Modeling and performance evaluation of PEM fuel cell by controlling its input parameters

Accepted Manuscript Modeling and Performance Evaluation of PEM Fuel Cell by Controlling its Input Parameters

Sudarshan L. Chavan, Dhananjay B. Talange PII:

S0360-5442(17)31246-X

DOI:

10.1016/j.energy.2017.07.070

Reference:

EGY 11258

To appear in:

Energy

Received Date:

10 May 2017

Accepted Date:

11 July 2017

Please cite this article as: Sudarshan L. Chavan, Dhananjay B. Talange, Modeling and Performance Evaluation of PEM Fuel Cell by Controlling its Input Parameters, Energy (2017), doi: 10.1016/j.energy.2017.07.070

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ACCEPTED MANUSCRIPT

Modeling and Performance Evaluation of PEM Fuel Cell by Controlling its Input Parameters Sudarshan L Chavan Department of Electrical Engineering College of Engineering(COEP) Pune, India. [email protected]

Dhananjay B. Talange Department of Electrical Engineering College of Engineering(COEP) Pune, India. [email protected]

Abstract Fuel cell technology is one of the most promising, emissions free, energy conversion technology under renewable energy systems because of its wide ability in most of the commercial applications like electrical vehicles, building cogeneration and standby power supply. Mathematical models are trusted as important tools for designing and performance analysis of fuel cell based systems. Many mathematical models based on thermal, electrochemical and electrical steady states as well as dynamic have been reported in literature to evaluate performance of Proton Exchange Membrane (PEM) fuel cell, but all these models are complex and needs huge amount of data for modeling and performance testing. The present paper proposes simple, but more realistic MARTLAB SIMULINK model for PEM fuel cell to evaluate its performance under different operating conditions. The performance of the proposed model is compared with single practical, 25cm2 active area, PEM fuel cell for model validation. The presented model is also valid for a stack having any number of cells. Key words: PEM fuel cell, Mathematical Model, Performance analysis, Simulink model. 1.

Introduction Continuous uses of fossil fuels for energy generation produces greenhouse gases, increases global warming and adversely affect the environment and human life. Fuel cells are energy generating devices which convert chemical energy of supplied fuel into electrical energy with negligible environmental effect. There are various types of fuel cells operating at different temperatures, amongst all; the PEM fuel cell is very popular due to its simple structure, quick start, high power density, low operating temperature and negligible environmental effects [1]. Because of the increasing interest in PEM fuel cell various mathematical models have been reported in literature to represent its operational performance. The model described in [2] represent a dynamic model of PEM fuel cell which needs measurement of fuel cell voltage, current and temperature. Large numbers of parameters are required to be obtained by calculation from measured quantities. Effect of temperature on output parameters is investigated in this model. In [3] electrical equivalent model based on thermodynamics and electrochemical phenomena is presented, also thermal model based on fuel cell thermal energy balance is described. The parameters required for the analysis of the model are obtained by conducting tests on the practical PEM fuel cell. In [4] a dynamic model of PEM fuel cell is presented and a nonlinear regression method with constant parameter model describing maximum likelihood estimation problem is used to determine model parameters. Technique used to find model parameters is very complicated. In [5] three different models, steady state model, dynamic model consisting of small signal model and large signal model which includes effect of double layer capacitance and MATLAB simulink model are presented. In MATLAB simulink model simplified and detailed models are described. Only in detailed model the effect variation of input parameters on output parameters can be analyzed. In [6] steady state model of PEM fuel cell is presented in MATLAB. Effect of variation of input parameters on cell output parameters is not investigated in this model. The model presented in [7] investigate the performance of steady state and dynamic model of PEM fuel cell. Dynamic model includes effect of charge double layer, fuel cell body dynamics effect and electrode channel fuel flow dynamics. Performance is investigated with different input parameters for short and long time intervals. Effect of temperature and heat produced on cell output parameters is not considered. In [8] MATLAB simulink steady state and dynamic model of PEM fuel cell is presented. As this model needs large no of input parameters, therefore it is very complex. In [9] mathematical model of PEM fuel cell is presented and Simulated Annealing optimization algorithm is used to estimate model parameters. Validation of model with data from practical fuel cell is also

