Implementation of SHE-PWM Switching Method for AC/AC Converters

Transcription

1 J. Basic. Appl. Sci. Res., ()-9,, TextRoad Publication ISSN 9-3 Journal of Basic and Applied Scientific Research Implementation of SHE-PWM Switching Method for AC/AC Converters Hassan Feshki Farahani,* and Somayeh Salehi Feshki Department of Electrical Engineering, Ashtian Branch, Islamic Azad University, Ashtian, Iran Department of Electrical Engineering, Ashtian Branch, Islamic Azad University, Ashtian, Iran ABSTRACT Power electronic convertors switching especially AC/AC converters (AC choppers) are of great importance. Different switching methods for AC choppers have been presented so far that each has its own advantages and disadvantages. In this paper, a switching strategy based on selective harmonics elimination is proposed. In this method, different harmonics can be desirably selected from output and then they can be removed. In this type of switching, the output is changed between two sinusoidal values which can lead to TDH reduction. According to harmonics application and importance, desired number of harmonics can be chosen. In this study, this switching has been investigated for three following modes. Amplitude control without harmonics elimination, elimination of th and 7 th harmonics and output amplitude control and elimination of th, 7 th, th and 3 th harmonics with output amplitude control are the mentioned modes. For each mode, the relevant equations and switching angels have been calculated. To verify the efficiency of the proposed method, a sample AC chopper has been simulated by PSpice and the obtained results have been analyzed and investigated. KEY WORDS: AC Chopper, SHEM Switching, Inverter, Selective Harmonics Elimination, PSpice. I. INTRODUCTION One of the most important needs of industry equipments is continuous variation of AC voltage. There are different techniques for AC voltage variation that among them, one can mention AC/AC converters. This method continuously changes voltage but one of its disadvantages is producing harmonics in voltage variation process which is undesirable. Another method of voltage variation is using tap changers which has some disadvantages and advantages. The down point of this method is that voltage variation is not continuous and several output voltage values are discreetly changed but in comparison with AC/AC converter, it does not inject any harmonics to the grid. These mentioned problems and limitations for AC voltage variation should be modified. One of the ways to modify is to use AC choppers. In this method, output voltage varies between two sinusoidal values (upper and lower binderies). Each band is chosen by user and has considerable effect on AC chopper operation. Different switching methods for AC choppers are presented which each one have advantages and disadvantages. In [], a sample AC chopper with two taps is presented. In this circuit, a series transformer has been used to compensate output voltage. The switching method used in this paper is PWM. In [-3] voltage regulation has been done using semiconductor devices. In these circuits, cost is considered as objective design. In [], PWM method has been used to control AC choppers. Among the advantages, linear control of fundamental component amplitude and output voltage harmonics elimination can be mentioned. In [], differences between conventional and electronic tap changers have been investigated. Some modifications for conventional tap changer controller have been proposed as well. N. Burany proposed a switching strategy for matrix converters using IGBT s, or similar fast unidirectional switches, to solve the ac commutation problem. It is based on detecting the polarity of the load current and voltage and assuring a permanent freewheeling path for the current during the process [6]. This solution and some variants have been widely used in matrix converters [7-], and it is also suitable for any direct AC/AC converters [-]. In this paper the solution is adapted for voltage regulation in fast chopped two-tap changers and new solutions to guarantee a safe commutation are analyzed and tested. The other switching strategy which is usually used for DC/AC converters is selective harmonic elimination (SHE) [-8]. In this study, SHE switching method for an AC chopper is presented. In this method, different harmonics can be desirably selected and eliminated from the output. Besides, in this paper, harmonics equations and switching angles have been obtained and by these equations, harmonics up to 3 th order have been eliminated. To verify the presented method, a sample AC chopper has been simulated by PSpice software and the obtained results have been tested. The paper structure is as follow: in part III, the equations of voltage waveform and switching angles for selective harmonic elimination are proposed. In part IV, the simulation results are studied and investigated and finally in V, the conclusion section is presented. II. AC CHOPPER AND ITS EQUATION Chopper circuit is shown in Fig.. In this figure, two four-quadrant switches have been used. AC output voltage can be varied by controlling these switches. Different controlling methods for these switches have been presented which in this paper; SH-PWM switching method is proposed. In this method, fundamental component amplitude can be controlled by *Corresponding Author: Hassan Feshki Farahani, Department of Electrical Engineering, Ashtian Branch, Islamic Azad University, Ashtian, Iran. Tel.: + 98 (9) 99; fax: hfeshki@yahoo.com

