# Real Optimisation of a PV System Based on Hysteresis Controllers over Sun: Design, Implementation, and Comparative Study

Authors: Houda Brahmi; Rabiaa Gammoudi; Rachid Dhifaoui
Journal: Journal of Engineering
 (2021)

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## Abstract

This paper presents two strategies for controlling photovoltaic power based on hysteresis controllers. These regulators adjust the photovoltaic current and voltage in order to supply the load with maximum power. The regulators are designed, produced, and tested within the ERCO-INSAT research unit. The proposed structures are experienced, and the results prove the robustness of the controls and confirm their abilities to maintain op timal power in real time. We also presented the mathematical model of the photovoltaic system, a dynamic model taking into account the variation of the climatic parameters as well as the internal parameters of the models such as the series and shunt resistances. Simulation results are validated by an experimental test that confirms the effectiveness of the current and voltage controllers carried out. This simulation is already based on the use of real solar radiation and temperature scenarios recorded by a digital oscilloscope via the intermediary of the sensors. The two techniques are ensured by the use of the Dspace card to control the DC/DC converter and to implement the chosen controls.


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## Body

## 1. Introduction

Following the report published by the International Energy Agency in 2018, the global energy consumption and demand in 2030 will grow by 45%. This increase is due to the demographic development and especially the industrialization in the countries which have a number of inhabitants exceeding the two billion (China, India, etc. ) [1–4].On one hand, conventional nonrenewable resources, such as coal, oil, natural gas, and uranium, occupy almost the majority of world production of electric energy. This domination in production can cause a risk of exhaustion of resources called “fossil.”On the other hand, an environmental problem arises since this type of energy resource causes much damage to the environment such as emissions of greenhouse gases that cause the increase in pollution and global warming. Therefore, to make the supply of electricity more environmentally friendly, the exploitation of new sources of energy production called “renewable energy” is essential [5–10].One of these nonpolluting energies is photovoltaic energy. This nonexhaustible source, respecting the environment, makes it possible to produce energy through a direct transformation of solar radiation into electrical energy. This conversion is achieved through the use of solar cells also called “photovoltaic” (PV) and is mainly based on a physical phenomenon “photovoltaic effect.”The commercialization of photovoltaic energy can be in the form of panels or in the form of PV generators.The photovoltaic panels are characterized by the nonlinearity of their output characteristics which are influenced by environmental factors (temperature and illumination). To take advantage of the reliable use of this source, it is necessary to reach and use adequately the maximum of its energy [11–15].Powering a system from a photovoltaic source is among the most widely used applications and is the subject of several research works [16]. From a practical standpoint, these applications are difficult to implement.To ensure a continuous optimal operation, an adaptation between the photovoltaic source and the load is necessary. This adaptation is performed by the insertion of a static DC/DC converter which must be controlled by an optimum operating point tracking system. Different methods of maximum power extraction are proposed by the literature [17–19].In January 1968, A. F. Boehringer developed the first MPPT control law suitable for a photovoltaic energy source. This control is based on an adaptive control algorithm that keeps the system running at its maximum power point. The principle of this command is still valid, and it is now applied to other more efficient digital algorithms with an improvement in the response time and the search precision of the PPM [20].The other maximum power extraction methods are classified into three main families; the first is the family of methods based on proportionality relations which are also called “indirect or static methods.” The results developed in [21] show the very great importance dedicated to climatic factors which make it possible to determine the maximum power point. These methods are generally relative to a well-defined installation. We find the control in voltage regulation and the control in regulation current.The methods of the second family are called “high performance algorithm commands” or “direct or dynamic methods.”They use measurements of the voltage and current values of the PV panels used. Among these methods, we find the “Perturb and Observ” (P&O) method and the “incremental conductance” method. The research developed in [22–31] shows that these algorithms are essentially based on the variation of these measurements (current, voltage).There is also the family of variable structure methods. The developments presented in [32,33] show the principle of the methods. The principle of this approach consists essentially in forcing the system to reach a given surface called “sliding surface” and to stay there until reaching equilibrium.There is also the family of intelligent methods such as “'the genetic algorithm, neural network, and fuzzy logic” The advantage of techniques based on fuzzy logic is that they can work with imprecise input values and they do not need a high precision mathematical model. In addition, they can deal with nonlinearities [34,35].In recent years, the use of control by neural networks, in various fields of application, does not cease increasing because it operates from a black box which does not require detailed information on the functioning of the system [36–39].Genetic algorithms are very relevant for global structural optimization problems (problems with several constraints). As they allow great freedom in the configuration and implementation of the various processing operations [40].The work developed and presented in this article is based essentially on the establishment of a test bench for the extraction of maximum photovoltaic power. It is recommended that the bench is as complete as possible in terms of equipment and logistics control and optimization to ensure a core of research and development to enhance this type of application.The main objective of the study carried out in this work is to analyze the principle of maximum power operation based on two real hysteresis controllers and to present the prototypes of these regulators.The hysteresis regulator is commonly used in industry thanks to its sensitivity to follow references with precision. This effectiveness is proven especially on a practical level.The different works [41–43] show that this technique is based on controlling the converter so that the variations in current or voltage are limited in a band surrounding the references. Depending on the operating conditions, the switching frequency of the switches follows a random variation.Subsequently, we will proceed to the implementation of these controls techniques whose test bench consists essentially of a photovoltaic generator installed on the roof of the research unit with a maximum power of 500 W, a DC-DC converter (buck, push-pull), and a resistive load. The command part is ensured by a PC integrating a DS1104 dSpace card. The experimental part is accompanied by a simulation based mainly on the use of the two real and random scenarios of solar radiation and temperature. These scenarios are recorded via a digital oscilloscope (METRIX-OX 7104). Solar radiation and temperature are measured, first, by two sensors which are designed and produced by our research team. The experimental results presented in this work are recorded for a period of 15 minutes, which allows us to properly test the effectiveness of these two regulators.


