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Journal of productivity and development 1(3) 2015:57-68

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Abstract

The main objective of this paper is a comparative investigate in enhancement of damping power system oscillation via

coordinated design of the power system stabilizer (PSS) and Static Var Compensator(SVC)and STATic synchronous

COMpensator(STATCOM). The design problem of FACTS-based stabilizers is formulated as a GA based optimization

problem. In this paper eigenvalue analysis method is used on small signal stability of single machine infinite bus (SMIB)

system installed with SVC and STATCOM. The generator is equipped with a PSS. The proposed stabilizers are tested on a

weakly connected power system with different disturbances and loading conditions. This aim is to enhance both rotor angle

and power system stability. The eigenvalue analysis and non-linear simulation results are presented to show the effects of

these FACTS-based stabilizers and reveal that STATCOM exhibits the best effectiveness on damping power system

oscillation.

Keywords: Damping Oscillations, PSS, SVC, STATCOM, Coordination Design, Optimization, Power System Stability

Introduction:

Electromechanical oscillations have been observed in many power systems [1],[2],[3]. The oscillations may be

local to a single generator or generator plant(local oscillations), or they may involve a number of generators

widely separated geographically (inter-area oscillations). Electromechanical oscillations are generally studied

by modal analysis of a linearized system model [2],[4].The synchronizing power is defined as the component of

real power in phase with the rotor angle deviation, while the damping power is defined as the component of the

real power in phase with the rotor speed deviation. However, lack of damping power causes oscillatory

instability, while lack of synchronizing power causes a periodic instability. Such lack of synchronizing power

and damping power occurs particularly in power systems with long transmission line.To enhance system

damping, the generators are equipped with power system stabilizers (PSSs) that provide supplementary

feedback stabilizing signals in the excitation systems. PSSs extend the power system stability limit by

enhancing the system damping of low frequency oscillations associated with the electromechanical modes [5–

8].

Despite the potential of modern control techniques with different structures, power system utilities still prefer

the conventional lead-lag power system stabilizer (CPSS) structure [9–11]. Kundur et al. [11] have presented a

comprehensive analysis of the effects of the different CPSS parameters on the overall dynamic performance of

the power system. It is shown that the appropriate selection of CPSS parameters results in satisfactory

performance during system upsets. The advent of high-power electronic equipment to improve utilization of

transmission capacity, as Envisaged in the concept of flexible alternating current transmission systems

(FACTS) controllers, provides a system planner with additional leverage to improve the stability of a system.

FACTS controllers like static var compensator (SVC),thyristor controlled series compensator (TCSC), static

synchronous compensator (STATCOM), static synchronous series compensator (SSSC), and unified power

flow controller (UPFC) can provide variable shunt and/or series compensation [12]. Recently, to improve

overall system performance, many researches were made on the coordination between FACTS controllers and

PSS on damping power system oscillation [13–17]. Barati et al. [18] presented a coordinated PSS, SVC and

TCSC control for a synchronous generator. Nonlinear optimization algorithm was presented to coordinate

parameters adjustment for a TCSC, a SVC and a PSS in a power system[19]. In [20], a gain adjustment

approach for a TCSC, a SVC and a PSS was introduced and the effect of gain tuning on oscillation modes and

on overall power system performance are investigated. The availability of high power gate-turn-off thyristors

Damping Power System Oscillationswith Single and Coordinated

Design of the Power System Stabilizer and FACTS Controllers

J.Barati1, S.S. Mortazavi

2, o.rahat

3

1Electrical Engineering Department, Ramhormoz Branch, Islamic Azad University, Ramhormoz, Iran 2Electrical Engineering Department, ShahidChamran University, Ahvaz, Iran

2 Electrical Engineering Department, Ramhormoz Branch, Islamic Azad University, Ramhormoz, Iran


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has led to the development of a STATCOM which is one of the FACTS devices connected in shunt and to

improve transmission stability and to dampen power oscillations.

The Phillips–Heffron model of the single machine infinite bus(SMIB) power system with FACTS devices is

obtained by linearizing non-linear equations around a nominal operating point of the power system [21].

