VSG Stability and Coordination Enhancement under ... - MDPI

electronics Article

VSG Stability and Coordination Enhancement under Emergency Condition Aazim Rasool 1,2, * , Xiangwu Yan 1 , Haaris Rasool 3 , Hongxia Guo 2 and Mansoor Asif 4 1 2 3 4

*

Department of Electrical Engineering, North China Electric Power University, Baoding 071003, China; [email protected] Goldwind Science and Technology, Co. Ltd., Beijing 100176, China; [email protected] Electrical Engineering and Power Electronics Department, Vrije Universiteit Brussel, 1050 Brussels, Belgium; [email protected] Department of Electronics System Engineering, Hanyang University, Ansan 15588, Korea, [email protected] Correspondence: [email protected]; Tel.: +86-156-1189-7523

Received: 17 August 2018; Accepted: 14 September 2018; Published: 17 September 2018

Abstract: Renewable energy sources are integrated into a grid via inverters. Due to the absence of an inherent droop in an inverter, an artificial droop and inertia control is designed to let the grid-connected inverters mimic the operation of synchronous generators and such inverters are called virtual synchronous generators (VSG). Sudden addition, removal of load or faults in the grid causes power and frequency oscillations in the grid. The steady state droop control of VSG is not effective in dampening such oscillations. Therefore, a new control scheme, namely bouncy control, has been introduced. This control uses a variable emergency gain, to enhance or reduce the power contribution of individual VSGs during a disturbance. The maximum power contribution of an individual VSG is limited by its power rating. It has been observed that this control, successfully minimized the oscillation of electric parameters and the power system approached steady state quickly. Therefore, by implementing bouncy control, VSGs can work in coordination to make the grid more robust. The proposed controller is verified through Lyapunov stability analysis. Keywords: virtual synchronous generator (VSG); parallel VSGs; lyapunov stability analysis; optimization; multiple VSGs coordination; island microgrid; reliability

1. Introduction With the increases in the growth of renewable energy sources (RES)-based distributed generators (DG), the parallel connection of DG sources to form a microgrid has emerged as a commercially and technically feasible solution. A microgrid usually comprises of multiple DGs of different types, such as renewable energy sources (RES), non-renewable energy source and energy storage system (ESS). RES are dependent on the environmental condition and are usually uncontrollable (or offer marginal control), and therefore the presence of controllable sources is necessary for the steady operation of a microgrid. A centralized control called an energy management system (EMS) controls all the parallel operating DGs in microgrid; based on the electrical parameters of grid. EMS can be operated in a grid-connected microgrid as well as in an island-mode microgrid. There are two main types of microgrid control: (i) control via communication, a centralized control that has comparatively a slower response (e.g., secondary or tertiary control); and (ii) control not requiring communication, a decentralized control that offers faster response toward any change in active and reactive power of a microgrid (e.g., primary control). [1–4]. The hierarchical control structure to normalize the operation of an islanded alternating current (AC) microgrid experiencing

Electronics 2018, 7, 202; doi:10.3390/electronics7090202

www.mdpi.com/journal/electronics

Electronics 2018, 7, 202

2 of 18

communication link failures is presented in [5]. In a microgrid, a droop control is normally used as a primary control due of its decentralized nature. It provides a firm coordination between multiple DGs operating in parallel. Different types of droop control are discussed in literature e.g., P-ω, P-V, Q-V, etc. [6–9].A drawback of droop control is a lack of inertia. In a conventional power system, a main source of electricity is a synchronous generator (SG), which has an inherent droop and inertia control that helps to synchronize multiple synchronous generators and share a real and reactive power equally among them. Moreover, because of its inherent inertia, it brings a system back to its steady state quickly after any disturbance. The control of inverter which resembles the characteristics of synchronous generator, in terms of real and reactive power sharing ability and droop-control, was first proposed in [10], and was further developed for parallel inverters in [7]. The virtual synchronous generator (VSG) was first proposed in [11], because of its capability to stabilize using virtual rotational inertia; along with a droop control. The inverter control strategies that mimic synchronous generator have been presented as virtual synchronous generator [12], followed by virtual synchronous machines (VSM) in [13], virtual synchronous machine (VISMA) in [14], and synchronverter in [15]. However, VSG still has some weaknesses compared to synchronous generator due to its inappropriate sharing of active and reactive transient power (unsuitable coordination) and the lack of overload capability to ride through large oscillations that can cause severe oscillation problem at the time of disturbance in a microgrid [16]. A VSG control technique based on Hamilton approach is introduced to enhance the robustness of a system in [17].The alternate moment of inertia is a technique that uses different inertia coefficient to increase the damping of a system during oscillation [18], the smaller inertia is used to enhance the dynamic response of an inverter [19], the proper increase in damping ratio by observing the derivative of power, reactive power, voltage and the phase difference to solve the output power oscillation presented in [20], the power oscillation is damped by using a virtual stator reactance in [16], and sharing transient load by using the generator emulation method presented in [21] are a few techniques to address this issue.

