If AC current and voltage were always in phase, the average power over a complete cycle would be equal to the product of the current and voltage and power could be measured in watts. However, this is a theoretical situation because there is always some reactance present in an AC circuit that keeps the current and voltage out of phase. Where phase difference is minimal, a reasonable approximation of actual power can be determined as the product of current (I) and voltage (E), which yields watts (W). This is the formula for determining actual power in a DC circuit.

However, when voltage and current are out of phase, current can be negative and voltage positive and vice versa at various times during each cycle. As a result, the value of power is less than the product of E x I. The terms volt-amperes (VA) or kilovolt- amperes (kVA) express the product of the effective values of voltage and current in an AC circuit. To determine useful or actual power, the volt-ampere product must be multiplied by a value called the power factor (PF).

Power in a single-phase AC circuit is found from

P (watts) = EI x PF

or

By transposing the second equation,

Thus, power factor is defined as the ratio of the actual power in watts to the voltamperes of an AC circuit. When the current and voltage are in phase, power is equal to E X I and the power factor is unity. When current and voltage are out of phase by 90° (as in a purely capacitive or inductive circuit), the power factor is zero. In this situation no actual power is produced. However, in circuits that contain both resistance and reactance, the value of PF lies between 1 and 0, and it depends on the relative values of resistance and reactance in the circuit.

According to the convention used in discussing power factor, voltage in an inductive circuit leads current, and in a capacitive circuit voltage lags current. Power factor can be expressed as either a decimal or a percentage. Some typical average power factors encountered in the operation of electrical equipment are expressed as percentages:

• Incandescent lamps—95 to 100 percent
• Large induction motors carrying rated load—85 to 90 percent
• Fractional-horsepower induction motors—60 to 75 percent

Current lags voltage both in lamps and motors, which are inductive loads. Current in an AC circuit is considered to consist of a component in phase and a component out of phase with the voltage,

The in-phase component is called active or real because, when multiplied by voltage,it gives the useful or real power in watts or kilowatts. The out-of-phase component is called reactive because it contributes nothing to the real power of the circuit. The product of the reactive component of the current and voltage is called reactive power or reactive volt-amperes, and it is measured in vars (volt-amperes reactive) or kilovars. If there were no capacitive component to cancel part of the inductive component, voltage and current would be out of phase by 90 electrical degrees.

In above Figure the greater the phase angle , the greater is the value of the reactive component. The cosine of the phase angle is the ratio of the active current to the total current. Because the actual power is the voltage multiplied by the active component of current,

where P = power, E = voltage, and I= current.
Thus the power factor of an AC circuit is equal to the cosine of the phase angle. The cosine of 0° is 1 and the cosine of 90° is 0, so as the phase angle is reduced, the power factor approaches 1.

POWER FACTOR CORRECTION

The efficiency of power generation, transmission, and distribution systems is improved when they are operating near-unity power factor. The most cost-effective way to obtain near-unity power factor is with the use of high-voltage power factor capacitors.
Capacitors provide leading reactive current that can reduce the lagging inductive current in the system. An advantage of this method for power factor correction is that capacitors can be installed near the load. Another unit of equipment, called a synchronous condenser ,can provide continuous power factor correction without the use of capacitors.

A synchronous condenser is a synchronous motor operated without a mechanical load for improving power factor. By overexciting its field, a synchronous condenser will operate at a very low leading power factor. The only input power required is that necessary to supply its losses. When used at the end of a long transmission line, the synchronous condenser neutralizes the effects of lagging power factor loads, thus improving the regulation of the transmission line.