Comparative performance evaluation of SMES–SMES, TCPS–SMES and SSSC–SMES controllers in automatic generation control for a two-area hydro–hydro system

Electrical Power and Energy Systems 33 (2011) 1585–1597

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Comparative performance evaluation of SMES–SMES, TCPS–SMES and SSSC–SMEScontrollers in automatic generation control for a two-area hydro–hydro system

Praghnesh Bhatt a, Ranjit Roy b,⇑, S.P. Ghoshal c

a Department of Electrical Engineering, Charotar Institute of Technology, Charotar University of Science and Technology, Changa 388 421, Gujarat, Indiab Department of Electrical Engineering, S. V. National Institute of Technology, Surat 395 007, Gujarat, Indiac Department of Electrical Engineering, National Institute of Technology, Durgapur 713 209, West Bengal, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 February 2010Received in revised form 31 October 2010Accepted 9 December 2010Available online 5 October 2011

Keywords:Automatic generation controlCRPSOHydraulic generation unitSMESSSSCTCPS

0142-0615/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijepes.2010.12.015

⇑ Corresponding author. Tel.: +91 9904402937; faxE-mail addresses: pragneshbhatt.ee@ecchanga.

rediffmail.com (R. Roy), [email protected]

This paper presents the automatic generation control (AGC) of an interconnected two-area multiple-unithydro–hydro system. As an interconnected power system is subjected to load disturbances with changingfrequency in the vicinity of the inter-area oscillation mode, system frequency may be severely disturbedand oscillating. To compensate for such load disturbances and stabilize the area frequency oscillations,the dynamic power flow control of static synchronous series compensator (SSSC) or Thyristor ControlledPhase Shifters (TCPS) in coordination with superconducting magnetic energy storage (SMES) are pro-posed. SMES–SMES coordination is also studied for the same. The effectiveness of proposed frequencycontrollers are guaranteed by analyzing the transient performance of the system with varying load pat-terns, different system parameters and in the event of temporary/permanent tie-line outage. Gains of theintegral controllers and parameters of SSSC, TCPS and SMES are optimized with an improved version ofparticle swarm optimization, called as craziness-based particle swarm optimization (CRPSO) developedby the authors. The performance of CRPSO is compared to that of real coded genetic algorithm (RGA)to establish its optimization superiority.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

In power systems, changes in the load affect the frequency andbus voltages in the systems. For small changes in the load the fre-quency deviation problem can be separated or decoupled from thevoltage deviation. The problem of controlling the real power outputof generating units in response to changes in system frequency andtie-line power interchange within specified limits is known as loadfrequency control (LFC). It is generally regarded as a part of auto-matic generation control (AGC) and is very important in the opera-tion of power systems [1]. With the increase in size and complexityof modern power systems, inadequate control may deteriorate thefrequency and system oscillation might propagate into wide arearesulting in a system blackout. However, most of the solutions pro-posed so far for AGC have not been implemented due to systemoperational constraints associated with thermal power plants. Themain reason is the non-availability of required stored energy capac-ity other than the inertia of the generator rotors.

Fast-acting energy storage system provides storage capacity inaddition to the kinetic energy of the generator rotors which canshare sudden changes in power requirement and effectively damp

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electromechanical oscillations in a power system. An attempt touse battery energy storage system (BESS) to improve the LFCdynamics of West Berlin Electric Power Supply has appeared in[2]. The problems like low discharge rate, increased time requiredfor power flow reversal and maintenance requirements have led tothe evolution of superconducting magnetic energy storage (SMES)for their applications as load frequency stabilizers.

A superconducting magnetic energy storage (SMES) which iscapable of controlling active and reactive powers simultaneously[3] is expected as one of the most effective and significant stabi-lizer of frequency oscillations. The viability of superconductingmagnetic energy storage (SMES) for power system dynamic perfor-mance improvement has been reported in [4,5].

Moreover, in the future competitive electricity market, variouskinds of apparatus with large capacity and fast power consumptionmay cause a serious problem of frequency oscillation. Especially, ifthe frequency of changing load is in the vicinity of the inter-areaoscillation mode (0.2–0.8 Hz), the oscillation of system frequencymay sustain and grow to cause a serious stability problem if noadequate damping is available [6]. Static synchronous series com-pensator (SSSC) is one of the important members of FACTS family[7] which can be installed in series with the transmission lines.With the capability to change its reactance characteristic fromcapacitive to inductive, the SSSC is very effective in controllingpower flow [8]. Ngamroo et al. [9] proposed the application of SSSC

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Nomenclature

i subscript referred to area (1, 2)j subscript referred to generation units (1–4)f nominal system frequency (Hz)PRi rated power of area i (MW)Hi inertia constant of area i (s)Di load damping coefficient in area iBi frequency bias of area iKi integral gain of area iDPDi incremental load change in area i (p.u.)DPmj incremental generation change of unit j (p.u.)TGj hydro governor time constant of unit j (s)TRj governor reset time constant of unit j (s)TWj water starting time constant of unit j (s)RPj permanent speed regulation for governor of unit jRTj temporary speed regulation for governor of unit japfj area participation factor of unit ja12 area capacity ratio �PR1=PR2ð ÞDxi incremental p.u. rotor speed deviation of area iDfi frequency deviation of area i (Hz)T12 tie - line synchronizing coefficientKf frequency gainTSSSC time constant for SSSC (s)TPS time constant for TCPS (s)

KSMES gains for SMESKSSSC gains for SSSCTSMES time constant for SMES (s)Ku gains for TCPSDPSMES active power output deviation of SMESDPSSSC active power output deviation of SSSCDPTCPS active power output deviation of TCPSc1, c2 positive constants representing cognitive and social

learning rate, respectivelygBest group bestpBesti personal best of ith particlePcraz predefined craziness probabilityr1, r2, r3, r4 random numbers in the interval [0,1]vcraziness

i random number chosen uniformly in the interval½vmin

i ; vmaxi �

xki ; vk

i current position and velocity of ith particle at kth itera-tion, respectively

xkþ1i ; vkþ1

i modified position and velocity of ith particle at kthiteration, respectively

vmax, vmin maximum and minimum velocity of ith particle,respectively

1586 P. Bhatt et al. / Electrical Power and Energy Systems 33 (2011) 1585–1597

for frequency stabilization by locating SSSC in series with thetie-line between interconnected two-area power systems withthermal units. Das et al. [10] investigated the application of Thyris-tor Controlled Phase Shifters (TCPS) as a new ancillary service forthe stabilization of frequency oscillations of an interconnected hy-dro-thermal power system.

