Equivalent Circuit of Synchronous Motor

A synchronous motor is a doubly excited system which means it is connected to two electrical systems, where a three-phase ac supply is connected to the armature winding and a DC supply to the rotor winding. Figure-1 shows the per phase equivalent circuit of a three-phase synchronous motor.

Here,V is the voltage per phase applied to the motor, R_ais the armature resistance per phase, and $X_{s}$ is the synchronous reactance per phase. These two parameters (i.e. $R_{a}$ and $X_{s}$) give the synchronous impedance per phase ($Z_{s}$) of the motor.

From the equivalent circuit of the synchronous motor as shown in Figure-1, we can write its voltage equation as,

$$mathrm{mathit{V}:=:mathit{E_{b}+I_{a}Z_{s}}}$$

$$mathrm{Rightarrow mathit{V}:=:mathit{E_{b}+I_{a}left ( R_{a} +jX_{s}right )}}$$

Where, the bold letters represent the phasor quantities.

Therefore, the armature current per phase is given by

$$mathrm{I_{a}:=:frac{mathit{V-E_{b}}}{mathit{Z_{s}}}:=:frac{mathit{V-E_{b}}}{left ( mathit{R_{a}+jX_{s}}right )}:=:frac{mathit{E_{r}}}{mathit{R_{a}+jX_{s}}}}$$

Where,$mathit{E_{r}}$ is the resultant voltage in the armature circuit.

The armature current and synchronous impedance of a synchronous motor are the phasor quantities having magnitude and phase angle. Thus, the magnitude of the armature current is given by,

$$mathrm{left|I_{a} right|:=:frac{mathit{V-E_{b}}}{mathit{Z_{s}}}:=:frac{mathit{E_{r}}}{mathit{Z_{s}}}}$$

And, the magnitude of the synchronous impedance is given by,

$$mathrm{left|Z_{s} right|:=:sqrt{mathit{R_{a}^{mathrm{2}}+X_{s}^{mathrm{2}}}}}$$

The equivalent circuit and the above equations helps a lot in understanding the operation of a synchronous motor as,

• When the field excitation is such that $mathit{E_{b}=V}$, then the synchronous motor is said to be normally excited.

• When the field excitation is such that $mathit{E_{b}<V}$, then the synchronous motor is said to be under excited.

• When the field excitation is such that $mathit{E_{b}> V}$, then the synchronous motor is said to be over excited.

As we shall see in the next section that the excitation of the synchronous motor affects its power factor.

Power Factor of Synchronous Motor

One of the most important characteristics of a synchronous motor is that it can be made to operate at leading, lagging or unity power factor by changing the field excitation. The following discussion explains how the change in field excitation affects the power factor of a synchronous motor −

• When the rotor excitation current is such that it produces all the required magnetic flux, then there is no need of extra reactive power in the machine. Consequently, the motor will operate at unity power factor.

• When the rotor excitation current is less than that required, i.e., the motor is under-excited. In this case, the motor will draw reactive power from the supply to provide the remaining flux. Thus, the motor will operate at a lagging power factor.

• When the rotor excitation current is more than that required, i.e. the motor is over-excited. In this case, the motor will supply reactive power to the 3-phase line, and behaves as a source of reactive power. Consequently, the motor will operate at a leading power factor.

Hence, we may conclude that a synchronous motor absorbs reactive power when it is under-excited and delivers reactive power when it is over-excited.