Three Phase Grid-Tied Solar PV System: Modeling, Simulation, and MPPT Analysis using Artificial Neural Networks (ANN)

Photovoltaic generators offer a low-environmental-impact, economic, and socially beneficial approach for producing electrical energy competitively. Recently much emphasis has been placed on the generation of clean energy, which has received increased attention. These natural and clean energy sources must contain all items required for their functioning. In this study, solar photovoltaic (PV) systems connected to a grid were simulated. The proposed model of the solar PV system, DC-DC converter, converter, and grid interface was formed. In solar PV systems, Maximum Power Point Tracking (MPPT) is essential because it boosts the output power of the system, allowing for efficient PV array use and voltage regulation. The interface receives power from the solar PV system by maintaining a constant voltage of the DC converter grid. The Pulse Width Modulation (PWM) sine wave technique is used to generate pulses for the converter. Artificial neural networks (ANNs) are effective machine learning tools based on the structure of the human brain. The actual and expected outputs are used by the ANN to enhance its performance. MATLAB/Simulink was used to construct and test the simulation system model, and the results were presented.

Introduction

The integration of renewable energy resources and energy storage technologies constitutes an emergent trend propelled by ecological concerns to diminish greenhouse gas emissions and the surging demand for electrical energy. Photovoltaic (PV) systems in hybrid configurations have become increasingly popular as a clean and safe way to harness solar energy [1]. Additionally, it has no pollutants, requires little upkeep, and doesn't require electricity. A PV solar panel's power source is non-linear when its output power varies with temperature and sunlight. Because each individual solar cell has a low voltage (typically 0.6 V), there are two main categories of PV system applications in power systems: off-grid or autonomous applications and on-grid or interconnected applications. Photovoltaic systems that function autonomously can furnish electrical power to loads situated at considerable distances, which lack direct access to such resources. Grids are utilized as grid-connected applications to interchange power with utility grids and supply energy for local loads. Photovoltaic systems may benefit power system functioning by boosting the voltage profile and lowering energy losses in distribution feeders, as well as maintenance and loading costs. Transformer tap changers are used during rush hours.

PV systems still face substantial challenges and can generate negative impacts on the system and produce a non-equilibrium system, such as overloading of the feeders, and low efficiency, low dependability, harmonic pollution, and high investment costs that greatly limit the utilization. Solar irradiance changes can cause power output and voltage flickers that directly impact the penetration of photovoltaic systems in electric utilities [3]. The semiconductor solar cells are used to produce photovoltaic solar energy on systems in which there is a transformation of solar radiation into direct current, which is thus transformed into alternating current by power electronic DC-to-AC converters. As a result, unlike classic synchronous generators, they lack inertia. Additionally, their dynamic characteristics and interactions with electrical systems are controlled by converter elements and controls. Therefore, it is vital to evaluate the impacts of growing penetration of photovoltaic generation systems on the power system dynamics to ascertain their prospective influence on the operation and functioning of the power grid [4].

Renewable energy penetration was defined in a number of ways, including the percentage of energy supplied by renewable energy, generation relative for peak load, and its generation capacity relative for the system. The division of the main grid into smaller microgrid subsystems makes the network easier to administer and operate. This eliminates the need to rebuild the main grid architecture and permits greater penetration of a dependable power source, like PV [5], [6]. Maximum Power Point Tracking (MPPT) represents one of several control strategies that may be applied to PV systems to boost their efficiency. Both the voltage and the current produced by the PV array must be managed in the controller. This could lead to structural issues with PV systems, increasing the chance of failure while monitoring maximum power in unforeseen weather conditions [2], [7]. MPPT in grid-connected photovoltaic systems can be significantly changed for the better by using an ANN-based NARMA-L2 method, according to the study's hypotheses. In particular, it is predicted that the suggested method will be superior to the traditional methods in terms of tracking effectiveness, irradiance circumstances, stability under temperature variation, and faster converging to the maximum power point.

Materials and Methods

Photovoltaic Module

With the same user-friendly iconography and dialogue as the block libraries in MATLAB/Simulink, this work simulates photovoltaic modules step-by-step using a blocks subsystem. For a photovoltaic module, a large number of solar cells are connected in parallel and series circuits on a panel to achieve high power. PV is a collection of several modules that are electrically coupled in series-parallel configurations to produce the necessary voltage and current. The solar cells, which are essentially a (p-n) semiconductor junction, is the building block of the PV system. It produces direct current with a photovoltaic effect by directly converting solar radiation. Fig. 1 illustrates an equivalent circuit of a photovoltaic solar cell, including a diode that considers the most basic of circuits, connected with a current source in parallel [8].

