Development of High Efficiency Current-fed Quasi-Z-source Inverter for HEV Motor Drive

Dong Cao, Ford Motor Company,

Dearborn, MI, USA caodong@ieee.org

Qin Lei, and Fang Z. Peng Department of Electrical and Computer Engineering

Michigan State University, East Lansing, USA

Abstract— This paper presents the development and high efficiency design considerations of a current-fed quasi-Z-source inverter for hybrid electric vehicle (HEV) motor drive using reverse-blocking (RB) IGBT. In order to overcome the unidirectional power flow and the voltage buck operation inability problems of traditional current-source inverter for motor drive applications, a current-fed quasi-Z-source inverter (CF-qZSI) has been proposed. By adding a diode and a LC network, CF-qZSI is able to achieve bidirectional power flow and voltage buck operation function. In order to achieve high efficiency for CF-qZSI, proper modulation method selection and careful passive components design are needed. The space vector pulse width modulation (SVPWM) method for this inverter to achieve proper voltage gain and less switching loss is discussed. The active device and passive components stress are analyzed. A high efficiency coupled inductor for CF-qZSI is designed and developed. A 15 kW prototype of CF-qZSI is built, experimental results with the efficiency up to 98% are provided.

I. INTRODUCTION With the development of automotive industry, the high

efficiency, high power density and high reliability inverter is required for HEV traction drive. Voltage source inverter (VSI) has been used for HEV motor drive widely, however, several concerns have been raised which limits the VSI in future HEV motor drive application [1, 2]. The pulse modulated output voltage, huge input capacitor bank and potential shoot-through risk of the VSI may cause motor insulation degradation, bearing failure, EMI, cost and reliability problems [3]. The current source inverter (CSI) have been used for medium voltage motor drive for many years due to its high efficiency, sinusoid output voltage and inherent shoot-through protection capability [4-12]. Instead of the bulky dc-link capacitor in VSI, an inductor and ac filter capacitors are utilized in CSI, which is much smaller in size. But due to the inherent boost features of CSI, a buck converter has to be added in between the battery and the CSI to operate the motor at low speeds and to charge the battery during dynamic breaking [3, 13]. Also, due to the bipolar voltage stress of the switching devices of CSI, traditional IGBT with another series diode blocking positive and negative voltage has to be used, which increase system conduction loss and limits its application for HEV motor drive.

In order to overcome the disadvantages of traditional VSI and CSI, voltage-fed/current-fed Z-source inverter (VF-ZSI/CF-ZSI) has been proposed [14]. By adding a diode and a LC network to the traditional VSI, the VF-ZSI is able to boost the input voltage utilizing the shoot-through zero state. The boost dc-dc converter used in front of the traditional VSI to step-up the battery voltage in HEV power train can be eliminated. The total system cost is then reduced accordingly; the utilization of the shoot-through zero state also makes the ZSI less vulnerable to EMI noise and more reliable. The control and modulation of ZSI has also been investigated thoroughly in terms of boost voltage gain and output voltage quality [15-24]. The ZSI has been used for many applications, such as fuel cell-battery HEV, photovoltaic (PV), and uninterrupted power supply (UPS) [17, 25-33]. But the traditional VF-ZSI cannot operate at regenerative mode to charge the battery due to the diode and have problems to output low voltage [34]. Several VF/CF quasi-ZSIs (VF-qZSI/CF-qZSI) have been proposed recently with more features [35, 36]. With continuous input current, VF-qZSI is especially suitable for PV applications [37, 38]. Reverse-blocking IGBT (RB-IGBT) with bipolar voltage blocking capability has been developed recently, and it has been applied for matrix converter and CSI applications [39-46]. By using RB-IGBT, the total system cost and complexity of matrix converter and CSI can be reduced. The CF-qZSI with voltage buck-boost and regenerative capability using RB-IGBT has been used for HEV motor drive [47, 48]. The basic operation principle and features of CF-qZSI has been provided and verified. The detailed CF-qZSI development and design consideration in terms of proper PWM strategy selection, active device stress analysis, and passive components optimal design consideration are not covered in the literature.