• Microgrid isolation A microgrid is designed to operate in two basic modes: (i) island mode, and (ii) grid-connected mode. The transition to an island-mode or isolated microgrid can take place suddenly i.e., unscheduled or according to a schedule. In the scheduled transition, the main grid controller give a signal to a microgrid. This type of transition is relatively safe because of prior information of a disturbance. When a fault appears at the grid; that goes beyond the protection limits of a microgrid, then a microgrid opens the circuit breaker (CB) ‘1’ in Figure 1 to isolate itself from the main fault zone in a grid. It is an unscheduled type of transition (from grid-connected to island mode) and it can cause severe disturbance. The proper protection and control measures are needed to safeguard a power system under such disturbances. Microgrids are designed to operate in island mode under the standards defined in IEEE-1547.4. The local loads within an island mode microgrid operate from the distributed generators DGs. These DGs can be RES, fuel generators, and energy storage batteries. The standards in IEEE-1547.4 suggest that a microgrid should be able to support its local loads, when any contingency happens at a main grid or it should have a proper plan of load-shedding; in terms of critical or non-critical load, when microgrid generation is not sufficient to support its local loads. An island microgrid is usually sensitive toward any change because it does not have grid support to counter any disturbance. Therefore, the change in load or any similar operation that causes transient behavior in an island-microgrid must be keenly observed and countermeasures must be taken to alleviate disturbance.


3 of 18

Electronics 2018, 7, x; doi: FOR PEER REVIEW

www.mdpi.com/journal/electronic

Island-mode

Grid DG

VSG-1 L

Transformer

CB1

VSG-2 CB2

L CB3 L Load-1

89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117

118 119

CB4

Fault

DG

DG

L Load-2 Figure 1. Transition to island microgrid. Figure 1. Transition to island microgrid.

