Learning Automata based fuzzy MPPT controller for solar photovoltaic system under fast changing environmental conditions

Abstract

Optimization of fuzzy Maximum Power Point Tracking (MPPT) controller using Learning Automata (LA) algorithm is proposed in this paper. The optimal duty cycle of the DC-DC converter circuit is obtained using LA for various environmental conditions through learning process. The fuzzy MPPT controller is developed using the information collected by LA through the learning process. The proposed model is developed and tested using MATLAB for standard test conditions of PV, constant temperature and varying irradiation level, constant irradiation and varying temperature level, and varying temperature and varying irradiation level. The results obtained using the proposed fuzzy MPPT are compared with the conventional Perturb and Observe (P&O) MPPT and variable step size Fuzzy MPPT based PV system. The experimental set up is developed and the test is conducted under different conditions for the solar PV system with P&O MPPT and the proposed LA Fuzzy MPPT. The results show that the proposed LA based Fuzzy MPPT method is more accurate and its tracking response is faster.

Keywords

Learning Automata Pursuit Algorithm Maximum Power Point Tracking Fuzzy photovoltaic MATLAB

1 Introduction

The solar PV power generation is greatly influenced by the environmental conditions such as solar irradiation and the temperature. The PV cell has non-linear characteristics and it has unique point at which the output power is maximum for the given environmental conditions. The Maximum Power Point (MPP) changes whenever the solar irradiation or temperature varies. The P-V characteristics of a PV module under different solar irradiations and different temperature are shown in Fig. 1(a) and (b) respectively. The MPP corresponding to each condition is marked in the figures. The Maximum Power Point Tracking (MPPT) controllers are used to change the operating point of the DC-DC converter in solar PV system based on the changes in temperature or solar irradiation so that maximum power can be transferred from source to load.

A number of MPPT algorithms have been proposed in the literatures [1, 2]. The proposed MPPT algorithms vary in the input parameters used, speed of tracking and implementation. The MPPT algorithms are categorized as (a) indirect methods and (b) direct methods [1]. The indirect methods are also called as model based methods (or) offline methods. Similarly, the direct methods are also called as model free methods or online methods [2]. Open-circuit voltage method [3, 4], Short circuit current method [4, 5], Artificial Intelligence (AI) methods such as Artificial Neural Network [6], Genetic algorithm [7] and Fuzzy Logic [8, 9] based MPPT techniques are categorized as model based MPPT methods. Perturb & Observe (P&O) MPPT [10, 11], Incremental conductance (InC) MPPT [12, 13], Extremum Seeking Control (ESC) method [14, 15] are the model free MPPT methods. The combination of online and offline methods is called as hybrid method [2].

The open circuit voltage and short circuit current method use the physical values of the PV such as open circuit voltage (V_oc), short circuit current (I_sc) to generate the control signals. The open circuit voltage method requires periodical shedding of solar PV system for measurement of V_oc. Similarly, I_sc needs to be measured periodically for short circuit current method. Periodical shutdown causes power losses and make the algorithms less efficient.

Among the model based methods, P&O MPPT algorithm is the most widely used algorithm. P&O MPPT algorithm is simple and easy to implement [16]. But, it’s tracking speed is low and it is less efficient under frequently varying weather conditions. The InC MPPT has better performance than the P&O algorithm. But, this algorithm also suffers from oscillation around MPP. Moreover, its implementation is complex [16]. The ESC MPPT is comparatively more efficient and reaching the MPP under fast changing weather conditions is also guaranteed. But, hardware implementation of this MPPT technique is very difficult [2].

Fuzzy Logic uses the experience of human experts to monitor and control the process/system. Many fuzzy based MPPT controllers are proposed in literatures for solar PV system. The fuzzy MPPT controller uses either physical parameters or instantaneous values as inputs for MPP tracking. Fuzzy Logic based MPPT algorithm presented in [8] uses temperature and irradiation as input. The instantaneous output of PV module namely PV power and/or PV voltage, PV current are used as inputs in the work presented in [17].

The important issues in designing the Fuzzy Logic Controllers (FLC) are the formation of membership functions and the development of rule base. This is generally done by the human experts based on their experience. As the number of inputs or the number of variables increases the number of rules increases exponentially. In that case, it may not be possible to derive the complete set of rules based on expert knowledge and achieve good performance. The FLC is tuned by trial and error method to improve the performance. Tuning the controller by trial and error basis is a time consuming process and the satisfactory improvement is not guaranteed. Hence, Evolutionary algorithms are used for optimization of FLC.

