Adaptive neuro-fuzzy inference system based automatic generation control

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Available online at www.sciencedirect.com

Electric Power Systems Research 78 (2008) 1230–1239

Adaptive neuro-fuzzy inference system basedautomatic generation control

S.H. Hosseini ∗, A.H. EtemadiDepartment of Electrical Engineering, Sharif University of Technology, Tehran, Iran

Received 10 October 2006; received in revised form 26 August 2007; accepted 29 October 2007Available online 21 February 2008

bstract

Fixed gain controllers for automatic generation control are designed at nominal operating conditions and fail to provide best control performancever a wide range of operating conditions. So, to keep system performance near its optimum, it is desirable to track the operating conditions andse updated parameters to compute control gains. A control scheme based on artificial neuro-fuzzy inference system (ANFIS), which is trained by
he results of off-line studies obtained using particle swarm optimization, is proposed in this paper to optimize and update control gains in real-timeccording to load variations. Also, frequency relaxation is implemented using ANFIS. The efficiency of the proposed method is demonstrated viaimulations. Compliance of the proposed method with NERC control performance standard is verified.
2007 Elsevier B.V. All rights reserved.

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eywords: ANFIS; Automatic generation control; Frequency relaxation; Partic

. Introduction

Large scale power systems are normally composed of con-rol areas or regions representing coherent groups of generators1]. The various control areas are interconnected through tieines. The tie lines are utilized for contractual energy exchangeetween areas and provide inter-area support in case of abnormalonditions. Area load changes and abnormal conditions, suchs outages of generation, lead to mismatches in frequency andcheduled power interchanges between areas. Automatic gener-tion control (AGC) (also designated by load frequency control)s an essential mechanism in electric power systems which bal-nces generated power and demand in each control area in ordero maintain the system frequency at nominal value and the powerxchange between areas at its scheduled value. The concept ofGC in vertically integrated power systems is well discussed

n [2–4]. In the past decades, many research works have inves-igated AGC problem to improve its response in conventional
ower systems. Conventional proportional integral (PI) control5], decentralized control [6], adaptive control [7], state feed-ack based on optimal control [8], fuzzy logic control [9] and
∗ Corresponding author. Tel.: +98 912 2079440; fax: +98 21 66023261.E-mail addresses: [email protected] (S.H. Hosseini),

[email protected] (A.H. Etemadi).

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378-7796/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.epsr.2007.10.007

arm optimization

eural network based control [10] are some of the publishedesearches on this topic.

Currently, in many countries, the electric power industry is inransition from vertically integrated utilities, providing power ategulated rates, to an industry that will incorporate competitiveompanies selling unbundled power at lower rates. In a competi-ive electricity market, there will be many market players, such asenerating companies (GENCOs), distribution companies (DIS-Os), transmission companies (TRANSCOs), and independent

ystem operator (ISO). For stable and secure operation of aower system, the ISO has to provide a number of ancillary ser-ices. One of the ancillary services is the “frequency regulation”ased on the concept of the load frequency control (LFC). In theew power system structure, load-frequency control acquires aundamental role to enable power exchanges and to provide bet-er conditions for electricity trading. Therefore, in recent years,esearchers have devoted their efforts to adapt AGC schemeso deregulated power systems for better performance in theseompetitive markets. Decentralized AGC scheme [11], iterativeinear matrix inequalities algorithm based LFC [12], hybrid evo-utionary fuzzy PI control algorithm [13], control using genetic
lgorithms and linear matrix inequalities [14] are some of theecent works on this topic.
Fixed gain controllers are designed at nominal operatingonditions and fail to provide best control performance over

mailto:[email protected]

mailto:[email protected]

dx.doi.org/10.1016/j.epsr.2007.10.007

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S.H. Hosseini, A.H. Etemadi / Electric P

wide range of operating conditions. Therefore, to keep sys-em performance near its optimum, it is desirable to track theperating conditions and use updated parameters to computehe control gains. A fuzzy gain scheduling scheme for conven-ional PI and optimal controllers has been designed in [1]. Therominent feature of fuzzy and neural network based schemess that they provide a model-free description of control systems
nd do not require model identification. In this paper, a controlcheme based on adaptive neuro-fuzzy inference system and par-icle swarm optimization (PSO) which is one of the most recentptimization approaches inspired from the food search method
Seco

Fig. 1. Two-area AGC system block d

Systems Research 78 (2008) 1230–1239 1231

f birds is proposed for optimal gain scheduling intended forestructured power systems. Using this method, the gains arepdated in real time and better dynamic and steady state responses obtained. Also, a frequency relaxation method is proposedhich deactivates both the primary and secondary frequency

ontrols whenever the magnitude of estimated frequency devi-tion is smaller than a threshold value, called deadband limit.
eparate ANFIS networks are used for modeling the nonlin-ar properties of the frequency relaxation. The simulations arearried out in presence of the generation rate constraint (GRC)f steam turbines because ignoring GRC leads to nonrealistic
iagram in restructured scenario.

