# An Intelligent Maximum Power Point Using a Fuzzy Log Controller under Severe Weather Conditions

Authors: Khaled Bataineh
Journal: International Journal of Photoenergy
 (2018)

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## Abstract

This study is aimed at providing a comparison between fuzzy systems and convectional P&O for tracking MPP of a PV system. MATLAB/Simulink is used to investigate the response of both algorithms. Several weather conditions are simulated: (i) uniform irradiation, (ii) sudden changing, and (iii) partial shading. Under partial shading on a PV panel, multipeaks appeared inP-V characteristics of the panel. Simulation results showed that a fuzzy controller effectively finds MPP for all weather condition scenarios. Furthermore, simulation results obtained from the FLC are compared with those obtained from the P&O controller. The comparison shows that the fuzzy logic controller exhibits a much better behavior.


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## Body

## 1. Introduction

Due to global warming along with high prices of fossil fuel and its hazards on the environment, searching for other renewable green sources of energy drew the attention of the world. Solar energy is considered the main source of renewable energy. Solar energy is a permanent, nonpolluting, and low-running-cost source of energy. Photovoltaic (solar cell) systems are one of the most favorable systems, and their installation is spreading widely. Photovoltaic (PV) systems can be connected to a grid or can be used as stand-alone systems [1, 2]. The power generated from a PV panel depends on the amount of solar irradiance, cell temperature, and load [3–5].Maximum power point tracking is essential to keep the system operating at its optimal power. Up to date, the overall PV efficiency reaches around 15%. Raising the power generated from PV systems can be achieved by tracking the maximum power point of the output power-voltage curve. This curve may contain multilocal maximum points under partially shaded conditions [6]. Employing MPPT techniques is considered the most economic way of improving the overall efficiency of the system compared with methods that rely on improving solar cell fabrication [7].Several methods for finding MPP are developed over the last three decades [7–14]. These methods vary in terms of requiring sensors, cost, efficiencies, complexity, correct tracking when sudden shading or temperature changes, and convergence speed. Esram and Chapman presented a review of 19 methods for finding MPP [8]. Generally, the techniques are classified into three classes: offline, online, and hybrid methods. Offline methods are the short-circuit current (SCC) method, open-circuit voltage (OCV) method, look-up table method, and curve-fitting-based [9] and artificial intelligence (AI) algorithms. Online methods are the extremum seeking control (ESC) method, ripple correlation control (RCC) method, hill climbing (HC) method [10], incremental conductance (IC) method, and perturbation and observation (P&O) method [11] and modified P&O [12, 13].As mentioned previously, when a PV system is subjected to a partially shaded condition, multiple peaks appeared in theP-V curve. Conventional methods such as P&O, hill climbing, IC, direct search algorithm, and line search algorithm with the Fibonacci sequence method could miss the global MPP [8, 14–16]. To overcome the problem with the conventional methods, several researchers have proposed several improvements. Because of the fact that the P&O method uses a fixed step size when tracking MPP, variable step size methods are developed to improve the steady-state performance and dynamic response of the PV system [17]. It has been shown that the small step size causes low oscillations during steady-state weather conditions but with a slower response. On the other hand, a larger step size leads to a faster response but with higher oscillations at steady-state conditions. Moreover, the performance of such systems reduces significantly due to the random nature of weather conditions. Tafticht et al. proposed a new method that combines nonlinear expression that is based on the open-circuit voltage with the P&O method to improve the tracking efficiency of MPP [18]. Recently, a new approach has been suggested by Heydari-doostabad et al. based on extremum seeking control (ESC) [19]. It takes the advantage of a band-pass filter (BPF) using a high-pass filter (HPF) and a low-pass filter (LPF) by only passing input power frequencies that include derivatives of PV with respect to its voltage, and so the system will operate at the global maximum point. Noguchi et al. [20] proposed a short-circuit pulse-based MPPT with fast scan on the P-V curve to identify the proportional parameter which is commonly used in a current-based MPPT [21]. Although the proposed method successfully found the global maximum point, momentary power loss is accompanied with additional extra cost. To avoid this extra power loss, Kazmi et al. proposed a controller that fluctuates the converter’s duty cycle from zero to one to measure the open-circuit voltage and the short-circuit current and then computes the optimum voltage and current [22]. Based on the computed values, in single step, the operating point is moved to the optimal operating point. The conventional hill climbing algorithm is utilized to keep the system operating around the maximum point. Although the system finds global maximum, significant loss in power is experienced. Utilizing the particle swarm optimization algorithm under abnormal weather conditions results in a long computation time to reach the maximum operating point [23].Intelligent systems such as neural networks (NN) and fuzzy logic controllers (FLC) have been used successfully in tracking the maximum power point of PV to decrease computation power requirement, while increasing the speed and efficiency of the tracking [2]. They are robust and relatively simple to design. However, they require complete knowledge of the operation of the PV system by the designer. Othman et al. validated the ability of FLC to find MPP compared to the P&O algorithm [24]. Punitha et al. used a modified IC method with NN to supply Vref and compared the results with those of the FLC and P&O approach to validate their proposed method [25]. Results showed the highest performance with the least response time when using ANN with IC. Subiyanto et al. presented a new method using a Hopfield neural network (HNN) to tune FLC parameters to enhance robustness and accuracy [26, 27]. Although fuzzy control has a good ability dealing with the nonlinear system, its main drawback is the generation of cumulative error due to continuous integral calculus. Most FLC-based MPPT techniques take the error (et) and the change in error (det/dt) as inputs. However, the requirement of differentiation not only increases the complexity of calculation but also may induce large amounts of errors from merely small amounts of measurement noise. The main objective of this study is to compare between conventional P&O and fuzzy logic controller MMPT algorithms under several extreme weather conditions. To carry out the comparison, computer-aided simulations are used to validate the results.


