  We show how distributed control of reactive power can serve to regulate
voltage and minimize resistive losses in a distribution circuit that includes a
significant level of photovoltaic (PV) generation. To demonstrate the
technique, we consider a radial distribution circuit with a single branch
consisting of sequentially-arranged residential-scale loads that consume both
real and reactive power. In parallel, some loads also have PV generation
capability. We postulate that the inverters associated with each PV system are
also capable of limited reactive power generation or consumption, and we seek
to find the optimal dispatch of each inverter's reactive power to both maintain
the voltage within an acceptable range and minimize the resistive losses over
the entire circuit. We assume the complex impedance of the distribution circuit
links and the instantaneous load and PV generation at each load are known. We
compare the results of the optimal dispatch with a suboptimal local scheme that
does not require any communication. On our model distribution circuit, we
illustrate the feasibility of high levels of PV penetration and a significant
(20% or higher) reduction in losses.
