2012 IEEE International Symposium on Intelligent Control (ISIC) Part of 2012 IEEE Multi-Conference on Systems and Control October 3-5, 2012. Dubrovnik, Croatia
Fuel Flow Control of a PEM Fuel Cell with MPPT Nabil Karami, Rachid Outbib
Nazih Moubayed
Laboratory of Sciences in Information and Systems (LSIS) Aix-Marseille University, Marseille, France
[email protected],
[email protected]
Department of Electrical and Electronics, Faculty of Engineering 1, Lebanese University, Tripoli, Lebanon
[email protected]
Abstract—In this paper, a Fuel Cell (FC) Maximum Power Point Tracking (MPPT) with fuel flow optimization is developed. The aim of this study is to extract the maximum power from a FC at different fuel flow rates and to protect the FC from over-current and voltage collapses across terminals. The system is composed of a tracker with a buck converter able to change the impedance and therefore the FC power. In order to illustrate our approach, simulation results show the behavior of the tracker at different fuel flow rates and verify the concept of maximum power tracking.
feedback controller was designed to maintain a necessary level of oxygen partial pressure in the cathode during variation of current demand for FC system with air and fuel supply subsystems. In [16-18], authors control the FC current output by controlling the fuel feeding.
I.
INTRODUCTION
Nowadays, FC's are considered as promising alternative solution for electrical energy generations in the future for mobile and stationary applications. This is due to their high efficiency and environmental friendliness. As for other industrial processes, optimizing the fuel consumption and extracting the maximum power represent some technological challenges in order to render FC a realistic solution for the future. The problem of extracting the maximum power in renewable energy was first done for processes like photovoltaic panels or wind turbines. The interest consists in orienting the process in such a way that the produced power is optimized [1-3]. There are several methods to search the optimal value of a function [4, 5] where the Perturb and Observe (P&O) is the most commonly used one based on its simple algorithm. The problem of extracting the maximum power from a FC has attracted the interest of authors [6-8] and different methodologies have been proposed. More precisely, the challenge is based on the tracking of the MPPT of the FC by controlling the gases flow, the pressure or the power converter. In the functioning of FC, the output depends on many operating parameters like cells temperature, anode and cathode pressures, relative humidity, the stoichiometry and the anode and/or cathode dry gas mole fraction. In fact, all these parameters have an impact on the produced FC voltage [9-12]. In the literature, many approaches are used to extract the maximum power of a FC and are of two kinds. The first kind is based on controlling the gases flow and/or the pressure and various methodologies are used. For instance, in [6, 13, 14] authors studied the MPPT of FC based on the control of a motocompressor group. In [15], a dynamic 978-1-4673-4600-9/12/$31.00 ©2012 IEEE
The second kind of approaches is based on the use of power converter interface at the FC output to control the output voltage and current. In this approach, power electronics is playing the main role in extracting the MPP [1924]. Besides to these two kinds of approaches, a hybrid methodology is developed in order to combine the advantages of the two approaches [8, 25]. The goal of this study is to apply the MPPT on a static FC model using the hybrid approach where a power converter and a fuel flow rate controller accomplish the maximum power tracking. In this study, we show that this approach offers an optimization of the fuel consumption and allows reaching the MPP at different fuel flow rates. Besides, protection of the FC is taken into consideration by designing a tracker that forbids the collapsing of the output voltage and therefore the protection against short-circuit and over-current absorption. In addition, the proposed control algorithm for MPPT protects over the degradation of the mechanical structure and the membrane by avoiding the overheating and the water excess formation. The paper is organized as follows. In the second section, the components of system under considerations are described. FC modeling is reviewed in the third section. In the fourth section, the strategy for tracking is introduced. The fifth section is dedicated to design the DC/DC converter and the PWM signal generator. In the sixth section, simulation results are presented in order to illustrate the performances of the tracking strategy for MPPT. Conclusion is given in section seven. II.
SYSTEM DESCRIPTION
The system consists of a static model of a Proton Exchange Membrane FC (PEMFC) with typical voltage of 0.57 Volt per cell. The FC used in this paper is the one predefined by SimPowerSystems toolbox of Matlab R2011a. The MPP is achieved at 24.23 Volt, 52 A, 1.26 kW at maximum fuel flow rate of 23.46 lpm. The system consists also of a MPPT block followed by a PWM signal generator that drives a buck converter. The system block diagram is shown in Figure 1. Theoretically, for every fuel flow rate, the FC generates a specific voltage and current. The role of the
289
tracker is to slide the current by acting on the buck converter so that the FC power reaches its maximum. The new current value determines a new fuel flow that will manage on the next cycle of the tracking process.
reactions. The basic expression for the PEMFC voltage is [12, 26-28]:
VFC
Ecell
E act
Econc
Eohmic
(4)
where VFC is the FC output voltage, Ecell represents the open circuit voltage, whereas Eact, Econc and Eohmic are the activation, the concentration, and the ohmic FC overvoltage respectively. In the ohmic region, the output voltage becomes linearly dependent to the current density with a slope determined mainly by the ionic resistance of the polymer electrolyte. When the FC operates in the concentration polarization region, depletion of reactants due to mass-transfer limitation causes the output voltage to decrease very rapidly to zero as illustrated in Figure 2.
