Optimal Control of Hybrid Photovoltaic-Thermometric Generator System Using GEPSO

Recently the concern about energy consumption across the globe has become more severe due to global warming. One essential way to address this problem is to maximize the efficiency of existing renewable energy resources and effectively eliminate their power losses. The previous studies on energy harvesting of photovoltaic (PV) modules try to cope with this problem using gradient-based control techniques and pay little attention to the significant loss of solar energy in the form of waste heat. To reconcile these waste-heat problems, this paper investigates hybrid photovoltaic-thermoelectric generation (PV-TEG) systems. We implement the generalized particle swarm optimization (GEPSO) technique to maximize the power of PV systems under dynamic conditions by utilizing the waste heat to produce electricity through embedding the thermoelectric generator (TEG) with the PV module. The removal of waste heat increases the efficiency of PV systems and also adds significant electrical power. As a control method, the proposed GEPSO can maximize the output power. Simulations confirm that GEPSO outperforms some state-of-the-art methods, e.g., the perturb and observe (PO), cuckoo search (CS), incremental conductance (INC), and particle swarm optimization (PSO), in terms of accuracy and tracking speed.


Introduction
In recent years, the excessive use of fossil fuels led to massive environmental which lead to better thermal conductivity. One plate is interconnected to a heat source while the other acts as a heat-sink source. To attain the desired level of output voltage from TEG, thermocouples are often connected in series-parallel configurations for higher power rating operations. In past, thermoelectric (TE) materials have been utilized as temperature sensors, but significantly improved in the conversion efficiency of TEG systems due to the advancement in manufacturing technology thereby focusing on renewable electricity generation has enormously increased the scope of TEG applications. In many industrial operations, heat recovery processes, and automobiles engines, the TEG modules can able to convert the waste heat into electricity without affecting the normal process of flow [8] [9] [10]. The energy efficiency of TEG normally ranges from 5% to 10% [11]. An increase in thermal and electrical performance of the TEG system can improve the efficiency level. In the meantime, the hybrid photovoltaic cell and thermoelectric generator (PV-TEG) system is widely discussed in research since it has potential improved power conversion efficiency.
To use the waste heat from PV cells by using the thermoelectric modules has been a key-motivation for studying the hybrid PV-TEG systems. In literature, numerous studies revealed that a sufficient increase in energy has been achieved by embedding TEG modules in PV-TEG system. Hybrid PV-TEG systems can address the problem of broad spectrum solar radiations by utilizing the power generating ability of both PV and TEG modules. In view of this fact, researches M. Ejaz DOI: 10.4236/jpee.2022. 103001 3 Journal of Power and Energy Engineering are being made to make hybrid PV-TEG systems more durable and efficient.
Several maximum power point tracking (MPPT) methods have been utilized to increase the power output of PV system and a dc-dc converter is used. The purpose of dc-dc converter is to control the reference voltage via modulated signal, as a result the system continuously track the maximum power point (MPP). The literature as documented in Refs. [12] [13] proposed the hybrid PV-TEG system instead of PV-based systems and obtained results showing the higher energy yield and eco-friendly environment. Further in Ref. [14], the implementation of PV-TEG systems for applications in water pumping systems substantiates that motor power output and the pump flow have increased. The hybrid PV-TEG presented in Ref. [15] confirmed that the energy output of hybrid PV-TEG systems has enhanced under various operating conditions. In addition, the control techniques to harvest the energy are playing a significant role in improving the energy conversion efficiency of hybrid PV-TEG systems. These techniques extract the optimal energy from the source and minimize power loss of the system through fixing the duty cycle of the dc-dc converter.
To date, many energy harvesting optimization algorithms [16] have been proposed in literature including incremental conductance (INC) [17], hill climbing (HC) [18], perturb and observe (P & O) [19] that are widely accepted because of their low complexity. Moreover, a sliding mode control (SMC) [20], inflection voltages method [21], fractional open circuit voltage [22] [23], and mathematical-graphical approach [24] are used. In standard conditions, i.e., uniform irradiance and temperature, these techniques can harvest energy quite effectively at a good convergence speed. Despite these facts, the continual oscillation occurring around MPP appears in the aforementioned MPPT techniques.
The oscillating nature at MPP causes a significant power loss in steady-state conditions. The gradient-based decision-making methods are insufficiently intelligent to deal with power loss caused by partial shading conditions (PSC) as documented in Ref. [25]. These undesired oscillations in voltage transients hinder the grid connectivity and reduce applications of PV-TEG in large-scale systems where time-sensitive stable control is a prime requirement under dynamic operating conditions.
To overcome the aforementioned problems, new metaheuristics algorithms are proposed in the literature. Among them, the bio-inspired optimization algorithms have been quite effective in dealing with MPP under nonlinear and stochastic issues [26]. Some typical bio-inspired approaches includes grey wolf optimization (GWO) [27], artificial bee colony (ABC) [28], genetic algorithm (GA) [29], Whale Optimization (WO) [30], cuckoo search (CS) [31], and particle swarm optimization (PSO) [32] so on. Although these approaches provide good results, however, still suffers from inefficient exploitation of solution in search space, procedural complexity, and their parameters need to be tuned properly.  [34], and artificial neural network (ANN) [35]. Nevertheless, these approaches can effectively deal with the nonlinear properties of the PV-curves but needs substantial computing resources, and enormous amounts of data for training, which rely on the previous knowledge of the systems.
In this paper, a novel hybrid PV-TEG system is implemented and to deal with the shortcomings of aforementioned techniques, a generalized particle swarm optimization (GEPSO) [36] based MPPT approach is proposed to fill the research gap for integrated PV-TEG system. The main contribution of this paper is iterated as  GEPSO provides a strong correlation among the exploration of the swarm particles and enhances the effectiveness and relative performance of the MPPT control.  The efficient tracking of proposed technique reduces the power losses and increase the energy conversion efficiency.  Results confirm the superiority of GEPSO in terms of tracking and settling time.
The structure of the paper is organized as follow: Section II explains the mathematical modeling of hybrid PV-TEG system and dc/dc boost converter. Section III presents a description of proposed control MPPT technique GESPO.
Section IV contains various case studies to validate the performance of the proposed method. Section V presents the summary of the work.

