Maximizing the Lifetime of Embedded Systems Powered by ∗ Fuel Cell-Battery Hybrids Jianli Zhuo1 , Chaitali Chakrabarti1 , Naehyuck Chang2 , Sarma Vrudhula3 1 Dept.
of Electrical Engineering, Arizona State University, Tempe, AZ, 85287, U.S. 2 School of CSE, Seoul National University, Seoul, Korea 3 Dept. of CSE, Arizona State University, Tempe, AZ, 85287, U.S.
[email protected],
[email protected],
[email protected],
[email protected] ABSTRACT
Compared to other alternative power source such as solar powers [3, 4, 5], fuel cells are easily controllable, have a stable power output and so have been widely used in automobiles, power plants, and more recently, portable applications. Fuel cells have limited load following capacity, ie, the power range is limited and the response is slow. Thus it is widely accepted that a hybrid power source (fuel cells plus secondary energy storage) is much more efficient than a fuel cell alone power source. A hybrid power system consists of a primary power source with high energy density and a secondary power source with high power density, and improves both the power capacity and the response time. The secondary power source could be a battery or an ultra capacitor or a combination [6]. Most of the prior work on fuel cell control has been in the context of hybrid automobiles. These include fuel cell models that capture the chemical kinetics, and mechanisms to control fuel cell operations [7, 8, 9]. Control techniques to coordinate the operations of the fuel cell, battery and super capacitor to achieve longer battery lifetime and higher system efficiency have also been proposed [10, 11]. The superiority of hybrid fuel cell/battery system over pure fuel cell systems has been demonstrated in terms of system efficiency, dynamic control requirement, etc in [7, 8]. Unfortunately, techniques developed for hybrid automobiles cannot be easily adapted for portable embedded systems. This is because while automotive systems are reactive, in an embedded system, the tasks can be executed in any manner as long as they meet a specified performance level. Thus for an embedded system powered by fuel cell-battery hybrids, techniques that jointly optimize the control parameters at the producer end (fuel cell and battery) and the consumer end (embedded processor) have to be developed. In this paper, we describe a procedure to enhance the lifetime of a DVFS based embedded system powered by a hybrid source. The hybrid power source is built with a PEM (Proton Exchange Membrane) fuel cell that works at room temperature and a Li-ion battery. The proposed procedure to enhance the fuel cell lifetime is built on top of an energy based optimization framework. Maximizing the fuel cell lifetime is equivalent to minimizing the overall energy loss, defined as the sum of the energy consumed by the load and the energy that is lost through the bleeder bypass when the battery is fully charged. The algorithm minimizes the energy loss by scaling the power of the DVFS based embedded system subject to deadline and battery constraints on the one hand and adjusting the fuel cell output power on the other hand. We first show how the energy based optimization framework can be used to set the fuel cell power output and DVFS setting for a single task, and then we describe the procedure for multiple tasks in a static (off-line) scheduling environment. Basically, we first determine the scaling factor that minimizes the energy consumption of the embedded system,
Fuel cells are a viable alternative power source for portable applications. They have higher energy density than traditional Li-ion batteries and can achieve longer lifetime for the same weight or volume. However, because of their limited power density, they can not track fluctuations in the load current fast. A hybrid power source, that consists of a fuel cell and a Li-ion battery, has the advantages of long lifetime and good load following capabilities. In this work, we consider the problem of extending the lifetime of a fuel-cell based hybrid source that is used to provide power to a DVFS processor. We propose a new algorithm that is built on top of an energy based optimization framework. The algorithm simultaneously adjusts the fuel flow rate (at the producer end), and judiciously scales the load current (at the consumer end) to minimize the energy loss of the hybrid system. Simulations on randomly generated task sets demonstrate the superiority of this algorithm with respect to an algorithm that does not allow adjustment of the fuel flow rate.
Categories and Subject Descriptors D.4.1 [Operating Systems]: Process Management—Scheduling
General Terms Algorithms
Keywords Fuel cell, Battery, Hybrid systems, DVFS system, Task scaling
1.
