# Roach Infestation Optimization MPPT Algorithm for Solar Photovoltaic System

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

- The paper proposes the RIO algorithm to track the GMPP of the PV system under uniform solar irradiance and partial shading conditions.
- The efficacy of the proposed RIO algorithm was tested in different unconstrained benchmark functions.
- The proposed RIO technique is realized to have an excellent searching performance in terms of contributing a better dynamic response, faster convergence time, higher tracking accuracy, and more robustness against the presence of the system uncertainties and load variations in the PV system as compared to PSO, P&O, and IC schemes.
- The gains of the PI-controller are optimized with some commonly used performance indices (i.e., evaluation criteria) such as ISE, ITSE, IAE, and ITAE. It is found that the values obtained in the RIO technique improve the dynamic response of the PV system as compared to the PSO technique.

## 2. Studied Photovoltaic (PV) System

_{s}and R

_{sh}are the intrinsic series and shunt resistor of the PV cell (Ω), respectively. I

_{sh}is the current through R

_{sh}. D

_{i}is the intrinsic diode. I

_{d}is diode current (A), I

_{sh}is shunt current (A), I

_{ph}is the light-generated current in the cell (A). V

_{pv}and I

_{pv}are the PV output voltage (V) and current (A), respectively. G is the solar irradiation (W/m

^{2}).

_{d}is the voltage across the diode (V).

_{s}and n

_{p}are the number of cells connected in series and parallel, q is the electron charge (C), K is Boltzmann’s constant (J/K), A is the p-n junction’s idealistic factor, T is the cell’s absolute temperature (°K), T

_{r}is the cell reference temperature (°K), I

_{ph}is the cell’s photocurrent (it depends on the solar irradiance and temperature), I

_{rs}is the cell’s reverse saturation current, I

_{sc}is the short-circuit current of the PV cell, V

_{oc}is the open-circuit voltage of the PV cell and G is the solar irradiance.

_{w}is the power electronics switch (e.g., MOSFET). D

_{1}is the freewheeling diode, C

_{1}is the input filter capacitor and D is the duty ratio.

_{w}) is regulated by the duty cycle (D), which is generated from the reference voltage signal (i.e., V

_{mpp}). The MPP and corresponding voltage signal (V

_{mpp}) of the PV system for different shading patterns are obtained from the RIO algorithm. The voltage error signal (V

_{err}) between V

_{mpp}and actual PV voltage (i.e., P

_{pv}) is given to proportional plus integral (PI)-controller to generate the desired PWM signal for MPPT and enhance the system dynamics. In this paper, different evaluation criteria such as integral of squared error (ISE), integral of time-squared error (ITSE), integral of absolute error (IAE), and integral of time-absolute error (ITAE) are employed for tuning the gains of the PI-controller. The mathematical minimization function is used for solving the ISE, ITSE, IAE, and ITAE evaluation criteria. The MATLAB/Simulink model of the studied PVS is shown in Figure 4. The modeling parameters of the PVS and DC-DC converter are given in Table 1 and Table 2, respectively. The detailed modeling and selection of the DC-DC converter components/parameters are taken from [41,42].

^{2}, the solar spectrum of air mass 1.5, and module temperature at 25 °C. Manufacturers of photovoltaic modules typically provide the ratings at only one operating condition (i.e., STC) [44,45]. However, the PV module operates over a large range of environmental conditions such as variations of solar irradiation, temperature, partial shading, etc., in the field. The suitability of a PV module technology for a particular site depends on five major factors which include the annual solar irradiation distribution, variations in the efficiency of PV module technology with solar irradiation, annual temperature distribution and module temperature coefficient, variations in the solar spectrum distribution, and rate of power degradation of the PV modules with time. Since temperature affects the amount of power we get from a solar system, the electrical efficiency of the PV module depends on ambient temperature, and it reduces when the temperature increases and vice versa [44,45]. The temperature coefficient implies how much will be the decrement in power output if the PV module temperature varies from STC. It is also true that this temperature coefficient varies from one type of solar cell technology to another [44].

## 3. Roach Infestation Optimization (RIO) Based MPPT Algorithm

^{l}

_{i}represents the velocity of ith particle/agent (i.e., cockroach) for the lth iteration, x

^{l}

_{i}is the current location for the lth iteration, ${p}_{i}^{best}$ is the best dark place (location) of the ith agent, C

_{0}and C

_{max}are constants and R

_{1}is a random number.

_{pv}) and current (I

_{pv}) from the PVS and subsequently regulates it by adjusting the duty ratio (D). The value of D is updated using the optimization algorithms to achieve the MPP as shown in Figure 4. In this work, the global peak power (G

_{P}) of the PV system is attained using the optimization algorithm to update D in the search process during both uniform irradiation/temperature and PSCs.

