# An Effective Method for Parameter Estimation of a Solar Cell

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}, 870 W/m

^{2}, 720 W/m

^{2}, and 630 W/m

^{2}) but also estimates minimum root mean square error even at a low level of irradiations. Furthermore, the statistical analysis validates that the average accuracy and robustness of the proposed algorithm are better than other algorithms. The best values of root mean square error generated by the proposed algorithm are $7.1700\times {10}^{-4}$ and $9.8412\times {10}^{-4}$ for single-diode and double-diode models. It is observed that the estimated parameters based on the optimization process are highly consistent with the experimental data.

## 1. Introduction

_{oc}), short circuit current (I

_{sc}), and current at maximum power point (I

_{mpp}) under standard test conditions (i.e., 1000 W/m

^{2}, 25 °C). The practical parameters vary at every instant with a change in weather conditions. The aging effects of PV also alter the parameters of the equivalent circuit [3,8,9].

## 2. Methodology

#### 2.1. PV Panel Model

#### 2.2. Objective Function

#### 2.3. Hybrid Algorithm

#### 2.3.1. Particle Swarm Optimization (PSO)

_{i}and velocity v

_{i}. The position of the particles represents the probable solution, and the velocity represents the rate of change of position of the particle concerning the current position. The particles change their positions with respect to the positions of the best particle. The velocity update equations are given by:

_{1}and c

_{2}are the acceleration parameter, r

_{1}and r

_{2}are the random number in the range [0, 1] and $w$ is the inertial weight vector which maintains balance between exploration and exploitation.

#### 2.3.2. Whale Optimization Algorithm (WOA)

#### Shrinking Movement

#### Spiral Movement

#### 2.3.3. Hybrid WOAPSO Algorithm

**Step 1**: Initialize the random population of search agents with position and velocity defined as:$${X}_{i}=\text{}\left({x}_{i}^{1},\dots \dots \dots \dots .{x}_{i}^{d},\dots \dots \dots .{x}_{i}^{n}\right),\text{}for\text{}i=1,2,\dots \dots \dots \dots .N$$$${V}_{i}=\text{}\left({v}_{i}^{1},\dots \dots \dots \dots .{v}_{i}^{d},\dots \dots \dots .{v}_{i}^{n}\right),\text{}for\text{}i=1,2,\dots \dots \dots \dots .N$$**Step 2**: Calculate the fitness of each search agent. If the problem is the minimization problem, then $\overrightarrow{{X}^{\ast}}$ is the position corresponding to the minimum fitness and for maximization problem $\overrightarrow{{X}^{\ast}}$ is the position corresponding to the maximum fitness. $\overrightarrow{{X}^{\ast}}$ is the best search agent.**Step 3**: Update the constant parameters A, C, using Equations (10) and (11) and l lying between [–1, 1] and p is the probability between 0 and 1.**Step 4**: If p < 0.5 and |A|$\ge $1, then select the random position of search agent (X*) in search space and update the position of search agent using Equations (9) and (13).

**Step 5**: Update the velocity of search agent based on the best position of search agent (X*) in the search space using the following equation:$${v}_{i}^{d}\left(t+1\right)=w\times {v}_{i}^{d}\left(t\right)+{c}_{1}\times {r}_{1}\times \left({X}^{\ast}-{x}_{i}^{d}\left(t\right)\right)$$**Step 6**: Update the position of the particles using Equation (17).**Step 7**: Go to step 3 until the termination criteria is met. The algorithm terminates when either maximum number of iterations or minimum error criteria is attained.**Step 8**: In the last iteration the returned value of $\overrightarrow{{X}^{\ast}}$ represents the global minimum and the position corresponding to it represents the solution of the problem.

#### 2.3.4. Implementation of WOAPSO for Parameter Extraction

#### Single-Diode Model

_{p}), series resistance (R

_{s}), shunt resistance (R

_{sh}), diode saturation current (I

_{SD}) and diode ideality factor (a

_{1}). The range of these parameters are [0–1, 0.001–0.5, 0–100, 0.01–0.5, 1–2].

#### Double-Diode Model

_{p}), series resistance (R

_{s}), shunt resistance (R

_{sh}), diode saturation currents (I

_{SD}, I

_{SD1}), and diode ideality factor (a

_{1}, a

_{2}). The range of these parameters are [0–1, 0.001–0.5, 0–100, 0.01–0.5, 0.01–0.5, 1–2, 1–2].

