IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 63, NO. 2, FEBRUARY 2016
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Enhanced Single-Phase Full-Bridge Inverter With Minimal Low-Frequency Current Ripple Guo-rong Zhu, Senior Member, IEEE, Haoran Wang, Biao Liang, Siew-Chong Tan, Senior Member, IEEE, and Jin Jiang, Senior Member, IEEE
Abstract—This paper describes a single-phase fullbridge inverter that possesses limited current ripple at the dc link while providing a sinusoidal square power at the ac output. This is achieved through the addition of an extra pair of switches and complementary control for the fullbridge inverter. The extra switches operate to prevent the double-line frequency ripple current from flowing into the input of the inverter. In doing so, the pulsation component of the sinusoidal square output power is confined to flow between the output capacitors and the load. Thus, the dc link input only supplies the dc component of the output power. Simulation and experimental results validating the proposed solution are presented. Index Terms—DC link, full-bridge inverter, limited current ripple.
I. I NTRODUCTION
S
INGLE-PHASE inverters play very important roles in various applications. Without a large capacitor at the dc link, the sine square output power delivered by a typical inverter will induce a nonnegligible low-frequency current ripple at the input of the inverter. This ripple, at twice the ac output voltage frequency, is detrimental to its input sources [1]–[3], particularly when it is a fuel cell [1] or photovoltaic (PV) system [2]. Techniques proposed for minimizing this ripple include the following: 1) placing a large capacitor at the dc link [4]; 2) utilizing two-stage converters with active control [5]–[10]; 3) incorporating active filter circuits at the dc link [11]–[14], [18]; and 4) using differential inverters with waveform control [15]–[17]. Most of the aforementioned solutions are applied at the dc input of the inverters instead of the dc output. With these approaches, there is a pulsation power that flows from the ac side, Manuscript received November 18, 2014; revised March 9, 2015 and June 23, 2015; accepted August 9, 2015. Date of publication October 16, 2015; date of current version January 8, 2016. This work was supported by the National Natural Science Foundation of China under Project 51107092. G. Zhu and B. Liang are with the School of Automation, Wuhan University of Technology, Wuhan 430070, China (e-mail: zhgr_55@ whut.edu.cn). H. Wang is with the Department of Energy Technology, Aalborg University, 9220 Aalborg East, Denmark (e-mail:
[email protected]). S.-C. Tan is with the Department of Electrical and Electronic Engineering, The University of Hong Kong, Pok Fu Lam, Hong Kong (e-mail:
[email protected]). J. Jiang is with the Department of Electrical and Computer Engineering, University of Western Ontario, London, ON N6A 5B9, Canada (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2015.2491881
Fig. 1. Enhanced single-phase full-bridge inverter circuit.
where it is induced, to the dc side where it is mitigated [4]–[14], [18]. However, confining the pulsation power at the ac side [15], [16] does result in a higher power-conversion efficiency than that achieved by mitigating at the dc side. Nevertheless, this comes at the expense of high-voltage stress on the capacitors of the inverter. In this paper, an enhanced single-phase full-bridge inverter along with a dedicated control methodology (known as the ripple confinement control) is proposed. This inverter achieves minimal low-frequency input current ripple by confining the pulsation power within the output capacitors at the ac side through voltage waveform control. The proposed alteration and control is an entirely different strategy as that presented in [15] and [16] and does not suffer from high-voltage stress. With the proposed technique, capacitors are utilized in both the positive and negative ranges. This results in smaller capacitors required for the same pulsating power as compared to conventional voltage waveform control approaches. II. P ROPOSED I NVERTER S YSTEM A. Inverter Circuit Fig. 1 shows the power circuit of the proposed inverter system. It comprises the four original switches of a conventional full-bridge inverter (T1 , T2 , T3 , and T4 ), two extra switches (T5 and T6 ) for pulsation power control, and two sets of ac filter capacitors (C1 and C2 ) and inductors (L1 and L2 ). Otherwise, no additional storage device is required. Here, C1 is equal to C2 , and L1 is equal L2 . Their respective total values are equal to that of the original capacitor and inductor used in a conventional full-bridge inverter with the same ratings and design specifications. Here, the output voltage is the difference between the
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equals the voltage of point A minus the voltage of point B, i.e., vo = vc1 − vc2
(1)
where vc1 and vc2 are respectively the voltages of ac capacitors C1 and C2 . These voltages are respectively controlled following (2) and (3) through switches T5 and T6 , while vo is maintained as a pure sinusoidal waveform. Note that (2) and (3) are asymmetrical vc1 =
1 Vmax sin(ωt) + F (t) 2
1 vc2 = − Vmax sin(ωt) + F (t). 2
Fig. 2. Proposed enhanced inverter and control system.
