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I IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 7 NO. 4 OCTOBER 1992 101 Optimum Control of N-Input K-Output Matrix Converters Pa010 Tenti, Senior Member, IEEE, Luigi Malesani, Member, IEEE, and Leopoldo Rossetto Abstract- Significant devel opment s of the genera l optimum control theory presented in a previous paper [3] are discussed for the specific case of multiphase matrix converters. Results hold, regardless of system configuration, input and output voltage waveforms, and loads. Applications to the most practical converter structures are illustrated, and implementation criteria of the optimum control meth od derived. Simulated results confirm the flexibility and effectiv eness of the approa ch. I. INTRODUCTION HREE-PHASE direct matrix converters, whose basic T onfiguration and control were originally introduced in [ 13, [2], have recently received increasing interest [4]- [8]. In fact, PWM direct conversion techniques do not require reactive elements (except for small filters needed to remove the modulation harmonics) and also allow pre- cise control of the phase and waveform o f converter input currents 161. Small-size, high-efficiency fast-response con verters can be devised accordingly, but a penalty is paid in terms of circuit complexity since a high number of bidirectional fully controlled switches is required. Even the latter problem is being overcome, since high-power, easy-to-drive, low-cost power semiconductors are now available. The major open problem regards control, which should enforce the desired output waveforms (while taking into account the inherent voltage/current limitations of the converter) and also optimize behavior on the supply side, by keeping input cu rrents sinusoidal and in phase with the line voltages. Solutions to this problem are available in the literature [l], [4], [6]-[8] for three-phase to three-phase matrix converters and under some simplifying assumptions (sinusoidal voltages, no energy loss). However, topologies other than three-phase to three-phase converters are of practical interest: fo r exam ple, three-phase to single-phase converters for multifrequency supplies for test/lab equip- ment, six-phase to three- phase or six-phase to single-phase converters for aircraft applications, multiphase rectifiers, etc. Moreover, for multiconverter systems, the control problem should be approached as a whole to optimize the global input/output behavior while avoiding useless energy exchanges between converters, which affect system Manuscript received June 8, 1990; revised May 6, 1992. The authors are with the Department of Electrical Engineering, Univer- IEEE Log Number 9202486. sity of Padova, 35131 Padova, Italy. efficiency [3]. Finally, for converters working, as active power filters [5], achieving input current waveforms fol- lowing nonsinusoidal references is mandatory. For the above reasons, developing a general control theory ca- pable of covering all converter topologies, connections, and operating modes is of prime interest. This problem was first approached in [3], in which a general optimum control theory was developed, based on the transformation of actual converter topology into a suitable equivalent structure. Optimum modulation laws referring to the latter structure were then derived in ana- lytical form, but the antitransformation problem remained open. In this paper the appli cation of the optimum control theory to N-input K-output matrix converters is discussed and general antitransformation criteria are developed. The most important converter configurations are then discussed in detail. 11. GENERAL EPRESENTATION F N-INPUT K-OUTPUT MATRIX ONVERTERS Since the results presented here are based on the optimum control theory discussed in [3], we first summarize The general representation of a N-input K-output voltage-fed matrix converter is shown in Fig. 1, in which u;-uX re supply voltages and u;I-uk are load voltages. Two fundamental hypotheses are made on the cofiverter system. First, outputs are assumed to be decoupled, so that each of them can be controlled independently. This assumption is well verified by all voltage-fed mattix converters, if the internal impedances of the supply are small enough. Second, as shown in Fig. 1, the system is assumed to be made up only of ideal, lossless switches and trans- formers. This implies that possible output voltages (cor- responding to all possible statuses of the converter switches) are independent of load currents and result from linear combinations of supply voltages. A . Single-Output Subsystems According to the above hypotheses, the N - to K-phase system of Fig. 1 can be split into a set of K N-phase to single-phase subsystems, a s shown in Fig. 2. In turn, each single-output subsystem can be represented either by the scheme of Fig. 3(a) sta r connection) or that of Fig. 3(b) 0885-8993/92 03.00 992 IEEE

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