Figure 1: System block diagram
III.
FUEL CELL MODELING
A FC is an electrochemical device that converts the chemical energy of a fuel and an oxidant to direct electrical current. In the case of hydrogen-oxygen FC, hydrogen (H2) is the fuel and oxygen (O2) is the oxidant. The total fuel reaction is: 1 2
H 2( g )
O 2 ( g ) o H 2 O( l )
electricity
(1)
A. Reversible voltage PEMFC model The maximum amount of electrical energy generated in a FC corresponds to the Gibbs free energy ûG, [12, 18, 19]:
Wel
'G
'H T'S
The overall nonlinear output voltage characteristic of a FC can be described by the theoretical formula given by the following Equation [29, 30]:
(2)
where G(joules) is the Gibbs free energy, H(joules) is the heat content (enthalpy of formation), T(K) represents the absolute temperature, and S(Joules/K) is the entropy of the system. Assuming that all of the Gibbs free energy can be converted into electrical energy, the maximum possible (theoretical) efficiency of a FC is a ratio between the Gibbs free energy and hydrogen higher heating value, K =ûG/ûH = 83%. Therefore, the theoretical voltage Eth of an electrochemical reaction of an H2/O2 PEMFC at standard conditions can be calculated from: Eth ,T
'H 0 T0
T 'S 0 nF
1.2297Volt
Figure 2: Fuel cell polarization curves and losses types
(3)
where ûH0 = -286 kJ/mol, ûS0 = -0.1634kJ/K/mol, T = 298.15K, F is the Faraday’s constant = 96.485 C/mol and n represents the electron pass round the external circuit for every mol of supplied hydrogen. B. Steady State Model The internal voltage of an FC is a nonlinear function of the FC current, internal temperature, and pressure of oxygen and hydrogen gasses. Like in batteries, FC output voltage is the difference between its internal voltage and its internal voltage drops, namely the activation, ohmic, and concentration voltage drops. These voltage drops are nonlinear functions of FC current, temperature, and chemical
VFC
Ecell
RT § I FC ln¨ 2DF ¨© i0
· ¸ ¸ ¹
RT § I FC ln¨1 2 F ¨© iL
· ¸¸ I FC Rint ¹
(5)
where IFC denotes the FC output current, i0 designs the exchange current which can be considered as the current density at which the overvoltage begins to move from zero, iL denotes the limiting current at which a reactant can be supplied to an electrode, . represents the charge transfer coefficient and Rint is the internal FC resistance.
C. Generic Fuel Cell Model Based on the study proposed in [31], a new approach of FC static modeling is proposed, where the FC model is obtained from the manufacturer datasheet. The proposed model represents a particular FC stack where the parameters such as pressures, temperature, compositions and flow rates of fuel and air vary. These variations affect the Tafel slope (A), the exchange current (i0) and the open circuit voltage (Ecell). The parameters (Ecell, i0, A) have to be updated based on the input pressures, flow rates, stack temperature and gases compositions. Ecell, i0 and A are modified as follows [10, 32]:
290
Ecell i0
K c En
zFk ( PH 2 Rh
PO2 )
(6) e
'G RT
(7)
A
RT zD F
between the FC and the load, can change the equivalent load resistance seen by the FC.
(8)
where R = 8.3145 J/(mol K), z is the number of moving electrons, En denotes the Nernst voltage (V), . represents the charge transfer coefficient. PH2 and PO2 (atm) stand for the inside stack partial pressure of hydrogen and oxygen respectively, k denotes the Boltzmann's constant, h represents the Planck's constant, ûG denotes the size of the activation barrier, T is the temperature of operation (K) and Kc denotes the voltage constant at nominal condition of operation.
A MPPT controller uses FC voltage, current and subsequently its power to find the MPP and then generates control instructions to the power converter. The algorithm given in Figure 3 starts first by calculating the value of the power P at zero Ampere. Next, the current is slightly increased and a new power value is calculated.
The rates of conversion (utilizations) of hydrogen (UfH2 ) and oxygen (UfO2 ) are determined as follows:
U fH 2 U fO2
60000.R.T .N . I FC z.F .Pfuel .Vlpm ( fuel ) .x%
(9)
60000.R.T .N .I FC z.F .Pair .Vlpm ( air ) . y %
(10)
where Pfuel denotes the absolute supply pressure of fuel (atm), Pair represents the absolute supply pressure of air (atm), Vlpm(fuel) stands for the fuel flow rate (l/min), Vlpm(air) stands for the air flow rate (l/min), x is the percentage of hydrogen in the fuel (%), y is the percentage of oxygen in the oxidant (%), and finally N designates the number of cells. The partial pressures and the Nernst voltage are determined as:
En
PH 2
(1 U fH 2 ) x% P fuel
PO2
(1 U fO2 ) y % Pair
1.229 (T
IV.
