Abstract
With the maturation of nonlinear systems, considerable endeavors have been made to provide valid and high-speed controllers to supervise superior and more complex systems. Artificial intelligence has been remembered as the head topic among designers in the last decade. One of the popular control techniques is fuzzy logic, which is known to provide a controller that simulates the behavior of an expert operator. On the other hand, due to the necessity of change in human energy sources and the popularity of solar energy, attention to the greatest utilization of this category of green resources has significantly increased. Maximum power point tracking (MPPT) in solar systems is a headed topic, with innovative methods being presented every day despite numerous articles. However, the less discussed topic is the choice of a fuzzy inference system. In this article, the two classes of Mamdani and Sugeno are discussed to introduce the best controller for extracting more power from a solar system by implementing both types and gaining an understanding of their differences. In addition, the influence of the number of input membership functions on the controller performance is investigated. Therefore, two different input membership functions are given to each fuzzy system model. It should be noted that fuzzy system setup has been done by genetic algorithm to respond to the mortal desire to automate various processes, which is a subset of artificial intelligence. Accordingly, four different fuzzy systems have been designed and implemented on a solar system. The results were tested and summarized in various radiations in MATLAB Simulink.
1. Introduction
Several governments have pushed to promote green energy in recent years, and numerous efforts have been undertaken to eliminate fossil fuels from the world’s energy portfolio [1]. Renewable resources come in various forms, but specific sources best suit each geographical zone. Nevertheless, solar-based resources are available in most areas as the superior option, and associated investment is economically viable for governments [2]. With the increasing expansion of solar systems globally in domestic and industrial sectors, much emphasis has been dedicated to efficiency [3]. Maximum power point tracking (MPPT), based on the “maximum power transfer theorem” in electrical circuits, is a popular method for reaching this critical goal. Accordingly, MPPT is placed between the panel and load, including a converter and controller. The controller sets the converter’s duty cycle to equalize the panel’s resistance and the load [4]. Many attempts have been made to modify this supplementary part; for example, in [5], various converters and electric circuits are presented. In [6], the emphasis is on the control design.
Since the controller’s role is pivotal, various solutions have been proposed and improved. Generally, controllers seek to minimize the voltage-power graph’s slope to zero, achieving maximum power and enhancing system efficiency [7]. MPPT controllers are classified into three main categories assessing their operational process, structure, and employed algorithm.
The first type is offline controllers, the most basic designs and often operate based on the precollected data. The look-up table approach is a well-known example in which the voltage of the panel or cell is measured to understand the system state, and the duty cycle value is derived by referring to past data [8]. Due to its strong dependence on previous data, a vast database is required for proper operation. So, it necessitates data collection in varied climate cases, which is complex and time-consuming, and consequently, it needs a large amount of memory. Furthermore, while increasing the controller’s accuracy with more available data, this circumstance slows the decision-making process. So, offline approaches do not provide satisfactory performance [9]. Other well-known methods include the Temperature algorithm, Open Circuit Voltage Technique [10] a Short Circuit Current Technique [11].
Online controllers, the second category, find the suited converter’s duty cycle with trial-and-error, which is their chief drawback. Perturb and observation is the widespread method used despite novel and innovative practices because of their low production costs [12, 13]. This method increases the amount of voltage with a specific value at the first step, and then the amount of power is measured and compared to its previous value. If a rise in voltage results in an increase in power, the trend will be maintained; otherwise, the voltage will fall. While using these algorithms, three principal fractures should be considered: first, significant available fluctuation negatively influences the system’s efficiency and stability. Second, it may get stuck in local minima while achieving the optimal operating point. Third, the approach’s accuracy is proportional to the number of adjustments to discover optimal values. or feedback control [14], incremental condition, and modified incremental conditions are other samples of this category.