This paper focuses on the development and high efficiency design considerations of CF-qZSI for HEV motor drive applications. Firstly, the output voltage gain control method of CF-qZSI is discussed. Instead of using the shoot-through zero state to boost the input voltage in VF-ZSI, the CF-qZSI utilizes the open-circuit zero state to step down the input voltage. The corresponding simple, constant and maximum current boost control can be proposed in accordance with the simple, constant and maximum voltage boost control in VF-

978-1-4673-4355-8/13/$31.00 ©2013 IEEE 157

ZSI. With different control methods, the output voltage and the device stress are different. The implemented SVPWM using the constant control method with less switching loss and passive components ripple is also discussed. Then, the active device stress analysis and total device stress ratio with different controls are provided and summarized. The passive components design including the capacitor, diode selection and coupled inductor design is addressed. Finally, the experimental results of CF-qZSI operated in constant torque mode and constant power mode are provided with efficiency up to 98.2%.

II. OPERATION PRINCIPLE AND PWM METHOD SELECTION

Fig. 1 shows the main circuit structure of the proposed current-fed quasi-Z-source Inverter with continuous input current. Six RB-IGBT S1 ~ S6 are used as the main switches, and the input inductor L3 is coupled with the inductors L1 and L2 of the Z-source network. The current of the L1, L2 and L3 are all continuous. The ∆ connected capacitor filter is at the output side, which is the same as the traditional current-source inverter. There are nine switching states for traditional current source inverter, while eleven possible switching states can be achieved for the CF-qZSI inverter. Due to the quasi-Z-source network, two extra open zero states with S1, S3, and S5 opened or S2, S4, and S6 opened can be realized. These two open zero states are forbidden in the traditional current source inverter, since a close loop is always required for a current source, otherwise switching device voltage breakdown will happen. The Z-source network makes these two open zero state possible with additional current loop. These open zero states provides the unique buck-boost feature to the inverter. Fig. 2 shows the CF-qZSI equivalent circuits of open zero state and the traditional switching state viewed from the dc-link.

inV

1S

4S

3S

6S

5S

2S

ab c M/G

3L inI

ai

1C

1L 2C

2L

1D

aC

bCcC

Fig. 1. RB-IGBT based CF-qZSI with continuous input current main circuit

structure for motor drive application.

(a) (b)

Fig. 2. Equivalent circuit of CF-qZSI viewed from dc-link when the inverter bridge is in (a) State I: open zero state (b) State II: one of the nine traditional

switching states,

Fig. 2(a) shows the state I, which is the open zero state. During state I, the inverter bridge is equivalent to an open circuit. Fig. 2(b) shows the state II, which is one of the nine traditional switching states, including six active states and

three short zero states. During state II, the inverter bridge can be considered as a voltage source. During one switching period, assume that opD and nopD is the duty ratio of the state I and state II. And

1op nopD D+ = (1) Due to the circuit symmetry, we have

1 2L LI I= (2) And during the state II, we have 1 2i in L Li I I I= + + , as

shown in Fig. 2(b) According to the capacitor C1 and C2 charging balance, we have,

( ) ( )1 2 0L in op L nopI I D I D+ + − = (3)

( ) ( )2 1 0L in op L nopI I D I D+ + − = (4) By solving the above equations, we have

1 21 2

opL L in

op

DI I ID

= =−

(5)

1 21

1 2i L L in in

opi I I I I

D= + + =

− (6)

ii can be considered as the input current for a current-fed inverter with SPWM control strategy, and M is the modulation index, the output line current peak value xi (x=a, b, or c) can be written as,

3 32 2 1 2

x i inop

Mi Mi ID

= =−

(7)

The output line RMS current _l rmsI can be written as,

_3

1 22 2 2x

l rms inop

i MI ID

= =−

(8)

According to the input and output power balance, we have,

3 cos2 2ll x

in inv iV I ϕ= (9)

Where llv is the output line to line voltage peak value, cosϕ is the power factor.

By plug in (7) into (9), we have,

( )4 1 23 cos

opll in

Dv V

M ϕ−

= (10)

According to (10), we can determine the output voltage value. And according to (5) and (8), we have

1 2 _2 23

L L op l rmsI I D IM

= = (11)

Similarly to a voltage source inverter by using a sinusoid voltage reference for the carrier based PWM method, the current source inverter can use a sinusoid current reference instead. Therefore, the three carrier-based control methods for traditional VF-ZSI, simple, constant, and maximum boost control methods can be used for the CF-qZSI [15-16], except the voltage reference signals are replaced with current reference signals.

