Digital Control Techniques Based on Voltage Source Inverters in

electronics Review

Digital Control Techniques Based on Voltage Source Inverters in Renewable Energy Applications: A Review Sohaib Tahir 1,2 , Jie Wang 1, *, Mazhar Hussain Baloch 1,3 and Ghulam Sarwar Kaloi 1,4 1

2 3 4

*

School of Electronic, Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200000, China; [email protected] (S.T.); [email protected] (M.H.B.); [email protected] (G.S.K.) Department of Electrical Engineering, COMSATS Institute of Information Technology, Sahiwal 58801, Pakistan Department of Electrical Engineering, Mehran University of Engineering & Technology, Khairpur Mirs 67480, Pakistan Department of Electrical Engineering, Quaid e Awam University of Engineering & Technology, Larkana 77150, Pakistan Correspondence: [email protected]

Received: 4 December 2017; Accepted: 2 February 2018; Published: 7 February 2018

Abstract: In the modern era, distributed generation is considered as an alternative source for power generation. Especially, need of the time is to provide the three-phase loads with smooth sinusoidal voltages having fixed frequency and amplitude. A common solution is the integration of power electronics converters in the systems for connecting distributed generation systems to the stand-alone loads. Thus, the presence of suitable control techniques, in the power electronic converters, for robust stability, abrupt response, optimal tracking ability and error eradication are inevitable. A comprehensive review based on design, analysis, validation of the most suitable digital control techniques and the options available for the researchers for improving the power quality is presented in this paper with their pros and cons. Comparisons based on the cost, schemes, performance, modulation techniques and coordinates system are also presented. Finally, the paper describes the performance evaluation of the control schemes on a voltage source inverter (VSI) and proposes the different aspects to be considered for selecting a power electronics inverter topology, reference frames, filters, as well as control strategy. Keywords: voltage source inverters (VSI); voltage control; current control; digital control; predictive controllers; advanced controllers; stability; response time

1. Introduction Nowadays, energy demand is getting increased with the passage of time and distributed generation (DG) power systems especially through wind, solar and fuel cells as well as their related power conversion systems are conferred immensely. Many problems like grid instability, low power factor and power outage etc. for power distribution have also been increased with increase in energy demand [1]. However, DG power systems are found to be a sensible solution for such problems as they have relatively robust stability and causes additional flexibility balance. Moreover, their utilization can also improve the distribution networks management and carbon release is also reduced. VSIs are extensively necessitated for the commercial purpose as well as for the industrial applications as they play a key role in converting the DC voltage and current, usually produced by various DG applications, into AC before being discharged into the grid or consumed by the load. Several control systems are introduced, various schemes are proposed and numerous techniques are updated in order to facilitate the control of three-phase VSI. The objectives of these control schemes are to constrain the high and low-frequency electromagnetic pollution and to inject the active power with zero power factor into the Electronics 2018, 7, 18; doi:10.3390/electronics7020018

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grid [2]. The smooth and steady sinusoidal waveform can be a good input to a load for getting the most suitable response, therefore, the output of the inverter, which normally enjoys special standards and characteristics, should be controlled for providing an aforementioned waveform to load and grid. Generally, it is observed that several problems are caused in linking the DG power system to a grid or grid to load in bidirectional inverters, i.e., grid instability, distortion in the waveform, attenuation as well as major and minor disturbances. Hence, in order to overcome these problems and to provide high-quality power, appropriate controllers with rapid response, compatible algorithm, ability to remove stable errors, less transit time, high tracking ability, less total harmonic distortion, THD value and smooth sinusoidal output should be designed. Various controllers are designed for achieving these qualities. The cascade technologies are introduced in the literature comprises of an inner current loop and outer voltage loop [3–12]. As the inner-loop current controller plays a fundamental role in closed-loop performance, various control approaches like PI [3–6], H∞ [7,8], deadbeat [9–11,13] and µ-synthesis [11] are extensively applied. Outer voltage loop in the aforementioned cases refines the tracking ability and decreases the tracking error. In case of no input limitations, aforesaid PI controllers are the best choice for stabilizing the inner loop performance. However, input constraints restrict their performance and no optimization is usually observed by using PI controllers. The deadbeat control method is proposed in [9] to enhance the closed-loop performance but unfortunately, it was found highly sensitive to the disturbances, parameters mismatches and measurement noise. Later on, some observed based deadbeat controllers are introduced in order to provide compensation for these discrepancies, however, a trade-off was observed between phase margin and closed-loop performance [9,10]. Afterwards, H∞ controllers in [7,8] are offering robust output response instead of input constraints, however, guaranteeing only the local stability like the µ-synthesis controller in [12]. Several other manuscripts are also amalgamated with literature for fulfilling the demand of electric power regarding fulfilling the environmental principles concerning green-house effects [14–18]. Various structures and topologies for interconnecting DGs are presented in [19–21] for parallel operation and in [22–24] for independent operation. For this reason, various control strategies are anticipated for stabilizing the system to control the voltage and frequency in case of unbalanced load and nonlinear loads. Many researchers have proposed several schemes for designing the controller in order to refine the quality of output voltage of DC to AC inverter. In [25], a control scheme is presented for a DG unit in islanded mode, this control technique is suitable for balanced load conditions for a DG unit when it is electronically coupled. However, this technique is constrained to small load variations and remain unable to stabilize the system in large load variations. A robust controller is proposed in [26] for balanced as well as unbalanced systems. However, it fails to address non-linear load properly. In [27], a repetitive control is implemented for controlling the inverters but the relatively slow response and absence of a systematical technique for stabilizing the error dynamics are the core problems. In [28], the uncomplicatedly designed controller is used to mitigate the load disturbances up to a significant extent through a feedforward compensation element, however, it is only restricted to balanced load conditions. In [29], a spatial repetitive control technique is implemented for controlling the current in a single-phase inverter. The results are satisfactory under non-linear load conditions; however, it is not guaranteeing the optimal tracking ability for a three-phase inverter. In [30], a discrete-time sliding mode current controller is proposed, it is optimally operating to control the system at a sudden load change, an unbalanced load and a nonlinear load, however, the system is quite intricate. In [31], the voltage and frequency controller is presented through a discrete-time mathematical model in order to operate the distributed resource units. This technique is achieving good voltage regulations under different load conditions but the results are not verified through the experimental setup. In [32], a controller is proposed having an adaptive feedforward compensation method applied through a Kalman filter for estimating the variation in parameters, the response was robust; however, tuning of covariance matrices are not appropriately described in the paper. In [33], a corresponding controller is recommended for distributed generation systems in grid applications, the anticipated controller is good in handling the grid disturbances and handling the nonlinearities, however, it is not suitable

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variation in parameters, the response was robust; however, tuning of covariance matrices are not appropriately described in the paper. In [33], a corresponding controller is recommended for Electronics 2018, 7, 18 3 of 37 distributed generation systems in grid applications, the anticipated controller is good in handling the grid disturbances and handling the nonlinearities, however, it is not suitable in stand-alone mode in stand-alone mode due the nonexistence of voltage loop. controller In [34,35],isthe adaptive controller is due to the nonexistence of to voltage loop. In [34,35], the adaptive used and voltage tracking used and voltage tracking achievedisprecisely. Theunder systemsystems is guaranteed undervariations, systems parameter is achieved precisely. Theis system guaranteed parameter however, variations, complexity inand computation exists and a value certainispre-defined is needed for complexityhowever, in computation exists a certain pre-defined needed for value parameters. In [36], parameters. In [36], controller an output based voltageoncontroller basedharmonic on the resonant harmonic filters is presented. an output voltage the resonant filters is presented. It measures the Itcapacitor measures the capacitor current and current in theUnbalanced same sensor.voltage Unbalanced voltage current and load current inload the same sensor. condition and condition harmonic and harmonic are in compensated in this controller. THDdefined value is not defined distortion are distortion compensated this controller. However, THDHowever, value is not appropriately, therefore, it is complicated tocomplicated assess the quality of the control technique based appropriately, therefore, it is to assess thecontroller. quality ofAn theadaptive controller. An adaptive control proportional derivative controller is presented in [37], for a pulseinwidth inverter operation technique based proportional derivative controller is presented [37], modulated for a pulse width modulated in islanded distributed generation system, voltage system, regulation under numerous load conditions inverter operation in islanded distributed generation voltage regulation under numerous loadis evaluated,isthough it is not easyittois achieve suitablethe control gains as pargains the designing conditions evaluated, though not easythe to achieve suitable control as par the procedure designing specified in the paper. Moreover, voltage and frequency are optimally controlled, active and reactive procedure specified in the paper. Moreover, voltage and frequency are optimally controlled, active and power unbalancing is aptly is compensated throughthrough small signal of inverters in [38]. in [38]. reactive power unbalancing aptly compensated smallmodeling signal modeling of inverters The key key purpose purpose of of this this study study isis to to provide provide aa comprehensive comprehensive review review of of the the digital digital control control The strategies for different three-phase inverters in stand-alone as well grid-connected modes. strategies differenttypes typesofof three-phase inverters in stand-alone as as well as grid-connected Correspondingly, explanation, discussion and and comparison of of thethe various are modes. Correspondingly, explanation, discussion comparison variouscontrol control strategies strategies are describedin inthis thismanuscript manuscriptin indetail. detail. described Themanuscript manuscriptisisorganized organizedas: as:classification classificationofofvoltage voltagesource source inverters described Section The inverters is is described in in Section 2. 2. Section 3 discusses the characteristics of control systems, followed by a depiction of reference Section 3 discusses the characteristics of control systems, followed by a depiction of reference frames frames in Section 4. The control strategy in decoupled dq frame and time-delay sampling scheme for in Section 4. The control strategy in decoupled dq frame and time-delay sampling scheme for VSI VSIdepicted are depicted in Sections 5 and 6 respectively. overview the mostcommonly commonlyused usedfilters filtersand and are in Sections 5 and 6 respectively. AnAn overview of of the most dampingtechniques techniques is illustrated in Sections and 8 respectively. The grid synchronization damping is illustrated in Sections 7 and 87 respectively. The grid synchronization techniques techniques by modulation techniques Sections 9 and 10 of the respectively. manuscript, followed byfollowed modulation techniques are describedare in described Sections 9 in and 10 of the manuscript, respectively. Moreover, control Techniques along theirare pros. & cons. in areSection described in Section Section 12, 11. Moreover, control Techniques along with their pros.with & cons. described 11. In In Section 12,analysis comparative analysis and goals for are theelaborated. researchersWhereas, are elaborated. Whereas, comparative and future goals forfuture the researchers conclusions are conclusions are drawn in Section 13. drawn in Section 13. 2. 2. Classification Classificationof ofVSIs VSIs There There are are various various types, types, in inwhich whichthe theinverters invertersare arecategorized. categorized. Figure Figure 11 shows shows the the complete complete detail of categories in which voltage source inverters are classified. detail of categories in which voltage source inverters are classified. High Power Drives

Indirect Conversion

Voltage Source Inverters

Multilevel VSI

Cascaded H-Bridge VSI

Current Source Inverters

Load Commutated Inverter

2-level HighPower VSI

Neutral Point Diode Clamped VSI

Direct Conversion

Cycloconverters

PWM-CSI

Flying Capacitor VSI

Figure 1. 1. Classification Classification of of voltage voltagesource sourceinverters inverters(VSIs) (VSIs)in inhigh highpower powerdrives. drives. Figure

2.1. Multilevel Diode Neutral-Point Clamped Inverter Multilevel inverter (MLI) was proposed in 1975, its design was like a cascade inverter with diodes facing the source. This inverter was later transformed into a Diode Clamped Multilevel Inverter,

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2.1. Multilevel Diode Neutral-Point Clamped Inverter Electronics 2018, 7, 18

of 37 Multilevel inverter (MLI) was proposed in 1975, its design was like a cascade inverter 4with diodes facing the source. This inverter was later transformed into a Diode Clamped Multilevel Inverter, which is also named as a Neutral-Point Clamped Inverter (NPC) [39]. In thisinverters, type of which is also named as a Neutral-Point Clamped Inverter (NPC) [39]. In this type of multilevel multilevel inverters, the integration voltage clamping diodes indispensable. Anisordinary DCthe integration of voltage clampingof diodes is indispensable. Anis ordinary DC-bus separated by bus is separated by an even number of bulk capacitors connected in series with a neutral point in the an even number of bulk capacitors connected in series with a neutral point in the middle of the line middle of the line that is dependent on the levels In of the inverter. In FigureNPC-MLI 2, a five-level NPCthat is dependent on the voltage levels ofvoltage the inverter. Figure 2, a five-level is shown, MLI shown, herediodes the clamping diodes are interlinked to M-1 pairs if M considered here is the clamping are interlinked to M-1 regulatory pairsregulatory if M is considered as is voltage levelsas of voltage levels of the inverter. the inverter. +

Sa

Vdc 2

Da

Ca

Sb

Vdc 4

Sc Db

Cb

Sd

Vdc

Load

Dc

n

S′a

D′a

D′b

S′b

Cc V - dc 4

Cd Vdc 2 -

Dc′

S′c

S′d

Figure Figure2. 2.Five-level Five-leveldiode diodeneutral-point neutral-pointclamped clampedinverter. inverter.

The neutral point converter was designed by Nabae, Takahashi and Akagi in 1981, this was The neutral point converter was designed by Nabae, Takahashi and Akagi in 1981, this was basically a three-level diode-clamped inverter [40]. A three-phase Three-level diode-clamped inverter basically a three-level diode-clamped inverter [40]. A three-phase Three-level diode-clamped inverter is shown in Figure 3. is shown in Figure 3. The NPC-MLI is considered as an important device in conventional high-power ac motor drive The NPC-MLI is considered as an important device in conventional high-power ac motor drive applications like mills, fans, pumps and conveyors, moreover, it also offers solutions for industries applications like mills, fans, pumps and conveyors, moreover, it also offers solutions for industries including chemicals, gas, power, metals, oil, marine, water and mining. The back-to-back including chemicals, gas, power, metals, oil, marine, water and mining. The back-to-back configuration configuration of inverters for reformative applications is also considered as a major plus point of this of inverters for reformative applications is also considered as a major plus point of this topology, used, topology, used, for example, in regenerative conveyors, mining industry and grid interfacing of for example, in regenerative conveyors, mining industry and grid interfacing of renewable energy renewable energy sources like wind power [41]. sources like wind power [41]. There are several benefits as well as drawbacks of multilevel diode-clamped [39,42]. A common There are several benefits as well as drawbacks of multilevel diode-clamped [39,42]. A common dc dc bus is shared by all the phases, this results in the reduction of capacitance requirements of the bus is shared by all the phases, this results in the reduction of capacitance requirements of the inverter. inverter. Due to this reason, implementation of a back-to-back topology is not only credible but can Due to this reason, implementation of a back-to-back topology is not only credible but can also be also be applied practically for performing different operations in an adjustable speed drive and a applied practically for performing different operations in an adjustable speed drive and a high-voltage high-voltage back-to-back inter-connection. The capacitors can be recharged as a group. On back-to-back inter-connection. The capacitors can be recharged as a group. On fundamental frequency, switching efficacy is relatively higher. However, real power flow is problematic in case of a single

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fundamental frequency, switching efficacy is relatively higher. However, real power flow is problematic in case of a single inverter as the intermediate dc levels will tend to overcharge or inverter asdue the to intermediate dc levels will tend overcharge discharge due to inappropriate discharge inappropriate monitoring andtocontrol. The or number of clamping diodes are monitoring and control. The number of clamping diodes are quadratically associated with the number quadratically associated with the number of levels, which can be unwieldy for units with a high of levels,ofwhich number levels.can be unwieldy for units with a high number of levels.

+

Vdc 2

C1

n

Sa

Sa

Sa

Sb

Sb

Sb

Sc

Sc

Sc

Sd

Sd

Sd

Vdc

-

Vdc 2

C2

a

b

c

Figure Figure3.3.Three-level Three-leveldiode diodeneutral-point neutral-pointclamped clampedinverter. inverter.

