In a cell, losses are proportional to the resistance in the corresponding circuit. Losses in a cell occur due to multiple processes, including the reflection of incident light at the cell surface, the absorption of photons without electrons and free holes, and the redistribution of electrons and voids. The following equation expresses the solar cell’s distinctive behavior as shown in Figure 2 (Chatrenour et al., 2017). I p v = I p h − I D − I S H (1) Where current PV (Ipv), diode current (ID), and diode voltage (Vd). I_SH = V_pv + I_pv, where Ipv is the output current, Vpv is the input voltage, RS and RSH are the solar cell’s corresponding series and parallel resistance, and RS/RSH is the leakage current. Shockley diodes have a voltage-current characteristic, and that characteristic can be written as a formula for the diode current, ID. I D = I O e v D a V t − 1 (2) Here, Io is the reverse saturation current; VD = Vpv + IpvRS is the diode voltage; a is the diode ideal constant;

V t = N s ⋅ k b e T T is the operating temperature of the solar cell; Ns is the number of series cells; kb is the Boltzmann constant; e is the electron charge; and T is the diode’s thermal voltage. Adding Eq. 2 to the first equation yields the solar panel’s defining equation, which is as follows: I P V = I p h − I o e V P V + I P V R S a V t − 1 − V P V + I P V R S R S H (3)

The value of the photovoltaic current Ipv is related to the variations in light intensity and temperature as shown in Eq. 3.

In order to maintain a constant load voltage between the PV array and inverter, a DC-DC boost converter is employed (Necaibia et al., 2017). As the voltage produced by PV systems is typically insufficient to power loads directly, this is an essential component of PV applications. In this study, a novel ANN control based MPPT approach was implemented to maximize power output from a DC-DC boost converter before feeding it into the input of an RS MLI. By calculating the duty cycle for the converter switch and running at a high switching frequency, Maximum Power Point Tracking (MPPT) is a technique for getting the most power out of PV panels. If the converter is in continuous conduction mode, the current through the inductor is always present (Abdullah et al., 2012). We provide duty cycle, inductor (L), and capacitor (C) formulas below. V o u t V i n = 1 1 − D (4) i n d u c t o r L = V i n × D × T Δ i L (5) C a p a c i t o r   C = V o u t × D R × Δ V o u t × f (6)

Vin and V0 are the boost converter’s input and output voltages; D is the duty cycle. D > 1 means output voltage > input voltage. Figure 3 depicts a DC-DC boost converter with PV integration and the ANN control based MPPT approach for maximizing PV duty cycle.

When a boost converter is used in conjunction with a PV array, it is discovered that the average current from the PV array increases as the duty cycle rises, resulting in a decrease in the voltage from the PV array as a whole. In order to raise the PV array’s break-even point, D modifies its V-I characteristic. When D is decreased, the average current from a PV array drops while the voltage is raised. If the PV array’s operating point moves to the right, it means the array’s output has been modified. In order to keep the DC voltage output at the VSC terminal constant, the DC-DC converter’s value of D is automatically adjusted using the perturb and absorb MPPT approach.

In (Yahya and Yahya, 2023), DC-DC boost converter technology to track the maximum power of a photovoltaic (PV) system using a maximum power point tracking (MPPT) controller based on a modified version of particle swarm optimization (MPSO). A DC-DC boost converter was utilized to increase the input DC voltage of the PV module. The boost converter supplied power for the DC-AC multilevel PWM inverter, which supplied the output AC voltage to a single inductive load. It is common practise to employ cascaded multilayer inverters to condition power in renewable energy applications due to its simplicity and low cost. Modulations in the DC link capacitor voltage result in low order harmonics and inter harmonics at the output of the multilevel inverter. The lowest number of harmonics is achieved using phase disposition pulse width modulation (PDPWM). Energy from the inverter cells.

