# Maximum Power Point Tracking for Photovoltaic Systems under Partial Shading Conditions Using Bat Algorithm

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## Abstract

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## 1. Introduction

## 2. Characteristics of Photovoltaic Systems

_{o}is the diode saturation current, T

_{k}is the operating temperature at 25 °C (a standard value), q is the electron charge constant that possesses a constant value of 1.602 × 10

^{−19}°C, and A and K are the ideality factor and Boltzmann constant, respectively. In addition, V

_{pv}and I

_{pv}are the PV voltage and current, respectively, and the solar-generated current (I

_{ph}) is determined by Equation (5). Contrary to a series resistor (R

_{s}), the parallel resistor (R

_{sh}) is ignored in the modeling process in some cases because it typically possesses high values that exert an insignificant effect on the output current. Where K

_{i}is the temperature coefficient and T

_{dif}= T

_{k}− T

_{r}is the deviation of the operating temperature.

## 3. Proposed Methodology

#### 3.1. Bat Algorithm

- Bats use echolocation to determine distance and can differentiate obstacles from their prey effectively.
- Bats fly in random directions at a velocity of v
_{i}from position x_{i}to search for prey using the echolocation of a fixed frequency f_{min}with varying wavelength λ and loudness of A. Bats automatically adjust the wavelength (or frequency) of the emitted pulses and the rate of pulse emission r ∈ [0, 1] based on the proximity to the targeted prey/food. - Loudness varies from a large positive value of A to a minimum constant value A
_{min}. The initial population, that is, the number of virtual bats is randomly generated, and ranges from 5 to 30. After determining the initial fitness of the population for the defined objective function, the fitness values are updated based on the movement, pulse rate, and loudness of the bat and then modified based on the global optimum position.

_{max}. New solutions generate every iteration by modifying the pulse frequency and assuming that the wavelength maintains a constant value. For each individual bat in the search space, the velocity v

_{i}and the location x

_{i}are updated based on several rules, which also contribute to the bats’ rate of convergence to an optimized global position. These rules are given by

_{i}and loudness A

_{i}are updated accordingly as the iterations progress. As the global optimum position approaches the prey/food, the loudness decreases and the rate of pulse emission increases.

_{i}, the rate of emission r

_{i}is updated based on the following expressions. As the bats become closer to the global optimum, the pulses’ rate of emission increases and the loudness A decreases. These relationships are mathematically expressed as Equations (10) and (11).

_{i}, the rate of emission r

_{i}are 0.7 and 0.5 respectively.

_{i}is within the range [0, 1]. Figure 5 illustrates the visual representation of the process of bat echolocation system for finding the global optimum position [37] and the process of obtaining the modified position and velocity vectors using the BAT algorithm. Followed by this the flowchart explaining the flow of the optimization process using the bio-inspired BA is shown in Figure 6. This section presents the detailed explanation of the mathematical concept of BA. The deployment of the BA in finding the MPPT of the PV system under three different PS conditions is explained in the following section.

#### 3.2. Implementation of the Bat Algorithm in the Maximum Power Point Tracking

_{n}refers to the number of bats that participate in the optimization, and the objective function is the PV output power measured for each duty cycle signal. An appropriate stopping condition is required for the algorithm to end the tracking process and finalize an appropriate duty cycle for a steady-state operation. A predefined algorithm iteration is considered in many studies for the stopping conditions of optimization. In this study, the stopping condition occurs when the fitness difference of all participating bats is less than a small predefined error or when the iteration count crosses the predefined iteration count which could be configured when running the simulation results. This is the place where the optimization algorithm converges.

_{i}) represents the PV output power for the ith particle in the search space, and ∆ denotes the minimum variation that reinitializes the algorithm to find the new GMPP.

## 4. Results and Discussion

_{in}= C

_{out}= 100 μF, C

_{s}= 50 μF, L = 200 μH, and R

_{load}= 50 ohm.

