Active Power and Reactive Power

Reactive power means Voltage and Current are not in phase and therefore during a cycle (say 20ms for 50 Hz), the power flow reverses during a part of the cycle. You can simply draw a voltage sine wave, a current sine wave 45 degrees lagging and instantaneous power wave (product of V & A instantaneous values every 1ms) to visualize the phenomena. You will realize that power loops exist above and below the X axis; these would be equal for 90 degrees phase difference, when power factor is 0.

Reactive power is a resonance phenomenon. It is the power the oscillates between the driving point inductance and capacitance as seen by the douce. As such it's phase shifted in time by 90 degrees from active (real) power and generates I squared r losses. It reduces the ability of generators to produce active power and transmission lines to carry active power. It can be generated by over or under excitation of generators (in accordance with their reactive power capability curves) or by the operation of Static VAR compensators that generally have fixed cap banks (thyristor switched cap banks are sometimes applied as well) and which phase shift active power through the use of power electronic switching of and thyristor switched reactors, or finally, by the installation of switchable capacitors or reactors (power inductors). Mathematically VARs are loosely coupled to active power. However practically speaking sufficient VARs are required to support voltage in order to allow the transfer of reveal power. Positive VARs support or boost voltage and negative (inductive) VARs buck or draw voltage down.

Actually, it is the phase angle difference between the two ends of the line that causes the active (real) power to flow, not the voltages. That is if the voltage phase angle of one end of a line ("From Bus") is greater than the voltage phase angle of the other end of a line ("To Bus"), then the direction of active power will be from "From Bus" to "To Bus". The direction of reactive power on a line, however, will depend on voltage magnitudes on both end of the line. That is the reactive power will flow from the bus or node with a higher voltage magnitude to the other end of the line with smaller voltage magnitude. In general, however, the reactive power is a local phenomenon and unlike active power it cannot be transmitted over long distances. That is if reactive power is needed to support a voltage at a station bus, then, it should be produced locally for that station.

P = (Vs*Vr*sin[theta])/X
Q ={ (Vs*Vr*cos[theta])/X} - (Vr^2)/X
P = real (active) power; Q = reactive power
Vs = sending end bus voltage
Vr = receiving end bus voltage
theta = phase angle difference between sending and receiving end bus voltages
X = reactance connected between sending and receiving end busses

In this equation resistance is considered negligible because reactance is usually larger than resistance. Equation changes slightly when resistance is accounted.

Though we didn't mention it but the power transfer equations changes slightly when dealing with a salient pole generator.

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