Solar and wind power dominate the renewable energy market due to their low environmental impact and high irradiation and kinetic energy output, respectively. Figure 4 depicted wind energy conversion system (WECS), purpose of WECS is to exploit the kinetic energy of wind for use in mechanical power generation. Low efficiency, non-linearity and unpredictability in wind speed, and high construction cost are all factors that prevent widespread adoption of wind energy (Manwell et al., 2010). Therefore, a control algorithm is necessary to optimize performance and cut expenses. Using a wind turbine, one can convert wind energy into electricity DWT. DWT are made up of blades and a motorized device. An AC-DC and DC-DC converter are required on the control side. In this study, a horizontal wind turbine with variable speed was used. Since variable speed turbines can generate electricity at varying wind speeds, they have a higher efficiency rating than fixed speed turbines (Nurzaman et al., 2017). In this study, a permanent-magnet synchronous generator is used (PMSG). PMSG’s high efficiency at low speeds has made it a popular choice for use in small-scale wind turbines. On the control side, an ANN control based MPPT algorithm locates and maintains the turbine’s maximum power point, maximizing its efficiency. Here, we present a DC-DC boost converter that is managed by a ANN control based MPPT algorithm and integrated into a wind power generation setup. In this paper, we’ll go over the results of a simulation test of ANN control based MPPT controllers for a residential wind turbine run through the Simulink MATLAB modelling environment.

Wind turbines’ peak mechanical power, stated as (Abdullah et al., 2011) P max = 1 2 ρ C p A V w 3 (7) Where ρ is the density of the air (in kg/m3), A is the swept area of the rotor blades (in m2), and Vw is the speed of the wind (in metres per second). Cp is the power coefficient, is written as (Gite and Pawar, 2017). c p = c 1 C 2 λ i − C 3 β − C 4 e 5 − C λ i + C 6 λ (8) 1 λ i = 1 λ + 0.08 β − 0.035 β 3 + 1 (9) λ = ω m * R V w (10)

C1 to C6 are rotor-specific. In this paper, C1 = 20, C2 = 140, C3 = 0.4, C4 = 28, C5 = 21, and C6 = 0.068.

Figure 5 is an electrical circuit schematic that depicts the PMSG, rectifier, and boost converter all in one convenient location. This model’s goal is to find the relationship between DC grid load current and turbine.

The current in dq reference frame represented as d d t i s d i s q = − R s L s d − L s d L s q ω e L s d L s q ω e R s L s q i s d i s q + 1 L s d 0 0 1 L s q v s d v s q ( 11) Thus, the expression for the mechanical equivalent torque of an electromagnetic force and the mechanical torque of a machine can be written as T e = N Ψ f + L s d − L s q i s d i s q (12) T m = P ω m = 1 2 ρ π R 2 C P V w 3 ω m (13)

Hence the rotor speed can be calculated d ω d t = T e − T m − B ω m j t + j p (14)

A MPPT algorithm known as P&O is utilized to improve performance is shown in Figure 6. The turbine will be operating at its maximum possible efficiency with the help of MPPT. P&O algorithms function by modifying a control parameter and observing the resulting change in output (Kavaskar and Mohanty, 2019). This algorithm is simple, effective, and does not call for any additional hardware or sensors. Δ P = P k − P k − 1 (15)

Delta D rises when P is positive and Vs. is negative. If P and the voltage change are positive, delta D will fall. Delta D decreases for a positive voltage change and negative P. If both P and the voltage change are negative, then delta D is too (Alsafasfeh et al., 2012).

Both the input voltage and output current of the PV array play a role in the I-V and P-V curves that define the PV module. Insulation-voltage and potential-voltage plots. This graphic depicts as MPP at a given temperature and radiation level (where 25°C is assumed for the temperature and 100 W/m2 is assumed for the radiation level). This is the sweet spot for maximizing both power output and efficiency from a PV module. In this case, the MPP is the general maximum, which is another name for the MPP.

Solar cell current (a) and power output (voltage) (b) are shown as a function of solar irradiance (W/m2) in Figure 8. The two most important parts of a PV system are the DC-DC boost converter and the DC-AC VSI. As a result of the boost converter, the 280 V DC maximum power point of the PV unit is increased to 480 V (to 500 V). To achieve maximum power tracking, the MPPT controller’s incremental conductance approach was used to vary the DC-DC boost converter’s duty cycle in response to changes in solar irradiance. We analyzed a three-level IGBT bridge circuit for a PV inverter (VSI) using pulse width modulation (switching frequency of 1980 Hz). The inverter uses synchronous reference frame theory and two-control to regulate the AC voltage at the output. The inverter’s 260 V AC output is increased to 4.16 kV so that it can be connected to the IEEE-13 bus power system network.

Using a Figure 10 diagram of the MV distribution power system’s solar PV and wind integrated power network, this part discusses the identification of HIF using intelligent classifiers following the below 4steps.