INTRODUCTION
Fuel cells are clean power sources that have attracted a great deal of attention in recent years. Fuel cells have a distinct advantage over batteries in that they have very high energy density compared to batteries. They are thus expected to generate power longer (4 to 10x) than a battery package of the same size and weight [1, 2]. ∗This research was funded in part by the NSF grant (CSR-EHS 05059540), the Consortium for Embedded Systems, ASU, and LG Yonam Foundation.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. ISLPED’06, October 4–6, 2006, Tegernsee, Germany. Copyright 2006 ACM 1-59593-462-6/06/0010 ...$5.00.
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0.8
and then determine the fuel cell power that minimizes the wasted energy. This is an extension of our prior work presented in [12], where the fuel cell output power was assumed to be fixed and the scaling factor of the DVFS based embedded system was the only control knob. The rest of the paper is organized as follows. Section 2 describes the fuel cell/battery characteristics and provides an overview of the hybrid system. The fuel cell efficient algorithm which jointly controls the DVFS scaling factor and the fuel cell current is explained in Section 3. Section 4 presents the performance of the proposed algorithm for randomly generated task set. The paper is concluded in section 5.
2.
Efficie n cy
0.7
0.1 0
1X Fuel cell
15
20
3X Fuel cell
vout
Battery Fuel cell output power
Fuel cell output voltage
10 Power(W)
ing the power density of the Li-ion battery and the energy density of the fuel cell. Figure 3 shows how, in order to ensure system safety, a fuel cell only system may be over-designed if the load current variance is large (max load current is 3X of the average load current). This would result in increase in total size and weight of the fuel cell. Since the Li-ion battery can supply the additional current when necessary, a fuel cell in conjunction with the battery is more efficient with respect to power/energy density and size/weight.
Load following Unstable chemical reaction w/fuel flow rate control
Practical maximum power
5
Figure 2: Fuel cell stack efficiency and fuel cell system efficiency of the fuel cell used in our work (measured values)
The I-V-P characteristic curves of the fuel cell are shown in Figure 1. They can be explained by electron transfer phenomenon that occurs at very low currents, and mass transport phenomenon that occurs at high currents. From the curves, we see that as the current density increases, the voltage drops, and that the power first increases then drops. The operating point of the fuel cell is typically set around P= 23 maxpower, and not P=maxpower because of stability considerations.
Theoretical maximum power
FC system efficiency
0.4
0.2
2.1 Fuel cell/battery characteristics
Higher fuel efficiency
FC stack efficiency
0.5
0.3
OVERVIEW OF THE HYBRID SYSTEMS
Higher power output
0.6
Iave
1X Fuel cell and battery hybrids 3Iave
iout
Figure 3: Advantage of using hybrid power source
Voltage Power
2.2 Fuel cell hybrid system Fuel cell current
The hybrid system under consideration is shown in Figure 4. The hybrid power source consists of a sodium borohydride (NaBH4 ) PEM (Proton Exchange Membrane) fuel cell system that works at room temperature and a Li-ion battery. The fuel cell system has an output power PF . The Li-ion battery has a fixed capacity and is capable of providing multiple levels of output power. The charging and discharging of the battery is controlled by the charge management system (CMS). At the consumer end is a dynamic voltage scalable (DVFS) processor based embedded system whose load power, PL , is a function of several variables such as the processor supply voltage, the power management state of various peripherals, and the type of energy management policy used. When PF < PL , the Li-ion battery provides PL − PF ; when PF > PL , the Li-ion battery is charged. If the battery gets fully charged and PF > PL , then the excess power is dissipated through the bleeder circuit. The hybrid control system accepts the state of the embedded system as input, and then determines the action of the power source. Specifically, the controller can adjust the fuel cell output power by adjusting the fuel rate flow (expressed in milliliter/second) as well as the air flow. At the consumer end, the load power can be adjusted by task scheduling, processor frequency/voltage scaling, memory frequency scaling, etc. In this paper, we show how a combination of the dynamic frequency/voltage scaling at the consumer end and fuel cell power adjustment at the producer end can help achieve a longer lifetime for the hybrid power system. The optimization metric in embedded systems powered by fuel
