1. Introduction
The photovoltaic system comprises a photovoltaic module array and a power conditioner that perform maximum power point tracking (MPPT). The power output of a photovoltaic module array is influenced by environmental factors, such as irradiance and temperature changes. Therefore, a photovoltaic module array must be controlled with a maximum power tracking controller, which enables the array to continue to yield maximum power output irrespective of variations in solar radiation and other environmental factors.
Several conventional maximum power point trackers are currently applied in commercialized power conditioners. Among them, the most commonly used ones are perturbation and observation (P&O) trackers [
1] and power feedback trackers [
2]. P&O trackers continuously increase regular perturbations to adjust the power output while comparing the current power output with the pre-adjusted power output until the maximum power point is determined. Advantages of P&O trackers include a simple structure and low electrical network cost. However, due to the effect of continuously increasing perturbation, the power output oscillates around the real maximum power point. Power feedback trackers detect the output voltage and power output of photovoltaic module arrays. To determine whether the photovoltaic system works at its maximum power point level, the rate of change of the power output is calculated in relation to the output voltage. When the rate of change is nonzero, the output voltage is increased or decreased until a zero rate of change is obtained. In power feedback, the problem of oscillation around the real maximum power point occurring with P&O is improved and power loss is avoided. However, the cost of power feedback controllers is higher than that of P&O controllers because accurate sensing elements are required to guarantee the precision of power feedback tracking.
In recent years, the optimization technology of solar energy harvesting systems have been developed and widely used. In Reference [
3], the proposed maximum power point tracking (MPPT) algorithm is based on the use of a negative feedback control loop and the proposed approach avoids the need for additional hardware, such as voltage or current sensors, microcontrollers, etc. Therefore, this method is particularly amenable to hardware-efficient implementation. However, this method is only used in low power systems, and in the case that the PV module is not shaded. An improved 0.8
Voc-model-based global maximum power point tracking (GMPPT) method based on the shading information is proposed in Reference [
4]. The location of the GMPP is determined directly by the shading rate, as a result the proposed method omits the comparing procedure of the traditional 0.8
Voc-model-based method. However, the detection method of shading rate needs to install additional switches, so it will increase the cost of the whole system. On the other hand, it will also reduce the stability of the system. The method is unique in achieving maximum output power by cross-layer optimization of poly-silicon solar cells and power converter circuits is proposed in Reference [
5]. This method can improve the output power of the solar energy harvesting system by 16%, but it can only be applied to solar cells, not the PV module array system. An analytic solution for solar energy harvesting embedded systems is first proposed in Reference [
6], which ensures uninterrupted operation at a maximized minimum utilization. Although the proposed algorithm is applicable to any harvesting source for presuming an appropriate energy estimator, it cannot be used in the maximum power point tracking for photovoltaic system.
Under shading or malfunction conditions, the output power–voltage (P–V) curve of a photovoltaic module array exhibits multi-peak characteristics [
7]. A local maximum power point rather than a global one may be obtained under shading or malfunction conditions if conventional MPPT techniques are applied. Scholars have developed various intelligent MPPT techniques for application in photovoltaic module arrays that are shaded or malfunctioned. The most commonly used techniques include gray wolf optimization (GWO) [
8], ant colony optimization (ACO) [
9], artificial bee colony (ABC) [
10], adaptive velocity particle swarm optimization (AVPSO) [
11], and modified particle velocity-based particle swarm optimization (PSO) [
12]. GWO is a swarm intelligence algorithm inspired by the hunting behaviors of gray wolves. The algorithm involves a hierarchical division of gray wolves into four strata. Hunting tasks, such as leading, encircling, attacking, and protecting, are assigned to gray wolves of different hierarchies to perform global optimization. The advantages of GWO include a simple structure and the requirement of only few parameters. However, the optimization process is at risk of falling into a local optimum. ACO is an optimization algorithm that performs optimal search by imitating the habitual behaviors of ant foraging. Ants release pheromones on their path to guide ants coming after them. The shorter the paths leading to the food site, the higher the amount of pheromones released, and vice versa. The ants that follow select the path to the food site according to the quantity of pheromones released. ACO requires few set parameters and possesses a simple structure. However, it requires a long time for searching and its speed of convergence is low. ABC imitates the job division of bees and divides bees into scouts, employed bees, and onlookers. The scouts randomly select directions in seeking food resources and convey messages of the found resource through dance. These messages are followed by employed bees, who are in charge of collecting food. Onlookers integrate all the messages and direct the employed bees in selecting the best collection path. ABC requires few parameters, and its speed of convergence is fast. However, because the speed of tracking and the algorithm stability are influenced by the number of scouts, ABC might require a long time for response tracking. AVPSO and modified particle velocity-based PSO are intelligent algorithms improved on the basis of PSO. Modified particle velocity-based PSO can alleviate the problem of falling into a local optimum, which enhances its stability. However, it has disadvantages, such as a long tracking time. In modified particle velocity-based PSO, particles are tracked in a single direction rather than being blindly tracked. However, the algorithm has disadvantages, such as complex calculations and requirement of additional iterations.
