Improved efficient bounding method for DC contingency analysis using reciprocity properties

The efficient bounding method for DC contingency analysis is improved using reciprocity properties. Knowing the consequences of the outage of a branch, these properties provide the consequences on that branch of various kinds of outages. This is used in order to reduce computation times and to get rid of some difficulties, such as those occurring when a branch flow is close to its limit before outage. Compensation, sparse vector, sparse inverse and bounding techniques are also used. A program has been implemented for single branch outages and tested on the actual French EHV 650 bus network. Computation times are 60% of the efficient bounding method. The relevant algorithm is described in detail in the first part of this paper. In the second part, reciprocity properties and bounding formulas are extended for multiple branch outages and for multiple generator or load outages. An algorithm is proposed in order to handle all these cases simultaneously