At the time of loading, unloading, or a fault, the oscillation in power and frequency of VSG At the time of loading, unloading, or a fault, the oscillation in power and frequency of VSG arises arises that may lead to instability of an overall system or even termination in a worst case situation. that may lead to instability of an overall system or even termination in a worst case situation. The The stabilization of VSG is evaluated on the basis of its ability to eliminate oscillations from the stabilization of VSG is evaluated on the basis of its ability to eliminate oscillations from the microgrid. microgrid. The oscillation improvement by considering the droop coefficient has been done by our The oscillation improvement by considering the droop coefficient has been done by our research research group in [22]. The angular frequency of VSG is considered for varying J and D in previous group in [22]. The angular frequency of VSG is considered for varying J and D in previous research. research. VSG utilizes a phase locked loop (PLL) technique to obtain frequency and phase of grid for VSG utilizes a phase locked loop (PLL) technique to obtain frequency and phase of grid for the sake the sake of synchronization [23]. of synchronization [23]. In this research, a new parameter ‘emergency gain’ is introduced to dampen the oscillation of VSG In this research, a new parameter ‘emergency gain’ is introduced to dampen the oscillation of during an emergency condition. The equation is derived to show the dependency of a parameter on a VSG during an emergency condition. The equation is derived to show the dependency of a parameter derivative of angular frequency. The final swing equation for the additional parameter is also presented. on a derivative of angular frequency. The final swing equation for the additional parameter is also A ‘bouncy control algorithm’ is designed to define the variable values of emergency gain; it enhances presented. A ‘bouncy control algorithm’ is designed to define the variable values of emergency gain; the stability of a microgrid. It basically improves the transient time by varying the dependence of it enhances the stability of a microgrid. It basically improves the transient time by varying the change in power on the VSG. The control is designed, such that ∆P and δP (derivative of change dependence of change in power on the VSG. The control is designed, such that P and  P in power) are influencing the sensitivity of VSG power during the recovery. Lyapunov stability analysis (derivative of change in power) are influencing the sensitivity of VSG power during the recovery. is implemented to show the effectiveness of the scheme [18,24,25]. The energy function of synchronous Lyapunov stability analysis is implemented to show the effectiveness of the scheme [18,24,25]. The generator is built within a simulation to investigate the disturbance in a system. This technique can be energy function of synchronous generator is built within a simulation to investigate the disturbance also be implemented to improve the coordination of VSGs that are operating as a source or a load in in a system. This technique can be also be implemented to improve the coordination of VSGs that are an island microgrid; developed in [26,27]. operating as a source or a load in an island microgrid; developed in [26,27]. The basic operation of a VSG is presented in Section 2. The emergency power control and its sub The basic operation of a VSG is presented in Section 2. The emergency power control and its sub sections: (a) bouncy control, and (b) Lyapunov stability analysis are presented in Section 3. In Section 4, sections: a) bouncy control, and b) Lyapunov stability analysis are presented in section 3. In section experiments and results are described. The conclusion of this work is presented in Section 5. 4, experiments and results are described. The conclusion of this work is presented in section 5. 2. Basic Operation of Virtual Synchronous Generator (VSG) 2. Basic Operation of Virtual Synchronous Generator (VSG) The block diagram of VSG control is shown in Figure 2. The control is designed in the The block diagram of VSG controlfrequency is shown in 2. Theiscontrol designed the dq-axis. dq-axis. The reference rotational of Figure the dq-axis ‘ωo ’ inisan isolatedinsystem, while in The areference rotational frequency of the dq-axis is ‘ ’ in an isolated system, while in a grid o grid-connected VSG, it adopts the rotational frequency of the grid. The double voltage current connected VSG, it adopts theVSG rotational of the grid. The order double voltage current controller is used in this controlfrequency system. The basic second swing equation forcontroller VSG control is used in thisin VSG control(1). system. order swing equation VSG control is shown is shown Equation It hasThe twobasic parts:second (i) a mechanical part, whichfor controls the rotor motion by in Equation It has two a mechanical part,control whichthe controls rotor using P −(1). ω control, andparts: (ii) an (i) electrical part, which stator the voltage bymotion using Qby − using V control. P   control, and (ii) an electrical part, which control the stator voltage by using Q  V control. Pre f − Pe ∂(ω − ω g ) = − D (ω − ω g ) (1)  (  g ) Pref  Pe J ω (1) J   D( ∂tg ) t  Ere f = E + I (r a + jx a ) (2) Eref  E  I ( ra  jxa ) (2) where Pref is the reference power provided by the governor, Pe is the measured output power, D is the droop coefficient, J is the virtual inertia, ω is the virtual angular frequency of VSG, and  g is


4 of 18

Electronics 2018, 7, x; doi: FOR PEER REVIEW Electronics 2018, 7, x; doi: FOR PEER REVIEW

www.mdpi.com/journal/electronic www.mdpi.com/journal/electronic

120 the angular frequency ofpower the grid or power common coupling Pref *output maximum Pre f is the reference provided by the governor, Pe is the(PCC). measured power, D is * is the 120 where the angular frequency of the grid or power common coupling (PCC). P is the maximum ref the droop coefficient, J is the virtual inertia, ω is the virtual angular frequency of VSG, and ω is the 121 instantaneous power by VSG source. ‘ E ’ is the excitation electromotive force and ‘ I ’ is theg stator 121 angular instantaneous power by VSG source. ‘ E ’ is the excitation electromotive force and ‘ I ’ is the stator ∗ or powerand common coupling (PCC).winding Pre f is in thesynchronous maximum instantaneous 122 current.frequency ‘ r ’ and ‘ of ’ aregrid a resistance a reactance of stator generator. x the 122 power current. ‘ ara ’ and ‘ xa a ’ are a resistance and a reactance of stator winding in synchronous generator. by VSG source. ‘E’ is the excitation electromotive force and ‘I’ is the stator current. ‘r a ’ and ‘x a ’ areactance ref DDpof ( Pstator  Prefwinding ) are a resistance and in synchronous generator. (3) ref p ( P  Pref ) (3) uuuuref DDq ((QQQQref )) ref

q

123 123 124 124

ωref= ωre f − D p ( P − Pre f ) (3) Equation (2) shows the basic active angular ( P   ), and reactive power u =power upower Dand − Qre f )frequency q (Q re f − and Equation (2) shows the basic active angular frequency ( P   ), and reactive power and voltage ( Q  V ) droop control equations. and voltage ( Q  V ) droop control equations.

