IET Generation, Transmission & Distribution

Research Article

Variation of UPFC controllable parametersduring power swing and their impacts ondistance relay

ISSN 1751-8687Received on 31st August 2016Revised 5th January 2017Accepted on 27th January 2017doi: 10.1049/iet-gtd.2016.1375www.ietdl.org

Jalal Khodaparast1, Mojtaba Khederzadeh1 , Filipe Faria da Silva2, Claus Leth Bak2

1Electrical Engineering Department, Shahid Beheshti University, Tehran 165895371, Iran2Department of Energy Technology, Aalborg University, Aalborg 9220, Denmark

E-mail: m_khederzadeh@sbu.ac.ir

Abstract: Unified power flow controller (UPFC) has impact on the performance of distance relay during power swing. Generally,power system's parameters oscillate during power swing and since UPFC operation depends on some of these parameters (busvoltage, active and reactive power), the UPFC injects oscillated series voltage and draws oscillated shunt current. Theseoscillating series voltage and shunt current influence distance relays, as the impedance seen by a distance relay during powerswing changes in UPFC-compensated lines. This study shows how and why series voltage and shunt current change duringpower swing. Moreover, the admittance swing characteristic is proposed in this study and effects of series and shunt branchesof UPFC on the admittance seen by a distance relay during power swing have been examined.

1 IntroductionGenerally, it is necessary to evaluate the impacts of flexible ACtransmission systems (FACTS) devices on distance relays indifferent conditions of power system (steady state, fault, transientand power swing). Since FACTS devices lead to variations of linecurrent and bus voltage, they affect the performance of a distancerelay during different conditions [1–5].

Unified power flow controller (UPFC) is a widely knownFACTS device used to control the power flow of a transmissionline and to improve the system stability. In lines with UPFC, aconventional distance relay is influenced in the form of over-reaching or under-reaching the fault point during a short-circuitevent [6, 7]. Many publications are devoted to the evaluation of theperformance of distance relay applied for protection of a linecompensated by FACTS devices. In [8, 9], the impacts of UPFC ondistance relays are discussed and an adaptive protection schemebased on phase component approach and an adaptive protectionscheme using artificial neural network are proposed, respectively.In [10], it is demonstrated that static VAR compensator (SVC) andstatic synchronous compensator (STATCOM) cause mal-operationof the distance relay in calculating the impedance, faulty-phasedetection and also delays in operation. In [11], an adaptive schemeis proposed for protection of transmission line with SVC tomitigate the mal-operation of distance relay. Reference [12]presents a new algorithm based on synchronised measurement foradaptive setting of distance relay in transmission line compensatedby STATCOM. In [13], the impacts of different modes of thyristorcontrolled series compensation (TCSC) on distance relay areanalysed. In [14], a new method is proposed based on post-faultdata for fault analysis in compensated line by TCSC. A methodbased on average of voltage and current and according tosuperimposed current in TCSC-compensated line is proposed in[15]. In [16–19], the effects of series compensations on theperformance of the distance relay are examined.

In spite of extensive research on the impacts of FACTS devicesin the performance of distance relay during a fault, limited worksreport their impacts during a power swing. For example, threemethods for power swing detection, impedance decrease, swingcentre voltage and power derivative are studied in [20] for fixedcapacitor compensated lines. A method based on negative sequencecomponent is proposed in [21] to discriminate the power swingfrom a fault in a fixed capacitor compensated line. In [22], theimpacts of UPFC on the power swing impedance characteristics areexamined, i.e. the variations of the radius and the centre point of

circular characteristic are studied. It is shown that parameters oftransmission line (ABCD) would change in the presence of UPFC.On the basis of the definitions of these parameters and the steady-state model of UPFC, new parameters (A′B′C′D′) are extractedcontaining the data of UPFC.

In this paper, the behaviour and performance of UPFC isexamined during power swing by analysing the variations of UPFCcontrollable parameters (series voltage and shunt current). Thevariations of these parameters are formulated in this paper and it isdemonstrated that consideration of these parameters as constantvalues leads to invalid results (will be explained next) duringpower swing. Another contribution of this paper is proposingadmittance swing characteristic to make analysis easier. Since it ispossible to analyse series and shunt branches impacts individuallyin admittance plane, this plane has been selected and power swingadmittance characteristic is proposed in this paper. Finally, theimpacts of variations of controllable parameters of UPFC onadmittance seen by distance relay are investigated in this paper.

Different cases are defined in simulation section to examine theperformance of UPFC in different ways. Two different powersystems are used in simulation section. The first one is two-machine equivalent system and the second one three-machinepower system. According to these two power systems, five cases(Case 1, Case 2, Case 3, Case 4 and Case 5) are defined. The firstfour cases (Cases 1–4) analyse the performance of UPFC in two-machine equivalent system in different conditions (phasor model ofUPFC and power swing in steady-state condition, phasor model ofUPFC and power swing is simulated by phase modulation, phasormodel of UPFC and power swing is simulated by amplitudemodulation, detailed model of UPFC and power swing is simulatedby phase modulation). The last case (Case 5) analyses theperformance of UPFC in three-machine power system, in whichdetailed model of UPFC is used and power swing is simulated bytriggering and clearing a fault in power system.