ACCEPTED MANUSCRIPT presented. In [10] steady state and dynamic model of PEM fuel cell is presented. Effect of mass flow rates of reactants, pressure of reactants and temperature on cell output parameters is investigated. Presented model is comparatively simple but it needs large no of input parameters for analysis. Model presented in [11] describe dynamic behavior of PEM fuel cell. Dynamics of reactants is modeled to investigate effect on terminal voltage. The presented model is simple but effect of most of the performance parameters such as operating temperature, reactants partial pressure change, flow rate change is not considered. In [12] dynamic model using electrical equivalent circuit is presented in MATLAB and in PSPICE. Thermodynamic characteristics are also included in the model. Effect of reactants partial pressure change and temperature is investigated on output parameters. The model uses large number of equations to investigate cell performance and hence it is very complex. Model described in [13] implemented a test protocol on non functioning PEM fuel cell to find its parameters. Only electrical terminal behavior can be investigated using this type of model. In [14] electrical circuit equivalent model is presented and direct loading test conducted on practical PEM fuel cell to find equivalent circuit parameters. Optimization of calculated parameters is not considered. In [15] Electrical circuit equivalent model of PEM fuel cell is presented in MATLAB. Least square optimization polyfit algorithm is used to find parameters of equivalent circuit. Validation of simulation and practical results also presented. This model is most suitable to describe terminal behavior of PEM fuel cell. In [16] the effect of inverter ripple on cell performance is investigated. Most of the models described in literature are depends on electrical equivalent, thermal, electrochemical or material based, however none of them is suitable to describe terminal behavior of PEM fuel cell at all operating conditions. In this paper MATLAB SIMULINK model is presented to investigate performance of PEM fuel cell by controlling its various input parameters at different operating conditions. 2

Mathematical Model for PEM Fuel Cell. In PEM fuel cell, current generated by the cell is depends on number of moles of hydrogen and oxygen reacting in a chemical reaction. This current can be find out either from mass flow rate of supplied hydrogen or oxygen and it is given by equation 1 or 2. 𝐼 = 95719.25 ∗

𝑀𝐹𝐻2

(1)

𝑁

or 𝐼 = 12060.63 ∗

𝑀𝐹𝑂2

(2)

𝑁

Where MFH2: Mass flow rate of hydrogen in g/s, MHO2: Mass flow rate of oxygen in g/s, N: Number of cells. Actual current produced by the fuel cell is always less than this current because the supplied hydrogen and oxygen are not 100% utilized. Some part of supplied hydrogen or oxygen always exhaust without reacting. If x is hydrogen utilization factor and y is oxygen utilization factor then actual current produced by fuel cell can be expressed as 𝐼 = 𝑥 * 95719.25 ∗

𝑀𝐹𝐻2 𝑁

(3)

or 𝐼 = 𝑦 * 12060.63 ∗

𝑀𝐹𝑂2 𝑁

(4)

Generally sufficient amount of oxygen supply is always available and therefore the hydrogen flow rate is mostly used to find current generated by fuel cell. At a particular flow rate of supplied hydrogen, the flow rate of oxygen should be such that the number of

ACCEPTED MANUSCRIPT electrons supplied to the cathode through external circuit should react with oxygen to form water and therefore oxygen flow rate is again important. 2.1 Voltage Generated by Fuel Cell Open circuit voltage generated by the fuel cell is actually depends on number of factors, but, in general, the voltage developed by fuel cell at a specific temperature and pressure is depends on Gibbs free energy change and number of moles of electrons supplied 0 when one mole of supplied hydrogen reacts. The reversible open circuit voltage (𝐸 ) is given by [1] ∆𝐺

𝐸0 = 2F

(5)

Where ΔG: Change in Gibbs free energy due chemical reaction at anode and cathode, F: Faraday constant ΔG is depends on change in enthalpy and entropy in a chemical reaction and it also depends on operating temperature and state of output product. The Gibbs free energy change is given by (6)

ΔG = ΔH - TΔS

Table 1. shows Gibbs free energy change(ΔG), enthalpy change (ΔH ) and entropy change (ΔS) due reactions at anode and cathode at various operating temperatures. Table 1: Gibbs Free Energy Change with Temperature [1]. Temp.(0C) ΔH (KJ/mole) ΔS (KJ/mole) ΔG (KJ/mole) 100 -242.6 -0.0466 -225.2 300 -244.5 -0.0507 -215.4 500 -246.2 -0.0533 -205.0 700 -247.6 -0.0549 -194.2 900 -248.8 -0.0561 -183.1 As ΔG is depends on the temperature, therefore the open circuit voltage changes with temperature. Actual open circuit voltage developed by the fuel cell is depends on temperature and pressure of the reactants (H2 and O2) and product (H2O). Nernst equation, shown in equation 7, is generally used to find relation between standard potential developed by the fuel cell and actual potential at various temperature and pressures of reactants and products [1]. 𝑅𝑇

