# Three-Phase Circuits

IN THIS CHAPTER

12.1 Introduction

12.2 Three-Phase Voltages

12.3 The Y-to-Y Circuit

12.4 The Δ-Connected Source and Load

12.5 The Y-to-Δ Circuit

12.6 Balanced Three-Phase Circuits

12.7 Instantaneous and Average Power in a Balanced Three-Phase Load

12.8 Two-Wattmeter Power Measurement

12.9 How Can We Check … ?

12.10 DESIGN EXAMPLE—Power Factor Correction

12.11 Summary

Problems

PSpice Problems

Design Problems

## 12.1 Introduction

In this chapter, we will begin to analyze three-phase circuits. These circuits consist of three parts: a three-phase source, a three-phase load, and a transmission line. The three-phase source consists of either three Y-connected sinusoidal voltage sources or three Δ-connected sinusoidal voltage sources. Similarly, the circuit elements that comprise the load are connected to form either a Y or a Δ. The transmission line is used to connect the source to the load and consists of either three or four wires. These circuits are described using names that identify the way in which the source and the load are connected. For example, the circuit shown in Figure 12.3-1 has a Y-connected three-phase source and a Y-connected load. The circuit in Figure 12.3-1 is called a Y-to-Y circuit. The circuit in Figure 12.5-1 has a Y-connected three-phase source and a Δ-connected load. The circuit in Figure 12.5-1 is called a Y-to-Δ circuit.

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