Improved Performance of a Single-Phase to Three-Phase Converter using a 4-Switch

Quasi Z-Source Inverter

F. Khosravi1, N. A. Azli2, A. Kaykhosravi Power Electronics and Drive Research Group (PEDG), Energy Research Alliance,

Faculty of Electrical Engineering Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Malaysia

farshadgoli@fkegraduate.utm.my1 naziha@ieee.org2

Abstract— This paper proposes an improved space vector pulse width modulation (PWM) control method for a 4-switch single-phase to three-phase converter using a Quasi Z-source (QZs) network that can be utilized in induction motor drive applications. Without using any extra filtering circuits, this method can work well to reject the effect of DC-link voltage ripple on the inverter output voltage, which can be accomplished by either power supply or voltage variations in the 4-switch structure. This closed-loop control strategy recognizes and senses any unbalanced voltage that occur across two split capacitors and by applying the changes in the vector’s activation interval time, the three-phase output voltage can be balanced. In traditional methods, the DC-link voltage without ripple is often achieved at the expense of larger DC-link capacitors that lead to a bulky and heavy DC-link filter with slow response and increase in cost. The simulation results of the proposed control method demonstrate its efficiency and the potential of the structure to be further developed.

I. INTRODUCTION

Over the years, three-phase motors, more than single-phase motors have been the main consideration in industries due to certain parameters such as; efficiency, torque ripples and power factor. In rural areas, in order to operate machine tools and rolling mills as well as in low-power industrial application for robotics, where a three-phase utility may not be available, high-performance converters are typically used to run the three-phase motor drives. Low losses and cost-effectiveness are the very important properties for these converters [1].

In [2-9] various single-phase to three-phase converters have been proposed with at least 6 switches. An alternative for the reduction of losses in these converters is that the number of power switches is reduced. Many components-minimized structures are proposed in literatures [10-12]. Some efforts have also been made in the improvement of control strategies applied in high-efficiency induction motors Adjustable Speed Drives (ASDs) [13-15].

For all 4-switch structure converters proposed by various researchers, the existence of a ripple-free and fixed DC-supply is very important in producing balanced three-phase output voltages. An advanced DC supply is usually the solution at the expense of higher capacitor values that lead to bulky and heavy DC-filter which in turn contributes to slow response and increase in cost. In addition, unbalance in the AC supply and the use of a diode rectifier to provide the DC-voltage generates

abnormal DC-voltage harmonics, which can affect the load with sub harmonics [16]. Optimum and cost-effective operation of electrical power requires having a balanced three-phase AC supply. In [16] a unique modulation strategy is proposed to compensate the ripple of the DC-Link voltage but this is strictly designed for a three-phase inverter with three legs (six switches) without any extra filtering.

In [1], a new cost-effective structure of a 4-switch single-phase to three-phase converter using a Quasi Z-source (QZs) network for induction motor drive applications is proposed. In comparison to the traditional 6-switch structure, the proposed circuit reduces the cost of the system, switching losses and the complexity of the control method as well as the interface circuits used to generate the trigger signals. In addition, the QZs network, similar to the Z-Source network uses a unique LC network with added advantages, such as; lower component ratings, reduced source stress, reduced component count and simplified control strategies for ASDs that require a large range of gain [1].

In this paper without using any extra filtering circuits, the proposed structure as depicted in Fig. 1 can work well to reject the effect of the DC-link voltage ripple on the inverter output voltage, which can be accomplished by either power supply or voltage variations in the 4-switch structure. This closed-loop control strategy recognizes and senses any unbalanced voltage that occurs across the two split capacitors and by applying the changes in the vector’s activation interval time, the three-phase output voltage can be balanced.

II. THE PROPOSED STRUCTURE

Fig.1 shows the single-phase to three-phase converter that employs a 4-switch Quasi Z-Source inverter. This circuit topology can overcome the problems faced by the traditional circuits for the same application. It employs a special LC network of different type, which is connected between the load and the power supply. The main circuit of the QZs inverter and the proposed structure with their operating principles are as depicted in [1] and [17], respectively.

For the proposed structure as shown in Fig. 1, one phase leg of the load is connected to the midpoint of two split capacitors with, · (1)

2012 IEEE International Conference on Power and Energy (PECon), 2-5 December 2012, Kota Kinabalu Sabah, Malaysia

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This structure employs the zero shoot-through state to buck or boost the voltage of the DC bus to the desired output voltage by gating ON both the upper and lower switches of the same phase leg. Assuming the QZs network to be considered is a symmetrical circuit, it can be written for the network; Ceq = C2 and L1 = L2, where; Ceq is equivalent capacitance of two split series capacitors.

