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Design and experimental implementation of time delay control for air supply in a polymer electrolyte membrane fuel cell system
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Design and experimental implementation of time delay control for air supply in a polymer electrolyte membrane fuel cell system Ya-Xiong Wang a, Dong-Ji Xuan b, Young-Bae Kim a,* a b
Department of Mechanical Engineering, Chonnam National University, Gwangju, Republic of Korea College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou, China
article info
abstract
Article history:
This paper studies the air flow control for preventing the starvation and/or obtaining the
Received 4 December 2012
maximum net power of a Polymer Electrolyte Membrane (PEM) fuel cell system using time
Received in revised form
delay control (TDC). Feedforward and feedback controls are utilized simultaneously to
7 May 2013
prevent air shortage during the transient response of the fuel cell operation. The TDC al-
Accepted 10 June 2013
gorithm design is created with a low-order dynamic model, and its superior performances
Available online 13 July 2013
are proven using a real-time control experiment. The optimal air excess ratio is calculated experimentally given the variation of the external load, and the net power increase is discussed by comparison with the results obtained from fixed air excess ratio. The Ballard
Keywords: Modeling
of
polymer
electrolyte
membrane fuel cell system
1.2 kW PEM fuel cell system is used for the experiments as a test rig, and the LabView system is used for the real-time air flow control. The superiority of the TDC performance is
Time delay control
proven by comparison with other control algorithms such as the proportionaleintegral
Air flow control
control (PIC), feedforward control, and the original manufacturer’s control. The proposed
Power optimization
control algorithm can improve PEM fuel cell system performance by preventing air shortage and/or by obtaining higher performance. Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Using the polymer electrolyte membrane (PEM) fuel cell in the fuel cell-based hybrid vehicle has many advantages. The PEM fuel cell-based hybrid vehicle can be started quickly, produces almost zero emission and low noise, and operates under relatively lower temperatures. It has higher efficiency than a vehicle equipped with an internal combustion engine. However, ancillaries such as a humidifier, cooler, and compressor are needed to obtain the best operating performance and prevent possible operation malfunction in using PEM as a hybrid vehicle. A regular PEM fuel cell system is presented in Fig. 1. The PEM fuel cell should provide efficient power
delivery to meet sudden high-power requirements; as vehicle operation involves quick start, stop, acceleration, and deceleration. Fuel cell power comes from fuel (hydrogen) oxidation at the anode and oxidant (oxygen) reduction at the cathode. If adequate oxygen and hydrogen cannot be supplied within a short interval, the fuel cell performance can decline, resulting in failure to provide quick acceleration response to the vehicle. Sometimes, air starvation will occur if the air inflow is too low, which eventually shortens fuel cell life expectancy [1]. Thus, many researchers have studied air flow control to prevent starvation. In providing the air flow control algorithm for the PEM fuel cell, developing an accurate fuel cell model is compulsory. Many studies constructing the PEM fuel cell
* Corresponding author. Tel.: þ82 62 5301677. E-mail address: [email protected] (Y.-B. Kim). 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2013.06.040
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Fig. 1 e The schematic diagram of a PEM fuel cell system.
model have been conducted using various approaches. Numerous accurate PEM fuel cell models, including the species, pressure, overpotential, temperature, and water distributions inside the fuel cell, have been developed using tools with computational fluid dynamics (CFD) [2e6]. Although these CFD models can provide exact fuel cell characteristics at the specific fuel cell location, the use of CFD modeling for control purposes is almost impossible because CFD models have degrees of freedom in tens of thousands, that is, state variables. Therefore, control engineers have separately developed control-oriented models with lower degrees of freedom. Most of the control-oriented models are classified as zero-dimensional or one-dimensional. Very few twodimensional models are developed [7,8]. One- or twodimensional models are normally used to analyze the water distribution inside the gas diffusion layer (GDL). If the effect of the water or its distribution, which is normally used for humidification control or water management, is not considered, a zero-dimensional model is sufficient for controlling air flow. Pukrushpan et al. proposed a zero-dimensional PEM fuel cell model including stacks, cooler, humidifier, and compressor [9]. Their control-oriented model includes mass flow rate of hydrogen and oxygen, pressure, and compressor rpm as a state variable. Similar models were developed by Vahidi et al. [10], Bao et al. [11], del Real et al. [12], McKay et al. [13], Karnik et al. [14], and Kim [15,16]. Although these models present fuel cell physical characteristics effectively (i.e., the relationship between cell voltage and cell current), they include many state variables for use in real-time control, and they require formidable experiments to obtain exact model parameters. Therefore, most models mentioned above are only used in simulation to verify the efficacy of their control algorithms in preventing air starvation. In a similar manner, Chiu et al. [17] and Na et al. [18] developed the state-space
linearized fuel cell model using pressure and species mass fractions as state variables without identifying the model parameters in the electrical engineering field. A transfer function between air flow inputs and PEM fuel cell outputs has been used for real-time control. For example, Wang et al. [19] conducted experiments to obtain the transfer function between air flow rates as an input and cell voltage as an output using exhaustive experiments to control cell voltage using robust control algorithm such as HN. A similar transfer function model was created by Yang et al. [20] using recursive least square algorithms. Arce et al. [21] also extracted the transfer function model between the compressor input and air excess ratio using experiments for real-time control. In regulating the PEM fuel cell output voltage or air excess ratio, conventional proportionaleintegralederivative (PID) control [8], LQG control [9,11], fuzzy control [22], neural network control [23], time delay control [15,16] or model predictive control (MPC) [10] have been applied without real plant validation. In real plant validation, Wang et al. [19] and Yang et al. [20] used HN and adaptive control, respectively, to regulate the fuel cell voltage output. However, their model utilized multivariable transfer matrices rendering the control system complex. Arce et al. [21] used MPC to regulate the air excess ratio. Although their experimental result was good to regulate the air excess ratio, their MPC algorithm was linear and it was too complex to apply in the real system. In the present paper, double control actions of feedforward control and TDC compensation are used to regulate the air excess ratio to prevent starvation and to obtain maximum net power of the stack. TDC can compensate for the error dynamics that might occur due to imperfect feedforward control action. The transfer function between air flow input and air excess ratio output is determined via experiments to design the TDC algorithm. The better dynamic performance of the
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TDC to prevent starvation and to achieve maximum net power is compared with the PIC and original manufacturer’s controller of the 1.2 kW Ballard PEM fuel cell system. The main contributions of the present paper are developing a simple but effective PEM fuel cell system model to design TDC and utilizing this model for real-time control. Superior TDC control characteristics for regulating the air excess ratio and for obtaining the maximum net power will be discussed. This is the first paper to apply TDC in regulating air flow to the PEM fuel cell system in real-time.
2.
PEMFC model
Ballard PEMFC with 1.2 kW has been used for air excess control to prevent starvation and/or to achieve the net power maximization in our experiment. The system is composed of 46 cells, each with a 110 cm2 membrane electrode assembly (MEA). The system is widely used by many researchers worldwide and is equipped with a self-controlled algorithm to prevent abnormal operation. It is also equipped with a selfhumidifier and is air-cooled by a small fan. Hydrogen is supplied from the pressurized tank through a regulating valve, which controls the anode pressure to render small pressure difference to the cathode side because large pressure difference between cathode and anode compartments can induce the membrane stress and shorten the fuel cell life. Oxygen supply is achieved from a compressor, whose air flow can be regulated through compressor input voltage. The fuel cell system is equipped with a manufacturer-made on-board controller to measure the fuel cell variables and to control the air flow depending on the required load. If insufficient hydrogen and/or oxygen is delivered to produce the required external power, the on-board controller automatically shuts down the system to prevent further fuel cell system damages. In the present paper, the manufacturer’s on-board controller is overridden by a PCI-6229 controller from National Instrument only to control compressor air flow. Other controls such as anode purging, humidifier, and fan control are performed by the manufacturer control algorithms. The present real-time controller receives the data from fuel cell sensors and computes the air flow using a 400 Hz sampling frequency. The real-time controller receives data from three sensors: stack voltage (Vst), stack current (Ist), and air flow supplied by a compressor (Win). The real-time controller output is the compressor voltage (Vcm), which controls the air flow rate depending on the required external power. As the air flow rate (Win) is a function of Vcm, the relation between these two variables can be obtained via experiment (Fig. 2) and can be represented as Win ¼ 1:862Vs3 þ 1:48Vs2 þ 2:65Vs ;
(1)
where Vs is the sensor output voltage measured at the air inlet stream line.
2.1.
