GENETIC ALGORITHM MODEL FOR PROFIT MAXIMIZATION OF GENERATING COMPANIES IN DEREGULATED ELECTRICITY MARKETS

Figures & data

FIGURE 1 Hourly market prices of energy.

FIGURE 2 Hourly forecasted demand with reserves.

TABLE 1 Data for the 20-Unit Problem Set

Unit	Unit	P ^min(i)	p ^max(i)	A(i)	B(i)	C(i)	T ^up(i)	T ^down(i)	X ^0(i)	D(i)	E(i)	CT(i)	R ^up(i)	R ^down(i)	Shut-Down
index, i	name	[MW]	[MW]	($/MW ^2h)	($/MWh)	($/h)	(h)	(h)	(h)	($/h)	($/h)	(h)	(MW/h)	(MW/h)	cost ($)
1	U18a	3.6	18	0.04175	15.7463	19.01	0	0	−1	0	0	1	6	5	0
2	U18b	3.6	18	0.04239	15.8712	19.04	0	0	−1	0	0	1	6	5	0
3	U18c	3.6	18	0.04411	16.0311	19.27	0	0	−1	0	0	1	6	5	0
4	U18d	3.6	18	0.04513	16.1724	19.44	0	0	−1	0	0	1	6	5	0
5	U30a	6	30	0.06975	26.2541	31.72	0	0	−1	30	30	2	12	15	0
6	U30b	6	30	0.07012	26.3911	31.74	0	0	−1	30	30	2	12	15	0
7	U30c	6	30	0.07237	26.5259	31.94	0	0	−1	30	30	2	12	15	0
8	U114a	22.8	114	0.01459	20.3148	11.57	3	2	−3	75	75	3	23	23	0
9	U114b	22.8	114	0.01567	20.4512	11.59	3	2	−3	75	75	3	23	23	0
10	U114c	22.8	114	0.01704	20.6219	11.77	3	2	−3	75	75	3	23	30	0
11	U150a	37.5	150	0.01921	26.7302	15.22	4	2	−3	105	105	4	38	38	0
12	U150b	37.5	150	0.02062	26.9095	15.25	4	2	−3	105	105	4	45	45	0
13	U150c	37.5	150	0.02242	27.1341	15.49	4	2	−3	105	105	4	45	45	0
14	U230a	80	230	0.00563	15.2835	44.85	5	3	−5	225	225	6	150	150	0
15	U230b	80	230	0.00575	15.2911	44.93	5	3	−5	225	225	6	225	150	0
16	U295a	103	295	0.01088	12.8875	6.78	5	4	−4	300	300	8	290	375	0
17	U295b	103	295	0.01133	12.8913	6.89	5	4	−4	300	300	8	290	375	0
18	U350a	140	350	0.00301	10.7601	32.96	8	5	−10	300	200	8	200	300	0
19	U400a	100	400	0.01059	8.3391	64.16	8	5	−10	500	500	8	250	250	0
20	U400b	100	400	0.01123	8.4511	64.36	8	5	−10	500	500	10	250	250	0

TABLE 2 20-Units ON/OFF Schedule by Genetic Algorithm

Unit	ON/OFF Schedule for the Hours 0–24
1	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0
9.5pt2	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0
9.5pt3	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0
9.5pt4	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0
9.5pt5	0	0	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0	0	0	0
9.5pt6	0	0	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0	0	0	0
9.5pt7	0	0	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0	0	0	0
9.5pt8	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0
9.5pt9	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0
9.5pt10	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0
9.5pt11	0	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0	0	0
9.5pt12	0	0	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0	0	0
9.5pt13	0	0	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0	0	0
9.5pt14	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0
9.5pt15	0	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0
9.5pt16	0	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0
9.5pt17	0	0	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0	0
9.5pt18	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0
9.5pt19	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0
9.5pt20	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	0	0
9.5pt

FIGURE 3 Total profit per hour for the 20-units problem set.

FIGURE 4 Total profit per generating unit for the 20-units problem set.

TABLE 3 Production (MW) Schedule for the 20-Units Problem Set

Unit Name	Production (MW) for the Hours 0–24
U18a	0	0	0	0	6	12	18	18	18	18	18	18	18	18	18	18	18	18	18	13	8	3.6	0	0	0
U18b	0	0	0	0	6	12	18	18	18	18	18	18	18	18	18	18	18	18	18	13	8	3.6	0	0	0
U18c	0	0	0	0	6	12	18	18	18	18	18	18	18	18	18	18	18	18	18	13	8	3.6	0	0	0
U18d	0	0	0	0	6	12	18	18	18	18	18	18	18	18	18	18	18	18	18	13	8	3.6	0	0	0
U30a	0	0	0	0	0	0	12	24	30	30	30	30	30	30	30	30	30	30	15	0	0	0	0	0	0
U30b	0	0	0	0	0	0	12	24	30	30	30	30	30	30	30	30	30	30	15	0	0	0	0	0	0
U30c	0	0	0	0	0	0	12	24	30	30	30	30	30	30	30	30	30	30	15	0	0	0	0	0	0
U114a	0	0	0	23	46	69	92	114	114	114	114	114	114	114	114	114	114	114	114	91	68	45	23	0	0
U114b	0	0	0	23	46	69	92	114	114	114	114	114	114	114	114	114	114	114	114	91	68	45	23	0	0
U114c	0	0	0	23	46	69	92	114	114	114	114	114	114	114	114	114	114	114	114	91	68	45	23	0	0
U150a	0	0	0	0	0	38	76	114	150	150	150	150	150	150	150	150	150	112	74	38	0	0	0	0	0
U150b	0	0	0	0	0	0	45	90	135	150	150	150	150	150	150	150	150	105	60	38	0	0	0	0	0
U150c	0	0	0	0	0	0	45	90	135	150	150	150	150	150	150	150	150	105	60	38	0	0	0	0	0
U230a	0	0	0	0	150	230	230	230	230	230	230	230	230	230	230	230	230	230	230	230	230	80	0	0	0
U230b	0	0	0	0	0	225	230	230	230	230	230	230	230	230	230	230	230	230	230	230	230	80	0	0	0
U295a	0	0	0	0	0	290	295	295	295	295	295	295	295	295	295	295	295	295	295	295	295	295	0	0	0
U295b	0	0	0	0	0	290	295	295	295	295	295	295	295	295	295	295	295	295	295	295	295	295	0	0	0
U350a	0	0	0	200	350	350	350	350	350	350	350	350	350	350	350	350	350	350	350	350	350	350	140	0	0
U400a	0	0	0	250	400	400	400	400	400	400	400	400	400	400	400	400	400	400	400	400	400	400	150	0	0
U400b	0	0	0	250	400	400	400	400	400	400	400	400	400	400	400	400	400	400	400	400	400	400	150	0	0

TABLE 4 Comparison of Lagrangian Relaxation and Genetic Algorithm Results for Up to 120-Unit Systems

		Genetic algorithm
		Total profit ($)
	Langrangian relaxation
Units	Total profit ($)	Best	Worst	Difference (%)
20	972 214	972 214	967 450	0.49
40	1 939 221	1 944 914	1 938 496	0.33
60	2 903 369	2 918 443	2 912 314	0.21
80	3 873 213	3 891 430	3 884 815	0.17
100	4 838 537	4 864 331	4 857 521	0.14
120	5 804 271	5 837 545	5 831 707	0.10