Chapter-4
AUTOMATIC GENERATION CONTROL OF MULTI-SOURCE POWER
GENERATION UNDER DEREGULATED ENVIRONMENT
4.1 INTRODUCTION
Electric power utilities throughout the world are currently undergoing major
restructuring processes and are adopting the deregulated market operation. Competition has been
introduced in power systems around the world based on the premise that it will increase the
efficiency of the industrial sector and reduce the cost of electrical energy of all customers. In
order to control electric power industry, government has set up some restructured rules and
economic incentives where the collection of those restructured rules called deregulation.
Deregulated system consists of generation companies (GENCOs), distribution companies
(DISCOs), transmission companies (TRANSCOs) and independent system operator (ISO).
Those entities like GENCO, TRANSCO, DISCO, ISO and many ancillary services do have
different roles to play and therefore have to be modelled differently. The more challenging issue
that has come up after deregulation is the ancillary service which is essential for maintaining the
electrical system security and reliability together. One of them is Automatic Generation Control
(AGC) that restores mismatches between generation and load and keeps the system stable.
Several authors have reported AGC in deregulated power system [34, 35]. The authors [34, 35]
represented price based simulation in deregulated power system.
Under the supervision of ISO, the DISCO can contract any amount of power from the
GENCO. These are implemented through DISCO participation matrix (DPM), the concept of
DPM and area participation factors (apf) are illustrated in [41]. The authors in [41] used
trajectory sensitivity to find out optimal parameters of the system using gradient Newton
algorithm. Many intelligent techniques such as genetic algorithm, bacteria forging optimization
algorithm (BFOA) etc., are used to optimize controller gains of AGC under deregulated power
system. In [45] the author reported GA based integral controller in multi area power system in
deregulated environment considering hydro-thermal power generating units. In [48], BFOA is
used in multi area thermal system under deregulated environment using non-integer control.
Decentralized controller [66] is also implemented in deregulated power system. In the above
literature, all authors have studied either thermal or hydro power plants. Keeping in view the
present power scenario, the combination of multi-source generators is more realistic for the study
of AGC. The control area may have the combination of thermal, hydro, gas, nuclear, renewable
energy sources, etc. [62]. It is quite apparent from literature survey that hardly any author has
reported multi sources generation system in deregulated power system. For this reason, the
thermal-gas power generating units are considered in two-area power system in this chapter as an
maiden attempt.
Ghoshal et al. [68] used a genetic algorithm (GA) to optimize controller gains of a multiarea hydro-thermal AGC system. Again, Ghosal [69] has proposed a scheme of GA/GA-SA
based fuzzy control for AGC of a multi area thermal generating system. He has reported better
results in comparison to his previous method. The premature convergence of GA degrades its
efficiency and reduces the search capability. Differential evolution (DE) is a branch of
evolutionary algorithms developed by Rainer Stron and Kenneth Price in 1995 for optimization
problems [55]. It is a population-based direct search algorithm for global optimization capable of
handling non-differentiable, non-linear and multi-modal objective functions, with few, easily
chosen, control parameters. DE differs from other Evolutionary Algorithms (EA) in the mutation
