An Active Filter for Fuel Cell Applications - Power and Energy Systems
An Active Filter for Fuel Cell Applications D. Franzoni, E. Santi, A. Monti, F. Ponci, D. Patterson #, N Barry * #
University of South Carolina Department of Electrical Engineering Email: [email protected] Abstract— Fuel cells are becoming a more attractive option for many remote power applications. One of the main wellknown problems of a fuel cell system is its slow dynamic response: the fuel cell system needs significant time to reach a new steady-state condition after a load change. Notice that fuel cell dynamics, in terms of time-constants, may be in the order of seconds while electrical loads are usually in the millisecond range. This slow dynamic response should be compensated to allow operation under quick load variation conditions. A separate energy storage device, such as a battery, can be used to supply power to the load during all transient periods in which the fuel cell is adapting its state according to the load request. This paper proposes a bidirectional converter to compensate for the fast load changes while the fuel cell system adjusts the fuel flow to deliver the necessary energy. Two control strategies are proposed: a current feed-forward control and a voltage feedback control. Simulink simulations have been developed to obtain insight about these control strategies, as well as about the behavior of the bi-directional converter. A 35W hardware prototype has been built to verify the control performance. Experimental results of both controls are in agreement with their simulations and therefore validate the proposed control strategies. Both control strategies perform well. The current feed-forward control has the advantage of being extremely fast - with responses of the order of one time step of the digital controller - but has the disadvantage of requiring a load current sensor.
III.
INTRODUCTION
In recent years, the escalating cost of conventional fuel and the increasing restrictions imposed by pollution laws have made efficient energy conversion systems based on fuel cell (FC) technology more attractive than they were in the past. A fuel cell stack is a device that converts the chemical energy of hydrogen into electricity as long as fuel (hydrogen) and oxidant (air) are supplied. In order to operate the fuel cell stack in an economical way for different power demands, fuel and oxidant flow may be dynamically adjusted as a function of load demand. The hydrogen fuel may be taken from a storage tank or generated using a reformer. Different dynamic time constants can be observed during FC operation due to chemical, mechanical and electrical phenomena occurring in the fuel cell and in the balance of plant. Typically, FC systems require few tenths of seconds for transitioning from one steady-state operating point to another [1]. In applications that require a fast dynamic response, the slow dynamics of a fuel cell system can be compensated by using a separate energy storage device, which provides power to the load during fast transients. The active filter solution shown in Fig. 1 has been proposed by the authors in [5]. It uses a bi-directional converter to interface the
University of Nebraska, USA * University of Cork, Ireland
energy storage device (a battery) with the fuel cell system. The converter is effectively connected in parallel with the fuel cell. The control strategy of the bi-directional converter manages the battery power in order to obtain a fast system response to quick load variations [5]. Therefore, the overall system is equivalent to a power source with a fast dynamic response (Fig. 1). This paper focuses on different control strategies for the active filter. The discussion begins with the characterization of the 35W-proton exchange membrane fuel cell stack PEM D35 used in this study, followed by a description of the proposed system. Two different control strategies are described and simulated. Experimental results for these control strategies are then provided and compared with simulation. Finally, the two control strategies are contrasted and relative advantages and disadvantages identified.
Fig. 1: The fuel cell by itself has slow dynamics, however the fuel cell/active filter combination shown in the dashed box is equivalent to a power source with fast dynamics.
IV.
CHARACTERIZATION OF THE FUEL CELL
An equivalent model for the fuel cell is needed to simulate and design a control strategy. A possible equivalent circuit for the PEM D-35 fuel cell is shown in Fig. 2 [2-3]. The DC voltage source E0 models the open circuit voltage, resistance Rr models ohmic losses, resistance Ra models the activation overvoltage and capacitance Ca models the effect of the charge double layer. The current interrupt technique [3][4] is used to quickly obtain the parameters of this behavioral model. In this technique the fuel cell provides a load current that is quickly brought to zero. The transient FC voltage can be used for parameter extraction.
used as input filter for the FC system. The 400µH inductance L has been designed for operation at 50kHz switching frequency with a peak current of 3A. Two sealed lead acid batteries (6V 8Ah) are connected in series on the low voltage side of the bi-directional converter. IRF540 MOSFETs are used as active switches and an IR2110 high-side driver is used to drive them. A diode is placed in series with the fuel cell to protect it against current backflow. Fig. 2: Equivalent electric circuit model of the fuel cell.
After the parameter extraction is performed, the behavior is compared with the experimental data for validation. Fig. 3 displays the comparison of the fuel cell voltage transient obtained from the equivalent circuit model and the PEM D-35 fuel cell system during a current interruption of 1A.
B. Control Stage. 1) Current Feed-forward Control The first proposed solution is to use current feedforward control. The current reference is determined according to the power flow requirement to and from the energy storage device [6]. Feed-forward from the load current is used to determine the current reference. Fig. 4 shows a block diagram of the control that uses the following control variables: battery voltage (Vb), actual current available from the fuel cell (iav), load current (iload), reference current for the active filter (iref), actual current from the active filter (iF), charging current (ich), which represents the desired battery charging current based on its state of charge, and current request to the fuel cell (ireq), calculated from the load current and the charging current.
Fig. 3: Comparison of the Fuel Cell voltage obtained from the equivalent circuit model and the PEM D-35 fuel cell system during a current interruption of 1A.
When the fuel cell current steps down to zero, the fuel cell voltage exhibits an instantaneous step increase. This step change is used to estimate Rr. Afterwards, the voltage increases more slowly to its final value. This transient is used to estimate the time constant defined by Ra and Ca. Capacitor Ca, which represents the charge double layer, discharges to zero and the FC terminal voltage rises exponentially to the open-circuit voltage. Notice that the equivalent circuit model cannot properly simulate high current density conditions where the assumption of negligible concentration losses does not hold. Table I lists the parameters values of the equivalent circuit model for the PEM D-35 fuel cell. TABLE I PARAMETERS OF EQUIVALENT CIRCUIT FOR THE PEM D-35 FUEL CELL SYSTEM
Parameter Ca Ra Rr
V.