Ghoshal et al. [11] have made a good attempt to stabilize thefrequency oscillations by coordinating Capacitive Energy Storage(CES) and TCPS in two-area thermal-hydro and hydro-diesel inter-connected systems to improve the transient performance of thesystem. Nanda et al. [12] have also considered an interconnectedhydro-thermal system in the continuous discrete mode using con-ventional integral (I) controller or proportional-integral (PI) con-troller. It is established that maximum deviation and settlingtime are same for both the controllers. Thus, it is quite relevantto consider the integral controller for the AGC loop.

Ghoshal et al. [13,14] used a genetic algorithm (GA) to optimizecontroller gains of a multi-area hydro-thermal AGC system simul-taneously more effectively than is possible with traditional ap-proach. The premature convergence of GA degrades its efficiencyand reduces the search capability. To overcome this problem, Gho-shal [15] has also proposed a more recent and powerful and com-putationally intelligent technique particle swarm optimization(PSO) to optimize the PID gains of the controller.

Literature survey shows that most of the earlier work in the areaof AGC pertains to an interconnected hydro-thermal system andrelatively lesser attention has been devoted to AGC of an intercon-nected hydro–hydro system involving hydro subsystems of widelydifferent characteristics. Thus, this paper addresses the AGC withinterconnected hydro dominated systems having multiple hydro–hydro subsystems with different area capacities. The impacts ofcoordinated controllers SMES–SMES, SSSC–SMES and TCPS–SMESon load frequency stabilization for such a hydro dominated systemhave been evaluated. The transient performance of these coordi-nated controllers are compared to establish their effectivenessone over another to suppress the area frequency oscillation andtie-line power exchange after the step load perturbation. In theview of the above, the objectives of the paper are as follow:

(i) To investigate the impacts of coordinated controllers SMES–SMES, SSSC–SMES and TCPS–SMES on dynamic response ofthe test system under load perturbation.

(ii) To examine the effect of system parameter variations, sinu-soidal load changes and tie-line outages on transient perfor-mance of the test system.

(iii) To obtain the optimized control parameters for SMES–SMES,SSSC–SMES and TCPS–SMES controllers by CRPSO and RGAand compare the effectiveness of the optimizationalgorithms.

2. Linearized models of an interconnected two-area multipleunits hydro–hydro system, TCPS, SSSC and SMES

The AGC system introduced in this work consists of two gener-ating areas of different capacities (Area 1: 1800 MW and Area 2:1200 MW). Each area comprises of two hydraulic generation units.The characteristics of hydro turbine differ widely from steam tur-bine in the following respects and hence, an attempt is made toexamine the frequency response of such a hydro dominated sys-tem in this work. Fig. 1 shows a linearized model of an intercon-nected two-area multiple-units hydro–hydro system for AGCstudy. The system parameters are given in Appendix.

2.1. Characteristic of hydraulic generation unit

The transfer function of the hydro turbine represents a non-minimum phase system. The initial power surge of a hydro turbineis opposite to that desired. A change in the gate position at the footof the penstock causes the pressure across the turbine to reduce.However, the flow does not change immediately due to water iner-tia causing the power of the turbine to reduce temporarily (the tur-bine mechanical power is the product of pressure and flow) [6].The initial opposite power surge lasts for 1–2 s depending on thewater starting time and the load step. Because of this phenomenon,during a generation deficit situation, the decelerating power (en-ergy) is higher for a hydro turbine compared to a steam turbinewith/without the reheat. Therefore, it would be of practical

Fig. 1. Linearized model of an interconnected two-area hydro–hydro system.

Fig. 3. A schematic of interconnected two-area hydro-hydro power system withTCPS in series with the tie-line.

P. Bhatt et al. / Electrical Power and Energy Systems 33 (2011) 1585–1597 1587

significance to explore the system performance having onlyhydraulic generation units for AGC. The complete block diagramof hydro turbine-governor system together with equivalent rotor/load is given in [6]. The transient response of a single hydraulicgeneration unit to a 0.1 per unit step change in load is shown inFig. 2. An initial opposite mechanical power change of turbinewhich is about 20% of load steps occurs and lasts for about 1.6 s.

2.2. Linearized model of TCPS applicable for AGC

The schematic of an interconnected two-area hydro–hydro sys-tem considering a TCPS in series with the tie-line is shown in Fig. 3.TCPS is placed near Area 1. Resistance of the tie-line is neglected.

Without TCPS, the incremental tie-line power flow from Area 1to Area 2 can be expressed as

0 5 10 15 20-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Time [Sec]

[pu]

Gate PositionMechanical PowerSpeed Deviation

Fig. 2. Transient response of a single hydraulic generation unit to a step change inthe load demand.

DP0tie12ðsÞ ¼

T12

sDx1ðsÞ � Dx2ðsÞ½ � ð1Þ

When a TCPS is placed in series with the tie-line, the current flow-ing from Area 1 to Area 2 can be written as

I12 ¼jV1j\ðd1 þuÞ � jV2j\ðd2Þ

jX12ð2Þ

From Fig. 3,

Ptie12 � jQ tie12 ¼ V�1I12 ¼ jV1j\� ðd1 þuÞ jV1j\ðd1 þuÞ � jV2j\ðd2ÞjX12

� �

ð3Þ

) Ptie12 � jQtie12 ¼jV1jjV2j

X12sinðd1 � d2 þuÞ � j

�jV1j2 � jV1jjV2j cosðd1 � d2 þuÞh i

X12ð4Þ

Separating the real parts of (4), we get

Ptie12 ¼jV1jjV2j

X12sinðd1 � d2 þuÞ ð5Þ

In (5), perturbing d1, d2 and u from their nominal values d01; d0

2 andu0 yields:

Fig. 5. Schematic of SSSC connected in series with the tie-line.

Fig. 6. Equivalent circuit of SSSC connected in series with the tie-line.


DPtie12 ¼jV1jjV2j

X12cos d0

1 � d02 þu0� �

sin Dd1 � Dd2 þ Duð Þ ð6Þ

(Dd1 � Dd2 + Du) is very small since, for a small change in realpower load, the variation of bus voltage angles as well as thevariation of TCPS phase angle are practically very small.

