35 coordinated design of a mb-pss and statcom controller to enhance power system stability · ·...

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –

6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 2, July- September (2012), © IAEME

352

COORDINATED DESIGN OF A MB-PSS AND STATCOM

CONTROLLER TO ENHANCE POWER SYSTEM STABILITY

1Gaber Shabib, and

2Youssef A. Mobarak

1Faculty of Energy Engineering, Aswan University, Egypt [email protected]

2Electrical Engineering Department, Faculty of Engineering, Rabigh, King Abdulaziz

University, Saudi Arabia, [email protected]

ABSTRACT

This paper solves the problem of power system stabilization by using the advanced static synchronous

shunt compensator STATCOM to increase the damping of electromechanical oscillations of the

power system and regulates the system voltage by absorbing or generating reactive power to the

system. Also, a multi-band power system stabilizer MB-PSS is developed in this paper to get a

moderate phase advance at all frequencies of interest in order to compensate for the inherent lag

between the field excitation and the electrical torque induced to ensure robust oscillation damping. A

combined control of STATCOM with MB-PSS is proposed also in this paper to give more increase of

the oscillation damping that improves power system stability. The application of these controllers is

applied to the multi-machine two-area power system using Matlab Toolbox.

Keywords: STATCOM, MB-PSS, Power System Stability, Oscillation Damping.

Nomenclature

ψd, ψq direct and quadrature axis component of stator flux

ed, eq direct and quadrature axis component of stator voltage

id, iq direct and quadrature axis component of stator current

rs stator resistance

Ed’, Eq

’ direct and quadrature axis transient voltage

ψkd, ψkq direct and quadrature axis damper flux linkage

Efd exciter voltage

KG speed governor gain

D the percentage of steady-state speed regulation or unit droop

TV the time constant of the vessel steam flow

P0 the steady-state vessel pressure

Q0 the steady-state mass flow out of the vessel

Vvessel the volume of the vessel

Kvessel the density change due to pressure changes in constant temperature

vsteam the specific volume of steam

T0 the vessel temperature

P2 ,P1 the boundaries of the smallest pressure interval

INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING &

TECHNOLOGY (IJEET)

ISSN 0976 – 6545(Print)

ISSN 0976 – 6553(Online)

Volume 3, Issue 2, July – September (2012), pp. 352-372

© IAEME: www.iaeme.com/ijeet.html

Journal Impact Factor (2012): 3.2031 (Calculated by GISI)

www.jifactor.com

IJEET

© I A E M E



353

v2 , v1 the specific volumes

PX the power of turbine X

K the turbine stage between draining points

Qk the mass flow in stage k

hink the inlet steam enthalpy of stage in k

houtk the outlet steam enthalpy of stage k

Xt a leakage reactance

m he modulation ratio defined by pulse width modulation (PWM)

K the ratio between the ac and dc voltage depending on the converter structure

Vdc the dc voltage

ψ the phase defined by PWM

Cdc the dc capacitor value

Idc the capacitor current

isd, isq the d- and q-components of the STATCOM current Is

Tdo’, Tdo

” transient and subtransient direct axis time constants (in sec.)

Tqo’, Tqo

” transient and subtransient quadrature axis time constants (in sec.)

TSR TSM the speed governor and servomotor time constants

xd, xd’, xd

” synchronous, transient and subtransient direct-axis reactances

xq, xq’, xq

” synchronous, transient and subtransient quad.- axis reactances

c1, c2, c3 constant

Kpac, Kiac Kpdc, Kidc ac and dc voltages proportional and integral gains

Cv-open,Cv-close,Copen,Cclose the valve’s rate limits and position limits

TSC,TRH1, TRH2,TCO steam chest, first reheater, second reheater, and crossover time constants

FVHP, FHP, FIP , FLP very-high-pressure (VHP), HP, IP, and LP turbines’ power fractions

PHP, PIP, PLP the HP turbine power, IP turbine power, and LP turbine power

1. INTRODUCTION Since 1960s, low frequency oscillations have been observed when large power systems are

interconnected by relatively weak tie lines. These oscillations may sustain and grow to cause

system separation if no adequate damping is available [1-5]. Nowadays, the conventional

power system stabilizer CPSS is widely used by power system utilities. Generally, it is

important to recognize that machine parameters change with loading make the machine

behavior quite different at different operating conditions. Since these parameters change in a

rather complex manner, a set of stabilizer parameters, which stabilizes the system under a

certain operating condition, may no longer yield satisfactory results when there is a drastic

change in power system operating conditions and configurations. Hence, power system

stabilizers PSSs should provide some degree of robustness to the variations in system

parameters, loading conditions, and configurations. H∞ optimization techniques [2] have been

applied to robust PSS design problem. However, the importance and difficulties in the

selection of weighting functions of H∞ optimization problem have been reported. In addition,

the additive and/or multiplicative uncertainty representation cannot treat situations, where a

nominal stable system becomes unstable after being perturbed [3]. Moreover, the pole-zero

cancellation phenomenon associated with this approach produces closed loop poles whose

damping is directly dependent on the open loop system [4].

On the other hand, the order of the H∞-based stabilizer is as high as that of the plant. This

gives rise to complex structure of such stabilizers and reduces their applicability. Kundur et

al. [4] 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. In addition, Gibbard [5] demonstrated that the CPSS provide satisfactory damping

performance over a wide range of system loading conditions. Robust design of CPSSs in



354

multi-machine power systems using genetic algorithm is presented in Ref. [6-7], where

several loading conditions are considered in the design process. Although PSSs provide

supplementary feedback stabilizing signals, they suffer a drawback of being liable to cause

great variations in the voltage profile and they may even result in leading power factor

operation under severe disturbances [8-9]. MB-PSS is based on multi-frequency variables

that this stabilizer can obtain to cope with all low, intermediate, and high frequencies

oscillations [10, 11]. The MB-PSS is developed in such a manner that it can be capable of

introducing moderate phase advance at all oscillations frequencies of interest in order to

compensate for the inherent lag between the field excitation and the electrical torque [7].

The recent advances in power electronics have led to the development of the flexible

alternating current transmission systems FACTS. Generally, a potential motivation for the

accelerated use of FACTS devices is the deregulation environment in contemporary utility

business. Along with primary function of the FACTS devices, the real power flow can be

regulated to mitigate the low frequency oscillations and enhance power system stability.