## 3. Results

^{2}at 33 °C. The SS2018P PV module is composed of 36 polycrystalline cells connected in series and generate the I-V data under different irradiance levels i.e., 1000 W/m

^{2}, 870 W/m

^{2}, 720 W/m

^{2}and 630 W/m

^{2}. The data collection consists of a total of 20 I-V measurements for solar cell and 27 for PV module. The values of current and voltage for solar PV module (SS2018P) are measured across variable resistive load (0.1–250 Ω, 2 A). The measured value of voltage and current at different irradiance level is presented in supplementary materials. For a reasonable comparison, the search ranges (i.e., upper and lower bound) for each parameter are tabulated in Table 1, which are the same as those being used by investigators in [27]. The proposed WOAPSO algorithm is implemented on MATLAB 2018a platform with Intel

^{®}core ™ i7-HQ CPU, 2.4 GHz, 16 GB RAM Laptop. In order to conduct the experiment, the sample size, and the estimated number of objective function evaluations are set at 30 and 50,000, respectively. Furthermore, a minimum of 30 separate runs are carried out to prevent the contingency.

#### 3.1. Parameter Estimation of Single-Diode Model Using WOAPSO

_{p}, I

_{sd}, a, R

_{s}, R

_{sh}) are required to be estimated for a single-diode model. Table 2 signifies the values of parameters optimized by WOAPSO and RMSE for the comparison. The WOAPSO algorithm provides the lowest RMSE of 7.1700 × 10

^{−4}than others (Table 2 and Table S2). Here RMSE values are acquired as the index for the evaluation of results with previously existing algorithms implemented by the researchers.

^{2}and 33 °C), all over the voltage range. The error relating the measurement results for each of 20 pair points is determined by IAE and RE, which is calculated by using Equations (18) and (19), respectively.

#### 3.2. WOAPSO for Parameter Estimation of Double-Diode Model

_{p}, I

_{sd}, I

_{sd1}, a

_{1}, a

_{2}, R

_{s}, R

_{sh}) are required to be optimized. The values of optimized parameters and minimum of RMSE are presented in Table 3. The characteristics curve in terms of current-voltage and power-voltage for the double-diode model is redrawn based on the best optimized parameters (Figure 4). It can be observed that the estimated data based on optimized parameters are in keeping with the experimental data set.

#### 3.3. WOAPSO for Parameter Estimation of SS2018P PV Module

_{p}, I

_{sd}, a, R

_{s}, R

_{sh}) for SDM of solar PV module at distinct levels of irradiance and constant temperature of 25 °C is presented in Table 4 and Tables S7–S9. The characteristics curve of current-voltage and power-voltage for solar PV module is redrawn based on best optimized parameters obtained by implementing the WOAPSO algorithm at a different level of irradiance, i.e., 1000 W/m

^{2}, 870 W/m

^{2}, 720 W/m

^{2}, and 630 W/m

^{2}and is depicted in Figure 5. It is found that the calculated data obtained by the WOAPSO is very effectively in keeping with the experimental data set. The curve of IAE between experimental and estimated values at 1000 W/m

^{2}, 870 W/m

^{2}, 720 W/m

^{2}, and 630 W/m

^{2}, is shown in Figure 6.

#### 3.4. Convergence Analysis

#### 3.5. Robustness and Statistical Analysis

## 4. Discussion

^{2}) are less than 0.0018 (Table S6). More importantly, the computational time for WOAPSO is less than other algorithms (Table 4). The average execution time of each algorithm on the three PV models is calculated and illustrated in Figure 9. The WOAPSO algorithm requires less time (about 26.1 s) than GWO, PSO, SCA, WOA, and PSOGSA, while GSA has the worst execution time of approximately 52 s.

