energies Article
An Enhanced Control Scheme Based on New Adaptive Filters for Cascaded NPC/H-Bridge System Jin-Wook Kang, Hoon Lee, Seung-Wook Hyun, Jintae Kim and Chung-Yuen Won * College of Information and Communication Engineering, Sungkyunkwan University, Suwon 16419, Korea;
[email protected] (J.-W.K.);
[email protected] (H.L.);
[email protected] (S.-W.H.);
[email protected] or
[email protected] (J.K.) * Correspondence:
[email protected]; Tel.: +82-031-290-7169 Received: 31 March 2018; Accepted: 20 April 2018; Published: 24 April 2018
Abstract: This paper studies the voltage fluctuation of dc-link generated in a 13-level cascaded neutral point clamped (NPC)/h-bridge (CNHB) with single-phase active front end (AFE) at the input side of each cell. The voltage fluctuation may deteriorate the power factor (PF) and current harmonics in the system. In this paper, new adaptive filters are proposed to overcome the problem. The center frequency of the proposed filters can be automatically varied, which allows to eliminate the specific harmonics in the dc-link well rather than the conventional one. Therefore, it can reduce the fluctuation of dc-link and maintain high PF and low current harmonic distortion without additional circuits externally or the current harmonics injection technique. As a result, capacitance for the dc-link can be optimally designed, and even cost and volume of the system can be reduced. This paper analyzes reasons of increasing voltage fluctuation theoretically and the conventional filter and proposed two types of adaptive filters are compared. In addition, the optimal design method of the dc-link capacitor necessarily used in NPC/h-bridge is presented. To verify the principle and feasibility of the proposed control method, a simulation and experiment are implemented with the CNHB system. Keywords: adaptive filter; NPC/h-bridge; cascaded inverter; multilevel converter; harmonics
1. Introduction In high power applications such as medium voltage motor drives, wind turbines, solar cells and vehicles etc., the multilevel topologies introduced in [1] have been widely applied to reduce the harmonic current on the grid, downsize the physical filter size and mitigate the switching losses of the used devices, in comparison with the conventional 2-level pulse width modulation (PWM) converter and inverter. These multilevel topologies allow the output voltage to be closer to sinusoidal wave by increasing the number of voltage levels, and reduce the harmonic distortion reported in the literature [2,3]. Among these topologies, the cascaded neutral point clamped (NPC)/h-bridge (CNHB) topology has the advantage of being easier to increase the output voltage than in other multilevel topologies such as the cascaded h-bridge, neutral point clamped, and flying capacitor, because of the possibility of modularization [4–6]. Figure 1 illustrates a multilevel topology widely used in applications where a rectifier is typically used in front of a system. These topologies have two major disadvantages. First, due to the diode rectifier, the regenerative energy generated from the load cannot be transmitted to the grid. Accordingly, it cannot be used in those applications that generate some regenerative energy, such as medium voltage motor drives, in high power applications. Second, important harmonics that are caused by switching noise, voltage fluctuation, and load variation are imposed on the input current. To solve out the problem, a phase shifting transformer is usually employed at the secondary side of the main transformer, however, it causes the system to be more complicated, and increases the cost Energies 2018, 11, 1034; doi:10.3390/en11051034
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To solve out the problem, a phase shifting transformer is usually employed at the secondary2 side Energies 11, out 1034the of 25 To2018, solve problem, a phase shifting transformer is usually employed at the secondary side
of the main transformer, however, it causes the system to be more complicated, and increases the cost of the main transformer, however, it causes the system to be more complicated, and increases the cost and volume as well. For further improvement of those factors mentioned previously, the CNHB is and volume as well. For further improvement of those factors mentioned previously, the CNHB is and volume well. further improvement those factors mentioned previously, the CNHB is usually usedasas an For active front end (AFE) of including regenerative capability, instead of the usually used as an active front end (AFE) including regenerative capability, instead of the usually used as an active front end (AFE) including regenerative capability, instead of the conventional conventional rectifier. This CNHB allows regenerative energy to be transferred from a load side to conventional rectifier. This CNHB allows regenerative energy to be transferred from a load side to rectifier. CNHB regenerative energy transferred load side as to the input the inputThis source, gridallows etc., and power factor (PF)toofbe each cell to befrom well acontrolled shown in source, Figure the input source, grid etc., and power factor (PF) of each cell to be well controlled as shown in Figure grid etc., and power factor (PF) of each cell to be well controlled as shown in Figure 2 [7–9]. 2 [7–9]. 2 [7–9].
Figure 1. Configuration of 13-level cascaded NPC/h-bridge system with diode rectifier. Figure 1. Configuration of 13-level cascaded NPC/h-bridge system with with diode diode rectifier. rectifier. NPC/h-bridge system
Figure 2. Configuration of 13-level cascaded NPC/h-bridge inverter with single-phase AFE rectifier. Figure 2. Configuration of 13-level cascaded NPC/h-bridge inverter with single-phase AFE rectifier. Figure 2. Configuration of 13-level cascaded NPC/h-bridge inverter with single-phase AFE rectifier.
However, as can be seen in Figure 2, since one cell has a single-phase NPC/h-bridge (NHB) However, as can be seen in Figure 2, since one cell has a single-phase NPC/h-bridge (NHB) However, as can be seen in Figure 2, since cell has a of single-phase NPC/h-bridge connected in series, voltage fluctuation with twiceone the frequency the input source inevitably (NHB) occurs connected in series, voltage fluctuation with twice the frequency of the input source inevitably occurs connected in series, voltage twice the frequency of thetoinput sourceit. inevitably occurs in the dc-link of each cell fluctuation so that an with additional circuit is needed eliminate Moreover, the in the dc-link of each cell so that an additional circuit is needed to eliminate it. Moreover, the in the dc-linkwith of each cellthe so inverter that an additional circuit is needed eliminate it. voltage Moreover, the component component twice output frequency in each to cell produces fluctuation of the component with twice the inverter output frequency in each cell produces voltage fluctuation of the with twice inverter output the frequency in each cell produces voltage fluctuation of the dc-link, and dc-link, andthe even deteriorates PF. dc-link, and even deteriorates the PF. even To deteriorates theproblems, PF. solve those the conventional approach [10] proposes a six-switch single-phase To solve those problems, the conventional approach [10] proposes a six-switch single-phase To solveconverter those problems, thesemiconductor conventional approach proposes single-phase AC/DC/AC with two switches [10] removed froma six-switch the h-bridge topology. AC/DC/AC converter with two semiconductor switches removed from the h-bridge topology. AC/DC/AC converter semiconductor switches AC/DC/AC removed from the h-bridge topology. However, it can be usedwith onlytwo in stand-alone single-phase systems not in multi-level However, it can be used only in stand-alone single-phase AC/DC/AC systems not in multi-level However, it can be used[11] onlyproposes in stand-alone single-phase systems not in the multi-level systems. Also literature a current harmonicsAC/DC/AC injection method to reduce voltage systems. Also literature [11] proposes a current harmonics injection method to reduce the voltage systems. Also literature [11] proposes a current harmonics injection method to reduce the voltage fluctuation of the dc-link. Current harmonics injection method results in aggravation of the THD fluctuation of the dc-link. Current harmonics injection method results in aggravation of the THD fluctuation of the dc-link. Current harmonics injection method results in aggravation of the THD
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characteristic of the inverter output current and it means that trade-off between inverter output current and dc-link capacitance should be considered for appropriate control objective. Therefore, in this paper, a control method based on new adaptive filters is proposed to reduce the voltage fluctuation and improve PF and current harmonics without additional sacrifice unlike the conventional methods. Additionally, the voltage fluctuation of dc-link affected by input and output frequency in a cell of CNHB is theoretically analyzed. This paper is organized as follows: Section 2 theoretically analyzes the components with specific harmonic current contents affecting dc-link voltage fluctuations by the input and output frequency, and introduces design of the dc-link capacitor through system modeling. Section 3 describes the conventional filter for reducing the dc-link variance component and introduces the proposed adaptive filter. Sections 4 and 5 give the simulation and experimental results for validation of the proposed control method based on the adaptive filter; and Section 6 provides the conclusion. 2. Analysis of the DC-Link in the CNHB System The CNHB topology consists of a plurality of converters and inverters, which are connected in series. One cell consists of a converter and an inverter, which includes two dc-link capacitors, eight switches and four clamping diodes [12]. Figure 1 shows that the diode rectifier is replaced with a converter, which has the advantage to control selectively current harmonic contents or replacement angle between the input voltage and current. It is also possible to utilize a general transformer or a multi winding transformer, instead of a complex phase shifting transformer, thereby reducing the volume and cost of the transformer in the system. However, since the converter of each cell is connected to the single-phase transformer as shown in Figure 3, the voltage fluctuation in the dc-link capacitor can be caused by both of the input power and load. As can be seen Figure 3, the specific harmonic components are generated in the dc-link capacitor. Meanwhile, the specific harmonic components are composed of the amount of voltage fluctuations generated by each frequency of the input side of the converter and the output side of the inverter [13]. This requires large dc-link capacitance, and in addition, adversely affects the durability and increases the overall volume of the system. These are the drawbacks of the system. Therefore, theoretical analysis of these harmonic components is needed. 2.1. Voltage Fluctuation Analysis in the DC-Link of One Cell The frequency of the input voltage is usually fixed at (50 or 60) Hz. Also, if the PF control of the grid is normally performed using the current controller of the NHB converter, the phase of input voltage and current is in-phase, as shown in Figure 3. The input voltage v g and current i g of the converter and the power of the converter can be expressed by Equations (1)–(3): v g (t) = Vpeak_g sin ω g t + φ phase_g
(1)
i g (t) = I peak_g sin ω g t + φ phase_g + φg
(2)
p g ( t ) = v g ( t )i g ( t ) =
n o 1 Vpeak_g I peak_g cos −φg − cos 2ω g t + 2φ phase_g + φg 2
(3)
where, Vpeak_g and I peak_g are the maximum values of input voltage and current, respectively; ω g is the angular speed of the input voltage; φ phase_g is the phase angle of the input voltage; and φg is the displacement angle of v g and i g . Meanwhile, cos −φg can be defined as the PF, because v g and i g are pure sinusoidal waveform, and the product of v g and i g in this single-phase system is divided into the active power component and reactivepower component vibrating at twice the frequency of the input voltage by cos 2ω g t + 2φ phase_g + φg .