Value 0.0133 F 1.5 Ω 0.5 Ω
DESCRIPTION OF THE SYSTEM
A. Power Stage The power stage used to implement the active filter is a bi-directional converter (see Fig. 1). The high voltage side of the bi-directional converter is connected to the PEM D35 fuel cell system. A 100µF input capacitance, Cin, is
Fig. 4 Current control block diagram
The FC block receives from the control current request signal ireq and outputs current available signal iav. Depending on the fuel cell system characteristics, this may represent an actual adjustment of fuel and air flow to the FC to accommodate the control request. In certain fuel cells flows are fixed. In that case it is desirable to make sure that the FC current changes at a fairly low rate to prevent flooding of the fuel cell. This can be achieved by making iav a low-pass filtered version of ireq with time constants of the order of several seconds. The control stage consists of four blocks (see Fig. 4): block A estimates the current needed to recharge the battery (ich); block B calculates the request current, ireq, as a sum of the load current (iload) and the charging current (ich); block C determines the reference current for the active filter (iref); and finally the hysteresis block defines the duty cycle to control the MOSFETs. This control has two different operating modes. The first is the discharging mode, in which the battery delivers its own power to the load to maintain the uninterrupted power flow since the fuel cell is unable to supply the power
absorbed by the load. Using ( 1 ) the reference current for the active filter is calculated:
iref = iload − iav
(1)
The second operating mode is the battery charging mode. The fuel cell is able to supply the power requested by the load. Therefore, the active filter could recharge the battery if necessary, while keeping the total current under the maximum allowed for the fuel cell. During this interval the reference current for the active filter is given by ( 2 ). iref = − min[(iav − iload ), ich ]
(2)
2) Voltage Feedback Control Another option is to use voltage feedback control to stabilize the bus voltage. Fig. 5 shows a block diagram of this control. The bus voltage Vbus is the controlled voltage. The control tries to keep the bus voltage at a reference value. From the fuel cell model of Fig. 2, the fuel cell voltage is given by VFC ( s ) = E0 − Z FC ( s) I FC ( s)
the load (see Fig. 4). The fuel cell is modeled using the equivalent electric circuit in Fig. 2. The active filter is modeled as a controlled current source, since the response of the hysteresis current loop can be considered instantaneous ( iF = iref ) as compared to the other system time constants. The battery is modeled as a large (1 F) capacitor. The equivalent electrical model of the system shown in Fig. 6 is described by the following equations: dvbus (t ) 1 (iFC (t ) − iload (t ) + iF (t )) = dt Cin
(5)
dva (t ) 1 = dt Ca
(6)
v (t ) iFC (t ) − a Ra
The control performance has been evaluated by applying a 100% step load increase from 0.38A to 0.76A.
(3)
The fuel cell internal impedance ZFC(s) is R ⋅R 1 + s ⋅ C a ⋅ a r Ra + R r Z FC ( s) = (Ra + Rr ) ⋅ 1 + s ⋅ C a ⋅ Ra
= 2 1 + 0.005 ⋅ s ( 4 ) 1 + 0.02 ⋅ s
The bus voltage is equal to the fuel cell voltage if the voltage drop of the series diode is neglected. Capacitor Cin of Fig. 1 is also neglected.
Fig. 5 Voltage feedback control block diagram
From (4), the fuel cell transfer function exhibits one pole at s = -50 (8Hz) and one zero at s = -200 (32Hz). The compensator is an integral compensator designed to give a crossover frequency of 300Hz. The integral action is used to increase the low-frequency loop gain. The load current and the open circuit voltage can be considered as disturbances. This control keeps the bus voltage constant. This may not be desirable, because at heavy load this may require the battery to provide power to the load indefinitely. It is possible to modify this control allowing slow variations of bus voltage according to the fuel cell static characteristic. Moreover, battery charging during periods of active filter inactivity should be implemented. This is left as future work. VI.
SIMULATION RESULTS
A simulation of both control strategies has been performed using Simulink. The power stage is the parallel combination of the fuel cell system, the active filter and
Fig. 6 Equivalent electrical model of the power stage system
A. Current Feed-forward Control Simulation The simulation of the step load response is shown in Fig. 7. The transient can be divided into two consecutive intervals. The first interval (discharging mode) begins when the load steps up and ends when the fuel cell current becomes equal to the reference value required by the load (Fig. 7(a)). At this point, the second interval (charging mode) begins and is complete only when the battery is fully recharged (Fig. 7(b)). The active filter current iF (Fig. 7(c)) is positive during the first interval since the bi-directional converter supplies power to the load; then it becomes negative during the second interval to recharge the battery; and finally it goes to zero when the battery is fully charged. Fig. 7(d) shows the fuel cell required and available currents. After the step load, the current request changes instantaneously to the new required value, but the available current from the fuel cell changes slowly as the fuel cell adjusts to the new power demand.
reduces this voltage drop and slows down the bus voltage variation.
(a)
(b)
Fig. 9 Step-up load variation of fuel cell only (no active filter). Load current, 0.2A/div, and fuel cell voltage, 1V/div. Time scale: 0.1s/div.
(c)
(d)
Fig. 7: Simulation results of a step-up load variation with current feedforward control: (a) Load current and fuel cell, (b) Bus voltage and battery voltage, (c) Active filter current, (d) Fuel cell request current and available current. Time scale: 10s/div.