2 Power swing admittance characteristicNowadays, most distance relays monitor the apparent impedanceand make decision based on this parameter. However, our reasonfor utilisation of admittance in UPFC-compensated line is only tosimplify the analysis. The admittance plot is more convenient inUPFC-compensated line because it is possible to separate and soanalyses the impact of series and shunt part of UPFC on admittancetrajectory.

IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2017

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It is easier to study the effect of power swing on distance relayby considering two-machine equivalent system as shown inFig. 1a. EA and ZA represent an equivalent network on the left-hand side of the transmission line and EB and ZB on the right-handside. V1 leads V3 by the angle δ1 and V3 is considered as reference.Therefore, admittance seen by the distance relay (inuncompensated line) is (1)

YUN =IrelayVrelay

= |V1 |∠δ1 − |V3 |∠0|V1 |∠δ1

YLine = (1 − ( |k1 |∠ − δ1)

)YLine

(1)

where ( |V3 | / |V1 | ) = k1. On the basis of (1) we have:

(A) Each different ratio of k1 gives a different locus, but all arecircles. The same centre of all circles is (real(YLine), imag(YLine))and their radiuses are k1 ⋅ |YLine|. To demonstrate these conclusions,consider division of (1) by YLine, which results in (2)

YUN

YLine= 1 − k1 cos δ1 + jk1 sin δ1 = X1 + jY1 (2)

It is obvious the relationship between X1 and Y1 is (3)

(X1 − 1)2 + Y12 = k1

2 (3)

By changing 0 ≤ δ1 ≤ 2 ⋅ π, locus of (3) will be a circle with centrein (1, 0) and radius equal to k1. Multiplication of each side of (2)by YLine gives the locus of YUN. So, the amplitude of every point oncircle is multiplied by the |YLine| and its angle is added to ∠YLine.Finally, the locus of YUN will be a circle with constant centre in(real(YLine), imag(YLine)) and radius equal to k1 ⋅ |YLine|. Forexample, three of these circular characteristics (in terms ofk1 = 0.4, 1, 2.5) are shown in Fig. 2a.(B) If the phase difference (δ1) is constant and the magnitude ratio(k1) varies, then the locus of admittance seen by relay is a straightline which is resulted from multiplying a constant complex (CC)value by YLine, which is described in (4)

YUN = (1 − (k1 cos δ1 + jk1 sin δ1))YLine = CCYLine (4)

For example, four of these straight lines (in terms ofδ1 = 45∘, 135∘, 225∘, 315∘) are shown in Fig. 2a.(C) Admittance characteristic of transmission line is straight linewhich is obtained by inverse of line impedance characteristic. Thischaracteristic is also in Fig. 2a.(D) Different zones of a distance relay will be straight linesperpendicular to admittance characteristic of transmission line.Admittance characteristics of all three zones are shown in Fig. 2a.

To sum up, all of four kinds of characteristics mentioned in (A),(B), (C) and (D) sections can be shown in one figure (Fig. 2a).Fig. 2 is also provided to compare the impedance-based andadmittance-based swing characteristics. In Fig. 2, there are foursub-figures which are dually inverted of each other in impedance

and admittance planes. Figs. 2a and b show the general admittance-based swing characteristic and impedance-based swingcharacteristic, respectively. Three different zones of distance relay,swing loci of impedance/admittance for four constant valuesδ1 = 45∘, 135∘, 225∘, 315∘, swing loci of impedance/admittance forthree constant values k1 = 0.4, 1, 2.5. The principle use of thesecurves is that their interactions with impedance/admittancetrajectory serve to make the values of δ1 and k1 on these curves.

In Fig. 2, sub-figures (c) and (d) show an example of theimpedance/admittance trajectory during power swing both foruncompensated (Zun/Yun) and compensated condition (Z /Y). Forinstance just consider the uncompensated ones, when k1 = 1,impedance/admittance starts from δ1 = 45∘ in its first swing,reaches zone 3 and continues going inside of zone 3 and thenreaches till maximum δ1 = 77∘ and then comebacks and this processcontinues until it reaches an equilibrium point. Therefore, it ispossible to analyse the performance of power system during powerswing by both planes (impedance and admittance). However,impacts of series and shunt parts of UPFC on seen admittance areanalysable separately, so it is more practical to use admittanceplane.

3 Admittance seen by distance relay duringpower swing in UPFC-compensated lineIn this section, the admittance seen by a distance relay duringpower swing is examined. Mathematical equations of voltage andcurrent at relay point are extracted and admittance is calculatedbased on these two parameters. Moreover, the calculatedadmittance is analysed to obtain the range of admittance seen bydistance relay during power swing when UPFC operates accurately(i.e. in controllable region).