Hence, sin(Dd1 � Dd2 + Du) � (Dd1 � Dd2 + Du).Therefore,

DPtie12 ¼jV1jjV2j

X12cos d0

1 � d02 þu0� �

Dd1 � Dd2 þ Duð Þ ð7Þ

T12 ¼jV1jjV2j

X12cos d0

1 � d02 þu0� �

ð8Þ

Thus, (7) reduces to

DPtie12 ¼ T12ðDd1 � Dd2 þ DuÞ ð9Þ) DPtie12 ¼ T12ðDd1 � Dd2Þ þ T12Du ð10Þ

We also know,

Dd1 ¼Z

Dx1 dt and Dd2 ¼Z

Dx2 dt ð11Þ

From (10) and (11), we get,

DPtie12 ¼ T12

ZDx1 dt �

ZDx2 dt

� �þ T12Du ð12Þ

Laplace transformation of (12) yields

DPtie12ðsÞ ¼T12

sDx1ðsÞ � Dx2ðsÞ½ � þ T12DuðsÞ ð13Þ

As per (13), tie-line power flow can be controlled by controlling thephase shifter angle Du.

The phase shifter angle Du(s) can be represented as:

DuðsÞ ¼ Ku

1þ sTPSDErrorðsÞ ð14Þ

Therefore, (13) can be rewritten as

DPtie12ðsÞ ¼T12

sDx1ðsÞ � Dx2ðsÞ½ � þ T12

Ku

1þ sTPSDErrorðsÞ ð15Þ

If the speed deviation Dx1 is sensed, it can be used as the controlsignal (i.e. DError = Dx1) to the TCPS unit to control the TCPS phaseshifter angle which in turn, controls the tie-line power flow. Thus,

DuðsÞ ¼ Ku

1þ sTPSDx1ðsÞ ð16Þ

and the tie-line power flow perturbation becomes

DPtie12ðsÞ ¼T12

sDx1ðsÞ � Dx2ðsÞ½ � þ T12

Ku

1þ sTPSDx1ðsÞ ð17Þ

DPtie12ðsÞ ¼ DP0tie12ðsÞ þ DPTCPSðsÞ ð18Þ

where DPTCPSðsÞ ¼ T12Ku

1þsTPSDx1ðsÞ

The structure of TCPS as a frequency controller is shown inFig. 4. The per unit rotor speed deviation (Dxi, i = 1, 2), which pro-vides the information of each mode of interest, is used as the inputsignal for the controller. Kf is the gain block having the value equalto nominal system frequency. There are two parameters such asstabilization gain Ku and time constant TPS to be optimized forthe optimal design of the TCPS frequency controller.

Fig. 4. Structure of TCPS as a frequency controller.

2.3. Linearized model of static synchronous series compensator (SSSC)applicable for AGC

A SSSC employs self-commutated voltage-source switchingconverters to synthesize a three-phase voltage in quadrature withthe line current, emulates an inductive or a capacitive reactance soas to influence the power flow in the transmission lines [8]. Thecompensation level can be controlled dynamically by changingthe magnitude and polarity of injected voltage, Vq and the devicecan be operated both in capacitive and inductive mode. The sche-matic of an SSSC, located in series with the tie-line between theinterconnected areas, can be applied to stabilize the area frequencyoscillations by high speed control of the tie-line power throughinterconnection as shown in Fig. 5.

The equivalent circuit of the system (Fig. 5) is shown in Fig. 6,where the SSSC is represented by a series-connected voltage sourceVs accompanied by a transformer leakage reactance Xs. The SSSCcontrollable parameter is Vs, which in fact represents the magni-tude of the injected voltage Vs. The phasor diagram of the systemtaking into account the operating conditions of the SSSC is shownin Fig. 7. Note that the SSSC voltage Vs changes only the magnitudeof the current but not its angle. When Vs = 0 (Fig. 7a), the current I0

of the system is

I0 ¼Vm � Vn

jXTð19Þ

where XT = XL + XS. The angle of the current is given by

hc ¼ tan�1 Vn cos hn � Vm cos hm

Vm sin hm � Vn sin hn

� �ð20Þ

(a) (b)Fig. 7. Phasor diagram (a) Vs = 0 (b) Vs lagging I by 90�.

Fig. 8. Structure of SSSC as a frequency controller.


From Fig. 7b, (19) can be generalized as

I ¼ Vm � Vs � Vn

jXT¼ Vm � Vn

jXT

� �þ � Vs

jXT

� �¼ I0 þ DI ð21Þ

being DI is an additional current term due to the SSSC voltage Vs.The power flow from bus m to bus n can be written as

Smn ¼ VmI� ¼ Smn0 þ DSmn

Pmn þ jQ mn ¼ ðPmn0 þ DPmnÞ þ jðQ mn0 þ DQ mnÞ ð22Þ

where Pmn0 and Qmn0 are the real and reactive power flows respec-tively when Vs = 0. The change in real power flow caused by theSSSC voltage Vs is given by

DPmn ¼VmVs

XTsinðhm � aÞ ð23Þ

When Vs lags the current by 90�(a = hc � 90�), DPmn can be writtenas follows:

DPmn ¼VmVs

XTcosðhm � hcÞ ð24Þ

From (20), the term cos(hm � hc) in (24) can be written as

cosðhm � hcÞ ¼Vn

Vmcosðhn � hcÞ ð25Þ

From Fig. 7a, we have

cosðhn � hcÞ ¼ywxy

ð26Þ

being

yw ¼ Vm sinðhmnÞ ð27Þ

and

xy ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2

m þ V2n � 2VmVn cos hmn

qð28Þ

and hmn = hm � hn. Using the above relationship, the term DPmn canbe expressed as

DPmn ¼VmVn

XTsin hmn �

VsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2


q ð29Þ

From (22),

Pmn ¼ Pmn0 þ DPmn

Pmn ¼VmVn

XTsin hmn

þ VmVn

XTsin hmn �

VsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2


q0B@

1CA ð30Þ

By linearizing (30) about an operating point

D _Pmn ¼VmVn

XTcosðhm � hnÞðDhm � DhnÞ

þ VmVn

XTsin hmn �

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2


q DVs

0B@

1CA ð31Þ

D _Pmn ¼ TmnðDhm � DhnÞ þ K1DVs ð32Þ

where Tmn ¼VmVn

XTcosðhm � hnÞ

and K1 ¼VmVn

XTsin hmn �

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2


q ð33Þ

As

Dhm ¼Z

Dxm dt and Dhn ¼Z

Dxn dt

D _Pmn ¼ Tmn

ZDxm dt �

ZDxn dt

� �þ K1DVs

Laplace transformation of (33) yields,

D _PmnðsÞ ¼Tmn

sDxmðsÞ � DxnðsÞ½ � þ K1DVsðsÞ ð34Þ

As per (34), tie line power can be controlled by controlling DVs.The controller to change the SSSC voltage can be represented as:

DVs ¼1þ T1s1þ T2s

� �1þ T3s1þ T4s

� �K2

1þ TSSSC

� �DErrorðsÞ

If the speed deviation Dx1 is sensed, it can be used as the controlsignal (i.e. DError = Dx1) to the SSSC unit to control Vs which willalter the tie-line power flow between two areas and assist in stabi-lizing the frequency oscillations. Thus,

