Proceedings of 2013 IEEE International Conference on ID3013 Applied Superconductivity and Electromagnetic Devices Beijing, China, October 25-27, 2013

978-1-4799-0070-1/13/$31.00 ©2013 IEEE 30

Battery Charge-Discharge Control Strategy Based on the Single Z-Source Three-Level SVPWM Inverter

Ke Qing Qu, Qing Quan Niu, Chong Yang, Jin Bin Zhao College of Electrical Engineering,

Shanghai University of Electric Power, Shanghai, China

kqqu@shiep.edu.cn

Abstract—A battery charge-discharge control strategy which based on the single Z-source three-level space vector pulse width modulation (SVPWM) inverter and the designed corresponding closed-loop control system is proposed. The inverter can not only eliminate the transformer or DC/DC converter link in traditional system, but also realize charger-discharge control in the case of a large range of battery voltage changes. The stage charging control based on the current feed-forward decoupling, the constant discharging control based on the power feed-forward decoupling and the output voltage boost method in constant discharging control are researched. The simulations in Matlab/Simulink verified that it can achieve the constant voltage or current charging control under unity power factor as well as the grid-connected constant power discharging control with boosted output voltage.

Keywords-Z-source; three-level inverter; battery; SVPWM

I. INTRODUCTION Currently in the study of battery charge-discharge control

and storage inverter systems, to solve the matching problem of the battery voltage and grid voltage, most literature use the transformers or external DC/DC link to step up/down the inverter output voltage, which not only increases the investment, but also affect the conversion efficiency of the inverter. Z-source inverter is conducive to resolve this problem because of its buck/boost characteristics [1]. Although some simplified SVPWM strategies as well as topologies combined Z-source inverter and multi-level technology are proposed in some literature [2,3], but still less applied to energy storage control system. Therefore, this paper studies the single Z-source three-level space vector pulse width modulation (SVPWM) inverter, which is applied to the battery charge-discharge situation, and designed the corresponding closed-loop control system. The application of single Z-source three-level inverter technology can not only eliminate the transformer or DC/DC converter link to improve the efficiency, but also realize the charge-discharge control under the situation with large range changes of battery voltage, and be applicable to more kinds of battery energy storage system with different voltage level. Especially due to its boost characteristic, the desired output voltage of the battery pack is further reduced, therefore reduces the number of the series in battery pack and is suitable for future electric vehicle as well as other small battery pack’s charge-discharge control. As the three-level SVPWM control algorithm can improve the voltage utilization,

easy to be digital-realized, and has a more flexible combination of switch modes, which help to improve the efficiency and achieve better control effects [3].

This paper studies the energy storage control technology which based on the bi-directional single Z-source three-level inverter and its SVPWM modulation algorithm, expounds the shoot-through vector insertion strategy.

II. SYSTEM STRUCTURE AND PRINCIPLE

A. System Overview In the battery’s charge-discharge control system, the single

Z-source three-level NPC inverter is adopted as storage inverter. And in its SVPWM control strategy, the shoot-through states is inserted carefully to achieve the boost of the inverter’s output voltage. Based on this, the closed-loop control system is designed for each mode to achieve the corresponding charge-discharge control of storage battery.

Battery charging adopts the stage charging mode realized by using of the cascade dual closed-loop control structure. As stage charging is essentially the reasonable combination of constant voltage control and constant current control, battery charge control strategies can be divided into four different modes, respectively are conventional constant voltage charging, constant voltage charging with power limited, conventional constant current charging, and constant current charging with power limited.

Battery discharging use the constant power control strategy, which is realized through the direct power control mode based on power feed-forward decoupling. It can be divided into three different conditions, respectively are constant power control with unity power factor and boosted output voltage, constant power control with reactive power output, and constant power control when it transforms from rectifier state to inverter state.

