Single-phase and Three-phase AC Power Systems

Contents

1 Single-phase Power System
2 Three-phase Power systems

Single-phase Power System

To help us understand single-phase power system, consider the sine wave shown in figure 1(a) below of a 120 V_ac single-phase power connected to a plug.

Figure 1(a) 120 V_ac single-phase power waveform and a power plug

We know very well that, voltage is the difference in potential between two points. Therefore the sine wave in figure 1(a) shows only the voltage difference between prongs A and B for one complete cycle. For instance, in the first half of the cycle, prong A is more positive than B by upto 170 V, at exactly mid cycle (180°) there is no voltage difference between A and B. During the second half of the cycle, prong A has a negative voltage with respect to B.

The power utility company normally maintains the voltage of prong B at ground, which implies that it is not only the return path for the current but it is actually connected to a metal rod driven to the earth. Hence, the wire that goes to prong B is called the Neutral, return wire or cold side (normally white in color). The wire that goes to prong A is called the hot side because it carries the voltage (usually black in color). The third pin on the plug is the safety ground and is kept separate from the neutral wire until the actual grounding point. The ground wire is usually connected to the chassis or motor frame, which prevents a person from getting a shock from touching the electrical equipment since it is at the same potential as the earth.

The highest instantaneous voltage on prong A is 170 V(called V_peak or V_max) and is considerably higher than the AC designation of 120 V_ac (called V_rms) because the 120 V_ac represents the effective voltage if the power were constant over the whole cycle. V_rms = 0.7071 x V_max. Therefore, if we take our V_max to be 170 V in our case, then V_rms= 0.7071 x 170= 120 V_ac. Note that, the values of voltages and current on AC equipment are usually rms values unless otherwise stated.

Single-phase AC is supplied as 120 Vac and 240 Vac. The common line frequencies used are 60 Hz in the U.S. and 50 Hz in UK and most of the rest of the world.

Shipboard systems and aircrafts use 400 Hz. This is because the high frequency reduces the amount of iron needed in transformers and motors hence reducing weight.

Three-phase Power systems

Single-phase is the most common form of power for homes and businesses that don’t consume large amounts of power. Three-phase AC is widely used to transmit power, run AC motors and other heavy electrical equipment.

Three-phase power is produced by a three-phase generator that has three separate field windings 120° apart. We have 2 configurations used:

Star (wye) connection (Y-connection)
Delta-connection (Δ-connection)

Figure 1(b) star (wye) connection for three-phase AC

Figure 1(c) delta connection for three-phase AC

A schematic of a star-connection generator is illustrated in the left side of figure 1(d). One of each coil is connected to a common wire labelled N (Neutral) and the other ends of the coils are labelled A, B, and C which are the three-phase outputs.

Figure 1(d) Three-phase power system (star-connection)

The relationship of phase voltages A, B and C is illustrated in figure (e) which shows each phase voltage with respect to the neutral.

Figure 1(e) three-phase waveforms

Each phase makes a complete cycle in one period and is 120° apart; at any specific time, all phases add to 0 V. The phase sequence in this case is ABC.

Usually, three-phase power is distributed within a facility as star-connected. Figure 1(d) above illustrates a complete star-connected system where a three-phase generator is connected to a three-phase load e.g. a three-phase motor. If all the impedances (Z₁, Z₂ and Z₃) are the same, the system is said to be balanced and there would be no current in the neutral wire. Under these conditions, the neutral wire could be removed, and the motor would continue to run without a problem. In practice, it is unlikely than any specific facility would present a purely balanced load to the power lines, since each phase voltage if considered separately, can be used as a standard single-phase voltage. Therefore effort is usually made to keep the load on each phase equal.

Don’t miss out on key updates, join our newsletter List

The specified line voltage of a three-phase star-connected system is the vector sum of two individual phase voltages in series.

For a balanced star (wye) connected system:

Where,

V_Line = three-phase line voltage (voltage between any two lines)

V_Phase= individual phase voltage (voltage across one coil which for a star connected system, is also the voltage between a line and neutral)

For delta connected system, the line and phase voltages are the same.

Star connected three-phase power is mainly used for distribution within a facility because the neutral wire allows separate single-phase loads to be pulled off where needed.

Delta connected systems have no neutral wire and are inherently balanced. The power utility company normally uses three wires to transmit the three-phase power over the power lines. Once at the site, the power is converted to star (wye) connected power with special transformers designed for this purpose. The three-phase transformers can be made as one part or from 3 single-phase transformers as illustrated in figure 1(f) and 1(g).