Figure 1: I-V-P curves for room temperature fuel cell The chemical to electrical efficiency of a single fuel cell is proportional to its output voltage [13]. However, the efficiency of a fuel cell system is not only impacted by the fuel cell stack, but also impacted by other factors such as fuel utilization, fuel transform efficiency and power conditioning efficiency. Figure 2 shows the fuel cell efficiency curve of the room temperature fuel cell considered in our work. We can see that the system efficiency is 44-46% in the power range 5W to 18W. So in our work, we assume that the fuel cell system efficiency is a constant. The fuel cell power output can be varied in a certain range (load following region) by controlling the fuel input rate. The load following capability of the fuel cell is quite slow, as indicated in [2]. When the membrane is wet, it takes the fuel cell around 10 sec to generate the full current (corresponding to 2/3 of the max power). Assuming that the output increases linearly, it takes about 1 sec to adjust the fuel cell output current by 10%, which is quite long for embedded applications. A traditional battery (such as a Li-ion battery), on the other hand, has superior load following capabilities and can respond to the current change immediately. However, Li-ion batteries have much lower energy density (< 200Whr/kg) compared to the fuel cell (2000 Whr/kg) [14]. A hybrid power source has the advantage of provid-
425
Energy provider PF
Fuel cell system
CMS battery
fuel flow rate
where the first term is the dynamic power, the second term is the intrinsic power, and the last term is the static power [15, 16]. If we assume that for scaling factor sk , the voltage scales by sk , and both Pon and Istatic are constant, then the total power consumption of task Tk , Pk (sk ) is given by
Energy consumer PL
Embedded system
DC-DC
bleeder DVS scaling
batt. state
−1 Pk (sk ) = α1 · Pk (1) · s−3 k + α2 · Pk (1) + (1 − α1 − α2 ) · Pk (1) · sk
Hybrid control system Embedded system state
Fuel cell state
where Pk (1) is the total power consumption at sk = 1, α1 and α2 are the ratios of dynamic power to total power and intrinsic power to the total power at sk = 1. In this paper, we assume that α1 +α2 = 0.8. This implies that the static power is 20% of the total power. The load power PL seen by the power source is actually the DCDC inlet power. If we assume a constant DC-DC efficiency [17], then the load power equation for task Tk is given by
Figure 4: The schematic view of the hybrid system cell/battery hybrids is lifetime of the fuel cell. The lifetime is related to the fuel consumption of the fuel cell. We assume that a given volume (or weight) of fuel can provide a certain amount of energy. If the fuel energy consumption is less, as a result of lower energy consumed at the consumer end, the lifetime of the fuel cell is longer. So the objective of extending the lifetime of the fuel cell is transformed to minimizing the fuel energy consumption during task execution. Energy provider Fuel cell system
E fc E bat battery
−1 PL,k (sk ) = α1 · PL,k (1) · s−3 (4) k + α2 · PL,k (1) + (1 − α1 − α2 ) · PL,k (1) · sk
The metric to measure the performance of difference policies is the total energy consumption of the system, Etotal , which includes the load (embedded system) energy consumption Eload and the wasted energy through the bleeder, Ewaste. The scaling factor which minimizes Etotal is called as the optimal scaling factor, sopt . The scaling factor which only considers minimizing Eload is called sload . Table 1 provides a comprehensive list of all parameters.
Energy consumer Eload
Embedded system
E waste
Table 1: Definition of fuel cell system parameters PF,k the output power of the fuel cell. PFmax the maximum power in the load following range. PFmin the minimum power in the load following range. Bmax the charge capacity of the battery Tk the k − th task in the task profile sk voltage / frequency scaling factor of Tk , sk ≥ 1 τk the worst case execution time of Tk PL,k (sk ) the load power when task Tk is scaled by sk α1 the ratio of the dynamic power to the total power when sk =1 α2 the ratio of the intrinsic power to the total power when sk =1;
bleeder
Figure 5: The energy flow of the hybrid system The energy flow of the hybrid system is shown in Figure 5. At the energy provider end, E f c is the electrical energy provided by the fuel cell and Ebat is the energy provided by the battery. The battery works as an energy buffer. Assume that the initial state of charge of the battery is Bini and final state of charge is Bend . Then the energy provided by the battery is Ebat = Bini − Bend (if Ebat < 0, then the battery buffer stores energy). At the energy consumer end, Eload is the energy consumed by the embedded system and Ewaste is the energy wasted through the bleeder. Recall that when the battery is fully charged but PF > PL , the excess power is dissipated through the bleeder circuit. The energy flow is summarized by the following equation. E f c + Ebat = Eload + Ewaste
Bini k Bend k Eload Ewaste Etotal opt sk sload k
(1)
Our objective is to minimize the fuel energy consumption given by E f c + Ebat . This is equivalent to minimizing Eload + Ewaste , according to Equation (1).