D _PmnðsÞ ¼Tmn

sDxmðsÞ � DxnðsÞ½ �

þ K11þ T1s1þ T2s


� �K2

1þ TSSSC

� �Dx1ðsÞ ð35Þ

D _PmnðsÞ ¼Tmn

sDxmðsÞ � DxnðsÞ½ �

þ 1þ T1s1þ T2s


� �KSSSC

1þ TSSSC

� �Dx1ðsÞ ð36Þ

where KSSSC = K1K2

D _PmnðsÞ ¼ DP0mnðsÞ þ DPSSSCðsÞ ð37Þ

where

DPSSSCðsÞ ¼1þ T1s1þ T2s


� �KSSSC

1þ TSSSC

� �Dx1ðsÞ

The dynamic characteristic of SSSC controller for the frequencystabilization is shown in Fig. 8. The input signal of the proposedcontroller is the per unit rotor speed deviation (Dxi, i = 1, 2). Thestructure of SSSC for the frequency stabilization consists of twogain blocks with gain Kf equal to nominal frequency and KSSSC, aproportional block with the time constant of TSSSC and two stagephase compensation blocks as shown in Fig. 8. The phase compen-sation block with time constants T1, T2, T3 and T4 provides theappropriate phase-lead characteristics to compensate for the phaselag between input and the output signals. Thus, there are sixparameters such as K2 of stabilization gain KSSSC and time constantsTSSSC, T1, T2, T3 and T4 to be optimized for the optimal design of theSSSC frequency controller.

Fig. 9. Configuration of SMES in power system.

Fig. 10. Structure of SMES as a frequency controller.


2.4. Linearized model of superconducting magnetic energy storage(SMES) applicable for AGC

Fig. 9 shows the basic configuration of a SMES unit in the powersystem. The superconducting coil can be charged to a set value(which is less than the full charge) from the utility grid during nor-mal operation of the grid. The DC magnetic coil is connected to theAC grid through a Power Conversion System (PCS) which includesan inverter/rectifier. Once charged, the superconducting coil con-ducts current, which supports an electromagnetic field, with virtu-ally no losses. The coil is maintained at extremely low temperature(below the critical temperature) by immersion in a bath of liquidhelium.

When there is a sudden rise in the demand of load, the storedenergy is almost immediately released through the PCS to the gridas line quality AC. As the governor and other control mechanismsstart working to set the power system to the new equilibrium con-dition, the coil charges back to its initial value of current. Similar isthe action during sudden release of loads. The coil immediatelygets charged towards its full value, thus absorbing some portionof the excess energy in the system, and as the system returns toits steady state, the excess energy absorbed is released and the coilcurrent attains its normal value [4,5].

The structure for SMES as frequency stabilizer is modeled as thesecond order lead-lag compensator, similar to SSSC and is shown inFig. 10. The SMES is connected at the load point unlike connectingTCPS and SSSC in series with tie-line. For SMES–SMES coordination,there are six parameters in each area such as stabilization gain,KSMES and time constants TSMES, T1, T2, T3 and T4 to be optimizedfor the optimal design of the coordinated frequency stabilizer.

3. Mathematical problem formulation

The objective of AGC is to reestablish primary frequency regula-tion capacity, restore the frequency to its nominal value as quickly

as possible and minimize tie-line power flow oscillations betweenneighboring control areas. In order to satisfy the above require-ments, gains (KI1, KI2) of integral controller in AGC loop and SSSCparameters (KSSSC, TSSSC, T1, T2, T3 and T4), SMES parameters (KSMES,TSMES, T1, T2, T3 and T4) and TCPS parameters (Ku, TPS) are to beoptimized to have minimum undershoot (US), overshoot (OS)and settling time (ts) in area frequencies and power exchange overthe tie-line. In the present work, an Integral Square Error (ISE)criterion is used to minimize the objective function defined asFigure of Demerit (FDM) as follows:

FDM ¼X

Df 21 þ Df 2

2 þ DP2tie

h iDT ð38Þ

where DT is a given time interval for taking samples, Df, the incre-mental change in frequency and DPtie, the incremental change in tiepower. The objective function is minimized with the help of RGA orCRPSO based optimization techniques and the effectiveness of theoptimization algorithms has been compared.

4. Evolutionary computation techniques employed

4.1. Real coded genetic algorithm

Steps of real coded genetic algorithm (RGA) [16] are as follows:

(i) A set of population of chromosomes is created. Each chro-mosome contains some genes (optimizing variables).

(ii) The chromosomes are evaluated by a defined fitness func-tion. The better chromosomes will return lesser FDM in thisprocess.

(iii) Some of the chromosomes are selected to undergo geneticoperations for reproduction.

(iv) Genetic operations of crossover are performed.(v) After the crossover operation, the mutation operation

follows.(vi) After going through the mutation operation, the new off-

spring will be evaluated using FDM.

The new population will be formed when the new offspring re-places the chromosome with the smallest FDM value. After theoperations of selection, crossover and mutation, a new populationis generated. This new population will repeat the same process.


Such an iterative process will be terminated after the execution ofthe maximum iteration cycles.

4.2. Craziness-based particle swarm optimization

The PSO was first introduced by Kennedy and Eberhart [17]. It isan evolutionary computational model, a stochastic search tech-nique based on swarm intelligence.

Velocity updating equation:

vkþ1i ¼ vk

i þ c1� r1� ðpBesti � xki Þ þ c2� r2� ðgBest� xk

i Þ ð39Þ

Position updating equation:

xkþ1i ¼ xk

i þ vkþ1i ð40Þ

The following modifications in velocity help to enhance the globalsearch ability of PSO algorithm as observed in CRPSO [18].

