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# Power Flow in Synchronous Motor

## Losses in Synchronous Motor

The losses that occur in a synchronous motor can be divided into the following categories −

## Copper Losses or I^{2}R Losses

*Copper losses or I ^{2}R losses* occur in the armature winding and rotor winding of the motor. These losses occur due to the resistance of the windings.

## Core Losses

*Core losses* or *iron losses* occur in the iron parts of the synchronous motor. The core losses in the motor occur because the various iron parts of the machine are subjected to the varying magnetic field. The core losses consist of *eddy current loss* and *hysteresis loss*.

**Hysteresis Loss**- Hysteresis loss occurs in the cores of the synchronous motor since any given iron part is subjected to magnetic reversal as the magnetic field varies. When the magnetic reversal occurs, some amount of power has to be spent to overcome the magnetic friction, which is called as*hysteresis loss*. The hysteresis loss is given by,Hysteresis Loss,

$$\mathrm{P_{h}=K_{h}\:B^{1.6}_{max}\:fV\:Watts}$$

Eddy Current Loss,**Eddy Current Loss**- When the armature and rotor cores of the synchronous motor are subjected to the changing magnetic field, an EMF is induced in the cores which circulates eddy currents in the cores. The power loss due to these eddy currents is known as eddy current loss and is given by,$$\mathrm{P_{e}=K_{e}\:B^{2}_{max}\:f^{2}t^{2}V\:Watts}$$

## Mechanical Losses

In the synchronous motor, there are two types of mechanical losses viz. *friction losses* and *windage losses*. The friction losses occur due to the friction in the moving parts such as bearings etc. while the windage losses occur due to the friction between the moving parts of the machine and the air inside the motor’s casing.

## Miscellaneous Losses

All the losses in the synchronous motor which cannot be easily accounted for are known as *miscellaneous losses*.

## Power Flow in a Synchronous Motor

The input power (P_{i}) in a synchronous Motor is electrical in nature. There
occurs armature copper loss in the resistance of the armature winding. If the
armature copper losses are subtracted from the input power, then we get the
mechanical power (P_{m}) developed by the motor.

Further, core losses (i.e., eddy current and hysteresis losses) and mechanical losses (i.e., friction and windage losses) occur in the motor due to rotation of the moving parts. Thus, if the core losses and mechanical losses are subtracted from the developed mechanical power, then we get the mechanical power output (P_{o}) of the synchronous motor. This output power is available at the shaft of the synchronous motor.

The power flow diagram of the synchronous motor is shown in Figure-1.

## Power Flow Equations of Synchronous Motor

Consider an under-excited synchronous motor (i.e.,E_{f}<V) driving a mechanical load. Figure-2 shows the per phase phasor diagram of the motor.

As the synchronous motor is under-excited, thus it being operating at a lagging power factor cosφ. Also, in practice,X_{S}>>R_{a}, therefore, the armature current (I_{a}) lags the resultant voltage (E_{r})by about 90°. As we know, the input power
to the synchronous motor is electrical while the output power is mechanical.
Hence, the power flow equations of a synchronous motor are given as follows:
Input power per phase,

$$\mathrm{P_{i}=V\:I_{a}\:cosφ}$$

Mechanical power developed,

$$\mathrm{P_{m}=\frac{VE_{f}}{X_{S}}sinδ}$$

Armature Cu loss per phase

$$\mathrm{=I^{2}_{a}R_{a}=P_{i}-P_{m}}$$

Output power per phase,

$$\mathrm{P_{o}=P_{m}-(Core\: and\: Mech.Losses)}$$

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