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3-level NPC type 1-phase AC-DC Converter
Pg
DC-Link
Pcap
3-level NPC type 1-phase DC-AC Inverter
Grid, Transformer, Filter
vg
Induction Motor
fmotor : 0~frate[Hz]
vg(60[Hz]) 0
0
Em
im
ig
fgrid : 60[Hz]
0
Pm
ig(60[Hz]) t
im(20[Hz])
Em(20[Hz]) Pg(120[Hz])
t
Pactive
Pm(40[Hz])
t
Pcap
t
0
~ vDC
ΔvDC
VDC_average t
Figure 3. dc-link voltage fluctuation by the and output power in shingle phase Figure 3. Characteristics Characteristicsofof dc-link voltage fluctuation by input the input and output power in shingle NHB. phase NHB.
The output voltage and current of the inverter, and consequently the power, are represented as The output voltage and current of the inverter, and consequently the power, are represented follows: as follows: t) V peak_m V peak _ msin sin ω m vm (vt)m (= + φ (4) (4) m tt phase _m phase_m (t ) Ipeak_m I peak _ sin mmtt + φphase m (5) im (ti)m = +m φ (5) m sin ω _m phase_m mm is the where, VVpeak_m voltage and and current current of of the the inverter, inverter, ω peak _ m and IIpeak_m peak _ m are the maximum output voltage angular is the phase angle of the inverter output, angular speed speed of of the the output output voltage voltage of of the the inverter, inverter, φphase_m phase _ m is the phase angle of the inverter output, and φm is the phase difference between the output voltage and current of the inverter. Equations (4)–(6) and m is the phase difference between the output voltage and current of the inverter. Equations are also divided into the active power components expressed with a part of PF cos(−φm ), and the (4)–(6) are also divided into the active power components expressed with a part of PF cos m , and reactive power component oscillated with twice the output voltage frequency of the inverter expressed the reactive power component oscillated with a part of cos 2ωm t + 2φ phase_m + φm :with twice the output voltage frequency of the inverter expressed with a part of cos 2mt 2 phase _ m m : n o 1 pm (t) = vm (t)im (t) = V1peak_m I peak_m cos(−φm ) − cos 2ωm t + 2φ phase_m + φm (6) pm (t ) vm (t )im (t )2 V peak _ m I peak _ m cos m cos 2m t 2 phase _ m m (6) 2 Assuming that PF is well controlled using the current controller of the NHB converter, the NHB Assuming that PF is well controlled using the current controller of the NHB converter, the NHB converter receives as much power as the power consumed by the inverter, in order to control the converter receives as much power as the power consumed by the inverter, in order to control the dcdc-link voltage to the reference voltage. However, if the output voltage frequency of the inverter link voltage to the reference voltage. However, if the output voltage frequency of the inverter differs differs from the input voltage frequency of the converter, a fluctuation may occur in the dc-link voltage, from the input voltage frequency of the converter, a fluctuation may occur in the dc-link voltage, due to the difference between the oscillated reactive power components in Equations (3) and (6). Those components are presented in Equation (7).
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due to the difference between the oscillated reactive power components in Equations (3) and (6). Those components are presented in Equation (7). In order to control the dc-link voltage by the reference voltage, the NHB converter receives as much power from the input source as the active power required by the inverter. Therefore, Vpeak_m and I peak_m can be expressed as Equation (8) using Vpeak_g and I peak_g : pcap (t) = pm (t) − p g (t) = 21 Vpeak_m I peak_m cos(−φm ) − 12 Vpeak_g I peak_gcos −φg
− 12 Vpeak_m I peak_m cos 2ωm t + 2φ phase_m + φm + 12 Vpeak_g I peak_g cos 2ω g t + 2φ phase_g + φg
1 1 2 Vpeak_m I peak_m cos(− φm ) = 2 Vpeak_g I peak_g cos V I peak_g cos(−φg ) ∴ Vpeak_m I peak_m = peak_g cos (−φm )
− φg
(7)
(8)
By substituting (7) with (8), the instantaneous power on the dc-link capacitor can be defined as follows: cos(−φg ) pcap (t) = 12 Vpeak_g I peak_g { cos(−φ ) cos 2ωm t + 2φ phase_m + φm − cos 2ω g t + 2φ phase_g + φg } (9) m Equation (9) implies that if the frequency of the input voltage is different from the output voltage frequency of inverter, fluctuation of power can be generated in the dc-link. The dc-link current i DC and voltage v DC that can be generated by this power can be expressed as Equations (10) and (11): i DC (t) = v DC (t) =
=
1 CDC
Pcap (t) VDC
(10)
R
i DC (t) dt Vpeak_g I peak_g cos(−φg ) sin(2ωm t+2φ phase_m +φm ) 4CDC VDC { cos(−φm )ωm
−
sin(2ω g t+2φ phase_g +φg ) } ωg
(11)
If the frequency of the input voltage differs from the output voltage frequency of the inverter, as shown in Equation (11), the frequency of the dc-link voltage fluctuation is twice as large as either the output voltage frequency of the inverter, or the frequency of the input voltage. These two components eventually cause a voltage fluctuation of the dc-link capacitor. 2.2. Optimal Designing DC-Link Capacitor Figures 4–7 show the voltage fluctuation in the dc-link when the output voltage frequency of the inverter is different, using the Equation (11). In Figures 4–7, dc-link voltage VDC is 120 Vdc , capacitance of dc-link CDC is 4.5 mF, Vpeak_g is 89.81 Vpeak , φg is 2.1 rad/s, φm is 0 rad/s, ω g is 377 rad/s and magnitude of I peak_g and ωm are changed by V/f control. Each figure shows the dc-link voltage for the three cells making up the U phase of the inverter. When the output voltage frequency of the inverter is low as shown in Figures 4 and 5, the harmonic component’s frequency is twice the output voltage frequency of the inverter, which is composed of the 120 Hz harmonic component, which is twice the input voltage frequency. These cause the voltage fluctuation of the dc-link.
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Figure 4. Modeling of the dc-link voltage fluctuation depending on the output voltage frequency of Figure 4. Modeling Modeling of the dc-link voltage fluctuation depending on the output voltage frequency of Figure 4. Modeling of of the the dc-link dc-link voltage voltage fluctuation fluctuation depending dependingon on the the output output voltage voltage frequency frequency of of Figure f : 5[Hz] . the inverter at m f : 5[Hz] . the inverter at the inverter at f : 5 [ Hz ] . m m f 5[Hz] . the inverter at m
Figure 5. Modeling of the dc-link voltage fluctuation depending on the output voltage frequency of Figure 5. Modeling of the dc-link voltage fluctuation depending on the output voltage frequency of Figure Figure 5. 5. Modeling Modeling of of the the dc-link dc-link voltage voltage fluctuation fluctuation depending dependingon on the the output output voltage voltage frequency frequency of of f : 20 [Hz] the inverter at . m : 20 [Hz] . f the inverter at the the inverter inverter at at ffmmm : 20 [Hz] [Hz].
Figure 6. Modeling of the dc-link voltage fluctuation on output frequency Figure 6. 6. Modeling Modeling of of the the dc-link dc-link voltage voltage fluctuation fluctuation depending depending on on the the output output voltage voltage frequency frequency of of Figure Figure 6. Modeling of[Hz] the dc-link voltage fluctuation depending depending on the the output voltage voltage frequency of of f : 40 the inverter at . m f : 40 [Hz] the inverter at . m f : 40 [Hz] the the inverter inverter at at f mm : 40 [Hz]..
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Figure Figure 7. 7. Modeling Modelingof of the the dc-link dc-link voltage voltage fluctuation fluctuationdepending dependingon onthe the output output voltage voltage frequency frequencyof of the inverter at f m : 59 [Hz] . the inverter at f m : 59 [Hz].