Genetic Algorithm (GA) [18] has been applied to learn and optimize the rule base and membership functions of the FLC. The GA based optimization of FLC for MPPT in photovoltaic system is presented in [19]. The other technique used for optimizing the rules base of FLC is Adaptive Neuro-Fuzzy Inference System (ANFIS). In [20, 21] ANFIS based MPPT for a solar PV module is presented. The ANFIS based approach utilizes Neural Network (NN) to learn the rule base and membership functions. These optimization techniques are more complex, they require high performance processors [22] and large amount of data for training. In addition to that, the training process of both GA and ANFIS techniques are time consuming.

In this paper, we propose Learning Automata based Fuzzy MPPT (LA Fuzzy MPPT) for solar PV system. The approach used for learning the rule base of a fuzzy system in this work is simple, the proposed algorithm does not require large amount of data for training and the time taken for training is comparatively less. The other main advantage of this technique is that it doesn’t require experimental data for training.

2 Fuzzy MPPT based solar PV system

Figure 2 shows the block diagram of solar PV system with fuzzy MPPT. The output of PV source is fed to the load via DC-DC Converter. The operation of the DC-DC converter is controlled by the MPPT controller. The fuzzy logic controller has a set of membership functions (MF) for each input(s) and output(s), set of rules. Based on the membership functions and rule base, fuzzy controller provides a duty cycle to the converter for the given environmental conditions so that the maximum power is transferred to load. Here, the objective is to optimize the MFs of the inputs, output and to develop the optimized rule base.

In this work, the temperature (T in °C), and solar irradiation (G in W/m²) of the PV module are selected as inputs and the output of FLC is duty cycle (D). To develop an optimized fuzzy MPPT controller, 4 MFs are selected for each of the input. The MFs of the inputs are defined as Low (L), Medium (M), High (H), and Very High (VH). The number of MFs is selected as 4. Hence, 16 rules has to be developed i.e., one has to find the rules R₁₁, R₁₂, R₁₃,. . . . , R₄₄ (refer Table 1) using the available information.

A method to develop the rule base for the fuzzy system using the available information is explained in the next section.

3 Fuzzy system development using Learning Automata

The function of MPPT is to operate the DC-DC converter at optimal duty cycle. Operation of MPPT can be viewed as a Single Stage Decision Making Problem (SSDMP) where the decision to be made is finding the optimal duty cycle for the given environmental conditions. In this work, we used Learning Automata (LA) Algorithm [23, 24] to find the optimal duty cycle.

The learning process is performed using LA for a wide operating region (range of temperature and irradiation levels). The operating region is divided into a number of control zones. Then the optimal duty cycle for each control zone is computed using LA algorithm. The rule base R₁₁, R₁₂, R₁₃,. . . . , R₄₄ of the fuzzy MPPT controller is developed using the information collected through the learning process.

3.1 Learning Automaton

The block diagram representation of Learning Automaton is shown in Fig. 3. A learning automaton is an adaptive decision-making unit situated in a random environment that learns the optimal action through repeated interactions with its environment [26]. LA sends an action (a) to the PV system (Environment) and observes the reward (O (a)) from the PV system. In the case of MPPT controller, ‘a’ is the candidate duty cycle and O (a) is the output power of PV module corresponding to duty cycle ‘a’. The objective of LA is to find the best action from the set of actions at which the output power of PV system is maximum for the given environmental conditions.

LA consists of three vectors and a learning algorithm. $〈 P, A, q, Algo 〉$

where,

P : is the set of probabilities for selecting an action. P is called as the probability density function (pdf) $P = [P_{1}, P_{2}, P_{3}, . . . P_{n}]$

n is the number of actions in the action set. Initially $P_{1} = P_{2} = \dots = P_{n} = \frac{1}{n}$

$A$ : is the set of actions. Action sets are defined by the user for all the control zones $A = {a_{1}, a_{2}, a_{3}, \dots a_{n}}$

q : is the set of q values [q₁, q₂, q₃, … q_n]

Corresponding to each action a_j there is a q value which is denoted as q (a_j) or q_j. q (a_j) is the expected value of observation O (a_j). Mathematically, $q (a_{j}) = E [O (a_{j})]$ (1)

Intuitively, if q (a_i) > q (a_j) it means that a_i is better than a_j. Moreover, if q (a^*) ≥ q (a_j) for all j, then a^* is the optimal action. Thus, if one can find q (a^*), then the optimal action can be found. The Algo helps to find q (a^*).