It is assumed that the voltages across the capacitors are the same or equal to /2 (Uc11=Uc12=Uc /2). In this case, the amplitude of the per-phase three-phase output voltages may be not identical to each other as reported in [1]. This is because the control method employed in [1] is not capable of compensating the effect of ripples and imbalance on the two capacitor voltages.

Fig.1. The proposed single-phase to three-phase converter using the QZs

network

From Fig. 1 and the main equations in [1], the required equations can be expressed as follows: SD (2)

(3)

By combining the equations (2) and (3), it can be written for the proposed structure that,

(4) 1 (5) 1

where; SD, is the symbolic function of the zero shoot-through state. SD should be equal to 0 if the inverter is in the zero shoot-through state and 1 when the inverter is in the non shoot-through state.

D is the zero shoot-through duty cycle. If the shoot-through time interval is T0 while the switching period is Ts, D can be expressed as,

(6)

This structure which has been thoroughly discussed in [1] has two different control modes; zero shoot-through state and non shoot-through state (active state).

III. IMPROVED SPACE VECTOR PWM CONTROL METHOD FOR THE PROPOSED CIRCUIT

To take into account the effects of voltage variation or voltage ripple on the inverter output voltage, it is

assumed the voltages across the capacitors are not the same that is,

(7)

(8)

(9)

The zero shoot-through state of the inverter for a Wye-connected three-phase load is as shown in Fig. 2. In this interval, the output voltage and the voltage across the load are equal to zero. In this boost state, the network inductors will be charged by the network capacitors, over two separate LC loops.

Fig.2. The equivalent circuit for the proposed structure of the zero shoot-

through state

The voltage vectors are introduced as the line-to-neutral instantaneous load voltages uan, ubn, ucn, which can be obtained from the voltages ua0, ub0, uc0, and un0 as follows [18],

uan = ua0 – un0 = ua0 – (ub0 + uc0)

ubn = ub0 – un0 = ub0 – (ua0 + uc0) (10)

ucn = uc0 – un0 = uc0 – (ua0 + ub0)

In the analysis, switches S1, S2, S3 and S4 can be considered as IGBTs. When the switch is closed, it is represented by “1” while “0” indicates an open state for that switch. With this assumption and based on Fig. 1, the phase-to-ground voltages can be written as follows:

S (11) S

By combining equations (4), (10) and (11), the line-to-neutral voltages are calculated by considering the capacitor voltages and coefficient " " . The proposed structure in Fig. 1 has four non shoot-through voltage vectors, , , , , and one zero shoot-through voltage vector, . These voltage vectors are calculated according to the switching states.

According to Clark’s transformation, the components αβ of the aforementioned voltage vectors can be obtained as follows [19]: 10 √ √ (12)

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The five voltage vectors which support the formation of the required reference vector on the αβ plane, are calculated as follows,

і , і 1 5 (13)

Table 1 shows the details of the voltage vectors. The switching states, line-to-neutral load voltages and phase-

to-ground voltages are also given in this table. The existence of the U2 parameter in this table in comparison to Table 1 in [1], illustrates the influence of voltage variations in the split capacitors on all the voltage space vectors.

Table 1- Voltage space vectors for all switching states

S1 S2 S3 S4 ua0 ub0 uc0 uan ubn ucn Vectors

1 0 0 1 U2 Uin 0 · (2U2- Uin) · (2Uin- U2) · (U2+ Uin)

0 1 1 0 U2 0 Uin · (2U2- Uin) · (U2+ Uin) · (Uin- U2)

1 0 1 0 U2 Uin Uin · (U2- Uin) · (Uin- U2) · (Uin- U2)

0 1 0 1 U2 0 0 · U2 · U2 · U2

1 1 1 1 U2 0 0 · U2 · U2 · U2

From Table 1, the voltage space vectors can be rewritten as follows, · ( (2U2- Uin) + j√3 Uin ) · ( (2U2- Uin) - j√3 Uin ) . (U2- Uin ) (14) · ·

The voltage vectors are dependent on the value of " " which is related to Uin as given in equation (4). Equations (5) and (6) have illustrated that the voltage vectors are also dependent on " " which is the zero shoot-through time. For the ideal case which has been considered in [1], two capacitors have the same voltages and for T0 = 0.3Ts and K = 0.7, the location of the voltage vectors in the αβ coordinates are as shown in Fig. 3.

To provide a symmetrical switching pattern, average value of the voltage space vectors (Vref.) shown in Fig. 3 and calculations of the switching states are obtained for 1 2⁄ · as follows,

. /2 (15)

Where; /2 (16)

and ti is half of the ON gating time for the ith switch over one switching cycle.