## 2. Problem Identification

In the case where the PVG is directly coupled to the load, the operating point is the intersection between the electrical characteristic of the PVG and the load [17]. The corresponding power at this operating point is not necessarily equal to the maximum power available from the PV array (Figure 1).Figure 1
Evolution of the operating point with a direct link between the source and the load.In order to reach the maximum power point which corresponds to the optimum power generated by the PV generator, an adaptation stage must be inserted and provided with a control to ensure the follow-up of the MPP while acting in an automatic way on the duty cycle of the selected static converter.These commands are generally referred to in the literature as “Maximum Power Point Tracking” (MPPT). These techniques essentially consist in bringing each time the operating point of the photovoltaic generator to the MPP whatever the abrupt variations are in the load or the weather conditions.As a recap of the different problems of a PV system, we have the following:(i)
The strong dependence of the characteristics of a photovoltaic generator on climatic conditions.(ii)
The adaptation of the impedances between the source and the load in order to obtain an optimal operation.(iii)
The limits of use and the divergences of several algorithms for extracting maximum power.(iv)
The need for experimental validation in order to prove the effectiveness of an approach compared to others.(v)
Check and control the adapter device from current and voltage.


## 3. Solar PV System Configuration

The major drawback of the direct connection between the source and the load is the link between the power extracted from the source and an application that is often very far from the maximum power that can deliver the photovoltaic generator.So, the insertion of a static converter, continuous/continuous type, is necessary. This converter acts as an adapter between the source and the load. In order to reach the operating point which corresponds to the optimum power generated by the PV generator, the adaptation stage must be provided with a command to track the MPP while acting automatically on the duty cycle of the chosen static converter.These commands are generally named “Maximum Power Point Tracking” (MPPT). These techniques essentially consist in bringing each time the operating point of the photovoltaic generator to the MPP, whatever the sudden variations are in the load or the weather conditions [44–48].The principle of the proposed and implemented control solutions is given in Figure2. The structure is based on a push-pull converter and a buck converter.Figure 2
Structure of the study system.The interest in using this type of converter (push-pull) in this configuration is the increase of the GPV voltage. This converter operates with a gain of 20. So, we have an output voltage of the push-pull stage which is20×Vpv. Finally, the control is ensured through a buck converter and we have Vch=m×α×Vpv.The push-pull converter and the buck converter used in this system have the function of transforming the fixed resistorR into an equivalent variable one. In other words, the equivalent resistor Rβ=fα×R connected to the photovoltaic generator becomes a function value of the control variable α.


### 3.1. Modelling and Characterization of PV Generator

A solar cell is basically a diode having a p-n junction exposed to light. When the diode is sufficiently illuminated by sunlight, it generates an electric current in a load resistor. The principle of converting solar radiation into electrical energy is based on the “photovoltaic effect” [49–51]. The energy extracted from the photovoltaic system is one of the reliable natural energy sources because of its ecological nature.The electrical behaviour of photovoltaic cells is nonlinear; several works have approached this theme of modelling. We use in this work the model described by system (1) and (2). Figure3 shows the electrical circuit on which our model is based.Figure 3
Electrical model of a solar cell.The main purpose of this model is to estimate the operating point of the PV generator from three climate variables: solar radiation, temperature, and wind speed. This model integrates also the dynamic variation of series and shunt resistances:(1)fWϑW=exp−γϑW−1ϑW≥1,Tj=TA+273.15+33.75fWϑWEs,VT=NsnsKIKBQTj,Is=IsrVTVTr3expWgVTr−WgVT,Iph=EsIphr+KTVT−VTr,Voc=VTlog1+IphIs,Rs≃VTIsexp−VocVT,Rsh≃RsVTIsexp−RsIphVT,Ip−Npiph+NpisexpVp+Nsnsrs/NpIpNsnsvT−1+1NsnsrshVp+NsnsrsNpIp=0,(2)Wg=Nsnswg,VTr=298.15NsnsKIKBQ,KT=NpkTQNsnsKIKB.This model involves two parametersIsr and Iphr which correspond to the saturation current and photon current at the reference regime. The values of these quantities are evaluated respectively in open-circuit and short-circuit conditions.The PV characteristics for the photovoltaic generator describe previously by system (1) and (2), are plotted in Figures4 and 5 for various values of solar radiation and temperature.Figure 4
Output characteristics of a PV panel with solar radiation.
(a)(b)Figure 5
Output characteristics of a PV panel with junction temperature variation.
(a)(b)


#### 3.1.1. Influence of Solar Radiation

To show the influence of solar irradiance on the overall behaviour of a PV panel, we set the value of the junction temperature at 25°C. The curves of Figure4 reflect sufficiently the functional behaviour of the photovoltaic generator.So, we can note the following:(i)
The short-circuit current is very sensitive to solar irradiance. It increases proportionally with illumination, a condition imposed here by the mathematical model.(ii)
The optimum power has almost the same behaviour as the short-circuit current. The optimal trajectory is a curve of great positive slope according to the optimal tension.