E = 𝐸0 + 2𝐹ln

( ) 𝑃𝑟𝑒𝑎𝑐𝑡

𝑃𝑝𝑟𝑜𝑑

Where E0 : Open circuit voltage at standard temperature. R: Universal gas constant. T: Operating or actual temperature Preact: Product of partial pressure of reactants Pprod: Partial pressure of product. For a stack having N number of cells,

(7)

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Estack = N * E In PEM fuel cell, as it is working on low temperature, generally pure hydrogen and oxygen are used as reactants, therefore partial pressures and actual pressures of hydrogen and oxygen are considered same. If the pressures of hydrogen and oxygen on two sides of the electrolyte membrane are different than it causes the electrolyte membrane to rupture, if operated continuously for longer duration. Considering humidity of supplied hydrogen, oxygen and water produced at cathode, the partial pressures of water should be same on both sides of the membrane. To keep the membrane intact, the partial pressure of hydrogen, oxygen and water on two sides of membrane are considered same i.e. PH2=PO2 Considering this effect the Nernst equation can be modified to E = 𝐸0 + 2.154 ∗ 10 ‒ 5 ∗ T ∗ ln

(

𝑃3𝐻𝑦𝑑𝑟𝑜𝑔𝑒𝑛 𝑃2𝑊𝑎𝑡𝑒𝑟

)

(8)

One important point to be considered for PEM fuel cell that, as hydrogen is used as main fuel for this cell, the Nernst equation shows that, at constant oxygen and water pressure, open circuit voltage changes with hydrogen pressure. If hydrogen partial pressure changes from P2 to P1, then change in voltage can be expressed as ΔV = 6.46 ∗ 10 ‒ 5 ∗ T ∗ ln

( ) 𝑃2

(9)

𝑃1

Considering partial pressures of oxygen and water constant throughout the operation of PEM fuel cell, the open circuit voltage with change in partial pressure of hydrogen from P1 to P2 is given by E = 𝐸0 + 6.46 ∗ 10 ‒ 5 ∗ T ∗ ln

( ) 𝑃2

𝑃1

(10)

The actual fuel cell voltage is always less than this open circuit voltage due to three types of polarizations taking place inside fuel cell i.e. activation polarization, ohmic polarization and concentration polarization [1]. The activation polarization is due to slow reaction rate kinetics of the fuel at electrodes, the ohmic polarization is due to internal resistance offered by fuel cell and concentration polarization is due to mass transport limitations at higher values of current density. Although the electrolyte membrane is considered to be pure proton conductor, small amount of electrons always flow through the electrolyte membrane causes small amount of current through electrolyte membrane called as internal current. Due to this internal current, even though the cell is at open circuit, there is drop in potential. Considering the effect of internal currents, the three types of polarizations can be expressed as [1] 𝐸𝑎𝑐𝑡 = 𝐴 ∗ ln

( ) 𝑖 + 𝑖𝑥

(11)

𝑖0

(12)

𝐸𝑜h𝑚 = 𝑖 ∗ 𝑅

(

𝐸𝑎𝑐𝑡 = ‒ 𝐵 ∗ ln 1 ‒ Where

)

𝑖 𝑖𝐿

(13)

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A=

( ) : Tafel slope

B=

( ): For Hydrogen

B=

( ): For Oxygen

𝑅𝑇

2αF

𝑅𝑇 2F 𝑅𝑇 4F

α : Charge transfer coefficient 𝑖𝑥: Internal current density (mA/cm2) 𝑖𝐿: Limiting current density (mA/cm2) 𝑖: Cell current density (mA/cm2) 𝑖0: Exchange current density (mA/cm2) R: Area specific resistance of membrane (Ω-cm2) As activation polarization occurs when current density is very less, therefore the effect of internal current density is considered only on activation polarization. Considering effect of all polarizations, the fuel cell voltage can be expressed as V = 𝐸0 + 6.46 ∗ 10 ‒ 5 ∗ T ∗ ln

