Suboptimal AGC Strategy

1. Hybrid Stochastic Search Technique based Suboptimal AGC
Regulator Design for Power System using Constrained Feedback
Control Strategy
International Conference on ICMOC’ 2010
Organized by
EE Deptt., NIT (Durgapur) W.B.
Corresponding Author:
O. V. Singh
Department of Electrical Engineering
Maharishi Markandeshwar University, Mullana
Ambala, Haryana-133207,

2.  CONTENTS
 ABSTRACT
 INTRODUCTION
 SUBOPTIMAL PI REGULATOR DESIGN
 GENETIC ALGORITHM- SIMULATED ANNEALING (GASA)
BASED SUBOPTIMAL REGULATOR DESIGN
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES

3. ABSTRACT
 A new hybrid stochastic search technique is proposed to design of
suboptimal AGC regulator for a two area interconnected non reheat thermal
power system incorporating DC link in parallel with AC tie-line.
 In this technique, we are proposing the hybrid form of Genetic Algorithm
(GA) and simulated annealing (SA) based regulator.
 GASA has been successfully applied to constrained feedback control
problems where other PI based techniques have often failed. The main idea
in this scheme is to seek a feasible PI based suboptimal solution at each
sampling time. The feasible solution decreases the cost function rather than
minimizing the cost function.

4. INTRODUCTION
 Automatic generation control is one of the most important issues in
electric power system operation and control.
 The main objective of AGC in an interconnected power system is to
maintain frequency of each area and to keep tie-line power close to the
scheduled values by adjusting the real power outputs of the generators so
as to accommodate fluctuating load demands [1-4].
 From the work reported so far, it has been observed that the availability
of an accurate model of the system under study plays a crucial role in the
development of the most control strategies like optimal, suboptimal,
adaptive control etc [4].
 An interconnected power system contains different kinds of uncertainties
due to changes in system parameters and characteristics, loads variation,
therefore the operating points of a power system may change very much
randomly during a daily cycle.

5. Continue…
 All the reported methods are mostly time based on the state-space
approach and require information about the system states, which are not
usually known or available (Optimal Techniques).
 Suboptimal control technique does not require complete information
about the system. so, this technique is better than Optimal control
strategies.
Recent days; Genetic Algorithm, Particle Swarm Optimization, Fuzzy
Algorithm, Neural Network based methods and their hybrid forms [4] to
design Optimal AGC schemes.
 We are proposed a new Stochastic Search Technique, involving a
synergistic combination of Genetic Algorithm (GA) and Simulated
Annealing (SA) is used to get the suboptimal constrained feedback gains
of the PI regulator.

6. Continue…
 This approach used on the suboptimal constrained feedback of state
variables available as output variables and structures of ‘Q’ matrix for
AGC regulator.
 A two area non-reheat type power system model interconnected via
parallel EHVAC/HVDC links is considered for the study.
 The system dynamic performance has been obtained with the
implementation of designed AGC regulator considering 2% load
perturbation in either of the areas.
 The effect of the constrained and without constrained feedback control
strategy in the power systems is also presented.

7. FIGURE 1: Transfer Function Model of Interconnected Power
Systems Consisting of Non-Reheat Turbines
1 / R1
∆Pc1
Kg1
( 1+sTg1)
Kt1
( 1+sTt1)
∆Pg2
T12 / s
1 / R2
Kp2
(1+sTp2)
Kg2
( 1+sTg2)
Kt2
( 1+sTt2)
∆Ptie
+
+
a12
∆Pdc2
∆Xg2
_
_
_
+
_
∆Pc2
Kdc
1+sTdc
B1
1/s
B2
∫ACE1 dt
1/s
+
∆Xg1 ∆Pg1
∆Pdc1
Kp1
(1+sTp1)
∆Pd1
- -
-
∆Pd2
∆F2
-
+ _
∫ACE2 dt
+
∆F1
a12
+
+
a12
+
+
+
∆Pdc
AREA -1
AREA -2

8.
SUBOPTIMAL PI REGULATOR DESIGN
 A 2-area interconnected power system is described by a completely
controllable and observable linear time-invariant state space
representation as given by the following differential equations:
d/dt [x(t)] = A x(t) + B u(t) + Γ d(t) (1)
y(t) = C x(t) (2)
where, x(t) is a vector of system states, u(t) is a vector of control inputs,
and y(t) is a vector of measured outputs, and A, B, C and Γ are matrices
of compatible dimensions.
Output feedback control strategies [3] use only selected subsets of the
state variables for feedback purposes.
 When designing a suboptimal AGC regulator, constraints are imposed on
the structure of the feedback matrix so as to affect the feedback of the
desired state variables only.

9. Continue…
 output variables: u(t) = Ke Ye(t) (3)
Where Ke is an output feedback control matrix to be determined. This law
may also be expressed in terms of the state variables as:
u(t) = Ke CeXe(t) (4)
 The control laws defined by equations (3) or alternatively (4) are
equivalent if and only if the following constraint is satisfied:
Γe = Ke Ce (5)
Accordingly, the output feedback control problem may now be stated as
that of finding an output feedback control matrix Ke subject to constraints
(5). The method is based on the following theorem [2], which is
presented for the determination of such an output feedback control
matrix.

