09-11-2012, 02:19 PM
THREE-PHASE SYSTEMS
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BALANCED THREE-PHASE CIRCUITS
The generation, transmission and distribution of electric power is accomplished by
means of three-phase circuits. At the generating station, three sinusoidal voltages
are generated having the same amplitude but displaced in phase by 120Æ. This is
called a balanced source. If the generated voltages reach their peak values in the
sequential order ABC, the generator is said to have a positive phase sequence,
shown in Figure 2.11(a). If the phase order is ACB, the generator is said to have a
negative phase sequence, as shown in Figure 2.11(b).
In a three-phase system, the instantaneous power delivered to the external
loads is constant rather than pulsating as it is in a single-phase circuit. Also, threephase
motors, having constant torque, start and run much better than single-phase
motors. This feature of three-phase power, coupled with the inherent efficiency of
its transmission compared to single-phase (less wire for the same delivered power),
accounts for its universal use.
PER-PHASE ANALYSIS
The current in the neutral of the balanced Y-connected loads shown in Figure 2.2
is given by
In = Ia + Ib + Ic = 0 (2.19)
Since the neutral carries no current, a neutral wire of any impedance may be replaced
by any other impedance, including a short circuit and an open circuit. The
return line may not actually exist, but regardless, a line of zero impedance is included
between the two neutral points. The balanced power system problems are
then solved on a “per-phase” basis. It is understood that the other two phases carry
identical currents except for the phase shift.
We may then look at only one phase, say “phase A,” consisting of the source
VAn in series with ZL and Zp, as shown in Figure 2.8. The neutral is taken as datum
and usually a single-subscript notation is used for phase voltages.
If the load in a three-phase circuit is connected in a , it can be transformed
into a Y by using the -to-Y transformation. When the load is balanced, the
impedance of each leg of the Y is one-third the impedance of each leg of the , as
given by (2.18), and the circuit is modeled by the single-phase equivalent circuit.