# Optimization of photovoltaic power system: a comparative study

- Vishal Dabra
^{1}Email author, - Krishan Kumar Paliwal
^{1}, - Pardeep Sharma
^{1}and - Narender Kumar
^{1}

**2**:3

https://doi.org/10.1186/s41601-017-0036-2

© The Author(s) 2017

**Received: **29 September 2016

**Accepted: **22 January 2017

**Published: **8 February 2017

## Abstract

This paper presents a comparative study of P&O, fuzzy P&O and BPSO fuzzy P&O control methods by using MATLAB software for optimizing the power output of the solar PV grid array. The voltage, power output and the duty cycle of the solar PV array are well presented and analyzed with an algorithm. The model consists of 66 PV Cells connected parallel and 5 PV cells connected in series to make solar PV array. The BPSO Fuzzy method generates 43.4820 MW output power more than P&O method and 150 KW more than P&O fuzzy method. This also shows that the time response of the photovoltaic system reduces to perturbations and insures the continuity of the operation at the time in response to the continued maximum power point. It also eliminates the fluctuations around MPPT. Simulation results also revealed that BPSO fuzzy P&O controller is more effective as compare with P&O and fuzzy P&O models.

### Keywords

Photovoltaic Maximum power point tracking Particle Swarm Optimization Bacterial foraging optimisation Fuzzy logic## Introduction

Photovoltaic power generation offers the benefits of clean, non-polluting power generation, production of power close to the consumer with very little maintenance requirement, and of having a especially extensive life period [1]. Recently, the photovoltaic power generation is one of the best growing fields for the engineers. There are number of ways for maximizing the power output of a PV grid array. MPPT control method of PV system was proposed and estimated the process for every two perturb processes in search for the maximum power output of PV grid array. The estimate-perturb-perturb (EPP) method significantly improves the tracking accuracy and speed of the MPPT control [2]. Introduce the exercise of BFO and ABFO techniques to develop a well-organized forecasting model for prediction of various ranges of input parameters for getting maximum power output [3]. A Particle Swarm Optimization (PSO) method of MPPT for PV system was proposed and discussed the effect of various irradiation conditions with partial shading. They found that PV system output power was increased with PSO method [4]. Artificial neural network (ANN) method was proposed for a PV system to get maximum power point tracking (MPPT) and observed that new MPPT algorithm can search the MPP fast and exactly based on the feedback voltage and current with different solar irradiance and temperature of environment [5]. FLC and MPPT were based on a voltage control approach of the power converter with a discrete PI controller and eliminate fluctuation in output power of PV system for getting MPPT [6]. A new heuristic population-based search algorithm was proposed and compared SOA with recently reported optimization algorithms like bacteria foraging optimization (BFO) and genetic algorithm (GA). They found that SOA is more effective than either BFO or GA in finding the optimal transient performance [7]. Swarm intelligence with PO algorithm was proposed and analyized oscillations in the output power, voltage and current of the PV system [8]. Perturbation and observation (P&O) method was proposed to track the MPPT of PV system for getting maximum system efficiency and obtained maximum power of PV system when compare with traditional P & O [9]. A fuzzy logic method for the MPPT of a photovoltaic system under variable temperature and insolation conditions was proposed and obtained that the effiecieny of the PV system increases [10]. Compares 62 different techniques of MPPT and gave information of choosing right algorithm for desired output [11]. MATLAB based PV array model was developed and studied the effect of varying temperature and insolation conditions on the performance of the PV array [12]. A new MPPT algorithm using neuro fuzzy system was presented to get the maximum power across the inverter terminals [13]. MATLAB/Simulink based MPPT methods were discussed in terms of the dynamic response of the PV system to variations in temperature and irradiance, attainable efficiency, and implementation considerations [14]. FLC technique gives better and more reliable control for PV grid system with varying weather conditions [15]. Efficiency of MPPT system of the PV system was increased by 2% by using P&O method [16]. To get MPPT under different operating conditions only when all nonlinearities in the characteristic *I-V* curves were omitted [17]. A new BAT algorithm for MPPT control design was suggested to PV system based on Switched Reluctance Motor (SRM) PI controller and developed PI controller was used to reach MPPT by monitoring the voltage and current of the PV array. The performance of the developed BAT algorithm was compared with Particle Swarm Optimization (PSO) for different disturbances to confirm its robustness [18]. Nevertheless, PV system power is still considered to be more expensive. The cost reduction and MPPT of PV system is subject to extensive research. The objective of this paper is to compare the BFO-PSO model with P & O model and PSO model by using various membership functions of fuzzy logic for PV grid array to get maximum power output.

