Proceedings of NCPCE-12

Strategies and Operating Point Optimizationof STATCOM Control for Voltage UnbalanceMitigation in Three-Phase Three-Wire Systems

Kuang Li, Jinjun Liu, Zhaoan Wang, and Biao Wei

Abstract—Reactive power control through the static com-pensator (STATCOM) has gained wide attentions due to itsoutstanding performance. But for a STATCOM with traditionalcontrol strategies, unbalanced utility voltages will greatly affectthe performance of the STATCOM and, in severe cases, may evencause the shutdown of the STATCOM for overcurrent protection.This paper proposes novel control strategies to ensure normaloperation of STATCOM in three-phase three-wire systems whensevere system voltage unbalance occurs and, furthermore, tomitigate voltage unbalance at the point of common coupling(PCC) whether it is caused by the utility or load. The control laws,operation principles, compensation characteristics, and operatingpoint optimization of the proposed control strategies are analyzedand compared in detail. The power flow in the STATCOM andcorresponding dc-side voltage-control schemes for these controlstrategies are also introduced. It is shown that the proposedvoltage-controlled current source (VCCS) strategy and modifiedvoltage-controlled voltage source strategy are valid for voltageunbalance compensation, especially the VCCS strategy for lowrating under the same performance. Finally, the simulation andexperimental investigations were carried out with these threeparameter-optimized control strategies, respectively, for light andheavy load conditions. The results verified that the current passingthrough the STATCOM is under control and the voltage at thePCC is more balanced than before compensation. The compensa-tion performance of the STATCOM is thus proven satisfactory.

Index Terms—Control strategy, point of common coupling(PCC), static compensator (STATCOM), voltage-controlled cur-rent source (VCCS), voltage-controlled voltage source (VCVS),voltage unbalance.

I. INTRODUCTION

STATIC COMPENSATOR (STATCOM) is an advanced re-active power compensator that has attracted more attention

in recent years [1]–[5]. It can be used to control power factor,regulate voltage, stabilize power flow, and improve the dynamicperformance of power systems. STATCOM can also provide ad-ditional functions, such as harmonics compensator and load bal-ancer, as a potential trend during the past decade [6].

In practical operation, one problem that STATCOM has todeal with in utilities is system voltage unbalance [7]–[12],

The authors are with the School of Electrical Engineering, Xi’an Jiao-tong University, Xi’an, Shaanxi, China 710049 (e-mail: [email protected];[email protected]).

which is considered to be a power-quality (PQ) problem withincreasing concern especially at the distribution level theseyears. According to [13], there were quite some grids in whichvoltage unbalance factor exceeds 3% in the U.S. The situationin China is even worse. But in the IEC standard, the voltage un-balance factor must be below 2% during a long period of time.An excessive level of voltage unbalance can impose seriousimpacts on any equipment connected in the grid system. Theaffected equipment includes induction motors, variable speeddrive systems, and many other power-electronic equipment. Intraditional control strategies, a STATCOM is usually controlledas a positive-sequence voltage source [7]–[12]. Under balancedutility voltages, STATCOM works very well. But in unbalancedvoltage mains, a negative-sequence current will be inducedwhen it goes through the STATCOM, as the STATCOM is ashort circuit for a negative-sequence component. Due to thesmall system impedance, a small amount of negative- sequencecomponent in the supply voltage would lead to a very largeamount of negative-sequence current. Under this situation, theSTATCOM has to be put into standby mode to avoid overcur-rent [7]. Bedsides, under unbalanced supply voltages, there is

voltage ripples in the dc bus and current harmonic in theoutput current of the STATCOM, where is the line frequency.In order to suppress the dc bus ripple voltage of the STATCOM,a simple way is to increase the capacity of the dc capacitor.But it is no use to attenuate the voltage unbalance in the powermains [11].