and recombination phases. DE uses weighted differences between solution vectors to change the
population whereas in other stochastic techniques such as Genetic Algorithm (GA), perturbation
occurs in accordance with a random quantity. DE employs a greedy selection process with
inherent elitist features.
In view of the above discussion, the author has taken a maiden attempt to study the
automatic generation control of multi-source two-area power system under deregulated
environment where, each area consists of thermal-gas generating units. For this study, classical
controllers such as integral, proportional-integral, integral-derivative, and proportional-integralderivative are considered to reveal the performances, where the gains of these controllers are
optimized by using GA and DE algorithms. Further, to investigate the performances of proposed
controllers, three different cases namely base case, bilateral transaction case and contract
violation cases have been studied. Finally, the dynamic performances obtained both by GA and
DE algorithms are compared for the proposed deregulated AGC system.
4.2 SYSTEM INVESTIGATED
The AGC system considered is two equal area systems consisting of thermal and gas
generation units. Each area consists of two numbers of GENCOs and two numbers of DISCOs as
shown in Appendix-1. The thermal area is provided with a single reheat turbine having
appropriate generation rate constraint of 3% per min [8]. The gas generating unit is considered
with a gas turbine, whose parameters are adopted from [64], details of which is given in
Appendices-3A and 3B. The transfer function of two-area thermal-gas system is shown in Fig.
4.1. As there are more than one GENCOs in each area, area control error (ACE) signal has to be
distributed among them in proportion to their participation in the AGC. Coefficients that
distribute ACE to several GENCOs are termed as “ACE participation factors” (apf ). Note that
n
 apf
i 1
i
 1 where, n is the number of GENCOs. A DISCO in each area demands a particular
GENCO or GENCOs for load power. As there are more than one GENCOs and DISCOs in the
deregulated structure, a DISCO has freedom to have a contract with any GENCO for transaction
of power. A DISCO may have a contract with a GENCO on another control area also. These
demands must be reflected in the dynamics of the system. Since, a particular set of GENCOs are
required to follow the load demanded by a DISCO, information signals must flow from a DISCO
to that particular set of GENCOs specifying corresponding demands. This is achieved using the
concept of DPM i.e., DISCO participation matrix [41]. DPM helps to visualise the contracts
easier. As the name suggests, DPM shows the participation of DISCO in a contract with
GENCO. In DPM, number of rows is equal to the number of GENCOs and the number of
column equal to the number of DISCOs of the system. Thus, each ij entry of the matrix called as
“contract participation factor” corresponds to the fraction of a total load contracted by a DISCO
j from a GENCO i. The sum of all entries in a column in a matrix is unity. The steady state
power flow on the tie-line is given by:
 Ptie12,scheduled  (Demand of DISCOs in area-2 from GENCOs in area-1)-
(Demand of DISCOs in area-1 from GENCOs in area-2)
any given time, the tie-line power error is given by:
(4.1) At
 Ptie12,error   Ptie12,actual   Ptie12,scheduled
(4.2)
This error in tie-line power is used to generate ACE signal as in the normal AGC system.
e1 (t )  ACE1  B1f1  Ptie12,error
(4.3)
e2 (t )  ACE2  B2 f 2  Ptie21,error
(4.4)
 Ptie21,error  12  Ptie12,error
(4.5)
where,  12   Pr1 ; P r1 and Pr 2 are the rated power of area-1 and 2, respectively.
Pr 2
Accordingly, ACE2  B2 f 2   12 Ptie12,error
(4.6)
cpf 11