Air supply control
One of the primary objectives of this paper is to prevent air starvation when the supplied air is less than the consumed
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air. Starvation will occur when the fuel cell system requires sudden power increase, and starvation usually occurs during the transients. Starvation is one of the main causes of aging and degeneration of fuel cells [24]. When starvation occurs due to lack of oxygen and/or hydrogen, the performance of the fuel cell decreases given cell voltage drops. A rapid cell voltage drop can cause a burn through the surface of the membrane. Starvation is a very complicated phenomenon with causes and consequences that have been reported in the literature [25,26]. Low reactant flow rates may induce uneven flow sharing between the cells in the stack, leading to locally or completely starved cells [27]. Oxygen or hydrogen starvation can result in the generation of hydrogen in the cathode or oxygen in the anode. The presence of oxygen in the anode or hydrogen in the cathode leads to the reversal of the cell potential, which is a negative potential differential between the anode and the cathode. Cell potential reversal accelerates the corrosion of carbon components, such as backing layers with ensuing electro-catalyst corrosion, and eventually leads to damaged components. The best way to prevent oxidant starvation and to enable stable operation of the fuel cell is to supply the excess oxygen rapidly by increasing the air flow rate to the cathode. This increase is limited by the inertia of the compressors, and especially at fast load change, the risk of starvation is high [1]. Therefore, excessive air flow is necessary to prevent the sudden shortage of the oxygen during the fast load change. The excessive air ratio, lO2 , is defined as the ratio between the oxygen supplied to the cathode ðWO2 ;ca;in Þ and the oxygen made to react in the fuel cell stack ðWO2 ;reacted Þ as follows [21,28,29]: lO2 ¼
WO2 ;ca;in : WO2 ;reacted
(2)
The desired value of this value depends on the fuel cell itself and on the operating objective. For example, Pukrushpan et al. [28] proposed to regulate lO2 ¼ 2 for a 75 kW stack to guarantee safety and to provide high efficiency. Arce et al. [21] proposed lO2 ¼ 4 to prevent starvation and achieve relatively higher fuel cell net power. If the air excess ratio increases, more compressor power is required to supply higher oxygen flow rate, and the gross fuel cell power also increases due to the increase in oxygen and hydrogen partial pressures. If the air excess ratio decreases, the compressor power and gross fuel cell power both decrease. Moreover, if the air excess ratio is too small, then starvation may occur during the sudden change of the load. Therefore, the regulation of lO2 is a critical issue in preventing starvation as well as in obtaining the maximum fuel cell net power. In the present paper, we used two air excess ratios. The first one uses a fixed value, and the second is a varying lO2 to obtain the maximal net fuel cell power. The optimal lO2 is obtained from the experiment.
2.2.
Controlled variable
The oxygen excess ratio, lO2 , cannot be measured directly. It can be obtained from other sensor measurements. Based on the definition of lO2 , values of WO2 ;ca;in and WO2 ;reacted are necessary.
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120
Air Flow Rate (slpm)
100 80 60 40 Experimental Data Identification
20 0 1.6
1.8
2
2.2
2.4 2.6 2.8 Sensor Voltage (V)
3
3.2
3.4
3.6
Fig. 2 e Curve fit between the air flow rate and the compressor voltage.
The oxygen mass flow WO2 ;ca;in is available in the dry air Wa,ca,in at the cathode inlet as follows [28,29]:
The oxygen flow consumption in the reaction WO2 ;reacted is as follows:
WO2 ¼ xO2 Wa;ca;in
n$Ist : WO2 ;reacted ¼ MO2 $ 4F
(3)
The oxygen mass fraction xO2 ;ca;in can be calculated by xO2 ;ca;in
yO2 ;ca;in MO2 ¼ : yO2 ;ca;in MO2 þ 1 yO2 ;ca;in MN2
(4)
The oxygen mole fraction yO2 ;ca;in is assumed for the atmospheric air condition. The mass flow rate of dry air at the cathode inlet is Wa;ca;in ¼
1 Wca;in ; 1 þ uca;in
(5)
where uca,in is the humidity ratio obtained by uca;in ¼
Mv Pv;ca;in $ ; Ma;ca;in Pa;ca;in
(6)
where Mv is the molar mass of vapor, and Ma,ca,in is molar mass of air at cathode, which is calculated as follows [28,29]: Ma;ca;in ¼ yO2 ;ca;in MO2
þ 1 yO2 ;ca;in MN2 :
(7)
Pv,ca,in and Pa,ca,in are the vapor and dry air partial pressures, respectively. The relation between Pv,ca,in and Pa,ca,in is as follows:
Pv;ca;in ¼ fca;in Psat Tca;in ;
(8)
Pa;ca;in ¼ Pca;in Pv;ca;in ¼ Pca;in fca;in Psat Tca;in ;
(9)
with fca,in denoting the relative humidity of air at the cathode inlet. Tca,in is the inlet flow temperature of cathode, and Psat(T ) is the saturation pressure, which depends on the temperature as [29], log10 ðPsat Þ ¼ 1:69 1010 T4 þ 3:85 107 T3 3:39 104 T2 þ 0:143T 20:29:
(12)
The stack current Ist is applied to share the load current Inet and the current of auxiliary equipment Iaux, which includes the air compressor, cooling fan, and other components of the PEM fuel cell system. Therefore, the stack current can be obtained as follows: Ist ¼ Inet þ Iaux :
(13)
Given measured load current Inet and current of auxiliary Iaux, several experiments were conducted to obtain the information between the current Inet and compressor voltage Vcm [29]. The current of auxiliary Iaux consumed by the auxiliaries, a function of the compressor input voltage of Vcm, is expressed as follows: 2 Iaux ¼ a0 þ a1 Vcm þ a2 Vcm :
(14)
The air flow rate Wca,in is measured using an on-board sensor. Its characteristic curve is defined with a third degree polynomial as follows: 2 3 þ b3 Vsensor : Wca;in ¼ b1 Vsensor þ b2 Vsensor
(15)
Combined with Eq. (1) to Eq. (15), the estimation equation of oxygen excess ratio can be obtained in the following form: lO2 ¼
Wca;in $f pca;in ; Tca;in ; fca;in ; n; F; yO2 ;ca;in ; MO2 ; MN2 ; Mv : Ist
(16)
In calculating the oxygen excess ratio, two assumptions are made: relative humidity, fca,in, is 1, and the temperature is considered constant (with room temperature Tca,in ¼ 298.15 K).
3.
Control scheme
(10)
According to del Real et al. [12], pressure Pca,in depends not only on the air flow rate Wca,in, but also on the stack current Ist, which has been modeled by the following linear regression [29]: Pca;in ¼ 1:003 þ 2:1 104 Wca;in 475:7 106 $Ist : (11)
The PEM fuel cell system has multiple input variables (Eq. (16)), which indicates complex nonlinear behavior. Correct plant dynamic model should be identified, both theoretically and empirically, to control air flow effectively. This paper developed a double action of feedforward control and TDC
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compensation to track the set-point trajectory accurately and avoid a lengthy modeling process. The manipulated variable is a compressor voltage Vcm, and the control objective is regulating the oxygen excess ratio lO2 . The overall control scheme is presented in Fig. 3.
3.1.
Feedforward load compensation
The fuel cell system is equipped with the compressor and inlet manifold to deliver the required oxygen, which shows slower dynamics than the electrochemical reactions inside of the cell to provide instant load change. The load change is represented by Ist. Thus, applying feedforward control is feasible to compensate for the disturbance effect and therefore improve the performance of the controller. If the analytical model of the process is available, then a dynamic feedforward controller can be built. However, as the information of the exact process modeling is limited, and the disturbance dynamic is fast, an efficient compensator can be used using a static feedforward controller correlating the steady state values of the manipulable variable and the fuel cell current [28]. The relationship between the current and the desired air flow to be provided by the compressor can be determined experimentally. Therefore, the oxygen excess ratio is in line with the target value.
3.2.
Feedback using TDC
Excellent fuel cell models including the ancillaries have been developed by many researchers [9e21]. These models describe the transient behaviors when the sudden load changes apply. However, as mentioned in the introduction, these models have multiple variables representing the physical and electrochemical responses. Therefore, these models are not practical to use in controlling the air excess ratio real-time. For real-time control, a simpler controller is favorable, such as simple transfer functions used from Arce et al. [21], Wang et al. [19], and Yang et al. [20], respectively. Therefore, the use of a general linear model is justified while approaching fuel cell control form with a more general approach, which can be easily implemented. The feedback controller proposed in this paper utilized the TDC to regulate the air flow rate. TDC is a type of control technique that enables state variables to follow the dynamics of a reference accurately by utilizing the information of the plant input and output within a few sampling periods. TDC has the ability to adapt the control input in terms of the reference dynamics. TDC can also adapt some of the plant parameters variations or disturbance imparts to the system.
Feedforward Control Set-point
+
-
TDC
u +
Inet, Tca,in, Pca,in, d(t)
+
PEM Fuel Cell Plant
TDC also does not require gain-phase adjustments or tracking of the control variable. The soundness of this control algorithm, including its stability, controllability, and observability, has already been proven [30e32]. The drawback of using TDC is that it requires real-time knowledge of all state variables and their derivatives. However, the fuel cell dynamic will be a linear system with the first order dynamics as described below. Moreover, its state values can be directly measured. Therefore, no observer is needed to estimate the state variables. The remaining difficulty (i.e., deciding the derivative of the state variable) can then be resolved using numerical differentiation. Although TDC inherently suffers from noise in calculating the time derivative, it can still be utilized in our research without using an additional noise reduction technique with fast sampling time.
3.2.1.
