Economic power dispatch of power system with pollution control using multiobjective ant colony optimization

International Journal of Computational Intelligence Research, April, 2007 by Linda Slimani, Tarek Bouktir

Abstract: This paper presents solution of optimal power flow (OPF) problem of medium-sized power systems via an ant colony optimisation (ACO) metaheuristic method. The objective is to minimise the total fuel cost of generation and environmental pollution caused by fossil based thermal generating units and also maintain an acceptable system performance in terms of limits on generator real and reactive power outputs, bus voltages, shunt capacitors/reactors, transformers tap-setting and power flow of transmission lines. CPU times can be reduced by decomposing the optimisation constraints of the power system to active constraints manipulated directly by ACO, and passive constraints maintained in their soft limits using a conventional constraint load flow. Simulation results on the IEEE 30-bus network with 6 generators show that by this method, an optimum solution can be given quickly.

Keywords: Optimal Power Flow, Power Systems, Pollution Control, NOx emission, Metaheuristic, Ant Colony Optimisation.

I. Introduction

The optimal power flow (OPF) calculation optimises the static operating condition of a power generation-transmission system. The main benefits of optimal power flow are (i) to ensure static security of quality of service by imposing limits on generation-transmission system's operation, (ii) to optimise reactive-power/voltage scheduling and (iii) to improve economy of operation through the full utilisation of the system's feasible operating range and by the accurate coordination of transmission losses in the scheduling process. The OPF has been usually considered as the minimisation of an objective function representing the generation cost and/or the transmission loss. The constraints involved are the physical laws governing the power generation-transmission systems and the operating limitations of the equipment.

The optimal power flow has been frequently solved using classical optimisation methods. Effective optimal power flow is limited by (i) the high dimensionality of power systems and (ii) the incomplete domain dependent knowledge of power system engineers [1][2][3].

The first limitation is addressed by numerical optimisation procedures based on successive linearisation using the first and the second derivatives of objective functions and their constraints as the search directions or by linear programming solutions to imprecise models [4-7]. The advantages of such methods are in their mathematical underpinnings, but disadvantages exist also in the sensitivity to problem formulation, algorithm selection and usually converge to local minima [8].

The second limitation, incomplete domain knowledge, precludes also the reliable use of expert systems where rule completeness is not possible.

As modern electrical power systems become more complex, planning, operation and control of such systems using conventional methods face increasing difficulties. Intelligent systems have been developed and applied for solving problems in such complex power systems.

One of the most recent metaheuristic algorithms is the Ant Colony Optimisation (ACO) computational paradigm introduced by Marco Dorigo in his Ph.D. thesis in 1992 [9], and expanded it in his further work, as summarised in [10], [11], [12].

ACO methods have been successfully applied to diverse combinatorial optimisation problems including travelling salesman [13], [14], quadratic assignment [15], [16], vehicle routing [17], [18], [19], telecommunication networks [20], graph colouring [21], constraint satisfaction [22], Hamiltonian graphs [23], and scheduling [24], [25], [26].

ACO offer a new powerful approach to these optimisation problems made possible by the increasing availability of high performance computers at relatively low costs.

As the name suggests, these algorithms have been inspired in the real ant colonies behaviour. When searching for food, ants initially explore the area surrounding their nest in a random manner. As soon as an ant finds a food source, it evaluates quantity and quality of the food and carries some of the found food to the nest. During the return trip, the ant deposits a chemical pheromone trail on the ground. The quantity of pheromone deposited, which may depend on the quantity and quality of the food, will guide other ants to the food source. The indirect communication between the ants via the pheromone trails allows them to find shortest paths between their nest and food sources. This functionality of real ant colonies is exploited in artificial ant colonies in order to solve global optimisation searching problems when the closed-form optimisation technique cannot be applied.

ACO is characterised by the use of a (parameterised) probabilistic model that is used to generate solutions to the problem under consideration. The probabilistic model is called the pheromone model. The pheromone model consists of a set of model parameters, which are called the pheromone trail parameters. The pheromone trail parameters have values, called pheromone values. At run-time, ACO algorithms try to update the pheromone values in such a way that the probability to generate high-quality solutions increases over time. The pheromone values are updated using previously generated solutions. The update aims to concentrate the search in regions of the search space containing high-quality solutions. In particular, the reinforcement of solution components depending on the solution quality is an important ingredient of ACO algorithms. It implicitly assumes that good solutions consist of good solution components. To learn which components contribute to good solutions can help to assemble them into better solutions.