Recently, several FACTS devices have been implemented and installed in practical power

systems [12]. In the literature, a little work has been done on the coordination problem

investigation of excitation and FACTS-based stabilizers. Refs. [13-17] present a coordinated

PSS and SVC control for a synchronous generator. However, the proposed approach uses

recursive least squares identification, which reduces its effectiveness for on-line applications.

Rahim and Nassimi [15] presented optimum feedback strategies for both SVC and exciter

controls. However, the proposed controller requires some or all states to be measurable or

estimated. Moreover, it leads to a centralized controller for multi-machine power systems,

which reduces its applicability and reliability. Noroozian and Anderson [16] presented a

comprehensive analysis of damping of power system electromechanical oscillations using

FACTS, where the impacts of transmission line loading and load characteristics on the

damping effect of these devices have been discussed. Wang and Swift [12] have discussed

the damping torque contributed by FACTS devices, where several important points have been

analyzed and confirmed through simulations. However, all controllers were assumed

proportional and no efforts have been done towards the controller design.

On the other hand, it is necessary to measure the electromechanical mode controllability in

order to assess the effectiveness of different controllers and form a clear inspiration about the

coordination problem requirements [10, 13]. A comprehensive study of the coordination

problem requirements among PSSs and different FACTS devices has been presented in Refs

[18-21]. However, no efforts have been done towards the coordinated design of the stabilizers

investigated. By controlling the magnitude of the STATCOM voltage the reactive power

exchanges between the STATCOM and the transmission line [22-26]. One of the most

important advantages of the STATCOM is its behaviour during the voltage collapse at the

bus where it is located as it supplies almost a constant reactive power without being affected

by voltage variation across it. So far, conventional power system stabilizer PSS is still used as

an effective and economical facility to tackle the problem [14]. Many techniques have been

reported in the literature on the topic of coordinated design of PSS [27-31].

In this paper, a comprehensive assessment of the effects of the excitation and STATCOM

control when applied independently and also through coordinated application has been

carried out. Also, MB-PSS is developed in this paper to get a moderate phase advance at all

frequencies of interest in order to compensate for the inherent lag between the field excitation

and the electrical torque induced to ensure robust oscillation damping. A combined control of

STATCOM with MB-PSS is proposed also in this paper to give more increase of the



355

oscillation damping that improves power system stability. All these controllers are supplied

to the multi-machine two-area power system.

2. STUDIED SYSTEM AND MODELING

The studied system (Kundur's four-machine two-area test system) consists of two fully

symmetrical areas linked together by two 230 kV lines of 220 km length as shown in

Fig. (1). Despite its small size, it mimics very closely the behavior of typical systems

in actual operation [4]. Each area is equipped with two identical round rotor

generators rated 20kV/900MVA. The synchronous machines have identical

parameters [11], except for inertias which are H=6.5s in area 1 and H=6.175s in area

2. The parameters of the generators, turbines and exciters data are given in Appendix.

Thermal plants having identical speed regulators are further assumed at all locations,

in addition to fast static exciters with a gain on 200 [10]. The load is represented as

constant impedances and is split between the areas in such a way that area 1 is

exporting 413MW to area 2. Since the surge impedance loading of a single line is

about 140 MW, the system is somewhat stressed, even in steady-state.

Fig. 1: Single line diagram of four-machine two-area test system.

2.1. Power System Model

2.1.1 Generator:

The generator is represented by the sixth-order model comprising of the

electromechanical swing equation and the generator internal voltage equation [10-11].

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

equations:

( )ωω

∆−−=∆

DTTHdt

dem

2

1 (1)

∆ωωdt

dδo

= (2)

G1

G2 G4

1

5

6

2 11 12

9 10

4

8

7

3

20/230

0.0167

20/230

0.0167 20/230

0.0167

R=0.0025

X=0.0250

B/2=0.0437

R=0.0025

X=0.0250

B/2=0.043

R=0.001

X=0.010

B/2=0.0175

R=0.001

X=0.010

B/2=0.0175

R=0.011

X=0.110

B/2=0.19

25

R=0.0

X=0.005

R=0.0

X=0.005

Load A

967MW+j100MVAR

Qc=200MVAR

Load B

1767MW+j100MVAR

Qc=350MVAR

230KV, 220Km

G3

20/230

0.0167

Area 1

H=6.5

Area 2

H=6.175

STATCOM



356

where: ∆ω=ω-ωo is the deviation, in rad/s of rotor angular velocity from synchronous

velocity ωo=2πf, H is the p.u. inertia constant, Tm and Te are the p.u. mechanical and

electromagnetic torque, respectively, D is the damping coefficient. Figure (2) shows

the electrical model of the synchronous machine in the d-q frame.

The sixth order model is frequently employed in stability and control analysis. Its

stator transients (ψ˙d, ψ˙q) are considered so fast as to be negligible as far as transient

stability and its associated slow rotor oscillations, are concerned.

Fig. 2: Electrical model of the synchronous machine (q-d frame)

The following differential equations used to describe the electrical variables and the

two swing equations (1), (2) to describe the mechanical motion [4]. Two of the six

differential equations are used to describe the d and q axis components of the stator

fluxes as follows:

dsqd irψe0 ++= (3)

qsdq irψe0 +−= (4)

Four differential equations are required to describe rotor electrical dynamics in the

four windings assumed to be lying on the rotor.

