A Simplified Minimum DC-Link Voltage Control Strategy for ... - MDPI

energies Article

A Simplified Minimum DC-Link Voltage Control Strategy for Shunt Active Power Filters Yu Wang 1 , Yuewu Wang 2, *, Si-Zhe Chen 1 , Guidong Zhang 1 1

2

*

and Yun Zhang 1

School of Automation, Guangdong University of Technology, Guangzhou 510006, China; [email protected] (Y.W.); [email protected] (S.-Z.C.); [email protected] (G.Z.); [email protected] (Y.Z.) School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China Correspondence: [email protected]; Tel.: +86-150-9995-6175

Received: 11 August 2018; Accepted: 5 September 2018; Published: 12 September 2018







Abstract: The active power filter (APF) is a popular electrical device to eliminate harmonics in power systems. The rational design and effective control of DC-link capacitor voltage are important for implementing APF functions. In this study, the influences from the DC-link voltage on the APF compensating current characteristic and compensation performance are analyzed, and the reason to maintain DC-link voltage at a minimum value is investigated. On this basis, a simplified minimum DC-link voltage control strategy for APF is proposed. Compared with the existing DC-link voltage control strategies, the minimum DC-link voltage value in proposed strategy is only determined by the grid voltage and modulation ratio, reducing the calculation burden and the implementation difficulty in application, avoiding the interference from external parameters on the compensation effect. Additionally, the reference DC-link voltage varies at different values according to the grid voltage and modulation ratio. A shunt APF prototype is established and the experimental results verify the correctness and effectiveness of the analysis and proposed strategy. Keywords: active power filter; minimum DC-link voltage; compensating current characteristic; compensation performance; simplified DC-link voltage control strategy

1. Introduction With the rapid development of power technology, a large amount of nonlinear loads are widely installed in power grids. Nowadays, with the utilization and popularization of renewable energy, including wind power, solar photovoltaic power, and electric vehicles, new harmonic sources have emerged in modern grids. Therefore, a great many harmonics are generated and injected into the power grid, deteriorating the power quality and bringing great harm to the equipment and grid [1,2]. Therefore, he harmonic elimination has been of extensive concern and investigated. To eliminate harmonic pollution, passive filters were applied. However, they did not achieve an ideal compensation effect [3,4]. The active power filter (APF) is an attractive solution to eliminate the harmonics for power system. Additionally, APF has many advantages, such as high filtering accuracy, superior dynamic response, modularity and scalability, making it an ideal devices to compensate harmonics and improve power quality [5–7]. To improve APF performance, the existing literature mainly focuses on the topology, harmonic detection method, compensating current control, DC-link voltage control, modulation strategy, etc. [8–12]. The APF compensating currents are generated by the inductor voltage which is the voltage difference between grid source and DC-link capacitor, and the DC-link voltage mainly determines the current-generating capability in APF. Therefore, the DC-link voltage should be maintained at a high enough value, ensuring the APF produce the compensating currents and achieving an ideal Energies 2018, 11, 2407; doi:10.3390/en11092407

www.mdpi.com/journal/energies

Energies 2018, 11, 2407

2 of 14

compensation performance [13–15]. Therefore, the value design and stable control in APF DC-link voltage are important works, and they need detailed analysis and optimized designed. Fortunately, there are literature investigate the DC-link voltage control in APF specifically. Zhao et al. [16] analyzed the influence from the DC-link voltage on APF performance based on the Fourier transform and presents a design of DC-link voltage reference value. Cui et al. [17] analyzed the DC-link voltage control in hybrid APF under current-mode scheme, improving the DC-link voltage control during the start-up process. Hoon et al. [18] enhanced the DC-link voltage control in a three-level neutral-point diode clamped inverter based shunt APF by combining an inverted error deviation control. Luo et al. [19] proposed a hysteretic control and a controllable pulse width modulation rectifier to overcome the DC-link voltage instability in hybrid APF. Choi et al. [20] investigated the various DC-link voltage control strategies in a LC coupling hybrid APF for reactive power compensation. Mannen et al. [21] proposed a new control method with k-step compensator in three-phase APF to reduce the fluctuation in DC-kink voltage during load variation. Zainuri et al. [22] presented a new self-charging strategy with step size error cancellation to improve the DC-link voltage control in a shunt APF. Mannen et al. [23] proposed a novel DC-link voltage control strategy for APF with a small DC capacitor to obtain a high feedback gain for reducing the capacitor voltage fluctuation and ensuring harmonic compensation performance. Moreover, a sufficient DC-link voltage ensures satisfactory APF compensation performance, however, a higher DC-link voltage leads to larger switching loss and noise in the APF, and vice versa [24]. Therefore, to obtain a satisfactory compensation effect with lower switching loss and noise, the minimum DC-link voltage value and the corresponding control strategies were discussed in [25,26]. The existing literature investigated the minimum DC-link voltage design based on reactive power for power quality compensator and APF, decreasing the device capacity, power consumption, and installation cost. However, the relationship between DC-link voltage and compensating current characteristic including the switching frequency harmonic current and harmonic compensating currents had not been concerned yet. Although the switching frequency harmonic current can be attenuated by applying the optimized pulse width modulation strategy and LCL filter, the above methods cannot guarantee to eliminate the switching frequency harmonic current completely under varied working conditions, and the implementation process are complicated. Thus, the switching frequency harmonic current should be considered during the compensation performance analysis, and the reason to maintain the DC-link voltage at the minimum value also needs to be discussed in detail. Based on the analysis of minimum DC-link voltage, the controllers to maintain DC-link voltage at the minimum value were proposed. Lam et al. [27] investigated the relationship between the reactive power compensation and DC-link voltage in LC coupling hybrid APF was deduced, and proposed a minimum DC-link voltage controlled to reduce switching loss under reactive power compensation. However, the harmonic currents were not considered in this work. Then, Lam et al. [28] deduced the minimum DC-link voltage value based on harmonic currents and dynamic reactive power in LC coupling hybrid APF, and presented a minimum DC-link voltage controlled obtained the least switching loss and best compensating effect. However, the minimum DC-link voltage is determined by grid voltage, harmonic currents, reactive power and equivalent circuit parameters in APF, leading to the complicated analysis and calculation process. Moreover, the harmonic currents, reactive power and equivalent circuit parameters frequently vary in the practical applications, and the randomly variation may cause a frequent fluctuation in DC-link voltage value calculation, resulting in the deterioration and unreliability in DC-link voltage control in APF. Thus, the relationship between the DC-link voltage and the switching frequency harmonic current and compensation performance is studied in this paper, and the reason to maintain the DC-link voltage at the minimum value is presented. Additionally, to address the shortcomings in the existing minimum DC-link voltage strategies, this paper proposed a simplified minimum DC-link voltage control strategy. The DC-link voltage value under the proposed strategy is only determined by the grid voltage and modulation index, avoiding the complex calculation of the harmonic currents,