However, as the output voltage frequency of the inverter increases, different amplitude, phase, However, as the output voltage frequency of the inverter increases, different amplitude, phase, and ripple voltages can be generated in each cell, as shown in Figure 6. As the frequency of the and ripple voltages can be generated in each cell, as shown in Figure 6. As the frequency of the inverter output voltage becomes closer to the frequency of the input voltage, the more similar to a inverter output voltage becomes closer to the frequency of the input voltage, the more similar to a sine sine waveform that 120 Hz component is multiplied by the low frequency sine wave, as shown in waveform that 120 Hz component is multiplied by the low frequency sine wave, as shown in Figure 7. Figure 7. Thus, the maximum value of the voltage ripple is an important factor to be considered in the Thus, the maximum value of the voltage ripple is an important factor to be considered in the design of the system, because voltage fluctuation appearing in the dc-link can vary the maximum design of the system, because voltage fluctuation appearing in the dc-link can vary the maximum value of the amplitude for each cell. value of the amplitude for each cell. In Equation (11), the formula outside of the curly bracket is already fixed, or it is a controlled In Equation Error! Reference source not found., the formula outside of the curly bracket is constant value, while the expression inside the bracket has different values over time, but does not already fixed, or it is a controlled constant value, while the expression inside the bracket has different exceed the maximum and minimum values of sine and cosine, ±1. Therefore, the time when the values over time, but does not exceed the maximum and minimum values of sine and cosine, ±1. voltage of the dc-link reaches the maximum can be defined by Equation (12), and voltage of dc-link Therefore, the time when the voltage of the dc-link reaches the maximum can be defined by Equation becomes minimum can be expressed as Equation (13): Error! Reference source not found., and voltage of dc-link becomes minimum can be expressed as Equation Error! Reference source not found.): sin 2ωm t1 + 2φ phase_m + φm = 1 Vpeak_g I peak_g cos(−φg ) 1 (12) v DC (t) = v DC_max (t1 ) = 4C V { cos(−φm )ωm + ωg }, when DC DC sin 2ω 1 +φ = − mg t11 +22φ phase cos g phase_g V peak _ g I peak _ g _ m m g 1 1 { vDC (t ) vDC _ max (t1 ) }, when (12) 4C DCVDC cos m m g sin 2 2 1 t phase _ g g sin 2ωg 1t + 2φ m 2 phase_m + φm = −1 V I peak_g cos(−φg ) 1 (13) v DC (t) = v DC_min (t2 ) = peak_g 4CDC VDC {− ω g − cos(−φm )ωm }, when sin 2ω t + 2φ + φ = 1 g g 2 phase_g sin t 2 1 cos V peak _ g I peak _ g g }, when m 2 phase _ m m 1 { vDC (t ) vDC _ min (t2 ) (13) assumed 4 cos C V m mpower factor sin 2 2 1 t In order to calculate voltage simplify, cos − φ and cos φ is (− ) DC DC fluctuation g g m 2 _ g phase g g as 1. By subtracting the minimum voltage from the maximum voltage of the dc-link capacitor, the is In order to calculate voltage power factorthecos (13): g and(12)cosand m voltage fluctuation of the dc-link canfluctuation be defined simplify, as Equation (14) using Equations assumed as 1. By subtracting the minimum voltage from the maximum voltage of the dc-link Vpeak_m I peak_m ω g + ωm capacitor, the voltage fluctuation∆v ofDC the=dc-link can be defined as Equation Error! Reference source (14) 2C V ω g ωm not found.) using the Equations (12) and (13): DC DC Also, Equation (14) can be rearrangedVwith C DC , as follows: peak _ m I peak _ m g m vDC 2CDCI peak_m VDC Vpeak_m +mωm ωgg CDC = 2∆v DC VDC ω g ωm Also, Equation Error! Reference source not found.) can be rearranged with
(14) (15) CDC , as follows:
Thus, dc-link capacitors can be designed by selecting the maximum ripple voltage and substituting V peak _ m I peak _ m g m parameters used in the system. CDC (15) 2vDCVDC g m
Thus, dc-link capacitors can be designed by selecting the maximum ripple voltage and substituting parameters used in the system.
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3. Proposed Control Method Using Adaptive Filters 3. Proposed Control 3.1. Conventional FilterMethod Using Adaptive Filters 3.1. Conventional Filter Control characteristics of multilevel systems connecting with the grid have significant effects on the input PF and voltage fluctuation of the dc-link capacitor. In implementing the controller, various Control characteristics of multilevel systems connecting with the grid have significant effects on types of filters have been proposed to prevent unreliable control due to noise of the peripheral circuit the input PF and voltage fluctuation of the dc-link capacitor. In implementing the controller, various while eliminating specific harmonics [14–16]. Conventional filters typically include notch filter (NF), types of filters have been proposed to prevent unreliable control due to noise of the peripheral circuit band pass filter (BPF) and low pass filter (LPF). Among many types of conventional filters, NF has while eliminating specific harmonics [14–16]. Conventional filters typically include notch filter (NF), been widely used in industrial field. By analyzing transfer function and characteristic of NF, it is band pass filter (BPF) and low pass filter (LPF). Among many types of conventional filters, NF has possible to apply it to obtain reliable control. been widely used in industrial field. By analyzing transfer function and characteristic of NF, it is NF is a filter that can remove only desired harmonic components. NF has been studied for possible to apply it to obtain reliable control. controlling ripple component caused by second order harmonic component in various types of NF is a filter that can remove only desired harmonic components. NF has been studied for topology [17–23]. Figure 8 shows an equivalent circuit, block diagram and transfer function of an NF. controlling ripple component caused by second order harmonic component in various types of From the equivalent circuit of NF, a transfer function of the NF can be defined as follows: topology [17–23]. Figure 8 shows an equivalent circuit, block diagram and transfer function of an NF. From the equivalent circuit of NF, a transfer ofo2 the NF can be defined as follows: vo function s2 o (16) vi s 2 s2 + sω 2o2 vo o (16) = 2 Q vi s + ωQo s + ωo2 C 1 where o and Q RNFq C NF . 1 LNF C where ωo = L L NF. L NF C NF and Q = R NF NF
NF NF
Bode Diagram 100
Bandwidth [Q=1] Bandwidth [Q=0.1]
50
Magnitude (dB)
0 -50 -100
-156[dB] at 754[rad/s]
-150 -200 -250
-318[dB] at 754[rad/s]
-300
(a)
-350 90 Q=1 Q=0.1
vi
vo
1 RNFCNF
Phase (deg)
45
1 s
0
-45
1 LNFCNF
1 s
(b)
754[rad/s]
Transfer Function of NF -90 0 10
10
1
10
2
3
10 Frequency (rad/s)
10
4
10
5
10
6
(c)
Figure 8. Characteristics Figure 8. Characteristics and and configuration configuration of of NF NF (a) (a) Equivalent Equivalent circuit, circuit, (b) (b) Block Block diagram, diagram, (c) (c) Bode Bode plot of NF various Q-factor. plot of NF various Q-factor.
Using Equation (16), a block diagram and bode plot of NF can be drawn as shown in Figure 8b,c. Using Equation (16), a block diagram and bode plot of NF can be drawn as shown in Figure 8b,c. The transfer function of NF is composed of o as center frequency and Q as Q-factor based on The transfer function of NF is composed of ωo as center frequency and Q as Q-factor based on passive passive elements. elements. Figure Figure 8c 8c shows shows the the magnitude magnitude and and phase phase response response characteristics characteristics of of NFs NFs as as bode bode plot. plot. Attenuation occurs at the center frequency so that only harmonic component corresponding Attenuation occurs at the center frequency so that only harmonic component corresponding to to the the center frequency is blocked while output voltage v o is generated by input voltage vi of the NF without center frequency is blocked while output voltage vo is generated by input voltage vi of the NF harmonic component. In addition, and magnitude of attenuation are adjustedare byadjusted Q. With without harmonic component. In bandwidth addition, bandwidth and magnitude of attenuation increasing Q, bandwidth becomes smaller, which allows NF strongly removing harmonic by Q. With increasing Q, bandwidth becomes smaller, which allows NF strongly removing harmonic components placing at the center frequency. components placing at the center frequency. 3.2. 3.2. Proposed Proposed Adaptive Adaptive Filters Filters and and Control Control Method Method Conventional Conventional filter filter discussed discussed in in previous previous Section Section 3.1 3.1 have have fixed fixed cut-off cut-off frequency frequency or or center center frequency. Therefore, adaptive filters have been proposed so that the frequency of harmonic frequency. Therefore, adaptive filters have been proposed so that the frequency of harmonic
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components can vary varyevery everytime timedue duetoto change of system frequency [24–27]. In paper, this paper, components can change of system frequency [24–27]. In this seriesseries notch notch filter and (SNF) and decoupled band pass filter are (DBPF) are proposed as filters. adaptive This filter (SNF) decoupled band pass filter (DBPF) proposed as adaptive Thisfilters. subsection subsection discusses theoretical analysis of proposed filters to eliminate voltage fluctuation discusses theoretical analysis of proposed filters to eliminate voltage fluctuation that occurs inthat the occurs the dc-link capacitor described in Section 2, and improve PFside. of the input side. dc-linkincapacitor described in Section 2, and improve PF of the input 3.2.1. 3.2.1. Series SeriesNotch NotchFilter Filter Figure Figure 99 shows shows aa block block diagram diagram of of SNF SNF where where two two NFs NFs are connected in series.
Figure Figure9.9.Block Blockdiagram diagramof ofSNF. SNF.