3.
(3)
To simplify the analysis, we make the following assumptions: (1) the battery charge management system has 100% efficiency; (2) we only do inter-task scaling, so the load power and the fuel cell output power do not change during the execution of a single task; (3) the task sequence is determined apriori, we only consider voltage/frequency scaling of the tasks.
FUEL CELL EFFICIENT SCALING
3.1 Definitions
3.2 Motivational example
We begin with the notations that have been used in the rest of this paper. The hybrid power source is characterized by the fuel cell power, PF that has a value in the range [PFmin , PFmax ], and Bmax , the energy capacity of the Li-ion battery. For task Tk , the fuel cell power is PF,k , the battery stored energy at the beginning of the exeend cution is Bini k and at the end of the execution is Bk . Let sk be the frequency scaling factor while executing task Tk . The task execution time is then sk × τk , where τk is the worst case execution time at the highest frequency (corresponding to sk = 1). The total power consumption of the DVFS processor is given by 2 P = C ·Vdd · f + Pon +Vdd · Istatic
α1 + α2 = 0.8 in this chapter the battery charge value when task Tk starts the battery charge value when task Tk finishes energy consumed by the load (DC-DC inlet) energy wasted through bleeder bypass the total energy consumption, given by Eload + Ewaste the scaling factor which minimizes Etotal the scaling factor which minimizes Eload
Consider a DVFS system whose frequency can be scaled from 1 to 2.5 in steps of 0.1. The fuel cell power can vary in [5, 15]W. The battery capacity is Bmax = 1500J and the initial state of the battery is half of Bmax . The task configuration is given in Table 2. We first assume that we do not use the load following capability, and the fuel cell output power is fixed at PF = 15W. By applying Algorithm fc scale [12], we obtain the scaling profile and the energy metrics as shown in Figure 6(a). Now if we control both the fuel cell output power and the load power, we get significant energy savings. In the profile shown in Figure 6(b), the fuel cell power, PF,1 is set to 8.225 W and the load
(2)
426
Since Etotal = Eload + Ewaste , and Eload is minimized by scaling , Eload (PF,k , sload ) can be minimized if the fuel cell outfactor sload k k ) = 0. put power PF,k is set to a value that makes Ewaste (PF,k , sload k Bmax −Bini load k ≥ PF,k − PL,k (sk ) × This means, PF,k should satisfy τk
power, PL,1 is scaled to 5.1W for task T1 , and PF,2 is set to 5W and PL,2 is scaled to 4.99W for task T2 . The values of all three energy metrics are significantly smaller for this profile. For instance, Eload reduces from 5229J to 3907J and Etotal reduces from 5730J to 3924J. Thus the lifetime of the fuel cell can be extended significantly if the fuel cell has load following capabilities.
or PF,k ≤ PL,k (sload )+ sload k k
Bmax −Bini k . sload ×τk k
The value of PF,k should also
satisfy the charge constraint in Equation (7). So the range of PF,k is Table 2: Task parameters of the illustrative example τk 2min 5min
Tk T1 T2
Power (W)
PL (1) 15W 12W
α1 : α2 4:1 3:1
PF =15W
15
PL,1 (s=1.1) =12.3W
PL,2 (s=1)=12W PF =0
0
0
5
Power (W)
(a). Without load following, Algorithm
15
fc_scale
E load = 3906.7 J E waste = 17.3 J E total = 3924 J
PF,1 =8.225W
10
t (min) 15
10
PF,2=5W
0
PL,2 (s=1.8)=4.99W
PF =0 t (min)
0
5
10
(b). With load following, Algorithm
sload × τk k
, PL,k (sload )+ k
Bmax − Bini k sload × τk k
(8)
3.3.2 Determining PF,k and sload for a sequence of k tasks
5 PL,1 (s=2)=5.1W
Bini k
Now assume the load following range limits of the fuel cell under Ìconsideration is Ω = [PFmin , PFmax ]. If Φk overlaps Ω, that is / then PF,k could be set to any value in the overlapped Ψk Ω = Ì 0, region Ψ Ì k Ω. In our algorithm, we choose the largest value in Ψk Ω because then the battery can get charged more and it could benefit the next task Tk+1 (the charge constraint of Tk+1Ì will be / more relaxed if Bini k+1 is larger). In the case when Ψk Ω = 0, then we set PF,k to either PFmin or PFmax (set to the value which is closer to the set Ψk ), and then re-calculate the optimal scaling facopt tor sk by minimizing the function Etotal (PF,k , sk ) = Eload (sk ) + Ewaste (PF,k , sk ) under battery constraint and deadline constraint.