Energies 2018, 11, 2407

3 of 14

Energies 2018, 11, x FOR PEER REVIEW

3 of 14

reactive reactivepower, power,and andequivalent equivalentcircuit circuitparameters, parameters,significantly significantlyreducing reducingthe thenumber numberof ofcalculation calculation steps and computational burden, improving the real-time characteristic and reliability theAPF APF steps and computational burden, improving the real-time characteristic and reliability ofofthe in in practicalimplementation. implementation.Furthermore, Furthermore, theDC-link DC-linkvoltage voltagevalue value can can vary vary at practical the at different different levels levels according accordingtotothe thevaried variedgrid gridvoltage, voltage,maintaining maintainingthe theDC-link DC-linkvoltage voltageatatthe theminimum minimumvalue valuein invaried varied operating conditions. Moreover, the proposed control strategy can also be applied for unbalance operating conditions. Moreover, the proposed control strategy can also be applied for unbalanceload load compensation, enhancing the applicability of APF. compensation, enhancing the applicability of APF. The Thestructure structureof ofthis thispaper paperisisorganized organizedas asfollows: follows:the therelationships relationshipsbetween betweenthe theDC-link DC-linkvoltage, voltage, compensating compensatingcurrent currentcharacteristic, characteristic,and andcompensation compensationperformance performanceare areanalyzed analyzedininSection Section2.2.Based Based on the analysis, a simplified minimum DC-link voltage control strategy is proposed in Section on the analysis, a simplified minimum DC-link voltage control strategy is proposed in Section 3.3. To To verify verifythe thecorrectness correctnessand andfeasibility feasibilityof ofthe theanalysis analysisand andthe theproposed proposedstrategy, strategy,the theexperimental experimentalresults results in APFprototype prototypeare arepresented presented in Section 4. Finally, the conclusion this and study the inaa shunt shunt APF in Section 4. Finally, the conclusion of thisofstudy theand outlook outlook for future work are presented in Section 5. for future work are presented in Section 5. 2.2.Influences Influencesof ofDC-Link DC-LinkVoltage Voltageon onAPF APFCompensation CompensationPerformance Performance Figure Figure11presents presentsthe thetopology topologyof ofthree-phase three-phasefour-wire four-wire center-split center-split shunt shunt APF. APF.From Fromthe the figure, figure, uusxsx is the grid voltage, and u is the inverter output voltage. Besides, i , i and i are grid is the grid voltage, and ucxcx is the inverter output voltage. Besides, saisa, sb isb and iscsc are grid currents, currents, ica and icc are compensating currents, and iLa , i Lb and are load currents, and C dc is ica,, iicb cb and icc are compensating currents, and iLa, iLb and iiLc Lc are load currents, and Cdc is the the DC-link DC-link capacitor. U is the DC-link voltage, where U = U = 0.5U . R is the equivalent resistance dc dcU dcL dc capacitor. Udc is the DC-link voltage, where UdcU = UdcL = 0.5Udc. R is the equivalent resistanceof of inductor. A resistance R and a three-phase full bridge rectifier constitute the non-linear load. The L inductor. A resistance RL and a three-phase full bridge rectifier constitute the non-linear load. The LCL and the LCLfilter filterisisconsisted consistedofofLLCC, ,LLGG,, C CFF,, and the LCL LCL filter filter is is simplified simplified to to be be an an inductor inductorwith withthe thevalue valueLL ==LLCC + L . + LGG. From FromFigure Figure1,1,the thesingle-phase single-phaseequivalent equivalentcircuit circuitfor foreach eachphase phaseisispresented presentedin inFigure Figure2.2.From From the thefigure, figure,the theinverter inverteroutput outputvoltage voltageis: is: dicx di cx ucxu= u=sxu+ u ==usx ++RR××iicx + L× Lx + u u + L × dt cx cx sx Lx sx

dt

(1) (1)

Figure1. 1. Topology Topologyof ofthree-phase three-phasefour-wire four-wirecenter-split center-splitshunt shuntAPF. APF. Figure

From FromEquation Equation(1), (1),the theinverter invertervoltage voltagein inAPF APFcan canbe becalculated calculatedby bygrid gridvoltage, voltage,equivalent equivalent inductance, inductance,equivalent equivalentresistance, resistance,and andcompensating compensatingcurrent. current. Generally, the non-linear load currents iL contains the fundamental current iL1 and harmonic currents iLh:

Energies 2018, 11, 2407

4 of 14

Energies 2018, 11, x FOR PEER REVIEW

4 of 14

Generally, the non-linear load currents iL contains the fundamental current iL1 and harmonic ∞ currents iLh : iLx = iL1x + iLhx = I L1x cos(ωt + θ1 ) + ∞ I Lnx cos(nωt + θ n ) (2) iLx = iL1x + iLhx = IL1x cos(ωt + θ1 ) + n∑ I cos(nωt + θn ) (2) = 2 Lnx



n =2

L1x and the effective values of iL1 and iLhx. where IIL1x where andILhx ILhare x are the effective values of iL1 and iLh x .

The single-phase equivalent circuit of APF. Figure 2. The

Actually, , the harmonic Actually, APF APF compensating compensating current current iicc contains contains the the fundamental fundamental component component iic1 c1, the harmonic component i and also the switching frequency harmonic current i : csw component ich ch and also the switching frequency harmonic current icsw: icxi ==ic1x i ++ichx i + + iicswx

(3) (3) In Equation (3), the fundamental current ic1 , which compensates system power loss and maintains In Equation (3), the fundamental current ic1, which compensates system power loss and the DC-link voltage, is very small during a steady-state situation, and it is neglected during a maintains the DC-link voltage, is very small during a steady-state situation, and it is neglected during steady-state operation. a steady-state operation. Additionally, to compensate the load harmonics, the compensation component in compensating Additionally, to compensate the load harmonics, the compensation component in compensating current is equaled to the harmonic components in load current presented in Equation (2). Thus, current is equaled to the harmonic components in load current presented in Equation (2). Thus, the the compensating current ich is: compensating current ich is:  ∞ ∞  ichai= i=Lha == ∑ IILncos( cos(nnωt  i ωt + + θ n )θn )   cha Lha Ln   nn= 2  =2  ∞  ∞ ichbi= i=Lhb == ∑ IILncos[ cosn[n(ω (ωt θn ] (4) i t −− 2π2π/3 / 3) +)θ+ (4)  chb Lhb n n]  =2 Ln   n=2 ∞     ichc = iLhc = ∑∞ ILn cos[n(ωt + 2π/3) + θn ] ichc = iLhc =n I cos[ n (ω t + 2π / 3) + θ n ] =2 Ln  n=2 cx