In order to keep voltage unbalance under a permitted level,a lot of measures have been put forward. Among them, themethod of active series compensators or parallel compensatorshas been very attractive. Dynamic voltage restorers (DVRs),series power-quality conditioners (SPQCs), and active lineconditioners (ALCs) are the common examples of an activeseries unbalance compensator [13]. For parallel compensators,the STATCOM itself is actually a choice [10]–[12]. In [10],the STATCOM operates as a voltage-controlled voltage source(VCVS), and a modified single-phase synchronous frametransform is proposed to handle the unbalanced condition. Thetransform, however, suffers from additional time delay imposedby its requirement for filtering of the second harmonic. In[11], a quasi 48-pulse STATCOM and a pulsewidth-modulated(PWM) converter are proposed. The output negative-sequencevoltage of the PWM converter protects the STATCOM whensevere supply voltage unbalance occurs. But this still cannotmitigate the unbalanced voltages at the PCC. In [12], a sim-plified model of STATCOM was proposed for unbalance

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compensation. But the model-based control algorithm is easilyinfluenced by system parameters and the control scheme israther complicated.

In this paper, STATCOM is operated to control reactivepower under normal situations. When severe supply voltageunbalance occurs, STATCOM will be switched from reactivepower control to the voltage unbalance compensation function.It can also be switched to compensate the asymmetrical currentof the load according to practical requirements. In this way,the functions of the STATCOM are extended, which is also atendency in these years [6], [14]–[18]. This paper discussesin detail how to mitigate the supply voltage unbalance at thePCC with a STATCOM.

The configuration of the STATCOM is first introduced.With this configuration, three control strategies for voltageunbalance compensation are proposed: voltage-controlledcurrent source (VCCS) strategy, voltage-controlled voltagesource (VCVS) strategy, and modified VCVS strategy. Foreach control strategy, the principle for unbalanced voltagemitigation is analyzed in detail. To achieve the optimal perfor-mance, the parameter relationships are also investigated. Withthe characteristic curves, the optimal operation point can belocated. At this point, the unbalanced voltages at the PCC andthe capacity of the STATCOM reach the smallest value at thesame time. Moreover, the power flow between the STATCOMand the utility grid is also presented. And the control scheme tokeep the dc bus voltage constant is put forward. Finally, simu-lation and experiment tests under unbalanced supply voltages,respectively, for resistive and diode rectifier load conditionsare shown. It is verified that the overcurrent phenomenon ofthe STATCOM does not occur any more and the unbalancedvoltage at the PCC is greatly reduced than that before compen-sation. The compensation behavior of the STATCOM on thesystem voltage unbalance is satisfactory.

II. SYSTEM CONFIGURATION

The proposed configuration of the whole system is shownin Fig. 1, which targets 10 kV and 3 10-MVA rating of theSTATCOM. There is no transformer, and the STATCOM isdirectly connected in parallel with the three-phase load viaa small inductor for the attenuation of switching frequencycurrent ripples. The power converter of the STATCOM employsseveral series-connected IGBTs in each leg of the three-phasebridge circuit for medium-voltage blocking capability. The dccapacitors could be in series and parallel connections too. As thepower stage of the STATCOM is just a three-phase full-bridgetwo-level converter and the control of the system is simplerthan multilevel topologies provided that the voltage-sharingtechniques for the series-connected IGBTs can be solvedsuccessfully.

The STATCOM has multiple compensation functions and thecontrol strategies must be embedded into the control unit. InFig. 1, the block diagram of the control system is also shown.The grid voltages, the source currents, the output currents, andthe dc voltage of the STATCOM need to be detected accurately.

Fig. 1. Simplified system configuration of the STATCOM.

Fig. 2. Single-phase equivalent circuit for the distribution system with VCCS-controlled STATCOM.

These signals are sent into a digital signal processor (DSP) con-trol unit. In this paper, the control strategy is fully digitally im-plemented based on a TMS320F2812 DSP. And it does not re-quire any additional analog-to–digital or digital-to-analog con-version chips. The cost of the whole control system is very low,but the reliability is comparatively high. Simultaneously, a touchpanel is introduced in the control system, and it is very conve-nient to operate the STATCOM and monitor the system status.

III. CONTROL STRATEGIES AND OPERATING POINT

OPTIMIZATION FOR MITIGATION OF VOLTAGE UNBALANCE

In three-phase three-wire systems, the line-to-line voltageat the PCC does not contains any zero-sequence components.Therefore, only the negative-sequence voltage is considered forunbalance compensation. In this paper, all of the negative- andpositive-sequence quantities are denoted by subscripts and ,respectively, and the formulation is based on phasor analysis.

