First, no, I don't think there is any existing code to do exactly what you are suggesting, but it is trivial to write a short program that varies loads and generation in a loop, calling the OPF each time. Second, I purposely did not change these zonal reserve prices in the output. What this is displaying is the shadow price on each reserve constraint. In the general case, I don't think there is a single zonal price that reflects the effects of multiple constraints. The subtilty here comes from the fact that the zone definitions can be (and in this case are) overlapping. So the price of $5.50 actually comes by adding the shadow prices on both of the zonal constraints. In this example, since every node in zone 2 is also in zone 1, you might expect the zone 2 price to be the sum of the two multipliers. However, this does not work in the general case. Suppose you had 3 zones, defined as follows ... Zone 1: gens 1, 2, 3 Zone 2: gens 3, 4 Zone 3: gens 4, 5, 6 And suppose all of the reserve constraints were binding. What is the "zone 2 price"? By definition it is the sensitivity of the total system cost to changes in the zone 2 reserve requirement. Attached is an example (overlapping_reserves_eg.m) that demonstrates such a case and verifies the prices by perturbing each constraint. You can see how the dispatches change (and consequently how the system cost is affected) as the constraints are perturbed. So my thought is that the zonal reserve price should be defined as the multiplier on the corresponding reserve constraint, but each generator should be paid a price equal to the zonal price for all zones in which it is included. Comments? -- Ray Zimmerman Senior Research Associate 211 Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 |
overlapping_reserves_eg.m
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On Mar 18, 2011, at 3:56 PM, Santiago Chamba wrote:
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