125 125 126 126

Figure Figure2. 2. Angular Angular frequency frequencyand andactive activepower powercontrol controlof ofaavirtual virtualsynchronous synchronousgenerator generator(VSG). (VSG). Figure 2. Angular frequency and active power control of a virtual synchronous generator (VSG).

Equation (2) shows the basic active power and angular frequency (P − ω), and reactive power 127 The simplified active and reactive power controls of VSG are shown in Figure 2 and 3 127 and voltage The simplified active and reactive power controls of VSG are shown in Figure 2 and 3 (Q − V) droop control equations. 128 128 respectively. respectively. The simplified active and reactive power controls of VSG are shown in Figures 2 and 3 respectively.

129 129 130 130

Figure 3. 3. Voltageand and reactivepower power controlof ofVSG. VSG. Figure Figure 3.Voltage Voltage andreactive reactive powercontrol control of VSG.

131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138

3.3. Emergency EmergencyPower PowerControl ControlScheme Scheme 3. Emergency Power Control Scheme The TheVSG VSGsystem systemisisdesigned designedin inthe thedq-axis, dq-axis,while whileconsidering consideringthe theangular angularfrequency frequencyof ofthe thegrid grid The VSG system is designed in the dq-axis, while considering the angular frequency of the grid and and the the dq-axis dq-axis are aresame. same. The The intention intention of of using using the the dq-axis dq-axis is is to to separate separate the the effects effects of ofactive activeand and and the dq-axis are same. The intention of using the dq-axis is to separate the effects of active and reactive power. The 3-Φ voltages and currents are first measured in abc-axis. After converting them reactive power. The 3-Ф voltages and currents are first measured in abc-axis. After converting them reactive power. The 3-Ф voltages and currents are first measured in abc-axis. After converting them into and frequency frequency are aremeasured. measured.The Thechange changeinin power and frequency is detected into dq-axis, dq-axis, power power and power and frequency is detected for into dq-axis, power and frequency are measured. The change in power and frequency is detected for for selection G & J . VSG gives V and θ at its output, which in turns generate pulse width thethe selection of of & . VSG gives V and  at its output, which in turns generate pulse width G e J x the selection of Ge e & Jx x . VSG gives V and  at its output, which in turns generate pulse width modulation through voltage andand current looploop control. The The overall control of grid modulation(PWM) (PWM)after afterpassing passing through voltage current control. overall control of modulation (PWM) after passing through voltage and current loop control. The overall control of connected VSG is displayed in Figure 4. grid connected VSG is displayed in Figure 4. grid connected VSG is displayed in Figure 4.


5 of 18



139

Figure Figure 4. 4. Overall Overall control control of of grid-connected grid-connected VSG. VSG.

