A robust approach to chance constrained optimal power flow with renewable generation

Abstract

Abstract-Optimal Power Flow (OPF) dispatches controllable generation at minimum cost subject to operational constraints on generation and transmission assets. The uncertainty and variability of intermittent renewable generation is challenging current deterministic OPF approaches. Recent formulations of OPF use chance constraints to limit the risk from renewable generation uncertainty, however, these new approaches typically assume the probability distributions which characterize the uncertainty and variability are known exactly. We formulate a Robust Chance Constrained (RCC) OPF that accounts for uncertainty in the parameters of these probability distributions by allowing them to be within an uncertainty set. The RCC OPF is solved using a cutting-plane algorithm that scales to large power systems. We demonstrate the RRC OPF on a modified model of the Bonneville Power Administration network, which includes 2209 buses and 176 controllable generators. Deterministic, chance constrained (CC), and RCC OPF formulations are compared using several metrics including cost of generation, area control error, ramping of controllable generators, and occurrence of transmission line overloads as well as the respective computational performance.Index Terms-Wind power integration, power system economics, optimal power flow, wind power uncertainty, wind power variability, optimization methods, chance constrained optimization, distributionally robust optimization.

Uncertainty sets for wind power generation

“…3a) results in difficult nonconvexity in distributionally robust formulations (e.g., Eq. (27)-(28) in [4]). To avoid this nonconvexity, we assume that the range on the mean value in (Eq.…”

“…This RCC-OPF is implemented and tested on a large-scale system in [4]. In this letter, we interpret the set for the mean in terms of the wind power uncertainty, while the set for the variance is deemed as the wind power variability.…”

“…This method is suitable for uncertainty sets in the RUC [2] and RCC-OPF [3], [4], which can be interpreted in terms variability and uncertainty of WPG. The case study in [4] shows that the RCC-OPF model with these uncertainty sets outperforms several benchmarks in terms of several cost and reliability metrics. …”

Chance-Constrained Two-Stage Unit Commitment Under Uncertain Load and Wind Power Output Using Bilinear Benders Decomposition

“…Certainly, for some special cases, chance constraint can be converted into a closed form expression and the whole model can be reformulated into a regular mixed integer programming (MIP) model (e.g., [20,24,26,29]). In [30,31], such property is used to study chance constrained optimal power flow problems subject to uncertain parameters of the normal distribution.…”

A Randomized Algorithm for Chance Constrained Optimal Power Flow with Renewables

“…To avoid this difficulty, several assumptions are needed. For example, in papers [11], [12], they suppose that parameters are according to normal distributions and they deal with a chance constrained DC-OPF. In fact, since a chance constrained DC-OPF with the Gaussian setting has convexity, we can efficiently solve this problem.…”