ECONOMIC EMISSION DISPATCH SOLUTION USING PARALLEL SYNCHRONOUS PSO ALGORITHMS

This paper presents recent advances in applying parallel synchronous PSO algorithms for Optimal Power Flow in Combined Economic Emission Dispatch environment of thermal units while satisfying the constraints such as generator capacity limits, power balance and line flow limits. The use of orthogonal polynomials will give a very convenient means to obtain the equivalent cost function of the generating units. A general formulation and the development of Cascade Correlation algorithm to solve the environmentally constrained dispatch problem are presented. The objective is the minimization of the cost of operation, subject to all the usual and emissions constraints. The results obtained by the proposed method are better than any other evolutionary computation techniques proposed so far.


INTRODUCTION
Economic load dispatch is one of the main functions of electrical power management systems.The main objective of economic load dispatch is to minimize the fuel cost while satisfying the required equality and inequality constraints.One of those constraints which is always taken into account is the environmental constraint.That is minimization of pollution emission (NOx, CO2, SO2, small quantities of toxic metals, etc) in case of power plants [2].Recently, a global parallel synchronous PSO algorithm which is a kind of the probabilistic heuristic algorithm has been studied to solve the power optimization problems.The (PS-PSO) may find several sub-optimum solutions within a realistic computation time.Even if there is no guaranty that the PS-PSO may find the global optimal solutions in a finite time.The paper presents a methodology to overcome long computation times by applying simple Parallel Synchronous Particle Swarm Algorithms.The fast computation feature of the developed algorithm is advantageous and can be used in on line power system studies.

PROBLEM FORMULATION
The Economic Load Dispatch (ELD) and Emission Dispatch (ED) are solved separately.Suitable generating power units are leaved the total demand power after making the ELD and ED.According to the rest of total power demand, ELD and ED are made solution.When the total power demand and required constraints are suitable for all power system, EED is done.The total fuel cost and emission are calculated together in EED step [11].When the convergence is done the problem will be solved.There is a convergence whenever the cost circumstances are changed, such as it increases or decreases.
Then, generating unit's powers are saved.EED problem is composed of mainly two types of objective functions, ELD and ED subject to equality and inequality constraints.Each problem is detailed as follows:

Economic Load Dispatch
ELD problem is to find the optimal combination of power generation that minimizes the total fuel cost while satisfying the total demand and power system constraints.The fuel costs for power generation units should be defined.The total fuel cost function of ELD problem is defined as follows [1]: where i P is: the power output of i-th generator in MW; ) P ( F i : is the total fuel cost of electrical power generation in $/h; , , i i i a b c : are the cost coefficients of the i-th generator.

Emission Dispatch
The aim of ED problem is to minimize total emission of all thermal units.The amount of emission from a fossilbased thermal generator unit depends on the amount of power generated by the unit.Total emission generated also can be approximated as sum of a quadratic function and an exponential function of the active power output of the generators.The emission dispatch problem can be described as the optimization of total amount of emission release defined by as [12]: where ) P ( E i : Total emission release in Kg/hr; and , : are the emission function coefficients of the i-th generating unit.

Economic Emission Dispatch
An aggregating equation ( 1) to (2), the power dispatch problem is expressed as a bi-objective optimization problem as follows [12]: where i Pf : is the price penalty factor.
The ratio between the average fuel cost and the average emission for maximum power capacity of that plant is found: Equality constraints: Generation-demand balance as an equality constraint [2]:

