Efﬁcient Control of DC Microgrid with Hybrid PV—Fuel Cell and Energy Storage Systems

: Direct current microgrids are attaining attractiveness due to their simpler conﬁguration and high-energy efﬁciency. Power transmission losses are also reduced since distributed energy resources (DERs) are located near the load. DERs such as solar panels and fuel cells produce the DC supply; hence, the system is more stable and reliable. DC microgrid has a higher power efﬁciency than AC microgrid. Energy storage systems that are easier to integrate may provide additional beneﬁts. In this paper, the DC micro-grid consists of solar photovoltaic and fuel cell for power generation, proposes a hybrid energy storage system that includes a supercapacitor and lithium–ion battery for the better improvement of power capability in the energy storage system. The main objective of this research work has been done for the enhanced settling point and voltage stability with the help of different maximum power point tracking (MPPT) methods. Different control techniques such as fuzzy logic controller, neural network, and particle swarm optimization are used to evaluate PV and FC through DC–DC boost converters for this enhanced settling point. When the test results are perceived, it is evidently attained that the fuzzy MPPT method provides an increase in the tracking capability of maximum power point and at the same time reduces steady-state oscillations. In addition, the time to capture the maximum power point is 0.035 s. It is about nearly two times faster than neural network controllers and eighteen times faster than for PSO, and it has also been discovered that the preferred approach is faster compared to other control methods.


Introduction
The global energy demand is steadily increasing. Traditional energy sources emit greenhouse gases, so non-traditional energy sources such as solar PV and wind turbines were developed to be renewable, abundant in nature, cost-efficient, and widely used. Instead, use a source as FC has in this ever-increasing power demand. The majority of rural areas do not have access to reliable electricity. The initial investment cost to electrify rural areas was very high. Still, with the aid of DC microgrids based on renewable energy sources (RES) such as solar PV and FC with energy storage systems (ESS), implementation is simple and cost-effective [1,2]. In this current scenario, DC microgrids are more popular because of easy interfacing with distribution generation without interlinking AC/DC and DC/AC  [19] h designed a fuzzy logic-based MPPT controller for PV and FC applications. Figure 1 shows the distributed RES, ESS, DC load with grid-connected voltage sour converter. DC microgrids have more advantages such as high efficiency, reliability, an low environmental pollution than AC microgrid and do not have frequency, reacti power issues. Hence, it is easy to link with DC micro sources.

Mathematical Model of Solar PV and Fuel Cell
The mathematical equations are modeled and designed using MATLAB/Simulink (2019a, The Mathwork, Inc., Natick, MA, USA) for PV and FC, which is illuminated as follows:

Modelling of Solar PV
PV cells are electrical devices that transform solar energy into electricity using semiconducting devices that demonstrate the photovoltaic effect. The photovoltaic cell is used to describe electrical variables such as current, voltage, and resistance as they change in response to sunlight. The equivalent circuit of a solar cell is shown in Figure 2. When an electron collides with another electron in its bound state, electron conduction occurs, and these electrons are energized by the base energy provided by the semiconductor's bandgap. The equivalent circuit of PV [20] module contains a diode, light-created source, and resistance connected in parallel. Figure 3 shows the P-V and I-V characteristics [21][22][23] of solar cell, which is conditioned and screened for various irradiances at T = 25 • C. The following Equations (1)-(4) represent the mathematical equations for modeling solar cells.
where, I = total current (A); V = output voltage (V); T = temperature ( • C); q = electron charge; k i = short-circuit temperature coefficient; I sh = shunt resistance current; R s = Series Resistance; R sh = Shunt Resistance; k b = open-circuit voltage temperature coefficient and k = Boltzmann's constant; A = ideality factor; I ph = load current; I d = diode

Model Equations of FC
FC's fundamental model includes mass, thermal energy, momentum, organisms, an charge. This FC model is based on five equations. These equations are combined to form an electrochemical process to express reaction kinetics and electro-osmotic drag durin the polymer electrolyte process. Equations (5)-(10) represent the five equations for this F model in vector form:

Model Equations of FC
FC's fundamental model includes mass, thermal energy, momentum, organisms, and charge. This FC model is based on five equations. These equations are combined to form an electrochemical process to express reaction kinetics and electro-osmotic drag during the polymer electrolyte process. Equations (5)-(10) represent the five equations for this FC model in vector form:

Model Equations of FC
FC's fundamental model includes mass, thermal energy, momentum, organisms, and charge. This FC model is based on five equations. These equations are combined to form an electrochemical process to express reaction kinetics and electro-osmotic drag during the polymer electrolyte process. Equations (5)-(10) represent the five equations for this FC model in vector form.

