Page 33 - Appplied Mathematics for the Petroleum and Other Industries, 5th Edition

226 ADVANCED OIL INDUSTRY APPLICATIONS

For more detailed explanations of electrical power and the power factors,
see the Petroleum Extension (PETEX) publication entitled Basic Electronics for
the Petroleum Industry, fourth edition. Other PETEX publications that readers
should find helpful concerning the subjects covered in the chapter include Basic
Instrumentation, fourth edition; Diesel Engines and Electric Power, third edition,
revised; Drilling Fluids, Mud Pumps, and Conditioning Equipment; Practical Well
Control, fourth edition; The Blocks and Drilling Line, third edition, revised; Treat-
ing Oilfield Emulsions, fourth edition; and Gas and Liquid Measurement.

ELECTRICAL POWER AND POWER FACTOR EQUATIONS

In alternating current (AC) electrical systems, the equipment being powered
influences the form of power a transformer or generator delivers to the equip-
ment. Also, whether the system is single-phase or three-phase influences wire
and equipment sizing.
Three forms of electrical power exist in AC systems. They include—
1. apparent power, in kilovolt-amperes (kVA);
2. real power, in kilowatts (kW); and

3. reactive power, in kilovolt-amperes-reactive (kVARs).
Apparent power is the vector sum of the power in watts plus the reactive
power in volt-amperes reactive (VAR) in a circuit.
Real power is the component of apparent power that represents true work.
Real power is expressed in watts and equals volt-amperes multiplied by the
power factor.
Reactive power is the value of the power in an electric circuit obtained by
multiplying the effective value of the current in amperes, the effective value of
the voltage in volts, and the sine of the angular phase difference between cur-
rent and voltage.
In addition, a ratio of real power to apparent power is a measure of how
power is being delivered and used. This ratio is referred to as the power factor
and is expressed in equation form as:
kW W
pf = —— = —–
kVA VA
where
pf = power factor
kW = kilowatts
kVA = kilovolt-amperes
W = watts
VA = volt-amperes.

Petroleum Extension-The University of Texas at Austin
Apparent power is the result of multiplying voltage by current. Apparent
power is also considered to be the total power. On the other hand, the capacitors
and inductors in the load determine reactive power. Therefore, the power actu-
kVARs b c kVA ally doing work is the real power, in kW, which is subtracted from the apparent
power by the amount of reactive power.
a
kW A right triangle—a power triangle—shows the three forms of power (fig.
9.1). Side a of the triangle represents the amount of kW, side b represents the
Figure 9.1 Power triangle amount of kVARs, and the hypotenuse (side c) represents total power, or kVA.