TIME DOMAIN MODELLING AND ANALYSIS OF A COUPLEDDVR-STATCOM (UPFC) SYSTEM

Norberto Garcia Manuel Madrigal Enrique Acha

Department of Electronics & Electrical Engineering

University of Glasgow

Glasgow, Scotlandnorberto@elec.gla.ac.uk madrigal@elec.gla.ac.uk eacha@elec.gla.ac.uk

Abstract: The harmonic interaction of the DynamicVoltage Restorer (DVR) and the Static SynchronousCompensator (STATCOM) with their associated cou-pling transformers’ non-linearities is presented in thispaper. Henceforth, the analysis of these controllers hasbeen reported in the open literature by separate, takingno account of the harmonic interactions between themnor of their interactions with their associated trans-formers. Aiming at advancing the state of the art, thispaper presents a three-phase model for the DVR, theSTATCOM and the coupling transformers, which aredescribed by a set of ordinary differential equations,and used to study power quality and harmonics prob-lems. The DVR and the STATCOM are connected ina back-to-back tie scheme sharing a DC-link capacitor.The STATCOM provides the active power required tomaintain constant DC-link voltage and the DVR injectsa voltage in series with the load in order to compensatefor voltage sags and swells.

Keywords: Time domain simulations, DVR, STAT-COM, PWM, transformer non-linearities.

1 INTRODUCTION

One of the key aspects of power quality improvement inpower systems is the mitigation of voltage sags and swells.The development of the DVR based on Voltage SourceConverters (VSC) has made possible to protect customerswith critical loads from such voltage disturbances. Theuse of two synchronous voltage sources, one shunt con-nected and the other series connected, working in a co-ordinated fashion has been proposed in [1], and termedunified power flow controller (UPFC). In [2] the authorspresent the benefits of applying Static Synchronous Se-ries Compensators (SSSC) for power quality in transmis-sion systems, carrying out comparisons with more conven-tional solutions based on the use of thyristor-switched andthyristor-controlled series compensators. In [3], the ba-sic principles of UPFC operation have been extended toprovide not only shunt compensation, series compensationand phase shifting, but also harmonic isolation in the pres-ence of nonlinear loads. The study of a DVR response

using a low-level model and PSPICE is presented in [4],where the benefits and drawbacks of these kinds of con-verters are discussed.

In this paper, the DVR and the STATCOM, which arePWM-based converters, are modelled in C++ using a mod-ular approach, which enables simple structures of the sys-tem to be solved by dividing it into a number of subcircuits.

2 DVR-STATCOM MODEL

Fig. 1 shows the simplified schematic diagram for theDVR-STATCOM model. The objective of the STATCOMis to either supply or absorb active power to maintain con-stant DC-link voltage. The DVR operates very much likean AC generator, which supplies a series voltage during theevent of a sag or a swell in the incoming feeder.

As illustrated in Fig. 1 the main elements of the DVR-STATCOM model are the VSC, the shunt and series trans-formers and the control systems.

Bearing in mind that the aims of the STATCOM andDVR control systems are quite different, and that the shuntand series transformers may have different configurations,it is sensible from the modelling point of view to developa basic block model which includes the VSC, transformerand DC-link capacitor. Such a basic structure can then beused to represent not only the structure of a wide range ofSTATCOMs but also to represent a wide range of DVRs.This model has well defined variables which facilitate theinclusion of the transformer’s connection, turns ratio andPWM switching frequency. The section below describesthe model and associated control systems for the STAT-COM and DVR.

2.1 Transformer model

The shunt transformer in Fig. 1 is modelled as a delta-wyethree-phase transformer consisting of three single-phasetransformers. The series transformer also taken to consistof three single-phase transformers. Fig. 2 shows the equiv-alent circuit of one of the single-phase transformers usedin this research. Applying Kirchhoff voltage and currentlaws to this circuit the following three basic equations canbe obtained,

control systemDVR

control systemSTATCOM

STATCOM

DVR

Figure 1: Simplified schematic diagram for the DVR-STATCOM system.