Unlike conventional NF, SNF is used to eliminate two harmonic components of input voltage Unlike conventional NF, SNF is used to eliminate two harmonic components of input voltage vi . SNF is composed of two subfilters. Each subfilter is based on conventional NF. Subfilter #1 only vi . SNF is composed of two subfilters. Each subfilter is based on conventional NF. Subfilter #1 only removes harmonic component at fixed frequency g while subfilter #2 is used to eliminate removes harmonic component at fixed frequency ω g while subfilter #2 is used to eliminate harmonic harmonic components if their frequencyDifference is changed. Difference between subfilter#2#1is and components even if theireven frequency is changed. between subfilter #1 and subfilter that subfilter that subfilter #2an is external connected withblock. an external block. frequency m of subfilter #2 #2 is is connected with signal Center signal frequency ωmCenter of subfilter #2 is changed f m from theAdjusted external center signal block. Adjusted center subfilter #2 isexternal changed by variable external signalsignal by variable signal f m from the external block. frequency ωm changes parameter of subfilter #2 to remove variable harmonic components. As a result, one of fixed harmonic frequency m changes parameter of subfilter #2 to remove variable harmonic components. As a component input voltage vcomponent by subfilter variable harmonic i is eliminated result, one ofinfixed harmonic in input voltage#1.vi Aisanother eliminated by subfilter #1.component A another in output of subfilter #1 is then removed in adjustable subfilter #2. variable harmonic component in output of subfilter #1 is then removed in adjustable subfilter #2. From the transfer function of NF and block diagram of SNF, a total transfer function of the SNF From the transfer function of NF and block diagram of SNF, a total transfer function of the SNF can be defined with Equation (17): can be defined with Equation (17): 2 )2s2 + ( ω ω2 )2 s4s 4+((ω 2gg2 + ωm2m ) s ( g gm ) m vo vo = 4 3 2 2 2 2 2 () 2 vi m ( B(mBmg2 ω 2gB+ m(ω ) 2 g ω m )2 vsi4 +s( Bg (+ BgBmB s m s g+ Bg gBBmm) s)s2+ )sm3) s+ (ω(2g g+ω m +B g B m g)ω
(17) (17)
gg = 22·22π (60[Hz]) [rad/s] where = 2 22· 2π f m · [rad/s] . ]. mm where ω · (60[Hz]) [rad/sand ] andω f m [rad/s As shown in thethe center frequency ω g ofsubfilter #1 is set#1at is 754set rad/s for rad/s removing As inEquation Equation(17), (17), center frequency at 754 for g of subfilter harmonic components corresponding twice to frequency f of input voltage which is 60 Hz in this g f g of input voltage which is 60 removing harmonic components corresponding twice to frequency paper. Another harmonic component can be filtered at subfilter #2 where center frequency ωm is Hz in this paper. Another harmonic component can be filtered at subfilter #2 where center frequency changed by corresponding twice to variable frequency f m . Center frequency of subfilter #2 is adjusted m is changed by corresponding twice to variable frequency f m . Center frequency of subfilter #2 is by external signal f m so that the proposed SNF not only removes fixed harmonic component, but also adjusted external signal harmonic f m so that the proposed SNF not only removes fixed harmonic adjusts toby eliminate variable components. component, but also adjusts to eliminate variable harmonic components. The SNF transfer function has two bandwidths, denoted Bg and Bm . These can be defined by The SNF transfer function has two bandwidths, using each Q-factor and center frequency as follows: denoted Bg and Bm. These can be defined by using each Q-factor and center frequency as follows: ω Bg = Qg ωg m (18) Bmg = Q B Q (18) m Bm Q
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The magnitude and phase response characteristics of the SNF are shown in Figure 10 using bode magnitude response characteristics the SNF are shown 10 using bode g at 754 of rad/s, red dotted lineinFigure plot. The When SNF has and fixedphase center frequency m is set by external plot. When SNF has fixed center frequency ω g at 754 rad/s, red dotted line ωm is set by external signal signal f m at 503 rad/s while, blue line m is set by changed external signal f m at 628 rad/s. f m at 503 rad/s while, blue line ωm is set by changed external signal f m at 628 rad/s. Magnitude of red Magnitude red dotted −125while dB atmagnitude 503 rad/s while magnitude of blue line −123 dB at 628 dotted line of is − 125 dB at line 503 is rad/s of blue line is −123 dB at 628israd/s (−122 dB rad/s (−122 dB of attenuation at 754 rad/s in both cases). It shows that as changes, attenuation m of attenuation at 754 rad/s in both cases). It shows that as ωm changes, attenuation occurs in the occurs in the corresponding center frequency while variable harmonic components can beby eliminated corresponding center frequency while variable harmonic components can be eliminated adjusting by adjusting center of SNF. center frequency of frequency SNF.
503[rad/s]
754[rad/s] 754[rad/s]
628[rad/s]
-125[dB]
-123[dB]
-122[dB] -122[dB]
Transfer Function of SNF
Figure Figure10. 10.Bode Bodeplot plotof ofSNF SNFvarious variouscentral centralfrequency. frequency.
3.2.2. 3.2.2. Decoupled DecoupledBand Band Pass Pass Filter Filter Another Another adaptive adaptive filter filter DBPF DBPF is is proposed proposed in in this this paper. paper. Figure Figure 11 11 illustrates illustrates block block diagram diagram of of DBPF DBPF where where two two conventional conventional BPFs BPFs are are connected connected in inparallel. parallel.To To remove remove two two harmonic harmonic components components of of input input voltage voltage vvi ,, each each subfilter subfilter extracts extracts different differentharmonic harmoniccomponents componentsfrom frominput inputvoltage voltageviv. . i
i
Subfilter Subfilter #1 #1 only only extracts extractsharmonic harmoniccomponents componentsatatfixed fixedfrequency frequency ωg g while subfilter subfilter #2 #2 extracts extracts variable harmonic harmonic components. components. The Theextraction extractionfrequency frequencyarea areaof ofsubfilter subfilter #2 #2 can can be be changed changed since since variable center frequency frequency ω of subfilter #2 comes from the external signal block. Therefore, output of two center m of subfilter #2 comes from the external signal block. Therefore, output of two m subfilters becomes harmonic components of input voltage. DBPF subtracts output of two subfilters subfilters becomes harmonic components of input voltage. DBPF subtracts output of two subfilters from input input voltage input voltage cancan be be removed. TheThe DBPF can from voltage so so that thattwo twoharmonic harmoniccomponents componentsinin input voltage removed. DBPF have better characteristic of filtering than conventional BPFs since harmonics component is eliminated can have better characteristic of filtering than conventional BPFs since harmonics component is by decoupling frequency frequency areas where each output of subfilter one another. the eliminated by decoupling areas where each output ofoverlaps subfilterwith overlaps with one From another. transfer of BPF and block diagram of DBPF,ofaDBPF, total transfer functionfunction of the DBPF be From thefunction transfer function of BPF and block diagram a total transfer of the can DBPF defined as follows: can be defined as follows: 2 2 2 4 s4s + ((ω 2gg2 + ωm2m) s)2s + ((gω gmω ) 2m ) vo vo = 4 3 2 ))ss22+( B 2 )( vi vsi 4 +s( Bg(+ Bg BmB)ms3) s+ (2gg2+ sm ) 2g ωm )2 (ω ωm2m (mBmg2ω2g B+g Bm2g)ω s+ g ( mω
(19) (19)
gg = 22·22π (60[Hz]) where = 2 22· 2π f m · [rad/s] . ]. where ω · (60[Hz])[rad/s] [rad/sand ] andω f m [rad/s mm The center center frequency frequency ωgg of for removing removing one one of of fixed fixed The of subfilter subfilter #1 #1 is is defined defined at at 754 754 rad/s rad/s for harmonic components, derived from frequency f of input voltage. ω is changed by external g m harmonic components, derived from frequency f g of input voltage. m is changed by external signal, corresponding twice to variable frequency f m . Because of decoupling block of DBPF, difference signal, corresponding twice to variable frequency f m . Because of decoupling block of DBPF, between transfer function of SNF and DBPF is that second order term of denominator in transfer difference function ofbetween DBPF istransfer simpler function than thatof ofSNF SNF.and DBPF is that second order term of denominator in transfer function of DBPF is simpler than that of SNF.
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Figure Figure 11. 11. Block Block diagram diagram of of DBPF. DBPF.
DBPF also has two bandwidths expressed as Bg and Bm. It can be defined as follows: DBPF also has two bandwidths expressed as Bg and Bm . It can be defined as follows:
g
B ω Bgg = QQg (20) ω (20) Bm =Qm m Bm Q Figure 12 shows magnitude and phase response characteristics of DBPF using a Bode plot. When DBPF12has fixedmagnitude center frequency ω g response at 754 rad/s, red dottedofline ωmusing is set aby external signal Figure shows and phase characteristics DBPF Bode plot. When f at 503 rad/s and blue line ω is set by changed external signal f at 628 rad/s. Magnitude of red m m g at 754 rad/s, red dotted line mm is set by external signal fm DBPF has fixed center frequency dotted line is −125 dB at 503 rad/s while magnitude of blue line is −123 dB at 628 rad/s (−122 dB of at 503 rad/s and blue line m is set by changed external signal f m at 628 rad/s. Magnitude of red attenuation at 754 rad/s in both cases). As center frequencies ωm of the DBPF change according to the dotted line is −125 dB at 503 rad/s while magnitude of blue line is −123 dB at 628 rad/s (−122 dB of external signals, gain is attenuated in the corresponding frequency. This confirms that magnitude is attenuation at 754 rad/s in both cases). As center frequencies m of the DBPF change according to attenuated in the corresponding frequency as ωm changes. the external signals, gainmagnitude is attenuated the corresponding frequency.ofThis magnitude Figure 13 illustrates andinphase response characteristics twoconfirms proposedthat adaptive filters, is attenuated in the corresponding frequency as changes. m SNF and DBPF, using a Bode plot. Applied conditions are: bandwidth Qg = Qm = 10; center frequency 13 illustrates magnitude and phase response of two proposed adaptive ωm =Figure 691 rad/s, ωg = 754 rad/s in each filter. As can be seencharacteristics in Figure 13, magnitude characteristics of filters, SNF andare DBPF, using a Bode Applied conditions Qg = respectively). Qm = 10; center SNF and DBPF almost the same (−plot. 123 dB at 628 rad/s and −are: 122 bandwidth dB at 786 rad/s, 691 rad/s, g can = 754 in each As can be seen frequency Phase shift be rad/s estimated by filter. comparing each phaseinatFigure gain of13,−3magnitude dB in the m = characteristics Bode plot. It means that many have occurred of characteristics of SNF andhow DBPF are phase almostdelays the same (−123 dB at by 628phase rad/s response and −122 characteristic dB at 786 rad/s, filter. Phase shift characteristic of each filter illustrated in Figure 13 shows that DBPF has 50.8 degrees respectively). at 786 rad/s while SNF has 57.7 at 786 by rad/s. As shown Figure 13, SNF DBPF have Phase shift characteristics candegrees be estimated comparing eachin phase at gain of −3and dB in the Bode similar magnitude Since mutual interference of subfilter #1 and subfilter #2 plot. It means that characteristic. how many phase delays have occurred components by phase response characteristic of filter. are decoupled, phase delay of DPBF is less than that of SNF. As a result, DBPF shows better phase Phase shift characteristic of each filter illustrated in Figure 13 shows that has 50.8 degrees at response characteristic 786 rad/s while SNF hasthan 57.7 SNF. degrees at 786 rad/s. As shown in Figure 13, SNF and DBPF have similar magnitude characteristic. Since mutual interference components of subfilter #1 and subfilter #2 are decoupled, phase delay of DPBF is less than that of SNF. As a result, DBPF shows better phase response characteristic than SNF.
