10.2 SINGLE- AND THREE-PHASE SYSTEMS 455
- New primary resources (such as nuclear fusion and solar energy) for electric bulk power
generation
- Development of better means of generation (such as superconducting generators) and
transmission (such as six-phase)
- Emphasis on energy conservation (better utilization of electricity with less waste)
- Electric-energy storage facilities such as pumped storage, compressed gas, storage batteries,
and superconducting magnetic coils.
10.2 Single- and Three-Phase Systems
It would be very helpful if the reader would review Section 3.1 on sinusoidal steady-state phasor
analysis and Chapter 4 on three-phase circuits before studying this section.
Ac power has significant practical advantages over dc power in generation, transmission,
and distribution. One major drawback of the single-phase circuit is the oscillatory nature of the
instantaneous power flowp(t) as seen in Equation (3.1.36). The consequent shaft vibration and
noise in single-phase machinery are rather undesirable. A three-phase circuit, on the other hand,
under balanced conditions has constant, nonpulsating (time invariant), instantaneous power, as
seen from Equation (4.2.13); the pulsating strain on generating and load equipment is eliminated.
Also for power transmission, a balanced three-phase system delivers more watts per kilogram
of conductor than an equivalent single-phase system. For these reasons, almost all bulk electric
power generation and consumption take place in three-phase systems.
The majority of three-phase systems are four-wire, wye-connected systems, in which a
grounded neutral conductor is used. Some three-phase systems such as delta-connected and three-
wire wye-connected systems do not have a neutral conductor. Because the neutral current is nearly
zero under normal operating conditions, neutral conductors for transmission lines are typically
smaller in size and current-carrying capacity than the phase conductors. Thus, the cost of a
neutral conductor is substantially less than that of a phase conductor. The capital and operating
costs of three-phase transmission and distribution systems, with or without neutral conductors,
are comparatively much less than those of separate single-phase systems.
Ratings of three-phase equipment, such as generators, motors, transformers, and transmission
lines, are usually given as total three-phase real power in MW, or as total three-phase apparent
power in MVA, and as line-to-line voltage in kV.
Power
The essential concepts related to power have been presented in Sections 3.1 and 4.2. However,
for better clarity and understanding, those concepts are revisited in a slightly different form.
Thecomplex powerS ̄in a single-phase system is the complex sum of thereal(P) andreactive
(Q) power, expressed as follows:
S ̄=P+jQ=V ̄I ̄∗=I ̄I ̄∗Z ̄=I^2 Z θZ=VI θV−θI (10.2.1)
whereθVis the angle associated withV ̄(with respect to any chosen reference),θIis the angle
associated withI ̄(with respect to the same reference chosen),θZis the impedance angle,V ̄is
the rms voltage phasor,I ̄is the rms current phasor, andZ ̄=R±jXis the complex impedance
with a magnitude ofZ. Note that∗stands for complex conjugate. If the voltage phasorV ̄itself is
taken to be the reference,θV=0 andθImay be replaced byθwithout any subscript.
Thepower factorPF is given by the ratio of the real powerP(expressed in watts) to the
apparent powerS=
√
P^2 +Q^2 expressed in volt-amperes,