(i) Velocity updating as proposed in [18] may be stated as in thefollowing equation:

Del

ta f2

(Hz)

Fig. 11.control

vkþ1i ¼ r2� vk

i þ ð1� r2Þ � c1� r1� ðpBesti � xki Þ

þ ð1� r2Þ � c2� ð1� r1Þ � ðgBest� xki Þ ð41Þ

Local and global searches are balanced by random number r2 as sta-ted in (41). Change in the direction in velocity may be modeled as inthe following equation:

0 50 100

-0.3

-0.2

-0.1

0

Time (Sec)

Del

ta f1

(Hz)

0 50 100 150 200 250-0.015

-0.01

-0.005

0

Time (Sec)

0 50 100 150 200 250

-3

-2

-1

0x 10

-3

Time (Sec)

Del

ta P

tie (p

u)

RGA

CRPSO

RGA

CRPSO

RGA

CRPSO

0 50

-0.2

-0.1

0

0.1

Time (Sec)

Del

ta 1

(Hz)

0 50

-0.1

-0.05

0

0.05

Time (Sec)

Del

ta P

tie (p

u)

0 50-0.4

-0.3

-0.2

-0.1

0

0.1

Time (Sec)

Del

ta f2

(Hz)

RGA

CRPSO

RGA

CRPSO

RGA

CRPSO

(a) (b)Frequency and tie-line power responses of the test system after 10% step load in Area 1 f

ler.

vkþ1i ¼ r2� signðr3Þ � vk

i þ ð1� r2Þ � c1� r1

� ðpBesti � xki Þ þ ð1� r2Þ � c2� ð1� r1Þ

� ðgBest� xki Þ ð42Þ

In (42), sign (r3) may be defined as

signðr3Þ ¼�1 ðr3 6 0:05Þ1 ðr3 > 0:05Þ

(ii) Inclusion of craziness: diversity in the direction of birdsflocking or fish schooling may be handled in traditionalPSO with a predefined craziness probability. The particlesmay be crazed in accordance with the following equationbefore updating its position.

vkþ1i ¼ vkþ1

i þ Prðr4Þ � signðr4Þ � vcrazinessi ð43Þ

where Pr(r4) and sign(r4) are defined respectively as:

Prðr4Þ ¼1 ðr4 6 PcrazÞ0 ðr4 > PcrazÞ

ð44Þ

signðr4Þ ¼1 ðr4 P 0:5Þ�1 ðr4 < PcrazÞ

ð45Þ

During the simulation of PSO, certain parameters require properselection as PSO is much sensitive to the selection of input param-eters. The best chosen maximum population size = 50, maximum

100

100

100

0 20 40 60 80

-0.4

-0.2

0

Time (Sec)

Del

ta f1

(Hz)

0 20 40 60 80

-0.4

-0.2

0

Time (Sec)

Del

ta f2

(Hz)

0 20 40 60 80

-0.1

-0.05

0

0.05

Time (Sec)

Del

ta P

tie (p

u)RGA

CRPSO

RGA

CRPSO

RGA

CRPSO

(c)or: (a) SMES–SMES controller, (b) SSSC–SMES controller, and (c) TCPS–SMES


allowed iteration cycles = 100, best value of Pcraz = 0.2 (chosen afterseveral experiments), best values of c1 and c2 are c1 = c2 = 1.65. Thechoice of c1, c2 are very much vulnerable for PSO execution. The va-lue of vcraziness

i lies between 0.25 and 0.35. The novelty of CRPSO lieswith the fact of its faster convergence to the better optimal solutionas compared to its other counter parts.

5. Simulation results and discussion

Time domain simulation studies have been carried out on aninterconnected two-area multiple-units hydro–hydro systemshown in Fig. 1 after 10% step load perturbation in Area 1. It is ob-served that after the load disturbance, the area frequency responseis heavily perturbed. Hence, to suppress the oscillations and tohave the optimal transient response of area frequencies and tie-line power exchange, the impacts of (a) SSSC–SMES coordination,(b) TCPS–SMES coordination and (c) SMES–SMES coordinationhave been explored and discussed as below.

5.1. SSSC or TCPS in series with the tie-line near Area 1 and SMESlocated at the terminal of Area 2 or with SMES located at the terminalof each area

The linearized model of an interconnected two-area multiple-units hydro–hydro systems with SSSC or TCPS in series with the

Table 1Optimized parameters for SMES–SMES controller.

Input set of parameters R3 = R4 = 0.05 R3 = R4 = 0.02D2 = 1.0 D2 = 0.55T12 = 0.0866 T12 = 0.055

Optimized parameters CRPSO RGA CRPSO RGA

KSMES1 0.299 0.291 0.300 0.291TSMES1 0.024 0.033 0.032 0.032T1 0.129 0.155 0.231 0.133T2 0.027 0.029 0.019 0.019T3 0.645 0.595 0.774 0.724T4 0.251 0.216 0.240 0.122KSMES2 0.231 0.110 0.182 0.224TSMES2 0.022 0.031 0.030 0.030T1 0.198 0.229 0.178 0.112T2 0.026 0.611 0.019 0.586T3 0.681 0.018 0.729 0.011T4 0.116 0.211 0.255 0.119Ki1 �0.300 �0.259 �0.300 �0.253Ki2 �0.171 �0.129 �0.228 �0.181

Table 2Optimized parameters for SSSC–SMES controller.

Input set of parameters R3 = R4 = 0.05 R3 = R4 = 0.02D2 = 1.0 D2 = 0.55T12 = 0.0866 T12 = 0.055

Optimized parameters CRPSO RGA CRPSO RGA

KSSSC 0.297 0.282 0.243 0.274TSSSC 0.030 0.034 0.026 0.025T1 0.188 0.166 0.213 0.103T2 0.039 0.038 0.036 0.046T3 0.542 0.560 0.554 0.475T4 0.141 0.237 0.157 0.296KSMES 0.297 0.288 0.296 0.258TSMES 0.025 0.024 0.038 0.038T1 0.121 0.165 0.103 0.262T2 0.011 0.017 0.016 0.029T3 0.800 0.697 0.797 0.781T4 0.148 0.211 0.252 0.149Ki1 �0.171 �0.234 �0.192 �0.180Ki2 �0.167 �0.186 �0.141 �0.137

tie-line near Area 1 and SMES located at the terminal of areas isshown in Fig. 1.

The transient responses for the systems shown in Fig. 1 with theSMES–SMES, SSSC–SMES and TCPS–SMES coordination are de-picted in Fig. 11 after 10% load perturbation in Area 1. The resultsclearly indicate that the coordination of SMES–SMES, SSSC–SMESand TCPS–SMES can be effectively employed to dynamically stabi-lize the multiple-units hydro–hydro system and suppress the oscil-lations in area frequencies and the tie-line power exchange underload disturbance.

In order to guarantee the effectiveness of coordinated controlof SMES–SMES, SSSC–SMES and TCPS–SMES, governor speed reg-ulations and damping coefficient of Area 2 as well as synchroniz-ing power coefficients of tie-line are varied simultaneously. Thevariation of above parameters consists of 27 parameter-sets. Thegains of the integral controller and gains and time constants ofSSSC, TCPS and SMES are optimized individually through RGAand CRPSO optimization algorithms for all parameter-sets. The re-sults for a few sets of SMES–SMES, SSSC–SMES and TCPS–SMEScontrollers are given in Tables 1–3 respectively. The undershoot(US), overshoot (OS) and settling time (ts) of area frequenciesand tie-line power exchange along with minimized value ofFDM optimized through RGA and CRPSO for SMES–SMES, SSSC–SMES and TCPS–SMES controllers are presented in Tables 4–6,respectively.

