Application of Genetic Algorithm to Economic Load Dispatch

Abstract: The authors propose a genetic algorithm based approach to economic load dispatch (ELD) problem. The genetic algorithm (GA) is a searching or optimising algorithm based on natural evolution principles. Because of its capability to solve non-linear optimisation problems, the application of GAs to power systems is a promising area to explore. In the proposed paper, a brief introduction to GAs is given. The ELD approach is tested on a sample 4 generator system. Test results are given and compared with results obtained using conventional LaGrange multipliers method.

Keywords: genetic algorithm, economic load dispatch, power system control

Introduction

Intelligent systems are expected as a new methodology for solving difficult problems in power systems. Various 'intelligent' technologies are researched and applied to power system area. Expert systems, artificial neural networks, fuzzy logic, and evolutionary algorithms are examples of these technologies.

Evolutionary algorithms (EA) are computer-based problem solving systems which use computational models of some of the known mechanisms evolution as key elements in their design and implementation. A variety of evolutionary algorithms have been proposed in literature. The major ones are:

• genetic algorithms (GA),
• evolutionary programming,
• evolution strategies,
• classifier systems, and
• genetic programming.

EAs maintain a population of structures, that evolve according to rules of selection and other operators, that are referred to as search operators, (or genetic operators), such as recombination and mutation. Each individual in the population receives a measure of it's fitness in the environment. Exploiting the available fitness information, reproduction focuses on high fitness individuals. Recombination and mutation perturb those individuals, providing general heuristics for exploration.

Fig.1. Genetic Algorithm

The recombination operation is often referred to as crossover because of the way that biologists have observed strands of chromosomes crossing over during the exchange. In nature, an important source of diversity is mutation. In an EA, a large amount of diversity is usually introduced at the start of the algorithm, by randomising the genes in the population. Although EAs use stochastic processes, the results are distinctly non-random (better than random).[2]

A GA is a search algorithm based on the mechanics of natural selection and natural genetics. GA also is one of the effective methods for optimisation problems and it requires a formalization of problems and a fitness function definition.

A principal scheme of genetic algorithm is shown on Fig.1.

Genetic algorithm can be briefly described by the following cycle: Evaluate the fitness of all of the individuals in the population. Create a new population by performing operations such as crossover, fitness-proportionate reproduction and mutation on the individuals whose fitness has just been measured. Discard the old population and iterate using the new population.[2]

GAs are used for a number of different application areas. An example of this would be multidimensional optimisation problems in which the character string of the chromosome can be used to encode the values for the different parameters being optimised. In power systems, the GAs has been used to:

• contingency analysis and security assessment of power systems,
• economic load dispatch,
• loss reduction using power system reconfiguration,
• power system expansion planning, distribution network planning,
• power system restoration planning.

The genetic model of computation can be implemented by having arrays of bits or characters to represent the chromosomes. Simple bit manipulation operations allow the implementation of crossover, mutation and other operations. Examples of the crossover is shown on Fig.2.

Fig.2. Examples of the Crossover

One iteration is referred to as a generation. The first generation (generation 0) is a population of randomly generated individuals.

Premature convergence is one of the major difficulties with GA and in fact with most search algorithms. It has been observed that this problem is closely tied to the problem of losing diversity in the population. One source of it is occasional appearance of ‘super-individual(s)’ which in few generations takes over the population. To avoid premature convergence, GA parameters should be chosen carefully.

Application of Genetic Algorithm to Economic Load Dispatch

Economic Load Dispatch is one of the optimisation problems in power system operation. Since an optimisation is required under severe constraints, all constraints cannot be taken into account. ELD determines the optimal generation for each generator in order to minimise the total fuel costs subjects to equality constraints on power balance and inequality constraints on power outputs of generators. In some cases, transfer loses, generation rate changes and line flows can be also considered. The majority of planning tasks present mixed-integer optimisation problems dealing with the minimisation of transfer loses, efficient power generation and low-cost system operation. The complexity of these problems dramatically increases with the number of units due to their combinatorial nature.

A genetic-based algorithm was used [3] to solve a power system ELD problem. The algorithm utilised payoff information of perspective solutions to evaluate optimality. Thus, the constraints of classical LaGrangian techniques on unit curves were eliminated. Using an ELD problem as a basis for comparison, several different techniques were explored. Two unique GAs were also compared. The results were verified for a sample problem using a classical technique.

The authors [4] presented some modifications of GAs for improving performance of ELD in power system. They have been trying to find the best operating point for GAs to work with. Two levels of problems have been dealt with for performance improvement: the first is choosing a suitable genetic strategy; the second is tuning various parameter values for selected genetic strategies. Both levels have been tested on a six generators unit. The test results were compared regarding on-line and off-line system performances.

In this paper we present the GA approach to ELD problem. ELD studies are important to arrive at power system planning, control, and operation. The objective was to develop an ELD system computing various ELD solutions in real-time mode. This ELD system could be implemented in an on-line power system control approach. 4-generator test power system, shown in Fig.3 has been used to test the effectiveness of proposed method.

Fig.3. Sample Power System.

The power system was described using following equations and constraints:

where:
N_i - cost for the i-th generator (in Sk/MW),
P_i - i-th generator's power output (in MW),
P_iMIN - minimum power output of the i-th generator,
P_iMAX - maximum power output of the i-th generator.

After experiments, the following GA parameters were chosen:

Chromosome length (number of bits):	30
Population (number of chromosomes):	150
Maximum number of generations:	20
Crossover probability:	1
Mutation probability:	0.003
Convergence criterion:	0.0001

The fitness function was defined as:

The results obtained using the GA approach were compared with an optimum computed using standard Lagrange Multipliers method.

Test Results

Test results are shown in Fig.4. The test results show that the proposed approach is suitable for fast on-line economic load dispatch. As the GA starts from random starting point, GAs with 9 different starting points have been tested.

A comparison between GA-based and traditional (La Grange Multipliers Method - LMM, see the first row in the table below) method has been carried out. As shown in the table, the difference d between total costs computed using traditional (LMM) method and GA are small. However, the power outputs of generators differ significantly (3 MW). Thus, the GA approach is capable to compute several different solution while minimizing total operating costs.

Conclusion

This paper has described the GA-based system for economic load dispatch. The system has been implemented on the 4-generator model of power system. The GAs with different starting have been tested. An experimental comparison between GA-based and traditional method has been carried out. In the application reviewed, the results show that the GAs can solve complex problems in the power systems and their applications are promising area to explore.

References

1. Kolcun, M.; Benc, R.; Szathmary, P.; Genetic Algorithms In Power Systems; Proc. of 8th Scientific Conference Electro-Power Engineering '97; TU in Kosice; 1996; Stara Lesna; pp. 165-70;
2. Heitkoetter, J.; Beasley, D.; The Hitch-Hiker's Guide to Evolutionary Computation: A list of Frequently Asked Questions (FAQ), USENET: comp.ai.genetic. Available via anonymous FTP from rtfm.mit.edu:/pub/usenet/news.answers/ai-faq/genetic/; 1996; About 100 pp;
3. Sheble, G.B.; Brittig, K.; Refined genetic algorithm-economic dispatch example; IEEE Transactions on Power Systems; Vol.: 10 Issue: 1; USA; 1995; p. 117-24;
4. Song, Y.H.; Li, F.; Morgan, R.; Cheng, D.T.Y.; Effective implementation of genetic algorithms on power economic dispatch; IPEC '95. Proc. of the International Power Engineering Conference; Vol.1; Nanyang Technol. Univ. Singapore; 1994; p. 268-74;