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Exploiting the Random Nature of Transmission Capacity

Fortnightly Magazine - September 15 1998

capable of¼ remaining stable, following [any single contingency]¼ and

(3) After the dynamic power swings subside following a [single contingency]¼ all transmission facility loadings are within emergency ratings and all voltages are within emergency limits.

One weakness of this definition is that FCITC cannot be measured directly or simply, requiring instead laborious computer studies by a skilled specialist. A second weakness is that the definition requires subjective interpretation since it reflects planning and operating practices and procedures. A third weakness is that transmission capacity varies with time and with operating conditions, some of which are random.

These variations can prove significant. For instance, in recent years the nominal transmission capacity between British Columbia and Washington was 2,300 MW in the summer and 600 MW in the winter. The difference was due to the seasonal changes in generation and load patterns in British Columbia and the northwestern United States. The variation in actual hour-by-hour transmission capacity is probably much greater.

Figure 2 illustrates the highly variable nature of wheeling flows. The month-to-month variations are huge, with wheeling ranging from less than 40,000 MWh to nearly 300,000 MWh. The peak hourly wheeling was 1,998 MW, while the average was only 227 MW, giving an annual load factor of 11 percent. If another transaction, with lower priority, were to contend for transmission capacity, the existing wheeling flows would contribute a significant measure of randomness to the ATC.

Figure 3 makes the same point in a different way. This figure is striking because the wheeling charges for these transactions were based on the capacity reserved. The marginal wheeling cost as seen by the purchaser of the service, up to the capacity reserved, was zero - yet 50 percent of the transactions had load factors of 70 percent or less.

Computing Availability

Utilities have not used random models of transmission capacity for several reasons. One important reason is that, until recently, a practical way of computing random transmission capacity was not available.

Transmission system usage is variable because the flows are functions of a number of uncertainties, combined with operating policies and procedures. Key uncertainties include forced outages (contingencies) of generating units and hour-to-hour fluctuations in load, and these in turn affect dispatch, unit commitment, maintenance scheduling, etc., which in their turn affect flows.

Recently developed production simulation programs that include electrical models of the transmission system can compute random flows and transmission capacity. These programs simulate the dispatch and operation of the power system for combinations of the random variables. One type of production simulation program uses Monte Carlo sampling to develop a statistically significant set of outcomes of these variables. Another type combines these variables mathematically to capture the effects of all possible combinations, without sampling.

Either type can produce data like that shown in Figure 4. These are flow-duration curves, similar to the familiar load-duration curves, for several limiting lines and interfaces in a large region with about 65,000 MW of peak load.# A point (x,y) on one of the curves is the probability (x) that the flow is greater than or equal to