Continuity Equation
The electrodes present in the FC are made up of carbon fiber or carbon cloth. The reactant gases are spread over the CL, and the electrodes are restrained as a porous medium everywhere. The continuity equation for the porosity with the help of electrodes (ε) has given in Equation (5).
where = differential operator of a vector, ρ = liquid density, ε = porosity, U = floating speed vector and t = time.

Momentum Conservation
Navier-Stokes equation has given in Equation (6) and designed for a Newtonian fluid.

Conversion of Charge Equation
PEMFC is used in CL to conduct electrochemical reactions. The charge equations are an integral part of the FC, and this equation consists of two equations: electron removal above conductive solid phase and proton transference above the membrane. The oxygen diffusion flux (ODF) on the catalyst surface is used to calculate the current density (CD) that circulates along with CL. The CL's two-dimensional Poisson's equation is as follows: The sum of phase currents of solid (is) and membrane (im) during CL is equal to the total current (i), which is given in the following equation, Using Ohm's law, the transfer current density (Jt) with solid surface tension is given by,

Continuity Equation
The electrodes present in the FC are made up of carbon fiber or carbon cloth. The reactant gases are spread over the CL, and the electrodes are restrained as a porous medium everywhere. The continuity equation for the porosity with the help of electrodes (ε) has given in Equation (5).
where ∇ = differential operator of a vector, ρ = liquid density, ε = porosity, U = floating speed vector and t = time.

Momentum Conservation
Navier-Stokes equation has given in Equation (6) and designed for a Newtonian fluid.

Conversion of Charge Equation
PEMFC is used in CL to conduct electrochemical reactions. The charge equations are an integral part of the FC, and this equation consists of two equations: electron removal above conductive solid phase and proton transference above the membrane. The oxygen diffusion flux (ODF) on the catalyst surface is used to calculate the current density (CD) that circulates along with CL. The CL's two-dimensional Poisson's equation is as follows: The sum of phase currents of solid (i s ) and membrane (i m ) during CL is equal to the total current (i), which is given in the following equation, Using Ohm's law, the transfer current density (J t ) with solid surface tension is given by, where J t = transfer current density at time t, σ s = solid phase surface tension, σ m = membrane phase surface tension, ϕ s = solid phase flux, ϕ m = membrane phase flux.

Electrochemical Reaction Dynamics equation
The current density at time (J t ) is a classification of electrochemical reaction velocity, the concentration of species, and potential among the phase of the membrane and solid. The expression for Butler-Volmer (B-V) has expressed below, where, F = Faraday's constant, R = electrical resistance, J 0 = exchange current density, αj = charge transfer coefficient, α a and α c = transfer coefficients of cathode and anode. Λ = mol concentration of the reactant.

MPPT Techniques
The efficient yield of solar PV and FC has developed via different MPPT methods. Various types of MPPT techniques are there. From that, the utmost familiar MPPT methods are perturb and observe (P and O), incremental conductance technique (INC), the FLC, ANN, and particle swarm optimization (PSO) control methods. In this paper, power has been transferred to load with the help of MPPT to extract maximum power from hybrid (PV-FC) DC microgrid. DC/DC boost converter performs as an interface among load and hybrid (PV-FC) sources. The maximum power has been obtained by changing the duty cycle of the DC/DC converter with respect to the load impedance. Hence, the MPPT techniques for solar PV and FC are necessary to sustain the module functioning at its MPPT.

Particle Swarm Optimization (PSO)
Kennedy and Eberhart founded PSO [28][29][30] as an evolutionary computation strategy. Birds penetrating for food stimulate the PSO. Flocking is a mechanism through which birds classify their food sources, and it was through these flock activities, the PSO process was discovered. The search space directs moving particles to their known positions. When a better position is found, it will be used to direct the flock's movement. Since the method is ongoing, as is the execution, the appropriate outcome can be trusted but not guaranteed. The difference between PSO and conventional evolutionary computation approaches is that particle velocities are tuned while individual evolutionary positions are replaced; it's as if the particle swarm individual's "fate" is changed rather than their "state." Furthermore, PSO experiences partial optimism, which results in less precise measurements of its position and velocity in its Control. However, this algorithm does not solve the optimization or scattering problems. The flowchart for the PSO algorithm is shown in Figure 5.