2 Farahani and Feshki, creating notches in output waveform and different harmonics from different orders can be desirably chosen and then eliminated. It should be considered that choosing harmonics is desirable and it is up to users. In this paper, three different modes are investigated which are as follow: Mode I: Amplitude controlling without harmonics elimination Mode II: Amplitude controlling with elimination of th and 7th harmonics Mode III: Amplitude controlling with elimination of th, 7th, th and 3th harmonics Also, how to use this method for AC chopper switching is explained. Transf ormer S D Vin Ls D S Rload + Vout - Lp Ls S D D S A. Determining equations for mode I Fig. AC chopper circuit γ(t), β(t), V up (t), V down (t) and ut (t) wave forms of AC chopper are plotted in Fig.,. The output can be expressed using these signals. Two functions γ(t) and β(t) are complementary and regarding that these functions are even, as a result, they also have DC component. By writing Fourier Series for γ(t) waveform, it can be viewed that there are not any odd harmonics in output. The Fourier series of γ(t) can be written as: n n n cos sin(n ) cos sin(n ) 3 3 n n n,3,,7,... The relation between γ(t) and β(t) can be written as: ( t) (t) So, frequency spectrum of β(t) is written as: n cos sin(n ) 3 n n n n cos sin(n ) 3 n () () (3) By multiplying γ(t) and β(t) by two sinusoidal signals (according to Fig.), two other sinusoidal signals will be created as follow: V (t) (t) V sin( t) () V up down up, max (t) (t) V down, max sin( t) Where V up,max > V down,max. Output voltage waveform will be obtained by summing two equations () and (): V (t) V (t) V (t) out up sin( t) V down up,max (t) V down,max (6) (t) (t) () 3

3 J. Basic. Appl. Sci. Res., ()-9, (t) (t) V up (t) V down (t) (t) /3- /3- /3+ / Fig. Waveforms of γ(t), β(t), V up (t), V down (t) and ut (t) in mode I Where output voltage is an odd function and it is expected that there are no even harmonics in it. Equations (), (3) and (6), show that output voltage is a function of α. That is, by varying α, output voltage will be changed. By specifying Fourier series coefficients of γ(t) and β(t) and also the relation between these two signals and output voltage, Fourier series can be written for output voltage and all harmonics coefficients are obtained. The existent harmonics in output are of 6k± order and even harmonics amplitude is equal to zero. The fundamental component value of output voltage is as follow: Vup,rms Vdown,rms Vout,f Vdown,rms sin( ) (7) To control the amplitude between Vm and Vm, it is needed that α is varied from to 3 degrees. Furthermore, by varying output from Vm to Vm, modulation index is varied from to. So, modulation index can be written as: Vout,rms Vdown,rms m (8) V V up,rms down,ms The relation between modulation index and α angel is shown in Fig.3. According to this figure, the more α is increased, the higher the modulation index value is. In other words, as α is increased, the notch width is decreased and consequently the RMS value of output voltage will be increased. 3 [Degree] Modulation Index [%] Fig.3 relation between α and modulation index in mode I B. Determining equations for mode II In this mode, in addition to fundamental component amplitude control, the th and 7 th harmonics are also eliminated. Similarly to mode I, Fourier series for output voltage can be written here. Output voltage waveform for a cycle and a quarter of a cycle is plotted in Fig.. The th and 7 th harmonics can be removed by Fourier series. (t) [V] t (Degree) (t) [V] /6 /3-3 /3 - /3 + /3 + 3 / t (Degree) Fig. Output waveform a) for one cycle b) for quarter of waveform in mode II

4 Farahani and Feshki, 3 Degree Modulation Index(m) Fig. relation between α to α 3 and modulation index in mode II In this figure, there are not any odd harmonics (the function is odd). Fourier series for waveforms of γ(t) and β(t) can be expressed as following equations: n sin n n sin n 3 n sin n sin n 3 sin 3 6 sin n 3 n sin sin n 3 3 n n sin n sin n sin sin n 3 n 6 3 () sin n sin n sin n Fourier series coefficients and fundamental component are obtained using (6), (9) and (). Voltage fundamental component can be expressed as: 3 Vout,f 3 sin sin 8 sin 3 3 sin 3 sin sin The above equation shows that fundamental component is a function of α to α 3 angles. Therefore, by variation of these angles, the fundamental component of output voltage can be controlled from V up,rms to V down,rms. To remove th and 7 th harmonics, the relevant Fourier series coefficient should be equal to zero. Also to control amplitude, fundamental component will be equal to modulation index. So, finally there are three equations and four variables which can be solved for different values of modulation index and α to α 3 values will be obtained versus modulation index as it is shown in Fig.. C. Determining equations for mode III One of the other modes is mode III in which th, 7 th, th and 3 th harmonics are eliminated and output voltage fundamental component amplitude are controlled as well. In this mode, notches in a quarter of output voltage waveform are needed which is shown in Fig.6. () (9) (t) [V] t (Degree) (t) [V] /3- /3-3 /3- /3+ /3+3 /3+ / t (Degree) Fig.6 Output waveform a) for one cycle b) for quarter of waveform in mode III

