Voltage-Sourced Converters in Power Systems

4

Space Phasors and Two-Dimensional Frames

4.1 INTRODUCTION

Chapter 3 investigated control of the half-bridge converter. The half-bridge converter is the main building block of the three-phase voltage-sourced converter (VSC), and the three-phase VSC control deals with simultaneous control of three half-bridge converters. As discussed in Chapter 3, while only a proportional-integral (PI) compensator can enable a half-bridge converter system to track a DC command, the compensator must be of higher order and bandwidth if a sinusoidal command is to be tracked. In a three-phase VSC system, we are invariably interested in tracking sinusoidal voltage or current commands. Therefore, the compensator design task inherently faces the same hardships as discussed in Chapter 3 for a half-bridge converter system tracking a sinusoidal command. The αβ-frame and the dq-frame, the two main classes of two-dimensional frames, are introduced in this chapter to simplify the analysis and control.¹

The αβ-frame enables one to transform the problem of controlling a system of three half-bridge converters to an equivalent problem of controlling two equivalent subsystems. Moreover, the concept of instantaneous reactive power can be defined in the αβ-frame [41]. The dq-frame possesses the same merits as the αβ-frame, in addition to the following:

• If the control is exercised in the dq-frame, a sinusoidal command tracking problem is transformed to an equivalent DC command tracking problem. Hence, PI compensators ...