OPTIMAL ALLOCATION OF FACTS DEVICES FOR LOSS MINIMIZATION USING MOGA Basant Uikey
Electrical Engineering Department, Jabalpur Engineering College, Jabalpur
Abstract:- This work presents a new approach to find the optimal rating of FACTS controllers by using Genetic algorithm (GA) &multi objective genetic algorithm (MOGA).
Among various FACTs controllers, in this work Static Synchronous Series Compensator (SSSC) is considered. Objective of this work is to minimize the reactive power loss in the system by placing optimum rating of the SSSC. The proposed algorithm is an effective &
practical method in this direction. In this paper, to minimize real power loss and improve voltage profile new evolutionary optimization techniques have been applied namely Genetic algorithm (GA) technique to select the optimal parameters setting including rating of Static Synchronous Series Compensator Series (SSSC), MATLAB program is carried out on IEEE 30-bus system, for validation of proposed algorithm and for comparison purpose.
Keywords:- Voltage profile improvement, Genetic Algorithm, optimal siting and sizing, FACTS, distribution networks, MOGA (Multi-objective genetic algorithm)
1. INTRODUCTION
Reactive power compensation is provided to minimize power transmission losses, to maintain power transmission capability and to maintain the supply voltage. Series compensation is control of line impedance of a transmission line; with the change of impedance of a line either inductive or capacitive compensation can be obtained thus facilitating active power transfer or control. Series capacitive compensation was introduced decades ago to cancel a portion of the reactive line impedance and thereby increase the transmittable power.
Subsequently, within the FACTS initiative, it has been demonstrated that variable series compensation is highly effective in both controlling power flow in the lines and in improving stability [1-3].
The voltage sourced converter based series compensator, called Static Synchronous Series Compensator (SSSC) was proposed by Gyugyi in 1989 [4].
SSSC provides the virtual compensation of transmission line impedance by injecting the controllable voltage in series with the transmission line.
Several optimization techniques have been engaged to solve power system optimization problems in system planning, pricing and operation. Some of the known methods like linear programming, Newton OPF; quadratic programming may fail to find global optimum solution due to complexity of the problem. The conventional methods become more complex while dealing with multi objective and multi constraint systems.
Genetic Algorithm (GA) is simple and faster compared to conventional method; it offers a new and powerful approach to this optimization. In a power system a number of parameters such as line- flows, line overloading, real power losses, etc can be optimized. In this paper the line overloading minimization, real power loss minimization and optimal placement and sizing of SSSC are done using Genetic Algorithm (GA).
1.1 Genetic Algorithm
Genetic Algorithms are search mechanisms based on the Darwinian principle of natural evolution and were first described by John Holland (1975) [5], who presented them as an abstraction of biological evolution and gave a theoretical mathematical framework for adaptation.
Genetic Algorithms are search mechanisms based on natural selection and natural genetics. They operate on the law of coincidence, which takes advantage of pre-information in order to derive improvement from it.
Genetic Algorithms used for optimization are based on the principle of biological evolution. They are very different to many conventional methods in the sense that they simultaneously consider many possible solutions to the problem. The Genetic algorithm (GA) has been used to solve difficult engineering problems that are complex and difficult to solve by conventional optimization methods [6,7]. GA maintains and manipulates a population of solutions and implements a survival of the fittest
Vol. 05, Issue 10,October 2020 Available Online: www.ajeee.co.in/index.php/AJEEE strategy in their search for better
solutions.
The fittest individuals of any population tend to reproduce and survive to the next generation thus improving successive generations. Below fig shows the flow chart of GA
Figure 1. Typical flowchart of Genetic Algorithm
1.2 Multi Objective Genetic Algorithm (MOGA)
Multi-objective genetic algorithm [8-10] is an extension of classical GA. The main
difference between a conventional GA and a MOGA lies in the assignment of fitness to an individual. The rest of the algorithm is the same as that in a classical GA. In the Multi-objective GA, first, each solution is checked for its domination in the population. Two solutions x1 and x2 are compared on the basis of whether one dominates the other solution or not.
1.3 Optimal Placement and Sizing of SSSC for Minimization of Line Overloading and Real Power Loss
Line overloading and power loss is a major concern in the operation of power system. In this chapter, the task of overloading index and power loss reduction is performed by optimal placement of Static Synchronous Series Compensator (SSSC) using Multi- Objective Genetic Algorithm (MOGA), a series FACTS device that can be used for reducing power losses and for controlling the power flows in various lines.
However, due to the huge cost of the FACTS device, it is essential to find the optimal location and sizing of the device in a power system to obtain maximum benefits of the device. For implementation of Multi-Objective Genetic Algorithm (MOGA) approach for optimal placement and sizing of SSSC, first, overloading index for various single line outages are calculated using Newton- Raphson load flow method and equation (1), and the contingencies are ranked in the order of their severity. Then real power loss computed by the equation (2).
