Stochastic Modelling of Protection Systems: Comparison of Four Mathematical Techniques

Power system protection systems are designed to automatically take countermeasures against situations in power systems that are undesired. If these countermeasures are not taken the extent of the undesired situation will grow. This is an important aspect of the stochastic behaviour of power systems. A review is given of stochastic models of protection systems as described in literature. It is concluded that a standard is needed for the treatment of stochastic aspects of protection systems. This standard can be used as a basis for models and for collecting failure statistics. The proposed standard is based on a division of all protection system actions into correct operations, mal-trips and fail-to-trips. The mal-trips are divided into instantaneous mal trips and potential mal trips. Suggestions about the mathematical treatment of the stochastic protection system actions have been made. A small part of a power system, including one or more protection systems, is modelled by using four mathematical techniques: Markov theory, renewal theory, Petri nets and simulation. In these models the protection system can work correctly or fail to operate when short circuits occur. When the cost of maintenance and the cost of a fail ure to operate are defined, the optimal maintenance frequency can be determined. When using simulation this is the most difficult because of its statistical nature. Using the analytical techniques, this is much easier. When the model becomes more complex, the usefulness of the techniques changes. Markov models are still useful and relatively easy to handle, but only exponential distributions can be used. Renewal theory cannot be used for modelling large systems. Petri nets can be used, but they are difficult to design. The advantage over Markov models is that deterministic transition times between states can be incorporated into the model. Simulation is very suitable for modelling large systems. The main concerns are the large computational demands and the interpretation and processing of the statistical output.