#### 3.1.2. Influence of Junction Temperature

The curves of Figure5 are plotted at 1000 W/m2 and four values of junction temperature. These curves also sufficiently reflect the reality of the functional behaviour of the photovoltaic panel vis-à-vis the change in temperature:(i)
The short-circuit current is almost insensitive to the change in temperature.(ii)
Optimal power decreases with increasing temperature. The optimal trajectory constitutes a positive slope curve as a function of the optimal tension.


## 3.1. Modelling and Characterization of PV Generator

A solar cell is basically a diode having a p-n junction exposed to light. When the diode is sufficiently illuminated by sunlight, it generates an electric current in a load resistor. The principle of converting solar radiation into electrical energy is based on the “photovoltaic effect” [49–51]. The energy extracted from the photovoltaic system is one of the reliable natural energy sources because of its ecological nature.The electrical behaviour of photovoltaic cells is nonlinear; several works have approached this theme of modelling. We use in this work the model described by system (1) and (2). Figure3 shows the electrical circuit on which our model is based.Figure 3
Electrical model of a solar cell.The main purpose of this model is to estimate the operating point of the PV generator from three climate variables: solar radiation, temperature, and wind speed. This model integrates also the dynamic variation of series and shunt resistances:(1)fWϑW=exp−γϑW−1ϑW≥1,Tj=TA+273.15+33.75fWϑWEs,VT=NsnsKIKBQTj,Is=IsrVTVTr3expWgVTr−WgVT,Iph=EsIphr+KTVT−VTr,Voc=VTlog1+IphIs,Rs≃VTIsexp−VocVT,Rsh≃RsVTIsexp−RsIphVT,Ip−Npiph+NpisexpVp+Nsnsrs/NpIpNsnsvT−1+1NsnsrshVp+NsnsrsNpIp=0,(2)Wg=Nsnswg,VTr=298.15NsnsKIKBQ,KT=NpkTQNsnsKIKB.This model involves two parametersIsr and Iphr which correspond to the saturation current and photon current at the reference regime. The values of these quantities are evaluated respectively in open-circuit and short-circuit conditions.The PV characteristics for the photovoltaic generator describe previously by system (1) and (2), are plotted in Figures4 and 5 for various values of solar radiation and temperature.Figure 4
Output characteristics of a PV panel with solar radiation.
(a)(b)Figure 5
Output characteristics of a PV panel with junction temperature variation.
(a)(b)


### 3.1.1. Influence of Solar Radiation

To show the influence of solar irradiance on the overall behaviour of a PV panel, we set the value of the junction temperature at 25°C. The curves of Figure4 reflect sufficiently the functional behaviour of the photovoltaic generator.So, we can note the following:(i)
The short-circuit current is very sensitive to solar irradiance. It increases proportionally with illumination, a condition imposed here by the mathematical model.(ii)
The optimum power has almost the same behaviour as the short-circuit current. The optimal trajectory is a curve of great positive slope according to the optimal tension.


### 3.1.2. Influence of Junction Temperature

The curves of Figure5 are plotted at 1000 W/m2 and four values of junction temperature. These curves also sufficiently reflect the reality of the functional behaviour of the photovoltaic panel vis-à-vis the change in temperature:(i)
The short-circuit current is almost insensitive to the change in temperature.(ii)
Optimal power decreases with increasing temperature. The optimal trajectory constitutes a positive slope curve as a function of the optimal tension.


## 3.1.1. Influence of Solar Radiation

To show the influence of solar irradiance on the overall behaviour of a PV panel, we set the value of the junction temperature at 25°C. The curves of Figure4 reflect sufficiently the functional behaviour of the photovoltaic generator.So, we can note the following:(i)
The short-circuit current is very sensitive to solar irradiance. It increases proportionally with illumination, a condition imposed here by the mathematical model.(ii)
The optimum power has almost the same behaviour as the short-circuit current. The optimal trajectory is a curve of great positive slope according to the optimal tension.


## 3.1.2. Influence of Junction Temperature

The curves of Figure5 are plotted at 1000 W/m2 and four values of junction temperature. These curves also sufficiently reflect the reality of the functional behaviour of the photovoltaic panel vis-à-vis the change in temperature:(i)
The short-circuit current is almost insensitive to the change in temperature.(ii)
Optimal power decreases with increasing temperature. The optimal trajectory constitutes a positive slope curve as a function of the optimal tension.