voltages of two output capacitors (C1 and C2 ). Note that the same power circuit given in Fig. 1 has been adopted for ac/dc rectification under a different control scheme [12]. B. Control Strategy The proposed controller for the inverter comprises two independent feedback components, namely, the output voltage feedback control and the ripple confinement feedback control. The output voltage feedback control is based on a common pulse width modulation (PWM) voltage control technique, which controls only switches T1 −T4 to generate the desired sinusoidal output voltage vo . The ripple confinement control is achieved through the control of voltages vc1 and vc2 via switches T5 and T6 such that the pulsation power is confined by the output capacitors. Fig. 2 shows an overview of the proposed inverter system with the aforementioned control. The upper portion describes the control strategy for the ripple confinement, and the lower portion represents the control of the full-bridge inverter. For output voltage control, the voltage reference voref is compared with the output voltage vo , and the difference is fed into a proportional–integral (PI) compensator. The output of the PI compensator is compared with a triangular carrier signal to derive the duty cycles for T1 −T4 . For the ripple confinement control, only one capacitor voltage, either vc1 or vc2 , is necessary to be the control variable. Here, vc1 is chosen, and vcref is represented by (2), which is obtained by detecting the peak value of output voltage Vmax and the root-mean-square value of the output current for calculating its peak value Imax . The error between vc1 and vcref is the input of the PI compensator which is consequently modulated to generate the gate signals for T5 and T6 . C. Principle of Operation T1 −T4 are switched according to the bipolar voltage switching scheme of PWM full-bridge inverters. The output voltage
(2) (3)
Here, Vmax and ω are respectively the amplitude and frequency of vo , and F (t) is the required control function for confining the pulsation power. At unity power factor, the load power Pload is Pload = Vmax sin(ωt)Imax sin(ωt) = (Vmax Imax /2) − (VmaxImax /2)cos(2ωt). There are two components here, namely, the dc component Pdc = Vmax Imax /2 and the ac component Pload−pulsation = Vmax Imax cos(2ωt)/2, which represents the double-line frequency pulsation power of the load. In achieving the ripple confinement control, the ac component has to be provided by the capacitors such that the pulsation power flowing between the capacitors and the load must be instantaneously matched, i.e., Pc1 + Pc2 = Pload−pulsation
(4)
where pc1 and pc2 are respectively the power of capacitors C1 and C2 . Then, F (t) can be derived as F (t) = B sin(ωt + θ) (5) 4 /16)+(V 2 I 2 /4ω 2 C 2 ) where the amplitude B = 4 (Vmax max max 2 and the phase angle θ = (1/2) arccos(−(Vmax /4B 2 )) Refer to the Appendix for the derivation. D. Comments The presented controller introduces a waveform with only the fundamental frequency (50/60 Hz) into the capacitors’ voltage. By excluding any dc bias from the waveform function (unlike that in [14] and [15]), the fourth-harmonic current component is absent from the dc link (see Fig. 3). III. S IMULATION AND E XPERIMENTAL R ESULTS A. Simulation Results The simulation of the proposed inverter is performed based on the following ratings: 20-kHz switching frequency, vin = 200 V, C1 = C2 = 60 μF (ac capacitors), and L1 = L2 = 26.4 μH. Fig. 3 shows the voltage and current waveforms, which include the switch currents, capacitor currents, input current, capacitor voltages, and output voltage of the inverter with the proposed control. The switch currents of the respective arms are depicted in Fig. 3(a) (iT 1 , i2 ), Fig. 3(b) (iT 3 , iT 4 ), and
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Fig. 4. Laboratory prototype of the proposed full-bridge inverter system.
