DRAG & AVERSION PARTICLE SWARM OPTIMIZATION ALGORITHM FOR REDUCTION OF REAL POWER LOSS

This paper projects Drag & Aversion Particle Swarm Optimization (DAPSO) algorithm is applied to solve optimal reactive power problem. In DAPSO the idea of decreasing and increasing diversity operators used to control the population into the basic Particle Swarm Optimization (PSO) model. The modified model uses a diversity measure to have the algorithm alternate between exploring and exploiting behavior. The results show that both Drag & Aversion Particle Swarm Optimization (DAPSO) prevents premature convergence to enhanced level but still keeps a rapid convergence. Proposed Drag & Aversion Particle Swarm Optimization (DAPSO) has been tested in standard IEEE 118 & practical 191 bus test systems. Real power loss has been considerably reduced and voltage profiles are within the limits.


Introduction
The main objective of optimal reactive power problem is to minimize the real power loss and bus voltage deviation. Various numerical methods like the gradient method [1][2], Newton method [3] and linear programming [4][5][6][7] have been adopted to solve the optimal reactive power dispatch problem. Both the gradient and Newton methods have the complexity in managing inequality constraints. If linear programming is applied then the input-output function has to be uttered as a set of linear functions which mostly lead to loss of accuracy. The problem of voltage stability and collapse play a major role in power system planning and operation [8]. Evolutionary algorithms such as genetic algorithm have been already proposed to solve the reactive power flow problem [9][10][11]. Evolutionary algorithm is a heuristic approach used for minimization problems by utilizing nonlinear and non-differentiable continuous space functions. In [12], Hybrid differential evolution algorithm is proposed to improve the voltage stability index. In [13] Biogeography Based algorithm is projected to solve the reactive power dispatch problem. In [14], a fuzzy based method is used to solve the optimal reactive power scheduling method. In [15], an improved evolutionary programming is used to solve the optimal reactive power dispatch problem. In [16], the optimal reactive power flow problem is solved by integrating a genetic algorithm with a nonlinear interior point method. In [17], a pattern algorithm is used to solve ac-dc optimal reactive power flow model with the generator capability limits. In [18], F. Capitanescu proposes a two-step approach to evaluate Reactive power reserves with respect to operating constraints and voltage stability. In [19], a programming based approach is used to solve the optimal reactive power dispatch problem. In [20], A.Kargarian et al present a probabilistic algorithm for optimal reactive power provision in hybrid electricity markets with uncertain loads. This paper projects Drag & Aversion Particle Swarm Optimization (DAPSO) algorithm is applied to solve optimal reactive power problem. Newly R. Ursem has suggested a model called the Diversity-Guided Evolutionary Algorithm (DGEA) [21]. He redefines the traditional mutation operator, the Gaussian mutation, to be a directed mutation instead. The important issue is that this directed mutation, in general, increases the diversity, whereas normal Gaussian mutation is not likely to do this, because it simply adds Arbitrary noise from some distribution with a mean of zero, normally N(0;  2 ). Consequently, the DGEA applies diversitydecreasing operators (selection, recombination) and diversity-increasing operators (mutation) to alternate between two modes based upon a distance-to-average-point measure. The performance of the DGEA clearly shows its potential in multi-modal optimization. As [21] rightfully pinpoints, the diversity measure are traditionally used to analyze the evolutionary algorithms rather than guide them. We are great believers of adaptive controlling; that measuring and using different properties of the swarm/population while running, adds significant potential to the algorithm. We have therefore adopted the idea from Ursem with the decreasing and increasing diversity operators used to control the population into the basic PSO model. We find, it is a natural modification of the PSO , and the idea behind it is surprisingly simple. The modified model uses a diversity measure to have the algorithm alternate between exploring and exploiting behavior. We introduce two phases' Drag and Aversion. By measuring the diversity we let the swarm alternate between these phases. As long as the diversity is above a certain threshold d low the particles attract each other. When the diversity declines below d low the particles simply switch and start to repel each other until the threshold d high is met. With this simple scheme we obtain our modified model, which we have chosen to call the ARPSO modelthe attractive and repulsive PSO. Proposed Drag & Aversion Particle Swarm Optimization (DAPSO) has been tested in standard IEEE 118 & practical 191 bus test systems. Real power loss has been considerably reduced and voltage profiles are within the limits.