TDC algorithm
The following time invariant non-linear dynamical system is considered by assuming all state variables and their derivatives are observable [30]. _ xðtÞ ¼ f ðx; tÞ þ hðx; tÞ þ Bðx; tÞuðtÞ þ dðtÞ;
(17)
where x(t), u(t), f(x,t), h(x,t), and d(t) represent state vector, control vector, known dynamics, unknown dynamics, and disturbance, respectively. The purpose of the TDC is to design a controller to achieve the desired performance under external disturbances and system uncertainties. The required performance can be defined using the following time invariant reference model: x_ m ðtÞ ¼ Am xm ðtÞ þ Bm rðtÞ;
(18)
where xm(t) and r(t) are state vector and referenced input vector for the reference model. If error vector is defined as e(t) ¼ xm(t) x(t), then the desired error dynamics can be obtained as: _ ¼ Ae eðtÞ; eðtÞ
(19)
where Ae represents the error system matrix. If all characteristic values of Ae are located at the left half plane, then the errors will become zero as time passes. The error system is asymptotically stable. Therefore, the following equation can be achieved: Bðx; tÞuðtÞ ¼ f ðx; tÞ hðx; tÞ dðtÞ þ x_ m ðtÞ Ae eðtÞ:
(20)
Assuming that B(x,t) is not square, the left pseudo-inverse of B is used as Bþ ¼ (BTB)1BT. Hence, the approximated solution of u(t) can be obtained as u t ¼ Bþ x; t f f ðx; tÞ hðx; tÞ dðtÞ þ x_ m ðtÞ Ae eðtÞg:
(21)
If the unknown function h(x,t) þ d(t) is continuous, and the time delay L is sufficiently small, then the estimation of unknown function can be expressed as:
u ff Vcm
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O
Feedback Loop
Fig. 3 e Structure of the proposed control scheme.
b btzhðxðt LÞ; t LÞ þ dðt LÞ hðxðtÞ; tÞ þ d _ LÞ f ðxðt LÞ; t LÞ Bðxðt LÞ; t LÞuðt LÞ: ¼ xðt
(22)
In most cases, as the matrix B(x,t) is unknown or uncertain, the estimation of B(x,t) is always used. Then, combining Eq. (21) with Eq. (22), the TDC law can be described as
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n _ LÞ þ f ðxðt LÞ; t LÞ u t ¼ Bþ x; t f x; t xðt o b LÞuðt LÞ þ x_ m t Ae e t : þ Bðt
Table 1 e Coefficients of the fuel cell identification model. Mid-range power
(23)
First-order
The manipulated variable of the system from Eq. (23) can be expressed simply by making the time delay L have the same time period as the sampling time Ts or its integer multiple.
3.2.2.
Third-order
First-order
Third-order
b1 sþa1
n12 s2 þn11 sþn10 s3 þd12 s2 þd11 sþd10
b2 sþa2
n22 s2 þn21 sþn20 s3 þd22 s2 þd21 sþd20
a1 ¼ 10.14
d10 ¼ 5.1 104 d11 ¼ 8.178 103 d12 ¼ 38.64
a2 ¼ 12.69
d20 ¼ 7.444 104 d21 ¼ 8.743 103 d22 ¼ 41.20
b1 ¼ 22.31
n10 ¼ 1.101 105 n11 ¼ 2.858 103 n12 ¼ 0.4527
b2 ¼ 17.28
n20 ¼ 1.015 105 n21 ¼ 2.075 103 n22 ¼ 9.522
PEM fuel cell model for TDC
For easy implementation and to reduce the computational burden, the first order models of PEM fuel cell system are identified with the mid-range and high-load power operations. A certain level of current demand at mid-range power was set, and several step changes were applied to Vcm to obtain a dynamic model between these signals, namely, a compressor air flow rate and the air excess ratio, lO2 (Fig. 4). A linear model is obtained through auto-regression-meanaverage (ARMA) estimation. The third order linear models can provide the same fit for the data presented. Thus, a first order model is sufficient to account for the fuel cell dynamics (Fig. 4). The figure shows minimal difference in estimating the fuel cell dynamics between the first order and third order transfer function. The coefficients of the first order and the third order models are presented in Table 1, respectively. The first order model is selected in this paper to simplify TDC application. The open loop test for model identification at high-range power is also shown in Fig. 5. The state space models at different load levels are represented as follows:
High-range power
_ xðtÞ ¼ a1 x þ b1 u for mid-range power and
(24)
_ xðtÞ ¼ a2 x þ b2 u for high-range power:
(25)
3.2.3.
TDC design
The state variable for the reference model with the first order PEM fuel cell can be expressed as constant in the following: xm t ¼ lO2 ;ref :
(26)
Based on the tracking requirement, the derivative of the state variable can be simply obtained as x_ m ðtÞ ¼ 0:
(27)
rd
8
3 Order Identification
6
1 Order Identification Experimental Data
Oxygen Excess Ratio
st
4
2
0
20
40
60 Time (s)
80
100
120
(a) 8 Oxygen Excess Ratio
Oxygen Excess Ratio
8 6 4 2
18
19
20 Time (s)
(b)
21
22
6 4 2
48
49
50 Time (s)
51
52
(c)
Fig. 4 e Model identification result for mid-range power: (a) oxygen excess ratio fit; (b) expanded plot at 20 s; (c) expanded plot at 50 s.
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Oxygen Excess Ratio
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rd
6
3 Order Identification
5
1 Order Identification Experimental Data
st
4 3 2 1 0
0
20
40
60 Time (s)
80
100
120
6
6
5
5
Oxygen Excess Ratio
Oxygen Excess Ratio
(a)
4 3 2 1 0 18
19
20 Time (s)
21
4 3 2 1 0 48
22
49
(b)
50 Time (s)
51
52
(c)
Fig. 5 e Model identification result for high-range power: (a) oxygen excess ratio fit; (b) expanded plot about 20 s; (c) expanded plot about 50 s.
Then, the tracking error and error dynamics are expressed as e t ¼ lO2 ;ref lO2 t
(28)
the suitable time delay L of the PEM fuel cell system is selected as follows: L ¼ Ts ¼ 2:5 ms:
and e_ t ¼ Ae e t ¼ K lO2 ;ref lO2 t :
(29)
If K has a large negative value, then Eq. (28) is always convergent. In the real experiment, the data sampling time always impacts TDC controller design. After trial and error,
Control Monitoring
NI PCI System
Signal Conditioner Nexa Monitoring
(30)
Comparing Eqs. (24) and (25) with Eq. (17), f(x,t) ¼ a1, b þ ¼ 1=b1 are obtained. Replacing above B(x,t) ¼ b1, and B equations, substituting Eq. (29) into Eq. (23), and considering the different operation points, the input of the TDC can be written as follows: 1 ai lO2 t b l_ O2 ðt LÞ þ ai lO2 ðt LÞ u t ¼ bi þbi uðt LÞ K lO2 ;ref lO2 t ;
(31)
where ai ˛ {a1,a2}, b i˛ {b1,b2}, lO2 ðtÞ is the oxygen excess ratio at t instant, and b l_ O2 ðt LÞ is evaluated by the numerical approach, given as follows: b l_ O2 ðt LÞ ¼ Q lO2 ðt LÞ lO2 ðt 2LÞ ;
(32)
in which Q is a constant.
4. Nexa Power Module
Air Compressor
DC Electronic Load
Fig. 6 e A PEM fuel cell system test rig for real-time control.
Experimental results
The TDC, in conjunction with the static feedforward controller, was implemented in the 1.2-kW Nexa PEM fuel cell system. The test rig with the LabView controller with PCI-6229 control board is shown in Fig. 6. A 1.2-kW electrical loader
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Load (A)
30
20
10
0
0
10
20
30
40 Time (s)
50
60
70
80
0
10
20
30
40 Time (s)
50
60
70
80
0
10
20
30
40 Time (s)
50
60
70
80
70
80
70
80
70
80
Stack Current (A)
30
20
10
0
Stack Voltage (V)
40
35
Oxygen Excess Ratio
30
8 6 4
Oxygen Excess Ratio
0
0
10
20
30
40 Time (s)
50
60
8 6 4 FF Set-point
2 0
Oxygen Excess Ratio
TDC Set-point
2
0
10
20
30
40 Time (s)
50
60
8 6 4 PIC Set-point
2 0
0
10
20
30
40 Time (s)
50
60
Fig. 7 e Comparison of three control responses with fixed air excess ratio: (a) load variation; (b) stack current variation; (c) stack voltage variation; (d) air excess ratio variation using TDC; (e) air excess ratio variation using FF; (f) air excess ratio variation using PIC.
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from BP Solutions Co. is also used. The LabView is chosen as a real-time controller because it is easy to implement with various inputs and outputs, it provides easy graphic user interface modules, and it consists of rich software tools, such as derivative, integrator, and mathematical subprograms that can be applied in real time. The main objectives of the present control are as follows: (1) preventing starvation by maintaining a constant lO2 ¼ 4, and (2) obtaining the best performance by regulating the variable lO2 , where desired lO2 was obtained via experiments.
4.1.
Controller performance with fixed lO2
The first test consists of a fixed lO2 and a profile of several step changes in the load that covered the whole working range of the fuel cell system. The results are plotted in Fig. 7, where despite the change of current demand of the fuel cell, the control system is able to regulate the oxygen ratio within the required value. Despite the occurrence of sensor input noise from the current measurement, the lO2 indicates minimal noise in tracking the constant value of 4. Fig. 7(d)e(f) shows the air excess ratio control results using TDC, FF, and PIC, respectively. In addition, Fig. 8 represents the expansion version of the air excess ratio results during the transient period using three different control algorithms. The figures show that TDC has the smallest oxygen excess ratio variation statically or dynamically. The overall performance index using three control algorithms is presented in Table 2. As seen from the table, TDC exhibits the best steady-state and
Table 2 e Performance index comparison with the fixed air excess ratio. Performance index
TDC
FF
PID
MSE (steady state) MSE (transition)
0.2168 0.8971
0.4026 0.9217
0.4602 0.9810
476.5 14.0298 20.4544 15.0413 4.6381
1388.4 33.3573 25.2946 31.2000 10.4834
1794.2 57.4191 26.1428 47.9336 7.6049
SSE, SSE, SSE, SSE, SSE,
transient performances. Particularly at higher-range power operation, TDC exhibits better transient response, while TDC shows better steady-state response at mid-range power operation. The overshoot or undershoot and rising time between TDC and FF are not highly different. In other words, as the compressor dynamics and the air flow dynamics flowing into the cathode manifold are much slower than their speed in the electrochemical process, they cannot respond efficiently to the fast command of TDC or FF. Therefore, even though TDC has better control action than FF or PIC, the transient response of TDC cannot exhibit superior characteristics.