The last category includes modern control methods that are both precise and swift [15]. This category, known as intelligence controllers, initially consisted of novel controlling techniques such as Fuzzy Logic Controllers, Artificial Neural Networks (ANN), and sliding mode controllers. The most common among developers are fuzzy logic systems. In reference [16], the most common techniques in tracking the maximum power point are reviewed, and a fuzzy logic-based controller is one of them. They can monitor the system status, assess the condition, and execute the appropriate commands to attain the intended objective and remain stable, just like an expert operator. Unlike others, they are not database-dependent and have a minor dependency on system dynamics. In other words, they act as a human operator, optimally controlling the system without the requirement to understand its dynamics [17]. They operate based on the system’s state, which is assumed to be input. The decision is then made according to a rule base, and the relevant instructions are enforced as the output. These advantages motivate us to investigate the fuzzy controller in this study [18].
The complexity of the modern controllers’ design is crucial in their development. An artificial neural network, for example, must be trained [19]; designing a sliding mode controller is a chattering phenomenon and complex design [20], and fuzzy controllers require the presence of an expert as a reference for replicating the reasoning and decision-making process [21]. Because this technique directly influences the controller’s performance, experts combine these powerful controllers with refined algorithms to make the created controllers more precise and faster. So, another group called optimized controllers is introduced, which includes innovative techniques and metaheuristics algorithms such as ant colony (ACO), bee colony (BC), grey wolf (GWO), and particle swarm optimization (PSO). In [22], a fuzzy logic controller is presented, and the rule base is designed with the help of an ACO. Also, a remarkably matched combination of grey wolf optimization and sliding mode controller is designed. Although they can manage the system individually, researchers combine them and produce hybrid controllers to increase the accuracy and simplify the design of the intelligence group [23]. For example, we may refer to GWO-P&O [24], and PSO-fuzzy [25] approaches.
The topic that has yet to get more attention in the literature study on the various ways of creating fuzzy systems is the type of fuzzy inference system (FIS). A Mamdani-type fuzzy inference system is used in the majority of investigations. An experienced designer, heuristic algorithms, or combinations develop the rules base after partitioning the input and output domains into a specific number of subdomains. Thus, the best design is chosen to regulate the PV system. However, there are two types of fuzzy logic systems: Mamdani and Sugeno. The sole difference between these systems is their defuzzification process.
Mamdani fuzzy inference was initially proposed to develop a control system by synthesizing a set of linguistic control rules collected from experienced human operators. Mamdani systems are well-suited to expert system applications where the rules are developed from human expert knowledge since their rule bases are more intuitive and easier to understand. Each rule’s output is a fuzzy set produced from the FIS’s output membership function and implication technique. These fuzzy output sets are aggregated into a single fuzzy set using the FIS’s aggregation mechanism, and a final crisp output value is applied to the system through the defuzzification process [26].
Sugeno fuzzy inference employs singleton output membership functions that are either constant or a linear function of the input values. A Sugeno system’s defuzzification process is more computationally efficient than a Mamdani system because it employs a weighted average of a few data points rather than computing the centroid of a two-dimensional area. Because each rule is linearly dependent on the input variables, the Sugeno approach is excellent for acting as an interpolating supervisor of several linear controllers that will be applied to distinct operating states of a nonlinear dynamic system [27]. For example, a PV’s performance might vary dramatically depending on the light intensity and the temperature. Linear controllers, while simple to implement and adaptable to any weather situation, must be updated frequently and seamlessly to keep up with the changing state of the PV system. Sugeno inference systems are adapted to smoothly interpolating the linear gains applied over the input space; they are a natural and efficient gain scheduler [28], while the output surface of Mamdani systems is discontinuous. As a result, while Sugeno systems, unlike Mamdani systems, lack a clear external description, they perform well with linear, optimization, and adaptive techniques. It also adapts itself well to mathematical analysis. Considering the conducted study and obtained results, in this study, two main features in designing a controller for updating the duty cycle of present converters in the MPPT section are analyzed. First and most importantly, the performance of fuzzy-Mamdani and fuzzy-Sugeno is compared to pave the way for picking the best type used in PV systems. Secondly, the influence of input membership functions is examined by suggesting 3 and 5 membership functions for each. Consequently, four initial controllers are designed and, in the next stage, are optimized by employing a genetic algorithm.