A. VCCS Voltage Unbalance Mitigation Strategy andOperating Point Optimization

In the VCCS voltage unbalance mitigation strategy, thesingle-phase equivalent circuit of the power system is shownin Fig. 2. and , respectively, denote the fundamentalpositive- and negative-sequence voltage components of thepower supply. and represent the current and voltage ofthe STATCOM. is the voltage at the PCC.

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With this control scheme, the STATCOM is controlled as acurrent source. Its amplitude is determined by the unbalancedvoltage and an equivalent amplifying quantity of the STATCOM

. Here, a rotating factor is introduced for the phase-anglecontrol of the compensating current, as shown in the followingequation:

(1)

Generally, the load impedance is much larger than the gridimpedance. Therefore, here is not considered (i.e., )for simplification.

The unbalanced voltage at the PCC and the current of theSTATCOM are as follows:

(2)

(3)

In (2), the unbalanced voltage can be mitigated by in largevalue, which is realized with the STATCOM. It is clear that onlythe unbalanced current flows into the STATCOM. One merit ofVCCS control is that the current of the STATCOM is fully undercontrol whenever the voltage of the utility grid is balanced ornot. Therefore, the STATCOM could theoretically be operatedonline safely at all times.

In this case, the voltage across the STATCOM is composed oftwo components: 1) fundamental frequency positive-sequencevoltage and 2) negative-sequence voltage (voltage harmonicsnot considered), which are expressed as

(4)

(5)

In order to evaluate the required capacity of the STATCOM,two terms named equivalent voltage and equivalent current areintroduced [19]. The values of these two quantities are definedas

(6)

(7)

Thus, the rating of the STATCOM can be estimated by

(8)

Because there is no positive-sequence current flowingthrough the STATCOM, the equivalent current is derived as

(9)

So for the VCCS voltage unbalance mitigation strategy, therating of the STATCOM is

(10)

Fig. 3. Single-phase equivalent circuit of the distribution system with a VCVS-controlled STATCOM.

The relationships between , , , and are analyzedbased on the equivalent circuit and shown in Fig. 4(a) when

, . If is purely inductive,is the optimum value because , , and are minimum atthe same time.

In order to find out the optimum value for in a general way,assume . Then, from (2)

(11)

The condition is

(12)

Generally, the system impedance of the power grid is moreinductive than resistive. Therefore, it can be also assumed that

for simplicity.

B. VCVS Voltage Unbalance Mitigation Strategy andOperating Point Optimization

In the VCVS voltage unbalance mitigation strategy, thesingle-phase equivalent circuit of the power system is shown inFig. 3. The quantities definitions are the same as those in theVCCS scheme, except that denotes the connecting reactorof the STATCOM with the utility grid.

In this control strategy, the STATCOM is controlled as avoltage source, whose amplitude and phase angle are deter-mined by the unbalanced voltage at the PCC, amplifying factor

, and another rotating factor . The control law is shown asfollows:

(13)

If the load is not considered , the unbalancedvoltage at the PCC after compensation becomes

(14)

where not only , but also influences the compensation char-acteristic of the STATCOM. However, one thing that does notchange is that the larger the amplifying factor is, the more bal-anced the voltage at the PCC is.

With this control scheme, the voltage across the STATCOM isa negative-sequence component. The positive-sequence voltage

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Fig. 4. Relationship between U , I , S and rotating angel with three control strategies. (a) VCCS control strategy (k = 2). (b) VCVS control strategy(k = 2:5, Z = 0:9 p.u.). (c) Modified VCVS control strategy (k = 1:5, Z = 0:2 p.u.).

Fig. 5. Characteristic comparison between the VCCS strategy and the VCVS strategy. (a) The relationship between I and U . (b) The relationship betweenU and U . (c) The relationship between S and U .

is only dropped on the connecting reactor which, in this case,must be high impedance. Therefore, the equivalent voltage is

(15)

Unlike the VCCS control approach, here not only nega-tive-sequence current, but also positive-sequence current flowsthrough the STATCOM. They are, respectively, as follows:

(16)

(17)

In the same way, the capacity of the STATCOM can be eval-uated according to

(18)

The relationships between , , , and are shown inFig. 3(b). If is purely inductive, it can be obtained thatis the optimum value because , , and are minimum atthe same time.