B. Voltage Feedback Control Simulation The simulation of the step load response is shown in Fig. 8. The bus voltage transient lasts about 1ms. Immediately after the step, the fuel cell provides the entire extra load current and the bus voltage drops. The voltage feedback control increases the active filter current to compensates for the bus voltage drop (see Fig. 8b). After about 1ms the active filter provides the entire extra load current and the bus voltage goes back to the original value.
(a)
(b)
Fig. 8 Simulation results of a step-up load variation with voltage feedback control: (a) Bus voltage, (b) Active filter current. Time scale: 5ms/div
VII.
EXPERIMENTAL RESULTS
Both controls have been implemented using a dSpace DS1104 platform. The integration method used for the real-time implementation is Euler with a time step equal to 100µs. For both controls, reference active filter current iref is calculated digitally by dSpace. On the other hand, the hysteresis current control is implemented with analog circuitry. A step-up load change from 0.38A to 0.76A is performed to evaluate the dynamics of the control variables. The experimental results are compared with simulation results to validate both control strategies. All experimental results have been numerically filtered to eliminate undesired switching noise. Fig. 9 shows the fuel cell voltage during a load step without active filter. It can be seen that the fuel cell voltage drops initially by 0.4V and after about 0.1s by approximately 1V. It will be shown how the active filter
A. Experimental Results for Current Feed-forward Control The step-up load transient is shown in Fig. 10 through Fig. 14. Notice how the active filter control ensures that the fuel cell current of Fig. 10 follows the current available waveform of Fig. 11. Fig. 10 shows the evolution of the load current and the fuel cell current during the step-up load variation. Notice that the experimental load current reaches a final value after the load step that is somewhat higher than the simulation. This causes some differences in the current request waveform immediately after the step load as shown in Fig. 11. Fig. 10 also shows the comparison between the simulated and measured fuel cell current. We can notice that both waveforms show the same trend but with some time shift. This difference is at least in part due to the fact that the model of the battery is simply a capacitor. In reality the battery is a nonlinear power source that, when discharging, has a voltage drop due to its nonlinear internal resistance. The difference in the battery voltage shown in Fig. 14 causes a difference in the current request and consequently in the current available waveforms shown in Fig. 11. In this implementation the available current is just a low-pass filtered version of the request current. Fig. 12 displays the comparison between the simulated and the measured actual current from the active filter. Notice that before the stepup load variation, these two waveforms have the same current, 0.02A toward the battery, indicating that the battery is charging. When the step-up load variation occurs, the actual current from the active filter becomes positive and the battery supplies the load. The maximum value of the measured active filter current differs from the maximum value of the simulation result by 0.05A. Moreover, the difference in time between simulation and experimental results is again related to the nonlinearity of the battery since the available current is used to calculate the current reference for the active filter (see equations ( 1 ) and ( 2 )).
Fig. 10 Step-up load variation under current mode control. Load current and fuel cell current. Time scale: 2s/div.
Fig. 11 Step-up load variation under current feed-forward control. Current Request and Current Available. Time scale: 5s/div.
Fig. 12 Step-up load variation under current feed-forward control. Actual current from the Active Filter (Fuel Cell side). Time scale: 5s/div.
Fig. 13 Step-up load variation under current feed-forward control. Bus voltage. Time scale: 2s/div.
Fig. 14 Step-up load variation under current feed-forward control. Battery voltage. Time scale: 5s/div.
Fig. 14 displays the battery voltage. We can see that after the step-up load the voltage of the battery drops from 14.75V to 13V in around three seconds and then stays constant while the battery supplies power to the load. Then the fuel cell current reaches the load current value and the fuel cell current keeps increasing to supply the current to recharge the battery. The difference between experimental and simulated battery voltage is due to the fact that in simulation the battery has been represented simply as a large capacitor. Fig. 13 displays the comparison between simulated fuel cell and experimental fuel cell voltage. The active filter ensures that the current from the fuel cell does not exceed the available fuel cell current iav. It is important to realize that the goal of the control is not to keep the bus voltage perfectly constant, which would require the battery to supply power to the load indefinitely under heavy load conditions, but rather to slow down the transient current requests to the fuel cell to a value compatible with the fuel cell dynamics. The bus voltage drop is due to the static fuel cell characteristic, but the rate of its drop is determined by the available current iav time constant. Ideally, when the load changes, the active filter current should change instantaneously to provide the entire extra load current, so that the fuel cell current is unchanged. As the available current from the fuel cell increases over several seconds, the active filter current can slowly go back to zero. The slow fuel cell current variation is shown in Fig. 10 to Fig. 14. To evaluate the speed of response of the current control, a zoom around the step-up load variation is shown in Fig. 15 and Fig. 16. The top waveform represents the request current calculated in block B. We can see the computational time step used by dSpace (100 µs) to calculate the request current waveform. The transient starts when the load steps up and ends when the active filter has adjusted its output current to supply the total load step current. It can be divided in two intervals. The first interval (40 µs) goes from the step-up load instant to the moment the request current variable steps up (top waveform in Fig. 15). During this interval the FC current (middle waveform in Fig. 15) increases to supply entirely the load current while the active filter remains in recharging mode. The maximum duration of this latency interval is equal to the control sampling time of 100 µs. The second interval (20µs) goes from the moment in which the request current variable steps up to the moment in
which the actual active filter current (bottom waveform in Fig. 15) reaches the reference current value. This interval typically takes one or two switching periods (20-40µs for 50kHZ switching frequency). During this interval the active filter current increases and the FC current decreases while the load current remains constant. At the end of this second interval the active filter reaches the reference current value and the FC current returns dynamically to its initial value. In conclusion, the feed-forward current control is extremely fast: it compensates for a load step variation in a time close to one time step of the digital controller. From Fig. 15 one may notice that the fuel cell ripple current increases when the active filter supplies the load. This is due to the fact that the active filter current supplied to the bus is a square wave at the active filter switching frequency (see Fig. 1). An output filter could be added to the active filter to attenuate this current ripple and the bus voltage ripple shown in Fig. 16. Fig. 16 shows the bus voltage and the fuel cell current. Notice how the active filter stabilizes the bus voltage. The bus voltage drops by 0.2V for 100 µs immediately after the load step and then goes back to the initial value after the active filter compensates for the load change.