## 4. Controls Concepts

The performance of the converter depends on the control strategy adopted to generate the control signal (PWM). Many digital and analogue methods are available to control the converters (such as dynamic methods and static methods). Hysteresis control techniques are the most popular because they offer good stability of current and voltage, a very fast response, and robust control and are not complicated to implement.


### 4.1. Hysteresis Current Controller Concept

The basic structure of this regulation mode is given in Figure6:Figure 6
Structure of the hysteresis current controller system.Figure7 describes the principle of the hysteresis regulator used as a current controller. When the photovoltaic current Ipv deviates from the reference value of Δh/2, fixed by the band control of the hysteresis controller, the output current error exceeds the upper hysteresis band −Δh/2 and the switching signal C becomes low. In case the error is greater than +Δh/2, the switching signal C becomes high. If the error is now between −Δh/2 and +Δh/2, the switching signal does not switch [52,53].Figure 7
Principle of hysteresis regulator.Thus, the hysteresis controller generates a control signal C to control the converter switch in order to maintain the current errorΔi within its band. This logic signal is given by the following relation:(3)C=1,ifΔi≥+Δh2,C=0,ifΔi≤−Δh2.


#### 4.1.1. Design of Hysteresis Current Regulator

Referring to the principle of the hysteresis control described above, the developed control circuit is based around many operational amplifiers including the comparator, the inverting, and the summing amplifier. At this level, it is important to note that even for resistances having the same characteristics, most often we measure a deviation of value because of the tolerance. So, we have inserted in the circuit of Figure8 adjustable potentiometers in series with the resistors to compensate for this difference. On another aspect, to ensure the stability of the signals at the output of the AOPs, we attack these integrated circuits by their negative inputs, which is why we used a few unit gain amplifiers, although to reverse the input if necessary. To ensure the “galvanic” isolation of the masses between the control part and the power stage, the HCPL optcoupler 2531 based on a phototransistor is used. Figure 8 gives the detailed electronic diagram of the hysteresis current controller card where the IC1 circuit represents a unity gain inverting amplifier used to invert the reference signal of the current. A low amplitude signal oscillating around zero is added to the output of IC1 constituting the tolerance band, delivered by the circuit IC2. This addition is ensured by the summing circuit IC3 whose output is compared to the current in the load using the comparator IC4. Moreover, the result of the comparison, output of the circuit IC4, is an alternative signal oscillating between −Vcc and +Vcc. At first, this signal is complemented by IC5. In a second time, it is added using the summing IC6 a continuous offset component equal to −Vcc to eliminate its negative component. Finally, to exploit this signal to the control of buck converter, we opted to isolate the masses by an optocoupler HCPL 2531 IC7.Figure 8
Design of a hysteresis current regulator.Figure9 gives an overview of the electronic card of the hysteresis current controller.Figure 9
Overview of the card of hysteresis current controller.


#### 4.1.2. Simulation of PV System with Hysteresis Current Control

The test system considered in this paper is a PV system connected to a resistor load. The system has a PV array, a push-pull converter, and the buck converter. The PV system is simulated, using the one diode model presented in Section2. Each module consists of 36 photocells.To check the performance of the proposed regulator, a MATLAB/Simulink model of the PV system was initially developed. The parameters of the TITAN STP-12-50 type PV module are used for the PV generator model (the specifications are listed in Table1).Table 1
Parameters of the PV generator used in simulation.
Solar panel TITAN-12-50 cell type: EFG multicristallinNumber of series cellsns36Number of parallel PV arraysNp1Number of series PV arraysNs10Open-circuit voltage in STC (per one PV array)21 VShort-circuit current en STC (per one PV array)3.2 AOptimal voltage in STC (per one PV array)17.2 VOptimal current in STC (per one PV array)2.9 AOptimal power in STC450 WIn order to verify the robustness of the proposed approach, we have presented real scenarios where the solar radiation and temperature vary randomly. Figures10 and 11 show the evolution of the real solar radiation and temperature.Figure 10
Evolution of solar radiation.Figure 11
Evolution of temperature.Figure12 presents the evolution of the actual and the optimal currents. These results show that the Ipv current faithfully follows its reference which constitutes the objective of our control. So finally, we can confirm that the PV current converges towards its reference value, which is imposed by the solar radiation.Figure 12
Evolution ofIpv and Ipv_opt.Figure13 gives the exact movement of the two real and optimal powers of a PVG and a zoom of this movement. This figure allows us to conclude that our control responds appropriately, given the existence of a concordance between the two powers.Figure 13
Evolution of real and reference powers of PVG.Figures14 and 15 represent the evolution of the efficiency and the real voltage of the generator. This efficiency clearly shows the efficiency of this current control with a value close to 100%.Figure 14
Efficiency of thePv system.Figure 15
Evolution of real voltage of PVG.


### 4.2. Hysteresis Voltage Controller Concept

Figure16 presents the general structure of the hysteresis voltage controller system with its different blocks.Figure 16
Circuit of the studied system.