## 4. Results and Discussion

#### 4.1. P–V and I–V Characteristics Curves of the PV System

_{mpp}) at MPPT will be higher with a high value of peak power under different shading patterns, as observed in Figure 7. A similar analysis can be examined in Figure 8 that the corresponding PV current (I

_{mpp}) at MPPT will be higher with a high value of peak power.

_{p}), the corresponding voltage (V

_{mpp}), current (I

_{mpp}) and resistance (Z

_{mpp}) values at MPP of the PVS under the selected test patterns are given in Table 5.

#### 4.2. Performance Assessment of the RIO and PSO Algorithms for Different Benchmark Functions

_{min}).

#### 4.3. Performance Assessment of the RIO and PSO Algorithms for Tuning the PI-Controller Parameters

_{p}) and integral (K

_{i}) gains of the PI-controller using PSO and RIO algorithms. The above-mentioned four objective functions (f) are derived from the voltage error signal (V

_{err}) between the voltage at MPP (V

_{mpp}) and the actual PV voltage (V

_{pv}) as shown in Figure 4. The details about the ISE, ITSE, IAE, and ITAE functions can be found in [48,49].

_{err}) graph of each objective function. The simulation results are obtained from Figure 4 with load resistance (R) = 50 Ω.

_{err}performance indices such as the settling time (t

_{s}), maximum dip (V

_{derr}), and the optimal parameters of the PI-controller for RIO and PSO are listed in Table 7. From the results, it is found that the best results are obtained with ITSE for both RIO and PSO algorithms than IAE, ISE, and ITAE values. The same can be examined for other transitions of the uniform and partial shading conditions in the studied PV system (Figure 4).

#### 4.4. Comparison between Different Algorithms for MPPT

_{pv}and I

_{pv}are significant for identifying the MPP by the algorithms. The harvested actual PV power (P

_{pv}) of the PVS based on the results obtained from the P&O technique, incremental conductance (IC) method, PSO, and the proposed RIO algorithms are presented in Figure 11 and Figure 12. The simulation results are carried out under the same patterns as shown in Case-4.1 and the obtained PI-controller gains by the ITSE method.

_{pv}) is more oscillating (i.e., minimum chattering) in the conventional P&O and IC methods as compared to the PSO and the proposed RIO techniques. Moreover, the results obtained with the IC method are less oscillating than the P&O method. The same was examined in the case study, which is shown in Figure 12 and other partial shading conditions. Hence, from the results, it can be concluded that the bio-inspired PSO and RIO MPPT techniques have significantly improved search performance as compared to the conventional P&O and IC-based methodologies. These accomplishments of the bio-inspired algorithms were demonstrated by assessing the results with that of the conventional MPPT techniques such as P&O and IC for different uniform and PSCs in the PV system [8,40].

_{pv}) tracked by each technique of the PVS is presented in Table 8, as assessed in Figure 11 and Figure 12. Additionally, in order to evaluate the actual MPPT performance attained by both algorithms, the mathematical formulation for MPPT efficiency (η

_{MPPT}) is represented as follows [7]:

_{MPPT}is the maximum achievable power or true MPP of the PV system. P

_{pv}is the actual power extracted from the PV array which depends upon the ability of the MPPT technique to attain a closer value of the true MPP (values shown in Figure 11 and Figure 12). It is true that the higher the MPPT algorithm’s accuracy, the higher the η

_{MPPT}. The tracking efficiency of the MPPT algorithms for the PV system is shown in Table 8.

_{MPPT}varies with change in partial shading pattern due to the search behavior of the optimization algorithms being random in nature to track the optimal point/solution. Additionally, the convergence speed (i.e., searching process time) is the time that the PV system takes to achieve the steady-state value of P

_{pv}. The searching process time (t

_{c}) of the P&O, IC, and PSO techniques (Table 8) is more than that of the RIO technique for MPPT, as studied in Figure 11 and Figure 12. Furthermore, it can be seen that the value of t

_{c}is higher for the partial shading scenario as compared to the uniform irradiation on the PV panel.

#### 4.5. Comparison Performance Evaluation for the Presence of Uncertainty and Variation of Load (R)

_{signal}and P

_{noise}represent the average received signal power and noise power, respectively. V

_{signal}and V

_{noise}are the corresponding signal voltage and noise voltage, respectively.

_{mpp}. As a result, the GMPP can be tracked back for load variations. The value of Z

_{mpp}for different shading patterns is presented in Table 5. Changing the output load does not prevent the algorithm from effectively obtaining the proper MPP in RIO. The RIO algorithm is tested and compared with PSO, P&O, and IC schemes under different PCSs, variations of load, and the presence of uncertainties to prove the system’s robustness and reliability.

