Transmission - Economic Dispatch

With the flows in the network being calculated based on the precomputed shift factors, we can now compute an economic dispatch and optimal power flow i.e. the output levels of all plants that minimises total production cost and respects thermal limits of the transmission lines in the network.

The economic dispatch and optimal power flow for the 7-Node system is shown in Figure 1. PLEXOS reports the data on the lines in the system as in Table 1. Lines "2_5" and "4_5" are flowing at their thermal limits. There is a shadow price associated with the "2_5" limit. Table 2 shows the solution data for nodes. Note how the prices at each node are different: this is an example of nodal pricing (or locational marginal pricing) and is caused by the congestion on Line "2_5".

Table 1: Line Solution Data

Line	Max Rating (MW)	Min Rating (MW)	Flow (MW)	Loss (MW)	Marginal Loss (%)	Marginal Loss Factor	Is Congested (Yes/No) [1]	Shadow Price ($/MW)
1_2	120	-120	4.62	0	0	1	0	0
1_3	120	-120	15.38	0	0	1	0	0
1_2	120	-120	4.62	0	0	1	0	0
2_3	100	-100	19.23	0	0	1	0	0
2_4	100	-100	0	0	0	1	0	0
2_5	120	-120	120	0	0	1	-1	10.53
2_6	200	-200	130	0	0	1	0	0
3_4	222	-222	-115.38	0	0	1	0	0
4_5	60	-60	60	0	0	1	-1	0
5_7	200	-200	50	0	0	1	0	0
6_7_1	200	-200	40	0	0	1	0	0
6_7_2	200	-200	40	0	0	1	0	0

Table 2: Node Solution Data

Child Name	Phase Angle (degrees)	Load (MW)	Generation (MW)	Price ($/MWh
1	0	0	20	14.95
2	0.13	40	304.62	15
3	2.12	150	0	14.69
4	0.13	80	255.38	14.6
5	8.38	130	0	22.42
6	4.6	200	150	16.86
7	10.1	200	70	20.57

*Note that as a convention PLEXOS uses 0 for "No" and -1 for "Yes" in reporting Boolean type values.

Figure 1: 7-Node Economic Dispatch