Design of Full Order Optimal Controller for Interconnected Deregulated Power System for AGC

ISSN (e): 2250 – 3005 || Volume, 05 || Issue, 06 || June – 2015 ||
International Journal of Computational Engineering Research (IJCER)
www.ijceronline.com Open Access Journal Page 28
Design of Full Order Optimal Controller for Interconnected
Deregulated Power System for AGC
Mrs. Upma Gupta1,
Mrs. S.N.Chaphekar2
1
M.E. Scholar, PES's Modern College of Engineering, Pune India
2
Assistant Professor, PES's Modern College of Engineering, Pune India
I. Introduction
In the electric power system load demand of the consumer always keeps on changing, hence the system
frequency varies to its nominal value and the tie line power of the interconnected power system changes to its
scheduled value. AGC is responsible to control the frequency to its nominal value and maintain the tie line
power to its scheduled value, at the time of load perturbation in the system. In the conventional power system
the generation, transmission and distribution are owned by a single entity called a Vertically Integrated Utility
(VIU). In the deregulated environment Vertically Integrated Utilities no longer exist. However, the common
operational objective of restoring the frequency at its nominal value and tie line power to its schedule value
remain the same. In the deregulated power system the utilities no longer own generation, transmission and
distribution. In this scenario there are three different entities generation companies (GENCOs), transmission
companies (TRASCOs), distribution companies (DISCOs). As there are several GENCOs and DISCOs in the
deregulated environment, a DISCO has the freedom to have a contract with any GENCO for transaction of
power. A DISCO has freedom to contract with any of the GENCOs in their own area or another area. Such
transactions are called "bilateral transactions” and these contracts are made under the supervision of an impartial
entity called Independent System Operator (ISO). ISO is also responsible for managing the ancillary services
like AGC etc. The objective of this paper is to modify the traditional two area AGC system to take into account
the effect of Bilateral Contracts. The concept of DISCO participation matrix is used that helps in the
visualization and implementation of Bilateral Contracts. Simulation of the bilateral contracts is done and
reflected in the two-area block diagram. The full order optimal controller is used for accomplish the job of
AGC i.e to achieve zero frequency deviation at steady state, and to distribute generation among areas so the
interconnected tie line power flow match the prescribed schedule and to balance the total generation against the
total load.
II. Formulation of Model of AGC for deregulated power system
Consider a two-area system in which each area has two GENCOs (non reheat thermal turbine) and two DISCOs
in it. Let GENCO1 GENCO2, DISCO1 and DISCO2 be in area 1 and DISCO3, and DISCO4 be in area 2 as
shown in Fig. 1.
Abstract
This paper presents the design and simulation of full order optimal controller for deregulated power
system for Automatic Generation Control (AGC). Traditional AGC of two-area system is modified to
take in to the effect of bilateral contracts on the system dynamics. The DISCO participation matrix
defines the bilateral contract in a deregulated environment. This paper reviews the main structures,
configurations, modeling and characteristics of AGC in a deregulated environment and addresses the
control area concept in restructured power Systems. To validate the effectiveness of full order
optimal controller, a simulation has been performed using MATLAB and results are presented here.
The results for LFC and AGC for a deregulated interconnected power systems shows that the
optimal full order controllers perform better than classical integral order controllers .
Keywords: Automatic Generation Control, Area Control Error, ACE Participation Factor,
Bilateral Contracts, Contract Participation Factor, Deregulation, DISCO Participation Matrix, Full
Order Optimal Controller, Load Frequency Control.