E load = 5228.9 J E waste = 501 J E total = 5730 J
10 5
)− Φk = PL,k (sload k
D 15min 15min
15
Assume that there are n tasks (T1 , T2 ,...,Tn); all tasks arrive at time 0 and share the same deadline D. The total energy consumption Etotal during task execution is
fc_scale_ctrl
Figure 6: Motivational example: (a) no load following, (b) with load following.
Etotal (PF,1 , ..PF,n; s1 , .., sn ) =
n
∑ Etotal (PF,k , sk )
k=1
3.3 Algorithm
k=1
Eload (s1 , s2 , .., sn ) =
To minimize Etotal for a single task execution, the two parameters that need to be determined are the fuel cell system output PF,k opt and the task scaling factor sk . The task duration is sk × τk , and total energy consumption is Etotal (PF,k , sk ) = Eload (sk ) + Ewaste (PF,k , sk ). If we can minimize both Eload and Ewaste , then the total energy loss Etotal is minimized. The load power consumption Eload , wasted energy Ewaste , and the battery constraint are as follows:
(9)
n
∑
PL,k (sk ) × sk × τk
(10)
k=1 n
Deadline constraint
:
∑ (sk × τk ) ≤ D
(11)
k=1
These values can be determined analytically by the Lagrange multiplier approach for the given load power model. Since the objective function Eload (s1 , s2 , .., sn ) is a sum of convex functions Eload (sk ), and the deadline constraint is also a convex function, we can introduce a Lagrange multiplier λ and construct a function f (s1 , s2 , .., sn ) as follows
(5)
max Ewaste(PF,k , sk ) = max 0, PF,k − PL,k (sk ) sk τk + Bini (6) k −B Battery constraint : PL,k (sk ) − PF,k × sk × τk ≤ Bini k
k=1
load load Our objective is to find the scaling factors (sload 1 , s2 , ..., sn ) which minimize the load energy consumption ∑nk=1 Eload (sk ) under the deadline constraint, where sload is a specific value of sk . k
3.3.1 Determining PF,k and sopt k for a single task
Eload (sk ) = PL,k (sk ) × sk × τk
n
∑ Eload (sk ) + ∑ Ewaste(PF,k, sk )
=
The input to the task scaling algorithm is a sequence of tasks, along with their specifications (deadlines, WCETs, current), Bmax and the state of the battery, Bini k . Each task is scaled such that the total energy consumption Etotal is minimized subject to the deadline constraint and the battery constraint.
n
n f (s1 , .., sn ) = Eload (s1 , .., sn ) − λ ( ∑ sk τk ) + x2 − D k=1
(7) =
First, since Eload is independent of the fuel cell current PF,k , we minimize Eload . Recall that for every task, there exists a scaling factor sk which minimizes factor Eload−3(sk ). We call this scaling −1 . Since P (s ) = α · s + α + (1 − α − α ) · s × sload 1 2 1 2 L,k k k k k load 3 2×α1 PL,k (1), sk = α2 (if there is no deadline constraints). If smax is the maximum scaling factor determined by the deadline conk straint, then the scaling factor sload has to be bounded by smax k k .