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503[rad/s] 503[rad/s]
754[rad/s] 754[rad/s] 754[rad/s] 754[rad/s]
628[rad/s] 628[rad/s]
-125[dB] -125[dB]
-123[dB] -123[dB]
-122[dB] -122[dB] -122[dB] -122[dB]
Transfer Function Function of of DBPF DBPF Transfer
Figure 12. Bode plot of DBPF various center frequency. Figure Figure12. 12.Bode Bodeplot plotof ofDBPF DBPFvarious variouscenter centerfrequency. frequency.
628[rad/s] 628[rad/s] 628[rad/s] 628[rad/s]
754[rad/s] 754[rad/s] 754[rad/s] 754[rad/s]
-123[dB] -123[dB] -123[dB] -123[dB]
-122[dB] -122[dB] -122[dB] -122[dB]
-50.6[deg] at at 593[rad/s] 593[rad/s] -50.6[deg] -46.1[deg] at at 593[rad/s] 593[rad/s] -46.1[deg] 57.7[deg] at at 786[rad/s] 786[rad/s] 57.7[deg] 50.8[deg] at at 786[rad/s] 786[rad/s] 50.8[deg]
Figure 13. Comparison of SNF and DBPF in bode plot. Figure Figure13. 13.Comparison Comparisonof ofSNF SNFand andDBPF DBPFin inbode bodeplot. plot.
3.2.3. Control Method 3.2.3. 3.2.3.Control ControlMethod Method Figure 14 shows control block diagram of of the conventional conventional method method for for aaa one one NPC/h-bridge NPC/h-bridge Figure NPC/h-bridge Figure14 14shows showsaaa control control block block diagram diagram of the the conventional method for one converter cell. In this case, the voltage controller is affected by voltage fluctuation and harmonic converter cell. In this case, the voltage controller is affected by voltage fluctuation and converter cell. In this case, the voltage controller is affected by voltage fluctuation and harmonic harmonic components in the dc-link. In addition, the output signal of PI voltage controller is included in the components in the dc-link. In addition, the output signal of PI voltage controller is included components in the dc-link. In addition, the output signal of PI voltage controller is includedin inthe the harmonic components. Thus, current control is distorted since the input reference of current harmonic components. Thus, current control is distorted since the input reference of current harmonic components. Thus, current control is distorted since the input reference of current controller controller comes from the the output of of voltage controller controller included in the the harmonic harmonic components. components. controller comes from voltage included in comes from the output of output voltage controller included in the harmonic components. To overcome the the disadvantage disadvantageof ofthe theconventional conventional control method due to voltage voltage fluctuation To the disadvantage of the conventional control method due to fluctuation To overcome overcome control method due to voltage fluctuation and and harmonic components in the dc-link, the control block diagram with an adaptive filter for is and harmonic components in the dc-link, the control block diagram with an adaptive filter is harmonic components in the dc-link, the control block diagram with an adaptive filter is proposed proposed for aa one one NPC/h-bridge NPC/h-bridge converter cell as shown shown in Figure Figure 15. 15. proposed for converter cell a one NPC/h-bridge converter cell as shown in as Figure 15.in When a voltage controller is used to control the voltage of the dc-link, the actual voltage in the When a voltage controller is used to control the voltage of the dc-link, When a voltage controller is used to control the voltage of the dc-link,the theactual actualvoltage voltagein inthe the dc-link is used as an input to the proposed adaptive filter to eliminate harmonic components. At this dc-link is used as an input to the proposed adaptive filter to eliminate harmonic components. At this dc-link is used as an input to the proposed adaptive filter to eliminate harmonic components. At this time, the frequency of output voltage is given through DSP of the inverter so that adaptive filter can time, time,the thefrequency frequencyof ofoutput outputvoltage voltageis isgiven giventhrough throughDSP DSPof ofthe theinverter inverterso sothat thatadaptive adaptivefilter filtercan can set their center frequency as twice of the frequency of the output voltage of inverter. set their center frequency as twice of the frequency of the output voltage of inverter. set their center frequency as twice of the frequency of the output voltage of inverter. Therefore, harmonic harmonic components components in in the the dc-link dc-link corresponding corresponding to to twice twice the the input input voltage voltage of of Therefore, converter and and output output voltage voltage of of inverter inverter can can be be removed removed by by the the adaptive adaptive filter. filter. The The output output of of the the converter
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Therefore, harmonic components in the dc-link corresponding to twice the input voltage of Energies 2018, 11, x FOR PEER REVIEW 13 of 24 converter and output voltage of inverter can be removed by the adaptive filter. The output of the adaptive filter as feedback signal signal to to the the voltage voltage controller controller to to perform perform dc-link dc-link voltage voltage13control control Energies 2018, FOR PEER of 24 adaptive filter11,is isxused used as aaREVIEW feedback without harmonic components. Since the voltage controller can operate without harmonics, the current without harmonic components. Since the voltage controller can operate without harmonics, the adaptiveisfilter used as by a feedback signal to the voltage controller to perform voltage control 2. controller notisaffected harmonics from dc-link asdc-link described in Section current controller is not affected by harmonics fromvoltage dc-linkfluctuation voltage fluctuation as described in without harmonic components. Since the voltage controller can operate without harmonics, the With these procedures, the proposed control scheme with adaptive filter can reduce dc-link voltage Section 2. With these procedures, the proposed control scheme with adaptive filter can reduce dccurrent controller is notthe affected harmonics from dc-link voltage fluctuation as described in fluctuations improve powerby factor. link voltage and fluctuations and improve the power factor. Section 2. With these procedures, the proposed control scheme with adaptive filter can reduce dclink voltage fluctuations and improve the power factor. Phase Shift Unipolar PWM Control block diagram(Conventional)
Control block diagram(Conventional) *
v
ie*ds = 0
dc v*dc
vdc Filter vNF dc / BPFFilter / LPF
vs vs
PI Voltage Controller PI Voltage Controller
ie*ds = 0
vsqs vsqs
T( e) Transformation T(e)
veqs veqs
Low Pass Filter
veqs_LPF veqs_LPF
vs*
Phase Shift * Unipolar * PWM (Converter) a b
v
v
ds * Phase e Inverse v a Unipolar v*b Shift s* d-q v ds transformation Inverse PhasePWM Shift d-q Unipolar Reference -1 T ( ) e transformation PWM Generation s* qs Reference T -1(e) Generation vs* e377 qs
PI Current Controller PI Current PI Controller Current Controller PI
ie*qs Current e e NF / BPF / LPF ie*qs i qs i ds Controller e ve*ds = 0 e i qs ieds e s e e ve*ds = 0 v ds v ds v ds_LPF Park s Transformation e e Low Pass All Pass v ds v ds Filter v ds_LPF Filter Park All Pass Filter
(Converter)
e
is is
v
PI PI
All Pass Filter All Pass Filter
e377 isds
isds
isqs
isqs
e
e ieds
Park Transformation Park T(e) Transformation
ieds
T(e)
ieqs
ieqs
Figure 14. 14. Conventional Conventional control control block block diagram diagram of of NPC/h-bridge NPC/h-bridge converter. Figure converter. Figure 14. Conventional control block diagram of NPC/h-bridge converter.
Figure 15. Proposed control block diagram of NPC/h-bridge converter with new adaptive filters. Figure 15. Proposed control block diagram of NPC/h-bridge converter with new adaptive filters. Figure 15. Proposed control block diagram of NPC/h-bridge converter with new adaptive filters.
4. Simulation Results 4. Simulation Results In order to verify principle and feasibility of the proposed control method based on adaptive filters, the simulation has beenand developed theproposed PSIM software The simulation In order to verify principle feasibilityusing of the control program. method based on adaptive filters, the simulation has been developed using the PSIM software program. The simulation
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14 of 24 In order to verify principle and feasibility of the proposed control method based on adaptive filters, the simulation has been developed using the PSIM software program. The simulation schematic schematic in which the 13-level cascaded NPC/h-bridge is connected to the grid is illustrated in Figure in which the 13-level cascaded NPC/h-bridge is connected to the grid is illustrated in Figure 2. 2. The systems parameters of the simulation and experiment are shown in Table 1. The systems parameters of the simulation and experiment are shown in Table 1.
Table 1. Simulation and experiment parameters. Table 1. Simulation and experiment parameters. Parameter Value Unit Parameter Parameter Rated power of transformer
Turn ratio Rated power of transformer Turn ratio Rated power Rated power Rated voltage Rated voltage Rated current Rated current Rated power of each stack Rated power of each stack
Value 1.1
2:1 1.1 2:1 15 15 380 380 27.8 27.8 1.1 1.1
Unit Input voltage Parameter kW of each stack
turn kW turn kW kW Vrms Vrms Arms Arms kW kW
Value
Unit
Value V Unit 89
Filter inductance Input voltage of each stack 1 89 mH V Filter inductance Switching frequency 10 1 kHzmH Switching frequency 10 kHz DC-link voltage 120120 V V DC-link voltage DC-link capacitance DC-link capacitance 4 4 mF mF
Figure 16 shows shows aa simulation simulation waveform waveform with with one one ac/dc ac/dc converter and an inverter driven by applying the conventional control method consisting of a 120 Hz notch filter to to thethe dc-link feedback, as applying the conventional control method consisting of a 120 Hz notch filter dc-link feedback, introduced in Section 3.1 3.1 [28,29]. Before applying the the existing control, the the initial charge of the as introduced in Section [28,29]. Before applying existing control, initial charge of dc-link the dcis performed through the ramp function, and when the steady state is reached, the dc-link voltage link is performed through the ramp function, and when the steady state is reached, the dc-link voltage control notch filter. The output voltage of control is is performed performedthrough throughthe theconventional conventionalcontrol controlmethod methodwith with notch filter. The output voltage the inverter is controlled by by V/F control, at at that time thethe frequency of of thethe inverter output voltage is of the inverter is controlled V/F control, that time frequency inverter output voltage approximately 56.67 Hz. Figure 17 shows the steady-state result of Figure 16 in an enlarged view of is approximately 56.67 Hz. Figure 17 shows the steady-state result of Figure 16 in an enlarged view time. AsAs shown in Figure 17e, thethe output current of the inverter is close to atosinusoidal wave. of time. shown in Figure 17e, output current of the inverter is close a sinusoidal wave. However, areare mixed in the input current as shown in Figure 17c. However,ititcan canbe beseen seenthat thatmany manyharmonics harmonics mixed in the input current as shown in Figure As shown in Figure 17a, using the conventional control method, voltage control is performed except for 17c. As shown in Figure 17a, using the conventional control method, voltage control is performed the 120 Hz the actual voltage component of the dc-link. Therefore, the voltage controller except for component the 120 Hzincomponent in the actual voltage component of the dc-link. Therefore, the of the dc-link transfers the components of the specific frequency which are lower than 120 Hz to the voltage controller of the dc-link transfers the components of the specific frequency which are lower input of the Ascurrent a result,controller. it generates ingenerates the input current andin thethe effect of than 120 Hzcurrent to the controller. input of the Asharmonics a result, it harmonics input decreasing voltage fluctuation is alsovoltage insufficient. current andthe thedc-link effect of decreasing the dc-link fluctuation is also insufficient.