## 5. Conclusions

- The proposed WOAPSO is relatively accurate and reliable at delivering the solution in terms of RMSE as compared with other algorithms such as GSA, SCA, GWO, PSO, WOA, PSOGSA, and existing algorithms in the literature.
- The I-V and P-V characteristic curves and IAE results indicate that WOAPSO can generate the optimized value of estimated parameters for all the models of solar PV cell as compared with other algorithms.
- The statistical analysis clearly depicts the robustness of the proposed WOAPSO technique on parameter estimation problem at different operating conditions.
- The convergence curves demonstrate that the best values of estimated parameters are obtained by WOAPSO, and RMSE is $7.1700\times {10}^{-4}$ and $9.8412\times {10}^{-4}$ in the case of single- and double-diode respectively.
- At different irradiation levels (i.e., 1000 W/m
^{2}, 870 W/m^{2}, 720 W/m^{2}, and 630 W/m^{2}), the proposed WOAPSO algorithm is best in producing optimized parameters (I_{p}, I_{sd}, a, R_{s}, R_{sh}) and minimum value of RMSE for PV module even at a low level of irradiation (630 W/m^{2}).

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations and Symbols

I_{p} | Photo Diode Current |

I_{sd} | Reverse Saturation Current |

R_{s} | Series Resistance |

R_{sh} | Shunt Resistance |

a | Diode Ideality Factor |

RMSE | Root Mean Square Error |

PV | Photo Voltaic |

I-V | Current-Voltage |

P-V | Power-Voltage |

MPP | Maximum Power Tracking |

V_{oc} | Open Circuit Voltage |

I_{mpp} | Maximum Power Point Current |

I_{sc} | Short Circuit Current |

GBO | Gradient Based Optimizer |

HHO | Harris-Hawk optimizer |

HBO | Heap-Based Optimizer |

SMA | Slime Mould Algorithm |

GA | Genetic Algorithm |

DE | Differential Evaluation |

SA | Simulating Annealing |

PS | Pattern Search |

HS | Harmony Search |

CS | Cooku Search |

FPA | Flower Pollination Algorithm |

BFO | Bacterial Foraging Algorithm |

BM | Bird Mating |

ABSO | Artificial Bee Swarm Optimization |

PSO | Particle Swarm Optimization |

ITLBO | Improved Teaching-Learning Based Optimization |

WOA | Whale Optimization Algorithm |

CWOA | Chaotic Whale Optimization Algorithm |

LWOA | Levy flight trajectory based WOA |

BWOA | Binary Whale Optimization Algorithm |

HAGWO | Hybrid Approach Grey Wolf Optimization |

WOA-CBO | Whale Optimization Algorithm Colliding Bodies Optimization |

MWOA | Memetic Whale Optimization Algorithm |

WOA-SA | Whale Optimization Algorithm-Simulated Annealing |

WOA-MFO | Whale Optimization Algorithm-Moth Flame Optimization |

SC-WOA | Sine-Cosine Whale Optimization Algorithm |

WOA-PS | Whale Optimization Algorithm- Pattern Search |

BS-WOA | Brainstorm- Whale Optimization Algorithm |

SDM | Single-diode Model |

DDM | Double-diode Model |

IAE | Internal Absolute Error |

RE | Relative Error |

GSA | Gravitational Search Algorithm |

SCA | Sine Cosine Algorithm |

GWO | Grey Wolf Optimization |

PSOGSA | Particle Swarm Optimization Gravitational Search Algorithm |

MLBSA | Multiple Learning Backtracking Search Algorithm |

EHHO | Enriched Harris Hawks Optimization |

IJAYA | Improved Jaya Algorithm |

GOTLBO | Generalized Opposition-Based Teaching Learning Based Optimization |

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**Figure 3.**I-V and P-V characteristics curve for estimated and experimental values for single-diode model of R.T.C France solar cell.

**Figure 4.**I-V and P-V characteristics curve for estimated and experimental values for double-diode model of R.T.C France solar cell.

**Figure 5.**Characteristics curve of simulated and experimental values at different level of irradiance (

**a**) I-V curve and (

**b**) P-V curve for single-diode model of SS2018P PV module. Symbols represent the estimated data while the solid lines represent the measured data.

**Figure 6.**Internal absolute error between measured and simulated current for single-diode model of SS2018P PV module at different level of irradiance.

