Single Input Cerebellar Model Articulation Controller (CMAC) based Maximum Power Point Tracking for Photovoltaic System

Min-Kuang Wu and Slamet WidodoDepartment of Mechanical Engineering

Southern Taiwan UniversityYungkang City, Tainan County, Taiwan R.O.C

e-mail: slamet_ae39@yahoo.co.id

Abstract—In this paper, a single-input cerebellar modelarticulation controller (CMAC)-based maximum power point tracking (MPPT) for PV system is proposed. As a type of neural network based controller with simple computationthat results in fast learning, it is more suitable for hardware implementation. The single-input CMAC control system adopts two learning stages. During off-line learning stage the CMAC controller learns about the control surface of single input fuzzy logic controller (S-FLC). At the end of this stage, the CMAC controller is capable to approximate and imitate the behavior of S-FLC. Then, an on-line learning follows this process to improve the system stability. The linear interpolation is also used to improve its performance. Simulation results show that the proposed method can be used effectively to track the MPP of solar panel, provides fast response due to temperature and solar irradiation changing and has good performance at steady state.

Keywords-single-input CMAC; MPPT; boost converter; photovoltaic.

I. INTRODUCTION

There are a lot of maximum power point tracking (MPPT) methods for photovoltaic that have been proposed. However, this topic still attracts great attention from many researchers. The most popular method over all proposed methods is perturbation and observation method (P&O). The main advantage of this method is its simplicity. This method, however, has some drawbacks such as oscillation around maximum power point during steady state operation and failure to handle sudden change of solar radiation [1]. There are also some intelligent controllers proposed for this application such as fuzzy logic, neural network and sliding mode controller. These control systems are very good alternative of MPPT controller in term of performance. However, these control algorithms need highly computation effort [2] and require high cost for implementation.

In this paper, a single-input cerebellar model articulation controller (CMAC)-based MPPT is proposed. This work is based on previous work proposed in [3]. Originally, CMAC was introduced by Albus in 1970’s [4]. CMAC plays an important role in non-linear function approximation and system modeling. The main advantages of CMAC type networks are the simple computation that results in fast learning and the possibility of low-cost digital implementation [5].

The CMAC system adopts two learning stages: off-line and on-line learning. During off-line learning stage the CMAC controller learns about control surface of the

reference control system, in this case single input fuzzy logic controller (S-FLC) is used. Since it only uses single input, this control system is known as single-input CMAC. After off-line learning completed, the CMAC controller is capable to approximate and imitate the behavior of S-FLC. Then, an on-line learning follows this process to improve the system stability. The linear interpolation is also used to improve its performance. Some simulations are performed to evaluate effectiveness of the proposed method to track maximum power point (MPP) of solar panel under temperature and solar radiation changing.

II. PV CHARACTERISTIC

PV panel is a non-linear device. It is usually described by its I–V characteristics and by the equivalent circuit. In the present work, the called “Four-Parameters Model” as mentioned in [6] was used. It is simple, only needs some parameters that can be found easily from product catalogue and has capability to predict the performance of different single crystal and polycrystalline PV panels successfully[7].

Figure 1. PV equivalent circuit.

The PV current (Ipv) can be expressed as a function of the PV array voltage (Vpv):

� Ipv=Isc{1-K1 (exp(K2(Vpv)m) - 1)}� ����

where K1, K2 and m are coefficients which are defined as:

� K1=0.01175� ����

� K2=K4 / (Voc)m� ����

� K3=ln{(Isc(1+K1)-Impp) / (K1Isc)}� ����

2010 International Symposium on Computer, Communication, Control and Automation

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� K4=ln{(1+K1) / K1}� ���

� m=ln(K3/K4) / ln(Vmpp/Voc)� ���

where Voc, Isc, Impp and Vmpp are open-circuit voltage, short-circuit current, current and voltage at MPP respectively. I-V curve for any solar irradiation level (G) and temperature (Tc) can be obtained by using adaptation of (1) in the following equations: (at standard testing condition, G = Gstc = 1000 W/m2; Tc=Tstc=25 oC)

� �Tc = Tc – Tstc� ����

� Ipv = αsc (G/Gstc)�Tc + ((G/Gstc) – 1)Isc.stc� � ��

� �Vpv = - βoc �Tc - Rs �Ipv� ����

The new values of the photovoltaic voltage and current are given by:

Vpv_new = Vpv + �Vpv (10)

� Ipv_new = Ipv + �Ipv� �����

where αsc and βoc refer to temperature coefficient related short-circuit current and open-circuit voltage respectively. Some parameters of the of Siemens SP-75 PV panel which were used in this work are shown in Table I. Fig. 2 shows the I-V characteristic and the P-V characteristic of solar panel under different solar radiation (200–1000 W/m2) for the same Temperature = 25 oC.

0 5 10 15 20 250

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4

5

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nt

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80

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Figure 1. PV characteristic under different solar radiation level.

III. SYSTEM MODELING

A simple MPPT for PV system with a boost DC-DCconverter as shown in Fig. 2 was developed to test the effectiveness of the proposed method. The output voltage (Vo) of the converter can be expressed as:

�� �D

VV so �

�1

� �����

where D is the duty cycle of the converter. It can be seen that the input DC voltage Vs can be shifted to a high level.

This converter topology, for some applications, shows some advantages such as cheaper implementations and better dynamic response compared to the buck converter topology [8]. In this work, the PV system is modeled by using Matlab. The simulation parameters are switching frequency 20 kHz, input capacitance 100 µF, inductance 200 µH and output capacitance 150 µF.