� � ���� � �����

��� �� (1)

�� � ������ � �������

��� ��� (2)

�� � �� � �� � �� (3)

where

� ��

�

(4)

also,

�� � ���� (5)

Solving eqs. (1) and (2) for �� and �� respectively,

���

���

� � ��� � ��� �� � �� ��� � ���

��(6)

���

������� �

����� � ��

��� � �� ��� � ���

����(7)

Besides, the flux linkage associated with the magneticnon-linear characteristic of the core can be expressed as

�� ���

��(8)

Substituting eqs. (3) and (5) into (8), leads to the fol-lowing result,

��

��� �� ��� � �� � ��� (9)

The single-phase transformer saturation characteristic isrepresented by means of a polynomial characteristic. Itcorresponds to one leg of the three-phase transformer mea-sured in [5], which is well fitted by the following polyno-mial equation,

�� � ������ � ��������� �� � (10)

Therefore, the three-phase model for the delta-star con-nected transformer is given in Appendix A.

N1 2N

+

−

+

−

+

−

+

−

Ideal

2 2

’

22

2ea e

i

vv

i

lr

i

a l

i i

a r

r

p p s s

p s

c m

s

c

Figure 2: Equivalent circuit for a single-phase transformerwith parameters referred to the primary side.

2.2 VSC model

The VSC used in the STATCOM model is a three-phasesix pulse bridge, whereas the VSC used in the DVR com-prises three single-phase bridges to enable the DVR to in-ject individual series voltages to correct unbalanced sagsand swells.

Neglecting losses in the semiconductor switches, theVSC model may be represented by the following voltageand current relationships [6] [7],

�� ��

����

�� �

�� ��

����

�� ��� (11)

and

��� ���� �� ��

� �� ������

�� (12)

where ��, �� and �� are the switching functions that gov-ern the VSC.

The ordinary differential equation of the DC-link is,

����

���

�

���� (13)

where � is the capacitance of the DC capacitor.

3 Control schemes

In the PWM control scheme, the switching signals are ob-tained by comparing a sawtooth wave of frequency �� andthree sine waves of main frequency ��, according to thefrequency-modulation ratio ��

�� ���

��(14)

When the amplitude of the three sine waves is varied(���� ) with respect to the amplitude of the sawtoothsignal (�������), the amplitude modulation ratio is de-fined as

�� ����� ������� (15)

controlV^

PrefaultMaximum

DetectorFaultn+1

n

1

yy

Vdc

LLV

α , PWM

Figure 3: Fault detection for the DVR.

For the three single-phase VSCs used in the DVR, threeindependent amplitude modulation ratios are required.

3.1 DVR control system

Fig. 3 shows the control system used in the DVR for volt-age sag and swell mitigation. The control system basicallydetermines the amplitude and phase angle of the voltageto be injected by permanently monitoring the evolution ofthe voltages at the point of common coupling (PCC). Oncethe fault is detected, the series voltage to be injected is de-termined by comparing fault and prefault voltages at PCC.The DC-link voltage plays a key role in DVR operationand its rms value is fedback as an additional variable ofthe control system.

It is recommended in [8] that the line-to-line rms volt-age at the fundamental frequency in a three-phase PWMscheme should be expressed as,

�����

��

�������� �

��

���

��������

������� (16)

Therefore,

�������� ����

��

����

����

���(17)

where ����is the injected rms voltage at the fundamen-

tal frequency, ���� is the amplitude of the triangular signaland ��� is the rms voltage in the DC-link capacitor. Also,� is the phase angle of the PWM output signal.

3.2 STATCOM control system

The control system’s main aim is to enable a smooth op-eration of the VSC and to produce a synchronous outputvoltage waveform which not only forces the exchange ofreactive power but also the active power exchanged re-quired to maintain a constant DC-link voltage. A basicapproach for the indirect control of reactive power outputcan be implemented by varying the DC capacitor voltage.Alternatively, direct control may be exerted by controllingthe internal voltage, in which case the voltage in the capac-itor is kept constant (PWM converter) [9]. In [10], variousfeedback control strategies are presented to control the re-active power exchanged, with the voltage in the capacitorbeing controlled indirectly. The design of a STATCOMusing EMTP simulations, which varies the voltage in theDC capacitor, is presented in [7]. A decoupled control of

