Uncertainty in the System

Note that in the previous discussion we assume that all the parameters of the problem are known in advance. In other words, perfect information regarding the load forecast and the generating units is available. In practice, there is uncertainty associated with any electric generating power system. Among the factors that randomly affect the load on the system are generator failures, unexpected demands, and the available electricity for trade. Here is a closer look at these factors.

• Generator Failures: A given generator may be unavailable for use at any time due to unforeseen circumstances, such as mechanical problems, unscheduled maintenance, etc. The current strategy of most utilities is to maintain adequate operating reserves for these types of situations. At any given time, some of these operating reserves are available from sources such as a pumped storage plant, unloaded but synchronized generators, or quick-start combustion turbines.
• Inaccurate Forecast: Experienced schedulers forecast the load for each hour of the week in advance and continually update this forecast. To estimate the load on the system, a scheduler uses the data of the same week from previous years, the data of days with similar weather conditions, and his or her personal experience. Clearly, the real demand may deviate from the expected demand in any given hour.
• Other Factors: Electricity can be bought from or sold to other electric companies. The price per megawatt-hour varies depending on the time of day, the contracts governing the trade between these companies, the amount of electricity needed, the urgency of the electricity need, etc. All these options further provide randomness into the electric power generation system.

We suggest a scenario analysis approach for incorporating uncertainty into the model [Rockafellar and Wets 1991]. One can consider a set of possible demand scenarios, each of which represents a limited amount of information about the demand uncertainty. For instance, one scenario may represent the worst case load on the system, another may represent the most likely demand occurrence. Each scenario is assigned a weight that reflects the possibility of its occurrence in the future. In other words, the uncertainty about future demand is modeled by a number of possible demand instances.

Given the set of possible scenarios at any time period, one must make a decision that is feasible for all these scenarios; that is, the decision is non-anticipative. The previous requirement guarantees having enough capacity in the system to meet future loads under any possible scenario. Among these feasible decisions, we select the schedule that minimizes the average cost over all possible scenarios [Takriti, Birge, and Long 1994]. The interested reader is referred to Appendix B for more details. Numerical results indicate that incorporating uncertainty into the model results in substantial savings. Here, we present results obtained from applying our model to the system of the MEPCC.