Robust unit commitment with $$n-1$$ n - 1 security criteria

Abstract

The short-term unit commitment and reserve scheduling decisions are made in the face of increasing supply-side uncertainty in power systems. This has mainly been caused by a higher penetration of renewable energy generation that is encouraged and enforced by the market and policy makers. In this paper, we propose a two-stage stochastic and distributionally robust modeling framework for the unit commitment problem with supply uncertainty. Based on the availability of the information on the distribution of the random supply, we consider two specific models: (a) a moment model where the mean values of the random supply variables are known, and (b) a mixture distribution model where the true probability distribution lies within the convex hull of a finite set of known distributions. In each case, we reformulate these models through Lagrange dualization as a semi-infinite program in the former case and a one-stage stochastic program in the latter case. We solve the reformulated models The research of this author is supported by EPSRC Grant EP/M003191/1. using sampling method and sample average approximation, respectively. We also establish exponential rate of convergence of the optimal value when the randomization scheme is applied to discretize the semi-infinite constraints. The proposed robust unit commitment models are applied to an illustrative case study, and numerical test results are reported in comparison with the two-stage non-robust stochastic programming model.

Distributionally Robust Transmission Expansion Planning: A Multi-Scale Uncertainty Approach

“…More recently, DRO approaches have been applied to model uncertainty in power system problems such as congestion line management [19], economic dispatch [20], securityconstrained optimal power flow [21], risk-based optimal power flow with dynamic line rating [22], investment decisions in wind farms [23], and unit commitment (UC) [24]- [26]. Regarding the application of DRO to TEP (DRO-TEP) problem, to the best of the authors' knowledge only a few works have been published so far.…”

Robust optimization vs. stochastic programming incorporating risk measures for unit commitment with uncertain variable renewable generation

“…In this method, the uncertain parameter is represented as a random variable whose distribution is not known with certainty. A family of distributions may be specified by characteristics of its moments [16,47] or a fixed discrete support with a bound on the distances among probability vectors [20,49]. Two-stage formulations are proposed to optimize the expected cost with respect to the worst distribution in the specified family.…”

A distributionally robust optimization-based risk-limiting dispatch in power system under moment uncertainty

“…Mathematical methodologies introduced above provide some motivation for solving ED problems with ambiguous distribution information of random variables in power system analysis, see recent references . Papers proposed DRO‐based unit commitment (UC) via 2‐stage optimization.…”

“…[21][22][23][24] Papers 21,23 proposed DRO-based unit commitment (UC) via 2-stage optimization. In paper, 21 two types of ambiguous distribution are addressed: a moment model with just known mean values of the random supply variables, and a mixture distribution type with a convex hull of finite known distribution forms. Paper 23 studied UC problem under an ambiguous distribution set of first-order moment uncertainty (ie, mean condition).…”

“…The motivation of RRLD is same as in the references. [21][22][23][24] Comparing with references, [21][22][23] we use a different uncertainty set where a general ellipsoid version of the first and second moment information is considered. The selected ellipsoid set has some advantage to describe the action of random variable distribution.…”