Control of the Z-Source Inverter for FCHEV with

the Battery Connected to the Motor Neutral PointMiaosen Shen

Siemens VDO Automotive, Miaosen.shen@siemens.com

Stefan Hodek University of Kaiserslautern,

Germany,

Fang Z. Peng Michigan State University,

fzpeng@egr.msu.edu

Abstract: The Z-source inverter provides a simple single stage solution for fuel cell-battery hybrid electric vehicles (FCHEV). It utilizes an exclusive Z-source (LC) network to link the main inverter circuit to the fuel cell (or any dc power source). This paper presents the control of the Z-source inverter for FCHEV with the battery connected to the motor neutral point. By controlling the shoot-through duty cycle and modulation index, the inverter can produce any desired output ac voltage. By controlling the shift of the reference signal of the PWM signal, the undesirable operation modes of the Z-source inverter can be eliminated and the state of charge (SOC) of the battery can be controlled. Therefore there is no need for a separate dc/dc converter. These facts make the Z-source inverter highly desirable for use in hybrid electric vehicles, as the cost and complexity is greatly reduced when compared to traditional inverters. This concept and the control method will be demonstrated by simulation results.

I. INTRODUCTION

Fuel cells as one of the promising clean energy sources are considered as possible alternative power source for hybrid electric vehicles. Fuel cell vehicles (FCVs) have generated interest among government, environmentalists, and consumers. A FCV promises zero emission benefits of a battery-powered pure electric vehicle, with the driving range and convenience of a conventional internal combustion engine vehicle.

The recently presented Z-source inverter [1] is a suited converter for FCVs. The Z-source inverter employs a LC-network to connect the fuel cell to the inverter. This unique network allows the Z-source inverter to use shoot-through state and hence to boost the inverter dc-rail voltage above the fuel cell output voltage. The benefits of the Z-source inverter are lower costs, lower complexity, higher reliability and higher efficiency compared to traditional inverters or traditional boosted inverters for FCV.

For a vehicle, the demanded propulsion energy is ever changing. Therefore, a battery or a super capacitor is usually used as a secondary energy source to handle the load dynamics and the regenerative braking. In traditional systems, an extra dc/dc converter is usually used to interface the battery and the fuel cell, which increases the cost and system

complexity. With the Z-source inverter, this dc/dc converter can be eliminated. A configuration with a battery connected to the neutral point of the traction motor is proposed in this paper. With this configuration, only a Z-source inverter is needed, furthermore, the undesirable operation modes can be eliminated by effective control.

II. Z-SOURCE INVERTER AND OPERATION MODES

By using a unique LC network shown in Fig.1, the Z-source inverter can handle shoot through states when both switches in the same phase leg are on, and it can boost the output voltage by intentionally inserting some shoot through states. The detailed circuit analysis and characteristic are presented in [1], where the inductor current is assumed to be high enough that only two operation modes shown in Fig. (a) and (b) will appear, where the input diode is always assumed to be on during non-shoot through states. During non-shoot through state, assuming the current to the inverter bridge is ii,and the current through both inductors are the same and equal to iL, the current through the input diode, id, can be expressed by

02)( 2111 iLiLLCLd iiiiiiii . (1)

Fig.1. The Z-source inverter.

14851-4244-0655-2/07/$20.00©2007 IEEE

iL1

iL2

+ +

_ _vc1 vc2

+

_vo

off

(a) shoot-through mode

iL1

iL2

+

_

vi

+ +_ _vc1 vc2

+

_V0

iiiC1iC2

on

id

(b) non shoot-through mode

Fig. 2. Z-source inverter basic operation modes

As can be seen from (1), the diode will conduct only when the inductor current is higher than half of the load current. However, this condition is not always met. Under certain operation conditions, there could be more operation modes [2]. These new operation modes might cause higher current stress to the switches, and might increase the output harmonic.

