Despite significant economic and ecological effects, a higher level of renewable energy generation leads to increased uncertainty and variability in power injections, thus compromising grid reliability. In order to improve power grid security, we investigate a joint chance-constrained (CC) direct current (DC) optimal power flow (OPF) problem. The problem aims to find economically optimal power generation while guaranteeing that all power generation, line flows, and voltages simultaneously remain within their bounds with a pre-defined probability. Unfortunately, the problem is computationally intractable even if the distribution of renewables fluctuations is specified. Moreover, existing approximate solutions to the joint CC OPF problem are overly conservative, and therefore have less value for the operational practice. This paper proposes an importance sampling approach to the CC DC OPF problem, which yields better complexity and accuracy than current state-of-the-art methods. The algorithm efficiently reduces the number of scenarios by generating and using only the most important of them, thus enabling real-time solutions for test cases with up to several hundred buses.
Renewable energy sources (RES) has become common in modern power systems, helping to address decarbonization and energy security goals. Despite being attractive, RES such as solar and have low inertia and high uncertainty, thus compromising power grid stability and increasing the risk of energy blackouts. Stochastic (chance-constrained) optimization and other state-of-theart algorithms to optimize and control power generation under uncertainty either explicitly assume the distribution of renewables, or use data-driven approximations. The latter becomes time-consuming and inaccurate, esp. when optimizing over multiple time steps.This paper considers a discrete-time chance-constraint direct current optimal power flow control problem for minimizing power generation costs subjected to power balance and security constraints. We propose an importancesampling-based data-driven approximation for the optimal automated generation control, which allows to improve accuracy and reduce data requirements compared to stateof-the-art methods. We support the proposed approach theoretically and empirically. The results demonstrate the approach superior performance in handling generation uncertainty, enhancing the stability of renewable-integrated power systems, and facilitating the transition to clean energy.
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