R3 = R4 = 0.02 R3 = R4 = 0.06 R3 = R4 = 0.06D2 = 1.0 D2 = 0.55 D2 = 0.1T12 = 0.0230 T12 = 0.0866 T12 = 0.055

CRPSO RGA CRPSO RGA CRPSO RGA

0.300 0.296 0.300 0.288 0.300 0.2820.038 0.032 0.040 0.026 0.031 0.0260.235 0.251 0.263 0.157 0.183 0.1630.023 0.029 0.013 0.027 0.024 0.0300.565 0.556 0.538 0.578 0.758 0.7860.221 0.255 0.287 0.180 0.261 0.2290.162 0.128 0.171 0.113 0.216 0.1290.027 0.028 0.024 0.024 0.028 0.0300.154 0.274 0.177 0.249 0.278 0.1480.017 0.730 0.024 0.507 0.021 0.5520.745 0.011 0.599 0.015 0.645 0.0170.300 0.119 0.120 0.234 0.278 0.168�0.300 �0.221 �0.293 �0.252 �0.300 �0.193�0.171 �0.292 �0.155 �0.125 �0.127 �0.208

R3 = R4 = 0.02 R3 = R4 = 0.06 R3 = R4 = 0.06D2 = 1.0 D2 = 0.55 D2 = 0.1T12 = 0.0230 T12 = 0.0866 T12 = 0.055

CRPSO RGA CRPSO RGA CRPSO RGA

0.293 0.254 0.299 0.289 0.300 0.2980.026 0.032 0.039 0.027 0.027 0.0250.174 0.129 0.176 0.192 0.160 0.2280.038 0.036 0.047 0.034 0.048 0.0500.432 0.576 0.536 0.499 0.533 0.4050.286 0.210 0.297 0.120 0.141 0.1150.298 0.300 0.300 0.272 0.300 0.2830.035 0.025 0.023 0.033 0.025 0.0360.185 0.188 0.165 0.254 0.159 0.1100.019 0.022 0.011 0.018 0.013 0.0280.648 0.633 0.748 0.741 0.604 0.6770.281 0.182 0.261 0.119 0.222 0.297�0.199 �0.187 �0.190 �0.164 �0.189 �0.200�0.190 �0.125 �0.196 �0.147 �0.180 �0.177

Table 3Optimized parameters for TCPS–SMES controller.

Input set of parameters R3 = R4 = 0.05 R3 = R4 = 0.02 R3 = R4 = 0.02 R3 = R4 = 0.06 R3 = R4 = 0.06D2 = 1.0 D2 = 0.55 D2 = 1.0 D2 = 0.55 D2 = 0.1T12 = 0.0866 T12 = 0.055 T12 = 0.0230 T12 = 0.0866 T12 = 0.055

Optimized parameters CRPSO RGA CRPSO RGA CRPSO RGA CRPSO RGA CRPSO RGA

Ku 3.000 2.838 2.917 2.890 2.752 2.886 2.185 2.416 3.000 2.689TPS 0.200 0.196 0.051 0.165 0.059 0.170 0.082 0.211 0.013 0.079KSMES 0.300 0.253 0.300 0.262 0.291 0.220 0.300 0.249 0.274 0.214TSMES 0.033 0.029 0.032 0.036 0.040 0.030 0.033 0.029 0.022 0.038T1 0.213 0.159 0.299 0.207 0.221 0.203 0.192 0.236 0.129 0.241T2 0.017 0.016 0.017 0.015 0.022 0.023 0.022 0.020 0.025 0.024T3 0.771 0.718 0.787 0.630 0.515 0.585 0.800 0.684 0.753 0.580T4 0.265 0.239 0.299 0.213 0.238 0.281 0.300 0.259 0.208 0.221Ki1 �0.435 �0.291 �0.499 �0.278 �0.459 �0.412 �0.305 �0.352 �0.465 �0.378Ki2 �0.451 �0.325 �0.194 �0.167 �0.469 �0.480 �0.195 �0.186 �0.442 �0.442

Table 4Results of frequency response of test system with SMSE–SMES controller.

R3 = R4 = 0.05 R3 = R4 = 0.02 R3 = R4 = 0.02 R3 = R4 = 0.06 R3 = R4 = 0.06D2 = 1.0 D2 = 0.55 D2 = 1.0 D2 = 0.55 D2 = 0.1T12 = 0.0866 T12 = 0.055 T12 = 0.0230 T12 = 0.0866 T12 = 0.055

CRPSO RGA CRPSO RGA CRPSO RGA CRPSO RGA CRPSO RGA

Df1 (Hz) US �0.276 �0.286 �0.267 �0.277 �0.279 �0.283 �0.282 �0.288 �0.268 �0.280OS 0.062 0.058 0.062 0.058 0.059 0.049 0.061 0.051 0.062 0.049ts 100 95 90 95 90 95 90 90 95 85

Df2 (Hz) US �0.010 �0.013 �0.007 �0.007 �0.003 �0.004 �0.011 �0.013 �0.007 �0.009OS 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000ts 400 350 600 550 1400 1400 400 325 610 600

DPtie (pu) US �0.003 �0.003 �0.002 �0.002 �0.001 �0.001 �0.003 �0.003 �0.002 �0.002OS 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000ts 320 350 420 500 1200 1400 300 310 500 550

FDM 0.5369 0.5408 0.5446 0.5512 0.5404 0.5544 0.5431 0.5524 0.5404 0.6050

Table 5Results of frequency response of test system with SSSC–SMES controller.



Df1 (Hz) US �0.283 �0.301 �0.337 �0.326 �0.306 �0.326 �0.289 �0.293 �0.283 �0.291OS 0.058 0.068 0.068 0.061 0.062 0.065 0.059 0.057 0.060 0.062ts 95 75 80 85 85 85 85 95 80 90

Df2 (Hz) US �0.346 �0.369 �0.349 �0.393 �0.371 �0.355 �0.361 �0.382 �0.381 �0.401OS 0.045 0.062 0.075 0.086 0.073 0.073 0.041 0.048 0.044 0.052ts 120 100 90 80 120 80 100 110 60 95

DPtie (per unit) US �0.092 �0.093 �0.090 �0.096 �0.095 �0.092 �0.094 �0.092 �0.093 �0.093OS 0.017 0.019 0.016 0.016 0.018 0.016 0.018 0.016 0.018 0.018ts 85 80 85 80 95 85 80 95 80 90

FDM 0.9962 1.0232 1.1282 1.2256 1.0389 1.1045 1.0051 1.1442 1.1007 1.0845


5.2. Comparative optimization performances of the optimizationtechnique

The comparative convergence profiles with RGA and CRPSOoptimization algorithms for coordination controllers SMES–SMES,SSSC–SMES and TCPS–SMES are shown in Fig. 12. With regard toperformance of the optimizing techniques, as tabulated in Tables4–6, it may be concluded that the CRPSO based optimization ap-proach offers lower values of FDM for different operating condi-tions. Comparative transient performances after varying loadperturbation shown in Fig. 11 and convergence profiles of FDMshown in Fig. 12 for CRPSO and RGA based optimizations, assist

to conclude that CRPSO based optimization is better than RGAbased one. Thus, CRPSO may be accepted as a better optimizingtechnique and subsequent studies in the present work are basedon CRPSO technique.

