Modeling and Optimum Performance Analysis of Photovoltaic Arrays Using Fuzzy Logic Controller

1Nur Mohammad, 2M.R. Alam, 3Md. Asiful Islam3Quazi, 4Delwar HossainDept. of Electrical & Electronic Engineering

Chittagong University of Engineering & Technology, Bangladesh3Bangladesh University of Engineering & Technology, Bangladesh

1nureee_ruet@yahoo.com, 2mra_eeecuet@yahoo.com, 3asif0406041@gmail.com, 4qdhossain@yahoo.com

Abstract—This paper presents a detailed mathematical and simulation model of PV array including maximum power

point tracking-the electronic power conditioning (PCS) system, on MATLAB/Simulink platform. The model includes PV

module and array for easy use on simulation stage. The proposed model is designed with a user-friendly icon and a dialog

box like Simulink block libraries. Considering the effect of solar irradiance and temperature changes, the output current

and voltage of PV modules are simulated and optimized using this model. A fuzzy logic based maximum power point

tracker is also developed using the presented model. The maximum power point tracker is tested in changing

environment of irradiance and/or temperature. It can successfully track the maximum power point more precisely and

rapidly than conventional perturb and observe based controller in these situations. The overall test results validate the

efficiency of the model as well as the fuzzy controller which can be used in associated research works.

Keywords— Photovoltaic (PV) cell, Insolation, Solar power generation, Grid connected PV, Maximum power point tracking (MPPT)

I. INTRODUCTIONEnergy is one of the most indispensable parts for our living being in the world. Access to energy plays a crucial role

in accelerating economic growth and development activities of a country. However the existing power plants and

utility grid is not able to cover the demand fully. Moreover the extreme use of fossil fuels produces harmful gases

which tempted to destroy the natural ecosystem and trigger the environment pollution. Huge emission of carbon

dioxide is going to destroy the ozone layer of the universe as a result global warming is threat to all. On the other

hand, adequate photon energy (sunshine) which is available on the earth surface throughout the year. Solar energy in

a single day is sufficient for the entire inhabitant of the earth. Photovoltaic renewable energy system may be one of

the promising solutions to ease the existing energy crisis considerably in the world if it is avail in a sustainable

manner. Photovoltaic power generation using solar cells that can convert solar light energy directly to DC electricity

promises to be a clean, widely applicable renewable energy source. Sustainable growth of photovoltaic power

generation is also reducing dependence and pressure on fossil fuel significantly. Researchers have shown great

interest on photovoltaic (PV) systems and technology over the past decades. Advancement in cell efficiency and

system reliability has given wide acceptance of PV technology for both standalone and grid interactive power

generation. According to the renewable energy unit of European Commission, the capacity of installed grid

connected PV grew at an average rate of 37% per year over the years 2002-2008 [1].

Fig. 1: Grid Connected Photovoltaic Installations [2]

At the end of 2010, the installed capacity in the USA was nearly 11,000 megawatts (MW) and the worldwide

installed capacity was over 16,000 MW (fig. 1). Photovoltaic renewable energy is recognized worldwide as a cost-

effective, environmentally friendly solution to energy shortages. The output current vs. voltage curve of a

photovoltaic cell shows a non-linear characteristic. From this nonlinear relationship, it can be observed that there is a

unique point, under given illumination and temperature, at which the cell produces maximum

power, the so-called maximum power point (MPP). This point occurs when the rate of change

of the power with respect to the voltage is equal to zero [3]. The output power of PV cell varies with

depending mainly on the level of solar radiation and ambient temperature corresponding to a specific weather

condition. The MPP will change with external environment of PV cell. An important consideration in achieving high

efficiency in PV power generation system is to match the PV source and load impedance properly for any weather

conditions, thus obtaining maximum power generation. The tracking process of maximum power point is called

maximum power point tracking (MPPT).