140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161

The coordination coordination of of multiple multiple sources sources in in aa microgrid microgrid is is aa critical critical issue issue because because of of different different power power The rating, inertia inertiaand anddroop droopratio. ratio.The The response different sources is not same, for example; rating, response of of different sources is not the the same, for example; the the response a synchronous generator is much slower a VSG-based inverter controller. response of a of synchronous generator is much slower thanthan thatthat of aof VSG-based inverter controller. In In the same way, dynamic response twoVSG VSGcontrollers controllersconnected connectedininparallel parallelisisnot not identical; identical; the same way, thethe dynamic response ofoftwo mainly because because of of droop droop and and inertia, inertia, and and therefore therefore it it is is necessary necessary to to limit limit the the response response of of aa speedier speedier mainly source that that approaches provide a protection to source approaches to to its itsrated ratedpower powersooner. sooner.This Thisstrategy strategyhas hasananability abilitytoto provide a protection a swiftly responding source, whereas force other sources to response faster to bring equilibrium to to a swiftly responding source, whereas force other sources to response faster to bring equilibrium to the system. system. the The emergency emergency power power controller controller is is designed designed such such that that the the recovery recovery time time speeds speeds up up or or slows slows The down to to stabilize stabilize aa microgrid. microgrid. The The change change in in power power during during transition transition time time along along with with the the VSG VSG control control down parameters decide decide the the response response of VSG, which which in in turn turn define define the the stability stability of of aa system. system. In In any any control control parameters of aa VSG, of aa power thethe electric parameters strivestrive to maintain their stable during of powersystem, system, electric parameters to maintain theirpoint stable pointnormal duringoperation normal and returnand to return a stabletostate afterstate anyafter disturbance. In the view above consideration, the input operation a stable any disturbance. In theofview of above consideration, the parameters of VSG in active power ‘∆P’‘ΔP’ andand the the derivative of the active power ‘δP’ input parameters of i.e. VSGthe i.e.change the change in active power derivative of the active power ‘ (equal to dP/dt), is used to stabilize a microgrid; without altering the control parameters (e.g., inertia  P ’ (equal to dP / dt ), is used to stabilize a microgrid; without altering the control parameters (e.g., and droop of the VSG control. inertia and coefficient) droop coefficient) of the VSG control. The active activepower powertries triestoto approach stable point any disturbance. VSG control, The approach its its stable point afterafter any disturbance. In VSGIncontrol, droop droop coefficient thestability, static stability, the dynamic is dependent coefficient usuallyusually defines defines the static whereaswhereas the dynamic stability stability is dependent on both on both droop coefficient andHence, inertia.P-ω Hence, P-ω droopdefines control the defines newpoint stable of VSG droop coefficient and inertia. droop control new the stable of point VSG electric electric parameters, such asand power and frequency. angular frequency. Thefrequency angular frequency is considered as a parameters, such as power angular The angular is considered as a measure measure of theofstability ofand the therefore, VSG, and to therefore, improve a VSG or athe microgrid, of the stability the VSG, improveto the stabilitythe of astability VSG or of a microgrid, angular the angularstability frequency stability needs to be enhanced. frequency needs to be enhanced.

162

3.1. Bouncy Bouncy Control Control 3.1.

163 164 165 166 167

A bouncy bouncy control control is is designed designed to to assist assist the the stability stability of of VSG VSG during during overload/emergency overload/emergency condition condition A as shown in Figure 5. It offers two properties: (a) speed-up the response of a power delivery; as shown in Figure 5. It offers two properties: (a) speed-up the response of a power delivery; by by increasing sensitivity of VSG a system a definite time (emergency) when drop increasing the the sensitivity of VSG on aonsystem for for a definite time (emergency) when the the drop in in angular frequency is not a problem; (b) slow-down the response of VSG toward any change when angular frequency is not a problem; (b) slow-down the response of VSG toward any change when aa minimal angular angular frequency frequency variation variation is is needed. needed. minimal


6 of 18



Pd

Pe Pref

Gac

SW2

+

SW1

Pref Pe

+++

+

+

D

ω

x ÷



1/J

++

Gde

Pe > Pref Abnormal Condition

δΔP >0 δΔP 0 ∆P> 0 ∆P< 0 ∆P< 0

178 179 180 181 182 183 184 185 186 187 188 189 190 191 192

193 194 195 196

Table 1. Bouncy control of gain selector. d(P)/dt Slope ΔP (P-Prefd(P)/dt0 ΔP> 0 d(P)/dt0 d(P)/dt>0 ΔP< 0 d(P)/dt0

Slope Decelerating Accelerating Decelerating Accelerating Accelerating Decelerating Accelerating Decelerating

Ge

Ge G de Gde Gac 1 Gac 1 1

1

In bouncy control, the effect of power error is amplified/reduced at the time of disturbance. In bouncyerror: control, the effect of power error is amplified/reduced at the time of disturbance. (a) (a) amplifying In amplifying ∆P, the decelerating gain ‘Gde ’ has more influence on a system as amplifying In amplifying Pac, ’the decelerating has more a system as compared toerror: the accelerating gain  ‘G because the timegain of G‘acGdeis’ very small.influence When theondecelerating