III. EXISTING FCHEV CONFIGURATIONS USING THE Z-SOURCE INVERTER

For FCHEV, there are two power sources (fuel cell and battery) and one load, the power conditioner has to be able to interface all of them and control the power flow. Literature [5] proposed a configuration connecting a high voltage battery directly in parallel with one of the Z-source capacitor as shown in Fig.3. In this configuration, the inverter uses the shoot through duty ratio and modulation index to control the output voltage and the battery state of charge, also it is able to eliminate the undesirable operation modes [6]. In this configuration, the battery voltage is limited by the voltage rating of the inverter bridge during when the fuel cell is turned off and the inverter is running with 50% shoot through duty ratio. During this condition, the fuel cell is bypassed by the diode D2 and the voltage across the inverter bridge is twice of the battery voltage. Thus the battery voltage is limited and so is the output voltage range.

Another configuration is to use an extra dc/dc converter to interface the battery and one of the Z-source capacitors as shown in Fig.4. This configuration improves the performance at the cost of an extra dc/dc converter.

M

L1

L2

Batteryfuel

cellstack

VcVo ++__

D1

D2

C1

C2

Fig.3. Configuration with battery connected in parallel with one of the capacitors

Fig.4. Configuration using a dc/dc converter to interface the capacitor and battery

IV. PROPOSED SYSTEM CONFIGURATION AND CONTROL

Traction drive systems with the battery connected to the neutral point of the motor has been reported in [3, 4]. Based on these concepts, the Z-source inverter for FCHEV with battery connected to the neutral point of the motor is proposed as shown in Fig.5. This converter can be considered as combination of two converters: a Z-source inverter and a buck converter with the battery as the load as shown in Fig.6. Equivalently, the duty ratio of the buck converter is controlled by the average value of the reference signals, and shift the reference signals will change the voltage ratio of the capacitor voltage and the battery voltage. Therefore, there are three control freedoms in total, the shoot through duty ratio, D0, themodulation index, M, and the shift of the PWM reference signal, Vs. By shifting the reference signals, one can control the current to the battery to charge/discharge it.

(a) Configuration of the inverter system

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(b) Basic PWM scheme

Fig. 5: Configuration of the FCHEV and PWM scheme

Fig. 6: Equivalent buck converter

Pin

0

84

168

248

336

420

0 100 200 300Current (A)

Vol

tage

(V) (io, vo)

Fig.7. Fuel cell VI curve

There are basically two cases that have to be considered to control this configuration:

In the first case, the fuel cell is turned on. Assuming that the battery voltage is Vb, with the shift control, from the buck converter stand point, the capacitor voltage is determined by

bs

c VVD

DV

0

0

1)1(2

. (2)

On the other hand, based on the Z-source inverter characteristic, the relationship between the fuel cell voltage and the capacitor voltage is

cVDD

V0

00 1

21, (3)

which also determines the fuel cell power based on the fuel cell polarization curve for a given fuel flow rate as shown in Fig.7. At the same time, the output ac voltage to the motor can be controlled by the modulation index:

22ˆ 0VV

Mv cac . (4)

With this two power flows being controlled, the battery power will automatically match the difference of the two, thus the state of charge of the battery can be controlled.

In the second case the battery is fully charged and the vehicle is in low speed cruising mode, the fuel cell is turned off and bypassed by diode D, the vehicle becomes a battery powered HEV. In this case, the shoot-through duty ratio is defined by controlling the current through the inductors L1 and L2. According to [6] D0 should be adjusted to about 0.5. The relationship of the output voltage and modulation index is

22ˆ C

ac

VMv , (5)

where VC is the capacitor voltage. Reference signal shift may be needed to limit the maximum voltage across the switching devices which equals to 2VC. Assuming that the battery voltage is Vb, and the voltage rating of the inverter bridge is Vinv, to limit the voltage across the inverter lower than the rating, the capacitor voltage has to be less than half of Vinv. From (2), with shoot through duty ratio of 0.5 and battery voltage of Vb, the capacitor voltage is

25.01 inv

bs

c

VV

VV . (6)

Thus the reference shift Vs should be

5.02

inv

bs V

VV . (7)

Also, based on [6], the inductor current can be controlled to any desired value by controlling the shoot through duty ratio.

Besides these basic functions, this configuration can also eliminate undesirable operation modes [2, 6]. In the first case, the fuel cell power can be controlled independently, therefore, one can increase the fuel cell power to charge the battery so that the sum of the two inductor current will be higher than the load current and the undesirable operation modes can be eliminated. For the second case, the inductor current can be controlled to any desired value, one is able to eliminate the undesirable modes too.