**Figure 7.**Convergence curve of WOAPSO and other six algorithms for (

**a**) single-diode model (

**b**) double-diode model of R.T.C France solar cell and (

**c**) single-diode model of SS2018P PV module.

**Figure 8.**Boxplot graph of best RMSE in 30 runs for (

**a**) single diose model (

**b**) double-diode model (

**c**) polycrystalline SS2018P PV module.

Parameter | SDM/DDM | SS2018P PV Module | ||
---|---|---|---|---|

Lower Bound | Upper Bound | Lower Bound | Upper Bound | |

I_{p} (A) | 0 | 1 | 0 | 10 |

I_{sd}, I_{sd1} (µA) | 0.01 | 0.5 | 0 | 50 |

R_{s} (Ω) | 0.001 | 0.5 | 0.001 | 2 |

R_{sh} (Ω) | 0 | 100 | 0 | 2000 |

a, a_{1}, a_{2} | 1 | 2 | 0 | 100 |

Algorithms | I_{ph} (A) ± SD | I_{sd} (µA) ± SD | R_{s} (Ω) ± SD | R_{sh} (Ω) ± SD | a ± SD | RMSE |
---|---|---|---|---|---|---|

GSA | 0.7607 ± 0.0053 | 0.05 ± 0.0265 | 0.0339 ± 0.0076 | 63.7784 ± 4.304 | 1.5486 ± 0.0042 | $1.2012\times {10}^{-3}$ |

SCA | 0.7595 ± 0.0209 | 0.002 ± 0.034 | 0.0519 ± 0.0229 | 90.0685 ± 4.517 | 1.2641 ± 0.140 | $1.9123\times {10}^{-3}$ |

GWO | 0.7695 ± 0.0038 | 1 ± 0.193 | 0.0269 ± 0.0037 | 47.9136 ± 16.872 | 1.6232 ± 0.0311 | $9.4095\times {10}^{-4}$ |

PSO | 0.7383 ± 0.023 | 1 ± 0.023 | 0.0501 ± 0.0053 | 25.1251 ± 3.213 | 1.6605 ± 0.024 | $1.4320\times {10}^{-3}$ |

WOA | 0.7573 ± 0.0019 | 0.016 ± 0.0056 | 0.053 ± 0.0028 | 58.5839 ± 0.354 | 1.2476 ± 0.0043 | $9.9529\times {10}^{-4}$ |

PSOGSA | 0.7677 ± 0.0071 | 0.01 ± 0.006 | 0.0522 ± 0.0066 | 18.4587 ± 37.62 | 1.218 ± 0.0349 | $1.2400\times {10}^{-3}$ |

WOAPSO | 0.7597 ± 0.0012 | 0.499 ± 0.004 | 0.0342 ± 0.0007 | 83.0131 ± 0.027 | 1.5483 ± 0.001 | $7.1700\times {10}^{-4}$ |

Algorithms | I_{ph} (A) ± SD | I_{sd1} (µA) ± SD | I_{sd2} (µA) ± SD | R_{s} (Ω) ± SD | R_{sh} (Ω) ± SD | a_{1} ± SD | a_{2} ± SD | RMSE |
---|---|---|---|---|---|---|---|---|

GSA | 0.7641 ± 0.0079 | 0.05 ± 0.177 | 0.001 ± 0.1191 | 0.0344 ± 0.0091 | 37.780 ± 1.21 | 1.9943 ± 0.1756 | 1.5492 ± 0.1076 | $2.03\times {10}^{-3}$ |

SCA | 0.7623 ± 0.0097 | 0.0012 ± 0.059 | 0.001 ± 0.046 | 0.0595 ± 0.0067 | 52.4903 ± 24.02 | 2 ± 0.3030 | 1.2197 ± 0.2088 | $3.18\times {10}^{-3}$ |

GWO | 0.7609 ± 0.0026 | 0.3156 ± 0.0052 | 0.0001 ± 0.008 | 0.0323 ± 0.0015 | 65.6799 ± 6.5859 | 1.9426 ± 0.0625 | 1.5312 ± 0.0272 | $1.60\times {10}^{-3}$ |

PSO | 0.7676 ± 0.0016 | 0.0216 ± 0.027 | 0.0947 ± 0.234 | 0.0335 ± 0.012 | 54.9501 ± 5.4630 | 1.4606 ± 0.203 | 1.8363 ± 0.0137 | $2.90\times {10}^{-3}$ |

WOA | 0.76354 ± 0.0019 | 0.169 ± 0.0017 | 0.163 ± 0.0011 | 0.0410 ± 0.0022 | 35.7342 ± 0.7539 | 2 ± 0.034 | 1.4420 ± 0.0036 | $4.30\times {10}^{-3}$ |