( ) + 𝐴 ∗ ln ( ) + 𝑖 ∗ 𝑅 - 𝐵 ∗ ln (1 ‒ ) 𝑃2

𝑖 + 𝑖𝑥

𝑃1

𝑖0

𝑖 𝑖𝐿

(14)

2.2 Power loss and Efficiency. During energy transformation the fuel cell voltage changes from reversible open circuit voltage E0 to load voltage V, therefore the conversion loss can be expressed as Conversion loss = 𝑖 ∗ (𝐸0 ‒ 𝑉)

(15)

Power loss also taking place as a resistive loss due to internal resistance of fuel cell and can be expressed as Resistive loss = 𝑖2 ∗ 𝑅

(16)

Total power loss = 𝑖 ∗ (𝐸 - 𝑉) + 𝑖2 ∗ 𝑅

(17)

Open circuit voltage of the PEM fuel cell has highest value when all hydrogen supplied, its calorific value and enthalpy of formation were converted into electrical energy. Efficiency of PEM fuel cell is the measure of actual energy produced in terms of maximum possible energy. As voltage and efficiency are related to each other, the efficiency of PEM fuel cell can be expressed as [1] 𝑉

Cell Efficiency = 1.48 X 100 Where,

(18)

ACCEPTED MANUSCRIPT V is actual fuel cell voltage and 1.48 is corresponding to maximum open circuit voltage at liquid water product. The above expression for efficiency is valid only if all supplied hydrogen is utilized by fuel cell to produce energy. But in practice some hydrogen always exhaust without reacting and hence efficiency get affected by fuel utilization factor ‘k’ Actual Cell Efficiency = k ∗

𝑉 1.48

∗ 100

(19)

2.3 Cell Internal Resistance and Humidity. The internal resistance of the PEM fuel is sum of electrode resistance and resistance offered by the cell electrolyte membrane to the flow of H+ ions. But generally the resistance provided by electrolyte membrane is more significant compared to the resistance of electrodes and therefore the internal resistance of PEM fuel cell is considered equivalent to its membrane resistance. The electrolyte membrane resistance varies with the humidity of the supplied gases (Fuels). Use of higher humidified gases reduces membrane resistance which in turn lowers loss due to ohmic polarization. 2.4 Temperature Rise and Heat Produced. Heat generated due to chemical reaction is the primary source of heat in PEM fuel cell. This heat is depends on number of moles of hydrogen reacting in chemical reaction. Heat generated due to losses in membrane resistance, electrode resistance, various contact resistances and conversion loss are other sources of heat. Among these heat sources, heat produced due to chemical reaction and conversion loss are major sources of heat. The heat generated due to chemical reaction and conversion loss can be expressed as 𝐻𝑟 =

(

𝛥𝐻 * 𝑀𝐹𝐻2 2.016

)

𝐻c = I ∗ (E ‒ V)

(20)

(21)

Where, 𝛥𝐻: Change in enthalpy in chemical reaction Generated heat increases temperature of fuel cell and the increased temperature adversely affect some of the output parameters and therefore cell temperature is required to be limit by circulating coolant through the cell. The circulated coolant absorbs heat from the heat sink. Considering no loss taking place in heat sink, the heat absorb by coolant from heat sink can be expressed as 𝐻a = h ∗ A ∗ ΔT

(22)

Where A: contact area of coolant with respect to heat sink h: heat transfer coefficient. ΔT: Temperature difference between heat sink and coolant. The heat transfer coefficient is depends on velocity of the circulating coolant, diameter of the tubes through which coolant is circulating and system heat sink temperature. In simple way it can be expressed as h = ( 8.846 ∗ 10 ‒ 2 + 3.81 ∗ 10 ‒ 5 ∗ T) ∗ 𝑉w0.8 ∗ 𝐷 ‒ 0.2 Where, Vw: Velocity of circulating coolant (m/hr) D: Diameter of tube (m)

(23)

ACCEPTED MANUSCRIPT The net heat generated is depends on the heat generated by the fuel cell and heat absorbed by the coolant. Net heat produced is given by (24)

𝐻n = 𝐻a - 𝐻g

Where, Hg is total heat generated due to all sources of heat. Due to net heat generated the system temperature rise can be expressed as ΔT = C

𝐻n

(25)

∗ m

Where, C: Specific heat capacity of heat sink material (J/Kg 0K) m : mass of heat sink (Kg) 3.      