c1x

chx

cswx

Moreover, Moreover, since since the the APF APF usually usually uses uses pulse pulse width width modulation modulation (PWM) (PWM) technology technology to to generate generate the compensating currents, the compensating currents not only contain the required compensation the compensating currents, the compensating currents not only contain the required compensation component, but also also contain contain the theswitching switchingfrequency frequencyharmonic harmoniccurrent currenticsw icsw . Generally, component, but . Generally, thethe icswicsw cancan be be attenuated by applying the composite current tracking method, the space vector pulse width attenuated by applying the composite current tracking method, the space vector pulse width modulation (SVPWM), and and optimized However, the the above modulation (SVPWM), optimized designed designed LCL LCL filter. filter. However, above methods methods cannot cannot guarantee eliminating the switching frequency harmonic current completely under guarantee eliminating the switching frequency harmonic current completely under varied varied working working conditions, and their Therefore, the the switching conditions, and their implementation implementation processes processes are are also also complicated. complicated. Therefore, switching frequency harmonic current i should be considered during the compensating current analysis, csw frequency harmonic current icsw should be considered during the compensating current analysis, and and the switching frequency harmonic current i can be described as: csw the switching frequency harmonic current icsw can be described as: icswx cos(bωt i = = IIcswx cos( bωt + + θθsw )) cswx

cswx

sw

(5) (5)

where Icsw is the effective value of switching frequency harmonic current, and b = f sw /f. where Icsw is the effective value of switching frequency harmonic current, and b = fsw/f. Substituting Equations (4) and (5) into Equation (3), the APF compensating current ic can be described as:

Energies 2018, 11, 2407

5 of 14

Substituting Equations (4) and (5) into Equation (3), the APF compensating current ic can be described as: ∞

∑

icx = ic1x + ichx + icswx =

ILnx cos(nωt + θn ) + Icswx cos(bωt + θsw )

(6)

n =2

Then, in a three-phase symmetrical power system, the grid voltages are:  √   usa = √2Usn cos(ωt) usb = 2Usn cos(ωt − 2π/3)   u = √2U cos(ωt + 2π/3) sc sn

(7)

where Usn is the effective value of usa , usb and usc , and w is the fundamental angular frequency. Substituting Equations (4) and (7) into Equation (1), the inverter voltages can be described as:  ∞ √  2U + ILn [ R cos(nωt + θn ) − nωL sin(nωt + θn )] u = ∑  sn ca   n =1   ∞ √ 2π ucb = 2Usn + ∑ ILn { R cos[n(ωt − 2π 3 ) + θn ] − nωL sin[ n ( ωt − 3 ) + θn ]}  n =1   ∞ √   2π  ucc = 2Usn + ∑ ILn { R cos[n(ωt + 2π 3 ) + θn ] − nωL sin[ n ( ωt + 3 ) + θn ]}

(8)

n =1

Therefore, the inverter voltage can also be expressed as: ∞

uc = uc1 + uch + ucsw = Uc1 cos(ωt + ϕ1 ) +

∑ Ucn cos(nωt + ϕn ) + Usw cos(bωt + ϕn )

(9)

n =2

where uc1 is the fundamental component of uc , uch is used to produce compensating currents compensating load harmonics, and ucsw is the inverter voltage at switching frequency. Then, the mold length of inverter voltage vector is: Uc =k Uc1 e j(ωt+ ϕ1 ) +

∞

∑ Ucn e j(nωt+ ϕn ) + Usw e j(bωt+ ϕn ) k

(10)

n =2

From Equations (7)–(10), the maximal value of inverter voltage mold is: ∞

Uc−max = Uc1 +

∑ Ucn + Usw =

√

2Usn + R ×

n =2

∞

∞

n =2

n =2

∑ ( Icn + Icsw ) + ωL × ∑ (nIcn + Icsw )

(11)

To provide the sufficient DC-link voltage to generate compensating currents, the following equation needs to be satisfied: m Uc_max = Udc (12) 2 where m is modulation index. To compensate harmonic currents, the APF needs to produce a voltage exceed the maximal value of inverter voltage vector mold. From Equation (12), the minimum DC-link voltage can be obtained: Udc_min =

2 Uc−max m

(13)

During the steady-state operation, the DC-link voltage maintains at minimum value, and APF generates compensating currents to compensate the load harmonics. When the DC-link voltage becomes larger than the minimum value, the effective value of inverter output voltage increases. From

Energies 2018, 11, 2407

6 of 14

Equations (11)–(13), the DC-link voltage determines the ability of producing compensating currents, and following equations can be obtained: ∞ ∞ √ m Udc = 2Usn + R × ∑ ( Icn + Icsw ) + ωL × ∑ (nIcn + Icsw ) 2 n =2 n =2

(14)

Generally, the effective value of harmonic currents Ich are determined by harmonic detection algorithm calculated from the load currents, and they remain stable during steady-state operation. From Equation (14), the switching frequency harmonic current Isw can be described as: m 2 Udc

−

√

∞

∞

n =2

n =2

2Usn − R ∑ Icn − ωL ∑ nIcn

Icsw =

(15)

R + ωL

According to Equation (15), with the stable effective value of grid voltage Usn , equivalent inductance L, equivalent resistance R and compensating harmonic currents Ich calculated from load currents, the increase of DC-link voltage Udc may lead to the increase in effective value of switching frequency harmonic current Icsw . Generally, the total harmonic distortion (THD) is an important indicator of compensation performance, and it can be expressed as: s THD =

∞

∑

n =2

In 2 + Isw 2 I1 2

(16)

As can be seen from Equation (16), the THD is not only affected by the nth harmonic currents In , but also affected by the switching frequency harmonic current Isw . Therefore, according to Equations (15) and (16), the increase of DC-link voltage Udc leads to the increase of switching frequency harmonic current Icsw , thereby raising the THD value and deteriorate the compensation performance. Therefore, to prevent the increase of the DC-link voltage from deteriorating the compensation performance, the DC-link voltage should be maintained at the minimum value. 3. Proposed Simplified Minimum DC-Link Voltage Control Strategy Substituting Equations (7) and (8) into Equation (1), the inverter voltage can be described as:  ∞ √  uca = 2Usn + ∑ ILn [ R cos(nωt + θn ) − nωL sin(nωt + θn )]    n =2   ∞ √ 2π ucb = 2Usn + ∑ ILn { R cos[n(ωt − 2π 3 ) + θn ] − nωL sin[ n ( ωt − 3 ) + θn ]}  n =2   ∞ √   2π  ucc = 2Usn + ∑ ILn { R cos[n(ωt + 2π 3 ) + θn ] − nωL sin[ n ( ωt + 3 ) + θn ]}

(17)

n =2

Make the transformation of the inverter voltages from the stationary abc coordinate system to the stationary α-β coordinate system with coordinate transformation formula Tabc-αβ : "

ucα ucβ

#



 r " uca 2 1   = Tabc−αβ  ucb  = 3 0 ucc

1 − √2 3 2

−√12 − 23

#

 uca    ucb  ucc 

(18)

Energies 2018, 11, 2407

7 of 14

Substituting Equation (17) into Equation (18), the inverter voltages in the stationary α-β coordinate are:  ∞ √    ucα = 2Usn + ∑ ILn [ R cos(nωt + θn ) − nωL sin(nωt + θn )] n =2 ∞ ∞ √  1 2π   ucβ = √3 {3 2Usn + R ∑ ILn [cos(nωt + θn ) + 2 cos[n(ωt − 3 ) + θn ] − nωL ∑ ILn [sin(nωt + θn ) + 2 sin[n(ωt − n =2

n =2

2π 3 ) + θn ]}

(19)

