issn 1755-4535 voltage and current unbalance compensation

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Published in IET Power ElectronicsReceived on 8th April 2008Revised on 19th June 2009doi: 10.1049/iet-pel.2008.0094

ISSN 1755-4535

Voltage and current unbalance compensationusing a static var compensatorY. Xu1 L.M. Tolbert1,2 J.D. Kueck1 D.T. Rizy1

1Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA2The University of Tennessee, Knoxville, TN 37996-2100, USAE-mail: [email protected]

Abstract: A three-phase insulated gate bipolar transistor (IGBT)-based static var compensator (STATCOM) is usedfor voltage and/or current unbalance compensation. An instantaneous power theory is adopted for real-timecalculation and control. Three control schemes – current control, voltage control and integrated control – areproposed to compensate the unbalance of current, voltage or both. The compensation results of the differentcontrol schemes in unbalance cases (load current unbalance or voltage unbalance) are compared andanalysed. The simulation and experimental results show that the control schemes can compensate theunbalance in load current or in the voltage source. Different compensation objectives can be achieved, that is,balanced and unity power factor source current, balanced and regulated voltage or both, by choosingappropriate control schemes.

1 IntroductionPower quality issues, especially current harmonics, currentunbalance and voltage unbalance, have drawn much attentionand much research work has been performed in this area.One means of correcting these power quality problems isto provide non-active power compensation by a parallelcompensator. A static var compensator (STATCOM) is aneffective way to eliminate or mitigate the harmonics andunbalance in current [1, 2]. However, there are still nostandard definitions of instantaneous non-active power andinstantaneous non-active current [3–6].

Voltage unbalance is generally not as severe as currentunbalance; however, it may have a more severe impact onboth loads and power system equipment. The negativeimpact of voltage unbalance on induction motors has beenstudied in depth [7, 8]. Series-connected converter-basedcompensators have been proposed for voltage unbalancecompensation, voltage sag compensation and voltageregulation [9–13]. For both the compensation of voltageunbalance and load current harmonics, an active filter forvoltage regulation, together with passive filters (fifth andseventhth) for current harmonics compensation, is proposedin [14]. Whereas in [15], a series active filter and a parallel

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active filter are connected to perform both voltage andcurrent compensation tasks at the same time. A method ofvoltage unbalance mitigation using a STATCOM is alsopresented in [16].

The instantaneous power theory presented in [6] is usedfor the STATCOM presented in this paper because thedefinitions of instantaneous power and instantaneous non-active power are suitable for real-time non-active powercompensation purpose. This instantaneous power theorywill be elaborated in Section 3.

A feedback controller is presented in this paper to performboth voltage unbalance and current unbalance compensationin a STATCOM. The system can compensate the non-activepower component and the unbalance in the load currentand/or regulate and balance the system voltage. Aftercompensation, the three-phase utility voltages are balanceddespite the sources of the unbalance. Either one or boththe tasks can be performed at the same time, depending onthe compensation objectives and the compensation resultsto be achieved. The compensator can provide the non-active component in the load current such that the sourcecurrent is balanced and has unity power factor or it canregulate the system voltage to a certain level by generating

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or consuming non-active power. Thus, it can compensate thevoltage or current unbalance caused by the load.

2 System configurationThe system configuration of a parallel non-active powercompensator is shown in Fig. 1. The compensator isconnected in parallel with the load through a couplinginductor Lc and the rest of the system is simplified as aninfinite utility voltage source with a system impedance ofRs + jvLs. The parallel compensator is connected throughthe coupling inductor at the point of common coupling(PCC) and the PCC voltage is denoted as vt. The filteringcapacitor Cf is used to mitigate the ripple in thecompensator current ic. The compensator only provides(generates or consumes) non-active power and there is noenergy source connected to the DC link. The DC linkvoltage vdc is regulated by the compensator.

By providing a certain amount of non-active power, thecompensator can eliminate or mitigate the unwantedcomponents, such as non-active power, harmonics andunbalance in the load current; it can also regulate thevoltage vt to a certain level. The compensator can performthese two tasks individually or as an integrated control ofthe voltage and the current.