2.2. 2.2. Multilevel MultilevelCapacitor CapacitorClamped/Flying Clamped/Flying Capacitor Capacitor Inverter Inverter A Acorresponding corresponding topology topology for for the the NPC-MLI NPC-MLI topology topologyisisthe theFlying FlyingCapacitor Capacitor(FC), (FC),or orCapacitor Capacitor Clamped, depictedininFigure Figure4.4.As Asanan alternative clamping diodes, capacitors Clamped, MLI MLI topology, topology, ititisisdepicted alternative to to clamping diodes, capacitors are are used for holding the voltages to the referred values. In the NPC-MLI, M − 1 number of capacitors used for holding the voltages to the referred values. In the NPC-MLI, M − 1 number of capacitors are are integrated a shared DC-bus, where the level number the inverter and−2(M − 1) switchintegrated on aon shared DC-bus, where M is M theislevel number of theofinverter and 2(M 1) switch-diode diode regulatory pairs areThough, used. Though, for the FC-MLI, instead of clamping diodes, onecapacitors or more regulatory pairs are used. for the FC-MLI, instead of clamping diodes, one or more capacitors are used to produce the output voltages depends upon the position and the level of the are used to produce the output voltages depends upon the position and the level of the inverter. inverter. They are coupled to the midpoints of two regulatory pairs on the same position on each side They are coupled to the midpoints of two regulatory pairs on the same position on each side of of a midpoint [42], see capacitors C a , C b and C c in Figure 5. a midpoint [42], see capacitors Ca , Cb and Cc in Figure 5. The The basic basic difference difference is is the the usage usage of of clamping clamping capacitors capacitors in in place place of of clamping clamping diodes, diodes, as as using using them the number numberofofswitching switchingcombinations combinations capacitors block reverse voltages them increases increases the asas capacitors dodo notnot block reverse voltages [42]. [42]. Numerous switching states would be able to produce the same voltage level and the redundant Numerous switching states would be able to produce the same voltage level and the redundant switching switching states states would would also also be be available. available. DC DCside sidecapacitors capacitorsin inthis thistopology topologyhave haveaaladder-like ladder-likestructure structureand andthe thevoltage voltageon oneach eachcapacitor capacitor deviates from that of the other capacitor. The voltage increment between two adjacent legs deviates from that of the other capacitor. The voltage increment between two adjacent legs of of the the capacitors provides the size of the voltage steps in the output waveform. One advantage of the flyingcapacitors provides the size of the voltage steps in the output waveform. One advantage of the capacitor-based inverter is the isredundancies for inner voltage levels; i.e.,i.e., two flying-capacitor-based inverter the redundancies for inner voltage levels; twoorormore moreeffective effective switching amalgamations can produce an output voltage. switching amalgamations can produce an output voltage. Unlike the diode-clamped diode-clampedinverter, inverter, flying-capacitor inverter requires allswitches of the Unlike the thethe flying-capacitor inverter nevernever requires all of the switches to be on (conducting state) in a consecutive series. Moreover, the flying-capacitor inverter to be on (conducting state) in a consecutive series. Moreover, the flying-capacitor inverter has has phase redundancies, while diode-clampedinverters invertershave haveonly only the the line-line phase redundancies, while thethe diode-clamped line-line redundancies redundancies[40]. [40]. These These redundancies redundancies provide provide selective selectivecharging chargingand anddischarging dischargingof ofspecific specific capacitors capacitorsand anditit can can be be incorporated in the control system for the voltage balancing across the various levels. incorporated in the control system for the voltage balancing across the various levels.

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+

Sa

Vdc 2

Sb

Cd

Sc

Vdc 4 Cd

Cc Cb

Vdc n

V - dc 4

Ca

Cc Cb

Cd

Sd Load

S′a

Cc S′b

Cd

S′c -

Vdc 2 -

S′d

Figure 4. 4. Multilevel capacitor clamped/flying clamped/flying capacitor Figure Multilevel (Five-level) (Five-level) capacitor capacitor inverter. inverter.

There are several advantages and disadvantages of multilevel flying capacitor inverters [41,43]. There are several advantages and disadvantages of multilevel flying capacitor inverters [41,43]. Phase redundancies are offered for balancing the voltage levels between the capacitors. Active and Phase redundancies are offered for balancing the voltage levels between the capacitors. Active and reactive power flow can be regulated. The presence of various capacitors allows the inverter to ride reactive power flow can be regulated. The presence of various capacitors allows the inverter to ride through outages for short duration and deep voltage sags. However, the control system is complex through outages for short duration and deep voltage sags. However, the control system is complex for for tracking the voltage levels for all of the capacitors. Correspondingly, recharging all the capacitors tracking the voltage levels for all of the capacitors. Correspondingly, recharging all the capacitors to to the same voltage level and startup are complex. Switching operation and efficacy are poor for real the same voltage level and startup are complex. Switching operation and efficacy are poor for real power transmission. The installation of large numbers of capacitors is not much economical and it power transmission. The installation of large numbers of capacitors is not much economical and it also also makes the system bulky as compared to the clamping diodes in multilevel diode-clamped makes the system bulky as compared to the clamping diodes in multilevel diode-clamped converters. converters. Likewise, packing is also tougher in the inverters with a higher number of levels. The Likewise, packing is also tougher in the inverters with a higher number of levels. The five-level and five-level and three-level FC-MLIs are represented in Figures 4 and 5 respectively. three-level FC-MLIs are represented in Figures 4 and 5 respectively.

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+

Sa

Vdc + 2 Vdc 2

Sa

C1 C1

Vdc Vdc

n

Sb

Cb Cb

Sc

C2 C2

Vdc 2V - dc 2-

Sd

Sb

Cc

Sc Sc

Sc

Sd

Sd

Sd

-

Cc

Sc

Sc

-

Sb

Sb

Sb

Ca

n

Sa

Sa

Sb Ca

Sa

Sa

Sd

Sd

c

b

a

c

b

a

Figure5.5.Three-level Three-levelcapacitor capacitorclamped/flying clamped/flying capacitor capacitor inverter. inverter. Figure Figure 5. Three-level capacitor clamped/flying capacitor inverter.

2.3. Cascaded Cascaded H-Bridge H-BridgeInverter Inverter 2.3. 2.3. Cascaded H-Bridge Inverter Thereare areminimum minimum three voltage levels for a multilevel inverter using cascaded topologies. In There three voltage levels for for a multilevel inverter using cascaded topologies. In order There are minimum three voltage levels a multilevel inverter using cascaded topologies. In order to attain a three-level waveform, a single full-bridge or H-bridge inverter is considered. Each to attain a three-level waveform, a single full-bridge or H-bridge inverter is considered. Each inverter order to attain a three-level waveform, a single full-bridge or H-bridge inverter is considered. Each is inverter is provided withDC a separate DC source. Acascaded three-level cascaded inverter is shown in Figure 6. provided with a separate source. A three-level inverter is shown in Figure 6. inverter is provided with a separate DC source. A three-level cascaded inverter is shown in Figure 6. By using usingdifferent differentcombinations combinations ofthe the fourswitches, switches, Sa, Sb, Sc and and SSdd,, each each inverter inverter level level can can By By using different combinationsof of thefour four switches, SSaa,, SSbb, ,SSc cand Sd, each inverter level can V − V 0 and connecting dc source to the produce three different outputs voltage, i.e.,VV produce three different outputs , 0, and −Vdc dc by by connecting thethe dc source to the ac dcdc produce three different outputsofof ofvoltage, voltage,i.e., i.e., dc , 0 and −V dc by connecting the dc source to the output. − V can be obtained by turning on switches S and S whereas for obtaining V , switches S c dc b dc on switches switches andScScwhereas whereasforfor obtaining acacoutput. dcdc can −V V V,dca , canbe be obtained obtained by by turning turning on SSb band obtaining output.−V and Sd can be turned on. However, for achieving the output voltage on 0 level either Sa and Sb dc or Sc switches for achieving achievingthe theoutput outputvoltage voltage 0 level either switchesSaSand a andSd Sdcan canbe beturned turned on. on. However, However, for onon 0 level either Sa Sa and Sd can be turned on. The different full-bridge inverters must be connected in series in the way that and S b or S c and S d can be turned on. The different full-bridge inverters must be connected in series and Sb or Sc and Sd can be turned on. The different full-bridge inverters must be connected in series the finally produced voltage waveform should be the sum of the inverter outputs. Multilevel cascaded in in the waveformshould shouldbebethe thesum sumofof inverter outputs. theway waythat thatthe thefinally finallyproduced produced voltage waveform thethe inverter outputs. inverters are proposed for the applications such as static VAR generation (reactive power control), Multilevel for the the applications applicationssuch suchasasstatic staticVAR VAR generation Multilevelcascaded cascaded inverters inverters are are proposed proposed for generation an interface with renewable energy sources and for battery-based applications. The main reasons (reactivepower power control), control), an an interface interface with (reactive with renewable renewable energy energy sources sourcesand andforforbattery-based battery-based forapplications. preferring a The cascaded multilevel H-bridge inverter are the availability of possible output levels main reasons reasons for for preferring preferring aa cascaded areare thethe applications. The main cascaded multilevel multilevelH-bridge H-bridgeinverter inverter more than twice the number of dc sources [42–44]. The series of H-bridges enables the manufacturing availability possible output levels [42–44]. The series of of availability ofofpossible output levels more than than twice twicethe thenumber numberofofdcdcsources sources [42–44]. The series and packaging process easy, quick and and economical.process However, the requirement ofeconomical. a separate dc H-bridges enables themore manufacturing H-bridges enables the manufacturing and packaging packaging processmore moreeasy, easy,quick quickand and economical. source for each H-bridge constrains the applications of these inverters to the products having multiple However, therequirement requirement of aa separate separate dc thethe applications of of However, the of dc source source for foreach eachH-bridge H-bridgeconstrains constrains applications separate DC sources already or readily available. these inverters to the products having multiple separate DC sources already or readily available. these inverters to the products having multiple separate DC sources already or readily available.

C1

C1

S Sa a

S Scc B

A

B

A

Sb Sb

Sd Sd

C2

C2

Sa

Sc

Sa

Sc

B

A

B

A

Sb

Sb

C3

C3

Sd

Sd

Figure6.6.Cascaded Cascaded H-bridge H-bridge multilevel Figure multilevelinverter. inverter. Figure 6. Cascaded H-bridge multilevel inverter.

Sa A

Sc

Sa B

A

Sb

Sb

Sc

B

Sd

Sd

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2.4. Two-Level Three Phase VSI with an Output Filter 2.4. Two-Level Three Phase VSI with an Output Filter A simple two-level inverter is used to convert dc to ac output. It consists of six switches, IGBTs A simple two-level inverter is used to convert dc to ac output. It consists of six switches, IGBTs and and MOSFETs are the two most suitable switching components for these inverters. Due to simplicity MOSFETs are the two most suitable switching components for these inverters. Due to simplicity in in their structure and ability to handle the voltage by keeping the system stable, they are preferred their structure and ability to handle the voltage by keeping the system stable, they are preferred utmost in the industry and for commercial purpose due to their support in uninterruptible power utmost in the industry and for commercial purpose due to their support in uninterruptible power supply applications. These are usually connected to the load or the grid by using LC or LCL filter. supply applications. These are usually connected to the load or the grid by using LC or LCL filter. Various types of control systems are implemented by the researchers to improve their performance, Various types of control systems are implemented by the researchers to improve their performance, robustness and stabilization, compensating the power losses and lowering the THD value. SPWM or robustness and stabilization, compensating the power losses and lowering the THD value. SPWM SVPWM are mostly applied to these types of inverters for getting appropriate values. Two level three or SVPWM are mostly applied to these types of inverters for getting appropriate values. Two level phase VSI is shown in Figure 7. In Figure 7, the S1 to S3 and S1′ to0 S3′ 0shows the switches of the three phase VSI is shown in Figure 7. In Figure 7, the S1 to S3 and S1 to S3 shows the switches of the representsthe thevoltage voltageacross acrossthe thecapacitors, capacitors,C.C. inverter. inverter. Whereas, Whereas, uucc represents

S1

Vdc+

u1

-

S′1

S2

S3 LC Filter

u2

S′2

iL

u3

S′3

Three-Phase Load

L

Uc C

Figure Figure7.7.Two-level Two-levelthree threephase phaseVSI VSI with with an an output output LC LC filter. filter.

2.5. Three Phase Four-Leg VSI with an Output Filter 2.5. Three Phase Four-Leg VSI with an Output Filter Nowadays, a growing interest in using the three-phase four-leg inverters is observed from the Nowadays, a growing interest in using the three-phase four-leg inverters is observed from researchers’ due to their ability to handle the unbalanced loads efficaciously in four-wire systems the researchers’ due to their ability to handle the unbalanced loads efficaciously in four-wire [45,46]. In this topology, the neutral point is proposed by connecting the neutral path to the mid-point systems [45,46]. In this topology, the neutral point is proposed by connecting the neutral path to of additional fourth leg, as shown in Figure 8. IninFigure represents output voltage of o Figure thethe mid-point of the additional fourth leg, as shown Figure8,8. uIn 8, u the represents the output o

′ . SM and the LC filter, represents the pointthe neutral between two switches, voltage of thewhereas LC filter,M whereas M represents pointpoint neutral point between two switches, SMSand M 0 S . Even though the configuration in this topology does not need expensive and large capacitors and Even though the configuration in this topology does not need expensive and large capacitors and M produces lower lower ripple ripple on on the the DC DC link link voltage, voltage, however, however, using using two two extra extra switches switches lead lead to to aa complex complex produces control system [47]. Additionally, the split DC-link voltage is about 15% less as compared to the AC AC control system [47]. Additionally, the split DC-link voltage is about 15% less as compared to the voltage in this configuration [48]. voltage in this configuration [48]. Another topology topologycan canbe beusing usingsplit splitDC DClink, link,which whichisisthe themost mostcommon common way providing Another way of of providing a a neutral point to three-phase VSIs. This configuration can be provided by using two capacitors neutral point to three-phase VSIs. This configuration can be provided by using two capacitors i.e., i.e., splitting the DC-bus intoparts two by parts by ausing a pair of capacitors by connecting neutral splitting the DC-bus into two using pair of capacitors and by and connecting a neutrala path to path to the mid-point of these capacitors, as shown in Figure 9. Both these configurations have the mid-point of these capacitors, as shown in Figure 9. Both these configurations have several several advantages and disadvantages, however, the split dc-link is found unsuitablefor forhandling handling the the advantages and disadvantages, however, the split dc-link is found unsuitable unbalanced loads, loads, whereas, whereas, three-phase three-phase four four leg leg inverter inverter is is found found most most appropriate appropriate for for handling handling the the unbalanced non-linear and unbalanced load conditions. A comparison of different types of VSIs with respect to non-linear and unbalanced load conditions. A comparison of different types of VSIs with respect to their characteristics, control contents and complexity is described in Table 1. their characteristics, control contents and complexity is described in Table 1.