results of the control method applied in the single-phase NPC/hFigure 16. 16. Simulation Simulation results of conventional the conventional control method applied in the single-phase bridge converter (a) dc-link voltage,voltage, (b) input of the converter, (c) input of the NPC/h-bridge converter (a) dc-link (b)voltage input voltage of the converter, (c) current input current converter, (d) output voltage of the of inverter, (e) output current of theof inverter (200 ms/div). of the converter, (d) output voltage the inverter, (e) output current the inverter (200 ms/div).
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Figure 17. Simulation results of the conventional control method applied in the single-phase NPC/hFigure Simulation results of the conventional control method applied in the single-phase bridge converter (a) dc-link voltage,voltage, (b) input of the converter, (c) input of the NPC/h-bridge converter (a) dc-link (b)voltage input voltage of the converter, (c) current input current 17. output Simulation results the conventional control method applied in single-phase NPC/hconverter, (d) voltage ofofthe inverter, (e) output current of theofinverter (20 ms/div). of theFigure converter, (d) output voltage of the inverter, (e) output current thethe inverter (20 ms/div). bridge converter (a) dc-link voltage, (b) input voltage of the converter, (c) input current of the converter, (d) output voltage of the inverter, (e) output current of the inverter (20 ms/div).
Figure 18 (FFT) waveforms forfor thethe waveforms in Figure 17. The Figure 18 shows showsthe thefast fastFourier Fouriertransform transform (FFT) waveforms waveforms in Figure 17. 120 Hz ripple voltage component in the actual dc-link voltage is removed by the notch filter of the The 120 Hz ripple component the actual dc-link voltage removed by the notch17. filter Figure 18 voltage shows the fast Fourierin transform (FFT) waveforms foristhe waveforms in Figure Theof the conventional control method configured the input to the voltagebycontroller. However, 120 Hz ripple voltage component in the dc-link voltage is removed the notch filter of the the conventional control method configured in actual theininput to the voltage controller. However, the component component 113.33 which twice the output frequency of the inverter, Hz, is notand removed, conventional control method configured in theof input to the voltage controller. However, theflows of 113.33 Hzofwhich isHz twice the is output frequency the inverter, 56.67 Hz, is56.67 not removed, component of 113.33 Hz which is twice the output frequency of the inverter, 56.67 Hz, is not removed, and flows into the voltage controller. Therefore, when the output value of the current controller is into the voltage controller. Therefore, when the output value of the current controller is performed and flows into the d-q voltage controller. Therefore, when the output value ofasthe current controller is performed in reverse transform, this harmonic component is shown a harmonic component of in reverse d-q transform, this harmonic component is shown as a harmonic component of 173.33 Hz. performed inharmonic reverse d-qcomponent transform, this harmonic component is shown as a233.33 harmonic ofinput 173.33 Hz. This is aconverted to aof power Hzcomponent by a 60 Hz This harmonic component is converted to power ripple 233.33ripple Hz byof a 60 Hz input voltage, causing 173.33 Hz. This harmonic component is converted to a power ripple of 233.33 Hz by a 60 Hz input causing a voltage in this the dc-link, and generates this fluctuation generates current component avoltage, voltage fluctuation in thefluctuation dc-link, and fluctuation current component of 303.33 Hz in voltage, causing a voltage fluctuation in the dc-link, and this fluctuation generates current component of 303.33 Hz in the input current again. the input current again. of 303.33 Hz in the input current again.
Figure 18. FFT simulation resultsofofthe theconventional conventional control applied in the single-phase Figure 18. FFT simulation results controlmethod method applied in the single-phase NPC/h-bridge converter (a) actual dc-link voltage and output signal of the NF, (b) output signal NPC/h-bridge converter (a) actual dc-link voltage and output signal of the NF, (b) output signalofof the Figure FFT simulation results of the conventional control method applied in the single-phase the18. PI voltage controller, (c) reference voltage of the dc-link, (d) input current of the converter. PI voltage controller, (c) reference voltage of the dc-link, (d) input current of the converter. NPC/h-bridge converter (a) actual dc-link voltage and output signal of the NF, (b) output signal of the PI voltage controller, (c) reference voltage of the dc-link, (d) input current of the converter.
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Figure using the SNF adaptive filter, is Figure 19 19 shows shows the the result result of of simulations simulations using using the the SNF SNF adaptive adaptive filter, filter, which which is is one one of of the the Figure 19 shows the result of simulations which one of the proposed control method. As shown in Figure 19c, when the simulation is performed under the same proposed control control method. method. As As shown shown in in Figure Figure 19c, 19c, when when the the simulation simulation is is performed performed under under the the same same proposed conditions asin inthe theconventional conventionalcontrol control described above, it can be seen the input current is conditions as as in the conventional control described above, can be seen seen thatthat the input input current is close close conditions described above, itit can be that the current is close to a sinusoidal wave. The steady-state result waveform is shown in Figure 20. By removing to aa sinusoidal sinusoidal wave. wave. The The steady-state steady-state result result waveform waveform is is shown shown in in Figure Figure 20. 20. By By removing removing the the dcdcto the dc-link fluctuation component through the SNF, and then performing the voltage control, the link fluctuation component through the SNF, and then performing the voltage control, the voltage link fluctuation component through the SNF, and then performing the voltage control, the voltage voltage fluctuation of the dc-link andPF theof of the input current clearly betterthan thanthose those of of the fluctuation of the the dc-link dc-link and the the PF ofPFthe the input current areare clearly better than those of the fluctuation of and input current are clearly better the conventional control. Figure 21 shows the FFT analysis of the waveforms in Figure 20. As shown conventional control. control. Figure Figure 21 21 shows shows the the FFT FFT analysis analysis of of the the waveforms waveforms in in Figure Figure 20. 20. As As shown shown in in conventional in Figure 21, in the proposed control, since the output frequency component and the 120 Hz component Figure 21, in the proposed control, since the output frequency component and the 120 Hz component Figure 21, in the proposed control, since the output frequency component and the 120 Hz component of isis feedback, it it can bebe confirmed that only thethe dc of the the inverter inverterare arenot notshown shownwhen whenthe thedc-link dc-linkvoltage voltage is feedback, it can can be confirmed that only the of the inverter are not shown when the dc-link voltage feedback, confirmed that only component exists in the output of the voltage controller. dc component component exists exists in in the the output output of of the the voltage voltage controller. controller. dc
Figure19. 19. Simulation Simulationresults resultsusing usingthe theproposed proposed control method with the SNF adaptive filter. (a) dcdcFigure control method with thethe SNF adaptive filter. (a) dc-link Simulation results using the proposed control method with SNF adaptive filter. (a) link voltage, (b) input voltage of the converter, (c) input current of the converter, (d) output voltage voltage, (b) input voltage of theofconverter, (c) input current of theof converter, (d) output voltagevoltage of the link voltage, (b) input voltage the converter, (c) input current the converter, (d) output of the the inverter, inverter, (e) output output current of the the inverter inverter (200 ms/div). ms/div). inverter, (e) output currentcurrent of the inverter (200 ms/div). of (e) of (200
Figure 20. 20. Simulation Simulationresults resultsusing usingthe theproposed proposed control method with the SNF adaptive filter. (a) dcdcFigure Simulation results using the proposed control method with SNF adaptive filter. (a) control method with thethe SNF adaptive filter. (a) dc-link link voltage, (b) input voltage of the converter, (c) input current of the converter, (d) output voltage link voltage, (b) input voltage the converter, (c) input current the converter, (d) output voltage, (b) input voltage of theofconverter, (c) input current of theof converter, (d) output voltagevoltage of the of the the inverter, inverter, (e) output output current of the the inverter inverter (20 ms/div). ms/div). of (e) of (20 inverter, (e) output currentcurrent of the inverter (20 ms/div).
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Figure 21. FFT FFT simulation results results using the the proposed proposed control control method method with with the the SNF SNF adaptive adaptive filter. filter. (a) (a) Figure Figure 21. 21. FFTsimulation simulation resultsusing using the proposed control method with the SNF adaptive filter. actual dc-link dc-link voltage voltage and and output output signal signal of of the SNF, SNF, (b) (b) output output signal signal of of the PI PI voltage controller, controller, (c) (c) actual (a) actual dc-link voltage and output signalthe of the SNF, (b) output signalthe of thevoltage PI voltage controller, reference voltage of the dc-link, (d) input current of the converter. reference voltage of the dc-link, (d)(d) input current of the converter. (c) reference voltage of the dc-link, input current of the converter.
