6. FUEL CELL CONVERTER
Description Symbol Value
Max. input voltage VF Cmax 65 V Min. input voltage VF Cmin 35 V Rated input power PF Crat 1000 W Max. output voltage Vomax 48 V Min. output voltage Vomin 30 V
Switching frequency fs 25 kHz
Dead time TDT 800 ns
Inductance L 200μH
Inductor resistance RL 8 mΩ
Input capacitor Cin 2.35 mF
ESR ofCin RCin 9.35 mΩ
Output capacitor Co 4.7 mF
ESR ofCo RCo 4.66 mΩ
Diode forward voltage drop VF W 0.6 V On-resistance of switches RQ 2.05 mΩ Rise time of switches Trise 36 ns Fall time of switches Tf all 10 ns Table 6.3: Fuel cell converter specifications and parameters.
Therefore the diodeD2 carries all the current. The protection circuit is explained in Section 9.2 on page 128. Even though the synchronous rectifiers of switchQ1 and Q2 are utilized a relative large amount of the power is lost in the diodesD1in buck-mode (Figure 6.5 (a)) andD2in boost-mode (Figure 6.5 (b)). This power consumption can be reduced by lowering the dead-time of the pairs (Q1,Q3) and (Q2,Q4). At higher power levels the main contributor of the power consumption is the inductor due to higher current levels.
The converter efficiency has been measured for different input powers and output voltages. The input voltage of the converter is the voltage characteristic of the fuel cell, i.e. the higher power the lower input voltage. The converter input power is varied between 100 W to 1000 W for an output voltage of 30 V, 36 V, 42 V, 48 V, and 54 V.
The converter will therefore operate both in buck and boost mode. The results can be seen in Figure 6.6. The measurements in Figure 6.6(b) coincide well with the theoretic efficiency calculation in Figure 6.6(a).
6.3. Conclusion
100 200 300 400 500 600 700 800 900 1000 0
5 10 15 20
Output voltageVo = 30V
Converterloss[W]
Fuel cell power [W]
(a) PCin
PCo PQ1 PQ2 PQ3 PQ4 PD1 PD2 PL
100 200 300 400 500 600 700 800 900 1000 0
5 10 15 20
Output voltageVo = 48V
Converterloss[W]
Fuel cell power [W]
(b) PCin
PCo
PQ1
PQ2
PQ3
PQ4 PD1 PD2 PL
Figure 6.5: Loss inside the converter. (a) Output voltageVo = 30 V. (b) Output voltage Vo = 48 V.
6. FUEL CELL CONVERTER
100 200 300 400 500 600 700 800 900 1000 95.5
96 96.5 97 97.5 98 98.5 99 99.5
100 Simulation
Fuel cell power [W]
ConverterefficiencyηCon,FC[%]
(a)
Vo = 30V Vo = 36V Vo = 42V Vo = 48V Vo = 54V
100 200 300 400 500 600 700 800 900 1000 95.5
96 96.5 97 97.5 98 98.5 99 99.5
100 Measurements
Fuel cell power [W]
ConverterefficiencyηCon,FC[%]
(b)
Vo = 30V Vo = 36V Vo = 42V Vo = 48V Vo = 54V
Figure 6.6: Efficiency of the converter for different input powers and output voltages.
(a) Simulation results. (b) Experimental results.
78
7 Drive System
In this chapter the drive system is modeled. The drive system is here defined as the electric machines, which are used for propulsion, and the inverters which supply the machines. The models are used for calculating the power transferred through the electric machines and inverters.
7.1 ELECTRIC MACHINE
As for the case of the fuel cell and battery, many types of electric machines exist. The most suitable machine for the propulsion of a vehicle is a trade of among several parameters, but the machine should perform well in all or most of the following items [11, 93, 96]:
• High torque and power density
• High torque at low speed for acceleration and climbing
• High intermittent torque for short durations
• A wide speed range with sufficient torque capability
• A high efficiency in the whole area of the torque-speed-curve, in both motor and generator mode
• High reliability and robustness
• Low cost
Due to the requirement of high efficiency and reliability, usually only AC-motors are considered as DC-motors suffer from these issues. Three types of AC-machines are here considered for the propulsion. The small review is based on [11, 85, 88, 93, 96].
Induction Machine - IM This machine is a well known and proven technology, which is widely available. It has a high reliability, can operate in a hostile en-vironment, requires low maintenance, and has low cost. The drawback of this machine is a low efficiency and low power factor.
Permanent Magnet Synchronous Machine - PMSM This machine is also a proven technology. The PMSM has a high torque/power density, a high efficiency, and easily removal of heat due to the lack of rotor currents. Due to the magnets in-side the rotor this machine is more expensive to manufacture than the IM, the magnets can be destroyed due to over currents or too high temperature, and an uncontrolled rectification can take place if the speed becomes too high. Be-cause of the magnets this machine also has a short constant power region, which means that it might be necessary to use field weakening in order to obtain a high speed.