2. Photovoltaic System
In recent years, the growing desire of countries to use solar systems has led to significant advances in this industry. Day by day, the limitations of the panels are reduced, and as a result, the efficiency in converting the received irradiations into electrical energy has increased. On the other hand, artificial intelligence and new controllers have significantly increased PV systems’ efficiency. In a conventional solar system, there are three main parts (Figure 1):
2.1. Photovoltaic Panel
Solar panels are devices that can convert photons received from the sun into electrical energy. Panels come in various sizes and types depending on the installation location and the type of connected consumers. However, the general energy production process is the same in all of them. The generated power is highly dependent on environmental factors such as the amount of partial or total shadows on the panel, temperature, and radiation intensity. Therefore, besides paying attention to the required power, geographical location, weather conditions, and physical factors such as trees and buildings surrounding the PV system that may cause shadows on the surface of panels should be considered.
It should be noted that each specific temperature and radiation in which the panel is placed leads to a unique maximum power, and the quantity of generated power is also specific for each voltage and current of the panel terminals.
Under standard conditions, these values are obtained with testing panels in the factory, and they are conveyed to customers in datasheets in the form of P-V and I-V diagrams known as panel characteristics. An example of these graphs is given in Figure 2, which is related to the ENVIRO-PVM6/PVC-75/100/150/250/315 panel.
2.2. MPPT
MPPT stands for maximum power point tracking and refers to how the greatest amount of power can be extracted from the panel in any environmental situation (shadow, temperature, and radiation factors). There are various approaches to achieving this goal, but the general process is establishing the maximum power transfer theorem, one of the fundamental rules of electrical circuits. According to this principle, maximum power transfer from the source to the load occurs when the load and the source resistances match. The maximum power theorem is an efficient way to ensure maximum power feed to the load. In photovoltaic systems, a converter and a controller are used for this purpose.
2.3. Boost Converter
The equivalent circuit of a boost converter is shown in Figure 3.
This circuit uses an inductor, capacitor, diode, and a switch (MOSFET or IGBT) to increase the voltage on the left by a certain amount and transfer it to the right side where the load is located. It should be noted that the input can be considered a source with a constant current because the presence of the inductor results in a constant input current. Also, Pulse-Width Modulation (PWM) is responsible for turning the switch ON and OFF, which due to the performance limitations and complexity of the structure of the frequency-based type, PMW based on time is usually used.
Depending on the condition of the switch, two operating modes are defined for the converter: (1)ON
When the switch turns on (Figure 4), the whole current passes through the inductor and charges it. Also, the capacitor is being discharged by the load. The diode plays the role of isolating by preventing the current flow from the right side to the left of the circuit, so these two parts are isolated. (2)OFF
In the second mode, the switch is open (Figure 5).
The source current and the current generated by discharging the inductor, after passing through the diode, are divided between the capacitor and the load until the capacitor is charged and the inductor is discharged. After charging, the capacitor converts into an open circuit stage, and the entire current is transferred to the load; also, the inductor is considered a short circuit after discharge.
In a boost converter, the amount of voltage increase can be controlled by the time allocated to each of the above modes, called the duty cycle (D), and is obtained by,
In each system, there is a control section in order to determine the appropriate value of D.
2.4. Controller
Various methods that have been introduced so far for determining the duty cycle value can be divided into three categories: (1)Offline Algorithms. These algorithms are among the simplest and most rudimentary methods. The process is that D values for several temperatures and radiation are stored in a database, and the controller determines the appropriate D with available information. However, due to the limited amount of data, most situations are interpolated, which is inaccurate. Therefore, low accuracy and dependencies on extensive databases make these methods inapplicable.(2)Online Algorithms. In this category of algorithms, we see a significant increase in sensors, which with the information obtained from these sensors, the system status is determined and complex algorithms determine the value of D. Despite the accuracy of the system in detecting the situation at any time, the overall process is time-consuming, and also based on the test results, the system performance at low voltages is not acceptable.(3)Artificial Intelligence. Intelligent controllers are among the novel methods and have shown acceptable speed, accuracy, and performance. It should be noted that using these algorithms requires sufficient and accurate knowledge of the system. The controller used in this research is the integration of artificial intelligence and genetic algorithms, considered intelligent controllers.
