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Ibraheem et al. SpringerPlus 2014, 3:744http://www.springerplus.com/content/3/1/744

RESEARCH Open Access

Decentralized automatic generation control ofinterconnected power systems incorporatingasynchronous tie-linesIbraheem1, Naimul Hasan1 and Arkan Ahmed Hussein1,2*

Abstract

This Paper presents the design of decentralized automatic generation controller for an interconnected powersystem using PID, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The designed controllers aretested on identical two-area interconnected power systems consisting of thermal power plants. The areainterconnections between two areas are considered as (i) AC tie-line only (ii) Asynchronous tie-line. The dynamicresponse analysis is carried out for 1% load perturbation. The performance of the intelligent controllers based onGA and PSO has been compared with the conventional PID controller. The investigations of the system dynamicresponses reveal that PSO has the better dynamic response result as compared with PID and GA controller forboth type of area interconnection.

Keyword: Automatic generation control; Genetic algorithm; Particle swarm optimization; Ziegler and Nicholsmethod asynchronous tie-line

1. IntroductionModern Power system consists of large number of gen-erating units interconnected by transmission lines. Theinterconnection of the power systems enhance the sta-bility and become a viable tool to provide the almostuninterruptible power to load canters from generatingstations. The two power system areas may be con-nected through synchronous/asynchronous tie-lines.To provide a good quality of power, the operation ofpower system must be maintained at the nominal fre-quency and voltage profile. And it is achieved by con-trolling of real and reactive powers. A modern powersystem is divided into a number of control areas and eacharea is responsible for its own load and power inter-changes. If the input-output power balance is not main-tained, a change in frequency will occur which it highlyundesirable. In modern interconnected power system,automatic generation control (AGC) is used to maintain

* Correspondence: aalganabe@gmail.com1Department of Electrical Engineering, Faculty of Engineering andTechnology, Jamia Millia Islamia, New Delhi, India2Department of Electrical Engineering, Engineering College, Tikrit University,Tikrit, Iraq

© 2014 Ibraheem et al.; licensee Springer. ThisAttribution License (http://creativecommons.orin any medium, provided the original work is p

the system frequencies and tie-line power flows at thespecified nominal values.The automatic generations control of interconnected

power systems has become more significant as size andcomplexity of the system is going on increasing to meetout power demand. A large number of control tech-niques have been proposed by the researchers for thedesign of AGC regulators. In the early era, the AGCstrategies were proposed base on centralized controlstrategy (Quazza 1966; Elgerd & Fosha 1970; Aldeen &Trinh 1994; Fosha & Elgerd 1970). The limitation ofAGC centralized control strategy is that it requires theexchange of information from control areas spread overdistantly connected geographical areas along with theirincreased computational and storage complexities. Thedecentralized automatic generation control strategiesdeals the limitations of centralized power system very ef-fectively (Kawabata and Kido 1982; Park & Lee 1984;Calovic 1984; Aldeen and Marsh 1990,1991; Aldeen1991; Yang et al. 1998,2002). The researchers (Kumaret al. 1985) proposed the systematic distributed controldesign methods and achieved almost identical results

is an Open Access article distributed under the terms of the Creative Commonsg/licenses/by/4.0), which permits unrestricted use, distribution, and reproductionroperly credited.

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as obtained with the centralized strategies. The designof decentralized load frequency controllers based onstructured singular values and multiple control-structure constraints are discussed in (Kumar et al.1987; Shayeghi et al. 2007). The decentralized AGCregulator design based on the structured singular valueis designed for local area robust analysis, and an eigenvalue method is derived for tie-line robustness analysis(Tan & Zhou 2012). (Tan 2011) proposed a method toanalyze the stability of multi-area power system by ac-counting the inherent structure of the multi-areapower system. (Sudha and Vijaya Santhi 2011) pro-posed a Type 2 Fuzzy controller for decentralized twoarea interconnected power system with considerationof generation rate constraint.

2. Power system modelsIn this paper two power system models are consideredfor design of decentralized AGC regulators using PID,GA and PSO. The area interconnection in one powersystem model is only AC tie line and in the secondmodel Parallel AC/DC link is considered

3. State space modelThe linear time-invariant state space representation ofinterconnected power system is given by the followingequations:

_X ¼ AX þ BU þ ΓD ð1ÞY ¼ Cx ð2Þ

Where A, B, Γ are system, control and disturbancematrices and x, u and d are system control and disturb-ance vectors.Power system model–I:

X1�T ¼ �

Δf 1ΔPt1ΔPg1Δf 2ΔPt2ΔPg2ΔPtie12ACE1ACE2� �

U1½ � ¼ u1 u2�; D1½ � ¼ ½ΔPd1 ΔPd2½ �Power system model–II

X2½ �T ¼ Δf 1ΔPt1ΔPg1Δf 2ΔPt2ΔPg2ΔPtie12ACE1ACE2ΔPdc� �

U2½ � ¼ U1½ �; D2½ � ¼ D1½ �State equations:From the transfer function block diagram shown in