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+ +

S1 S1

SMSM CC

u1 u1

MM

VV dc dc

S′1S′1

S M′S M′

S 2S 2 u2 u2

S′2S′2

S3 S3 iL iL u3 u3

S′3S′3

- -

Filter LCLC Filter

I Load I Load

LL

Three-Phase Three-Phase Load Load U oU o

U Uc c

CC Neutral Wire Neutral Wire

Figure 8. Three-phase four-leg inverter with an output LC filter. Figure 8. Three-phase four-leg inverter with output filter. Figure 8. Three-phase four-leg inverter with anan output LCLC filter.

a a

+ + C C 1 1

Three-phase four Three-phase four inverter legleg inverter in in stand alone mode stand alone mode

Vdc Vdc C2

b b

c c

C - - 2

Figure 9. Schematic a Three-phase four-leg inverter with split DC-link. Figure 9. Schematic of of a Three-phase four-leg inverter with split DC-link. four-leg inverter with split DC-link. Table 1. Comparison different types of VSI in terms of design, implementation & complexity. Table 1. of different types of in of implementation & Table 1. Comparison Comparison of of different types of VSI VSI in terms terms of design, design, implementation & complexity. complexity. Characteristic Characteristic Characteristic

Cascaded Cascaded H-HCascaded Bridge VSI Bridge VSI H-Bridge VSI

NP-Diode NP-Diode NP-Diode Clamped VSI Clamped Clamped VSI VSI

Flying Flying Capacitor VSI Capacitor Capacitor VSIVSI

Flying

Design implementation Design && implementation Design & implementation complexity complexity complexity

High High High

Low Low Low

Medium Medium Medium

Specific Requirements Specific Requirements Specific Requirements

SeparateDC DC Separate SeparateDC sources sources sources

Clamping diodes Clamping diodes Clamping diodes

2L-VSI

2L-VSI 2L-VSI

Low LowLow

Additional

Additional Additional IGBTs/MOSFETs IGBTs/MOSFETs capacitors IGBTs/MOSFETs capacitors capacitors

Voltage/current Voltage/current Voltage balancing Voltage Voltage SetupVoltage/current Voltage balancing Setup Voltage balancing Voltage Setup regulation regulation regulation Modularity High Low High Low Modularity High Low High LowLow Modularity High Low High Fault tolerance ability Easy Difficult Easy Easy Fault tolerance ability Easy Difficult Easy Easy Fault tolerance ability Easy Difficult Easy Easy Reliability Medium Medium Medium-High High High Reliability Medium Medium Medium-High Reliability Medium Medium Medium-High High Converter Complexity Complexity Medium Medium Low-Medium High High Converter Medium Medium Low-Medium Converter Complexity Medium Medium Low-Medium High Controller Complexity Medium-High Medium-High Medium-High Medium Controller Complexity Medium-High Medium-High Medium-High Medium Medium Controller Complexity Medium-High Medium-High Medium-High Medium Power Quality Good Good Good Power Quality Good Good Good Medium Operational Power (MW) 3–6 3–7 3–6 3Medium Power Quality Good Good Good MV-IGBT, Operational Power (MW) 3 Operational Power (MW) 3–63–6IGCT 3–73–7 3–63–6 Switching devices MV-IGBT, MV-IGBT, IGCT LV-IGBT3 IGCT Switching devices MV-IGBT, IGCT MV-IGBT, IGCT MV-IGBT, IGCT LV-IGBT Switching devices MV-IGBT, IGCT MV-IGBT, IGCT MV-IGBT, IGCT LV-IGBT Control Concerns Control Concerns Control Concerns

Power Sharing Power Sharing Power Sharing

3. 3. Characteristics of of Control Systems Characteristics Control Systems 3. Characteristics of Control Systems There areare several parameters and characteristics through which a particular control system is is There several parameters and characteristics through which a particular control system There are several parameters and characteristics through which a particular control system is identified. Mainly, there are two characteristics of a control system are found i.e., analog or digital identified. Mainly, there are two characteristics of a control system are found i.e., analog or digital identified. Mainly, there are two characteristics of a control system are found i.e., analog or digital control systems. Both areare having some advantages and disadvantages, described as as follows: control systems. Both having some advantages and disadvantages, described follows: control systems. Both are having some advantages and disadvantages, described as follows:

3.1. Analog Control System 3.1. Analog Control System

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3.1. Analog Control System The control systems in which the input and output are designed and analyzed by continuous time analysis or Laplace transform (in s-domain) using state-space formulations. In analog control systems, the representation of the time domain variable is assumed to have infinite precision. Hence, the equations of state space model are differential equations. These systems can be designed without using a computer, microcontrollers or a programmable logic control (PLC). Implementation of analog signals is generally done by using Op-amps, capacitors etc. Robustness against crash or breakdown, having a wide dynamic range, analytical composition accessibility and continuous processing indicate numerous advantages of the analog control systems. However, slow processing speed, interference, complicated implementation in comparative logic, intelligent control systems, neural networks and MIMO are several disadvantages of analog control systems. 3.2. Digital Control System In digital control systems, modeling, designing, implementation and analysis is carried out in discrete-time or z-transformation domain. In digital control systems, as the name depicts that digital signals are analyzed. Therefore, time is sampled and quantized for state space equations. Additionally, as a digital computer has finite precision, extra attention is needed to ensure that error in coefficients, i.e., A/D conversion, D/A conversion etc. are not producing any disturbances or inadequate effects. In a digital controller, the output is a weighted sum of current as well as previous input and output samples, therefore, its implementation requires the storage of relevant values in a digital controller. Mostly, a digital controller is implemented via a computer, so, found most economical to control the plants. Moreover, it is relatively easier to constitute and reconstitute through software. Likewise, programs can be leveled to the confines of storage without any additional cost. Correspondingly, digital controllers are compliant with constraints of the program can be changed. Furthermore, the digital controllers are less responsive to the changes in environmental conditions, unlike the analog controllers. Flexibility, swift expansion, uncomplicated implementation in comparative logic, intelligent systems and MIMO, high accuracy as well as robustness against interference are several advantages of these systems. Though, low processing speed, low dynamic range and non-user-friendly interface are the several drawbacks of the digital control systems. The digital controllers are implemented with various technologies which are classified into three categories expressed as follows: 1. 2. 3.

Microcontroller Based implementation (MC) [49–51] Digital Signal processing-based implementation (DSP) [52–54] Field programmable gate array-based implementation (FPGA) [55–57]

In reliable scientific research, generally, DSP is used. Fixed point arithmetic and floating-point algorithms are mostly used in implementing the digital control technique by DSP. A traditional slow microprocessor is used normally in slow applications. However, an FPGA is found adequate in fast controllers, due to its abilities of bug fixing and to be reprogrammed in complex structures. A general structure of a closed loop grid connected digital control system, with an inner current loop and an outer voltage loop, is depicted in Figure 10. In this figure, a voltage source inverter with an output filter is considered. An AC bus is connected to point of common coupling, PCC. Moreover, coordinates transformation from abc to dq is achieved by a phase angle, PH. However, PLL represents the phase locked loop. The symbols S1 , S2 , S3 , S10 , S20 and S30 represents the switches, responsible for positive and negative sequences of the inverter output. The vdre f . and vqre f . represents the reference voltages in dq frame. SVPWM shows the space vector pulse width modulation technique for generating drive signals for a voltage source inverter. The voltage across capacitors, uc and current across inductors, i L are measured and transformed into a synchronized dq reference frame. The input voltage is computed in the dq frame on the basis of vre f . in the three-phase reference frame. The computed data is then transformed from rotating dq to abc reference frame. Afterward, the PWM technique would be selected accordingly.

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on the basis of v in the three-phase reference frame. The computed data is then transformed from Electronics 2018, 7, 18 ref . 11 of 37 rotating dq to abc reference frame. Afterward, the PWM technique would be selected accordingly.

S2

S1

iL

u2

-

S′3

P C C

L

u3

S′2

S′1

LCL Filter

ia ib ic

AC Bus

u1

Vdc +

S3

Uc

va , vb , vc

C

abc

id iq

+

iˆq

+

vdref .

vˆ

+ dc

+v ˆ

iq ref .

+

Digital voltage Controller

v + d +v

qc

vq ref .

+

q

PLL

abc

dq

Rq

Digital current Controller

idref .

iˆd

PH

dq

abc

SVPWM

Vˆref .

Rd

dq

PH

Figure Schematicdiagram diagramof of aa controlled controlled three-phase with a digital controller. Figure 10.10.Schematic three-phasegrid gridconnected connectedVSI VSI with a digital controller.

4. Reference Frames 4. Reference Frames Control systems are implemented in either a single phase or a three-phase synchronous Control systems are implemented in either a single phase or a three-phase synchronous reference reference frame. These frames are synchronized with each other through special formulation in order frame. These frames are synchronized with each other through special formulation in order to to be compatible for facilitating the modeling, design, analysis and transformation of one phase and be compatible for facilitating the modeling, design, analysis and transformation of one phase and three phase systems into other systems. Complex structures, especially for multi-level converters, can three phase systems into other systems. Complex structures, especially be simplified by using these reference frames describes as follows [1,58]. for multi-level converters, can be simplified by using these reference frames describes as follows [1,58]. 4.1. abc Reference Frame 4.1. abc Reference Frame A general three-phase system is said to be applied to abc frame without any transformation. An A general three-phase system is each said phase to be applied abcframe frame anystar transformation. individual controller is to be used for current intoabc butwithout Delta and connection Anhas individual controller is to be used for each phase current in abc frame but Delta and to be considered for designing a control system. Non-linear controllers are used instar thisconnection system hasdue to be considered for designing a control system. Non-linear controllers are used in this system due to their rapid dynamic response. to their rapid dynamic response. 4.2. dq Reference Frame 4.2. dq Reference Frame This frame is used in three-phase systems. Park’s Transformation is used for transforming the frame used in three-phase systems. Park’s is used for transforming abcThis frame intois dq frame. This transformation causesTransformation the current and voltage waveforms tothe beabc frame into dq frame. This transformation causes the current and voltage waveforms to be converted converted into a frame that rotates synchronously with the grid voltage. As a result, the variables are into a frame into that DC rotates synchronously with the be grid voltage. and As afiltered result, ifthe variables are converted converted variables and they can easily controlled required. into DC variables and they can easily be controlled and filtered if required. 4.3. αβ Reference Frame 4.3. αβ Reference Frame This frame is used in three-phase systems and sometimes sensationally in single phase systems too.This Grid current is transformed into systems a stationary frame from abc frame or single-phase frame is used in three-phase and reference sometimes sensationally in single phase systems frame bycurrent using Clark’s transformation. using this transformation controlorvariable can too. Grid is transformed into a Therefore, stationaryby reference frame from abc frame single-phase be transformed into sinusoidal quantities. frame by using Clark’s transformation. Therefore, by using this transformation control variable can be transformed into sinusoidal quantities. 5. The Control Strategy in Decoupled dq Frame 5. The In Control Strategy Decoupled dq Frameframe, decoupling is the most important issue to be a digital controlin scheme in dq reference discussed. Generally, balancedinand sinusoidal waveform canmost be obtained by adopting In a digital controlascheme dq interrupted reference frame, decoupling is the important issue to be ac voltage control in an inverter station. Therefore, the fundamental requirement is to simplify the discussed. Generally, a balanced and interrupted sinusoidal waveform can be obtained by adopting

ac voltage control in an inverter station. Therefore, the fundamental requirement is to simplify the control design [59]. The controller in an inverter station is based on a mathematical steady-state model in the synchronous reference frame. Moreover, during a balanced network state, the direction of the

control design [59]. The controller in an inverter station is based on a mathematical steady-state model in the synchronous reference frame. Moreover, during a balanced network state, the direction of the current injected into the loads is assumed as the reference direction. The mathematical representation of a steady-state model is expressed as following: Electronics 2018, 7, 18

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ubd = ω Lisq + usd (1)  = − + u ω Li u current injected into the loads is assumed as the reference direction. The mathematical representation sd sq  bq

of a steady-state model is expressed as following: In Equation (1), the terms ubd and ( u bq represents the voltages in dq frame under balanced u = ωLisq + usd the proportional and integrated controllers network conditions. Likewise, k p and k ibd represents (1) ubq = −ωLisd + usq and the equation by using aforementioned coefficients represents a PI controller. Correspondingly, Equation (1), the terms ubd voltages and ubq represents the voltagesisdin and dq frame under balanced network usd In and the bus in dq axis. However, the active and u sq represents isq represents conditions. Likewise, k p and k i represents the proportional and integrated controllers and the equation reactive current respectively. Commonly, the d-axis is fixed to the voltage source space vector, i.e., by using aforementioned coefficients represents a PI controller. Correspondingly, usd and usq represents the amplitude of the desired ac voltage space vector is kept constant and the value of u = 0 . Then the bus voltages in dq axis. However, isd and isq represents the active and reactive currentsqrespectively. Equation (1)the cand-axis be simplified as:the voltage source space vector, i.e., the amplitude of the desired ac Commonly, is fixed to voltage space vector is kept constant and the value of usq = 0. Then Equation (1) can be simplified as:

ubd = ω Lisq + usd ( ubd = ωLisq + usd ω Lisd ubqu ==−− ωLisd bq

(2) (2)

According to Equation (2), the control structure of the inverter station is shown in Figure 11, According to Equation (2), the control structure of the inverter station is shown in Figure 11, where a PI controller is employed in the ac voltage control [60]. Moreover, usref . is the reference where a PI controller is employed in the ac voltage control [60]. Moreover, usre f . is the reference voltage voltagecan which can be set accordingly for the desirable amplitude of voltage. AC bus voltage. which be set accordingly for the desirable amplitude of AC bus

usd +

-

KP +

usref .

0

+

isd

ωL

isq

ωL

usq-

Ki s

K KP + i s

bd uref .

+

udc

+ SVPWM -

PLL

+

u

bq ref .

The decoupling decoupling control strategy in dq reference frame. Figure 11. The

6. Time Delay Sampling Scheme for VSI Time samplingfor fordigital digital controllers is done by using a discrete time-domain analysis, i.e., zTime sampling controllers is done by using a discrete time-domain analysis, i.e., z-domain. domain. Two fundamental advantages of using z-domain analysis over s-domain (continuous time Two fundamental advantages of using z-domain analysis over s-domain (continuous time domain) domain) analysis for designing a current controller are: First the control implementation is achieved analysis for designing a current controller are: First the control implementation is achieved on on a computer-based system, i.e., the control calculation, sampling measurements and PWM signals a computer-based system, i.e., the control calculation, sampling measurements and PWM signals sequence sequence areinupdated discrete steps. Although, and hold is a characteristic are updated discretein time steps.time Although, this samplethis andsample hold feature is a feature characteristic of a control of a control system effectsasits as sampling per the referred sampling frequency. Secondly, the system and effects its and dynamics perdynamics the referred frequency. Secondly, the multiple time delays multiple time delays can be modeled by using a backshift operator, which affords no simplifications can be modeled by using a backshift operator, which affords no simplifications in linear control design, in linear control time design, unlike continuous timetime domain, the multiple delays were unlike continuous domain, where the multiple delays where were sampled using antime exponential term, sampled using an exponential which is approximated generally applyingeffect Taylor-series which is approximated generallyterm, by applying Taylor-series expansion. Thebysampling is a most expansion. The sampling effect is a most critical requirement to handle model uncertainties, issues in critical requirement to handle model uncertainties, issues in power supplies and relative disturbances. power supplies and relative Therefore, in order deal withshould aforementioned issues, Therefore, in order to deal withdisturbances. aforementioned issues, zero order to hold, ZOH be incorporated in zero order hold, ZOH should be incorporated in the control system. In ZOH, a pole or a zero is added the control system. In ZOH, a pole or a zero is added into the existed controller through the compensator. intofundamental the existed controller the compensator. The fundamental of this technique is The advantagethrough of this technique is its uncomplicated structureadvantage to be implemented on a system, though, it only affects a limited share of the overall delay. There are two basic sampling routines generally employed in the digital control systems, i.e., single updated sampling and double updated sampling [61]. A single-update sampling method comprises of the measurement samplings, in which calculated modulation indexes are updated once in every

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its uncomplicated structure to be implemented on a system, though, it only affects a limited share of the overall delay. There are two basic sampling routines generally employed in the digital control systems, i.e., Electronics 2018, 7, 18 13 of 37 single updated sampling and double updated sampling [61]. A single-update sampling method comprises of the measurement samplings, in which calculated modulation indexes are updated once switching period. Whereas, a double-update sampling sampling concept conferred to a PWMto concept which in every switching period. Whereas, a double-update concept conferred a PWMinconcept the measurement sampling and therefore, thetherefore, calculatedthe modulation are updated every in which the measurement sampling and calculatedindex modulation indextwice are in updated switching periodswitching [61]. The detailed single-update and single-update double-updateand sampling are shownsampling in Figure are 12, twice in every period [61]. The detailed double-update where, represents the switching period of present time slot. T(k − 1)slot. andHowever, T(k − 2) shownT(k) in Figure 12, where, T(k) represents thethe switching period of However, the present time shows the switching former time slots. T(k − 1) and T(k − 2) period shows of thethe switching period of the former time slots. Asingle-update single-updatePWM-technique PWM-technique with sampling the beginning of a switching A with sampling at theatbeginning of a switching period is period depictedis depicted in Figure In this technique, the modulation index isonce updated once in of beginning of a in Figure 12a. In this12a. technique, the modulation index is updated in beginning a switching switching period. A time domain of onetime sampling time is in introduced inloops. the control loops.isThis effect period. A time domain of one sampling is introduced the control This effect modeled is modeled withoperator a backshift operator taking into the account. with a backshift while takingwhile discrete timediscrete domaintime into domain the account. Figure 12b 12bshows showsanother anotherscheme schemeof ofaasingle-update single-updatePWM PWMsampling samplingin inwhich whichthe themodulation modulation Figure index isis updated updated in in middle middle of ofaaswitching switchingperiod. period. Therefore, Therefore, the the time time delay delay due due to to sampling sampling and and index updatingroutine routineis is mean value of two the two converter voltage reference i.e.,and actual and updating thethe mean value of the converter voltage reference values,values, i.e., actual former former cycles. controlTherefore, cycles. Therefore, thefunction transferoffunction of a single-update PWM technique with control the transfer a single-update PWM technique with sampling in sampling middle ofperiod a switching period is determined. middle of ainswitching is determined. Inthe thedouble-update double-updatesampling sampling concept, concept, sampling sampling and andupdating updatingoccurs occurstwice twicein ineach eachsampling sampling In period. In this this technique, technique, the modulation modulation index is is updated updated on on the the basis basis of of former former control control cycle’s cycle’s period. measurements. According measurements. According to to this this behavior, behavior, the the time-delay time-delay isis one one control control cycle. cycle. The Thepattern patternofofa adouble-update double-updatesampling samplingisispresented presentedininFigure Figure12c. 12c.

