The paper proposes an alternative and novel approach to the PWM duty cycles computation for Conventional Matrix Converters (CMC) fed by balanced, unbalanced or non-sinusoidal AC voltage sources. The presented solution simplifies the prototyping of direct modulation algorithms. PWM duty cycles are calculated faster by the smooth interpolation technique, using only vector coordinates, without trigonometric functions and angles. Both input voltages and output reference voltages are expressed by analytic signals in the proposed direct modulation. Input voltages are represented by the rotating vector collection in the two-dimensional Cartesian coordinate system. All reference output voltages are located inside the triangular surface, named here as the voltage synthesis field, formed by these rotating vectors. A certain degree of reference signals placement freedom allows to maximize the voltage transfer ratio to 0:866 with less switching compared to the Optimum-Venturini direct method. The proposed solution was verified by simulations and experiments for CMC3 × k. The comparison with the Optimum-Venturini modulation is included. The proposed PWM duty cycle computation approach can also be applied to multiphase CMC converters for any number of inputs as well as outputs.

This paper proposes the use of barycentric coordinates in the development and implementation of space–vector pulse–width modulation (SVPWM) methods, especially for inverters with deformed space–vector diagrams. The proposed approach is capable of explicit calculation of vector duty cycles, independent of whether they assume ideal positions or are displaced due to the DC–link voltage imbalance. The use of barycentric coordinates also permits a well–defined and universal approach to the problem of identifying the region in which the reference vector is located. It completely avoids the use of angles, trigonometric functions and inverse trigonometric functions and is chiefly based on matrix operations which are well suited for digital signal processor implementation. The proposed approach is exposed and validated for the special case of three–level neutral–point clamped (NPC) inverter controlled by a discontinuous space–vector PWM.

This paper proposes the generalized direct modulation for Conventional Matrix Converters (CMC) using the concept of analytical signals and barycentric coordinates. The paper proposes a novel approach to the Pulse Width Modulation (PWM) duty cycle computing, which allows faster prototyping of direct control algorithms. The explanation of the new idea using analytical considerations demonstrating the principles of direct voltage synthesis has been presented in the article. The study concerns mainly the CMC3 × 3 but solutions for 3 × n, 5 × 5, and 5 × 3 topologies have also been discussed. The transformation of instantaneous input voltages to analytic signals great permits for simple presenting of real input voltage conditions such as waveform type, asymmetry or other deformation like higher–order harmonics. The proposed interpolation methods allow for determining the values of PWM duty cycles using simple formulas based on the determinants of the 2nd–degree matrices. Therefore, the proposed method, which based on the barycentric coordinates, frees an algorithm from trigonometry and angles.

This article presents a fast direct pulsewidth modulation (PWM) algorithm for the conventional matrix converters developed in Verilog hardware description language. All PWM duty cycle calculations are performed in one cycle by an atomic operation designed as a digital module using field-programmable gate array basic blocks. The algorithm can be extended to any number of output phases. The improved version of the discontinuous direct analytic voltage PWM (DAV-PWM) method is proposed, in which the use of trigonometry, angles, and program loops has been eliminated. The proposed DAV-PWM is equivalent to the space vector modulation; it can be applied during input asymmetry and also allows for the control of the displacement input angle. The proposal has been verified using the circuit simulation in PSIM, digital structure modeling in ModelSim, and finally through an experiment.

This paper proposes and discusses a concept of a hybrid modulation for the control of modular voltage source inverters with coupled reactors. The use of coupled reactors as the integrating elements leads to significant reduction in the size and weight of the circuit. The proposed modulation combines novel coarsely quantized pulse amplitude modulation (CQ-PAM) and innovative space-vector pulse width modulation (SVPWM). The former enjoys very low transistor switching frequency and low harmonic elimination, while the latter ensures high resolution of amplitude control. The SVPWM is based on the use of barycentric coordinates. The feasibility of the proposed solution is verified by simulations and laboratory tests of a 12-pulse modular voltage source inverters with two-level and three-level component inverters.