Example

The case ﬁle lib/t/t_auction_case.m, used for this example, is a modiﬁed version of the 30-bus system that has 9 generators, where the last three have negative PMIN to model the dispatchable loads.

Table F-2:Generator Oﬀers

Generator	Block 1	Block 2	Block 3
	MW @ $/MWh	MW @ $/MWh	MW @ $/MWh
1	12 @ $20	24 @ $50	24 @ $60
2	12 @ $20	24 @ $40	24 @ $70
3	12 @ $20	24 @ $42	24 @ $80
4	12 @ $20	24 @ $44	24 @ $90
5	12 @ $20	24 @ $46	24 @ $75
6	12 @ $20	24 @ $48	24 @ $60

Table F-3:Load Bids

Load	Block 1	Block 2	Block 3
	MW @ $/MWh	MW @ $/MWh	MW @ $/MWh
1	10 @ $100	10 @ $70	10 @ $60
2	10 @ $100	10 @ $50	10 @ $20
3	10 @ $100	10 @ $60	10 @ $50

To solve this case using an AC optimal power ﬂow and a last accepted oﬀer (LAO) pricing rule, we use:

mkt.OPF = 'AC';
mkt.auction_type = 1;

mpc = loadcase('t_auction_case');
offers.P.qty = [ ...
12 24 24;
12 24 24;
12 24 24;
12 24 24;
12 24 24;
12 24 24 ];

offers.P.prc = [ ...
20 50 60;
20 40 70;
20 42 80;
20 44 90;
20 46 75;
20 48 60 ];

bids.P.qty = [ ...
10 10 10;
10 10 10;
10 10 10 ];

bids.P.prc = [ ...
100 70 60;
100 50 20;
100 60 50 ];

[mpc_out, co, cb, f, dispatch, success, et] = runmarket(mpc, offers, bids, mkt);

>> co.P.qty

ans =

   12.0000   23.3156         0
   12.0000   24.0000         0
   12.0000   24.0000         0
   12.0000   24.0000         0
   12.0000   24.0000         0
   12.0000   24.0000         0

>> co.P.prc

ans =

   50.0000   50.0000   50.0000
   50.2406   50.2406   50.2406
   50.3368   50.3368   50.3368
   51.0242   51.0242   51.0242
   52.1697   52.1697   52.1697
   52.9832   52.9832   52.9832

>> cb.P.qty

ans =

   10.0000   10.0000   10.0000
   10.0000         0         0
   10.0000   10.0000         0

>> cb.P.prc

ans =

   51.8207   51.8207   51.8207
   54.0312   54.0312   54.0312
   55.6208   55.6208   55.6208

In other words, the sales by generators and purchases by loads are as shown summarized in Tables F-4 and Tables F-5, respectively.

Table F-4:Generator Sales

Generator	Quantity Sold	Selling Price
	MW	$/MWh
1	35.3	$50.00
2	36.0	$50.24
3	36.0	$50.34
4	36.0	$51.02
5	36.0	$52.17
6	36.0	$52.98

Table F-5:Load Purchases

Load	Quantity Bought	Purchase Price
	MW	$/MWh
1	30.0	$51.82
2	10.0	$54.03
3	20.0	$55.62

F.2 Example