The basis for the application of stochastic methods can be found in the inherent randomness of system loads, or irregular fluctuations of system parameters such as the capacity of transmission lines, which may have a pronounced effect on the control functions of a power system. In the dynamic modeling, this type of uncertainty is usually represented by small random perturbations. The other type of uncertainty may represent large perturbations in the dynamic system modeling which are usually originated by random component outages. From the point of view of a system operator or planner, replicating both types of uncertainties in the dynamic model is important. This has been achieved with the development of software packages that apply certain aspects of the theory of stochastic systems to stability assessment of large scale power systems.
The following papers illustrate work in this field of study:
1. C. O. Nwankpa, S. M. Shahidehpour and J. Qiu, "A class of load perturbations in reliability evaluation of electric power systems," Journal of Electric Machines and Power Systems, Vol. 17, No. 4, pp. 233--257, 1989.
2. C. O. Nwankpa and S. M. Shahidehpour, "Colored noise modelling in the reliability evaluation of electric power systems," Journal of Applied Mathematical Modelling, Vol. 14, No. 7, pp. 338--351, July 1990.
3. C. O. Nwankpa, S. M. Shahidehpour and Z. Schuss, "Analysis of small disturbances of transmission lines in dynamic stability studies," Accepted by International Journal of Systems Science.
4. C. O. Nwankpa and S. M. Shahidehpour, "A probabilistic approach to bulk power transmission systems analysis," Proceedings 21st North American Power Symposium, Oct. 1989, Rolla, Mo., pp. 88--94.
5. C. O. Nwankpa and S. M. Shahidehpour, "Inclusion of small random perturbations in structure preserving model for power systems reliability studies," Proceedings of IASTED Conf.: Power High Tech '89, Valencia, Spain, July, 1989, pp. 471--475.
6. C. O. Nwankpa and S. M. Shahidehpour, "A class of power network reliability problems via colored noise modeling," Proceedings of IEEE International Symposium on Circuits and Systems, New Orleans, La, May 1--3, 1990, pp. 164--167.
7. C. O. Nwankpa and S. M. Shahidehpour, "Effect of small load fluctuations on power system voltage stability studies," Proceedings of American Control Conference, San Diego, Ca., May 23--25, 1990, pp. 2106--2110. C. O. Nwankpa and S. M. Shahidehpour,
8. "A new approach to the indication of voltage collapse in electric power systems," Proceedings of 10th Power Systems Computation Conference, Graz, Austria, August 19--24, 1990.