Modeling of PV Cells
Photovoltaic PV cell can be modeled as a semiconductor diode with a pn-junction in which electron-hole pairs are formed when the light strikes at the junction [18]. The current of an ideal PV cell is proportional to the amount of irradiation being received from the sun. A pictorial representation of the PV model using current source, diode, and resistor combinations is illustrated in Figure 1. The PV cell output current I ph is given by:  The PV module is formed by connecting multiple PV cells, linked in series to achieve necessary voltage and connected parallel to get the desired level output current. The current-voltage relation for PV cell can be expressed as: where V pv , q, I sat , k, T, N p , N s and n represent the output voltage, electron charge, reverse saturation current, Boltzmann constant, temperature of PV cells, number series-parallel connected PV cells, and diode ideality factor, respectively. The efficiency of PV module can be calculated using Equation (3) as: where P  is cross-section area in m 2 and G is the irradiation in W·m −2 of the PV panel.
The output of PV system changes with respect to variations in atmospheric conditions/environmental inputs such as irradiance and temprature. The characteristic I-V curve is shown in Figure 2(a) while P-V curve in Figure 2

Modeling of Thermoelectric Generator (TEG)
Thermoelectric generator TEG is typically built by connecting thermometric solid-state devices in series [8]. The equivalent electrical circuit is shown in Figure 4. The temperature difference across two ends of junctions produces an electromotive force so-called the Seebeck effect. The induced voltage due to Seebeck effect is expressed as follows: where T H , T C represents the hot-and cold-side surfaces temperature, and κ represents the corresponding Seebeck coefficient. The Equation (5) can be used to calculate the Seebeck coefficient as: where th  is the number of thermocouples, p θ , n θ are the Seebeck coefficients. The output current, voltage and power of TEG are computed as: where R L , R int are the applied load and internal resistance of TEG system. The R int is determined by: where C σ is the copper strip electrical conductivity, A t is the cross-sectional area of thermometric, A C is the copper strip cross-sectional area, L is thermocouple length, L C is the copper strip length, and β is the electrical conductive of thermocouple material, respectively. The TEG gathers heat flux on the hot-side and emits on the cold-side. In addition to Seebeck effect κ during the energy conversion, the Thomson and Peltier effects are also induced [8]. Notably, when load is applied the electric current drives through across the junctions of the material. The influence of Thomson effect on TEG module is so far neglected due to its minimal impact on the resistive load R L . The energy equation for the TEG module is given by [1]: The variables in the above equation are defined as; ( )

Modeling of Hybrid PV-TEG Generator
The hybrid photovoltaic-thermometric generator PV-TEG power module [12] is designed to change the maximum solar irradiation into electricity. PV cells typically employ a little amount of incoming solar irradiation to create electricity while converting a substantial amount of solar irradiation into waste heat. Thus, the temperature of PV cells increases, which leads to a degradation of the energy efficiency of the PV system. Figure 5 depicts a typical hybrid PV-TEG module layout. The proposed system consists of TEG with heat-sink that makes use of waste heat energy from PV system to increase power generation and decrease the temperature of PV cells. PV array serves as a heat source for the TEG and heat sink is placed on the TEG cold-side. The heat sink ensures the sufficient temperature differential across its two terminals. Furthermore, heat sink reduces the ambient temperature of PV cell, as a result improving energy conversion efficiency of the PV-TEG system. The energy conversion efficiency of hybrid PV-TEG system is formulated as: The PV arrays and TEG can be connected parallel or serially for the hybrid system; however, extra power electronic switches are required for parallel connections, increasing power losses. On the other hand, the serial connection of PV and TEG has fewer power switches and less power loss. The energy efficiency of the PV power system mainly depends on the ratio of energy generated to the quantity of solar input power per unit area while TEG's depends on the amount of input heat energy at the hot end to the amount of heat energy emitted at the cold end. In this hybrid model, the PV temperature act as TEG input and electrical energy is produced at its output.