Design of Full Order Optimal Controller…
For LFC or AGC conventional model is used which is just the extension of the traditional Elgerd model [3]. In
this AGC model, the concept of disco participation matrix (DPM) is included to incorporate the bilateral load
contracts. DPM is a matrix with the number of rows equal to the number of GENCOs and number of columns
equal to the number of DISCOs in the system. The DPM shows the participation of a DISCO in a contract with
GENCO. For the system described in Fig 1, the DPM is given as
Where Cpf refers to "contract participation factor." ,
Thus ijth entry corresponds to the fraction of the total load power contracted by DISCO j from GENCO i. The
sum of all the entries of particular column of DPM is unity.
Whenever the load demanded by a DISCO changes, it is reflected as a local load in the area to which this
DISCO belongs. As there are many GENCOs in each area, ACE signal has to be distributed among them in
proportion to their participation in the AGC. "ACE (Area Control Error) participation factor (apf)" are the
coefficient factors which distributes the ACE among GENCOs. If there are m no of GENCOs then
.
In deregulated scenario a DISCO demands a particular GENCO or GENCOs for load power. These demands
must be reflected in the dynamics of the system. Turbine and governor units must respond to this power
demand. Thus, as a particular set of GENCOs are supposed to follow the load demanded by a DISCO,
information signals must flow from a DISCO to a particular GENCO specifying corresponding demands. Here,
we introduce the information signals which were absent in the conventional scenario. The demands are
specified by (elements of DPM) and the pu MW load of a DISCO. These signals carry information as to which
GENCO has to follow a load demanded by which DISCO.
The block diagram for two area AGC in a deregulated power system is shown in Fig 2. In this model the
schedule value of steady state tie line power is given as
ΔPtie1-2,scheduled =(demand of DISCOs in area 2 from GENCOs in area1)-(demand of DISCOs in area 1 from
GENCOs in area2)
At any given time, the tie line power error, ΔPtie1-2,error is defined as-
ΔPtie1-2,error = ∆Ptie1-2,actual - ΔPtie1-2,scheduled
This error signal is used to generate the respective ACE signals as in the traditional scenario
errortie
PfBACE ,21111 

errortie
PfBACE ,12222 

Where
errortie
r
r
errortie
P
P
P
P ,21
2
1
,12 

Pr1 and Pr2 are the rated powers of area 1 and area 2, respectively. Therefore
errortie
PafBACE ,2112222 

Where
In the block diagram shown in figure 2, ∆PL1,LOC and ∆PL2,LOC represents the local loads in area 1 and area 2
respectively.
∆PL1, ∆PL2 , ∆PL3 and ∆PL4 represents the contracted load of DISCO1, DISCO2, DISCO3 and DISCO4
respectively.

III. Design of full order optimal Controller
The theory of optimal control is concerned with operating a dynamic system at minimum cost. The
case where the system dynamics are described by a set of linear differential equations and the cost is described
by a quadratic functional is called the LQ problem. The optimal control problem for a linear multivariable
system with the quadratic criterion function is one of the most common problems in linear system theory. it is
defined below:
................(1)
Given the completely controllable plant, where x is the n1 state vector, u is the p1 input vector. A is the n
n order of real constant matrix and B is the np real constant matrix. Desired steady -state is the null state
x=0
The control law
...................(2)
Where K is pn real constant unconstrained gain matrix, that minimizes the quadratic performance index .
The design of a state feedback optimal controller is to determine the feedback matrix ‘K’ in such a way that a
certain Performance Index (PI) is minimized while transferring the system from an initial arbitrary state
x(0) 0 to origin in infinite time i.e., x( ) = 0 .Generally the PI is chosen in quadratic form as:
........................(3)
where, ‘Q’ is a real, symmetric and positive semi-definite matrix called as ‘state weighting matrix’ and ‘R’ is a
real, symmetric and positive definite matrix called as ‘control weighting matrix’.
The matrices A, B, Q & R are known. The optimal control is given by u = − Kx,‘K’ is the feedback gain matrix
given by;
.......................(4)
where, ‘S’ is a real, symmetric and positive definite matrix which is the unique solution of matrix Riccati
Equation:
.....................(5)
The closed loop system equation is;
..................(6)
The matrix is the closed loop system matrix. The stability of closed loop system can be tested
by finding eigen values of .
IV. State Space Modeling AGC System in Deregulated Environment
The two area AGC system considered has two individual area connected with a tie line. The deviation in each
area frequency is determined by considering the dynamics of governor, turbines, generators and load
represented in that area. The state space model of representation of AGC model is given by
........................(7)
This model of AGC is shown in Fig.2 .Where x is state vector, u is control vector p is disturbance vector and q
is the bilateral contract vector. A, B, Ґ and β are the constant matrix associated with state control, disturbance
and bilateral contract vector respectively.
In our system we can identify total 13 states. All these vectors and matrix are given by -
The State Vector ‘x’ (13×1),  
T
xxxxxxxxxxxxxx 13121110987654321
 where
 
T
tieMMMMGVGVGVGV
PdtACEdtACEPPPPPPPPffx 21214321432121 
  ;
.............(8)
Control Vector ‘u’ (2×1)  
T
uuu 21
 ; ..........................(9)
Disturbance vector 'p' (2×1)
 
T
dd
PPp 21

;............................(10)
Bilateral Contract Vector 'q' (4×1)
 
T
LLLL
PPPPq 4321

.......................(11)