4.2.
8 Oxygen Excess Ratio
Oxygen Excess Ratio
Variable lO2 tracking for net power optimization
A variable setting for the reference of lO2 was proposed based on the load current to obtain the maximum efficiency of the fuel cell. The reference of variable lO2 was decided based on
6 5 4 3 2 1 9.5
10 Time (s)
4
20 Time (s)
Oxygen Excess Ratio
4 3 2
30 Time (s)
30.5
20.5
TDC FF PIC Set-point
8
5
1 29.5
6
2 19.5
10.5
6 Oxygen Excess Ratio
t ¼ [0, 80] s t ¼ [9.5, 10.5] s t ¼ [19.5, 20.5] s t ¼ [29.5, 30.5] s t ¼ [39.5, 40.5] s
6
4
2 39.5
40 Time (s)
40.5
Fig. 8 e Expanded plot of air excess ratio variation: (a) at 10 s; (b) at 20 s; (c) at 30 s; (d) at 40 s.
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1000
Table 3 e Performance index comparison with the optimal air excess ratio.
Inet=30A Inet=28A
900
Inet=26A
Net Power (W)
800
Performance index
TDC
Nexa
MSE (steady state) MSE (transition)
0.2131 0.3473
0.2646 0.4829
373.8 7.1825 6.6645 5.3258 4.2588
581.1 16.5207 16.7724 9.6417 11.7474
Inet=24A Inet=22A
700
Inet=20A
Maximum Net Power Inet=18A
600
SSE, SSE, SSE, SSE, SSE,
Inet=16A
500
Inet=14A Inet=12A
400
t t t t t
¼ ¼ ¼ ¼ ¼
[0, 80] s [9.5, 10.5] s [19.5, 20.5] s [29.5, 30.5] s [59.5, 60.5] s
Inet=10A
1
Oxygen Excess Ratio
300
2
3
4 5 6 Oxygen Excess Ratio
7
8
9
8 6
4
2 10
15
20 Load (A)
25
30
Fig. 9 e Decision curves for obtaining optimal air excess ratio: (a) net power change depending on the air excess ratio and external power; (b) curve fit for the optimal air excess ratio with load variation.
the experiments (Fig. 9). The figure presents the relation between net power and lO2 depending on the load change. lO2 should be changed depending on the load change to obtain the maximum fuel cell net power. Therefore, the abilities of the controller while tracking a variable set point for the oxygen excess ratio are an important issue for fuel cell control. This scenario is the same for the controller that the manufacturer provides for the fuel cell. Considering a variable reference, not only can higher efficiency be obtained but the dangers of starvation can also be prohibited by setting an appropriate value of lO2 whenever required load is large. Therefore, a sudden request for more power is possible given the unavoidable drop of oxygen in the stack. Using the same test load profile, the TDC and the original manufacturer’s controller are tested, and their results are presented in Fig. 10. This test aims to exhibit better dynamic
6
Oxygen Excess Ratio
Oxygen Excess Ratio
6
5
4
3
2 9.5
10 Time (s)
3
20 Time (s)
20.5
5
5
Oxygen Excess Ratio
Oxygen Excess Ratio
4
2 19.5
10.5
6
4 3 2 1 29.5
5
30 Time (s)
30.5
4
3 Nexa TDC Set-point 2 59.5
60 Time (s)
60.5
Fig. 10 e Comparison of optimal air excess ratio variation: (a) at 10 s; (b) at 20 s; (c) at 30 s; (d) at 60 s.
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Net Power (W)
1000 800 600 400 200
0
10
20
30
40 Time (s)
50
60
70
80
0
10
20
30
40 Time (s)
50
60
70
80
Net Power (W)
1000 800 600 400 200
Fig. 11 e Net power variation: (a) manufacturer’s controller; (b) TDC.
performance of the TDC given the varying lO2 reference conditions. Whenever an increase of the load is considered, the undershoot of lO2 might be a problem. This scenario leads to an immediate decrease of available oxygen, and the controller can only overcome this issue via the slow dynamics of the compressor and its supply manifold. Therefore, a sudden decrease of lO2 can lead to oxygen starvation. Thus, fast oxygen supply to the fuel cell is necessary to increase the optimal power and to prevent the starvation. The performance of the TDC can be assessed by comparing the control action in two different ways. On one hand, the recovery toward the desired reference under the load change is improved (Fig. 10). This improvement is due to the combined contributions of the feedforward controller and TDC. In the case of sudden load increase, TDC exhibits better performance by reducing the settling time from 400 ms to 50 ms (Fig. 10(c)). In a similar way, when the sudden decrease of the load occurs, the TDC settling time reduces from 300 ms to 100 ms (Fig. 10(d)).
These results show that the TDC provides oxygen faster to the fuel cell, providing higher efficiency conditions, which can be crucial in the case of continuous changing loads. Table 3 summarizes the steady-state and transient error comparisons between TDC and manufacturer’s controller and reveals that the TDC provides better control performance. An additional benefit of the proposed control scheme is that the control signal is significantly smoother, which leads to more even delivery of power (Fig. 11). The maximum power fluctuation from the original controller is 50 W, while the TDC reduces it to maximum 20 W. This significant reduction of the power fluctuation can also increase the stack lifetime. Finally, the net power efficiency comparison is made (Fig. 12). The TDC can provide almost 3.5% more power than the original manufacturer’s control scheme. Although only 1.2 kW of fuel cell is used in the paper, this increase of power efficiency cannot be ignored if longer fuel cell operation time or a high-power fuel cell is considered.
900
Filtered Net Power (W)
5.
Maximum Power Tracking Constant Set-point=4 Nexa Controller
800
700
600
500
400
300
0
10
20
30
40 Time (s)
50
60
70
Fig. 12 e Net power variation by changing the air excess ratio.
80
Conclusion
This study is based on the real-time control of PEM fuel cell technology, the Nexa power module. The study focuses on the accurate but simple control using TDC to prevent oxygen starvation and/or to obtain the maximum efficiency of the PEM fuel cell. The major contributions of this research are summarized as follows: first, the simple transfer functions between compressor voltage input and air excess ratio of the PEM system model are identified via experiments for midpower and high-power ranges. The obtained transfer functions represent the whole range of operation in accordance with the wide range of load variation. Second, TDC is designed and applied to prevent oxygen starvation and to achieve better performance. The proposed control scheme succeeds in reducing the settling time and power fluctuation better than the manufacturer’s controller. Optimal air excess ratio is
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determined via experiments to achieve the best efficiency. Maximum 3.5% of net power increase is achieved compared with the manufacturer control scheme or fixed air excess ratio scheme using the optimal air excess ratio. The technique utilized in this paper provides a solution that can be implemented easily, both in terms of modeling the process and reducing the computational burden for the realtime controller.
Acknowledgements This research was supported by Chonnam National University Research Fund in 2013.