#### 4.2.1. Design of Hysteresis Voltage Regulator

Two voltage control options have been designed: the first is internal (or open loop) control while the second is external (or closed loop). However the two voltage control options are identical in their basic designs with the current regulator described previously; the only difference is that, for the internal control, we control the voltage across a capacitor of an RC circuit, filtering the control signal which drives the chopper. But, for the external control, the quantity to be controlled is measured by a suitable sensor external to the regulator.The external regulator, operating in a closed loop, consists in controlling the voltage applied to the resistive load so that the latter supplies a DC voltage at a reference value. This regulator has the same structure as the current regulator described above, except that the inputv (t) is a voltage measured by a suitable sensor at the output of a rectifier bridge, connected in parallel with the load. The two types of voltage regulator are placed in the same box shown in Figure 17. The type of control (internal or external) is selected by a simple changeover switch.Figure 17
Overview of the card of hysteresis voltage controller.


#### 4.2.2. Simulation of PV System with Hysteresis Voltage Control

While using the same simulation parameters as the current command, and with real scenarios, we found these results which respectively show the evolution of solar radiation Figure18 and temperature Figure 19.Figure 18
Evolution of solar radiation.Figure 19
Evolution of temperature.Both actual and optimal voltages are shown in Figure20. This result clearly proves that the voltage Vpv always remains in the vicinity of Vref despite the change in climatic conditions. So, we can conclude about the profitability of this type of control.Figure 20
Evolution of real and optimal voltages of PVG.As usual, both real and optimum powers are recorded. Always thePpv power is very close to its reference as shown in Figure 21.Figure 21
Evolution of real and reference powers of PVG.From the ratio between the two powers (measured active power and optimal active power), we recorded the efficiency which always shows the good response of this type of command which is based on the control of voltages Figure22.Figure 22
Efficiency of thePv system.


### 4.3. Comparative Study

In this part, we will try to compare (more or less) the two approaches studied from a power point of view. Figures23 and 24 clearly show the evolution of “DeltaP” which presents the power difference between two successive points. Then, with the scenarios used, the current control shows more efficiency in following the maximum power than the voltage control as shown in Table 2.Figure 23
Evolution of “DeltaP” of current control.Figure 24
Evolution of “DeltaP” of voltage control.Table 2
Values of “DeltaP.”
DeltaPminmaxHysteresis current control040Hysteresis voltage control−11060The ease of implementing different methods has an important influence on the decision to select one MPPT technique among the others.Therefore, these techniques are characterized by their ease of implantation. Although the operating point is close to the PPM, the major drawback of this type of method is sometimes the estimation ofIcc and Vco.


### 4.4. Experimental Results

Figure25 gives a global view of photovoltaic panels installed on the roof of the laboratory of the ERCO Research Unit at INSAT. This Solar System is composed of ten identical panels having the characteristics indicated in Table 1.Figure 25
PV generator installed on ERCO-INSAT.To validate the previously proposed models, we exploited these photovoltaic panels in connection with a load resistance.Figure26 shows the experimental test bench used to implement and study the proposed MPPT performances. This test bench consists essentially of a PV generator, an illuminance sensor, a temperature sensor, a voltage, and current sensors, all of which are designed and built within the ERCO-INSAT research unit, a push-pull converter, a buck converter, dSpace card DS1104 and control panel, and finally a variable resistive load of 400 W power. The variation of the load value is ensured by 7-step switches.Figure 26
Configuration of the experimental set used.


### 4.5. Experimental Results of PV System with Hysteresis Current Control

For the experimental results, we used just five modules connected in parallel to supply the resistive load. That means in the STC conditions (E=1000W/m2 and T=25°C), we have Pm=250W, Vm=17.2V, and Im=5.7A.Figures27 and 28 show, respectively, the evolution of temperature and solar radiation.Figure 27
Evolution of temperature.Figure 28
Evolution of solar radiation.The behaviour of the voltage and power photovoltaic shows that the MPPT algorithm is robust despite the rapid changes in solar radiation and temperature.Figures29 and 30 , respectively, illustrate the evolution of photovoltaic power Ppv and voltage Vpv.Figure 29
Evolution of photovoltaic power.Figure 30
Evolution of photovoltaic voltage.Figures31 and 32 give the change of the two real and reference currents and the variation of the operating point in the plane Ppv-Ipv.Figure 31
Evolution ofIpv and Iref.Figure 32
Evolution of operating point inPpv-Ipv plane.The experimental results show that the proposed MPPT approach has a fast response under rapid solar irradiance variations.


### 4.6. Experimental Results of PV System with Hysteresis Voltage Control

With the same generator as the previous method, we also tried to implement this technique, the lighting and temperature scenarios are shown by Figures33 and 34 .Figure 33
Evolution of solar radiation.Figure 34
Evolution of temperature.Figures35 and 36 , respectively, present the variation of real current as a function of time and especially the monitoring of the maximum voltage.Figure 35
Evolution of real current of PVG.Figure 36
Evolution of optimal and real voltages.


## 4.1. Hysteresis Current Controller Concept

The basic structure of this regulation mode is given in Figure6:Figure 6
Structure of the hysteresis current controller system.Figure7 describes the principle of the hysteresis regulator used as a current controller. When the photovoltaic current Ipv deviates from the reference value of Δh/2, fixed by the band control of the hysteresis controller, the output current error exceeds the upper hysteresis band −Δh/2 and the switching signal C becomes low. In case the error is greater than +Δh/2, the switching signal C becomes high. If the error is now between −Δh/2 and +Δh/2, the switching signal does not switch [52,53].Figure 7
Principle of hysteresis regulator.Thus, the hysteresis controller generates a control signal C to control the converter switch in order to maintain the current errorΔi within its band. This logic signal is given by the following relation:(3)C=1,ifΔi≥+Δh2,C=0,ifΔi≤−Δh2.