Boost Converter
Boost converter adequate provided voltage between PV array and load resistance R L [37]. It has ability to control signal via duty cycle which allows the PV array to operate at optimal point. The characteristic equations for the input-output capacitance, output voltage, inductor, and other electrical parameters are presented from Equation (12) to Equation (16).
( ) where d b is the duty cycle of dc/dc boost converter, V i , V o are the input and output voltage, C i is input and C o is output capacitor and L is the inductor to reduce the ripple current.

PSO MPPT Algorithm
Kennedy and Eberhart first proposed particle swarm optimization PSO based MPPT approach in 1995 which utilizes the idea of swarms like fish and birds.
PSO is built upon a collection of group members termed as particles which represent solutions and coordinate with each other using social interactions and experience models. The particles begin exploring for food/shelter randomly in a search area. Once the goal is achieved, the information is conveyed to other searching members. After being transitioned into the optimization process, this  (17) is used to update the location of each particle at each function iteration and the particle flies to a different position which is determined by a fitness function that analyzes each solution quality. The velocity of the particles is determined by Equation (18) as: where j pbest represents the best fitness value of particle j, gbest represents the best fitness value of the whole swarm, c 1 and c 2 are the constriction factor (for limiting the velocity of the particles), w denotes the inertia weights (for regulating the global search), and r 1 and r 2 represent random numbers.

GEPSO MPPT Algorithm
This paper employs energy harvesting algorithm so-called generalized particle swarm optimization GEPSO [36] that enhances the original PSO performance and its effectiveness for MPPT control problem. This approach uses a dynamic weight adjustment mechanism to enhance the updating formula for particle velocity. In Equation (17) where ψ represents the constriction parameter and can be determined by: and w 1 in Equation (19) represents the inertia weight which is dynamically updated in each function iteration as follows: Throughout the searching process, 1 i w will always be equal to or greater than a minimal inertia value. As the swarm's best fitness function improves compared to its previous function iteration, 1 i w also increases proportionally. Thus, with the improvement of gbest , the effect of the current velocity direction increases, leading to deeper exploitation of the existing solution. On contrary to that 1 i w Journal of Power and Energy Engineering decreases whenever the worst value of the fitness function appear compared to the previous function iteration, which prevents the particles from moving along their past direction and leads to more exploration of the search space. Figure 6 shows the updating of particle's positions in two consecutive function iterations of the GEPSO algorithm [36]. The position and velocity of the particle are initialized by Equation (22) and Equation (23) as: The third term in Equation (19) increases the interrelation between particles and ensures the swarm more swiftly converge towards optimum solutions. The impact of random velocities, leads to improve swarm exploration in many unexplored regions of the search space. The parameters in the first three terms in Equation (19) significantly improve the algorithm's performance.
In general terms for the hybrid PV-TEG system, the fitness function is modeled as the output power. The corresponding search for optimum control value can be defined as d k in the possible set of solutions D using the fitness function a global optimum, otherwise it is called a local optimum of ( ) P d in D. The flowchart and pseudo-code of the overall process of GEPSO are presented in Figure 7 and Figure 8, respectively.

Results and Discussion
The performance testing setup consists of four serially connected PV modules with a boost converter that provides an interface between PV-TEG output and load resistance. MPPT controller generates the optimum duty cycle depending upon the sensors data. The results of generalized particle swarm optimization

Case 1: Varying Temperature with Constant Irradiance
The GEPSO is tested under varying temperature to verify its effectiveness. The temperature gradient is summarised in Figure 10

Case 2:
Step-Change in Irradiance with Constant Temperature

Case 3: Partial Shading
Case 3 deals with partial shading conditions PSC for which irradiation pattern is shown in Table 2

Case 4: Complex Partial Shading
This type of shading is caused by extensive partial shading of a significantly large number of series-connected PV modules. In this situation, several peaks are generated, which are closely related. In complex partial shading condition, the PV curve is shown in Figure 14(b) where 12 PV modules are serially attached and applied irradiance pattern is listed in  Figure 17 shows the proposed GEPSO algorithm can track the GMPP with a fewer number of iterations and in less time than others.

Case 5: Hybrid PV-TEG System
In the proposed hybrid PV-TEG energy module, the maximum power extraction ability of MPPT methods is examined under STC. Figure 17

Case 6: Non-Uniform Temperature on TEG
This case deals with the unequal distribution of temperature on TEGs due to non-uniform irradiance on PV modules. Figure Figure 19(a) and the duty cycle comparison of implemented methods are illustrated in Figure 19

Conclusion
This paper proposes a GEPSO based energy harvesting technique for PV and hybrid PV-TEG systems under various operating conditions. A comprehensive comparison is made with the standard MPPT techniques, including PSO, CS, and INC, respectively. The GEPSO technique is designed for strongly correlate search particles so that it can achieve quick convergence towards globally optimum solutions rapidly. In addition, the random velocity terms are introduced into the GEPSO technique and improvising the swarm exploration in unexplored regions of interest of the search space. Moreover, the comprehensive case studies validate the effectiveness and advantages of GEPSO for harvesting maximum energy. The outcomes demonstrated that GEPSO can outperform some state-of-the-art energy harvesting techniques, making the PV system generates more energy under different environmental conditions.