## Methods of MPPT

All MPPT controller work towards to set an optimal duty cycle of boost converter so that voltage generated by PV array can be boosted to desire. The following methods are used for getting MPPT of PV array.

### Particle swarm optimization method

Particle swarm optimization (PSO) method is a population based stochastic optimization technique. The system is initialized with a population of random solutions and searches for optimum power generations. PSO has been successfully applied in many areas: function optimization, artificial neural network training, fuzzy system control, and other areas where GA can be applied [14].

### Perturbation & observation method

The mainly used method for MPPT is P&O. P&O method algorithm exercises simple feedback arrangement and tiny measured parameters. In this method, the module voltage is periodically given a perturbation and power output is compared with that at the previous perturbing cycle. This perturbation causes the power output of the solar module varies. If the power increases due to the perturbation then the perturbation is continued in the same direction [17]. After getting the maximum power, MPP is zero and in next instant decreases and hence after that the perturbation reverses as. When the steady state is arrived the algorithm oscillates around the MPP [14, 16].

### Bacterial foraging optimization method

Bacteria Foraging Optimization Algorithm (BFOA) is a novice to the family of nature-inspired optimization algorithms. A bacterium moves by taking small steps while searching for nutrients, is called chemotaxis and key idea of BFOA is mimicking chemotactic movement of virtual bacteria in the observation area. During foraging of the real bacteria, locomotion is achieved by a set of tensile flagella. Flagella help an *E.coli* bacterium to tumble or swim, which are two basic operations performed by a bacterium at the time of foraging. When they rotate the flagella in the clockwise direction, each flagellum pulls on the cell. That results in the moving of flagella independently and finally the bacterium tumbles with lesser number of tumbling whereas in a harmful place it tumbles frequently to find a nutrient gradient [7, 14, 19].

## Fuzzy logic control for MPPT

Fuzzy logic rules sets

E \ CE | NB | NS | ZE | PS | PB |
---|---|---|---|---|---|

NB | ZE | ZE | PB | PB | PB |

NS | ZE | ZE | PS | PS | PS |

ZE | PS | ZE | ZE | ZE | NS |

PS | NS | NS | NS | ZE | ZE |

PB | NB | NB | NB | ZE | ZE |

## Methodology adopted

_{local}for the PSO. In PSO minimum value index from the J

_{local}and corresponding bacteria’s position is termed as the local best position of particle for each bacteria. The velocity of each particle is further updated from random initial velocity to a PSO tuned velocity by using the formula given in Eq. 4.

where, *c*
_{1}
*c*
_{2} and *R*
_{1}, *R*
_{2} are initialized initially.

The chemotactic and swarming loop continues till all initialized steps are completed. In each loop PSO updates the direction of bacteria and move the bacteria into the direction of fast convergence. Reproduction steps take place for bacteria with high fitness function values. To disperse or kill the weak bacteria, a probability of 0.25 is defined as the deciding probability. If random probability is higher than it, bacteria are dispersed or vice versa. Result will be positions of bacteria with minimum fitness function output. These positions are membership function’s tuned variables for fuzzy logic controller.

Range values for input ‘E’ to fuzzy controller

Membership functions | Range parameters |
---|---|

Trapezoidal | [−inf −0.032 x(1) x(2)] |

Triangular | [x(1) x(2) 0] |

Triangular | [x(2) 0 x(3)] |

Triangular | [0 x(3) x(4)] |

Trapezoidal | [x(3) x(4) 0.032 inf] |

## Matlab model of PV grid

## Results and Discussion

^{−4}s is considered for model simulation. It is divided into three sub models each for P&O MPPT control, Fuzzy P&O algorithm control and BFO tuned fuzzy P&O MPPT control. For easy user access a block for fuzzy controller tuning is provided separately so that clear comparison between algorithms can be visualised. Modelling of all three sub blocks provided is same except MPPT control part. To check the results, initially the V-I curve and P-V curve of PV array is plotted for different radiation intensity. Figure 6 shows the curve for that and nonlinear characteristics of PV array are depicted from these. Every curve has a unique maximum point which is called maximum power point. We worked towards raising the value of this point. Note that with decrease in radiation intensity MPP point also reduces.

