A Hybrid Particle Swarm Optimization and Single-Objective Slap Swarm Optimization Algorithm Based MPPT Strategy

Under inhomogeneous irradiance conditions, multiple peak characteristic of P-V curve reduces the efficiency of conventional trackers like incremental conductance control. A hybrid particle swarm optimization and single-objective slap swarm optimization algorithm (PSO-SOSSOA) based which is applied to maximum power point tracking (MPPT) strategy is presented. The PSO-SOSSOA adopts the particle swarm optimization algorithm in the early period of the algorithm operation and a modified single-objective slap swarm optimization algorithm (SOSSOA) in the remaining period. The simulation results reveal that the PSO-SOSSOA can successfully deal with global MPPT and exhibits performance advantages in terms of efficiency, search speed, and power oscillation compared with the SOSSOA.


Introduction
A photovoltaic (PV) array that receives a uniform solar irradiance exhibits a single peak maximum power point on the P-V characteristic curve. In this situation, Maximum Power Point Tracking (MPPT) can be realized by traditional incremental conductance control strategy, Perturb ＆ Observe control strategy, etc. [1,2]. However, when a PV array is in the partial shading state, the P-V characteristic curve of the PV array presents multiple peak points because of the hot spot effect. The above traditional control strategies are prone to fall into local optimal solutions and cannot be used to search for the global optimal value accurately. Therefore, some swarm intelligence control strategies with global search capability have been proposed. Particle swarm optimization (PSO) algorithm was introduced to the MPPT control strategy [3]. Such approach ensures that the PV array operates at the maximum power point (MPP). But it has the disadvantage of a long convergence time. An MPPT method based on an improved chicken swarm optimization algorithm [4] brought adaptive inertia weights and random factors to improve the exploration ability. Salp Swarm Optimization (SSO) Algorithm is used to deal with the problem of global MPPT [5]. However, there is a large power oscillation in the early period of the MPPT strategy.
This paper proposes a hybrid PSO and single-objective salp swarm optimization algorithm (PSO-SOSSOA) based MPPT strategy. In the early period of the PSO-SOSSOA operation, the PSO algorithm is utilized to reduce power oscillation and to narrow the search range. In the remaining period of the operation, a modified SOSSO algorithm is utilized to reduce the search time.

Particle swarm optimization
PSO is a bio-inspired metaheuristic approach based on the behavior of birds proposed by Kennedy and Eberhart [6]. PSO algorithm can be utilized to search the global MPP of PV system under the condition of local shading. The particle location of PSO is replaced by the duty ratio i D of DC-DC converter in PV system. i D is updated by equation (1).
where l is known as the current iteration, i v is considered to be the speed of particle i. i v is updated by where ω is known as the inertia weight, pbest,i D is the current best duty ratio of particle i, gbest D is the current best duty ratio founded by all particles, 1 c is the acceleration constant that controls the movement of particle i towards pbest,i D , 2 c is the acceleration constant that controls the movement of particle i towards gbest D .

Single-objective salp swarm optimization
Single-objective salp swarm optimization (SOSSO) is another bio-inspired metaheuristic approach based on the swarming behavior of slaps [7]. Salps form a swarm that resembles a spiral chain for better movement and foraging. Salp spiral-like chain consists of a leader and followers. Leader leads the movement at the forefront of the chain, and the rest of salps update their positions as followers.
When the SOSSO algorithm (SOSSOA) is applied to global MPPT of PV system, the salp position is regarded as the duty ratio i D . The duty ratio of leader is updated using equation (3) where 1 D is the duty ratio of leader, F is the food position which is the current best duty ratio of the swarm gbest D , lb D and ub D are the lower and upper boundaries of duty ratio, respectively. 2 k and 3 k are random constants between 0 and 1. The parameter 1 k is utilized to balance exploitation and exploration of SOSSO, and it is calculated as equation (4) 2 1 where L is considered to be the total number of iterations. The duty ratio of salp followers is updated according to Newton's equation of motion as follows： where i D is the duty ratio of salp follower i, 2 i ≥ , the time t of the algorithm is the number of iterations. The initial speed 0 v is set to 0. The acceleration a is the ratio of . Substituting the above concepts into equation (5), the following equation (6) is obtained The salp swarm utilizes equation (3) and equation (6) to simulate the motion of the spiral-like chain. In each iteration, the fitness values of all salps are computed. The salp with the best fitness value is selected as the leader, other salps are the followers.

Hybrid PSO-SOSSO algorithm
When PV modules of a PV array receive different solar irradiance, the SOSSOA is used to realize MPPT because of the characteristics of SOSSOA. However, in the early period of the SOSSOA operation, the output power of the PV array fluctuates violently because the duty ratio (lead salp position) changes greatly, and the speed of SOSSO searching for the global MPP is relatively slow. To address these mentioned problems, the PSO and the SOSSOA are combined to obtain a hybrid PSO-SOSSO algorithm (PSO-SOSSOA). In the early period of the PSO-SOSSOA operation ( 1/ 3 l L < ⋅ ), the use of PSO can gradually reduce the variation range of duty ratio and power fluctuation during the search process. In the remaining period of the operation, the SOSSOA is modified to meet performance requirements.

Initialization
Both the particle location of PSO and the salp position of SOSSO are considered to be the duty ratio

Modification of SOSSOA
After the search of PSO, the individuals gather in the surrounding area where the global MPP is located at, and the individual search space of SOSSO becomes smaller. Therefore, the variation of the leader duty cycle is reduced by modifying the equation (4). The equation (4) can be rewritten as where γ is the reduction factor between 0 and 1.
In the process of searching for the global MPP by following individual, the global optimal duty cycle may exist near current best duty ratio of any individual. Therefore, in order to improve the search efficiency and speed, the equation (6) can be modified as

Determination of stop and restart conditions
If the change step size of all individual duty ratio ( ( ) ( 1)) D l D l − − become less than a threshold, or if the iteration count l reaches the total number of iterations L, the PSO-SOSSOA will stop and generate the optimal duty ratio.
If solar irradiance or shading condition suddenly changes, the PSO-SOSSOA will start over. The judgment method is shown in the following formula (9) array, new array, last array, last The Flowchart of PSO-SOSSOA is provided in Figure 1.  Figure 4 and Figure 5. In Figure 4, The MP values found by PSO-SOSSOA and SOSSOA are both 549.05W. The convergence time of PSO-SOSSOA is 0.99s, while that of SOSSOA is 1.44s. In Figure 5, The MP value found by PSO-SOSSOA and SOSSOA is 386.94W and 386.78W respectively, and search time is 0.99s and 1.35s respectively. The above simulation results reveal that the PSO-SOSSOA and the SOSSOA can basically realize MPPT, but the search efficiency of PSO-SOSSOA is better than that of SOSSOA under the inhomogeneous irradiance condition 2. The average time taken by PSO-SOSSOA and SOSSOA to converge to MP is 0.99s and 1.395s respectively. This demonstrates that the PSO-SOSSOA significantly improves the search speed as compared to the SOSSOA. As illustrated in Figures 4 and 5, the power oscillation of PSO-SOSSOA is significantly smaller than that of SOSSOA.

Conclusion
A hybrid PSO-SOSSOA for PV MPPT is proposed in this paper. The simulation results reveal that the proposed PSO-SOSSOA can search and locate the global MP under different inhomogeneous irradiance conditions. The PSO-SOSSOA not only improves the search speed and efficiency, but also reduces power oscillation as compared to the SOSSOA.