Constant Voltage Constant Frequency Control for Single Phase Three Level Inverter
Nihat Öztürk
Rıdvan Canbaz
Emre Çelik
Electrical and Electronics Engineering Department, Gazi University, Faculty of Technology, Ankara, Turkey
[email protected],
Electrical and Electronics Engineering Department, Gazi University, Faculty of Technology, Ankara, Turkey
[email protected]
Electrical and Electronics Engineering Department, Gazi University, Faculty of Technology, Ankara, Turkey
[email protected]
Abstract—This paper proposed a single-phase three-level inverter that has constant voltage constant frequency (CVCF) operation system. Harmonic analyses with linear and nonlinear loads have been realized to measure the robustness of the proposed technique. It has been shown that the proposed technique has 15% less harmonic distortion and better performance than the conventional inverter for the same load and switching frequency. The constant voltage and frequency used feedback PI control blocks. The system stability was analyzed with the help of Bode curves. The proposed control schema is verified by MATLAB/Simulink results and the results prove that the proposed method is able to achieve not only low harmonic distortion but constant voltage and constant frequency for various operating conditions. Keywords: Multi-level inverter, CVCF control, harmonic distortion.
I.
INTRODUCTION
Voltage source pulse width modulation (PWM) inverters have been widely used in industrial applications such as uninterruptible power supplies, variable speed drivers, and renewable energy source [1]. One of the disadvantages of voltage source pulse width modulation (PWM) inverters is that the PWM rectangular voltage and current waveforms cause turn-on and turn-off losses that limit the operating frequency [2,3]. A variety of switching techniques have been proposed to reduce the amount of losses in the PWM inverters. Techniques for reducing switching losses and switching stress, in the form of snubber circuits, are also well established. Furthermore, different switching techniques are also used to reduce both switching losses and switching stress [4-5]. One of them this technique is multilevel inverter topology. Multilevel inverter topologies (MLIs) are increasingly being used in medium and high power applications due to their many advantages such as low power dissipation on power switches, low harmonic contents and low electromagnetic interference (EMI) outputs. The selected switching technique to control the inverter will also have an effective role on harmonic elimination while generating the ideal output voltage. [6]. Three different topologies have been proposed for multilevel inverters: diode-
clamped (neutral-clamped), capacitor-clamped (flying capacitors) and cascaded multi cell with separate dc sources [7]. Constant-voltage constant-frequency (CVCF) PWM DC/AC inverters are widely employed in various AC power conditioning systems such as variable speed drive, automatic voltage regulators and uninterruptible power supply systems. A good power supply should have the nominal constant output under disturbances and uncertainties, optimum dynamic response to disturbances, and it remains stable under all operating conditions. Total Harmonic Distortion (THD) of output voltage is one important index to evaluate performance of inverters. Nonlinear loads causing distortion are major sources of THD in AC power systems. [8-12]. In this study, a three-level inverter CVCF added superiority. Thus, harmonics are minimized without requiring high switching frequency. Harmonic analyses with linear, nonlinear loads and also third harmonic injection have been realized to measure the robustness of the proposed technique. Analyses has shown that the proposed technique has about 45% less harmonic distortion and better performance than the conventional inverter for the same load and switching frequency. The constant voltage and frequency used feedback PI control blocks. The system stability was analyzed with the help of Bode curves. The proposed control schema is verified by MATLAB/Simulink results and the results prove that the proposed method is able to achieve not only low harmonic distortion but constant voltage and constant frequency for various operating conditions. II.
SINGLE PHASE THREE LEVEL INVERTER
The diode clamped multi-level inverter proposed by Nabae, Takashi, and Akagi in 1981 was named as neutral point converter and was essentially a three-level diode clamped inverter as shown in Figure1. [13].
The circuit diagram of a single-phase full-bridge voltagesource CVCF inverter is shown in Figure2. Since the switching frequency is much higher than the natural frequency of the output LC filter, the dynamics of inverter are mainly determined by its LC filter. Dead-time effect and inevitable loss in every part of the inverter offered a litter damping. The damping effect can be summarized as a small resistor connected in series with the filter inductor.
Figure 1. Diode clamped multi-level inverter circuit
Figure 2. Single-phase three-level inverter contr
Figure3 shows the circuit model of an inverter. The voltage source U can take five values: +E, +E/2 0, -E/2 and -E. The state equations of the inverter are [14]. ⎡ . ⎤ ⎡ 0 ⎢V c ⎥ ⎢ ⎢ . ⎥=⎢ 1 ⎢ i ⎥ ⎢− ⎣ L ⎦ ⎣ L
1 ⎤ ⎡ V ⎥ ⎢0 ⎡ ⎤ c C +⎢ ⎥ ⎢ ⎥ 1 r − ⎥⎣iL ⎦ ⎢ L⎦ ⎣L
−
1⎤ C ⎥ ⎡U ⎤ ⎥⎢ ⎥ 0 ⎥⎣ I ⎦ ⎦
(1)
The transfer function of the proposed inverter model can be found using Eq.1
1 LC LC 1 s2 + s+ RC LC
10 fg ≤ fr ≤ ( fsw / 2 )
(3)
fg =Main wave frequency fr =Cut-off frequency fsw =Switching frequency
Figure 3. The circuit model of LC filter.