To obtain a set of identical three-phase voltages on the load, and for calculating the switching times, the following equations must be met. · · cos· · sin (17)

Where " " is the so-called coefficient for amplitude tuning, and it can be adjusted by the maximum magnitude of the voltage space vector.

Fig.3. Arrangement of voltage vectors in αβ coordinates for K = 0.7 and

in the ideal case

According to the mentioned five vectors and in order to have a one change status for all switches in a switching cycle, calculation of the switching times is done for the two zones as follows,

A. Zone One: 0 180

In this zone, average value of the voltage space vectors is calculated with four vectors, all vectors except 2. 0

Thus: √3 · 2⁄ . 3 √3 · 4⁄ (18) 2⁄

B. Zone Two: 180 360

In this zone, average value of the space vectors is calculated with four vectors, all vectors except 1.

2012 IEEE International Conference on Power and Energy (PECon), 2-5 December 2012, Kota Kinabalu Sabah, Malaysia

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0

Thus: √3 · 2⁄ . √3 3 · 4⁄ (19) 2⁄

The pulse patterns of switches for both zones are shown in Fig. 4. The switching frequency has been fixed to 10 kHz.

(a)

(b)

Fig.4. Pulse patterns for switches in the improved space vector PWM control method in (a) Zone one (b) Zone two

IV. SIMULATION RESULTS

In order to capture the advantages of the improved space vector PWM control method applied in the proposed structure, the converter is connected to a three-phase Wye-connected RL load with parameters given as follows.

RL = 10 Ω

Lf = 15 mH

Simulations have been conducted in Matlab/Simulink environment and results have been obtained to show the effectiveness of the improved space vector PWM control method. The QZs network has been simulated by considering the following parameters:

L1 = L2 = 100 µH, C2 = 150 µF, C11 = C12 = 300 µF

C = 470 µF, 190 2 . 50.

Fig. 5 shows the waveforms of the three-phase current which flows through the three-phase load in non shoot- through state, D = 0.0. The maximum values of these currents are equal 3.8 A. The load currents are perfectly symmetrical although the voltages across the two split capacitors are not the same as shown in Fig. 7. The voltage variations on these capacitors may have occurred either by the input voltage ripples or by the current

through the phase leg " " via midpoint connection of the capacitors. As shown in the Fig.7, the capacitor’s voltage also has ripples with frequency that is equal to the input voltage frequency that is 50Hz. The voltage difference between the average values of the two split capacitor’s voltage is around 10 Volts, which can be sensed by the control system and applied in the timing equations.

Fig. 6 depicts the total harmonic distortion (THD) of the load currents. In comparison to the traditional structure [13], the proposed converter with the improved space vector PWM control method has a smaller current percent THD of 3.73%.

(a)

(b)

Fig.5. Waveforms of the three-phase current flowing through the load

(a) Normal view (b) Zoomed for D = 0.0

Fig.6. Harmonic spectra of the load currents

Fig.7. Voltages of the QZs network capacitors for D = 0.0

Furthermore, this control method can also work well for the proposed structure while voltage sag is occurring at the input voltage. For the shoot through state, it is

2012 IEEE International Conference on Power and Energy (PECon), 2-5 December 2012, Kota Kinabalu Sabah, Malaysia

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assumed that the input voltage waveform remains constant, therefore the magnitude of the output voltages and currents will be increased based on the rate of zero shoot through time that is related to equation (2).

Fig. 8 shows the waveforms of the three-phase current which flows through the three-phase load in shoot- through state, D = 0.1. The maximum values of these currents are equal to 4.7 A. The load currents are also perfectly symmetrical in this state, although the voltages across the two split capacitors are not the same as shown in Fig. 9.

Fig.8. Waveforms of the currents flowing through the load for D = 0.1

Fig.9. Voltages of the QZs network capacitors for D = 0.1

V. CONCLUSION

The results in this paper have proven that the improved SVPWM control method for the 4-switch Quasi Z-Source single-phase to three-phase converter without any extra filtering circuit is a more efficient algorithm. The results have been presented in two cases; non shoot-though state (D = 0.0) and shoot-trough state (D = 0.1). The voltage variations on the capacitors may have occurred either by the input voltage ripple or by the current through the phase leg " " via midpoint connection of the capacitors which can lead to imbalance in the inverter output. However, by recognizing and sensing the unbalanced voltages that occur across the two capacitors and applying the changes in the vector’s activation interval time, the improved SVPWM control method has produced balanced output currents and voltages for the three-phase loads. In addition, the THD of the load current is less in comparison with that of the traditional circuits.

ACKNOWLEDGMENT The authors would like to thank the Research

Management Centre (RMC) of Universiti Teknologi Malaysia and the Ministry of Higher Education (MOHE) for the funding of this project through Vote Number Q.J130000.7123.00H87.