158

Table I Comparison of normalized output voltage and normalized inductor currents with three different control strategies

opD values due to M ll

in

vV

versus M ll

in

vV

versus opD _

in

l rms

II

versus opD 1

_

L

l rms

II

versus opD

Simple boost 1opD M= − 4 2 1

3cosMMϕ

−⎛ ⎞⎜ ⎟⎝ ⎠

4 1 23cos 1

op

op

DDϕ

⎛ ⎞−⎜ ⎟−⎝ ⎠

2 6 1 23 1

op

op

DD

⎛ ⎞−⎜ ⎟−⎝ ⎠

2 63 1

op

op

DD

⎛ ⎞⎜ ⎟−⎝ ⎠

Constant boost 312

opMD = −

4 3 13cos

MMϕ

⎛ ⎞−⎜ ⎟⎜ ⎟⎝ ⎠

2 3 1 23cos 1

op

op

DDϕ

⎛ ⎞−⎜ ⎟−⎝ ⎠

1 221

op

op

DD

⎛ ⎞−⎜ ⎟−⎝ ⎠

21

op

op

DD

⎛ ⎞⎜ ⎟−⎝ ⎠

Maximum boost 3 312

opMD

π= −

4 3 33 cos

MM

ππ ϕ

⎛ ⎞−⎜ ⎟⎜ ⎟⎝ ⎠

2 3 1 2cos 1

op

op

DDπ ϕ

⎛ ⎞−⎜ ⎟−⎝ ⎠

3 2 1 21

op

op

DDπ

⎛ ⎞−⎜ ⎟−⎝ ⎠

3 21

op

op

DDπ

⎛ ⎞⎜ ⎟−⎝ ⎠

Fig. 3 shows the three current boost control reference

signals for CF-qZSI to generate open zero state with different voltage gain, or different voltage step down ratio. Similar to the voltage boost control methods for VF-ZSI, three different current reference signals are used for the current boost control. In order to generate open zero state, the simple boost control uses two straight lines as reference, the maximum boost control uses the three phase current reference envelop as reference, the constant boost control utilizes two sinusoid envelop curve as reference, as shown in Fig. 3. These three current references for current boost control are same formula with the three voltage boost control in [15-16]. Hence, the

opD relationship with M of these three current boost control methods are the same with the shoot-through duty cycle relationship with M in the voltage boost control methods, which can be summarized in the second column of Table I. By plugging in these three opD and M relationships to (8), (10), and (11), we can derive the normalized output voltage relationship with opD , M, and normalized inductor current relationship with opD , as shown in Table I. Fig. 4 and Fig. 5 shows the illustration of the normalized voltage and current in Table I assuming power factor equals to 1. The input voltage is chosen as the base voltage, the output voltage gain and voltage step down feature of three different control methods can be shown clearly in Fig. 4(a). As shown in Fig. 4(a), the purple dot line shows the CF-qZSI output voltage capability without any open zero state, which is the same as the traditional CSI. The red solid line, the blue dash line and the green dash dot line shows the output voltage capability of simple boost control, constant boost control and maximum boost control respectively. When the voltage gain is larger than two, the diode 1D in the Z-source network will conduct. Therefore, region A is forbidden region if the diode is used in the Z-source network. If the diode 1D is replaced by an active switch, the CF-qZSI is able to operate at region A. Region B is the motoring region, the peak output voltage is from 0 to 2 inV . Region C is regenerative region. Although maximum boost control is able to output the minimum voltage with certain open zero duty cycle as shown in Fig. 4(b), it is not usually selected during the operation. Similar to the maximum boost control in VF-ZSI, the maximum boost control for CF-qZSI will also suffer low frequency current ripple, which is not preferred for practical operation. And constant boost control is usually selected with lower voltage gain with certain open state duty cycle as shown in Fig. 4(b) and less inductor current stress as shown in Fig. 5. When opD equals to 0.5, the input dc current is zero, only circulating current exists in the circuit.

Simple Boost

Maximum Boost

Constant Boost

*opI

*opI

*opI

*aI

*cI *

bI

02

π 56

π3

π 23

π6

π θ

Fig. 3. Three current boost control methods with different voltage gain.

2−

0

4

2

0.2 0.4 0.6 0.8 1 1.15

Simple Boost

Maximum Boost

Constant Boost

W/O open zero state

Region A

Region B

Region C

M

ll

in

VV

Simple Boost

Maximum Boost

Constant Boost

0.20.10 0.3 0.50.4opD

ll

in

VV

1.5

1

0.5

0

(a) (b)

Fig. 4. Normalized peak output line-to-line voltage at three different control methods. (a) versus modulation index M (b) versus open zero state duty cycle

Dop.