Fig.2: Two area AGC model in deregulated power system
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
0000000000022
00000000000
100000000000
000
1
0000000
1
0
0000
1
000000
1
0
00000
1
000000
1
000000
1
00000
1
000
1
000
1
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0000
1
000
1
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1
000
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1
000
1
00
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1
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1
1212
122
1
444
333
222
111
14
33
22
11
2
212
2
2
2
2
2
1
1
1
1
1
1
1
TT
aB
B
TTR
TTR
TTR
TTR
TT
TT
TT
TT
T
ka
T
k
T
k
T
T
k
T
k
T
k
T
A
gg
gg
gg
gg
TT
TT
TT
TT
P
P
P
P
P
P
P
P
P
P
P
P
P
P

..........(12)

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
00
00
00
0
0
0
0
00
00
00
00
00
00
4
4
3
3
2
2
1
1
Tg
apf
Tg
apf
Tg
apf
Tg
apf
B
, .................(13)
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
00
00
00
00
00
00
00
00
00
00
00
0
0
2
2
1
1
p
p
p
p
T
k
T
k
.....................(14)

,
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



0000
)()()()(
)()()()(
0000
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00
241412231312423212413112
2414231342324131
4
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4
42
4
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3
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3
33
3
32
3
31
2
24
2
23
2
22
2
21
1
14
1
13
1
12
1
11
2
2
2
2
1
1
1
1
cpfcpfacpfcpfacpfcpfacpfcpfa
cpfcpfcpfcpfcpfcpfcpfcpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
cpf
T
k
T
k
T
k
T
k
gggg
gggg
gggg
gggg
P
P
P
P
P
P
P
P

..........(15)
V. Design of full Optimal controller for AGC in Deregulated Environment
The design of a state feedback optimal controller is to determine the feedback matrix ‘K’ in such a way that a
certain Performance Index (PI) is minimized while transferring the system from an initial arbitrary state
x(0) 0 to origin in infinite time i.e., x( ) = 0.
Generally the PI is chosen in quadratic form as given by equation (3)
where, ‘Q’ is a real, symmetric and positive semi-definite matrix called as ‘state weighting matrix’ and ‘R’ is a
real, symmetric and positive definite matrix called as ‘control weighting matrix’. The matrices Q and R are
determined on the basis of following system requirements.
1) The excursions (deviations) of ACEs about steady values are minimized. In this model, these excursions are;
and .......................(16)
........................(17)
2) The excursions of about steady values are minimized. In this model, these excursions are x11 & x12
.
3) The excursions of control inputs u1 and u2 about steady values are minimized.
Under these considerations, the PI takes a form;
.....(18)

Fig. 3 Simulation model of two area AGC in deregulated system with Optimal Controller
This gives the matrices Q (13×13) and R (2×2) as:
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

2
122121
212
2
2
1
2
1
10000000000
0100000000000
0010000000000
0000000000000
0000000000000
0000000000000
0000000000000
0000000000000
0000000000000
0000000000000
0000000000000
00000000000
00000000000
aBaB
BaB
BB
Q
...................(19)
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
10
01
R
..................(20)
The matrices A, B, Q & R are known. The optimal controller gain matrix can be obtained by using equations (4)
to (6).
VI. Simulation Result
A. Case 1:
Consider a case where all the DISCOs contract with the GENCOs for power as per the following DPM:
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
25.25.04.
1.4.01.
3.25.5.2.
35.1.5.3.
DPM

It is assumed that each DISCO demand s 0.1 pu MW power from GENCO as defined by cpfs in DPM matrix
and each GENCO participates in AGC as defined by following apfs: apf1 = 0.75, apf2 = 0.25, apf3 = 0.5 and
apf4 = 0.5.
The system in figure 3 simulated using the above data and the system parameters given in Appendix -I . The
result of the simulation has shown in Figure 4.
The off diagonal elements of DPM corresponds to the contract of a DISCO in one area with a GENCO in
another area.
The schedule power on the tie line in the direction from area1 to area2 is -
= [0.1(0.1+0.25)+0.1(0.3+0.35)] -[0.1(0.1+0.4)+0.1(0+0)]
= 0.05 pu MW
The desired generation of a GENCO in pu MW can be expressed in terms of Contract Participation Factor
(cpfs) and the total demand of DISCOs as
Where is the total demand of DISCO j and are given by DPM.
At steady state power generated by GENCOs -
= 0.3(0.1) + 0.5(0.1)+ 0.1(0.1)+ 0.35(0.1) = 0.125 pu MW
= 0 .125 pu MW; = 0.06 pu MW; = 0.09 pu MW
Fig. 4a: Frequency Deviations (Hz) for area 1 & area 2, case1
Fig. 4a shows the dynamic responses of frequency deviations in two areas (i.e., ∆f1 and ∆f2).The frequency
deviation in each area goes to zero in the steady state.
The schedule power on the tie line in the direction from area1 to area2 is .05 pu MW. Fig. 4b shows the actual
Tie line power flow between two area at steady state is also .05 pu MW. So the deviation in tie line power at
steady state become zero .
Fig. 4c & 4d show the power generated by GENCO1, GENCO2, GENCO3 & GENCO4 in steady state. The
results are matching from our calculations.
0 5 10 15
-0.4
-0.2
0
0.2
0.4
time (sec)
FreqdeviationArea1(Hz)
0 5 10 15
-0.4
-0.3
-0.2
-0.1
0
0.1
time (sec)
FreqDeviationinArea2(Hz))
I
Optimal
I
Optimal

