Application of Barycentric Coordinates in Space Vector PWM Computations

Abstract

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 spacevector 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.INDEX TERMS Space-vector PWM, three-level NPC inverter, barycentric coordinates.

Direct Modulation for Conventional Matrix Converters Using Analytical Signals and Barycentric Coordinates

“…A mathematical expression for computing the PWM duty cycles can be constructed in an explicit algebraic form based on the triangle vertices coordinates in two-dimensional Cartesian reference frame [38]. Considering the vectors arrangement illustrated in Fig.…”

Analytical Formulation and Minimization of Voltage THD in Staircase Modulated Multilevel Inverters With Variable DC Ratios

“…One of the major challenges of MLI operation is output voltage THD minimization while maintaining desired MI [4]. This is achieved either by fundamental-frequency switching, such as SCM or by high-frequency control strategies, such as pulse width modulation (PWM) and space vector modulation (SVM) [4], [5]. While PWM and SVM may provide better overall performance, they may not be suitable for high power applications due to higher switching losses.…”

A New Concept of PWM Duty Cycle Computation Using the Barycentric Coordinates in a Three–Dimensional Voltage Vectors Arrangement

“…Growing complexity of VSI topologies entails a significant increase in the complexity of Pulse Width Modulation (PWM) methods suitable for these inverters. This paper addresses the above problem by proposing an effective 3D-SVM computing algorithm based on barycentric coordinates [6] for 3-level 4-leg diode-clamped VSI. The proposed algorithm can be applied for 4-wire 3-phase applications such as DSTATCOM, multi-source Hybrid Energy Storage Systems, Active Power Filter [4], [7]- [13], local small power PV generation plant, uninterruptible power supply of various factories, offices, residential houses, etc.…”

“…Moreover, none of the mentioned space-vector diagram transformations are applicable to 4-wire, 4-legs inverters. Analysis and comparison of the mentioned transformation methods with barycentric coordinates for 3-wire system can be found in [6]. One of the few attempts (applicable for 4-wire systems) to compute the duty cycles of the actual (i.e.…”

“…Section III contains a brief introduction the used 3D-SVM modulation and barycentric coordinates in the modulation algorithm. Proposed modulation algorithm is based on [20] but developed by balancing DC-link voltages [21]- [24], accurate generation of output voltages regardless of unbalanced capacitor voltages [18], [19], fast duty cycles calculations algorithm based on barycentric coordinates [6] and optimal switching state sequence. Experimental results are introduced in Section IV to validate the effectiveness of the proposed duty cycle computation.…”