2.5. Load
The loads adjoined to the solar panels are no longer restricted to common applications and low-voltage types of equipment. With the expansion of smart cities and smart power grids, solar panels are used in diverse sectors. In this study, to emphasize the attention on the performance of controllers, a simple resistor is used as the consumer.
3. Proposed Controller
Due to modern technology and society’s passion for high speed and accurate systems that can regulate advanced processes with minor errors, the controllers are expanding at an incredible rate. Therefore, we witness novel techniques to boost the performance of systems every day and needless from human observation and leadership. Fuzzy logic systems are among the most trustable options used in various sections. According to this renown, it is selected as the central controller in this study. Despite exactness and speed, flexibility in the design of every single phase is another feature that makes this controller flourish. The critical sections and the reason for considering that type of structure for the proposed controller are mentioned as follows, and the general layout of a fuzzy logic system is presented in Figure 6.
3.1. Fuzzy Inference System
The first phase in designing a fuzzy controller is choosing the appropriate inference system. Particularly, they are bifurcated in Sugeno and Mamdani. There is no clear way to peaking the appropriate type except considering the previous experiences in designing such controllers and sufficient wisdom of the system. Consequently, both types have been dissected in this study, and the outcome is presented in the last section.
4. Mamdani Fuzzy Controller Design with 9 Rules
After reviewing and comparing the systems presented in the previous section, considering the obtained results, the fuzzy controller is designed to be applied to metaheuristic algorithms.
This controller is of the Mamdani type with two inputs equal to the slope of the voltage-power diagram and its changes, which are stated in the following equations:
Looking again at the power characteristic, it can be seen that in spaces far from the peak, the slope of the graph is constant on both sides; while approaching the peak, the slope changes and approaches zero.
As shown in Figure 7, the main components in the Mamdani fuzzy controller are the fuzzification part, the defuzzification part, the rule base, and the inference engine.
The proposed system consists of two inputs with membership functions shown in Figure 8, which represent the slope and slope changes of the graph and are expressed as follows:
Normalization makes it possible to achieve the appropriate behavior simply by optimizing the coefficients K1 and K2, which reduces the computation cost and causes more effortless adaptability in the case of any change in panels. In other words, the controller does not depend on the system. In other words, if the inputs are out of the suitable range for control, by minimum changes and resetting the above coefficients, it will be compatible with the new system.
The output of the controller is a number in the range of 0-1, which is applied to a time-based phase modulation (PWM) that produces pulses to fire the IGBT of the converter. On the other hand, the produced pulses determine the ON and OFF periods of the IGBT. The membership functions for output are presented in Figure 9. Figure 10 shows the MPPT section in MATLAB/Simulink.
5. Optimization of FLC
As mentioned earlier, in some articles, the system has five membership functions for each input and output [29]. The purpose of this article is to simplify the controller as much as possible. So the number of membership functions has been reduced to three. Also, with the assumption of membership functions as fixed and symmetric, the optimized parameters are only nine fuzzy rules and two input coefficients (K1 and K2).
The simplification of the cost function is also done so that instead of zeroing the slope of the P-V diagram, which requires more calculations, the output power is employed directly (Equation (4)). If the cost function assumes the sum of the square of the control signal, which is denoted by Y and is equal to the inverse of power, Equation (5) is obtained for the cost function. Also, the control signal is multiplied by 100 to aggrandize it (20).
5.1. Input and Output Parameters
The next phase is determining the number of inputs and outputs. The parameters that influence the decision-making process and the way controllers rule the system with their consideration of them must be specified as inputs, and orders for regulating the system and reaching the desired goal are considered as outputs. In a PV system, the final goal in maximum power point tracking is to find the pick point of the P-V characteristic of the connected panel by changing the converter duty cycle and resetting the duty cycle in case of a change in environmental conditions. So, inputs are the generated power and voltage that the maximum power point (MPP) changes according to them, and output is the duty cycle. So, here, the inputs are as follows:
5.2. Specify Input and Output Membership Functions (MFs)
5.2.1. Input MF
After acquiring the required information about each input and output, membership functions should be designed. In a fuzzy system, inputs that are crisp values and incomprehensible to the fuzzy logic, are first obtained and converted to the degree of belonging to one or more membership functions (MFs). This step, called fuzzification, habilitate the inputs for argument processing and analysis. This step is the same in both Sugeno and Mamdani inference systems. There are diverse types, and the wide spreads are triangular, Gaussian, z-shape, and sigmoid. In this study, all of the membership functions are of triangle type and in the range of -1–1. In order to investigate the effects of the number of membership functions on the performance of fuzzy systems, for each inference system, two types are considered: (a)three membership functions for each input(b)five membership functions for each input
Therefore, a total of 4 fuzzy controllers have been designed. The related plots are illustrated in Figures 11 and 12.
