# A New Affinely Adjustable Robust Model for Security Constrained Unit Commitment under Uncertainty
## 6 Conclusions  
This paper presented a new affinely adjustable robust model to solve the security constrained unit commitment problem considering uncertainty of intermittent generation sources and demand. The affine policies were only applied for the variables of the dispatch as adjustable variables in the event of the realization of uncertain variables. This approach keeps the non-anticipativity condition (\(\tau\leq t\)), i.e., only uncertain information known from past periods and the current period is considered. In addition, a user-cut based algorithm was implemented to generate \(N-1\) security constraints in the solution of the model. This algorithm merges the linear sensitivity factors (PTDF, LODF, and OTDF) and some logical and functional rules that allow for defining the feasible region of the problem only with the \(N-1\) binding constraints--a feature that improves the computational efficiency for the proposed model. Computational experiments showed that (1) the algorithm proposed in this paper, based on user cuts, is computationally efficient for evaluating \(N-1\) security constraints within the proposed AARO-SCUC model; (2) high quality solutions can be obtained in short run times by considering only information revealed from the current period and few periods in the past (\(t-2\leq\tau\) or \(t-3\leq\tau\) ). That is, it is not necessary to consider, for example, uncertain information disclosed for 23 past periods and the current one (\(t-24\leq\tau\)) to obtain good solutions. This behavior could be determined mainly by the non-anticipativity condition \(\tau\leq t\) of the dispatch variables. Furthermore, through the AGC, power systems have the particularity of correcting the inconveniences produced by the deviations of the forecast errors just at the instant \(t\). (3) A post-hoc analysis using Monte Carlo simulations shows that all the solutions of the model are robust for any condition where the realizations of the uncertainty variables are less than or equal to the maximum level of uncertainty used within the optimization process. In addition, there seems to be an inverse relationship between the level of uncertainty revealed of past periods considered  
Figure 8: Zoom of Figure 7.  
Figure 7: Number of violated constraints vs. materialization of forecast errors, 24-bus system. and the number of violated constraints for variable realizations outside the maximum level of uncertainty. The proposed model was optimized under uncertainty boxes bounded by maximum uncertainty levels. An important topic for future work is to consider unbounded uncertainty sets in order to always obtain a good performance of the model solution (feasible solutions) for realizations of the uncertain variable outside the uncertainty set. To reach this goal, a potential procedure based on global robust optimization may be implemented. Another important research opportunity for the reduction of the conservatism of the solution is to consider ellipsoidal uncertainty sets, using the criterion proposed by [68]. This also allows for the modeling of spatio-temporal dependencies of solar and wind generators. This, however, will change the structure of the AAROUC model since it results in nonlinear decision rules requiring the solution of mixed-integer second-order cone programming models. Conceptualization, C.C.M.-C., J.E.S.-A. and A.J.-D.; Data curation, J.E.S.-A. and C.C.M.-C.; Formal analysis, C.C.M.-C., J.E.S.-A., J.M.L.-L., A.J.-D. and J.G.V. ; Funding acquisition, A.J.-D., J.M.L.-L. and J.G.V. ; Investigation, C.C.M.-C. and J.E.S.-A. ; Methodology, C.C.M.-C.; Project administration, A.J.-D., J.M.L.- and J.G.V. ; Resources, C.C.M.-C., J.E.S.-A., A.J.-D., J.M.L.-L. and J.G.V. ; Software, J.E.S.-A. and C.C.M.-C.; Supervision, A.J.-D., J.M.L.-L. and J.G.V. ; Validation, C.C.M.-C. and J.E.S.-A. ; Visualization, C.C.M.-C. and J.E.S.-A. ; Writing--original draft, C.C.M.-C. and J.E.S.-A. ; Writing--review and editing, A.J.-D., J.M.L.-L. and J.G.V. ; All authors have read and agreed to the published version of the manuscript.