Fig. 15 Step-up load variation under current feed-forward control. Zoom in of the step-up load transient. Request current, fuel cell current and active filter inductor current. Time scale: 100µs/div.
experimental bus voltage and Fig. 18 shows a comparison of simulated and experimental current from the active filter during the 0.38A step load. The control brings the bus voltage back to steady state in about 1 ms and the maximum deviation is 0.3 V.
Fig. 17 Step-up load variation under voltage mode control. Comparison between simulated bus voltage and experimental bus voltage. Time scale: 1ms/div.
Fig. 18 Step-up load variation under voltage mode control. Comparison between simulated and experimental active filter current. Time scale: 1ms/div.
Fig. 19 Hydrogen purge under voltage control. Top trace: bus voltage, 1V/div; bottom trace: active filter current, 200mA/div. Time scale: 0.5s/div.
Fig. 16 Step-up load variation under current feed-forward control. Zoom in of the step-up load transient. Top trace: bus voltage, 2V/div, middle trace: fuel cell current, 200mA/div. Time scale: 100µs/div.
B. Experimental Results for Voltage Feedback Control Fig. 17 shows a comparison of the simulated and
In many FC systems a hydrogen purge is periodically performed to clear waste products on the hydrogen side of the fuel cell. This causes a drop in pressure and a dip in the FC voltage. The voltage feedback control compensates this drop and provides a more stable bus voltage. Fig. 19 shows an oscilloscope capture during purging. The top waveform is the bus voltage and the bottom waveform is the current from the active filter. Notice how the active
filter current increases during the purge interval supporting the fuel cell voltage. As a result the bus voltage is not affected by the purge. The series diode prevents current back feed into the fuel cell. VIII.
DISCUSSION
The main objective of the active filter is to compensate for the slow dynamics of the fuel cell system. The choice of connecting both the fuel cell and the active filter in parallel with the DC bus has the advantage that additional losses of the active filter stage occur only when there is a load increase or during the recharging mode of operation, but not in steady-state condition with a constant load. A disadvantage of this solution is that the DC bus voltage has a static characteristic similar to the fuel cell characteristic, with non-negligible voltage droop as a function of load. The amount of droop can be estimated from the fuel cell equivalent circuit model of Fig. 2, which shows a dc internal resistance equal to Ra + Rr = 2Ω . The active filter could compensate for this droop, but this would require the battery to provide power to the load for an indefinite time under high load condition. The current feed-forward control shown in Fig. 4 performs a dual function: when the load during a transient requires more power than the fuel cell can provide at that time, the converter draws the necessary power from the battery; otherwise, it keeps the battery charged. The current drawn from the fuel cell is precisely controlled so that it does not exceed the current that the fuel cell is capable of providing at any given time, but at the same time fast load current dynamics are provided by the battery through the active filter. During a step load transient, the fuel cell current is equal to the available current, as can be seen from Fig. 10 and Fig. 11. The current feed-forward control provides a very fast response to load variation, close to one time step of the digital controller, since the system reacts as soon as the measured load current changes, without going through a feedback loop. A potential disadvantage of this control is that, being basically an open-loop control, it is sensitive to model inaccuracies. For example, the active filter hysteresis control actually controls the current on the battery side, not the current on the active filter side. Therefore, the reference current to the hysteresis control has to be scaled by a factor equal to the ratio of bus voltage and battery voltage. In the implementation a constant factor is used that does not take into account variations of these voltages due to loading and to the state of charge of the battery. This error could be compensated by calculating the actual voltage ratio obtained from measurements. Another disadvantage of this control is that a load current sensor is needed.
The voltage feedback control as implemented in Fig. 5 does not manage the battery state-of-charge and does not adjust to variations of available current from the fuel cell. Adding these features to the basic control described here is left as future work. An advantage of this control is that it does not need a load current sensor. Another advantage is that it is capable of compensating for disturbances on the dc bus other than load variations. For example, the control can stabilize the bus voltage during hydrogen purge. It is interesting to compare the response time of the two controls for the same load step as shown in Fig. 15 through Fig. 18. The feed-forward control is about ten times faster than the feedback control and has a response time of about one time step of the digital control. IX.
CONCLUSION
Given the increasing interest in FC systems, this work discusses a power conditioner (active filter) that compensates for the slow dynamics of the FC. The active filter is a bidirectional converter connected to an energy storage device (a battery) able to provide fast load current dynamics. A simple equivalent circuit model for the fuel cell is used for control design and for simulations. FC model parameters are extracted using the current interrupt technique. Two different control strategies are proposed: current feed-forward control and voltage feedback control. Simulations have been developed to obtain insight of the control strategies and finally a prototype has been built to validate the control approaches and to compare the performance of the two control strategies. There is good agreement between simulation and experimental results. ACKNOWLEDGMENT This work was supported by the U.S. Office of Naval Research under Grant N00014-02-1-0623. REFERENCES [1] [2] [3] [4] [5]
[6]
A.J. Appleby, F.R. Foulkes, Fuel Cell Handbook (New York: Van Nostrand Reinhold 1989) Laminie, J.E, and Dicks, A 2000, Fuel Cell Systems Explained, John Wiley & Sons, Chistester, England. M. Smith, K. Cooper, D. Johnson, L. Scribner, “Comparison of Fuel Cell Electrolyte Resistance Measurement Techniques”, Fuel Cell, April/May 2005. J. R. J. Larminie, Current interrupt technique for circuit modeling, 1994. E. Santi, D. Franzoni, A. Monti, D. Patterson, F. Ponci, N. Barry, “A Fuel Cell Based Domestic Uninterruptible Power Supply”, APEC 2002, Volume: 1 ,10-14 March 2002 Pages:605 - 613 vol.1 W. Tang, F. C. Lee, R. B. Ridley, I. Cohen, “Charge Control: Modeling, Analysis, and Design”, in IEEE Trans Power Electronics, Vol. 8, No 4, pp. 396 – 403, October 1993.