In Equation (19), since the values of harmonic components and their arithmetic combinations are Energies 2018, 11, x FOR PEER REVIEW 7 of 14 small compared with effective value of grid voltage Usn , they can be ignored to simplify the calculation. Therefore, the mold(19), length of the the values inverter voltage vector is: In Equation since ofoutput harmonic components and their arithmetic combinations are small compared with effective value q of grid voltage √ Usn, they can be ignored to simplify the 2 + u2 = (20) |Uc | = sn calculation. Therefore, the mold length of theuinverter voltage vector is: cα cβoutput2U

ucα2 + ucβ2 = U sn harmonics, the APF inverter voltage (20) To produce compensating currentsUto eliminate the2load c = exceeds the maximal value of inverter voltage vector. Substituting Equation (20) into Equation (13), To produce compensating currents to eliminate the load harmonics, the APF inverter voltage the following equation is obtained: exceeds the maximal value of inverter voltage vector. Substituting Equation (20) into Equation (13), the following equation is obtained: 2√ Udc_min = 2Usn + Umar (21) m2 U dc _ min = 2U sn + U mar (21) m where Umar is the voltage margin with a small value to control the switching frequency harmonic whereand Umarother is the voltage current factors.margin with a small value to control the switching frequency harmonic current and other Thefactors. control diagram of the proposed strategy is presented in Figure 3. From the figure, the DC-link control value diagram the proposed strategy is presented Figure 3. From the grid figure, the DCvoltageThe reference is of initially set to be a minimum valueincalculated by the voltage and link voltage reference value is initially set to be a minimum value calculated by the grid voltage and modulation index according to Equation (21), reducing the power consumption and switching modulation index the according to Equation the power consumption and switching loss. Additionally, grid voltage may (21), varyreducing occasionally in practical application, leadingloss. to the Additionally, the grid voltage may vary occasionally in practical application, leading to the frequent frequent change of DC-link voltage reference value. To solve this issue, the DC-link voltage value change of DC-link voltage reference value. To solve this issue, the DC-link voltage value under the under the proposed strategy is classified into certain levels according to different ranges of the grid proposed strategy is classified into certain levels according to different ranges of the grid voltage for voltage for selection. Thus, the reference DC-link voltage maintains at a constant value within a selection. Thus, the reference DC-link voltage maintains at a constant value within a specific range. specific range. Furthermore, the DC-link voltage reference value under proposed strategy varies Furthermore, the DC-link voltage reference value under proposed strategy varies adaptively with adaptively with the change of grid voltage, maintaining DC-link voltage at the minimum value in the change of grid voltage, maintaining DC-link voltage at the minimum value in varied operating varied operating conditions. conditions.

Figure Thecontrol controlblock blockof ofproposed proposed simplified simplified minimum strategy. Figure 3.3.The minimumDC-link DC-linkvoltage voltagecontrol control strategy.

Compared with the existing minimum DC-link voltage control strategy, the proposed minimum DC-link voltage is only determined by the grid voltage and modulation index, avoiding the influence from variations of equivalent parameters, reactive power and harmonic currents, thus improving the stability, reliability, and real-time characteristic of APF. Additionally, the proposed DC-link voltage minimum value avoids complex calculation of equivalent parameters, harmonic currents, and reactive power, reducing the calculation burden of processor. The comparison of calculation burden

Energies 2018, 11, 2407

8 of 14

Energies 2018, 11, x FOR PEER REVIEW

8 of 14

Compared with the existing minimum DC-link voltage control strategy, the proposed minimum DC-link voltage is only determined by the and grid voltage and modulation index, avoiding the influence and 16 multiplications and divisions, the calculation in [28] contains 20 additions and from variationsand of equivalent parameters, reactive power and harmonic thusburden improving subtractions eight multiplications and divisions. This brings a largecurrents, calculation to thethe stability, reliability, and real-time characteristic APF. Additionally, the proposed DC-link processor. By applying the proposed strategy,ofthe addition and subtraction calculations arevoltage not needed, value and the number of the multiplication and division reducesharmonic to three,currents, thus reducing the minimum avoids complex calculation of equivalent parameters, and reactive calculation burden on processorburden and improving the real-time characteristics for APF. burden between power, reducing the calculation of processor. The comparison of calculation the conventional and the proposed minimum DC-link voltage control strategy is listed in Table 1. Table 1. Comparison of calculation burden under proposed and conventional strategies. The minimum DC-link voltage calculation in [27] contains four additions and subtractions and 16 Minimum DC-Link Addition and Subtraction Times Multiplication and Division Times multiplications and divisions, and the calculation in [28] contains 20 additions and subtractions and Voltage Strategy (Within the 20th Harmonics) (Within the 20th Harmonics) eight multiplications and divisions. This brings a large calculation burden to the processor. By applying Strategy in Ref. [27] 4 16 the proposed strategy, calculations are not needed, Strategy in Ref. the [28] addition and subtraction 20 8 and the number of the multiplication andStrategy division reduces to three,0 thus reducing the calculation burden on processor and Proposed 3 improving the real-time characteristics for APF. 4. Experiment Verification Table 1. Comparison of calculation burden under proposed and conventional strategies.

Figure 4 presents a shunt APF prototype established in laboratory, and the parameters are shown in TableDC-Link 2. Without APF, the grid current contains a large number of harmonics, and the THD Minimum Addition and Subtraction Times Multiplication and Division Times of theVoltage experimental is 23.63%. Based on the deduction, the the APF20th minimum DC-link Strategygrid current (Within the 20th Harmonics) (Within Harmonics) voltage under the proposed simplified strategy can be calculated from Equation (21). Thus, with the Strategy in Ref. [27] 4 16 gridStrategy voltagein URef. sn = 220 [28]V, the minimum DC-link 20 voltage Udc-ref = 630 V. When the8Udc = 620 V, lower thanProposed minimumStrategy value 630 V, the experimental0 results are shown in Figure 5. From 3the figure, the grid current after compensation still contains a large number of harmonics, and it is not an ideal sine waveform. Furthermore, 4. Experiment Verificationthe grid current THD after compensation is 11.05%, and it does not ideally compensate performance. The results illustrate that, when Udc is lower than the minimum value, APF Figure 4 presents a shuntthe APF prototype laboratory, and the parameters are shown cannot largely compensate harmonics andestablished achieve anin ideal compensation performance. in Table 2. Without APF, the grid current contains a large number of harmonics, and the THD of the Table Parameters of APF and experimental experimental grid current is2.23.63%. Based onprototype the deduction, the APFsetup. minimum DC-link voltage under the proposed simplified strategy can be calculated from Equation (21). Thus, with the grid Parameters Symbol Value voltage Usn = 220 V, the minimum DC-link voltage Udc-ref = 630 V. When the Udc = 620 V, lower than Grid Voltage Usn 220 V minimum value 630 V, the experimental results are shownf in Figure50 5. Hz From the figure, the grid current Grid Frequency after compensation still contains a large number of harmonics, and it is not an ideal sine waveform. Switching Frequency fsw 9.6 kHz Furthermore, the grid current THD after compensation is 11.05%, and it does not ideally compensate Equivalent Inductance L 0.45 mH performance. The results illustrate that, when U is lower than the minimum value, APF cannot Equivalent Resistance dc R 0.2 ohm largely compensate the harmonics achieve an ideal DC-linkand Capacitance Cdcu,compensation CdcL 10,000 performance. uF

Figure 4. 4. The The APF Figure APF prototype. prototype.

