MINIMIZATION OF REAL POWER LOSS BY ENHANCED GREAT DELUGE ALGORITHM

This paper presents Enhanced Great Deluge Algorithm (EDA) for solving reactive power problem. Alike other local exploration methods, this Enhanced Great Deluge Algorithm (EDA) also swap general solution (fresh_Config) with most excellent results (most excellent_Config) that have been found by then. This deed prolong until stop conditions is offered. In this algorithm, new solutions are selected from neighbours. Selection strategy is different from other approaches. In order to evaluate validity of the proposed Enhanced Great Deluge Algorithm (EDA) algorithm, it has been tested on standard IEEE 118 & practical 191 bus test systems and compared to other standard reported algorithms. Results show that Enhanced Great Deluge Algorithm (EDA) reduces the real power loss and voltage profiles are within the limits.


Introduction
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. The Great Deluge algorithm (GD) [21] is a generic algorithm and it alike to the hill-climbing and simulated annealing algorithms. The name comes from the resemblance of a great deluge a person climbing a hill will try to move in any direction that does not get his or her feet wet in the anticipate to find a way up as the water level increases. In this work, we utilize a Great Deluge (GD) algorithm that was introduced by Dueck [21] and applied by Burke et al. [22] in different optimization problem to solve the reactive power problem. In proposed Enhanced Great Deluge Algorithm (EDA) model, global and local characters of the algorithms are used in a competent way. In order to evaluate validity of the proposed Enhanced Great Deluge Algorithm (EDA) algorithm, it has been tested on standard IEEE 118 & practical 191 bus test systems and compared to other standard reported algorithms. Results show that Enhanced Great Deluge Algorithm (EDA) reduces the real power loss and voltage profiles are within the limits.

Problem Formulation
The optimal power flow problem is treated as a general minimization problem with constraints, and can be mathematically written in the following form: subject to g(x,u)=0 (2) and h(x, u) ≤ 0 where f(x,u) is the objective function. g(x.u) and h(x,u) are respectively the set of equality and inequality constraints. x is the vector of state variables, and u is the vector of control variables. The state variables are the load buses (PQ buses) voltages, angles, the generator reactive powers and the slack active generator power:

Active Power Loss
The objective of the reactive power dispatch is to minimize the active power loss in the transmission network, which can be described as follows: or where g k : is the conductance of branch between nodes i and j, Nbr: is the total number of transmission lines in power systems. P d : is the total active power demand, P gi : is the generator active power of unit i, and P gsalck : is the generator active power of slack bus.

Voltage Profile Improvement
For minimizing the voltage deviation in PQ buses, the objective function becomes: = + × (9) where ω v : is a weighting factor of voltage deviation.
VD is the voltage deviation given by:

Equality Constraint
The equality constraint g(x,u) of the ORPD problem is represented by the power balance equation, where the total power generation must cover the total power demand and the power losses: = + (11) This equation is solved by running Newton Raphson load flow method, by calculating the active power of slack bus to determine active power loss.

Inequality Constraints
The inequality constraints h(x,u) reflect the limits on components in the power system as well as the limits created to ensure system security. Upper and lower bounds on the active power of slack bus, and reactive power of generators: Upper and lower bounds on the bus voltage magnitudes: Upper and lower bounds on the transformers tap ratios: Upper and lower bounds on the compensators reactive powers: Where N is the total number of buses, N T is the total number of Transformers; N c is the total number of shunt reactive compensators.

Enhanced Great Deluge Algorithm
Great deluge algorithm replaces common solution (fresh_Config) with best results (most excellent_Config) that have been found by then. This action continues until stop conditions is offered. In this algorithm, novel solutions are chosen from neighbours. In great deluge algorithm these results are satisfactory which their values are equal or better than the value of Water Level (WL). Value of WL also increases at a fixed pace in each step. Augment of WL persist until value of WL equals with the finest result accomplished ever. In this step, the algorithm is repeated several times and if better result is not obtained, it comes to the end. The primary amount of WL is equal with the primary results (f(s)). In this work, at the beginning of the search, the level is set to be initial water level. The water level, level, is decreased by β in each of the iteration where β is based on the estimated quality (est.q). The pseudo code for the GD to solve clustering problems is shown in Fig. 1. Fig. 1 shows that, the algorithm starts by initializing the required parameters as in Step-1 by setting the stopping condition (N.iters), estimated quality of the final solution (est.q), the initial water level (level), decreasing rate (β), maximum number of not improving solutions (not_improving_length_GD). Again, note that the initial solution is generated using K-Means (So).
In the improvement phase (Step-2), neighbourhood structures N1 and N2 are applied to generate candidate solutions (in this case, five candidate solutions are generated), and the best candidate is selected as the candidate solution (Sworking) as shown in Step-2.1. In this work there are two cases to be taken into consideration as follows: is better than f(SArrange), then Sworking is accepted as a current solution (Ssource ← Sworking), and the best solution is updated (SArrange ← Sworking) as shown in Step-2.2. The level will be updated by the value β (i.e. level = level -β).

Case 2: Worse solution If f(Sworking) is less than f(SArrange)
, then the quality of Sworking is compared against the level. If it is less than or equal to the level, then Sworking is accepted, and the current solution is updated (Ssource ← Sworking). Otherwise, Sworking will be rejected. The level will be updated by the value β (i.e. level = level -β). The counter for the non-improving solution is increased by 1. If this counter is equal non_improving_length_GD, then the process terminates. Otherwise, the process continues the stopping condition is met (i.e. Iterations> N.iters), and return the best solution found SArrange. (Step-2). Note that in this work the est.q is set to 0, and non_improving_length_GD is set to 10.

Algorithm of great deluge algorithm
Step Step-2: Improvement (Iterative) Phase repeat ( while termination condition is not satisfied) Step-2.

iters (termination condition is met)
Step-3: Termination phase Return the best found solution SArrange However, there are three drawbacks in employing the GD algorithm are : (i) in GD the estimated quality (est.q) of the final solution is very hard to investigate, as each dataset has it is own performance (ii) in GD the acceptance criterion is based on level which is decreased based on the estimated quality that is decreased continuously without control, and (iii) in GD the neighbourhood structure i.e. N1 and N2 are not really effective as it is based at random. Therefore, Enhanced Great Deluge Algorithm (EDA) is proposed to overcome these drawbacks. EDA structure resembles the original structure of the GD algorithm, but the basic difference is in term of updating the level. In MGD, we have introduce a list that keeps the previous level value at the time when the better solution is obtained (i.e. SArrange = Sworking). When the maximum number of iteration of no improved GD (not_improving_length_GD) is met, then the level is updated by a new level that is arbitrarily selected.

Enhanced great deluge algorithm for solving reactive power problem
Step Step-2: Improvement (Iterative) Phase repeat ( while termination condition is not satisfied) Step-2.

iters (termination condition are met)
Step-3: Termination phase Return the best found solution SArrange.

Simulation Results
At first Enhanced Great Deluge Algorithm (EDA) algorithm has been tested in standard IEEE 118-bus test system [23].  Table 1, with the change in step of 0.01.