3 Instantaneous power theoryAn instantaneous non-active power theory [6] is adopted tocalculate the instantaneous variables based on themeasurements (vt, il, ic and vdc) and to implement control,depending on the compensation objectives and controlschemes. In a three-phase system with a voltage vector v(t)and a current vector i(t) (vectors for voltage and current are

Figure 1 System configuration of a STATCOM for voltageand current unbalance compensation

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denoted in bold)

v(t) = [v1(t), v2(t), v3(t)]T (1)

i(t) = [i1(t), i2(t), i3(t)]T (2)

The instantaneous power p(t) and the average power P(t) overthe averaging interval [t 2 Tc, t] are defined by (3) and (4)

p(t) = vT(t)i(t) =∑3

k=1

vk(t)ik(t) (3)

P(t) = 1

Tc

∫t

t−Tc

p(t) dt (4)

Theoretically, the averaging interval Tc can be chosenarbitrarily from zero to infinity and for different Tc values, theresulting active and non-active currents will have differentcharacteristics. However, in practice, a specific value of Tc ischosen according to the specifications of the system. Forexample, in a periodic system with period T, Tc is chosen asthe integer multiples of T/2 and all the definitions areconsistent with the standard definitions. The detaileddiscussion of choice of Tc is presented in [17]. A three-phasesinusoidal system with voltage fundamental period T isstudied in this paper and in this case, Tc is normally chosenas T/2 to eliminate current harmonics.

The instantaneous active current ia(t) and instantaneousnon-active current in(t) are defined by (5) and (6),respectively

ia(t) = P(t)

V 2p (t)

vp(t) (5)

in(t) = i(t) − ia(t) (6)

In (5), the voltage vp(t) is the reference voltage, which ischosen based on the characteristics of the system and thecompensation results to be achieved. In the three-phasesinusoidal system being studied, if the system voltage onlycontains a fundamental component and is balanced, thenthe reference voltage is usually chosen as the system voltageitself; otherwise the positive sequence component of thefundamental component of the system voltage is usuallychosen as the reference voltage so that fundamental andbalanced compensation results can be achieved. Vp(t) is therms value of the reference voltage vp(t), that is.

Vp(t) =��1

Tc

∫t

t−Tc

vTp (t)vp(t) dt

√(7)

The rms values of the voltage v(t) and the current i(t) are,respectively

V (t) =��1

Tc

∫t

t−Tc

vT (t)v(t) dt

√(8)

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I (t) =��1

Tc

∫t

t−Tc

iT(t)i(t) dt

√(9)

The definitions in (4) and (7) are average and rms values overaveraging interval Tc, whose instantaneous values maychange with time t because they are the average values overthe interval [t 2 Tc, t]. In practice, Tc is not arbitrarilychosen. In a system with periodic voltages and currents, Tc

is chosen as the integral multiples of T/2 (where T is theperiod of the system). By choosing this Tc, the definitions(4), (8) and (9) are constants and the same as theconventional definitions.

The standard definitions apply to three-phase sinusoidalsteady-state balanced systems and in this case, the proposedinstantaneous definitions are consistent with the standarddefinitions when Tc is chosen as the integral multiples ofT/2 (where T is the period of the system). Theinstantaneous definitions extend the standard definitions tocases that are single phase, non-sinusoidal, unbalanced ornon-periodic.

The definitions in this instantaneous non-active powertheory are all consistent with the standard definitions forthree-phase fundamental sinusoidal systems. They are alsovalid in other various cases, such as single-phase systems,non-sinusoidal systems and non-periodic systems as well,by changing the averaging interval Tc and the referencevoltage vp(t) [6]. More specifically, a three-phase systemwith unbalanced voltage, unbalanced current or both, is thestudy objective in the paper. In this theory, all thedefinitions are instantaneous values; therefore they aresuitable for real-time control and provide advantages forthe design of control schemes, which will be discussed inthe next section.