Fig. 1. Equivalent basic circuit of photovoltaic solar cell.

Load current $I_L$ represented a photocurrent cell $R_s$ and $R_{sh}$ are core series and shunt resistors associated with the cell, respectively. Generally, the values of $R_s$ are very small, so they can be neglected to simplify the analysis, and that of $R_{sh}$ is very large. Module photocurrent:

(1) $$\begin{array}{r}{I}_{Ph}=[I_{SCr}+K_i(T-298)]\text{*}\mathrm{\lambda }/1000\end{array}$$

Saturation reverse current ($I_{rs}$):

(2) $$\begin{array}{r}{I}_{rs}=I_{SCr}/[exp(q{V}_{OC}/N_{s}kAT)-1]\end{array}$$

Saturation current I_o changes with the cell temperature, which is given as:

(3) $$\begin{array}{r}{I}_o=I_{rs}{\left[{\frac{T}{T}}_r\right]}^{3}exp\left[\frac{q\ast E_{g0}}{Bk}\{\frac{1}{T_r}-\frac{1}{T}\}\right]\end{array}$$

The output PV module’s current is:

(4) $$\begin{array}{rl}& I_{PV}={}_{N_P}\ast _{I_{Ph}}\\ & -{}_{N_P}\ast _{I_O}[exp\left\{\frac{q\ast (V_{pv}+I_{PV}{R}_{s)}}{N_{s}AkT}\right\}-1]\end{array}$$

Maximum Power Point Tracking (MPPT)

Maximum Power Point Tracking (MPPT) is a method employed in electronics to control and satisfy optimized power output. applied to the modules of Photovoltaic (PV) to allow them to generate the maximum possible power they can produce. Fig. 2 illustrates that the photovoltaic cell operates at a specific point where the combination of current and voltage produces the highest power output. Maintaining the PV array consistently at this optimal point is a significant challenge; therefore, various algorithms have been developed to achieve accurate and efficient MPPT control.

Fig. 2. Block diagram of the MPPT Control system.

Based on the Maximum Power Transfer Theorem, a circuit delivers the greatest power when the impedance of the source is equal to that of the load. A boost converter is connected to the solar panel on the source side to raise the output voltage. Adjusting the converter’s duty cycle allows the source impedance to align with the load impedance. Among these techniques, the Perturb and Observe (P&O) and Incremental Conductance methods are the most widely used, despite their limitations, such as oscillations around the maximum power point (MPP) and reduced accuracy during severe weather variations. These methods typically employ monitoring with a fixed iteration step that is chosen based on the tracking speed and accuracy requirements [9].

Observing Fig. 3, At a specific level of solar irradiation (for instance, 1000 watts/m²), point A represents the Maximum Power Point (MPP). At this point, the following equation is derived:

(5) $$\begin{array}{r}\frac{dP}{dV}=0\end{array}$$

Fig. 3. Incremental conductance method flow chart.

When the operation shifts to point B or point C, it is represented by (6) and (7), respectively.

(6) $$\begin{array}{r}\frac{dP}{dV}>0\end{array}$$

(7) $$\begin{array}{r}\frac{dP}{dV}<0\end{array}$$

The MPPT technique is designed to continuously monitor and ensure that the system operates at its maximum power point (point A). There are several traditional approaches used for this purpose; five of the most common are listed below, although we’ll focus on describing only the first one.

1. Incremental Conductance approach.

2. Perturb and Observe approach.

3. Voltage_O/C approach.

4. Current_S/C approach

5. Voltage_Constant approach.

Incremental Conductance Method

The incremental conductance approach depends on the principle that the derivative of the photovoltaic output power $P_{pv}$ with respect to the panel voltage $V_{pv}$ becomes zero at the maximum power point. The control algorithm, illustrated in Fig. 3, is more challenging and complex to implement than earlier techniques, as it requires division operations where the denominators can sometimes be zero. When reaching the maximum power point, Vpv oscillates around the optimum value V_pv, MPP. These oscillations lead to power losses that increase proportionally with the step-size disturbance. A large step size enables the MPPT algorithm to respond rapidly to sudden changes in operating conditions like irradiance or temperature; however, it also introduces higher steady-state oscillations and greater power loss. Conversely, a small step size minimizes these oscillations under stable or slowly varying conditions, but it reduces the system’s ability to react quickly to abrupt environmental variations in temperature or solar radiation [10].