The design problem is transformed into an optimization problem and GA optimization techniques are employed

to search for the optimal PSS and FACTS controller‟s parameters.

In this paper the eigenvalue analysis and the nonlinear simulation results are used for small signal stability of

single machine infinite bus (SMIB) system installed with PSS and FACTS controllers. This analysis shows that

coordinated design of PSS and STATCOM-based controllers has significant performance to promote the

damping power system oscillations compared with SVC-Based controllers.

I. SYSTEM MODEL

I.1. Generator model

The power system is represented by a single machine infinite-bus(SMIB) with FACTS devices is shown in

Fig.1. The generator is equipped with a PSS. The generator has a local load of admittance Y L = g + jb . The

transmission line has impedances of Z=R + jX. The SVC and STATCOM are used at the middle point in

transmission line for power oscillations damping. The system is modeled for low frequency oscillations studies

and the linearized power System model is used for this purpose. The generator is represented by the 3rd

order

model consisting of the electromechanical swing equation and the generator internal voltage equation. The

dynamics of rotor angle δ and velocity ω is described by the so called swing equations:

(1)

' ' '

1

1 /

/

b

m e

q fd d d d q do

P P D M

E E x x i E T

II.2

Exciter and PSS

Fig. 2 shows the IEEE Type-ST1 excitation system is considered in this work. It can be described as:

(2) /fd A ref pss fd AE K V V u E T

V

G

Vb

VSC

YL

Vm

Z/2 Z/2

IDC

SVC

i

iL

il1

iSVC

il2

STATCOMCDC

Xt

o DCV CV

is

C

ψ

Figure 1. SMIB with PSS and FACTS Devices


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The inputs to the excitation system are the terminal voltage V and reference voltage Vref . K A and T A ,

respectively are represented the gain and time constants of the excitation system.

In equations (1) and (2): Pe and V are related by the following equations:

e d d q qP V i V i

(3)

1/2

2 2

'

:

d q q

d q

q q d d

V x i

V V V

V E x i

(4)

Where xq is the q-axis reactance of the generator. Moreover, Fig. 2 shows the transfer function of the PSS. It

consists of an amplification block, a wash out block and two lead-lag blocks [9]. The objective of the washout

block is to act as a high pass filter that eliminates DC offset. The lead-lag blocks provide the appropriate phase-

lead characteristic to compensate for the phase lag between the exciter input and the generator electrical torque.

The output of the PSS is limited to guarantee that the PSS does not counteract the voltage regulator action of the

AVR.

31

2 4

11

1 1 1

ST STSTK

ST ST ST

1

A

A

K

ST

Min

Max

Max

Min

fdE'

refV

V

PSSU

Lead Lag PSS

Figure 2. IEEE Type-ST1 excitation system with

PSS

II.3 SVC -Based Stabilizer

The complete SVC controller structure with a lead-lag compensator is shown in Fig. 3. The susceptance of the

SVC, B, could be expressed as:

(5 )

/REFSVC S SVC SVC SVC SB K B U B T

31

2 4

11

1 1 1

ST STSTK

ST ST ST

Min

Max

Max

Min

SVCB

SVCU

refSVCU

+-

Lead LagControler

1

S

S

K

ST

Figure 3. SVC with lead-lag controller

Referring to Fig.1, the d and q components of the machine current i and terminal voltage V can be written as:

(7 )d q

d q

i i ji

V V jV


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(8 )

By linearizing eqns. 1 and 2 it is possible to obtain:

(9 )

' ' '

/

/

/

b

e

q fd d d d q do

fd fd A A

P D M

E x x i E T

E E K V T

Where

(10

)

'1 2

'3 4

'5 6

e q PB SVC

do q fd qB SVC

q vB SVC

P K K E K B

K sT E E K K B

V K K E K B

Where K1-K6 , KPB, KqB and KvB are linearization constants. substituting eqn. 10 into eqn. 9 one can obtain the

linearized model of the power system installed with the SVC as[18]:

(11 )

1 2

34

' ' '' '

5 6

0 00 377 0 0

00

10 0

10

PB

pss

qB

q

do do doq do Sfd

A A A vBAfd

A A A A A

KK KD

UMM M M

KKKE

T T T T BE

K K K K K KK

T T T T T

VC

In short;

(12 )P x A x B u

Here, the state vector X is [∆δ , ∆ω , ∆E'q, ∆Efd ]

T, and the control vector U is [UPSS , ,∆B]

T. K1-K6,Kp,Kq and Kv

are linearization constant.

