PSO based Direct Power Control for a Multifunctional Grid Connected Photovoltaic System

Received May 28, 2017 Revised Jan 14, 2018 Accepted Jan 28, 2018 This paper presents a grid-connected photovoltaic system (PV) used as a shunt active power filter (SAPF) to provide the power factor correction, harmonic elimination, reactive power compensation and to simultaneously supply power from a PV system to the utility. A direct power control (DPC) method is used for controlling the system to feed the photovoltaic energy in synchronization with grid and provide power quality improvement. The PI parameters of DC-link voltage controller are tuned using the Particle Swarm Optimization (PSO) algorithm without the need for an exact mathematical model of system. This PI-PSO controller gives better results for robustness, harmonic minimization and reduces the overshoot and undershoots of PI controller. The overall control of system is tested in Matlab/Simulink environment. Then, the simulations results demonstrate the robustness and feasibility of proposed method. Keyword:


INTRODUCTION
The solar energy is the most popular source among the alternative energy resource without emission of pollutants energy conversion is done [1]. In an effort to use the solar energy effectively, a great deal of research has been done on the grid-connected photovoltaic generation systems. In PV systems connected to the grid, the inverter that converts the output direct current (DC) of the solar modules to the alternate current (AC) is receiving increased interest in order to generate power to utility [2].
Today, the widespread use of nonlinear loads in power systems causes circulation of harmonics and reactive currents in the distribution lines [3] [4]. If the grid-connected PV system is applied to nonlinear loads, the power quality is relatively poorer. To avoid these problems, the grid-connected PV system should not only supply active power to the system via MPPT, but also improve the power quality (low THD and unity power factor) [5].
By modifying the control of the inverter, active filtering feature can also be included in the PV interfacing inverter and thus saves the cost of additional active filter. Various control types of shunt active filter were presented in the literature [6]. In this article, we propose the direct power control (DPC). The DPC strategy is based on the instantaneous active and reactive power comparators. The active power command is provided from a dc-bus voltage controller block, while the reactive power command is directly given from the outside of the controller. Errors between the commands and the estimated feedback power are input to the hysteresis comparators [7] [8].
In the DPC technique, the active power is delivered from the outer proportional-integral (PI) controller. This PI controller is formulated as an optimization problem [9]. In this work, we propose the use of the particle swarm optimization (PSO) method to search for the optimal parameters of a PI controller. DPC based on classical PI regulator and PSO algorithm is developed and a comparison study is presented. To show the performances, a numerical simulation is performed.

SYSTEMS CONFIGURATIONS
The structure of the grid-connected PV system is shown in Figure. 1. It consists of a photovoltaic array connected through a dc-dc boost converter to a three-phase inverter that is connected to a grid through a simple filter and nonlinear load.

PV Array Model
The PV module is the unity of base for the construction of a PV array. We have used the PV module model of a single diode. This model is the most commonly used due to good results [10]. The current-voltage relationship is given by:    Figure.4 shows the equivalent circuit of the DC-DC boost converter. These converters can be described using ordinary differentiation equations as follows:

Boost Converter Modeling
(1 ) D: is the duty cycle. The switch is on for a period equal to DT, and the switch is off for an interval time equal to (1 -D) T.

Maximum Power Point Tracking
Several publications on MPP methods are regularly published in the literature. For our study, we chose the MPPT algorithm of P&O. P&O method is one of the popular methods to track the maximum-power point and probably the most frequently used in practice, mainly due to its easy implementation. [11] [12]. The working principle of P&O is depicted by the flow chart in Figure.

Active Power Filter
The structure of the active filter consists essentially of two parts, a power and a control part. The power part consists of an inverter, a coupling filter and a source of energy. The control part is used to control the switching of semiconductor elements forming the inverter from the power part. Au through appropriate control strategies, it is possible to generate harmonic signals at the output of the inverter to offset those present on the power grid, such as. [13] s lf i i i  (6) i s : current of source.; i l : current of the load; i f : current compensation.

DIRECT POWER CONTROL
The main idea of the direct power control (DPC) originally proposed by Ohnishi (1991) and further developed by Noguchi and Takahachi in 1998, is similar to the direct torque control (DTC) of induction machines. Instead of flux and torque, the active power (P) and reactive power (q) are selected as two instantaneous magnitudes to control [14] [7]. The figure .2 shows the configuration of the direct power control without voltage sensor for a three phase inverter. The estimated values of (p s ) and (q s ) in terms of the three phase line currents and voltages can be derived as: [14] s S S S P jQ  (7) . . .

S sa sa sb sb sc sc
The phase of the power-source voltage vector is converted to the digitized signal N  Error! Reference source not found.. For this purpose, the working plane (α, β) is divided into 12 sectors in Figure. 7. The sectors can be numerically determined by the following equation. [7].
Or: N= 1,2,3….12 is the number of the sector

Hysteresis control and switching table
The references of reactive power (qref) and active power (pref) are compared with the estimated reactive (qs) and active (ps) values. Errors between the commands and the estimated feedback power are input to the hysteresis comparators and digitized to the signals Sp and Sq. The output signal of the active power controller is defined: And similarly for the reactive power controller as: For all sectors the switching table proposed is represented in the Table 1.