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DC | Direct Current |

GMPP | Global Maximum Power Point |

IAE | Integral of Absolute Error |

ISE | Integral of Squared Error |

ITAE | Integral of Time-Absolute Error |

ITSE | Integral of Time-Squared Error |

MATLAB | MATrix LABoratory |

MOSFET | Metal-Oxide Field Effect Transistor |

MPP | Maximum Power Point |

MPPT | Maximum Power Point Tracking |

PSC | Partial Shading Condition |

PSO | Particle Swarm Optimization |

PV | Photovoltaic |

PVS | Photovoltaic System |

RIO | Roach Infestation Optimization |

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**Figure 1.**Global cumulative solar PV capacity in 2019 [3].

**Figure 2.**Classification of some common MPPT control methods [4].

**Figure 6.**A 4S structure of PV array system (

**a**). Pattern-1, (

**b**). Pattern-2, (

**c**). Pattern-3, (

**d**). Pattern-4.

**Figure 9.**Convergence characteristic graph for: (

**a**). Langerman-5 function, (

**b**). Bohachevsky-1 function.

**Figure 10.**Dynamic response of voltage error (V

_{err}) graph for: (

**a**). RIO algorithm, (

**b**). PSO algorithm.

**Table 1.**Studied solarex MSX60 PV module parameters [43].

System Parameters/Data | Symbol | Value |
---|---|---|

For One PV Module | ||

Maximum power for 1000 W/m^{2} and 25 °C | ${P}_{pv}^{max}$ | 59.90 W |

Voltage at MPP for 1000 W/m^{2} and 25 °C | ${V}_{pv}^{max}$ | 17.1 V |

Current at MPP for 1000 W/m^{2} and 25 °C | ${I}_{pv}^{max}$ | 3.5 A |

Open-circuit voltage | V_{oc} | 21.0 V |

Short-circuit current | I_{sc} | 3.74 A |

Series resistance | R_{s} | 0.10363 Ω |

Shunt resistance | R_{sh} | 283.3724 Ω |

Ideality factor | A_{0} | 1.5406 |

Temperature coefficient of Isc | 0.00247%/°C | |

Temperature coefficient of V_{oc} | −0.8%/°C |

System Parameters/Data | Symbol | Value |
---|---|---|

Capacitor | C | 464 μF |

Input filter capacitor | C_{1} | 10 μF |

Inductor | L | 1.14 mH |

Switching frequency | f_{s} | 50 kHz |

Load resistance | R | 40 Ω, 50 Ω, 60 Ω |

Optimization Algorithm | Parameter | Symbols | Value |
---|---|---|---|

RIO * | Cockroach parameter | C_{0} | 0.4 |

Cockroach parameter | C_{max} | 1.4 | |

PSO | Cognitive parameter | c_{1} | 1.2 |

Social parameter | c_{2} | 1.6 | |

Weight parameter | w | 0.4 |

Shading Pattern | Module-1 | Module-2 | Module-3 | Module-4 | |
---|---|---|---|---|---|

Pattern-1 at 25 °C | Uniform shading | 1000 | 1000 | 1000 | 1000 |

Pattern-2 at 25 °C | Uniform shading | 600 | 600 | 600 | 600 |

Pattern-3 at 25 °C | Partial shading | 1000 | 800 | 600 | 400 |

Pattern-4 at 25 °C | Partial shading | 800 | 600 | 400 | 200 |

Pattern-5 at 20 °C | Uniform shading | 1000 | 1000 | 1000 | 1000 |

Pattern-6 at 20 °C | Partial shading | 800 | 600 | 400 | 200 |

Pattern-7 at 50 °C | Uniform shading | 1000 | 1000 | 1000 | 1000 |

Patterns | G_{p} (W) | V_{mpp} (V) | I_{mpp} (A) | Z_{mpp} (Ω) |
---|---|---|---|---|

Pattern-1 | 239.600 | 68.400 | 3.500 | 19.5428 |

Pattern-2 | 137.919 | 66.455 | 2.07537 | 32.0207 |

Pattern-3 | 115.856 | 52.6927 | 2.19871 | 23.96538 |

Pattern-4 | 76.5723 | 52.3029 | 1.46402 | 35.7255 |

Pattern-5 | 250.314 | 71.7273 | 3.4898 | 20.5534 |

Pattern-6 | 80.4385 | 54.8416 | 1.46674 | 37.3901 |

Pattern-7 | 176.991 | 52.3176 | 3.383 | 15.4648 |

Functions [38] | DD | Search Space | Statistical Values | PSO | RIO * |
---|---|---|---|---|---|