II.4 STATCOM-Based Stabilizers

As shown in Fig.1, The STATCOM consists of a three phase gate turn-off (GTO) – based voltage source

converter (VSC) and a DC capacitor . The STATCOM model used in this study is founded well enough for the

low frequency oscillation stability problem. The STATCOM is installed through a step- down transformer with

a leakage reactance of Xt . The voltage difference across the reactance produces active and reactive power

exchange between the STATCOM and the transmission network. The STATCOM resembles in many respects a

synchronous compensator, but without the inertia. The STATCOM is one of the important FACTS devices and

can be used for damping electromechanical oscillations in a power system to provide stability improvement.

This study examines the application of STATCOM for damping electromechanical oscillations in a power

system.

The VSC generates a controllable AC voltage source V CVo DC behind the leakage reactance. The voltage

difference between the STATCOM-bus AC voltage Vm(t) and Vo(t) produces active and reactive power

exchange between the STATCOM and the power system, which can be controlled by adjusting the magnitude

CVDC and the phase . In Fig. 1, we have [22]:

(13 )

(cos sin ) , , ( cos sin )DC DCs sd sq sd sq

DC DC

dV I CV CV CV j I I jI I Io DC DC dt C C


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where C = mk , k is the ratio between the AC and DC voltage depending on the converter structure, m is the

modulation ratio defined by pulse width modulation (PWM) ; V DC is the DC voltage;and ψ is the phase defined

by PWM. Furthermore, DCC is the DC capacitor value and DCI is the capacitor current while sdI and sqI are

the d and q components of the FACTS current sI respectively. Fig. 4 illustrates the block diagram of

STATCOM AC/DC voltage PI controller with a damping stabilizer. The proportional and integral gains are

KACP, KACI and KDCP, KDCP for AC and DC voltages respectively. The STATCOM damping stabilizers are lead-

lag structure where KC and Kψ are the stabilizer gains, Tw is the washout time constant, and T1C, T2C, T3C, T4C,

T1ψ, T2ψ, T3ψ, and T4ψ are the stabilizer time constants.

Min

Max

Max

Min

refV

DCIDCP

KK

S

1

1 CST

C

CU

ConverterDynamics

PI AC Voltage Regolature

Max

refV

DCIDCP

KK

S

1

1 CST

ConverterDynamics

PI DC Voltage Regolature

VAC

VDC

1 3

2 4

1 1

1 1 1

w C C

w C C

ST ST STK

ST ST ST

Figure 4. STATCOM AC/DC Voltage Regulator

with supplementary damping control in the AC

control loop

III.4 Linearizing Model STATCOM

In electromechanical mode damping stabilizers analysis, the linearized incremental model around a nominal

operating point is usually employed [23]. Linearizing the expressions of id and iq and substituting into the linear

form of (1)-(4),(7)-(9) and (13) yield the following linearized expressions.

i s is the current flow from STATCOM , and the d-q axis measure is:

(14)

'7 8 11

'9 10 12

sin cos

cos sin

d q b q DC

d q b q DC

C i C i V C E CV

C i C i V C E CV

(15)

Solving (14) and (15) simultaneously, id and iq expressions can be obtained.