Figure12. 12. Time delay model delay model (sampling at beginning) (b) Figure model of ofaaVSI VSI(a) (a)single-update single-updatetime time delay model (sampling at beginning) single-update time delay model (sampling (b) single-update time delay model (samplingatatmiddle) middle)(c) (c)double-update double-updatetime timedelay delaymodel model for for aa VSI. VSI.

7. Output Output Filters Filters for forInverters Inverters 7. The harmonics harmonics reduction reduction is is the the foremost foremost priority priority of of the the researchers researchers while while designing designing aa power power The electronicsor oran anelectrical electricalsystem. system.Therefore, Therefore,an anoutput outputfilter filterisisused usedfor forthis thispurpose. purpose.An An output outputfilter filter electronics uses the controlled phenomenon of switching the semiconductor devices for harmonics reduction. uses the controlled phenomenon of switching the semiconductor devices for harmonics reduction. Thereare arenumerous numeroustopologies topologiesof ofsuch suchfilters filtersintroduced introducedin inthe theliterature literatureby bycombining combiningthe theinductor inductor There (L)and andcapacitor capacitor(C) (C)i.e., i.e.,L, L,LC LCand andLCL LCLfilters filtersunified unifiedwith withthe theinverters inverterstototheir theiroutput. output. (L) 7.1. L-Filter L-Filter 7.1. Inhigh highswitching switching frequency frequency inverters, inverters, the the first first order orderL-filter L-filterisisconsidered consideredas asthe themost mostsuitable suitable In filter. However, inductance decreases the dynamics of the whole system. filter. However, inductance decreases the dynamics of the whole system. 7.2. 7.2. LC-Filter LC-Filter An An LC LC filter filter isisaasecond-order second-orderfilter filterhaving havingsubstantially substantially sophisticated sophisticated damping damping behavior behavior as as compared L-filter. This filter topology is relatively easiereasier to design and it isand a compromise between comparedtotoanan L-filter. This filter topology is relatively to design it is a compromise the valuesthe of values inductance and capacitance. The cut-off needs the relatively higher higher value between of inductance and capacitance. The frequency cut-off frequency needs the relatively of inductance whereas the voltage quality can be improved through the higher value of capacitance. value of inductance whereas the voltage quality can be improved through the higher value of The value of resonant frequency is dependent on the impedance of the grid when the system is connected to the grid supply. An LC-filter is mostly preferred in standalone mode. The three-phase

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capacitance. The value of the of resonant resonant frequency frequency is is dependent dependent on on the the impedance impedance of of the the grid grid when when the 14 of 37 system is connected to the grid supply. An LC-filter is mostly preferred in standalone mode. The system is connected to the grid supply. An LC-filter is mostly preferred in standalone mode. The three-phase three-phase two-level two-level and and three-phase three-phase four four legs legs voltage voltage source source inverters inverters with with an an integrated integrated LC LC filter filter are shown in Figures 7 and 8 respectively. two-level and three-phase four legs voltage source inverters with an integrated LC filter are shown in are shown in Figures 7 and 8 respectively. Figures 7 and 8 respectively. 7.3. 7.3. LCL-Filter LCL-Filter 7.3. LCL-Filter An An LCL LCL filter filter is is aa third third order order filter, filter, mostly mostly used used for for the the grid-tied grid-tied inverters. inverters. The The lower lower frequency frequency An LCL in filter is a third order filter, mostly usedThis for the grid-tied inverters. The lower frequency is preferable presence of aforementioned filters. filter supports the comparatively is preferable in presence of aforementioned filters. This filter supports the comparatively healthier healthier is preferablebetween in presence of aforementioned filters. This This filterfilter supports thebe comparatively healthier decoupling the filter and the grid impedance. should precisely designed decoupling between the filter and the grid impedance. This filter should be precisely designed by by decoupling between the filter and the gridof impedance. This filter should be precisely designed by taking taking into into consideration consideration the the parameters parameters of the the inverters. inverters. Otherwise Otherwise even even the the smaller smaller values values of of taking into can consideration the parameters ofstates the inverters. Otherwise even the thesmaller smallerinductance values of inductance bring resonance and unstable into the system. However, inductance can bring resonance and unstable states into the system. However, the smaller inductance inductance can bring resonance and unstable states into the system. However, the smallerLCL inductance can can provide provide optimized optimized current current ripple ripple diminishing diminishing values. values. A A three-phase three-phase VSI VSI with with an an LCL filter filter is is can provide optimized current ripple diminishing values. A three-phase VSI Thevenin with an LCL filter is V Z shown in Figure 13. Where, and represents the Thevenin voltage and impedance th th shown in Figure 13. Where, V and Z represents the Thevenin voltage and Thevenin impedance shown in Figure 13. Where, Vthth and Zththrepresents the Thevenin voltage and Thevenin impedance respectively. the complexity of the control system inflated significantly and the dynamic respectively. However, However, the complexity complexity of of the the control control system system inflated inflated significantly significantly and and the the dynamic dynamic respectively. However, the performance of the inverter can perhaps be affected when relatively complex filter structures are performance of the inverter can perhaps be affected when relatively complex filter structures are performance of the inverter can perhaps be affected when relatively complex filter structures are employed. Thus, these topologies are most suitable for high power applications, which employ low employed. Thus, these topologies are most suitable for high power applications, which employ low employed. Thus, these topologies are most suitable for high power applications, which employ low switching Figures 14 and 15 show the switching frequencies. frequencies. However, However, Figures 14 14 and and 15 15 show show the the one-leg one-leg block block diagram diagram of of aaa single-phase single-phase switching frequencies. However, Figures one-leg block diagram of single-phase and three-phase grid-connected systems, respectively. Where, represents pulse width K pwm represents the and three-phase grid-connected systems, respectively. Where, the pulse width width K and three-phase grid-connected systems, respectively. Where, Kpwm represents the pulse pwm modulation the system, whereas, and i g represents the modulation characteristic of the , iu,,c , u Lc ,, LLg, ,i L and the grid side i , ii i represents u modulation characteristic characteristic of of the system, system, whereas, whereas, uuuggg, ,,uiu i ucg, Lig , i Li , i gi and i g represents the voltage, inverter side voltage, voltage across capacitor, grid side inductance, inverter side inductance, grid grid side side voltage, voltage, inverter inverter side side voltage, voltage, voltage voltage across across capacitor, capacitor, grid grid side side inductance, inductance, inverter inverter side side inverter side current and grid side current respectively. inductance, inverter side current and grid side current respectively. inductance, inverter side current and grid side current respectively. capacitance. Electronics 2018,The 7, 18 value

SS1 1

SS2 22

u1 u11

+ + V Vdc dc -

u2 u 22

-

S′ S′11

S′ S′22

SS3 33 LCL Filter LCL Filter

IL I LL

u3 u 33

S′ S′33

Z th Z thth

L L

Uc U cc

Vth Vthth

C C

Figure 13. A Three-phase voltage source inverter in grid-connected mode. Figure 13. A Three-phase voltage source inverter in grid-connected mode.

iiref . ref ref ..

K K pwm pwm

u uiii

+ + +

Σ Σ --

ii + 1 1 L s i i ++ Liii s

--

Σ Σ

1 1Cs Cs

u ucc +++

ug ugg

--

ig i gg

1 1L s Lggg s

Σ Σ

Figure 14. One-leg block diagram of a single-phase grid-connected system. Figure 14. One-leg block diagram of a single-phase grid-connected system.

iiref . ref ref ..

+ + +

--

Σ Σ

G G((ss))

ui uii

+ + +

Σ Σ --

K K((ss))

K K pwm pwm

uuk k

+ + +

Σ Σ --

ii i 11 i L s i Lii s

--

Σ Σ

ic icc

+ + +

11 Cs Cs

uu c c

--

ug ugg

Σ Σ

Figure 15. One-leg block diagram of a dual-loop current control strategy for VSI. Figure control strategy strategy for for VSI. VSI. Figure 15. 15. One-leg One-leg block block diagram diagram of of aa dual-loop dual-loop current current control

11 L Lgggss

ig i gg

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8. Damping Techniques for Grid-Connected VSIs 8. Damping Techniques for Grid-Connected VSIs In the grid-connected applications, LCL filter is highly preferred due to its harmonic suppressing capability. In this case, the voltage across the point of common coupling PCC is controlled in In the grid-connected applications, LCL filter is highly preferred due to its harmonic suppressing synchronism with the current. Therefore, it becomes possible to regulate the active and reactive capability. In this case, the voltage across the point of common coupling PCC is controlled in power injected intothe thecurrent. grid according to the requirement. ThetoLCL filterthe offers a resonance frequency synchronism with Therefore, it becomes possible regulate active and reactive power which can be a source of instability in the closed-loop system. This problem is stated by injected into the grid according to the requirement. The LCL filter offers a resonance frequencyvarious which researchers in the literatureinand strategies areisproposed solveresearchers it [62–65]. can be a source of instability the numerous closed-loopdamping system. This problem stated by to various Damping methods be classified intostrategies two groups. Passiveto damping and (ii) Active damping. in the literature andcan numerous damping are (i) proposed solve it [62–65]. Damping methods can be classified into two groups. (i) Passive damping and (ii) Active damping. 8.1. Passive Damping 8.1. Passive PassiveDamping damping is to inserting passive elements in the filter for reduction of the resonant peak

in thePassive systemdamping [32]. Generally, passive damping schemes never control is to inserting passive elements in thedesire filterany for amendments reduction of in thethe resonant strategy. Though, approachespassive changedamping attenuation of the filter, as aany result of which losses peak in the system these [32]. Generally, schemes never desire amendments in the increases [18,32,34]. The passive damping techniques, presented generally in the literature, results in control strategy. Though, these approaches change attenuation of the filter, as a result of which losses the addition of a simple resistordamping in series techniques, with the filter capacitor [63]. The drawback of this increases [18,32,34]. The passive presented generally in major the literature, results in technique is aofreduction filter attenuation, increasing losses and large filter volume [62]. A the addition a simple in resistor in series with the filter power capacitor [63]. The major drawback of this general schematic of passive damping control strategy for a grid connected VSI is shown in Figure technique is a reduction in filter attenuation, increasing power losses and large filter volume [62]. 16.general schematic of passive damping control strategy for a grid connected VSI is shown in Figure 16. A

iref . +

-

Σ

G ( s)

ui

K pwm

1

-

uk +

Σ -

1

Li s

ii +

Σ

ic

Cs

R

+

Σ

+

uc

ug

Σ

1

ig

Lg s

Figure 16. One-leg block diagram of a passive damping control strategy for a grid-connected VSI.

8.2. Active 8.2. Active Damping Damping The active active damping damping methods methods are proposed to to overcome overcome the the drawbacks drawbacks associated associated with with the the The are proposed passive damping modifications in in thethe control policy in passive damping techniques. techniques.Active Activedamping dampingtechniques techniquesoffer offer modifications control policy order to afford closed loop damping [65,66]. The active damping techniques are classified into in order to afford closed loop damping [65,66]. The active damping techniques are classified into3 incorporated 3groups, groups,i.e., i.e.,single singleloop, loop,multi-loop multi-loopand andcomplex complexcontrollers. controllers. Single Single loop loop methods methods are are incorporated to damp without supplementary supplementary measurement. measurement. These These methods comprise of of to damp the the LCL LCL filter filter resonance, resonance, without methods comprise low pass filter-based method, virtual flux estimation method, sensor-less method, splitting capacitor low pass filter-based method, virtual flux estimation method, sensor-less method, splitting capacitor method, notch-filter method. Generally, single-loop methods are method, notch-filter method methodand andgrid gridcurrent currentfeedback feedback method. Generally, single-loop methods found relatively robust during uncertainty in in parameters and are found relatively robust during uncertainty parameters andvariation variationiningrid grid inductance inductance [62]. [62]. Multiloop methods explore additional measurements. This group comprises of capacitor current Multiloop methods explore additional measurements. This group comprises of capacitor current feedback, capacitor average current control techniques. However, the feedback, capacitorvoltage voltagefeedback feedbackand andweighted weighted average current control techniques. However, third group of active damping methods is based on complex control structures. This outcome of these the third group of active damping methods is based on complex control structures. This outcome of techniques is usually a suitable andand a robust dynamic include these techniques is usually a suitable a robust dynamicresponse response[67]. [67].These These techniques techniques include predictive control, control, state-space state-space controllers, controllers, adaptive adaptive controllers, controllers, sliding controller and and vector vector predictive sliding mode mode controller control. Additionally, when LCL filter is selected, there are two options for current control: grid control. Additionally, when LCL filter is selected, there are two options for current control: grid current current or converter current. Various techniques are proposed but there exists a disagreement in the or converter current. Various techniques are proposed but there exists a disagreement in the literature literature thesolution suitableofsolution of these and itthat is agreed that the current control strategy about the about suitable these issues andissues it is agreed the current control strategy should be should be carefully selected. An active damping technique with a damping resistance as well as a carefully selected. An active damping technique with a damping resistance as well as a harmonic harmonic compensator are described in [65]. A general schematic of active control damping controlfor strategy compensator are described in [65]. A general schematic of active damping strategy a grid for a grid connected VSI is shown in Figure 17. connected VSI is shown in Figure 17.

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iref . +

-

Σ

G(s)

ui +

Σ

K(s)

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K pwm

-

uk +

Σ

1

Li s

ii

-

Σ

ic +

1

uc Cs

-

ug

Σ

1

ig

Lg s

-

Figure 17. One-leg block diagram of an active damping control strategy for a grid-connected grid-connected VSI. VSI.

9. Grid Techniques 9. Grid Synchronization Synchronization Techniques The grid The grid voltage voltage must must be be synchronized synchronized with with the theinjected injectedcurrent currentinina autility utilitynetwork networkforfora significant output. In synchronization algorithm, phase of the grid voltage vector is considered and a significant output. In synchronization algorithm, phase of the grid voltage vector is considered and control variables variables i.e., i.e., grid grid voltages voltages and and grid grid currents currents are are synchronized synchronized by by using using it. it. Various Various methods methods control are introduced in literature for extracting the phase angle [68]. Some commonly used techniques are introduced in literature for extracting the phase angle [68]. Some commonly used techniques found found in credible research are discussed as: in credible research articlesarticles are discussed as: Technique 9.1. Zero-Crossing Technique The simplest method to implement is Zero-Crossing method. However, it is not considered on largerscale scale due to poor performances reported in the literature. Especially, during voltage a larger due to poor performances reported in the literature. Especially, during voltage variations, variations, ample values of and harmonics are observed. ample values of harmonics notchesand are notches observed. 9.2. Filtering of Grid Voltages The grid grid voltages voltages can canbe befiltered filteredininthe thedqdq frame well as the in the αβ reference frame. frame as as well as in αβ reference frame. The The performance of zero-crossing method is improved voltage filtering [68].However, However, performance of zero-crossing method is improved by by voltage filtering [68]. it it is isa acomplicated complicatedprocess processtotoextract extractthe thephase phaseangle angleout out of of utility utility voltage, voltage, especially especially during during a fault condition. This method uses the arctangent function to realize the phase angle. Generally, a delay is observed in processing a signal while while using using the the filtering filtering method. method. Therefore, designing of the filter must be considered critically. critically. 9.3. Phase Locked 9.3. Phase Locked Loop Loop Technique Technique The phase locked locked loop, loop,PLL PLLtechnique techniqueisisconsidered considered state-of-the-art method to obtain The phase asas thethe state-of-the-art method to obtain the the phase angle of the grid voltages. The PLL is implemented in dq-synchronous reference frame. phase angle of the grid voltages. The PLL is implemented in dq-synchronous reference frame. In this In this case, the coordinates transformation to dq is and preferred andvoltage, referenceuˆ voltage, uˆ d case, the coordinates transformation from abcfrom to dqabc is preferred reference d would be would be set to zero for realizing the lock. A general schematic of PLL technique is depicted in set to zero for realizing the lock. A general schematic of PLL technique is depicted in Figure 18. A PI Figure 18. A PI regulator is generally used to control the reference variable. Afterward, the grid regulator is generally used to control the reference variable. Afterward, the grid frequency is frequency is integrated in the system and utility voltage angle is acquired after passing through integrated in the system and utility voltage angle is acquired after passing through a voltagea voltage-controlled oscillator, VCO. This voltage angle is then fed into the αβ to dq transformation controlled oscillator, VCO. This voltage angle is then fed into the αβ to dq transformation module for module for transforming into the synchronous reference frame. transforming into the synchronous reference frame. This technique is found the most suitable for rejecting notches, grid harmonics and other This technique is found the most suitable for rejecting notches, grid harmonics and other disturbances. However, additional improvements are needed to handle the unsymmetrical voltage disturbances. However, additional improvements are needed to handle the unsymmetrical voltage faults. Especially, filtering techniques to filter the negative sequence should be proposed in case of faults. Especially, filtering techniques to filter the negative sequence should be proposed in case of unsymmetrical voltage faults, as second-order harmonics are propagated by the PLL system and unsymmetrical voltage faults, as second-order harmonics are propagated by the PLL system and reflected in the obtained phase angle. Moreover, it should be assured to estimate the phase angle of the reflected in the obtained phase angle. Moreover, it should be assured to estimate the phase angle of positive sequence of the grid voltages during unbalanced grid voltages [68]. the positive sequence of the grid voltages during unbalanced grid voltages [68].

