Abstract
This paper, presents the particle swarm optimization-based fuzzy logic controller (PSO FLC) design for load frequency control in a two-area interconnected hydrothermal power system. Flexible alternating current transmission system devices and energy storage devices are being installed to improve the reliability and stability of the system under dynamic conditions. One such devices namely thyristor-controlled phase shifter (TCPS) is connected in series with the tie-line to damp out the power swings and frequency oscillations. Similarly at the terminal of one control area, a fast acting energy storage device of superconducting magnetic energy storage (SMES) is connected to meet the sudden changes in demand. The existing conventional controllers are unable to provide the satisfactory performance over a wide range of operating conditions due to system nonlinearity and plant parameter variations. To improve the dynamic performance of the system, this work proposes an intelligent tuning approach using a combination of particle swarm optimization (PSO) and fuzzy logic technique. In this work, PSO algorithm is employed for the optimal selection of membership function parameters of the proposed fuzzy PI, TCPS and SMES controllers by minimizing the time domain objective function. The simulation study is performed by the proposed PSO FLC in a two-area interconnected power system. To show the effective performance of the proposed controller, a comparative study has been made with the conventional, genetic algorithm and fuzzy logic-based optimized controller under varying load conditions.
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- \(T_{p1}\), \(T_{p2 }\) :
-
Generator time constants
- \(K_1, K_2\) :
-
Generator gains
- \(T_{gi}\) :
-
Thermal unit governor time constant
- \(T_{ri, }\)T\(_{ti }\) :
-
Thermal unit reheat time constant
- \(K_{ri }\) :
-
Reheater gain
- \(T_{w }\) :
-
Hydro unit water time constant
- \(T_{Ri}\), \(T_{Hi }\) :
-
Hydro turbine time constants
- \(T_{hi }\) :
-
Hydro unit governor time constant
- \(R_{i}\) :
-
Governor speed regulation of the units of two areas (\(i = 1, 2\))
- \(P_{r1}\), \(P_{r2 }\) :
-
Rated area capacities (\(a12 = P_{r1}/P_{r2})\)
- \(T_{12 }\) :
-
Synchronizing coefficient
- \(B_{i}\) :
-
Frequency bias coefficient (\(i =1, 2\))
- \(T_{s }\) :
-
Settling time
- \(T_{p }\) :
-
Peak time
- \(K_\mathrm{TCPS }\) :
-
Gain constant of TCPS
- \(T_\mathrm{TCPS }\) :
-
Time constant of TCPS
- \(K_\mathrm{SMES }\) :
-
Gain constant of SMES
- \(T_\mathrm{SMES }\) :
-
Time constant of SMES
- \(T_{1}\), \(T_{2}\), \(T_{3}\), \(T_{4 }\) :
-
Time constants of phase compensation block
- \(K_\mathrm{p}\), \(K_\mathrm{i}\) :
-
Proportional and integral gain of PI controller
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Appendix
Appendix
Power system data
\(B_{1} = B_{2} = 0.545\) Hz/pu MW; \(T_{12} = 0.545\) pu;
\(R_{1} = R_{2} = 2.4\) Hz/pu MW; \(P_{r1} = P_{r2} = 1500\) MW;
Nominal load = 1250 MW (each area)
Generator data
\(T_{p1 }= T_{p2 }= 20 \mathrm{s}; K1=K2=120\) Hz/pu MW.
Thermal unit data
\(T_{g1 }= T_{g2 =} 0.08\,\mathrm{s}; T_{r1 }= T_{r2 }= 10.2 \)s;
\(T_{t1 }= T_{t2 }= 0.3\,\mathrm{s}; K_{r1 }=K_{r2 }= 3\) Hz/pu MW.
Hydro unit data
\(T_{R1 }= T_{R2 }= 4.9 \mathrm{s}; T_{h1 }= T_{h2 }= 0.2\) s
\(T_{H1 }= T_{H2 }= 28.75\,\mathrm{s}; T_{w }= 1\) s
TCPS data
Rating = 2 MVA; \(\Phi _\mathrm{min} = -10^{\circ }; \Phi _\mathrm{max} = 10^{\circ }\);
\(K_\mathrm{TCPSmin} = -2; K_\mathrm{TCPSmax} = 2; T_{TCPS} = 1.5\) s;
SMES data
Rating = 1.25 MVA; \(K_\mathrm{SMESmin} = 0.2\);
\(K_\mathrm{SMESmax} = 4; T_\mathrm{SMES }= 0.01\) s;
\(T_{1 }= 0.3\,\mathrm{s}; T_{2 }= 0.02\,\mathrm{s}; T_{3} = 0.8\,\mathrm{s}; T_{4} = 0.4\) s.
PI controller data
\(K_\mathrm{pmin} = -10; K_\mathrm{pmax} = 10; K_\mathrm{imin} = -2; K_\mathrm{imax} = 2\).
PSO parameters
No of particles = 50; \(c_{1} = c_{2} = 2; W_\mathrm{max} = 0.9\);
\(W_\mathrm{min }= 0.2; \mathrm{Iter}_\mathrm{max }= 50; V_\mathrm{max} = 0.2; V_\mathrm{min }= -0.2\)
GA parameters
No of generation = 100; population size = 50;
Cross over probability = 0.6;
Mutation probability = 0.03.
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Jeyalakshmi, V., Subburaj, P. PSO-scaled fuzzy logic to load frequency control in hydrothermal power system. Soft Comput 20, 2577–2594 (2016). https://doi.org/10.1007/s00500-015-1659-8
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DOI: https://doi.org/10.1007/s00500-015-1659-8