Energies 2018, 11, 2407

9 of 14

Table 2. Parameters of APF prototype and experimental setup. Parameters

Symbol

Value

Grid Voltage Grid Frequency Switching Frequency Equivalent Inductance Equivalent Resistance DC-link Capacitance

Usn f f sw L R Cdcu , CdcL

220 V 50 Hz 9.6 kHz 0.45 mH 0.2 ohm 10,000 uF

Energies 2018, 2018, 11, 11, xx FOR FOR PEER PEER REVIEW REVIEW Energies

of 14 14 99 of

Figure 5. 5. Voltage Voltageand andcurrent currentwaveforms waveformswhen whenU Usn sn = 220 V V and and U dc-ref 620 V.V. Figure Voltage = 220 Udc-ref 620V. and current waveforms when U sn 620 dc-ref===

Then, when when U Udcdcdc===640 640V, V,higher higherthan thanthe theminimum minimumvalue value630 630V, V, the the experimental experimentalresults results are are Then, when U 640 V, higher than the minimum value 630 V, the experimental results are Then, shown in Figure 6a. The load harmonics are greatly compensated, and the grid currents are nearly shown in in Figure Figure 6a. 6a. The The load load harmonics harmonics are are greatly greatly compensated, compensated, and and the the grid grid currents currents are are nearly nearly shown sinusoidalwaveforms. waveforms.Additionally, Additionally,the thegrid gridcurrent currentdistortions distortionsare arealmost almosteliminated, eliminated,and andthe thegrid grid sinusoidal waveforms. Additionally, the grid current distortions are almost eliminated, and the grid sinusoidal current THD after compensation is 5.65%, thus satisfying the international standards. In addition, current THD after compensation is 5.65%, thus satisfying the international standards. In addition, the current THD after compensation is 5.65%, thus satisfying the international standards. In addition, the the experimental voltages and currents with U = 660 V are shown in Figure 6b. Compared with experimental voltages voltages and and currents currents with with U Udcdc == 660 660 V V are are shown shown in in Figure Figure 6b. 6b. Compared Compared with with the the dc experimental the voltages currents VU and = thecurrents grid currents after compensation are voltages and and currents withwith Udcdc ==U640 640 V640 and U dc = =U 660 V,660 theV, grid currents after compensation compensation are both both dc =V dc V, voltages and currents with U and dc 660 the grid after are both nearly sinusoidal waveforms, and harmonic components are largely compensated. Therefore, nearly sinusoidal waveforms, and harmonic components are largely compensated. Therefore, when nearly sinusoidal waveforms, and harmonic components are largely compensated. Therefore, when when the DC-link voltage becomes higher minimum value, APFachieves achievesan an ideal ideal the DC-link voltage becomes higher thanthan the the minimum value, thethe APF achieves an ideal the DC-link voltage becomes higher than the minimum value, the APF compensationperformance. compensation performance. compensation

(a) (a)

(b) (b)

Figure 6. Voltage and current currentwaveforms waveformswhen whenUU Usnsnsn=== 220 220V, V,UU Udc-ref dc-ref = ==640 640 V and 660 660 V. V.(a) (a)U Udc-ref dc-ref = ==640 640 Figure waveforms when V, dc-ref (a) U dc-ref Figure6. 6. Voltage Voltage and 640 V V and and V. 640 V; and (b) U dc-ref = 660 V. V; 660 V.V. V; and and (b) (b) U Udc-ref 660 dc-ref= =

With the increase increase of of DC-link DC-link voltage voltage value, value, the the THD THD values values of of simulation simulation and and experiment experiment grid With the experimentgrid grid With current aftercompensation compensationwith with the different U dc are are presented presented in Table Table 3, and thewith THDs with current after thethe different UdcU are presented in Table 3, and3, theand THDs different current compensation with different dc in the THDs with different DC-link voltages voltages are presented presented in7.Figure Figure 7. The Theillustrate results illustrate illustrate that,the when the DC-link DC-link DC-link voltages are presented in Figurein The results that, when DC-link voltage different DC-link are 7. results that, when the voltage becomes lowerthe than the minimum minimum value, APF cannot cannot compensate harmonics completely, and becomes lower than minimum value,value, APF APF cannot compensate harmonics completely, andand the voltage becomes lower than the compensate harmonics completely, the compensation compensation performance performance even even deteriorates deteriorates with with the the decrease decrease of of DC-link DC-link voltage. voltage. Additionally, Additionally, the when the the DC-link DC-link voltage voltage becomes becomes larger larger than than the the minimum minimum value, value, the the increase increase of of DC-link DC-link voltage voltage when cannot improve improve the the APF APF compensation compensation performance, performance, but but increases increases the the THD THD of of grid grid current current and and cannot deteriorates the compensation effect. deteriorates the compensation effect.

Energies 2018, 11, 2407

10 of 14

compensation performance even deteriorates with the decrease of DC-link voltage. Additionally, when the DC-link voltage becomes larger than the minimum value, the increase of DC-link voltage cannot improve the APF compensation performance, but increases the THD of grid current and deteriorates Energies 2018, 11, x FOR PEER REVIEW 10 of 14 the compensation effect.

Figure Figure7.7.The Thegrid gridcurrent currentTHD THDvalue valuewith withthe thevariation variationof ofthe theDC-link DC-linkvoltage. voltage.

