Dynamic Energy Management

We present a unified method, based on convex optimization, for managing the power produced and consumed by a network of devices over time. We start with the simple setting of optimizing power flows in a static network, and then proceed to the case of optimizing dynamic power flows, i.e., power flows that change with time over a horizon. We leverage this to develop a real-time control strategy, model predictive control, which at each time step solves a dynamic power flow optimization problem, using forecasts of future quantities such as demands, capacities, or prices, to choose the current power flow values. Finally, we consider a useful extension of model predictive control that explicitly accounts for uncertainty in the forecasts. We mirror our framework with an object-oriented software implementation, an open-source Python library for planning and controlling power flows at any scale. We demonstrate our method with various examples. Appendices give more detail about the package, and describe some basic but very effective methods for constructing forecasts from historical data.Comment: 63 pages, 15 figures, accompanying open source librar

Risk-Averse Model Predictive Operation Control of Islanded Microgrids

In this paper we present a risk-averse model predictive control (MPC) scheme for the operation of islanded microgrids with very high share of renewable energy sources. The proposed scheme mitigates the effect of errors in the determination of the probability distribution of renewable infeed and load. This allows to use less complex and less accurate forecasting methods and to formulate low-dimensional scenario-based optimisation problems which are suitable for control applications. Additionally, the designer may trade performance for safety by interpolating between the conventional stochastic and worst-case MPC formulations. The presented risk-averse MPC problem is formulated as a mixed-integer quadratically-constrained quadratic problem and its favourable characteristics are demonstrated in a case study. This includes a sensitivity analysis that illustrates the robustness to load and renewable power prediction errors

Robust Optimal Power Flow with Wind Integration Using Conditional Value-at-Risk

Integrating renewable energy into the power grid requires intelligent risk-aware dispatch accounting for the stochastic availability of renewables. Toward achieving this goal, a robust DC optimal flow problem is developed in the present paper for power systems with a high penetration of wind energy. The optimal dispatch is obtained as the solution to a convex program with a suitable regularizer, which is able to mitigate the potentially high risk of inadequate wind power. The regularizer is constructed based on the energy transaction cost using conditional value-at-risk (CVaR). Bypassing the prohibitive high-dimensional integral, the distribution-free sample average approximation method is efficiently utilized for solving the resulting optimization problem. Case studies are reported to corroborate the efficacy of the novel model and approach tested on the IEEE 30-bus benchmark system with real operation data from seven wind farms.Comment: To Appear in Proc. of the 4th Intl. Conf. on Smart Grid Communication