−1 × PL,k (1) × sk τk ∑ α1 · s−3 k + α2 + (1 − α1 − α2 ) · sk n
k=1
−λ ×
n
∑ (sk × τk ) + x2 − D
(12)
k=1
where we include x2 in the function because the deadline constraint is not a equation. We calculate the partial derivative of f (s1 , s2 , .., sn ) w.r.t. to each
427
sk , x and λ, and set the partial differential functions to value zero. ∂f = α2 − 2α1 s−3 (1) − λ τk = 0, ∀k ≤ n (13) P L,k k ∂sk n ∂f (14) = ∑ (sk × τk ) − D = 0 ∂λ k=1 ∂f = 2×x×λ = 0 (15) ∂x The solution of Equation (15) can be either λ = 0 or x = 0. If λ = 0, then the the simultaneousequations in Equation (13) have
4.1 Experimental setting The DVS system supports CPU scaling factor from 1 to 2.5 with steps of 0.1. In addition, we vary the value of PL (1) and the ratio α1 : α2 for each task. The task set used in the experiments is a task graph where the task order is already scheduled beforehand, and all tasks share the same deadline. Here each task sequence consists of 50 to 100 tasks. Each task has τk from 1 to 2 min. The task density is µ = ∑nk=1 τDk , where D is the deadline. µ varies from 0.3 to 0.7. For each task density value, we run 100 task sequences, and then get the average values for all the feasible cases. The battery capacity is set to Bmax = 15KJ, the initial value is assumed to be half of the capacity. The fuel cell load following range is [5,15]W. When we apply Algorithm fc scale for no load following case, we set a constant fuel cell output power PF = 15W. We assume that the fuel cell is shut down after all the tasks are completed. Since the task execution time is in the order of minutes and the battery capacity is quite large, we assume that the additional charge/dischage because of the delay in adjusting PF,k (≈ 1 sec for 10% change) is handled by the battery.
load . 1 an unconstrained solution: sk = 3 2×α α2 = sk If λ = 0 and x = 0, the solution (s1 , s2 , ..sn , λ), x for the n + 1 functions in Equation (13) and Equation (14) exists, but it is difficult to find analytically. However, Equation (13) tells us that the value of (s1 , s2 , .., sn ) which minimizes the objective function should satisfy the condition PL,k (sk ) × sk s = PL, j (s j ) × s j s ≤ k
j
is also 0, ∀ j, k ≤ n. If α1 : α2 is identical for all tasks, then sload k identical for all tasks and the value can be obtained by evenly distributing the slack to all tasks. When α1 : α2 is different from each other, we can find these values numerically. After we determine sload , we find the value of PF,k which mink imizes wasted charge and satisfies charge constraint for each indiopt vidual task. Note that it may be necessary to re-calculate sk if Ì / Ψk Ω = 0.
4.2 Experiment 1: Embedded system w/o load power variance In this simulation, we investigate the performance of the proposed algorithm for an embedded system where the load power PL (1) is the same for all tasks. Assume that PL,k (1) = 15W. The power ratio α1 : α2 is different from task to task, and randomly (based on the uniform distribution) chosen from the range [3, 7]. Table 3 shows the total energy consumption Etotal , load energy consumption Eload , wasted energy Ewaste for the different algorithms. The energy consumption values in Table 3 show that the total energy consumption, Etotal , of Algorithm fc scale ctrl is much lower than fc scale.
3.3.3 Algorithm description The proposed fuel cell efficient task scaling algorithm consists of three main steps. The details are shown in Algorithm 1. opt Step1: Calculate the scaling factor sk of the task sequence based on unlimited load following range (line 1). Step2: Determine PF,k based on the load following range (lines 5-9). opt Step3: Re-determine sk to minimize the total energy consumption (line 10).
Table 3: Experiment 1: Performance comparison when PL,k (1) = 15W, and α1 : α2 varies randomly between 3 to 7 Item µ 0.7 0.5 0.3 fc scale 99.60 100.16 100.42 Etotal (KJ) fc scale ctrl 75.09 72.17 73.86 fc scale 99.57 100.13 100.40 Eload (KJ) fc scale ctrl 75.09 67.67 67.48 fc scale 0.03 0.03 0.02 Ewaste (KJ) fc scale ctrl 0 4.49 6.38
Algorithm 1 Task Scaling Algorithm fc scale ctrl opt opt 1: Determine (sopt 1 ,s2 ,..,sn ) by assuming unlimited load following
range.