University of South Carolina Department of Electrical Engineering Email: [email protected] Abstract— Fuel cells are becoming a more attractive option for many remote power applications. One of the main wellknown problems of a fuel cell system is its slow dynamic response: the fuel cell system needs significant time to reach a new steady-state condition after a load change. Notice that fuel cell dynamics, in terms of time-constants, may be in the order of seconds while electrical loads are usually in the millisecond range. This slow dynamic response should be compensated to allow operation under quick load variation conditions. A separate energy storage device, such as a battery, can be used to supply power to the load during all transient periods in which the fuel cell is adapting its state according to the load request. This paper proposes a bidirectional converter to compensate for the fast load changes while the fuel cell system adjusts the fuel flow to deliver the necessary energy. Two control strategies are proposed: a current feed-forward control and a voltage feedback control. Simulink simulations have been developed to obtain insight about these control strategies, as well as about the behavior of the bi-directional converter. A 35W hardware prototype has been built to verify the control performance. Experimental results of both controls are in agreement with their simulations and therefore validate the proposed control strategies. Both control strategies perform well. The current feed-forward control has the advantage of being extremely fast - with responses of the order of one time step of the digital controller - but has the disadvantage of requiring a load current sensor.
III.
INTRODUCTION
In recent years, the escalating cost of conventional fuel and the increasing restrictions imposed by pollution laws have made efficient energy conversion systems based on fuel cell (FC) technology more attractive than they were in the past. A fuel cell stack is a device that converts the chemical energy of hydrogen into electricity as long as fuel (hydrogen) and oxidant (air) are supplied. In order to operate the fuel cell stack in an economical way for different power demands, fuel and oxidant flow may be dynamically adjusted as a function of load demand. The hydrogen fuel may be taken from a storage tank or generated using a reformer. Different dynamic time constants can be observed during FC operation due to chemical, mechanical and electrical phenomena occurring in the fuel cell and in the balance of plant. Typically, FC systems require few tenths of seconds for transitioning from one steady-state operating point to another [1]. In applications that require a fast dynamic response, the slow dynamics of a fuel cell system can be compensated by using a separate energy storage device, which provides power to the load during fast transients. The active filter solution shown in Fig. 1 has been proposed by the authors in [5]. It uses a bi-directional converter to interface the
University of Nebraska, USA * University of Cork, Ireland
energy storage device (a battery) with the fuel cell system. The converter is effectively connected in parallel with the fuel cell. The control strategy of the bi-directional converter manages the battery power in order to obtain a fast system response to quick load variations [5]. Therefore, the overall system is equivalent to a power source with a fast dynamic response (Fig. 1). This paper focuses on different control strategies for the active filter. The discussion begins with the characterization of the 35W-proton exchange membrane fuel cell stack PEM D35 used in this study, followed by a description of the proposed system. Two different control strategies are described and simulated. Experimental results for these control strategies are then provided and compared with simulation. Finally, the two control strategies are contrasted and relative advantages and disadvantages identified.
Fig. 1: The fuel cell by itself has slow dynamics, however the fuel cell/active filter combination shown in the dashed box is equivalent to a power source with fast dynamics.
IV.
CHARACTERIZATION OF THE FUEL CELL
An equivalent model for the fuel cell is needed to simulate and design a control strategy. A possible equivalent circuit for the PEM D-35 fuel cell is shown in Fig. 2 [2-3]. The DC voltage source E0 models the open circuit voltage, resistance Rr models ohmic losses, resistance Ra models the activation overvoltage and capacitance Ca models the effect of the charge double layer. The current interrupt technique [3][4] is used to quickly obtain the parameters of this behavioral model. In this technique the fuel cell provides a load current that is quickly brought to zero. The transient FC voltage can be used for parameter extraction.
used as input filter for the FC system. The 400µH inductance L has been designed for operation at 50kHz switching frequency with a peak current of 3A. Two sealed lead acid batteries (6V 8Ah) are connected in series on the low voltage side of the bi-directional converter. IRF540 MOSFETs are used as active switches and an IR2110 high-side driver is used to drive them. A diode is placed in series with the fuel cell to protect it against current backflow. Fig. 2: Equivalent electric circuit model of the fuel cell.
After the parameter extraction is performed, the behavior is compared with the experimental data for validation. Fig. 3 displays the comparison of the fuel cell voltage transient obtained from the equivalent circuit model and the PEM D-35 fuel cell system during a current interruption of 1A.
B. Control Stage. 1) Current Feed-forward Control The first proposed solution is to use current feedforward control. The current reference is determined according to the power flow requirement to and from the energy storage device [6]. Feed-forward from the load current is used to determine the current reference. Fig. 4 shows a block diagram of the control that uses the following control variables: battery voltage (Vb), actual current available from the fuel cell (iav), load current (iload), reference current for the active filter (iref), actual current from the active filter (iF), charging current (ich), which represents the desired battery charging current based on its state of charge, and current request to the fuel cell (ireq), calculated from the load current and the charging current.
Fig. 3: Comparison of the Fuel Cell voltage obtained from the equivalent circuit model and the PEM D-35 fuel cell system during a current interruption of 1A.
