POSTER 6, PRAGUE MAY 4 Enhanced Two-Phase Single Leg Matrix Converter: Analysis, Modelling and Verification Roman KOŇARIK Department of mechatronics and electronics, Faculty of electrical engineering, University of Zilina, Slovakia roman.konarik@fel.uniza.sk Abstract. The paper deals with analysis and modelling of a new type of single- supplied AC/AC converter with two outputs. It consists of single-leg half-bridge matrix converter loaded by the resistive-inductive load in series connection. There are two problems solved in this paper: a) creating a second output shifted by 9 degrees from the original one, and providing frequency control of both orthogonal systems for supplying a two- electrical machine. As simulation results are given: harmonic analysis of the voltage of both s; maximal possible reachable current waveform under R-L load with parametric changes of the time constant of the load. The simulation is resulting in a recommendation for the fair and right design of the converter, and demands to single- or two input supply voltage, respectively, under passive R-L or motoric load. Keywords Matrix converter, VSI converter, single- connection, half bridge connection, bidirectional switch.. Introduction and Motivation The matrix converter topology has become well known after substitution of thyristor devices in cycloconverters by switched-off elements acting in the high-frequency range, in 7-8-years [4]-[7]. Matrix converter replaces two energy conversion by one energy conversion only because within converter is not any energy storage element. Since classical electric conversion uses DC link converters with rather bulky smoothing capacitors, direct matrix converters operate without of DC-link circuit. One of the main advantages of that is unity power factor on its input side. Another advantage is that this converter offers sinusoidal input and harmonic output quantity and bi-directional energy flow [3], [8]. Two induction motor can be supplied either from two single converters or one three- VSI inverter [9]-[], [4]. Another way is using of two matrix converters in half-bridge connection [5]-[7]. Thanks to the absence of any energy storage element, the instantaneous power on input must be the same as the power on the output side. In MxC, it is possible to control the angle between the voltages and current on the input - the output angle differs from input. Another advantage is that the forms of waveforms at the two sides are independent. So the input could be two- AC and output DC, or both could be DC or both could be AC. To save the number power switching elements is also possible to use the one-leg connection of the converter []-[]. The proposed system, in comparison with the conventional system currently used, reduces the number of power switching elements of the converter. Single leg voltage source inverter (Fig.) was presented in []. This topology can work in two operation modes. UAC V C C Driver S S C Main Auxiliary Fig.. Single leg voltage source inverter - pair of contacts and denote solid state relay. In the first operation mode (relay in position ) called Full speed operation, the main is fed by AC voltage source and auxiliary by single leg voltage source inverter. It is necessary to sense AC voltage and ensure 9 shift for auxiliary. In the second operation mode (relay in position ) called Reduced speed operation, the main and auxiliary s are fed by single leg voltage source inverter. Voltage frequency, therefore speed of induction machine, is given by inverter. 9 shift for the auxiliary is ensured by capacitor C. connected in series with auxiliary. Simulation experiments of above scheme have been done and will be presented at the next ELEKTRO 6 International Conference []. M
ROMAN KOŇARIK, ENHANCED TWO-PHASE SINGLE LEG MATRIX CONVERTER. Single Leg Two-Phase Matrix Converter From single leg voltage source inverter was derived schematic for single leg matrix converter (Fig. ). The main reason for such a measure was a strongly non-harmonic current waveform of auxiliary current both in full- and reduced speed regimes, [8]. It is important to note that sinusoidal PWM modulation cannot be used because of decreased magnitude of auxiliary voltage (5 % of the main ), Fig. 5. UAC/ UAC/ V S S C Main Auxiliary M Driver Fig.. Single leg two- matrix converter - symbols S and S denote bi-directional switches; pair of contacts and denotes solid state relay Note that it has to be used AC source with a neutral point. Otherwise, the autotransformer is necessary, Fig. 3. Fig. 5. Voltage of auxiliary of MxC basic scheme for full speed regime and its fundamental harmonic. So, we need double voltage for auxiliary or to use motoric load for half voltage supply. Besides, there are many higher harmonics sum of them, see the figure having negative acting on resulting torque of fed IM motor. Ratio of higher harmonics RMS value and supply voltage RMS expressed as total harmonic distortion of aux voltage is Fig. 3. Single leg two- matrix converter scheme for full speed regime - symbols BiS denote bi-directional switches. Basic Scheme of Enhanced TPSLMxC Converter and its Analysis The basic scheme of the enhanced two- singleleg matrix converter are derived from two- single-leg MxC converter, Fig. 3, first time published in 5, [3], [8]. Improving of the scheme in full speed regime is based on the addition of resonant L resc res components into auxiliary, Fig. 4. Firstly, analysis of the scheme with the passive load will be done. THD u [%] = = U rms U rms U rms = = 3 86 %. () Similar problem with non-harmonic current occurs at reduced speed regime due to the non-harmonic supply voltage; see Fig. 6 for 33.33 Hz [8]. u [pu].5 -.5 -.5.5.5n.T Fig. 6. Principle voltage waveform and its referenced fundamental harmonics at frequency of 33.33 Hz So, the equivalent scheme for enhanced circuit of auxiliary in full speed regime is shown in Fig. 7. Fig. 4. Basic scheme of TPSLMxC for full speed regime.