Problem formulation
The objective of the reactive power optimization problem is to minimize the active power loss in the transmission Network as well as to improve the voltage profile of the system. Adjusting reactive power controllers like Generator bus voltages, reactive Power of VAR sources and transformer taps performs reactive Power scheduling.
The control vector constraints The dependent vector constraints The power flow constraint

Basic Particle Swarm Optimization
The basic Particle Swarm Optimization (PSO) model consists of a swarm of particles moving in an n-dimensional, real valued search space of possible problem solutions. For the search space, in general, a certain quality measure, the fitness, is defined making it possible for particles to compare different problem solutions. Every particle has a position vector x and a velocity vector v. Moreover, each particle contains a small memory storing its own best position seen so far p and a global best position g obtained through communication with its fellow neighbor particles. This information flow is obtained by defining a neighborhood topology on the swarm telling particles about immediate neighbors.
The intuition behind the PSO model is that by letting information about good solutions spread out through the swarm, the particles will tend to move to good areas in the search space. At each time step t the velocity is updated and the particle is moved to a new position. This new position is simply calculated as the sum of the previous position and the new velocity: The update of the velocity from the previous velocity to the new velocity is, as implemented in this paper, determined by: )), Where  1 and  2 are real numbers chosen uniformly and at Arbitrary in a given interval, usually

Drag & Aversion Particle Swarm Optimization (DAPSO)
We define the Drag phase merely as the basic PSO algorithm. The particles will then attract each other, since in general they attract each other in the basic PSO algorithm because of the information flow of good solutions between particles. We define the second phase aversion, by "inverting" the velocity-update formula of the particles: In the Aversion phase the individual particle is no longer attracted to, but instead repelled by the best known particle position vector g(t) and its own previous best position vector p(t).
In the Drag phase the swarm is contracting, and consequently the diversity decreases. When the diversity drops below a lower bound, d low , we switch to the Aversion phase, in which the swarm expands due to the above inverted update-velocity formula (9). Finally, when a diversity of d high is reached, we switch back to the Drag phase. The result of this is an algorithm that alternates between phases of exploiting and exploring -Drag and aversionlow diversity and high diversity. The Drag & Aversion Particle Swarm Optimization (DAPSO), algorithm is shown in Fig. 1  The first of the two new functions, setDirection determines which phase the algorithm is currently in, simply by setting a sign-variable, dir, either to 1 or -1 depending on the diversity. In the second function, calculateDiversity, the diversity of the swarm (in the pseudo-code stored in the variable "diversity"), is set according to the diversity-measure:   (10) where S is the Swarm, [S] is the swarmsize, [L] is the length of longest the diagonal in the search space, N is the dimensionality of the problem, p ij is the j' th value of the I' th particle and pj is the j' th value of the average point p. Note that this diversity measure is independent of swarmsize, the dimensionality of the problem as well as the search range in each dimension.
Finally, the velocity-update formula, eqn. (9) is changed by multiplying the sign-variable direction to the two last terms in it. This decides directly whether the particles attract or repel each other:

Drag & Aversion Particle Swarm Optimization Algorithm for Reactive Power problem
The proposed Reactive Power Optimization algorithm using the ARPSO can be expressed as follows: Step 1. Initial searching points and velocities of agents are generated.
Step 2. Ploss to the searching points for each agent is calculated using the load flow calculation. If the constraints are violated, the penalty is added to the loss (evaluation value of agent).
The fitness function of each particle is calculated as: total real power losses of the n -th particle max G, and otherwise 0 Step 3. Pbest is set to each initial searching point. The initial best evaluated value (loss with penalty) among pbests is set to gbest.
Step 5. Update the velocity from previous velocity to the new velocity using eqn. (8).
Step 6. To new function applied. i. setdirection ii. Calculate Diversity to control swarm. Step 7.Ploss to the new searching points and the evaluation values are calculated.
Step 8. If the evaluation value of each agent is better than the previous pbest, the value is set to pbest. If the best pbest is better than gbest, the value is set to gbest. All of gbests are stored as candidates for the final control strategy.
Step 9. If the iteration number reaches the maximum iteration number, then stop. Otherwise, go to Step 4. If the voltage and power flow constraints are violated, the absolute violated value from the maximum and minimum boundaries is largely weighted and added to the objective function (1) as a penalty term. The maximum iteration number should be determined by pre-simulation. As mentioned below, PSO requires less than 100 iterations even for large-scale problems.

Simulation Results
At first Drag & Aversion Particle Swarm Optimization (DAPSO) algorithm , has been tested in standard IEEE 118-bus test system [26].  Table 1, with the change in step of 0.01.