Evolutionary Techniques of GAMS used in Optimization of economic load dispatch in Power system

Evolutionary Techniques of GAMS used in Optimization of economic load dispatch in Power system

Evolutionary Techniques of GAMS used in Optimization of economic load dispatch in Power system

Arun Kumar Uchchkotiya 1, Rameshwar Singh 2, A.S Trivedi 3

Student , Electrical , NITM , GWALIOR, INDIA 1 Asst.prof , Electrical , NITM , GWALIOR, INDIA 1 Proff , Electrical , NITM , GWALIOR, INDIA 1

Abstract

In the electric power supply systems, there exist a wide range of problems involving optimization processes. Among them, the power system scheduling is one of the most important problems in the operation and management ANY power system optimization problems including economic dispatch (ED) have noconvex characteristics with heavy equality and inequality constraints . The objective of ED is to determine an optimal combination of power output to meet the demand at minimum cost while satisfying the constraints. For simplicity, the cost function for each unit in the ED problems has been approximately represented by a single quadratic function and is solved using mathematical programming techniques .Economic load dispatch has the objective of generation allocation to the power generators such that the total fuel cost is minimized and all operating constraints are satisfied. Generally ELD is solved without accounting for transmission constraints, however, in deregulated power system environment Economic load dispatch (ELD) has the objective of generation allocation to the power generators such that the total fuel cost is minimized and all operating constraints are satisfied. Generally ELD is solved without accounting for transmission constraints, however, in deregulated power system environment. A number of traditional methods are used for solving ELD and other power system problems. During the last decade soft computing methods like particle swarm optimization (PSO),GA and lemda iteration method have been increasingly proposed for complex optimization problems. The paper reviews and compares the performance of the proposed PSO,GA and iteration method variants with traditional solver GAMS for economic dispatch on TWO standard test systems having different sizes and complexity levels. A large 38-unit power system is included for validating the results.

Keywords: Optimization of Economic load dispatch ,GAMS, Electric power generation; Thermal generator constraints;

1. Introduction

   Most of power system optimization problems including economic dispatch (ED) have complex and nonlinear characteristics with heavy equality and inequality constraints [1]. Economic dispatch is one of the most important problems to be solved in the operation and planning of a power system Power utilities try to achieve high operating efficiency to produce cheap electricity. GA [7] Competition exists in the electricity supply industry in generation and in the marketing of electricity. The operating cost of a power pool can be reduced if the areas with more economic units generate larger power than their load, and export the surplus power to other areas than their load, and export the surplus power to other areas with more expensive units. On the other hand, ELD is one of the most crucial issues of present energy management system. The objective of ELD in a power system is to discover the best possible combination of power output for all generating units which will minimize the total fuel cost as well as satisfying load and operational constraints. The ELD problem is extremely complex to work out because of its large dimension, a non-linear objective function, and various constraints. several analysis on the ELD have been carried out till now, suitable improvements in the unit outputs scheduling can contribute to significant cost savings [3]The benefits thus gained will depend on several factors like the characteristics of a pool, the policies adopted by utilities, types of interconnections, tie-line limits and load distribution in different areas. Therefore, transmission capacity constraints in production cost analysis are important issues in the operation and planning of electric power systems. Soft computing based approaches are also becoming very popular. Although these methods do not always guarantee global best solutions, they often achieve a fast and near global optimal solution. Recently covariance matrix adapted evolutionary strategy has been proposed problems. Large dimension problems are difficult to optimize using soft computing methods, as these techniques take a long

   time to converge; on the other hand, traditional methods like the GAMS solver computes the best result almost instantaneously. Many researchers have been done for the problem as reported in the literature [8] [9]. At the early time, the objective function of the ED problem was approximately represented by a single quadratic function so that mathematical programming techniques could be implemented to solve it This paper proposes some modified PSO GA local minima and enhance global search. [10]There has been phenomenal growth in mathematical programming techniques and development of computer codes to solve large scale optimization models over the past four to five decades. There has also been noteworthy development in relational database for improved data organization and transformation capabilities.. A number of efficient modelling languages have been developed which makes use of both the development in improved database management and mathematical programming techniques. One of the most popular and flexible languages among these is the General Algebraic Modelling System (GAMS) [2]. GAMS module was originally developed through a World Bank funded study in 1988.

2. The General Algebraic Modelling System (GAMS) solvers

The General Algebraic Modelling System (GAMS) is specifically designed for modelling linear, nonlinear and mixed integer optimization problems. [2] The system is particularly very advantageous with large, complex problems. GAMS allows the user to concentrate on the modelling problem by making the setup simple. GAMS is especially useful for handling large, complex, one-of-a-kind problems which may require many revisions to establish an accurate model.. The user can change the formulation quickly and easily, and can even change from one solver to another. Similarly the use can easily convert from linear to nonlinear optimization option with little trouble.[2] GAMS main window show in the fig 1 and fig 2 show .

Fig. 1 GAMS main window

the optimization solver ,in GAMS modelling system solve the different problems of linear, nonlinear and mixed integer optimization problems.