GoldStein-Price | Best (f_{min}) | 8.39 × 10^{−5} | 6.56 × 10^{−5} | ||

5 | [−200, 200] | Mean | 8.40 × 10^{−5} | 6.61 × 10^{−5} | |

SD | 9.20 × 10^{−7} | 8.95 × 10^{−7} | |||

Perm | Best (f_{min}) | 6.63 × 10^{−6} | 5.93 × 10^{−6} | ||

5 | [−200, 200] | Mean | 6.63 × 10^{−6} | 5.99 × 10^{−6} | |

SD | 0.33 × 10^{−7} | 0.31 × 10^{−7} | |||

Langerman-5 | Best (f_{min}) | 4.86 × 10^{−7} | 2.74 × 10^{−7} | ||

5 | [−200, 200] | Mean | 4.88 × 10^{−7} | 2.79 × 10^{−7} | |

SD | 0.57 × 10^{−9} | 0.52 × 10^{−9} | |||

Bohachevsky-1 | Best (f_{min}) | 8.75 × 10^{−6} | 7.41 × 10^{−6} | ||

5 | [−200, 200] | Mean | 8.77 × 10^{−6} | 7.41 × 10^{−6} | |

SD | 1.83 × 10^{−8} | 1.67 × 10^{−8} | |||

Ackley | Best (f_{min}) | 0 | 0 | ||

5 | [−200, 200] | Mean | 0 | 0 | |

SD | 0 | 0 |

Function (f) | Algorithm | |||||||
---|---|---|---|---|---|---|---|---|

PSO | RIO * | |||||||

V_{derr} | t_{s} (ms) | K_{p} | K_{i} | V_{derr} | t_{s} (ms) | K_{p} | K_{i} | |

ISE | −0.0135 | 205.85 | 0.915 | 7.402 | −0.012 | 195.57 | 0.875 | 7.017 |

ITSE | −0.012 | 187.03 | 0.827 | 6.917 | −0.0105 | 155.73 | 0.78 | 6.157 |

IAE | −0.015 | 215.65 | 0.975 | 8.157 | −0.013 | 199.56 | 0.915 | 7.573 |

ITAE | −0.018 | 231.12 | 0.997 | 8.894 | −0.014 | 206.15 | 0.986 | 8.439 |

Pattern | MPPT Algorithm | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

P&O [18] | IC [17] | PSO [23] | RIO * | |||||||||

P_{pv} (W) | η_{MPPT} (%) | t_{c} (ms) | P_{pv} (W) | η_{MPPT} (%) | t_{c} (ms) | P_{pv} (W) | η_{MPPT} (%) | t_{c} (ms) | P_{pv} (W) | η_{MPPT} (%) | t_{c} (ms) | |

Pattern-1 | 235.766 | 98.400 | 184.963 | 236.001 | 98.498 | 158.843 | 236.209 | 98.585 | 113.964 | 237.659 | 99.190 | 58.451 |

Pattern-2 | 135.319 | 98.398 | 181.057 | 135.843 | 98.495 | 157.345 | 135.903 | 98.538 | 113.819 | 136.807 | 99.194 | 58.459 |

Pattern-3 | 113.545 | 98.006 | 178.671 | 113.594 | 98.048 | 155.650 | 113.651 | 98.097 | 124.856 | 114.502 | 98.862 | 67.208 |

Pattern-4 | 75.069 | 98.038 | 176.496 | 75.084 | 98.057 | 156.924 | 75.128 | 98.113 | 124.572 | 75.703 | 98.865 | 67.211 |

Pattern-5 | 246.311 | 98.401 | 180.107 | 246.579 | 98.508 | 158.256 | 246.769 | 98.584 | 113.963 | 248.288 | 99.191 | 58.453 |

Pattern-6 | 78.831 | 98.002 | 181.398 | 78.840 | 98.013 | 157.681 | 78.922 | 98.115 | 124.857 | 79.526 | 98.866 | 67.203 |

Pattern-7 | 174.153 | 98.397 | 184.521 | 174.433 | 98.502 | 159.782 | 174.479 | 98.581 | 124.857 | 175.555 | 99.189 | 67.203 |

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**MDPI and ACS Style**

Pradhan, C.; Senapati, M.K.; Ntiakoh, N.K.; Calay, R.K.
Roach Infestation Optimization MPPT Algorithm for Solar Photovoltaic System. *Electronics* **2022**, *11*, 927.
https://doi.org/10.3390/electronics11060927

**AMA Style**

Pradhan C, Senapati MK, Ntiakoh NK, Calay RK.
Roach Infestation Optimization MPPT Algorithm for Solar Photovoltaic System. *Electronics*. 2022; 11(6):927.
https://doi.org/10.3390/electronics11060927

**Chicago/Turabian Style**

Pradhan, Chittaranjan, Manoj Kumar Senapati, Nicholas Kakra Ntiakoh, and Rajnish Kaur Calay.
2022. "Roach Infestation Optimization MPPT Algorithm for Solar Photovoltaic System" *Electronics* 11, no. 6: 927.
https://doi.org/10.3390/electronics11060927