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232 S.H. Hosseini, A.H. Etemadi / Electric P

esults. The simulation results demonstrate the effectiveness ofhe proposed method. The compliance of proposed method withERC recent control performance standard is verified.

. System model

.1. Block diagram and state space realization

The traditional AGC of a two-area system has been modi-ed in [15] to take into account the effect of bilateral contractsn the dynamic response of the automatic generation controlystem. In this approach, the concept of “DISCO participationatrix” (DPM) is introduced to clarify the contracts betweenENCOs and DISCOs in the entire control areas. DPM is an× m matrix which n is the number of GENCOs and m is the

umber of DISCOs in control areas. DPM is comprised of “con-ract participation factors” (cpf); cpfij corresponds to the fractionf the total load power contracted by DISCO j from GENCO i.he sum of all the entries in a column in this matrix is unity. Intwo-area system with two GENCOs and two DISCOs in eachrea, the DPM is as follows:

PM =

⎡⎢⎢⎢⎣

cpf11 cpf12 cpf13 cpf14




⎤⎥⎥⎥⎦ (1)

s there are many GENCOs in each area, area control errorACE) signal has to be distributed among GENCOs in proportiono their participations in the AGC. Coefficients that distribute
CE to several GENCOs are termed as “ACE participation fac-
ors” (apfs) in [15]. The scheduled steady state power flow onhe tie line is given as

a

(

(

Acl =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

−1

TP10

KP1

TP1

KP1

TP10 0

0−1

TP20 0

KP2

TP2

K

T

0 0−1

TT10 0 0

0 0 0−1

TT20 0

0 0 0 0−1

TT30

0 0 0 0 0−T

−1

2πR1TG10 0 0 0 0

−1

2πR2TG20 0 0 0 0

0−1

2πR3TG30 0 0 0

0−1

2πR4TG40 0 0 0

B1

2π0 0 0 0 0

0B2

2π0 0 0 0

T12

2π

−T12

2π0 0 0 0

Systems Research 78 (2008) 1230–1239

�Ptie1−2,scheduled

= (demand of DISCOs in area II from GENCOs in area I)

− (demand of DISCOs in area I from GENCOs in area II)

(2)

At any given time, the tie line power error �Ptie1−2,error isefined as

Ptie1−2,error = �Ptie1−2,actual − �Ptie1−2,scheduled (3)

he tie line power error vanishes in the steady state. The blockiagram for AGC in a two-area deregulated system is shown inig. 1. The local load variations in areas I and II are denoted byPL1,LOC and �PL2,LOC, respectively. The state space equation

f the system is as follows:

˙ = Aclx + Bclu (4)

here x is the state vector and u is the load variations of DIS-Os and local loads. The state matrices and vectors are given in

5)–(7).

.2. Proposed method for GRC implementation

As noted earlier in Section 1, ignoring generation rate con-traint (GRC) leads to nonrealistic results. But GRC is nonlinearnherently and the system cannot be modeled with state spacef GRC is included in the block diagram directly. Therefore, arief algorithm is proposed to include the GRC of each gener-ting unit in one solution step of the state space equations. Thislgorithm is described as follows:

1) Take the inputs such as model parameters, GRC of each unit,initial state, etc.

2) Solve the state space Eq. (4) for the Tsampling period.

0 0 0 0 0 0 −KP1

TP1

P2

P20 0 0 0 0 0

KP2

TP2

1

TT10 0 0 0 0 0

01

TT20 0 0 0 0

0 01

TT30 0 0 0

1

T40 0 0

1

TT40 0 0

−1

TG10 0 0

−K1apf1

TG10 0

0−1

TG20 0

−K1apf2

TG20 0

0 0−1

TG30 0

−K2apf3

TG30

0 0 0−1

TG40

−K2apf4

TG40

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

(5)

0 0 0 0 0 0 1

0 0 0 0 0 0 −1

0 0 0 0 0 0 0

⎥⎥⎥⎥⎥⎦

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3) If the generation rate of any unit has violated its GRC, setits generation to the maximum possible value.