2: k=1, flag=0; 3: WHILE k ≤ n DO 4: Input: task Tk with τk , sload , battery with Bmax and Bini k k . Bini
k 5: Plow = PL,k (sopt k ) − sopt ×τ ; k
6: Phigh = PL,k (sopt k )+
k
Bmax −Bini k opt sk ×τk
;
7: if Plow > PFmax then PF,k = PFmax , flag=1 end if; 8: if Phigh < PFmin then PF,k = PFmin , flag=1 end if; 9: if flag==0 then PF,k = min(Phigh ,PFmax ); opt 10: else determine sopt k by minimizing Echm (sk ), and adjust s j for k < j ≤
4.3 Experiment 2: Embedded system with load current variation Next, we vary the load power, PL,k (1) for each task. The load power is randomly chosen based on the uniform distribution in the range [10,15]W. The power ratio α1 : α2 is still randomly chosen from the range [3, 7]. Table 4 compares the energy performance of the different algorithms. In this case, the difference between Algorithm fc scale ctrl and fc scale is larger than when the load power is constant (as in Experiment 1). Recall that in Algorithm fc scale, PF = 15W which is based on the highest load power value 15W. When the load current variance is quite high (a realistic scenario since different tasks may use different resources) and the fuel cell power has been set to a high value, then many a time Ewaste is high since the battery is not big enough to hold all the excess charge. In such scenarios, changing the fuel cell current PF reduces Ewaste and Etotal as shown in Table 4.
opt
11: 12: 13: 14: 15: 16:
4.
n if sk changes; end if execute task Tk by sopt k till it finishes; max ,Bini + (P − P (sopt )) × sopt × τ ); Bend = min(B F,k L.k k k k k k if Bend k < 0 then return FAILURE; end else Bini k+1 = Bk , k=k+1, flag=0; end if END WHILE
SIMULATION RESULTS
In this section, we compare the performance of the proposed algorithm fc scale ctrl with the algorithm fc scale [12] which is proposed for minimizing the total energy consumption of a hybrid system with fixed fuel cell output power PF .
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Table 4: Experiment 2: Performance comparison when PL,k (1) varies within [10,15]W and α1 : α2 varies between 3 to 7 Item µ 0.7 0.5 0.3 fc scale 94.751 95.482 95.813 Etotal (KJ) fc scale ctrl 59.981 65.786 67.872 fc scale 79.926 80.212 80.370 Eload (KJ) fc scale ctrl 59.952 54.120 54.007 fc scale 14.825 15.271 15.443 Ewaste (KJ) fc scale ctrl 0.029 11.666 13.865
tem. Simulations on randomly generated task sets demonstrated the superior performance of this algorithm compared to the algorithm that does not allow adjustment of the fuel flow rate. In deriving the procedure, we assumed that the fuel cell power efficiency is constant. In the near future, we will take a more detailed look at the fuel cell system efficiency as a function of the output power. Also, to account for a more realistic scenario, we will include the delay of the fuel cell load following. This can typically be handled by proper off-line scheduling. But for very short task durations, we may experience uncertainty that is not trivial to handle by off-line methods.
4.4 Experiment 3: Configuration of the hybrid power source
6. ACKNOWLEDGEMENT We sincerely thank Dr. Don Gervasio and Sonja Tasic (Flexible Display Center, ASU), and Kyungsoo Lee (School of Computer Science and Engineering, SNU) for help with the fuel cell setup and measurement.
