8. DESIGN
f fLP,2
-+ +
-pBus,FC
pBus,Bat pBus,UC
-pBus,Load
pBoP
pAux
pLight
pHeat +++++
pInv,L fLP,1 f
1
+ 2
pInv,R
FC-LP-filter Saturation
Bat-LP-filter
Bat-switch
Power flow Bus
connection
pFC
pFC* pBus,FC*
+ +
+
pBus,UC,charge* pBus,Bat,charge*
+
0 1
2 FC-switch
3 Bus connection
Figure 8.5: System level block diagram of energy management strategy.
situation the switch "FC-switch" in Figure 8.5 therefore is in position 2. During normal operation it is in position 1.
The switch "Bat-switch" in Figure 8.5 is used to divide the bus power between the battery and ultracapacitors. When the ultracapacitors are the only energy storage device, the switch is in position 1. Thereby the battery bus power contribution is zero, and the ultracapacitors therefore provide that part of the load power that the fuel cell is not able to deliver. When the battery is the only energy storage device, the switch is in position 3. Thereby the ultracapacitor bus power contribution becomes zero, and the battery provides the difference between the fuel cell bus power and bus load power. When both the battery and ultracapacitors are presented the switch is in position 2. In this situation, the battery contribution is also determined by a low-pass filter (Block "Bat-LP-filter" in Figure 8.5). This filter has a higher bandwidthfLP,Bat thanfLP,F C of the fuel cell filter. However, the bandwidth is chosen sufficiently low, so that the load power due to the short term accelerations and braking of the vehicle is fed to the ultracapacitors. In this way the battery assists the fuel cell stack with the base part of the load power, and the ultracapacitors take care of the peak powers. It may be understood, that if the fuel cell power rating is sufficiently high, the battery in this situation is only utilized during the heating-up of the fuel cell stack. However, if the fuel cell stack power rating is very small, the battery will be the main source of energy to the electric machines, and the only function of the fuel cell is to charge the battery and ultracapacitors during standstill. The choice of cut-off frequency is a trade-off between the sizing of the battery and ultracapacitor. If the frequency is too low, the energy requirement of the ultracapacitor might be too big, and if the frequency is too high the power requirement of the battery becomes too big. By trial-and-error method it turns out, that fLP,Bat = 20 mHz provides a sufficient balance between the power and energy distribution of the battery and ultracapacitor.
In Figure 8.6(a) the fuel cell, battery, and ultracapacitor contribution to the load power is shown for case 7 with a fuel cell power rating of PF C,rat = 2500 W, where both the battery and ultracapacitor are present. It is seen that the fuel cell provides the base power, the battery delivers the power requirement of low frequency, and the 102
8.5. Energy Management Strategy
ultracapacitors handle the fast peak powers. Therefore, in this way the ultracapacitors act as a high-pass filter. In Figure 8.6(b) the state-of-charge of the battery is shown.
Due to the heating requirement in the start of the plot, i.e. from time 420 min the load power is high. As the battery in this situation should provide the power, the state-of-charge drops quite fast. At time 426 minthe fuel cell has reached the correct temperature, and therefore it starts to produce power. The fuel cell power rating is sufficient for the shown example, so the battery can be charged while the truck is being used. The ultracapacitor voltage can be seen in Figure 8.6(c). When the truck is in passive mode the ultracapacitor is fully charged.
The proposed energy management strategy shares ideas with the one presented in [1], where a diesel generator, battery, and ultracapacitor hybrid are investigated.
In that work the diesel generator is operated at the point where it has the highest efficiency, and the ultracapacitor is also acting as a high pass filter. However, if a fuel cell is operated at the point of maximum efficiency only a small fraction of the power capability is used. Therefore, in order to utilize as much of the nominal power as possible, the fuel cell should try to follow the load. Therefore the "FC-LP-filter" is used.
Charging Strategy
In Figure 8.5 it is shown how the load power is divided between the fuel cell stack, battery, and ultracapacitors. When the state-of-charge of the battery is 1, and the ultra-capacitor voltage is below its reference voltage, the fuel cell charges them, provided by availability of extra power. The battery is charged with the current level2IBat,10.
pBus,Bat,charge∗ =
2IBat,10vBat SoCBat <1
0 SoCBat ≥0 [W] (8.71)
The 10 hour current depends on the number of parallel strings, i.e.
IBat,10 =NBat,pQBat,10,Base
10 h [A] (8.72)
Due to the health of the ultracapacitors, it is of high importance that they are not overcharged. When the vehicle is used, i.e. active, the ultracapacitors have to cap-ture the braking energy, which means that they should not be fully charged. When the vehicle is active, it is chosen to charge the ultracapacitors to a value between the maximum and minimum voltage, so there is a buffer of equal size for the energy due to braking and accelerating. The ultracapacitor voltage reference is therefore:
v∗U C =
V
U C,max+VU C,min
2 Truck active
VU C,max Truck inactive [V] (8.73)
When the truck is inactive the ultracapacitor is charged to the maximum voltage.