Although grid currents currents with with varied variedDC-link DC-linkvoltages voltagesare aredifferent, different,it itis is difficult Although the the THDs THDs of of grid difficult to to recognize from the voltage and current waveforms. Thus, the values of compensating current in recognize from the voltage and current waveforms. Thus, the values of compensating current in each each varied DC-link voltages are presented in Table 4. From the table, with the increase orderorder withwith varied DC-link voltages are presented in Table 4. From the table, with the increase of the of the DC-link voltage, the values of each order in compensating currents vary slightly, due to DC-link voltage, the values of each order in compensating currents vary slightly, due to the the compensating compensating currents currents strictly strictly following following the the reference reference compensating compensating currents currents obtained obtained from from the the harmonic harmonicdetection detectionsection. section. However, However,the theswitching switchingfrequency frequencyharmonic harmoniccurrent currentincrease increaseobviously obviously with of the theDC-link DC-linkvoltage. voltage.AsAs mentioned above, THD is calculated withthe the increase increase of mentioned above, the the THD is calculated with with everyevery order order in compensating the current, including the switching frequency harmonic current. Therefore, in compensating the current, including the switching frequency harmonic current. Therefore, the the increase of the DC-link voltage leads to the increase of the switching frequency harmonic current, increase of the DC-link voltage leads to the increase of the switching frequency harmonic current, leading THD value, butbut notnot thethe improvement of the compensation effect, and and the leadingtotothe theincrease increaseofofthe the THD value, improvement of the compensation effect, influence becomes moremore serious withwith the further increase of the voltage. Therefore, when the the influence becomes serious the further increase ofDC-link the DC-link voltage. Therefore, when DC-link voltage is higher than the minimum value, the increase of the DC-link voltage cannot improve, the DC-link voltage is higher than the minimum value, the increase of the DC-link voltage cannot but brings but the deterioration in the compensation effect. To avoid the deterioration the compensation improve, brings the deterioration in the compensation effect. To avoid theindeterioration in the and achieve an and idealachieve compensation theperformance, DC-link voltage should bevoltage maintained a compensation an idealperformance, compensation the DC-link shouldat be minimum value. maintained at a minimum value. Moreover, when the effective value of grid voltage varies form Usn = 220 V to 198 V, the required minimum DC-link voltage changes Udc-ref = 575 accordingly. Under the proposed strategy, Table 3.value Comparison of to THD values withVdifferent DC-link voltages. the DC-link voltage varies adaptively and maintains at a new minimum value, as shown in Figure 8. THD Value Additionally, the dynamic behavior of currents during the transient is not obvious. This is because Cases Simulation Experiment the transient is not caused by a variation of the load, but caused by a variation of the grid voltage, Without APF 23.63% 22.39% resulting in a variation of the DC-link voltage. In the APF, the dynamic in current control loop is much 600 V 32.08% 35.25% faster than that in voltage control loop, thus the disturbance from the voltage loop causes a very small 620 V 10.42% 11.05% current distortion during the transient. Thus, with the DC-link voltage obtained by the proposed 640 V 4.94% 5.65% strategy, the load harmonic currents are still significantly compensated and the grid current distortion 660 V 4.53% 5.52% is almost eliminated. After compensation, DC-link Voltage the THD of the grid current is 5.52%. The results verify that, 680 V 5.08% 5.82% under the proposed strategy, the DC-link voltage can vary adaptively to maintain the minimum value 700 V 5.47% 6.17% with the varied grid voltage situation and ensure the ideal APF compensation performance. 720 V 5.96% 6.58% 740 V 6.22% 6.82% Table 4. The values of compensating current in each order with varied DC-link voltages.

Current Orders Fundamental 5th 7th 11th 13th 17th

640 V 45.88 A 8.57 A 4.25 A 3.41 A 2.39 A 2.21 A

660 V 46.85 A 8.59 A 4.32 A 3.43 A 2.45 A 2.22 A

680 V 46.55 A 8.58 A 4.30 A 3.43 A 2.39 A 2.22 A

740 V 46.87 A 8.59 A 4.32 A 3.35 A 2.41 A 2.21 A

Energies 2018, 11, 2407

11 of 14

Table 3. Comparison of THD values with different DC-link voltages. THD Value

Cases Without APF Energies 2018, 11, x FOR PEER REVIEW

19th 23rd 25th 29th Switching Frequency

DC-link Voltage

600 V 620 V 640 V 660 V 1.65 A 680 V 1.55 A 700 V 1.30 A 720 V 1.18 A 740 V

0.55 A

Simulation

Experiment

22.39%

23.63%

32.08% 10.42% 4.94% 1.68 A 4.53% 1.65 A 1.56 A 5.08% 1.57 A 5.47% 1.32 A 1.31 A 5.96% 1.20 A 6.22% 1.19 A

35.25% 11.05% 5.65% 1.68 A 5.52% 1.57 A 5.82% 6.17% 1.31 A 6.58% 1.20 A 6.82%

0.73 A

0.95 A

0.82 A

11 of 14

Table 4. The values of compensating current in each order with varied DC-link voltages.

Moreover, when the effective value of grid voltage varies form Usn = 220 V to 198 V, the required V V V accordingly. 680 VUnder the proposed 740 V minimumCurrent DC-linkOrders voltage value 640 changes to Udc-ref660 = 575 strategy, 45.88 Aand maintains 46.85atAa new minimum 46.55 A value, as shown 46.87 Ain Figure 8. the DC-linkFundamental voltage varies adaptively 5thdynamic behavior 8.57 A 8.59 A the transient 8.58isAnot obvious. 8.59 A is because Additionally, the of currents during This 7th 4.25 A 4.32 A 4.30 A 4.32 A the transient is not caused by a variation of the load, but caused by a variation of the grid voltage, 11th 3.41 A 3.43 A 3.43 A 3.35 A resulting in a variation of the DC-link theA APF, the dynamic control loop is 13th 2.39 A voltage. In 2.45 2.39 A in current 2.41 A much faster than that in voltage control loop, thus the disturbance from the voltage loop causes a 17th 2.21 A 2.22 A 2.22 A 2.21 A 19th 1.65 A 1.68 A 1.65 A 1.68 A very small current distortion during the transient. Thus, with the DC-link voltage obtained by the 23rd the load harmonic 1.55 Acurrents are1.56 A 1.57 proposed strategy, stillA significantly1.57 compensated and theAgrid current 25th 1.30 A 1.32 A 1.31 A 1.31 A distortion is almost grid 29th eliminated. After 1.18 Acompensation, 1.20the A THD of the 1.19 A current is 5.52%. 1.20 A The results verify that, under the proposed strategy, the DC-link voltage can vary adaptively to maintain the Switching 0.55 A 0.73 A 0.82 A 0.95 A Frequency minimum value with the varied grid voltage situation and ensure the ideal APF compensation performance.

Figure8.8.Voltage Voltage and and current current waveforms waveforms when when the the grid grid voltage voltage U Usn variesfrom from220 220VVto to198 198V. V. snvaries Figure

Furthermore, the experiment results in an unbalanced load are shown in Figure 9. From the figures, Furthermore, the experiment results in an unbalanced load are shown in Figure 9. From the the grid current in a, b, and c phases before compensation are 35.8 A, 45.3 A, and 37.8 A, respectively. figures, the grid current in a, b, and c phases before compensation are 35.8 A, 45.3 A, and 37.8 A, When applying the proposed strategy in APF, the load harmonics are greatly compensated, and the grid respectively. When applying the proposed strategy in APF, the load harmonics are greatly currents are all sinusoidal waveforms and 45.2 A, 46.8 A, and 45.8 A in a, b, and c phase, respectively. compensated, and the grid currents are all sinusoidal waveforms and 45.2 A, 46.8 A, and 45.8 A in a, Moreover, the neutral line current is in = 11.2 A with the unbalance load, as shown in Figure 10a. After b, and c phase, respectively. Moreover, the neutral line current is in = 11.2 A with the unbalance load, compensation by the APF under the proposed the DC-link voltage strategy, the neutral current drops to as shown in Figure 10a. After compensation by the APF under the proposed the DC-link voltage about in = 1.7 A, as shown in Figure 10b. The experimental results show that the APF under proposed strategy, the neutral current drops to about in = 1.7 A, as shown in Figure 10b. The experimental DC-link voltage strategy can also compensate the neutral current in unbalanced load application, results show that the APF under proposed DC-link voltage strategy can also compensate the neutral reducing the influence from neutral current to the system, and the unbalanced load phenomenon is current in unbalanced load application, reducing the influence from neutral current to the system, eliminated effectively. Therefore, the proposed strategy can be applied in the unbalanced load situation and the unbalanced load phenomenon is eliminated effectively. Therefore, the proposed strategy can and also achieves an ideal APF compensation performance. be applied in the unbalanced load situation and also achieves an ideal APF compensation performance.