5.2.2. Output MF
In designing a fuzzy controller, the first difference is defining the output membership functions. In a Mamdani system, the output-MF is a degree of one or more membership functions; Therefore, membership functions are similar to input-MF, and the same process is repeated. In this design, 9 output MFs are considered for both Mamdani systems with 3 and 5 input MFs (Figure 13). The process of the Mamdani inference system is presented in Figure 14.
Nevertheless, in Sugeno inference systems, there are no observable functions, and instead, constant numbers or linear equations of input values are defined. This change allows designers to take advantage of a different way of reasoning and determining the appropriate output and provide them with more flexible controllers. In this type, the final output is equal to the weighted average of all rules’ outcomes and is presented in the following:
Consequently, each rule generates two values: (i)—Rule output level, which is either a constant value or a linear function of the input values:
Here, andare the values of input 1 and input 2, respectively, and , , and are constant coefficients. For a zero-order Sugeno system,is a constant (). In this design, is a constant number. (ii)—Rule firing strength derived from the rule antecedent,
Here, and are the membership functions for inputs 1 and 2, respectively.
The output of each rule is the weighted output level, which is the product of and .
The process of the Sugeno inference system is presented in Figure 15.
5.2.3. Rule Base
The last and most critical part of creating a fuzzy system is representing the “if-then” rules. This section clarifies each input value and what the output should be. This part must be able to conduct equivalently to the brain of an expert; accordingly, it is mainly characterized by a professional who is vastly acquainted with the system and how it should react in the face of diverse circumstances. Recently, optimization algorithms have been employed to do this obligation, and in this study, a Genetic algorithm is used. Therefore, initial versions of the rule base are designed, which cannot supervise the system properly; and in the next phase, they will be updated by a Genetic algorithm.
It should be noted that if the control is to be suited, enough rules should be defined that thoroughly cover all the possible conditions. In the fuzzification, the value of each input is given to one or a combination of more than one MFs, and the rules should cover any possible combination of MFs. Accordingly, considering as the number of membership functions of the first input and for the second input, the number of rules must be equal to the following:
6. Optimization
The algorithm used to optimize the fuzzy system is called the Genetic algorithm, which is inspired by the behavior of genes in organisms and has become one of the most well-known techniques in optimization. In genetics, each individual has a series of chromosomes that make up their gene. To reproduce in a population, the parent’s genes are combined to form the child’s gene eventually. Consequently, in a genetic algorithm, each parameter that must be set is a chromosome, and the sum of the adjustable variables of the system constitutes a gene. By generating several answers for a system, one generation is created, and the next generation is the result of combining the genes of the previous generation.
In evolution, the ultimate goal is to find outstanding people who own superior genes. In addition, to create the best offspring, the genes of the principal people of the previous generation must be combined and the genes of the weakest people removed. For accomplishing this goal, a criterion is needed to define for determining superior and weak genes, which is defined as a cost function and as follows:
Also, considering the differences in the Sugeno and Mamdani types, the chromosomes are defined in two ways, which are discussed below:
6.1. Mamdani
The algorithm generates random numbers (equal to the number of rules) specified and sets each number equal to the “then” section of one of the rules as follows: where and are, respectively, equal to the number of first and second input MF and is generated natural number So, the output MFs are constant, but the allocated MF for each rule differs.
