So far, we have learnt all about single-phase circuits. Let us step-up to the three-phase ac circuit.
A single-phase ac power system consists of a generator connected through a pair of wires (a transmission line) to a load.
Make sure to read what is ac circuit first.
Make sure to read:
- What is phasor
- Impedance and admittance
- Kirchhoff’s laws for ac circuit
- Power calculation in ac circuit
And its applications:
- Phase shifter circuit and formula
- AC bridge
- AC op-amp
- Capacitance multiplier circuit
- Wien bridge oscillator
Three-Phase AC Circuits
Figure.(1a) depicts a single phase two wire system, where Vp is the rms magnitude of the source voltage and Ø is the phase.
What is more common in practice is a single-phase three-wire system, shown in Figure.(1b).
It contains two identical sources (equal magnitude and the same phase) that are connected to two loads by two outer wires and the neutral.
For example, the normal household system is a single-phase three-wire system because the terminal voltages have the same magnitude and the same phase.
Such a system allows the connection of both 120 V and 240 V appliances.
|Figure 1. Single-phase systems: (a) two-wire type, (b) three-wire type.|
Circuits or systems in which the ac sources operate at the same frequency but different phases are known as polyphase.
Figure.(2) shows a two-phase three-wire system, and Figure.(3) shows a three-phase four-wire system.
As distinct from a single-phase system, a two-phase system is produced by a generator consisting of two coils placed perpendicular to each other so that the voltage generated by one lags the other by 90°.
|Figure 2. Two-phase three-wire system|
By the same token, a three-phase system is produced by a generator consisting of three sources having the same amplitude and frequency but out of phase with each other by 120°.
Since the three-phase system is by far the most prevalent and most economical polyphase system, discussion in this chapter is mainly on three-phase systems.
|Figure 3. Three-phase four-wire system|
Three-phase systems are important for at least three reasons.
First, nearly all-electric power is generated and distributed in three-phase, at the operating frequency of 60 Hz (or ω = 377 rad/s) in the United States or 50 Hz (or ω = 314 rad/s) in some other parts of the world.
When one-phase or two-phase inputs are required, they are taken from the three-phase system rather than generated independently.
Even when more than three phases are needed—such as in the aluminium industry, where 48 phases are required for melting purposes—they can be provided by manipulating the three phases supplied.
Second, the instantaneous power in a three-phase system can be constant (not pulsating).
This results in uniform power transmission and less vibration of three-phase machines.
Third, for the same amount of power, the three-phase system is more economical than the single- phase.
The amount of wire required for a three-phase system is less than that required for an equivalent single-phase system.
After we learn about three phase circuit, we will learn:
- Balanced three phase voltage
- Balanced three phase power
- Unbalanced three phase power
- Three phase power measurement
We also discuss the analysis of the power formula for a balanced system and power formula for unbalanced three-phase systems.
Finally, we apply the concepts developed in this chapter to three-phase power measurement and residential electrical wiring. You will also learn how to do three-phase power measurement.