POSTER 6, PRAGUE MAY 4 3 U aux R aux L aux adding a resonant LC filter. The first way needs to have higher voltage as demanded fundamental harmonic. So, it will be taken into account later on. The third options could be the combination of both methods. Fig. 7. Equivalent scheme for enhanced circuit of auxiliary (without LC resonant components). In this circuit, the voltage of aux is possible to express as u aux (t) = sign[sin(ωt)]abs[cos(ωt)]. () di(t) dt U aux Thus, for current = τ i(t) + τ R u aux(t) (3) 3. Design of LC Filter for Enhancement of Auxiliary Phase Current The design of LC filter for enhancement of auxiliary current of TPSLM converter has been done using []. We have decided to use the serial resonance LC filter for fundamental harmonic. Then L res = U ω res P ; C res = P ω res U (7) Then, see Fig., the circuit can be described by two differential equations for i L and u C. i k+ = ( T τ ) i k + T τ R u auxk = = F i k + G R u auxk (4) where τ = L T R, and T can be chosen as T = and τ = T ; 36 Then F =.9944 and G = ( F ) =.56 and u aux k = sign [sin ( π π k)] abs [cos( k)] (5) 8 8 Using direct and inverse Z-transformation [9], [] and/or special approach [] one can obtain i k = F k + G R F l {u k (l+) }. (6) l=k The simulation result is shown in Fig. 8 Fig. 9. Completing of auxiliary by LC resonant circuit tuned to the geometric center of the frequency range, 33.33 Hz. System of differential equations for that circuit gives di L dt = τ i L L u C + τ R u aux du C dt = C i L (8) where L= L res+l aux. The design of resonant components using [] is described in Chap. 3. L res C res R aux L aux Fig.. Equivalent scheme for enhanced circuit of auxiliary with LC resonant components. Fig. 8. Voltage and current waveforms of MxC basic scheme for full speed regime. The improvement of the auxiliary current waveform is possible either by using sinusoidal PWM modulation or System equations can be simplified into matrix form as d dt ( i L u C ) = A ( i L u C ) + B R u aux (9)
4 ROMAN KOŇARIK, ENHANCED TWO-PHASE SINGLE LEG MATRIX CONVERTER After time discretization, we obtain ( i L = F u ( i L + G C u )k+ C )k R (u aux) k () Where, for chosen T = T ; τ = T F 36 =.9944 and G = ( F ) =.56. (u aux ) k = sign [sin ( π π k)] abs [cos( k)]. () 8 8 ( i L u C )k Consequently = F k + G R F l {u k (l+) } () l=k The simulation results are shown in Fig..5 piecewise linear voltage source in LTSpice was used for reading the text file exciting voltage values. The SPICE simulation shows the strong non-harmonic current waveform in both modes, full speed mode Fig. 3 and reduced speed mode Fig. 5. The improvement of the current harmonics in both modes when LC filter is used is shown in Fig. 4 and Fig. 6. Parameters of the system: R-L load: R= Ω; L=8 mh Operating frequency: 5Hz and 33.33 Hz LC filter parameters are: L res=94.mh, C res=µf for 5 Hz L res=76mh, C res=7.9µf for 33.33Hz.5 -.5 - -.5 -...3.4.5.6.7.8.9 3 Fig.. Principle voltage waveform of i Lres and u Cres in auxiliary at frequency of 5 Hz (33.33 Hz) 4. Verification of TPSLMxC Scheme by LTSpice Circuit Simulator Fig. 3. Voltage and current waveforms in auxiliary at frequency of 5 Hz Fig.. Simulation scheme in LTSpice. Fig. 4. Voltage and current waveforms in auxiliary at frequency of 5 Hz with LC filter tuned to this frequency The exciting voltage waveform was created in m file script in Matlab and the values exported in to a text file. A
POSTER 6, PRAGUE MAY 4 5 L res=.86 H, C res=4.54 µf for 33.33Hz of the aux The final value of the capacitor C res in reduced speed mode for the aux is the serial combination of the 9 shift capacitor and the calculated capacitor of the LC filter. Fig. 5. Voltage and current waveforms in auxiliary at frequency of 33.33 Hz Fig. 7. Current waveforms in main and auxiliary at frequency of 5 Hz (full speed mode) Fig. 6. Voltage and current waveforms in auxiliary at frequency of 33.33 Hz with LC filter tuned to this frequency. 5. Modelling and Simulation Experiments with Motor Load in Simulink Environment Two- induction motor has been used with a TPSLMxC converter. The parameters of the motor are: Main winding stator Rs = 64 Ω, Ls =.H Main winding rotor Rr = 8 Ω, Lr =.5H Auxiliary winding stator Ras = 58.85Ω, Las =.95H Main winding mutual inductance Lms = H Operating frequency: 5Hz and 33.33Hz LC filter parameters are: Full speed mode L res=. H, C res=9 µf for 5 Hz of the aux Reduced speed mode with sinusoidal PWM modulation L res=.9 H, C res=7.856 µf for 33.33Hz of the main Fig. 8. Current waveforms in main and auxiliary at frequency of 5 Hz with LC filter (full speed mode) Fig. 9. Current waveforms in main and auxiliary at frequency of 33.33 Hz (reduced speed mode)
