Introduction to Electric Circuits

112 Three-phase a.c. circuits

Now

VAB = 2 VAN COS 0 = 2 VAN COS 30 ~ = 2 VAN ~/3/2 : ~/3 VAN

But VAB = VL and VAN = Vpn SO that

V L -" W/3 VpH (5.2)

Summarizing, we can say that in a balanced three-phase star connection:

9 the line current equals the phase current (IL = IPH);

* the line voltage is ~3 times the phase voltage and leads it by 30 ~

(VL = V'3 VpH/-30~

9 the phase current is equal to the phase voltage divided by the phase

impedance (IpH -- VpH/ZPH);

9 the phase angle is given by ~b = tan -~ (XL/RL) where XL and RL are the load

reactance and resistance, respectively;

9 the power factor is given by cos ~b.

It is also worth noting here that in a star connection the star point is available

which means that 'mixed' (three-phase and single-phase) loads can be supplied

from the same supply. This is particularly useful in power distribution net-

works.

Example 5.1

Three 10 s resistors are connected in star to a three-phase supply whose line

voltage is 440 V. Calculate (1) the voltage across each resistor, (2) the line

current, (3) the current in each phase if one of the resistors becomes open

circuited.

Solution

The connection is shown in Fig. 5.10.

Figure 5.10

VL = 440V

A

1

VpH l ~ 10~'~