Consider the compensated equivalent system as shown inFig. 1b. According to this figure, two new parameters, seriesvoltage (Vse) and shunt current (Ish), enter power system as a resultof UPFC performance. In this condition, the relay current (Irelay) is(5)

Irelay = Ise + Ish (5)

where Ise and Ish are currents of series and shunt branches,respectively. Series current is (6)

Ise = |V2 |∠δ2 − |V3 |∠0ZLine

=|V1 |∠δ1 + |Vse | ρ′ − |V3 |∠0

ZLine(6)

where ZLine is the impedance of transmission line, ρ′ is angle Vsewith respect to reference (V3) and voltage at Bus 2 is V2 = |V2 |∠δ2.

The shunt branch of UPFC has two major tasks. The first one issupporting demanded active power for series branch and thesecond one is injecting/absorbing reactive power at Bus 1.Therefore, the shunt current drawn by shunt branch consists of twoparts: one part (Ish

(1)) is drawn to provide demanded active power forseries branch to keep power flow of Bus 2 at its reference valueand the other part (Ish

(2)) is drawn because of reactive powercompensation for shunt branch to keep the amplitude of bus

Fig. 1  Two-machine equivalent system(a) Uncompensated, (b) Compensated

2 IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2017

voltage (|V1|) at its reference value. Therefore, shunt current isobtained as (7)

Ish = Ish(1) + Ish

(2) = | Ish |∠θsh (7)

Admittance seen by distance relay is obtained by Irelay/Vrelay whichgives (8)

Y =IrelayVrelay

=Ise + Ish|V1 |∠δ1

(8)

Therefore, based on (5)–(8), admittance seen by distance relayduring power swing in UPFC-compensated line is (9)

Y = YUN + YSE + YSH

YUN = YLine − YLine|V3||V1|

∠ − δ1

YSE = YLine|Vse||V1|

∠(ρ′ − δ1)

YSH =|Ish||V1|

∠(θsh − δ1)

(9)

where series voltage is Vse = |Vse |∠ρ′ and shunt current isIsh = | Ish |∠θsh. According to (9) and compared to (1), theadmittance seen by a distance relay during power swing incompensated lines includes three parts, where one part is the sameas uncompensated line (YUN) and the other two parts are resultedfrom compensating performance of series (YSE) and shunt (YSH)branches of UPFC during power swing.

To analyse admittance seen by distance relay during powerswing in UPFC-compensated line, it is better to examine each partindividually.

Part1(YUN): Let it first be assumed that both the injected seriesvoltage Vse and the shunt current Ish are zero. Then, the admittance

is similar to (1) described by circles with radius k1 ⋅ |YLine| aroundthe centre defined by (real(YLine), imag(YLine)) in G, B plane.

Part2(YSE): Assume now that Vse ≠ 0 and Ish = 0. It followsfrom (9) that the admittance seen in this condition changes from itsuncompensated value as function of magnitude(|YLine | ⋅ |Vse | / |V1|) and angle (ρ′ − δ1 − θLine), where θLine is theangle of the line impedance. Since this angle is an unrestrictedvariable, the boundary of admittance region for this condition isobtained from a complete rotation of phasor with maximummagnitude r1 [r1 is defined in (10)]. This region is a circle with acentre defined by YUN and the radius of r1

(real(Y(δ1, ρ′) − YUN(δ1)))2 + (imag(Y(δ1, ρ′) − YUN(δ1)))2

=|YLine | |Vse|

|V1| Max

2

= r12

(10)

Part3(YSH): Assume now that Vse = 0 and Ish ≠ 0. The sameexplanation can be made in this condition, with the admittance seenin this condition changing from its uncompensated value asfunction of magnitude (|Ish | / |V1|) and angle of (θsh − δ1). In thiscondition, admittance will be inside of circular region with a centredefined by YUN and the radius of (r2). This region can be describedby (11)

(real(Y(δ1, θsh) − YUN(δ1)))2 + (imag(Y(δ1, θsh) − YUN(δ1)))2

=|Ish||V1| Max

2

= r22

(11)

TOTAL(Y): Now suppose that Vse ≠ 0 and Ish ≠ 0. The admittancein this condition will be the accumulation of previous two circularregions creating a larger circular region with a centre defined byYUN and the radius of (r3). This region is

Fig. 2  Swing characteristic(a) Admittance-based swing characteristic, (b) Impedance-based swing characteristic, (c) Example of the admittance trajectory, (d) Example of the impedance trajectory

IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2017

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(real(Y(δ1, ρ′, θsh) − YUN(δ1)))2 + (imag(Y(δ1, ρ′, θsh) − YUN(δ1)))2

=|YLine | |Vse | + | Ish|

|V1| Max

2

= r32

(12)

The area inside this circle defines all admittance values obtainableby controlling Vse and Ish. These circular regions are shown inFigs. 3a and b. In Fig. 3a, some regions are illustrated when K1 = 1and δ1 is 15∘, 30∘, 45∘, 60∘ and 75∘, whereas in Fig. 3b, some regionsare illustrated when δ1 = 45∘ and K1 = 0.30, 0.65, 1.00, 1.35, 1.70.According to Figs. 3a and b and mathematical formulations (9),admittance characteristic in compensated line will be different fromuncompensated line. In uncompensated line, the admittancetrajectory moves on the uncompensated characteristic. However,by entering new complex values (complex series voltage andcomplex shunt current) in admittance formulation, the admittanceseen by distance relay in UPFC-compensated line deviates from itsuncompensated position. While UPFC operates inside controllableregion, admittance seen by distance relay is inside a circular regionwith centre on uncompensated line admittance (YUN) and radiusmaximum of (r3). The boundary of this region depends on rating ofUPFC.