5.3. Comparative transient performance evaluation of SMES–SMES,SSSC–SMES and TCPS–SMES controllers for the test system

Case 1: Application of 10% step load with nominal parameters.The comparative transient responses of SMES–SMES, SSSC–

SMES and TCPS–SMES controllers are shown in Fig. 13 after 10%load perturbation in Area 1. It is observed that the system with

Table 6Results of frequency response of test system with TCPS–SMES controller.



Df1 (Hz) US �0.489 �0.503 �0.621 �0.671 �1.092 �1.159 �0.547 �0.580 �0.592 �0.666OS 0.081 0.075 0.107 0.089 0.318 0.359 0.086 0.086 0.104 0.102ts 50 45 45 40 30 30 55 45 45 35

Df2 (Hz) US �0.390 �0.460 �0.349 �0.430 �0.301 �0.385 �0.364 �0.473 �0.391 �0.508OS 0.067 0.066 0.083 0.076 0.129 0.191 0.055 0.080 0.070 0.079ts 70 75 50 70 50 45 80 55 60 55

DPtie (per unit) US �0.121 �0.118 �0.100 �0.105 �0.075 �0.076 �0.103 �0.116 �0.098 �0.098OS 0.021 0.018 0.017 0.013 0.021 0.023 0.016 0.017 0.017 0.014ts 45 45 30 45 30 30 60 60 35 35

FDM 1.0710 1.1054 1.1400 1.4084 2.7518 3.2595 1.0969 1.2000 1.1653 1.5017

0 20 40 60 80 1000.52

0.54

0.56

0.58

0.6

Number of Iteration

Figu

re o

f Dem

erit

0 20 40 60 80 1000.9

1

1.1

1.2

1.3

1.4

1.5

1.6

Number of Iteration

Figu

re o

f Dem

erit

0 20 40 60 80 1001

1.2

1.4

1.6

1.8

Number of IterationFi

gure

of D

emer

it

CRPSORGA

CRPSORGA

CRPSORGA

(a) (b) (c)Fig. 12. Figure of demerit for nominal sets of parameters: (a) SMES–SMES controller, (b) SSSC–SMES controller, and (c) TCPS–SMES controller.


SMES placed in both areas gives minimum undershoot and over-shoot in frequency oscillations as well as tie-line power exchangeas compared to SSSC–SMES and TCPS–SMES controllers. However,the oscillations in frequency of Area 2 and tie-line power take long-er time to settle. On the other hand, SSSC–SMES and TCPS–SMEScontrollers are very effective to quickly suppress the oscillationsin area frequencies and tie-line power. Fig. 14 shows the compar-ison of Figure of Demerit values obtained by CRPSO algorithm forthe performance evaluation of the controllers for different sets ofparameter. The performance of TCPS–SMES controller is highlysensitive with the variation in system parameters and gives veryhigher undershoot and overshoot particularly for the system hav-ing low synchronizing coefficients of tie-line. On the other hand,SMES–SMES controller and SSSC–SMES controller are uniformlyeffective to suppress the frequency oscillations, always giving con-sistent FDM values for different sets of parameters. Though the fre-quency oscillations and tie-line power take a longer time to settlewith SMES–SMES controller, it gives the least value of undershootand overshoot as compared to other coordinated controllers, thusproducing the least value of FDM for different input sets ofparameters.

Case 2: Application of sinusoidal load change to the systems withnominal parameters.

The sinusoidal load change is imposed on Area 1 in order to eval-uate the effectiveness of the coordinated frequency stabilizersagainst the varying load patterns. The expression for sinusoidal loadchange containing low sub-harmonic terms is assumed as follow.

DPL1 ¼ 0:03 sinð4:36tÞ þ 0:05 sinð5:3tÞ � 0:1 sinð6tÞ ð45Þ

Fig. 15 depicts the dynamic response of the system after applyingthe sinusoidal load change. The coordinated control of the devicescan effectively limit the oscillations in frequency of both the areasand tie-line power. It should be noted that the oscillations are lim-ited but do not get damped out, since the sinusoidal load distur-bances in both areas occur continuously from 0 to 30 s.

Case 3: Application of 10% step load with nominal parameters inthe event of tie-line outage.

The frequency response of the system has also been observed inthe event of tie-line fault. For the simulation, two conditions offaults are assumed. (a) Tie-line outage occurs at t = 10 s and is re-stored at t = 15 s, (b) Tie-line outage occurs at t = 10 s and doesnot restore. The frequency responses for the system under tie-lineoutage condition are shown in Figs. 16 and 17.

In the events of temporary tie-line outages, the system expe-riences severe fluctuations as long as the fault persists. The oscil-lations quickly damp out after the restoration of the tie-line andthe system regains its stable operation which can be noticedfrom Fig. 16. In the events of permanent tie-line outage, boththe areas are operating in islanding mode. The frequency of Area1 is highly disturbed; the oscillations sustain, grow and eventu-ally lead to system instability in Area 1 in case of SSSC–SMESand TCPS–SMES controllers as shown in Fig. 17. However, thepresence of SMES in Area 2 absorbs the disturbances and

0 20 40 60 80 100

-0.4

-0.2

0

Time (Sec)

Del

ta f1

(Hz)

0 20 40 60 80 100-0.4

-0.3

-0.2

-0.1

0

0.1

Time (Sec)

Del

ta f2

(Hz)

0 20 40 60 80 100

-0.1

-0.05

0

0.05

Time (Sec)

Det

a Pt

ie (p

u)

SMES placed in both areasSSSC - SMES CoordinationTCPS - SMES Coordination



Fig. 13. Comparative dynamic responses for SMES–SMES, SSSC–SMES and TCPS–SMES controllers after 10% step load change in Area 1.