Boost Converter

A boost converter has embedded elements such as inductors, switches, diodes, and capacitance; see Fig. 4. The operation of a boost converter can be divided into two modes [11]: the first mode applies when the switch SW is turned on at t = Ton, as shown in Fig. 5. When the input current increases, it passes through the inductor L and the switch SW, allowing energy to be stored in the inductor. The second operating mode starts when the switch turns off at t = T_off. At this point, the current that previously flowed through the switch is redirected through L (inductor), D (diode), C (capacitor), and R (load), as illustrated in Fig. 6. The inductor current gradually decreases until the switch is turned on again in the next cycle, transferring the stored energy from the inductor to the load [11]. as (8) demonstrated, output voltage was higher than input voltage.

Fig. 4. Main circuit of boost converter.

Fig. 5. First mode of boost converter circuit.

Fig. 6. Second mode of boost converter circuit.

(8) $$\begin{array}{r}{V}_{out}=\frac{1}{(1-D)}\ast V_{in}\end{array}$$

The output voltage is represented as $V_{out}$, the duty cycle as a D, and the input voltage as Vin, which would be the voltage generated by the solar panel.

For the converter to function in continuous conduction mode, the inductance must be set so that the inductor current I_L remains continuous and does not drop to zero. Therefore, the value of L can be calculated using (9).

(9) $$\begin{array}{r}{L}_{min}=\frac{(1-D{)}^2\ast D\ast R}{2\ast f}\end{array}$$

Minimum inductance Lmin = (D ^* R)/F, where D represents the duty cycle, while R denotes the output impedance, and F is the switching frequency of the switch SW. The output capacitance to provide the desired output voltage ripple is determined by the equation:

(10) $$\begin{array}{r}{C}_{min}=\frac{D}{R\ast f\ast V_r}\end{array}$$

If $C_{min}$ is the minimum capacity, D is the ring, R is the output resistance, f is the switching frequency of switch SW, and Vr is the output voltage ripple factor. To express Vr, the equation below:

(11) $$\begin{array}{r}{V}_r=\frac{\mathrm{\Delta }{V}_{out}}{V_{out}}\end{array}$$

The PV voltage source is connected to a DC-AC converter, as illustrated in Fig. 7. To smooth the DC voltage, it is applied to both levels of the IGBT converter, generating 50 Hz. The IGBT converter uses Pulse Width Modulation (PWM) at a carrier frequency of 2 kHz. From Fig. 8, two PI controllers are used in the voltage regulator circuit; the first one regulates load voltage by applying transformation of abc to dq and dq to abc, while the second PI is tuning the index modulation.

Fig. 7. DC-AC PWM converter circuit.

Fig. 8. Block diagram of the voltage control.

(12) $$\begin{array}{rl}& V_d=\frac{2}{3}(V_a\sin \left(wt\right)+V_b\sin (wt-2\pi /3)\\ & +V_c\sin (wt+2\pi /3))\end{array}$$

(13) $$\begin{array}{rl}& V_q=\frac{2}{3}(V_a\cos \left(wt\right)+V_b\cos (wt-\frac{2\pi }{3})\\ & +V_c\cos (wt+2\pi /3)\end{array}$$

(14) $$\begin{array}{r}{V}_o=\frac{1}{3}(V_a+V_b+V_c)\end{array}$$

where w represents the rotation speed of the reference frame (rad/s). The abc transformation also applied to the three-phase current case, and the voltage variables (V_a, V_b, V_c, V_d, V_q, and V_o) were directly replaced with the current variables. I_a, I_b, I_c, I_d, I_q, and I_o. A voltage vector is the first output of the voltage regulator; it contains three modulation signals that are fed into the PWM generator to produce six-pulses in the converter. The second output modulation index returns. After approximately 50 ms, the system reaches a steady state; the harmonics generated by the converter are effectively attenuated by the LCL filter.