( )( )( )

−′

′−−′′−

−′

′−′′−′+

−′

′−′′−′′−′−

′=′

2ld

ddldd2

ld

ddddkd2

ld

ddddqqfd

do

qxx

xxxxi

)xx(

)x)(xxx(ψ

)xx(

)x)(xxx(EEE

T

1E& (5)

( )( )( )

−′

′−−′′+

−′

′−′′−′−

−′

′−′′−′′+′−

′=′

2lq

qqlqq2

lq

qqqqkq2

lq

qqqqdd

qo

dxx

xxxxi

)xx(

)x)(xxx(ψ

)xx(

)x)(xxx(EE

T

1E& (6)

( )[ ]dldqkddo

kd ixxEψT

1ψ −′−′+−

′′=& (7)

( )[ ]qlqdkqqo

kq ixxEψT

1ψ −′−′−−

′′=& (8)

The following algebraic equations:

ddld

ddkd

ld

ldqd ix

xx

xxψ

xx

xxEψ ′′−

−′

′′−′+

−′

−′′′= (9)

qqlq

qqkq

lq

lqdq ix

xx

xxψ

xx

xxEψ ′′−

−′

′′−′+

−′

−′′′−= (10)

Which relate internal voltages and fluxes with output stator currents, along with the

following relationship for the electromagnetic torque:

+

+ +

R'kq2

R'kq1

L'1kq1

Rs

-

-

-

+

+

- ωR ψd L1

iq Vq Lmq

q axis

i'kq1

i'kq

V'kq1

V'kq2

L'1kq2

R'kd

Rs

-

-

-

+

- + ωR ψq L1

id Vd Lmd

d axis

i'kd

i'fd

V'kd

V'fd

+

L'1kd

L'1fd

R'fd



357

dqqde iψiψT −= (11)

2.1.2 Exciter and PSS:

An excitation system for the synchronous machine and regulate its terminal voltage in

generating mode. The excitation system is implementing a DC exciter described in

[10], without the exciter's saturation function. The basic elements that form the

excitation system depicted in Fig. (3), the voltage regulator and the exciter. It can be

described as;

( )( )fdPSSrefaa

f

.

EuvVKT

1E −+−= (12)

f

ee

f EsTK

1V

+= (13)

Low-pass filter time constant Tr, in seconds, of the first-order system that represents

the stator terminal voltage transducer. Regulator gain and time constant Ka and Ta, of

the first-order system representing the main regulator. Exciter gain Ke and time

constant Te of the first-order system representing the exciter. Transient gain reduction

time constants Tb, and Tc of the first-order system representing a lead-lag

compensator. Damping filter gain and time constant Kf and Tf of the first-order system

representing a derivative feedback. Regulator output limits and gain Efd-min and Efd-max

are imposed on the output of the voltage regulator, and Vref is the reference voltage. A

conventional lead–lag PSS is installed in the feedback loop to generate a stabilizing

signal Upss:

Fig. 3: Excitation system with PSS model.

In Eq. (12), the terminal voltage v can be expressed as: 2q

2dd vvv += (14)

qqd ixv = , and d'd

'qq ixEv −= (15)

Where xd, and xq are the d-axis, and q-axis reactance’s of the generator

1sT

1T

b

c

+

+s

1sT

K

a

a

+

ee KsT

1

+

1sT

K

f

f

+

s

1sT

1

r +

+

+

+

+

+ 4

3

2

1

w

w

sT1

sT1

sT1

sT1

sT1

sTK

Efs max

Efs min

Vf

upss max

upss min

Δω

Lead-lag comp. Regulator

Lead-lag PSS

Vref

vd

vq

Upss

+ -

+

-

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976

6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 2, July

2.1.3 Governor and Turbine Model

A typical overview of primary control in a stea

functional blocks include the governor speed changer, speed governor, speed

controlled valves, and turbine systems. All the equipments with some simplification

can be mathematically represented by simple block

one control valve CV between the steam generator and HP turbine is assumed [1

Also, the models are built without intercept valves, fast valving. Boiler pressure is

assumed to be constant [10].

Fig. 4: Steam unit primary control blocks.

The block diagram of Fig. (5) shows an approximate model for a typical mechanical

hydraulic speed-governing system. In the figure, T

and servomotor time constants, respectively. Also, C

represent the valve’s rate limits and position limits, respectively. Although it is

possible to extract the parameters of the governor model using dimensions and

physical parameters [20], we just confine the study to the turbine model. Thus, for the

governor model, only speed governor gain is taken into account using K

where D is the percentage of steady

parameters are considered to be typical values [1

Fig. 5: Simple mechanical

The steam chest and inlet piping to the first turbine cylinder and reheaters

crossover piping introduce delays between valve movement and change in steam flow.

The main objective in modeling the steam system for dynamic studies is to represent

these delays. Also, the configuration of turbines affects the model. There may be

tandem compound or cross compound configuration. Also in each of these categories,

single or double reheat stages may exist. Figure (6), three common configurations for

tandem compound units are presented. The general model for the turbine system can

represent all tandem compound configurations. Figure (7) T

steam chest, first reheater, second reheater, and crossover time constants, respectively.


6553(Online) Volume 3, Issue 2, July- September (2012), © IAEME

358

Governor and Turbine Model:

A typical overview of primary control in a steam unit is presented in Fig. (4),

functional blocks include the governor speed changer, speed governor, speed


can be mathematically represented by simple block-based models. In the models, only

one control valve CV between the steam generator and HP turbine is assumed [1


Fig. 4: Steam unit primary control blocks.

The block diagram of Fig. (5) shows an approximate model for a typical mechanical

governing system. In the figure, TSR and TSM are the speed governor

and servomotor time constants, respectively. Also, Cv-open, Cv-close, Copen


to extract the parameters of the governor model using dimensions and

], we just confine the study to the turbine model. Thus, for the

governor model, only speed governor gain is taken into account using K

ntage of steady-state speed regulation or unit droop. Other

parameters are considered to be typical values [14].

Fig. 5: Simple mechanical-hydraulic speed-governing model.

The steam chest and inlet piping to the first turbine cylinder and reheaters




dem compound or cross compound configuration. Also in each of these categories,



t all tandem compound configurations. Figure (7) TSC, TRH1, TRH2, and T



September (2012), © IAEME

m unit is presented in Fig. (4), the

functional blocks include the governor speed changer, speed governor, speed relay,


based models. In the models, only

one control valve CV between the steam generator and HP turbine is assumed [11].


The block diagram of Fig. (5) shows an approximate model for a typical mechanical-

are the speed governor

open, and Cclose


to extract the parameters of the governor model using dimensions and

], we just confine the study to the turbine model. Thus, for the

governor model, only speed governor gain is taken into account using KG=100/D,

state speed regulation or unit droop. Other

The steam chest and inlet piping to the first turbine cylinder and reheaters and




dem compound or cross compound configuration. Also in each of these categories,



, and TCO are




Also, FVHP, FHP, FIP and FLP, are very

power fractions, respectively.

Fig. 6: Three common tandem compound configurations of steam turbines

Fig. 7: General model for tandem compound configuration of turbines.

