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Design of a maximum power point trackingbased PID controller for DC converter of standalone PV system
Journal of Electrical Systems and Information Technology volume 9, Article number: 9 (2022)
Abstract
Standalone photovoltaic system (PV) produces a variance in the output voltage under variable irradiation and temperature, and variable load conditions, resulting in control challenges. The research scope is to maintain a constant output load voltage despite variations in input voltage or load. The use of a DC converter ensures that the output voltage of such systems remains constant regardless of changes in the production voltage and load. The control on a DC boost converter is employed to solve this problem. This paper presents the design of a maximum power point trackingbased (MPPT) DC converter controller for such a system. The MPPTbased PID has been proposed as a control approach and implemented to the system DC converter. Incremental Conductance (IC) algorithm has been employed as an MPPT in association with an optimized PID. The Particle Swarm optimization technique (PSO) has been used to optimize the proposed PID through selected cost function. The PV system with the loaded converter is modeled and simulated using the MATLAB/Simulink environment. The system performance is displayed using a family of curves under different operating conditions and disturbances.
Introduction
Recently, academics have focused on renewable energy assets such as wind turbines and solar panels to reduce the use of fossil fuels, which are the primary source of ecological natural contaminations. One of the most significant challenges in the creation of wind and solar energy is that, due to the stochastic nature of wind speeds and solar radiation, they usually include uncertainty. In this regard, the current uncertainty surrounding assets such as wind and solar units makes it important to evaluate the distribution system's arranging strategy to ensure a reliable execution. PV module power generation is primarily determined by solar irradiation, ambient temperature, and module characteristics [1].
Solar energy which can be directly generated from sun using photovoltaic (PV) installations is powerful enough to replace the need of conventional electricity sources, especially in urban or islanded areas. Such standalone energy sources operate under uneven lighting conditions. They represent the most conventional systems that produce a variance in the output voltage under variable irradiation and temperature, and also variable load conditions, resulting in control challenges. To achieve the peak efficiency, each PV array is connected in series through a DC–DC converter that performs perarray distributed maximum power point tracking [2].
A great attention has been paid to the control and robustness of the PV systems due to the change in either temperature, irradiation or even the connected load. Maximum Power Point Tracking (MPPT) has been used to improve and ensure that such systems are more efficient. PID controller for the DC converter of the standalone PV systems based on Maximum Power Point Tracking (MPPT) has been suggested in the literature. Mirza Fuad Adnan has presented in [3], the design and simulation of a DC–DC boost converter with PID controller to enhance the overall performance of the system. Their main aim was to achieve better conversion efficiency, minimizing the harmonic distortion and improving power factor while keeping size and cost of the converter within acceptable range. A PID controller has been applied to the boost converter achieving an improved voltage regulation considering only the variable irradiation and temperature. More research work has been introduced in the literature [4,5,6,7] discussing the same concept of implementing PID controller to PV systems either in standalone form or when being in grid connected form.
Improved model reference adaptive control scheme with PID controller is proposed in [8] to increase the stability and reliability of adaptive control. There are two loops in this upgraded version: an inner loop and an outer loop. With a PID controller, the inner loop acts as a typical feedback loop, while the outer loop acts as an adaptive control for parameter adjustment. This proposed method outperforms the standard model reference adaptive control method [8].
The PID controller generates a signal that consists of three terms: The proportional (P) action causes a direct proportionate change in the input (manipulated variable) to the error signal. The integral (I) action causes a change in the input proportionate to the integral of error, with the primary goal of removing offset. The derivative (D) action, on the other hand, is employed to speed up the reaction or to stabilize the system, and it produces a change in the input proportionate to the error signal's derivative [9].
In [10], simulations show that the FOPID controller outperforms the PID controller in terms of performance, but the PID controller outperforms the FOPID controller in terms of position tracking under disturbance [10].
In this paper, an optimal PID (OPID) and an MPPTbased PID controllers are designed to control the boost converter of a standalone PV system. This is the novelty in this work. Eberhart and Kennedy proposed PSO, a populationbased stochastic search technique. The original inspiration for the PSO algorithm came from a concept of community behavior in animals like fish schooling and bird gathering. When birds or insects look for food or migrate in the search space, it is based on communication of individual knowledge and natural learning. The popularity of PSO in recent decades has been attributed to its simple structure and the fact that it just requires a few parameters to change the algorithm [11].
Performance of the two controllers in the presence of different operating points and disturbances is compared by carrying out simulation using the MATLAB/Simulink environment and displaying the system performance using a family of curves for the purpose of validating the proposed controllers.
The major contributions made by this research article are as follows:

1.
MPPTbased PID controller for a DC–DC boost converter control scheme is formulated for a standalone PV system connected to a resistive load, using IC for realtime estimation of the MPP during the PV system operation.

2.
The proposed control scheme has been figured out in such a way that it should be simple to understand and easy to implement.

