Abstract
AbstractThe need to de‐carbonize the current energy infrastructure, and the increasing integration of renewables pose a number of difficult control and optimization problems. Among those, the optimal power flow (OPF) problem—i.e., the task to minimize power system operation costs while maintaining technical and network limitations—is key for operational planning of power systems. The influx of inherently volatile renewable energy sources calls for methods that allow to consider stochasticity directly in the OPF problem. Here, we present recent results on uncertainty quantification for OPF problems. Modeling uncertainties as second‐order continuous random variables, we will show that the OPF problem subject to stochastic uncertainties can be posed as an infinite‐dimensional L2‐problem. A tractable reformulation thereof can be obtained using polynomial chaos expansion (PCE), under mild assumptions. We will show advantageous features of PCE for OPF subject to stochastic uncertainties. For example, multivariate non‐Gaussian uncertainties can be considered easily. Finally, we comment on recent progress on a Julia package for PCE.
Highlights
We are witnessing a paradigm shift in the production of electrical energy: the tremendous effort to generate electricity from renewable energy sources is unprecedented
With the influx of renewable energy sources and production of electrical energy at lower-scale voltage levels the traditional modus calls for a critical assessment
The task of delivering electrical energy to consumers in a cost-optimal way whilst respecting engineering limits such as generation limits and line limits is posed as a nonlinear optimization problem, the so-called optimal power flow problem (OPF) [1]
Summary
We are witnessing a paradigm shift in the production of electrical energy: the tremendous effort to generate electricity from renewable energy sources is unprecedented. The task of delivering electrical energy to consumers in a cost-optimal way whilst respecting engineering limits such as generation limits and line limits is posed as a nonlinear optimization problem, the so-called optimal power flow problem (OPF) [1]. These problems are used for planning, dispatching, and operating the electric power system. Probabilistic forecasts are used that model the value to be forecast as a random variable [2] This in turn affects the way the OPF problem is solved. We show how the OPF problem can be formulated in the presence of uncertainties and how it can be solved in terms of a deterministic proxy problem
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