# Variable resistor & inductor connected to alternator

1. Mar 24, 2015

### CraigH

A simple 2 pole alternator (a synchronous generator), is powered by a steam turbine. The amount of steam to the turbine is kept constant with a constant pressure $p$, flow rate $\dot{q}$, and power $P$.

If a variable resistor, inductor, and capacitor are connected in series to the electrical power output of the generator, what will be the effect on the turbine and generator ?

The frequency of electrical power supplied by the generator must remain constant, because it is a synchronous generator so the frequency of electrical power output is inherently locked to the frequency of the prime mover. (In this case the steam turbine, which is constant).

So what is the effect on the turbine and generator?

I understand that it is something to do with the torque angle of the generator. A bigger electrical load increases the torque angle, but why?

Also, when the torque angle increases from zero the field of the stator no longer perfectly aligns with the field of the motor, so now a back emf is generated across the generator$^1$. But how exactly does this all change when the resistance, inductance, and capacitance of the electrical load is changed?

$^1$ This is a separate question, but why does a non zero load angle mean a back emf is generated? What is the relationship between torque angle and back emf? Am I also correct in saying that this back emf is out of phase with the "normal" voltage induced because of the rotating field of the rotor, and hence the generator also supplies reactive power as well as real power?

2. Mar 27, 2015

### Hesch

If a resistor is connected, it will consume active power.
An inductor will comsume reactive power.
A capacitor will produce reactive power.

The generator must produce or consume all these types of power (nobody else to do it). In case of reactive power, the angle between generated voltage and current will be ±90 degrees. In case of active power, the angle will be 0 degrees. When active and reactive power are combined, the angle between voltage and current will be somewhere in between 0 and 90 degrees. This phaseshift will influence the torque angle.

But even if you connect only a resistor, the angle between the magnetic fields from the stator and the rotor will change, because the resistor consumes active power, and therefore the gap between the rotor and the stator must yield a torque. This torque increases as the angle increases from 0 (minimum torque) to ±90 degrees (maximum torque). The torque is proportional to sin(angle).

The calculations regarding the torque angle are complex, because the generator has inductance and resistanse in its stator, which are included in the circuit as a whole.

3. Mar 27, 2015