298)
44.43 zF
RT ln( PH 2 PO2 1 / 2 ) zF
(11) (12) (13)
MAXIMUM POWER POINT TRACKING TECHNIQUE
Figure 3: MPPT algorithm
When examining the typical FC polarization and power curves illustrated in Figure 2, a point of maximum power is observed. This point depends on the fuel flow that feeds the FC. Therefore, there exist some conditions in which the FC produces the maximum power for the supplied fuel flow. There are various methods to find extremum value of a function (which have been developed mostly for photovoltaic arrays), such as Perturb and Observe (P&O) [4], Incremental Conductance [5], short-circuit current method [33], and the open-circuit voltage method [34]. Considering its simple algorithm, P&O is the most commonly used method.
The MPPT Simulink block is shown in Figure 4. At every cycle, input power and current are subtracted from the previous power and current values respectively. The ratio of power over current (ûPFC / ûIFC) is compared to zero in order to decide the direction of the next current perturbation.
The P&O algorithm works by periodically perturbing IFC and observing the resulting change on the output power ûPFC. By comparing the direction of the perturbation to the observed ûPFC, the direction of the next perturbation is determined, and the process is repeated until ûPFC = 0 (ideally) is obtained. In practice, for P&O, IFC must be constantly perturbed in order to keep the algorithm active, hence ûPFC = 0 cannot occur and the system will typically oscillate around the MPP. A DC-DC power converter, placed 291
Figure 4: MPPT Simulink block design
V.
DC/DC SYNCHRONOUS BUCK DESIGN
A. PWM duty cycle generation The PWM signal is generated by comparing a signal level control with a repetitive saw-tooth waveform of 10 kHz (Fig. 5). The generator is designed to deliver two PWM signals in opposite phase to control the synchronous buck converter.
20 Amps. Notice that in Figure 8.a, the power curve will not drops and the voltage will not collapse. The same scenario of extracting the maximum power of the FC is repeated at a fuel flow of 23.46 lpm (Fig. 7.b and 8.b).
Figure 5: PWM Signal generator
B. Model of synchronous buck DC–DC converter The state-space averaged model describing the voltage and current dynamics of the synchronous DC–DC buck converter shown in Figure 6 are given by: vout (t )
C
di L (t ) dt v out (t ) i L (t ) R
VFC (t )D (t )
dv out (t ) dt
L
(14)
Figure 7: Variation of voltage, current, power and duty cycle at (a): 5 lpm, (b): 23.46 lpm
(15)
where L is the inductance, C denotes the capacitance, R represents the loading resistance, VFC and vout are the input and the output voltages respectively, iL denotes the inductor current and . designates the duty cycle.
Figure 8: Power and voltage variation versus current at (a): 5 lpm, (b): 23.46 lpm Figure 6: Synchronous Buck converter
VI.
SIMULATION RESULTS
A. Simulation with power tracker By connecting the MPPT, the system is able to reach the maximum power. Many simulations are done at different fuel flow rates. From Figure 7.a, and Figure 8.a, the fuel flow rate is fixed to 5 lpm. The maximum power reached is 500 Watt at
B. Simulation with power tracker at different fuel flow rates In this step, the tracker is simulated with a fuel flow rate step variation from 5 to 20 lpm. As mentioned in the subsection A, at 5 lpm the maximum power that can be extracted from the FC is at 20 Amps. When an extra fuel is added, the FC is able to deliver more power. Figure 9 shows the power and voltage variations at different fuel flow rates with no voltage collapsing.
292
current sensors, the system is able to extract the maximum power at any fuel flow rates.
voltage
MPP @ 20lpm
di
re ct io n
MPP @ 20lpm
Tr ac ki ng
power
MPP @ 5lpm
Trac king direc tion
MPP @ 5lpm
current
current
Figure 9: Power and voltage variation with fuel flow
C. Simulation with power tracker and fuel flow controller Based on the generic model of [31], Equation (9) can be modified and a relationship between the fuel flow rate and the current is expressed as: Vlpm ( fuel )
60000.R.T .N .I FC z.F .Pfuel .U fH 2 .x%
(16)
Assuming a constant temperature and pressure, Equation (16) shows a linear relationship between the current IFC and the fuel flow Vlpm(fuel). At T = 55 degree Celsius and at Pfuel = 1.5 bars (optimum operating points), Equation (16) is simplified to:
Vlpm( fuel )
0.2346. I FC
(17)
Based on Equation (17), the simulation of Figure 10 shows that the tracker as far as the electrical output power controls the flow.
Figure 11: Complete Simulink Design
VII. CONCLUSION A maximum power point tracker and fuel controller are studied and simulated in this study. The fuel cell is modeled in two different static representations. The P&O control algorithm is applied using a buck converter. Results show a good behavior of the controller with high efficiency. Maximum power is extracted from the FC at different fuel flow rates. One more important advantage of using the MPPT is its ability to forbid the FC voltage to collapse and forbid current to go beyond critical limits, which protect FC from degradation and increase its lifetime. REFERENCES [1]
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Figure 10: MPPT with fuel flow control
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