To mitigate issues related to growth of variable smart loads and distributed generation, distribution system operators (DSO) now make it binding for prosumers with inverters to operate under pre-set rules. In particular, the maximum active and reactive power set points for prosumers are based on local voltage measurements to ensure that inverter output does not cause voltage violations. However, such actions may restrict the range available for local energy management, thus reducing the profit which prosumer would otherwise have made. This work analyses the loss of arbitrage opportunity and ability to perform voltage regulation for active prosumers due to inverter operational rules and location along a radial distribution network (DN). We model the arbitrage opportunity as a linear programming based local control for load and energy storage output based on electricity price variations, while ensuring that active and reactive injection limits are respected at finer time scales. We observe that relative feeder location determines the effect of inverter rules on arbitrage profits, with more adverse losses for prosumers located farther away from the substation. Subsequently, we propose a hybrid control policy that helps minimize this locational discrepancy while regulating the nodal voltage. Case studies are presented using three identical prosumers located at different parts of a test network. We observe that the proposed hybrid policy reduces the locational disparity to less than 1.4% between prosumers connected at the head and end of the feeder.

In recent years, electricity generation has been responsible for more than a quarter of the greenhouse gas emissions in the US. Integrating a significant amount of renewables into a power grid is probably the most accessible way to reduce carbon emissions from power grids and slow down climate change. Unfortunately, the most accessible renewable power sources, such as wind and solar, are highly fluctuating and thus bring a lot of uncertainty to power grid operations and challenge existing optimization and control policies. The chance-constrained alternating current (AC) optimal power flow (OPF) framework finds the minimum cost generation dispatch maintaining the power grid operations within security limits with a prescribed probability. Unfortunately, the AC-OPF problem's chance-constrained extension is non-convex, computationally challenging, and requires knowledge of system parameters and additional assumptions on the behavior of renewable distribution. Known linear and convex approximations to the above problems, though tractable, are too conservative for operational practice and do not consider uncertainty in system parameters. This paper presents an alternative data-driven approach based on Gaussian process (GP) regression to close this gap. The GP approach learns a simple yet non-convex data-driven approximation to the AC power flow equations that can incorporate uncertainty inputs. The latter is then used to determine the solution of CC-OPF efficiently, by accounting for both input and parameter uncertainty. The practical efficiency of the proposed approach using different approximations for GP-uncertainty propagation is illustrated over numerous IEEE test cases.