gain ‘Gde ’ isto greater than 1 thengain it increases the sensitivity (P When − Pre f ),the and therefore, compared the accelerating ‘ Gac ’ because the timeofofpower very small. decelerating Gac isdifference VSG reach the power faster than and speeds up the recovery( time. gaintries ‘ Gdeto ’ is greater than 1 reference then it increases thebefore sensitivity of power difference ), the and P  PrefAt normal condition, both gains Gac and Gde remain at ‘1’. (b) reducing error: When a VSG is connected therefore, VSG tries to reach the power reference faster than before and speeds up the recovery time. in parallel with other VSGs, then in this case, reducing the response of an individual VSG (crossing its At the normal condition, both gains Gac and Gde remain at ‘1’. (b) reducing error: When a VSG is rated limit) can enhance the stability of an overall microgrid. In reducing ∆P, both accelerating and connected in parallel with other VSGs, then in this case, reducing the response of an individual VSG decelerating gains should be provided with a value less than ‘1’ to slow down the response. (crossing its rated limit) can enhance the stability of an overall microgrid. In reducing P , both When the power error goes higher from Pre f , bouncy control is activated. Once the control starts, accelerating and decelerating gains should be provided with a value less than ‘1’ to slow down the it remains active until the power returns to its reference value (or new stable value). The bouncy response. control equation of an emergency condition is given in Equations (3)–(6). Our focus remains on Gde as When the power error goes higher from Pref , bouncy control is activated. Once the control it has significant dependence on the settling time. In contrast, Gac has comparatively less significance starts, on it. it remains active until the power returns to its reference value (or new stable value). The bouncy control equation of an emergency is given in Equation (3)–(6). Our focus remains Ge × ( Precondition (4) f − Pmeas ) = ∆P × Ge on Gde as it has significant dependence on the settling time. In contrast, Gac has comparatively less The conventional swing equation of VSG control in Equation (1) is changed after implementing significance on it. bouncy control, such that the ∆P is increasing or decreasing by factor Gde and Gac during the time Ge  ( Prefand P Ge of power deceleration acceleration Ge is the general term for an emergency gain (4) meas )  P respectively. (Gac & Gde ). The conventional swing∂(equation (1) is changed after implementing Ge ×control ( Pre f −in Pe Equation ) ω − ω g ) of VSG J ΔP is increasing = − by D (ω − ωgG ) and G during the time (5) bouncy control, such that the or decreasing factor de ac ∂t ω of power deceleration and acceleration respectively. Ge is the general term for an emergency gain ( Gac & Gde ).


7 of 18

The relationship of the old and new (after adding a new parameter in control) derivative of the change in frequency is derived to show the dependence of a newly introduced parameter in Equation (6). It can be seen from Equation (6), when the value of ‘x’ is set to ‘1’ then the VSG works •

normally. To reduce the response of δω 1 , the value of ‘x’ regulate to less than ‘1’, which makes the •

second part of Equation (6) negative and eventually reduces δω 1x . When the value of ‘x’ is greater than •

‘1’ then it makes a second term positive, and therefore the response of δω 1x increases as compared •

to δω 1 . Hence, it speeds-up the recovery time. •

J1 δω 1x =

x ∗ ∆P1 − D1 ∆ω1 ω1

•

•

∆P1 ω1 ( x − 1 ) ∆P1 J1 ω1 (1 − x )

J1 δω 1x = J1 δω 1 + •

•

δω 1x = δω 1 −

(6)

(7)

Investigating the effect of this method on the overall frequency deviation of a parallel connected VSG in a microgrid, we are calculating the equivalent frequency deviation and adding the effect of the proposed control into it. The criterion of frequency deviation is decided based on its operating power. When all the VSGs are under the rated electric parameters of a system then the frequency deviation can be increased for a limited time after any disturbance to achieve a quick response; by contrast, when the power of any VSG goes beyond the rated power, then the slow response toward any disturbance is introduced to enhance the stability of a VSG operation and island microgrid. •

•

•

δω eq = δω 1 + δω 2 •

•

•

(8)