Artificial Neural Network
The computational tool that represents nonlinear systems has been said to be ANN [31][32][33]. ANN consists of biological neurons, which contain weight and bias to interconnect each other by transferring signals. The weights related to input values go together with the learning rule in the training process. The output y j of ANN has given in Equation (11), where f = activation function, x i = input signal and w ij = weight between input and output, b = bias value. The output neuron E, obtained as follows, where y di = desired value of output neuron i and y i = actual output.

Artificial Neural Network
The computational tool that represents nonlinear systems has been said to be ANN [31][32][33]. ANN consists of biological neurons, which contain weight and bias to interconnect each other by transferring signals. The weights related to input values go together with the learning rule in the training process. The output yj of ANN has given in Equation (11), where f = activation function, xi = input signal and wij = weight between input and output, b = bias value. The output neuron E, obtained as follows, where ydi = desired value of output neuron i and yi = actual output. In this paper, a quasi-Newton back propagation algorithm has been used for weight mean square error (MSE). With the help of a minimum number of neurons per layer, maximum accuracy has been obtained by carrying out more trials. The ANN that is developed in this paper, the input layer contains 1 neuron, the hidden layer has 10 neurons, and the output layer has 1 neuron. The neurons in the input layer and the hidden layers' sigmoidal activation functions are used, and the neurons in the output layer linear activation function are used. The structure of ANN used in this paper is shown in Figures 6 and 7. In this paper, a quasi-Newton back propagation algorithm has been used for weight mean square error (MSE). With the help of a minimum number of neurons per layer, maximum accuracy has been obtained by carrying out more trials. The ANN that is developed in this paper, the input layer contains 1 neuron, the hidden layer has 10 neurons, and the output layer has 1 neuron. The neurons in the input layer and the hidden layers' sigmoidal activation functions are used, and the neurons in the output layer linear activation function are used. The structure of ANN used in this paper is shown in Figures 6 and 7.

Fuzzy Logic Controller
The linguistic variables and their ranges are determined with the help of the main control variables. With the help of these control variables, the fuzzy logic controller (FLC)

Fuzzy Logic Controller
The linguistic variables and their ranges are determined with the help of the main control variables. With the help of these control variables, the fuzzy logic controller (FLC)

Fuzzy Logic Controller
The linguistic variables and their ranges are determined with the help of the main control variables. With the help of these control variables, the fuzzy logic controller (FLC) [34][35][36][37] is designed. The human's specific intellect and understanding for developing the membership functions are essential for making the perception. Figures 8 and 9 depict an FLC-based MPPT controller and an FLC rule viewer and sur-face viewer, respectively. Consider the input variables error E (k) and shift in error DE when determining the fuzzy membership functions (k). As a result of these input signals, linguistic variables are obtained. Change of Control (Duty cycle D (k)) is the contribution of the fuzzy membership function. Figure 10 shows the proposed MPPT [38] control scheme with membership feature fuzzy controller for E (k), DE (k), and D (k). With the use of the intuition method, a triangular membership function was used to obtain E (k) membership values and DE (k). The E (k) and DE (k) (−2, 2) intervals are set. To classify some unique input, a triangular style membership feature is proposed for an individual dominant fuzzy subset. Fuzzy rules for the hybrid (PV-FC) scheme are presented in Table 1.

