1. Introduction
In recent years, the development of renewable energy has played a high profile as it helps reduce the use of fossil fuels, mitigates the greenhouse effect, and reduces air pollution. Among them, the photovoltaic power generation system has the advantages of no fuel consumption, low maintenance cost, and environmental protection, which expands its market share year by year. However, the limitations of the photovoltaic power generation system include low conversion efficiency and the significant effect of the maximum output power point influenced by the environment. In order to overcome these problems, it is necessary to develop MPPT control technologies to enhance efficient energy conversion. Most MPPT control strategies perform well under stable weather conditions. However, when the photovoltaic power generation system is installed in a cloudy area with a rapid irradiance fluctuation due to unstable weather conditions, the MPPT controller may not be capable of handling the mentioned irradiance even if there is enough insolation. This limits the application and development of the photovoltaic power generation system accordingly. In order to solve this problem, it is important to develop new MPPT algorithms with good transient responses. In addition, when the photovoltaic module array is partially shaded, there will be multiple peaks presented in its output P–V characteristic curve, resulting in multiple local maximum power points (LMPPs). Conventional MPPT technology has difficulties in searching the GMPP because searching stops when any peak is reached, degrading the tracking performance of the photovoltaic power generation system. In addition, as shading is common for large photovoltaic power generation systems, it is necessary to develop a new MPPT algorithm that can quickly and accurately find the GMPP even when shading occurs. In order to fully grasp the significant business opportunities of photovoltaic power generation systems and to expand the market of renewable energy-related industries, it is important and urgent to develop a new MPPT method with good transient responses and the ability to search for the best solution in the whole area. Based on this, it is very important to develop an intelligent MPPT algorithm with fast tracking speeds, simple architecture, low cost, high accuracy, and low energy loss for photovoltaic power generation systems under shading conditions.
A photovoltaic power generation system is composed of a photovoltaic module array, a power conditioner, and a transmission and distribution system, wherein the power conditioner is also capable of tracking the maximum power point [
1,
2,
3,
4]. Due to the output power of a photovoltaic module array varying based on the intensity of insolation and temperature, photovoltaic module arrays shall be controlled by the maximum power point tracker, to ensure the maximum power delivered by photovoltaic module arrays regardless of insolation or temperature.
Based on different conditions of insolation and ambient temperature on the photovoltaic module array, there will be corresponding power–voltage (P–V) characteristic curves generated accordingly. Currently, there are many traditional maximum power point tracking methods [
5,
6,
7] applied in power conditioners, in which perturbation and observation (P and O) [
6] and power feedback [
7] are most widely used. The perturbation and observation method is characterized by a simple structure, fewer required parameters, and a low circuit cost. It will change the output power by continuously applying a fixed perturbation and determines the perturbation direction by comparing the output power before and after the change until the maximum power point is tracked. Unfortunately, power is lost easily during such a tracking process, so there will be a trade-off between tracking speed and the step size. On the other hand, the power feedback method makes logic decisions based on the variations in output power and voltage of photovoltaic module arrays, and it determines whether the photovoltaic module arrays are working at the maximum power point by calculating the ratio of the output power to the output voltage. When the slope of power-to-voltage is not equal to zero, it will adjust the output voltage by either increasing or decreasing until the zero slope is obtained. The power feedback method can improve the oscillation issue around the maximum power point and reduce the power loss observed in the perturbation and observation method; however, considering its drawbacks, it is impossible to make a precise measurement on the sensing elements in the real circuit, so it is unlikely to operate at the zero slope.
When the photovoltaic module array is shaded or failed, there will be more than one maximum power point (MPP) observed in the power–voltage characteristic curve of the photovoltaic module array. However, only the local maximum power point (LMPP) can be tracked by the traditional maximum power point tracker, but not the global maximum power point (GMPP) [
8,
9].