10. State Space Model of the power systems
 The state space representation of the systems under consideration may be
given by the following equation 1.
State Vector x(t)=[ΔPtieΔF1ΔPg1ΔXg1∫ACE1dtΔF2ΔPg2ΔXg2∫ACE2dtΔPdc]
Control Vector u(t) = [ΔPc1 ΔPc2]
Disturbance Vector P(d) = [ΔPd1 ΔPd2]
Output Vector Y(t) = [ΔPtie ΔF1 ∫ACE1 ΔF2 ∫ACE2]
 The Design of suboptimal AGC regulator based on constrained and without
constrained feedback control strategy using ‘Qc’ [3] and ‘Q’ is a 10x10
identity matrix. The System data are given in the APPENDIX.

11. System Coefficient Matrices
 The structure of state, control and disturbance matrices (A, B, and Г)
may be derived from the model.
 The control cost-weighting matrix ‘R’ is a 2x2 dimensional identity
matrix. The state cost weighting matrix Qc is designed based on the
concept of controllability and observability.

12. GENETIC ALGORITHM- SIMULATED ANNEALING
(GASA) BASED SUBOPTIMAL REGULATOR DESIGN
 The GASA heuristic incorporates Simulated Annealing (SA) in the
selection criteria of Genetic Algorithm (GA) [5-6].
 The solution string comprises of suboptimal using only feedback of
states which are available as output should be incorporated while dealing
with suboptimal control problems. Its gains are encoded as a string of
real numbers.
 The GASA heuristic employs Blend crossover and a mutation operator
suitable for real number representation to provide it a better search
capability.
 The objective is to minimize the Tie-line power flows augmented with
penalty terms corresponding to transient response specifications in the
regulator output and frequency.

13. Flow Chart: GASA Technique based Suboptimal AGC
Regulator using constrained feedback control strategy

14. RESULTS
FIGURE 3: Response of change in F1
FIGURE 4: Response of change in F2
FIGURE 5: Response of change in IACE

15. DISCUSSION
For the simulation study, MATLAB-7.8 software is used. The step load
perturbation is 2% at area-1 in the power system model study.
FIGURE 3 to 5 shows the dynamic response curves of change in
frequency of the area-1, area-2 and tie line power flows of the power
system with and without constrained respectively compared with the
proposed suboptimal control.
It is clear from the overshoots and settling times in GASA case is very
much less than those obtained by suboptimal PI regulator with
constrained PI(C) and without constrained PI. The results gives that the
settling time of PI suboptimal regulators is 50% longer than the proposed
regulator’s.

16. CONCLUSION
 It has been reported that the proposed control technique is effective and
provides significant improvement in the system performance. In
addition, the proposed suboptimal regulator is very simple and easy to
implement since it does not require complete information about system
states.
 Therefore, the proposed regulator fulfills the necessity of the two area
interconnected power system. The results obtained have been compared
with those obtained from PI based suboptimal AGC regulator cases. The
system states for PI suboptimal regulator also checked for constrained
and without constrained matrices of the system. Hence, the proposed
GASA suboptimal regulator is recommended to generate good quality
and secure electric power.

17. APPENDIX
 Nominal Parameters of Thermal System Investigated: f= 50, Pr1 = Pr2
= 2000, H1 = H2 = 5, Tt1= Tt2 = 0.3, Tg1 = Tg2 = 0.08 , Kp1 = Kp2 = 1,Kg1=
Kg2= 1, D1= D2= 8.33 10-3
, a12 = -1, R1= R2=2.4, Ptiemax = 200, B1 = B2 =
0.425, δ1 - δ2= 30 0
, 2πT12= 0.545, Kdc= 1, Tdc= 0.2
 Parameters used for GASA: Number of Parents=100, Number of
Children=10, Max. number of Iterations=200, Crossover
Probability=0.6, Mutation Probability=0.01

18. REFERENCES
1. M. Athans and P. Falb, Optimal Control: An introduction to the theory
and its application, McGraw-Hill, New York, 1966.
2. B. C. Moore, “Principle components analysis in linear system:
controllability, observability, and model reduction”, IEEE Trans.
Automatic Control, AC-26(1), pp. 17-31, 1981.
3. Naimul Hasan, “Suboptimal automatic generation control strategies in
interconnected power system with ac/dc links,” Ph.D. Thesis, Deptt. of
Electrical Engg., Jamia Millia University, New Delhi, India, 2008.
4. Ibraheem, P. Kumar and Kothari, “Recent philosophies of automatic
generation control strategies in power systems”, IEEE Trans. Power
System, vol. 11, no. 3, pp. 346-357, February 2005.
5. D.Bhagwan Das, C. Patvardhan,” Reactive Power Dispatch with a
hybrid stochastic search technique”, International Journal of Electrical
Power and Energy Systems, 24(2002) 731-736.
6. Omveer Singh, D. Bhagwan Das,” Design of Optimal State Feedback
Controller for AGC using a Hybrid Stochastic Search”, IEEE
Conference, POWERCON 2008, India.

19. THANK YOU!