B. Stage Charging Control Based on Current Feed-Forward Decoupling The system which based on the single Z-source three-level

SVPWM inverter adopts stage charging mode for battery’s charging control. Its control system applies the cascade double-loop control structure. The inner rings are all the current control structure based on current feed-forward decoupling, while the outer ring is designed according to the specific control objectives. The dual closed-loop control systems for

The project is supported by Shanghai Pujiang Program (project number: 12PJ1403900) and Innovation Program of Shanghai Municipal Education Commission (Grant No. 13ZZ132)

31

four different charging modes are all similar except for the outer ring part. Therefore, only take constant voltage charging with power limited as an example to elaborate the battery charge control system.

*di

*du du

ωL

PI

ωL

PI0* =qi

*qu qu

qidi

de

0=qe

au

bu

cudq/abc

SVPWM

as bs cs

ae be ce ai bi ci

PI*dcu

dcu

abc/dq

ae be ce

ai bi ci

gθ

abc/dqgθ de

gθ

ae be ce

PLLgθ

dcudcu dci

mindci/P**ˆdcu

dcu′dci

Figure 1. System block diagram of constant voltage charging with power limited.

Fig. 1 is system block diagram of the constant voltage charging with power limited. It adopts the dual closed loop which consists of the dc-side voltage outer ring and the grid-side current inner ring to realize the constant voltage charging with power limited. In Fig. 1, the current maximum grid-allowed charging power P* is given by superior Power Grid Dispatch Center. P* divided by the actual charging current Idc, then the allowed charging voltage U’

dc for right now can be obtained. Compare U’

dc with the settled conventional constant charging voltage reference value U *

dc, output the smaller one and make it to be the new charging voltage reference value under conditions of limited power. The specific circumstances are as shown in Table I.

TABLE I. SELECTION OF CHARGING VOLTAGE REFERENCE VALUE WITH POWER LIMITED

Conditions Charging voltage reference value

U’dc > U *

dc U *dc

U’dc < U *

dc U’dc

U’dc = U *

dc Udc or U *dc

New charging voltage reference value goes through the dc-side voltage outer loop, then the q-axis current component’s reference value can be obtained and sent to inner control loop. Through inner loop’s current feed-forward decoupling, the input signal of the space voltage vector used for the SVPWM control can be obtained. And by the SVPWM modules, generates bridge-arm switches’ control signal and eventually to control the single Z-source three-level inverter accordingly.

Constant current charging mode is relatively similar with the constant voltage charging. Only in the outer control ring part, it requires to change into the dc-side current outer ring control, so as to realize the constant charging current in dc side.

C. Constant Power Discharging Control Based on Power Feed-Forward Decoupling For discharging control, it adopts the constant power

discharging mode. Through the direct power control based on

power feed-forward decoupling, realize the grid-connected constant power discharge. The purpose of using power feed-forward decoupling is to achieve the separate control of the inverter’s output active and reactive power.

Fig. 2 is system block diagram of the constant power discharging control. In Fig. 2, firstly, by sampling and calculation, to get the grid-side output active and reactive power’s instantaneous values. Then through the power feed-forward decoupling, obtains the input signals of the space voltage vector used for the SVPWM control. And also by the SVPWM modules, generates bridge-arm switches’ control signals, which are used to control the single Z-source three-level inverter accordingly to achieve the grid-connected constant power discharge of battery.

Figure 2. System block diagram of grid-connected constant power discharging.

D. Output Voltage’s Boost in Constant Power Discharging Based on the traditional SVPWM, with careful insertions of

the upper and lower shoot-through states (by turning on the upper three or lower three switches from one bridge arm simultaneous), it’s able to create a new SVPWM algorithm applies to the single Z-source three-level inverter, by which it can achieve the output voltage’s boost in constant power discharging [4].

III. PARAMETER DESIGN OF CLOSED LOOP Take charging control as an example to describe the design

of the closed-loop PI parameters. For discharging control, it becomes much easier to debug the parameters because there are only two PI regulators within the control loop. Its parameters’ design can refer to the charging control’s situation.