II. PHOTOVOLTAIC ARRAY MODEL

The photovoltaic array is an arrangement of several modules connected in series/parallel to get a suitable power and

voltage. The basic element of the photovoltaic array is the solar cell which usually uses a p-n junction diode in a

physical configuration to produce photovoltaic electricity. Solar cell is basically a p-n junction fabricated in a thin

wafer or layer of semiconductor.. Being exposed to the sunlight, photons with energy greater than the band-gap

energy of the semiconductor are absorbed and create some electron-hole pairs proportional to the incident irradiation

as shown in figure 3. Under the influence of the internal electric fields of the p- n junction, these carriers are swept

apart and create a photocurrent which is directly proportional to solar insolation [4]. PV system naturally exhibits a

nonlinear I-V and P-V characteristics which vary with the intensity of sunlight exposed and cell temperature.

Fig. 2: PV Module in the Renewable energy Lab of CUET. Fig. 3: PV Cell Structure, Module and Array.

A PV cell is represented by a simplified equivalent circuit as the one given in Fig. 4 and by an equation as in (1).

(1)

Here, q is charge of electron, n is the ideality factor of cell which depends on the PV technology [5], k is Boltzmann

constant (1.38×10-23), Icell is cell output current, Iph is photocurrent which is a function of cell operating temperature

and solar irradiance, Io is reverse saturation current of diode, Rs is series resistance of cell, Tc is cell operating

temperature and Vcell is cell output voltage. Photocurrent mainly depends on the solar insolation and cell’s working

temperature which

(2)

Where, Isc is the short circuit current at 25o C temperature (reference) and 1kW/m2

irradiance, K1 is cell’s short

circuit current temperature co-efficient, G is the solar insolation in kW/m2, To is the cell’s reference temperature.

Fig. 4: Simplified equivalent circuit of a solar cell.

Also, the cell’s saturation current varies the cell’s operating temperature which may expressed as,

(3)

In (3), Iso is the cell’s reverse saturation current at reference temperature and solar radiation 1kW/m2, Eg is the bang-

gap energy of the semiconductor used in the cell. Iso can be found from the following equation,

(4)

In (4), Voc is the open circuit voltage under standard condition and Ns is the no. of cells connected in series. An even

more exact mathematical description of a solar cell, which is called the double exponential model, is derived from

the physical behavior of solar cell constructed from polycrystalline silicon. This model is composed of a light-

generated current source, one diode, a series resistance and a parallel resistance [6]. However, there are some

limitations to develop expressions for the V-I curve parameters subject to the implicit and nonlinear nature of the

model. The shunt resistance Rp is inversely related with shunt leakage current to the ground. In general, the PV

efficiency is insensitive to variation in Rp and the shunt-leakage resistance can be assumed to approach infinity

without leakage current to ground. On the other hand, a small variation in Rs will significantly affect the PV output

power.

III. DERIVING MODEL PARAMETERS

The model parameters can be found from the manufacturer’s data sheet supplied with the PV module. The most

important model parameters are the open circuit voltage, Voc and short circuit current, Isc under specified test

conditions (at temperature 25oC, AM1.5 and irradiance 1kW/m2). Voltage and current at maximum power are also

specified for that particular condition. Given the PV open circuit voltage Voc at reference temperature and ignoring

the shunt-leakage current, the reverse saturation current at reference temperature can be approximately obtained as,

(5)Here, Ns is the number of cells in series in the PV module.

IV. GENERALIZED PV MODEL CHARACTERISTICS

As the output power from a PV module varies with the variation in insolation as well as temperature, we have

considered these parameters in the development of our PV simulation model. The model is developed in masked

subsystem form with several stages in Matlab/Simulink platform [7]-[14]. The Voc, Isc (in standard condition

mentioned above), To, n, Eg, K1 are taken as input parameters from the user. Voc=22.2V and Isc=5.45A used by us is

from the datasheet of the Brand and Model: Solerex-MSX-40 PV module which is available in the Renewable

Energy Laboratory of EEE department in CUET. One of the samples is shown in figure 2; where Ns is 36 and no. of

parallel path (Np) is 1. The values of Ns and Np can also be given as input parameters. Both Rs and Rp are calculated

in the initialization option of the masked subsystem. This initialization is carried out every time at the starting of

simulation. Both directly coupled dc load and ac load after inversion are connected at the output of the array and the

simulation results resemble the actual results. Only the current vs. voltage and power vs. voltage curves at the output

of the PV array for different irradiances and temperatures are shown in Fig. 5-6. The output curves at the dc and ac

loads are not shown here for concision.

Fig. 5: Output Current -Voltage and Power - Voltage characteristics for different insolation.