When the fuel cell current steps down to zero, the fuel cell voltage exhibits an instantaneous step increase. This step change is used to estimate Rr. Afterwards, the voltage increases more slowly to its final value. This transient is used to estimate the time constant defined by Ra and Ca. Capacitor Ca, which represents the charge double layer, discharges to zero and the FC terminal voltage rises exponentially to the open-circuit voltage. Notice that the equivalent circuit model cannot properly simulate high current density conditions where the assumption of negligible concentration losses does not hold. Table I lists the parameters values of the equivalent circuit model for the PEM D-35 fuel cell. TABLE I PARAMETERS OF EQUIVALENT CIRCUIT FOR THE PEM D-35 FUEL CELL SYSTEM
Parameter Ca Ra Rr
V.
Value 0.0133 F 1.5 Ω 0.5 Ω
DESCRIPTION OF THE SYSTEM
A. Power Stage The power stage used to implement the active filter is a bi-directional converter (see Fig. 1). The high voltage side of the bi-directional converter is connected to the PEM D35 fuel cell system. A 100µF input capacitance, Cin, is
Fig. 4 Current control block diagram
The FC block receives from the control current request signal ireq and outputs current available signal iav. Depending on the fuel cell system characteristics, this may represent an actual adjustment of fuel and air flow to the FC to accommodate the control request. In certain fuel cells flows are fixed. In that case it is desirable to make sure that the FC current changes at a fairly low rate to prevent flooding of the fuel cell. This can be achieved by making iav a low-pass filtered version of ireq with time constants of the order of several seconds. The control stage consists of four blocks (see Fig. 4): block A estimates the current needed to recharge the battery (ich); block B calculates the request current, ireq, as a sum of the load current (iload) and the charging current (ich); block C determines the reference current for the active filter (iref); and finally the hysteresis block defines the duty cycle to control the MOSFETs. This control has two different operating modes. The first is the discharging mode, in which the battery delivers its own power to the load to maintain the uninterrupted power flow since the fuel cell is unable to supply the power
absorbed by the load. Using ( 1 ) the reference current for the active filter is calculated:
iref = iload − iav
(1)
The second operating mode is the battery charging mode. The fuel cell is able to supply the power requested by the load. Therefore, the active filter could recharge the battery if necessary, while keeping the total current under the maximum allowed for the fuel cell. During this interval the reference current for the active filter is given by ( 2 ). iref = − min[(iav − iload ), ich ]
(2)
2) Voltage Feedback Control Another option is to use voltage feedback control to stabilize the bus voltage. Fig. 5 shows a block diagram of this control. The bus voltage Vbus is the controlled voltage. The control tries to keep the bus voltage at a reference value. From the fuel cell model of Fig. 2, the fuel cell voltage is given by VFC ( s ) = E0 − Z FC ( s) I FC ( s)
the load (see Fig. 4). The fuel cell is modeled using the equivalent electric circuit in Fig. 2. The active filter is modeled as a controlled current source, since the response of the hysteresis current loop can be considered instantaneous ( iF = iref ) as compared to the other system time constants. The battery is modeled as a large (1 F) capacitor. The equivalent electrical model of the system shown in Fig. 6 is described by the following equations: dvbus (t ) 1 (iFC (t ) − iload (t ) + iF (t )) = dt Cin
(5)
dva (t ) 1 = dt Ca
(6)
v (t ) iFC (t ) − a Ra
The control performance has been evaluated by applying a 100% step load increase from 0.38A to 0.76A.
(3)
The fuel cell internal impedance ZFC(s) is R ⋅R 1 + s ⋅ C a ⋅ a r Ra + R r Z FC ( s) = (Ra + Rr ) ⋅ 1 + s ⋅ C a ⋅ Ra
= 2 1 + 0.005 ⋅ s ( 4 ) 1 + 0.02 ⋅ s
The bus voltage is equal to the fuel cell voltage if the voltage drop of the series diode is neglected. Capacitor Cin of Fig. 1 is also neglected.
Fig. 5 Voltage feedback control block diagram
From (4), the fuel cell transfer function exhibits one pole at s = -50 (8Hz) and one zero at s = -200 (32Hz). The compensator is an integral compensator designed to give a crossover frequency of 300Hz. The integral action is used to increase the low-frequency loop gain. The load current and the open circuit voltage can be considered as disturbances. This control keeps the bus voltage constant. This may not be desirable, because at heavy load this may require the battery to provide power to the load indefinitely. It is possible to modify this control allowing slow variations of bus voltage according to the fuel cell static characteristic. Moreover, battery charging during periods of active filter inactivity should be implemented. This is left as future work. VI.
SIMULATION RESULTS
A simulation of both control strategies has been performed using Simulink. The power stage is the parallel combination of the fuel cell system, the active filter and
Fig. 6 Equivalent electrical model of the power stage system
A. Current Feed-forward Control Simulation The simulation of the step load response is shown in Fig. 7. The transient can be divided into two consecutive intervals. The first interval (discharging mode) begins when the load steps up and ends when the fuel cell current becomes equal to the reference value required by the load (Fig. 7(a)). At this point, the second interval (charging mode) begins and is complete only when the battery is fully recharged (Fig. 7(b)). The active filter current iF (Fig. 7(c)) is positive during the first interval since the bi-directional converter supplies power to the load; then it becomes negative during the second interval to recharge the battery; and finally it goes to zero when the battery is fully charged. Fig. 7(d) shows the fuel cell required and available currents. After the step load, the current request changes instantaneously to the new required value, but the available current from the fuel cell changes slowly as the fuel cell adjusts to the new power demand.
reduces this voltage drop and slows down the bus voltage variation.
(a)
(b)
Fig. 9 Step-up load variation of fuel cell only (no active filter). Load current, 0.2A/div, and fuel cell voltage, 1V/div. Time scale: 0.1s/div.
