Probability measures of fuzzy events in power systems

The various reserve capacity states are not predictable accurately due to uncertain operation of the power system and also due to uncertain changes in the required demand. Hence, the reserve capacity states are considered as fuzzy events and they are subjectively defined. The probability values of being in the same state or transferring from one state to another state are also not known precisely due to the uncertain shape of the load curve. The probability values have been assigned after a great deal of discussion with Load Despatch Centre experts. The application of fuzzy set theory allows the inclusion of professional wisdom, knowledge and intruition into an analytical scheme. The foregoing power system example is intended merely to demonstrate possible ways of defining some of the concepts of probability theory in a more general setting in which the fuzzy events are allowed.