1. Introduction

The term "power electronics" is used for a family of electrical circuits which convert electrical energy from one level of voltage/current/frequency to other using semiconductor-based switches. The switching process in power electronic converters is called modulation, and development of optimum modulation strategies has been the subject of research in power engineering during several past decades. Electrical power conversion has evolved as new topologies, switching devices, control, and modulation strategies have been proposed. Each group of power electronic converters has its own preferable modulation approach optimizing the circuit performance, addressing such issues as switching frequency, distortion, losses, and harmonics generation. Only voltage source inverters modulation will be discussed below.

Before turning to specific issues of modulation, one needs to establish a common basis to compare the modulation schemes. Different merits are used to evaluate a particular pulse

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width modulation (PWM) implementation: diminished harmonics [1], filtered distortion performance factors [2], and the root-mean-square (RMS) harmonic ripple current [3]. In this text, analytical solutions to PWM strategies are used to compare magnitude of various harmonic components. This approach has a number of advantages [4].

Firstly, the conventional method of determining harmonic components of a switched waveform using fast Fourier transform (FFT) of the waveform is sensitive to the time resolution of the simulation and periodicity of the overall waveform. Moreover, it ensures that intrinsic harmonic components of PWMs are not affected by such factors as simulation round off errors, dead time, switch ON-state voltages, DC bus ripple voltages, etc.

Secondly, PWM strategies can be compared at exactly the same phase leg switching frequency.

And thirdly, the first-order weighted total harmonic distortion (WTHD) is used for a quick comparison of PWMs since it has a physical meaning (the normalized current ripple expected into an inductive load when fed from the switched waveform) and often used performance indicator.

The rest of the paper is organized as follows. In Section 2, information on the double Fourier series expansions and necessary relations is given. Essentials on PWM are provided in Section 3. Different voltage inverter topologies and their analytical PWM solutions are presented in Section 4. Harmonic distortion factors of the introduced inverter topologies, different modulation schemes are compared in Section 5, and a summary on the chapter is given in Section 6.
