Contents I. Introduction
The demand for high power equipment in industries have increased up to megawatt levels. As a result, multilevel inverters (MLIs) have drawn more attention to meet the increasing demand of power ratings and power quality with low harmonics. Various topologies of multilevel inverters have been proposed. Multilevel inverter modulation using SVPWM almost often utilize simplified space vector modulation techniques, which invariably involve trigonometric calculations for their implementation. The implementation of carrier-based pulse-width modulation (PWM) schemes is simpler as compared to SVPWM due to easier selection of carrier and modulation signals. Carrier-based PWM schemes for MLIs simply involve comparison of carrier signals with identified modulating signals. Among the modulation techniques for MLIs, carrier-based pulse-width modulation (PWM) is preferred over space vector pulse-width modulation (SVPWM). It is preferred because SVPWM involves complex calculations to synthesize the reference voltage using the nearest three vectors and to select the appropriate vector from the available redundant vectors [1], [2]. Multilevel inverter modulation using SVPWM often uses simplified space vector modulation techniques, which mostly require trigonometric calculations for implementation. Basically, idea behind SVM is to divide the available voltage levels in the inverter into sectors with active vectors. Each sector represents a different arrangement of active vectors that can be generated by the inverter. The reference space vector is then created by determining the appropriate combination of active vectors based on its position. The SVM algorithm calculates the switching times required to achieve the desired output voltage vector. It considers the angle and magnitude of the reference space vector and compares it with the available voltage vectors. By switching between these voltage vectors at the appropriate times, the desired output voltage waveform using seven-segment switching scheme [3] is generated by the inverter. On the other hand, the implementation of carrier-based PWM schemes is simpler due to the direct selection of carrier and modulation signals. Carrier-based PWM schemes for MLIs involve the simple comparison of carrier signals with modulating signals. Nonetheless, SVPWM offers certain advantages. It allows better utilization of the dc-link voltage and provides flexibility in implementing the switching pattern [4]. Additionally, it is easier to implement digitally since the number of steps involved in modulation process does not increases as the number of levels increases [5]. It also provides better control of the harmonic content in the output and improves the overall efficiency of the inverter. As a result, SVPWM remains a popular alternative to carrier-based PWM techniques for multilevel inverter modulation. The conventional two-level SVM is a fairly established and mature technique. However, extension of the technique to MLIs gets complicated. As the number of inverter output voltage levels increase, the number of space vectors in the space vector diagram becomes n3, where n is the number of levels of the multilevel inverter (for example- for 3 level inverter, number of space vectors is 27 and for 5 level inverters, it becomes 125). Dividing the space vector diagram into component two-level diagrams, using non-orthogonal coordinate systems such as K – L coordinates, g – h coordinates, imaginary coordinates, α-β coordinates, are some of the methods available in the literature to simplify the SVM of multilevel inverters [2]. A common drawback of most of these methods is that they involve reverse transformation to the original a – b – c coordinate system to select from the available redundant vectors. The space vector modulation of MLIs is quite complex on account of the large number of stationary vectors available from an inverter. The identification of the nearest three vectors is quite tedious unless specialized mathematical tools are used. One such tool is the imaginary coordinate transformation technique [6]. Yuan et.al [7] proposed a technique using the imaginary coordinate system wherein the reverse transformation to the a – b – c coordinate system was avoided. However, to facilitate this, the complexity of the algorithm was increased significantly.