+
cpf 21
DISCO1
cpf 12
+

+
+
cpf 31
+
+
cpf 41
1
B1
+

apf
DISCO2
cpf 42
Thermal power plant with reheat turbine
+

1  s K r1 T r1
1  s T r1
1
1  s T G1
+
+
-
1
1  s T t1
+
11
PID
controller
+
cpf 32
+
R1
apf
+
1
R2
+
cpf 22
+
-
12
1
cg  sbg

+
1  s T CR
1 sT F
1 s X G
1 sY G
+
1
1 sT
P d
K PS 1
1  T P1
f 1
CD
Gas turbine power plant
+
2  T 12
s

-
1
a12
1
R2
R
+

apf
21
PID
controller
+
+
+
apf

22
+
-
a12
Thermal power plant with reheat turbine
1
+

1
1  s T G1
+
1
cg  sbg
1  s K r1T r1
1  s T r1
1 s X G
1 sY G
+
B2
1
1  s T t1
1  s T CR
1 sT F
1
1  s T CD
+
+
-
K PS 1
1  T P1
f
2
P d
Gas turbine power plant
+
cpf 13
cpf 23
DISCO3
+


+
cpf 14
+
cpf 24
+
cpf 33
cpf 43
+


+
+
cpf 34
DISCO4
cpf 44
Fig. 4.1 Transfer function model of multi-source two-area system under deregulation
The nominal system parameters are given in Appendix-4
Since, in the considered two-area system, there are two GENCOs and two DISCOs in each area.
The corresponding DPM is
 cpf 11 cpf 12
 cpf
cpf 22
21

DPM   
cpf
cpf 32
31

 cpf 41 cpf 42
 cpf 13
 cpf 23

 cpf 33
 cpf 43
cpf 14 
cpf 24 
 
cpf 34

cpf 44 
(4.7)
From the above equation, the block diagonals of DPM refers to local demands whereas, off
diagonal blocks correspond to the demands of the DISCOs in one area to the GENCOs in another
area.
4.3 DESIGN OF CONTROLLERS
The proportional integral derivative controller (PID) is the most popular feedback
controller used in the process industries. It is a robust and easily understood controller that can
provide excellent control performance despite the varied dynamic characteristics of process plant.
As the name suggests, the PID algorithm consists of three basic modes, the proportional mode,
the integral and the derivative modes. A proportional controller has the effect of reducing the rise
time, but never eliminates the steady-state error. An integral control has the effect of eliminating
the steady-state error, but it may make the transient response worse. A derivative control has the
effect of increasing the stability of the system, reducing the overshoot, and improving the
transient response. Proportional integral (PI) controllers are the most often type used today in
industry. A control without derivative (D) mode is used when: fast response of the system is not
required, large disturbances and noises are present during operation of the process and there are
large transport delays in the system. Derivative mode improves stability of the system and
enables increase in proportional gain and decrease in integral gain which in turn increases speed
of the controller response. PID controller is often used when stability and fast response are
required. In view of the above, I, PI, ID and PID structured controllers are considered in the
present chapter.
Design of PID controller requires determination of the three main parameters,
proportional gain ( K P ), integral gain ( K I ) and derivative gain ( K D ). Similarly, for PI
controller proportional gain ( K P ) and integral gain ( K I ) are to be determined. For design of ID
controller K I and K D are to be determined. The controllers in both the areas are considered to be
different, so that proportional gains are K P1 , K P 2 ; integral gains are K I 1 , K I 2 and derivative gains
are K D1 , K D2 . The integral square error (ISE) criterion is considered as the objective function for