4 Control schemes for unbalancecompensationIn a three-phase power system, voltages or currents arebalanced if the amplitudes of the three-phase voltages orcurrents are equal and the phase angles between consecutivephases are equal as well, which is 2p/3 radians in a three-phase case. From the standpoint of the compensatorconnected in parallel with a load, there are two kinds ofunbalance; one is an unbalanced load and the other one isan unbalanced voltage source (could be caused by otherloads or by the generators in the system). In the first case,the load current il is not balanced, which results inunbalance in the voltage vt as well because of the differencein voltage drop through the conductors caused by theunbalanced currents. If the unbalanced load is compensatedso that a balanced current is drawn from the utility, thenthe voltage vt will also be balanced, that is, the unbalanceis compensated in the load current compensation. Whereasin the second case, the load draws unbalanced current


because of the unbalanced voltage vt. This unbalance canonly be compensated with voltage regulation by theSTATCOM. After compensation, the three-phase PCCvoltages are balanced and the load draws balanced currentfrom the utility, however, the three-phase utility currentsare still unbalanced because of the compensation currentsinjected by the STATCOM. Because the PCC voltage isbalanced after the compensation, the unbalance caused bythe voltage source does not have impact on the load.

In this section, a current unbalance compensation controlscheme and a voltage unbalance compensation controlscheme are presented and compared and an integratedcontrol which combines the two control schemes togetheris also presented.

4.1 Current unbalance compensation

The control diagram of current control is shown in Fig. 2.The non-active component in the load current is calculatedby the instantaneous power theory in Section 3 [(5) and(6)] and this non-active component is provided by thecompensator; therefore a balanced, unity power factorsource current is drawn from the utility. The compensatoroutput voltage vc is controlled so that the compensatorcurrent tracks the reference i∗c, as shown in (10)

v∗c = vt + KP1(i∗c − ic) + KI 1

∫t

0

(i∗c − ic) dt (10)

The output of the PI controller is the difference between theinverter output voltage vc and the PCC voltage vt, which isalso the voltage drop on the coupling inductance. In steadystate, the proportional term [the second term in (10)] iszero and the integral term [the third term in (10)] is thevoltage drop on the coupling inductance

i∗c = i∗c1+i∗c2 (11)

The reference compensator current i∗c has two components,i∗c1 and i∗c2. The first component i∗c1 is the non-activecomponent in the load current calculated by theinstantaneous power theory. The system is assumed to beideal in the instantaneous power theory; however, there arelosses in the real compensator. Therefore if there is noactive power provided to the compensator, the DC linkcapacitor voltage vdc varies. Vdc is the average value of the

Figure 2 Current control diagram

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DC link voltage vdc over one system fundamental cycle. Toregulate the DC link voltage, some active power is drawnfrom the utility to meet the losses. This active current isreferred to as i∗c2, which is in phase with the PCC voltagevt. Therefore a control loop is designed as shown in (12)

i∗c2 = KP2(V ∗dc − Vdc) + KI2

∫t

0

(V ∗dc − Vdc) dt

[ ]vt (12)

The sum of i∗c1 and i∗c2 is the current that the compensatorneeds to provide, which is i∗c as shown in (11).

4.2 Voltage unbalance compensation

In power systems, most voltage unbalance conditions are dueto magnitude inequalities, whereas the phase angles are equal(2p/3) or nearly equal; therefore in this paper, unbalancedvoltages with unequal magnitudes are considered and thiskind of voltage unbalance can be compensated by a parallelcompensator by providing non-active power. The principleis to control the compensator so that its output is onlynon-active power (if losses are neglected), which isaccomplished by keeping the compensator output voltagevc in phase with the voltage vt and controlling the three-phase magnitudes of vc independently. In each phase,when the magnitude of vc is larger than that of vt, thecompensator generates non-active power; if the magnitudeof vc is smaller than that of vt, the compensator consumesnon-active power. By controlling the three-phasemagnitudes of the compensator voltage vc individually, therms values of the three-phase voltages of vt are controlledat a given level V∗

t, as shown in (13).

