Interval Mathematics Applied to Multiperiod Optimal Power Flow

The main tools for the operation and planning of electrical power systems are Power Flow (PF) and Optimal Power Flow (OPF). However, the analysis performed by these tools delivers deterministic values, that disregard uncertainties that occur in electrical systems. Such uncertainties are mainly caused by data error of lines, transformers, demand, and generation of alternative sources forecasting. A strategy to incorporate these uncertainties in the tools is through Interval Math (1M), which allows the inclusion of data intervals instead of single points. This strategy is performed only once, unlike probabilistic methods that run exhaustive simulations. Thus, the objective of this work is to incorporate 1M into a Multiperiod Optimal Power Flow (MOPF) to consider load and generation data uncertainties, after the deterministic optimization. The uncertainty ranges are added via Krawczyk Method, which determines an optimal interval of operation. The MOPF realizes the dispatch of power generation and reserve spinning along 24 hours of a hydro-thermal-wind system. The proposed method was compared with results obtained from traditional exhaustive simulations carried out with the southern Brazilian system with 33 Buses. The results obtained were close to the values of the random analysis, with uniformity.