PSOGSA | 0.7611 ± 0.0041 | 0.432 ± 0.0171 | 0.01 ± 0.0021 | 0.0347 ± 0.0042 | 61.72 ± 18.7135 | 1.9 ± 0.0183 | 1.5489 ± 0.0144 | $1.48\times {10}^{-1}$ |

WOAPSO | 0.7601 ± 0.0007 | 0.5 ± 0.0020 | 0.5 ± 0.0027 | 0.0311 ± 0.0005 | 100 ± 0.4345 | 1.5755 ± 0.0043 | 1.7314 ± 0.0015 | $9.8412\times {10}^{-4}$ |

**Table 4.**Comparison of proposed WOAPSO with different parameter estimation methods for SS2018P PV module (1000 W/m

^{2}).

Parameters | Algorithms | ||||||
---|---|---|---|---|---|---|---|

GSA | SCA | GWO | PSO | WOA | PSOGSA | WOAPSO | |

I_{ph} (A) | 1.0959 ± 0.0037 | 1.1742 ± 0.011 | 1 ± 0.024 | 1.1796 ± 1.009 | 1.181 ± 0.0103 | 1.168 ± 0.053 | 1.1707 ± 0.0025 |

I_{sd} (µA) | 0.001 ± 0.2246 | 0.0092 ± 0.388 | 0.001 ± 0.0759 | 0.001 ± 0.707 | 0.019 ± 1.034 | 0.001 ± 1.358 | 0.0074 ± 0.0348 |

R_{s} (Ω) | 0.001 ± 0.0253 | 0.0011 ± 0.0187 | 0.001 ± 0.0022 | 0.0022 ± 0.583 | 0.0024 ± 0.007 | 0.0075 ± 0.0342 | 0.2 ± 0.0017 |

R_{sh} (Ω) | 455.5284 ± 13.67 | 139.676 ± 19.5323 | 100 ± 0.842 | 1308.079 ± 2.466 | 18.166 ± 10.71 | 2000 ± 4.63 | 177.219 ± 0.026 |

a | 53.5976 ± 0.2493 | 1.4147 ± 1.021 | 1.2628 ± 0.0399 | 1.2429 ± 0.252 | 1.289 ± 0.6784 | 1.246 ± 0.24 | 1.3939 ± 0.0068 |

RMSE | $1.68\times {10}^{-1}$ | $1.51\times {10}^{-3}$ | $1.59\times {10}^{-1}$ | $5.13\times {10}^{-3}$ | $7.82\times {10}^{-4}$ | $3.22\times {10}^{-3}$ | $7.6714\times {10}^{-4}$ |

CPU time (s) | 17 | 12.45 | 9.3 | 10 | 7.56 | 13.17 | 7.81 |

Model | Algorithm | RMSE | |||
---|---|---|---|---|---|

Min | Mean | Max | SD | ||

Single-diode model | GSA | $1.2012\times {10}^{-3}$ | $5.4701\times {10}^{-3}$ | $2.4211\times {10}^{-1}$ | $1.3129\times {10}^{-3}$ |

SCA | $1.9123\times {10}^{-3}$ | $9.6515\times {10}^{-3}$ | $2.1642\times {10}^{-1}$ | $9.4066\times {10}^{-3}$ | |

GWO | $9.4095\times {10}^{-4}$ | $1.0441\times {10}^{-3}$ | $1.3506\times {10}^{-3}$ | $1.4050\times {10}^{-5}$ | |

PSO | $1.4320\times {10}^{-3}$ | $1.2534\times {10}^{-3}$ | $1.4074\times {10}^{-3}$ | $1.1520\times {10}^{-4}$ | |

WOA | $9.9529\times {10}^{-4}$ | $9.2032\times {10}^{-4}$ | $7.1240\times {10}^{-3}$ | $9.0250\times {10}^{-3}$ | |

PSOGSA | $1.2400\times {10}^{-3}$ | $1.7660\times {10}^{-3}$ | $5.2460\times {10}^{-3}$ | $1.9880\times {10}^{-3}$ | |