PARALLEL SYNCHRONOUS PARTICLE SWARM OPTIMIZATION
Parallel synchronous optimization algorithms work best when three conditions are met.First, the optimization has total and undivided access to a homogeneous cluster of computers without interruptions from other users.Second, the analysis function takes a constant amount of time to evaluate any set of design variables throughout the optimization.Third, the number of parallel tasks can be equally distributed among the available processors.If any of these three conditions is not met, the parallel optimization algorithm will not make the most efficient use of the available computational resources [13].
Particle Swarm Optimization (PSO) was first proposed by Kennedy and Eberhart in 1995.This technique was inspired from the choreography of a bird flock and can be seen as a distributed behavior algorithm that performs multidimensional search.According to PSO, the behavior of each individual is affected by either the best local or the best global individual to help it fly through a hyperspace.Moreover, an individual can learn from its past experiences to adjust its flying speed and direction.Therefore, by observing the behavior of the flock and memorizing their flying histories, all the individuals in the swarm can quickly converge to near-optimal geographical positions with well-preserved population density distribution [13].
In a PSO system, a swarm of individuals (called particles) fly through the search space.Each particle represents a candidate solution to the optimization problem.The position of a particle is influenced by the best position visited by itself (own experience) and the position of the best particle in its neighborhood (the experience of neighboring particles).When the neighborhood of a particle is the entire swarm, the best position in the neighborhood is referred to as the global best particle, and the resulting algorithm is referred to as a Gbest PSO.When smaller neighborhoods are used, the algorithm is generally referred to as a lbest PSO.The performance of each particle is measured using a fitness function that varies depending on the optimization problem [14].
While several modifications to the original PSO algorithm have been made to increase robustness and computational throughput, one of the key issues is whether a synchronous or asynchronous approach is used to update particle positions and velocities.The sequential synchronous PSO algorithm updates all particle velocities and positions at the end of every optimization iteration [13].
Each particle i is represented as a D-dimensional position vector ) t ( x i and has a corresponding instantaneous velocity vector ) t ( v i .Furthermore, it remembers its individual best value of fitness function and position L x which has resulted in that value.During each iteration t, the velocity update rule is applied on each particle in the swarm.The g x is the best position of the entire swarm and represents the social knowledge [4]. )) where ω : called inertia weight and during all iterations decreases linearly from start ω to end ω ; Next, the position update rule is applied: The PSO updates the particles in the swarm using equations ( 6) and ( 7).This process is repeated until a specified number of iterations are exceeded, or velocity updates are close to zero.The quality of particles is measured using a fitness function which reflects the optimality of a particular solution.

ALGORITHM
The algorithm for solving the combined emission and economic dispatch problem using Parallel Synchronous PSO method is given below:

Compute
End-For Until some convergence criteria is satisfied.

SIMULATION RESULTS
The proposed approach is tested on the IEEE 30-bus system [4].
The fuel cost equations in $/h for the three generators are:  The loss coefficient matrix is: The proposed Parallel Synchronous PSO methods have been successfully employed and the results were obtained for IEEE 30-bus system using MATLAB software.

CONCLUSION
This paper introduces a new approach based on parallel synchronous PSO algorithms to study the power system Economic Emission dispatch which is formulated as a constrained optimization problem.Incorporating with the proposed constraint handling technique, parallel synchronous PSO algorithms successfully achieved the global optimal solution of the EED problem consisting of 3 generators and were able to obtain the solutions better than the known best solution reported in the literature for the EED problem.Furthermore, the 3 test was conducted to demonstrate that the performance of method is statistically significant.
The better computation efficiency and convergence property of the proposed parallel synchronous PSO algorithms show that it can be applied to a wide range of optimization problems.
demand (MW); L P : Transmission losses (MW); ij B : are the elements of loss coefficient matrix technique.D. Inequality Constraints: Generation power should be within the minimum output min i P − and the maximum output diagonal matrices with random diagonal elements drawn from a uniform distribution between 0 and 1; ISSN 1335-8243 (print) © 2011 FEI TUKE ISSN 1338-3957 (online) www.aei.tuke.skwww.versita.com/aei 2 1 and ϕ ϕ : are scalar constants that weight influence of particles' own experience and the social knowledge.
For each particle I = 1:to m Do Randomly initialize

Table 1
Results of optimization process (synchronous PSO)