the present work which is described in equation (4.8).
J  ISE 
t sim
 f   f   P 
2
1
2
2
2
Tie
 dt
(4.8) where,
0
f1 and f 2 are the system frequency deviations in area-1 and area-2, respectively; PTie is the
incremental change in tie-line power and t sim is the time range of simulation. The problem
constraints are the controller parameter bounds. Therefore, the design problem can be formulated
as the following optimization problem.
Minimize J
subject to K P min  K P  K P max , K I min  K I  K I max K D min  K D  K D max
,
(4.9)
(4.10)
where, J is the objective function and K P min , K I min ; K P max , K I max and K D min , K D max are
the minimum and maximum value of the control parameters. As reported in the literature, the
minimum and maximum values of controller parameters are chosen as 0 and 2.0, respectively.
4.4 RESULTS AND ANALYSIS
4.4.1 Implementation of DE algorithm
Simulations were conducted on an Intel, core 2 Duo CPU of 2.4 GHz based computer in
the MATLAB (R2010a) environment. The flow chart of the DE algorithm employed in the
present study is already given in Fig. 2.4 which described in section 2.4.3. A series of simulation
has been performed to properly tune the DE parameters to reduce the objective function. Table
4.1 shows the outcomes of DE parameters variation where, 50 independent runs are performed
for each parameter variation. Based on the results obtained from Table 4.1, the parameters for
further simulation studies considered in the present chapter are: a population size of NP=50,
generation number of G=90, step size of F=0.7 and crossover probability of CR =0.3. The
strategy employed is DE/best/1/exp. Optimization is terminated when the pre-specified number
of generations for DE is reached. One more important factor that affects the optimal solution
more or less is the range for unknowns. In the very first run of the program, i.e, first iteration, a
wider solution space is explored and after getting the initial solution the solution space is
shortened nearer to the values obtained in the previous iteration. Here, the lower and upper
bounds of the gains are chosen as 0 and 2, respectively.
Table 4.1 Study of tuning of DE parameters
Parameters
Np
F
CR
Average of
Max.
Min.
Std. Dev.
ISE
of ISE
of ISE
of ISE
10
1.3858
1.7136
1.0803
0.225074
20
1.37755
1.7485
1.0342
0.234971
30
1.44094
1.9153
1.1125
0.235593
40
1.4976
1.9484
1.0481
0.247296
50
1.4239
1.8391
0.9952
0.210464
0.1
1.34788
1.7485
1.0813
0.22114
0.3
1.469253
1.9259
1.0342
0.251433
0.5
1.497607
1.9484
1.0481
0.247296
0.7
1.44342
1.8391
0.9952
0.204003
0.9
1.4144
1.9153
1.1125
0.232506
0.1
1.478147
1.9259
1.0342
0.259239
0.3
1.381753
1.6205
1.032
0.169625
0.5
1.37976
1.6359
1.0768
0.183741
0.7
1.537327
1.8691
1.2188
0.221018
0.9
1.344693
1.7136
1.0803
0.217211
Other parameters
Gen(G)=90;F=0.1;CR=0.9
Gen(G)=90;NP=50;CR=0.9
Gen(G)=90;Np=50;F=0.7
4.4.2 Base case
Consider a case where the GENCOs in each area participate equally in AGC, i.e., ACE
participation factors are: apf 1  0.5 ; apf 2  1  apf 1  0.5 ; apf 3  0.5 ; apf 4  1  apf 3  0.5
It is assumed that the load change occurs only in area-1. Thus, the load is demanded only by
DISCO1 and DISCO2. DISCO3 and DISCO4 do not demand any load from GENCOs, thus
corresponding cpfs in DPM matrix are zero. Let this load demand for DISCO1 and DISCO2 be
0.1 pu.MW for each of them. The DPM matrix is given by:
 0 . 5 0 .5
 0 . 5 0 .5