To account for losses in an actual system, the referencecompensator voltage is shifted a small phase angle u∗ sothat a small amount of active power is drawn by thecompensator as shown in (14). The phase angle u∗ iscontrolled so that the DC link voltage vdc is maintained ata given value. The control diagram is illustrated in Fig. 3

v∗c = 1 + KP1(V ∗

t − Vt) + KI1

∫t

0

(V ∗t − Vt) dt

[ ]vt(vt − u∗)

(13)

u∗ = KP2(V ∗dc − Vdc) + KI2

∫t

0

(V ∗dc − Vdc) dt (14)

In Fig. 3, the first input of the phase angle shift block is thecompensator reference voltage calculated by the voltageregulation requirement. This compensator reference voltageis phase shifted in the phase angle shift block and thephase shift angle u∗ is determined by the DC link voltagecontrol loop, which is the second input of the phase angleshift block.


4.3 Integrated compensation

Can the compensator regulate the voltage and compensatethe load non-active power at the same time? An integratedcompensation is proposed which approaches this goal. Thecontrol diagram is shown in Fig. 4, which is essentially acurrent control loop integrated with the voltage regulation.The reference current contains three components, the loadnon-active component i∗c1, the voltage regulationcomponent i∗c3 and the DC link control component i∗c2,where i∗c1 and i∗c2 are the same as in Section 4.1 and thevoltage regulation component i∗c3 is

i∗c3 = KP3(V ∗t − Vt) + KI3

∫t

0

(V ∗t − Vt) dt

[ ]vt vt − p

2

( )(15)

The integrated control combines the current loop and thevoltage control loop together. The two control loops canwork independently by shutting down the other control loop(changing the control gains to zero) or work together. Thisprovides the flexibility for the STATCOM to perform bothvoltage and current controls without any hardwarereconfiguration. From Fig. 4, gains for PI controller 1 wouldbe determined first which determines the magnitude of thecompensator’s inverter output voltage to compensate for loadnon-active current, then PI controller 3 gains modify themagnitude of the inverter output voltage for non-activepower for voltage regulation and finally PI controller 2 gainsare chosen which modify the inverter output voltage phaseangle to draw a small amount of active power for inverterlosses and to regulate the DC link voltage.

Figure 4 Control diagram of the integrated current andvoltage control

Figure 3 Voltage control diagram


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In all three control schemes, the controllers are applied tothe three phases separately so that the voltage or current ofeach phase is controlled separately. KP for the controllers isdetermined by how fast the STATCOM responds to stepchange in the voltage. A larger KP will result in a fasterresponse, but too large will result in overshoot by thecompensator. KI is determined by the maximum expecteddifference between two steady-state operating conditions. IfKI is too large, then stability issues arise even with steady-state conditions.

5 Simulation resultsIn the simulations presented in this section, the ac systemvoltage rating is 480 V (line-to-line rms value). Theminimum DC link voltage is 784 V [18], whereas in thesimulations the DC link voltage is 2200 V because theunbalance compensation requires a much higher DC voltage.

Considering there are two kinds of unbalance – loadunbalance and voltage source unbalance – and there arethree control schemes – current control, voltage control andintegrated control – all the combinations of compensationand their results are listed in Table 1. The compensationresults of the source current and the PCC voltage arecompared. If the unbalance is caused by the load, thecompensation results using different control schemes areshown in the third column in the table. If the unbalance iscaused by the voltage source, the compensation results areshown in the fourth column. In the load unbalance case, thevoltage is automatically balanced if the unbalance in the loadis compensated. In the voltage source unbalance case, it ismore complicated. The voltage can be compensated to bebalanced or unbalanced depending on the compensationobjectives. If a balanced voltage is desired for the load, itincreases the source current unbalance and consequently, itdeteriorates the power factor.

The simulation results of load unbalance compensation andvoltage source unbalance compensation are shown below.

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Experimental results of load unbalance compensation arepresented in the next section.

5.1 Load unbalance compensation

The three-phase load current together with phase a voltage isshown in Fig. 5a. The current is unbalanced and lagging thevoltage. There is no compensation from t ¼ 0 s to t ¼ 0.4 sand and the rms values of the voltage vt, the source currentis and the compensator current ic are shown in Figs. 5b, 5eand 5f, respectively. Current compensation is performedfrom t ¼ 0.4 s to t ¼ 0.8 s to achieve balanced sourcecurrents and unity power factor (in phase with the voltage).As shown in the control diagram in Fig. 2, the parametersof PI controller 1 (non-active current control) areKP ¼ 100 and KI ¼ 1000, respectively and the parametersof PI controller 2 ( DC link voltage control) are KP ¼ 0.01and KI ¼ 0.1, respectively. The voltage is balanced sincethe load now draws balanced current from the utility andthe magnitude is increased (Fig. 5b).