Fig.4b: Actual Tie line power ( pu MW), case 1
Fig.4c: Generated Power by GENCO1 & GENCO2 (pu MW) case 1
0 5 10 15
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
time (sec)
ActualTielinePower(puMW)
0 5 10 15
0
0.05
0.1
0.15
0.2
time (sec)
GENCO1Power(puMW))
0 5 10 15
0
0.05
0.1
0.15
0.2
time (sec)
GENCO2Power(puMW))

Fig.4d: Generated Power by GENCO3 & GENCO4 (pu MW), case 1
B. Case 2: Contract Violation
It may be happen that a DISCO violate a contract by demanding more power than that specified in the contract.
This excess power is not contracted out to any GENCO. This uncontracted power must be supplied by the
Gencos in the same area as the DISCO. It must be reflected as a local load of the area but not as the contracted
demand.Now consider DPM as below
Now in this case all the Discos contract with the Gencos for power as per the following DPM-
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
0025.3.
7.125.0
0025.2.
3.025.5.
DPM
It is assumed that each DISCO demand s 0.1 pu MW power from GENCO as defined by cpfs in DPM matrix
and DISCO1 demand 0.1 pu MW of excess power. ACE participation factors are apf1=0.75, apf2=1-apf1=
0.25, apf3= 0.5, apf4=1-apf3=0.5.
The total local load in area I = Load of DISCO1 + Load of DISCO2
= (0.1 + 0.1) + 0.1= 0.3 pu MW
Similarly, the total local load in area II = Load of DISCO3 + Load of DISCO4
= (0.1 + 0.1) = 0.3 pu MW (no un contracted load)
Schedule tie line power flow is 0.05 from area 2 to area 1.
The system in figure 3 simulated again ,using the above data and the system parameters given in Appendix -I .
The result of the simulation has shown in figure 5.
Fig. 5a: shows the dynamic responses of frequency deviations in two areas (i.e., ∆f1 and ∆f2).The frequency
deviation in each area goes to zero in the steady state.
Fig. 5b: shows the tie line power deviation between two area. The actual tie line power .05 pu MW which flows
from area 2 to area 1.Scheded tie tie line power is also .05, in the steady state deviation goes to zero.
Fig 5c & 5d show the power generated by GENCO1, GENCO2,GENCO3 & GENCO4 in the steady state. The
generation of GENCO3 & GENCO4 are not affected by the excess load of DISCO1. The un contracted load of
0 5 10 15
0
0.05
0.1
0.15
0.2
time (sec)
GENCO3Power(puMW))
0 5 10 15
0
0.05
0.1
0.15
0.2
time (sec)
GENCO4Power(puMW))

DISCO1 is reflected in generation of GENCO1 & GENCO2. The ACE participation factor decide the
distribution of un contracted load in the steady state. Thus this excess load is taken up by the GENCOs in the
same area as that of the DISCO making the un contracted demand.
Fig. 5a: Frequency Deviations (Hz) for area 1 & area 2, case2
Fig.5b: Actual Tie line power ( pu MW), case 2
0 5 10 15
-0.6
-0.4
-0.2
0
0.2
0.4
Time (sec)
FreqdeviationArea1(Hz)
0 5 10 15
-0.4
-0.2
0
0.2
0.4
Time (sec)
FreqDeviationinArea2(Hz))
I
Optimal
I
Optimal
0 5 10 15
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
Time (sec)
ActualTielinePower(puMW)

Fig.5c: Generated Power by GENCO1 & GENCO2 (pu MW), case 2
Fig.5d: Generated Power by GENCO3 & GENCO4 (pu MW), case 2
The value of 'k' optimal controller gain matrix, find out with the help of MATLAB program is given below.