A. Parameter Design of the Inner Ring No matter which kind of battery charging mode it is, the

inner ring are all the current control structure that based the current feed-forward decoupling. Fig. 3 is a block diagram of the inner current control structure. According to Fig. 3, the system’s closed-loop transfer function can be got, that is

iIiP

iIiPci KsRKLs

KsKsG+++

+=)(

)( 2 (1)

Then design the corresponding current regulator. According to (1), choose typical I-type system and assume that

32

LR

KK

iP

iI = (2)

Take (2) into (1), and the new transfer function of the current inner loop can be written as follows

sTKLs

KsGciP

iPci +

=+

=1

1)(

)( (3)

where Tc = L / KiP is the inertia time constant. *di

sKK iI

iP + du diRsL +

1

Figure 3. Inner current control diagram.

Define the system’s band width is just the corresponding frequency value when the closed-loop gain value takes -3 dB, that is

203

210

)(1

11

1)(−

=+

=+

=TsT

sGcc

ciω

(4)

From (4), there is

1=ccTω (5)

According this, the current inner loop parameter settings can be got

⎩⎨⎧

==

RKLK

ciI

ciP

ωω (6)

B. Parameter Design of the Outer Ring Take conventional constant voltage charging as an example

to describe the design of outer loop control parameters. For other charging modes, the corresponding parameters’ design all can refer to this.

Under d-q coordinate system, write the KAL equation about the dc-bus capacitor’s pole column in Fig. 1, then through Laplace transformation, it becomes

dc

rddqqdc i

sCRsCiSiSU 1

/11)(

23 =

++= (7)

where Sn (n = d, q) is the expression of switching function under the d-q coordinates, Rr is the battery internal resistance.

During the design of inner current loop, as is using the typical I-type system which can be approximately equivalent to a first-order inertial system, the current inner equivalent inertia time constant can be expressed as 3Ts. And considering the outer ring itself has a certain sampling delay, merge the small inertia time constants from both the inner and outer ring, and choose the corresponding equivalent proportional gain as 0.75. Fig. 4 is a diagram of the outer voltage control after merger.

*dcu

sKK uI

uP + dcudi14

75.0+⋅ sTs sC

1

Figure 4. Outer voltage control diagram.

Make the control block diagram in Fig. 4 simplified, and then the system transfer function can be written as follows

)14()(75.0)( 2 +⋅

+≈s

uIuPcu TsCs

KsKsG (8)

Then design the corresponding voltage regulator. According to (8), choose typical II-type system and assume that

⎪⎩

⎪⎨⎧

=

=

s

uI

uPu

TTKK

4

τ (9)

Take (9) into (8), through simplification and deformation, it becomes

)1(

)1(75.0)( 2 ++=

sTCssKsG

u

uuPcu τ

τ (10)

According to this and the parameter tuning formulas for typical II-type system, the voltage outer loop parameter settings can be obtained as follows

⎪⎩

⎪⎨⎧

⋅=

+=

ThTh

hK

u

u

τ222

1 (11)

where h = τu / T is the bandwidth.

Reasonable outer PI parameters can be obtained by selecting an appropriate value of h.

IV. SIMULATION Build the battery charge-discharge control system’s models

in Matlab/Simulink. The simulation parameters are as follows, battery internal resistance R = 5 Ω, dc-voltage-divide capacitors CS1 = CS2 = 4000 μF, Z-source-network capacitors CS1 = CS2 = 220 μF and inductors L1 = L2 = 1 mH, SVPWM ratio k = 0.65, three-phase power grid’s phase voltage is 220 V and the frequency is 50 Hz, grid-side inductance L3 = L4 = L5 = 800 mH, system’s switching frequency fS = 2.5 kHz, simulation time is 0.4 s.

A. Simulation of the Battery’s Charging Control The simulation is carried out under the mode of constant

voltage charging with power limited. The battery’s voltage Udc = 800 V. As there is no need to boost the output voltage for the battery’s charging, set the inverter’s boost ratio B = 1. The voltage reference value of the conventional constant voltage charging is U*

dc = 900 V. Set at the moment of 0.2 s, the grid-side maximum allowed charging power P* reduces from 20 kW to 14 kW, system begins to transform from conventional constant voltage charging mode to constant voltage charging mode with power limited. Fig. 6 is the system’s simulation waveforms.