4 Variations of series voltage and shunt currentduring power swingSince the admittance seen by a distance relay in UPFC-compensated line is related to series voltage and shunt current, it isnecessary to analyse the variations of these parameters duringpower swing. When a power swing occurs in a line which iscompensated by UPFC, the compensation parameters (Vse, Ish)change during time based on UPFC control aims (keep active andreactive power at their references). Therefore, series voltage andshunt current are not CC values and change during power swing.

Consider the compensated equivalent system as shown inFig. 1b with transmission line with impedance ZLine = R + jX. Thecomplex power at Bus 2 (which is controlled by UPFC) is (13)

S2 = V2I2∗ (13)

where S2 is the complex power, V2 is the voltage phasor and I2 isthe current phasor at Bus 2. Since the line currents at the beginningand end of transmission line are equal (I2 = I3), the complex powerat Bus 2 is calculated as (14)

S2 = V2V2

∗ − V3∗

ZLine∗ = |V2 |∠δ2

|V2 |∠ − δ2 − |V3 |∠0ZLine

∗ (14)

On the basis of (14) and by separating the real and imaginary parts,(15) is extracted

real(S2ZLine∗ ) = |V2 |2 − |V3 | |V2 | cos(δ2)

imag(S2ZLine∗ ) = − |V3 | |V2 | sin(δ2)

(15)

Since the control aim of UPFC is to keep the active and reactivepowers at their reference values (S2 = Pref + jQref) and according to(15), identity sin2(δ2) + cos2(δ2) = 1 and by some mathematicalsimplifications we have (16)

a1X2 + b1X + c1 = 0

a1 = 1b1 = − |V3 |2 − 2 imag(S2ZLine

∗ )c1 = real(S2ZLine

∗ )2 + imag(S2ZLine∗ )2

(16)

Therefore, the desired amplitude and phase angle of V2 (forreaching the desired power flow) are (17) and (18)

|V2 | = −b1 ± b12 − 4a1c1

2a1(17)

δ2 = sin−1 imag(S2ZLine∗ )

|V2|(18)

According to (17), there are two values for |V2| based on being + orin - equation. Selection between these two signs is related toachievement of the control objectives of UPFC. Hence, in order toachieve the desired power flow (Pref and Qref) at the compensatedbus (Bus 2), the amplitude and phase of V2 have to satisfy (17) and(18), respectively. On the basis of principle of UPFC, phasor of V2is provided by adding series voltage to V1 as (19)

|V2 |∠δ2 = |V1 |∠δ1 + |Vse |∠ρ′ (19)

When a power swing occurs, V1 changes during power swing andconsequently Vse should change during time [based on (19)] tokeep V2 constant. It is worthy of note that it is assumed changes areinside the controllable region of UPFC, so it can compensate allchanges due to power swing. Therefore, the series voltage iscontrolled voltage source during power swing with amplitude (20)and angle (21)

|Vse(t) |= ( |V2 | cos δ2 − |V1(t) | cos δ1(t))2 + ( |V2 | sin δ2 − |V1(t) | sin δ1(t))2

(20)

ρ′(t) = tan−1 |V2 | sin δ2 − |V1(t) | sin δ1(t)|V2 | cos δ2 − |V1(t) | cos δ1(t)

(21)

Fig. 3  Admittance regions(a) Admittance regions when K1 = 1 and δ1 is 15∘, 30∘, 45∘, 60∘, 75∘, (b) Admittance regions when δ1 = 45∘ and K1 = 0.30, 0.65, 1.00, 1.35, 1.70

4 IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2017

where |Vse(t)|, ρ′(t), |V1(t)| and δ1(t) are time-variant parametersduring power swing and |V2| and δ2 are time-invariant during powerswing.

Shunt current during power swing drawn by the shunt branch ofUPFC consists of two parts (Ish(t) = Ish

(1)(t) + Ish(2)(t)), where Ish

(1)(t) isin-phase with V1 to provide demanded active power in seriesbranch, as described by (22)

Ish(1)(t) =

Psh(t) = Pse(t)|V1(t)|

∠δ1(t) (22)

where Pse(t) = |Vse(t) | ⋅ | Ise | cos(ρ′ − ∠Ise) is needed active powerin series branch which is assumed equal to Psh(t). The other part ofshunt current [Ish

(2)(t)] is perpendicular to V1 and keeps |V1| constantby reactive power compensation (Qsh) (23)

Ish(2)(t) =

Qsh(t)|V1(t)|

∠(δ1(t) ± 90∘) (23)

where ± depends on shunt current mode (+ is related to injection ofreactive power and - is related to absorbing reactive power). On thebasis of (22) and (23), shunt current drawn by UPFC is also time-variant parameter during power swing.