Fig. 6: Output Current -Voltage and Power-Voltage characteristics for different temperature

VI. MAXIMUM POWER POINT TRACKING METHODSThe power supplied by PV arrays depends on the irradiation intensity, temperature, and PV array voltage. Usually,

the PV output voltage changes with temperature, while the PV output current changes mainly with insulation. The

photovoltaic system displays an inherently nonlinear current-voltage (I-V) relationship as well as power-voltage (P-

V), requiring an online search and identification of the optimal maximum operating power point as given in figure 7.

MPPT controller is a power electronic DC/DC converter or DC/AC inverter system inserted between the PV array

and its electric load to maximize the available photovoltaic energy utilization. In figure 8 of general MPPT system,

during the period when open circuit voltage is sensed, S is closed and Q is opened. This will disconnect the power

conditioner and load from the module. The capacitor C gets charged to a voltage that is proportional to V oc. Then S

is open and Q is closed for normal operation of the module and load. It is to be noted that, the duty cycle for

switching S should be very small, less than 1%, so that the normal operation is not affected.

Fig. 7: (I-V) and (P-V) characteristics of a PV array [4]. Fig. 8: PV panel with General MPPT system

The algorithm works as follow, since there is no reference cell and still we need to have the Vmp value for

comparison, we need to have to measure the Voc of the same cell. This is done with the help of switch S. While

measuring Voc, it is need to be disconnecting rest of the circuitry. This is done with active switch Q. A voltage V

proportional to the module voltage is measured. This voltage is compared with a reference Vmp*.If these two

voltages match, maximum power is transferred to the load through the DC-DC converter. If these two voltages do

not match, then error signal is generated. Depending on the polarity of the error signal, duty cycle is increased or

decreased such that voltages match. The use of MPPT can make full use of the system capacity and thus reducing

the cost of the system. A number of methods for MPPT have been reported in the literatures [16].

VII. A NOVEL FUZZY LOGIC CONTROLLER FOR MPPT

Due to a nonlinear current voltage characteristic of PV cells, it is difficult to track the MPP. The situation gets worse

when the solar irradiance and/or cell operating temperature changes. Numerous techniques have been proposed so

far to realize MPP. These MPPT methods vary in complexity, sensors required, convergence speed, cost, range of

effectiveness, implementation hardware, popularity, and in other respects. Among them constant voltage method,

the perturb-and observe (P&O) method, the incremental conductance method etc. are most common [16]-[17].The

P&O MPPT algorithm is mostly used, due to its ease of implementation. A drawback of P&O MPPT technique is

that, at steady state, the operating point oscillates around the MPP giving rise to the waste of some amount of

available energy and the system accuracy is low [18]. Incremental Conductance method has measurement

parameters as same as P&O method. However, from derivation of this method, it can be seen that it has no

consideration about change of temperature. In a nutshell, in fast changing environment these conventional MPPT

methods face a great deal of difficulty to track the actual MPP. To overcome the difficulties of commonly used

MPPT methods a unique fuzzy logic controller is proposed in this paper. The proposed controller can track the MPP

not only accurately but also its dynamic response is very fast in response to the change of environmental parameters

in comparison with the conventional MPPT algorithms.

A fuzzy control system essentially embeds the experience and intuition of a human plant operator and sometimes

those of a designer and/or researcher of a plant. The design of a conventional control system is normally based on

the mathematical model of a plant. If an accurate mathematical model is available with known parameters a

controller can be designed for specified performance. But in some cases an accurate mathematical model is not

always available. Moreover, the response of a conventional controller is not always precise and fast enough if load

and system parameters vary abruptly. In these situations, fuzzy logic controller (FLC) can be a very good alternative

[19]. FLC can achieve robust response of a system with uncertainty and nonlinear characteristics. It has the

advantages of working with imprecise inputs, not needing an accurate mathematical model, and handling

nonlinearity. A MPP search based on fuzzy heuristic rules, which does not need any parameter information, consists

of a stepwise adaptive search, leads to fast convergence and is sensorless with respect to sunlight and temperature

measurements [21]. The control objective is to track and extract maximum power from the PV arrays for a given

solar insolation level and cell operating temperature. The maximum power corresponding to the optimum operating

point is determined for a different solar insolation level and temperature. A block diagram of the entire fuzzy logic

controller based MPPT system is shown in Fig. 9.