Fig 2. Optimization solver

Using the tools show in the table 1 and table 2,recently use of GAMS are using the different area show in the table 3 and worldwide use this tools show the fig.3 The basic structure of a mathematical model coded in GAMS has the

components: sets, data, variable, equation, model and output The tool kit in GAMS gives algorithms for each category of problem. GAMS also has the unique feature of providing a common language that can make use of a variety of solvers

Fig 3 Academic + Commercial Users Worldwide OF GAMS

Table 1: Structure of GAMS model [2]

Table 2 Methods of Solving Optimization Problems.[3,4]

Table 3 GAMS Are Using The Different Area[4]

3. Economic load dispatch Formulation

The objective of an ELD problem is to find the optimal combination of power generations that minimizes the total generation cost while satisfying an equality constraint and inequality constraints. The fuel cost curve for any unit is assumed to be approximated by segments of quadratic functions of the active power output of the generator. For a given power system network, the problem may be described as optimization (minimization) of total fuel cost as defined by (1) under a set of operating constraints

(1)

where is FT total fuel cost of generation in the system ($/hr), ai, bi, and ci are the cost coefficient of the i th generator, Pi is the power generated by the i th unit and n is the number of generators. The cost is minimized subjected to the following generator capacities and active power balance constraints.

(2)

where Pi, min and Pi, max are the minimum and maximum power output of the i th unit.

where PD is the total power demand and PLoss is total transmission loss. The transmission loss PLoss can be calculated by using

B matrix technique and is defined by (4)

where Bij s are the elements of loss coefficient matrix B

(3)

(4)

4 Results and Discussions

The performance of traditional optimization approach using the NLP minimization module of GAMS has been compared with DE,BBO, Iteration method and PSO, for two test cases having different sizes and complexity levels as described below. Simulations were carried out using MATLAB 7.0.1 on a Pentium IV processor, 2.8 GHz. with 1 GB RAM.

1. Description of the test cases

   The performance of traditional optimization approach using the NLP minimization module of GAMS has been compared GA, Iteration method and PSO and its variants for two test cases .

   1. Test case I: This system is taken from [ 5] . It has 4-generating units supplying a total load of 520 MW. Transmission losses are neglected while minimizing cost function given by eq. (1) subject to constraints given by (2) .The fuel-cost characteristics are given in Table 4.[5]

   2. Test case 2: This system is taken from [6] . It has 38-generating units supplying a total load of 8550 MW. Transmission losses are neglected while minimizing cost function.

      Test Case -1

      This system comprises of 4 generating units and the input data of 4-generator system are given in cost coefficients of generating unit Table 4.[5] Here, the total demand for the system is set to 530 MW. and different load demand 200 to 1200 MW The obtained results for the 4-generator system using the GAMS are given in Table 6 and the results are compared with those from pso classical ,pso accelerated and gradient method . in finding a global optimal solution presented In The Table [5].

      Table 4 cost coefficients of generating unit [5]

2. Comparison of Results for 4 unit system

   The minimum cost reported for the 4 unit system with pso classical and pso accelerated or gradient method are 12919.96$ or 12919.76 [5 ].The best cost $ 12919.75 has obtained by the GAMS and Result has compared with PSO ,gradient method show in table 5 .

   Table 5 Comparison of Results for 4 unit system

3. Effect of load variation for 4 unit system

   Load was changed from the test case (I ) 200 MW to 1200 MW) and it was found that the system did not convergence for 800 MW. It can be seen from Table 6. And show in the fig 4.with increase in load the optimal cost was found to increase.

   Table 6 : Results of optimal dispatch with changing

4. Effect of Generator Outage contingency

   In practical power system operation power generators often become faulty and are not available. In this paper each generator is considered out of service one by one for load demands of 200, 300, 400, 500, 6000, 700 , 800, 900 ,1000 and 1100 MW for test case I. Comparison of best results of one by one generator outage can be seen from Table 7 and graphical representation is shown Figure 5. Results of optimal dispatch with generator outage contingency for load demand 400 has been shown in Table 8.so that outage of Gen1 maximum cost of

   $10544.753 was computed. Least operational cost ( $10785.296) was found for outage of Gen.4.

   Fig 4: Generator for different load demands (Test case I)

   Table 7 : Comparison of best results of one by one generator out for different loads (test case I )

   Fig 5: Generator outage cases for different load demands (Test case I)

   Table 8 :Results of optimal dispatch with generator outage contingency (test case I: PD=400 MW)

   Test case 2

   The coefficient of fuel cost and maximum and minimum power limits are given in table 10 [6].The power demand is to be 8550 (MW).The results corresponding to DE/BBO,BBO,PSO,NEWPSO and GAMS are detailed in section table 9 .the comparison of results of all methods shown in table 9.

   Table 10: Fuel cost coefficient of Test case I Table 9 comparison of best result load (8550MW)

1. Conclusion

This paper presents an efficient and simple approach for solving the economic load dispatch (ELD) problem The performance of PSO variants was compared with traditional NLP solver GAMS for economic dispatch problem of four test cases. Soft computing techniques like the PSO use random operators for achieving the optimal result therefore in every fresh trial, these methods converge to different solutions near the global best solution. The traditional NLP algorithm like the GAMS uses mathematical operations to achieve the best solution so they are always consistent and converge to the unique global minimum solution. The time taken by soft computing techniques is quite large as compared to GAMS. The time requirement increases tremendously with problem complexity (like the inclusion of losses) and with increase in problem size. No such issue is there with GAMS.

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