WOAPSO | $7.1701\times {10}^{-4}$ | $7.8030\times {10}^{-4}$ | $1.3436\times {10}^{-3}$ | $2.4290\times {10}^{-6}$ | |

Double-diode model | GSA | $2.0330\times {10}^{-3}$ | $4.7041\times {10}^{-3}$ | $2.6058\times {10}^{-1}$ | $1.5796\times {10}^{-3}$ |

SCA | $3.1800\times {10}^{-3}$ | $1.7932\times {10}^{-3}$ | $1.2470\times {10}^{-1}$ | $7.7256\times {10}^{-2}$ | |

GWO | $1.6000\times {10}^{-3}$ | $2.6901\times {10}^{-3}$ | $8.2830\times {10}^{-2}$ | $2.6995\times {10}^{-3}$ | |

PSO | $2.9000\times {10}^{-3}$ | $4.9713\times {10}^{-3}$ | $3.3402\times {10}^{-2}$ | $3.5833\times {10}^{-2}$ | |

WOA | $4.3000\times {10}^{-3}$ | $5.2967\times {10}^{-3}$ | $1.8698\times {10}^{-2}$ | $3.9481\times {10}^{-3}$ | |

PSOGSA | $1.4812\times {10}^{-1}$ | $1.4833\times {10}^{-1}$ | $1.4732\times {10}^{-1}$ | $1.0977\times {10}^{-2}$ | |

WOAPSO | $9.8412\times {10}^{-4}$ | $1.2481\times {10}^{-3}$ | $1.9312\times {10}^{-3}$ | $1.0581\times {10}^{-3}$ | |

SS2018P module model | GSA | $1.6877\times {10}^{-1}$ | $1.9462\times {10}^{-1}$ | $2.0011\times {10}^{-1}$ | $4.4500\times {10}^{-3}$ |

SCA | $1.5149\times {10}^{-3}$ | $5.2657\times {10}^{-3}$ | $2.0345\times {10}^{-1}$ | $1.0058\times {10}^{-2}$ | |

GWO | $1.5938\times {10}^{-1}$ | $1.5940\times {10}^{-1}$ | $5.2494\times {10}^{-1}$ | $1.6793\times {10}^{-2}$ | |

PSO | $5.1329\times {10}^{-2}$ | $1.2512\times {10}^{-2}$ | $2.6323\times {10}^{-1}$ | $1.9334\times {10}^{-2}$ | |

WOA | $7.8164\times {10}^{-4}$ | $1.8268\times {10}^{-3}$ | $2.1078\times {10}^{-2}$ | $1.3639\times {10}^{-3}$ | |

PSOGSA | $3.2258\times {10}^{-3}$ | $3.9510\times {10}^{-3}$ | $2.2333\times {10}^{-1}$ | $4.0336\times {10}^{-3}$ | |

WOAPSO | $7.6714\times {10}^{-4}$ | $7.4601\times {10}^{-4}$ | $7.5388\times {10}^{-4}$ | $7.4516\times {10}^{-5}$ |

**Table 6.**Ranking of the proposed WOAPSO and other compared algorithms on three PV models according to the Friedman test.

Algorithms | Friedman Ranking | Final Ranking |
---|---|---|

GSA | 3.9 | 4 |

SCA | 5.91 | 6 |

GWO | 3.36 | 3 |

PSO | 6.53 | 7 |

WOA | 2.05 | 2 |

PSOGSA | 5.22 | 5 |

WOAPSO | 1 | 1 |

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**MDPI and ACS Style**

Sharma, A.; Sharma, A.; Averbukh, M.; Jately, V.; Azzopardi, B.
An Effective Method for Parameter Estimation of a Solar Cell. *Electronics* **2021**, *10*, 312.
https://doi.org/10.3390/electronics10030312

**AMA Style**

Sharma A, Sharma A, Averbukh M, Jately V, Azzopardi B.
An Effective Method for Parameter Estimation of a Solar Cell. *Electronics*. 2021; 10(3):312.
https://doi.org/10.3390/electronics10030312

**Chicago/Turabian Style**

Sharma, Abhishek, Abhinav Sharma, Moshe Averbukh, Vibhu Jately, and Brian Azzopardi.
2021. "An Effective Method for Parameter Estimation of a Solar Cell" *Electronics* 10, no. 3: 312.
https://doi.org/10.3390/electronics10030312