Appendix C: Examples for Locational Marginal Price 122 Case 2: Figure C.2 shows case 2. In this case, generator 1 can not supply both loads because of the transmission constraint. Hence, 50 MW of load 2 is supplied by the generator 2. If 1 MW load is added to bus 1, this 1 MW load is supplied by generator 1. Therefore, LMP of bus 1 is equal to $10/MWhr. If 1 MW load is added to bus 2, this 1 MW load is supplied by generator 2. Therefore, LMP of bus 2 is equal to $15/MWhr. Due to transmission congestion LMPs are not equal in this case. LMP: 10$10/MWhr 100 MW Bid: $20/MWhr 400 MW @ $10/MWhr dispatched 300 MW 1 Limit: 200 MW 2 200 MW Fig. C.2- 2 bus system – case 2 200 MW @ $15/MWhr dispatched 50 MW LMP: 15 $10/MWhr 250 MW Bid: $20/MWhr Case 3: In cases 1 and 2 LMPs of buses are smaller than bid of their loads. Hence, the loads are not curtailed. Case 3 is similar to case 2; except bid of load 2 is $12/MWhr. Figure C.3 shows case 3. Due to transmission constraint, generator 1 can not supply more that 200 MW of load 2. If the rest of load 2 is supplied by generator 2, LMP of bus 2 will be $15/MWhr (like case 2) which is greater than bid of load 2. Hence, load 2 is curtailed till LMP of bus 2 decreases to bid of load 2 i.e. $12/MWhr. In fact each load can be modelled with a load which is curtailed never and an imaginary generator with the bid of load. For example, load of buses of 2 can be modelled with a 250 MW load and an imaginary generator with bid $12/MWhr. The load is supplied fully and curtailed never. Figure C.4 shows the imaginary generator. In this case first generator of bus 1 is dispatched till reach transmission constraint. After that, imaginary generator is dispatched since its bid is smaller that bid of generator 2. If 1 MW load is added to bus 1, this 1 MW load is supplied by generator 1. Therefore, LMP of bus 1 is equal to $10/MWhr. If 1 MW load is added to bus 2, this 1 MW load is supplied by imaginary generator. Therefore, LMP of bus 2 is equal to $12/MWhr. The value of load curtailment is equal to dispatched value of imaginary generator. In this case, imaginary generator produces 50 MW. This means load of bus 2 is curtailed 50 MW, and only 200 MW of it is supplied. Because of the transmission congestions LMPs are not equal in this case.