Figures 22–24 22–24 show show the the simulation simulation result result waveform waveform with with the the DBPF DBPF adaptive adaptive filter filter applied. applied. This This Figures Figures 22–24 show the simulation result waveform with the DBPF adaptive filter applied. This was performed performed under under the the same same conditions conditions as as the the simulations simulations mentioned mentioned above. above. DBPF DBPF also also was has was has performed under the same conditions as the simulations mentioned above. DBPF also has characteristics characteristics similar to the steady state waveform using SNF, because it forms a notch angle for two characteristics similar to the steady state waveform using SNF, because it forms a notch angle for two similar to theinsteady stateway waveform SNF, because it forms a notch angle for two frequencies in frequencies the same same as SNF. SNF.using In addition, addition, since the the voltage control is performed performed using only only frequencies in the way as In since voltage control is using the way as SNF.excluding In addition,the since the voltage controlcomponent is performedgenerated using onlyinthe dc dc-link, component, the same dc component, component, voltage fluctuation the the the dc excluding the voltage fluctuation component generated in the dc-link, the excluding the voltage fluctuation component generated in the dc-link, the harmonics mixed in theisinput harmonics mixed in the input current are reduced, and the voltage fluctuation of the dc-link also harmonics mixed in the input current are reduced, and the voltage fluctuation of the dc-link is also current are reduced, and the voltage fluctuation of the dc-link is also decreased. decreased. decreased.
Figure 22. Simulation results using the proposed control method with thethe DBPF adaptive filter. (a) Figure 22. Simulation Simulationresults resultsusing usingthe the proposed control method with DBPF adaptive filter. Figure proposed control method with the DBPF adaptive filter. (a) dc-link voltage, (b)input input voltage ofthe theofconverter, converter, (c)input input current of the theconverter, converter, (d)output output voltage (a) dc-link voltage, (b) input voltage the converter, (c) current input current of the converter, (d) voltage output dc-link voltage, (b) voltage of (c) of (d) of the inverter, (e) output current of the inverter (200 ms/div). voltage of the inverter, (e) output current of the inverter (200 ms/div). of the inverter, (e) output current of the inverter (200 ms/div).
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Simulation results using the proposed control method with thethe DBPF adaptive filter. (a) Figure 23. 23. Simulation Simulationresults resultsusing usingthe the proposed control method with DBPF adaptive filter. Figure proposed control method with the DBPF adaptive filter. (a) dc-link voltage, (b) input input voltage of the theofconverter, converter, (c) input input current of the the converter, converter, (d) output output voltage (a) dc-link voltage, (b) input voltage the converter, (c) current input current of the converter, (d) voltage output dc-link voltage, (b) voltage of (c) of (d) of the inverter, (e) output current of the inverter (20 ms/div). voltage of the inverter, (e) output current of the inverter (20 ms/div). of the inverter, (e) output current of the inverter (20 ms/div).
Figure 24. 24. FFT FFT simulation simulation results results using using the the proposed control method with the DBPF adaptive filter. Figure simulation results using the proposed proposed control control method method with with the the DBPF DBPF adaptive adaptivefilter. filter. (a) actual dc-link voltage and output signal of the DBPF, (b) output signal of the PI voltage controller, (a) actual dc-link voltage and output signal of of the the DBPF, DBPF, (b) output output signal signal of of the the PI PI voltage voltagecontroller, controller, (c) reference reference voltage voltage of of the the dc-link, dc-link, (d) (d)input inputcurrent currentof ofthe theconverter. converter. (c) the dc-link, (d) input current of the converter.
Simulation results of of conventional NF, NF, proposed proposed SNF SNF and and DBPF DBPF applied applied in in single-phase single-phase NPC/hNPC/hSimulation Simulation results results ofconventional conventional NF, proposed SNF and DBPF applied in single-phase bridge converter are analyzed by comparing characteristics of dc-link voltage, THD and power factor bridge converterconverter are analyzed comparing characteristics of dc-link voltage, THD and power NPC/h-bridge are by analyzed by comparing characteristics of dc-link voltage, THDfactor and of input input current current as as shown shown in in Table 2. 2. The The proposed proposed SNF SNF shows shows superior superior reduction reduction of of voltage voltage of power factor of input current asTable shown in Table 2. The proposed SNF shows superior reduction of fluctuation as as 10.9 10.9 V. V. Furthermore, Furthermore, voltage voltage fluctuation fluctuation of of the the proposed proposed DBPF DBPF is is 10.9 10.9 V, V, which which is is fluctuation voltage fluctuation as 10.9 V. Furthermore, voltage fluctuation of the proposed DBPF is 10.9 V, which is smaller than the 11.4 V of the conventional NF. The characteristic of the THD is improved by smaller thanthe the11.4 11.4 V the of the conventional NF.characteristic The characteristic of the THD is improved by smaller than V of conventional NF. The of the THD is improved by proposed proposed control method, which is 2.38% in SNF and 2.36% in DBPF. Compared to conventional proposed control method, which is 2.38% in SNF 2.36% in DBPF. Compared to conventional control method, which is 2.38% in SNF and 2.36% in and DBPF. Compared to conventional control method control method method with with NF, NF, proposed proposed SNF SNF and and DBPF DBPF has has better better power power factor, factor, which which is is 0.99 0.99 in in SNF SNF and and control with NF, proposed SNF and DBPF has better power factor, which is 0.99 in SNF and DBPF. As a result, DBPF. As As aa result, result, proposed proposed control control method method with with two two adaptive adaptive filters filters not not only only reduces reduces the the dc-link dc-link DBPF. voltage fluctuation, but also improves the characteristics of THD and power factor of input current. voltage fluctuation, but also improves the characteristics of THD and power factor of input current.
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proposed control method with two adaptive filters not only reduces the dc-link voltage fluctuation, Energies 2018, 11, x FOR PEER REVIEW 19 of 24 Energies 2018, 11, x FOR PEER REVIEW 19 of 24 but also improves the characteristics of THD and power factor of input current. Table 2. Comparison of the characteristics of the ac/dc converter for different control methods. Table 2. 2. Comparison Comparison of of the the characteristics characteristics of of the the ac/dc ac/dc converter Table converter for for different different control control methods. methods. Control Method VDC _ Max [V] VDC _ Min [V] VDC [V] THD [%] Power Factor [V] VDC _ Min [V] VDC [V] THD [%] Power Factor Control Method VVDC _ Max [V] Control Method VDC_Min [V] 4VDC [V] THD [%] Power Factor DC_Max Conventional NF 126.1 114.6 11.4 17.03 0.98 Conventional 126.1 114.6 11.4 17.03 0.98 0.98 Conventional NFNF 126.1 114.6 11.4 17.03 Proposed SNF 125.4 114.5 10.9 2.38 0.99 Proposed SNF 125.4 114.5 10.9 Proposed SNF 125.4 114.5 10.9 2.382.38 0.99 0.99 Proposed DBPF 125.4 114.5 10.9 2.36 0.99 0.99 Proposed DBPF 114.5 10.9 2.36 Proposed DBPF 125.4 114.5 10.9 2.36 0.99
5. Experiment Experiment Results Results 5. 5. Experiment Results An experiment experimentwas wasperformed performedtotoverify verifythe thefeasibility feasibility the proposed control method applied An ofof the proposed control method applied in An experiment was performed to verify the feasibility of the proposed control method applied a cascaded NPC/h-bridge system.The Theconfigurations configurationsofofthe theexperimental experimentalsystem systemand andpower powerstacks stacks aincascaded NPC/h-bridge system. in a cascaded NPC/h-bridge system. The configurations of the experimental system and power stacks are as asfollows followsFigures Figures25–28, 25–28,and andthe theexperimental experimentalparameters parametersas asin inTable Table1.1. are are as follows Figures 25–28, and the experimental parameters as in Table 1. The controller is implemented on TMS320F28377s, and that of the floating point point microcontroller microcontroller The controller is implemented on TMS320F28377s, and that of the floating The controller is implemented on TMS320F28377s, and that of the floating point microcontroller unit at at 200 200 MHz MHz rate rate frequency. frequency. The The switching switching and and sampling sampling frequency frequency isis 10 10kHz. kHz. The The power power is is unit unit at 200 MHz rate frequency. The switching and sampling frequency is 10 kHz. The power is supplied to to the the cascaded cascadedNPC/h-bridge NPC/h-bridge inverter through the cascaded NPC/h-bridge NPC/h-bridge converter. supplied converter. supplied to the cascaded NPC/h-bridge inverter through the cascaded NPC/h-bridge converter.
Figure 25. Configuration of the experiment system. Figure 25. 25. Configuration Configuration of of the the experiment experiment system. system. Figure
Figure 26. Experimental setup 1 of the 13-level cascaded NPC/h-bridge system. Figure 26. Experimental setup 1 of the 13-level cascaded NPC/h-bridge system. Figure 26. Experimental setup 1 of the 13-level cascaded NPC/h-bridge system.
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Figure 27. Experimental setup 2 of the 13-level cascaded NPC/h-bridge system. Figure 27. Experimental setup setup 22 of of the the 13-level system. Figure 27. Experimental 13-level cascaded cascaded NPC/h-bridge NPC/h-bridge system.
Figure 28. Experimental setup 3 of the one-stack NPC/h-bridge. Figure 28. Experimental setup 3 of the one-stack NPC/h-bridge. Figure 28. Experimental setup 3 of the one-stack NPC/h-bridge.