As is shown in Fig. 6, at the beginning, the charging power needed for the battery to maintain its constant voltage charging is about 18 kW, meanwhile the maximum allowed charging power from the grid is 20 kW, which means the remaining power of the grid is sufficient. At 0.2 s when the grid-side maximum allowed charging power dropped from 20 kW to 14 kW, system transforms to the constant voltage charging with power limited to continue the charge for battery.

33

P/W

t/s

U/V

I/A

t/s

U/V

I/A

t/s

I/A

U/V

U

/V

t/s

Q/v

ar

P/W

t/s

U/V

I/A

t/s

During the whole process of the system’s transformation from conventional constant voltage charging to constant voltage charging with power limited, grid-side phase voltage is always synchronized to the phase current, which shows that through the closed-loop control, it achieves the system’s rectifying operation under unity-power factor.

(a)

(b)

(c)

Figure 5. Waveforms of constant voltage charging with power limited: (a) Waveform of the charging power; (b) Waveforms of the charging voltage and current; (c) Waveforms of the grid-side phase voltage and current.

B. Simulation of the Battery’s Discharging Control The simulation is carried out under the mode of constant

power control with unity power factor and boosted output voltage. The battery’s voltage Udc = 500 V at this time. Make the inverter’s boost ratio B = 1.5. The settled reference value of the active power output from the battery to the grid is P* = 6000 W, reactive power Q* = 0. Fig. 6 is the system’s simulation waveforms.

As is shown in Fig. 6, after about 0.02 s, the system reaches a steady state. The battery voltage is 500 V, each dividing capacitor withstands the voltage of 250 V. As the boost ratio B is set to 1.5, through the unique single Z-source three-level inverter’s boost operating which realized by the corresponding SVPWM control algorithm with shoot-through states carefully inserted, the peak value of the inverter’s phase voltage output reached about 375 V and the line voltage’s peak value reached about 750 V, which witnesses the realization of output voltage’s boost. And meanwhile, the output current waveform also maintained a good degree of sine.

During the whole process of the battery discharging, grid-side phase voltage and phase current always maintain a phase difference of 180°, which indicates that through the closed-

loop control, it realizes the constant power control with boosted output voltage and unity power factor under the grid-connected inverting operation.

(a)

(b)

(c)

Figure 6. Waveforms of constant power control with unity power factor and boosted output voltage: (a) Waveforms of the inverter’s output; (b) Waveforms of the grid-side active and reactive power output; (c) Waveforms of the grid-side phase voltage and current.

V. CONCLUSION The system is able to achieve the constant voltage or

current charging control under unity power factor as well as the constant power discharging control with boosted output voltage. The rightness and validity of the proposed battery charge-discharge control strategies are verified with the simulation in Matlab/Simulink.

REFERENCES [1] J. Rabkowski, “The bidirectional Z-source inverter as an energy

storage/grid interface,” The International Conference on ‘Computer as a Tool’, pp. 1629-1635, Warsaw, Poland, 9-12 September 2007.

[2] F. Gao, P. C. Loh, F. Blaabjerg, and D. M. Vilathgamuwa, “Dual Z-source inverter with three-level reduced common-mode switching,” IEEE Transactions on Industry Applications, vol. 43, no. 6, pp. 1597-1608, 2007.

[3] L. Yan, W. Xu, and X. Yan, “Research based on SVPWM method of three level inverter,” 30th Chinese Control Conference, pp. 4513-4515, Yantai, China, 22-24 July 2011.

[4] P. C. Loh, S. W. Lim, F. Gao, and F. Blaabjerg, “Three-level Z-source inverters using a single LC impedance network,” IEEE Transactions on Power Electronics, vol. 22, no. 2, pp. 706-711, 2007.