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




147.10108.108.023.023.571.571.128.128.312.080.
147.01023.023.108.108.128.128.571.571.080.312.
k
0 5 10 15
0
0.05
0.1
0.15
0.2
0.25
Time (sec)
GENCO1Power(puMW)
0 5 10 15
0
0.05
0.1
0.15
0.2
Time (sec)
GENCO2Power(puMW)
0 5 10 15
0
0.05
0.1
0.15
0.2
0.25
Time (sec)
GENCO3Power(puMW)
0 5 10 15
0
0.05
0.1
0.15
0.2
Time (sec)
GENCO4Power(puMW)

Hence the control inputs:
u1= -.312 x1 +.08 x2 -.571 x3 -.571 x4 + .128 x5 +.128 x6 -.108 x7 -.108 x8 + .023 x9 +.023 x10+ x11 - .147 x13
u1= .080 x1 -.312 x2 +.128 x3 +.128 x4 -.571 x5 -.571x6 -.023 x7 +.023 x8 -.108 x9 -.108 x1+ x12 + .147 x13
The eigen values of 'A' open loop system are
[0, 0, -0.444 + 3.63i, -0.444-3.63i, -0.823 + 3.02i, -0.823 - 3.02i, -0.778, -13.4, -13.4, -2.50, -2.50, -
12.5, -12.5 ]
Two eigen values are zero and remaining have negative real parts indicating that, the system is marginally stable
before applying the optimal control strategy.
The eigen values of 'Ac' closed loop system are
[-13.3996 -13.3804 -0.8468 + 3.7432i -0.8468 - 3.7432i -1.1232 + 3.1450 -1.1232 - 3.1450i -
0.8032 + 0.2435i
-0.8032 - 0.2435i -0.4590 -12.5000 -12.5000 -2.5000 -2.5000 ]
All eigen values of ‘Ac’ have negative real parts indicating that the system is asymptotically stable after
applying optimal control strategy.
APPENDIX I
Pr1 = Pr2 2000 MW
R1 = R2= R3 = R4 2.4 Hz /pu MW
K1= K2 .6558
Kp1 = Kp2 120
Tp1 = Tp2 24
B1 = B2 .429
T12 .0707 MW / radian
TT1 =TT2 =TT3 =TT4 .4
Tg1 = Tg2 = Tg3 = Tg4 .08
Ptie max 200 MW
VII. CONCLUSION
This work gives an overview of AGC in deregulated environment which acquires a fundamental role to
enable power exchanges and to provide better conditions for the electricity trading. The important role of AGC
will continue in restructured electricity markets, but with modifications. Bilateral contracts can exist between
DISCOs in one control area and GENCOs in other control areas. The use of a “DISCO Participation Matrix”
facilitates the simulation of bilateral contracts. Models of interconnected power systems in deregulated
environment have been developed for integral as well as optimal control strategies. The state equations and
control equations have been successfully obtained and full State feedback optimal controller has designed .The
models have also been tested for system stability before and after applying closed loop feedback control and it
has been observed performance is much better in case of full state feedback optimal controller as compare to
integral controller.
References
[1] J. Kumar, K. Ng, and G. Sheble, “AGC simulator for price-based operation: Part I,” IEEE Trans. Power Systems, vol.12,no. 2,
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May 1997.
[3] O. I. Elgerd and C. Fosha, “Optimum megawatt-frequency control of multiarea electric energy systems,” IEEE Trans. Power
Apparatus & Systems, vol. PAS-89, no. 4, pp. 556–563, Apr. 1970.
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[5] R. Christie and A. Bose, “Load-frequency control issues in power systems operations after deregulation,” IEEE Trans. Power
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Meeting, Seattle, WA, July 15–21, 2000.
[7] V. Donde, M. A. Pai, I. A. Hiskens ,“ Simulation of Bilateral Contracts in an AGC System After Restructuring” IEEE Trans.
Power Systems, vol. 16, no. 3, August 2001.
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Publishers, 1998.
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[10] P. Kundur," Power System Stability and Control," McGraw-Hill, 1994
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[12] Hadi Saadat, "Power System Analysis "TATA McGraw Hill 1991

Design of Full Order Optimal Controller for Interconnected Deregulated Power System for AGC

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