In order to find out the optimum value for in a general way,assume , ,

. Then

(19)

The condition is

(20)

Fig. 5 shows the characteristics comparison between theVCCS strategy and the VCVS strategy with as a variableparameter. The equivalent current of the STATCOM with theVCCS control is much smaller than that with the VCVS con-trol. The equivalent voltage, however, is not the case. Thus, therating of the STATCOM becomes different under the same un-balanced voltage level. It is obvious that the VCCS mitigationstrategy is more favorable, as shown in Fig. 5(c).

C. Modified VCVS Voltage Unbalance Mitigation Strategy

In fact, the output voltage of the STATCOM in the VCVScontrol scheme is only composed of the fundamental nega-tive-sequence component, as shown in (16). Therefore, theSTATCOM is a short circuit for the positive-sequence voltage.In order to prohibit the resulting large current from flowing

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Fig. 6. Characteristic comparison between the VCCS strategy and the modified VCVS strategy. (a) The relationship between I and U . (b) The relationshipbetween U and U . (c) The relationship between S and U .

into the STATCOM and to ensure the PCC voltages at a per-mitted level, the inductance of the linking reactor betweenthe STATCOM and the grid must be very high, for example,

. On one hand, it makes the cost and volumeof the system increase greatly. On the other hand, the highinductance deteriorates the unbalance mitigation capability ofthe STATCOM. To solve this contradiction and to improve thesystem performance in a reasonable manner, a modified VCVScontrol strategy is proposed.

The control law for the modified VCVS strategy is as follows:

(21)

where represents the fundamental positive-sequencevoltage at the PCC. The output positive-sequence voltage cancancel with the positive-sequence voltage at the PCC; therefore,it can eliminate the positive-sequence current flowing into theSTATCOM. Theoretically, the positive-sequence current of theSTATCOM will be

(22)

Since the negative-sequence component is the same as that in theprevious VCVS strategy, the unbalance compensation perfor-mance of the STATCOM is unchanged too. The only differenceis that the STATCOM outputs the positive-sequence voltage, be-sides the negative-sequence voltage. So the equivalent voltagewithout the load becomes

(23)

Therefore, the rating of the STATCOM is

(24)

The relationships between , , , and are shownin Fig. 4(c). If is purely inductive, is also theoptimum value because , , and are minimum atthe same time.

Fig. 6 shows the characteristics comparison between themodified VCVS strategy and the VCVS strategy with asthe variable parameter. In Fig. 6, the equivalent current of theSTATCOM with the VCCS control is also smaller than thatwith the modified VCVS control. But the equivalent voltagesare very close. Nevertheless, the capacity of the STATCOMwith the VCCS strategy is still a little smaller than that with themodified VCVS strategy under the same unbalanced voltagelevel. If the linking reactor could be too small to be ne-glected, these two lines could overlap each other. It means thatfrom the outside characteristic, these two control strategieshave no difference when is very small. But in application,

should have a certain value (e.g., 0.1 p.u.). Therefore, ingeneral, the VCCS mitigation strategy is a little better than themodified VCVS control strategy.

IV. POWER-FLOW ANALYSIS AND DC BUS VOLTAGE CONTROL

From the energy point of view, the compensation operation isthe power exchange between the STATCOM and the utility grid.Therefore, the analysis of the electric power consumed by theSTATCOM is absolutely necessary. Only when the STATCOMabsorbs little active power, is the control strategy applicable.

In the VCCS strategy, only the negative-sequence currentflows into the STATCOM. Thus, for the positive-sequencecomponent, the active power is

(25)

For the negative-sequence component, the active power is

(26)

According to (1)

(27)

from (12), is close to 90 , which leads to being very small.With proper control, the dc bus voltage of the STATCOM couldbe stable.