Values of old and new range of membership functions

Membership functions | Input (Error) | Input (change in error) | Output (derivative of error) | |||
---|---|---|---|---|---|---|

Old values | New values | Old values | New values | Old values | New values | |

NB | [−Inf −0.032 −0.016 -0.008] | [−Inf −0.032 −0.001952 −0.0007866] | [−Inf −100 -80 -40] | [−Inf −100 −2.503 −0.8948] | [−Inf 0 0.1 0.3] | [−Inf 0 0 0] |

NS | [−0.016 -0.008 0] | [−0.001952 −0.0007866 0] | [−80 -40 0] | [−2.503 −0.8948 0] | [0.1 0.3 0.5] | [0 0 0.5] |

ZE | [−0.008 0 0.008] | [−0.0007866 0 0.0001318] | [−40 0 40] | [−0.8948 0 1.043] | [0.3 0.5 0.7] | [0 0.5 0.848] |

PS | [0 0.008 0.016] | [0 0.0001318 0.000451] | [0 40 80] | [0 1.043 2.603] | [0.5 0.7 0.9] | [0.5 0.848 0.8499] |

PB | [0.008 0.016 0.032 Inf] | [0.0001318 0.000451 0.032 Inf] | [40 80 100 Inf] | [1.043 2.603 100 Inf] | [0.7 0.9 1 Inf] | [0.848 0.8499 1 Inf] |

*W*/

*m*

^{2}for 4 s and 800

*W*/

*m*

^{2}for next 1 s. Since DC voltage is the evaluation parameter for the stability of the PV grid model. The PV array output power by three methods is plotted in Figs. 10 and 11. The generated power is highest by our proposed method amongst all three with a sharp dip at 4 s time as irradiation is decreased from 1000

*W*/

*m*

^{2}to 800

*W*/

*m*

^{2}.

## Conclusions

We analyzed the simulation of three methods of control: P&O and fuzzy P&O controllers and BPSO tuned fuzzy P&O controller and compared the obtained simulation results, by subjecting the controlled system to the same environmental conditions. Results revealed that the generation of 99.71 MW of power from 66 parallel connected and 5 series connected PV cells with BPSO fuzzy P&O controller whereas fuzzy P&O controller and P&O controller has generated just 99.56 MW and 56.228 MW of power, respectively. This also shows that the time response of the photovoltaic system reduces to perturbations and insures the continuity of the operation at the time in response to the continued maximum power point. It also eliminates the fluctuations around MPPT. Simulation results also proposed BPSO fuzzy P&O controller is more effective as compare with P& O and fuzzy P&O system.

## Nomenclature

*CE* change in error

*DC* duty cycle

*E* error

*k* time

*P*(*k*) Output power of PV panel

*P*(*k-1*) Output power of PV panel

*V*(*k*) Voltage of PV panel

*V*(*k-1*) Voltage of PV panel

### Future scope

The controller’s results can be compared to other methods of control such as the use of neural networks controllers to optimize the PV boost converter.

## Declarations

### Acknowledgment

The authors acknowledge help for this work from Er. Naveen Vashisth to prepare some steps in algorithm used.

### Authors’ contributions

VD carried out research work related to the photovolatic array, participated in the problem formulation, suggested the methodology adpoted, also participated in the formation of algorithm by using MATLAB and drafting of the manuscript. KKP participated in the algorithm designing, simulation work and analysis. PS participated in the study and performed the MATLAB based analysis. NK participated to develop methodology adopted and helped to draft the manuscript. All authors of this research paper have directly participated in the planning, execution, or analysis of this study. All authors of this research paper have read and approved the final version submitted.

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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