5 J. Basic. Appl. Sci. Res., ()-9, Fourier series of γ(t) and β(t) functions can be written as () and (3): n sin n sin n sin n sin n n sin n 3 sin n sin n sin n 3 sin n 3 _ sinn 3 n sin n sinn sin n sin n n 3 sinn sin n sinn 3 sin n sinn sinn sin n 3 3 (3) () The relation between fundamental component and α to α angles can be written as () which can be controlled by varying these angels: Vout,f 3 sin sin sin 3 sin sin sin () 3 3 sin 3 sin sin This equation is a function of α to α 3. Also in this case by suitably choosing switching angles, output voltage amplitude can be controlled between V down,rms to V up,rms. The relation between modulation index and switching angles is plotted in Fig.7. These relations are obtained from solving five nonlinear equations. 3 Degree Modulation Index(m) Fig.7 relation between α to α and modulation index in mode III 3 III. SIMULATION RESULTS To verify the presented switching method, it has been used for a sample AC chopper and has been simulated. Voltage V down,max =V and V up,max =9V and output frequency is considered equal to Hz. The load is resistive and is equal to Ω. This simulation has been accomplished by PSpice software which is presented for each mode in following parts. A. Results of Mode I For this case, output voltage waveform is shown in Fig.8a in which voltage is varied between two sinusoidal values. In this mode, modulation index is considered about 6% and only fundamental component is controlled. Maximum output voltage is varied from V to 9V by changing modulation index. Output voltage frequency spectrum is plotted in Fig.8b from which it is clear that there are not any even harmonics in output and harmonics of 6k± order are remained. The first harmonic frequency is Hz or th order and its amplitude is about 3% of fundamental component amplitude. 6

6 Farahani and Feshki, V V -V s ms ms ms ms Time V (.,66.6) (a) V (.,3.66) V Hz.KHz.KHz.7KHz.KHz (b) Fig.8 waveforms of a) output voltage b) spectral frequency of chopper in mode I obtained from simulation B. Results of Mode II In this mode, by creating more notches in output voltage as shown in Fig.9a, fundamental component amplitude can be controlled and also th and 7 th harmonics can be eliminated. Therefore, it is expected that output voltage spectral frequency does not contain th and 7 th harmonics which is obviously shown in Fig.9b. In this case, modulation index and output frequency are also considered 6% and Hz respectively. The first remained harmonic in output voltage is th harmonic ( Hz) and its amplitude is approximately 6% of that for fundamental component. V V -V s ms ms ms ms Time V (.,63.) (a) V (.,.36) V Hz.KHz.KHz.7KHz.KHz (b) Fig.9 waveforms of a) output voltage b) spectral frequency of chopper in mode II obtained from simulation C. Results of Mode III In this case, by creating notches in a quarter of voltage waveform according to Fig.a, the fundamental component amplitude is controlled along with elimination of th, 7 th, th and 3 th harmonics. Fig.b verifies the fact that output 7

7 J. Basic. Appl. Sci. Res., ()-9, voltage frequency spectrum does not contain mentioned harmonics as expected before. The modulation index is considered 6% and the first harmonic frequency is 8Hz (or 7 th harmonic order) and its amplitude is 7. % of fundamental component amplitude. V V -V s ms ms ms ms Time V (.,6.) (a) V (8.,.3) V Hz.KHz.8KHz.KHz (b) Fig. waveforms of a) output voltage b) spectral frequency of chopper in mode III obtained from simulation D. Modulation index variation and its effect on output harmonics Modulation index variation can change output voltage harmonics. To investigate this change, modulation index is decreased from 6% to 3% and spectral frequency for mode I to III is shown in Fig. to Fig.3 respectively. V (.,.8) V (.,8.) V Hz.KHz.KHz.7KHz.KHz Fig. spectral frequency of output voltage in mode I with 3% modulation index V (.,.98) V (.,3.883) V Hz.KHz.KHz.7KHz.KHz Fig. spectral frequency of output voltage in mode II with 3% modulation index V (.,.93) V (8.,.33) V Hz.KHz.KHz.7KHz.KHz Fig.3 spectral frequency of output voltage in mode III with 3% modulation index 8

