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produced by a generator at bus 1 to serve a load at bus 3, two-thirds of that energy would flow over the direct line, 1-3, while one-third would flow over the longer routes of lines 1-2 and 2-3.

We assume that there are three merchant firms, A, B and C, each of which serves 300 MW of load at each bus; so each merchant serves 900 MW of load and each bus has a 900-MW aggregate load. The merchant firms each have one generator at each bus, with the italicized capacities and per-megawatt-hour incremental costs shown. For simplicity, we assume that the merchant firms do not exercise market power and, therefore, that they bid their incremental costs.

If there are no transmission constraints, each generator's energy output would be as indicated to the right of its incremental cost. Every generator with a cost below $18 per megawatt-hour would operate at maximum, every generator with a cost above $18 per megawatt-hour would produce no power, and C1, the $18 per megawatt-hour generator, would provide exactly the quantity of power that is required to balance supply and demand. If price equaled $18 per megawatt-hour at each bus, then all generators willingly would dispatch themselves, as shown in Figure 3.

Because so much cheap power is available at bus 1 and power is so expensive at bus 3, the unconstrained dispatch leads to 700 MW of flows through line 1-3. Given that we assume loads to be fixed, some action must be taken to redispatch generation so that the line flow is brought down to its 600-MW limit.

The New York and PJM ISOs use bids from market participants to find the least-cost generation dispatch. They then set the price at each power system bus equal to the bid-based "cost" of getting one extra megawatt to that bus, given that all transmission constraints are respected. The price at each bus thus equals the best market price available to serve that bus while respecting constraints.

Figure 4 shows the resulting dispatch and prices, the latter of which are determined from the incremental costs of the two marginal generators: unit B1 at $15 per megawatt-hour and unit A2 at $25 per megawatt-hour. Because a load increment at bus 1 would be served by unit B1, the price at bus 1 is $15 per megawatt-hour. For a similar reason, the price at bus 2 is $25 per megawatt-hour. Bus 3 is trickier. Because of how generator dispatch affects loads over the constrained line 1-3, a 1-MW load increment at bus 3 is most cheaply served by increasing output by 2 MW at bus 2 while reducing output by 1 MW at bus 1. That produces a bus 3 price of $35 per megawatt-hour (= 2 x $25 - 1 x $15).[Fn.4]

Not coincidentally, the prices shown in Figure 4 induce the lowest-cost-possible dispatch of this power system. At each bus, the lowest-cost generators operate at maximum, the highest-cost generators produce no power, and the generators with incremental costs equal to price provide exactly the quantities of power that