• Create disturbances in MATLAB/Simulink to obtain faulty existing data.

The DWT is a powerful method for separating a transient signal into its constituent parts, which it then displays in the domain of time-frequency instead of the conventional time domain (Elkalashy et al., 2008). The basic concept is to analyze the signal by expanding and contracting it. A continuous signal f (t) is defined in both CDWT and DWT, with the definition provided by Eq. 16. C W T a , b = 1 a   ∫ − ∞ ∞ f t * h t − b a d t (16)

The mother wavelet is the initial point from which a wavelet feature is formed. CDWT is an alternate method for avoiding the same resolution issue that plagues STFT. In contrast to the DWT technique, however, this one has low redundancy during signal reconstruction. The DWT is an effective data technique for signal analysis because it permits the signal to be sampled with distinct peaks. For decades, this sophisticated and powerful instrument has been employed to regulate the safety switches. There are other ways to compute time and frequency information, such as with a fast Fourier transform (FFT), a short-time Fourier transform (STFT), or a continuous- (CDWT), but DWT has been utilized because of its quick computing speed and precision (Chen et al., 2016). Since this is the case, we can express DWT as Eq. 17. D W T m , k = 1 a 0 m ∑ n f n * h k − n a 0 m a 0 m (17)

Algorithm

Below (Chen et al., 2016) we display the various decomposition levels of the signal X(n). Here are the procedures for signal decomposition:

First, through a denoising process, the original X(n) is decomposed into a series of levels.

Choosing a subset of levels from which to reconstruct the signal is the second stage.

Third, re-create the signal using the values you’ve chosen.

In Step 4, you’ll choose the sampling rate, window size, decomposition levels, and mother wavelet.

Where n and m are integers, h is the wavelet function, a 0 m and n a 0 m are sizing and interpretation constants, respectively. By using DWT, one can separate a signal into its low-frequency g(n) and high-frequency h(n) approximation and detailed coefficients, respectively as shown in Figure 11. This process of successive approximation is repeated until the signal has been decomposed into a large number of low-resolution sub-signals. In comparison to the Haar wavelet, the Daubechies 4 (db4) is a more effective frequency extractor, it was chosen as the mother wavelet for fault detection in this work. And unlike Coiflet and Meyer wavelets, it reduces signal redundancy and satisfies Parsevall’s theorem (Daubecheis, 1992). The condition shown in Eq. 18 represents the optimal decomposition of L-levels N = 2 L (18) Where N is the level, and L is the length. B = F 2 L + 1 (19)

From Eqs. 19, B is the level-to-level bandwidth in hertz, and F is the sample rate in hertz. In order to divide the signal into its component parts, a sampling rate of 20 kHz is being considered, with each phase of the current signal receiving 800 samples over a length of 5,000 points. Using Eq. 18, we can determine the different band frequencies that were captured at each level, and they are as follows: Approximation is made using the detailed coefficient d4, which represents frequencies from 5 to 2.5 kHz, 2.5 to 1.25 kHz, 1.25 to 0.625 kHz, and 0.625 to 0.3125 kHz, respectively. In the proposed study, the mother wavelet of db4 is used with detailed coefficients on 5 levels for varied fault current signals captured throughout each cycle.

NNRBFs are trained with data sets generated from short circuit simulations at all line sections accounting for four different types of failures, and then applied to the problem of fault detection in a simulated DG-based distribution system. By analyzing the three-phase currents coming from the main source at the feeding substation, it is possible to identify a single-phase-to-ground fault, a phase-to-phase fault, a two-phase-to-ground fault, or a three-phase fault. In order to standardize the fault currents in the three-phase output at the main source or feeder substation, the maximum fault currents for each fault type are calculated. This equation is used to standardize currents (Yu et al., 2008): I n o r m a l = I I max (20)

The maximum fault current, or Imax, is the product of the fault current and the fault type, and it varies depending on the nature of the defect. The normalized three-phase fault currents are used to classify various fault types. With k input neurons and m hidden neurons, the NNRBF is a three-layer feed-forward neural network. The input layer feeds data into the hidden layer, while the hidden layer is made up of neurons with radial basis activation functions. In Figure 12 we see a typical NNRBF, and in Figure 12 we see an NNRBF used for training.

