Before we get back to our three-node network, we'll illustrate out-of-merit dispatch with a simple example. The figure below shows a two-node electricity network with only one transmission line. The marginal cost of generator 1 is $10/MWh and the marginal cost of generator 2 is $30/MWh. Total demand is 100 MWh. Assume that each generator could produce as much power as you want.
The perfect economic dispatch here would be g1* = 100 MWh, g2* = 0 MWh. (If you don't understand why, go back and look at the section on economic dispatch with constant marginal cost.) Total system cost is $10 MWh × 100 MWh = $1,000.
Now, assume that there is a flow limit on the transmission line of 80 MW. If generator 1 produces more than 80 MW, the transmission line would become overloaded. So the system operator has to back off on generator 1 and increase power on generator 2. The adjusted economic dispatch that respects the transmission constraint is g1* = 80 MWh, g2* = 20 MWh. Total system cost is $10 MWh × 80 MWh + $30 MWh × 20 MWh = $1,400.
The system cost of transmission congestion is defined as:
(Total system cost with congestion) - (Total system cost if all transmission constraints were eliminated)
In our example, the system cost of transmission congestion is $1,400 – $1,000 = $400. This is also the value to the system of increasing the flow limit on the transmission line. If capacity on the transmission line could be expanded for less than $400, it would save money. If expanding capacity on the transmission line would cost more than $400, then it makes more economic sense to live with the congestion and use the more-expensive generator at node 2 more often.
This example illustrates what some students find to be a counterintuitive economic result for transmission: that it may be optimal to have some amount of transmission congestion. Simply having congestion does not mean that the transmission system is working inefficiently.