Mathematical Problems in Engineering

Research Article

The Improved Binary-Real Coded Shuffled Frog Leaping Algorithm for Solving Short-Term Hydropower Generation Scheduling Problem in Large Hydropower Station

Table 4

The best computational solutions of economic load distribution (ELD) and unit commitment (UC) corresponding to 75m, 88m, and 107m water head.

(a) 75m water head


Period(h)	Load distribution (MW)
	Left-bank
	VGS						ALSTOM
	1#	2#	3#	4#	5#	6#	7#	8#	9#	10#	11#	12#	13#	14#

1	550	550	550	550	550	550	570	570	Down	Down	Down	Down	Down	Down
2	550	550	550	550	550	550	570	570	Down	Down	Down	Down	Down	Down
3	560	560	550	550	550	550	570	570	Down	Down	Down	Down	Down	Down
4	590	590	590	590	590	590	600	600	Down	Down	Down	Down	Down	Down
5	560	550	550	550	550	550	Down	Down	570	Down	Down	Down	Down	Down
6	560	550	550	550	550	550	Down	Down	570	Down	Down	Down	Down	Down
7	560	550	550	550	550	550	Down	Down	570	Down	Down	Down	Down	Down
8	560	550	550	550	550	550	Down	Down	570	Down	Down	Down	Down	Down
9	560	550	550	550	550	550	Down	Down	570	Down	Down	Down	Down	Down
10	550	550	550	550	550	550	550	550	550	Down	Down	Down	Down	Down
11	560	560	560	560	560	560	570	570	570	Down	Down	Down	Down	Down
12	550	550	550	550	550	550	570	570	570	Down	Down	Down	Down	Down
13	550	550	550	550	550	550	560	550	550	Down	Down	Down	Down	Down
14	550	550	550	550	550	550	570	Down	570	Down	Down	Down	Down	Down
15	550	550	550	550	550	550	570	Down	570	Down	Down	Down	Down	Down
16	550	550	550	550	550	550	570	Down	570	Down	Down	Down	Down	Down
17	550	550	550	550	550	550	570	Down	570	Down	Down	Down	Down	Down
18	550	550	550	550	550	550	570	Down	570	Down	Down	Down	Down	Down
19	560	560	560	560	560	550	570	570	570	570	Down	Down	Down	Down
20	560	560	560	560	550	550	570	570	Down	570	Down	Down	Down	Down
21	590	590	590	570	570	570	580	580	Down	580	Down	Down	Down	Down
22	590	590	590	570	570	570	580	580	Down	580	Down	Down	Down	Down
23	560	550	550	550	550	550	570	Down	Down	Down	Down	Down	Down	Down
24	560	550	550	550	550	550	570	Down	Down	Down	Down	Down	Down	Down

	Right-bank
	Orient power				ALSTOM				HEC				UC
	15#	16#	17#	18#	19#	20#	21#	22#	23#	24#	25#	26#	UC

1	500	Down	500	Down	540	Down	Down	Down	490	480	480	Down	11111111000000101010001110
2	500	Down	500	Down	540	Down	Down	Down	490	480	480	Down	11111111000000101010001110
3	520	Down	520	Down	540	Down	Down	Down	510	510	510	Down	11111111000000101010001110
4	560	Down	540	Down	610	Down	Down	Down	520	520	520	Down	11111111000000101010001110
5	520	520	Down	520	540	Down	Down	Down	510	510	510	490	11111100100000110110001111
6	520	520	Down	520	540	Down	Down	Down	510	510	510	490	11111100100000110110001111
7	520	520	Down	520	540	Down	Down	Down	510	510	510	490	11111100100000110110001111
8	520	520	Down	520	540	Down	Down	Down	510	510	510	490	11111100100000110110001111
9	520	520	Down	520	540	Down	Down	Down	510	510	510	490	11111100100000110110001111
10	490	490	Down	490	510	510	Down	Down	470	470	470	470	11111111100000110111001111
11	520	520	Down	520	540	540	Down	Down	510	510	510	510	11111111100000110111001111
12	520	500	Down	500	Down	540	Down	Down	490	490	490	490	11111111100000110101001111
13	490	490	Down	490	Down	530	Down	Down	480	480	480	480	11111111100000110101001111
14	520	520	Down	520	Down	Down	Down	Down	510	510	490	490	11111110100000110100001111
15	520	520	Down	520	Down	Down	Down	Down	510	510	490	490	11111110100000110100001111
16	520	520	Down	520	Down	Down	Down	Down	510	510	490	490	11111110100000110100001111
17	520	520	Down	520	Down	Down	Down	Down	510	510	490	490	11111110100000110100001111
18	520	520	Down	520	Down	Down	Down	Down	510	510	490	490	11111110100000110100001111
19	520	520	520	520	Down	Down	Down	Down	510	510	510	510	11111111110000111100001111
20	520	520	520	520	Down	Down	Down	Down	510	510	510	510	11111111010000111100001111
21	520	520	520	520	Down	560	Down	Down	510	510	510	510	11111111010000111101001111
22	520	520	520	520	Down	560	Down	Down	510	510	510	510	11111111010000111101001111
23	520	520	520	Down	Down	540	Down	Down	510	510	510	490	11111110000000111001001111
24	520	520	520	Down	Down	540	Down	Down	510	510	510	490	11111110000000111001001111