(16)

'7 8 11

'9 10 12

cos cos cos sin

sin sin sin cos

d q b q DC DC

d q b q DC DC DC

C i C i V C E C V V C CV

C i C i V C E C V V C CV

(17)

Solving (16) and (17) simultaneously, Δid and Δiq can be expressed as:

(18)

'19 21 23 25 27

'20 22 24 26 28

d q DC

q q DC

i C C E C V C C C

i C C E C V C C C

(19)

The constants C7-C28 are expressions of: '

0 0 0 0 0, , , , , , , ,L d q q d qZ Y x x i i E C

The constants C1-C24 are expressions of:

(20)

'

d q q

q q d d

v x i

v E x i

(21)


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Using Equations (∆Id) and (∆Iq), the following expressions can be easily obtained

(22

)

'1 2e q pDC DC pC pP K K E K V K C K

(23

)

' '3 4( )do q fd qDC DC qC qK sT E E K K V K C K

(24

)

'5 6 q vDC DC vC vv K K E K V K C K

(25

)

'7 8DC q DC DC CV K K E K V K C K

Where K1-K8, KDCP , KPC, Kpψ, KqDC, KqC, Kqψ, KvDC, KvC , Kvψ , KDC, K∆C, and K∆ψ are linearization constants.

The above linearizing procedure yields the following linearized power system model

(26)

1 2

34

' '

5 6

7 8 9

0 377 0 0 0 0 0

0

10

'

10

00

pDC

qDC

qq do dodo do

fdA A A vDC

fdDC

A A A A

DC

KK KD

M M M M

KKKE

T TT TE

K K K K K KVT T T T

K K KV

0

0

0

0

pC P

PSSqC q

do do

A vC A vA

A A A

C

K K

M Mu

K KC

T T

K K K KK

T T T

K K

Using vector representation, the above equation can be written as:

(27) P x A x B u

Here, the state vector X is [∆δ , ∆ω , ∆E'q, ∆Efd , ∆VDC ]

T, and the control vector U is [UPSS , ∆C, ∆ψ]

T. K1-

K9,Kp,Kq, Kv and K∆ are linearization constant.

II. PROBLEM FORMULATION

II.1. Stabilizer Structure

The commonly used lead-lag structure is chosen in this study. The transfer function of the stabilizer is:

(28) 31

2 4

11

1 1 1

w

w

sT sTsTu K y

sT sT sT

where u and y are the stabilizer output and input signals respectively, K is the stabilizer gain, Tw is the washout

time constant, and T1, T2, T3, and T4 are the stabilizer time constants. From the viewpoint of the washout

function, the value of TW is not critical and may be in the range of 1–20 s [19]. In the lead–lag structured

controllers, the washout time constants Tw is usually prespecified [14,20].In the present study a washout time

constant Tw = 10 s is used. The controller gain K and time constants T1, T2 , T3 and T4 are to be determined.

Furthermore, In the design of a robust damping controller, selection of the appropriate input signal is a main

issue. Input signal must give correct control actions when a disturbance occurs in the power system. Both local

and remote signals can be used as control. However, local control signals, although easy to get, may not contain

the desired oscillation modes. For local input signals, line active power, line reactive power, line current

magnitude and bus voltage magnitudes are all candidates to be considered in the selection of input signals for

the FACTS power oscillation damping controller [25].

Similarly, generator rotor angle and speed deviation can be used as remote signals. However, rotor speed seems

to be a better alternative as input signal for FACTS-based controller [26]. In this study, the input signal of the

proposed damping stabilizers is the speed deviation, Δω.


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II.2. Objective Function

A widely used conventional lead–lag structure for both PSS and FACTS-based stabilizers, shown in Figs. 2, 3,4

and 5, is considered. In this structure, the washout time constant Tw is usually prespecified. It is worth

mentioning that the damping controller is designed to minimize the electromechanical mode oscillation while

the internal PI controllers are designed to minimize the variations in ac and dc voltages of the STATCOM.

Therefore, the following weighted-sum multi objective function is proposed in order to coordinate among the

damping stabilizers and the internal ac and dc PI controllers. Therefore, to increase the system damping to

electromechanical modes, an objective function J defined below is proposed.

(29) 0

( )simt t

J t dt

In the above equations tsim is the simulation time. It is aimed to minimize this objective function in order to

improve the system response in terms of the settling time and overshoots.

II.3. Optimization problem

In this study, it is aimed to minimize the proposed objective function J. The problem constraints are the PSS

and FACTS controller parameter bounds. Therefore, the design problem can be formulated as the following

optimization problem.