4) Repeat steps 2 and 3 until the GRC of no unit is violated.

Applying the above algorithm enables us using the state spaceodel and simultaneously considering GRC of generating units.

cl =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

−KP1

TP1

−KP1

TP10

0 0−KP2

TP2

0 0 0

0 0 0

0 0 0

0 0 0cpf11

TG1

cpf12

TG1

cpf13

TG1cpf21

TG2

cpf22

TG2

cpf23

TG2cpf31

TG3

cpf32

TG3

cpf33

TG3cpf41

TG4

cpf42

TG4

cpf43

TG4

cpf31 + cpf41 cpf32 + cpf42 −(cpf13 + cpf23

−(cpf31 + cpf41) −(cpf32 + cpf42) cpf13 + cpf23

0 0 0

. Proposed control scheme

.1. Integral gain optimization

As mentioned earlier, fixed gain controllers are designed atominal operating conditions and fail to provide best controlerformance over a wide range of operating conditions. It is

=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

�ω1

�ω2

�PGV1

�PGV2

�PGV3

�PGV4

�PM1

�PM2

�PM3

�PM4∫ACE1dt∫ACE2dt

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

and u =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

�PL1

�PL2

�PL3

�PL4

�PL1,LOC

�PL2,LOC

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)

�Ptie1−2

esirable to keep system performance near its optimum. There-ore, the presented method tracks different system operating

Atut


0−KP1

TP10

−KP2

TP20

−KP2

TP2

0 0 0

0 0 0

0 0 0

0 0 0cpf14

TG10 0

cpf24

TG20 0

cpf34

TG30 0

cpf44

TG40 0

(cpf14 + cpf24) 0 0

cpf14 + cpf24 0 0

0 0 0

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)

onditions and updates the integral gains according to the realime disturbances in an online manner. Thus, the objectiveunction of the optimization of the performance of the systemepicted in Fig. 1 is defined as [2]

=∫ ∞

0{α(�Ptie,error)

2 + β[(�f1)2 + (�f2)2]} dt (8)

he coefficients α and β are assumed to be equal to 1. It isssumed that sampling period is Tsampling. In order to keepystem performance near optimum, the power system datas gathered at each Tsampling seconds. Now, the optimal val-es of integral gains K1 and K2, which are shown in Fig. 1nd correspond to the disturbances of load demands, shoulde calculated in order to minimize (8). PSO is used for theurpose of minimization with fitness function of (8). A briefescription about PSO is given in Appendix A.1. The inputsre �PL1, �PL2, �PL3, �PL4, �PL1,LOC and �PL2,LOC. Thetness function is evaluated and the population is updated iter-tively until the optimum is obtained or the stopping criterionetermines to finish the calculations. The gains K1 and K2 arebtained and the control system is updated with new gains untilhe next sampling time at which the aforementioned actions arearried out again.

For large power systems consisting of several control areasnd many GENCOs, the optimization process may take a longime which is not desirable for online control actions. Thus,
NFIS is used to decrease the optimization time. A brief descrip-
ion about ANFIS is given in Appendix A.2. The first step insing ANFIS is to train it. Hence several hundred probable dis-urbances of the aforementioned six �PL s are considered. These

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isturbances are combinations of the load variations in the rangef −0.1 to 0.1 puMW. Therefore for each of the six disturbances,our values of −0.1, −0.03, 0.03 and 0.1 are considered. Finally,he training set consists of 4096 (46) elements. Then, the optimalains of K1 and K2 are computed for each of these disturbancessing PSO method and the objective function (8). After gather-ng these data, we are ready to train ANFIS. For each gain, oneeuro-fuzzy network is trained. After computing the optimalains, two matrices with 4096 rows and 7 columns (six columnsor load variation and the last one representing the optimal gain),ne matrix for each gain, is fed to ANFIS for training. When theraining is done, the two trained neuro-fuzzy networks can esti-ate the optimal gains for any disturbances taken place in the

ower system and online control can be implemented. It shoulde noted that the efficiency of ANFIS can be enhanced by choos-ng a bigger training set. The proposed method can be applied tomall and intermediate power systems easily. However, althoughll of the time-consuming computations are carried out offline,or large and very large power systems, computation time will beomehow exorbitant and more powerful computers or advancedomputing techniques will be necessary.