### 4.1.1. Design of Hysteresis Current Regulator

Referring to the principle of the hysteresis control described above, the developed control circuit is based around many operational amplifiers including the comparator, the inverting, and the summing amplifier. At this level, it is important to note that even for resistances having the same characteristics, most often we measure a deviation of value because of the tolerance. So, we have inserted in the circuit of Figure8 adjustable potentiometers in series with the resistors to compensate for this difference. On another aspect, to ensure the stability of the signals at the output of the AOPs, we attack these integrated circuits by their negative inputs, which is why we used a few unit gain amplifiers, although to reverse the input if necessary. To ensure the “galvanic” isolation of the masses between the control part and the power stage, the HCPL optcoupler 2531 based on a phototransistor is used. Figure 8 gives the detailed electronic diagram of the hysteresis current controller card where the IC1 circuit represents a unity gain inverting amplifier used to invert the reference signal of the current. A low amplitude signal oscillating around zero is added to the output of IC1 constituting the tolerance band, delivered by the circuit IC2. This addition is ensured by the summing circuit IC3 whose output is compared to the current in the load using the comparator IC4. Moreover, the result of the comparison, output of the circuit IC4, is an alternative signal oscillating between −Vcc and +Vcc. At first, this signal is complemented by IC5. In a second time, it is added using the summing IC6 a continuous offset component equal to −Vcc to eliminate its negative component. Finally, to exploit this signal to the control of buck converter, we opted to isolate the masses by an optocoupler HCPL 2531 IC7.Figure 8
Design of a hysteresis current regulator.Figure9 gives an overview of the electronic card of the hysteresis current controller.Figure 9
Overview of the card of hysteresis current controller.


### 4.1.2. Simulation of PV System with Hysteresis Current Control

The test system considered in this paper is a PV system connected to a resistor load. The system has a PV array, a push-pull converter, and the buck converter. The PV system is simulated, using the one diode model presented in Section2. Each module consists of 36 photocells.To check the performance of the proposed regulator, a MATLAB/Simulink model of the PV system was initially developed. The parameters of the TITAN STP-12-50 type PV module are used for the PV generator model (the specifications are listed in Table1).Table 1
Parameters of the PV generator used in simulation.
Solar panel TITAN-12-50 cell type: EFG multicristallinNumber of series cellsns36Number of parallel PV arraysNp1Number of series PV arraysNs10Open-circuit voltage in STC (per one PV array)21 VShort-circuit current en STC (per one PV array)3.2 AOptimal voltage in STC (per one PV array)17.2 VOptimal current in STC (per one PV array)2.9 AOptimal power in STC450 WIn order to verify the robustness of the proposed approach, we have presented real scenarios where the solar radiation and temperature vary randomly. Figures10 and 11 show the evolution of the real solar radiation and temperature.Figure 10
Evolution of solar radiation.Figure 11
Evolution of temperature.Figure12 presents the evolution of the actual and the optimal currents. These results show that the Ipv current faithfully follows its reference which constitutes the objective of our control. So finally, we can confirm that the PV current converges towards its reference value, which is imposed by the solar radiation.Figure 12
Evolution ofIpv and Ipv_opt.Figure13 gives the exact movement of the two real and optimal powers of a PVG and a zoom of this movement. This figure allows us to conclude that our control responds appropriately, given the existence of a concordance between the two powers.Figure 13
Evolution of real and reference powers of PVG.Figures14 and 15 represent the evolution of the efficiency and the real voltage of the generator. This efficiency clearly shows the efficiency of this current control with a value close to 100%.Figure 14
Efficiency of thePv system.Figure 15
Evolution of real voltage of PVG.


## 4.1.1. Design of Hysteresis Current Regulator

Referring to the principle of the hysteresis control described above, the developed control circuit is based around many operational amplifiers including the comparator, the inverting, and the summing amplifier. At this level, it is important to note that even for resistances having the same characteristics, most often we measure a deviation of value because of the tolerance. So, we have inserted in the circuit of Figure8 adjustable potentiometers in series with the resistors to compensate for this difference. On another aspect, to ensure the stability of the signals at the output of the AOPs, we attack these integrated circuits by their negative inputs, which is why we used a few unit gain amplifiers, although to reverse the input if necessary. To ensure the “galvanic” isolation of the masses between the control part and the power stage, the HCPL optcoupler 2531 based on a phototransistor is used. Figure 8 gives the detailed electronic diagram of the hysteresis current controller card where the IC1 circuit represents a unity gain inverting amplifier used to invert the reference signal of the current. A low amplitude signal oscillating around zero is added to the output of IC1 constituting the tolerance band, delivered by the circuit IC2. This addition is ensured by the summing circuit IC3 whose output is compared to the current in the load using the comparator IC4. Moreover, the result of the comparison, output of the circuit IC4, is an alternative signal oscillating between −Vcc and +Vcc. At first, this signal is complemented by IC5. In a second time, it is added using the summing IC6 a continuous offset component equal to −Vcc to eliminate its negative component. Finally, to exploit this signal to the control of buck converter, we opted to isolate the masses by an optocoupler HCPL 2531 IC7.Figure 8
Design of a hysteresis current regulator.Figure9 gives an overview of the electronic card of the hysteresis current controller.Figure 9
Overview of the card of hysteresis current controller.