(c)
(d)
Fig. 7: Simulation results of a step-up load variation with current feedforward control: (a) Load current and fuel cell, (b) Bus voltage and battery voltage, (c) Active filter current, (d) Fuel cell request current and available current. Time scale: 10s/div.
B. Voltage Feedback Control Simulation The simulation of the step load response is shown in Fig. 8. The bus voltage transient lasts about 1ms. Immediately after the step, the fuel cell provides the entire extra load current and the bus voltage drops. The voltage feedback control increases the active filter current to compensates for the bus voltage drop (see Fig. 8b). After about 1ms the active filter provides the entire extra load current and the bus voltage goes back to the original value.
(a)
(b)
Fig. 8 Simulation results of a step-up load variation with voltage feedback control: (a) Bus voltage, (b) Active filter current. Time scale: 5ms/div
VII.
EXPERIMENTAL RESULTS
Both controls have been implemented using a dSpace DS1104 platform. The integration method used for the real-time implementation is Euler with a time step equal to 100µs. For both controls, reference active filter current iref is calculated digitally by dSpace. On the other hand, the hysteresis current control is implemented with analog circuitry. A step-up load change from 0.38A to 0.76A is performed to evaluate the dynamics of the control variables. The experimental results are compared with simulation results to validate both control strategies. All experimental results have been numerically filtered to eliminate undesired switching noise. Fig. 9 shows the fuel cell voltage during a load step without active filter. It can be seen that the fuel cell voltage drops initially by 0.4V and after about 0.1s by approximately 1V. It will be shown how the active filter
A. Experimental Results for Current Feed-forward Control The step-up load transient is shown in Fig. 10 through Fig. 14. Notice how the active filter control ensures that the fuel cell current of Fig. 10 follows the current available waveform of Fig. 11. Fig. 10 shows the evolution of the load current and the fuel cell current during the step-up load variation. Notice that the experimental load current reaches a final value after the load step that is somewhat higher than the simulation. This causes some differences in the current request waveform immediately after the step load as shown in Fig. 11. Fig. 10 also shows the comparison between the simulated and measured fuel cell current. We can notice that both waveforms show the same trend but with some time shift. This difference is at least in part due to the fact that the model of the battery is simply a capacitor. In reality the battery is a nonlinear power source that, when discharging, has a voltage drop due to its nonlinear internal resistance. The difference in the battery voltage shown in Fig. 14 causes a difference in the current request and consequently in the current available waveforms shown in Fig. 11. In this implementation the available current is just a low-pass filtered version of the request current. Fig. 12 displays the comparison between the simulated and the measured actual current from the active filter. Notice that before the stepup load variation, these two waveforms have the same current, 0.02A toward the battery, indicating that the battery is charging. When the step-up load variation occurs, the actual current from the active filter becomes positive and the battery supplies the load. The maximum value of the measured active filter current differs from the maximum value of the simulation result by 0.05A. Moreover, the difference in time between simulation and experimental results is again related to the nonlinearity of the battery since the available current is used to calculate the current reference for the active filter (see equations ( 1 ) and ( 2 )).
Fig. 10 Step-up load variation under current mode control. Load current and fuel cell current. Time scale: 2s/div.
Fig. 11 Step-up load variation under current feed-forward control. Current Request and Current Available. Time scale: 5s/div.
Fig. 12 Step-up load variation under current feed-forward control. Actual current from the Active Filter (Fuel Cell side). Time scale: 5s/div.
Fig. 13 Step-up load variation under current feed-forward control. Bus voltage. Time scale: 2s/div.
Fig. 14 Step-up load variation under current feed-forward control. Battery voltage. Time scale: 5s/div.
Fig. 14 displays the battery voltage. We can see that after the step-up load the voltage of the battery drops from 14.75V to 13V in around three seconds and then stays constant while the battery supplies power to the load. Then the fuel cell current reaches the load current value and the fuel cell current keeps increasing to supply the current to recharge the battery. The difference between experimental and simulated battery voltage is due to the fact that in simulation the battery has been represented simply as a large capacitor. Fig. 13 displays the comparison between simulated fuel cell and experimental fuel cell voltage. The active filter ensures that the current from the fuel cell does not exceed the available fuel cell current iav. It is important to realize that the goal of the control is not to keep the bus voltage perfectly constant, which would require the battery to supply power to the load indefinitely under heavy load conditions, but rather to slow down the transient current requests to the fuel cell to a value compatible with the fuel cell dynamics. The bus voltage drop is due to the static fuel cell characteristic, but the rate of its drop is determined by the available current iav time constant. Ideally, when the load changes, the active filter current should change instantaneously to provide the entire extra load current, so that the fuel cell current is unchanged. As the available current from the fuel cell increases over several seconds, the active filter current can slowly go back to zero. The slow fuel cell current variation is shown in Fig. 10 to Fig. 14. To evaluate the speed of response of the current control, a zoom around the step-up load variation is shown in Fig. 15 and Fig. 16. The top waveform represents the request current calculated in block B. We can see the computational time step used by dSpace (100 µs) to calculate the request current waveform. The transient starts when the load steps up and ends when the active filter has adjusted its output current to supply the total load step current. It can be divided in two intervals. The first interval (40 µs) goes from the step-up load instant to the moment the request current variable steps up (top waveform in Fig. 15). During this interval the FC current (middle waveform in Fig. 15) increases to supply entirely the load current while the active filter remains in recharging mode. The maximum duration of this latency interval is equal to the control sampling time of 100 µs. The second interval (20µs) goes from the moment in which the request current variable steps up to the moment in
which the actual active filter current (bottom waveform in Fig. 15) reaches the reference current value. This interval typically takes one or two switching periods (20-40µs for 50kHZ switching frequency). During this interval the active filter current increases and the FC current decreases while the load current remains constant. At the end of this second interval the active filter reaches the reference current value and the FC current returns dynamically to its initial value. In conclusion, the feed-forward current control is extremely fast: it compensates for a load step variation in a time close to one time step of the digital controller. From Fig. 15 one may notice that the fuel cell ripple current increases when the active filter supplies the load. This is due to the fact that the active filter current supplied to the bus is a square wave at the active filter switching frequency (see Fig. 1). An output filter could be added to the active filter to attenuate this current ripple and the bus voltage ripple shown in Fig. 16. Fig. 16 shows the bus voltage and the fuel cell current. Notice how the active filter stabilizes the bus voltage. The bus voltage drops by 0.2V for 100 µs immediately after the load step and then goes back to the initial value after the active filter compensates for the load change.