Similarly, in the VCVS strategy, only the negative-sequencevoltage is generated by the STATCOM. Although there is pos-itive-sequence current, the positive-sequence voltage is zero.Thus, for the positive-sequence component, the active power

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Fig. 7. Detection of the fundamental negative-sequence component in PCCvoltages and control algorithm for constant dc voltage. (a) System voltageswithout harmonic distortion. (b) System voltages with heavy harmonicdistortion.

is also zero. For the negative-sequence component, the activepower is

(28)

According to (13) and (16)

(29)

As shown in (20), is close to 0 . Generally, the resistance ofcould be neglected. In this condition, is very small too.

Thus, the control strategy is applicable.In the modified VCVS control strategy, although positive se-

quence voltage exists, the positive-sequence current becomeszero. So the positive-sequence active power is equal to zero. Andthe negative-sequence active power is the same as that shown in(29).

From the mentioned analysis with the three control strategies,the STATCOM is shown to consume only a small amount of ac-tive power besides absorbing or generating almost all of the re-active power necessary for unbalance compensation. Therefore,the STATCOM could operate normally.

Fig. 7(a) shows the detection method for the fundamentalnegative-sequence component in load voltages when the systemvoltage is hardly harmonics distorted. In that case, the utilityonly contains fundamental positive- and negative-sequencevoltages, which become dc and ac components, respectively,in the – frame. Then a 64-point moving average process isused in the low-pass filter (LPF) to remove the ac component.Therefore, only the dc component remains. With the inversetransformation, the positive components , , and are

obtained. After subtraction from the total voltage quantities,and used as the control reference signal of the STATCOM, thefundamental negative-sequence component is obtained.

If the utility voltage contains a lot of harmonics, the methodin Fig. 7(a) does not work effectively. The detected signal wouldalso be harmonic contaminated. Therefore, another unbalancedvoltage detection method is introduced as shown in Fig. 7(b). Inthis case, the transformation matrix is correspondingly modifiedso that only the negative-sequence voltage of the utility becomesdc component in the – frame. Actually, this can be achievedby switching the positions of two columns in the trans-formation matrix. Thus, only with low-pass filters (LPFs) andinverse transformation, can the exact detection for the controlreference signal of the STATCOM be realized.

The reference detection methods shown in Fig. 10 are sim-ilar to those used in harmonic current separation based on theinstantaneous reactive power theory. The only deference is thatthe detection objects become the three-phase voltages.

In order to ensure that the STATCOM is working properly,the dc bus voltage has to be controlled to a certain stable level.The dc bus voltage control scheme is also shown in Fig. 7(a).In this paper, a single voltage control loop is adopted. The errorsignal between the dc bus voltage and its reference isregulated with a PI controller. The output of the PI regulator isadded to the channel signal in the – frame. Therefore, thecertain positive-sequence component is generated at the funda-mental frequency with the same phase angle of the PCC posi-tive-sequence voltage after inverse transformation. Since the de-tected signal is used as the reference for the STATCOM currentin the VCCS control strategy, it will then generate certain pos-itive-sequence currents besides the currents for voltage unbal-ance mitigation. The generated positive-sequence currents alongwith the same phase angle as the PCC positive-sequence voltagewill produce certain active power, which is used to adjust thedc-side voltage of the STATCOM.

For the case of utility voltages with severe harmonics or thecase of using VCVS control strategies, the control diagram isshown in Fig. 7(b). The principle of adjusting the necessary ac-tive power flow in the STATCOM to control the dc-side voltagedoes not change.

V. SIMULATION AND EXPERIMENT RESULTS

In order to verify the three control strategies for voltage un-balance mitigation, detailed computer simulation investigationsin the time domain have been carried out with PSIM6.0. Foreach control strategy, two kinds of loads are studied: resistiveload and rectifier load ( , )where , , and .

Fig. 8 shows the simulation waveforms with the STATCOMunder the VCCS control. After the STATCOM is put into opera-tion at 0.04 s, the PCC voltage becomes more balanced. Thenegative-sequence voltage approaches a very small extent,even zero. More evidence is that the load current is also symmet-rical after compensation. A corresponding result is the increaseof the current in the STATCOM and the power supply. The miti-gation performance of the STATCOM is outstanding, regardless

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Fig. 8. Simulation results with the VCCS control strategy (L = 0:3 mH). (a) Resistive load. (b) Diode rectifier load.

Fig. 9. Simulation results with the VCVS control strategy (L = 40 mH). (a) Resistive load. (b) Diode rectifier load.