1.5

0.5

2

0

1

0 0.20.1 0.3 0.50.4opD

_

in

l rms

II

Simple Boost

Maximum Boost

Constant Boost

1

0.5

1.5

00.20.10 0.3 0.50.4

1

_

L

l rms

II

Simple Boost

Maximum Boost

Constant Boost

opD (a) (b)

Fig. 5. (a) Normalized input inductor current stress versus Dop (b) Normalized Z-source inductor current stress versus Dop.

Fig. 6 shows the generated PWM control signal using two extra open zero state current reference in one switching cycle. ia

*, ib* and ic* are the three current reference signal, ip* and in*

are the two open zero state reference signal. The case shown in Fig. 6 can represent one of the switching states of simple boost control or constant boost control method. The maximum boost control replaces all the traditional short zero states with the open zero states, which can be considered as a special case of Fig. 6 when 0 0T = . As shown in Fig. 6, the open zero state

opT is inserted in to the traditional short zero state 0T , which increases the device switching times. By using the SVPWM

159

method, all the switching vector positions can be selected, to achieve better harmonic performance and minimum switching loss. Fig. 7 shows the case by combining two traditional zero state 0T as shown in Fig. 6 to one state, and it is inserted into the middle of the active vector 1T and 2T . In the real implementation, the PWM method shown in Fig. 7 is recommended with relatively low switching loss, the detailed analysis of the harmonic and switching loss benefits for this switching pattern has already been summarized in [49].

1S

2S

3S4S

5S6S

*ai

*bi

*ci

*pi

*ni

1T 2T0T 0T 0T 2T 1T 0T 2Top

2Top opT

Fig. 6. Carrier based method PWM control using two extra open-state zero state reference to generate open zero state that are inserted into the traditional

zero states.

2T 2T0T 0T1T 1T 2opTopT2opT

Fig. 7 PWM method by combining and selectively placing the zero vector

III. ACTIVE DEVICES DESIGN GUIDELINES In order to select the active switching device properly with

different control methods, the device voltage and current stress should be estimated. In this section, the switching device voltage stress, current stress is analyzed and summarized. Since the input of the CF-qZSI is the battery in HEV traction drive application, the input voltage is selected to be the voltage base for the device voltage stress analysis. And the output voltage is determined by the input voltage and inverter voltage gain. And for HEV traction drive, the current of the inverter is determined by the motor, therefore the rms value of the load current is selected to be the current base for the device. The device current stress should also be selected according to the highest current for the motor drive. At low low speed, the motor operates at constant torque mode, and the device peak current stress is determined during this mode. And during the constant torque mode, the CF-qZSI operated at buck mode with zero open state. Table II summarizes the main switching devices (RB-IGBT) as well as the z-source network diode voltage and current stress. The switch current stress is the average device current during one switching period. And the switch peak current stress is the device peak current value during one switching period. The inductor current ripple is not included in the peak current stress in Table II. In the practical design, the inductor current ripple should also be considered.

According to Table II, the switch and diode voltage stress during the buck mode is 2 inV . And according to Fig. 4(a), during the boost mode, the peak output line-line voltage is also 2 inV , which means the peak voltage appears on the device is 2 inV± since the output voltage could be positive or negative. Therefore, reverse blocking switching device such as RB-IGBT is required. The voltage spike across the device during the switching should also be considered during the practical design, which is determined by the device internal stray inductance, the output capacitor busbar stray inductance, and the device switching turn off di/dt. The RB-IGBT voltage rating selection should consider 2 inV plus the device turn off voltage spike. Fig. 8 shows the diode average and peak current versus open-state duty cycle with three control methods. When the open state duty cycle equals to 0.5, the device has the peak current stress. This means the device current rating or thermal design should be selected according to this case with 0.5 open state duty cycle.

Table II Switching Device and Diode 1D Stress Summary

versus opD versus M

Switch and diode voltage stress, 2 inV 2 inV

Switch average current stress _2

3l rmsI _

23

l rmsI

Diode average current stress _2

1op

l rmsop

D ID−

( )_

2 2 3

3l rms

MI

M

−

Switch and diode peak current stress _

21

l rmsop

ID−

_2 2 1

3l rmsI

M

0.20.10 0.3 0.50.4opD

1

0.5

1.5

0

Simple Boost

Maximum Boost

Constant Boost

_D ave

lrms

II

0.20.10 0.3 0.50.4opD

2.5

1.5

3.5

1

2

3

Simple Boost

Maximum Boost

Constant Boost

Dpk

lrms

II

(a) (b)

Fig. 8 Diode average and peak current stress versus open zero state duty cycle opD with three control methods.