6 ROMAN KOŇARIK, ENHANCED TWO-PHASE SINGLE LEG MATRIX CONVERTER Fig.. Current waveforms in main and auxiliary at frequency of 33.33 Hz with LC filter (reduced speed mode) 6. Conclusion The paper brings analysis, modelling and computer simulation of an enhanced one-leg matrix converter. Analysis and worked-out simulation experiment results have shown, that use of the LC filter can significantly improve the harmonic of the current waveform in both main and auxiliary windings. This improvement has been shown in LTSPICE simulation with an auxiliary voltage source and simple RL load and also in MATLAB-Simulink simulation width complete model of one leg MxC converter and two AC motor drive. It should also be noticed that the simple LC resonant tank is always tuned to only one frequency, and therefore, the operation of the MxC converter is also limited to this one frequency. To eliminate this disadvantage, we suppose to use a switched capacitor [3], [4] which capacity can be continuously changed and adapted to actual requirements given by resonant frequency. It will be done in the next work. [4] A. Zuckerberger, D. Weinstock, A. Alexandrovitz, "Single- Matrix Converter," IEE Proc. on Electric Power App., Vol. 44(4), pp. 35-4, Jul. 997. [5] S. Jeevananthan, P. Dananjayan, R. Madhavan, Novel Single-Phase to Single-Phase Cyclo-Conversion Strategies: Mathematical and Simulations Studies, Int l Journal of Power and Energy Systems, Vol. 7, No. 4, pp. 44-43, 4. [6] B. Dobrucký, P. Špánik, M. Kabašta, Power electronic two- orthogonal system with HF input and variable output, Electronics and electrical engineering (Elektronika ir elektrotechnika), No. (89), pp. 9-4, 9. [7] P. Chlebiš, P. Šimoník, and M. Kabašta, The Comparison of Direct and Indirect Matrix Converters, in Proc. of PIERS Int l Conf., Cambridge, USA, July 5-8,, pp. 3-33. [8] P. Štefanec, B. Dobrucký, One Leg MxC Analysis and Modelling, 5 International Conference on Electrical Drives and Power Electronics (EDPE), The High Tatras, -3 Sept. 5. [9] R. Vích, Z-transformation and some of its Utilization (in Czech). SNTL Mathematical Seminar, Prague, 983. [] I.V. Blagouchine, E. Moreau, Analytic method for the computation of the total harmonic distortion by the Cauchy method of residues, IEEE Transactions on Communications, Vol. 59, No. 9, Sept., pp. 478-49. [] T.K. Moon, W.C. Stirling, Mathematical methods and algorithms for signal processing, Prentice Hall, New York,, Chap. 3. [] B. Dobrucký, M. Beňová, M. A. R. Abdamula S. Kaščák, Design Analysis of LCTLC Resonant Inverter for Two-Stage -Phase Supply System, Automatika - Journal for Control, Measurement, Electronics, Computing and Communications, 3, vol. 54, no. 3, pp. 99-37. [3] A. Lettenmainer, D. Novotny, and T. A. Lipo, Single- induction motor with an electronically controlled capacitor, IEEE Transactions on Industry Applications, vol. 7, no, 988, pp. 38 43. [4] V. Vodovozov, N. Lillo, and Z. Raud, Single-Phase Electric Drive for Automotive Applications, in Proc. of Int l Symp. on Power Electronics, Electrical Drives, Automation and Motion SPEEDAM 4, Ischia, 4, pp. 93-98. About Author Roman KOŇARIK was born in Slovakia. He is currently a postgraduate student at the University of Zilina, Faculty of electrical engineering, Department of mechatronics and electronics. His research interests lie in the fields of analog electronics, power electronics and control systems theory. Acknowledgements The paper was supported from Slovak Grant Agency VEGA by the grant No. /98/5. References [] M. Chomát, and T. Lipo, Adjustable-Speed Single-Phase IM Drive With Reduced Number of Switches, IEEE Transactions on Industry Applications, vol. 39, no. 3, pp. 89-85, May/June 3. [] S. Kaščák, T. Laškody, M. Praženica, R. Koňarik, Current Control Contribution to a Single-Phase Induction Motor Fed by Single-Leg VSI Inverter, accepted paper for ELEKTRO 6 Int l Conference, the High Tatras, Slovakia, May 6, pp. (TBA). [3] B. Dobrucký, T. Laškody, M. Praženica, A Novel Supply System for Two- Phase Induction Motor by Single Leg Matrix Converter Elektronika ir elektrotechnika, ISSN 39-5, vol., no. 4, 5.