# Constant Q, Variable P

#### scothoward

I am currently doing a simulation in PowerWorld where there is simply a generator transmission line and load. The Q (reactive power) of the load is being kept constant and the P (real power) of the load is being increased from 0 to Q.

From this, the load bus voltage is being plotted against the P drawn from the generator. The curve should first be downward (lower bus voltage when increased power is being drawn) and then at some point (~P = 0.5Q) flatten out and then continue upwards (higher bus voltage when increased power is being drawn). I do not understand why this would happen. Wouldn't higher P lead to higher S, which in turn leads to higher current, more losses and lower load bus voltage?

Where is my understanding wrong?

#### m.s.j

Where is my understanding wrong?
It seems for evaluation of generator out put voltage you just considered voltage drop due to generator internal impedance, however you should consider armature reactions too. The voltage EA is the internal generated voltage produced in one phase of a synchronous generator. If the machine is not connected to a load (no armature current flowing), the terminal voltage will be equivalent to the voltage induced at the stator coils. This is due to the fact that there are no current flow in the stator coils hence no losses. When there is a load connected to the generator, there will be differences between EA and V. These differences are due to:

a) Distortion of the air gap magnetic field by the current flowing in the stator called armature reaction.
b) Self inductance of the armature coil
c) Resistance of the armature coils

When the rotor is spun, a voltage EA is induced in the stator windings. If a load is attached to the terminals of the generator, a current flows. But a 3-phase stator current flow will produce a magnetic field of its own. This stator magnetic field will distorts the original rotor magnetic field, changing the resulting phase voltage. This effect is called armature reaction because the armature (stator) current affects the magnetic field, which produced it in the first place. The armature reaction voltage can be modeled as an inductor in series with the internal generated voltage.
If the stator self-inductance is called LA (reactance is XA) while the stator resistance is called RA, then the total difference between EA and V is:

V=EA- jXIA – jXAIA- jRAIA
= EA- jXSIA –RAIA

Where XS = X + XA

For a given phase voltage and armature current, a larger internal voltage EA is needed for lagging loads than for leading loads. Thus, a larger field current is needed to get the same terminal voltage because EA= k.FLUX.ω because ω must be kept constant to keep constant frequency.

Alternatively, for a given field current and magnitude of load current, the terminal voltage is lower for lagging loads and higher for leading loads. Refer to attached page.

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