Fig. 3. Simulation voltage and current waveforms of the inverter with the proposed control.
Fig. 3(c) (iT 5 , iT 6 ), respectively. Each current pair is 180◦ out of phase. Capacitor currents (ic1 , ic2 ) can be imbalanced because of the imbalanced voltages on the capacitors. With these capacitor voltage settings, the pulsation power is confined at the ac side. Consequently, the input current ripple is suppressed [see Fig. 3(e)]. B. Experimental Results Fig. 4 shows the laboratory setup of the proposed inverter. It has been constructed with the same parameters as that of the simulation. The control is implemented using an ARM controller. Fig. 5(a) shows the voltage and current waveforms of the proposed inverter system without the ripple confinement control that is operating in steady state under a resistive load. Fig. 5(b) shows the same set of waveforms with the ripple confinement control. As shown in the figures, the same output
Fig. 5. Experimental voltage and current waveforms of the inverter (a) without waveform control and (b) with waveform control.
voltage vo is obtained with both control methods, even though the capacitor voltages are asymmetrical in the case of Fig. 5(b). To confine the pulsation power at the ac side, the powers of the capacitors contain an additional component, 2CF(t)F (t) [refer to (A5)]. Therefore, the capacitor voltages contain F (t) [see (2) and (3)] and are of a larger amplitude than that without the ripple confinement control. As a result, the input current ripple with the ripple confinement control [see Fig. 5(b)] is much smaller than that without the ripple confinement control [see Fig. 5(a)]. The experimental results are similar to the simulation results.
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Fig. 6. Frequency characteristic of the input current of the inverter (a) without waveform control and (b) with waveform control.
Fig. 7. Experimental voltage and current waveforms of the inverter under a resistive–capacitive load (a) without waveform control and (b) with waveform control.
Fig. 6(a) and (b) show respectively the frequency spectrum characteristics of the input current of the inverter without and with the ripple confinement control. Without ripple confinement control, the 100-Hz current ripple (amplitude of 0.36 A) is 87.8% of the dc current (0.41 A). With ripple confinement control, the 100-Hz current ripple (amplitude of 0.06 A) is 13.9% of the dc current (0.43 A). The low-frequency current ripple is significantly mitigated. Moreover, the 200-Hz current ripple is below 0.01 A at all times. To further show the validity of the proposed method, the control of the prototype is modified based on a similar derivation, to cater for loads that comprise reactive components. Fig. 7 presents the results of the proposed inverter system with a resistive–capacitive RC load. It is illustrated that, under the RC load, the proposed inverter also achieves a ripple-confined input current (from 0.53 to 0.24 A). Similarly, the system is applicable for resistive–inductive load.
Fig. 8. Flow paths of the double-frequency ripple current of the inverter (a) without and (b) with ripple confinement control.
IV. F URTHER A NALYSIS A. Analysis of Pulsation Power’s Flow Paths With the ripple confinement control, the flow paths of the double-frequency ripple current are altered from that shown in Fig. 8(a) to that in Fig. 8(b). The solid line in Fig. 8(a) depicts the full-bridge inverter with the equivalent LC filter (2C = C1 = C2 , and L = 2L1 = 2L2 ), and the dotted line depicts the additional switches. Here, ripple flows through T1 , T2 , T3 , T4 , and the dc source. In Fig. 8(b), all the switches operate under the proposed control method to alter the flow path of the pulsation power. Here, the ripple
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TABLE I C OMPARISON A MONG D IFFERENT M ETHODS
Fig. 9. Current stresses on the various components.