3.
Through PID controller, the MPPT is guaranteed with a superior performance to the proposed system and conventional PID and IC based MPPT techniques.
The system modeling
System modeling is perhaps an important phase in addition to the other forms of system control design work. The system model depends on the aims of the simulation. If the objective is to predict the behavior of a system before it is built, a good system model should support the designer with important information about the system dynamics, and so on. Because of the difficulty involved in solving nonlinear equations, all the governing equations will be put together in block diagram form and then simulated using MATLAB’s Simulink environment. Simulink will solve these nonlinear equations numerically and provide a simulated response of the system dynamics [12]. The proposed system under study comprises a PV array, boost converter, an MPPTbased PID and PWM controller in addition to a resistive DC load. The model for each of the system elements is derived as follows:
PV system model
Figure 1 displays the standalone PV system to be considered in this work. The operation of the proposed system should operate at the strategies of: maximum power point operation, boosting the voltage of the PV array to the desired level of the load voltage, battery backup units with charge regulators and load matching.
Figure 2 displays the complete electrical equivalent circuit for PV cells which can be represented by two equations as:
Based on Eqs. (1) and (2), the MATLAB Simulink block for the PV array has been considered in the system modeling by setting the array parameters in accordance with the selected data given in Appendix A. Figure 3 displays the I–V and P–V characteristics of the module and the array of the considered PV system.
Boost converter model
The boost converter of Fig. 4 with a switching period of T and a duty cycle of D is considered as a part of the proposed standalone PV system. Assuming continuous conduction mode of operation, the state space equations when the main switch is ON are given by Eq. (3), [13].
and when the switch is OFF are shown by Eq. (4):
Figure 5 illustrates Eqs. (3) and (4) in MATLAB Simulink using a simulated boost converter circuit with a control signal applied to the gate of the switching element in order to get the desired switching operation of the converter and obtain the states \(i_{L} \left( t \right)\) and \(v_{o} \left( t \right)\) [14,15,16].
Maximum power point tracking (MPPT) algorithms
Maximum power point tracking MPPT is used in PV systems to maximize the output power of photovoltaic cells. MPPT can be achieved through the implementation of an electronic circuit, programmed algorithm, or it may be simulated in MATLAB Simulink environment. It varies the electrical operating point of the modules so that they are able to deliver maximum power [17]. Several algorithms for MPPT are proposed and introduced in the literature including: perturb and observe, open circuit voltage, short circuit current, incremental conductance algorithms, in addition to the neural networks and fuzzy logic [17]. The selection of the algorithm depends on the complexity of system and the time taken to track the maximum power point. In this work, the proposed method to track the maximum power for the standalone PV system is the incremental conductance IC algorithm using MATLAB/Simulink.
Incremental conductance algorithm
In this algorithm, it is needed to apply two voltages sensor and two current sensors for sensing both the output voltage and current of the PV array. The maximum power point is achieved when the slope of the P–V curve has a value of zero, this can be explained as:
The Flow chart of the incremental conductance MPPT algorithm is displayed in Fig 6, [18].
MPPTbased PID controller
In most of the applications, it is needed to maintain the output voltage of converter as constant regardless the changes in the load or input voltage. The DC–DC power converters are sited in middle stage of most of electrical power systems; their input is connected to solar cells, and output is connected to the load. Both input and output sides are prone to sudden changes in values, slow transient response increase losses in the system and leads to reduction in efficiency.
Several methods have been proposed by researchers to control output voltage of DC–DC converters. This paper proposes an MPPTbased PID controller to be implemented to the converter as described in Figs. 7 and 8.
Nowadays, the PID controller is the most widely used, it is used to optimize the system performance like the stability, the voltage regulation, rapidity and the precision. The proposed PID controller is illustrated in Fig. 9 [19]. The PID tuning and optimization can be carried out by many algorithms Genetic, Ant Colony, Particle Swarm, Harmony, and other algorithms presented in the literature [20]. In this work, the Particle Swarm Optimization (PSO) has been employed to get the gains of the optimal PID (OPID) and the MPPTbased PID proposed controllers. Figure 10 represents the flowchart of PSO algorithm [21].
The PID controller can be described as illustrated in Eq. (7) [22]:
The parameters of OPID and MPPTbased PID controllers have been designed and optimized using the PSO technique with the objective function that is chosen to be the Integral Time Square Error (ITSE) which can be defined as in Eq. (8) to minimize the squared error:
In addition, among the evolutionary computation, the updated velocity and position for each particle in the swarm can be calculated using the current velocity and the distance from the particle best solution p_{besti} and the global best solution g_{besti} by employing Eqs. (9) and (10) [23, 24]:
Initialization parameters used for PSO are: population size = 30, maximum number of iterations = 2000, minimum and maximum velocities are 0 and 2, cognitive and social acceleration coefficient C1 = 2, C2 = 1.4, minimum and maximum inertia weights are 0.6 and 0.9.
Results and discussion
Maximum power point trackingbased PID controller for DC converter of standalone PV system is employed to maintain a constant output voltage despite variations in load and input voltage due to the variable of irradiation and temperature. With the parameters of the OPID and MPPTbased PID controllers have been designed using PSO technique and the abovementioned objective function, the proposed system simulation has been carried out using MatLabR2017b. The parameters of the PV array model are given in the appendix. Figure 11 displays the Simulink model for the system under study. To validate the effectiveness of the proposed controllers, the system has been tested and disturbed under three case studies:

Running the system under constant converter input voltage, i.e., constant temperature and irradiance for the PV array.