Energies 2018, 11, 2407 Energies 2018, 2018, 11, 11, xx FOR FOR PEER PEER REVIEW REVIEW Energies

(a) (a)

12 of 14 12 of of 14 14 12

(b) (b)

Figure 9. Three-phase load and and grid grid currents currentswith withthe theunbalance unbalanceload loadwhen whenUU U sn = 220 V and Udc-ref = Figure 9. 9. Three-phase Three-phase load = Figure currents with the unbalance load when 220VVand andUUdc-ref dc-ref = snsn== 220 640 V. (a) Before compensation; and (b) after compensation. 640 V. V. (a) Before compensation; and (b) after compensation. 640

(a) (b) (a) (b) sn = 220 V and Udc-ref = 640 V. (a) Figure 10. Neutral line current with the unbalance load when U sn = = 640 V. (a) Figure when U Usn Figure 10. 10. Neutral Neutral line line current current with with the the unbalance unbalance load load when = 220 220 V V and and U Udc-ref dc-ref = 640 V. (a) Without compensation; compensation; and and (b) (b) with with compensation. compensation. Without Without compensation; and (b) with compensation.

Conclusions 5. Conclusions Conclusions 5. APF compensating compensating current This paper paper analyzes analyzes the the influence influence from from DC-link DC-link voltage voltage on on the the APF current This characteristic and and compensation compensation performance, performance, and and establishes establishes the the relationships relationships between between the the DC-link DC-link characteristic current is voltage and switching frequency harmonic established. The increase of the DC-link voltage voltage and switching frequency harmonic current is established. The increase of the DC-link voltage lead to the increase of the switching frequency harmonic current, thus raising the THD value and may to the increase of the switching frequency harmonic current, thus raising the THD value may lead to the increase of the switching frequency harmonic current, thus raising the THD value deteriorating the compensation performance. Thus, to Thus, achieve ideal compensation performance, and deteriorating the compensation compensation performance. Thus, to toanachieve achieve an ideal ideal compensation compensation and deteriorating the performance. an and to reduce switching loss and power consumption in the APF, the DC-link voltage should be performance, and to reduce switching loss and power consumption in the APF, the DC-link voltage performance, and to reduce switching loss and power consumption in the APF, the DC-link voltage maintained at the minimum value level. should be be maintained maintained at at the the minimum minimum value value level. level. should minimum DC-link voltagecontrol controlstrategy strategyfor forthe theAPF APFis isproposed. proposed. On this basis, a simplified minimum DC-link voltage control strategy for the APF is proposed. On this basis, a simplified minimum DC-link voltage Compared strategies, the Compared with the existing minimum DC-link voltage strategies, the reference DC-link voltage in Compared with the existing minimum DC-link voltage strategies, the reference DC-link voltage in the proposed proposed strategy strategy is is only only determined determined by by the the grid grid voltage voltage and and the the modulation modulation ratio, ratio, avoiding avoiding the the the calculation of harmonic currents, reactive equivalent complex calculation of harmonic currents, reactive power, and parameters, reducing the complex calculation of harmonic currents, reactive power, and equivalent parameters, reducing the calculation burden burden of characteristic and reliability of calculation burden of the the processor processor and and improving improving the the real-time real-time characteristic characteristic and reliability reliability of the the calculation practical implement. implement. Therefore, Therefore, the the proposed proposed strategy strategy can can be be an solution for APF in in practical Therefore, the proposed strategy can be an optimized optimized solution solution for the the APF application. APF in practical APF in practical application. Author Contributions: All authors authors contributed contributed improving improving the the quality quality of of the the manuscript. manuscript. Specifically, Specifically,Y.W. Y.W. Author Contributions: All All Author Contributions: authors contributed improving the quality ofand theperformed manuscript. conceptualized the idea of this research, carried out the theoretical analysis, theSpecifically, experiments.Y.W. Y.W. conceptualized the idea of this research, carried out the theoretical analysis, and performed the experiments. conceptualized thedesign idea ofofthis carried out the theoretical analysis, and performed the S.C. experiments. contributed to the theresearch, methodology and experiments, writing, and revising the paper. provided Y.W. contributed to the the design of the thelanguage, methodology and experiments, experiments, writing, and revising revising the paper. paper. S.C. S.C. important comments on the structure, and format of the paper. G.Z. designed the methodology and Y.W. contributed to design of methodology and writing, and the provided important comments on the structure, language, and format of the paper. G.Z. designed the experiment setup. Y.Z.comments contributed the structure, writing andlanguage, revising the provided important ontothe andpaper. format of the paper. G.Z. designed the methodology and experiment setup. Y.Z. contributed to the writing and revising the paper. methodology experiment setup. Y.Z. contributed to the writing and revising the paper. Funding: Thisand work was funded by the National Natural Science Foundation of China under grant no. U1501251 and no. 51307025, and the Science and Technology Planning Project of Guangdong Province grant Acknowledgments: This work was supported by the National Natural Science Foundation of Chinaunder under grant Acknowledgments: No. 2017B090907011.This work was supported by the National Natural Science Foundation of China under grant no. U1501251 U1501251 and and no. no. 51307025, 51307025, and and the the Science Science and and Technology Technology Planning Planning Project Project of of Guangdong Guangdong Province Province under under no. grant No. 2017B090907011. grant No. 2017B090907011.

Energies 2018, 11, 2407

13 of 14

Acknowledgments: This work was supported by the National Natural Science Foundation of China under grant no. U1501251 and no. 51307025, and the Science and Technology Planning Project of Guangdong Province under grant No. 2017B090907011. Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3. 4. 5. 6. 7.

8. 9. 10.

11.

12. 13.

14. 15.

16.

17.

18.

19.