0

0

π α

+

+

−

−

2π

Comparison

ComparisonV

ODEs

K

KV

V

V

e

e V

VV

PI

PI Amplitude

anglePhase

pattern

ramp

ramp

dcdc_ref

ref

rms

rms

dc

dc

1

2pcc

ydc

control

Switching

ypcc

Figure 4: Structure of the control system.

the active and reactive powers exchanged between a STAT-COM using PWM and the electric system is presented in[11]. The control system presented in this paper, shown inFig. 4, is an alternative solution. The key functions of thiscontrol system are to maintain constant voltage at the PCCand to keep constant voltage at the DC capacitor. Thesetwo tasks are carried out by means of two independent PIcontrollers. Since the output signals of these controllersare used to generate the switching pattern of the VSC, theoutput signals are the phase angle and amplitude of the sinewaves used by the PWM scheme.

As shown in Fig. 4, the error signals are

��� � ������� � ��� (18)

� �� � ���� � ���� (19)

The ODEs for the two controllers can be expressed as

����

������ � �� ���

(20)

�� ��

���� �� � �� � ��

(21)

and

�� � � � �� � � �� � ��� (22)

�� � � � �� � � �� � � �� (23)

where� constant in PI controller time constant in PI controllerSince the rms values for the voltages are updated every

seconds, being the period of the system, �� � � and �� � � are also updated at each period �.

The signals ��� and � �� are compared with ramps sig-nals and multiplied by constants �� and ��, respectively,in order to obtain the angle � and the amplitude ��������within PWM control scheme limits.

4 CASE STUDIES

Fig. 5 shows a three phase system which feeds a linear loadthrough an equivalent transmission line. A fix capacitorbank is used as well as a DVR-STATCOM for voltage sagand swell mitigation.

VSCshunt seriesVSCn:

1

PCC

V

CAPACITOR

Vseries

load

SHUNT STATCOM DVR LOAD

Figure 5: Test system.

4.1 Analysis of the transient response of theshunt transformer

Large inrush currents have been reported in the shunt-connected transformer, after fault clearing, of a full sizeUPFC prototype [12] . This phenomenon is closely relatedto STATCOM operation, in particular, its transformer en-ergization. This has provided the motivation for carryingout the study reported in this section.

The STATCOM control system maintains constant volt-age at the DC-link capacitor and is also responsable forthe exchange of reactive power with the external systems.This is done by varying the �� relation in the PWM con-trol scheme. Taking into account this characteristic, Fig.6 shows the first cycle of the inrush current injected bythe STATCOM when the VSC produces a fundamental-frequency voltage (� �������� ) at its terminals of 0.7, 1and 1.3 p.u., respectively for 1 p.u. at the PCC. Further-more, the impact of varying the relation �� is also shownin these figures, for �� � �� ��� ��� ��� . Moreover,the ideal case is also shown in this figure, at �� � ��,which corresponds to a purely sinusoidal waveform gener-ated by the VSC.

It can be observed from this figure, that at low valuesof �� , the inrush current presents distortion mainly dueto the VSC. Ans when the � �������� is larger than thevoltage at PCC, the distortion is dominated by those har-monics generated by the transformer saturation. It shouldbe noticed that this should be the case when the STATCOMinjects reactive power. The critical condition is for low��

and large � �������� .The peaks of the first cycle of the inrush currents have

values of 3.2, 0.01 and 3.1 p.u. for phase a, b and c, respec-tively, when the transformer is operated in open-circuit (re-sults not shown). However, the peaks of the inrush currentsare attenuated when the � �������� is connected to thetransformer. The control of the reactive power injection

9

27

45

63

81

99

0.05 0.052 0.054 0.056 0.058 0.06 0.062 0.064 0.066

−2

−1

0

1

2

3

4

mf

time, s

Cur

rent

, p.u

.

Phase A

(a)

9

27

45

63

81

99

0.05 0.052 0.054 0.056 0.058 0.06 0.062 0.064 0.066

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

mf

time, s

Cur

rent

, p.u

.Phase A

(b)

9

27

45

63

81

99

0.05 0.052 0.054 0.056 0.058 0.06 0.062 0.064 0.066

−3

−2

−1

0

1

2

3

mf

time, s

Cur

rent

, p.u

.