PI controller
The regulation of the continuous voltage of inverter is ensured by a regulator of PI type. The error between the voltage of the capacitor V dc and the reference voltage V dcref is used as an input to PI Controller  (13) Where, k P is the proportional constant gain and k i is the integral constant gain. These gains are tuned by using Particle Swarm Optimization (PSO).

PARTICLE SWARM OPTIMIZATION
The particle swarm optimization (PSO) algorithm was first described in 1995 by Kennedy and Eberhart [15] [16]. The technique has evolved greatly since then. PSO is a stochastic, population based evolutionary computer algorithm for problem solving. In a PSO system, a swarm of individuals (called particles) fly through the search space. Each particle represents a candidate solution to the optimization problem. The position of a particle is influenced by the best position visited by itself (i.e., its own experience) and the position of the best particle in its neighbourhood (i.e., the experience of neighboring particles). When the neighbourhood of a particle is the entire swarm, the best position in the neighbourhood is referred to as the global best particle, and the resulting algorithm is referred to a global best PSO. When smaller neighbourhoods are used, the algorithm is generally referred to a local best PSO. The performance of each particle (i.e., how close the particle is from the global optimum) is measured using a fitness function that varies depending on the optimization problem. Each particle in the swarm is represented by the following characteristics [15] [17]: x i is the current position of the particle; v i is the current velocity of the particle; y i is the personal best position of the particle is the neighbourhood best position of the particle. The personal best position of particle i is the best position visited by particle i so far. Let F denote the objective function. Then the personal best of a particle at time step t is updated as: For the gbest model, the best particle is determined from the entire swarm by selecting the best personal position. If the position of the global best particle is denoted by the vector then:  ( 1) ( ) ( 1) This process is repeated until a specified number of iterations is exceeded, or velocity updates are close to zero. The quality of particles is measured using a fitness function which reflects the optimality of a particular solution. The following steps summarize the basic PSO algorithm: Unitl some convergence criteria is satisfied

Objective function formulation
In this study, the PSO algorithm is proposed to tune the PI parameters of voltage controller by minimizing the cost function. So that, the proportional (kp) and integral (ki) gains of PI controller is defined as the problem parameters that should be optimized.
Thus, each individual of population is composed of the controller parameters kp and ki. Then, the optimization problem of PI controller is formulated as the minimization of the integral time absolute error ITAE and of the maximum overshoot. Therefore, the objective function is defined as: n: is the total number of points for which the optimization is carried out. ts: is the time rang of simulation or simulation period.

SIMULATION RESULTS AND ANALYSIS
The system depicted in Figure.1 and 6 has been simulated using the SimPowerSystem with Sfunction of Matlab/Simulink installed on a computer system with Intel Core i5-4210 CPU, 1.70 GHz speed and 4GO of memory. Parameters used in simulation are as follows:  The source current and its spectrum before connecting SAPF feed by PV system are illustrated in Figure 9. The results show that the system is affected by the nonlinear load during the operation. Where, the Total Harmonic Distortion (THD) of the supply current is high and equals 27.57%. To verify the performances and robustness of the proposed control and the research algorithm of maximum power point tracking (MPPT), a variable profile irradiance to sweep all modes of operation of our system is done. Figure 10 shows the solar irradiance level starts from 0 W/m 2 , then increases to 600 W/m 2 , after that decreases to 200 W/m 2 and finally increases to 1000 W/m 2 .  We can observed from [0.3s-0.5s] and [0.8s-1s] , the opposite phase between voltage and current source and the negative sign of the utility active power (Ps), meaning the filter current has information of harmonic and PV array currents to ensure elimination of harmonic and injection of current to the load. The dc link voltage returns to its reference value in few milliseconds, without overshoot and undershoots, as shown in Figure 12e, demonstrates the superiority of the PI-PSO controller compared to its counterpart PI controller. Figure 13 show harmonic spectrum of source current at 0 W/m². The active filter decreases the total harmonic distortion (THD) from 27.57% to 1.83% with PI controller. However, with PI-PSO controller the THD is increased to 1.28% which proves the effectiveness of the proposed controller. Performance of proposed control is evaluated in term of THDi level behavior under fast changing irradiation as well as changing operation modes as shown in Table 5.   The simulation result shows that the improved particle swarm optimization PI control has a smaller overshoot during radiation change, low rise time and low source current THD compared to its counterpart PI controller. It can be concluded that the DPC with PI-PSO gives betters results for robustness, harmonic minimization and inject the maximum active power available from the PV array into the load and/or grid.

CONCLUSION
In this paper, a PSO based direct power control for a multifunctional grid connected photovoltaic system is investigated. the simulation results show a significant enhancement by applying the DPC with PI-PSO controller in comparison with classical DPC in termes of response time, overshoot, THD and stability the systeme under irradiation changes.The optimization of the gains of PI controller for dc link voltage by using PSO algorithm presents a perfect efficiency to reduce the overshoot and undershoot of PI controller and gives better results for robustness and harmonic minimization.