MATLAB SIMULINK Model To develop mathematical model for PEM fuel cell following assumptions are used. Both hydrogen and oxygen flow is required to generate the current by fuel cell but only hydrogen flow rate is used to find current developed by fuel cell. Flow rate of hydrogen required to generate current is decided from minimum mole flow rate of either hydrogen or oxygen. Water is considered as coolant to extract heat from fuel cell. Heat sink is considered to be loss less. Only heat generated by chemical reaction at 27 0C and heat generated due to conversion loss are considered as sources of heat. Only membrane resistance is considered as internal resistance of fuel cell.

MATLAB SIMULINK is an userfriendly tool for modeling, simulating and analyzing dynamic systems. It provides support for developing graphical block diagrams, evaluation of developed system performance and refinement of system design. Developed MATLAB SIMULINK model consists of number of subsystems and sub-subsystems. Some important system and subsystem models are given below with short explanation of logic used. 3.1 Main Model of PEM Fuel Cell. The main model of PEM fuel cell gives its performance analysis with respect to various input parameters. The various input parameters required for analysis are listed in table 2. Table 2: Fuel Cell Model Input Parameters Sr. No Input Parameter 1 No of cells in a stack (N) 2 MEA active area (S) 3 Mass flow rates of hydrogen (MFH2) 4 Mass flow rates of oxygen (MFO2) 5 Exchange current density( i0) 6 Internal current density( ix) 7 Limiting current density( iL) 8 H2 and O2 Humidity 9 Coolant velocity (Vw) 10 Resistive Load variation limit (300 Ω -1 Ω) 11 Hydrogen partial pressure change 12 Heat sink initial temperature (T)

Unit cm2 SLPM SLPM mA/cm2 mA/cm2 mA/cm2 % m/hr Ω % 0K

ACCEPTED MANUSCRIPT 13 14 15

Coolant initial temperature (Tc) Activation polarization constant (A) Concentration polarization constant (B)

0K -

The displays connected to this model gives variation of various output parameters of the PEM fuel cell. The output parameters are: Cell output voltage(V), Current density (mA/cm2), Cell Power density (W/cm2), Cell Efficiency, Output heat, System temperature and Total power loss (W/cm2). The main SIMULINK model of PEM fuel cell is shown in figure 1. Numbers of subsystems are used to find various output parameters of PEM fuel cell. Figure 2 shows system model to find all output parameters of PEM fuel cell.

Figure1. Main Model of PEM fuel cell.

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Figure 2. System Model for Output Parameters.

3.2 Modeling of Cell output Parameters. Reversible open circuit voltage developed by PEM fuel cell is basically depends on Gibbs free energy change, cell operating temperature and state of output product (liquid or steam). Lookup table is used to find Gibbs free energy at various operating temperatures and hence open circuit voltage. Equations 8 to 14 are used to find cell output voltage. Cell output current is depends on three parameters, current generated by fuel cell through chemical reaction, load current and limiting current of fuel cell. Voltage generated by fuel cell is supplied to the load to generate load current. The load current is compared with fuel cell chemical reaction current and cell limiting current to decide cell output current. Cell output current becomes load current as long as it is less than the cell chemical reaction current or cell limiting current. If load current excides cell reaction current or cell limiting current then that respective current becomes cell output current. Considering hydrogen utilization factor 85%, the chemical reaction current can be found from equation 3. Conversion loss taking place inside the cell and power loss due to internal resistance of cell are considered as major sources of power loss. Increase in these losses affects terminal voltage as well as efficiency of the fuel cell. As efficiency of fuel cell is a function of terminal voltage, therefore efficiency of cell can be expressed in terms of cell terminal voltage. Equations 15 to 17 are used to find power loss taking place inside the PEM fuel cell where as equation 18 is used to find cell efficiency. Figure 3 shows combinations of subsystems to find power loss and efficiency. Heat generated in fuel cell increases its temperature which is required to be limit by use of coolant. Equations 20 to 25 are used to find heat output and fuel cell system temperature. 4.

Performance Analysis. Before investigating effect of various input parameters on cell output parameters, the performance of developed model is compared with the performance of single 25 cm2 active area practical PEM fuel cell at same operating conditions. Performance of both simulink model and practical cell is investigated at following input parameters,  Operating temperature: 65 0C.  H2 mass flow rate: 0.32 SLPM.  O2 mass flow rate : 1.75 SLPM.