Phase A

(c)

Figure 6: Inrush current vs � �������� .

0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.30

100

200

300

400

% T

HD

i

0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3−40

−20

0

20

40

% IP

N

0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.30

40

80

120

% T

HD

i

0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3−1

0

1

% IP

N

0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.30

100

200

300

Voltage VSC Fund., p.u.

% T

HD

i

0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3−40

−20

0

20

% IP

N

Phase A

Phase B

Phase C

Figure 7: ����� and ���� vs � ������� .

is achieved by adjusting the voltage � ������� , whereincreases in reactive power injections are achieved by in-creasing � ������� . It is observed that this also resultsin attenuation of the inrush currents but at the expense ofgenerating harmonic distortion. A condition that seems toattenuate inrush currents while keeping a reasonably lowharmonic distortion is when the voltage � ������� equalsthe voltage at PCC.

Fig. 7 summarizes the effects on the inrush currents ofvarying the voltage � ������� from 0.7 to 1.3 p.u. Forthe computation of the ����, Fast Fourier Transforms(FFT) were applied assuming that the first cycles of theinrush currents were periodic. Moreover, Fig. 7 showsthe peak of the inrush current for each phase normalized,with respect to the peak of the inrush current, when thetransformer is energized in open-circuit (%IPN). As ob-served from Fig. 7 phase a, for a voltage � �������

equal to 1 p.u., the %IPN decreases by approximately 20%,with the ����� being 100%. If the voltage � �������

is increased the %IPN is further reduced but at the ex-pense of increasing the �����. Conversely, if the volt-age � ������� is reduced then the %IPN is increased and����� is reduced. The response of phase c is similarto the phase a. The %IPN of phase b shows an almostconstant value around 0%, this is due to the fact that thecurrent at fundamental frequency is to small (no reactivepower transfer) compared with the harmonics generated bythe VSC.

4.2 Analysis of the relation between the seriestransformer and its VSC

It is well accepted that the fundamental-frequency com-ponent in the output voltage of a PWM three-phase VSCvaries linearly with � (for � � ���) [8]. Also, the har-monics are centered around � and its multiples. How-ever, the amplitudes of these harmonics do not vary lin-early with �.

In order to study the harmonic distortion introducedby the DVR into the AC system during mitigation of

1 2 30

50

100

150

200

% T

HD

v

1 2 30

0.1

0.2

0.3

0.4

Vfu

nd

1 2 30

0.25

0.5

0.75

1

% T

HD

v

1 2 30

0.025

0.05

0.075

0.1

Vfu

nd

1 2 30

50

100

150

200

turns ratio

% T

HD

v

1 2 30

0.1

0.2

0.3

0.4

Vfu

nd

Phase A

Phase B

Phase C

Figure 8: THDv at ���� vs turns ratio.

voltage disturbance at PCC, the turns ratio of the trans-former is varied and the control system adjusts the voltage� ���� taking due account of the transformer’s turnsratio.

Fig. 8 shows the %THD and the fundamental-frequencycomponent ������ of ���� . From this figure, it can beobserved that the %THDv decreases almost linearly withincreases in turns ratio. It should be remarked that the%THDv observes this behaviour since when the turns ra-tio is increased the control system of the DVR determinesa higher � to compensate the disturbance.

Turns ratio of 1, 2 and 3 correspond to values of � �

����� ����� ��� for a 30% sag and � � ���� ����� ����

for the 20% swell, respectively. As seen from the resultsshown in Fig. 8, %THD reduces almost linearly when �

increases.

4.3 Dynamic performance of the combinedDVR-STATCOM system

The test system shown in Fig. 5 is simulated with noSTATCOM during the first three cycles of simulation. TheSTATCOM is switched on just after the third cycle pro-ducing a fundamental-frequency component in the voltage� ������ equal to 1 p.u. using a � � ��. The seriestransformer uses a turn ratio of 2:1.