[14]
[15]
[16]
[17]
[18]
[19]
references [20] [1] Danzer MA, Wittmann SJ, Hofer EP. Prevention of fuel cell starvation by model predictive control of pressure, excess ratio, and current. J Power Sources 2009;190:86e91. [2] Cordiner S, Lanzani SP, Mulone V. 3D effects of watersaturation distribution on polymeric electrolyte fuel cell (PEFC) performance. Int J Hydrogen Energy 2011;36:10366e75. [3] Wang ZH, Wang CY, Chen KS. Two-phase flow and transport in the air cathode of proton exchange membrane fuel cells. J Power Sources 2001;94:40e50. [4] Dutta S, Shimpalee S, Van Zee JW. Numerical prediction of mass-exchange between cathode and anode channels in a PEM fuel cell. Int J Heat Mass Transfer 2001;44:2029e42. [5] Meng H, Wang CY. Model of two-phase flow and flooding dynamics in polymer electrolyte fuel cells. J Electrochem Soc 2005;152:A1733e41. [6] Kim YB. Study on the effect of humidity and stoichiometry on the water saturation of PEM fuel cells. Int J Energy Reserch 2012;36:509e22. [7] Chen YS. A segmented model for studying water transport in a PEM fuel cell. PhD thesis, Univ Michigan 2009. [8] Ahn JW, Choe SY. Coolant controls of a PEM fuel cell system. J Power Sources 2008;179:252e64. [9] Pukrushpan JT, Huei P, Stefanopoulou A. Control-oriented modeling and analysis for automotive fuel cell systems. Tran ASME Dyn Syst. Meas Control 2004;126:14e25. [10] Vahidi A, Stefanopoulou A, Peng H. Model predictive control for starvation prevention in a hybrid fuel cell system. Proc ACC 2004;1:834e9. [11] Bao C, Ouyang M, Baolian Y. Modeling and control of air stream and hydrogen flow with recirculation in a PEM fuel cell systemdII. Linear and adaptive nonlinear control. Int J Hydrogen Energy 2006;31:1897e913. [12] del Real AJ, Arce A, Bordons C. Development and experimental validation of a PEM fuel cell dynamic model. J Power Sources 2007;173:310e24. [13] McKay DA, Siegel JB, Ott W, Stefanopoulou A. Parameterization and prediction of temporal fuel cell voltage
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behavior during flooding and drying conditions. J Power Sources 2008;178:207e22. Karnik AY, Stefanopoulou A, Sun J. Water equilibria and management using a two-volume model of a polymer electrolyte fuel cell. J Power Sources 2007;164:590e605. Kim YB. Improving dynamic performance of protonexchange membrane fuel cell system using time delay control. J Power Sources 2010;195:6329e41. Kim YB, Kang SJ. Time delay control for fuel cells with bidirectional DC/DC converter and battery. Int J Hydrogen Energy 2010;35:8792e803. Chiu LY, Diong B, Gemmen RS. An improved small-signal model of the dynamic behavior of PEM fuel cells. IEEE Trans Ind Appl 2004;40:970e7. Na WK, Gou B. Feedback-linearization-based nonlinear control for PEM fuel cells. IEEE Energy Convers 2008;23:179e90. Wang FC, Chen HT, Yang YP, Yen JY. Multivariable robust control of a proton exchange membrane fuel cell system. J Power Sources 2008;177:393e403. Yang YP, Liu ZW, Wang FC. An application of indirect model reference adaptive control to a low-power proton exchange membrane fuel cell. J Power Sources 2008;179:618e30. Arce A, del Real AJ, Bordons C, Ramirez D. Real-Time implementation of a constrained MPC for efficient airflow control in a PEM fuel cell. IEEE Ind Elec 2010;57:1892e905. Mammar K, Chaker A. Fuzzy logic control of fuel cell system for residential power generation. J Electrical Engineering 2009;60:328e34. Haiskos J, Sarimevis H, Zervas PL, Markatos NC. Operational optimization and real-time control of fuel-cell systems. J Power Sources 2009;193:258e68. Schmittinger W, Vahidi A. A review of the main parameters influencing long-term performance and durability of PEM fuel cells. J Power Sources 2008;180:1e14. Yousfi-Steiner N, Mocoteguy P, Candusso D, Hissel D. A review on polymer electrolyte membrane fuel cell catalyst degradation and starvation issues: causes, consequences and diagnostic for mitigation. J Power Sources 2009;194:130e45. Qu S, Li X, Hou M, Shao Z, Yi B. The effect of air stoichiometry change on the dynamic behavior of a proton exchange membrane fuel cell. J Power Sources 2008;185:302e10. Liu Z, Yang L, Mao Z, Zhuge W, Zhang Y, Wang L. Behavior of PEMFC in starvation. J Power Sources 2006;157:166e76. Pukrushpan JT, Stefanopoulou A, Peng H. Control of fuel cell breathing. IEEE Control Syst Mag 2004;24:14e25. Gruber JK, Doll M, Bordons C. Design and experimental validation of a constrained MPC for the air feed of a fuel cell. Control Eng Pract 2009;17:874e85. Youcef-Toumi K, Fullbrigge K. Application of decentralized time-delay controller to robot manipulators. Proc IEEE Robotics Automation 1989:1786e91. Youcef-Toumi K, Reddy S. Analysis of linear time invariant systems with time delay. ASME J Dyn Syst Meas Control 1992;57:544e55. Jung JH, Chang PH, Kang SH. Stability analysis of discrete time delay control for nonlinear systems. Proc ACC 2007:5995e6002.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Design and experimental implementation of time delay control for air supply in a polymer electrolyte membrane fuel cell system Ya-Xiong Wang a, Dong-Ji Xuan b, Young-Bae Kim a,* a b
Department of Mechanical Engineering, Chonnam National University, Gwangju, Republic of Korea College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou, China
article info
abstract
Article history:
This paper studies the air flow control for preventing the starvation and/or obtaining the
Received 4 December 2012
maximum net power of a Polymer Electrolyte Membrane (PEM) fuel cell system using time
Received in revised form
delay control (TDC). Feedforward and feedback controls are utilized simultaneously to
7 May 2013
prevent air shortage during the transient response of the fuel cell operation. The TDC al-
Accepted 10 June 2013
gorithm design is created with a low-order dynamic model, and its superior performances
Available online 13 July 2013
are proven using a real-time control experiment. The optimal air excess ratio is calculated experimentally given the variation of the external load, and the net power increase is discussed by comparison with the results obtained from fixed air excess ratio. The Ballard
Keywords: Modeling
of
polymer
electrolyte
membrane fuel cell system
1.2 kW PEM fuel cell system is used for the experiments as a test rig, and the LabView system is used for the real-time air flow control. The superiority of the TDC performance is
Time delay control
proven by comparison with other control algorithms such as the proportionaleintegral
Air flow control
control (PIC), feedforward control, and the original manufacturer’s control. The proposed
Power optimization
control algorithm can improve PEM fuel cell system performance by preventing air shortage and/or by obtaining higher performance. Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Using the polymer electrolyte membrane (PEM) fuel cell in the fuel cell-based hybrid vehicle has many advantages. The PEM fuel cell-based hybrid vehicle can be started quickly, produces almost zero emission and low noise, and operates under relatively lower temperatures. It has higher efficiency than a vehicle equipped with an internal combustion engine. However, ancillaries such as a humidifier, cooler, and compressor are needed to obtain the best operating performance and prevent possible operation malfunction in using PEM as a hybrid vehicle. A regular PEM fuel cell system is presented in Fig. 1. The PEM fuel cell should provide efficient power
delivery to meet sudden high-power requirements; as vehicle operation involves quick start, stop, acceleration, and deceleration. Fuel cell power comes from fuel (hydrogen) oxidation at the anode and oxidant (oxygen) reduction at the cathode. If adequate oxygen and hydrogen cannot be supplied within a short interval, the fuel cell performance can decline, resulting in failure to provide quick acceleration response to the vehicle. Sometimes, air starvation will occur if the air inflow is too low, which eventually shortens fuel cell life expectancy [1]. Thus, many researchers have studied air flow control to prevent starvation. In providing the air flow control algorithm for the PEM fuel cell, developing an accurate fuel cell model is compulsory. Many studies constructing the PEM fuel cell
* Corresponding author. Tel.: þ82 62 5301677. E-mail address: [email protected] (Y.-B. Kim). 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2013.06.040
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Fig. 1 e The schematic diagram of a PEM fuel cell system.
model have been conducted using various approaches. Numerous accurate PEM fuel cell models, including the species, pressure, overpotential, temperature, and water distributions inside the fuel cell, have been developed using tools with computational fluid dynamics (CFD) [2e6]. Although these CFD models can provide exact fuel cell characteristics at the specific fuel cell location, the use of CFD modeling for control purposes is almost impossible because CFD models have degrees of freedom in tens of thousands, that is, state variables. Therefore, control engineers have separately developed control-oriented models with lower degrees of freedom. Most of the control-oriented models are classified as zero-dimensional or one-dimensional. Very few twodimensional models are developed [7,8]. One- or twodimensional models are normally used to analyze the water distribution inside the gas diffusion layer (GDL). If the effect of the water or its distribution, which is normally used for humidification control or water management, is not considered, a zero-dimensional model is sufficient for controlling air flow. Pukrushpan et al. proposed a zero-dimensional PEM fuel cell model including stacks, cooler, humidifier, and compressor [9]. Their control-oriented model includes mass flow rate of hydrogen and oxygen, pressure, and compressor rpm as a state variable. Similar models were developed by Vahidi et al. [10], Bao et al. [11], del Real et al. [12], McKay et al. [13], Karnik et al. [14], and Kim [15,16]. Although these models present fuel cell physical characteristics effectively (i.e., the relationship between cell voltage and cell current), they include many state variables for use in real-time control, and they require formidable experiments to obtain exact model parameters. Therefore, most models mentioned above are only used in simulation to verify the efficacy of their control algorithms in preventing air starvation. In a similar manner, Chiu et al. [17] and Na et al. [18] developed the state-space
linearized fuel cell model using pressure and species mass fractions as state variables without identifying the model parameters in the electrical engineering field. A transfer function between air flow inputs and PEM fuel cell outputs has been used for real-time control. For example, Wang et al. [19] conducted experiments to obtain the transfer function between air flow rates as an input and cell voltage as an output using exhaustive experiments to control cell voltage using robust control algorithm such as HN. A similar transfer function model was created by Yang et al. [20] using recursive least square algorithms. Arce et al. [21] also extracted the transfer function model between the compressor input and air excess ratio using experiments for real-time control. In regulating the PEM fuel cell output voltage or air excess ratio, conventional proportionaleintegralederivative (PID) control [8], LQG control [9,11], fuzzy control [22], neural network control [23], time delay control [15,16] or model predictive control (MPC) [10] have been applied without real plant validation. In real plant validation, Wang et al. [19] and Yang et al. [20] used HN and adaptive control, respectively, to regulate the fuel cell voltage output. However, their model utilized multivariable transfer matrices rendering the control system complex. Arce et al. [21] used MPC to regulate the air excess ratio. Although their experimental result was good to regulate the air excess ratio, their MPC algorithm was linear and it was too complex to apply in the real system. In the present paper, double control actions of feedforward control and TDC compensation are used to regulate the air excess ratio to prevent starvation and to obtain maximum net power of the stack. TDC can compensate for the error dynamics that might occur due to imperfect feedforward control action. The transfer function between air flow input and air excess ratio output is determined via experiments to design the TDC algorithm. The better dynamic performance of the
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 8 ( 2 0 1 3 ) 1 3 3 8 1 e1 3 3 9 2
TDC to prevent starvation and to achieve maximum net power is compared with the PIC and original manufacturer’s controller of the 1.2 kW Ballard PEM fuel cell system. The main contributions of the present paper are developing a simple but effective PEM fuel cell system model to design TDC and utilizing this model for real-time control. Superior TDC control characteristics for regulating the air excess ratio and for obtaining the maximum net power will be discussed. This is the first paper to apply TDC in regulating air flow to the PEM fuel cell system in real-time.
2.