Algo : The algorithm which updates the behavior of automaton based on the observation and q values.

Pursuit Algorithm (PA) [25] is used as a tool by LA for learning the optimal actions. During the training process, the Pursuit Algorithm observe the rewards, update the q values through iterative process and find the optimal action for all the selected control zones. After successful learning, the data collected through the learning will be used to develop the fuzzy system.

3.2 Learning of Optimal actions

The learning process starts with the selection of number of actions, action set values and initialization of P , q values. In PA, P and q are initialized based on number of actions. The number of actions selected for each control zone is n = 10. Therefore, $P = [\frac{1}{n}, \frac{1}{n}, \frac{1}{n}, \frac{1}{n}, \frac{1}{n}, \frac{1}{n}, \frac{1}{n}, \frac{1}{n}, \frac{1}{n}, \frac{1}{n}]$

The q value is initialized as “zero” for all actions. $q = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]$

The iteration process will be initiated after initialization. The algorithm updates P and q values in a systematic way after each iteration. In each iteration, the algorithm selects a duty cycle from the action set. This duty cycle is sent to the PV system and the power output of PV module corresponding to the selected duty cycle is obtained. As far as the LA is concerned, the obtained output power is the observation. Based on the received observation, the values of P , q and the greedy action are updated. Greedy action (a_g) is the action which has the maximum estimate of q value [24]. Greedy action can be obtained using, $q^{k} (a_{g}) = max_{a \in A} q^{k} (a)$ (2) or $a_{g} = \underset{a \in A}{arg max} q^{k} (a)$ (3)

Let us say, in k^th iteration based on the probabilities P^k, an action a^k is selected. For the selected action a^k LA receives the observation which is O (a). Based on O (a), the q (a) value is updated using the equation $q^{k + 1} (a) = q^{k} (a) + α_{k} [O (a) - q^{k} (a)] .$ (4)

If the current observation O^k (a) is more than the present estimate of q (a); the new estimate q^k+1 (a) will be slightly increased. Similarly, if the current observation is less than the present estimate, then the new estimate q^k+1 (a) will be slightly decreased.

Thus, by repeatedly taking random actions and by receiving observations for several times q^k (a) converge to q (a). A small fixed value (say, 0.1) can be used for α.

Now, the probability of all actions (pdf) are updated by increasing the probability for choosing the greedy action and decreasing the probability of all other actions. The equations to update the probabilities are ${\begin{matrix} p^{k + 1} (a_{g}) = p^{k} (a_{g}) + β (1 - p^{k} (a_{g})), \forall a \in A = a_{g} \\ p^{k + 1} (a) = p^{k} (a) - β p^{k} (a), \forall a \in A \neq a_{g} \\ 0 < β < 1 \end{matrix}$ (5) where, β is the probability learning rate.

The processes starting from sending an action to the environment to updating the probability of all actions complete one iteration. The iteration is repeated until one of the probability in the pdf is almost 1 (say 0.99). The greedy action corresponding to the point of convergence will be the optimal action.

The algorithm repeats the same procedure and finds the optimal duty cycle for all the 16 control zones from C₁₁ to C₄₄. The detained explanation for the algorithm can be found in [25 –27]. The flowchart of learning optimal actions using Pursuit Algorithm is shown in Fig. 4. The data collected through LA learning process is used to develop fuzzy system. This makes the FLC more reliable and accurate. Moreover, the FLC directly gives the duty cycle as output based on the inputs and hence, the response is faster.

4 Simulation results and discussion

Learning Automata is developed using MALTAB. The range of temperature and irradiation values selected for learning process are T = 16°C to 43°C and G = 0 to 1300W/m² respectively. To compute the optimal duty cycles, the selected range of temperature and irradiation values are divided into 16 control zones as given in Table 2.

4.1 Computation of Optimal duty cycle for control zones using LA

The method of computing optimal duty cycle for one control zone, namely, C₃₂ is explained below. The irradiation values between 600W/m² and 900W/m², the temperature between 22°C and 28°C are the values corresponds to the control zone C₃₂. The optimal duty cycle for the midpoint values of the control zone is found using LA and the rule R₃₂ is defined based on the obtained result. The midpoint values of the control zone C₃₂ are T = 25°C and G = 750W/m².