There are several calculations taken into account during NNRBF training. Input k-dimensional vector X is used to calculate a scalar value by the network, which is then output. Y = f X = w 0 + ∑ i = 1 m w i ϕ D i (21) Where (Di) is the RBF and (w0) is the bias, (wi) is the weight parameter, (m) is the number of hidden-layer nodes, and (m) is the bias.

The Gaussian function is used as the RBF in this investigation, and it is given by. ∅ D i exp − D i 2 σ 2 (22) D i = ∑ j = 1 k X j − C j i 2 (23)

Di is the distance between the input vector X and each data centre, where is the radius of the cluster represented by the centre node. Di, the distance between two points, is typically calculated using the Euclidean norm and is presented as a cypher layer in (Yu et al., 2008). Figure 13 depicts the training procedures for the RBFNN and how they are implemented.

The RBFNNs were implemented in the MATLAB software for the fault detection technique, and training data was generated in the Dig SILENT Power Factory 14.0.523 software by simulating various faults created at the 5th BUS of each line. We can extract the fault distance from each source and the number of defective lines from the RBFNNs’ target vector by running simulations. Here, we break down the inputs and outputs of the training data that was used to hone the generated RBFNNs.

Table 1 describes that comparison between coefficients of phase a, b, c currents and NNRBF output of phase a, b, c and ground resistance of 20 Ω at bus 5. Conventional fault types like LG, LL, LLG, and both LLLG and HIF occurrence are used here.

Table 2 describes that comparison between coefficients of phase a, b, c currents and NNRBF output of phase a, b, c and ground resistance of 10 Ω at bus 5. Conventional fault types like LG, LL, LLG, and both LLLG and HIF occurrence are used here. In no fault case ground current value is high at 20 Ω when compared to 10 Ω it means when resistance is high ground current value will be very low and vice versa.

Here, we present the simulation results for the IEEE 13-bus power network that included both PV and Wind. We simulated the PV and Wind method we intend to use to detect and identify HIF in the MV distribution network. To test the viability of the strategy, we run a MATLAB/Simulink simulation of the distribution model shown in Figure 7. In Figure 14A, we can see the time-varying current signal during the typical feeder state, which lasts for 0.25s. The HIF analysis was run alongside simulations of various power system failures to prove the viability of the proposed method. The three-phase current waveform during this time period is shown in Figure 14B in the event of an HIF fault and a single line to ground (LG). As can be seen in Figures 14C, D, the magnitude of the fault current and voltage in the case of an HIF fault in phase C of a three-phase system are small. It is shown in Figures 14E, F that if an LG fails in phase A of a three-phase system, the amplitude of the current signal is quite large, making it challenging to detect HIF in power systems. To address these issues in real time, we extracted the features using a DWT analysis, which decomposes the signal across the temporal and frequency domains. Every cycle, DWT is applied to 800 samples of the phase current signal at four different levels of decomposition. There is a different spectrum of frequencies represented by each tier; Table 1 displays the calculated SD values for each of the detailed coefficient levels and the final decomposed level (d4) (d1, d2, d3, and d4). In this paper, we present a DWT analysis of the A, B, and C stages of the system under normal conditions. Table 2 summarizes the results of the DWT analysis performed on faults with different fault resistance, such as LL, LLG, and three-phase faults, and the SD characteristics derived from these faults that were used to train classifiers to identify HIF in the system. There were 13 buses in the system, and each one had a fault applied to it so that the DWT data could be collected and used to train and test the classifiers. In this research, we used eighty percent of the data for training our classifiers and twenty percent for testing. The current setup consists of three input neurons (representing the various potential root causes of the issue) and a single output neuron (the precise count of faulty lines). Mean square error (MSE) is a common metric used to evaluate the efficacy of neural networks. All RBFNNs are considered well-trained if their MSE is less than 0.0002 and they have undergone no more than 38 training epochs. After faults are categorized, RBFNNs are put through their paces. Initial network simulation and data collection were performed in MATLAB/Simulink, covering both steady-state and transient conditions as well as the occurrence of common faults like LG, LL, LLG, and LLLG, and even HIF. As shown in Figures 14A–F, the normal operation of the power grid results in an asymmetrical current waveform due to the distribution of electrical demand.

Table 3 describes the comparison on various classification methods and % accuracy ‘ X ’ represents the fault type/parameter which is not considered for classification, and ‘/’ represents the occurrence of fault.