^{2}, two that receive 300 W/m

^{2}, one that receives 400 W/m

^{2}, one that receives 600 W/m

^{2}, and two that receive 1000 W/m

^{2}levels of solar irradiance. Figure 8a shows the P–V curve for this condition. Under this condition, the GMPP occurs in the initial part of the duty cycle search space. Figure 8b shows that the proposed MPPT technique tracks the GMPP by approximately t = 0.7 s. Several conventional methods based on the hill climbing approach cannot track the GMPP under this condition.

^{2}, two receive 200 W/m

^{2}, two receive 600 W/m

^{2}, one receives 800 W/m

^{2}, and three receive 1000 W/m

^{2}. Figure 10a presents the resulting P–V characteristic, while Figure 10b shows the performance of the proposed method. The fast convergence and accuracy of the proposed method are thus demonstrated as the GMPP, which is accurately tracked in less than 1 s.

_{Mmax}) and (P

_{Mmin}) is the minimum measured power values among all 15 tests. The tracking power efficiency (P

_{EE}), which is used to evaluate the results, is a part of the arithmetic mean value and actual global maximum power value tracked by the proposed algorithm under partial shading conditions (P

_{EE}= (P

_{M}/P

_{A}) × 100).

_{EE}%) of 99.8%. Thus, the proposed system performs with better accuracy when tracking the GMPP under different partial shading conditions, varied load and stochastic weather condition. To compare the performance of the proposed algorithm for tracking GMPP with the existing approaches, a comparison study was carried out on evaluating the parameters of simplicity, efficiency, tracking capability, speed, dependency, reliability and response to load variation parameters associated with the different approaches. The traditional algorithms like Incremental conductance have a greater advantage in terms of the simplicity of the method but the efficiency and the accuracy of the approach is not as effective as the proposed BA. The proposed algorithm tracks the GMPP of the PV system under PS conditions more effectively than the dividing rectangles (DIRECT) algorithm, which uses the dividing process to select the exploration range or searching area. The proposed bat algorithm completely scans the tracking space before estimating the GMPP of the system whereas the DIRECT method eliminates a part of the search space to make it faster.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Photovoltaic (PV) cell equivalent circuit [14].

**Figure 2.**Output characteristic curves under PS conditions: (

**a**) I_V characteristic of PV cell in reverse bias region; (

**b**) P_V curve of PV array under partial shading conditions [14]. MPP: maximum power point.

**Figure 3.**VI curve of (

**a**) Buck converter (

**b**) Boost converters (

**c**) Buck-boost, Cuk and SEPIC (single-ended primary-inductor converter) converters.

**Figure 8.**(

**a**) P–V curve of the PV array with shading pattern 1; (

**b**) Simulation results for the PV array under partial shading. GMPP: global maximum power point, LMPP: local maximum power point. For further evaluation of the proposed approach, the second pattern is simulated under the condition in which the GMPP occurs as the last peak in the output P–V curve and involves 10 modules that receive varying irradiance levels. Of these modules, two receive 100 W/m

^{2}, two receive 200 W/m

^{2}, two receive 400 W/m

^{2}, one receives 600 W/m

^{2}, and three receive 1000 W/m

^{2}each. Figure 9a depicts the output P–V curve resulting from this condition. Figure 9b shows the proposed method tracks of the GMPP at approximately t = 0.8 s, which is considered a short tracking time.

**Figure 9.**(

**a**) P–V curve of the PV array with shading pattern 2; (

**b**) Simulation results for the PV array under partial shading. GMPP: global maximum power point, LMPP: local maximum power point.

**Figure 10.**(

**a**) P–V curve of the PV array under partial shading pattern 3; (

**b**) Simulation results for the PV array under partial shading. GMPP: global maximum power point, LMPP: local maximum power point.