6.2. Sugeno
Generated values equal output MFs, which accept constant numbers, considering equal to the number output-MFs and P(b) is generated integer number in the range of
7. Results
The fuzzy systems debated in the previous sections are constructed with the help of the MATLAB software toolbox and are accommodated by the genetic algorithm. The optimized controllers are connected to thoroughly similar PV systems to compare the controllers’ performance extensively. The presented diagram shows the power generated by the controlled fuzzy system discussed with the proposed methods (Figure 16). During the conducted test, the value of temperature is constant and equal to 30cantograds, while the irradiation changes in equal intervals (800, 500, 1000, 900, and 600 ()).
Considering the raise period occurred in the initial interval, all controllers are showing approximately equal performance except for Mamdani-25; however, all of them reach steady state simultaneously (Figure 17).
After reaching the steady state, the performance of Mamdani-9 falls and provides the lowest power, and the fluctuations are not desirable.
In Figure 18, the irradiation change accrues, increasing from 500 to 1000 (). All controllers can greatly find the MPP; however, Sugeno-9 performed better in this process, but the Mamdani-9 could not generate as much power as others after reaching the steady state.
When radiation decreases from 1000 to 900 (), all the controllers have good power to reach a steady state. The only point is the greater number of fluctuations in Mamdani-25, which leads to a decrease in average power and thus a decrease in productivity. Nevertheless, the maximum achieved in all methods is approximately 49.7 w (Figure 19).
In the last change of radiation, which reaches , irregular fluctuations are again seen in the first controllers, but the other two controllers still have acceptable performance. We also see the same behavior of all controllers in terms of achieving a stable state (Figure 20).
By comparing the first and second intervals, it can be concluded that the performance of the first two controllers decreases at lower radiations. So, the most stable and trustworthy method is Sugeno-9.
In this section, the behavior of the controller in variable load is analyzed among several methods including ANN. To simulate this situation, a variable resistor is used instead of a fixed resistor that acts as a consumer. In the first period, it is equal to 30 ohms (0 to 0.01); in the second period, it is 40 ohms (0.01 to 0.02), and in the last period, it is 45 ohms (0.02 to 0.03). As shown in Figure 21, all four controllers can follow the changes, but as expected, the ANN cannot have the highest power, and large fluctuations can be observed. However, fuzzy-based controllers show acceptable behaviors. The output power of Sugeno and Mamdani controllers is similar. By using the mentioned controllers, there is an increase or decrease in every change of condition, whereas the FIS controller is not like this and reaches its peak.
Based on the data presented in Figure 21, it is easy to see that as the output resistance increases, the power is reduced.
8. Conclusions
Maximum utilization of solar panels and artificial intelligence are two hot topics that have attracted much attention. This article tried to achieve significant results by merging the two topics. So, four fuzzy controllers were presented and compared to achieve the maximum power of a PV system. The prototype controllers, which were designed with minimal knowledge of the system, were tuned by a genetic algorithm to discuss the magnitude of the optimization algorithms in the controller design. It was also shown that increasing membership obedience does not necessarily increase fuzzy controlling power. According to the simulation results and microscopic comparison, we can see that the Sugeno controller with three input membership functions, which was introduced in the article as Sugeno-9, showed a more stable behavior than other controllers.
Abbreviations
| MPPT: | Maximum power point tracking |
| : | Duty cycle |
| : | The period in which the IGBT switch is close |
| : | The period in which the IGBT switch is open |
| : | fuzzy input in the moment |
| : | Generated voltage in the moment |
| : | Generated power in the moment |
| : | Rule output level |
| : | Values of fuzzy input 1 |
| : | Values of fuzzy input 2 |
| , , : | Constant coefficients |
| : | Rule firing strength |
| : | membership functions for inputs |
| : | The number of membership functions |
| : | Desired power |
| Sugeno-9: | The optimized Sugeno fuzzy system with 3 input membership functions |
| Sugeno-25: | The optimized Sugeno fuzzy system with 5 input membership functions |
| Mandani-9: | The optimized Mamdani fuzzy system with 3 input membership functions |
| Mandani-25: | The optimized Mamdani fuzzy system with 5 input membership functions. |
Data Availability
Data will be available on request. For data-related queries, kindly contact Baseem Khan (baseem_khan04@rediffmail.com).
Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.