In the chorological production cost model that treats the load and operating status of units at each time period with uncertain, load level is a random variable for each time period, or even a stochastic process in the whole time horizon; the operating status of each unit is a stochastic process – Markov Chain in the whole time horizon. Different to the chorological method, the non-chorological method accommodates the load model and unit operating status model with some practical simplification to reduce the complication of the calculation dramatically.

The load model is represented as the load duration curve, as a probability distribution expressed in terms of hours that the load is expected to equal or exceed the value on the horizontal axis. This is a monotonically decreasing function with increasing load and could be converted to a “pure” probability distribution by dividing by the number of hours in the load interval being modeled. The following is an example to convert the load - time curve to load duration curve.

The

The units operating status is simplified from Markov Chain to discrete operating status within the output range, since units often suffer partial outages where the units must be derated for some period of time.

The production cost model uses the thermal-unit heat rate characteristics that are linear segments. This type of heat rate characteristics is essential to the development of an efficient probabilistic computational algorithm since it results in stepped incremental cost curves. This simplifies the economic scheduling algorithm since any segment is fully loaded before next is required.

The easiest way to explain and grasp the probabilistic procedure of thermal unit scheduling is as follow:

If there is a segment of capacity with a total of C MW available for scheduling, if we denote

q= the probability that C MW are unavailable and p= 1-q= the probability or “availability” of this segment.

Then after this segment has been scheduled, the probability that needing x MW or more is now . Since the occurrence of loads and unexpected unit outages are statistically independent events, the new probability distribution is a combination of mutually exclusive events with the same measure of need for additional capacity. This is

We note that the generation requirements for any generating segment are determined by the knowledge of the distribution that exists prior to the dispatch of the particular generating segment. That is the value of determine the required hours of operation of a new unit. The area under the distribution for x between zero and the rating of the unit loading segment determines the requirements for energy production. Assuming the particular generation segment being dispatched is not perfectly reliable, there will be a residual distribution of demands that cannot be served by this particular segment because of its forced outage.

Let us represent the forced outage rate for a generation segment of C MW and , the distribution of unserved load prior to scheduling the unit. Assume the unit segment to be scheduled is a complete generating unit with an input-output cost relation

The unit will be required hours, but on average it will be available only hours. The energy required by the load distribution that could be served by the unit is . The unit can only generate (1-q)E because of its expected unavailability.

The cost for this period =

Having scheduled the unit, there is a residual of unserved demands due to the forced outage of the unit. The recursive algorithm for the distribution of the probability of unserved load may be used to develop the new distribution of unserved demand after the unit is scheduled. That is

The process may be repeated until all units have been scheduled and a residual distribution remains that gives the final distribution of unserved demand.