Fig.9: Functional block of FLC based MPPT system [20]

The fuzzy controller consists of three functional blocks as fuzzification, Fuzzy rule base and Defuzzification.These functions are described as follows:

a. Fuzzification

The proposed FLC in this paper takes one input which is the slope (n) of the power vs. voltage curve at a samplinginstant n and gives output the change in voltage for the sampling instant . The variable and

are expressed as follows:

Where and are the power and voltage of PV array, respectively. So, and are zero at the

maximum power point of a PV array. In Fig. 10, the membership function of the input and output variables is shown

which is assigned eleven fuzzy sets, including positive very big (PVB), positive big (PB), positive medium (PM),

positive small (PS), positive very small (PVS), zero (ZE), negative very small (NVS), negative small (NS), negative

medium (NM), negative big (NB) and negative very big (NVB). The membership functions are denser at the center

in order to provide more precise output at the MPP. zero (ZE), negative very small (NVS), negative small (NS),

negative medium (NM), negative big (NB) and negative very big (NVB). The membership functions are denser at

the center in order to provide more precise output at the MPP.

b. Fuzzy rule base

The fuzzy rule base should be such that it can generate an output which is change in voltage based on the

magnitude of the input, to operate the PV array at a voltage corresponding to MPP. At MPP, the input

variable is zero. So, the output, change in voltage should also be zero. But, a mean should be there to avoid the PV array voltage locking in a local maximum rather than proceed towards the actual value. Rule Base Table for Fuzzy Logic controller is given in table 1.

Fig. 10 The membership functions of input and output variables.

Table 1: Rule Base Table for Fuzzy Logic controller

Input NVB NB NM NS NVS ZE PVS PS PM PB PVB

Output NVB NB NM NS NVS ZE PVS PS PM PB PVB

C. DefuzzificationThe most common center of gravity method for defuzzification is used in this paper. It computes the center of

gravity from the final fuzzy space, and yields a result which is highly related to all of the elements in the same fuzzy

set.

VIII. RESULT AND DISCUSSION

As mentioned previously, the common methods to track MPP have several drawbacks. Among them, the P&O

method shows slow tracking speed and oscillations about MPP. In this paper the performance of FLC is compared

with that of P&O method to show FLC’s superiority in tracking MPP over other conventional methods. The

simulation results are shown in Fig.12-14. Simulation is performed from 0 to 0.5s. The irradiance and temperature

profile are shown in Fig. 11 during this period. In P&O method, if step size of input variable is very small, the

accuracy in tracking MPP is high but tracking speed becomes too slow. On the other hand if the step size is

increased, accuracy deteriorates (oscillation about a mean point occurs) but tracking speed increases. Both accuracy

and speed of tracking cannot be achieved simultaneously in this simultaneously. The proposed fuzzy logic based

method is even better with respect to conventional fuzzy methods which can produce unexpected results when

abrupt parameter changes occur in real time. The simulation results of P&O method shown here has step size

relatively large to match the tracking speed of that of FLC. But in this case it shows increased oscillation. At the

start of simulation, output of the PV array is assumed to be set at zero.

Fig. 11: Irradiance and temperature changes during simulation.

Fig. 12 Output voltage at different environmental condition with FLC (red) and conventional P&O controller (blue).

Fig. 13: Output current at different environmental condition with FLC (red) and conventional P&O controller (blue).

Fig. 14: Output power at different environmental condition with FLC (red) and conventional P&O controller (blue).

IX. CONCLUSION

A complete generalized model of PV array along with fuzzy logic based MPPT controller is developed in this paper.

The simulation results give encouraging output on the performance of PV system and thus validate the effectiveness

of the model. The model is also simple and user friendly.Fuzzy logic toolbox of Simulink is used to achieve the

FLC. The specialty of this FLC is that the rule base is very simple which increases the speed of computation of the

processor. That is why the proposed FLC can track the MPPT very fast and accurately even if the environment

changes abruptly. The performance of the proposed controller is compared with that of a conventional P&O

controller and the worth of the fuzzy controller is obvious. The proposed controller can be used in any real PV

system with the help of digital signal processor to get good results.

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