Stochastic optimization for power management in radial distribution networks with renewable photovoltaic generation

The stochastic nature of solar renewable power poses challenges in distribution networks with high-penetration photovoltaic (PV) generation in terms of maintaining adequate generation to satisfy end-users as well as accomplishing voltage regulation. However, real power control of modern programmable electric loads and reactive power compensation from the power electronic interfaces of PV generators offer opportunities to overcome these challenges to eventually achieve customer satisfaction and minimize costs for the operation of distribution systems. To cope with the random and intermittent nature of solar generation, this thesis introduces a stochastic optimization model for real and reactive power management in such distribution systems with a large number of residential-scale PV generation units. Decision variables include demand response schedules of programmable loads, as well as reactive power consumption or generation by the PV inverters in a fashion adaptive to the uncertain real power generation. Voltage regulation is also addressed in the stochastic optimization framework through enforcement of suitable constraints or using principles of risk-averse optimization. A decentralized solver based on the alternating direction method of multipliers (ADMM) is also developed featuring closed-form updates per node and communication only between neighboring nodes. Numerical tests are provided to demonstrate the superior performance of applying this stochastic optimization model for power management in large distribution networks compared to other proposed schemes in the literature.