From t ¼ 0.8 s to t ¼ 1.2 s, the integrated compensation isperformed. The reference line-to-neutral rms voltage is set to277 V. The actual voltage is regulated at 277 V and balanced.As the control diagram shown in Fig. 4, the parameters of PIcontroller 1 (non-active current control) are KP ¼ 80 andKI ¼ 1000, respectively, the parameters of PI controller 2(DC link voltage control) are KP ¼ 0.01 and KI ¼ 0.1,respectively and the parameters of PI controller 3 (PCCvoltage control) are KP ¼ 2 and KI ¼ 20, respectively.With the integrated control, the source current is leadingthe voltage because there is some non-active powerprovided by the compensator to the utility to boost thevoltage and the magnitude of the source current isincreased some as shown in Fig. 5e. At both the currentcompensation and the integrated compensation, thecompensator current is unbalanced and more non-activecurrent is flowing to the system at the integratedcompensation condition. Choosing too large controllergains can result in instability issues and controller gains are

Table 1 Voltage and current unbalance control

Controlschemes

Compensationresults

Load unbalance Voltage source unbalance

voltage control source current balanced, pf = 1 unbalanced, pf = 1

PCC voltage balanced, regulatedmagnitude

balanced, regulated magnitude

current control source current balanced, pf ¼ 1 balanced, pf ¼ 1

PCC voltage balanced, unregulatedmagnitude

unbalanced, unregulated magnitude

integratedcontrol

source current balanced, pf = 1 balanced, pf = 1 unbalanced, pf = 1

PCC voltage balanced, regulatedmagnitude

unbalanced, regulatedmagnitude

balanced, regulatedmagnitude

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to some degree based on expected load current unbalance orresulting voltage unbalance.

As listed in Table 1, the voltage or the source currentbalance can be achieved using either current control orvoltage control. In current control, the voltage magnitude isnot regulated, but the source current is controlled to unitypower factor, whereas in integrated control, the voltagemagnitude is regulated, but the source current is notcontrolled to unity power factor (usually a leading power

factor because non-active power is provided to the utility toboost the voltage).

5.2 Voltage source unbalancecompensation

If the voltage source is unbalanced, the current compensationcan make the source current balanced and unity power factor,whereas the voltage compensation can make the voltagebalanced and magnitude regulated, as shown in Table 1. If

Figure 5 Load current unbalance compensation (simulation)

a Load current (A)b PCC rms voltage (V)c Source current (current control)d Source current (integrated control)e Source current rms (A)f compensator current rms (A)

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the integrated control is used, either a balanced source currentor a balanced voltage can be achieved, depending on thecompensation objective.

Fig. 6 shows the simulation results of the current controland the integrated control with balanced voltage ascompensation objective. The PI controllers’ parameters arethe same as in the case presented in the previous Section.The load current is shown in Fig. 6a with phase a voltage.The load current is lagging the voltage and is slightly

unbalanced because of the unbalanced voltage. There is nocompensation from t ¼ 0 s to t ¼ 0.4 s and the rms valuesof the voltage, the source current and the compensatorcurrent are shown in Figs. 6b, e and f, respectively.

Current compensation is performed from t ¼ 0.4 s tot ¼ 0.8 s and the source current is balanced and unitypower factor (in phase with the voltage). The voltage is stillunbalanced since the compensator only provides thecompensation of the load current unbalance and non-active

Figure 6 Simulation of voltage source unbalance compensation (balanced voltage is desired)

a Load current (A)b PCC rms voltage (V)c Source current (current control)d Source current (integrated control)e Source current rms (A)f Compensator current rms (A)

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power and the unbalance in the voltage remains. Themagnitude of the voltage is increased. The load now drawsbalanced current from the utility despite the unbalancedvoltage. This is done by choosing the positive sequence ofthe voltage as the reference voltage vp(t) in (5). Fromt ¼ 0.8 s to t ¼ 1.2 s, the integrated compensation isperformed with the reference line-to-neutral rms voltage setto 277 V. The voltage is regulated at 277 V and balanced.The source current is leading the voltage because there issome non-active power provided by the compensator to theutility and the source current is not balanced as shown inFig. 6e. For both the current compensation and theintegrated compensation, the compensator current isunbalanced and more non-active current is flowing to thesystem at the integrated compensation condition.