PEMFC model
Ballard PEMFC with 1.2 kW has been used for air excess control to prevent starvation and/or to achieve the net power maximization in our experiment. The system is composed of 46 cells, each with a 110 cm2 membrane electrode assembly (MEA). The system is widely used by many researchers worldwide and is equipped with a self-controlled algorithm to prevent abnormal operation. It is also equipped with a selfhumidifier and is air-cooled by a small fan. Hydrogen is supplied from the pressurized tank through a regulating valve, which controls the anode pressure to render small pressure difference to the cathode side because large pressure difference between cathode and anode compartments can induce the membrane stress and shorten the fuel cell life. Oxygen supply is achieved from a compressor, whose air flow can be regulated through compressor input voltage. The fuel cell system is equipped with a manufacturer-made on-board controller to measure the fuel cell variables and to control the air flow depending on the required load. If insufficient hydrogen and/or oxygen is delivered to produce the required external power, the on-board controller automatically shuts down the system to prevent further fuel cell system damages. In the present paper, the manufacturer’s on-board controller is overridden by a PCI-6229 controller from National Instrument only to control compressor air flow. Other controls such as anode purging, humidifier, and fan control are performed by the manufacturer control algorithms. The present real-time controller receives the data from fuel cell sensors and computes the air flow using a 400 Hz sampling frequency. The real-time controller receives data from three sensors: stack voltage (Vst), stack current (Ist), and air flow supplied by a compressor (Win). The real-time controller output is the compressor voltage (Vcm), which controls the air flow rate depending on the required external power. As the air flow rate (Win) is a function of Vcm, the relation between these two variables can be obtained via experiment (Fig. 2) and can be represented as Win ¼ 1:862Vs3 þ 1:48Vs2 þ 2:65Vs ;
(1)
where Vs is the sensor output voltage measured at the air inlet stream line.
2.1.
Air supply control
One of the primary objectives of this paper is to prevent air starvation when the supplied air is less than the consumed
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air. Starvation will occur when the fuel cell system requires sudden power increase, and starvation usually occurs during the transients. Starvation is one of the main causes of aging and degeneration of fuel cells [24]. When starvation occurs due to lack of oxygen and/or hydrogen, the performance of the fuel cell decreases given cell voltage drops. A rapid cell voltage drop can cause a burn through the surface of the membrane. Starvation is a very complicated phenomenon with causes and consequences that have been reported in the literature [25,26]. Low reactant flow rates may induce uneven flow sharing between the cells in the stack, leading to locally or completely starved cells [27]. Oxygen or hydrogen starvation can result in the generation of hydrogen in the cathode or oxygen in the anode. The presence of oxygen in the anode or hydrogen in the cathode leads to the reversal of the cell potential, which is a negative potential differential between the anode and the cathode. Cell potential reversal accelerates the corrosion of carbon components, such as backing layers with ensuing electro-catalyst corrosion, and eventually leads to damaged components. The best way to prevent oxidant starvation and to enable stable operation of the fuel cell is to supply the excess oxygen rapidly by increasing the air flow rate to the cathode. This increase is limited by the inertia of the compressors, and especially at fast load change, the risk of starvation is high [1]. Therefore, excessive air flow is necessary to prevent the sudden shortage of the oxygen during the fast load change. The excessive air ratio, lO2 , is defined as the ratio between the oxygen supplied to the cathode ðWO2 ;ca;in Þ and the oxygen made to react in the fuel cell stack ðWO2 ;reacted Þ as follows [21,28,29]: lO2 ¼
WO2 ;ca;in : WO2 ;reacted
(2)
The desired value of this value depends on the fuel cell itself and on the operating objective. For example, Pukrushpan et al. [28] proposed to regulate lO2 ¼ 2 for a 75 kW stack to guarantee safety and to provide high efficiency. Arce et al. [21] proposed lO2 ¼ 4 to prevent starvation and achieve relatively higher fuel cell net power. If the air excess ratio increases, more compressor power is required to supply higher oxygen flow rate, and the gross fuel cell power also increases due to the increase in oxygen and hydrogen partial pressures. If the air excess ratio decreases, the compressor power and gross fuel cell power both decrease. Moreover, if the air excess ratio is too small, then starvation may occur during the sudden change of the load. Therefore, the regulation of lO2 is a critical issue in preventing starvation as well as in obtaining the maximum fuel cell net power. In the present paper, we used two air excess ratios. The first one uses a fixed value, and the second is a varying lO2 to obtain the maximal net fuel cell power. The optimal lO2 is obtained from the experiment.
2.2.
Controlled variable
The oxygen excess ratio, lO2 , cannot be measured directly. It can be obtained from other sensor measurements. Based on the definition of lO2 , values of WO2 ;ca;in and WO2 ;reacted are necessary.
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120
Air Flow Rate (slpm)
100 80 60 40 Experimental Data Identification
20 0 1.6
1.8
2
2.2
2.4 2.6 2.8 Sensor Voltage (V)
3
3.2
3.4
3.6
Fig. 2 e Curve fit between the air flow rate and the compressor voltage.
The oxygen mass flow WO2 ;ca;in is available in the dry air Wa,ca,in at the cathode inlet as follows [28,29]:
The oxygen flow consumption in the reaction WO2 ;reacted is as follows:
WO2 ¼ xO2 Wa;ca;in
n$Ist : WO2 ;reacted ¼ MO2 $ 4F
(3)
The oxygen mass fraction xO2 ;ca;in can be calculated by xO2 ;ca;in
yO2 ;ca;in MO2 ¼ : yO2 ;ca;in MO2 þ 1 yO2 ;ca;in MN2
(4)
The oxygen mole fraction yO2 ;ca;in is assumed for the atmospheric air condition. The mass flow rate of dry air at the cathode inlet is Wa;ca;in ¼
1 Wca;in ; 1 þ uca;in
(5)
where uca,in is the humidity ratio obtained by uca;in ¼
Mv Pv;ca;in $ ; Ma;ca;in Pa;ca;in
(6)
where Mv is the molar mass of vapor, and Ma,ca,in is molar mass of air at cathode, which is calculated as follows [28,29]: Ma;ca;in ¼ yO2 ;ca;in MO2
þ 1 yO2 ;ca;in MN2 :
(7)
Pv,ca,in and Pa,ca,in are the vapor and dry air partial pressures, respectively. The relation between Pv,ca,in and Pa,ca,in is as follows:
Pv;ca;in ¼ fca;in Psat Tca;in ;
(8)
Pa;ca;in ¼ Pca;in Pv;ca;in ¼ Pca;in fca;in Psat Tca;in ;
(9)
with fca,in denoting the relative humidity of air at the cathode inlet. Tca,in is the inlet flow temperature of cathode, and Psat(T ) is the saturation pressure, which depends on the temperature as [29], log10 ðPsat Þ ¼ 1:69 1010 T4 þ 3:85 107 T3 3:39 104 T2 þ 0:143T 20:29:
(12)
The stack current Ist is applied to share the load current Inet and the current of auxiliary equipment Iaux, which includes the air compressor, cooling fan, and other components of the PEM fuel cell system. Therefore, the stack current can be obtained as follows: Ist ¼ Inet þ Iaux :
(13)
Given measured load current Inet and current of auxiliary Iaux, several experiments were conducted to obtain the information between the current Inet and compressor voltage Vcm [29]. The current of auxiliary Iaux consumed by the auxiliaries, a function of the compressor input voltage of Vcm, is expressed as follows: 2 Iaux ¼ a0 þ a1 Vcm þ a2 Vcm :
(14)
The air flow rate Wca,in is measured using an on-board sensor. Its characteristic curve is defined with a third degree polynomial as follows: 2 3 þ b3 Vsensor : Wca;in ¼ b1 Vsensor þ b2 Vsensor
(15)
Combined with Eq. (1) to Eq. (15), the estimation equation of oxygen excess ratio can be obtained in the following form: lO2 ¼
Wca;in $f pca;in ; Tca;in ; fca;in ; n; F; yO2 ;ca;in ; MO2 ; MN2 ; Mv : Ist
(16)
In calculating the oxygen excess ratio, two assumptions are made: relative humidity, fca,in, is 1, and the temperature is considered constant (with room temperature Tca,in ¼ 298.15 K).
3.
Control scheme
(10)
According to del Real et al. [12], pressure Pca,in depends not only on the air flow rate Wca,in, but also on the stack current Ist, which has been modeled by the following linear regression [29]: Pca;in ¼ 1:003 þ 2:1 104 Wca;in 475:7 106 $Ist : (11)
The PEM fuel cell system has multiple input variables (Eq. (16)), which indicates complex nonlinear behavior. Correct plant dynamic model should be identified, both theoretically and empirically, to control air flow effectively. This paper developed a double action of feedforward control and TDC
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compensation to track the set-point trajectory accurately and avoid a lengthy modeling process. The manipulated variable is a compressor voltage Vcm, and the control objective is regulating the oxygen excess ratio lO2 . The overall control scheme is presented in Fig. 3.
3.1.
Feedforward load compensation
The fuel cell system is equipped with the compressor and inlet manifold to deliver the required oxygen, which shows slower dynamics than the electrochemical reactions inside of the cell to provide instant load change. The load change is represented by Ist. Thus, applying feedforward control is feasible to compensate for the disturbance effect and therefore improve the performance of the controller. If the analytical model of the process is available, then a dynamic feedforward controller can be built. However, as the information of the exact process modeling is limited, and the disturbance dynamic is fast, an efficient compensator can be used using a static feedforward controller correlating the steady state values of the manipulable variable and the fuel cell current [28]. The relationship between the current and the desired air flow to be provided by the compressor can be determined experimentally. Therefore, the oxygen excess ratio is in line with the target value.
3.2.