Assuming a steam vessel as in Fig. (7), using the continuity equation, the time

constant of steam crossing the vessel can be written as:

vesselvessel

0

0V KV

Q

PT =

steamvessel

v

1

PK

∂

∂=

where TV is the time constant of the vessel steam flow, P

pressure, Q0 and is the steady-

the vessel, and Kvessel is the density change due to pressure changes in constant

temperature, vsteam is the specific volume of steam at assumed constant temperature of

the vessel, and T0 is the vessel temperature which is assumed to be constant. Often,

the volume of the vessel for reheater, crossover, and chest cannot be determined



359

, are very-high-pressure VHP, HP, IP, and LP turbines’

fractions, respectively.

(a) without reheat,

(b) single reheat

(c) double reheat



vessel as in Fig. (7), using the continuity equation, the time

constant of steam crossing the vessel can be written as:

vessel (16)

0T

(17)

is the time constant of the vessel steam flow, P0 is the steady

-state mass flow out of the vessel. Vvessel is the volume of

is the density change due to pressure changes in constant

is the specific volume of steam at assumed constant temperature of

is the vessel temperature which is assumed to be constant. Often,




pressure VHP, HP, IP, and LP turbines’



vessel as in Fig. (7), using the continuity equation, the time

is the steady-state vessel

is the volume of

is the density change due to pressure changes in constant

is the specific volume of steam at assumed constant temperature of

is the vessel temperature which is assumed to be constant. Often,




360

exactly and has to be derived using available data. For calculating Kvessel, the tabulated

thermodynamic data of steam can be used [23].

Assume P2 and P1 to be the boundaries of the smallest pressure interval which include

the vessel pressure in steam thermodynamic specific volume table. Also, v2 and v1 are

the specific volumes corresponding to P1 and P2. Then, Kvessel can be approximately

written as follows:

vesselT12

12vessel

PP

v1v1K

−

−= (18)

Note that in tabulated thermodynamic data, the specific volume is given at different

pressures for various temperatures. The exact temperature of our vessel may not be

available in the table. In such cases, a linear interpolation for gaining the specific

volume is common. Using (16) and (17), time constants for steam chest, reheaters, and

crossover can only be estimated. Often, the above equation parameters cannot be

stated exactly or temperature steadiness is not always provided.

Another important parameter set of the turbine model are the power fractions. These

fractions determine the way that each turbine contributes to total turbine system

power. Assuming the rated output power as a per unit basis, we have:

1FFF LPIPHP =++ (19)

To determine each of these fractions, two useful parameters a1 and a2 can be defined

as follows:

1HP

LP

HP

LP aP

P

F

F== , 2

HP

IP

HP

IP aP

P

F

F== (20)

where PHP, PIP, and PLP are HP turbine power, IP turbine power, and LP turbine

power, respectively. For calculating the turbine power, we need the steam enthalpy on

each stage and mass flow which is available from the heat balance map. The power of

each turbine is simply estimated via the following:

( )∑ −=k

outkinkkX hhQP , X=HP, IP, LP (21)

where PX is the power of turbine X, k indicates the turbine stage between draining

points, Qk is the mass flow in stage k, hink is inlet steam enthalpy of stage in k, and

houtk is the outlet steam enthalpy of stage k. Solving (18), (20), we have:

21HP

aa1

1F

++= ,

21

2IP

aa1

aF

++= ,

21

1LP

aa1

aF

++= (22)

Thus, the turbine model parameters can all be estimated. Note that for calculating the

turbine power as a weighted sum of the turbine sections, the turbine thermodynamic

process was assumed to be pure isentropic and mechanical losses are neglected.

Nevertheless, these assumptions are common for turbine thermodynamic studies [27].

2.2 Static Synchronous Compensator (STATCOM)

The STATCOM resembles in many respects a synchronous compensator, but without

the inertia. The basic electronic block of a STATCOM is the Voltage Source

Converter VSC, which in general converts an input dc voltage into a three-phase

output voltage at fundamental frequency, with rapidly controllable amplitude and



phase angle. In addition to this, the controller has a coupling transformer and a dc

capacitor. The control system can be designed to maintain the magnitude of the bus

voltage constant by controllin

voltage. The STATCOM is based on a solid state synchronous voltage source which

generates a balanced set of three sinusoidal voltages at the fundamental frequency

with rapidly controllable amplitude and

STATCOM is shown in Fig. (8).

Fig. 8: STATCOM connected to a transmission line.

The STATCOM is represented by a first order differential equation relating the

STATCOM dc capacitor voltage and current. The

transformer with a leakage reactance of X

VSC and a dc capacitor. The STATCOM model used in this study is found good

enough for the low frequency oscillation stability problem [

controllable ac voltage Vo given by:

V� � CV��∠ψ

where C=mk, m the modulation ratio defined by pulse width modulation

ratio between the ac and dc voltage depending on the converter structure, V

voltage, and ψ is the phase defined by PWM. The magnitude and the phase of V

be controlled through m and ψ respectively.

By adjusting the STATCOM ac voltage V

exchange between the STATCOM and the power system can be controlled through

the difference between Vo and the STATCOM

governed by:

V��

��

�� I��

Where Cdc is the dc capacitor

the d- and q-components of the STATCOM current I

components of the Id can be expressed as:

I� ��

′ ��ψ

��′ ��

Where c1, c2, and c3 are constants.



361



voltage constant by controlling the magnitude and/or phase shift of the VSC output



with rapidly controllable amplitude and phase angle. The configuration of a

STATCOM is shown in Fig. (8).

Fig. 8: STATCOM connected to a transmission line.


STATCOM dc capacitor voltage and current. The STATCOM consists of a stepdown

transformer with a leakage reactance of Xt, a three phase gate turn-off GTO


enough for the low frequency oscillation stability problem [26]. The VSC generates

given by:

(23)

where C=mk, m the modulation ratio defined by pulse width modulation

ratio between the ac and dc voltage depending on the converter structure, V

is the phase defined by PWM. The magnitude and the phase of V

olled through m and ψ respectively.