Now it is necessary that the DC voltage generated by the converter, which is the link to the grid, be AC. The purpose of this network controller is to keep the DC link voltage at a fixed value irrespective of the output power range. The goal of this controller is DC voltage regulation and control of reactive power; it uses vector control in the rotating reference system with the vector voltage. In accordance with the fundamental of energy conversion and ignoring the losses of the converter, the total instantaneous power in the output terminal AC should be equal to the moment of power in the DC link. According to the (12)–(14):

(15) $$\begin{array}{r}{V}_{dc}{I}_{dc}=v_a{i}_a+v_b{i}_b+v_c{i}_c\end{array}$$

The 3-phase instantaneous active and reactive power using the following equations:

(16) $$\begin{array}{r}P=V_a\ast I_a+V_b\ast I_b+V_c\ast I_c\end{array}$$

(17) $$\begin{array}{rl}& Q=1/\\ & \sqrt{3[(V_b-V_c)\ast I_a+(V_c-V_a)\ast I_b+(V_a-V_b)\ast I_c]}\end{array}$$

Proposed Method

The neural network predictive controller available in the Deep Learning Toolbox™ utilizes a neural network model of a nonlinear plant to forecast its future behavior. Based on these predictions, the controller computes the control input that maximizes plant performance within a defined future time horizon. The process begins with identifying the neural network plant model (system identification), which is then employed by the controller to anticipate the plant’s future performance. In this study, the NARMA-L2 architecture is implemented using MATLAB’s Neural Network Toolbox. The system identification process can be outlined in the following steps:

a) The first step in applying feedback linearization (or NARMA-L2 control) involves identifying the target system. A neural network is trained to model the system’s forward dynamics. The NARMA-L2 model is a widely used framework for representing general discrete-time nonlinear systems.

b) The next step is to design a nonlinear controller that enables the system output to follow a desired reference trajectory.

The main drawback of this controller is that training a neural network to minimize the mean square error requires dynamic backpropagation, which is relatively slow. A practical alternative is to employ approximate models to represent the system. In this section, the controller is designed using the NARMA-L2 approximate model Plant Identification. The MPPT technique can help appreciably increase a photovoltaic system's power through control parameter modification. The main benefit of the MPP after using NN is the decrease in the steady-state oscillation [12]. Table I showed the specific parameters of the neural network. The boost converter control based on the NARMA-L2 approach is simulated in the MATLAB-SIMULINK environment, as illustrated in Fig. 9.

Table I. The Specific Parameters of the Neural Network

Network architecture
Size of hidden layer	4
Sampling interval (sec)	0.0001
No. Delayed plant inputs	1
No. Delayed plant outputs	2
Training data
Training samples	5000
Maximum plant input	2
Minimum plant input	−2
Maximum interval (sec)	3
Minimum interval (sec)	2
Maximum plant output	2
Minimum plant output	3
Training parameters
Training epochs	200

Fig. 9. Boost converter with ANN model in MATLAB simulation.

Simulation Results and Discussion

The photovoltaic module parameters were considered as a reference input in the simulation model. Table II summarized the characteristic parameters of PV modules and their corresponding values.

Table II. Electrical Characteristics Data of PV Module

Parameters	Magnitude
V OC	66 V
I SC	25.44 A
P R	240.5 W
V mp	54.2 V
I mp	23.25 A
Ns	2
T aK	30 to 70) C)
T rK	25 C
G /1000	kW/m2 = 1

Where the parameters that are represented in Table I refer to open-circuit voltage (Voc), short-circuit current I_SC, rated power, voltage maximum power, current maximum power, number of cells that are in series connection Ns, number of cells that are in parallel connection Np, operating temperature and reference temperature of modules, and irradiance (an instantaneous measurement of solar power over some area), respectively, where Vpv = Voc, Np = 1, Ns = 36. The power of the photovoltaic module is a nonlinear function of the ambient temperature and the intensity of solar radiation. When a PV cell is exposed to solar radiance, it converts a portion of the incident solar energy directly into electrical energy, resulting in output characteristics exhibiting current-voltage (I-V) and power-voltage (P-V), which describe the performance of the PV module in different operating conditions [13]. The power generation of photovoltaic cells decreased, affected by an increase in ambient temperature, while all other circumstances remained constant, as seen in Fig. 10. The emerging power from photovoltaic cells increased as the light's intensity grew; see Fig. 11. The Maximum Power Point (MPP), or P_m, is a special maximum output power for solar cells under a specific light intensity. The previously mentioned data indicates that light intensity and ambient temperature have a high impact on the outcome power of PV cells. Thus, PV arrays must maximize the use of control tracking power points under different environmental conditions to guarantee the maximum output power [14].

Fig. 10. PV characteristic curves at constant irradiations and various temperatures; (a) I-V curves, (b) P-V curves.