Fig. 10. Voltage stresses on the various components.
flows through T1 , T2 , T3 , T4 , and the additional switches T5 and T6 . B. Stress Comparison of Circuit Components Fig. 9 depicts the current stresses on the various components of the inverter with and without the proposed control method. Without the ripple confinement control, the current stresses on T1 , T2 , and L1 increase, while those on T3 , T4 , and L2 decrease, with T5 and T6 switched off. Fig. 10 depicts the voltage stresses on the various components of the inverter with and without the proposed control. As shown, the voltage stresses on the switches are identical for both cases. However, with the ripple confinement control, the voltage stresses on the capacitors are higher. C. Comparison Among Different Power Decoupling Methods The comparisons of these methods from the number of devices and voltages stress are in Table I. From the comparison among different methods in Table I, it can be found that the control complexity of the system is reduced by adding an additional pair of switches. Compared with the power decoupling method, the proposed method reuses the LC filter as the decoupling storage elements to reduce the number of elements and cost. Moreover, the capacitor voltages of the inverter with existing voltage waveform control [15], [18] contain both the dc-bias and ripple parts, which result in only having the positive half of the capacitors’ capacity being used for storing the pulsating power. This leads to high capacitor voltage stress (see Fig. 11).
Fig. 11. Voltage stress of the output capacitors under the traditional control method and the proposed method.
With the proposed method, the entire capacity of the capacitors (positive and negative sides) will be utilized to support the same pulsation power, which follows: pc−pulsation =
1 CΔu2 2
(6)
where Δu is the value from peak to valley of the capacitor voltage. Therefore, the voltage stress of capacitors is smaller with the proposed technique (see Fig. 11). Moreover, smaller capacitors will be required to buffer the same pulsation power. V. C ONCLUSION A single-phase full-bridge inverter system that achieves limited double-frequency ripple at the dc link is proposed. Without any additional storage device, the pulsation power is confined between the load and ac capacitors through two additional switches and a feedback control for injecting a fundamental frequency waveform to the capacitors’ voltages. The proposed method can eliminate the dc electrolytic capacitor and achieve a lower voltage stress on the capacitors than traditional methods. Furthermore, this solution is applicable to loads with reactive components. A PPENDIX Assuming that the output current of the inverter is given as io = Imax sin(ωt)
(A1)
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where Imax is the amplitude of the output current, then the ripple power of the load is pload−pulsation =
Vmax Imax cos(2ωt). 2
(A2)
From (2) and (3), the currents of capacitors C1 and C2 (assuming C1 = C2 = C) are, respectively, 1 dvc1 =C Vmax ω cos(ωt) + F (t) (A3) ic1 = C dt 2 1 dvc2 = C − Vmax ω cos(ωt) + F (t) (A4) ic2 = C dt 2 where F (t) is the first-order time derivative of F (t). The total power on these two capacitors is pc1 + pc2 = vc1 · ic1 + vc2 · ic2 1 ωCV2max sin(2ωt) + 2CF(t)F (t). 4 By substituting (A2) and (A5) into (4), we have
(A5)
=
Vmax Imax 1 ωCV2max sin(2ωt) + 2CF(t)F (t) = cos(2ωt) 4 2 (A6) which can be rearranged to give
2 θ θ A A A F (t)= sin ωt+ + cos ωt+ +k− 4ω 2 4ω 2 4ω (A7) where k is an integral constant and 2 I2 4 Vmax ω 2 Vmax max . (A8) A= + 2 16C 64
