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Single-Phase Z-Source Inverter

Yu Tang, Shaojun Xie, Chaohua Zhang

College of Automation Engineering, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China

Abstract- This paper proposes a novel single-phase Z-source inverter topology with input and output sharing the same ground. It is simple in structure and only utilizes two switches while keep the voltage transfer ratio the same as the full-bridge inverter. One-cycle control is adopted and high efficient constant frequency control can be achieved without accurate model of the converter. The unique feature of proposed topology is verified by operating principle, simulation and experimental results. This topology can be used in distributed power systems where dual grounding is needed. Index Terms—Single-phase, Z-source inverter, one-cycle control.

1. INTRODUCTION In a traditional single-phase voltage-source inverter, the bridge structure is often used. For full-bridge inverter topology, four switches are required, thus presents a high cost. The half-bridge inverter only utilizes two switches and seems more economical, but the output voltage is lower than half the input voltage, and the voltage balance of the input divider capacitors must be kept which may increase the complexity of control. The four switches buck/boost/buck-boost inverters proposed in [1] consists of two identical buck/boost/buck-boost dc-dc converters sharing the same dc input while the load is across the two output, therefore these topologies are complex in structure. The distributed power generation inverter has to operate normally under the dual-grounding circumstance when considering maintenance safety, that means the input and output of the inverter must sharing the same ground[2]. The above mentioned topologies cannot meet this requirement, therefore an isolated converter must be added in the front stage which increase the system complexity and cost greatly. An inverter topology with inherent common ground for input and output was proposed for grid-connected

application in [3], but it requires a split dc input voltage source and four switches, so it is lack of practice. Z-source converter can provide unique features that cannot be obtained in traditional voltage-source and current-source converter. Recently, the research on Z-source is mainly focused on the three-phase Z-source inverter in which the Z-source network is used as the front stage [4-6]. The three-phase Z-source inverter can provide the shoot-through of the phase-legs and buck-boost ability compared to traditional topologies. In this paper, a novel single-phase Z-source inverter topology is presented based on the unique feature of the Z-source. The proposed topology utilizes only two switches and is simple, in addition, the input and output share the same ground. One cycle control has the ability to reject the input perturbation instantly, and is insensitive to system model [8-9]. By adopting one cycle control, high efficient constant frequency control can be achieved. The feasibility of the proposed topology and its one cycle control strategy is analyzed in detail and verified by simulation and experiments. 2. SINGLE-PHASE Z-SOURCE INVERTER TOPOLOGY There are two basic Z-source converter topologies [7], including voltage-fed and current-fed, as shown in Fig.1. The Z-source networks are symmetric in these topologies. S1 and S2 are turned on and off in complement. Defining the duty ratio of S1 as D, then we can get the relationship between voltage ratio and D of voltage-fed and current-fed topologies, respectively: vo v D 2D ? 1 = ， o = (1) vi 2 D ? 1 vi D ?1

(a) voltage-fed Fig.1 Basic topologies of Z-source converter

(b) current-fed

978-1-4244-1874-9/08/$25.00 ?2008 IEEE

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Fig.2 shows the voltage gain versus D of voltage-fed and current-fed topologies, respectively. For voltage-fed topology, it clearly shows that there are two discontinuous operation regions. For current-fed topology, we can see that the output voltage vary continuously. When D is less than

0.5, output voltage is in-phase with input voltage. When D is greater than 0.5, output voltage is out-of-phase with input voltage. This unique feature can be utilized to realize DC-AC power conversion, as shown in Fig.3.

(a) voltage-fed Fig.2 Voltage gain versus D of two basic topologies

(b)

current-fed

Fig.3 (a) shows the basic single-phase Z-source inverter topology. vi=vC can be derived easily in steady state from Fig.3(a), then we can get the improved topology with input and output sharing the same ground, as shown in Fig.3(b).

The unsymmetrical Z-source network is composed of input voltage source vi, capacitor C, and inductors L1, L2, where L1 and L2 can be coupled inductors with any coupled factor.

(a) basic topology Fig.3 Single-phase Z-source inverter topology

(b) improved topology

3. OPERATING PRINCIPLE OF SINGLE-PHASE Z-SOURCE INVERTER

The duty ratio of S1 is D and the coupled inductor of L1 and L2 is M. Two states exist in one switching period, and Fig.4 shows their equivalent circuits. In state 1, switch S1 is turned on and S2 is turned off. The time interval in this state is DT, where T is the switching period, as shown in Fig. 4 (a). We can get

In state 2, S2 is turned on and S1 is turned off. The time interval in this state is (1-D)T, as shown in Fig. 4 (b). We can get

diL 2 ? diL1 ? L1 dt + M dt = vi ? vo ? ? L diL 2 + M diL1 = v ? v C o ? 2 dt dt ? ?C dvC = ?i L2 ? dt ? dv ?C f o = iL1 + iL 2 ? io ? dt

diL 2 ? diL1 ? L1 dt + M dt = ?vC ? ? L diL 2 + M diL1 = ?v i ? 2 dt dt ? ?C dvC = i L1 ? dt ? dv ?C f o = ?io ? dt

From (2) and (3), we can get the averaged equation

(3)

(2)

1267

diL 2 ? diL1 ? L1 dt + M dt = D(vi ? vo ) ? (1 ? D)vC ? ? L diL 2 + M diL1 = D(v ? v ) ? (1 ? D)v C o i ? 2 dt dt ? ?C dvC = ? Di + (1 ? D)i L2 L1 ? dt ? dv ?C f o = D(iL1 + iL 2 ) ? io ? dt

