Study Comparison Between Enhanced Firefly and Differential Evolution to Solve the Maximum Power Point Tracking Problem

The energy prerequisite of the world is always expanding. The expanding energy requests put a great deal of weight on the classical energy sources (oil, gas and coal). Be that as it may, the fossil fuel-based energy sources are restricted in amount and furthermore cause ecological contamination. The negative impacts of the traditional energy sources can be overcome by making utilization of sun's vitality. This source will never harm the earth [1]. In photovoltaic (PV) source generators, the electrical energy straightway produces by changing over the energy of sunlight based radiation [2]. With a flow in the utilization of non-traditional energy sources, PV compositions are by and large progressively utilized in several applications [3]. Notwithstanding, a noteworthy test in utilizing a PV source is to handle the circumstances like unstable atmospheric conditions [4]. The characteristic of a photovoltaic system emphatically relies on upon the operating ecological conditions, for example, temperature and solar insolation [5]. The PV systems ought to work at the maximum power point, so as to accomplish maximum efficiency. Then and in order to obtain maximum power, the MPP tracking (MPPT) is inserted between the photovoltaic frameworks and the load [6]. Babu et al. [7] do an endeavor for maximum power point tracking by providing amendments to particle swarm optimization method, taking in the consideration the selection of the initial value. The basic combination of this technique adds strengthen in order to follow global peak power precisely with the influence of change in ecological situation together with steady state oscillations of very nearly to zero, quicker dynamic reaction, and easy enforcement. Accurate estimation is executed for various situations of partial shading and lastly the outcomes acquired are contrasted with other techniques. MPPT using genetic algorithm (GA) for PV system is displayed by Kumar et al. [8]. It is incorporated with a unit of battery storage as power source unit in standalone mode. Photovoltaic supply relies on upon solar irradiance, site position and ecological factors such as temperature, and wind. In this way photovoltaic output is fluctuating in quality and the insertion of non linear load leads to make the circumstance more ticklish. In order to get wanted evaluated voltage, DC-DC converter is utilized. Where, battery storage unit goes about as secondary supply to guarantee continuous power source. In present work, different artificial intelligence methods have been suggested to solve the problem of Maximum power point tracking with the use of buck-boost converter. In this paper, in order to draw all the power supplied from the PV system different optimization methods are proposed to control the duty cycle. The remnant of the paper is arranged as follows: section one gives some introduction about the paper, a brief explanation of buck-boost converter is given in section two. Section three discussed the proposed optimization algorithms. The results and their simulations are given in section four. The last section presented the conclusion.

The use of artificial intelligent is increased rapidly nowadays. Where different concepts have been used to find or modified many optimization algorithms [13].

3.1 Differential evolution

Nowadays, among the real-parameter and the most capable stochastic optimization techniques, differential evolution (DE) is utilized [14]. The main features that are promoted this algorithm; first, the capability to find the global optimum solution paying little respect to the values of initial parameters. Second, fast rate of convergence. Finally, little usage of parameters [15]. Genetic algorithm is like DE in terms of the principle of work. Be that as it may, as opposed to GA— which depends basically on the operation of the crossover to produce the variation in the population, differential evolution uses the mechanism of the mutation to search the possible regions in the search space. Using the generations of mutation, crossover and selection, DE can enhance the population of solutions [16]. DE has turned out to be a hopeful technique for optimization of multimodal objective functions. It is exceptionally easy to comprehend and to execute. DE is likewise especially simple to work with [17]. The algorithm begins with members which are produced randomly by using the uniform distribution. A trial solution is resulted by using mutation and crossover producers at every iteration. Then the operation of selection is used to find the best solutions into the next generation. The population advances iteration by iteration till the algorithm reach the maximum generation [18].

3.1.1 Initialization

An initial population of N candidate solutions or individuals is first generated and is used as the parent population of the first iteration or generation. The premier individuals ought to spread to the all search space in so far as possible using the population which is randomized uniformly in the space bounded by minimum and maximum limits [18].

Thus, real encoding can be used for each member (mem) as follows [17]:

$\operatorname{mem}_{j k}=L L_{j k}+$ rand $*\left(L H_{j k}-L L_{j k}\right)$     (5)

where, LH_jk and LL_jk denote the upper and lower bounds of each chromosome, rand is a random number chosen from the range [0, 1], k=1, .., N, and j=1, …, d.