5 Simulation resultsVariations of series voltage and shunt current during power swingand the impacts of these variations on admittance seen by adistance relay during steady state and power swing are examined inthis section. Both fully detailed model of compensated powersystem (power system and UPFC) and its simple model are used inthis section. The simple model is used at the first to illustrate thetheoretical concept more clearly and then detailed model is used tovalidate the results.

To analyse UPFC performance in different conditions, fivedifferent cases are provided. The Case 1 is the assessment of UPFC(phasor model) performance in steady-state condition. The Case 2is simulation of UPFC (phasor model) performance during powerswing (sinusoidal changes of δ1) and the Case 3 consists in thesimulation of UPFC (phasor model) performance during powerswing (sinusoidal changes of |V1|). Case 4 examines theperformance of detailed model of UPFC during power swing andCase 5 simulates three-machine power system with detailed modelof UPFC.

5.1 UPFC performance during steady state (investigation byphasor model of UPFC)

Phasor model of UPFC-compensated power system (Fig. 1b) isprogrammed in MATLAB. This model is programmed based on(13)–(23) to model the basic performance of UPFC simply. Data ofthe power system is presented in the Appendix section. Generatorsare considered programmed ideal voltage source which has the

options of phase and amplitude modulations. Distance relay isinstalled in Bus 1 and impedance is calculated by phasor of voltageover phasor of current.

5.1.1 Case 1: UPFC performance without power swing(steady-state condition): First, assume there is no power swing inpower system (δ1 = 45∘). Initially, Pref = + 0.707 pu andQref = + 0.2929 pu (these values are related to uncompensatedcondition). However, at t = 0.5 s, Pref is changed to +0.72 pu andQref is kept constant at 0.2929 pu. Moreover, since |V1| is equal toits reference value during simulation, Qsh is zero. Simulationresults of this condition are tabulated in Table 1. According toTable 1, two columns are compared and some conclusions and theirreasons can be summarised as:

• Since there is no power swing in this condition, amplitude andangle of V1 are constant.

• To track new reference values for active and reactive powersflowing at Bus 2, UPFC forces V2 to change (Its angle isincreased and its amplitude is decreased compared withuncompensated condition). Voltages of both columns are shownin Fig. 4a.

• On the basis of calculated series voltage and current, seriesactive power (Pse) is calculated by UPFC. This is −0.032 pu incompensated condition, which shows that direction of activepower inside UPFC block is from series to shunt branch.

• Since amplitude of V1 equals to reference value (Vref = 1 pu),reactive power compensation of shunt branch (Qsh) is zero,second part of shunt current (Ish

(2)) is zero and just first part (Ish(1))

of shunt current is present. On the basis of (16), since Pse isnegative, angle of shunt current ∠Ish

(1) = − 135∘ = 45∘ − 180∘.Moreover, amplitude of shunt current (|Ish

(1)|) increases to 0.032because of increasing in active power in compensated column ofTable 1.

• Active and reactive powers at Bus 2 equal reference values, as aresult of meeting UPFC control aims.

• The active power at Bus 1 is the same as Bus 2 in both columnsof Table 1, because shunt active power (Psh) and series activepower (Pse) are equal.

• The admittance seen by a distance relay changes when referencevalues of UPFC change. The impact of UPFC on admittanceseen by distance relay when reference value of UPFC change isshown in Fig. 4b. According to this figure, uncompensatedadmittance (YUN) is 0.7075 − j0.2929 pu. However, theadmittance in compensated condition (Y) changes to0.72 − j0.2662 pu, which is the summation of series admittance(YSE), shunt admittance (YSH) and uncompensated admittance(YUN).

Fig. 4  Both columns of Table 1(a) Voltages, (b) Admittances

IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2017

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5.2 UPFC performance during power swing (investigation byphasor model of UPFC)

Generally, power swing is created when two generators or groupsof generators are fluctuating with respect to each other. So, theresultant signal in this condition is superposition of two signalswith different frequencies as (24)

y(t) = Aa cos(ωat + ϕa) + Ab cos(ωbt + ϕb) (24)

where Aa and Ab are amplitudes, ωa and ωb are angular frequenciesand ϕa and ϕb are phase angles of two sinusoidal signals a and b.On the basis of trigonometric identity, adding these two sinusoidalsignals results in (25)

y(t) = Am cos(ωat + ϕa + ϕm)

Am = Aa2 + Ab

2 + 2AaAb cos((ωb − ωa)t + ϕb − ϕa)

ϕm = ArctanAa sin((ωb − ωa)t + ϕb − ϕa)

Aa + Ab cos((ωb − ωa)t + ϕb − ϕa)

(25)

It is clear from (25) that the effect of this type of superposition is tomodulate both the amplitude and phase of the signal during powerswing. Therefore, it is necessary to consider both amplitude andphase of signal as modulated signals. So, both amplitude and phasemodulation are included in this section. However, in order toanalyse the results conveniently, amplitude modulation and phasemodulation are examined separately (Case 2 and Case 3). It isworth noting that combination of both of them will also beexamined in Case 5 (three-machine power system).