## 2. PV Modeling and Characteristics

Detailed description of PV modeling can be found in [2]. I-V nonlinear characteristic curves are shown in Figure 1. Partial shading occurs when radiation is not equally distributed on PV cells. The current generated by shaded cells is decreased. This leads to the reduction in the overall power generated from the PV system. In order to understand such phenomena, a PV array system with modules connected in series is considered. Under partial shading conditions, multiple peaks are presented in the P-V characteristic (see Figure 2).Figure 1
Effect of irradiance changes onI-V characteristics.Figure 2
Characteristic curves of PV under partial shading.


## 3. MMPT Algorithm

In this section, a brief description about the P&O controller and fuzzy logic controller is given.


### 3.1. P&O Controller

A detailed description of the P&O controller can be found in [28–30]. The flow chart of the P&O algorithm is shown in Figure 3. The basic idea of this controller is to provoke perturbation by acting (decrease or increase) on the PWM duty cycle and observing the effect on the output PV power. The algorithm can be summarized as follows; after recording the present power levels produced by the system, the algorithm performs a perturbation to the operating point by means of changing the duty cycle and measures the resulting power accordingly. If there is an increase in the power levels, another iteration is performed in the same direction. Otherwise, iteration in the reverse direction is carried out. The peak is detected when the power oscillates about a certain value; i.e., increasing and decreasing the duty cycle result in less power levels.Figure 3
Flowchart of the P&O algorithm.To generate maximum power, a DC-DC boost converter is used and placed between the source and the load. To simulate the P&O algorithm, the PV system composed of a PV panel, a boost DC-DC converter, MPPT, and resistive load is built as shown in Figure4. In this work, a boost converter controlled by the MPPT algorithm is used to track MPP. Voltage gain of the converter is given as [31]
(1)VoVs=11−D.Figure 4
Schematic diagram of the PV system with MPPT.The minimum values of inductance and capacitance of the converter necessary for stability (listed in Table1) are given as [31]
(2)Lmin=DR1−D22Fs,Cmin=VoDFsΔVoR.Table 1
DC-DC booster converter design values.
Electrical characteristic
Values
Inductance
9 × 10−4 H
Output capacitor
0.001 F
Input capacitor
1 × 10−9 F
Resistance load
28.18 ΩThe P&O algorithm has been implemented in a Simulink model to control the duty cycle of the switching signal of the converter.∆V and ∆P are used to detect irradiation variations, and the algorithm determines the value of the duty cycle necessary to attain the maximum power point on the load. It changes the duty cycle value by a step size (s) which is determined by the designer.


### 3.2. Proposed Fuzzy Logic Controller

The proposed FL MPPT logic diagram shown in Figure5 has two inputs (power and ∆V) and one output (D). Triangular shape membership functions have been used. The fuzzy inference is carried out using a Mamdani-type system. The defuzzification uses the center of gravity to compute the output of this FLC which is the duty cycle:
(3)D=∑j=1nμDj−Dj∑j=1nμDj.Figure 5
General diagram of a fuzzy controller.The proposed fuzzy rules of the system are shown in Table2. These two input variables and the control action for the tracking of the maximum power point are illustrated in Figure 5.Table 2
Rules of the fuzzy controller.
∆V↓\P→
Very low
Low
Medium
High
Very high
Very low
Very low
Very low
Medium
High
Very high
Low
Very low
Very low
High
High
Very high
Medium
Medium
Medium
Medium
Medium
Very high
High
Medium
Medium
High
Medium
Very high
Very high
Low
Low
Medium
High
Very highBased on the results of the Simulink model, tuning of the rules is performed to design the fuzzy logic controller. Values of fuzzy controller inputs are compared with twenty-five rules of the system and are implicated with the membership functions. The implication has been chosen to be an “and” operator that chooses minimum values of membership functions. The implicated rules were aggregated using a maximum method. Figure6 shows the surface view for the relation between fuzzy inputs and output. A centroid method has been selected for defuzzification by calculating the center of mass of the aggregated membership function. The crisp value represents the duty cycle of the switching signal that triggers the IGBT in the boost converter.Figure 6
Surface view for fuzzy inputs (P, dV) vs. output (D) (adappted from Allataifeh et al. [2]).