DPM    
 0
0
 0
0
0
0

0
0
0
0 


0
0 
Simulation has been carried out by considering 4% regulation (R), the gains of the controllers are
optimized using GA and proposed DE algorithms and are given in Table4.2.
Table 4.2 Gain values of different controllers
Type of controller
DE optimized
GA optimized
KI1
0.3604
0.3341
I controller
KI2
0.3107
0.3799
PI controller
KI1
0.2997
0.4072
KI2
0.1999
0.2799
KP1
0.0341
0.791
KP2
0.1226
0.2126
KI1
0.973
0.8883
KI2
0.649
0.8922
KD1
0.3673
0.3191
KD2
0.7083
0.5866
KI1
1.3065
0.9819
KI2
0.3903
0.7219
KD1
1.0959
0.7899
KD2
0.4993
0.7163
KP1
0.8495
0.169
KP2
0.0767
0.1727
ID controller
PID controller
Overshoot, undershoot and settling time of ∆f1, ∆f2 and ∆Ptie for I, PI, ID and PID controllers are
given in Table 4.3. As seen from this table, the objective function values are improved with
proposed DE optimised PID/ID/PI/I controllers by 42.5%, 37.13%, 2.55% and 0.44%,
respectively, compared to GA optimised controllers. The overshoot and undershoot of ∆f1, ∆f2
and ∆Ptie with PID, PI and ID controllers optimised with DE are improved as compared to those
obtained by GA technique. However, for I controller, overshoot and undershoot are found to be
less in GA optimisation compared to DE algorithm. The improvement in settling times for ∆f1
are found to be 10.29%, 6.76%, 9.28% and 9.66%, respectively, by I, ID, PI and PID controllers.
Similarly, for ∆f2 these are 9.76%, 37.65%, 8.72% and 33.58% by I, ID, PI and PID controllers,
respectively. The improvement in settling time for ∆Ptie is found to be 21.67% for PID controller.
The dynamic performances of I, ID, PI and PID controllers are shown in Figs. 4.2-4.4 using GA
optimized values.
In Figs. 4.5-4.6, the change in generations, i.e., ∆PG1 and ∆PG2 of GENCOs for different
controllers optimized using GA is shown. It is observed from these two figures that both the
GENCOs generate same power. Similarly, dynamic performances of different controllers with
DE algorithm are shown in Figs. 4.7-4.9. The change in generations, i.e., ∆PG1 and ∆PG2 of
GENCOs for different controllers optimized using DE algorithm is shown in Figs.4.10-4.11. In
both the cases, generation of GENCOs generate the same power 0.1p.u MW. With regard to the
performances of different controllers it is observed that, PID controller offers lesser value of
objective function and also reduces the settling time of frequency deviations of both the control
areas and change in tie-line power than those obtained by I, PI and ID controllers, as shown in
Table 4.3. So, for further investigation the PID controller is only considered.
0.2
0.1
f1
0
-0.1
PID controller
ID controller
I controller
PI controller
-0.2
-0.3
-0.4
0
5
10
15
20
25
Time in sec
Fig. 4.2 Frequency deviation of area-1 for base case with GA
