Increasing penetration of distributed energy resources complicate operations of electric power distribution systems by amplifying volatility of nodal power injections. On the other hand, these resources can provide additional control means to the distribution system operator (DSO). This paper takes the DSO perspective and leverages a data-driven distributionally robust decision-making framework to overcome the uncertainty of these injections and its impact on the distribution system operations. We develop an AC OPF formulation for radial distribution systems based on the LinDistFlow AC power flow approximation and exploit distributionally robust optimization to immunize the optimized decisions against uncertainty in the probabilistic models of forecast errors obtained from the available observations. The model is reformulated to be computationally tractable and tested on multiple IEEE distribution test systems. We also release the code supplement that implements the proposed model in Julia and can be used to reproduce our numerical results, see [27].

Distribution locational marginal prices (DLMPs) facilitate the efficient operation of low-voltage electric power distribution systems. We propose an approach to internalize the stochasticity of renewable distributed energy resources (DERs) and risk tolerance of the distribution system operator in DLMP computations. This is achieved by means of applying conic duality to a chance-constrained AC optimal power flow. We show that the resulting DLMPs consist of the terms that allow to itemize the prices for the active and reactive power production, balancing regulation, and voltage support provided. Finally, we prove the proposed DLMPs constitute a competitive equilibrium, which can be leveraged for designing a distribution electricity market, and show that imposing chance constraints on voltage limits distorts the equilibrium.

Distribution system operators (DSOs) world-wide foresee a rapid roll-out of distributed energy resources. From the system perspective, their reliable and cost effective integration requires accounting for their physical properties in operating tools used by the DSO. This paper describes an decomposable approach to leverage the dispatch flexibility of thermostatically controlled loads (TCLs) for operating distribution systems with a high penetration level of photovoltaic resources. Each TCL ensemble is modeled using the Markov Decision Process (MDP). The MDP model is then integrated with a chance constrained optimal power flow that accounts for the uncertainty of PV resources. Since the integrated optimization model cannot be solved efficiently by existing dynamic programming methods or off-the-shelf solvers, this paper proposes an iterative Spatio-Temporal Dual Decomposition algorithm (ST-D2). We demonstrate the merits of the proposed integrated optimization and ST-D2 algorithm on the IEEE 33-bus test system.

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