In recent years, many scholars have proposed various intelligent maximum power point tracking methods [
10,
11,
12,
13,
14,
15,
16,
17] in response to such multi-peak values caused by some shaded modules in the photovoltaic module array [
18]. The most popular algorithms include ant colony optimization (ACO) [
11], artificial bee colony algorithms (ABC) [
12], and particle swarm optimization (PSO) [
13,
14]. Ant colony optimization [
11] is characterized by fewer parameters and a simple structure, but its searching speed is slow. As a probabilistic algorithm for optimizing routes, it imitates the foraging habits of ants, leaving pheromones along the routes to guide those ants behind. Because more pheromones will remain in shorter foraging routes, those ants behind can determine their foraging routes based on the pheromone concentration, therefore saving time spent in random search. On the other hand, the artificial bee colony algorithm [
12] works by the separation of duties in a bee colony, wherein worker bees, responsible for finding food sources, transmit information of food size and direction through dancing to increase the yield of food, while onlooker bees collect all information to guide the worker bees to choose the best collection routes. Although fewer parameters are required and the convergent speed is faster in the artificial bee colony algorithms, the tracking speed and stability are both affected by the number of scout bees, leading to a longer tracking response time. For particle swarm optimization [
13,
14] originating from research on the predation behavior of birds, it is based on the information sharing among individuals in the swarm, making the movement of the entire swarm evolve from disorder to order during the solution space to obtain the optimal solution. The PSO algorithm proposed in reference [
13,
14] does not use a complex calculation process and expensive hardware equipment, but treats the partial shading of the photovoltaic module as a mathematical problem and finds the optimal solution through the mutual traction and improvement between particles, thereby achieving the search for the global maximum power points. Compared with other evolutionary algorithms, the PSO method only needs few evolutionary swarms, but it is easy to obtain regional solutions instead of accurate search results. In the firefly search algorithm proposed by Sundareswaran, when the behavior where the firefly with weak light follows the behavior of the firefly with strong light is simulated in searching for the GMPPs, it considers the voltage point of each sample as the light emitted by the firefly, thereby updating the voltage operating point continuously until the MPP is found [
15]. However, when the photovoltaic module array is partially shaded, the traditional firefly search algorithm will be trapped in the LMMP during tracking and fail to track the GMMP. In addition, some scholars have proposed MPPT technology based on artificial neural networks. For example, Gowid et al. used open-circuit voltage, short-circuit current, irradiance, and fill factor as input parameters for artificial neural networks (ANNs), and voltage and current at the MPP as output parameters [
16]. Although this method can track quickly with great accuracy, it requires an additional irradiance meter and cannot provide the correct fill factor. On the other hand, Lin et al. used the voltage, current, and temperature at the current operating point as the input of the ANN, and used the voltage of the MPP as the output [
17]. Although it can effectively reduce the number of input parameters, it is still difficult to apply to the actual photovoltaic power generation system due to complicated equations caused by too many hidden layers.
Based on the above reasons, an improved cuckoo search algorithm [
19] for tracking the maximum power point of a photovoltaic module array with some modules shaded or failed is presented. It has the advantages of few parameters, simple structure, and easy-to-understand principle, as well as a shorter tracking time by automatically adjusting its step factor. In this paper, an improved cuckoo search algorithm is evolved from traditional ones, wherein its maximum power point tracker has a better tracking speed response and steady-state performance even when the characteristic curve of the photovoltaic module arrays presents multi-peak values due to the shading or failure of some modules. The research results of this paper can be further used to estimate the power generation loss of the photovoltaic module array under different shading conditions in the future and its long-term power generation and evaluate the sustainable economic efficiency photovoltaic power generation system under shade [
20].
This paper is divided into five sections. The first section is an introduction to the composition of photovoltaic power generation systems and a briefing on the existing conventional MPPT method and intelligent MPPT method, as well as their advantages and disadvantages. The second section describes the shading characteristics of the photovoltaic module array and the P–V output characteristics curve when some modules are shaded. In the third section, we first introduce the operating principle of the traditional cuckoo algorithm and its iteration formula, and then explain the improvement strategy of the improved cuckoo algorithm proposed in this paper for the iteration formula. In the fourth section, Matlab software is used to simulate the MPPT of the photovoltaic module array under different shading conditions based on the traditional cuckoo algorithm and the improved cuckoo algorithm. The simulation results are used to compare the tracking speed response and stability performance of the proposed improved cuckoo algorithm and the traditional cuckoo algorithm. Finally, the study’s conclusions are presented in the fifth section, and future research directions are discussed.