3.1.2 Mutation

The enforcement of mutation step is the fundamental distinction between differential evolution and other evolutionary methods. In differential evolution, the operation of mutation does the vector differences between the current individuals of population in order to find the value and the orientation of perturbation which is utilized to the member subject of the operation of the mutation. This operator is basically in charge of protecting a population powerful as well as for seeking new regions. DE is considered as self-adjusting algorithm where it derives the perturbations from the differences between the individuals, rather than utilizing a predefined probability in order to apply the mutation. In DE, the "self-adjusting" means: while the individuals reach to the optimal solution, any randomly selection distinction vector will reduce in size. Ultimately the distinction vector approximates to zero then this operator will be debilitated, in case the individuals reach to a solitary result. Then the vectors which are recently perturbed are created by append the weighted distinction to different vector. Based on the kind of the problem, different schemes where suggested for a number of options [17]. Three methods of mutation actualized here were DE/rand/1, DE/current-to-best/1, and DE/rand/1/either/or, which encase the accompanying strides:

DE scheme 1/rand/1 [19]:

$V_{T_{k, g}}^j=x_{r 1, g}^j+F\left(x_{r 2, g}^j-x_{r 3, g}^j\right)$     (6)

where, $V_{T_{k, g}}^j$ is the trial vector, r1, r2, r3 {1, 2, …., N}, r1≠r2≠r3≠k. F is a scale factor greater than zero. In order to control the increasing in the differential variation, real number F is used. F represents the mutation factor, g is the number of generation.

DE scheme 2/current-to-best/1 [17]:

In order to provide a means to enhance the greed of the scheme, an additional control variable λ is introduced. Thus, a perturbed vector is generated according to Eq. (7).

$V_{T_{k, g}}^j=x_{k, g}^j+\lambda\left(x_{\text {best }, g}^j-x_{k, g}^j\right)+F\left(x_{r 2, g}^j-x_{r 3, g}^j\right)$     (7)

DE scheme 2/rand/1/either/or [20]:

$V_{T_{k, g}^j}^j=x_{r 1, g}^j+0.5(F+1) *\left(x_{r 2, g}^j+x_{r 3, g}^j-2 x_{r 1, g}^j\right)$      (8)

3.1.3 Crossover (recombination)

From the mutation operation the perturbed vector will produce. Then go through the operation of the crossover to raise the variety of the members and in order to not trap in a local minimum. As per to the kth vector and its associated vector, this operator results a new trial vector as follows:

$u_{k, g}^j=\left\{\begin{array}{cc}V_{T_{k, g}}^i & \text { if }\left(\text { rand }^j(0,1) \leq C_r \text { or } j=j_{\text {rand }}\right. \\ x_{k, g}^j & \text { if }\left(\text { rand }^j(0,1)>C_r \text { or } j=j_{\text {rand }}\right.\end{array}\right\}$      (9)

where, C_r is a crossover factor in the range [0,1].

3.1.4 Selection

Actually, the step of selection in differential evolution is straightforward, because it checks the situations where the trial vector can go through the members. Comparison between the two fitness functions will perform due to the trial vector that result will just exchange with the original member if and only if has better fitness.

$x_{k, g+1}=\left\{\begin{array}{ll}u_{k, g} & \text { if } f\left(u_{k, g}\right) \leq f\left(x_{k, g}\right) \\ & x_{k, g} \quad \text { else }\end{array}\right\}$       (10)

Finally, the DE can be summarizing as follows [21]:

1: Generate an initial population=(x₁, x₂, x₃, …., x_N)

2: Repeat

3:   for k=1 to N do

4:    Generate a new trial vector y

5:   if f(y)<f(x_k) then insert y into new generation Q

6:         else insert x_k into new generation Q

7:    end if

8:   end for

9:   P=Q

10: Until stop criteria is met

In design the DE, the user must choose the key parameters that control DE, i.e., population size (N), boundary constraints of optimization variables, mutation factor (F), crossover rate (C_r) and the stopping criterion [18].

3.2 Enhanced firefly algorithm

The bioluminescence operations are in charge of the fireflies flashing light. During the life time of fireflies, many contradictions about the concepts behind the cause and significance of flashing light, hence a big part of those thoughts being associated with the intermarriage stage [22, 23]. The basic job of flashing light is to build the intermarriage copartner, and in this stage the operations of bioluminescence is recognized as luminescent emanation. The one of a kind symbol of the flashing floodlight is the sign for their preparedness on intermarriage and outcomes of like correct shining emission operation is to fetch both the fireflies of similar class for sex. One class firefly is the photinus, then amongst them the masculine firefly uses compendious signal manner and female firefly interacts to it in a limit time period. Various kinds of firefly introduce special intermarriage practices on different situations [24]. They, have a place with group of Lampyridae, are little winged insects equipped for delivering a cool light so that to pull the mates [25]. It is supposed to have a capacitor-like mechanism, which gradually fills with the charge till the specific limit is come to, at which fireflies discharge the energy as light, after which the cycle does again [26]. Yang, created this algorithm which is inspired by the light attenuation with the separation and fireflies' mutual attraction, instead of by phenomenon of the fireflies’ light flashing. In order to modify the FA, the search locally is performed to raise the exploration and abilities of the search of the algorithm, then guarantee that the convergence will be rapid. FA is allowed to search for the global optima for a given objective function [25]. Thus, FA can avoid the falling in local optima.