Vo = G (s) = Vi
Cut-off frequency fr is chosen between main wave frequency fg and switching frequency fsw for elemination of outside noises. The most appropriate value of cut-off frequency is calculated on equation 3.
(2)
The single-phase three-level inverter produces different switching signals from conventional two-level and three-phase three-level inverter [16]. The proposed inverter control model was simulated in MATLAB/Simulink environment. The voltage across the load is taken as the feedback in this study. An error signal is obtained by subtracting the actual output from the reference set point, which is passed through the PI controller producing the control signal. As for the PI parameters, they are found to be Kp=0.075 and Ki=0.213 by means of the Ziegler-Nichols method. The switching signals are produced by comparing the control signal with the carrier signals. The switching signals of
the single-phase three-level inverter are shown in Figure4. In this paper, sinusoidal pulse width modulation technique is used. In this method, a high frequency triangular carrier signal is compared with the more low-frequency sine. Gate signals are then generated by the results of the comparing. Figure4
presents the basic PWM method for the proposed control of the single-phase three-level diode-clamped inverter. The PWM technique is realized using four triangular signals shifted and differently compared with the control signal [16].
Figure 4. Production of switching signals for single-phase three-level inverter.
Figure5 shows the switching signals for the single-phase diode-clamped three-level inverter. These signals are generated with the help of the circuit given in Figure4.
(a) Figure6. The bode curve for proposed inverter.
Figure6 shows the bode diagram of the system. If gain and angle margins are positive, then the system will be stable. The gain and angle margins of the designed system are calculated as |-180|-|-15|=165 and 0-|-110|=100, respectively. Since the two results are positive, the designed system is stable. The proposed and conventional inverters operated under the same conditions. The obtained results are reported in Table 1. It can be seen that harmonic distortion for the linear loads is less than those for the nonlinear loads. The inverter parameters used in this study are also given in Table 2. TABLE I COMPARISON OF TWO AND THREE-LEVEL INVERTERS Linear Load Switching Frequency
(b) Figure5. The produced switching signals for single-phase three-level inverter a) Circuit for switching signal production b) Switching signals.
Harmonic Distortion (THD %)
Two Level Three Level Two Level Three Level
Nonlinear Load
5kHz
5kHz
5kHz
5kHz
3.37
3.44
1.49
2.19
TABLE II INVERTER PARAMETERS
DC bus voltage Switching frequency Filter inductor Filter capacitor Load
100 V 5 kHz 1mH 10μF 20Ω
so that the order of the lowest harmonic will be 13th [17]. The generation of the switching signals with third harmonic injection PWM method is as shown in Fig.9 and Fig.10.
Figure 9. The third harmonic of MATLAB / Simulink in the production.
Figure7. The FFT analysis of the two-level inverter for the resistive load (R = 20Ω). Figure10. The third harmonic reference signal is superimposed.
In case of harmonic the carrier signal, output harmonics was observed to be less in the three-level inverter. Table 3 shows the comparison between two and three-level inverters with third harmonic injection.
Figure8. The FFT analysis of the three-level inverter for the resistive load (R = 20Ω).
Fast Fourier Transform (FFT) analyses of the two inverters were made in Matlab/Simulink environment. These results are shown in Figure7 and Figure8. It has shown that 150 and 250Hz high-harmonic production. It can be clearly seen from these figures that the three-level inverter has eliminated 3rd, 5th and 7th harmonics. The addition of the third harmonic makes it possible to increase the maximum amplitude of the fundamental component in the reference and output voltages. Harmonic elimination techniques, which are suitable for fixed output voltage, increase the order of harmonics and reduce the size of the output filter. However, these advantages should be weighed against increase in switching losses of power devices and iron losses in transformer due to high harmonic frequencies. It is not always necessary to eliminate tripled harmonics, which are not normally present in three-phase connections. Therefore, in three-phase inverters, it is preferable to eliminate 5th, 7th and 11th harmonics of the output voltages,
TABLE III COMPARISON BETWEEN TWO AND THREE-LEVEL INVERTERS WITH THIRD HARMONIC INJECTION. Linear Load Switching Two Level 5kHz Frequency Three Level 5kHz Harmonic Two Level 8.74 Distortion Three Level 6.57 (THD %)
III.