5.2.1 Case 2: UPFC (phasor model) performance duringpower swing (sinusoidal change of δ1): This case isprogrammed to examine the phase modulation during power swing.In this step of analysis, sinusoidal variation of δ1 is considered. Tosimulate the power swing phenomenon, displacement angle of V1 isconsidered as (26)

δ1(t) = δ10 + k sin(2π f slipt) (26)

Three different time intervals with different conditions areprogrammed for this case. Initially, power system is inuncompensated condition and there is no power swing in powersystem during 0 ≤ t < 0.5 s; next, reference values of UPFCchanges at t = 0.5 s (Pref increases to 0.72 pu) and so power system

is compensated during 0.5 ≤ t < 1 s; and finally power swing iscreated in compensated power system at t = 1 s [variation δ1 isbased on (26)] and so power system is in compensated and inpower swing condition during 1 ≤ t < 3 s.

Variation of displacement angle δ1(t) in this case is shown inFig. 5a, which its power swing condition is based on (26) wherek = 0.22, δ1

0 = 45∘ and f slip = 0.5 Hz. Here, k is selected 0.22 toenforce UPFC operates inside region of its performance. On thebasis of control aim of UPFC, this device should provide time-varying series voltage and shunt current to compensate variation ofpower in transmission line. Amplitude and phase of both seriesvoltage and shunt current are shown in Fig. 5b.

According to Fig. 5, Vse and Ish change during time because δ1

changes during power swing. Variation of these parameters can beexplained based on (20) and (21). Fig. 5b completely demonstratesthat considering constants Vse and Ish during power swing is notcorrect and it is necessary to be considered as time-variantparameters in analysis.

Fig. 5c shows active and reactive at Bus 1 and Bus 2 in Case 2.According to this figure, UPFC can cancel variations in active andreactive powers at Bus 2 and keep them constant at their referenceduring power swing (1 < t < 3 s). Since series active power (Pse) isconsidered equal to shunt active power (Psh), active power at Bus 1equals to active power at Bus 2. However, reactive power at Bus 1is different from Bus 2 and changes during power swing.

Admittance analysis can easily validate the impacts of UPFC onadmittance seen by a distance relay during power swing.Comparison between admittance in uncompensated and UPFC-compensated line is shown in Fig. 5d [only the admittance of firstswing (1 < t < 1.5 s) is shown in this figure]. According to thisfigure, uncompensated admittance (YUN) moves on uncompensatedadmittance swing characteristic (K1 = 1) during power swing.However, admittance in compensated line (Y) moves in a differentway because Y = YUN + YSE + YSH. Moreover, since |V1| and activepower at Bus 1 are constant during power swing, the real part ofadmittance is constant (0.72 pu). These results demonstrate thatUPFC changes admittance trajectory during power swing and thatchange is related to variation of series voltage and shunt currentduring power swing.

In [22], the impacts of UPFC on the power swing blockingcharacteristics are examined and it is shown that centre and radiusof impedance trajectory change in compensated line. However,there is an impractical hypothesis in analysis part of this paperwhich series voltage and shunt current are considered constant(steady-state model of UPFC is considered during power swing).To compare [22] with our paper, both of them are simulated for thesame condition (reference values of UPFC are equal touncompensated condition and power swing is started at t = 1 s) andtheir results are shown in Fig. 6.

The simulation result of our paper is shown in Fig. 6a.According to Fig. 6a, uncompensated trajectory (YUN) moves onuncompensated characteristic (k1 = 1) and also compensatedtrajectory (Y) is inside the defined area [combination of differentcircle with radius r3 based on (12)]. These results validate that theproposed idea in our paper that we need an area for showing thevariation of swing trajectory during power swing in compensatedline. On the other hand, the proposed method in [22] is simulated(Vse and Ish are considered constant values: Vse = 0.17∠ − 40∘ andIsh = 0.028∠54.8∘) and its result is shown in Fig. 6b. According toFig. 6b, Moravej et al. [22] just provide new circular swingcharacteristic for compensated condition. Although theuncompensated trajectory (ZUN) moves on uncompensatedcharacteristic, the compensated trajectory (Z) does not move oncompensated characteristic and cuts it only in one point. Therefore,we can conclude that considering constant value for Vse and Ishleads to wrong results.