Type of Controller | Voltage Equations | Current Equations | Impedance Equations |
---|---|---|---|

Buck | ${V}_{in}=\frac{1}{D}\xb7{V}_{out}$ | ${I}_{in}=D\xb7{I}_{out}$ | ${Z}_{in}=\frac{1}{{D}^{2}}\xb7{Z}_{out}$ |

Boost | ${V}_{in}=\left(1-D\right)\xb7{V}_{out}$ | ${I}_{in}=\frac{1}{\left(1-D\right)}\xb7{I}_{out}$ | ${Z}_{in}={\left(1-D\right)}^{2}\xb7{Z}_{out}$ |

Buck-boost | ${V}_{in}=-\frac{\left(1-D\right)}{D}\xb7{V}_{out}$ | ${I}_{in}=-\frac{D}{\left(1-D\right)}\xb7{I}_{out}$ | ${Z}_{in}=\frac{{\left(1-D\right)}^{2}}{{D}^{2}}\xb7{Z}_{out}$ |

Ćuk | ${V}_{in}=-\frac{\left(1-D\right)}{D}\xb7{V}_{out}$ | ${I}_{in}=-\frac{D}{\left(1-D\right)}\xb7{I}_{out}$ | |

SEPIC | ${V}_{in}=\frac{\left(1-D\right)}{D}\xb7{V}_{out}$ | ${I}_{in}=\frac{D}{\left(1-D\right)}\xb7{I}_{out}$ |

**Table 2.**Parameters of the PV-AE125MF5N PV module at standard test conditions, Temperature = 25 °C and Insolation = 1000 W/m

^{2}.

Parameter | Value/Unit |
---|---|

Maximum power rating (P_{max}) | 125 W |

Open circuit voltage (V_{oc}) | 21.8 V |

Short circuit current (I_{sc}) | 7.9 A |

Maximum power voltage (V_{mp}) | 17.3 V |

Maximum power current (I_{mp}) | 7.23 A |

Test Condition | P_{A} (exp) | P_{Mmax} (BA) | P_{Mmin} (BA) | P_{M} (BA) | P_{EE} (%) |
---|---|---|---|---|---|

Scenario 1 | 365.7 | 365.7 | 364.1 | 365.2 | 99.8 |

Scenario 2 | 280.4 | 280.4 | 278 | 279.4 | 99.8 |

Scenario 3 | 503 | 503 | 497.1 | 466.1 | 99.9 |

Evaluated Parameter | Incremental Conductance [6] | DIRECT [3] | P&O [7] | PSO [11] | DE [12] | DEPSO [14] | Proposed Method (BA) |
---|---|---|---|---|---|---|---|

GMPP tracking capabilities | Low | Moderate | High | High | High | High | High |

Efficiency | Low (Under PSC) | High | High | High | High | High | Very High |

Simplicity | Simple | Moderate | Moderate | Moderate | Moderate | Moderate | Moderate |

Speed | Very High | Moderate | Moderate | Moderate | High | Moderate | High |

Reliability | Low | Moderate | High | High | High | Moderate | High |

Location dependency | Yes | No | Yes | Yes | No | No | No |

Steady-state oscillation | Yes | No | No | No | No | No | No |

Response to load variation | Moderate | Slow | Slow | Slow | Fast | Fast | Fast |

Tuning Dependency | Low | High | High | High | Moderate | Moderate | Moderate |

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## Share and Cite

**MDPI and ACS Style**

Seyedmahmoudian, M.; Kok Soon, T.; Jamei, E.; Thirunavukkarasu, G.S.; Horan, B.; Mekhilef, S.; Stojcevski, A.
Maximum Power Point Tracking for Photovoltaic Systems under Partial Shading Conditions Using Bat Algorithm. *Sustainability* **2018**, *10*, 1347.
https://doi.org/10.3390/su10051347

**AMA Style**

Seyedmahmoudian M, Kok Soon T, Jamei E, Thirunavukkarasu GS, Horan B, Mekhilef S, Stojcevski A.
Maximum Power Point Tracking for Photovoltaic Systems under Partial Shading Conditions Using Bat Algorithm. *Sustainability*. 2018; 10(5):1347.
https://doi.org/10.3390/su10051347

**Chicago/Turabian Style**

Seyedmahmoudian, Mehdi, Tey Kok Soon, Elmira Jamei, Gokul Sidarth Thirunavukkarasu, Ben Horan, Saad Mekhilef, and Alex Stojcevski.
2018. "Maximum Power Point Tracking for Photovoltaic Systems under Partial Shading Conditions Using Bat Algorithm" *Sustainability* 10, no. 5: 1347.
https://doi.org/10.3390/su10051347