.2. Frequency relaxation

By frequency relaxation or deadband control we mean thathere is no response from generators when the frequency variesn range of f0 ± fdeadband where f0 is the nominal frequencynd fdeadband is the limit of deadband. Reduction of movementn generators and reduction in regulation energy costs (thosenergy costs incurred by AGC in balancing supply and demandn real-time) are two benefits of frequency relaxation [16]. But,he deadband is nonlinear inherently and its modeling is com-licated. For modeling frequency relaxation, an ANFIS basedethod is proposed. First, ANFIS should be trained. ANFIS

tructure for frequency estimation for the end of current sam-ling period is shown in Fig. 2. The four inputs of ANFIS forrequency estimation are the disturbances of two areas (local
oad variations), frequency and rate of change of frequency athe end of previous sampling period. The output of ANFIS ishe frequency of the control area at the end of current samplingeriod.
Fig. 2. ANFIS structure for frequency estimation.

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Systems Research 78 (2008) 1230–1239

In order to form the training set, two random load varia-ion curves (similar to Fig. 6) are generated each lasting 4000

related to 2000 sampling periods based on a 2-s samplingeriod. For each sampling period, a random load variation in theange of −0.1 and 0.1 is generated for each local load. Then,sing these 2000 random values, the two load variation curvesre constructed. Randomly generated local load variations pluseros for �PL1, �PL2, �PL3 and �PL4, implying constant DIS-Os demands just for simplicity, are fed into the control system,erforming optimal gain scheduling and obtaining the responsef the system needed for training the ANFIS, which are fre-uency and rate of change of frequency at all sampling periods.e could also consider demand variations for DISCOs and still

he main concept would be the same but, these variations haveinor effects since they are compensated very quickly by GEN-Os through bilateral contracts. Using the obtained results, theve columns of the input training matrix could be determined.he first two columns are the load variations at the beginningf each sampling period which is given by the two randomlyenerated load curves. The frequency and the rate of change ofrequency at the end of the previous sampling period and the fre-uency at the end of current sampling period, all obtained fromhe response of the system, form columns three to five of theraining matrix. Thus, the training matrices, one for each area,onsisting of 5 columns and 2000 rows, are created and nowhey can be fed into ANFIS networks for training. When theraining is done, the network can estimate frequency related tohe end of current sampling period in each area for any occurredisturbances.

At the beginning of each sampling period, the final fre-uency of that period is computed for the current disturbances. If0 − fdeadband < fi < f0 + fdeadband where fi is the frequencyf control area i at the end of current sampling period, then theontrol loops are deactivated. Otherwise, the control loops wille active until next sampling time, at which the above processs carried out again. The flowchart of proposed online controlcheme is shown in Fig. 3.

. Simulation results

The test system shown in Fig. 1 is used to illustrate theehavior of the proposed method. The parameters of the testystem are given in Appendix B. For ANFIS, the followingettings were used: Gaussian membership function, two mem-ership functions for each input, hybrid optimization method andpoch = 5. PSO settings were as follows: population size = 20,1 = c2 = 2, ωmax = 0.9, ωmin = 0.4, maximum speed = 2.RC was set to 3% per minute.

.1. Integral gains optimization

In this section, the results of optimal gain scheduling are pre-ented. Two cases are considered. In the first case, it is assumed
hat the load variations occurs only in area I. In the second case,he load variations occur in both areas. The amounts of timepent to compute optimal gains using PSO and ANFIS are com-ared. It can be seen that using PSO for each disturbance is not

S.H. Hosseini, A.H. Etemadi / Electric Power Systems Research 78 (2008) 1230–1239 1235

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4

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Fp

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Fig. 3. Flowchart of proposed control scheme.

ractical, however, ANFIS responses quickly enough for onlineontrol.