By adjusting the STATCOM ac voltage VB or Vo, the active and reactive power


and the STATCOM-bus voltage Vm. The dc v

��cosψ� I��sinψ" (24)

is the dc capacitor value and Idc is the capacitor current while i

components of the STATCOM current Is, respectively. The d

can be expressed as: ψ�#$��δ

, and I� � ��ψ�#$��δ

�� (25)

are constants.





g the magnitude and/or phase shift of the VSC output



phase angle. The configuration of a


STATCOM consists of a stepdown

off GTO-based


VSC generates

(23)

where C=mk, m the modulation ratio defined by pulse width modulation PWM, k the

ratio between the ac and dc voltage depending on the converter structure, Vdc the dc

is the phase defined by PWM. The magnitude and the phase of Vo can

, the active and reactive power


. The dc voltage Vdc is

(24)

is the capacitor current while isd and isq are

, respectively. The d- and q-axis

(25)



362

Figure (9) illustrates the block diagram of STATCOM ac and dc voltage PI controller.

The proportional and integral gains are Kpac, Kiac and Kpdc, Kidc for ac and dc voltages,

respectively [26-28].

Fig. 9: STATCOM PI controller for (a) ac voltage, and (b) dc voltage

2.3 Multi-Band Power System Stabilizer (MB-PSS)

A PSS can be viewed as an additional block of a generator excitation control or AVR,

added to improve the overall power system dynamic performance, especially for the

control of electromechanical oscillations. Thus, the PSS uses auxiliary stabilizing

signals such as shaft speed, terminal frequency and/or power to change the input

signal to the AVR. This is a very effective method of enhancing small-signal stability

performance on a power system network. The main characteristics of the MB-PSS

model are shown in Fig. 10(a). As for conventional PSS, the MB-PSS comprises three

main functions, the transducers, the lead-lag compensation and the limiters. Two

speed deviation transducers are required to feed the three band structure used as lead-

lag compensation. Four adjustable limiters are provided, one for each band and one

for the total PSS output. The low band is taking care of very slow oscillating

phenomena such as common modes found on isolated system. Hydro-Quebec system

is a good example with its 0.05 Hz global mode.

The intermediate band is used for inter-area modes usually found in the range of 0.2 to

1.0 Hz. The high band is dealing with local modes, either plant or intermachines, with

a typical frequency range of 0.8 to 4.0 Hz. The speed deviation transducers are both

derived from machine terminal voltages and currents. The first one, so called ∆ωL. is

associated with the first two bands. Its measurement is accurate in the 0 to 2.0 Hz

range. ∆ωH., the second transducer, is designed for the high band with a frequency

range of 0.8 to 5.0 Hz. The MB-PSS also provides two tunable notch filters to reject

the high frequency torsional modes found on turbo-generators. These are tuned for the

first two torsional modes of a given machine. With a simple and efficient setting

method such as the one presented here, it is possible to set the PSS with only two high

level parameters per band. Doing so, the whole lead-lag compensation circuit is

specified with six parameters. They are the three filter central frequencies FL, FI, FH

and gains KL, KI, KH, Being plain band-pass filters, only the first block in each

branch is involved. Time constants and gains are derived from simple equations for

the high band case.



K&'' � K&'( �T&* � T&( �

*π+

T&' � ,-�

., and T

K&' � K&* � .

.�

Central time constants TH2, and T

frequency FH while the symmetrical time constants, T

constant ratio R. Equation (29) is used to derive branch gains K

unit gain for the differential filter. The band gain is therefore equal to K

technique allows us to represent the MB

10(b).

(a) IEEE PSS4B model of the MB

(b)

Fig. 10: MB

The performance of the MB-PSS will now be assessed using stability simulations on

the actual Hydro-Quebec power system. To do so, an analytical approach, previously

described in [28]. The aim of this type of analysis is to identify the electromechanical

behavior of the system by developing a MIMO (Multiple Inputs Multiple Outputs)



363

1 (26) '

+-√. (27)

T&1 � T&(R (28)

.��.��*.�'

(29)

, and TH7 are directly derived from the filter central

frequency FH while the symmetrical time constants, TH1, and TH8 are computed using

constant ratio R. Equation (29) is used to derive branch gains KH1 and KH2

unit gain for the differential filter. The band gain is therefore equal to K

technique allows us to represent the MB-PSS in a simplified model as shown in Fig.

(a) IEEE PSS4B model of the MB-PSS

(b) MB-PSS simplified model

Fig. 10: MB-PSS conceptual representation.

PSS will now be assessed using stability simulations on

Quebec power system. To do so, an analytical approach, previously

im of this type of analysis is to identify the electromechanical




are directly derived from the filter central

are computed using

H2 to obtain a

unit gain for the differential filter. The band gain is therefore equal to KH. This

PSS in a simplified model as shown in Fig.

PSS will now be assessed using stability simulations on

Quebec power system. To do so, an analytical approach, previously

im of this type of analysis is to identify the electromechanical




364

type of conventional linear model (A,B,C,D) fulfilling the following state equations

[25, 30]:

x4�' � Ax4 � Bu4 (30)

y4 � Cx4 � Du4 (31)

In large power systems, participation factors corresponding to the speed deviation of

generating units can be used for initial screening of generators on which to add PSS.

However, a high participation factor is a necessary but not sufficient condition for a

PSS at the given generator to effectively damp oscillation. Following the initial

screening a more rigorous evaluation using residues and frequency response should be

carried out to determine the most suitable locations for the stabilizers.

3.1 PSS Tuning

The MB-PSS settings were easily selected by varying the center frequency and gain of

each band so as to achieve a nearly flat phase response between 0.1Hz and 5Hz. The

dω-PSS settings with two changes [11]: a gain increase from 20 to 30 and the addition

of a 15-ms transducer time constant. The frequency responses of these PSSs as shows

Bode Plot of the PSS in Fig. (11).This figure confirms that the MP-BSS phase is

effectively flat around 20-40 degrees in the frequency range of interest. The dω-PSS

has an overall poor phase shape, especially around 1-2 Hz, which makes it unable to

cope with faster local or intermachine modes in multi-unit power plants. By contrast,

the dPa-PSS has a good combination of strong gain and phase advance above 0.3 Hz,

although it is unpractical at low frequency where it shows a 180 deg phase advance,

which actually has a destabilizing effect despite the rather small low-frequency gain.