7. DRIVE SYSTEM
Switched Reluctance Machine - SRM This machine has a simple and robust struction, and is therefore relatively cheap to produce. The SRM has a long con-stant power region, but suffers from high acoustic noise, high torque ripple, and a poor power factor which results in high inverter current ratings.
Due to the surroundings where the truck will operate, i.e. parks, and cemeteries, etc., it is important that the machine is silent, which eliminates the SRM. The GMR Truck is a low speed vehicle, which means that it is not necessary with a long constant power region. Due to the high load capability (up to 1000 kg) and the requirement of being able to climb steep roads (15 %slope) a high torque is required in the whole speed range. These issues and the fact that the physical space is limited in the truck favors the PMSM when compared to the IM. It is assumed that the fuel cell stack will be more costly than the electric machines. For this reason it is important with a high efficiency, in order to decrease the fuel cell power rating. The high efficiency again favors the PMSM, and therefore this is selected.
Modeling
AC machines are often modeled in the dq-reference frame, which rotates with the velocity of the stator field. Thereby the sinusoidal currents, voltages, and flux linkages become constant, which is simpler. The dq-model of a PMSM is given by [62]:
vd =Rsid+Lddid
dt −ωeLqiq [V] (7.1)
vq =Rsiq+Lqdiq
dt +ωeLdid+ωeλpm [V] (7.2) τe = 3
2 P
2 (λpmiq+ (Ld−Lq)idiq) [Nm] (7.3) τe =Js
dωs
dt +Bvωs+sign(ωs)τc +τs [Nm] (7.4) pEM = 3
2(vdid+vqiq) [W] (7.5)
ps =ωsτs [W] (7.6)
ωe = P
2ωs [rad/s] (7.7)
80
7.1. Electric Machine
where vd [V] D-axis voltage vq [V] Q-axis voltage id [A] D-axis current iq [A] Q-axis current
pEM [W] Electric power of the machine τe [Nm] Electromechanical torque τs [Nm] Shaft torque
ωe [rad/s] Electric angular velocity ωs [rad/s] Shaft angular velocity Rs [Ω] Phase resistance Ld [H] D-axis inductance Lq [H] Q-axis inductance
Bv [Nms/rad] Viscous friction coefficient τc [Nm] Coulomb friction
λpm [Vs/rad] Flux linkage of the permanent magnet P [−] Number of poles
The dq-model in Equation (7.1)- (7.7) includes resistive loss and mechanical loss.
The core loss, which becomes higher at high speeds are neglected in order to simplify.
Efficiency
The efficiency is defined as ηEM =
ps
pEM ps ≥0
pEM
ps ps <0 [−] (7.8)
In order to investigate the efficiency, the theoretic efficiency of a motor with pa-rameters in Table 7.1 is calculated.
Stator resistance Rs 9.62 mΩ
D-axis inductance Ld 28.7μH
Q-axis inductance Lq 47.2μH
Permanent magnet flux linkage λpm 9.71 mWb
Poles P 12
Moment of inertia Js 18.2·10−3kgm2 Viscous friction coefficient Bv 1·10−3Nms/rad
Coulomb friction τc 0.1 Nm
Table 7.1: Parameters of PMSM used for efficiency investigation.
The efficiency contour of the machine with the parameters in Table 7.1 is shown in Figure 7.1. The efficiency is calculated when using Id = 0 control. This control property does not utilize the reluctance torque due the difference in the inductances in the d-axis and q-axis, but this control property is simpler. It is seen that the efficiency increases with higher shaft angular velocity and torque. However, if the core losses were taken into account, the efficiency would probably be lower at high speed, as they are proportional with the speed squared [82].
7. DRIVE SYSTEM
101010 20 20
20
30 30
30
30 30
40 40
40
40 40 40
50
50
50 50 50 50
60
60
60 60 60 60
70
70
70 70 70 70
80
80
80
80 80
80 90
90
Shaft angular velocityωs[rad/s]
Shafttorqueτs[Nm]
0 50 100 150 200 250
1 2 3 4 5 6 7 8 9 10 11
Figure 7.1: Efficiency plot of a PMSM forId= 0control. The labels in the contour lines displays the efficiency in%.
The maximum efficiency of the PMSM used for illustration is ηEM = 90.4 %.
At the maximum speed ωs,max = 279 rad/s and torque τs,max = 11 Nm the ma-chine has a power factor angle of φEM(τs,max, ωs,max) = 0.53 rad and efficiency of ηEM (τs,max, ωs,max) = 0.90.