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PLL Controller ωr Loop filter + +

PI

+

ω

VCO

1 s

θ

-

Transformation Module

uβ

abc

uα αβ

dq

uq

αβ

ud

ua ub uc

Figure technique. Figure18. 18.General Generalschematic schematicofofa athree-phase three-phasePLL PLL technique.

10. 10.Modulation ModulationSchemes Schemes InInpower powerelectronics electronicsconverters, converters,the themajor majorproblem problemisisthe thereduction reductionininharmonics. harmonics.PWM PWMcontrol control techniques techniquesprovide providethe themost mostsuitable suitablesolution solutionfor forharmonics harmonicsreduction. reduction.AAsinusoidal sinusoidaloutput outputhaving having controlled controlledvalues valuesofoffrequency frequencyand andmagnitude magnitudeisisthe thecore corepurpose purposefor forusing usingthese thesePWM PWMtechniques. techniques. Primarily, PWM techniques are are classified into into threethree majormajor categories i.e., Triangular Comparison-based Primarily, PWM techniques classified categories i.e., Triangular ComparisonPWM Space Space Vector-based PWMPWM (SV-PWM) and and Voltage look-up table-based PWM based(TC-PWM), PWM (TC-PWM), Vector-based (SV-PWM) Voltage look-up table-based PWM (VLUT-PWM). (VLUT-PWM). 10.1. Based PWM 10.1.Triangular TriangularComparison Comparison Based PWM InInTriangular (TC-PWM) techniques, techniques,PWM PWMwaves wavesare areproduced produced TriangularComparison Comparisonbased based PWM PWM (TC-PWM) byby the the combination ordinary triangular carrier a fundamental modulating reference signal. combination of of an an ordinary triangular carrier andand a fundamental modulating reference signal. The The triangular carrier signal hasrelatively relativelyvery veryhigher higherfrequency frequency than than that triangular carrier signal has that of ofaafundamental fundamentalmodulating modulating reference signal. The magnitude and frequency of the fundamental modulating referencereference signal control reference signal. The magnitude and frequency of the fundamental modulating signal the magnitude and frequency of the central module in the grid side. PWM and Synchronous PWM control the magnitude and frequency of the central module in the grid side. PWM and Synchronous (SPWM) are the core techniques to be mentioned in TC-PWM [69]. PWM (SPWM) are the core techniques to be mentioned in TC-PWM [69]. 10.2. Space Vector Based PWM 10.2. Space Vector Based PWM In SVPWM techniques, the revolving reference vectors provide the reference signals. In SVPWM techniques, the revolving reference vectors provide the reference signals. The The magnitude and frequency of central module in grid side are controlled by the frequency and magnitude and frequency of central module in grid side are controlled by the frequency and magnitude of the revolving reference vectors respectively. This technique was first introduced to magnitude of the revolving reference vectors respectively. This technique was first introduced to generate vector based PWM in the three-phase inverters. However, nowadays it is expanded to various generate vector based PWM in the three-phase inverters. However, nowadays it is expanded to other newly introduced inverters. SV-PWM is considered to be the more advanced technique for PWM various other newly introduced inverters. SV-PWM is considered to be the more advanced technique generation for getting qualified sinusoidal output with low THD values [69]. for PWM generation for getting qualified sinusoidal output with low THD values [69]. 10.3. Voltage Look-Up Table-Based PWM 10.3. Voltage Look-Up Table-Based PWM In VLUT-PWM, a new method is introduced to obtain the voltage reference based on the current In VLUT-PWM, a new method is introduced to obtain the voltage reference based on the current reference for an inverter. The major advantage of this technique is its compatibility and simplicity with reference for an inverter. The major advantage of this technique is its compatibility and simplicity the load conditions. The switching frequency in this technique is usually taken significantly lower as with the load conditions. The switching frequency in this technique is usually taken significantly compared to various other presented techniques [52]. lower as compared to various other presented techniques [52]. 11. Control Techniques 11. Control Techniques Connecting the grid to the distributed generation system plays a key role and if bit negligence Connecting the grid to the distributed generation system plays a keyi.e., rolethe and if bit negligence is shown in implementing this procedure, a number of problems can arise grid uncertainty is shown in implementing this procedure, a number of problems can arise i.e., the grid uncertainty and disturbance, so in order to overcome this situation, a suitable controller must be designed for it. so in order to overcome situation, a suitable controller must be designed for it. Inand thisdisturbance, section, the most appropriate controlthis techniques are described according to their applications. In this section, the most appropriate control techniques are described according tofor their applications. Various single loop and multiloop control systems are discussed in the literature power droop Various single loop and multiloop control systems are discussed in the literature for power droop control, voltage and current control. In which inner loop is for current regulation and outer loop is

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control, voltage and current control. In which inner loop is for current regulation and outer loop is voltage regulation[13,70,71]. [13,70,71].InInFigure Figure19, 19,the thecategorization categorizationof of classical classical an an advanced control forfor voltage regulation technique is depicted clearly. clearly. Inverters Control Schemes

Predictive Control

Hysteresis Based Control Trajectory Based Control Deadbeat Control

Sliding Mode Control

Model Predictive Control (MPC) MPC with finite control set (FCS)

Voltage Control

Current Control

MPC with continuous control set (CCS)

Intelligent Control

Hysteresis Control

Artificial Neural Network (ANN) Control

Fuzzy Control FuzzyANN based Control

Linear Control

Current Control

Current Control

Direct Power Control (DPC)

Field Oriented Control (FOC)

Direct Torque Control (DTC)

Voltage Oriented Control (VOC)

Advance Control Techniques

Classical Control Techniques

Figure techniques for for VSIs. VSIs. Figure 19. 19. Classification Classification of of control control techniques

11.1. Classical Techniques 11.1. Classical Control Control Techniques The classical classicalcontrollers controllers include the category of controllers for or adding or subtracting a The include the category of controllers for adding subtracting a proportion proportion and adjusting the system accordingly. These controllers involve proportional (P), and adjusting the system accordingly. These controllers involve proportional (P), proportional proportional(PI), integration (PI), proportional integral derivative (PID) and proportional derivative (PD) integration proportional integral derivative (PID) and proportional derivative (PD) controllers. controllers. Theseare controllers are as considered the most fundamental controllers in the for These controllers considered the most as fundamental controllers in the industry forindustry controlling controlling linear systems and considered as the base of control theory. Lot of work in literature is linear systems and considered as the base of control theory. Lot of work in literature is being done being done on these controllers [49–52,72–78]. The fundamental benefits of implementing these on these controllers [49–52,72–78]. The fundamental benefits of implementing these controllers are controllers theirthemselves ability to tune themselves to the requirement of thesimple plant and their their abilityare to tune according to theaccording requirement of the plant and their structure. simple structure. Moreover, they are the most commonly used controllers on commercial levels, so Moreover, they are the most commonly used controllers on commercial levels, so easily available. easily available. However, theirresponse trackingtime ability, andstable ability to handle stable error However, their tracking ability, andresponse ability totime handle error are relatively lowerare as relatively lower as compared to modern state-of-the-art controller. The schematic of a digital PI compared to modern state-of-the-art controller. The schematic of a digital PI controller for controlling controller for controlling a three-phase with an LC filterisinshown stand-alone mode shown in 20, Figure a three-phase VSI with an LC filter in VSI stand-alone mode in Figure 20.is In Figure ia f , 20. In Figure 20, , and represents the filter current across phase a, b and c respectively. i i i af the bf filter current cf i and i represents across phase a, b and c respectively. Likewise, v , v and v bf

cf

a

b

c

characterizes phase a, b and c respectively. Likewise, i and iq represents the current , vbvoltage and vacross Likewise, Likewise, va the c characterizes the voltage across phase a, b dand c respectively. across the d and q axis respectively. Moreover, Sa , Sb and Sc represents the switching commands across id and i q represents the current across the d and q axisq respectively. Moreover, Sa , Sb and Sc phase a, b and c respectively. Correspondingly, Vred f . and Vre f . symbolizes the reference voltages along d and switching commands across phase a, b and c respectively. Correspondingly, Vref drepresents and q axisthe respectively. . q

Vref . symbolizes the reference voltages along d and q axis respectively.

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vdc

+ -

vdc

+

q ref . q ref .

v

v

PI

+

PI

PI

PI PI

vq

vq

abcabc dq dq

viq viq vid vid

Sa SSab

+ -

Sc

LC Filter iL

LC LFilter

iL

SSb

iaf ibf icf iaf ibf icf U

c

L

Uc c

Three-Phase Load

Three-Phase Load

C

C

iaf iibfaf iicfbf icfva vvab vvbc vc

+ -

rq - +PI r q idf -iqf idf iqf

SVPWM SVPWM

implementationof PI control scheme d vref rd + v .+ implementationof PIPIcontrol scheme d PI d vref-. + rd +vd

va vb vc

Analogue to

va vb vc

Digitalto Analogue Converter Digital Converter

Figure 20. Schematic of PI control algorithm for aa VSI. VSI. Figure of aaaPI PIcontrol controlalgorithm algorithmfor for Figure20. 20. Schematic Schematic of a VSI.

11.2. PR 11.2. PR Controllers 11.2. PRControllers Controllers PRPRcontrollers controllers are the combination of proportional proportionaland andresonant resonantcontrollers. controllers. The frequencies PR and resonant controllers. The frequencies controllersare arethe thecombination combination of of proportional The frequencies closer to resonant frequency are integrated by the integrator. Therefore, phase shift or stationary error closertotoresonant resonant frequency frequency are byby thethe integrator. Therefore, phase phase shift orshift stationary error closer areintegrated integrated integrator. Therefore, or stationary dodonot This controller can be in both both ABC and αβ frames. Due gain near not occur. ThisThis controller cancan be applied applied in ABC and αβ frames. Due to to high gain near error dooccur. not occur. controller be applied in both ABC and αβ frames. Due tohigh high gain near resonant frequencies, this controller has the ability to eliminate the steady-state errors of electrical resonant frequencies, this controller has the ability to eliminate the steady-state errors of electrical resonant frequencies, this controller has the ability to eliminate the steady-state errors of electrical quantities. the network frequency equal the resonant frequency. quantities.The Theresonant resonantcontroller controller maintains maintains the equal toto the resonant frequency. quantities. The resonant controller maintains thenetwork networkfrequency frequency equal to the resonant frequency. It is capable of adjusting the frequency according to changes in grid frequency. However, an It is capable of adjusting the frequency according to changes in grid frequency. However, an accurate It is capable of adjusting the frequency according to changes in grid frequency. However, an accurate accurate tuningis alwaysneeded neededfor for optimal optimal results to to thethe frequency tuning always needed optimal and this thistechnique techniqueisis foundsensitive sensitive the frequency tuning isisalways for results and and this technique isfound found sensitive to frequency variations[30,31]. [30,31].These Thesecontrollers controllers are are relatively relatively better inin terms of of their tracking variations [30,31]. relatively betterthan thanPIPI PIcontrollers controllers in terms of their tracking variations These controllers are better than controllers terms their tracking ability and response time. If used with a harmonic compensator, they can optimally handle THD. ability and response time. time. If ability and response If used used with with a harmonic harmonic compensator, compensator, they they can can optimally optimally handle handle THD. THD. Their capabilitytotohandle handlecurrent current in in grid-connected grid-connected inverters isisalso remarkable. However, damping Their capability inverters also remarkable. However, Their capability to handle current in grid-connected inverters is also remarkable. However, damping damping issuesstill still exist.The The active and and passive damping adjustments and integration in in a system with a issues issues still exist. exist. Theactive active andpassive passivedamping dampingadjustments adjustmentsand andintegration integration ina asystem systemwith witha harmonic compensator are somehow, the complicated issues. Moreover, they do not have aresomehow, somehow, the complicated Moreover, they dooutstanding not have aharmonic harmonic compensator compensator are the complicated issues.issues. Moreover, they do not have outstandingability ability toto handle handle stable stable error error and phase shift. The limitation to tohandle specific outstanding and phase shift. The limitation handle ability to handle error and phase shift. The limitation to handle frequencies i.e.,specific closer frequencies i.e., stable closer to resonant frequencies is also a drawback of thesespecific controllers. A PR controller frequencies i.e., closer to resonant frequencies is also a drawback of these controllers. A PR controller towith resonant frequencies is also HC, a drawback of these controllers. PR controller a harmonic a harmonic compensator, in stand-alone mode for a VSI isAshown in Figurewith 21. Structures with a harmonic compensator, HC,mode in stand-alone mode for a in VSI is shown in Figure 21.ofStructures compensator, HC, in stand-alone for a VSI is shown Figure 21. Structures a simple of a simple PR controller and a discrete PR controller are shown in Figures 22 and 23, respectively. of acontroller simple PRand controller and PR a discrete PR controller are shown in22 Figures 22 respectively. and 23, respectively. PR a discrete controller are shown in Figures and 23, Where, Where, Ts represents the sampling period, ω represents the grid angular frequency. However, ω T Where, represents the sampling period, represents the grid angular frequency. However, Ts represents the sampling period, ω represents the grid angular frequency. However, K p and Kr s K p and Kr denotes the proportional and resonant coefficients respectively. The PR controller with denotes the proportional and resonantand coefficients The PR controller with a harmonic K and denotes the proportional resonantrespectively. coefficients respectively. The PR controller with Kp r a harmonic compensator is proposed in [65]. compensator is proposed in [65]. a harmonic compensator is proposed in [65]. vdc

+ vdc

Implementation of PR control technique d ref .+

viq

i df

i qf

vˆβ

PR

abc abc dq dq

v id

vˆβ

Sa SSba

+ -

SScb

Sc iaf ibfiaficfibfviacfvbvvac vb vc

+ - - + - vˆq q v -i df viˆqfq ref .v id - viq ref .

αβ αβ

-v q

SVPWM SVPWM

Implementation of PRvˆ control technique vˆd + α PR ˆ vˆα v + HC d PR + + PR HC

dq

v

d ref .+

dq

v

LC Filter iL

iL

iaf ibf icf

Uc

iaf ibf icf C

L

LC Filter Three-Phase Load Three-Phase L Load

Uc C

Analogue to Digital Converter to Analogue

va

vb vc

va

vb vc

Digital Converter

Figure21. 21.General General schematic schematic of VSI. Figure of aa PR PRController Controllerand andHC HCfor fora athree-phase three-phase VSI.

Figure 21. General schematic of a PR Controller and HC for a three-phase VSI.

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KP

+

KP

Reference value Reference value

+

Kr



+ −

Kr

+





+



−



+



Output Output

 

Figure 22. General structure of a PR Controller.

Kp

Figure Figure 22. 22. General General structure structure of of aa PR PR Controller. Controller.