Finally, even though the low-frequency shaping of the dω-PSS is satisfactory in

overall, its DC rejection (washout) is not efficient enough, providing five time less

attenuation than the MB-PSS.

Fig. 11: Frequency responses of these PSSs as Bode Plot of the PSS tuning

3. RESULTS AND DISCUSSIONS

3.1 System without STATCOM or MB-PSS The 4-machine 2-area test system was subjected to a three phase fault at the mid-point

of the one transmission lines and cleared after 200 ms. In this case; the system didn't



365

have any stabilizer such as PSS or FACTS devices. Therefore, the system stability

was affected by this three-phase fault and led the system to be unstable. The responses

of the test system are shown in Fig. (12). The performance of the rotor angle δ, speed

deviation ∆ω, the terminal voltage Vt, the field excitation voltage Efd, acceleration

power Pa and tie line power Ptie in the two area system are shown below.

(a) Rotor angle δ14, in deg. (b) Speed Deviation dω1, pu.

(c) Voltage Terminal Vt1, pu. (d) Exciter Voltage Efd1, pu.

(e) Acceleration Power Pa1, pu. (f) Power Tie Line Ptie, MW

Fig. 12: Four-machine two-area test system with 3-Φ fault and without MB-PSS or

STATCOM

3.2 System with STATCOM device and without MB-PSS

If the STATCOM controller is added to the above test system (4-machine 2-area

system) and subjected to the same 3-Φ fault, then the system response maintain to be

stable and the oscillations nearly damped. Figure (13) shows the performance of the

rotor angle δ, speed deviation dω, the terminal voltage Vt, the field excitation voltage

Rotor Angle - delta 1-4

-50

0

50

100

150

200

0 10 20 30 40 50

time, sec.

delt

a,

de

g.

Speed Deviation - dw1

1

1.002

1.004

1.006

1.008

1.01

1.012

1.014

0 10 20 30 40 50

time, sec.

dw

1,

pu

Terminal Voltage - Vt1

0.97

0.99

1.01

1.03

1.05

1.07

0 10 20 30 40 50time, sec.

Vt1

, p

u

Exciter Voltage - Efd1

0

1

2

3

4

5

6

7

0 10 20 30 40 50

time, sec.

Efd

1, p

u

Acceleration Power - Pa1

-0.22

-0.12

-0.02

0.08

0.18

0.28

0 10 20 30 40 50

time, sec.

Pa

1,

pu

Tie-line Power - Ptie

-300

-100

100

300

500

700

0 10 20 30 40 50

time, sec.

Pti

e,

pu



366

Efd, acceleration power Pa and tie line power Ptie when the disturbance of 3-Φ fault has

occurred in the two-area system with STATCOM controllers of +/-500MVA

converter rating fixed at each end of the two areas.




Fig. 13: Four-machine two-area test system with STATCOM controller under 3-Φ

fault

3.3 System with MB-PSS and without STATCOM

If the MB-PSS is used with the exciter of each machine in the test system (4-machine

2-area system), and the system is subjected to the same 3-Φ fault, then the system

response maintain to be stable and the oscillations are damped. Figure (14) shows the

performance of the rotor angle δ, speed deviation dω, the terminal voltage Vt, the field


0

10

20

30

40

50

60

70

80

0 10 20 30 40 50time, sec.

delt

a 1

-4, deg

.

w ith STATCOM


0.996

0.998

1

1.002

1.004

1.006

0 10 20 30 40 50time, sec.

dw

1, p

u

w ith STATCOM


0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

0 10 20 30 40 50

time, sec.

Vt1

, p

u

w ith STATCOM

Exciter Voltage Efd1

-1

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50

time, sec.

Efd

1, p

uw ith STATCOM


-0.2

-0.1

0

0.1

0.2

0.3

0 10 20 30 40 50

time, sec.

Pa

1,

pu

w ith STATCOM

Tie line Power - Ptie

0

100

200

300

400

500

600

700

0 10 20 30 40 50time, sec.

Pti

e, p

u

w ith STATCOM



367

excitation voltage Efd, acceleration power Pa and tie line power Ptie when the

disturbance of 3-Φ fault has occurred in the two-area system which have excitation

control by MB-PSS [13].




Fig. 14: Four-machine two-area test system with multi-band power system stabilizer

(MB-PSS) under 3-Φ fault

3.4 System with Combined Control of STATCOM Controller and with Excitation

Control of (MB-PSS)

When the combination of the STATCOM and the MB-PSS were added to the two-

area system, this leads to a significant increase of the oscillation damping and leads to

Rotor Angle -delta1-4

32

36

40

44

48

0 2 4 6 8 10 12time, sec.

delta, sec.

w ith MB-PSS


0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

0 5 10 15 20time, sec.

dw

1, pu

w ith MB-PSS


0.95

1

1.05

1.1

1.15

1.2

1.25

0 2 4 6 8 10 12

time, sec.

Vt1

, p

u

w ith MB-PSS

Exciter Voltage - Efd1

-1

1

3

5

7

9

11

13

0 2 4 6 8

time, sec.

Efd

1, p

uw ith MB-PSS


-0.33

-0.23

-0.13

-0.03

0.07

0.17

0.27

0 1 2 3 4 5 6 7

time, sec.

Pa1, p

u

w ith MB-PSS


180

280

380

480

580

680

0 2 4 6 8time, sec.

Pti

e, p

u

w ith MB-PSS



368


180

280

380

480

580

680

0 1 2 3 4 5 6 7 8time, sec.

Ptie, pu

STATCOM

MB-PSS

the improvement of the power system stability. Comparing with the previous results,

the combination between STATCOM and MB-PSS gives more stable performance of

the system parameters. Figure (15) shows the performance of the disturbance of 3-Φ

fault occurred in the two-area system which have combined control of MB-PSS and

STATCOM.




Fig. 15: Four-machine two-area test system with combined STATCOM controller and

MB-PSS under 3-Φ fault

3.5 Comparison between the Three Cases (STATCOM, MB-PSS, and Combined) When the combination between the STATCOM and the MB-PSS is added to the two-

area system, this is result in a significant increase in damping oscillation which leads


20

25

30

35

40

45

50

0 2 4 6 8 10 12

time, sec.

delta 1

-4, deg.