REFERENCES [1] F. Khosravi, N. A. Azli, A. Kaykhosravi, “A New Single-Phase to

Three-Phase Converter using Quasi Z-Source Network,” IEEE Applied Power Elec. Colloquium (IAPEC), pp. 46-50, 2011.

[2] N. Mohan, T.M. Underland and R.J. Ferraro, “Sinusoidal Line Current Rectification with a 100 kHz B-SIT Step-up Converter,” IEEE PESC Conf. Rec, pp. 92-98, 1984.

[3] P. Enjeti and A. Rahman, “A New Single-Phase Three-Phase Converter with Active Input Current Shaping for Low Cost AC Motor Drives,” IEEE. Tran. On IA, Vol. 29, No. 4, 1990.

[4] S.B. Bekiarov and A. Emadi, “A New On-Line Single-Phase to Three-Phase UPS Topology with Reduced Number of Switches,” IEEE Conference, Proc. PESC3, pp. 451-456, 2003.

[5] M.D. Bellar, M. Aredes, J.L. Siklva, L.G.B. Rolim, F.C. Aquino and V.C. Peterson, “Comparative Analysis of Single-Phase to Three-Phase Converters for Rural Electrification,” IEEE Conf. on IEs, Vol. 2, pp. 1255-1260, 2004.

[6] H. Haga, K. Ohishi and K. Sumida, “Unity Power Factor Control Method of Single-Phase to Three-Phase Power Converter without Reactor and Electrolytic Capacitor,” IEEE, EPE Conference, pp. 1-7, 2005.

[7] X. Yang, R. Hao, X. You and T.Q. Zheng, “A New Topology for Operating Three-Phase Induction Motors Connected to Single-Phase Supply,” IEEE Conference, ICEMS, pp. 1391-1394, 2008.

[8] X. Yang, R. Hao, X. You and T.Q. Zheng, “A New Single-Phase to Three-Phase Cycloconverter for Low Cost AC Motor Drives,” Proc. ICIEA 3rd IEEE Conf., pp. 1752-1756, 2008.

[9] E.C. Santos, C.B. Jacobina, J.A.A. Dias, “Active Power Line Conditioner Applied to Single-Phase to Three-Phase Systems,” IEEE Conference on Industrial Electronic, pp. 148-153, 2009.

[10] H.W. Broeck and H. Ch. Skudelny, “Analytical Analysis of the Harmonic Effects of a PWM AC Drive,” IEEE Trans. Power Electronic, Vol. 3, No. 2, pp. 216-223, 1988.

[11] P.N. Enjeti, A. Rahman and R. Jakkli, “Economic Single-Phase to Three-Phase Converter Topologies for Fixed and Variable Frequency Output,” IEEE Trans. Power Electronic, Vol. 8, No.3, pp. 329-335, 1993.

[12] F. Blaabjerg, S. Freysson, H.H. Hansen and S. Hansen, “A New Optimized Space-Vector Modulation Strategy for a Component-Minimized Voltage Source Inverter,” IEEE Transaction on Power Electronics, Vol. 12, No. 4, 1997.

[13] M.N. Uddin, T.S. Radwan and M.A. Rahman, “Performance Analysis of a Four Switch 3-Phase Inverter Fed IM Drives,” IEEE Conference, pp. 36-40, 2004.

[14] B.K. Bose, Power Electronics and AC Drives, Englewood Cliffs, NJ: Prentice Hall, 1986.

[15] M. N. Uddin, T.S. Radwan and M.A. Rahman, “Performances of Fuzzy Logic Based Indirect Vector Control for Induction Motor Drive,” IEEE Trans. On Industry Applications, Vol. 38, No. 5, pp. 1219-1225, 2002.

[16] P. Enjeti and W. Shireen, “A New Technique to Reject DC-Link Voltage Ripple for Inverters Operating on Programmed PWM Waveforms,” IEEE Trans. Power Electron., Vol.7, pp.171–179, 1992.

[17] J. Anderson and F.Z. Peng, “Four Quasi Z-Source Inverters,” IEEE Power Electronic Conf., pp. 2743-2749, 2008.

[18] F. Blaabjerg, H.H. Hansen and S. Hansen, “A New Optimized Space-Vector Modulation Strategy for a Component-Minimized Voltage Source Inverter,” IEEE Trans. On Power Electronics, Vol. 12, No. 4, 1997.

[19] P.Q. Dzung, L.M. Phuong, P.Q. Vinh, N.M. Hoang and T.C. Binh, “New Space Vector Control Approach for Four Switch Three Phase Inverter (FSTPI),” IEEE PEDS Conf., pp. 1002-1008 , 2007.

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