The output voltage range is an important factor determining the performance of the inverter. To maximize the

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available output voltage, the voltage across the inverter bridge should be the rated value, Vinv, given the capacitor voltage is Vc, the fuel cell voltage should be

invs

binvco V

VD

VDVVV

0

0

1)1(42 . (8)

To get this relationship of the capacitor voltage and fuel cell voltage, based on (3), the shoot through duty ratio should be

invs

b

VVD

VDD

)1()1(21

0

00 . (9)

Therefore the shift of the reference can be expressed as a function of the battery voltage and the shoot through duty ratio in order to keep the inverter bridge voltage to its allowable level:

012D

V

VV

inv

bs (10)

Assume that the maximum constant boost control [11] is used, the available modulation index under this condition is

)211(3

23

)1(200

0

inv

bs

V

VDD

VDM . (11)

Thus the available output voltage is

invinv

binvout V

V

VDDVMV *)211(

31*

21

00 (12)

Therefore, the available output voltage is related to the shoot through duty ratio as well as the battery voltage as shown in Fig.8.

Compare to the other two configurations shown in Fig.3-4, the obtainable output voltage range is higher than the first configuration and lower than the second configuration with the same inverter bridge voltage rating provided a proper battery is chosen. For this configuration, there is no extra dc/dc converter is needed. However, there might be some dc current flowing through the machine, which increases the motor copper loss, therefore the machine needs to be oversized a little bit. Thus the cost of this configuration is also in between of the other two configurations.

V. SIMULATION RESULTS

In order to verify the validity of the proposed configuration and the analysis, simulation is conducted. The parameters of the inverter in simulation are L1=L2=160µH,C1=C2=1000µF, switching frequency of 10 kHz. In simulation 1 (Fig. ) the fuel cell outputs a constant power of 30kW. The motor power is changed from 24kW to 39kW. To handle the load dynamics while keeping the fuel cell power constant, the battery gets charged and discharged respectively. As can be seen from the simulation results, the fuel cell voltage and

current maintains after the step change of the load, and the battery current has a step change to meet the load power.

In simulation 2 (Fig. ) a low output power and low motor speed is simulated, usually the load power factor is relatively low for induction machine under this operation condition. The load power factor used in simulation is cos =0.256, D0=0,M=0.2, Vo=350V, Vb=175V, switching frequency of 10 kHz. Due to the low power factor a self-boost would occur and force shoot through state to happen [2]. By introducing a small amount of reference signal shift, this can be avoided as shown in Fig.10. The inverter input voltage is constant, which means that no self-boost is present. Also, the motor current is pure sinusoidal with a dc element, which is the current charging the battery to avoid undesirable operation modes.

0.20.30.40.50.60.7

00.1

0.20.3

0.4

0

0.1

0.2

0.3

0.4

0.5

0.6

shoo

t thr

ough

dutyra

tioD0

Vb/Vinv

outp

ut p

hase

pea

k vo

ltage

/Vin

v

Fig. 8. Obtainable output voltage versus shoot through duty ratio and battery voltage.

In simulation 3 the battery has to be discharged. Therefore the fuel cell is turned off and the load is still in low power factor condition. The parameters used in simulation are power factor cos =0.256, V0=350V, D0=0.5, M=0.25, Vb=160V.The inverter bridge is assumed to be rated for 400V. When the fuel cell is turned off, the battery has to supply the motor power and hence gets discharged. As shown in the simulation results in Fig.11, the output voltage and current are pure sinusoidal, the current has a negative dc bias, which is the current discharging the battery. Also the voltage across the inverter bridge is well controlled.

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Fig. 9: Simulation results of load dynamics

VI. CONCLUSION

A new configuration using the Z-source inverter for fuel cell hybrid electric vehicles is proposed in this paper with the battery connected to the motor neutral point. With this configuration, there are three control freedoms: the modulation index, shoot through duty ratio, and reference signal shift. The inverter is able to control the output power as well as the battery SOC with these control freedoms. The configuration and analysis are verified with simulation. Compare to other configurations, the proposed configuration provides a medium performance solution with medium cost.

ACKNOWLEDGMENT

This work was partially supported by the National Science Foundation under Grant 0424039.

Fig. 10: Simulation results of a low power factor

Fig. 11: Simulat fuel cell power ion results of zero

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