.1.1. Case 1In this case, all GENCOs participate equally in AGC, i.e.,

pfi = 0.5 where i = 1, 2, 3, 4. DPM matrix is assumed to be

PM =

⎡⎢⎢⎢⎣

0.50 0.50 0.00 0.00

0.50 0.50 0.00 0.00

0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00

⎤⎥⎥⎥⎦

he following load variations are considered: �PL1 = 0.05 pu,PL2 = 0.05 pu,�PL1,LOC = 0.1 pu and no disturbances occur

n area II. The optimal gains found using the proposed algorithmre K1 = 0.9 and K2 = 0.1. The response of the system withhese gains is compared with the response of optimal value of

1 = K2 = 0.6588 found in [15]. Frequency deviations in twoontrol areas and Ptie1−2,error are shown in Fig. 4. It can be seenhat the responses of the system are not considerably different,owever, the value of the objective function for the fixed gains is.23, but its value for the optimal gains found using the proposedethod is 0.20 which is better to some extent. It took 51 s tond the two optimal gains using PSO but, the two trained ANFISetworks responded immediately. It is obvious that using PSOirectly in order to find the optimal gains for each disturbances impractical.

.1.2. Case 2In this case, all GENCOs participate equally in AGC, i.e.,

pfi = 0.5 where i = 1, 2, 3, 4 like case 1. DPM matrix isT0

ig. 4. System response for case 1. (a) �f1. (b) �f2. (c) �Ptie,error. Solid:roposed method, dashed: optimal gains found in [15].

ssumed to be

PM =

⎡⎢⎢⎢⎣

0.50 0.25 0.00 0.30

0.20 0.25 0.00 0.00

0.00 0.25 1.00 0.70

⎤⎥⎥⎥⎦

0.30 0.25 0.00 0.00

he following load variations are considered: �PL1 =.01 pu, �PL2 = 0.02 pu, �PL3 = −0.05 pu, �PL4 = 0.1 pu,

1236 S.H. Hosseini, A.H. Etemadi / Electric Power Systems Research 78 (2008) 1230–1239

Fp

�

f0pfP

aaf

csoA

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a(Iaat

aimplementation. Simulation results showed that the number ofcontrol pulses sent out to generating units after frequency relax-ation implementation is reduced by 71% which means that thegenerators wears and tears are reduced considerably. Fig. 7

ig. 5. System response for case 2. (a) �f1. (b) �f2. (c) �Ptie,error. Solid:roposed method, dashed: optimal gains found in [15].

PL1,LOC = −0.1 pu and �PL2,LOC = 0 pu. The optimal gainsound using the proposed algorithm are K1 = 1.1 and K2 =.82. The response of the system with these gains is com-ared with the response of optimal value of K1 = K2 = 0.6588ound in [15]. Frequency deviations in two control areas and
tie1−2,error are shown in Fig. 5. It can be seen that the overshootsnd settling time of the responses are somewhat better usingdaptive optimal gains found here. The values of the objectiveunction using the fixed gains found in [15] and the variable gains
F(

Fig. 6. Load variation of the two control areas.

omputed here are 0.12 and 0.09, respectively which demon-trates that the computed gains are more appropriate. The timef computing the optimal gains using PSO was 58 s, but theNFIS response was immediately and practical.

.2. Frequency relaxation

Fig. 6 shows the per unit load variation profiles of Tehrannd Fars utilities recorded by Iran Grid Management CompanyIGMC), for 8 h on 18 January 2006, between 16:00 and 24:00.t is assumed that the load variations of �PL1,LOC and �PL2,LOCre similar to this figure and the contracted demands of DISCOsre constant and do not have any variations. Tsampling is assumedo be 2 s [19].

The proposed algorithm was applied to these real load vari-tions twice, once without and once with frequency relaxation

ig. 7. System response to load variations. (a) Without frequency relaxation.b). With frequency relaxation.

ower

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hows the frequency deviation of the first control area withoutnd with implementing frequency relaxation method with dead-and limit of 0.15 Hz. It can be seen that frequency deviation isuch more in the second case which correspondingly reflects a

onsiderable reduction in control actions.

.3. Compliance with NERC standard

For decades, members of North American Electric Reliabil-ty Council (NERC) used Control Performance Criteria (CPC)o measure their control performance which consisted of A1, A2,1 and B2 criteria [17]. Since these criteria lack sufficient tech-ical justifications, recently NERC has introduced new controlerformance criteria (CPS) based on extensive analytical studies18]. Control areas are required to be no less than 100% com-liant with CPS1 and no less than 90% compliant with CPS2.PS1 is defined as

PS1 = (2 − CF) × 100% (9)

here compliance factor (CF) is defined as

F = CF12−month

ε21

(10)

nd CF12−month is given as

F12−month = AVG12−month

[(ACE

−10B

)1× �f1

](11)

here ε1 is a constant derived from a targeted frequency bound,is the frequency bias setting, �f1 is the clock-minute aver-

ge of frequency deviation, AVG12−month means computing theverage over a 12-month period and (ACE/ − 10B)1 is thelock-minute average of ACE divided by the control area’s fre-uency bias.