Feedback using TDC
Excellent fuel cell models including the ancillaries have been developed by many researchers [9e21]. These models describe the transient behaviors when the sudden load changes apply. However, as mentioned in the introduction, these models have multiple variables representing the physical and electrochemical responses. Therefore, these models are not practical to use in controlling the air excess ratio real-time. For real-time control, a simpler controller is favorable, such as simple transfer functions used from Arce et al. [21], Wang et al. [19], and Yang et al. [20], respectively. Therefore, the use of a general linear model is justified while approaching fuel cell control form with a more general approach, which can be easily implemented. The feedback controller proposed in this paper utilized the TDC to regulate the air flow rate. TDC is a type of control technique that enables state variables to follow the dynamics of a reference accurately by utilizing the information of the plant input and output within a few sampling periods. TDC has the ability to adapt the control input in terms of the reference dynamics. TDC can also adapt some of the plant parameters variations or disturbance imparts to the system.
Feedforward Control Set-point
+
-
TDC
u +
Inet, Tca,in, Pca,in, d(t)
+
PEM Fuel Cell Plant
TDC also does not require gain-phase adjustments or tracking of the control variable. The soundness of this control algorithm, including its stability, controllability, and observability, has already been proven [30e32]. The drawback of using TDC is that it requires real-time knowledge of all state variables and their derivatives. However, the fuel cell dynamic will be a linear system with the first order dynamics as described below. Moreover, its state values can be directly measured. Therefore, no observer is needed to estimate the state variables. The remaining difficulty (i.e., deciding the derivative of the state variable) can then be resolved using numerical differentiation. Although TDC inherently suffers from noise in calculating the time derivative, it can still be utilized in our research without using an additional noise reduction technique with fast sampling time.
3.2.1.
TDC algorithm
The following time invariant non-linear dynamical system is considered by assuming all state variables and their derivatives are observable [30]. _ xðtÞ ¼ f ðx; tÞ þ hðx; tÞ þ Bðx; tÞuðtÞ þ dðtÞ;
(17)
where x(t), u(t), f(x,t), h(x,t), and d(t) represent state vector, control vector, known dynamics, unknown dynamics, and disturbance, respectively. The purpose of the TDC is to design a controller to achieve the desired performance under external disturbances and system uncertainties. The required performance can be defined using the following time invariant reference model: x_ m ðtÞ ¼ Am xm ðtÞ þ Bm rðtÞ;
(18)
where xm(t) and r(t) are state vector and referenced input vector for the reference model. If error vector is defined as e(t) ¼ xm(t) x(t), then the desired error dynamics can be obtained as: _ ¼ Ae eðtÞ; eðtÞ
(19)
where Ae represents the error system matrix. If all characteristic values of Ae are located at the left half plane, then the errors will become zero as time passes. The error system is asymptotically stable. Therefore, the following equation can be achieved: Bðx; tÞuðtÞ ¼ f ðx; tÞ hðx; tÞ dðtÞ þ x_ m ðtÞ Ae eðtÞ:
(20)
Assuming that B(x,t) is not square, the left pseudo-inverse of B is used as Bþ ¼ (BTB)1BT. Hence, the approximated solution of u(t) can be obtained as u t ¼ Bþ x; t f f ðx; tÞ hðx; tÞ dðtÞ þ x_ m ðtÞ Ae eðtÞg:
(21)
If the unknown function h(x,t) þ d(t) is continuous, and the time delay L is sufficiently small, then the estimation of unknown function can be expressed as:
u ff Vcm
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O
Feedback Loop
Fig. 3 e Structure of the proposed control scheme.
b btzhðxðt LÞ; t LÞ þ dðt LÞ hðxðtÞ; tÞ þ d _ LÞ f ðxðt LÞ; t LÞ Bðxðt LÞ; t LÞuðt LÞ: ¼ xðt
(22)
In most cases, as the matrix B(x,t) is unknown or uncertain, the estimation of B(x,t) is always used. Then, combining Eq. (21) with Eq. (22), the TDC law can be described as
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n _ LÞ þ f ðxðt LÞ; t LÞ u t ¼ Bþ x; t f x; t xðt o b LÞuðt LÞ þ x_ m t Ae e t : þ Bðt
Table 1 e Coefficients of the fuel cell identification model. Mid-range power
(23)
First-order
The manipulated variable of the system from Eq. (23) can be expressed simply by making the time delay L have the same time period as the sampling time Ts or its integer multiple.
3.2.2.
Third-order
First-order
Third-order
b1 sþa1
n12 s2 þn11 sþn10 s3 þd12 s2 þd11 sþd10
b2 sþa2
n22 s2 þn21 sþn20 s3 þd22 s2 þd21 sþd20
a1 ¼ 10.14
d10 ¼ 5.1 104 d11 ¼ 8.178 103 d12 ¼ 38.64
a2 ¼ 12.69
d20 ¼ 7.444 104 d21 ¼ 8.743 103 d22 ¼ 41.20
b1 ¼ 22.31
n10 ¼ 1.101 105 n11 ¼ 2.858 103 n12 ¼ 0.4527
b2 ¼ 17.28
n20 ¼ 1.015 105 n21 ¼ 2.075 103 n22 ¼ 9.522
PEM fuel cell model for TDC
For easy implementation and to reduce the computational burden, the first order models of PEM fuel cell system are identified with the mid-range and high-load power operations. A certain level of current demand at mid-range power was set, and several step changes were applied to Vcm to obtain a dynamic model between these signals, namely, a compressor air flow rate and the air excess ratio, lO2 (Fig. 4). A linear model is obtained through auto-regression-meanaverage (ARMA) estimation. The third order linear models can provide the same fit for the data presented. Thus, a first order model is sufficient to account for the fuel cell dynamics (Fig. 4). The figure shows minimal difference in estimating the fuel cell dynamics between the first order and third order transfer function. The coefficients of the first order and the third order models are presented in Table 1, respectively. The first order model is selected in this paper to simplify TDC application. The open loop test for model identification at high-range power is also shown in Fig. 5. The state space models at different load levels are represented as follows:
High-range power
_ xðtÞ ¼ a1 x þ b1 u for mid-range power and
(24)
_ xðtÞ ¼ a2 x þ b2 u for high-range power:
(25)
3.2.3.
TDC design
The state variable for the reference model with the first order PEM fuel cell can be expressed as constant in the following: xm t ¼ lO2 ;ref :
(26)
Based on the tracking requirement, the derivative of the state variable can be simply obtained as x_ m ðtÞ ¼ 0:
(27)
rd
8
3 Order Identification
6
1 Order Identification Experimental Data
Oxygen Excess Ratio
st
4
2
0
20
40
60 Time (s)
80
100
120
(a) 8 Oxygen Excess Ratio
Oxygen Excess Ratio
8 6 4 2
18
19
20 Time (s)
(b)
21
22
6 4 2
48
49
50 Time (s)
51
52
(c)
Fig. 4 e Model identification result for mid-range power: (a) oxygen excess ratio fit; (b) expanded plot at 20 s; (c) expanded plot at 50 s.
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Oxygen Excess Ratio
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rd
6
3 Order Identification
5
1 Order Identification Experimental Data
st
4 3 2 1 0
0
20
40
60 Time (s)
80
100
120
6
6
5
5
Oxygen Excess Ratio
Oxygen Excess Ratio
(a)
4 3 2 1 0 18
19
20 Time (s)
21
4 3 2 1 0 48
22
49
(b)
50 Time (s)
51
52
(c)
Fig. 5 e Model identification result for high-range power: (a) oxygen excess ratio fit; (b) expanded plot about 20 s; (c) expanded plot about 50 s.
Then, the tracking error and error dynamics are expressed as e t ¼ lO2 ;ref lO2 t
(28)
the suitable time delay L of the PEM fuel cell system is selected as follows: L ¼ Ts ¼ 2:5 ms:
and e_ t ¼ Ae e t ¼ K lO2 ;ref lO2 t :
(29)
If K has a large negative value, then Eq. (28) is always convergent. In the real experiment, the data sampling time always impacts TDC controller design. After trial and error,
Control Monitoring
NI PCI System
Signal Conditioner Nexa Monitoring
(30)
Comparing Eqs. (24) and (25) with Eq. (17), f(x,t) ¼ a1, b þ ¼ 1=b1 are obtained. Replacing above B(x,t) ¼ b1, and B equations, substituting Eq. (29) into Eq. (23), and considering the different operation points, the input of the TDC can be written as follows: 1 ai lO2 t b l_ O2 ðt LÞ þ ai lO2 ðt LÞ u t ¼ bi þbi uðt LÞ K lO2 ;ref lO2 t ;
(31)
where ai ˛ {a1,a2}, b i˛ {b1,b2}, lO2 ðtÞ is the oxygen excess ratio at t instant, and b l_ O2 ðt LÞ is evaluated by the numerical approach, given as follows: b l_ O2 ðt LÞ ¼ Q lO2 ðt LÞ lO2 ðt 2LÞ ;
(32)
in which Q is a constant.
4. Nexa Power Module
Air Compressor
DC Electronic Load
Fig. 6 e A PEM fuel cell system test rig for real-time control.