5.2.2 Case 3: UPFC (phasor model) performance duringpower swing (sinusoidal change of |V1|): This case is

Table 1 Simulation results of Case 1Parameters Pref = 0.707Qref = 0.2929

(uncompensated)Pref = 0.72Qref = 0.2929

(compensated)|V1 | , pu 1 1δ1, deg 45 45|V2 | , pu 1 0.9744δ2, deg 45 47.64|Vse | , pu 0 0.052ρ′, deg 0 166|Ish | , pu 0 0.032

θsh, deg 0 −135

Pse = Psh, pu 0 −0.032

P1, pu 0.7070 0.72Q1, pu 0.2929 0.2662P2, pu 0.7070 0.72Q2, pu 0.2929 0.2929Y, pu 0.7075 − j0.2929 0.72 − j0.2662YSE, pu 0 0.0449 + j0.0266

YSH, pu 0 −0.032 + 0j

6 IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2017

programmed to examine the amplitude modulation during powerswing. So, sinusoidal variation of |V1| is considered based on (27)

|V1 | (t) = |V1 |0 + kv sin(2π f slipt) (27)

During 0 ≤ t < 0.5 s, power system is in uncompensated conditionand there is no power swing in power system. At t = 0.5 s, activepower reference of UPFC increases to 0.72 pu, and finally powerswing is simulated based on (27) and is started at t = 1 s. Variationof |V1| in this case is shown in Fig. 7a, which is based on (27)where kv = − 0.022, |V1 |0 = 1 and f slip = 0.5 Hz. Amplitude andphase of both series voltage and shunt current in this case areshown in Fig. 7b which shows that UPFC provides time-varyingseries voltage and shunt current during power swing. Fig. 7c showsactive and reactive at Bus 1 and Bus 2 in Case 3. According to thisfigure, UPFC can cancel variations in active and reactive powers atBus 2 and keep them constant at their reference during powerswing (1 < t < 3 s). Moreover, admittance movements [only theadmittance of first swing (1 < t < 1.5 s)] for uncompensated andUPFC-compensated line are shown in Fig. 7d. According to thisfigure, uncompensated admittance (YUN) moves on uncompensated

admittance swing characteristic (δ1 = 45∘) during power swing.However, admittance in compensated line (Y) moves in a differentway which demonstrates that UPFC changes admittance trajectoryduring power swing.

5.3 UPFC performance during power swing (investigation bydetailed model of UPFC)

In this section, two cases (Case 4 and Case 5) are examined, inwhich detailed model of UPFC is utilised that is presented in demoof Simulink/MATLAB and models complete behaviour of UPFC.Detailed model of UPFC consists of two major parts: electrical andcontrol parts.

i. Electrical part: Series and shunt converters in detailed modelof UPFC use voltage-sourced converter (VSC) connected tothe secondary side of a coupling transformer. The VSCs usegate turn-off thyristors to synthesise a square-wave voltagesignal from a DC voltage source. Four three-level inverters areused to build a semi-sinusoidal voltage waveform whichamplitude of each odd harmonic (n) of a three-level inverter is

Fig. 5  Results of Case 2(a) Variation of δ1, (b) Variation of series voltage and shunt current, (c) Active and reactive powers at Bus 1 and Bus 2, (d) Admittance seen by distance relay

Fig. 6  Comparison(a) Proposed method in this paper, (b) Proposed method in [22]

IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2017

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Vn =4Vdcnπ sin σ

2 (28)

where Vdc is the voltage of DC link and σ is the conductionangle. Moreover, special interconnections of transformers(phase-shifting transformers which provide phase shift of±7.5 ∘) are used to neutralise harmonics contained in the squarewaves. By utilisation of these phase-shifting transformers andchoosing the appropriate conduction angle for the three-levelinverter, UPFC generates a 48-step voltage.

ii. Control part: Control of shunt branch regulates voltage at itsterminal by controlling the amount of reactive power injectedinto or absorbed from the power system. The control systemconsists of different parts. A phase-locked loop (PLL) whichsynchronises gate turn-off thyristor pulses to the systemvoltage. The output of the PLL is used to compute d and qcomponents of voltage and current in measurement blocks.Two proportional–integral (PI) controllers are used for voltageregulator and current regulator. The output of the currentregulator is angle which is phase shift of the inverter voltagewith respect to the system voltage (for providing demandedactive power by series branch). Finally, firing pulses generatorwhich produces pulses for the four inverters.

Control of series branch is used to manage power flow. The seriesbranch injects a voltage Vse in series with the transmission line.The control system of series branch consists of different parts. PLLwhich its task is synchronisation. The output of the PLL is used tocompute d and q components of voltage and current inmeasurement blocks. The measured active and reactive powers arecompared with reference values to produce errors. These errors areused by two PI regulators to produce the reference values of d andq components of Vse to be synthesised by the VSC. Finally, firingpulses generator which produces pulses for four inverters.

5.3.1 Case 4: Investigation in two-machine equivalentsystem: To validate the extracted conclusions by precise model ofUPFC during power swing, detailed model of UPFC is allocated intwo-machine equivalent system (simulated by Simulink of