[6] L. Zhang, X. Ruan, and X. Ren, “Second-harmonic current reduction and dynamic performance improvement in the two-stage inverters: An output impedance perspective,” IEEE Trans. Ind. Electron., vol. 62, no. 1, pp. 394–404, Jan. 2015. [7] B. Gu, J. Y. Zhang, L. H. Zhang, B. F. Chen, and J. S. Lai, “Control of electrolyte-free micro-inverter with improved MPPT performance and grid current quality,” in Proc. IEEE APEC, 2014, pp. 1788–1792. [8] P. F. Ksiazek and M. Ordonez, “Swinging bus technique for ripple current elimination in fuel cell power conversion,” IEEE Trans. Power Electron., vol. 29, no. 1, pp. 170–178, Jan. 2014. [9] J. M. Galvez and M. Ordonez, “Swinging bus operation of inverters for fuel cell applications with small dc-link capacitance,” IEEE Trans. Power Electron., vol. 30, no. 2, pp. 1064–1075, Feb. 2015. [10] M. Su, P. Pan, X. Long, Y. Sun, and J. Yang, “An active power-decoupling method for single-phase ac-dc converters,” IEEE Trans. Ind. Informat., vol. 10, no. 2, pp. 461–468, Feb. 2014. [11] X. Cao, Q. C. Zhong, and W. L. Ming, “Ripple eliminator to smooth dcbus voltage and reduce the total capacitance required,” IEEE Trans. Ind. Electron., vol. 62, no. 4, pp. 2224–2235, Apr. 2015. [12] W. Cai, L. Jiang, B. Liu, S. Duan, and C. Zou, “A power decoupling method based on four-switch three-port dc/dc/ac converter in dc microgrid,” IEEE Trans. Ind. Appl., vol. 51, no. 1, pp. 336–343, Jan./Feb. 2015. [13] T. Shimizu, T. Fujita, G. Kimura, and J. Hirose, “A unity power factor PWM rectifier with dc ripple compensation,” IEEE Trans. Ind. Electron., vol. 44, no. 4, pp. 447–455, Aug. 1997. [14] P. T. Krein, R. S. Balog, and M. Mirjafari, “Minimum energy and capacitance requirements for single-phase inverters and rectifiers using a ripple port,” IEEE Trans. Power Electron., vol. 27, no. 11, pp. 4690–4698, Nov. 2012. [15] I. Serban, “Power decoupling method for single-phase h-bridge inverters with no additional power electronics,” IEEE Trans. Ind. Electron., vol. 62, no. 8, p. 1, Aug. 2015. [16] G. R. Zhu, S. C. Tan, Y. Chen, and C. K. Tse, “Mitigation of lowfrequency current ripple in fuel-cell inverter systems through waveform control,” IEEE Trans. Power Electron., vol. 28, no. 2, pp. 779–792, Feb. 2013. [17] W. Li et al., “Topology review and derivation methodology of singlephase transformerless photovoltaic inverters for leakage current suppression,” IEEE Trans. Ind. Electron., vol. 62, no. 7, pp. 4537–4551, Jul. 2015. [18] T. Yi, F. Blaabjerg, and P. C. Loh, “Decoupling of fluctuating power in single-phase systems through a symmetrical half-bridge circuit,” IEEE Trans. Power Electron., vol. 30, no. 4, pp. 1855–1865, Apr. 2014.
If k = A/4ω, F (t) contains no dc component such that F (t) = B sin(ωt + θ) where
(A9)
4 V 2 I2 Vmax + max2 max 16 4ω C 2
2 1 Vmax θ = arccos − . 2 4B 2
B=
4
(A10) (A11)
R EFERENCES [1] A. Cardenas, K. Agbossou, and N. Henao, “Development of power interface with FPGA-based adaptive control for PEM-FC system,” IEEE Trans. Energy Convers., vol. 30, no. 1, pp. 296–306, Mar. 2015. [2] Y. Liu, H. Abu-Rub, B. Ge, D. Sun, and H. Zhang, “Comprehensive modeling of single-phase quasi-Z-source photovoltaic inverter to investigate low-frequency voltage and current ripples,” IEEE Trans. Ind. Electron., vol. 62, no. 7, pp. 4194–4202, Jul. 2015. [3] Y. Ohnuma, K. Orikawa, and J. Itoh, “A single-phase current-source PV inverter with power decoupling capability using an active buffer,” IEEE Trans. Ind. Appl., vol. 51, no. 1, pp. 531–538, Jan./Feb. 2015. [4] C. Cecati, A. D. Aquila, and M. Liserre, “A novel three-phase single-stage distributed power inverter,” IEEE Trans. Power Electron., vol. 19, no. 5, pp. 1226–1233, Sep. 2004. [5] P. Alemi, Y. C. Jeung, and D. C. Lee, “DC-link capacitance minimization in t-type three-level ac/dc/ac PWM converters,” IEEE Trans. Ind. Electron., vol. 62, no. 3, pp. 1382–1391, Mar. 2015.
