What is the fundamental differences between the conventional AC Power Flow (CPF) & Harmonic Power Flow (HPF)? Is HPF simply a combination of CPFs at different frequencies? Instead of finding the set \$\{V, \theta ,P ,Q\}\$ for all nodes, does HPF deal with finding the set \$\{V_h ,\theta_h, P_h, Q_h\}\$?
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Sinusoidal AC active power is the product of the RMS values of the voltage, the current, and the cosine of the phase angle between them. Reactive power is the product of the RMS values of the voltage, the current, and the sine of the phase angle between them.
The active or reactive power for each individual harmonic would be calculated in the same way using the RMS values of individual harmonic voltages and currents. The harmonic power would presumably be defined as the sum of the individual harmonic powers and the total power would be the fundamental power plus the harmonic power.
The apparent power for the fundamental is the square root of the sum of the squares of the active and reactive powers.
The total apparent power including the fundamental and harmonic components is the RMS value of the total current waveform multiplied by the RMS value of the total voltage waveform.
In a system with a supply that has very little harmonic distortion and a nonlinear load, there can be a large apparent power due to harmonic currents drawn by the load. The reactive power of the fundamental components can be easily calculated, but I am not sure how to calculate the total reactive power due to the fundamental voltage and the harmonic currents. Since reactive power flow is normally a continuous exchange of energy back and forth between capacitive and reactive storage elements, it is difficult to picture the energy exchange in a system of this type.