For a given embedded system, if we know the application domain and the corresponding load power variance, then it is possible to come up with a set of candidate configurations which satisfy the energy performance and then choose the configuration that satisfies the weight/size requirement. To illustrate this, consider the set of tasks with utilization µ = 0.7 in Experiment 1 that have load power value PL (1) which is 15W, and α1 : α2 which varies randomly between 3 to 7. First, assume that we have already chosen the battery with Bmax = 64kJ and that the initial charge Bini is half of Bmax . We vary the fuel cell load following range increasing the value of PF max from 5W in steps of 1W, and the value of PFmin is set to PFmax /3. Figure 7(a) plots the system performance, Etotal (averaged over 100 random task sets) as a function of PFmax . The infeasible region corresponds to the case when PFmax is too small so that the tasks cannot complete with sufficient power or the state of charge of the battery falls below a certain value (it is set to half of Bini in this experiment) at the end of the task profile. Figure 7(a) shows that PFmax = 6W is sufficient for this particular system, and that increasing PFmax does not change the system performance. Now if we have a smaller battery, say, Bmax = 16kJ, then PFmax should be chosen to a value not less than 8W, as shown in Figure 7(b). Since the feasible regions in Figure 7(a) and (b) have the same energy performance, we can choose any candidate configuration from the feasible region without any performance degradation. The final choice will depend on the availability of the components as well as the weight and size requirements. Etotal(KJ)
7. REFERENCES [1] D. Gervasio, S. Tasic, and F. Zenhausern, “A room temperature micro-hydrogen-generator,” Journal of Power Sources, vol. 149, pp. 15–21, 2005. [2] D. Gervasio, “Fuel-cell system for hand-carried portable power,” International Fuel Cell R&D Forum, Nov. 2005. [3] P. H. Chou and D. Li, “Maximizing efficiency of solar-powered systems by load matching,” in ISLPED’04, August 2004. [4] V. Raghunathan, A. Kansal, J. Hsu, J. Friedman, and M. B Srivastava, “Design considerations for solar energy harvesting wireless embedded systems,” in IPSN’05, April 2005. [5] X. Jiang, J. Polastre, and D. Culler, “Perpetual environmentally powered sensor networks,” in IPSN’05, April 2005. [6] J. P. Zheng, T. R. Jow, and M. S. Ding, “Hybrid power sources for pulsed current applications,” IEEE Trans. Aerospace and Electronic Sys., vol. 37, no. 1, pp. 288–292, 2001. [7] Y. Guezennec, Ta-Young Choi, G. Paganelli, and G. Rizzoni, “Supervisory control of fuel cell vehicles and its link to overall system efficiency and low-level control requirements,” in Proc. American Control Conf. (ACC), 2003, vol. 3, pp. 2055–2061. [8] A. Vahidi, A. Stefanopoulou, and Huei Peng, “Model predictive control for starvation prevention in a hybrid fuel cell system,” in Proc. American Control Conf. (ACC), 2004, vol. 1, pp. 834–839 vol.1. [9] A. Nasiri, V. S. Rimmalapudi, A. Emadi, D. J. Chmielewski, and S. Al-Hallaj, “Active control of a hybrid fuel cell-battery system,” in Proc. Intl’l Power Electronics and Motion Control Conf. (IPEMC), 2004, vol. 2, pp. 491–496. [10] Z. Jiang, L. Gao, and R. A. Dougal, “Flexible multiobjective control of power converter in active hybrid fule cell/battery power sources,” IEEE Transactions on Power Electronics, vol. 20, no. 1, pp. 244–253, Jan 2005. [11] M. J. Gielniak and Z. J. Shen, “Power management strategy based on game theory for fuel cell hybrid electric vehicles,” in Proc. Vehicular Technology Conference (VTC), 2004, vol. 6, pp. 4422–4426. [12] J. Zhuo, C. Chakrabarti, N. Chang, and S.Vrudhula, “Extending the lifetime of fuel cell based hybrid systems,” in 43rd DAC, July 2006. [13] J. Larminie and A. Dicks, Fuel Cell Systems Explained, John Wiley & Sons, LTD, 2000. [14] C. K. Dyer, “Fuel cells and portable electronics,” in Symposium on VLSI circuits (digest of technical papers), June 2004, pp. 124–127. [15] R. Jejurikar, C. Pereira, and R. Gupta, “Leakage aware dynamic voltage scaling for real-time embedded systems,” in 41st DAC, June 2004, pp. 275–280. [16] J. Zhuo and C. Chakrabarti, “System-level energy-efficient dynamic task scheduling,” in 42nd DAC, June 2005, pp. 628–631. [17] Y. Choi, N. Chang, and T. Kim, “Dc-dc converter-aware power management for battery-operated embedded systems,” in 42nd DAC, June 2005, pp. 895–900.
Etotal(KJ)
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~75 Infeasible region
Infeasible region
feasible region
feasible region
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(b) Bmax = 16kJ
Figure 7: Different configurations: (a) when Bmax = 64kJ, PFmax = 6W is sufficient, (b) when Bmax = 16kJ, PFmax = 8W is sufficient.
5.
CONCLUSION AND FUTURE WORK
In this paper, we presented a procedure to increase the lifetime of fuel cell/battery hybrids. The procedure, built on top of an energy based optimization framework, simultaneously adjusts the fuel flow rate (at the producer end), and judiciously scales the load current (at the consumer end) to minimize the energy loss of the hybrid sys-
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