Guo-rong Zhu (M’11–SM’15) was born in Hunan, China. She received the Ph.D. degree in electrical engineering from the Huazhong University of Science and Technology, Wuhan, China, in 2009. From 2002 to 2005, she was a Lecturer with the School of Electrical Engineering, Wuhan University of Science and Technology, Wuhan. From 2009 to 2011, she was a Research Assistant/Research Associate in the Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong. She is currently an Associate Professor with the School of Automation, Wuhan University of Technology, Wuhan. Her main research interests are focused on the areas of power electronics and control and the reliability of power electronics systems. Haoran Wang received the B.S. and M.S. degrees in control science and engineering from the Wuhan University of Technology, Wuhan, China, in 2012 and 2015, respectively. From August 2013 to September 2014, he was a joint training research student with the Department of Electrical Engineering, Tsinghua University, Beijing, China. He is currently a Research Assistant with the Department of Energy Technology, Aalborg University, Aalborg East, Denmark. His research interests include power decoupling techniques in single-phase conversion systems and the reliability of capacitors in power converters.
ZHU et al.: SINGLE-PHASE FULL-BRIDGE INVERTER WITH MINIMAL LOW-FREQUENCY CURRENT RIPPLE
Biao Liang received the B.Eng. degree in electrical engineering and automation from South China Agriculture University, Guangzhou, China, in 2013. He is currently working toward the Master’s degree in electrical engineering at the Wuhan University of Technology, Wuhan, China. From August 2014 to September 2015, he was a joint training research student with the Department of Electrical Engineering, Tsinghua University, Beijing, China. His research interests include power decoupling techniques in single-phase conversion systems and power system reliability.
Siew-Chong Tan (M’06–SM’11) received the B.Eng.(Hons.) and M.Eng. degrees in electrical and computer engineering from the National University of Singapore, Singapore, in 2000 and 2002, respectively, and the Ph.D. degree in electronic and information engineering from the Hong Kong Polytechnic University, Hong Kong, in 2005. From October 2005 to May 2012, he was subsequently, a Research Associate, Postdoctoral Fellow, Lecturer, and Assistant Professor in the Department of Electronic and Information Engineering, Hong Kong Polytechnic University. From January to October 2011, he was a Senior Scientist in the Agency for Science, Technology and Research (A∗Star), Singapore. He is currently an Associate Professor in the Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong. He was a Visiting Scholar at the Grainger Center for Electric Machinery and Electromechanics, University of Illinois at Urbana–Champaign, Urbana, IL, USA, from September to October 2009, and an Invited Academic Visitor of the Huazhong University of Science and Technology, Wuhan, China, in December 2011. His research interests are focused on the areas of power electronics and control, LED lighting, smart grids, and clean energy technologies. Dr. Tan serves extensively as a reviewer for various IEEE/Institution of Engineering and Technology (IET) TRANSACTIONS and journals on power electronics, circuits, and control engineering. He is an Associate Editor of the IEEE T RANSACTIONS ON P OWER E LECTRONICS. He is a coauthor of the book Sliding Mode Control of Switching Power Converters: Techniques and Implementation (CRC Press, 2011).
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Jin Jiang (M’90–SM’94) is a Senior Industrial Research Chair Professor in the Department of Electrical and Computer Engineering, University of Western Ontario, London, ON, Canada. His research interests are in the areas of dynamics and control of power plants and power systems, integration of renewable energy resources in the form of microgrids, fault-tolerant control of safety-critical systems, and instrumentation and control of nuclear power plants.