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

Set of Parameters

Figu

re o

f Dem

erit

SMES Placed in Both AreasSSSC - SMES CoordinationTCPS - SMES Coordination

Fig. 14. Figure of demerit for input sets of parameters for SMES–SMES controller,SSSC–SMES controller and TCPS–SMES controller (Set 1: 0.05, 1, 0.0866), (Set 2:0.02, 0.1, 0.0866), (Set 3: 0.02, 0.55, 0.06), (Set 4: 0.02, 1, 0.02), (Set 5: 0.06, 1, 0.02),(Set 6: 0.06, 0.55, 0.0866), (Set 7: 0.01, 0.55, 0.02), (Set 8: 0.1, 1, 0.06), (Set 9: 0.1,0.1, 0.0866).

0 5 10 15 20 25 30-0.4

-0.2

0

0.2

0.4

Time (Sec)

0 5 10 15 20 25 30Time (Sec)

0 5 10 15 20 25 30Time (Sec)

Del

ta f1

(Hz)


-0.1

-0.05

0

0.05

0.1

Del

ta f2

(Hz)

-0.1

-0.05

0

0.05

0.1

Del

ta P

tie (p

u)



Fig. 15. Comparative dynamic responses for SMES–SMES, SSSC–SMES and TCPS–SMES controllers after application of sinusoidal load change in Area 1.


frequency of Area 2 gets stabilized, even with the permanent out-age of the tie-line. It is to be noticed that the system with SMESplaced in both areas is working satisfactory even in islandingmode after the permanent tie-line outage. The presence of SMESin both the areas effectively suppresses the frequency oscillationsand restores the system operation even in the absence of tie-linepower support.

6. Conclusion

The significant contributions of this paper are as follow:

(a) The comprehensive mathematical model of an intercon-nected two-area multiple units hydro–hydro system fittedwith SSSC, TCPS in series with tie-line and SMES placed atthe terminal of area has been presented in this paper.

(b) The linearized models of SSSC and TCPS are developed asapplicable for automatic generation control.

(c) The coordinated controllers SMES–SMES, SSSC–SMES andTCPS–SMES are very effective in frequency control, produc-ing consistent results against varying system parameters,different load changes and in the event of temporary tie-lineoutage. However, SSSC–SMES and TCPS–SMES controllershave failed to stabilize one of the islanded areas where SMESis not installed in the event of permanent tie-line outage. Onthe other hand, SMES–SMES controller shows its effective-ness over SSSC–SMES and TCPS–SMES controllers to stabilizethe system even with permanent outage of the tie-line.

(d) SMES–SMES controller offers the least undershoot and over-shoot in frequency deviations and tie-line power exchangesas compared to SSSC–SMES controller and TCPS–SMES con-troller. The TCPS–SMES controller shows the highest under-shoot and overshoot but it is very effective to quicklysuppress the frequency oscillations and tie-line poweroscillations.

(e) The effectiveness of TCPS-SMES controller for frequency sta-bilization is very sensitive to system parameters variations,particularly for low tie-line synchronizing coefficient.

0 50 100

-0.2

-0.1

0

0.1

Time (Sec)

Det

a f1

(Hz)

0 20 40 60 80 100-0.5

0

0.5

Time (Sec)

Det

a f1

(Hz)

0 20 40 60 80

-0.4

-0.2

0

0.2

0.4

Time (Sec)

Det

a f1

(Hz)

0 50 100 150 200 250-15

-10

-5

0

5x 10-3

Time (Sec)

Det

a f2

(Hz)

0 20 40 60 80 100-0.4

-0.3

-0.2

-0.1

0

0.1

Time (Sec)

Det

a f2

(Hz)

0 20 40 60 80-0.4

-0.3

-0.2

-0.1

0

Time (Sec)

Det

a f2

(Hz)

0 50 100 150 200 250-3

-2

-1

0x 10-3

Time (Sec)

Det

a Pt

ie (p

u)

0 50 100

-0.1

0

0.1

0.2

Time (Sec)

Det

a Pt

ie (p

u)

0 20 40 60 80

-0.1

-0.05

0

0.05

Time (Sec)

Det

a Pt

ie (p

u)

(a) (b) (c)Fig. 16. Comparative dynamic response for the test system after 10% step load with: (a) SMES–SMES controller, (b) SSSC–SMES controller, (c) TCPS–SMES controller fortemporary tie-line outage (Case a).

0 50 100-0.3

-0.2

-0.1

0

0.1

Time (Sec)

Del

ta f1

(Hz)

0 50 100-20

-10

0

10

20

Time (Sec)

Del

ta f1

(Hz)

0 50 100-1

-0.5

0

0.5

1x 105

Time (Sec)

Del

ta f1

(Hz)

0 50 100-10

-5

0

5x 10-3

Time (Sec)

Del

ta f2

(Hz)

0 50 100-0.4

-0.3

-0.2

-0.1

0

Time (Sec)

Del

ta f2

(Hz)

0 50 100-0.4

-0.3

-0.2

-0.1

0

Time (Sec)

Del

ta f2

(Hz)

0 50 100-3

-2

-1

0x 10-3

Time (Sec)

Del

ta P

tie (p

u)

0 50 100-0.1

-0.05

0

Time (Sec)

Del

ta P

tie (p

u)

0 50 100

-0.1

-0.05

0

Time (Sec)

Del

ta P

tie (p

u)

(a) (b) (c)Fig. 17. Comparative dynamic response for the test system after 10% step load with: (a) SMES–SMES, (b) SSSC–SMES, (c) TCPS–SMES controllers for permanent tie-line outage(Case b).



(f) Between the two optimization techniques considered,CRPSO based optimization yields true optimal solution ascompared to RGA.

Thus, coordinated controllers SMES–SMES, SSSC–SMES andTCPS–SMES may be successfully implemented for load frequencystabilization of an interconnected two-area multiple-units hy-dro–hydro system.

Appendix A

f = 60 Hz; H1 = H2 = 3 s; D1 = D2 = 1; B1 = B2 = 20.5;PR1 = 1800 MW; PR2 = 1200 MW; a12 = 1.5; T12 = 0.0866;RP1 = RP2 = RP3 = RP4 = 0.05; RT1 = RT2 = RT3 = RT4 = 0.05;TG1 = TG2 = TG3 = TG4 = 0.2 s; TR1 = TR2 = TR3 = TR4 = 0.2 s;TW1 = TW2 = TW3 = TW4 = 1.0s; apf1 = apf2 = apf3 = apf4 = 0.5;Vm = Vn = 1 pu, hmn = 30�, BaseMVA = 1000 MVA.

References

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Documents

Comparative performance evaluation of SMES–SMES, TCPS–SMES and SSSC–SMES controllers in automatic generation control for a two-area hydro–hydro system