TABLE I. PV PANEL PARAMETER

PV array power (Ppv) 75 W

Maximum power point current (Impp) 4.4 A

Maximum power point voltage (Vmpp) 17.0 V

Maximum power point power (Pmpp) 75 W

Short circuit current (Isc) 4.8 A

Open circuit voltage (Voc) 21.7 V

Temp. coefficient : short-circuit current (αsc) 2.06 mA/oC

Temp. coefficient : open-circuit voltage (βoc) -77 mV/oC

Figure 2. Structure of the single input CMAC-based MPPT.

IV. SINGLE INPUT CMAC-BASED MPPTThe CMAC is a simple and fast associative memory

type neural network based on the local approximation [8]. A CMAC model example is shown in Fig. 3. In this work, it was only one single input used. Each input state which is called signed distance (ds) is corresponding with small part active element (n) of total memory element (Ne). The active elements are also associated with active weights (w)which are used to determine the CMAC output. It is usually symbolized as association vector (a(ds)) in binary form e.g. in Fig. 3, n = 3, Ne = 13, the associative vector is [0 1 1 1 0 0 0 0 0 0 0 0 0]. In this work n = 4 and Ne = 343 were chosen. The output of the CMAC, then is determined by using following formula,

� � �� �

��Ne

i

Ne

dsaiiiicmac wwau

1 1)(:

� �����

During learning process the weight values are adjusted to minimize the error between target output (ud) and CMAC output (ucmac). In this work least mean square (LMS) algorithm was used for this purpose,

� � � � � �� � � � � �� �kukukdsaNe

kwkw cmacd �������1 (14)

where α is learning rate which the value can be chosen arbitrary within [0,1] and in this work was set to be 1.

Figure 3. Single-input CMAC model.

There are three main stages for designing the CMAC based MPPT: generating of the learning target, the off-line learning and the on-line learning.

A. Generating of learning targetThe CMAC is used to control the operating voltage of

solar panel so that the maximum power can be extracted. Since CMAC is a neural network type controller, it needs a control reference as learning target. In this case single input fuzzy logic controller (S-FLC) was used. The derivation of PV power over voltage (dP/dV) and variation of the voltage (dV) were used and treated as input pair (e,ė). Thereafter, these values were transformed into single input variable ds by using signed distance function. Actually, this function calculates the distance of the actual state (e,ė) from the switching line, ė + λe = 0. It can be positive or negative according to the position of the actual state as shown in Fig. 4. The signed distance for a general point P(e,ė) is defined as follows [9,10]:

�21 �

��

��

eeds� � ����

where λ is slope of the switching line. This value (ds), then is used as input variable of S-FLC.

Triangular shape function was chosen as membership function of the input variables. The input variable then wascategorized into several linguistic value such as NB (negative big), NS (negative small), ZE (zero), PS (positive small) and PB (positive big). In this work, thirteen fuzzy subsets were used for input variable ds and also for output variable Dstep. The fuzzy inference wascarried out by using Sugeno’s method. This incremental step value then was used to adjust the operating voltage of the PV to get maximum power

Figure 4. Derivation of signed distance as shown in [3].

B. Off-line learning

The main purpose of this stage is to train the CMAC so that after the completion of this stage it will be able to imitate the behavior of the reference controller; in this case it is S-FLC. Initially, the CMAC table is empty and then the CMAC contents, stored at the locations addressed by input ds, are updated at each step by learning rule as mentioned in (14). The control output of S-FLC is used as target output (ud (k)).

C. On-line learningActually, when the off-line learning has been

completed, the CMAC has ability to perform as S-FLC. On-line learning, however, is still needed to ensure its stability. It is performed by using the following modified learning rule,

� � � � � �� � � � � �� �kykrkdsaNe

kwkw �������1 (16)

in this work y(k) refers to actual dP/dV and r(k) refers to reference dP/dV=0 where the power delivered by solar panel is maximum. Further, to improve the generalization ability at the off-line stage, linear interpolation scheme is also applied between two neighboring state outputs.

V. SIMULATION RESULTS

Comparison of control surface between S-FLC and single-input CMAC based MPPT can be seen in Fig. 5. It is obvious that CMAC can imitate the control behavior of S-FLC very well. It also indicates that learning process hasbeen conducted successfully.

To evaluate effectiveness of the proposed method, some simulations were performed to compare the performance of the proposed method with the conventional fixed step size perturbation and observation (P&O) MPPT method. The simulations were made by using Matlab and configured under the same conditions. The sampling period used for the P&O algorithm was chosen as 0.01 s. Therefore, the duty cycle of the power converter wasupdated every 0.01 s. The performance of P&O (with a fixed step size 0.01) and CMAC based MPPT methods under step change of solar radiation from 200 W/m2

(temperature T = 25 oC) to 800 W/m2 (temperature T = 35 oC) at 0.5 s is shown in Fig. 6.

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-0.1

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Co

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utp

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S-CMAC

Figure 5. Control surface of S-FLC and S-CMAC.

0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.610

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Figure 6. Tracking performance under solar radiation and temperaturechanging.

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 155

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Figure 7. Performance comparison at steady state.

It can be seen obviously that the proposed method provides better dynamic response due to weather condition

change. It reaches maximum power faster than traditional P&O. It also has better performance at steady state. As shown in Fig. 7, the oscillations occurred in P&O are greatly reduced. It means the proposed method can greatly reduce the power loss.

VI. CONCLUSION

In this paper, the single input CMAC based MPPT has been presented. The main advantages of this controller are its simple computation results in fast learning, and its possibility for low-cost digital implementation. Through learning process, it can learn and imitate the control behavior of the reference controller. In this case single input fuzzy logic controller (S-FLC) was used as areference. The simulation result of the proposed MPPT method under different weather conditions (solar irradiation and temperature) shows the effectiveness of the proposed method for tracking the maximum power point of the solar panel.

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