In steady state, we get

The realization of one cycle controlled single-phase Z-source inverter is shown in Fig.5. Fig.6 shows the principle waveforms in steady state. When clock signal arrives, S1 is turned off and S2 is turned (4) on, then vds(S1) is integrated from zero, the integration value is

vint = k ∫ (vC + vi ? vo ) dt

0

t

(8)

Where k is integration factor, when the integration value reaches vi-vref, the integrator resets, then S1 is turned on and S2 is turned off. D is determined as

?vC = vi ?v ? o = 2D ? 1 ? vi D ? ?iL1 = io ? 1? D ?iL 2 = iL1 ? D

Suppose vo = V sin wt , substituting to (5), we get

D= 1 2 ? A sin ω t

k∫

(5)

(1? D )Ts

0

(vC + vi ? vo ) dt = vi ? vref

(9)

The average value of vds(S1) is

Vds1 =

1 Ts

∫

(1? D )Ts

0

(vC + vi ? vo )dt = K (vi ? vref )

(10)

Where K = 1/ kTs =1。 (6) In steady state, the average voltage across inductor L1 is 0, we get

While A = V / vi Substituting (6) to (5), we get

Vds1 = vi ? vo

From (10) and (11), we get (7)

(11)

iL 2 = io (1 ? A sin ω t )

vi ? vref = vi ? vo

Therefore

(12)

4. ONE-CYCLE CONTROL STRATEGY

vo = vref

(13)

(a) state 1 Fig.4 Equivalent circuits in one switching period

(b) state 2

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Fig.5 One cycle controlled single-phase Z-source inverter

Fig.6 Principle waveforms

5. SIMULATION AND EXPERIMENTAL RESULTS

To verify the proposed topology and its one cycle control strategy, simulation and experimental results were given. The parameters were: input voltage vi=150V, output voltage vo=90V(50Hz), Z-source inductors L1=L2=300 μ H, the coupled factor is 0.6, Z-source capacitor C =470 μ F, output

filter capacitor Cf=20 μ F, the switching frequency is 45kHz and the dead time is 1 μ s. Fig7 (a) and (b) shows the simulation results under no load and resistance load R=25 Ω , respectively. Fig7(c) shows simulation results when the load varied between no load and R=25 Ω . Fig.7 (d) shows the simulation results when input voltage varied.

(a) no load

(b) R=25 Ω

(c) load varied Fig.7 Simulation results

(d) input voltage varied

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Same parameters were used in experiments. Fig.8 (a) shows the waveforms of vo and vds(S1) under no load. Fig.8 (b) shows the waveforms of vds(S1) and vint under no load.

Fig.8 (c) shows the waveforms of vo and vds(S1) under R=25 Ω . The experimental results coincide with the simulation results well.

μ

(a) vo and vds(S1) under no load (b) vds(S1) and vint under no load

(c) vo and vds(S1) under R=25 Ω Fig.8 Experimental results

6. Conclusion Traditional single-phase inverter topologies cannot achieve the common ground of the input and output, so they cannot be used in conditions where dual grounding is needed. To solve this problem, a novel single-phase Z-source inverter topology with inherent common ground for input and output has been given. Operation principle and its one cycle control strategy is analyzed in detail, and verified by simulation and experimental results. REFERENCES

[1] N. Vázquez, J. Almazan, J. ?lvarez, C. Aguilar, and J. Arau, “Analysis and experimental study of the buck, boost and buck-boost inverters,” IEEE PESC, Charleston, SC, 1999, pp. 801–806. [2]Y. S. Xue, L. C. Chang, S. B. Kj?r, “Topologies of single-phase inverters for small distributed power generators: an overview,” IEEE Trans. on Power Electronics, vol.19, no.5, pp.1305-1314, September

2004. [3] N. Kasa, T. Iida, and H. Iwamoto, “An inverter using buck-boost type chopper circuits for popular small-scale photovoltaic power system,” IEEE IECON, San Jose, CA, 1999, pp. 185–190. [4] F. Z. Peng, “Z-source inverter,” IEEE Trans. on Industry Applications, vol. 39, no. 2, pp. 504-510, March/April 2003. [5] M. S. Shen, J. Wang, A. Joseph, F. Z. Peng, et al, “Constant Boost control of the Z-source inverter to minimize current ripple and voltage stress,” IEEE Trans. on Industry Applications, vol. 42, no. 3, pp. 770-777, May/June 2006. [6] P. C. Loh, D. M. Vilathgamuwa, Y. S. Lai , G. T. Chua, et al, “Pulse-width modulation of Z-source inverters,” IEEE Trans. on Power Electronics, vol. 20, no. 6, pp. 1346-1355, November 2005. [7] X. P. Fang，Z. M. Qian and F. Z. Peng, “Single-phase Z-Source PWM AC-AC converters,” IEEE Power Electronics Letters, vol.3, no.4, pp.121-124, December 2005. [8] K. M. Smedley and S. Cuk, “One-cycle control of switching converters,” IEEE Trans. on Power Electronics, vol.10, no. 6, pp. 625-633, November 1995. [9] K. M. Smedley and S. Cuk, “Dynamics of one-cycle controlled Cuk converter,” IEEE Trans. on Power Electronics, vol. 10, no. 6, pp: 634-639, November 1995.

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