Figure 29 shows the output phase voltage waveforms on phase a, b, and c for the phase shift Figure 29 shows the output voltage cascaded waveforms on phase a, b,system. and c for shift PWM (PS-PWM) scheme appliedphase to a 13-level NPC/H-bridge As the onephase can see in Figure 29 shows the output phase voltage cascaded waveforms on phase a, b, and c for the phase shift PWM (PS-PWM) scheme applied to a 13-level NPC/H-bridge system. As one can see in Figure(PS-PWM) 29, the output voltage of step 13 appears. Figure NPC/H-bridge 30 shows a slightly enlarged view ofsee each PWM scheme applied to a13 13-level cascaded system. As one canof in Figure 29, thePS-PWM output voltage of step appears. Figure 30 scheme, shows athe slightly enlarged view each phase. Since is implemented as a unipolar PWM inverter stack of each cell is Figure 29, the output voltage of step 13 appears. Figure 30 shows a slightly enlarged view of each phase. Sincethrough PS-PWM is implemented as a voltage unipolar PWM scheme, thestages, inverter stack of each cell is modulated a carrier whose output is divided into five and each stack is phase phase. Since PS-PWM is implemented as avoltage unipolar PWM scheme, the inverter of each cell is modulated through a carrier whose output is divided into fivesteps. stages, andstack each stack is phase shifted by 120°. Thus, each phase can obtain an output voltage in 13 modulated through a carrier whose output voltage is divided into five stages, and each stack is phase shifted by 120°. Thus, eachexperimental phase can obtain an output 13 steps. Figure 31◦shows the waveform of thevoltage dc-linkin voltage of the single-phase NPC/hshifted by 120 . Thus, each phase can obtain an output voltage in 13 steps. Figure 31 shows the experimental waveform of the the input dc-link voltage of current, the single-phase NPC/hbridge converter, the output voltage of the inverter, side system and the inverter Figure 31 shows the experimental waveform of the dc-link voltage of the single-phase bridge the output voltage of sequence the inverter, the input sidethe system current, and thecontrolled inverter outputconverter, current. After the initial charge was performed, dc-link voltage was NPC/h-bridge converter, the output voltage ofwas theperformed, inverter, the input side system current, and output current. After the initial charge sequence the dc-link voltage was controlled to reach the output steady state, andAfter the inverter was driven. the inverter current. the initial charge sequence was performed, the dc-link voltage was to reach the steady state, and the inverter was driven. controlled to reach the steady state, and the inverter was driven.
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Figure 29. Waveforms of each phase voltage of the the inverter. inverter. Figure 29. 29. Waveforms Waveforms of of each each phase phase voltage voltage of of Figure the inverter. Figure 29. Waveforms of each phase voltage of the inverter.
Figure 30. Waveforms of the phase voltage of each cell in a-phase. Figure 30. Waveforms of the phase voltage of each cell in a-phase. Figure 30. Waveforms of the phase voltage of each cell in a-phase. Figure 30. Waveforms of the phase voltage of each cell in a-phase.
Figure 31. Waveforms of the singe-phase NPC/h-bridge converter operation using the proposed Figure 31. Waveforms of the singe-phase NPC/h-bridge converter operation using the proposed control method. control method. Figure 31. Waveforms of the the singe-phase singe-phase NPC/h-bridge NPC/h-bridge converter proposed Figure 31. Waveforms of converter operation operation using using the the proposed Figures 32–34 shows the dc-link ripple waveform when the control sequence of Figure 31 reaches control control method. method. Figures 32–34 shows the dc-link ripple waveform when the control sequence of Figure 31 reaches
steady state by applying the proposed control. The inverter power frequencies of (20, 40, and 56.67) steady state by applying the proposed control. The inverter power frequencies of (20, 40, and 56.67) Figures 32–34 shows the dc-link ripple waveform the control sequence of Figureto31twice reaches Hz are applied, respectively. Simulation results show when that ripple voltage corresponding the Figures 32–34 shows the Simulation dc-link ripple waveform the control sequence of Figure reaches Hz are applied, respectively. results show when that ripple voltage corresponding to31 twice the steady state by applying the proposed control. The inverter power frequencies of (20, 40, and 56.67) output state voltage frequency ofproposed the inverter, and ripple voltage corresponding to twice the system steady by applying control. inverter power frequencies to of (20, 40,the andsystem 56.67) output voltage frequencythe of the inverter, andThe ripple voltage corresponding twice Hz are applied, respectively. Simulation resultslike show that ripple voltage corresponding to twice the voltage frequency are generated in the dc-link the waveform. The components that fluctuate Hz are applied, respectively. Simulation results show that ripple voltage corresponding to twice the voltage frequency are generated in the dc-link like the waveform. The components that fluctuate the output voltage frequency of the inverter, and to ripple voltage corresponding to twice the system voltagevoltage of the frequency dc-link are extracted according the frequency throughtothe proposed filter, and output of the inverter, and ripple voltage corresponding twice the system voltage voltage of the dc-link are extracted according to the frequency through the proposed filter, and voltage are generated in the dc-link like the waveform. The components that fluctuate the removedfrequency when performing the voltage control, thereby reducing the power factor of the input side frequency are generated in the the waveform. The components fluctuate voltage removed when performing thedc-link voltagelike control, thereby reducing the powerthat factor of thethe input side voltage of the dc-link extracted according to the frequency through the proposed filter, and system current, and theare ripple of the dc-link. system current, and the ripple of the dc-link. removed when performing the voltage control, thereby reducing the power factor of the input side system current, and the ripple of the dc-link.
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of the dc-link are extracted according to the frequency through the proposed filter, and removed when performing the voltage control, thereby reducing the power factor of the input side system current, and the2018, ripple thePEER dc-link. Energies 11, xof FOR REVIEW 22 of 24 Energies 2018, 11, x FOR PEER REVIEW Energies 2018, 11, x FOR PEER REVIEW
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Figure 32. Waveform of the voltage fluctuation in the dc-link. dc-link. (Output frequency frequency ofinverter inverter at20 20 Hz). Figure32. 32.Waveform Waveform of of the the voltage voltage fluctuation fluctuation in Figure in the the dc-link. (Output (Output frequency of of inverterat at 20Hz). Hz). Figure 32. Waveform of the voltage fluctuation in the dc-link. (Output frequency of inverter at 20 Hz).
Figure 33. Waveform of the voltage fluctuation in the dc-link. (Output frequency of inverter at 40 Hz). Figure 33. Waveform of the voltage fluctuation in the the dc-link. (Output (Output frequency of of inverterat at 40Hz). Hz). Figure33. 33.Waveform Waveform of of the the voltage voltage fluctuation fluctuation in in Figure the dc-link. dc-link. (Output frequency frequency of inverter inverter at40 40 Hz).
Figure 34. Waveform of the voltage fluctuation in the dc-link. (Output frequency of inverter at 56.67 Hz). Figure 34. Waveform of the voltage fluctuation in the dc-link. (Output frequency of inverter at 56.67 Hz). Figure 34.34. Waveform ofof the (Output frequency frequencyofofinverter inverteratat56.67 56.67 Hz). Figure Waveform thevoltage voltagefluctuation fluctuationin in the the dc-link. dc-link. (Output Hz).
6. Conclusions 6. Conclusions 6. Conclusions This paper proposed new adaptive filters for the 13-level cascaded NPC/h-bridge systems. It can This paper proposed new adaptive filters for the 13-level cascaded NPC/h-bridge systems. It can reduce thepaper voltage fluctuation at the dc-link and improve current harmonic systems. distortionIt and This proposed new adaptive filterscapacitor for the 13-level cascaded NPC/h-bridge can reduce the voltage fluctuation at the dc-link capacitor and improve current harmonic distortion and PF as well in the system. reduce the voltage fluctuation at the dc-link capacitor and improve current harmonic distortion and PF as well in the system. PF asTheoretical well in the analysis system. of the NPC/h-bridge system discovered voltage fluctuation component by Theoretical analysis of the NPC/h-bridge system discovered voltage fluctuation component by the input side ofanalysis the converter and the outputsystem side ofdiscovered the inverter. In addition, a dc-link capacitor Theoretical of the NPC/h-bridge voltage fluctuation component by the input side of the converter and the output side of the inverter. In addition, a dc-link capacitor design considering these components was described. the input side of the converter and the output side of the inverter. In addition, a dc-link capacitor design considering these components was described. Conventional filter,components such as the was analyzed its magnitude and phase response design considering these wasNF described. Conventional filter, such as the NF was analyzed its magnitude and phase response characteristic. Unlike the such conventional filterwas to extract the its harmonic components at the fixedConventional filter, as the NF analyzed magnitude and phase response
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6. Conclusions This paper proposed new adaptive filters for the 13-level cascaded NPC/h-bridge systems. It can reduce the voltage fluctuation at the dc-link capacitor and improve current harmonic distortion and PF as well in the system. Theoretical analysis of the NPC/h-bridge system discovered voltage fluctuation component by the input side of the converter and the output side of the inverter. In addition, a dc-link capacitor design considering these components was described. Conventional filter, such as the NF was analyzed its magnitude and phase response characteristic. Unlike the conventional filter to extract the harmonic components at the fixed-frequency region, the proposed adaptive filters have the advantage of reducing two harmonic components at the variable-frequency region. Two proposed adaptive filters, SNF and DBPF are introduced, and applied to the proposed control method. In this paper, simulation and experiment were performed and presented to verify the proposed filters and control method as well as their feasibility. From them, the proposed method resulted in better performance of smaller dc-link voltage fluctuation and lower current harmonic distortion. The voltage regulation can be reduced from 9.6% to 9.1%, and the THD of the input current is drastically reduced from about 17.03% to about 2.4%. Given the results, it is expected that the proposed control method with adaptive filter is one of good candidates for multi-level cascaded NPC/h-bridge systems. Author Contributions: Jin-Wook Kang and Seung-Wook Hyun conceived and designed the experiment; Jintae Kim, Seung-Wook Hyun and Hoon Lee performed the experiment; Jin-Wook Kang and Hoon Lee analyzed the theory. Jintae Kim and Hoon Lee wrote the manuscript. Jintae Kim and Chung-Yuen Won participated in research plan development and revised the manuscript. All authors have contributed to the manuscript. Acknowledgments: This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea. (Nos. 20152020105720, 20162010103830). Conflicts of Interest: The authors declare no conflict of interest.
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