30
Table 4.3 Undershoot (US), overshoot (OS) and settling time (ST) for
base case with different controllers using GA and DE algorithms
Type of controllers
∆f1
I controller
∆f2
∆ptie
Parameters
DE optimised
GA optimised
OS
US
ST
OS
US
ST
OS
US
ST
0.2301
-0.425
17.43
0.1619
-0.2153
18.58
0.0164
-0.0694
13.49
0.2698
0.2242
-0.4252
19.43
0.1603
-0.2163
20.59
0.164
-0.0695
13.52
0.271
OS
US
ST
OS
US
ST
OS
US
ST
0.2203
-0.4237
17.4
0.1515
-0.2137
18.53
0.0135
-0.0691
13.34
0.2627
0.2488
-0.421
19.18
0.1706
-0.2126
20.3
0.0183
-0.677
13.3
0.2695
OS
US
ST
OS
US
ST
OS
US
ST
0.1477
-0.3494
5.79
0.0563
-0.1522
5.2
0.0085
-0.0516
1.88
0.1028
0.1559
-0.3576
6.21
0.0616
-0.1582
8.34
0.0091
-0.0533
1.88
0.1635
OS
US
ST
OS
US
ST
OS
0.0409
-0.2574
5.52
0.012
-0.0946
4.51
0.0057
0.0503
-0.2916
6.11
0.0138
-0.1191
6.79
0.0086
OBJ
∆f1
∆f2
PI controller
∆ptie
OBJ
∆f1
ID controller
∆f2
∆ptie
OBJ
∆f1
∆f2
PID controller
∆ptie
US
ST
-0.0315
1.88
0.0548
OBJ
-0.0397
2.4
0.0935
f2
0.1
0
PID controller
ID controller
I controller
PI controller
-0.1
-0.2
0
5
10
15
20
25
30
Time in sec
Fig. 4.3 Frequency deviation of area-2 for base case with GA
0.02
 Ptie
0
-0.02
PID controller
ID controller
I controller
PI controller
-0.04
-0.06
0
5
10
15
20
25
Time in sec
Fig. 4.4 Change in tie-line power for base case with GA
30
0.1
 PG1
0.08
0.06
0.04
PID controller
ID controller
I controller
PI controller
0.02
0
0
5
10
15
20
25
30
Time in sec
Fig. 4.5 Generation of GENCO1 for base case with GA
0.2
 PG2
0.15
0.1
PID controller
ID controller
I controller
PI controller
0.05
0
0
5
10
15
20
25
30
Time in sec
Fig. 4.6 Generation of GENCO2 for base case with GA
0.2
0.1
f1
0
-0.1
PID controller
ID controller
I controller
PI controller
-0.2
-0.3
-0.4
0
5
10
15
Time in sec
20
25
30
Fig. 4.7 Frequency deviation of area-1 for base case with DE
f2
0.1
0
PID controller
ID controller
I controller
PI controller
-0.1
-0.2
0
5
10
15
20
25
30
Time in sec
Fig. 4.8 Frequency deviation of area-2 for base case with DE
 Ptie
0
-0.02
PID controller
ID controller
I controller
PI controller
-0.04
-0.06
0
5
10
15
20
25
Time in sec
Fig. 4.9 Change in tie line power for base case with DE
30
0.1
 PG1
0.08
0.06
0.04
PID controller
ID controller
I controller
PI controller
0.02
0
0
5
10
15
20
25
30
Time in sec
Fig. 4.10 Generation of GENCO1 for base case with DE
0.2
 PG2
0.15
0.1
PID controller
ID controller
I controller
PI controller
0.05
0
0
5
10
15
20
25
30
Time in sec
Fig. 4.11 Generation of GENCO2 for base case with DE
4.4.3 Bilateral transaction case
In this case, all DISCOs are in contract with all GENCOs for transaction of power.
DISCOs contract with the GENCOs as per the following DPM matrix. It is assumed that each
DISCO’s demand is 0.1puMW power from GENCOs as defined by cpfs in DPM matrix.
 0 .5
 0 .2

