Transmission Expansion Planning in Deregulated Power ... - tuprints

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Transmission Expansion Planning in Deregulated Power ... - tuprints

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.

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