Figure 1, the following equations are obtained:

_x1 ¼ −1

Tp1x1 þ Kp1

Tp1_x2−

Kp1

Tp1x7−

Kp1

Tp1ΔPd1 ð3Þ

_x2 ¼ −1Tt1

_x2 þ 1Tt1

x3 ð4Þ

_x3 ¼ −1

R1Tg1_x1−

1Tg1

x3 þ 1Tg1

u1 ð5Þ

_x4 ¼ −1

Tp2x4 þ Kp2

Tp2x5 þ Kp2

Tp2x1−

Kp2

Tp2ΔPd2 ð6Þ

_x5 ¼ −1Tt2

x5 þ 1Tt2

x6 ð7Þ

_x6 ¼ −1

R2Tg2x4−

1Tg2

x6 þ 1Tg2

u2 ð8Þ

_x7 ¼ 2πT 0x1−2πT 0x3 ð9Þ_x8 ¼ B1x1 þ x7 ð10Þ_x9 ¼ B2x4−x7 ð11Þ

From the above equations, System, control and dis-turbance matrices can be obtained as given below:State matrix ‘A’, Control matrix ‘B’, and disturbance

matrix Γ for power system model-I are as follows below.The same matrices can be obtained for the power systemmodel-II.

A ¼

−1=Tp1 Kp1=Tp1 0 0 0 0 −Kp1=Tp1 0 00 −1=Tt1 1=Tt1 0 0 0 0 0 0

−1=R1Tg1 0 −1=Tg1 0 0 0 0 0 00 0 0 −1=Tp2 Kp2=Tp2 0 Kp2=Tp2 0 00 0 0 0 −1=Tt2 1=Tt2 0 0 00 0 0 −1=R2Tg2 0 1=Tg2 0 0 0

2πT0 0 0 −2πT 0 0 0 0 0 0B1 0 0 0 0 0 0 0 00 0 0 B2 0 0 0 0 0

2666666666666664

3777777777777775

B ¼

0 00 0

1=Tg1 00 00 00 1=Tg20 00 00 0

2666666666666664

3777777777777775

Γ ¼

−Kp1=Tp1 00 00 00 −Kp2=Tp20 00 00 00 00 0

2666666666666664

3777777777777775

The area control error for area-1 is defined as:

ACE1 ¼ ΔPtie1 þ B1Δf 1 ð12Þand the feedback control for Area-1 takes the form

u1 ¼ −K1 sð ÞACE1 ð13Þwhere K1(s) is the local LFC controller for area-1.According to (Tan 2009,2010), a decentralized controller

can be designed assuming that there are no tie-line powerflows, In this case the local feedback control will be

u1 ¼ −K1 sð ÞB1Δf 1 ð14Þ

4. A control scheme for an interconnectedpower system4.1 Tuning of AGC parameterThe AGC regulator has the objective to minimize areacontrol error (Xue et al. 2007). The AGC regulators

Figure 1 Transfer function model of power system.

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having single output as a control signal based on PID isgiven below;

u tð Þ ¼ KP e tð Þ þ 1Ti

Z t

0e τð Þdτ þ Td

de tð Þdt

� �ð15Þ

where u(t) is the control input for governor , e(t) theerror , The tuning process of PID controller gain isdone by Ziegler and Nichols (ZN) method (Asttrom &Hagglund 1995). The proportional, integral and deriva-tive gains are calculated for the critical ultimate gain,Ku and oscillation of ultimate time period, Tu. Thesegains are shown below in Table 1.

4.2 Genetic algorithmThe genetic algorithm is a nature inspired optimizationtechnique (Goldberg 1989). There are some sequentialsteps to be followed in developing the GA for automaticgeneration control. The Chromosomes Structure is builtup with the initial set of random population in the formchromosomes which consists of genes as binary bits.These binary bits are then decoded to give proper string

Table 1 Gains of PID controller

Controllers Proportional gain Integral gain Derivative gain

P 0.5 Ku

PI 0.4 Ku 0.8 Tu

PID 0.6 Ku 0.5 Tu 0.12 Tu

for optimization. The new population are regeneratedwhich is to be converged at global optimum by thespecified selection, crossover and mutation operators.Elitism is applied to save and use previously found bestpartner in subsequent fittest generation of population.The processes stop as soon as convergence criterion is

satisfied.The flow chart of the GA algorithm used in this work

is shown in Figure 2.