Minimize J

Subject to : min max min max min max min max

1 1 1 2 2 2 3 3 3 4 4 4

min max min max min max

min max min max min max min max

, , ,

, ,

, , ,

PSS PSS PSS ACP ACP ACP ACI ACI ACI

DCI DCI DCI DCP DCP DCP C C C

T T T T T T T T T T T T

K K K K K K K K K

K K K K K K K K K K K K

The proposed approach employs genetic algorithm [14] to solve this optimization problem and search for

optimal set of the controller parameters. Based on the linearized power system model, Genetic Algorithm (GA)

has been applied to the above optimization problem to search for optimal settings of the proposed stabilizer. In

this study, PSS and FACTS-based damping controllers as discussed in the following combination cases:

Case 1: without compensation (base case)

Case 2: Single and coordinated compensation Design Approach (PSS and SVC)

Case 4: STATCOM internal AC and DC PI voltage controllers with PSS and C-based damping stabilizer.

Case 5: STATCOM internal AC and DC PI voltage controllers with PSS and ψ-based damping stabilizer.

III. SIMULATION RESULTS

Simulations on the SMIB system (shown in Fig. 1) are performed to evaluate the effectiveness of the PSS and

FACTS controllers to damping power system oscillations and its design by the methods proposed using GA in

the paper are demonstrated by example power systems. The relevant parameters of the power system are given

in Appendix. To validate the effectiveness of the proposed controllers, two different operating conditions

(Normal & Heavy) as given in Table 1 are considered. Parameters for the proposed stabilizers are given in

Table 2.

TABLE I: LOADING CONDITIONS

Loading Pe (pu) Qe (pu)

Normal 1.0 0.015

Heavy 1.1 0.4


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III.1. Eigenvalues Analysis

The system eigenvalues and their damping ratios with and without PSS, SVC and STATCOM (single and

coordinated design) for nominal and heavy loading conditions are given in Tables 3-5, respectively.

The eigenvalue analysis reveals the effectiveness of GA Based single and coordinated of PSS and FACTS –

Based controllers to damping power system oscillations and power system stability Enhancement.

TABLE II: OPTIMAL PARAMETER SETTING OF THE PROPOSED STABILIZERS

Controlle

r optimal

paramete

r

Single design Coordinated design

PSS SVC PSS SVC

C-based

Stabiliz

er

ψ-based

Stabilize

r

T1 0.561 0.280

1

0.189

4 0.795

0.492 0.0092

T2 0.100

0

0.300

0

0.100

0

0.300

0

0.5000 0.5000

T3 0.267

1

0.012

4

0.137

2

0.518

6

0.720 0.138

T4 0.100

0

0.300

0

0.100

0

0.300

0

0.5000 0.5000

K 16.02

1 310 61.45 87.18

41.50 53.65

KPAC -- -- -- -- 513.5 340.3

KIAC -- -- -- -- 30.32 798.0

KPDC -- -- -- -- 287 171.06

KIDC -- -- -- -- 915.56 831.6

TABLE I: SYSTEM EIGENVALUES IN NOMINAL LOADING CONDITION, SINGLE AND COORDINATED

DESIGN

Single Design Coordinated Design

No

Control

PSS SVC STATCO

M only

PSS&SVC C-based

Stabilizer

ψ-based

Stabilizer

-

0.3±j4.96

-

1.93±j3.55

-

0.72±j5.98

-1.082±

j2.658

-2.04±j1.74 -1.15± j1.29 -3.068±

j0.863

TABLE II: SYSTEM EIGENVALUES IN NOMINAL LOADING CONDITION, SINGLE AND COORDINATED

DESIGN


No

Control

PSS SVC STATCO

M only

PSS&SV

C

C-based

Stabilizer

ψ-based

Stabilizer

-

0.49±j3.69

-

1.02±j2.4

-

0.53±j5.54

-0.717±

j1.854

-

3.212±j3.95

-1.611±

j2.50

-2.72± j2.30


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TABLE III: DAMPING OF SYSTEM ELECTROMECHANICAL MODE IN BOTH OF LOADING

