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Home Excitation Characteristics of IronCore Reactors Power  
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Power
The real power consumed in a circuit is the average of the instantaneous values over a given period of time. For ac circuits, the real power is the average taken over one or more complete cycles. Thus, if a complex voltage wave is expressed by
and a complex current wave by
the real power is then obtained as follows
where the product v(t)i(t) results in the following series
It is not necessary to integrate every term in the series represented in Eq. 534 in order to evaluate the series. However, by considering 9 of the several typical terms, the integral can be evaluated in a simpler manner. Let us first consider the first term in the series of Eq. 534 as follows
Then consider the product of the n^{th} voltage harmonic and the n^{th} current harmonic when n may have any integral value 1, 2, 3, etc.
There is also in Eq. 537 the series of crossproducts represented by the term
which can be reduced to
The average value of the term above, taken over a complete cycle, is zero. From this it is apparent that the real power associated with a voltage harmonic of a given order and a current harmonic of a different order is zero. Therefore, the expression for the power obtained by carrying out the integration of Eq. 533 becomes
In Eq. 538, the angle
or the angle by which the n^{th} current harmonic lags or leads the n^{th} voltage harmonic, and
where PF_{n} is the power factor associated with the n^{th} voltage harmonic and the w^{th} current harmonic. In the case of a sinusoidal voltage and a nonsinusoidal current, the power is the product of the effective value of the voltage, the effective value of the fundamental in the current, and the cosine of the angle by which the fundamental in the current is displaced from the voltage. The same consideration applies to a sinusoidal current and nonsinusoidal voltage.


Home Excitation Characteristics of IronCore Reactors Power 