CONCLUSION
This paper presents a single-phase three-level inverter for CVCF control including a PI controller. The proposed threelevel inverter and conventional inverter have been tested under the same operational conditions to achieve a comparative study. Consequently, it has been observed that the proposed single-phase three-level inverter can successfully reduce the harmonics for the linear and nonlinear loads. Simulation results show that the proposed control strategy is capable of supplying for both linear and nonlinear loads with excellent voltage regulation and minimum harmonic distortion in the load voltage. The inverter operates in PWM mode without the switching transition times. The technique can easily be applied to the PWM inverter structure in switching control algorithms without any restriction. Furthermore, the proposed technique can also be used for UPSs in order to decrease the harmonic distortion.
ACKNOWLEDGEMENT This work was supported by the Gazi University Scientifically Research Project under Grant 07/2011-20. REFERENCES [1]
Wang C.M, “Zero-voltage-switching DC/AC inverter”, Electric Power Applications, IET, vol.1, pp.387-394, 2007.
[2]
Chung H., Hui S.Y.R., and Tse K.K., “Reduction of power converter EMI emission using soft switching technique”, IEEE Transaction on Electromagnetic Compability, vol.40, pp.282-287,1998..
[3]
Guo Z., and Kurokawa F., “Control and PWM Modulation Scheme for dead-Time Compensation of CVCF Inverters”, 31st International Telecommunications Energy Conference, 2009. INTELEC 2009, pp.1-6, 2009.
[4]
Chuang Y.C., Chuang H.S and Ke Y.L., “Design and Implementation of Battery Charger with Zero-Voltage-Switching-Resonant Converter for Photovoltaic Arrays”, Industrial and Commercial Power Systems Technical Conference, 2006, pp.1-6, 2006.
[5]
Bal G. and Öztürk N., “A Novel Control Technique for Soft Switching Sinusoidal PWM Inverter”, Electric Power Components and Systems, vol. 39, no.1, pp. 31-45, 2011.
[6]
Çolak I., Kabalci E. and Bayindir R., “Review of multilevel voltage source inverter topologies and control schemes”, Energy Conversion and Management, vol. 52, pp.1114–1128, 2011.
[7]
Rodríguez, J., Lai, J.S., and Peng F., Z., “Multilevel Inverters: A Survey of Topologies, Controls, and Applications”, IEEE Trans.on Industrial Electronics, vol. 49, no:4, pp.724-738, 2002..
[8]
Zhou K., Wang D., and Low K.S., “Periodic errors elimination in CVCF PWM DC/AC converter systems: repetitive control approach”, Control Theory and Applications, IEE Proceedings, Vol.147, 694-700, 2000.
[9]
Keliang Z. and Danwei W., “Unified robust zero-error tracking control of CVCF PWM converters, Circuits and Systems I: Fundamental Theory and Applications”, IEEE Transactions on, vol. 49, pp. 492-501, 2002.
[10] Ye Y., Zhang B., Zhou K., Wang D., and Wang Y., “High-performance cascade-type repetitive controller for CVCF PWM inverter: analysis and design”, Electric Power Applications, IET, vol.1, 112-118, 2007. [11] Bal G., Öztürk N. and Bekiroğlu E., “Investigation of switching losses for sinusoidal PWM zero current switching inverter and resonant link inverter”, Industrial Electronics, 2009. IECON '09. 35th Annual Conference of IEEE, 590-594, 2009.. [12] Aydemir M.T. and Evran F., “Operation principles of a switched capacitor snubber circuit suggested for half-bridge DC/DC converters”, International Journal of Electronics, vol. 96, no. 1, pp. 29–42, 2009. [13] A. Nabae, I. Takahashi, and H. Agaki, “A new neutral-point-clamped PWM inverter”, IEEE Trans. IA. vol.17, pp. 518-523, 1981. [14] Li Jim, Yong K., and Jian C., “A Novel Fuzzy-Repetitive Control Scheme for Inverters”, Proceedings of the 2002 IEEE, International Symposium on Intelligent Control, Vancouver. Canada October 27-30, pp. 104-109, 2002. [15] Sefa, I.; Altin, N.; Ozdemir, S.; Demirtas, M.; , "dSPACE based control of voltage source utility interactive inverter," Power Electronics, Electrical Drives, Automation and Motion, 2008. SPEEDAM 2008. International Symposium on, pp.662-666, 11-13 June 2008. [16] Stala Robert, “Individual MPPT of Photovoltaic Arrays with Use of Single-Phase Three-Level Diode-Clamped Inverter” IEEE Trans IA, pp. 3456 – 3462. [17] Deepthi J. and Saxena S. N., “Study of Variation of THD in a Diode Clamped Multilevel Inverter with respect to Modulation Index and
Control Strategy”, 2nd International Conference and workshop on Emerging Trends in Technology (ICWET) 2011,