Olivares, D.E.; Mehrizi-San, A.; Etemadi, A.H.; Chang, Y.R. Trends in microgrid control. IEEE Trans. Smart Grid 2014, 5, 1905–1919. [CrossRef] Rakpenthai, C.; Uatrongjit, S.; Watson, N.R. On harmonic state estimation of power system with uncertain network parameters. IEEE Trans. Power Syst. 2013, 28, 4829–4838. [CrossRef] Zobaa, A.F.; Aleem, S.H.E.A. A new approach for harmonic distortion minimization in power systems supplying nonlinear loads. IEEE Trans. Ind. Inform. 2014, 10, 1401–1412. [CrossRef] Beres, R.N.; Wang, X.; Liserre, M.; Blaabjerg, F.; Bak, C.L. A review of passive power filters for three-phase grid-connected voltage-source converters. IEEE J. Emerg. Sel. Top. Power Electron. 2016, 4, 54–69. [CrossRef] Hoon, Y.; Radzi, M.A.M.; Hassan, M.K.; Mailah, N.F. Control algorithms of shunt active power filter for harmonics mitigation: A review. Energies 2017, 10, 2038. [CrossRef] Swain, S.D.; Ray, P.K.; Mohanty, K.B. Improvement of power quality using a robust hybrid series active power filter. IEEE Trans. Power Electron. 2017, 32, 3490–3498. [CrossRef] Monroy-Morales, J.L.; Campos-Gaona, D.; Hernandez-Angeles, M.; Pena-Alzola, R.; Guardado-Zavala, J.L. An active power filter based on a three-level inverter and 3D-SVPWM for selective harmonic and reactive compensation. Energies 2017, 10, 279. [CrossRef] Fabricio, E.L.L.; Junior, S.C.S.; Jacobina, C.B.; de Rossiter Correa, M.B. Analysis of main topologies of shunt active power filters applied to four-wire systems. IEEE Trans. Power Electron. 2018, 33, 2100–2112. [CrossRef] Bosch, S.; Staiger, J.; Steinhart, H. Predictive current control for an active power filter with LCL-filter. IEEE Trans. Ind. Electron. 2018, 65, 4943–4952. [CrossRef] Musa, S.; Radzi, M.A.M.; Hizam, H.; Wahab, N.I.A.; Hoon, Y.; Zainuri, M.A.A.M. Modified synchronous reference frame based shunt active power filter with fuzzy logic control pulse width modulation inverter. Energies 2017, 10, 758. [CrossRef] Tareen, W.U.K.; Mekhielf, S. Three-phase transformerless shunt active power filter with reduced switch count for harmonic compensation in grid-connected applications. IEEE Trans. Power Electron. 2018, 33, 4868–4881. [CrossRef] Panigrahi, R.; Subudhi, B. Performance enhancement of shunt active power filter using a kalman filter-based H∞ control strategy. IEEE Trans. Power Electron. 2017, 32, 2622–2630. [CrossRef] Morales, J.; De Vicuña, L.G.; Guzman, R.; Castilla, M.; Miret, J. Modeling and sliding mode control for three-phase active power filters using the vector operation technique. IEEE Trans. Ind. Electron. 2018, 65, 6828–6838. [CrossRef] Tan, K.H.; Lin, F.J.; Chen, J.H. DC-Link voltage regulation using RPFNN-AMF for three-phase active power filter. IEEE Access 2018, 6, 37454–37463. [CrossRef] Ribeiro, R.L.A.; Rocha, T.O.A.; Raphaell, M.S.; Euzeli, C.S.; Antonio, M.N.L. A robust DC-link voltage control strategy to enhance the performance of shunt active power filters without harmonic detection schemes. IEEE Trans. Ind. Electron. 2015, 62, 803–813. [CrossRef] Zhao, G.; Liu, J.; Yang, X.; Wang, Z. Analysis and specification of dc side voltage in parallel active power filter regarding compensation characteristics of generators. In Proceedings of the 2008 IEEE Power Electronics Specialists Conference, Rhodes, Greece, 15–19 June 2008. Cui, X.X.; Lam, C.S.; Dai, N.Y.; Choi, W.H.; Wong, M.C. Study on DC voltage control of hybrid active power filters. In Proceedings of the 2011 6th IEEE Conference on Industrial Electronics and Applications, Beijing, China, 21–23 June 2011. Hoon, Y.; Radzi, M.A.M.; Hassan, M.K.; Mailah, N.F. DC-link capacitor voltage regulation for three-phase three-level inverter-based shunt active power filter with inverted error deviation control. Energies 2016, 9, 533. [CrossRef] Luo, A.; Shuai, Z.K.; Shen, Z.J.; Zhu, W.J.; Xu, X.Y. Design considerations for maintaining DC-side voltage of hybrid active power filter with injection circuit. IEEE Trans. Power Electron. 2009, 24, 75–84. [CrossRef]

Energies 2018, 11, 2407

20. 21. 22.

23.

24. 25.

26.

27. 28.

14 of 14

Choi, W.H.; Lam, C.S.; Wong, M.C.; Han, Y.D. Analysis of DC-link voltage controls in three-phase four-wire hybrid active power filters. IEEE Trans. Power Electron. 2013, 28, 2180–2191. [CrossRef] Mannen, T.; Fujita, H. Dynamic control and analysis of DC-capacitor voltage fluctuations in three-phase active power filters. IEEE Trans. Power Electron. 2016, 31, 6710–6718. [CrossRef] Zainuri, M.A.A.M.; Radzi, M.A.M.; Soh, A.C.; Mariun, N.; Rahim, N.A. DC-link capacitor voltage control for single-phase shunt active power filter with step size error cancellation in self-charging algorithm. IET Power Electron. 2016, 9, 323–335. [CrossRef] Mannen, T.; Fujita, H. A DC capacitor voltage control method for active power filters using modified reference including the theoretically derived voltage ripple. IEEE Trans. Ind. Appl. 2016, 52, 4179–4187. [CrossRef] Vahedi, H.; Shojaei, A.A.; Dessaint, L.A.; Al-Haddad, K. Reduced DC-Link voltage active power filter using modified PUC5 converter. IEEE Trans. Power Electron. 2018, 33, 943–947. [CrossRef] Lam, C.S.; Cui, X.X.; Wong, M.C.; Han, Y.D. Minimum DC-link voltage design of three-phase four-wire active power filters. In Proceedings of the 2012 IEEE 13th Workshop on Control and Modeling for Power Electronics (COMPEL), Kyoto, Japan, 10–13 June 2012. Lao, K.W.; Dai, N.Y.; Liu, W.G.; Wong, M.C. Hybrid power quality compensator with minimum DC operation voltage design for high-speed traction power systems. IEEE Trans. Power Electron. 2013, 28, 2024–2036. [CrossRef] Lam, C.S.; Choi, W.H.; Wong, M.C.; Han, Y.D. Adaptive DC-link voltage-controlled hybrid active power filters for reactive power compensation. IEEE Trans. Power Electron. 2012, 27, 1758–1772. [CrossRef] Lam, C.S.; Wong, M.C.; Choi, W.H.; Cui, X.X.; Mei, H.M.; Liu, J.Z. Design and performance of an adaptive low-DC-voltage-controlled LC-hybrid active power filter with a neutral inductor in three-phase four-wire power systems. IEEE Trans. Power Electron. 2014, 61, 2635–2647. [CrossRef] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).