Kp +

Kr Reference value Kr Reference value



+ −



z−1

Ts

z−1

Ts

+



+ +



+

−

+

 

+

Ts

+

ω2

T

+ +

Output

 Output  +

−1

z

+

z−1

ω s z + z−1 of a discrete PR Controller. Figure 23. Structure −1

2

Figure 23. Structure of a discrete PR Controller. 11.3. LQG Control Technique Figure 23. Structure of a discrete PR Controller.

integration of Kalman filter with an LQR controller gives rise to an LQG controller. In this LQG Control Technique 11.3.The LQG Control technique, Kalman Filter, as well as an LQG controller, can be designed independently of each other. integration of Kalman filter filter with with an LQR LQR controller controller gives gives rise rise to an LQG controller. In this The integration Kalman This control scheme isofvalid for both linear time-invariant systems as well as for linear time-varying Kalman Filter, Filter, as well well as as an an LQG LQG controller, controller, can can be be designed designed independently ofeach eachother. other. technique, Kalman of systems. LQG control technique facilitates the designing of a linear independently feedback controller for an valid for both linear time-invariant systems as well as for linear time-varying This control scheme is uncertain nonlinear control system [79–81]. An LQG control structure with a Kalman estimator is facilitates the designing of a linear controller for an uncertain systems. LQG LQGcontrol controltechnique technique facilitates the designing of a feedback linear feedback controller for an shown in Figure 24. Where, ue represents the known input and yc is the estimated nonlinear control system [79–81]. An LQG control structure with a Kalman estimator is shown uncertain nonlinear control system [79–81]. An LQG control structure with a Kalman estimator is noise/disturbance. The Kalman estimator provides the optimal to the continuous or discrete in Figure Where, represents known input and ycsolution isinput the estimated ue the shown in24. Figure 24. ueWhere, represents the known and yc noise/disturbance. is the estimated estimation problems. The Kalman estimator optimalprovides solutionthe to the continuous or to discrete estimationorproblems. noise/disturbance. Theprovides Kalman the estimator optimal solution the continuous discrete estimation problems.

ue uyce

Kalman estimator Kalman estimator

xˆ

-K

Output

-K

Output yc Figure Figure24. 24.Structure Structureof ofan anLQG LQGcontroller. controller. xˆ

Figure 24. Structure of an LQG controller. 11.3.1. 11.3.1.Linear LinearQuadratic QuadraticRegulator Regulator The linear quadratic regulator 11.3.1. Linear Quadratic The linear quadraticRegulator regulator(LQR) (LQR)technique techniqueisisfound foundoptimal optimalfor forsteady steadyas aswell wellas as transient transient states [82–84]. As the name depicts, this control technique is a combination of linear and quadratic statesThe [82–84]. As the name depicts,(LQR) this control technique is a combination of linear and quadratic linear quadratic regulator technique is found for steady as well asthe transient functions, where the dynamics ofofthe system are described byby aoptimal set of of linear equations andand costcost of functions, where the dynamics the system are described a set linear equations the states [82–84]. As the name depicts, this control technique is a combination of linear and quadratic the system is a quadratic function. The cost function parameters are considered critically while of the system is athe quadratic function. The cost function parameters are considered critically while functions, where dynamics of the system are described byapproach a set of linear equations and the cost of designing the controller. LQR algorithm is an automatic for finding a suitable statedesigning the controller. LQR algorithm is an automatic approach for finding a suitable state-feedback the system is a quadratic function.with The state cost feedback function parameters are considered critically feedback controller. Pole placement controller provides the system with a while high controller. the Polecontroller. placementLQR with algorithm state feedback controller provides the system with aa high degree of designing is an automatic approach for finding suitable degree of freedom and makes it simpler to implement. This method is characteristically steadystateand freedom and makes Pole it simpler to implement. method is characteristically it can be feedback controller. placement with stateThis feedback controller provides thesteady systemand with a high degree of freedom and makes it simpler to implement. This method is characteristically steady and

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it can be employed evenof if the some of theparameters system parameters are unknown. However, in the finding employed even if some system are unknown. However, exertion exertion in finding exact the exact weighting factors limits the applications of LQR control scheme. Moreover, it has aof weighting factors limits the applications of LQR control scheme. Moreover, it has a discrepancy discrepancy of tracking accuracy during[83–85]. load changes [83–85]. tracking accuracy during load changes 11.3.2. 11.3.2. Linear Linear Quadratic Quadratic Integrator Integrator In (LQI) scheme, cost cost minimization is considered critically. This In linear linear quadratic quadraticintegrator integrator (LQI) scheme, minimization is considered critically. technique is implemented for nullifying the steady-state error between actual grid voltage and This technique is implemented for nullifying the steady-state error between actual grid voltage reference grid voltage during load variations [82]. An integral term used with LQ control is foris and reference grid voltage during load variations [82]. An integral term used with LQ control minimizing the the tracking error produced bybyuncertain for minimizing tracking error produced uncertaindisturbances disturbancesinininstantaneous instantaneousreference reference voltage. Optimal gains for providing adequate tracking with zero steady-state voltage. Optimal gains for providing adequate tracking with zero steady-stateerror errorare arerelatively relatively simpler technique. TheThe rapid dynamic response, accurate tracking abilityability and simpler to to attain attainby byusing usingthis this technique. rapid dynamic response, accurate tracking relatively simpler designing procedure provide thisthis technique a benefit over and relatively simpler designing procedure provide technique a benefit overother othertechniques. techniques. However, complications in extracting the model and phase shift in voltage tracking However, complications in extracting the model and phase shift in voltage trackingeven evenininnormal normal operative operative condition condition are are the the major major drawbacks drawbacks of of this this scheme. scheme. 11.4. 11.4. Hysteresis Hysteresis Control Control Technique Technique Hysteresis Hysteresis control control is is considered considered as as aa nonlinear nonlinear method method [86–93]. [86–93]. The Thehysteresis hysteresiscontrollers controllersare are used used to to track track the the error error between between the the referred referredand andmeasured measuredcurrents. currents.Therefore, Therefore,the thegating gatingsignals signalsare are generated on the basis of this reference tracking. Hysteresis bandwidth is adjusted for error removal generated on the basis of this reference tracking. Hysteresis bandwidth is adjusted for error removal in reference tracking. in reference tracking. This This isis an an uncomplicated uncomplicatedconcept conceptand andhas hasbeen beenused usedsince sinceanalog analogcontrol control platforms were intensively used. This technique does not require a modulator; therefore, the platforms were intensively used. This technique does not require a modulator; therefore, the switching switching frequency of an inverter is dependent on the hysteresis bandwidth operating conditions frequency of an inverter is dependent on the hysteresis bandwidth operating conditions and filter and filter parameters [94]. The major drawback of hysteresis is its uncontrolled parameters [94]. The major drawback of hysteresis controller controller is its uncontrolled switchingswitching frequency; frequency; however, researchers are working on improving this controller and several works however, researchers are working on improving this controller and several works are presented are and presented and several arethe proposed in the literature. Main advances in this are several techniques aretechniques proposed in literature. Main advances in this technique aretechnique direct torque direct (DTC)and [87,88,95,96] andcontrol direct power control (DPC) [97–99]. DPC, active and controltorque (DTC)control [87,88,95,96] direct power (DPC) [97–99]. In DPC, active In and reactive powers reactive powers are directly controlled, however, in DTC torque and flux of the system are controlled. are directly controlled, however, in DTC torque and flux of the system are controlled. Error signals are Error signals produced by hysteresis controllers signals by the look-up produced by are hysteresis controllers and drive signalsand aredrive generated byare thegenerated look-up according to the according to the magnitude of the error signals. Hysteresis controllers require very high frequency magnitude of the error signals. Hysteresis controllers require very high frequency for constraining the for constraining the variables in hysteresis band limits, whenever implemented onshown a digital variables in hysteresis band limits, whenever implemented on a digital platform as inplatform Figure 25. as shown in Figure 25. Moreover, switching losses are very high in this type of controllers. So, Moreover, switching losses are very high in this type of controllers. So, Hysteresis controllers are found Hysteresis controllers found inappropriate for high power applications. inappropriate for highare power applications.

vdc

+ LC Filter a + iref .

-

b + iref . -

icref .+-

iL

Sa Sb Sc

iaf ibf icf

L

Three-Phase Load

Uc

C

iaf ibf icf

Analogue to Digital Converter

Figure 25. A Hysteresis control technique for VSI. Figure 25. A Hysteresis control technique for VSI.

11.5. Sliding Mode Control 11.5. Sliding Mode Control The sliding mode control is considered to be an advanced power control technique for the The sliding mode control is considered to be an advanced power control technique for the power power converters. It fits into the family of adaptive control and variable structure control [100–104]. converters. It fits into the family of adaptive control and variable structure control [100–104]. Sliding

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mode control is a non-linear technique, whereas it can be instigated to both non-linear as well as Sliding mode control is a non-linear technique, whereas it can be instigated to both non-linear as well linear systems [100]. In Figure 26, a sliding mode control along with SVM/PWM is presented. Where, as linear systems [100]. In Figure 26, a sliding mode control along with SVM/PWM is presented. βv represents the gain, λ is a strictly positive constant and φ is a trade-off between the tracking Where, β v represents the gain, λ is a strictly positive constant and φ is a trade-off between the tracking errorand andsmoothing smoothing of control the control discontinuity. The sliding controller voltage error of the discontinuity. The sliding controller producesproduces the voltagethe references references in a converter for generating the drive signals. A predefined trajectory is executed and the in a converter for generating the drive signals. A predefined trajectory is executed and the control control variable slideitalong it [102–104]. The and robust andresponse stable response is achieved variable is forcedistoforced slide to along [102–104]. The robust stable is achieved even ineven the in the system parameters variation or load disturbances by implementing sliding mode control system parameters variation or load disturbances by implementing sliding mode control technique. technique. Thisiscontroller is more and of removing stable error as compared to the This controller more robust androbust capable of capable removing the stable the error as compared to the classical classical controllers. However, some drawbacks in implementing a sliding mode control are difficulty controllers. However, some drawbacks in implementing a sliding mode control are difficulty in finding findingsliding a suitable sliding and of limitation ofrate sampling rate thatthe degrades the performance of ainsuitable surface andsurface limitation sampling that degrades performance of SMC will SMC will beWhenever degraded.tracking Whenever tracking a variable reference,phenomenon the chattering phenomenon is be degraded. a variable reference, the chattering is another drawback another drawback of SMC technique. As a result, overall system efficacy is reduced [105,106] of SMC technique. As a result, overall system efficacy is reduced [105,106].

vdc

+ -

implementation of sliding modecontrol

β vref .

λ βv

+ -

-

+

-

-

1

+ -

+

φ

PWM Modulator

+

+

LC Filter

Sa Sb

iL

Sc

iaf ibf icf

-

L

Three-Phase Load

Uc

C

βv

iaf ibf icf va vb vc

iaf ibf icf va vb vc

1 C

Analogue to Digital Converter

va

vb vc

Figure 26. 26. A A Sliding Sliding mode mode control control technique technique on on aa VSI. VSI. Figure

11.6. Partial Feedback Controllers 11.6. Partial Feedback Controllers There are several techniques presented for conversion of non-linear systems to linear systems There are several techniques presented for conversion of non-linear systems to linear systems for their uncomplicated computation. Partial feedback controllers are one of the most effective and for their uncomplicated computation. Partial feedback controllers are one of the most effective and forthright techniques for transforming the non-linear systems into the linear ones. By this technique, forthright techniques for transforming the non-linear systems into the linear ones. By this technique, a system can be converted either partially or fully into a linear system, depends on the system a system can be converted either partially or fully into a linear system, depends on the system constraints. Linearity in a system is attained by the cancellation of the nonlinearities inside the constraints. Linearity in a system is attained by the cancellation of the nonlinearities inside the system. system. So, these systems can be controlled by using the linear controllers whenever a non-linear So, these systems can be controlled by using the linear controllers whenever a non-linear system is fully system is fully transformed into a linear system i.e., exact feedback linearization method. However, transformed into a linear system i.e., exact feedback linearization method. However, if it is partially if it is partially converted into a linear system then it is known to be partial feedback linearization. converted into a linear system then it is known to be partial feedback linearization. PFL controller is PFL controller is implemented in [104,106–109]. In PFL, it is difficult to ensure the stability of implemented in [104,106–109]. In PFL, it is difficult to ensure the stability of complicated renewable complicated renewable energy system applications. However, an independent subsystem can be energy system applications. However, an independent subsystem can be obtained from PFL for obtained from PFL for constraining the extensive use of this method. Moreover, in order to deal with constraining the extensive use of this method. Moreover, in order to deal with these problems, these problems, exact feedback linearization (EFL) is a forthright and model-based technique for exact feedback linearization (EFL) is a forthright and model-based technique for scheming nonlinear scheming nonlinear control techniques. EFL receipts the built-in nonlinearity characteristic of the control techniques. EFL receipts the built-in nonlinearity characteristic of the system under deliberation system under deliberation and consents the conversion of a nonlinear structure into a linear one, and consents the conversion of a nonlinear structure into a linear one, algebraically. EFL removes algebraically. EFL removes nonlinearities of a system through nonlinear feedback, as a result, the nonlinearities of a system through nonlinear feedback, as a result, the transformed system is not reliant transformed system is not reliant on an operating point on an operating point. 11.7. Repetitive Repetitive Control Control 11.7. The plug-in plug-in scheme scheme (PIS) (PIS) and and internal internal model model (IM) (IM) principle principle are are the the basic basic concepts concepts of of repetitive repetitive The control(RC). (RC).RC RCuses usesan anIMP IMPwhich whichisisinincorrespondence correspondence model a periodic signal. In order control toto thethe model of of a periodic signal. In order to to derive this model, trigonometric Fourier series expansion is used. If the model of reference is fed derive this model, trigonometric Fourier series expansion is used. If the model of reference is fed into intoclosed the closed loop path, optimal reference tracking be obtained. Moreover, it isrobust foundagainst robust the loop path, optimal reference tracking can be can obtained. Moreover, it is found against disturbances and has the ability to reject them. RC mostly deals with periodic signals. Closed

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disturbances and has the ability to reject them. RC mostly deals with periodic signals. Closed loop behavior of the and REVIEW Magnitude response of the corecore factors used for for analyzing the loop behavior ofsystem the system Magnitude response of IM the are IM the are the factors used analyzing Electronics 2018, 7, x FOR PEER and 23 of 37 performance of the repetitive controller in case of frequency variation or any other uncertainty in the the performance of the repetitive controller in case of frequency variation or any other uncertainty in loop behavior of the system and Magnitude response of the IM are the core factors used for analyzing system. Both these factors indicate the performance sagging in case of variation or uncertainty in the the system. Both these factors indicate the performance sagging in case of variation or uncertainty in the performance of repetitive controller in case of frequency or other uncertainty reference signal. In presence of a of periodic disturbance, RC intends to attain zero tracking errorinwhen the reference signal. Inthe presence a periodic disturbance, RCvariation intends toany attain zero tracking error the system. Both these factors indicate the performance sagging in case of variation or uncertainty in a periodic or a constant command is referred to it. RC has anhas ability to locate an error, time-period when a periodic or a constant command is referred to it. RC an ability to locate an aerror, a timethe reference signal. In presence of a periodic disturbance, RC intends to attain zero tracking error before and fine-tunes the next command the feedback control systemcontrol for eliminating the period before and fine-tunes the next according command toaccording to the feedback system for when a periodic or a constant command is referred to it. RC has an ability to locate an error, a timeobserved error. iterror. lacks However, the ability to physical noise.handle For this purpose,noise. an LPF can be eliminating the However, observed it handle lacks according the ability physical period before and fine-tunes the next command to to the feedback control system For for this used.eliminating Kalman’s filtering approach is also noticeable to remove this noise [27,110–113]. The general purpose, an LPFthe canobserved be used. Kalman’s filtering approach is also noticeable to remove this noise error. However, it lacks the ability to handle physical noise. For this structure of aThe repetitive isofshown in Figure 27. [27,110–113]. general structure a repetitive controller is also shown in Figure 27. purpose, an LPF cancontroller be used. Kalman’s filtering approach is noticeable to remove this noise [27,110–113]. The general structure of a repetitive controller is shown in Figure 27. Repetitive Controller +

Time delay Time delay function

+

+ Reference Reference values

function

Repetitive Controller

Stabilizing Stabilizing Controller

Low-pass Low-pass filter

-

Disturbance +

+

+

+

values

+

Disturbance

Controller

filter

+

+

Nominal Nominal Controller

+

Plant

Plant

Controller

+

+

+

Output

Output

-

Figure 27.27. Block diagram ofRepetitive Repetitivecontrol control algorithm. Figure 27. Block control algorithm. Figure Blockdiagram diagramof of Repetitive algorithm.