δω eqx = δω 1x + δω 2 3.2. Flowchart The flowchart of a bouncy control is shown in Figure 6. The system is initializing with Ge = 1 and three phase voltages and currents are measured in a simulation through voltmeter and ammeter, respectively. In the actual system, the voltages and currents are first changed from abc-axis to dq-axis. However, in the flowchart, it is unnecessary to show a transformation. Power and frequency are acquired from the data obtained through measurement. The method of acquisition without using PLL is presented in [28]. Power and frequency are being measured continuously, so the change in power and (∆P) and derivate of power (δP) can easily be detected. These parameters are the key factors in the execution of emergency control. The selecting criteria Ge ’ from ‘∆P’, and ‘δP’, can be seen in Table 1. The algorithm is designed to limit the contribution of power to the grid when the VSG reaches to its maximum power, therefore only ∆P > 0 is considered to change gains in a bouncy control, while the gain is unchanged at the time when ∆P < 0 (it can be introduced in future studies). When ∆P > 0, it further detects the power derivative ‘δP’ to find out whether the curve is positive or negative. ‘texe ’ is the time of execution of simulation, when the time ‘t’ is less than the execution time ‘texe ’, the system keeps updating ‘Ge ’ in the simulation. Emergency control ends with the termination of the simulation.


8 of 18



Start Set Initial values of gain=1 Transient Simulation Acquisition V & I Measure Power and Angular frequency Detect ΔP,δP ΔP > 0 YES YES

δP > 0

Ge=Gac

NO

Ge=1

NO

Ge=Gde Update Ge t < texe

YES

NO

End

229

Figure6.6.Flowchart Flowchartofofbouncy bouncycontrol. control. Figure

230

3.3. 3.3.Lyapunov LyapunovStability StabilityAnalysis Analysis

231 232 233 234 235 236 237 238 239 240 241 242 243

The power controller strategy is justified by implementing transient system analysis by Theemergency emergency power controller strategy is justified by implementing transient system analysis using the online Lyapunov method. Evaluation of the Lyapunov function through transient simulation by using the online Lyapunov method. Evaluation of the Lyapunov function through transient helps to calculate energy function of the VSG, which turnwhich represents the stability of system.of simulation helpsthe to calculate the energy function of the in VSG, in turn represents thethe stability Itthe hassystem. few advantages over small signal state-space stability: (i) there is no need to solve non-linear It has few advantages over small signal state-space stability: (i) there is no need to solve differential of equation a system;of(ii) assumptions are required; (iii) it does not itchange a non-linear equation differential a no system; (ii) no assumptions areand required; and (iii) does not system into linear, so it has accurate results. Due to these advantages, the Lyapunov method has been change a system into linear, so it has accurate results. Due to these advantages, the Lyapunov method commonly used by researchers. has been commonly used by researchers. However, in the Lyapunov is to to find find the theLyapunov Lyapunovfunction. function.ItItshould shouldbe However, in the Lyapunovmethod, method,the the main main task task is bedesigned designedsuch suchthat thatthe thefunction functiongives gives zero zero output output value at a stable condition. The similar value at a stable condition. The similaronline online optimization technique to improve control parameters optimization technique to improve control parametersby byreducing reducingthe thefitness fitnessvalue valueofofananobjective objective function; function;depending dependingononthe theerror errorofofananelectric electricparameters parametersisispresented presentedinin[29]. [29].The TheLyapunov Lyapunovfunction function for a synchronous generator is presented in [18,25] by calculating the energy function. for a synchronous generator is presented in [18,25] by calculating the energy function.As AsVSG VSGisisa a replica soso this energy function could bebe implemented inin VSG control. replicaofofsynchronous synchronousgenerator, generator, this energy function could implemented VSG control. 1 2 VV=VVK +V VPP =  2ω ooJ∆ω J  2−[ P[ P (−δr)r + ) Pmax Pmax(cos (cosδ−cos cosδr)]r )] reref f (δ K 2

(9) (9)