Fig. 10. Simulation results with the modified VCCS control strategy (L = 0:3 mH). (a) Resistive load. (b) Diode rectifier load.

of the linear resistive loads in Fig. 8(a) or for nonlinear rectifierloads [Fig. 8(b)].

Figs. 9 and 10, respectively, show the simulation waveformswith the STATCOM under the VCVS control and under the

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Fig. 11. Experiment waveforms under the VCCS strategy with rectifier load (f = 3:2 kHz). (a) Unbalanced PCC voltages without the STATCOM (t: 5 ms/divu: 150 V/div). (b) Nearly balanced PCC voltages with the STATCOM (t: 5 ms/div u: 150 V/div). (c) Unbalanced load current without the STATCOM (t: 5 ms/divi: 20 A/div). (d) Nearly balanced load current with the STATCOM (t: 5 ms/div i: 20 A/div).

Fig. 12. Experiment waveforms with the STATCOM under rectifier load (f = 3:2 kHz). (a) Nearly balanced PCC voltages with the VCVS control strategy. (b)Nearly balanced PCC voltages with the modified VCVS control strategy. (a) t: 5 ms/div u: 150 V/div; (b) t: 5 ms/div u: 150 V/div.

modified VCVS control. It is verified by the simulation wave-forms that undoubtedly the two strategies can mitigate the un-balanced voltages at the PCC under any load condition.

Furthermore, experiment investigations have been carriedout on an established reduced scale prototype STATCOM with3.2-kHz switching frequency. The prototype is rated at 380V/50 kVA. The unbalanced supply voltage is obtained througha programmable ac source Chroma 6590, whereand . Fig. 11 shows the PCC voltage and loadcurrent waveforms before and after compensation. It is seen inFig. 11(a) that the voltage at the PCC is little distorted but highlyunbalanced originally. After the STATCOM is put into oper-ation, the three-phase PCC voltage becomes almost balancedas shown in Fig. 11(b). It means that the negative-sequencevoltage was almost fully compensated by the STATCOM withthe proposed VCCS control strategy. Fig. 11(c) and (d) are theload current waveforms before and after the STATCOM works.

Fig. 12(a) is the voltage waveforms at the PCC with theVCVS control strategy. Compared with Fig. 11(b), it is clearly

shown that the amplitude of the voltage under the VCVScontrol has greatly decreased. This phenomenon is caused bythe linking reactor between the STATCOM and the grid. Thesmaller the reactor is, the larger the positive-sequence currentof the STATCOM is, and the smaller the positive-sequencevoltage at the PCC is. Fig. 12(b) is the voltage waveforms atthe PCC with the modified VCVS control strategy, which issimilar to the results in Fig. 11(b). Because of the similarity tothose in the VCCS control strategy, the load current waveformsin the VCVS and the modified VCVS control strategies are notshown here.

From the experimental results, it is obvious that the supply-voltage unbalance problem can be mitigated effectively by theSTATCOM with the proposed VCCS and modified VCVS con-trol strategies.

VI. CONCLUSION

In this paper, novel control strategies are proposed forSTATCOM to compensate for the utility voltage unbalance ei-

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ther caused by the asymmetric load or upstream supply source.Through extensive theoretical analysis, computer simulation,and experimental tests on a hardware prototype of STATCOM,the following conclusions are obtained.

1) The STATCOM can be utilized to compensate thevoltage unbalance at the PCC.

2) The VCCS and modified VCVS control strategies haveproven to be valid for utility voltage unbalance mitiga-tion with STATCOM. And the VCCS control strategy ismore preferable for a low rating under the same com-pensation performance.

3) An optimum operation point exists when realizing thetwo control strategies. At this point, the STATCOMshows the best compensation characteristics.

4) When compensating utility voltage unbalance, theSTATCOM can be controlled to absorb almost onlyreactive power. Only a small amount of active power isconsumed for stabilizing the dc capacitor voltage.

A full-scale 10-kV/3-MVA STATCOM is under constructionfor distribution level compensation. The description of the full-scale setup construction, the implementation approach, and al-gorithms of control strategies for reactive power control andsystem voltage unbalance mitigation, and tests of field instal-lation will be reported in future publications.

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