Chance Constrained Voltage Regulation via Affine Inverter Control Policies
Voltage control plays an important role in the operation of electricity distribution networks. Especially with increasing penetration of solar power generation in distribution networks, rapid and substantial changes in voltage magnitude can occur. However, with the revised IEEE 1547 standard, smart inverters can participate in voltage regulation by injecting or absorbing reactive power and can facilitate other network-wide objectives, such as minimization of thermal losses. To cope with the stochastic nature of the solar power generation and random fluctuations of user real and reactive power consumption, this thesis introduces a stochastic optimal power flow where the control actions are expressed as affine functions of uncertain quantities. Voltage security constraints are also introduced in a stochastic optimization framework as probabilistic constraints. Assuming the uncertainties follow a Gaussian distribution, the resulting optimization problem is shown to be a second-order cone program. We illustrate the results using real data taken from Pecan Street and tested on standard distribution test feeders which include the IEEE-13 feeder, the SCE -47 feeder, a modified SCE-47 feeder with overvoltage and the UKGDS-95 feeder.