**American Electric Power** named **Michael Rencheck** senior vice president and chief nuclear officer for its D.C. Cook Nuclear Plant in Bridgman, Mich. The **American Public Power...**

## Exploiting the Random Nature of Transmission Capacity

y MW. For example, there is a 50 percent probability that the flow on line B will exceed 1,200 MW in the negative direction in any given hour. Figure 4 covers one year.

Notice that at least some of these curves do not represent a gaussian random variable. Furthermore, the flows on the various lines and interfaces are not necessarily independent, nor are they perfectly correlated. Table 1 gives the correlation coefficients for the various line/interface pairs for another system. The fact that the distributions are not gaussian, and that correlations are complex, means that classical system theory is not very useful in analyzing available transmission capacity, or ATC. The analysis needs to be based on a production simulation program that can model how the system is really operated.

A first cut at the probabilistic ATC for one of these lines or interfaces is the difference between the total thermal transmission capacity and the scheduled transfers.

Subtracting a reliability margin reflecting the flows that would result from the worst possible contingency can refine this first cut. This reliability margin is random, since which contingency is the worst will depend on the state of the system. The fact that the flow on the outage worst contingency element is also uncertain compounds the randomness. But these effects can be modeled in the production simulation program.

Current production-simulation programs cannot compute limits due to voltage or stability problems. Where such limits exist, they can be calculated using other techniques and combined with the limits found by the production-simulation program.

The resultant probabilistic ATC can be expressed as a table or represented graphically as a curve like the one in Figure 1.

Using Probabilistic

Availability

How can using probabilistic transmission capacity reduce risks, increase transmission system usage and revenues, and aid in transmission system planning? For simplicity and clarity, let's look at a sample system instead of a real one using the interface whose probabilistic ATC is given in Table 2. Three wheeling transactions (A, B, and C) contend for this transfer capability. At any given hour, each transaction will need either 150 MW of transfer capability, with probability 0.7, or none, with probability 0.3. The transactions are statistically independent.

CONVENTIONAL DETERMINISTIC MODELING. Suppose the transmission service provider (TSP) decides that the deterministic transmission capacity is 300 MW. As in Figure 1, this means that only about 30 percent of the time will the actual transmission capacity be lower than this amount. Suppose also that the wheeling tariff is $1.67/kW per month, or $20/kW per year. The transmission provider will accommodate only transactions A and B and will charge $6 million per year.

How reliable is the service? Assume that when a transaction must be curtailed, TSP in real time randomly selects either A or B to curtail (probability = 0.5). A transaction will need to be curtailed when two conditions are met: 1) The transmission capacity is reduced, and 2) the transaction is active. Table 3 shows that transaction A will be curtailed with probability 0.0963 - almost 10 percent of the time. Since the