Fig. 15 Step-up load variation under current feed-forward control. Zoom in of the step-up load transient. Request current, fuel cell current and active filter inductor current. Time scale: 100µs/div.
experimental bus voltage and Fig. 18 shows a comparison of simulated and experimental current from the active filter during the 0.38A step load. The control brings the bus voltage back to steady state in about 1 ms and the maximum deviation is 0.3 V.
Fig. 17 Step-up load variation under voltage mode control. Comparison between simulated bus voltage and experimental bus voltage. Time scale: 1ms/div.
Fig. 18 Step-up load variation under voltage mode control. Comparison between simulated and experimental active filter current. Time scale: 1ms/div.
Fig. 19 Hydrogen purge under voltage control. Top trace: bus voltage, 1V/div; bottom trace: active filter current, 200mA/div. Time scale: 0.5s/div.
Fig. 16 Step-up load variation under current feed-forward control. Zoom in of the step-up load transient. Top trace: bus voltage, 2V/div, middle trace: fuel cell current, 200mA/div. Time scale: 100µs/div.
B. Experimental Results for Voltage Feedback Control Fig. 17 shows a comparison of the simulated and
In many FC systems a hydrogen purge is periodically performed to clear waste products on the hydrogen side of the fuel cell. This causes a drop in pressure and a dip in the FC voltage. The voltage feedback control compensates this drop and provides a more stable bus voltage. Fig. 19 shows an oscilloscope capture during purging. The top waveform is the bus voltage and the bottom waveform is the current from the active filter. Notice how the active
filter current increases during the purge interval supporting the fuel cell voltage. As a result the bus voltage is not affected by the purge. The series diode prevents current back feed into the fuel cell. VIII.
DISCUSSION
The main objective of the active filter is to compensate for the slow dynamics of the fuel cell system. The choice of connecting both the fuel cell and the active filter in parallel with the DC bus has the advantage that additional losses of the active filter stage occur only when there is a load increase or during the recharging mode of operation, but not in steady-state condition with a constant load. A disadvantage of this solution is that the DC bus voltage has a static characteristic similar to the fuel cell characteristic, with non-negligible voltage droop as a function of load. The amount of droop can be estimated from the fuel cell equivalent circuit model of Fig. 2, which shows a dc internal resistance equal to Ra + Rr = 2Ω . The active filter could compensate for this droop, but this would require the battery to provide power to the load for an indefinite time under high load condition. The current feed-forward control shown in Fig. 4 performs a dual function: when the load during a transient requires more power than the fuel cell can provide at that time, the converter draws the necessary power from the battery; otherwise, it keeps the battery charged. The current drawn from the fuel cell is precisely controlled so that it does not exceed the current that the fuel cell is capable of providing at any given time, but at the same time fast load current dynamics are provided by the battery through the active filter. During a step load transient, the fuel cell current is equal to the available current, as can be seen from Fig. 10 and Fig. 11. The current feed-forward control provides a very fast response to load variation, close to one time step of the digital controller, since the system reacts as soon as the measured load current changes, without going through a feedback loop. A potential disadvantage of this control is that, being basically an open-loop control, it is sensitive to model inaccuracies. For example, the active filter hysteresis control actually controls the current on the battery side, not the current on the active filter side. Therefore, the reference current to the hysteresis control has to be scaled by a factor equal to the ratio of bus voltage and battery voltage. In the implementation a constant factor is used that does not take into account variations of these voltages due to loading and to the state of charge of the battery. This error could be compensated by calculating the actual voltage ratio obtained from measurements. Another disadvantage of this control is that a load current sensor is needed.
The voltage feedback control as implemented in Fig. 5 does not manage the battery state-of-charge and does not adjust to variations of available current from the fuel cell. Adding these features to the basic control described here is left as future work. An advantage of this control is that it does not need a load current sensor. Another advantage is that it is capable of compensating for disturbances on the dc bus other than load variations. For example, the control can stabilize the bus voltage during hydrogen purge. It is interesting to compare the response time of the two controls for the same load step as shown in Fig. 15 through Fig. 18. The feed-forward control is about ten times faster than the feedback control and has a response time of about one time step of the digital control. IX.
CONCLUSION
Given the increasing interest in FC systems, this work discusses a power conditioner (active filter) that compensates for the slow dynamics of the FC. The active filter is a bidirectional converter connected to an energy storage device (a battery) able to provide fast load current dynamics. A simple equivalent circuit model for the fuel cell is used for control design and for simulations. FC model parameters are extracted using the current interrupt technique. Two different control strategies are proposed: current feed-forward control and voltage feedback control. Simulations have been developed to obtain insight of the control strategies and finally a prototype has been built to validate the control approaches and to compare the performance of the two control strategies. There is good agreement between simulation and experimental results. ACKNOWLEDGMENT This work was supported by the U.S. Office of Naval Research under Grant N00014-02-1-0623. REFERENCES [1] [2] [3] [4] [5]
[6]
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