STATCOM

MB-PSS

Speed Deviation - dw 1

0.995

0.997

0.999

1.001

1.003

1.005

0 4 8 12 16 20time, sec.

dw

1, pu

STATCOM

MB-PSS

Terminal Voltage Vt1

0.92

0.97

1.02

1.07

1.12

1.17

0 2 4 6 8 10 12

time, sec.

Vt1

, pu

STATCOM

MB-PSS

Exciter voltage - Efd1

-1

1

3

5

7

9

11

13

15

0 2 4 6 8time, sec.

Efd

1, pu

STATCOM

MB-PSS


-0.35

-0.25

-0.15

-0.05

0.05

0.15

0.25

0.35

0 2 4 6 8

time, sec.

Pa1, pu

STATCOM

MB-PSS



369

to improve the power system stability. Comparison between the three cases

(STATCOM, MB-PSS, and Combined) is shown in Fig. (16). The combination

STATCOM and MB-PSS gave more stable performance of the system parameters.

(a) Rotor angle δ14, in deg.

(b) Speed Deviation dω1, pu.

Fig. 16: Four-machine two-area test system with combined STATCOM controller and

MB-PSS under 3-Φ fault

4. CONCLUSIONS

In this study, the power system stability enhancement via STATCOM device and MB-

PSS are presented and discussed. The coordination between the STATCOM controller

and the MB-PSS is taken into consideration to improve the system transient stability

as well as the system voltage regulation. The electromechanical mode is more

controllable through based stabilizers. The proposed stabilizers have been tested on a

Kundur's four-machine two-area power system with three-phase fault disturbance and

Rotor Angle, delta 1-4

20

25

30

35

40

45

50

55

60

0 10 20 30 40 50time, sec.

delta, deg.

STATCOM

MB-PSS

Combined

Speed Deviation, dw1

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

0 10 20 30 40 50time, sec.

dw

1, pu

STATCOM

MB-PSS

Combined



370

loading conditions. The nonlinear simulation results show the effectiveness and

robustness of the proposed STATCOM controller and power system stabilizer to

enhance the system stability.

REFERENCES

[1] Sauer PW, Pai MA. Power system dynamics and stability. Englewood Cliffs, NJ, USA:

Prentice-Hall; 1998.

[2] Asgharian R. A robust H∞ power system stabilizer with no adverse effect on shaft torsional

modes. IEEE Trans Energy Conv., pp. 475–481, 1994.

[3] Kwakernaak H. Robust control and H∞ optimization—tutorial. Automatica, pp.255–273, 1993.

[4] Kundur P, Klein M, Rogers GJ, Zywno MS. Application of power system stabilizers for

enhancement of overall system stability. IEEE Trans PWRS, pp. 614–626, 1989.

[5] Gibbard MJ. Robust design of fixed-parameter power system stabilizers over a wide range of

operating conditions. IEEE Trans PWRS, pp.794–800, 1991.

[6] Heniche A., Kamwa I., and Grondin R., “Torsional-Mode Identification for Turbogenerators

with Application to PSS Tuning”, IPST’05 in Montreal, Canada on June 19-23, 2005.

[7] Mahran AR, Hogg BW, El-Sayed ML. Coordinated control of synchronous generator

excitation and static VAR compensator. IEEE Trans Energy Conv., pp. 615–622, 1992.

[8] K. R. Padiyar, and Nagesh Prabhu, Design and performance evaluation of subsynchronous

damping controller with STATCOM, IEEE Transactions on Power Delivery, Vol. 21, No. 3,

pp.1398-1405, july 2006

[9] Behrooz Vahidi, Mohammad Reza Bank Tavakoli, and Wolfgang Gawlik, Determining

parameters of turbine’s model using heat balance data of steam power unit for educational

purposes, IEEE Transactions on Power Systems, Vol. 22, No. 4, pp. 1546-1552, November

2007.

[10] “IEEE Recommended Practice for Excitation System Models for Power System Stability

Studies”, IEEE St. 421.5-2002.

[11] Mobarak Y. A., " A Simulink Multi-Band Power System Stabilizer", Journal of Engineering

Sciences, Assiut University, Vol. 35, No. 2 pp. 489-507, March 2007.

[12] Wang HF, Swift FJ. A unified model for the analysis of FACTS devices in damping power

system oscillations. Part I. Single-machine infinite-bus power systems. IEEE Trans PWRD, pp.

941–946, 1997.

[13] Abido MA, Abdel-Magid YL. Analysis and design of power system stabilizers and FACTS

based stabilizers using genetic algorithms. 14th Power Systems Computation Conference

PSCC, June 24–28, 2002.

[14] Y. A. Mobarak, “Power System Stabilization Using a Combination of Static VAR

Compensator and Multi-Band Power System Stabilizer”, International Review of Automatic

Control (I.RE.A.CO.), Praise Worthy Prize, Vol. 4, No. 1, pp. 94-101, January 2011.

[15] Rahim A, Nassimi S. Synchronous generator damping enhancement through coordinated

control of exciter and SVC. IEE Proc Gener Transm Distrib, pp. 211–218, 1996.

[16] Noroozian M, Anderson G. Damping of power system oscillations by use of controllable

components. IEEE Trans PWRD, pp. 2046–2054, 1994.

[17] M. Ahmadzadeh, S.S. Mortazavi, A. Saeedian, A novel method of coordinating PSSs and

FACTS devices in power system stability enhancement, WSEAS transactions on Power

systems, 2009.

[18] A. Ahmed, Y. A. Mobarak, O. Amer, “Power System Damping Enhancement via Coordinated

Design of PSS & TCSC”, Journal of Engineering Sciences (JES), Assiut University, Egypt,

Vol. 39, No. 1, pp. 113-122, January 2011.

[19] Du W, Wu X, Wang HF, and Dunn R, Feasibility study to damp power system multi-mode

oscillations by using a single FACTS device, Int. J Electric Power Energy System, Vol.32, pp.

645-655, 2010.



371

[20] Youssef A. Mobarak, “SVC, STATCOM, and Transmission Line Rating Enhancments on

Induction Generator Driven by Wind Turbine", International Journal of Electrical Engineering

and Technology (IJEET), Volume 3, Issue 1, pp. 326-343, Jan- June 2012.

