Enriched Firefly Algorithm for Solving Reactive Power Problem

In this paper, Enriched Firefly Algorithm (EFA) is planned to solve optimal reactive power dispatch problem. This algorithm is a kind of swarm intelligence algorithm based on the response of a firefly to the light of other fireflies. In this paper, we plan an augmentation on the original firefly algorithm. The proposed algorithm extends the single population FA to the interacting multi-swarms by cooperative Models. The proposed EFA has been tested on standard IEEE 30 bus test system and simulation results show clearly the better performance of the proposed algorithm in reducing the real power loss.


Introduction
Various algorithms utilized to solve the reactive power problem.Various numerical methods like the gradient method [1]- [2], Newton method [3] and linear programming [4]- [7] have been utilized to solve the optimal reactive power dispatch problem.The problem of voltage stability and collapse play a key role in power system planning and operation [8].Evolutionary algorithms such as genetic algorithm have been already utilized to solve the reactive power flow problem [9]- [11].In [12], Hybrid differential evolution algorithm is utilized to improve the voltage stability index.In [13] Biogeography Based algorithm have been used to solve the reactive power dispatch problem.In [14], a fuzzy based methodology 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 proposes Enriched Firefly Algorithm (EFA) to solve reactive power dispatch problem.Our proposed EFA approach is good in exploration and exploitation for searching the global near optimal solution, when compared to other literature surveyed algorithms.A firefly algorithm (FA) is a population-based algorithm enthused by the social behaviour of fireflies [21], [22].Fireflies converse by flashing their light.Dimmer fireflies are attracted to brighter ones and move towards them to mate [23].FA is extensively used to solve reliability and redundancy problems.A class of firefly called Lampyride also used pheromone to attract their mate [24].The proposed Enriched Firefly Algorithm (EFA) extends the single population FA to the interacting multi-swarms by cooperative Models [25].The proposed EFA algorithm has been evaluated on standard IEEE 30 bus test system.The simulation results show that our proposed approach outperforms all the entitled reported algorithms in minimization of real power loss.

Objective function
The Optimal Power Flow problem is considered as a common minimization problem with constraints, and can be written in the following form: 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: The control variables are the generator bus voltages, the shunt capacitors and the transformers tap-settings: or Where N g , N t and N c are the number of generators, number of tap transformers and the number of shunt compensators respectively.

Active power loss
The objective of the reactive power dispatch is to minimize the active power loss in the transmission network, which can be mathematically 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: 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)

Inequality Constraints
The inequality constraints h(x,u) imitate 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: (12) , ∈ 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.

Proposed Enriched Firefly Algorithm
There are three ideal rules amalgamated into the unique Firefly algorithm (FA), i) all fireflies are unisex so that a firefly is attracted to all other fireflies ii) a firefly's attractiveness is proportionate to its brightness seen by other fireflies.For any two fireflies, the dimmer firefly is attracted by the brighter one and moves towards it, but if there are no brighter fireflies nearby means then firefly moves arbitrarily iii) the brightness of a firefly is proportional to the value of its objective function.According to the above three rules, the degree of attractiveness of a firefly is planned by the following equation: (17) where β is the degree of attractiveness of a firefly at a distance r, β 0 is the degree of attractiveness of the firefly at r= 0, r is the distance between any two fireflies, and γ is a light absorption coefficient.
The distance r between firefly i and firefly j located at x i and x j respectively is calculated as a Euclidean distance: The movement of the dimmer firefly i towards the brighter firefly j in terms of the dimmer one's updated location is determined by the following equation: The third term in (19) is included for the case where there is no brighter firefly than the one being considered and rand is a random number in the range of [0, 1].

Basic Firefly Algorithm
[Step 1] fireflies are arbitrarily placed within the exploration range, supreme attractiveness is , the light absorption is γ, randomization parameter is , maximum number of iterations is T; the position of fireflies is arbitrary distributed. [ Step 2] Compute the fluorescence brightness of fireflies.Compute the objective function values of Firefly Algorithm that use the enriched Firefly Algorithm as the largest individual fluorescence brightness value . [ Step 3] Modernize the position of firefly.When the firefly is no only attracted by a brighter firefly but also prejudiced by the historical best position of group, the position formula is updating as function (20).The brightest fireflies will modernize their position as the following function: Where 1 is the global optimal position at generation t. [Step 4] Recalculate the fluorescence brightness value by using the distance measure function after updating the location and penetrating the local area for the toughest fluorescence brightness individual, modernizing the optimal solution when the target value is enriched, or else unchanged. [ Step 5] When reach the maximum iteration number T , record the optimal solution, otherwise repeat step (3), ( 4), ( 5) and start the next search.The optimal solution is also the global optimum value and the global optimum image threshold is the corresponding threshold value , at the position .

Enriched Firefly Algorithm
In order to overcome the early convergence of classical FA, Cooperative optimization model is amalgamated into FA to construct an Enriched FA in this paper.In order to progress the balance between the exploration and exploitation in EFA we suggest a modification of Eq. ( 21) used in traditional FA.The goal of the modification is to reinstate balance between exploration and exploitation affording increased possibility of escaping basin of attraction of local optima.In the suggested EFA ,the firefly find a brighter firefly when iterative search use Firefly Algorithm ,then move towards with a certain step, but the direction of movement will bounce under the influence of the historical best position of group.The direction that towards blend with the direction that towards the historical best position of group is the deflect direction, in this way each search is affected by better solutions thereby improving the convergence rate.The principle of Firefly Algorithm with the influence of the historical best position of group .Suppose any firefly in the probing range is attracted by a brighter firefly and influenced by the historical best position of group, then the original direction of movement will change and move towards the optimal direction, thus speeding up the convergence rate.
In the proposed EFA, Eq. ( 20) of old-style FA based on constants values of and is modified by Eq. ( 21) Using new variables, and .In this case, the fireflies are adjusted by: Schematic procedure of Firefly Algorithm with the influence of the historical best position of group.The movement of a firefly is attracted to another more brighter firefly with the influence of the historical best position of group is determined by where is the updating position of firefly, is the initial position of firefly which play an important role in balancing the global Table 3 shows the proposed approach succeeds in keeping the control variables within limits.Table 4 summarizes the results of the optimal solution obtained by various methods.

Conclusion
In this paper, the EFA has been effectively implemented to solve Optimal Reactive Power Dispatch problem.The proposed algorithm has been tested on the standard IEEE 30 bus system.Simulation results show the robustness of proposed EFA method for providing better optimal solution in decreasing the real power loss.The control variables obtained after the optimization by EFA is within the limits.

Table 1 .
fireflies under the influence of the historical best position of group, 1 2 ⁄ is the arbitrary parameter that can avoid the result falling into local optimum., 4 transformer-tap settings, and 2 bus shunt reactive compensators.Bus 1 is slack bus and 2, 5, 8, 11 and 13 are taken as PV generator buses and the rest are PQ load buses.Control variables limits are listed in Table1.Preliminary Variable Limits (PU)

Table 3 .
Values of Control Variables After Optimization

Table 4 .
Comparison Results