Fig. 7 shows the simulation results of the integratedcontrol with balanced source current as the compensationobjective. There is no compensation from t ¼ 0 s tot ¼ 0.2 s and integrated control from t ¼ 0.2 s to t ¼ 0.8 s.The average value of the three-phase rms voltages isregulated at 277 V; therefore the non-active power providedfrom the compensator is equal in each phase. Fig. 7c showsthe source current, which is leading the voltage. In Fig. 7d,


it shows that the source current is nearly balanced whenthe integrated control is performed. The reason that theunbalance is not completely compensated is because of thelimited DC link voltage of the inverter. In the simulation,the DC link voltage is already set at 2200 V, which ismuch higher than the minimum DC voltage requirement(784 V) mentioned at the beginning of this section.Because of the unbalanced three-phase output of theinverter current, a very high DC link voltage is required togenerate a much higher inverter output voltage vc than thePCC voltage vt. If the inverter only performs balancedcompensation, the DC link voltage can be much lower(1000 V in the simulations).

6 Experimental resultsA Powerex POW-R-PAKTM configurable insulated gatebipolar transistor (IGBT)-based three-phase inverter wasused as the inverter for the STATCOM. The ac systemvoltage rating is 208 V (line-to-line rms value). The DClink voltage of the inverter is 450 V. DanfysikULTRASTABw 866 current transducers were used formeasuring the load current and the compensator current.LEM CV 3–500 voltage transducers were used for

Figure 7 Simulation of voltage source unbalance compensation (balanced source current is desired)

a Load current (A)b PCC rms voltage (V)c Source current (integrated control)d Source current rms (A)


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measuring the PCC voltage and the inverter DC link voltage.dSPACE, a real-time control platform, is used to implementthe Simulink controller on hardware to perform the real-timecontrol of the compensator. In all the experiments, the DClink voltage control loop parameters are KP ¼ 0.2 andKI ¼ 0.05, respectively.

6.1 Load unbalance compensation

An unbalanced resistive and inductive (RL) load is tested inthis experiment. The inductors of the RL load are not equalin each phase; therefore the three-phase load currents are notbalanced, as shown in Fig. 8b. The system line-to-neutralrms voltage is 120 V. The load resistor is 10.8 V in eachphase and the load inductors are 30, 10 and 10 mH,respectively. The coupling inductor is 10 mH in eachphase; the DC link voltage is 450 V. The three-phasesystem voltages are balanced, which is shown in Fig. 8a.The source current after compensation together with thephase a voltage is shown in Fig. 8c. The source current isnearly balanced compared to the load current and in phasewith the voltage. The compensation current is shown inFig. 8d, which is unbalanced and 908 out of phase with thevoltage. Current control is used in the experiment, that is,the compensation objective is to provide the unbalancecomponent and the non-active component in the load

Power Electron., 2010, Vol. 3, Iss. 6, pp. 977–988: 10.1049/iet-pel.2008.0094

current so that the source current is balanced and unitypower factor.

Current control is used in the experiment, that is, thecompensation objective is to provide the unbalancecomponent and the reactive component in the load currentso that the source current is balanced and unity powerfactor. The PI controller parameters are KP ¼ 40 andKI ¼ 1, respectively.

The unbalance of the three-phase currents is calculated as

Iunbalance =max{|Ia − Ib|, |Ib − Ic|, |Ic − Ia|}

Avg(Ia, Ib, Ic)(16)

where

Avg(Ia, Ib, Ic) = (Ia + Ib + Ic)/3 (17)

The rms values of the three-phase load currents and thesource currents after compensation are listed in Table 2.The unbalance of the load currents and the sourcecurrents is also listed in the table. The unbalance of theload current is 38.97% and the unbalance of the sourcecurrent is improved to 4.92% after compensation. A seriescompensator is a more effective method to compensatevoltage source unbalance than this parallel compensator.