CPS2 is defined as

PS2 =[

1 − violations

total periods − unavailable periods

]×100% (12)

he average of area control error over clock-ten-minutes isefined as

CEav =∣∣∣∣

∑ACE

nsamples−10 min

∣∣∣∣ (13)

iolations clock-ten-minutes{0 if ACEav ≤ L10

1 if ACEav > L10(14)

here L10 is defined as

10 = 1.65 × ε10 × ((−10Bi) × (−10Bs))1/2 (15)

here ε10 is a constant derived from the targeted frequencyound, and Bi is the frequency bias of the control area, and
s is the sum of the frequency bias settings of the control areas
n the respective interconnection [11]. The calculations showedhat the proposed algorithm is more than 100% (129% exactly)ompliant with CPS1 and 100% compliant with CPS2.

(


. Conclusions

A new control scheme for AGC based on adaptiveeuro-fuzzy inference system (ANFIS) and particle swarm opti-ization was proposed considering generation rate constraint.or a two-area test system, integral gains K1 and K2 were calcu-

ated adaptively in real-time according to load variations in theontrol areas. Also, frequency relaxation was implemented usingNFIS. The simulation results showed that adaptive controlains obtained according to the changes in demands, improvehe dynamic and steady state system responses resulting frombtaining lower values of the objective function. The time con-umed for computing optimal gains using PSO directly is toouch for real-time control and is not practical. However, the

rained ANFIS response time is reasonable and practical. Twoealistic load variations were considered and the response ofhe system was obtained using the proposed algorithm in whichoth optimal gain scheduling and frequency relaxation methodere applied. The frequency relaxation resulted in considerable

eduction in generator movement. The compliance of proposedethod with NERC control performance standard was veri-ed.

ppendix A. Theoretical background

Particle swarm optimization and adaptive neuro-fuzzy infer-nce system are used in this paper. In this section they areescribed briefly.

.1. Particle swarm optimization

The particle swarm optimization is a robust stochastic evo-utionary computation technique based on the movement andntelligence of swarms [20]. The particle swarm optimizationas been shown to be effective in optimizing difficult mul-idimensional discontinuous problems in a variety of fields21].

In the literature of PSO, there are some important keywordshat are described below [22].

Particle refers to each individual in the swarm. All parti-les should accelerate their movements toward the personal andverall best locations. Position is the place of a particle in a N-imensional space of solutions. Fitness is a function that takeshe position of a particle and returns a scalar number that showshe goodness of that position and is the objective function; likether evolutionary algorithms. pbest is the best position that aarticle encountered in the search process and had the best fit-ess value. gbest is the global best position of all particles in thewarm which has the highest fitness and each particle knows it.ach particle should change its position with a specified velocity

oward a better position.The PSO algorithm can be described as follows:

1) Define the fitness function and solution space: fitnessfunction is the interface between the physical world andoptimization method. The fitness function should be definedto show the goodness of a solution by a single number.

1 ower Systems Research 78 (2008) 1230–1239

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The parameters to be optimized are limited in a predefinedreasonable range that specifies the solution space.

2) Initialize swarm location and position randomly: each par-ticle should start with an initial location and velocity(magnitude and direction) at the beginning of the searchprocess. These initial values are generated randomly andthe initial location of each particle is its pbest and the bestinitial location of the swarm is the initial gbest.

3) Flying toward the optimum: each particle compares its cur-rent location with its pbest or gbest using the fitness functionand if its current fitness is worse, flies to an appropriate loca-tion. The velocity of the movement depends on pbest andgbest as is calculated using the following equation:

vk+1i = ωvk

i + c1 × rand1 × (pbest − xki )

+c2 × rand2 × (gbest − xki ) (A.1)

where vki is velocity of particle i at iteration k, ω is weighting

function, c1 and c2 are weighting factors which determinethe convergence behavior of PSO; c1 is a factor determininghow much the particle is influenced by the memory of itsbest location and c2 is a factor determining how much theparticle is influenced by the rest of the swarm and bothare typically set equal to 2, rand1 and rand2 are randomnumbers between 0 and 1, xk

i is current position of particlei at iteration k, pbesti is the pbest of particle i, and gbest isthe best value so far in the group among the pbests of allparticles. The following weighting function is usually used:

ω = ωmax − ωmin

itermax× iter (A.2)

where ωmax is the initial weight, ωmin is the final weight,itermax is the maximum iteration number, and iter is thecurrent iteration number. Once the velocity is determined,particles move according to the following equation:

xk+1i = xk

i + �t × vk+1i (A.3)

where �t is the time step usually chosen to be 1.4) Repeat: the previous step is repeated for each time step and

the pbest related to each particle and the gbest are updatedand the process is finished when the termination criteriais met. Maximum number of iterations is one of the mostcommon criteria for the algorithm to stop. Fig. A.1 showsthe particle swarm algorithm.