## 3.1. P&O Controller

A detailed description of the P&O controller can be found in [28–30]. The flow chart of the P&O algorithm is shown in Figure 3. The basic idea of this controller is to provoke perturbation by acting (decrease or increase) on the PWM duty cycle and observing the effect on the output PV power. The algorithm can be summarized as follows; after recording the present power levels produced by the system, the algorithm performs a perturbation to the operating point by means of changing the duty cycle and measures the resulting power accordingly. If there is an increase in the power levels, another iteration is performed in the same direction. Otherwise, iteration in the reverse direction is carried out. The peak is detected when the power oscillates about a certain value; i.e., increasing and decreasing the duty cycle result in less power levels.Figure 3
Flowchart of the P&O algorithm.To generate maximum power, a DC-DC boost converter is used and placed between the source and the load. To simulate the P&O algorithm, the PV system composed of a PV panel, a boost DC-DC converter, MPPT, and resistive load is built as shown in Figure4. In this work, a boost converter controlled by the MPPT algorithm is used to track MPP. Voltage gain of the converter is given as [31]
(1)VoVs=11−D.Figure 4
Schematic diagram of the PV system with MPPT.The minimum values of inductance and capacitance of the converter necessary for stability (listed in Table1) are given as [31]
(2)Lmin=DR1−D22Fs,Cmin=VoDFsΔVoR.Table 1
DC-DC booster converter design values.
Electrical characteristic
Values
Inductance
9 × 10−4 H
Output capacitor
0.001 F
Input capacitor
1 × 10−9 F
Resistance load
28.18 ΩThe P&O algorithm has been implemented in a Simulink model to control the duty cycle of the switching signal of the converter.∆V and ∆P are used to detect irradiation variations, and the algorithm determines the value of the duty cycle necessary to attain the maximum power point on the load. It changes the duty cycle value by a step size (s) which is determined by the designer.


## 3.2. Proposed Fuzzy Logic Controller

The proposed FL MPPT logic diagram shown in Figure5 has two inputs (power and ∆V) and one output (D). Triangular shape membership functions have been used. The fuzzy inference is carried out using a Mamdani-type system. The defuzzification uses the center of gravity to compute the output of this FLC which is the duty cycle:
(3)D=∑j=1nμDj−Dj∑j=1nμDj.Figure 5
General diagram of a fuzzy controller.The proposed fuzzy rules of the system are shown in Table2. These two input variables and the control action for the tracking of the maximum power point are illustrated in Figure 5.Table 2
Rules of the fuzzy controller.
∆V↓\P→
Very low
Low
Medium
High
Very high
Very low
Very low
Very low
Medium
High
Very high
Low
Very low
Very low
High
High
Very high
Medium
Medium
Medium
Medium
Medium
Very high
High
Medium
Medium
High
Medium
Very high
Very high
Low
Low
Medium
High
Very highBased on the results of the Simulink model, tuning of the rules is performed to design the fuzzy logic controller. Values of fuzzy controller inputs are compared with twenty-five rules of the system and are implicated with the membership functions. The implication has been chosen to be an “and” operator that chooses minimum values of membership functions. The implicated rules were aggregated using a maximum method. Figure6 shows the surface view for the relation between fuzzy inputs and output. A centroid method has been selected for defuzzification by calculating the center of mass of the aggregated membership function. The crisp value represents the duty cycle of the switching signal that triggers the IGBT in the boost converter.Figure 6
Surface view for fuzzy inputs (P, dV) vs. output (D) (adappted from Allataifeh et al. [2]).