11.7.1. Fuzzy Control 11.7.1. Fuzzy Control 11.7.1. Fuzzy Control This control technique belongstotothe the family of of intelligent control systems. TheThe PI controller is This PI PI controller is This control control technique techniquebelongs belongs to thefamily family ofintelligent intelligentcontrol controlsystems. systems. The controller replaced by a fuzzy logic controller in this technique as shown in Figure 28. Where, v fz. is the replaced by by a fuzzy logic controller in in this technique is replaced a fuzzy logic controller this techniqueasasshown shownininFigure Figure28. 28.Where, Where,vvfzf.z. isis the the fuzzified output voltage.However, However, its block diagram is shown in Figure 29. In 29. a fuzzy controller, the fuzzified output voltage. its block diagram is shown in Figure In a fuzzy controller, fuzzified output voltage. However, its block diagram is shown in Figure 29. In a fuzzy controller, the tracking error of load current and its derivative are given as the input. This controller design is the tracking of load current and derivative are givenasasthe the input.This Thiscontroller controllerdesign design is is tracking errorerror of current and its its derivative are given dependent on load the awareness, knowledge, skills and experience of the input. converter designer in terms of dependent on the awareness, knowledge, skills and experience of the converter designer in terms of dependent on involvement. the awareness, experience of the converter in terms of functions Dueknowledge, to non-linear skills natureand of the power converters, the systemdesigner can be stabilized functions involvement. Due to non-linear nature of the power converters, the system can be stabilized functions involvement. Due to non-linear nature of the power converters, the system can be in case of parameters variation even if the exact model of the converter is unknown. Fuzzy stabilized logic in case of parameters variation even if the exact model of the converter is unknown. Fuzzy logic controllers are also variation categorizedeven as non-linear controllers probably the best controllers amongst in case of parameters if the exact modeland of the converter is unknown. Fuzzy logic controllers are also categorized as non-linear controllers and probably the best controllers amongst the repetitive [113–116]. However, strong assumptions andthe adequate experienceamongst are the controllers are alsocontrollers categorized as non-linear controllers and probably best controllers repetitive controllers [113–116]. strong and on adequate experience are required in required incontrollers fuzzification of However, this controller. Asassumptions it is dependent the input experience and draw are the repetitive [113–116]. However, strong assumptions andsystem adequate conclusions according to theAs setitofisrules assigned tothe them during the process of their modelingaccording and fuzzification of this controller. dependent on system input and draw conclusions required in fuzzification of this controller. As it is dependent on the system input and draw to thedesigning. set of according rules assigned toset them during the process of their modeling and designing. conclusions to the of rules assigned to them during the process of their modeling and

designing.

vdc

implementationof fuzzy control technique vref +. iref .

vref +.

Fuzzy Controller

abc

abc

idf iqf viq vid

-

dq

-

dq idf iqf viq vid

+ - d dt

v fz.

vdc

Sa Sb

LC Filter

+ -

iL

Three-Phase Load

L

LC Filter

SSa c Sb

iaf ibf icf

Uc

iL

L

C

Sc

iaf ibf icf via vib vic va vb vc af bf cf

iref .

Controller

+ d dt

SVPWM

+

SVPWM

v fz. + implementationof fuzzy control Fuzzytechnique

+ -

iaf ibf icf Analogue to Digital Converter

Uc

va

Analogue to Digital Converter

Figure 28. A Fuzzy control algorithm topology on a VSI. Figure 28. A Fuzzy control algorithm topology on a VSI.

Figure 28. A Fuzzy control algorithm topology on a VSI.

C

vb vc

va

vb vc

Three-Phase Load

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Reference values Electronics 2018, 7, x FOR PEER REVIEW Reference values

i(t)

Defuzzification

Fuzzification

i(t)

Defuzzification

Fuzzification

Output 24 of 37

Output

Rule base decision

Fuzzy Controller

Rule base decision

Fuzzy Controller

Figure algorithm. Figure 29. 29. Block Block diagram diagram of of Fuzzy Fuzzy control control algorithm.

11.7.2. Artificial Neural Network FigureControl 29. Block diagram of Fuzzy control algorithm. 11.7.2. Artificial Neural Network Control The Artificial neural network Control (ANN) controllers are the fundamental form of the controllers 11.7.2. Artificialneural Neuralnetwork Network The Artificial (ANN) controllers are the fundamental form of the controllers based based on the human-thinking mode. It consists of a number of artificial neurons to behave as a on the human-thinking mode. It consists of controllers a number are of artificial neuronsform to behave as a biological The Artificial neural network (ANN) the fundamental of the controllers biological human brain. The reference tracking error signals are given through a suitable gain or a human brain. reference tracking error signals are through a suitable gaintoorbehave a scaling based on The the human-thinking mode. It consists of agiven number of artificial neurons as afactor scaling factor (S) as input to the ANN for generating the switching signals into the power converters. human brain. The reference errorsignals signalsinto are given through a suitableThis gainapproach or a (S) asbiological input to the ANN for generating thetracking switching the power converters. This approach is used for achieving thefor constant switching operation in into power converters. ANN can scaling factor (S) as input to the switching ANN generating signals the power converters. is used for achieving the constant operationthe inswitching power converters. ANN can be used in both be used in both online as well offline modes whileswitching operatingoperation it on system control. It has high tolerance This is used for achieving the constant power canfaults online as approach well offline modes while operating it on system control. It in has highconverters. tolerance ANN level to level be to faults because of itsasability to estimate the function mapping. Its topology ishas shown in Figure 30. used in both online well offline modes while operating it on system control. It high tolerance because of its ability to estimate the function mapping. Its topology is shown in Figure 30. level to faults becausecan of itsbe ability to estimate function topologyperformance is shown in Figure Fuzzy and ANN combined to the achieve anmapping. optimalItscontrol in a30.power Fuzzy and ANN can be combined to achieve an optimal control performance in a power Fuzzy and ANN can be combined to achieve an optimal control performance in a power the converter [113–115]. ANN does not need a converter model for its operation, however, converter [113–115]. ANN does not need a converter model for its operation, however, the operational converter [113–115]. ANN does not need a converter model for its operation, however, thewhile operational behavior of a power converter should be precisely known to the designer/operator behavior of a power converter should be precisely known to the designer/operator while while designing operational behavior of a power converter should be precisely known to the designer/operator designing the ANN control system. the ANN control designing the system. ANN control system. v

vdcdc+

implementationof ANN control technique implementationof ANN control technique q vref .

k

k

k

iL

SScc

iafiafibf iibfcf icfU C

dq

dq

af bf cf

+ +- + - + k q vref . - - vviqid viq idf iiqfdf iqf

LC Filter

SSa a SSbb

abc

abc

iafi ibfi icfi vavvabvvbc vc

vid

+

SVPWM SVPWM

d d vref . + vref . + +

+ -

Analogue to

Analogue Digital to Digital Converter Converter

c

iL

LC Filter L

L

Three-Phase Three-Phase Load Load

Uc

C

va v vb vvc v a b c

Figure SchematicofofArtificial Artificial Neural control forfor VSIs. Figure 30.30. Schematic NeuralNetwork Network control VSIs. Figure 30. Schematic of Artificial Neural Network control for VSIs. 11.8. Robust Controllers

11.8. Robust Controllers Controllers 11.8. Robust In robust control theory, a control system vigorous against uncertainties and disturbances is In robust control a control system vigorous uncertainties andAll disturbances is offered. offered. The basic theory, aim is to attain the stability invigorous case against of inadequate modeling. the In robust control theory, a control system against uncertainties anddescriptions, disturbances is The basic aim is to attain the stability in case of inadequate modeling. All the descriptions, criteria and criteria and limitations should be appropriately defined in order to get robust control. This controller offered. The basic aim is to attain the stability in case of inadequate modeling. All the descriptions, limitations appropriately defined in order to getin robust This controller guarantees guarantees the be stability and high performance of closed-loop systemcontrol. multivariable systems [117]. the criteria andshould limitations should be appropriately defined order even to getinrobust control. This controller stability and high performance of closed-loop system even in multivariable systems [117]. guarantees the stability and high performance of closed-loop system even in multivariable systems [117]. 11.8.1. H-Infinity Controllers

11.8.1. H-Infinity Controllers The expression H∞ control originates from the term mathematical space on which the 11.8.1. H-Infinity Controllers optimization takes place: H∞ isoriginates consideredfrom as a the space of mathematical matrix-valued functions are the The expression H∞ control term space onthat which The expression H∞ control originates from term plane. mathematical on system, which the investigative and confined in the open right-half of thethe complex In this typespace of control optimization takes place: H∞ is considered as a space of matrix-valued functions that are investigative optimization place:problem H∞ isis formulated consideredand as then a space of matrix-valued that are first of all,takes the control mathematical optimization functions is implemented and confined in the open right-half of the complex plane. In this type of control system, first of all, i.e., selection the bestin element according to criterion from theplane. set of In obtainable Hinvestigative and of confined the open right-half of the complex this typealternatives. of control system, the control problem is formulated and thenpertinent mathematical optimization issystems. implemented i.e., selection infinity control techniques are generally for the multivariable The impact of a first of all, the control problem is formulated and then mathematical optimization is implemented of theperturbation best element according to criterion from the set of obtainable alternatives. H-infinity control can be reduced by using H-infinity control techniques in a closed loop system subject to i.e., selection of the best element according to criterion from the set of obtainable alternatives. Hinfinity control techniques are generally pertinent for the multivariable systems. The impact of a perturbation can be reduced by using H-infinity control techniques in a closed loop system subject to

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techniques are generally pertinent for the multivariable systems. The impact of a perturbation can be reduced by using H-infinity control techniques in a closed loop system subject to the problem formulation. The impact can be measured either in terms of performance or stabilization of the Electronics 2018, 7, x FOR PEER REVIEW 25 of 37 system. However, modeling of the system should be well-defined for implementation of these control techniques. Moreover, H-infinity control have another discrepancy of high computational the problem formulation. The impact cantechniques be measured either in terms of performance or stabilization complications. In However, case of non-linear limitations, control system cannot handle them well of the system. modeling systems of the system should bethe well-defined for implementation of these and response time also increases However, these controllers implemented and of well defined control techniques. Moreover,[118]. H-infinity control techniques haveare another discrepancy high computational complications. In case of non-linear systems limitations, the control system cannot in [111,112,119]. handle them well and response time also increases [118]. However, these controllers are implemented

11.8.2. µ-Synthesis and well definedControllers in [111,112,119]. Mu-synthesis is based on the multivariable feedback control technique, which is used to handle 11.8.2. μ-Synthesis Controllers

the structured as well as unstructured disturbances in the system. Where µ mentions the singular Mu-synthesis is based on the multivariable feedback control technique, which is used to handle value that is reciprocal of the multivariable stability margin. The basic purpose is to mechanize the the structured as well as unstructured disturbances in the system. Where μ mentions the singular synthesis of multivariable feedback controllers that are insensitive to uncertainties of the plant and be value that is reciprocal of the multivariable stability margin. The basic purpose is to mechanize the able synthesis to attain the anticipated feedback performance objectives. This methodtoisuncertainties well described in plant [120,121]. of multivariable controllers that are insensitive of the and be able to attain the anticipated performance objectives. This method is well described in [120,121].

11.9. Adaptive Controllers

11.9. Adaptive Controllers An adaptive controller is designed to have the ability of self-tuning, i.e., to regulate itself

spontaneously according to variations in thetosystem parameters. It does not i.e., require initial conditions, An adaptive controller is designed have the ability of self-tuning, to regulate itself spontaneously according to variations in the system parameters. requiretoinitial conditions, system parameters or limitations for its implementation dueIt does to itsnot ability modify the control system parameters or limitations for itsRecursive implementation to itsand ability to modify the control law most law according to system requirements. least due squares Gradient descent are two according to system requirements. Recursive least squares and Gradient descent are two most commonly known technique for parameters estimation in adaptive controllers. The structure commonly known technique for parameters estimation in adaptive controllers. The structure of a of a typical adaptive controller is shown in Figure 31. In the literature, some credible research typical adaptive controller is shown in Figure 31. In the literature, some credible research articles and articles and state-of-the-art techniques for adaptive controllers are found in [14,37,53,55,113,122–125]. state-of-the-art techniques for adaptive controllers are found in [14,37,53,55,113,122–125]. These Thesecontrollers controllers applicable both dynamic as well as static processes. However, the complicated areare applicable forfor both dynamic as well as static processes. However, the complicated computational process leads to exertion in its implementation. computational process leads to exertion in its implementation. Parameters tuning

Reference values

Controller Parameters

Controller

Control Signal

Plant

Output

Figure 31.Block Blockdiagram diagram of algorithm. Figure 31. ofAdaptive Adaptivecontrol control algorithm.

Predictive Controllers 11.10.11.10. Predictive Controllers Predictive controllers are commenced as a propitious control technique for electronics inverters. Predictive controllers are commenced as a propitious control technique for electronics inverters. The system model is considered critically and then imminent behavior of the control variables is The system is considered critically and then imminent behavior of the and control is predictedmodel conferring to the specified criterion. It is an uncomplicated technique can variables handle predicted conferring to the specified criterion. It is an uncomplicated technique and can handle multivariable systems efficiently. Moreover, it can handle the system with several limitations or nonmultivariable efficiently. it can handle withresponse severaland limitations or linearities. systems It is generally preferredMoreover, due to its prompt static as the wellsystem as dynamic ability non-linearities. It iserrors. generally preferred due to its prompt as well dynamictoresponse to handle stable However, its computational analysisstatic is complex asas compared classical and controllers. is further categorized intoitsDeadbeat control and Model control. It canto refer ability to handleItstable errors. However, computational analysis is Predictive complex as compared classical to literature [105,125–127] for predictive controllers. A comparison of predictive control techniques controllers. It is further categorized into Deadbeat control and Model Predictive control. It can refer to on basis of their pros.for andpredictive cons. is described in Table literature [105,125–127] controllers. A 2. comparison of predictive control techniques on

basis of their pros. and cons. is described in Table 2. 11.10.1. Deadbeat Control

Deadbeat control technique is the most authentic, competent and attractive technique in terms of low THD value, frequency as well as rapid transient response. Differential equations are derived

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11.10.1. Deadbeat Control Deadbeat control technique is the most authentic, competent and attractive technique in terms Electronics 2018, 7, x FOR PEER REVIEW 26 of 37 of low THD value, frequency as well as rapid transient response. Differential equations are derived and discretized in this type systemforfor controlling the dynamic behavior of theThe system. and discretized in this typeof of control control system controlling the dynamic behavior of the system. controlsignal signal is predicted predicted for period forfor attaining the the reference value. Its effective The control forthe thenew newsampling sampling period attaining reference value. Its effective Electronics 2018, 7, x FOR PEER REVIEW 26 of 37 dynamic performance and highbandwidth bandwidth simplify simplify the control for for thisthis typetype of controller. dynamic performance and high thecurrent current control of controller. Error compensation is a specialty of a deadbeat controller. However, its major discrepancy is its is its Error compensation isthis a specialty of asystem deadbeat controller. However, its major discrepancy and discretized in type of control for controlling the dynamic behavior of the system. The sensitivity for network parameters and accurate mathematical filter modeling [13,54,56,128–135]. control is predicted for the new period for attaining the reference value.[13,54,56,128–135]. Its effective Its sensitivity forsignal network parameters andsampling accurate mathematical filter modeling topology is shown in Figure 32, where a disturbance observer, a state estimator and a digital deadbeat dynamic and high bandwidth the current controlafor this estimator type of controller. Its topology is performance shown in Figure 32, where asimplify disturbance observer, state and a digital ˆ Error compensation iscontrol a specialty of a deadbeat controller. its major discrepancy its the d represents controller are used the voltage and current a However, VSI.of The coefficient deadbeat controller areto used to control the voltage and of current a VSI. The coefficient disˆ represents sensitivity for network parameters and accurate mathematical filter However, modeling [13,54,56,128–135]. Its ˆ v output of disturbance observer comprises of current and voltage. and represents vˆ q d the output of disturbance observer comprises of current and voltage. However, vˆ d and vˆ q represents topology is shown in Figure 32, where a disturbance observer, a state estimator and a digital deadbeat the controlled voltage across d-axis and the controlled voltage across d-axis andq-axis q-axisrespectively. respectively. ˆ controller are used to control the voltage and current of a VSI. The coefficient d represents the output of disturbance observer comprises of current and voltage. However, vˆd and vˆ represents

vdc

implementationof deadbeat control scheme

q

the controlled voltage across d-axis and q-axis respectively. + L

+ -

iaf ibf icf i

Uc

Three-Phase Load

LC Filter Three-Phase Load

L

C L

Sc

Uc

iaf ibf icf Analogue to Digital Converter

va

C

va

Analogue to Digital Converter

abc

Disturbance Observer Observer

vβ

dq

Disturbance

vˆq

iL

vdc

SSac Sb

abc

dˆ

z

vvαβ

iaf ibf icf viafa ivbfb ivcfc va vb vc

vq

−1

vvˆqd

dq

estimator

SVPWM SVPWM

dˆ State

d

αβ idf iqf vid ivdfiq iqf vid viq

q vref .