Because of the aforementioned reasons, a teacher-learning-based optimization (TLBO) algorithm [
13] was used in this study as the logic for MPPT control on the modules of a photovoltaic module array in shading or malfunction conditions. The advantages of this algorithm include few set parameters, a simple structure, and easy-to-understand principles, as well as scatter search and memory characteristics similar to those of ACO. Therefore, the TLBO algorithm is suitable for continuous range search. However, it has the disadvantage of a long tracking time due to its fixed teaching factors. This drawback was improved through an improved TLBO algorithm [
14] extended on the basis of an existing TLBO algorithm proposed by the author previously. An increased tracking speed and precision could be obtained by the maximum power point tracker with the improved algorithm when a multi-peak phenomenon was observed in the characteristic curve of the photovoltaic module array due to some modules operating under shading or malfunction conditions. But, in this method, only two random students learn from each other, rather than the students in the whole class learn from the students with the best grades. Therefore, this method does not have the ability to automatically adjust teaching factors, so it does not achieve the best performance.
Because the computation process of the existing maximum power point tracking method described above is very complex or it may take a long time to track the maximum power point, this paper proposes an improved TLBO algorithm, which makes the computation process simple and can shorten the tracking time.
In this paper,
Section 2 described the P–V and I–V characteristic curves for a PV module array under normal and shaded module conditions. Then,
Section 3 described briefly the algorithm and implementation procedure of the proposed improved TLBO method to track the global maximum power points when applied to multi-peaked output characteristic curves of PV module arrays. The simulation results of a conventional TLBO algorithm, TLBO algorithm proposed in Reference [
10] and the proposed TLBO global MPP tracker under shaded or malfunctioning conditions is presented in
Section 4. Finally, in
Section 5, some experimental results are made to demonstrate the effectiveness of the proposed MPP tracker.
2. Malfunction and Shading Effects of Photovoltaic Module Arrays
When some modules of photovoltaic module arrays are shaded, their total power output decreases due to their reduced output voltage and electric current. When some modules malfunction, they can form circuits through the bypass diode, to allowing other modules continue to function appropriately and thereby maintaining a certain amount of power output for the module array. Moreover, the modules with low output voltage can be protected from the current intrusion of other normal modules by applying a blocking diode. Thus, damage to the photovoltaic modules can be avoided. The photovoltaic modules used in this study were SANYO HIP 2717 photovoltaic modules [
15]. Their electrical parameter specifications are presented in
Table 1 [
15]. Solar Pro [
16] software was used to simulate the output characteristic curves of the modules.
Figure 1 and
Figure 2 display the simulated P–V and current–voltage (I–V) characteristic curves of a photovoltaic module in the standard test condition (air mass: 1.5, solar irradiance: 1000 W/m
2, and temperature: 25 °C) without shade or with diverse percentages of shade.
Figure 3 illustrates the P–V and I–V characteristic curves of a photovoltaic module array with a four series and one parallel structure and one module under 30% shade. Because the photovoltaic module array is made up of four photovoltaic modules in series, one of which is shaded by 30%, and the rest is not shaded. Consequently, there are two kinds of irradiation conditions, it will appear two peaks in the P–V characteristic curve of a PV module array. The rest of the situation, and so on. Therefore, a multi-peak phenomenon and a considerable decrease in the maximum power output can be observed in the P–V characteristic curve.
Figure 4 illustrates the P–V and I–V characteristic curves of a photovoltaic module array with a four series and one parallel structure and one module that malfunctioned. Due to the malfunction of the module in question, no output current was observed. Moreover, the current outputs of the normal modules flowed to the load through the bypass diode of the malfunctioning module. Thus, a normal operation of the photovoltaic module array could be maintained; however, the total power output of the array was equal to the power output of only three modules.