Running the system under variable converter input voltage, i.e., variable temperature and irradiance for the PV array.

Running the system under load change disturbance.
For each case study, the converter output voltage, current and power responses are displayed in the form of families of curves for the purpose of validation the proposed controllers under the abovementioned condition as elaborated in the following:
Simulation of the PV system with MPPTbased PID controller under constant input voltage
In this case, the PV standalone system has been considered to be running under constant converter input voltage, i.e., constant temperature and irradiance for the PV array. The responses of the converter output voltage, current, and power responses associated with this case are displayed in Fig. 12b–d. From these responses, it is clear that MPPTbased controller succeeded in reducing overshoot and minimizing the settling time.
Simulation of the PV system with MPPTbased PID controller under variable input voltage
In this case, the PV standalone system has been considered to be running under variable converter input voltage, i.e., variable temperature and irradiance for the PV array as shown in Fig. 13a. The responses of the converter output voltage, current and power responses associated with this case are displayed in Fig. 13b–d. From these responses, it is clear that MPPTbased controller succeeded in reducing overshoot and minimizing the settling time.
Simulation of the PV system with MPPTbased PID controller under load change disturbance
In this case, the PV standalone system has been considered to be running under a load change disturbance, where the load current and power have been increased in two steps by adding a parallel load to the main system load using two C. Bs as shown in Fig. 14a. The responses of the converter output voltage, current and power responses associated with this case are displayed in Fig. 14b–d. From these responses, it is clear that MPPTbased controller succeeded in reducing overshoot and minimizing the settling time.
Conclusion
One of the most promising sources of electricity is renewable green energy. It is a free source that does not have a reserve amount. Aside from other renewable green energy sources, photovoltaic solar energy is another major option for reducing emissions. PV solar cells are a versatile energy source since they can be deployed practically everywhere there is sunlight.
The novelty of this paper is to present a design of an MPPTbased PID controller for a DC–DC boost converter control of a standalone PV system to maintain a constant output voltage at different disturbances. Incremental conductance MPPT and Particle Swarm Optimization algorithms have been used. The results illustrated that the voltage, current and power system responses with the proposed controller under different disturbances had less overshoot, lower steady state error, and smaller settling time compared with optimized PID controller noticing that the results were obtained by using the same optimization technique for the two controllers. The effectiveness of the proposed controller has been tested by implementing different disturbances including variable temperature, variable irradiation, and load change disturbances.
Scope of future
Future research directions could include the following:

Designing of Fuzzy controller and Fuzzy PID controller.

Under partial shading conditions, compare the proposed control strategies to alternative MPPT algorithms (PSC).
Availability of data and materials
Available.
Abbreviations
 PV:

Photovoltaic
 MPPT:

Maximum power point trackingbased
 IC:

Incremental Conductance
 PSO:

Particle Swarm optimization technique
 OPID:

Optimal PID
 T:

Switching period
 D:

Duty cycle
 ITSE:

Integral Time Square Error
 p _{ besti } :

Particle best solution
 g _{ besti } :

Global best solution
 C1:

Cognitive coefficient
 C2:

Social acceleration coefficient
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Acknowledgements
We thank all the distinguished professors, the administration of the College of Engineering in Helwan, the Presidency of the Department of Power Engineering and the Department of Graduate Studies.
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FAM made the initial preparations for writing the research and doing the Simulink of model. MEB made adjustments in writing, correcting it, and reducing the citation rate, the final results of Simulink of model were produced. SS and SM did the final review. All authors read and approved the final manuscript.
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Appendix: Selected PV module to supply the practical system
Appendix: Selected PV module to supply the practical system
Model  100 WPV module 

Maximum power (Wp)  100 Wp 
Maximum power voltage (V)  18 
Maximum power current (A)  5.55 
Open circuit voltage (V)  21.6 
Short circuit current (A)  6.11 
Number of series cells (Ns)  36 
Number of parallel cells (Np)  1 
Temperature coefficients of Isc (%)  + 0.002/℃ 
Temperature coefficients of Voc (%)  − 0.2355/℃ 
Cell series resistance Rs (Ω)  0.0001 
Cell shunt resistance Rsh (Ω)  1000 
Temperature Range  − 40°℃ to + 80°℃ 
Standard Test Conditions  1000 w/m^{2} AM1.5 25°℃ 
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Mohammed, F.A., Bahgat, M.E., Elmasry, S.S. et al. Design of a maximum power point trackingbased PID controller for DC converter of standalone PV system. Journal of Electrical Systems and Inf Technol 9, 9 (2022). https://doi.org/10.1186/s43067022000505
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DOI: https://doi.org/10.1186/s43067022000505
Keywords
 PV system
 Standalone PV systems
 DC–DC converter
 Boost converters
 MPPT algorithms
 IC algorithm
 PID optimization