Figure 8 Three-phase unbalanced RL load compensation (experiment)

a System voltage against (t)b Load current il (t)c Source currentd Compensation current ic (t)

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6.2 Single phase load on three-phasesystem compensation

Fig. 9 shows a single-phase load in a three-phase system. Fig. 9ais the three-phase system voltage, which is fundamental,sinusoidal and balanced. An RL load is connected betweenphases a and b and the three-phase load currents are shownin Fig. 9b. The phase a current and the phase b current areequal in magnitude and opposite in phase and the phase ccurrent is zero. The rms values of the load currents arelisted in the second column in Table 3. The rms value ofphase c current is not zero because of the measurementerror and noise. This single-phase load in a three-phasesystem can be viewed as an extreme case of load current

Table 2 RMS values of current unbalance compensation

Il, A Is, A

Phase a 8.06 8.11

Phase b 9.00 7.95

Phase c 11.81 8.35

Iunbalance, % 38.97 4.92

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unbalance. The unbalance of the three-phase load currentsis listed in Table 3, which is 137.17%.

Current control is used in the experiment. The PI controllerparameters are KP ¼ 40 and KI ¼ 1, respectively. The sourcecurrent after compensation is shown in Fig. 9c. Themagnitudes of phase a and phase b source currents are reducedand there is a current in phase c. The rms values of the three-phase source currents are shown in the third column ofTable 3 and the unbalance of the source current is improvedto 22.42%. The values of phases a and b are reduced and thethree phases are more balanced after compensation.

Table 3 RMS current values of single-phase loadcompensation

Il, A Is, A

Phase a 7.20 4.44

Phase b 7.22 4.97

Phase c 0.43 3.97

Iunbalance, % 137.17 22.42

Figure 9 Single-phase load in a three-phase system (experiment)

a System voltage against (t)b Load current il (t)c Source current is (t)d Compensation current ic(t)


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7 ConclusionsA three-phase IGBT-based STATCOM is proposed forvoltage and/or current unbalance compensation. Aninstantaneous power theory is used for real-time calculationand control. Three control schemes – current control,voltage control and integrated control – are proposed tocompensate unbalanced voltage, unbalanced current or both.

The instantaneous power theory is suitable for STATCOMapplication, because it can provide real-time calculation andcontrol for the compensator. The definitions of instantaneousactive current and instantaneous non-active current arefeasible for voltage and current unbalance compensationbecause the definitions of the three-phase voltages andcurrents are independent of each other.

Three control schemes are proposed. Either currentunbalance (caused by the load) or voltage unbalance(caused by other loads or generators in the system) can becompensated using the STATCOM. Differentcompensation objectives can be achieved, that is, balancedand unity power factor source current, balanced andregulated voltage or both, by choosing appropriate controlschemes. The integrated control has the flexibility toimplement current control and voltage control separately ortogether. Thus, a STATCOM can perform both voltageunbalance compensation and/or current unbalancecompensation without any hardware reconfiguration, whichbrings flexibility to the compensation system and reducescapital costs. In practice, because of the limited DC linkvoltage, sometimes the STATCOM cannot achieve 100%compensation.

8 AcknowledgmentsThis manuscript has been prepared by the Oak RidgeNational Laboratory, Oak Ridge, Tennessee 37831,managed by UT-Battelle for the US Department of Energyunder contract DE-AC05-00OR22725.

The submitted manuscript has been authored by acontractor of the US Government under Contract No.DE-AC05-00OR22725. Accordingly, the US Governmentretains a non-exclusive, royalty-free license to publish fromthe contribution, or allow others to do so, for USGovernment purposes.

9 References

[1] JAIN S.K., AGARWAL P., GUPTA H.O.: ‘A control algorithm forcompensation of customer-generated harmonics andreactive power’, IEEE Trans. Power Deliv., 2004, 19,pp. 357–361

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issn 1755-4535 voltage and current unbalance compensation

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