modeling and control of the pemfc power interface

MODELING AND CONTROL OF THE PEMFC POWER INTERFACE NICU BIZON*, MIHAI OPROESCU*

*University of Pitesti, Pitesti, Romania, [email protected] ABSTRACT. This paper presents an investigation of the nonlinear phenomena in the PEM-Fuel Cells (PEMFC) power interface. The boost converter is used into an Energy Generation System (EGS) as power interface between the PEMFC as energy source and the battery stack as energy storage device. The simulation results show that the boost converter behavior can be improved using a well designed control surface. The used Simulink models for the EGS blocks and some design consideration are presented, too. KEYWORDS: Energy generation system, fuel cell, energy storage device, boost converter, hysteretic control, Simulink models.

1.

The energy generation system

The typical Energy Generation System (EGS) with Energy Storage Device (ESD) is presented in figure 1.

Figure 1. A typical energy generation system with energy storage

The boost converter is ideally suited for interfacing the inverter system with the PEMFCs. Based on the load conditions, the boost stage can be commanded to draw a specific amount of current from the fuel cell with a ripple well defined by the frequency, size of the inductor, and duty ratio. In this paper we investigate the EGS topology presented in figure 2.

Figure 2. The analyzed EGS

The inverter system will need to respond to dynamic load conditions. However, the chemistry of the fuel cell cannot respond instantaneously to these load dynamics. The function of the battery bank is to provide momentary ride through capability while the fuel cell adjusts to the new operating point. On average, the state of charge of the battery bank has no net change: any energy supplied to the load by the battery during a transient must be replenished from the fuel cell once the chemistry has reached

steady state condition. Therefore, the current command for the boost converter must include the average load current as well as the battery charging current. The advantages and drawbacks of each current control method are seen into the fast- and slowscale instabilities of an EGS, with a PEM-Fuel Cell and a battery stack as slow processes and with a boost converter that gives the fast-scale instabilities of the system in order to optimize the power conversion. The boost converter interface model shown in figure 1 is described by four differential equations that expands the system to a four order system (with four variables: output voltage - vout, PEMFC voltage – Vin, voltage over the Cstorage - : vC_storage and inductor current - iL ). 2.

EGS modeling

Battery model Usually, a lead-acid battery for the ESD is a low price solution. Generally, a battery model is complex because the storage device has many model parameters such as capacity, dead-cell voltage, discharge impedance, self-discharge impedance, and shunt capacitance. In order to simplify the simulations it is used a simple model for a sealed lead acid battery (SLA) [1,2]. The battery is modeled as a capacitor for energy storage Cstorage, a DC offset voltage Voffset and a series resistance Rs to limit the short circuit current (figure 2). In this paper, the 60V/7Ah battery pack structure (5 batteries, 6 cells/battery and 2,45V max/cell) it is used. The value of series resistance is taken as 80mΩ/cell (as suggested in [3]). The calculated equivalent series resistance of the pack is RS=5⋅80 mΩ=0,4 Ω. The typical “dead cell” voltage for SLA battery technology is about 1,75V. Therefore the total offset voltage is Voffset=5⋅6⋅1,75 V=52,5 V. Finally, the energy stored in the capacitor can be calculated. First we calculate the maximum battery pack voltage: Vmax=5⋅6⋅2,45 V=73,5 V. So, the maximum storage capacitor voltage must be the difference between the maximum expected battery voltage and the deadcell voltage: VC_storage= Vmax - Voffset =21 V. For the 7Ah batteries we obtain Q=7 Ah⋅3600sec/hour=25200 C and the value for the modeled storage capacitance is Cstorage=Q/ VC_storage =1200 F. The EDS Simulink model is presented in figure 3.

Figure 3. The EDS Simulink model

Obviously, the addition of the battery to the boost converter output change the control characteristic that must consider the required battery charging parameters in the control law generation [4] (see figure 4). The solid line in figure 4.a represents the boundary control law (named boundary control with current taper-BCCT). This is a function of both current limits and battery voltage. Regardless of the commanded current, as the batteries charge and the voltage increases (over knee voltage Vknee , to the maximum value Vmas , the inductor peak current will back off to preventing “boiling” of the batteries. In order to minimize the PEMFC current ripple a 2-D control surface is proposed using a fuzzy system for control surface generation as o function of both current ripple and battery voltage (Figure 4.b) 2

a) BCCT 1-D

b) BCCT 2-D Figure 4. Current control law

PEMFC model The fuel cell electrical equivalent model has a rather large capacitance shunting the device. The equivalent circuit for this model is shown in figure 5, where Re is the electrolyte and contact resistance (=Rohm), Rct is the charge transfer resistance (it is this the same as activation loss), Cd is the double charge layer capacitance, Zd is the diffusion impedance also called the concentration loss or Warburg impedance [5,6].