4.3 Particle Swarm Optimization (PSO)Particle swarm optimization (PSO) is a population-basedstochastic optimization technique which is based on thesocial behavior of bird flocking, fish schooling andswarming theory (Kennedy & Eberhart 1995; Eberhart &Kennedy 1995). In the PSO method, a swarm consists of aset of individuals named as particles are specified by theirposition and velocity vectors (xi(t), vi(t)) at each time. Inan n-dimensional solution space, each particle is treated asan n-dimensional space vector and the position of the ith

particle is presented by xi = [xi (1), xi(2), …, xi(n)]; then itflies to a new position by the velocity represented by vi =[vi(1), vi(2), …, vi(n)]. The best position for ith particle rep-resented by pbest,i = [pbest,i(1), pbest,i(2), …, pbest,i(n)] isdetermined according to the best value for the specifiedobjective function and this global best position is repre-sented as gbest = (gbest,1, gbest,2, …, gbest,n). For the next it-eration, the position xik and velocity vik corresponding to

Figure 2 Flowchart of GA based optimization technique.

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the kth dimension of ith particle are updated using the fol-lowing equations:

vik t þ 1ð Þ ¼ w:vik þ c1:rand1;ik pbest;ik tð Þ� �

þ c2:rand2;ik gbest;k tð Þ−xik tð Þ� �

ð16Þ

xi;k t þ 1ð Þ ¼ xik tð Þ þ vik t þ 1ð Þ ð17Þwhere i = 1, 2, …, n is the index of particles, w is the in-ertia weight, rand1,ik and rand2,ik are random numbers inthe interval [0 1], c1 and c2 are learning factors, and trepresents the iterations.The flow chart of PSO as implemented for optimization

is shown in Figure 3.

5. Simulation results and discussionThe dynamic responses of various system states of inter-connected decentralized power system are obtained forAGC regulators designed using PID, GA and PSO. Thesimulation work is carried out using MATLAB softwarewith numerical data shown in appendix A. In this paperboth AC tie-line and parallel AC/DC tie-line as areainterconnection are considered for the investigations.The time responses are plotted for various system states

with implementation of designed AGC regulators con-sidering 1% load perturbation in area-1. The Figures 4and 5 show the dynamic responses of the frequency de-viations in area-1 and area-2 respectively. The investiga-tions of these plots inferred that with PSO controller,the oscillation, overshoot decreases as compared withGA and PID controller and also the settling time is fas-ter in the case of time response with PSO with AC/DCtie-line compared to those offered by GA and PID.Figure 6 represents the tie-line power flow deviation be-tween the two areas. The analysis reveals that the pro-posed controllers are capable to mitigate the deviationsin tie-line power flows. The PSO controller has the su-periority to the GA and PID in terms of over shoots andsettling time. The Figures 7 and 8 are plotted for thearea control error for area 1&2 respectively, the Figure 7shows that the PSO controller has the best over shootand settling time. The Figure 8 shows that the overshootand settling time with GA controller is comparable withPSO and PID.

6. ConclusionThe AGC regulators are designed using PID, GA andPSO for two-area interconnected decentralized power

Figure 3 Flowchart of PSO optimization technique.

Figure 4 Dynamic response for Δf1.

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Figure 5 Dynamic response for Δf2.

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system. The area interconnections are considered as ACtie-line and parallel AC/DC tie-lines. Investigations ofresults are presented that inferred the superiority PSOcontroller in comparison to PID and GA. The compari-sons have been made between the power system model-Iand power system model-II consisting of AC tie-line andparallel AC/DC tie-line. The positive effect of DC link in

Figure 6 Dynamic response for Ptie12.

parallel to AC tie-line is also clearly visible in the time re-sponse plots of all states with the designed regulators.

Nomenclature

i subscript referring to area i (i =1,2)Δfi frequency deviation of Area (Hz)

Figure 7 Dynamic response for ACE1.

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ACEi area control error,ΔPti incremental change in power generation,ΔPgi incremental change in governor valve position,ΔPtie tie-line power deviation,Tgi governor time constant for the ith areasubsystem (s),Tti turbine time constant for the ith area subsystem (s),Tpi plant model time constant for the ith areasubsystem (s),

Figure 8 Dynamic response for ACE2.

Tij synchronizing coefficient between the ith and jtharea subsystem (p.u. MW),Kpi plant gain for the ith area subsystem,Ri speed regulation due to governor action for the itharea subsystem,χi (t) states of the i

th area subsystem,ui(t) control input for the ith area subsystem.ZN Ziegler and Nichols control methodACE Area Control Error

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Competing interestsThe authors declare that they have no competing interests.

Authors’ contributionsAAH has studied intelligent optimization techniques such as "GA and PSO"and implemented for Decentralized AGC of two area interconnected powersystem. NH has supervised and reviewed the work carried out here in thispaper to the best for the good understanding of the researchers. IB has finetuned the modeling of the decentralized interconnected power system andsimulation results. The authors have read and approved the final manuscript.

Received: 5 October 2014 Accepted: 4 December 2014Published: 16 December 2014

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doi:10.1186/2193-1801-3-744Cite this article as: Ibraheem et al.: Decentralized automatic generationcontrol of interconnected power systems incorporating asynchronoustie-lines. SpringerPlus 2014 3:744.

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