Marginal pricing of harmonic injections: an analysis of the resulting payments

Marginal pricing of harmonic injections can be shown to encourage each member of the network to independently act in such a way that the harmonic profile of the system is optimized. A problem encountered with marginal pricing is that loads can be charged complex amounts for their injections. This paper demonstrates that the real part of the amount charged for any injection reflects the "in-phase" component of that current, which will either increase or decrease the prevailing harmonic voltages. The imaginary part charged to a load reflects the quadrature component of their injections, which has no effect on the voltage magnitudes, at the margin. Each load need only be liable for the real amount they are charged, which has a direct correspondence with the total payments due.