## 4.1.2. Simulation of PV System with Hysteresis Current Control

The test system considered in this paper is a PV system connected to a resistor load. The system has a PV array, a push-pull converter, and the buck converter. The PV system is simulated, using the one diode model presented in Section2. Each module consists of 36 photocells.To check the performance of the proposed regulator, a MATLAB/Simulink model of the PV system was initially developed. The parameters of the TITAN STP-12-50 type PV module are used for the PV generator model (the specifications are listed in Table1).Table 1
Parameters of the PV generator used in simulation.
Solar panel TITAN-12-50 cell type: EFG multicristallinNumber of series cellsns36Number of parallel PV arraysNp1Number of series PV arraysNs10Open-circuit voltage in STC (per one PV array)21 VShort-circuit current en STC (per one PV array)3.2 AOptimal voltage in STC (per one PV array)17.2 VOptimal current in STC (per one PV array)2.9 AOptimal power in STC450 WIn order to verify the robustness of the proposed approach, we have presented real scenarios where the solar radiation and temperature vary randomly. Figures10 and 11 show the evolution of the real solar radiation and temperature.Figure 10
Evolution of solar radiation.Figure 11
Evolution of temperature.Figure12 presents the evolution of the actual and the optimal currents. These results show that the Ipv current faithfully follows its reference which constitutes the objective of our control. So finally, we can confirm that the PV current converges towards its reference value, which is imposed by the solar radiation.Figure 12
Evolution ofIpv and Ipv_opt.Figure13 gives the exact movement of the two real and optimal powers of a PVG and a zoom of this movement. This figure allows us to conclude that our control responds appropriately, given the existence of a concordance between the two powers.Figure 13
Evolution of real and reference powers of PVG.Figures14 and 15 represent the evolution of the efficiency and the real voltage of the generator. This efficiency clearly shows the efficiency of this current control with a value close to 100%.Figure 14
Efficiency of thePv system.Figure 15
Evolution of real voltage of PVG.


## 4.2. Hysteresis Voltage Controller Concept

Figure16 presents the general structure of the hysteresis voltage controller system with its different blocks.Figure 16
Circuit of the studied system.


### 4.2.1. Design of Hysteresis Voltage Regulator

Two voltage control options have been designed: the first is internal (or open loop) control while the second is external (or closed loop). However the two voltage control options are identical in their basic designs with the current regulator described previously; the only difference is that, for the internal control, we control the voltage across a capacitor of an RC circuit, filtering the control signal which drives the chopper. But, for the external control, the quantity to be controlled is measured by a suitable sensor external to the regulator.The external regulator, operating in a closed loop, consists in controlling the voltage applied to the resistive load so that the latter supplies a DC voltage at a reference value. This regulator has the same structure as the current regulator described above, except that the inputv (t) is a voltage measured by a suitable sensor at the output of a rectifier bridge, connected in parallel with the load. The two types of voltage regulator are placed in the same box shown in Figure 17. The type of control (internal or external) is selected by a simple changeover switch.Figure 17
Overview of the card of hysteresis voltage controller.


### 4.2.2. Simulation of PV System with Hysteresis Voltage Control

While using the same simulation parameters as the current command, and with real scenarios, we found these results which respectively show the evolution of solar radiation Figure18 and temperature Figure 19.Figure 18
Evolution of solar radiation.Figure 19
Evolution of temperature.Both actual and optimal voltages are shown in Figure20. This result clearly proves that the voltage Vpv always remains in the vicinity of Vref despite the change in climatic conditions. So, we can conclude about the profitability of this type of control.Figure 20
Evolution of real and optimal voltages of PVG.As usual, both real and optimum powers are recorded. Always thePpv power is very close to its reference as shown in Figure 21.Figure 21
Evolution of real and reference powers of PVG.From the ratio between the two powers (measured active power and optimal active power), we recorded the efficiency which always shows the good response of this type of command which is based on the control of voltages Figure22.Figure 22
Efficiency of thePv system.


## 4.2.1. Design of Hysteresis Voltage Regulator

Two voltage control options have been designed: the first is internal (or open loop) control while the second is external (or closed loop). However the two voltage control options are identical in their basic designs with the current regulator described previously; the only difference is that, for the internal control, we control the voltage across a capacitor of an RC circuit, filtering the control signal which drives the chopper. But, for the external control, the quantity to be controlled is measured by a suitable sensor external to the regulator.The external regulator, operating in a closed loop, consists in controlling the voltage applied to the resistive load so that the latter supplies a DC voltage at a reference value. This regulator has the same structure as the current regulator described above, except that the inputv (t) is a voltage measured by a suitable sensor at the output of a rectifier bridge, connected in parallel with the load. The two types of voltage regulator are placed in the same box shown in Figure 17. The type of control (internal or external) is selected by a simple changeover switch.Figure 17
Overview of the card of hysteresis voltage controller.