Fig. 9 shows the time domain solution of the currentsinjected by the STATCOM. As observed from this figure,inrush currents appear in the shunt transformer when theSTATCOM is switched on after the third cycle. The pe-riodic steady-state solution of the system takes place afterthe 33rd cycle and for the next 17 cycles. After the 50th cy-cle, and for the next 10 cycles, a 30% sag and a 20% swelloccur at PCC in phases and �, respectively. To counteractthese faults the DVR responds by injecting a series voltagein order to mitigate the voltage fault. Figs. 10 and 11 showthe time domain solution of voltage � ��� and a close upof voltage � ��� during fault mitigation. Figs. 12 and 13show the current across the load and the DC-link voltage,respectively.

0 0.2 0.4 0.6 0.8 1 1.2−4

−2

0

2

4

time, s

Cur

rent

, p.u

.

0 0.2 0.4 0.6 0.8 1 1.2−0.4

−0.2

0

0.2

0.4

time, s

Cur

rent

, p.u

.

0 0.2 0.4 0.6 0.8 1 1.2−4

−2

0

2

time, s

Cur

rent

, p.u

.STATCOM on Steady−State Fault Fault clearing

Phase A

Phase B

Phase C

Figure 9: STATCOM currents.

From Fig. 9 it can be observed that during the fault con-dition larger currents, compared with the prefault currents,flow in the shunt transformer. This effect is associated withthe fact that during the fault condition, the STATCOM isconnected at PCC with unbalanced voltages. The pres-ence of these currents during fault condition may be avoidif a STATCOM with three single-phase converters is usedinstead of a single three-phase converter, since individualcontrol phase may be achieved.

It can also be observed from Figs. 9 and 12 that the in-rush current injected at PCC does not influence the loadcurrent thanks to the adequate performance of the STAT-COM control system which maintains constant DC-linkvoltage (see Fig. 13). This figure shows a small ripplein the DC-link voltage during the fault. Furthermore, thecontrol system implemented for the DVR is good enoughtto maintain constant the load current during the sag andswell, as it can be observed in Fig. 12. From Figs. 10and 11 it can be observed that the voltages ������� injectedby the three single-phase converters cause harmonic distor-tion associated with the�� and the unipolar PWM schemeused.

5 CONCLUSIONS

A new time domain model for the coupled DVR-STATCOM system has been presented in this paper in or-der to study power quality and harmonic problems. Thethree-phase model includes VSCs, transformers and con-trol system, which are applied to mitigate voltage sags andswells.

Interactions between the VSC and transformers havebeen studied. Typical inrush currents in the shunt trans-formers have been detected during STATCOM switching.The influence of an adequate control of �� and �� in theVSC transient currents has been demonstrated.

No effects have been detected on the DVR during STAT-COM inrush currents. This is due to the correct perfor-mance of the STATCOM control system which maintains

0 0.2 0.4 0.6 0.8 1 1.2−2

−1

0

1

2

time, s

Vol

tage

, p.u

.

0 0.2 0.4 0.6 0.8 1 1.2−2

−1

0

1

2

time, s

Vol

tage

, p.u

.

0 0.2 0.4 0.6 0.8 1 1.2−2

−1

0

1

2

time, s

Vol

tage

, p.u

.

Phase A

Phase B

Phase C

Figure 10: Voltages at ����.

0.9 0.905 0.91 0.915 0.92 0.925 0.93−2

−1

0

1

2

time, s

Vol

tage

, p.u

.

0.9 0.905 0.91 0.915 0.92 0.925 0.93−2

−1

0

1

2

time, s

Vol

tage

, p.u

.

0.9 0.905 0.91 0.915 0.92 0.925 0.93−2

−1

0

1

2

time, s

Vol

tage

, p.u

.Phase A

Phase B

Phase C

Figure 11: Voltages at ����.

0 0.2 0.4 0.6 0.8 1 1.2−0.2

−0.1

0

0.1

0.2

time, s

Cur

rent

, p.u

.

0 0.2 0.4 0.6 0.8 1 1.2−0.2

−0.1

0

0.1

0.2

time, s

Cur

rent

, p.u

.

0 0.2 0.4 0.6 0.8 1 1.2−0.2

−0.1

0

0.1

0.2

time, s

Cur

rent

, p.u

.