The severity of a contingency can be evaluated by an overloading index:- OLI= lϵ nl 2nW ( ∆SlSlmaxavg )2n (1) Where n =2, nl is the no. of overloaded lines.
1. S l max is the rated capacity of line, 2. S l avg is the average capacity of line, 3. ΔS lavg = S l avg – S l max
The second objective of this dissertation is to determine the optimal location and sizing of SSSC in the power system to minimize the real power loss. The real power loss describe as:-
PL = Nj=1gk[Vi2+ Vj2− 2ViVjcos(δi− δj)] (2) Subjected to the following equality constraints:−
Pgi− Pdi− VNj=1 i Vj Yij cos(δij− Ѳij)=0 (3) Qgi − Qdi− VNj=1 i Vj Yij sin(δij− Ѳij)=0 (4)
Pgimin ≤ Pg ≤ Pgimax ∀i∈ NG, Qmingi ≤ Qg ≤ Qmaxgi ∀i∈ NG, Vjmin ≤ Vj≤ Vjmax ∀i∈ NG, Qmingi ≤ Qg ≤ Qmaxgi ∀i∈ NG, XSSSCmin ≤ Xi ≤ XSSSCmax
Where PL is the power loss in the kth line, ntl is the number of lines in the system, N is the set of buses, NG is the set of generation buses, Yij Is the magnitude of ij element in admittance matrix, θij phase angle of ij element in admittance matrix, Pgi and Qgi are the active and reactive power generation at bus i, Pdi and Qdi are the active and reactive power load at bus i, Vi is the voltage magnitude at bus i, δij is the phase angle, XSSSC is the reactance of SSSC.
After computing OLI for various lines, the lines are ranked in decreasing order of overloading index. For placement of SSSC, the lines connected between two generation buses are ignored irrespective of their OLI values. Highest values of OLI are selected as possible locations for SSSC. For these possible locations of SSSC, Genetic algorithm has been applied for determining the optimal location and size of SSSC.
2. RESULT
Result of real power loss and over loading index with and without SSSC placement using GA and MOGA are shown below.
Figure 2. Results of Real power Loss with and without SSSC placement using Genetic Algorithm
Figure 3. Results of Overloading Index with and without SSSC placement using Genetic Algorithm
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Figure 4. Results of Overloading Index with and without SSSC placement using MOGA Algorithm
Figure 5. Results of Real Power loss with and without SSSC placement using MOGA Algorithm
3. CONCLUSION
In this paper, genetic algorithm (GA) and multi-objective genetic algorithm (MOGA) has been proposed for optimal placement and sizing of SSSC for over loading index and real power loss minimization under single line outage contingencies of a power system,. IEEE 30-bus system is used.
It has been observed that SSSC optimum location for one contingency may not be optimum for other contingencies and more than one SSSC are required to minimize over loading and power losses simultaneously under various contingencies. In future work, the same approach may be applied for large size power system. Other FACTS devices can also be considered for loss minimization and over loading index enhancement in a power system.
REFRENCES
1. N. G. Hingorani and L. Gyugyi, Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems, IEEE Press, New York, 2000.
2. R. M. Mathur and R. K. Varma, Thyristor- based FACTS Controllers for Electrical Transmission Systems, IEEE Press, Piscataway, 2002.
3. Y. H. Song, Flexible AC Transmission Systems (FACTS). The Institution of Electrical Engineers, London, 1999.
4. L. Gyugyi, “Solid-state control of electric power in ac transmission systems”, International Symposium on Electric Energy Conversion in Power Systems, Invited paper, No T-IP 4, Capn, Italy, 1989.
5. John Holland, “Adaptation in natural and artificial system”, Ann Arbor: University of Michigan press 1975.
6. D.E. Goldberg, Genetic Algorithms for Search, Optimization, and Machine Learning, Addison–Wesley, Reading, MA, 1989.
7. R. Narmatha Banu, D. Devaraj „Optimal Power Flow for Steady state security enhancement using Genetic Algorithm with FACTS devices‟, 2008 IEEE Region 10 Colloquium and the Third ICIIS, Kharagpur, INDIA December 8-10, 2008.
8. D.E. Goldberg, Genetic Algorithms for Search, Optimization, and Machine Learning, Addison–Wesley, Reading, MA, 1989.
9. K. Deb, „Multi-objective Optimization Using Evolutionary Algorithms‟. John Wiley &
Sons, Ltd., New York, pp. 209–213, 2005.
10. C.M. Fonseca, P.J. Fleming, An overview of evolutionary algorithms in multi-objective optimization, Evolutionary Computation, vol.3 (1), pp. 1–16, 1995.
11. Prashant Kumar Tiwari, Yog Raj Sood
„Optimal Location of FACTS Devices in Power System Using Genetic Algorithm‟, 2009 World Congress on Nature &
Biologically Inspired Computing (NaBIC 2009).