## 4. Simulation Results and Discussion

The performance of the proposed FLC is evaluated using MATLAB/Simulink. The electrical specifications of the PV cell areIsc=4.75A, Voc=0.6V, and Rs=5.1×10−3Ω. The simulated model consists of 72 cells connected in series to form a PV module. A partially shaded model is simulated by connecting two modules in series allowing each module to receive different levels of irradiation. The P&O MPPT controllers and FLC were simulated under the following tests: (i) uniform irradiation, (ii) sudden changing, and (iii) partial shading. The values of power listed in Table 3 demonstrate that a significant increase in the power output is obtained by using FLC.Table 3
Comparison between output power values with and without MPPT.
Case no.
Irradiance level (W/m2)
Output power (W) (without MPPT)
Output power (W) (with MPPT)
% increase
1
800
102.5
123.2
20.7%
2
600
64.9
87
34%
3
500
45
70.8
57%
4
300
21.4
38.7
80%Figure7 shows that the FLC has a great ability to find MP in extremely short time when a PV panel is subjected to sudden changes of irradiation (full shading conditions). To accurately investigate the performance of the FLC, the tracking error and tracking efficiency are defined [3]:
(4)efficiency=PpvPmpp×100%,error=Pmpp−PpvPmpp×100%.Figure 7
Comparison between fuzzy and P&O partial shading.
(a)
Partial shading—1000 to 800 W/m2
(b)
Partial shading—800 to 500 W/m2
(c)
Partial shading—600 to 400 W/m2
(d)
Partial shading—500 to 300 W/m2Power values on the load after applying FLC have been compared with the nominal values of the maximum power points for several cases of uniform irradiation and partial shading. Results listed in Table4 show that the FLC has efficiently found the MPP for all uniform irradiation and partial shading scenarios studied.Table 4
Values of model outputs.
Case no.
Condition
Ir1 (W/m2)
Ir2 (W/m2)
Nominal power (W)
Power after fuzzy (W)
Efficiency
1
Uniform irradiation
1000
1000
149
149
100%
2
Uniform irradiation
900
900
133
133
100%
3
Uniform irradiation
800
800
118
117.5
99.6%
4
Uniform irradiation
700
700
102.5
101.5
99%
5
Uniform irradiation
600
600
87.2
87
99.8%
6
Uniform irradiation
500
500
71.3
70.8
99.3%
7
Uniform irradiation
400
400
56.5
56
99%
8
Uniform irradiation
300
300
41.5
41
99%
9
Uniform irradiation
200
200
26.6
24.5
92%
10
Partial shading
1000
800
126.3
126
99.8%
11
Partial shading
900
600
95.7
94
98%
12
Partial shading
800
500
79.5
79
99.4%
13
Partial shading
700
500
78.2
78
99.7%
14
Partial shading
600
400
62.3
62
99.5%
15
Partial shading
900
300
61.4
60
97.7%
16
Partial shading
700
300
48
47.5
99%
17
Partial shading
500
300
46.3
46
99.4%To further prove the ability of FLC to track the MPP under partial shading, a comparison between the proposed algorithm and the P&O algorithm is conducted. Results listed in Table5 show that the P&O algorithm is trapped at local peaks while the fuzzy controller finds the global peak. Figure 7 shows the output power for the fuzzy controller compared with the P&O algorithm at different cases. The irradiation applied on the simulated model at this case is equal on the whole panel and suddenly decreased partially at 0.2 s. The fuzzy controller found the peak at the first part with accuracy greater than that of the P&O algorithm. After partial shading being applied on 36 cells of the PV panel, the fuzzy controller tracked the global maximum power point while the P&O algorithm is trapped at the local peaks. The fuzzy controller has reached the global point with an efficiency of 99% while the P&O controller failed to reach this point. The fuzzy controller detects irradiation changing by detecting changes in voltage and power values of the PV system. This controller has the ability to change the duty cycle by a precise difference depending on membership functions. P&O changes the value of the duty cycle by a fixed step every time irradiation changes. Because of the fixed step value, it does not reach the necessary precise value of the duty cycle to get a maximum power from the system and gets trapped at local maximum under partial shading conditions due to its way of tracking by looking for the first peak in power values.Table 5
Comparison between the fuzzy controller and P&O.
Ir1 (W/m2)
Ir2 (W/m2)
Local peak (W)
Global peak (W)
Output of P&O (W)
Output of fuzzy (W)
1000
800
71.24
126.3
68
126
800
500
55.7
79.5
53
79
600
400
41.5
62.3
39
61
500
300
34
46.3
31
46


## 5. Conclusions

In this study, the fuzzy logic controller (FLC) for maximum power point tracking (MPPT) of a photovoltaic system under variable insolation conditions has been developed to track the maximum power point of the PV system. A MATLAB/Simulink model consists of a PV panel and a boost converter with FLC connected to a resistive load that has been built in order to evaluate the performance of the proposed controller. The proposed system showed its ability to recover from sudden changes and maintain stability under partial shading conditions. A comparison between the performance of the proposed FLC and perturbation and observation controller has been made. The results show that the fuzzy logic controller has reached the global point with an efficiency of 96% while the P&O controller failed to reach this point.



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