In order to make an electrical system operation planning robust to the possibility of failures (contingencies), different models and approaches have been proposed to determine a dispatch of generators capable of ensuring the system  survival (i.e., capable of meeting the demand) even if one or two components fail. To this end, the safety criteria known as n1 and n2 are adopted worldwide in various electrical systems as an efficient and practical way of mitigating load shed in the event of contingencies. However, these criteria started to be questioned due to recent blackouts brought about by simultaneous failures of different system components.
Unlike what is usually said, multiple contingencies are more common and dangerous than natural independent faults. The main reason for this lies in the complexity of the dynamic stability of power systems. In addition, the protection system, that operates in parallel to the supply system, is not free of failures. Thus, natural faults can cause subsequent contingencies (dependent on earlier contingencies) due to the malfunction of the protection mechanisms or the instability of the overall system. These facts drive the search for more stringent safety criteria, for example, nK, where K can be greater than two.
The computational complexity and the size (number of constraints and variables) of the optimization models traditionally used to consider the criterion nK in operation planning problems is very high and extremely dependent on the parameter K. For K equal 2, it is still possible to solve such models when considering real systems, with a few hundred power plants. However, for K more than 2, these models become computationally intractable because of the exponential growth in the number of constraints and variables of the optimization model. This is due to the need of enumerating all the possible contingencies in the mathematical dispatch model.
In the present work, we study a new approach to the electrical system operation planning problem capable of incorporating the safety criterion nK, where K can be greater than 2. First, we formulated the problem using a mathematical modeling technique called Robust Optimization. This allows us to select the worst case of contingency, which let us to avoid enumerating all the possible contingencies. Such technique has been successfully applied disregarding the transmission network. This approach becomes unfeasible when we take into account the network, as well as the possibility of contingencies in its transmission lines. Thus our research seeks to solve an open problem.
