Different Power Types in ac Circuits, Power Factor effect and correction

Power in ac circuits:  The power of an ac circuit is very seldom equal to the direct product of the volts and amperes. To calculate the power of a single phase ac circuit, the product of the volts and amperes must be multiplied by the power factor.

Apparent power is the term applied to the product of voltage and current in an ac circuit. It is expressed in voltamperes (VA) or in kilovolt-amperes (kVA) or megavolt-amperes (MVA).

Power factor is the ratio of the true power or watts to the apparent power or volt-amperes. The power factor is expressed as a decimal or in percentage. Thus power factors of 0.8 and of 80 percent are the same. In giving the power factor of a circuit, state whether it is leading or lagging. The current is always taken with respect to the voltage. A power factor of 0.75 lagging means that the current lags the voltage. The power factor may have a value anywhere between 0 and 1.0 but can never be greater than 1.0.

EXAMPLE In the fig.  below, which shows a single-phase circuit, the ammeter I reads 10 A, and the voltmeter E 220 V. The apparent power is the product of volts and amperes, or IE =10 * 220 = 2200 VA. But the wattmeter  W reads 1870 W. A wattmeter always indicates real or true power. Therefore the power factor (for a

single-phase circuit) is

The cosine of the angle of lag or lead is equal to the power factor.

The symbol θ, the Greek letter theta, is often used to designate the angle of lag or lead; hence power factor is sometimes referred to as    cos θ (cosine theta). This means the cosine of the angle θ.

The power factor in a noninductive circuit, one containing resistance only, is always 1, or 100 percent; i.e., the product of volts and amperes in such a circuit gives true power.

The power factor in a circuit containing inductance or capacitance may be anything between 0 and 1 (0 and 100 percent), depending on the amount of inductance or capacitance in the circuit.

Typical power factors of various kinds of central-station loads are as follows:

Incandescent Lighting. 1.0.

Incandescent Lighting with Small Step-Down Transformers. 0.95 to 0.98.

Incandescent Street-Lighting Series Circuits. 0.6 to 0.8

Sodium-Vapor Street Lighting, Parallel Circuits. 0.8 to 0.85.

Sodium-Vapor Street Lighting, Series Circuits. 0.5 to 0.7.

Fluorescent Lighting. 0.5 to 0.95, depending on type of auxiliary used.

Mercury-Vapor Lighting. 0.5 to 0.95, depending on type of auxiliary used.

Single-Phase Induction Motors; Squirrel-Cage Rotor. 1⁄20 to 1 hp, power factor, 0.55 to 0.75, average 0.68 at rated load: 1 to 10 hp, power factor, 0.75 to 0.86, average 0.82 at rated load.

Polyphase Induction Motors; Squirrel-Cage Rotor. 1 to 10 hp, power factor, 0.75 to 0.91, average 0.85 at rated load; 10 to 50 hp, power factor, 0.85 to 0.92, average

0.89 at rated load.

Polyphase Induction Motors; Phase-Wound Rotors. 5 to 20 hp, power factor, 0.80 to 0.89, average 0.86 at rated load; 20 to 100 hp, power factor, 0.82 to 0.90, average 0.87 at rated load.

Induction-Motor Loads in General. Power factor, 0.60 to 0.85, depending on whether motors are carrying their rated loads.

Rotary Converters, Compound-Wound. Power factor at full load can be adjusted to practically 100 percent. At light loads it will be lagging and at overloads slightly leading.

Rotary Converters, Shunt-Wound. Power factor can be adjusted to any desired value and will be fairly constant at all loads with the same field rheostat adjustment. Rotary converters, however, should not be operated below 0.95 power factor leading or lagging at full load or overload.

Small Heating Apparatus. This load has the same characteristics as an incandescent- lighting load. The power factor of the load unit is practically 1, but the distributing transformers will lower it to some extent.

Arc Furnaces. Power factor, 0.80 to 0.90.

Induction Furnaces. Power factor, 0.60 to 0.70.

Electric-Welding Transformers. Power factor, 0.50 to 0.70.

Synchronous Motors. Adjustment between 0.80 power factor leading to a power factor of 1. (1) Operating power factors above 0.95 will be obtained only when practically all the load consists of synchronous motors or converters which can be operated at practically a power factor of 1. (2) Power factors of 0.90 to 0.95 can be safely predicted only when the load is entirely incandescent lighting or heating or when a large non-inductive load, such as synchronous motors or converters, is used with a smaller proportion of inductive motor load. (3) For the average central station load, consisting of lighting and motor service, a power factor of 0.80 should be assumed. (4) A power factor of 0.70 should be assumed for a plant having a large proportion of induction motors, fluorescent lighting, electric furnaces, or electric- welding load.

Kilowatts and kilovolt-amperes  (General Electric Company). The term kilowatt (kW) indicates the measure of power which is all available for work. Kilovolt-amperes (kVA) indicate the measure of apparent electric power made up of two components, an energy component and a wattless or induction component. Kilowatts indicate real power and kilovolt-amperes apparent power. They are identical only when current and voltage are in phase, i.e., when the power factor is 1.

Ammeters and voltmeters indicate total effective current and voltage regardless of the power factor, while a wattmeter indicates the effective product of the instantaneous values of emf and current. A wattmeter, then, indicates real power. Standard guarantees on ac generators are made on the basis of loads at 80 percent power factor. However, it must not be inferred that a given generator will deliver its rated power output at all power factors. The generator rating in kilowatts will be reduced in proportion to the power factor and probably in a greater ratio if the power factor is very low. The method of rating ac generators by kilovolt-amperes instead of by kilowatts is now in general use. In discussing an ac load, it is well to state it in terms of kilowatts, power factor, and kilovolt-amperes, thus: 200 kW, 80 percent power factor (250 kVA). This shows that the current in the circuit corresponds to 250 kVA and heats the generator and conductors to that extent but that only 200 kW is available for doing work. An illustration of the distinction between kilowatts and kilovolt-amperes is given in fig. below:

Effects of low power factor. It is sometimes considered that the wattles component of a current at low power factor is circulated without an increase of mechanical input over that necessary for actual power requirements. This is inaccurate because internal work or losses due to this extra current are produced and must be supplied by the prime mover. Since these extra losses manifest themselves in heat, the capacity of the machine is reduced. Moreover, wattless components of current heat the line conductors, just as do energy components, and cause losses in them. The loss in any conductor is always    W = I²  X  R

Where W = the loss in watts, I = the current in amperes in the conductor, and R = the resistance in ohms. It requires much larger equipment and conductors to deliver a certain amount of power at a low power factor than at a power factor close to 1.

Correction of low power factor. In industrial plants, excessively low power factor is usually due to under-loaded induction motors because the power factor of motors is much less at partial loads than at full load. If motors are under-loaded, new motors of smaller capacity should be substituted. Power factor can be corrected (1) by installing synchronous motors which, when overexcited, have the property of neutralizing the wattless or reactive components of currents or (2) by connecting static capacitors across the line.

Source: American Electricians' Handbook