IV. PASSIVE COMPONENTS DESIGN GUIDELINES The current stress and voltage stress of the Z-source

network passive components and input inductor also needs to be analyzed to design the proper capacitor and inductor.

A. Z-source Capacitor Design Since the two Z-source capacitor is on dc side, and the

inductor voltage under steady state is zero, the voltage stress of the capacitor C1 and C2 is the input voltage inV . In order to select the capacitor correctly, the capacitor rms current should be calculated. The Z-source capacitor current is near zero during the boost operation mode without open zero state, so only the current stress under buck mode with open zero state is considered. According to Fig. 2, the capacitor C2 current is

160

1in LI I+ , during the open zero state, and 2LI− during other states. Since inductor currents are the same due to (2), we have

( ) ( )( )2 2_ 1 11C rms op in L op LI D I I D I= + + − − (12)

According to (5) ,(8), and (12), we have

( )__

2 2 13

l rmsC rms op op

II D DM

= − (13)

According to the opD value versus M of the three control methods in Table I, we can derive the _C rmsI value versus

opD of the three control methods as shown in Table III. The capacitance requirement can be calculated as,

1C

L in Sop

VI I C fDΔ+ = (14)

Where Sf is the switching frequency. Plug in (5) and (8)into (14), we have,

( ) _1 2 2

3op op l rms

C S

D D ICM V f

−=

Δ (15)

Plug the M and Dop relationship in Table I, and assume the capacitor voltage ripple is about 10% of the Vin we can derive the capacitance requirement versus Dop. Table III summarizes the capacitor current stress as well as the capacitance value requirement versus Dop under three different control methods.

Table III Capacitor current stress and capacitance selection under three control methods

_C rmsI versus opD C versus opD

Simple boost _2 213

l rms op

op

I DD−

_2 2310%

l rmsop

in S

IDV f

Constant boost _21

opl rms

op

DID−

_210%

l rmsop

in S

IDV f

Maximum boost _3 21

l rms op

op

I DDπ −

_3 210%

l rmsop

in S

IDV fπ

Fig. 9(a) shows the capacitor rms current versus Dop under

three control methods. Fig. 9(b) shows the normalized capacitance requirement versus open-state duty cycle assuming _ / 2l rms in SI V fπ is the base.

1.5

0.5

2

0

1

0.20.10 0.3 0.50.4opD

_

_

C rms

l rms

II

Simple Boost

Maximum Boost

Constant Boost

60

20

0

40

0.20.10 0.3 0.50.4opD

_

2l

rms

inS

CI V

fπ

Simple Boost

Maximum Boost

Constant Boost

(a) (b)

Fig. 9 Capacitor design under three control methods. (a) Normalized capacitor rms current versus opD (b) Normalized capacitance versus opD

B. Input and Z-source coupled inductor design The current stress of the input inductor L3 and two Z-

source inductors L1 and L2 has already been calculated in Table I and illustrated in Fig. 5. If three independent inductors are designed, the total magneto motive force (MMF) of these inductors are

1 2 1 3 2ind in L LMMF N I N I N I= + + (16) Where N1, N2, and N3 is number of turns of each inductor,

indMMF is the total MMF of three independent inductors. The total stress of input inductor and one of the Z-source inductor can be illustrated as Fig. 10. Fig. 10 shows that, with the change of open zero duty cycle, the summation of the input inductor current stress and one of the Z-source inductor current stress is the same. This means if the input inductor and Z-source inductors are coupled in one core, the total MMF can be reduced. According to Fig. 5, the peak current stress of the input inductor and the Z-source inductors are the same. Assuming the number of turns of each inductor are the same,

3indMMF NI= (17) And we also have,

2coupleMMF NI= (18) Where, coupleMMF is the total MMF of the three inductors

coupled in one core. Since the total MMF of the coupled inductor can be reduced by one third compared to the independent inductor design, the total inductor size of the coupled inductor design should be smaller than the independent case. Therefore, a coupled inductor using one core for the input and Z-source inductors should be designed.