From the electrical specification of the selected PV module (MSX 60PV) and the DC-DC converter, we know that the duty cycle for the selected control zone is in between 0.20 and 0.29. Now, the single decision to be made is, finding the optimal duty cycle from the set of predefined duty cycles $A_{32} = {0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27}$ . To achieve this, the learning automaton interacts with the PV system and optimizes the pdf corresponding to the optimal duty cycle for the selected zone. The converter circuit is operated by the duty cycle given from the learning automaton. The output power of PV module corresponding to the duty cycle is observed by LA. Based on the output power, LA updates the pdf. The process is repeated until the optimized pdf is achieved.

The iteration process to find the optimal pdf starts with the uniformly distributed pdf. The algorithm chooses the random duty cycle and updates the pdf based on the observation and selects the greedy action for the updated pdf for the next iteration. After a number of iterations the algorithm finds the optimal action at which the output power is maximum and selects the same action as greedy action repeatedly. The optimized pdf after completion of the learning process for the selected case is depicted in Fig. 5. The probability of the optimal action is greater than 0.99 and the other action is less than 0.01.

Based on the result, the 3rd action in the action set is the optimal action i.e., the optimal duty cycle for T = 25°C and G = 750W/m² is D = 0.20. The optimized pdf for all the control zones are obtained in a similar way using the duty cycle set assigned by the user for all the control zones.

4.2 Fuzzy logic controller

The membership functions for the inputs of FLC are formed using the range of temperature and irradiation values selected to train the LA.

The rule base of LA Fuzzy MPPT is developed using the optimized pdf and optimal action for the operating regions obtained through the learning process. The MFs of the inputs T, G and the output D are shown in Fig. 6(a), (b) and (c) respectively. The surface view is shown in Fig. 6(d).

4.3 Simulation of Solar PV system with LA Fuzzy MPPT

The Simulink model of PV system with Fuzzy based MPPT is shown in Fig. 7. Solarex MSX 60 PV Module is selected as source and DC-DC Boost converter is adapted as power conditioning unit.

The PV system with LA Fuzzy MPPT is developed in MATLAB/Simulink. A standalone solar PV system with P&O MPPT, Variable Step Size (VSS) fuzzy MPPT and the proposed MPPT are simulated for (i) Standard Test conditions (STC) of PV Module (ii) Uniform temperature and varying irradiation (iii) Uniform irradiation and varying temperature and (iv) Varying temperature and varying irradiation. The simulation results are presented and discussed in the following subsections.

4.3.1 Standard Test Conditions (STC)

Figure 8 shows the waveforms of output power obtained from the PV system with P&O MPPT, VSS Fuzzy MPPT based PV system and the proposed LA fuzzy MPPT based PV system for STC. The maximum output power of MSX60 PV under STC is 60 W. The output power obtained by simulating the LA Fuzzy MPPT based PV system is 59.93 W. The output power matches well with the manufacturer’s data sheet information. This confirms that the duty cycle given by the proposed system is accurate. From Fig. 8, it can be seen that the P&O MPPT controller takes long time to reach the MPP. Moreover, it oscillates around the MPP after reaching the MPP. The Fuzzy MPPT takes less time to reach MPP when compared to the P&O MPPT. But, the proposed MPPT method has faster response and reached MPP very quickly compared to the other methods.

4.3.2 Uniform temperature and varying irradiation

In this case, the temperature of the module is kept constant (T = 27°C) and the irradiation is varied. The irradiation is 800W/m² from 0 to 50 ms 950 W/m² from 50 ms to 100 ms. The output power for the selected conditions is shown Fig. 9(a). The output voltage of the PV module is presented in Fig. 9(b).

The LA Fuzzy MPPT responded quickly whenever the changes occur in the environmental conditions and also the duty cycle given by the controller is more accurate comparing to the other MPPT controllers.

4.3.3 Uniform irradiation and varying temperature

Here, the irradiation of PV module is maintained constant and the temperature is varied. The irradiation is kept at G = 900W/m². The temperature is maintained at 27°C from t = 0 to 50 ms. At 50 ms, the temperature is decreased to 19°C and maintained till 100 ms. Figure 10(a) shows the output power of PV with P&O MPPT, fuzzy MPPT and LA Fuzzy MPPT. The output voltage of PV for the selected conditions is shown in Fig. 10(b). The results obtained under uniform irradiation and varying temperature matches to the desired values. It means that the optimal duty cycles learned by the LA MPPT and the rule base generated based on information obtained by LA are accurate.