Simulink model of DC Microgrid
The hybrid DC microgrid Simulink model using MATLAB comprises DC-DC boost converters, PV, FC, FLC, ANN, PSO-based MPPT method, and resistive load. This proposed hybrid DC microgrid has been developed with the help of MATLAB simulation software. The system parameters for PV, FC, boost converter, DC-DC bidirectional converter, supercapacitor, and battery are illustrated in Table 2. Figure 11 illustrates MATLAB Simulink model of hybrid DC microgrid, and Figures 12-14 show the subsystem of FC, DC-DC bidirectional converter and boost converter, model of FLC.  Figure 15a,b shows the solar PV irradiance of 980 W/m 2 for t < 1 s and 800 W/m 2 for t > 1 s with constant temperature T = 25 • C and nominal charging and discharging characteristics of an energy storage system. In this proposed system, the hybrid DC microgrid comprises solar PV with a boost converter, FC with a boost converter, Supercapacitor with bidirectional converter, and battery with bidirectional converter. The aforementioned simulations comprise FLC, ANN, and PSO-based MPPT. Figures 16-18 illustrate solar PV power with (FLC, ANN, and PSO) and without MPPT controller.        Figure 15a,b shows the solar PV irradiance of 980 W/m 2 for t < 1 s and 800 W/m 2 for t > 1 s with constant temperature T = 25 °C and nominal charging and discharging characteristics of an energy storage system. In this proposed system, the hybrid DC microgrid comprises solar PV with a boost converter, FC with a boost converter, Supercapacitor with bidirectional converter, and battery with bidirectional converter. The aforementioned simulations comprise FLC, ANN, and PSO-based MPPT. Figures 16-18 illustrate solar PV power with (FLC, ANN, and PSO) and without MPPT controller.  Similarly, Figure 19 shows the output power of FC with (FLC, ANN and PSO) and without an MPPT controller. Figures 20 and 21 show the output voltage, current, power, and state of charge (SOC) of battery and supercapacitor with the use of a bidirectional converter. Using FLC, the performance of solar PV has risen to 1402 W from 845 W, which is a rise of 66%, then FC has raised to 1278 W from 787 W, which is a rise of 62%. Using    Similarly, Figure 19 shows the output power of FC with (FLC, ANN and PSO) and without an MPPT controller. Figures 20 and 21 show the output voltage, current, power, and state of charge (SOC) of battery and supercapacitor with the use of a bidirectional converter. Using FLC, the performance of solar PV has risen to 1402 W from 845 W, which is a rise of 66%, then FC has raised to 1278 W from 787 W, which is a rise of 62%. Using ANN, the performance of solar PV has risen to 1335 W to 845 W, which is a rise of 58% then FC has raised to 1208 W from 787 W, which is a rise of 53%. Similarly, by using the PSO algorithm, the performance of solar PV has raised to 1260 W from 845 W, which is a rise of 49% then FC has raised to 1188 W from 787 W, which is a rise of 51%.     It clears that FLC gives the best performance for this proposed hybrid Dc microgrid when compared to ANN and PSO algorithm. Table 3 gives the comparative analysis of power for PV and FC without MPPT and with FLC, ANN, and PSO algorithm-based MPPT.  Table 4 shows the comparison of settling time, overshoot, and undershoot for the proposed hybrid DC microgrid with the help of FLC, ANN, and PSO algorithm. The simulation results, which were obtained for the hybrid DC microgrid, tabulated in Table 4. Hence, with the help of different controllers, the enactment of the hybrid structure has been detected and analyzed. The Simulation analysis for hybrid DC microgrid using MATLAB/Simulink has been done to compute the maximum power of the DC load (resistive load) with different controllers.
algorithm-based MPPT controller. Table 4 shows the comparison of settling time, overshoot, and undershoot for the proposed hybrid DC microgrid with the help of FLC, ANN, and PSO algorithm. The simulation results, which were obtained for the hybrid DC microgrid, tabulated in Table 4. Hence, with the help of different controllers, the enactment of the hybrid structure has been detected and analyzed. The Simulation analysis for hybrid DC microgrid using MATLAB/Simulink has been done to compute the maximum power of the DC load (resistive load) with different controllers.  algorithm-based MPPT controller. Table 4 shows the comparison of settling time, overshoot, and undershoot for the proposed hybrid DC microgrid with the help of FLC, ANN, and PSO algorithm. The simulation results, which were obtained for the hybrid DC microgrid, tabulated in Table 4. Hence, with the help of different controllers, the enactment of the hybrid structure has been detected and analyzed. The Simulation analysis for hybrid DC microgrid using MATLAB/Simulink has been done to compute the maximum power of the DC load (resistive load) with different controllers.    algorithm-based MPPT controller. Table 4 shows the comparison of settling time, overshoot, and undershoot for the proposed hybrid DC microgrid with the help of FLC, ANN, and PSO algorithm. The simulation results, which were obtained for the hybrid DC microgrid, tabulated in Table 4. Hence, with the help of different controllers, the enactment of the hybrid structure has been detected and analyzed. The Simulation analysis for hybrid DC microgrid using MATLAB/Simulink has been done to compute the maximum power of the DC load (resistive load) with different controllers.

Conclusions
In this paper, a hybrid DC microgrid with various control techniques has been proposed to achieve maximum power point in solar PV and FC. The MPPT method improves the settling time of the proposed hybrid DC microgrid, according to the results obtained using different control techniques such as FLC, ANN, and PSO algorithm. When compared to other control methods, FLC has a higher efficiency rating. The results show that the fuzzy MPPT approach for forecasting hybrid DC microgrid output has a high level of precision, effectiveness, and reliability. This research has been applied to both grid and stand-alone systems. As a result of this research into different control techniques for MPPT systems, it is now possible to choose a particular MPPT process for various applications. We will investigate the possibility of implementing the appropriate control methods to other types of DC-DC converters as well as to control a DC microgrid with advanced DC-DC converter topologies in future research.