DPM   
0
0.3
0.25  0 0.3
0.25  0 0 

 

0.25 1 0.7 
0.25  0 0 
Let, each GENCO participates in AGC as defined by following apfs:
apf 1  0.75 ; apf 2  1  apf 1  0.25 ; apf 3  0.5 ; apf 4  1  apf 3  0.5
With the above apf values, GENCOs participate in AGC. The apfs only affect the transient
behaviour of the system, not the steady state behaviour. The optimum gain values, speed
regulation (Ri) for the PID controller are obtained using GA and DE optimization algorithms and
the values are given in Table 4.4.
Table 4.4 Gain values of PID controller and speed regulation (Ri) for
bilateral transaction and contract violation cases by DE and GA
For bilateral transaction
Parameters
For contract violation
DE
GA
DE
GA
KI1
1.2251
0.9934
1.3424
0.8693
KI2
1.4309
1.0955
1.4304
0.5797
KD1
0.990
0.9509
1.0421
0.5499
KD2
0.8277
0.947
0.919
0.145
KP1
0.7795
0.2963
1.1908
0.853
KP2
0.9013
0.7447
1.0861
0.6221
R1
3.0784
3.8896
3.1743
3.5095
R2
4.9809
6.8678
8.1454
5.1325
Dynamic performances of PID controller using GA and DE algorithms are shown in
Figs.4.12-4.14. From these figures, the overshoot of ∆f1 and ∆f2 are found to be improved by
33.14% and 34.07% using DE algorithm as compared to GA. Overshoot, undershoot and settling
time obtained for PID controller using both GA and DE algorithms are given by Table 4.5. As
given in this table, the settling times of ∆f1, ∆f2 and ∆Ptie are improved by 13.04%, 9.26% and
3.75%, respectively, using proposed DE tuned controller compared to GA technique. Also, the
objective function is improved by 32.7% using DE algorithm compared to GA. Figs. 4.15-4.18
show the generations of GENCOs for bilateral transaction case using DE and GA algorithms
with PID controller.
0.1
0
f1
-0.1
-0.2
-0.3
DE tuned PID controller
GA tuned PID controller
-0.4
-0.5
0
5
10
15
20
25
30
Time in sec
Fig. 4.12 Frequency deviation of area-1 for bilateral transaction case
0.1
0.05
f2
0
-0.05
-0.1
-0.15
DE tuned PID controller
GA tuned PID controller
-0.2
0
5
10
15
20
25
30
Time in sec
Fig. 4.13 Frequency deviation of area-2 for bilateral transaction case
DE tuned PID controller
GA tuned PID controller
0.04
 Ptie
0.02
0
-0.02
0
5
10
15
20
25
30
Time in sec
Fig. 4.14 Change in tie-line power for bilateral transaction case
 PG1
0.1
0.05
DE tuned PID controller
GA tuned PID controller
0
0
5
10
15
20
25
30
Time in sec
Fig. 4.15 Generation of GENCO1 for bilateral transaction case
DE tuned PID controller
GA tuned PID controller
 PG2
0.1
0.05
0
0
5
10
15
20
25
Time in sec
Fig. 4.16 Generation of GENCO2 for bilateral transaction case
30
 PG3
0.15
0.1
0.05
0
DE tuned PID controller
GA tuned PID controller
0
5
10
15
20
25
30
Time in sec
Fig. 4.17 Generation of GENCO3 for bilateral transaction case
DE tuned PID controller
GA tuned PID controller
0.12
0.1
 PG4
0.08
0.06
0.04
0.02
0
0
5
10
15
20
25
30
Time in sec
Fig. 4.18 Generation of GENCO4 for bilateral transaction case
Table 4.5 Overshoot, undershoot and settling time by DE and GA
for bilateral transaction and contract violation cases
Parameters
∆f1
∆f2
∆Ptie
Bilateral transaction case optimised
DE
GA
OS
0.0988
0.1478
US
-0.4664
-0.4949
ST
10.87
12.5
OS
0.0683
0.1036
US
-0.2158
-0.2076
ST
11.47
12.64
OS
0.05
0.05
US
-0.0186
-0.0309
ST
3.08
3.2
Contract violation case optimised
DE
GA
0.1093
0.1177
-0.6192
-0.7542
11.71
17.19
0.0641
0.0474
-0.2089
-0.3856
12.49
17.43
0.05
0.05
-0.015
-0.0449
3.47
4.25
OBJ
0.4945
0.7348
0.7605
1.2967
4.4.4 Contract violation case
DISCO may demands more power than that of the specified contract. The excess of
power must be supplied by the GENCOs of the same area as the DISCOs. Let us consider
DISCO1 demands 0.1puMW of excess power, the extra power reflects as local load of the area.
So the local load of area-1 is
∆PL1,loc= load of DISCO1(0.1)+load of DISCO2(0.1)+0.1=0.3 pu MW.
The local load of area-2 remains same as the second case i.e., 0.2 pu MW. The DPM matrix
remains same as the second case. The power generation of area-2 i.e., GENCO3and GENCO4
remains same as before. The un-contracted load of DISCO1 is reflected in generation of
GENCO1 and GENCO2. The dynamic performances of PID controller using GA and DE
algorithms are given in Figs. 4.19-4.21. Overshoot of ∆f1 is improved by 7.45% using DE
technique compared to GA. Generation of all GENCOs are shown in Figs. 4.22-4.25 when
computed by both in GA and DE algorithms.