Phase A

Phase B

Phase C

Figure 12: Load currents.

0 0.2 0.4 0.6 0.8 1 1.21

1.1

1.2

1.3

1.4

1.5

1.6

time, s

Vol

tage

, p.u

.DC link

Figure 13: DC link voltage.

constant DC-link voltage even in the presence of inrushcurrents, and also the system configuration. Besides, theDVR control system feedsback the DC-link voltage in or-der to considered any posible fluctuation in this voltage.

The harmonic distortion introduced by the DVR duringvoltage mitigation is closely associated with turns ratio ofthe series transformer, ��, �� and the PWM scheme im-plemented.

References

[1] L. Gyugyi, “Dynamic Compensation of AC Trans-mission Lines by Solid-State Synchronous VoltageSources”, IEEE Transactions on Power Delivery, Vol.9, No. 2, pp. 904-911, April 1994.

[2] L. Gyugyi, C.D. Schauder and K.K. Sen, “Static Syn-chronous Series Compensator: A Solid-State Ap-proach to the Series Compensation of TransmissionLines”, IEEE Transactions on Power Delivery, Vol.12, No. 1, pp. 406-417, January 1997.

[3] J.H.R. Enslin, J. Zhao and R. Spee, “Operation of theUnified Power Flow Controller as Harmonic Isola-tor”, IEEE Transactions on Power Electronics, Vol.11, No. 6, pp. 776-784, November 1996.

[4] G.T. Heydt, W. Tan, T. LaRose and M. Negley,“Simulation and Analysis of Series Voltage BoostTechnology for Power Quality Enhancement”, IEEETransactions on Power Delivery, Vol. 13, No. 4, pp.1335-1341, October 1998.

[5] E.P. Dick and W. Watson, “Transformer Models forTransient Studies Based on Field Measurements”,IEEE Transactions on Power Apparatus and Systems,Vol. PAS-100, No.1, pp. 409-419, January 1981.

[6] E. Acha and M. Madrigal, “Power Systems Harmon-ics”, John Wiley & Sons, 2001.

[7] B. Han, G. Karady, J. Park and S. Moon, “Interac-tion Analysis Model for Transmission Static Com-pensator with EMTP”, IEEE Transactions on PowerDelivery, Vol. 13, No. 4, pp. 1297-1302, October1998.

[8] N. Mohan, T.M. Undeland and W.P. Robbins, “PowerElectronics: Converters, Applications and design”,John Wiley & Sons, 1995.

[9] N.G. Hingorani and L. Gyugyi, “UnderstandingFACTS: Concepts and Technology of Flexible ACTransmission Systems”, IEEE Press, 2000.

[10] P. Rao, M.L. Crow and Z. Yang, “STATCOM Con-trol for Power System Voltage Control Applications”,IEEE Transactions on Power Delivery, Vol. 15, No. 4,pp. 1311-1317, October 2000.

[11] P. Garcia and A. Garcia, “Control System for aPWM-Based STATCOM”, IEEE Transactions onPower Delivery, Vol. 15, No. 4, pp. 1252-1257, Oc-tober 2000.

[12] C. Schauder, L. Gyugyi, M. Lund, D. Hamai, T. Ri-etman, D. Torgerson and A. Edris, “Operation of theUnified Power Flow Controller (UPFC) Under Prac-tical Constraints”, IEEE Transactions on Power De-livery, Vol. 13, No. 2, pp. 630-639, April 1998.

Appendix A

�

��

��������������

���������������������

���

���

��������������

� �

��������������

������������������

������������������

��������������

�

��������������

������

���������������

��������������

(24)

where matrix A is defined as,

� �

������������

�� � � �� � � �� � �

� �� � � �� � � �� �

� � �� � � �� � � ����

��� � �� � � ��� � �

���

��� � �� � � ��� �

� ���

��� � �� � � ���

��

��� � ��� � � ��� � �

���

��� � ��� � � ��� �

� ���

��� � ��� � � ���

������������

(25)

where � ���������

�, � �

�������������

, � � �����

,and ��, �� and �� are the line voltages on the delta sideof the transformer.