Figure 5.The PEMFC equivalent circuit

Figure 6. The PEMFC u-i characteristic

The proposed model it is based on well know and simple analytical description [5-8]. The losses due to irreversibility’s will be determined in terms of three main groups: Activation losses, Ohmic losses and Concentration losses (figure 6). By adding, the cell voltage is determined in terms of the drawn current (iL) and PEM area (APEM). The J. Larminie relation used for PEMFC modeling is:

(

)

i +i E = E0 − i +i R −A ln l n l n ohmic act  i  0

  i +i +B ln1 − l n  conc  i max  

  , i =i / A PEM  l L 

The proposed relation used for PEMFC modeling is:

 i spec + in E = E 0 − (i spec + in )Rohmic − Aact ln  i0

  i spec + i n  k2   + Bconc ln λk1 Psys 1−  i λk3 P k 4   max sys  

   The  

k1÷k4

correction coefficients of the PEMFC model can be obtained by different methods (see table 1 and 3). The identification algorithm was presented and tested for different real and simulated situations in [9,10]. A short presentation of the identification methodology using genetic algorithm will be following presented. The structured used for genetic algorithm follow next structure: • 7 constants: E 0 , I n , I 0 , I max , Rohmic , Aact and Bconc . These values are physical constants and their values will be established by the user from physical specifications. • 6 parameters λ , Psys , k1 , k 2 , k 3 and k 4 .

3

These values are linear independent, but in the formula they appear grouped in two regions. First region include values for λ , Psys , k1 and k 2 and second region include values for λ , Psys , k 3 and k 4 . If we denote α = λk P k , β = λk P k , and x = il + i n , the formula for E become: 1

2

3

4

E = E 0 − xRohmic − Aact ln

  x x + Bconc ln α 1 − i0   i max β

    

In this case, there are only two variables Table 1. PEMFC model parameters for λ = 1 and Psys = 2 that must be determined by the genetic Parameter Value Value Value using ”least using using genetic algorithm: α and β . A gene will have two squares” J. Larminie algorithm chromosomes with values between 0 and 10. method relation [5] method The best performance was obtained for: 0.967 0.97 1.2 Eo / [Volts] 2
populations with 100 peoples; 2.755 2.7 2 in / [mA/cm ] 2
a 100% mutation probability; 0.074 0.067 0.074 i0 / [mA/cm ] imax / [A/cm2]
a 5% of old genes; 0.6 0.9 0.624 ROhmic / [Ω]
an 80% percent of new entities for new 0.02 0.03 0.021 Aact / [Volts] 0.034 0.06 0.035 population from combinations; Bconc / [Volts] 0.16 0.05 0.162
100 reference points; 0.531 0.5 N/A k2
a dynamic size for mutation established 0.515 0.5 N/A k3 from difference between entity values and 0.012 0 N/A k1 reference values. 0.018 0 N/A k4
a 5% of new random entities. The combination is made from two genes and generates one gene. First n chromosomes was provided by first gene, where n is a random number between 0 and N (total number of chromosomes): N=2 in this case. The parents from combination are chosen with a roulette algorithm that ensure as a good entity have a greater probability to be used for combination that a poor entity. The fitness function F is based on a sum of absolute differences in references points: F=

m

∑ (abs(calculated value − reference value) + 1) m

where m is the number of reference points. The entities used for combination are chosen from all population using an algorithm named “roulette” that raises more probably the entities with a good fitness. First, the algorithm computes the sum of fitness values, SumF , and than generate a random number between 0 and SumF . Considered that entities are placed on a line of length SumF the random number indicates only one entity. The parents for combination are selected applying twice the roulette algorithm (figure 7). In figure 8 are presented some results using proposed PEMFC model: Best entity

1

10

100

Figure 7. Best entity evolution

4

1000

Figure 8. The PEMFC characteristics for different values of the PEMFC model parameters: λ and Psys

