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3.2 Power Factor. Power factor occurs only in AC circuits and is defined as
the ratio of real power to apparent power.  Power factor is also the cosine of
the phase angle between the voltage and current signals.  Figure 9-1 provides
a graphic representation of power factor.  When the current signal crosses the
x-axis after the voltage signal, the power factor is said to be lagging. If
it crosses the x-axis before the voltage signal, the power factor is leading.
Power factor values can range from leading 0.2 to lagging 0.2, with an optimum
value of 1.  Typically power factor ranges from between 0.75 and 0.95, lagging.
3.2.1 Apparent Real, and Reactive, Power.  Real power is actual power used by
a piece of equipment and converted ultimately into work. Reactive power is not
converted into work but is a measure of the stored energy (either capacitive
or inductive) that must be constantly transferred between the source of power
and the end equipment.  Motors require reactive power to magnetize their
coils. For each sinusoidal cycle of the voltage provided to the motor, the
magnetic field builds up and collapses.  Reactive power Is borrowed as the
magnetic field is built up and, as the magnetic field collapses, the power is
returned. Apparent power is power a utility must generate to operate the
equipment. It contains components of both real and reactive power as shown on
the bottom of Figure 9-1.  If the power factor is equal to 1 (voltage and
current signals coincide), then real and apparent power are equal.  However,
because of the power factor effect, the utility must generate a greater amount
of power than required by online equipment for useful work.  Since apparent
power is defined as volts times amps, this requires the utility to generate
more current.  In addition to costing more money, the increased amperage
flowing through transmission lines and into the equipment causes both to heat,
which hastens deterioration and adversely affects regulation in transformers.
Since reactive power does not register on watthour meters but results in added
expense to the utility, the added cost is passed on to the customer in the
form of a power factor charge.
3.3 Demand.  Demand is defined as average power used during some
utility-selected time period.  Power is usually expressed in kilowatts and
normal industry standards for time are 15- or 30-minute intervals, but
occasionally are as long as 60 minutes.  In Figure 9-2, a 15-minute time
interval from 0900 to 0915 is used to illustrate demand. During this interval
load varies as shown: 300 kW for the first 5 minutes, 400 kW for the next 5
minutes, and 800 kW for the last 5 minutes.  The average power used during
this 15-minute period is 500 kW, shown as a dotted line.  This dotted line is
"demand value" or simply "demand" for that 15-minute interval. Note that the
area under the dotted line (demand) is exactly equal to the area under the
solid line (varying load).  This leads to yet another definition of demand.
Demand is that value of power which, if held constant over the interval, will
account for the same consumption of energy as the real power.  Figure 9-3 is
an actual demand graph over four time intervals.  As before, demand for each
time interval is shown by the dotted line with actual power consumed
represented by the solid line.  Again for each interval, area under the dotted
line is equal to area under the solid line. If demand shown in the second
interval was the highest demand for the entire billing period, it would be
called peak demand and would be the value used by utility companies for


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