4.3.4 Varying temperature and varying irradiation

The PV system with different MPPT controllers is operated under varying temperature and irradiation. From 0 to 50 ms the temperature is kept at 26°C and the irradiation is maintained as 900 W/m². The temperature is changed to 22°C and the irradiation is changed to 800 W/m² at 50 ms and maintained until 100 ms. From 100 ms to 150 ms again the temperature and irradiation are changed to 30 °C and 1000W/m² respectively. The temperature and irradiation variations are depicted in Fig. 11(a) and (b) respectively.

The Duty cycle generated by different MPPT controllers for the selected conditions are plotted in Fig. 12 (a). The duty cycle of LA Fuzzy MPPT controllers is comparatively more precise and constant for all the conditions. The duty cycle has changed immediately whenever the changes occurred in the environmental conditions.

The output power for the varying temperature and irradiation is shown in Fig. 12(b). The P&O MPPT and Fuzzy MPPT took more time to reach the MPP when compared with the proposed MPPT. The proposed MPPT reached MPP within 2 ms in all cases.

Figure 12(c) shows the output voltage obtained for the selected cases. The output voltage of P&O MPPT based PV system has ripples due to the oscillation of duty cycle. The ripple in the output voltage is shown in Fig. 12(d).

5 Hardware implementation

A hardware setup is developed and the proposed LA Fuzzy MPPT controller is experimentally validated. The developed hardware is shown in Fig. 13. The regulated power supply is used as source and a DC-DC Boost Converter is used as a power conditioning unit. PIC 16F887 Microcontroller is used for pulse generation. The driver circuit is powered by a voltage regulator circuit which is powered from external source. National Instrument’s data acquisition card and transducers are used for data processing.

The developed hardware is operated under various conditions with P&O MPPT. The variations in input voltage input current of the P&O MPPT based solar PV system is shown in Fig. 14(a) and (b) respectively The duty cycle response of the P&O algorithm is shown in Fig. 14(c).

It can be seen from the figures that the duty cycle increase or decrease in steps until it reach the MPP and it has oscillation. It can also be noted that whenever the change has occurred in the input(s), the P&O starts tracking towards the new MPP by decreasing or increasing the perturbation values in steps. It takes approximately 10 to 15 steps to reach the MPP and the duty cycle has oscillation after reaching the MPP. The power output of the solar PV system with P&O MPPT is shown in Fig. 14(d).

The solar PV system is operated under various voltage and current levels with LA Fuzzy MPPT and the performance of the proposed MPPT is validated. The input voltage variation is shown in Fig. 15(a) and the variation in input current is shown in Fig. 15(b). Figure 15(c) is the duty cycle generated by the LA optimized Fuzzy MPPT.

The LA fuzzy MPPT adapt to the changes quickly and gives a fixed duty cycle immediately. The duty cycle generated by the LA Fuzzy MPPT is more accurate and it has no oscillation. Hence, it helps reduce the oscillation in the output power. The output power of solar PV system with proposed LA fuzzy MPPT for the given input is shown in Fig. 15(d).

The experimental results show that the proposed LA fuzzy MPPT produces accurate duty cycle corresponding to the changes occurs at the input of the solar PV system. Moreover, the duty cycle has no oscillation. Thus, the performance and efficiency of LA Fuzzy MPPT based PV system is better when compared to the other MPPT methods.

6 Conclusion

A standalone solar PV system with optimized Fuzzy MPPT controller for fast changing environmental conditions is presented in this paper. A new optimization technique using Learning Automata based approach is proposed for development of fuzzy MPPT. Optimization of the output membership functions and the rule base development of the fuzzy MPPT is achieved by the information collected using Learning Automata for various environmental conditions through a learning process. The tracking performance of the proposed LA Fuzzy MPPT method is analyzed by simulating the model for several conditions such as uniform irradiation level and fast changing environmental conditions. The simulation results obtained from the proposed MPPT based PV system is compared with P&O MPPT and fuzzy MPPT. The hardware is implemented for the proposed LA optimized fuzzy MPPT based system and the performance is validated experimentally. Similarly, the hardware results obtained from P&O MPPT based system for several conditions and the results are discussed. The obtained results are satisfactory. The proposed MPP has faster tracking response and the duty cycle has better accuracy.

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