.2. ANFIS

Adaptive neuro-fuzzy inference systems represent a neuraletwork approach to the design of fuzzy inference systems [23].ince their introduction, ANFIS networks have been widely con-idered in the technical literature and successfully applied tolassification tasks, rule-based process controls, pattern recog-ition problems, and so on. An ANFIS network makes use of a
upervised learning algorithm to determine a nonlinear modelf the input–output function, which is represented by a train-ng set of numerical data. Since under proper conditions it cane used as a universal approximator [24], an ANFIS network is
r

i

Fig. A.1. PSO flowchart.

articularly suited for solving function approximation problemsn several engineering fields.

In general, the problem to be solved is the approximation ofn unknown function y = f (x), f : Rn → R. Using an ANFISetwork, the function is approximated through a fuzzy inferenceystem constituted by M rules of Sugeno first-order type. Theth rule, k = 1, . . . , M, has the following form:

if z1 is B(k)1 , z2 is B

(k)2 , . . . , and zn is B(k)

n then y(k)

=n∑

j=1

a(k)j zj + a

(k)0 (A.4)

here z = [z1, z2, . . . , zn] is the input pattern and y(k) is theutput associated with the rule. Each rule is characterizedy membership functions (MFs) μ

B(k)j

(zj) of the fuzzy input

ariables B(k)j , j = 1, . . . , n, and by the coefficients a

(k)j , j =

, . . . , n, of the crisp output. Several options are possible forhe fuzzification of crisp inputs, the composition of input MFs,nd the way rule outputs are combined. Usually, these choicesnsure a more compact representation of the first-order Sugenoule, i.e.,

f z is B(k) then y(k) =n∑

j=1

a(k)j zj + a

(k)0 (A.5)

ower

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neering, power systems, from School of ElectricalEngineering, Sharif University of Technology, 2007,


here B(k) is the overall fuzzy input variable and μB(k) (z) is theorresponding MF, which is also called the firing strength (oreight) of the kth rule. The usual choices adopted for ANFISetworks also yield the following structure of the fuzzy inferenceystem:

˜ =∑M

k=1μB(k) (z) × y(k)

∑M

k=1μB(k) (z)

(A.6)

here y is the estimate, for a given input z, of the actual value= f (z) [25].

ppendix B. Numerical values of the model

= 60 Hz system frequency.= 5 s inertia constant.= 2.4 Hz/pu regulation.= 0.0083 pu/Hz load frequency characteristic.

g = 0.08 s speed governor time constant.t = 0.3 s turbine time constant.p = 20 s power system time constant.p = 120 Hz/pu power system gain.= 0.425 pu frequency bias control.

12 = 0.545 pu synchronizing power coefficient.RC = 3%/min generation rate constraint.

12 = −1.

eferences

[1] J. Talaq, F. Al-Basri, Adaptive fuzzy gain scheduling for load frequencycontrol, IEEE Trans. Power Syst. 14 (1) (1999) 145–150.

[2] O.I. Elgerd, C. Fosha, Optimum megawatt-frequency control of multi-area electric energy systems, IEEE Trans. Power App. Syst. 89 (4) (1970)556–563.

[3] O.I. Elgerd, Electric Energy Systems Theory: An Introduction, McGraw-Hill Inc., New York, 1982.

[4] N. Jaleeli, D.N. Ewart, L.H. Fink, Understanding automatic generationcontrol, IEEE Trans. Power Syst. 7 (3) (1992) 1106–1122.

[5] J. Nanda, B.L. Kaul, Automatic generation control of an interconnectedpower system, IEE Proc. Gener. Transm. Distrib. 125 (5) (1978) 385–390.

[6] N. Bekhouche, A. Feliachi, Decentralised estimation for the automatic gen-eration control problem in power systems, in: Proceedings of the 1992 IEEEConference on Control Applications, (2), pp. 626–631.