[21] Shayeghi H, Safari A, and Shayanfar HA, PSS and TCSC damping controller coordinated

design using PSO in multi-machine power system, Energy Conversion and Management,

Vol.51, pp.2930-2937, 2010.

[22] S.F. Faisal, A.H.M.A. Rahim, J.M. Bakhashwain, A robust STATCOM controller for a

multimachine power system using particle swarm optimization and loop-shaping, International

Journal of Electrical, Computer, and Systems Engineering, pp. 64-70, 2007.

[23] Mohammad Reza Safari Tirtashi Ahmad Rohani Reza Noroozian, PSS and STATCOM

controller design for damping power system oscillations using fuzzy control strategies,

Proceedings of ICEE 2010, May 11-13, 2010

[24] S. Panda, N.P. Padhy "Optimal location and controller design of STATCOM for power system

stability improvement using PSO" Journal of the Franklin Institute, pp. 166-181, 2008.

[25] Mohammad Reza, Ahmad Rohani & Reza Noroozian, PSS and STATCOM controller design

for damping power system oscillations using fuzzy control strategies, 18th Iranian conference

on Electrical Engineering, pp. 901-906, 2010.

[26] Y. A. Mobarak, “Power Systems Voltage stability Assessment Using STATCOM ”,

International Review of Automatic Control (I.RE.A.CO.), Praise Worthy Prize, Vol. 4, No. 2,

pp. 259-266, March 2011.

[27] Mahdiyeh Eslami, Hussain Shareef, Azah Mohamed, Mohammad Khajehzadeh, Optimal

location of PSS using improved PSO with chaotic sequence, International Conference on

Electrical, Control and Computer Engineering, Pahang, Malaysia, pp. 253-258, June 21-22,

2011.

[28] J. Barati, S. S. Mortazavi, A. Saidian, Analysis and assessment of FACTS-based stabilizers for

damping power system oscillations using genetic algorithms, International Review of

Electrical Engineering, Vol. 5, No.6, pp 2819-2827, 2010.

[29] A.B. Khormizi & A.S. Nia, Damping of power system oscillations in multi-machine power

systems using coordinate design of PSS and TCSC, 10th EEEIC, pp. 1-4, 2011.

[30] Furini MA, Pereira ALS, and Araujo PB, Pole placement by coordinated tuning of power

system stabilizers and FACTS-POD stabilizers, Int. J Electric Power Energy System, Vol.33,

pp. 615-622, 2011.

[31] Youssef A. Mobarak, "Novel Controllers for Reactive Power Compensation by using

STATCOM", ICGST International Journal on Automatic Control and System Engineering

(ACSE), Vol. 12, Issue 1, pp. 9-20, June 2012.

Appendices

1- MB-PSS Simplified Settings Mode [11]:

K=1, FB=0.2Hz, KE=20, FI=0.9Hz, KI=25, FH=12Hz, KH=145, VLmax=0.075pu, VImax=0.15pu,

VHmax=0.15pu, VSmax=0.15pu

2- STATCOM parameters [26]: 230 KV, ±500 MVAR

R=0.0073pu,L=0.22pu,Vdc=40KV,Cdc=±375µF, Vref =1.0pu, Vac regulator gains Kp = 5, Ki = 1000,

Vdc regulator gains Kp = 0.1e-3, Ki = 20e-3

3- Synchronous Generator [4, 14]:

Xd=1.8pu,Xd'=0.3pu,Xd

''=0.25pu,Xq=1.7pu,Xq

'=0.55pu,Xq

''=0.25pu,Xl=0.2pu,Rs=0.0025pu,Tdo

'=8sec,T

do''=0.03sec,Tqo

'=0.4sec, Tqo''=0.05sec,H=6.5sec, p=4

4- Excitation System [4, 10]:

Tr=0.02sec, Ka=300, Ta=0.001, Ke=1, Te=0, Tb=0, Tc=0, Kf=0.001, Tf=0.1sec, Efmin= -11.5, Efmax=11.5

5- Steam Turbine and Governor [10, 11]:

Kp=1, Rp=0.05, Dz=0, Tsr=0.001, Tsm=0.15, and Vgmin=-0.1, Vgmax=0.1pu/s, gmin=0, gmax=4.496, and

T2=0, T3=10, T4=3.3, T5=0.5, and F2=0.5, F3=0.5, F4=0, F5=0, and H3=0.24897, H4=0, H5=0, and

K12=83.47, K23=42.702, K34=0, K45=0pu/rad, and D2=2.4832, D3=0.4, D4=0, D5=0pu, torque/pu speed

deviation.



372

Biographies

Gaber Shabib: He received his B.Sc. degree in electrical engineering from Al-

Azhar University with excellent with honor degree. In October 1982 he joins the

electrical engineering, King Fahad University of Petroleum and Minerals,

Dhahran Saudi Arabia as a research assistant. In December 1985 he received his

M.Sc. degree in electrical engineering from King Fahad University of Petroleum

and Minerals. In November 1987 he joins the Qassim Royal Institute, Qassim,

Saudi Arabia as a lecturer. He received his Ph.D. degree from Menoufia University, Egypt, in 2001.

He joined Aswan High Institute of Energy, South Valley University, Aswan, Egypt in 1999. He joined

Digital Control Laboratory, Tsukuba University, Japan as a visiting Professor 2006–2007. His

research interests are power system stability, control, Self tuning control, Fuzzy logic techniques,

Digital control techniques all as applied to power systems.

Youssef A. Mobarak was born in Egypt. He received his B.Sc. and M.Sc.

degrees in Electrical Engineering from South Valley University, Aswan, Egypt,

in 1997 and 2001 respectively and Ph.D. from Cairo University, Egypt, in 2005.

He joined Electrical Engineering Department, High Institute of Energy, South

Valley University as a Demonstrator, as an Assistant Lecturer, and as an

Assistant Professor during the periods of 1998–2001, 2001–2005, and 2005–2009

respectively. He joined Artificial Complex Systems, Hiroshima University, Japan

as a Researcher 2007–2008. Also, he joined King Abdulaziz University, Rabigh, Faculty of

Engineering 2010 to present. His research interests are power system planning, operation, and

optimization techniques applied to power systems, Nanotechnology materials via addition nano-scale

particles and additives for usage in industrial field.

35 coordinated design of a mb-pss and statcom controller to enhance power system stability · ·...

Documents