Thereby the ultracapacitor is fully utilized and an extra buffer is provided for the self discharging
When the ultracapacitors are charged by the fuel cell, the maximum charging power will be the rated fuel cell power PF C,rat. For the configurations with both a battery and ultracapacitor, the battery will provide the base power to the loads when
8. DESIGN
420 425 430 435 440 445 450
−5000 0 5000 10000
Case 7, PF C,rat = 2500W
Time [min]
Poweratbus[W]
(a) pBus,Load
pBus,U C
pBus,Bat
pBus,F C
420 425 430 435 440 445 450
0.2 0.4 0.6 0.8 1
Time [min]
Batterystate-of-chargeSoCBat[-]
(b)
420 425 430 435 440 445 450
20 25 30 35 40 45 50
Time [min]
UltracapacitorvoltagevUC[V]
(c)
Figure 8.6: Results of applying energy management strategy when both a battery and ultracapacitor acts as energy storage devices. (a) Bus powers. (b) State-of-charge of battery. (c) Ultracapacitor voltage.
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8.5. Energy Management Strategy
the fuel cell is heating-up. In order to reduce the stress of the battery, it is in this situation therefore decided not to charge the ultracapacitors. The charging power is therefore
PBus,U C,charge=
0 Heating required
PF C,rat No heating required [W] (8.74)
The proposed energy management strategies in Figure 8.5 suggest that the fuel cell and battery are operated in a smooth way. However, in order to insure that the ultracapacitors are not overcharged, it might be necessary to disconnect them when the voltage approaches VU C,max. Thereby the fuel cell or battery will be operated in a discontinuous way, which is not desirable. In order to avoid an abrupt change of power of the fuel cell and battery, the ultracapacitor should stop "asking" for charging power before it reaches the reference voltage v∗U C. The equivalent capacitance of the combination of the series and parallel structure of the ultracapacitor base module is when fully charged given by
Ceq = NU C,p NU C,s
Ceq,max,Base [F] (8.75)
If it is neglected that the capacitance depends on the actual voltage, the energy that needs to be put into a capacitor with voltagevU C before it is charged tov∗U C is given by
EU C,charge = 1
2CeqvU C∗ 2− 1
2CeqvU C2 [J] (8.76)
Due to the lowpass filters in front of the fuel cell and battery, they will still provide power a few time constants after an inverse step has been applied. This energy should therefore be exactly enough to charge the ultracapacitor to the desired voltage. After the inverse step the output of the lowpass filters is exponentially falling. The energy of this falling power is the initial power times the time constant. Therefore from Equa-tion (8.76), the required charge power at the inverse step should be
PU C,charge,req =
⎧⎨
⎩
EU C,charge
τLP,F C Case 2, 4, and 6
EU C,charge
τLP,Bat Case 7, 8, 9, and 10 [W] (8.77)
where τLP,F C [s] Time constant of the FC-LP-filter τLP,Bat [s] Time constant of the Bat-LP-filter
The ultracapacitor should therefore stop "asking" for power when the power cal-culated in Equation (8.77) becomes smaller than the actual fuel cell powerpF C. The requested ultracapacitor charging power at the bus is therefore
pBus,U C,charge∗ =
⎧⎪
⎨
⎪⎩
PBus,U C,charge PU C,charge,req > pF C 0 |PU C,charge,req| ≤pF C
−PBus,U C,charge PU C,charge,req <−pF C
[W] (8.78) Due to the charging energy in Equation (8.76) the requested ultracapacitor charging power at the bus in Equation (8.78) can also be negative. This is useful when the
8. DESIGN
904 906 908 910 912 914 916 918
−3000
−2000
−1000 0 1000 2000 3000
Case 2,PF C,rat = 4000W
Time [min]
Shaftpowerps[W]
(a)
904 906 908 910 912 914 916 918
−4000
−2000 0 2000 4000
Time [min]
Power[W]
(b) Fuel cellpF C
UC charge reference at buspBus,UC,charge∗
904 906 908 910 912 914 916 918
38 40 42 44 46 48
Time [min]
Ultracapacitorvoltage[V]
(c) Actual,vUC
Reference,v∗UC
Figure 8.7: Charging strategy for ultracapacitor. Case 2, PF C,rat = 4000 W. (a) Shaft power. (b) Fuel cell power and ultracapacitor charge reference power at the bus. (c) Actual and reference ultracapacitor voltage.
106