[7] J. Kanniah, S.C. Tripathy, O.P. Malik, G.S. Hope, Microprocessor-basedadaptive load-frequency control, IEE Proc. Gener. Transm. Distrib. 131 (4)(1984) 121–128.

[8] M. Aldeen, A fresh approach to the LQR problem with application topower systems, in: Proceedings of the International Power EngineeringConference, Singapore, vol. 1, 1993, pp. 374–379.

[9] G.A. Chown, R.C. Hartman, Design and experience with a fuzzy logic
controller for automatic generation control (AGC), IEEE Trans. PowerSyst. 13 (3) (1998) 965–970.
10] D.K. Chaturvedi, P.S. Satsangi, P.K. Kalra, Load frequency control: a gen-eralised neural network approach, Electrical Power Energy Syst. 21 (1999)405–415.


11] B. Tyagi, S.C. Srivastava, A decentralized automatic generation controlscheme for competitive electricity markets, IEEE Trans. Power Syst. 21(1) (2006) 312–320.

12] H. Bevrani, Y. Mitani, K. Tsuji, Robust decentralised load-frequency con-trol using an iterative linear matrix inequalities algorithm, IEE Proc. Gener.Transm. Distrib. 151 (3) (2004) 347–354.

13] C.F. Juang, C.F. Lu, Load-frequency control by hybrid evolutionary fuzzyPI controller, IEE Proc. Gener. Transm. Distrib. 153 (2) (2006) 196–204.

14] D. Rerkpreedapong, A. Hasanovic, A. Feliachi, Robust load frequencycontrol using genetic algorithms and linear matrix inequalities, IEEE Trans.Power Syst. 18 (2) (2003) 855–861.

15] V. Donde, M.A. Pai, I.A. Hiskens, Simulation and optimization in an AGCsystem after deregulation, IEEE Trans. Power Syst. 16 (3) (2001) 481–489.

16] G.A. Chown, B. Wigdorowitz, A methodology for the redesign of fre-quency control for AC networks, IEEE Trans. Power Syst. 19 (3) (2004)1546–1554.

17] North American Electric Reliability Council (NERC), Control Perfor-mance Criteria Training Document, in operating manual, 1996, pp.cpc.1–cpc.20.

18] Automatic Generation Control, 2005 [Online]. Available: http://www.nerc.com.

19] M.L. Kothari, J. Nanda, L. Hari, Selection of sampling period for auto-matic generation control, Int. Elect. Mach. Power Syst. 25 (10) (1997)1063–1077.

20] J. Kennedy, The particle swarm: social adaptation of knowledge, in: Pro-ceedings of the International Conference on Evolutionary Computation,1997, pp. 303–308.

21] R.C. Eberhart, Y. Shi, Evolving artificial neural networks, in: Proceed-ings of the 1998 International Conference on Neural Networks and Brain,Beijing, PR China, 1998, pp. PL5–PL13.

22] J. Robinson, Y. Rahmat-Samii, Particle swarm optimization in electromag-netics, IEEE Trans. Antennas Propagat. 52 (2) (2004) 397–407.

23] J.S. Jang, ANFIS: adaptive-network-based fuzzy inference system, IEEETrans. Syst. Man Cybern. 23 (3) (1993) 665–685.

24] B. Kosko, Fuzzy systems as universal approximators, IEEE Trans. Comput.43 (11) (1994) 1329–1333.

25] M. Panella, A. Stanislao Gallo, An input–output clustering approach tothe synthesis of ANFIS networks, IEEE Trans. Fuzzy Syst. 13 (1) (2005)69–81.

Seyed Hamid Hosseini (M’89) received B.S. degreein 1983 from University of Oklahoma, Norman, OKand M.S. and Ph.D. degrees from Iowa State Uni-versity, Ames, IA in 1985 and 1988, all in electricalengineering. Since 1988, he has been with the elec-trical engineering department of Sharif Universityof Technology, Tehran, Iran. His research interestsinclude power system operation, optimization, andplanning.

Amir Hossein Etemadi was born in Iran. He receivedhis B.S. degree in electrical engineering from Schoolof Electrical and Computer Engineering, University ofTehran, 2005 and his M.S. degree in electrical engi-

Tehran, Iran. His research interests include power sys-tem reliability, operation, protection and distributionsystem optimization.

http://www.nerc.com

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Adaptive neuro-fuzzy inference system based automatic generation control