‘V’ is ‘V’ the is energy function of transient system whenwhen fault fault or any occurs. ‘δ’ is‘ a ’ 244 wherewhere the energy function of transient system or disturbance any disturbance occurs. angleangle of VSG. ‘δr ’ is ‘the stable is the power. power. ‘P’ is the 245 power is a power of VSG. is theat angle at point. stable Pin point. Pininput is thereference input reference ‘ Poutput ’ is the  r ’angle electrical power. It can be seen from Equation (9), the energy function is divided into two sections: 246 output electrical power. It can be seen from Equation (9), the energy function is divided into two kinetic energy ‘VK ’, and (ii) potential energy ‘VP ’. The kinetic energy is positive during oscillations, 247 (i)sections: (i) kinetic energy ‘ VK ’, and (ii) potential energy ‘ VP ’. The kinetic energy is positive during as the inertia and change in angular frequency is equal to or greater than zero. The potential energy 248 has oscillations, as the inertia and change in angular frequency is equal to or greater than zero. The a negative sign, so the magnitude of a second term must be less than zero or the first term during 249 oscillations; potential energy has a negative sign, so the magnitude of a second term must be less than zero or the to satisfy V > 0. 250 first term during oscillations; to satisfy V  0 . 251 The kinetic energy ‘ VK ’ is dependent on the variable ‘  ’–change in frequency, nominal 252 frequency ‘ o ’, and virtual inertia coefficient ‘J’. It can be assumed from the Equation (10), the kinetic 253 energy is present in a system due to change in frequency ‘  ’, when the system is at the stable


9 of 18

The kinetic energy ‘VK ’ is dependent on the variable ‘∆ω’–change in frequency, nominal frequency ‘ωo ’, and virtual inertia coefficient ‘J’. It can be assumed from the Equation (10), the kinetic energy is present in a system due to change in frequency ‘∆ω’, when the system is at the stable condition i.e., ω = ω g ; then ‘∆ω = 0’, consequently there is no kinetic energy in a system (VK = 0). It can be observed from Equation (4) that emergency gain ‘Ge ’ is influencing the derivative of ω, when the ‘Ge ’ increases the change in angular frequency also rises and vice versa. To enhance the angular frequency stability, it is better to take Ge less than 1, which in turn reduces the change in angular frequency. 1 VK = ωo J∆ω 2 (10) 2 The potential energy ‘Vp ’ is dependent on the power and the phase angle of VSG. When there is a phase difference in the VSG with respect to the grid, then there is an existence of potential energy in the system. The reference power angle ‘δr ’ has basically ‘0’ value at a grid. At the stable condition, δ is equal to δr , therefore the term (δ − δr ) and (cos δ − cos δr ) are equal to zero, consequently there is no more potential energy in a system VP = 0. When the disturbance appears in a system, emergency gain is activated; it directly influences the potential energy of a system. The main purpose of implementing emergency gain is to provide the independent control during abnormal conditions of the VSG. As it can be seen from Equation (9), potential energy has a negative sign, therefore it causes declining behavior on the energy function. So, the increase in potential energy ‘VP ’ causes the reduction in overall energy ‘V’. Hence, it improves the responsiveness of a system. By contrast, when the emergency gain is set lower than 1 then the potential energy ‘VP ’ falls, consequently, the overall energy takes a longer time to stabilize. VP = Pre f (δ − δr ) + Pmax (cos δ − cos δr ) (11) At the stable condition, the transient energy is supposed to be at zero. When any disturbance occurs in a system, the energy becomes positive that shows the system is under an abnormal condition. The derivative of the system transient energy must be negative to fulfill the Lyapunov stability criterion. The negative value shows that the transient system is returning back to the equilibrium state after the disturbance [18]. The derivative of ‘V’ in Equation (9) is taken by considering the variable ∆ω: .

V=

dV d∆ω = ωo J∆ω − D∆ω 2 dt dt

(12)

The above expression is a derivative equation of the system energy, it is necessary to be negative . to show its decaying behavior (V < 0). The second term − D∆ω 2 remains negative for D > 0, it is a damping factor. The first term of Equation (12) is negative when the system is approaching the equilibrium state. For the positive ∆ω (∆ω = ω − ω g ), the derivative of ∆ω is negative and for the negative ∆ω, the derivative of ∆ω is positive. Therefore, the first term maintains negative in either conditions. E = V + [ R + jX L ] ∗ Io (13) Zs = R + jX L = | Z |∠ ϕ The interlinking of the VSG inverter with a grid is demonstrated in Figure 7. The voltage generated from the VSG is represented by E∠δ, in which, E is the amplitude of the voltage, while ‘δ’ is the power angle of voltage. V ∠δr is the instantaneous voltage of a grid, ’V’ is the amplitude of the voltage and δr is 2018, the reference power of a grid which is ideally at ‘0’ (δr = 0).www.mdpi.com/journal/electronic X L and R are the line impedances. Electronics 7, x; doi: FOR PEER angle REVIEW

E