The performance criterion used to evaluate the PEMFC models is the identification accuracy given by RMS error function: ∑

( final calculated value − reference value )2

RMS _ error = 1 − m

m

Table 2. RMS errors Value using ”least squares” method 0.982

Value using genetic algorithm method 0.988

Value using fuzzy method 0.973

A first order system (with death time τPEMFC and time constant TPEMFC) it is used for the PEMFC dynamic behavior (where nCELL is stack cells number): VPEMFC = nCELL ⋅ E , Vin ( s ) =

VPEMFC ⋅ e− t / τ PEMFC 1 + TPEMFC ⋅ s

Using the above data, the fuel cell voltage is expected to be in the range of 42V to 52V based on nominal load current and normal operating conditions (see figure 5, where ncell=60 and APEM=60 cm2). However, the open cell voltage can be as high as 72V if the pre-load fails and must be designed for or protected against in the inverter design. The PEMFC Simulink model is presented in figure 9.

Figure 9. The PEMFC Simulink model

It is possible to model a fuel cell stack in a much more fundamental manner, incorporating electrochemistry, thermal characteristics, and mass transfer [11,12,13], but such a complicate model is not necessary for testing the inverter system electrical performances [14-21]. The obtained result with a well knowing fuzzy identification technique ([22]; from Matlab toolboxes) is following given. 1 Training Data ANFIS Output

0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 10. ANFIS model topology Figure 11. ANFIS output and training data set Table 3. Fuzzy system parameters that approximate a given PEMFC characteristic [System]

[Rules]

Name='anfisfc'; Type='sugeno'; Version=2.0 NumInputs=1; NumOutputs=1; NumRules=5 AndMethod='prod'; OrMethod='max' ImpMethod='prod'; AggMethod='max' DefuzzMethod='wtaver'

1, 1 (1) : 1 2, 2 (1) : 1 3, 3 (1) : 1 4, 4 (1) : 1 5, 5 (1) : 1

5

[Input1]

[Output1]

Name='input1' Range=[0 0.9] NumMFs=5 MF1='in1mf1':'gaussmf', [0.101872237607765 -0.00339123188884595] MF2='in1mf2':'gaussmf', [0.107133374218832 0.218233346431983] MF3='in1mf3':'gaussmf', [0.108355435945731 0.45209895667639] MF4='in1mf4':'gaussmf', [0.109273687791531 0.68804727709605] MF5='in1mf5':'gaussmf', [0.104032328545096 0.907618201388046]

Name='output' Range=[-0.000550170802689542 0.975370908592898] NumMFs=5 MF1='out1mf1':'linear', [-3.69106649911531 0.889681043738718] MF2='out1mf2':'linear', [-2.31399630457492 1.00826361645473] MF3='out1mf3':'linear', [-2.07624702288251 1.11374235747597] MF4='out1mf4':'linear', [-2.54632618748775 1.58816488038201] MF5='out1mf5':'linear', [-4.3646858782209 3.41039831842838]

Inherent in the fuel cell is a high intolerance for current ripple at low frequency or slower load transients [23]. Boost converter model Figures 2 show the complete circuit diagram of the boost converter. The current mode controlled boost converter is designed to operate in continuous conduction mode (CCM). The converter equation when operate in CCM is

Vout t = 1 − τ , where τ = on is the duty ratio [24]. For example, if input Vin T

voltage, output voltage and output power are Vin = 48V , Vout = 60V and ratio is

τ = 0,2

and I load

Pout = 900W

, respectively, the duty

P = out = 15 A ⇒ Rload = 4Ω . The average inductor current = IL is Vout

I out = 18,75 A . Series resistance of the inductor (RL) is 0.05 Ω in simulations, and 10 kHz 1 −τ 1 switching frequency f = is used. T IL =

Obviously, depending upon the value of iL at the beginning of the period and some circuit parameters, the switch may or may not turn off during a switching period. There are three possible types of operation in any switching period, as illustrated in figure 12 where in =iL(nT) and Iref =ILMAX.

Figure 12. Inductor current waveforms corresponding to three possible types of operation

Figure 13. The boost converter Simulink model

-

In order to compare the EGS control performances two type of the controller are used in simulated Simulink model (figure 14): a controller with a BCCT 1-D control law (named classic controller in figure 14); 6

-

a controller with a BCCT 2-D control law (named fuzzy controller in figure 14).