MATLAB). UPFC constructed by three-level, 48-pulse gate turn-off thyristor-based converters, one connected in shunt (is coupledto power system by transformer 200 MVA and 500 kV/30 kV) atbus Bus 1 and one connected in series (is coupled to power systemby transformer 200 MVA and 25 kV/25 kV) between buses Bus 2and Bus 3. Moreover, power swing is created by utilisation ofprogrammed voltage-source block which has the facility of phasemodulation. The same events as the previous simulation are alsoconsidered in this condition. First, power system is inuncompensated and steady state during 0 ≤ t < 0.5 s; second,reference values of UPFC changes at t = 0.5 s (Pref increases to0.72 pu) and so compensated power system is in steady stateduring 0.5 ≤ t < 1 s; moreover finally, power swing is created att = 1 s (variation δ1 is shown in Fig. 8a) and so power system is incompensated and power swing state during 1 ≤ t < 3 s. Seriesvoltage, shunt current, active power and reactive power at Bus 1and Bus 2 during whole of simulation are shown in Figs. 8b and c.In addition, the admittance seen by distance relay is also shown inFig. 8d. First, by comparing the simulation results presented inCase 2 and Case 4, it is possible to conclude that the programmedphasor model is an accurate model. Second, voltage series andshunt current provided by UPFC should be modelled as time-varying parameters during power swing. Finally, the admittanceseen by distance relay during power swing in compensated line isdifferent from uncompensated condition. It is worth noting that theripples in Fig. 8 are resulted from switching operation and controlequipment in detailed model of UPFC.

5.3.2 Case 5: Investigation in three-machine powersystem: In the previous cases, ideal voltage sources withamplitude and phase modulation capability are utilised to help inunderstanding phenomena. However, it is not usually encounteredin power systems. Controllers of synchronous generators affect thesystem response during power swings, so three-machine powersystem (is shown in Fig. 9a and its data is presented in [22]) issimulated in Simulink; which machines are modelled dynamicallyand governor and automatic voltage regulator (AVR) areconsidered for every machine. The compensated three-machinepower system is simulated by sampling frequency 30.72 kHz andthen measured voltage/current is pre-filtered by low-pass filter for

Fig. 7  Results of Case 3(a) Variation of |V1|, (b) Variation of series voltage and shunt current, (c) Active and reactive powers at Bus 1 and Bus 2, (d) Admittance seen by distance relay

8 IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2017

preventing aliasing phenomenon. To model distance relay,sampling rate of measured voltage and current are decreased byinteger factor 16 and are sent to discrete Fourier transform toestimate their phasors for calculation of impedance. Detailed modelof UPFC (the same configuration as Case 4) is installed at the left-end of transmission line L5 to control the active and reactivepowers at the Bus 2. The natural power flow (without UPFC) atBus 2 is P2 = 9.32 pu and Q2 = 0.66 pu. (Vbase = 500 kV andSbase = 100 MVA). The reference voltage of the shunt converter iskept constant at Vref = 0.9749pu. First, power system is in steady-states condition and UPFC is set to keep active and reactive powersat Bus 2 equal to their values in uncompensated condition. Next, att = 1 s, UPFC increases active power to 10 pu. A three-phase faultis simulated at t = 2 s at line L4 and is vanished after 0.07 s. Thisevent causes a power swing and is observed by the distance relay.Series voltage, shunt current, active power and reactive power atBus 1 and Bus 2, admittance trajectories for uncompensated andcompensated conditions during whole of simulation are shown inFigs. 9b–d. According to simulation results, series voltage andshunt current of UPFC during power swing are not constant andchange during time. Moreover, impedance trajectories shows that,uncompensated admittance trajectory (YUN) does not move exactlyon uncompensated characteristic (k1 = |D | = 0.9741 where D isone of the parameters of π model of transmission line) becauseamplitude of voltages changes during power swing. In addition,Fig. 9d shows that compensated admittance trajectory (Y) moves ina different way compared with YUN.

6 ConclusionBoth power swing and UPFC influence admittance seen bydistance relay. Moreover, power swing has effects on UPFCperformance so that the series voltage and shunt current providedby UPFC change during power swing. Finally, the admittance seenby a distance relay during power swing in compensated line byUPFC is different from an uncompensated line. In this paper,UPFC performance during power swing has been examined and ithas been demonstrated how interaction of power swing and UPFCchanges the admittance seen by distance relay during power swing.

According to simulation results, admittance in compensated lineconsists of three parts: uncompensated part, series part and shuntpart. It is demonstrated how the last two parts (resulted from UPFCoperation) force impedance trajectory in compensated line todeviate from uncompensated one. When UPFC operates inside ofits controllable region (active and reactive power (PQ) region), thisdeviation is limited to an admittance boundary, which is formulatedin this paper.

Fig. 8  Results of Case 4(a) Variation of δ1, (b) Variation of series voltage and shunt current, (c) Active and reactive powers at Bus 1 and Bus 2, (d) Admittance seen by distance relay

IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2017

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8 Appendix 8.1 Data of two-machine equivalent system

V3 = 1∠0,V1 = 1∠δ1,ZA = 0.1∠90∘,ZB = 0.1∠90∘,

ZLine = 1.0∠90∘

Amplitude values are in per unit (Vbase = 500 kV,Sbase = 100 MVA).

Fundamental frequency is 60 Hz.Distance relay zones: Mho characteristic (zones 1–3) with

radius 0.85 × |ZLine|, 1.2 × |ZLine| and 1.5 × |ZLine|, respectively.

Fig. 9  Results of Case 5(a) Three-machine power system, (b) Variation of series voltage and shunt current, (c) Active and reactive powers at Bus 1 and Bus 2, (d) Admittance seen by relay

10 IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2017