Deadbeat Controller

z

vvq

dq

ref . +

State estimator

LC Filter

Sa Sb

vα vˆd control scheme deadbeat −1

αβ

q vref v d.

Deadbeat vd implementationof Controller

dq

d vref .+

vb vc vb vc

Figure 32.Deadbeat Deadbeat control control topology VSIs. Figure 32. topologyfor for VSIs.

11.10.2. Model Predictive Control

Figure 32. Deadbeat control topology for VSIs. 11.10.2. Model Predictive Control

As the name depicts, a model of the system is used to predict the behavior of the system in model

11.10.2. Model Predictive Control As the name depicts, a model of the system is used to predict the behavior system in model predictive control (MPC) technique. A cost function criterion is defined in this typeofofthe control system, predictive (MPC) technique. A the cost function criterion isthe defined in of this ofincontrol As depicts, a model of system is used toThe predict behavior thetype system model system, whichcontrol canthe bename minimized for optimal control actions. controller adapts the optimal switching predictive control technique. cost function criterion iscontroller defined this type for of control system, which can be minimized optimal control actions. The adapts the optimal switching states according to (MPC) thefor cost functionA criterion. Forecast error can beinlessened current tracking which can be minimized for optimal control actions. The error controller adapts the optimal switching system limitations and non-linearities, as multiple inputs tracking and statesimplementing. according toMoreover, the cost function criterion. Forecast canas bewell lessened for current statessystems, according tohandled the costwell function criterion. Forecast error canpresent be lessened for considered current tracking output are by MPC. Control actions of the state are in order implementing. Moreover, system limitations and non-linearities, as well as multiple inputs and output Moreover, system and non-linearities, well as control, multipleitinputs to implementing. predict the control actions of thelimitations system in the next Like as deadbeat is alsoand found systems, are handled well by MPC. Control actions ofstate. the present state are considered in order to output systems, are handled well by MPC. Control actions of the present state are considered in order sensitive to system parameter variations [136–147]. The topology for implementation of MPC on VSI predicttothe control actionsactions of the in in the Like deadbeat control, it is also found predict the control of system the system thenext next state. state. Like deadbeat control, it is also found is shown in Figure 33, whereas, its control schematic is depicted in Figure 34. sensitive to system parameter variations Thetopology topology implementation sensitive to system parameter variations[136–147]. [136–147]. The for for implementation of MPCofonMPC VSI on VSI is shown in Figure 33, whereas, controlschematic schematic isisdepicted in Figure 34. is shown in Figure 33, whereas, its its control vdepicted in Figure 34. dc

+ -

implementationof MPC control scheme

vˆq

abcabc dq dq

Observer

vˆq

idf iiqfdf iqfviq vviqidvid

Observer Disturbance

vˆd

Sa Sba

vdc

LC Filter

+ -

iL iL

SSb

iaf ibf icf

LC Filter L

Uc

iaf ibf icf

c

Sc

iaf iibfaf iicfbf icfva vba vcb vc

Model Predictive q vd vref .ref - . + Controller Model Predictive q vref . Controller dˆ Disturbance dˆ

SVPWM SVPWM

MPC control vˆd scheme v implementationof + d ref .

Uc

L

C

C

Analogue to Digitalto Analogue Converter Digital Converter

va

va

Figure 33.33.Model Controltopology topology VSIs. Figure ModelPredictive Predictive Control forfor VSIs. Figure 33. Model Predictive Control topology for VSIs.

vb vc

vb vc

Three-Phase Load

Three-Phase Load

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MODEL PREDICTIVE CONTROLLER predicted control variables

Predictor Reference values +

Optimizer

+ Reference values

Plant

Output

-

Cost Function

Constraints

Figure 34. Block Diagram of Model Predictive Control algorithm.

11.11. Iterative 11.11. Iterative Learning Learning Scheme Scheme Iterative Learning butbut authentic technique for attaining zero Iterative Learning Scheme Scheme(ILS) (ILS)is isa complicated a complicated authentic technique for attaining tracking error. In this scheme, each control command is is executed zero tracking error. In this scheme, each control command executedand andthe thesystem systemisis examined examined and and then adjusted accordingly before each repetition. Highly accurate modeling of the system is essential then adjusted accordingly before each repetition. Highly accurate modeling of the system is essential for the the implementation implementation of of ILS; therefore, its its designing designing technique technique is is relatively relatively more more complicated complicated than than for ILS; therefore, other schemes. ofof removing thethe tracking error caused by the disturbances. The other schemes. ILS ILSisiscapable capable removing tracking error caused by periodic the periodic disturbances. next cycle is predicted by considering the learning gain, system adjustment in z-transform, tracking The next cycle is predicted by considering the learning gain, system adjustment in z-transform, tracking error at at each each repetition, repetition, control control function function of of the the designed designed controller controller and and the the error error function function between between error two consecutive consecutive iterations. iterations. two 12. Comparative Analysis and Future Research Goals VSIs are specially designed for converting DC to three-phase AC, therefore, control strategies the three-leg three-leg three-phase three-phase power power inverters. inverters. However, for MLIs, the control must be according to the three-phase power inverters. The The control policies of VSIs strategies must must be beinherited inheritedfrom fromthree-leg three-leg three-phase power inverters. control policies of in stand-alone modemode can be into into numerous categories depending uponupon similar and VSIs in stand-alone cancategorized be categorized numerous categories depending similar dissimilar considerations. Considering the PWM, VSIs VSIs can be into into two two categories i.e., and dissimilar considerations. Considering the PWM, canclassified be classified categories carrier-based modulation and and carrier-less modulation. The carrier-based modulation schemes such i.e., carrier-based modulation carrier-less modulation. The carrier-based modulation schemes as Selective Harmonic Elimination (SHE), (SHE), 3D SVPWM, Sinusoidal Pulse Width (SPWM) such as Selective Harmonic Elimination 3D SVPWM, Sinusoidal PulseModulation Width Modulation and Minimum-Loss Discontinuous PWMPWM (MLDPWM) based PWM techniques (SPWM) and Minimum-Loss Discontinuous (MLDPWM) based PWM techniqueshave have attained constant switching switching frequency. frequency. significant consideration due to their constant SPWM offers constant switching frequency and flexible control schemes; nevertheless, one major disadvantage of ofthis thistechnique technique is the compact efficacy the DC voltage [148]. The 3D-SVPWM disadvantage is the compact efficacy of theofDC voltage [148]. The 3D-SVPWM delivers delivers an adequate DC bus utilization and a standardized load curvature harmonic as curvature as to compared to an adequate DC bus utilization and a standardized load harmonic compared the SPWM the SPWMHowever, technique. However, it is complex nature to beonimplemented on theCorrespondingly, digital devices. technique. it is complex in nature to bein implemented the digital devices. Correspondingly, the SHE-PWM suggestsby a flexible controller by considering the switching angle. the SHE-PWM suggests a flexible controller considering the switching angle. However, the real-time However, the real-time enactment of this carrier-based modulation is quite of difficult. The capability enactment of this carrier-based modulation is quite difficult. The capability the MLDPWM under of the MLDPWM under conditions nonlinear is and unbalanced found its relatively nonlinear and unbalanced found relatively conditions admissible; is however, real-timeadmissible; execution however, its real-time executionHowever, is found very much circuitous. However, the carrier-less is found very much circuitous. the carrier-less modulation approaches such asmodulation flux vector approaches such as fluxa vector and hysteresis provide rapid-dynamic [149]. switching But, they and hysteresis provide rapid-dynamic response [149].a But, they sufferresponse from variable suffer from[91]. variable switchingthey frequency Additionally, they require composite switching tables frequency Additionally, require [91]. composite switching tables for their implementation. for their The implementation. conventional PI controllers encounter problems to eliminate the steady-state error. In order to PIcontroller controllers to eliminate steady-state In order solveThe thisconventional problem, a PR is encounter commonlyproblems used in the stationarythe reference frameerror. for regulating to solve this problem, a PR controller commonly used in the stationary reference frame for the output voltages of the VSIs due to itsis sophisticated explication in eliminating the steady-state regulating output voltages of the VSIs due to its sophisticated explication in eliminating the error, whilethe controlling sinusoidal signals. Additionally, it is competent in eliminating selective steady-state error, while controlling sinusoidal signals. Additionally, it is competent in eliminating harmonic uncertainties. selective harmonic uncertainties.

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It is also taken into consideration that the PR controller perceives the resonant frequency to offer gains at specific frequencies. Thus, the resonant frequency should be synchronized with the frequency of the microgrid. Hence, it can be said that it is very sensitive with respect to the variations in system frequency. The PI controller is also extensively used in the dqo frame and performs robustly with pure DC signals. Though, in order to allocate the control variables from the abc to the dqo frame, the phase angle of the microgrid should be known. Likewise, using cross-coupling and voltage feedforward terms are the secondary problems in implementing this method. In the stand-alone operating mode, VSIs primarily controls the power transfer, voltage and frequency of the system. Nevertheless, power quality can be enhanced by offering a suitable control technique in the inverter-based type DGs. As in VSIs, the auxiliary services for improvement in power quality embedded in the control assembly. In case of VSIs, compensation of unbalanced voltage, a lower value for total harmonic distortion, harmonic power-sharing schemes, power sharing between active/reactive powers, imbalance power, active/reactive power control and augmentation in power quality are critically considered and embedded in control schemes. VSIs are also applied on several applications in microgrid systems, extensively, for improving the power quality. This power control strategy is presented in [38]. However, a comprehensive review of various control strategies for microgrids is described in [150]. Moreover, using modular multilevel inverters can improve the modularity and scalability to meet reference voltage levels, efficiency in high power applications, reduction in harmonics in high voltage applications and size of passive filters as well as no requirement for dc-link capacitors [151]. In Table 3, different types of filters are suggested by various researchers based on the control systems. However, it is significant to use L-filters for low power applications having a simple design, nevertheless, L-filters are not found suitable in resonance state as well as for high power applications. So, LCL-filter is highly preferred in aforementioned system characteristics. The designing of this filter is comparatively complicated due to a few constrictions related to the system stability. The accuracy in designing and modeling of the system leads to better performance against resonance and harmonics. Nevertheless, the choice should be made according to the customer’s demand. The prime parameters should be chosen on the basis of system condition and intended tasks to be performed by the system. Afterward, the designing of power system and control system parameters should be finalized. This corresponding study incorporates the advantages and disadvantages of each controller in terms of stability, rapid response time, harmonic elimination, the nonlinearity of the system, unbalanced compensation and robustness against parameter variation. Various suitable control schemes for different types of VSIs are documented in this paper. However, their implementations for power generation and power quality improvement are still not perfect simultaneously. Moreover, each controller has its own benefits and obstructions. Therefore, it is not easy to decide that which control scheme is better than the others. These are significant subjects for the future research. On the basis of the analysis of former publications, appended research is suggested to be carried out in the aforementioned area. Regardless of the several investigations in this field, none of the proposed control techniques can be selected as an immaculate solution to meet al.l the requirements of power quality, i.e., harmonic/reactive/imbalance power-sharing and voltage unbalanced/harmonic/swell/sag and Interruption compensation at the same time. Therefore, further research should be focused on the novel power-electronics topologies to fulfill all aforementioned necessities simultaneously. Three-phase three-wire VSIs are now a well-developed and mature research topic with respect to their hierarchical control. But on the other hand, control hierarchies are not as well established for ML-VSIs, as for three-phase three-wire VSIs. It may be beneficial to consider ML-VSI system, as well as the primary, secondary and tertiary stages, whenever a control scheme is to be designed. Substantially, a lot of work is to be done for exploiting the new control approaches for ML-VSIs. In order to achieve enhanced performance, it is compulsory to use some innovative techniques such as robust, MPC and LQR control techniques.

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It is also observed through a number of studies that coupling among the phases is neglected whenever controlling an ML-VSI by means of a conventional PI controller, which results in a reduction of the system’s robustness. Hence, it can also be beneficial to implement decoupled phase voltage control to realize the referred response in time domain. A comparison of the credible research articles found in literature with respect to their control techniques, modulation schemes, control parameters, loop characteristics, employed filters and applications is described in Table 3. 13. Conclusions On the basis of research, conventional multilevel inverter topologies given in the previous sections, general and asymmetrically constituted ML-VSIs have been also reviewed in this paper. Several new hybrid topologies can be designed through the combinations of three main MLI topologies. Besides the combination of topologies, the trade-offs in MLI structures can be dealt by using H-MLIs that is formed using different DC source levels in inverter cells. PWM strategies that generate switching frequency at fundamental frequency are also introduced for H-MLIs for the switching devices of the higher voltage modules to operate at high frequencies only during some inverting instants. Due to numerous applications of conventional MLIs and flexibility to design the hybrid MLI topologies, this paper cannot cover all utilizations with MLIs but the authors intend to provide a useful basis to define the most proper control schemes and applications. In addition to these, the fundamental design and control principles of MLIs have been introduced as a result of a detailed literature survey. This paper has been destined to provide a reference to readers and the results given in this paper can also be extended with experimental studies. Table 2. Description of predictive controllers on the basis of their pros. & cons. Deadbeat Control

• • • •

-Modulator required -Fixed switching frequency -Low Computations -Limitations not undertaken

Trajectory Based control

• • • Predictive Control

-Modulator not required -Variable frequency -No cascaded structure

Hysteresis Based predictive control

• • •

-Modulator not required -Variable frequency -Uncomplicated structure

Model Predictive Control

• • • •

-Modulator required in case of continuous control set (CCS) and not required in case of finite control set (FCS). -Likewise, fixed switching frequency (CCS) and variable switching frequency exists in (FCS). -Online optimization and simple designing is included in case of FCS. -Constraints are considered in both cases

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Table 3. Digital control system characteristics in numerous credible scientific proposals. Application

Controller

Filter

Ref. Frame

Feedback

Modulation

Ctrl. Parameter

Ref.

General General General UPS General General DG DG DG DG General APF General DG General PV General UPS PV, APF PV, APF General General DG UPS General General General PV PV

adaptive Classic, PR Adp., Rpt. DB Rpt. Rpt C Classic Classic Classic Classic DB Adp., Rpt. DB Adp., MPC LQG PR, LQG Adp. Pred. Pred., Fuzzy SMC, Pred. DB Adp., DB DB DB, Rpt. MPC MPC MPC MPC Classic, Rpt.

LCL LCL L LC LC LCL LCL LC LC L L LC LCL LCL LCL L L LC L L L L L LC LCL L L L L

Single Phase Single Phase Single Phase Single Phase Single-Phase Single Phase abc, αβ abc, αβ abc, αβ abc, αβ abc, αβ abc, dq abc, dq abc, αβ abc, dq abc, αβ abc, αβ abc, dq abc, αβ abc, αβ abc, dq abc, dq abc, dq abc, αβ abc, abc abc, αβ abc, dq abc, dq abc, dq

Multi-loop Multi-loop Single-loop Multi-loop Single-loop Single-loop Single-loop Multi-loop Multi-loop Single-loop Single-loop Multi-loop Multi-loop Multi-loop Single-loop Single-loop Multi-loop Single-loop Multi-loop Multi-loop Single-loop Single-loop Single-loop Single-loop Single-loop Single-loop Single-loop Single-loop Single-loop

SPWM PWM SPWM PWM PWM PWM PWM SVPWM SPWM VLUT PWM SVPWM PWM SVPWM PWM SVPWM PWM SVPWM PWM PWM SVPWM PWM SVPWM PWM PWM PWM SVPWM SVPWM SVPWM

V, I I I V, I V I V, P V, I V, I V I I I I I I I V P P I I I V V, I I I I I

[51] [152] [105] [153] [101] [104] [47] [48] [49] [50] [52] [53] [54] [55] [66] [64] [107] [109] [108] [111] [113] [112] [116] [115] [122] [125] [128] [130] [97]

Acknowledgments: The National Natural Science Foundation of China supported this research work under Grant No. 61374155. Moreover, the Specialized Research Fund for the Doctoral Program of Higher Education PR China under Grant No. 20130073110030 is highly acknowledged. Author Contributions: Sohaib proposed the idea for writing the manuscript. Wang suggested the literature and supervised in writing the manuscript. Mazhar helped Sohaib in writing and formatting. Sarwar helped in modifying the figures and shared the summary of various credible articles to be included in this manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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