-

3. The EGS control

In current control mode we must allow for the situation where a light load produces a low average inductor current that causes the converter to operate in discontinues conduction mode (DCM). So, there are three possible states or circuit configurations that depend by the state (q1) of the electronic switch (controlled with command voltage vcommand) and the diode conduction state (q2). The EGS system may operate in discontinuous conduction mode (DCM) for some switching cycles, in addition to the usual continuous conduction mode (CCM) of operation. Thus, to study the chaotic behavior of such a system, we must take into account the possibility of occasional DCM operation in which the inductor current may fall to zero in some switching periods. For that a step load model we use (figure 15). Several tools are available for the analysis of nonlinear systems using current control mode [25]. In this paper we chose the clocked or no clocked peak current control, with or without hysteresis, and using the BCCT law (1-D or 2-D). The controller models (using a specific boundary control law [26,27]) are shown in figure 16.

Figure 14. Simulated Simulink model

Figure 15. The step load Simulink model

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Figure 16. Diagrams of the clocked peak current controller using the BCCT law 1-D (left) and 2-D (right)

Figure 17.a.The clocked peak current controller using the BCCT law 1-D (top) and 2-D (botom)

Figure 17.b.The no clocked peak current controller using the BCCT law 1-D (top) and 2-D (botom)

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Figure 17.c.The no clocked histeretic peak current controller using the BCCT law 1-D (top) and 2-D (botom)

4.

Simulation results

We analyze the system dynamic behavior using different control methods for a large load dynamic. Changing in the load dynamic is the most frequently case and the controller must be designed to give controllability for the EGS in any situation. Plotted circuit variables and used parameters are mention in every set of figures. Apparently, for a nominal regime with a PEMFC energy source (see figures 11-12) the dynamic of the variables is almost the same for different control implementations used in this paper. For a step nominal to light the PEMFC dynamic appear in evidence when a long simulation time is used. To speed up the simulations (time equivalent systems are presented in [26]), the battery and PEMFC time constants are reduced by 10, so the values used in simulations are Cstorage =120F, Cfilter = 0.01 F, TPEMFC =10 ms and τPEMFC = 1 ms (see figures 18).

Figure 18. The PEMFC dynamic

Using the presented current mode controller the EGS was tested for a step-up load (nominal to over-load) and a step-down (nominal to light-load), respectively. Some obtained simulation results are following presented (see figures 19-27). 5.

Conclusions

The simulation results shows that, in comparison with the no clocked control methods, the clocked control methods provides better dynamic response and small PEMFC current ripple, robustness against system uncertainty disturbances, and an implicit stability proof. The increased stability and small PEMFC current ripple are obtained by a proper designing of the control surface using a fuzzy system to generate the BCCT 2-D law. The PEMFC current ripple is smaller in that case because the PEMFC current ripple is one of the control surface variables. The control losing phenomena into an EGS high step load were reported. The PEMFC model can be used into EGS simulation to test the control methods and see the EGS behavior under different disturbances (figure 28).

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Figure 19. For a step-up load and a no clocked peak current controller using the BCCT law 1-D (blue) and 2-D (green)

Figure 20. For a step-down load and a no clocked current controller using the BCCT law 1-D (blue) and 2-D (green)

10

Figure 21. For a step-up load and a histeretic current controller using the BCCT law 1-D (blue) and 2-D (green)

Figure 22. For a step-down load and a histeretic current controller using the BCCT law 1-D (blue) and 2-D (green)

Figure 23. For a step-up load and a clocked peak current controller using the BCCT law 1-D (blue) and 2-D (green)

11

Figure 24. For a step-down load and a clocked peak current controller using the BCCT law 1-D (blue) and 2-D (green)

Figure 25. A zoom for a clocked peak current controller using the BCCT law 1-D (blue) and 2-D (green)

Figure 26. For a high step-down load and a clocked peak current controller using the BCCT law 1-D (blue) and

12

2-D (green)

Figure 27. For a high step-down load and a clocked peak current controller using the BCCT law 1-D (blue) and 2-D (green)

Figure 28. The Energy Generation System structure

Acknowledgments. The Grant #570/2006-2008 of the National University Research Council (CNCSIS) has supported part of the research for this paper.

References

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