Solving the Short-Term Scheduling Problem of Hydrothermal Systems via Lagrangian Relaxation and Augmented Lagrangian

Table 1

Thermal data.

Plant	Fuel	Fuel costs			Start-up costs			Power limits		Min. times		Ramp
		𝑥𝑘	𝑎0	𝑎1	𝑎2	𝑏0	ω	𝑏1	𝑝𝑡^min	𝑝𝑡^max	𝑡^up	δ	Δ
01	NUCLEAR	5,624.0	20.9	0.0002	45,000	12,500	4	70	657	9	9	150	180
02	NUCLEAR	5,624.0	16.3	0.0002	56,000	21,000	6	125	1,350	9	9	200	250
03	GAS	4,000.0	153.8	0.0005	420	250	1	200	923	2	2	70	35
04	GAS	1,200.0	117.0	0.0009	285	150	1	80	670	1	1	100	250
05	GAS	657.0	74.4	0.0052	85	42	1	90	869	1	2	100	300
06	GAS	723.0	11.8	0.0043	98	6	1	60	480	1	1	120	200
07	COAL	986.0	170.5	0.0089	3,226	1,613	7	12	132	4	6	50	70
08	COAL	1,183.0	129.0	0.0077	3,895	1,945	8	25	262	5	8	60	75
09	COAL	1,540.0	75.0	0.0062	4,691	2,345	9	20	100	10	20	50	50
10	GAS	755.3	143.0	0.0065	88	50	1	65	638	2	2	150	250
11	GAS	529.0	70.2	0.0051	61	35	1	71	638	2	2	150	250
12	GAS	866.0	80.6	0.0066	97	48	1	23	347	1	1	100	200