Overshoot, undershoot and settling time obtained by DE and GA algorithms for PID
controller is also given in Table-4.5. As given in this table, the settling times of ∆f1, ∆f2 and
∆Ptie are found to be improved by 31.88%, 28.38% and 18.35% with proposed technique as
compared to GA. To show the robustness of proposed controllers, contract violation (C.V) is
increased from 10% to 30% in steps of 10% and the dynamic responses are shown in Figs. 4.264.28 from which it is clear that the designed controllers are robust and perform satisfactorily for
different contract violation.
0
f1
-0.2
-0.4
-0.6
DE tuned PID controller
GA tuned PID controller
0
5
10
15
20
25
30
Time in sec
Fig. 4.19 Frequency deviation of area-1 for contract violation case
0
f2
-0.1
-0.2
-0.3
-0.4
DE tuned PID controller
GA tuned PID controller
0
5
10
15
20
25
30
Time in sec
Fig. 4.20 Frequency deviation of area-2 for contract violation case
DE tuned PID controller
GA tuned PID controller
0.04
 Ptie
0.02
0
-0.02
-0.04
0
5
10
15
Time in sec
20
25
30
Fig. 4.21 Change in tie-line power for contract violation case
0.2
 PG1
0.15
0.1
0.05
DE tuned PID controller
GA tuned PID controller
0
0
5
10
15
20
25
30
Time in sec
Fig. 4.22 Generation of GENCO1 for contract violation case
0.2
DE tuned PID controller
GA tuned PID controller
 PG2
0.15
0.1
0.05
0
0
5
10
15
20
25
Time in sec
Fig. 4.23 Generation of GENCO2 for contract violation case
30
0.2
 PG3
0.15
0.1
0.05
DE tuned PID controller
GA tuned PID controller
0
0
5
10
15
20
25
30
Time in sec
Fig. 4.24 Generation of GENCO3 for contract violation case
0.15
DE tuned PID controller
GA tuned PID controller
 PG4
0.1
0.05
0
0
5
10
15
Time in sec
20
25
30
Fig. 4.25 Generation of GENCO4 for contract violation case
0
f1
-0.2
-0.4
-0.6
0.3 C.V
0.4 C.V
-0.8
0.5 C.V
0
5
10
15
Time in sec
20
25
30
Fig. 4.26 Frequency deviation of area-1 for different values of contract violation
0.05
0
f2
-0.05
-0.1
-0.15
0.3 C.V
0.4 C.V
0.5 C.V
-0.2
-0.25
0
5
10
15
20
25
30
Time in sec
Fig. 4.27 Frequency deviation of area-2 for different values of contract violation
0.06
0.5 C.V
0.4 C.V
0.3 C.V
0.04
 Ptie
0.02
0
-0.02
-0.04
-0.06
0
5
10
15
20
25
30
Time in sec
Fig. 4.28 Change in tie-line power for different values of contract violation
4.5 CONCLUSION
AGC of interconnected multi-source two-area system under deregulated environment is
considered in this chapter. Thermal and gas generation units are considered in the two-area.
Thermal unit considering reheat turbine and appropriate value of GRC is taken. Performances of
different controllers are compared with GA and DE algorithms for base case. The controller
parameters are optimized using differential evolution (DE) optimization technique. Initially the
control parameters of DE algorithm are tuned by carrying out multiple runs of algorithm for each
control parameter variation. The best DE parameters are found to be: step size F=0.3, crossover
probability of CR =0.7, population size of NP=50 and generation of G=90. The parameters of
integral (I), integral derivative (ID) and proportional integral derivative (PID) controllers are
optimized employing tuned DE algorithm and GA. The superiority of the proposed approach has
been shown by comparing the results with GA technique for the same power system by using
various performance measures like overshoot, settling time and standard error criteria of
frequency and tie-line power deviation for base case. The critical study of the dynamic responses
reveals that PID controller is superior keeping in view of settling time and reduced oscillations
than other controllers. Controller gains and speed regulation (Ri) parameters are optimized using
DE and GA algorithms for bilateral transaction and contract violation cases also. For contract
violation case, higher values of (Ri) are obtained in case of DE, which results into economical
governor. With references to obtained values of settling time, overshoot and objective function by
both the algorithms, DE is found to perform better than GA for all the three cases, i.e., base case,
bilateral transaction and contract violation cases. Furthermore, it is also observed that the
proposed system is robust and is not affected by change in the contact violation condition, system
parameters and size of contract violation.
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