1.6

1.4

1.7

1.3

1.5

0.20.10 0.3 0.50.4opD

Simple boost

Maximum boost

Constant boost1

_

in L

l rms

I II

+

Fig. 10 The sum of input inductor and one Z-source inductor current stress.

Assume the inductor current ripple is about 30% of the inductor dc current, the inductance of Z-source inductor can be calculated as,

1 2130%

in op

L S

V DL LI f

= = (19)

And the inductance of the input inductor can be calculated as,

330%

in op

in S

V DLI f

= (20)

Plug (5), (8) and the relationship of M and Dop in Table I, we can derive the inductance requirement of three control methods versus Dop as shown in Table IV. Assuming the inductance base is _/ 2in S l rmsV f Iπ , Fig. 11 shows the illustration of normalized inductance requirement under three control methods. Fig. 11(a) shows Z-source inductor

161

inductance requirement assuming the current ripple is 30%. Fig. 11(b) shows the input inductor inductance requirement assuming the current ripple is 30%.

Table IV Inductance requirement under three control methods

1 2,L L versus opD 3L versus opD

Simple boost _

3(1 )30% 2 2

in op

S l rms

V Df I

−

( )( )_

3 130% 2 2 1 2

op opin

S l rms op

D DVf I D

−−

Constant boost _

(1 )30% 2

in op

S l rms

V Df I

− ( )

( )_

130% 2 1 2

op opin

S l rms op

D DVf I D

−−

Maximum boost _

(1 )30% 3 2

in op

S l rms

V Df I

π − ( )

( )_

130% 3 2 1 2

op opin

S l rms op

D DVf I D

π −−

1_

2l

rms

inS

LI

VT

π

0 0.20.1 0.3 0.50.4opD

6

10

14

12

8

16 Simple Boost

Maximum Boost

Constant Boost12

4

16

0

8

0 0.20.1 0.3 0.50.4opD

_2

inl

rms

inS

LI

VT

π

Simple Boost

Maximum Boost

Constant Boost

(a) (b)

Fig. 11 Normalized inductance requirement under three control methods assuming the current ripple is 30%. (a)Z-source inductor inductance

requirement. (b) input inductor inductance requirement.

C. Input and Z-source coupled inductor core and winding optimal selection strategy

1) Winding Selection Although helix copper bar winding is better in terms of

thermal performance than copper foil, the copper foil is still selected as the winding due to easier prototype making purposes. The number of turns selection criterion of helix winding is the same as the copper foil winding. Assuming the operating temperature is 100 ºC and the switching frequency for the inductor is 20 kHz. The skin depth of the copper can be calculated as

0

22 Sf

ρδπ μ

= (21)

Where ρ is the copper resistivity at 100 ºC, which is 2.3*10-8 Ωm, µ0 is the copper permeability which is about 1.26*10-6 N/A2. The skin depth δ can be calculated as 0.54 mm, so the copper foil with thickness 0.021 inch is selected. Since during the worst case, the inductor current is 120 A, assuming the copper current density is about 5 A/mm2, 2 inch width copper foil is selected. And the 5 mil thick Nomex paper is selected as the insulation material.

2) Core Material Selection The powder core from Chang Sung corporation (CSC) is

selected for the core design due to its soft saturation and low power loss features. Table V shows a summary of power core material comparison of CSC. The High Flux and Mega Flux material have high saturation flux feature, and High Flux material has less core loss, therefore, the High Flux material is

selected for the core design. After comparison, the High Flux 60µ material is selected as the inductor core.

Table V CSC’s core comparison by material

Bs (G) Core Loss DC Bias MPP 7000 Lower Better

High Flux 15000 Low Best Sendust 10,000 Low Good

Mega Flux 16,000 Medium Best

020406080

100120140

1 10 100 1000

Rel

ativ

e Per

mea

bilit

y

DC Magnetizing Force H(Oe)

High Flux 26uHigh Flux 60uHigh Flux 125u

Fig. 12. High Flux relative permeability change versus DC magnetizing

force.

