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Home Excitation Characteristics of IronCore Reactors CoreLoss Current and Magnetizing Current  
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CoreLoss Current and Magnetizing Current
The fundamental, 3rd, and 5th harmonic components of the current in a reactor are shown in Fig. 56. Such a current could also be the exciting current or noload current in a transformer. The fundamental component i_{exc1} is shown in Fig. 57 along with the flux wave Φ and induced voltage wave e. Sinusoidal flux variation is assumed. In Section 54 it was shown that in the case of sinusoidal voltage the harmonics in the current wave do not contribute to the real power. Therefore, core loss, i.e., hysteresis and eddycurrent losses, can be taken into account by taking the product of the induced emf and the component of the fundamental in the current that is in phase with the induced emf. This component of current is called the coreloss current and is represented by i_{c} in Fig. 57.
If the current wave representing the coreloss current ic is subtracted from the total fundamental component of current i_{exc1}, the result is a sine wave of current that is in phase with the flux wave Φ. If there were no harmonics, this latter component of current would be the magnetizing current. Under these conditions the two currents, i.e., coreloss and magnetizing currents, as well as the flux and the induced voltage, could be represented by the phasor diagram shown in Fig. 58. However, the magnitude of the exciting current is actually greater than that resulting from the fundamental component, as it does include all the harmonic components. Since the harmonics in the exciting current do not contribute to the real power if the induced voltage is sinusoidal, the coreloss component I_{c} in Fig. 58 is not affected by inclusion or exclusion of the harmonics. In accordance with Eq. 546, the exciting current has an rms or effective value of
It must be kept in mind that under ac excitation, in the absence of a dc component, only odd harmonics are present in the exciting current.
The following relationship is obtained from Eq. 548
Generally, phasor diagrams apply to sinusoidal quantities, but may be used to include nonsinusoidal currents and voltages if these are replaced by equivalent sinusoidal quantities, i.e., sinusoids that have the same rms or effective values. If the exciting current is represented by a phasor I_{exc} as in Fig. 59 and is treated as an equivalent sinusoidal current, the phasor difference expressed by the righthand side of Eq. 549 leads to a phasor that lags the coreloss current by 90°. The equivalent sinusoid represented by this phasor is called the magnetizing current, and from Eq. 549 is seen to be
Equation 550 suggests that the harmonic components be included in the magnetizing component of the exciting current. This facilitates the development of a phasor diagram and a simple equivalent circuit. A phasor diagram including the harmonics in the magnetizing current is shown in Fig. 59.


Home Excitation Characteristics of IronCore Reactors CoreLoss Current and Magnetizing Current 