## 4.2.2. Simulation of PV System with Hysteresis Voltage Control

While using the same simulation parameters as the current command, and with real scenarios, we found these results which respectively show the evolution of solar radiation Figure18 and temperature Figure 19.Figure 18
Evolution of solar radiation.Figure 19
Evolution of temperature.Both actual and optimal voltages are shown in Figure20. This result clearly proves that the voltage Vpv always remains in the vicinity of Vref despite the change in climatic conditions. So, we can conclude about the profitability of this type of control.Figure 20
Evolution of real and optimal voltages of PVG.As usual, both real and optimum powers are recorded. Always thePpv power is very close to its reference as shown in Figure 21.Figure 21
Evolution of real and reference powers of PVG.From the ratio between the two powers (measured active power and optimal active power), we recorded the efficiency which always shows the good response of this type of command which is based on the control of voltages Figure22.Figure 22
Efficiency of thePv system.


## 4.3. Comparative Study

In this part, we will try to compare (more or less) the two approaches studied from a power point of view. Figures23 and 24 clearly show the evolution of “DeltaP” which presents the power difference between two successive points. Then, with the scenarios used, the current control shows more efficiency in following the maximum power than the voltage control as shown in Table 2.Figure 23
Evolution of “DeltaP” of current control.Figure 24
Evolution of “DeltaP” of voltage control.Table 2
Values of “DeltaP.”
DeltaPminmaxHysteresis current control040Hysteresis voltage control−11060The ease of implementing different methods has an important influence on the decision to select one MPPT technique among the others.Therefore, these techniques are characterized by their ease of implantation. Although the operating point is close to the PPM, the major drawback of this type of method is sometimes the estimation ofIcc and Vco.


## 4.4. Experimental Results

Figure25 gives a global view of photovoltaic panels installed on the roof of the laboratory of the ERCO Research Unit at INSAT. This Solar System is composed of ten identical panels having the characteristics indicated in Table 1.Figure 25
PV generator installed on ERCO-INSAT.To validate the previously proposed models, we exploited these photovoltaic panels in connection with a load resistance.Figure26 shows the experimental test bench used to implement and study the proposed MPPT performances. This test bench consists essentially of a PV generator, an illuminance sensor, a temperature sensor, a voltage, and current sensors, all of which are designed and built within the ERCO-INSAT research unit, a push-pull converter, a buck converter, dSpace card DS1104 and control panel, and finally a variable resistive load of 400 W power. The variation of the load value is ensured by 7-step switches.Figure 26
Configuration of the experimental set used.


## 4.5. Experimental Results of PV System with Hysteresis Current Control

For the experimental results, we used just five modules connected in parallel to supply the resistive load. That means in the STC conditions (E=1000W/m2 and T=25°C), we have Pm=250W, Vm=17.2V, and Im=5.7A.Figures27 and 28 show, respectively, the evolution of temperature and solar radiation.Figure 27
Evolution of temperature.Figure 28
Evolution of solar radiation.The behaviour of the voltage and power photovoltaic shows that the MPPT algorithm is robust despite the rapid changes in solar radiation and temperature.Figures29 and 30 , respectively, illustrate the evolution of photovoltaic power Ppv and voltage Vpv.Figure 29
Evolution of photovoltaic power.Figure 30
Evolution of photovoltaic voltage.Figures31 and 32 give the change of the two real and reference currents and the variation of the operating point in the plane Ppv-Ipv.Figure 31
Evolution ofIpv and Iref.Figure 32
Evolution of operating point inPpv-Ipv plane.The experimental results show that the proposed MPPT approach has a fast response under rapid solar irradiance variations.


## 4.6. Experimental Results of PV System with Hysteresis Voltage Control

With the same generator as the previous method, we also tried to implement this technique, the lighting and temperature scenarios are shown by Figures33 and 34 .Figure 33
Evolution of solar radiation.Figure 34
Evolution of temperature.Figures35 and 36 , respectively, present the variation of real current as a function of time and especially the monitoring of the maximum voltage.Figure 35
Evolution of real current of PVG.Figure 36
Evolution of optimal and real voltages.


## 5. Conclusion

In this work, the interest in inserting an adaptation stage between the source and the load was discussed. The structure of buck and push-pull choppers has been adopted. The principle of a hysteresis controller has been exposed, tested, and implemented. These results essentially make it possible to present the advantages of these control approaches which offer good tracking of MPP and above all a very good conformity between the real current and voltage of the PVG and the reference values.The main objective of this research is to develop two MPPT controllers for a PV system in order to obtain maximum power with random scenarios of climatic factors. The simulation results as well as the experimental validation show a very great efficiency of the hysteresis regulators which has ensured essentially a very good control in current and voltage which causes the extraction of the optimum of power.Finally, the experimental validation was presented to confirm the results found by simulation. The test bench is based on the use of the DS1104 card in order to implement the adopted control structures.



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*Source: 6689121-2021-04-24.xml*