Experimental results
The TDC, in conjunction with the static feedforward controller, was implemented in the 1.2-kW Nexa PEM fuel cell system. The test rig with the LabView controller with PCI-6229 control board is shown in Fig. 6. A 1.2-kW electrical loader
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Load (A)
30
20
10
0
0
10
20
30
40 Time (s)
50
60
70
80
0
10
20
30
40 Time (s)
50
60
70
80
0
10
20
30
40 Time (s)
50
60
70
80
70
80
70
80
70
80
Stack Current (A)
30
20
10
0
Stack Voltage (V)
40
35
Oxygen Excess Ratio
30
8 6 4
Oxygen Excess Ratio
0
0
10
20
30
40 Time (s)
50
60
8 6 4 FF Set-point
2 0
Oxygen Excess Ratio
TDC Set-point
2
0
10
20
30
40 Time (s)
50
60
8 6 4 PIC Set-point
2 0
0
10
20
30
40 Time (s)
50
60
Fig. 7 e Comparison of three control responses with fixed air excess ratio: (a) load variation; (b) stack current variation; (c) stack voltage variation; (d) air excess ratio variation using TDC; (e) air excess ratio variation using FF; (f) air excess ratio variation using PIC.
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from BP Solutions Co. is also used. The LabView is chosen as a real-time controller because it is easy to implement with various inputs and outputs, it provides easy graphic user interface modules, and it consists of rich software tools, such as derivative, integrator, and mathematical subprograms that can be applied in real time. The main objectives of the present control are as follows: (1) preventing starvation by maintaining a constant lO2 ¼ 4, and (2) obtaining the best performance by regulating the variable lO2 , where desired lO2 was obtained via experiments.
4.1.
Controller performance with fixed lO2
The first test consists of a fixed lO2 and a profile of several step changes in the load that covered the whole working range of the fuel cell system. The results are plotted in Fig. 7, where despite the change of current demand of the fuel cell, the control system is able to regulate the oxygen ratio within the required value. Despite the occurrence of sensor input noise from the current measurement, the lO2 indicates minimal noise in tracking the constant value of 4. Fig. 7(d)e(f) shows the air excess ratio control results using TDC, FF, and PIC, respectively. In addition, Fig. 8 represents the expansion version of the air excess ratio results during the transient period using three different control algorithms. The figures show that TDC has the smallest oxygen excess ratio variation statically or dynamically. The overall performance index using three control algorithms is presented in Table 2. As seen from the table, TDC exhibits the best steady-state and
Table 2 e Performance index comparison with the fixed air excess ratio. Performance index
TDC
FF
PID
MSE (steady state) MSE (transition)
0.2168 0.8971
0.4026 0.9217
0.4602 0.9810
476.5 14.0298 20.4544 15.0413 4.6381
1388.4 33.3573 25.2946 31.2000 10.4834
1794.2 57.4191 26.1428 47.9336 7.6049
SSE, SSE, SSE, SSE, SSE,
transient performances. Particularly at higher-range power operation, TDC exhibits better transient response, while TDC shows better steady-state response at mid-range power operation. The overshoot or undershoot and rising time between TDC and FF are not highly different. In other words, as the compressor dynamics and the air flow dynamics flowing into the cathode manifold are much slower than their speed in the electrochemical process, they cannot respond efficiently to the fast command of TDC or FF. Therefore, even though TDC has better control action than FF or PIC, the transient response of TDC cannot exhibit superior characteristics.
4.2.
8 Oxygen Excess Ratio
Oxygen Excess Ratio
Variable lO2 tracking for net power optimization
A variable setting for the reference of lO2 was proposed based on the load current to obtain the maximum efficiency of the fuel cell. The reference of variable lO2 was decided based on
6 5 4 3 2 1 9.5
10 Time (s)
4
20 Time (s)
Oxygen Excess Ratio
4 3 2
30 Time (s)
30.5
20.5
TDC FF PIC Set-point
8
5
1 29.5
6
2 19.5
10.5
6 Oxygen Excess Ratio
t ¼ [0, 80] s t ¼ [9.5, 10.5] s t ¼ [19.5, 20.5] s t ¼ [29.5, 30.5] s t ¼ [39.5, 40.5] s
6
4
2 39.5
40 Time (s)
40.5
Fig. 8 e Expanded plot of air excess ratio variation: (a) at 10 s; (b) at 20 s; (c) at 30 s; (d) at 40 s.
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1000
Table 3 e Performance index comparison with the optimal air excess ratio.
Inet=30A Inet=28A
900
Inet=26A
Net Power (W)
800
Performance index
TDC
Nexa
MSE (steady state) MSE (transition)
0.2131 0.3473
0.2646 0.4829
373.8 7.1825 6.6645 5.3258 4.2588
581.1 16.5207 16.7724 9.6417 11.7474
Inet=24A Inet=22A
700
Inet=20A
Maximum Net Power Inet=18A
600
SSE, SSE, SSE, SSE, SSE,
Inet=16A
500
Inet=14A Inet=12A
400
t t t t t
¼ ¼ ¼ ¼ ¼
[0, 80] s [9.5, 10.5] s [19.5, 20.5] s [29.5, 30.5] s [59.5, 60.5] s
Inet=10A
1
Oxygen Excess Ratio
300
2
3
4 5 6 Oxygen Excess Ratio
7
8
9
8 6
4
2 10
15
20 Load (A)
25
30
Fig. 9 e Decision curves for obtaining optimal air excess ratio: (a) net power change depending on the air excess ratio and external power; (b) curve fit for the optimal air excess ratio with load variation.
the experiments (Fig. 9). The figure presents the relation between net power and lO2 depending on the load change. lO2 should be changed depending on the load change to obtain the maximum fuel cell net power. Therefore, the abilities of the controller while tracking a variable set point for the oxygen excess ratio are an important issue for fuel cell control. This scenario is the same for the controller that the manufacturer provides for the fuel cell. Considering a variable reference, not only can higher efficiency be obtained but the dangers of starvation can also be prohibited by setting an appropriate value of lO2 whenever required load is large. Therefore, a sudden request for more power is possible given the unavoidable drop of oxygen in the stack. Using the same test load profile, the TDC and the original manufacturer’s controller are tested, and their results are presented in Fig. 10. This test aims to exhibit better dynamic
6
Oxygen Excess Ratio
Oxygen Excess Ratio
6
5
4
3
2 9.5
10 Time (s)
3
20 Time (s)
20.5
5
5
Oxygen Excess Ratio
Oxygen Excess Ratio
4
2 19.5
10.5
6
4 3 2 1 29.5
5
30 Time (s)
30.5
4
3 Nexa TDC Set-point 2 59.5
60 Time (s)
60.5
Fig. 10 e Comparison of optimal air excess ratio variation: (a) at 10 s; (b) at 20 s; (c) at 30 s; (d) at 60 s.
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Net Power (W)
1000 800 600 400 200
0
10
20
30
40 Time (s)
50
60
70
80
0
10
20
30
40 Time (s)
50
60
70
80
Net Power (W)
1000 800 600 400 200
Fig. 11 e Net power variation: (a) manufacturer’s controller; (b) TDC.
performance of the TDC given the varying lO2 reference conditions. Whenever an increase of the load is considered, the undershoot of lO2 might be a problem. This scenario leads to an immediate decrease of available oxygen, and the controller can only overcome this issue via the slow dynamics of the compressor and its supply manifold. Therefore, a sudden decrease of lO2 can lead to oxygen starvation. Thus, fast oxygen supply to the fuel cell is necessary to increase the optimal power and to prevent the starvation. The performance of the TDC can be assessed by comparing the control action in two different ways. On one hand, the recovery toward the desired reference under the load change is improved (Fig. 10). This improvement is due to the combined contributions of the feedforward controller and TDC. In the case of sudden load increase, TDC exhibits better performance by reducing the settling time from 400 ms to 50 ms (Fig. 10(c)). In a similar way, when the sudden decrease of the load occurs, the TDC settling time reduces from 300 ms to 100 ms (Fig. 10(d)).
These results show that the TDC provides oxygen faster to the fuel cell, providing higher efficiency conditions, which can be crucial in the case of continuous changing loads. Table 3 summarizes the steady-state and transient error comparisons between TDC and manufacturer’s controller and reveals that the TDC provides better control performance. An additional benefit of the proposed control scheme is that the control signal is significantly smoother, which leads to more even delivery of power (Fig. 11). The maximum power fluctuation from the original controller is 50 W, while the TDC reduces it to maximum 20 W. This significant reduction of the power fluctuation can also increase the stack lifetime. Finally, the net power efficiency comparison is made (Fig. 12). The TDC can provide almost 3.5% more power than the original manufacturer’s control scheme. Although only 1.2 kW of fuel cell is used in the paper, this increase of power efficiency cannot be ignored if longer fuel cell operation time or a high-power fuel cell is considered.
900
Filtered Net Power (W)
5.
Maximum Power Tracking Constant Set-point=4 Nexa Controller
800
700
600
500
400
300
0
10
20
30
40 Time (s)
50
60
70
Fig. 12 e Net power variation by changing the air excess ratio.
80
Conclusion
This study is based on the real-time control of PEM fuel cell technology, the Nexa power module. The study focuses on the accurate but simple control using TDC to prevent oxygen starvation and/or to obtain the maximum efficiency of the PEM fuel cell. The major contributions of this research are summarized as follows: first, the simple transfer functions between compressor voltage input and air excess ratio of the PEM system model are identified via experiments for midpower and high-power ranges. The obtained transfer functions represent the whole range of operation in accordance with the wide range of load variation. Second, TDC is designed and applied to prevent oxygen starvation and to achieve better performance. The proposed control scheme succeeds in reducing the settling time and power fluctuation better than the manufacturer’s controller. Optimal air excess ratio is
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determined via experiments to achieve the best efficiency. Maximum 3.5% of net power increase is achieved compared with the manufacturer control scheme or fixed air excess ratio scheme using the optimal air excess ratio. The technique utilized in this paper provides a solution that can be implemented easily, both in terms of modeling the process and reducing the computational burden for the realtime controller.
Acknowledgements This research was supported by Chonnam National University Research Fund in 2013.
[14]
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