# Synchronous machine power factor and angle

I have a 8-pole synchronous machine (as a generator), which is rated to produce 1000 kVA. Its synchronous reactance is 0.4 Ohms. It is connected to a diesel engine with the grid frequency 60 Hz. The load is resistive type, 500 kW, 480 V. I need to calculate the speed, power factor and power angle.

I know the following:

• Speed can be calculated by: $n = 120 \cdot \frac{f}P$ , where $f$ is frequency (60 Hz) and $P$ are poles (8) ... and we get the result 900 rpm.
• Power factor can be calculated by: $\mathrm{PF} = \cos(\mathrm{PA})$, where $\mathrm{PF}$ is power factor, $\mathrm{PA}$ is power factor angle (is that the same as power angle?)

So, how can I calculate power factor and power angle?

There is a difference between the power factor and power angle calculations. Under ideal conditions, for a purely resistive load, there is a phase difference between the voltage and current. But we always have reactive components present, so there is an angle between the current and voltage. The cosine of the angle between the current and voltage is called the power factor.

The power angle is the angle between a generator's internal voltage and its terminal voltage.

This link at Rapid tables provides more detail on how to calculate the power factor:

The Power Factor is equal to the real or true power P in watts (W) divided by the apparent power |S| in volt-ampere (VA)....

For sinusoidal current, the power factor PF is equal to the absolute value of the cosine of the apparent power phase angle φ (which is also is impedance phase angle):

$PF = |\cos φ|$

PF is the power factor.

$φ$ is the apparent power phase angle.

This document discusses the power angle:

The phase angle $\delta$ between the terminal voltage $V_T$ and the excitation voltage $E_f$ in Fig. 53 is usually termed the torque angle. The torque angle is also called the load angle or power angle.

If the load is purely resistive, the power factor is 1 and the power angle is zero by definition.