8 Farahani and Feshki, Tabel. THD in different modulation index and operational modes Modulation Index THD Mode I Mode II Mode III The results of how modulation index variation affects THD are listed in Table.. According to obtained results, modulation index reduction leads to increase THD value. For instance, decreasing modulation index from 6.% to 3.6% in mode I causes THD increase from 8.7 to IV. CONCLUSION In this paper, a switching strategy for AC choppers has been presented based on selective harmonics elimination (SHE- PWM). In this method, by creating notches in output voltage and expressing waveform equations, a number of harmonics have been desirably chosen and eliminated. Besides, by output control between two sinusoidal values, THD has been decreased. Moreover, to evaluate the presented method, an AC chopper has been simulated using PSpice software. The obtained results have shown that different harmonics can be desirably eliminated from output using this method. Finally, the effects of modulation index variation on THD of output voltage have been investigated. According to results, decreasing modulation index leads to increase of THD. V. REFERENCES [] J. C. Campo, et al., "Dual-tap chopping stabilizer with mixed seminatural switching. Analysis and synthesis " IEEE Transactions on Power Delivery, vol., pp [] Y. H. Chung, et al., "Dynamic voltage regulator with solid state switched tap changer " Quality and Security of Electric Power Delivery Systems, 3. CIGRE/PES 3. CIGRE/IEEE PES International Symposium, pp. - 8, 3. [3] J. Faiz and B. Siahkolah, "Optimal configurations for taps of windings and power electronic switches in electronic tapchangers " IEE Proceedings- Generation, Transmission and Distribution, vol. 9, pp. 7 -,. [] G.-H. Choe, et al., "An improved PWM technique for AC choppers " IEEE Transactions onpower Electronics, vol., pp. 96 -, 989. [] J. Faiz, et al., "Differences between conventional and electronic tap-changers and modifications of controller," IEEE Transactions on Power Delivery, vol., pp. 3-39, 6. [6] N. Burany, "Safe control of four-quadrant switches," in Proc. IEEE Industry Applications Conference, IAS 89, pp. 9-9, 989. [7] L. Empringham, et al., "Intelligent commutation of matrix converter bi-directional switch cells using novel gate drive techniques," in Proc. IEEE Power Specialists Conf., Fukuoka, Japan, pp , 998. [8] A. Schuster, "A matrix converter without reactive clamp elements for an induction motor drive system," in Proc. IEEE Power Electronics Specialists Conf., Fukuoka, Japan, pp. 7-7, 998. [9] T. Svensson and M. Alakula, "The modulation and control of a matrix converter-synchronous machine drive," in Proc. European Conf. Power Electronics Applications, Florencia, Italy, pp , 99. [] M. Ziegler and W. Hofmann, "Semi natural two steps commutation strategy for matrix converters," in Proc. IEEE Power Electronics Specialists Conf., Fukuoka, Japan, pp , 998. [] P. Enjet and S. Choi, "An approach to realize higher power PWM AC controller," in Proc. IEEE Applied Power Electronics Conf. Expo., San Diego, CA, pp , 993. [] J. H. Kin and B. H. Kwon, "Three-phase ideal phase shifter using AC choppers," Proc. Inst. Elect. Eng., Elect. Power Appl, vol. 7, pp ,. [3] B. H. Kwon, et al., "Novel topologies of AC choppers," Proc. Inst. Elect. Eng., Elect. Power Appl, vol. 3, pp , 996. [] B. D. Min and B. H. Kwon, "Novel PWM line conditioner with fast output voltage controller," Proc. Inst. Elect. Eng., Proc. Elect. Power Appl, vol., pp. 8-9, 998. [] H. F. Farahani, "Investigation of Modulation Index, Operational Mode and Load Type on the SHEM Current Source Inverter," Journal of applied science, 8. [6] H. Sarabadani and H. F. Farahani, "Investigation the Effect of Load and Modulation Index on the -Level Voltage Source Inverter with SHE-PWM Switching," International Conference on Electrical Energy and Networks. [7] H. F. Farahani, "Modulation Index Effect on the -Level SHE-PWM Voltage Source Inverter," Engineering (Scientific Research), February. [8] H. F. Farahani and F. Rashidi, "A Novel Method for Selective Harmonic Elimination and Current Control in Multilevel Current Source Inverters," International Review of Electrical Engineering,Part A, February. 9