CONDITIONS, SINGLE AND COORDINATED DESIGN


Loading No

Control

PSS

only

SVC

only

STATCOM

only

PSS&SVC C-based

Stabilizer

ψ-based

Stabilizer

Normal -

0.0600

0.4776 0.1195 0.3783 0.7616 0.6628 0.9628

Heavy -

0.1310

0.3911 0.0968 0 .3608 0.6309 0.5393 0.7643

III.2. Non Linear TimeDomain Simulation

To assess the effectiveness of the proposed PSS and FACTS devices to improve the stability of SMIB

powersystem shown in Fig. 1 is considered for nonlinear simulation studies. 6-cycle 3-φ fault on the infinite bus

was created, at both loading conditions given in Table 1, to study the performance of the proposed controller.

The system data is given in the appendix. Figures 5-7 show the rotor angle response with above mentioned

disturbance at nominal and heavy loading conditions respectively. The response with coordinated design is

much faster, with less overshoot and settling time compared to CPSS and single design. It can be observed from

Figs. that, the coordinated design approach provides the best damping characteristic and enhance greatly the

first swing stability at two loading conditions. Response when CPSS and designed individually and in

coordinated manner at nominal and heavy loading conditions are compared and show in Figs.(5-7),respectively.

It is clear that the control effort is greatly reduced with the coordinated design approach.

(a) (b)

Figure 5. Machine rotor angle response for a six cycles fault with nominal(a) & heavy(b) loading conditions.

0 1 2 3 4 5 6-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time(s)

Ro

tor

An

gle

(ra

d)

0 1 2 3 4 5 6-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time(s)

Ro

tor

An

gle

(ra

d)


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Figure 6. Machine rotor angle responsefor a six cycles fault with nominal loading condition

Figure 7. Machine rotor angle for a six cycles fault with heavy loading condition

IV. Conclusion

In this study, the power system stability enhancement via PSS and FACTS device are presented and discussed

The stabilizer design problem has been formulated as a multi objective optimization problem, which was solved

by genetic algorithms (GA). The proposed stabilizers have been applied and tested on power system under

severe disturbance and different loading condition. It is also evident that the coordinated design of PSS and

FACTS-based stabilizer provides great damping characteristics and enhance significantly the system stability

compared to individual design. It is clear from the eigenvalues analysis that the system stability is greatly

enhanced with the proposed stabilizers. The eigenvalues results presented show that the system stability is

greatly enhanced with the coordinated design of the proposed stabilizers. The simulations results presented

show that both FACTS devices improve the system stability, furthermore the STATCOM-based stabilizer

provide a better effectiveness than SVC-based stabilizer on damping power system oscillation. Moreover it can

be seen that the coordinated PSS and ψ -based stabilizer provide better damping characteristics and enhances

the first swing stability greatly compared to the coordinated PSS and C-based stabilizer case.

0 1 2 3 4 5 60.8

1

1.2

1.4

1.6

1.8

2

Time(s)

Ro

tor

An

gle

(ra

d)

Conventional PSS[1]

Proposed PSS

Proposed SVC

Coordinated PSS & SVC

Coordinated PSS & C - Based Stabilizer

Coordinated PSS & - Based Stabilizer

0 1 2 3 4 5 61.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

Time(s)

Ro

tor

An

gle

(ra

d)

Conventional PSS[1]

Proposed PSS

Proposed SVC

Coordinated PSS & SVC

Coordinated PSS & C - Based Stabilizer

Coordinated PSS & - Based Stabilizer


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Acknowledgements

Funding support of this research was provided by the Islamic Azad University, Ramhormoz Branch,

khozestan, Iran. Moreover, this paper was derived from a plan named “Damping Low Frequency

Oscillationswith Single and Coordinated Design of the Power System Stabilizer and FACTS Controllers“.

Appendix

Power system data in per unit value:

M=9.26 ; Tdo=7.76 ; D=0; x=0.973 ;xd=0.19; xq=0.55 ; R=0.234 ; X=0.997 ; g=0.249 ; b=0.262 ; Kc=1.0 ;

Tc=0.05 ; |Efd|≤ 7.3 pu ; Vdc=1 , KA=20 , TA=0.01.

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