3) Number of turns Design Although winding and the core material are selected, the

shape of the core with proper cross section area (Ae) and effective magnetic length (le) and total number of turns (NT) should be selected properly. Assume the cross section area of the core is square. The desired core shape is shown in Fig. 13. And the total window width 0.06 mwidthW = in order to keep the 2 inch copper foil with about 10% insulation gap. The single layer winding thickness (Tthk) can be calculated with copper thick ness plus the Nomex paper thickness with about 20% margin, which is about 0.8 mm. And after the winding is finished about 10% gap between turns is designed to help cooling. Therefore, the window length can be calculated as,

03length T thkW N T k= (22) Where k0 is 1.1 with considering the 10% gap between

turns. The effective magnetic length can be calculated as,

2( )e width length el W W Aπ= + + (23) And according to Ampere’s law, we have

_ max2 T in eN I Hl= (24) Where Iin_max is the peak input current which is 120 A and

according to previous analysis, only 2NI is needed for the coupled inductor design. And according to Fig. 12, the relative permeability of the inductor can be calculated using a function of H, which is

( )r f Hμ = (25) The inductance can be calculated as,

0e

r Te

AL Nl

μ μ= (26)

By plugging the (22) ~ (25) to (26), we can derive that, the inductance can be calculated using a function of Ae and NT. Since the number of turns NT is a natural number, by changing Ae continuously, we can have different design with different NT, as shown in (27) and (28).

162

20

0( )

2( 3 )e

Twidth T thk e

AL f H NW N T k A

μπ

=+ +

(27)

20.5

T ein

S

N BAVT

Δ= (28)

Where ∆B is the peak to peak flux change, and TS is the switching period. And according to the High Flux 60µ material core loss density equation 2.27 1.321.46den ac SP B f= , and 0.5acB B= Δ we can calculate the total core loss since the core volume can be calculated as,

1.52 ( )core e width length eVol A W W A= + + (29) And copper volume with insulation paper can be

calculated as,

( )22 (3 )copper T thk e e widthVol N T A A W= + − (30)

And the total copper length of Z-source inductor can be calculated as,

( )4 T thk e TWdg N T A N= + (31)

Since during the Dop=0.5 the two Z-source inductor have the peak current stress 120 A, and when Dop is zero only the input inductor current is 120 A. Therefore, the copper loss of both Z-source inductor can be calculated as,

21_ max2copper L

cu cu

WdgP IThk Wdh

ρ= (32)

Where Thkcu is the copper thickness which is 0.021 inch, and Wdhcu is the copper width which is 2 inch. And IL1_max is 120 A. By adding the total copper and core size and adding copper and core loss we can derive the total inductor size and total power loss curve versus number of turns as shown in Fig. 14.

eA

x

x

lengthW

eA

x

xw

idthW

x

el

Fig. 13 Desired core shape.

1.4

1.6

1.8

2.0

2.2

2.4

110

120

130

140

150

160

5 10 15 20 25

Tot

al I

nduc

tor

Size

(L)

Tot

al P

ower

Los

s (W

)

Number of turns

Fig. 14 The total inductor size and total power loss versus number of turns.

Fig. 15 shows the designed core shape of the coupled inductor using changsung high flux 60u block cores and the 3D structure of the final winding and the inductor. The yellow color shows the Z-source inductor winding, and the green part shows the input inductor winding.

eA

4 cm

5 cm

5 cm

eA

4 cm6 cm

4 cm

el

4 cm

Fig. 15 The designed core shape and winding structure.

V. PROTOTYPE AND EXPERIMENTAL RESULTS Fig. 16 ~ Fig. 17 shows the experimental results and

measured efficiency of the CF-qZSI.

Effic

ienc

y

Voltage Gain0 10.5 1.5 2

98%

92%

100%

90%

96%

94%

88%

Fig. 16 Experimental results at 15 kW and efficiency curve at different

voltage gain.

V(250 V/div)

Ca CbV(250 V/div)

CcV(250 V/div)

PNV(200 V/div)

(20 μs/div)

(2 ms/div)DSV

(200 V/div)

Ca Cb CcV ,V ,V(250 V/div)

Zoomed in (20 μs/div)

Fig. 17 Experimental results of buck mode and boost mode.

VI. CONCLUSION This paper presents the development and optimal design

considerations of CF-qZSI. The constant boost control method should be selected, which can maximize the utilization of the open-circuit zero state with relatively low device and passive component stress. SVPWM control method with flexible vector selection and placement can be used to generate the PWM signal with relatively low switching loss and output harmonics. The open-circuit zero state can be kept the same in every switching period with the constant boost control. The active device stress analysis and passive component stress analysis are provided to select the proper device and components. The coupled inductor design method is also provided with relatively small size and high efficiency. The experimental results with measure efficiency curves are also provided to demonstrate the validity and features of the proposed circuit and design method.

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