Apparent Power

Historically, the introduction of the concepts of apparent power and power factor can be traced to the electric power industry, where large amounts of electric energy must be transferred from one point to another; the efficiency with which this transfer is affected is related directly to the cost of the electric energy, which is eventually paid by the consumer. Customers who provide loads which result in a relatively poor transmission efficiency must pay a greater price for each kilowatthour (kWh) of electric energy they actually receive and use. In a similar way, customers who require a costlier investment in transmission and distribution equipment by the power company will also pay more for each kilowatthour unless the company is benevolent and enjoys losing money.

Assume that the sinusoidal voltage V= V_m cos (⍵t + theta) is applied to a network and the resultant sinusoidal current is I = I_m cos (⍵t + phi). The phase angle by which the voltage leads the current is therefore (theta-phi). The average power delivered to the network, assuming a passive sign convention at its input terminals, may be expressed either in terms of the maximum values: P = (1/2)V_mI_m cos (theta-phi). If our applied voltage and current responses had been dc quantities, the average power delivered to the network would have been given simply by the product of the voltage and the current.

Applying this dc technique to the sinusoidal problem, we should obtain a value for the absorbed power which is “apparently” given by the familiar product V_effI­_eff. However, this product of the effective values of the voltage and current is not the average power; we define it as apparent power. Dimensionally, apparent power must be measured in the same units as real power, since cos (theta-phi) is dimensionless; but in order to avoid confusion, the term voltamperes (VA) is applied to the apparent power. Since (theta-phi) cannot have a magnitude greater than unity, it is evident that the magnitude of the real power can never be greater than the magnitude of the apparent power.

Apparent power is not a concept which is limited to sinusoidal forcing functions and responses. It may be determined for any current and voltage waveshapes by simply taking the product of the effective values of the current and voltage.

By: Jonald Sarmiento