Fig. 11. PV characteristic curves at constant temperature and various irradiations; (a) I-V curves, (b) P-V curves.

Photovoltaic solar resources connected to distribution networks change load conditions of the network they are connected to at the points, which are called points of common coupling (PCC). The implementation of this system is linked to the grid-connected mode; the addition of a controller in the AC part improves the system’s reliability. According to the IEEE 1547–2003 Standard for Interconnecting Distributed Resources with Electric Power Systems [15], photovoltaic (PV) solar converters are required not to actively control the voltage at the point of common coupling (PCC). Consequently, most PV systems are designed to function at a unity power factor, as this configuration enables the generation of greater real power [4].

Based on the above model and control method, the grid-connected PV generation system can be developed and executed in the MATLAB/Simulink environment, as illustrated in Fig. 12. Table III shows the grid-tied PV system parameters and their values (used and obtained) and the other system’s variables used in the proposed model.

Fig. 12. Photovoltaic system interconnected to the grid.

Table III. Specifications and Component Values of the Grid-Tied Photovoltaic System

Unit	Parameters	Value
IGBT Converter PWM	Snubber resistance	150 Ω
	Filter (LCL)	0.34 H, 0, 05 H/218e-6F
	Carrier frequency	2000 Hz
Photovoltaic (PV module)	ambient temperature	25°C
	Insolation/Irradiation	240 W/sqm
	Total number of cells in parallel	2
Grid side	Phase-to-phase rms	210 V
	Frequency	50 Hz
	V abc	122 V
	I abc	22A
Boost	Vdc/output	60 V
DC Bus	Voltage	65 V

Simulations with loads have been carried out, and good results have been obtained at different load parameters. However, to show that the trained system shows a better performance. Two simulation cases are studied and implemented according to models and control methods, and then the results (before and after).

a) Open loop system: without ANN, there is no controller.

b) Close loop system: An ANN controller is used.

The output voltage/current of the grid are in phase and have an expression of volts (V) and current (I). It is achieved by using three-phase measurement (voltage and current). The aim of controller design is to supply the maximum power at first from 400 radiation levels. The output automatically increases as sunlight intensifies, supplying power to the local load. When the PV array’s power generation decreases, the grid compensates by providing the required energy. On the assumption that through (0-1) s, solar irradiance is 400 W/m²; through (1-2) s, solar irradiance was 1000 W/m²; and through (2–3) s, solar irradiance returns to 600 W/m², that causes a drop in the PV current as shown in Fig. 13.

Fig. 13. Photovoltaic current (I_PV) in different solar irradiance values.

The comparative simulation results of the MPPT control and the proposed method obtained by ANN control are shown by the meaning of "before" and "after." Fig. 14 shows the voltage of the converter before and after the proposed control. It seems that the ANN has improved the signals of the converter, reducing losses caused by distortion of the converter's signals. As in reference [16], an NN-based MPPT controller was investigated where radiation varied with different steps in different regions.

Fig. 14. Converter’s voltage; (a) Before using ANN controller, (b) Afte using ANN controller.

The instantaneous PV power losses caused by the proposed method utilized in this paper without and with ANN (before and after). See Fig. 15 That PV operates in current source mode and provides continuous and stable power.

Fig. 15. Instantaneous photovoltaic (a) voltage, b) current, and c) power) V_PV, I_PV, P_PV.Simulation results of PV and the grid-connected converter validate the accuracy of the proposed model. Fig. 16 shows the output voltage and current of the converter at full load (FL) condition, and Fig. 17 shows the output waveform of ab load voltage.

Fig. 16. Output voltage/current: FL conditions.

Fig. 17. Load voltage Vl_ab.

Conclusions

This paper presented a solar photovoltaic PV generation system integrated into a three-phase grid. The maximum power extraction from the PV array was achieved via the application of a Maximum Power Point Tracking MPPT control system. The Artificial Neural Network ANN algorithm is employed to ensure higher dynamic performance of the proposed system, which is modeled and implemented in MATLAB-SIMULINK. The grid-tied DC/AC converter, which is constructed with a two-level IGBT design, operates at 50 Hz and is generated via a three-phase Pulse Width Modulation (PWM) strategy with a carrier frequency of 2 kHz. Based on simulation outcomes, the NARMA-L2 and an appropriate modulation approach are crucial for the reliable and precisely regulated power grid converter. The system parameters were tuned to achieve stable and efficient voltage and current at the PV side.

Conflict of Interest

The authors declare that they do not have any conflict of interest.