ACCEPTED MANUSCRIPT  

Hydrogen back pressure : 1.58 bar Oxygen Pressure: - 0.83 bar Figure 3. Subsystem for Cell output voltage, Power loss and Efficiency.

Polarization characteristics of simulation model and practical model are shown in figure 4 and 5. The two polarization characteristics are compared in figure 6. The nearly matching characteristic of simulation model and practical PEM fuel cell gives validation of simulink model.

Figure 4. Polarization Curve for Simulation Model

Figure 5. Polarization Curve for Practical PEM Fuel Cell.

ACCEPTED MANUSCRIPT

Figure 6. Comparison of Polarization Curves between Practical Cell and Simulated Model. Performance of PEM fuel cell simulink model can be analyzed by controlling almost all input parameters cited in table 1. Here performance is analyzed by controlling few parameters. 4.1 H2 flow rate: Hydrogen flow rate actually decides number of moles of hydrogen available for chemical reaction to produce fuel cell current. Hydrogen flow rate to be used, is depends on cell limiting current density and load demand. At a particular load, the hydrogen flow rate should be sufficient to satisfy load demand. If the hydrogen flow rate is not sufficient to satisfy load demand then cell voltage sharply reduces indicating fuel cell is not able to satisfy load demand. Figure 7 indicate hydrogen flow rate 2 SLPM is sufficient to satisfy load demand but flow rate 0.1 SLPM flow rate is not sufficient to satisfy load demand and hence cell voltage goes down. With large flow rate, cell temperature increases due to more number of moles of hydrogen reacting in a chemical reaction. Effect of hydrogen flow rate on cell terminal voltage, power density, cell efficiency and cell temperature is shown in figure 7, 8, 9 and 10.

Figure 7. Effect of H2 flow rate on cell terminal voltage.

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Figure 8. Effect of H2 Flow Rate on Cell Power Density.

Figure 9. Effect of H2 Flow Rate on Cell Efficiency.

Figure 10. Effect of H2 Flow Rate on Cell Temperature.

ACCEPTED MANUSCRIPT 4.2 H2 humidity: Working of PEM fuel cell is basically depends on proton conductivity of electrolyte membrane. Dry electrolyte membrane resist flow of H+ ions trough it, hence cell current decreases. Presence of water on both sides of polymer electrolyte membrane increases proton conduction rate or in other word decreases membrane resistance for the conduction of proton. Humidified hydrogen and oxygen increases water content in membrane, therefore decreases membrane resistance. The effect of hydrogen humidity on cell terminal voltage, power density and cell efficiency at constant flow rate of 0.5 SLPM is shown in figures 11, 12 and 13.

Figure 11. Effect of H2 Humidity on Cell Terminal Voltage.

Figure 12. Effect of H2 Humidity on Power Density.

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Figure 13. Effect of H2 Humidity on Cell Efficiency. 4.3 H2 Partial pressure: Nernst equation is generally used to find effect of partial pressures of hydrogen, oxygen and water on open circuit voltage of PEM fuel cell. Change in open circuit voltage in tern changes terminal voltage. Decrease in partial pressure of hydrogen decreases fuel cell terminal voltage. Effect of 20% decrease in partial pressure of hydrogen, keeping oxygen and water partial pressures constant, on PEM fuel cell terminal voltage is shown in figure 14. As terminal voltage is already very less, effect of partial pressure change is very less. This effect is considerable in fuel cell stack.

Figure 14. Effect of H2 Partial Pressure on Cell Terminal Voltage. 5. Conclusion Mathematical model of PEM fuel cell is developed in MATLAB SIMULINK and performance is analyzed by controlling some input parameters like hydrogen flow rate, hydrogen humidity and hydrogen partial pressure. Performance of the developed model is

ACCEPTED MANUSCRIPT compared with single 25 cm2 active area practical PEM fuel cell at same operating conditions. Nearly matching polarization curves of practical PEM fuel cell and developed PEM fuel cell model gives validation of developed model. ACKNOWLEDGMENT First author of this research paper is working as an Associate Professor in department of Electronics and Telecommunication at JSPM’s, Rajarshi Shahu College of Engineering, Pune, India and presenting his sincere thanks to Principal/Management for encouragement and support for this research work. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

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