# A New Affinely Adjustable Robust Model for Security Constrained Unit Commitment under Uncertainty
###### Abstract  
Currently, optimization models for the safe and reliable operation of power systems deal with two major challenges: the first one is the reduction of the computational load when considering \(N-1\) contingencies; the second one is the adequate modeling of the uncertainty of intermittent generation and demand. This paper proposes a new affinely adjustable robust model to solve the security constrained unit commitment problem considering these sources of uncertainty. Linear decision rules, which take into account the forecasts and forecast errors of the different sources of uncertainty, are used for the affine formulation of the dispatch variables, thus allowing the tractability of the model. Another major novelty is that the evaluation of the \(N-1\) security constraints is performed by incorporating a novel method, proposed in the literature, based on the user-cuts concept. This method efficiently and dynamically adds only the binding \(N-1\) security constraints, increasing the computational efficiency of the model when transmission line contingencies are considered. Finally, Monte Carlo simulations on the post-optimization results were run to demonstrate the effectiveness, feasibility and robustness of the solutions provided by the proposed model. p 2021 11 3987 2021  
and balance of the system. In order to mitigate the negative effects of uncertainty, new mathematical optimization models focus on incorporating the dynamic and unexpected variability of power systems. Conventional procedures and methods for the UC solution, under different conditions of uncertainty, have been widely applied by researchers [5; 6]. Dealing with the uncertainties of the UC problem through deterministic optimization (as in [7; 8]), where load and intermittent generation sources are based solely on forecasts, may not be adequate to correctly address the reliable balance between this type of sources and demand. Although this approach may be easy to implement and computationally more efficient, its greatest drawback lies in the overestimation of generation reserves, a circumstance that turns out to be economically inefficient for the system. On the other hand, stochastic optimization models for the UC (SOUC) address the behavior of the corresponding random variables through probability distributions that are modeled by a finite set of scenarios, each one with a given probability. This approach overcomes some of the drawbacks of deterministic formulations. However, considering a large number of scenarios in the SOUC hinders the computational tractability of the underlying mathematical models. [PERSON] and [PERSON] [9] discuss in detail the computational complexity of the SOUC. As an alternative, different techniques have been used to solve the SOUC efficiently (i.e., shortening the required solution times). These techniques include: Lagrangian relaxation--LR [5; 10; 11; 12; 13], Benders decomposition--BD [12; 14; 15; 16; 17], strong valid inequalities embedded in cutting plane approaches [18; 19], column generation [20; 21], and progressive hedging algorithms [22; 23; 24; 25; 26; 27; 28; 29; 30]. Likewise, the parallel implementation of the above techniques is also an alternative, e.g., LR [10] and BD [31]. The other major drawback of SOUC approaches is the difficulty that arises when trying to estimate the probability distribution of the stochastic variables. Alternatively, robust optimization of the UC (ROUC) does not require the definition of scenarios or the estimation of their realization probabilities. Instead, it defines an uncertainty set to optimize the response of the system over all possible realizations of the random variables, particularly the worst one [1]. Several authors have tackled the UC from the robust optimization perspective [32; 33; 34; 35; 36]. However, one major drawback appears, as a direct consequence of protecting the system against an improbable worst-case scenario: the obtained solution can be over-conservative [37].