(b) 88m water head


Period(h)	Load distribution (MW)
	Left-bank
	VGS						ALSTOM
	1#	2#	3#	4#	5#	6#	7#	8#	9#	10#	11#	12#	13#	14#

1	Down	Down	Down	Down	Down	Down	640	640	640	635	630	630	630	630
2	Down	Down	Down	Down	Down	Down	640	640	640	635	630	630	630	630
3	Down	Down	Down	Down	Down	Down	640	640	640	640	640	640	640	640
4	Down	Down	Down	Down	Down	Down	670	670	670	670	670	670	670	670
5	Down	Down	Down	Down	Down	Down	670	670	670	670	670	670	670	670
6	Down	Down	Down	Down	Down	Down	670	670	670	670	670	670	670	670
7	Down	Down	Down	Down	Down	Down	670	670	670	670	670	670	670	670
8	Down	Down	Down	Down	Down	Down	670	670	670	670	670	670	670	670
9	Down	Down	Down	Down	Down	Down	670	670	670	670	670	670	670	670
10	Down	660	660	Down	Down	Down	670	670	670	670	670	670	670	670
11	660	660	660	Down	Down	Down	660	660	660	660	660	660	660	660
12	650	650	650	Down	Down	Down	660	660	660	660	656	650	650	Down
13	641	640	640	Down	Down	Down	640	640	640	640	640	640	640	Down
14	670	670	Down	Down	Down	Down	670	670	670	670	670	Down	670	Down
15	670	670	Down	Down	Down	Down	670	670	670	670	670	Down	670	Down
16	670	670	Down	Down	Down	Down	670	670	670	670	670	Down	670	Down
17	670	670	Down	Down	Down	Down	670	670	670	670	670	Down	670	Down
18	670	670	Down	Down	Down	Down	670	670	670	670	670	Down	670	Down
19	660	660	660	660	Down	Down	660	660	660	660	660	Down	660	Down
20	640	640	640	480	Down	Down	639	639	639	639	639	Down	639	Down
21	660	660	660	660	Down	Down	670	670	670	670	670	Down	670	Down
22	660	660	660	660	Down	Down	670	670	670	670	670	Down	670	Down
23	670	Down	Down	670	Down	Down	670	670	670	670	670	Down	670	Down
24	670	Down	Down	670	Down	Down	670	670	670	670	670	Down	670	Down

	Right-bank
	Orient power				ALSTOM				HEC				UC
	15#	16#	17#	18#	19#	20#	21#	22#	23#	24#	25#	26#	UC

1	Down	Down	Down	Down	610	610	610	520	Down	Down	Down	Down	00000011111111000011110000
2	Down	Down	Down	Down	610	610	610	520	Down	Down	Down	Down	00000011111111000011110000
3	Down	Down	Down	Down	620	610	610	610	Down	Down	Down	Down	00000011111111000011110000
4	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	00000011111111000011110000
5	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	00000011111111000011110000
6	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	00000011111111000011110000
7	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	00000011111111000011110000
8	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	00000011111111000011110000
9	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	00000011111111000011110000
10	Down	Down	Down	Down	660	660	660	657	Down	Down	Down	Down	01100011111111000011110000
11	Down	Down	Down	Down	634	620	620	620	Down	Down	Down	Down	11100011111111000011110000
12	Down	Down	Down	Down	620	620	620	620	Down	Down	Down	Down	11100011111110000011110000
13	Down	Down	Down	Down	620	620	620	620	Down	Down	Down	Down	11100011111110000011110000
14	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	11000011111010000011110000
15	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	11000011111010000011110000
16	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	11000011111010000011110000
17	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	11000011111010000011110000
18	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	11000011111010000011110000
19	630	Down	Down	Down	650	634	620	620	Down	Down	Down	Down	11110011111010100011110000
20	580	Down	Down	Down	610	610	610	526	Down	Down	Down	Down	11110011111010100011110000
21	630	Down	Down	Down	660	650	650	650	Down	Down	Down	Down	11110011111010100011110000
22	630	Down	Down	Down	660	650	650	650	Down	Down	Down	Down	11110011111010100011110000
23	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	10010011111010000011110000
24	Down	Down	Down	Down	660	660	660	660	Down	Down	Down	Down	10010011111010000011110000

(c) 107m water head


Period(h)	Load distribution (MW)
	Left-bank
	VGS						ALSTOM
	1#	2#	3#	4#	5#	6#	7#	8#	9#	10#	11#	12#	13#	14#

1	590	590	590	590	Down	590	700	Down	700	Down	Down	700	Down	Down
2	590	590	590	590	Down	590	700	Down	700	Down	Down	700	Down	Down
3	590	590	590	590	Down	590	700	Down	700	Down	Down	700	Down	Down
4	700	700	590	590	Down	590	700	Down	700	Down	Down	700	Down	Down
5	700	700	700	590	590	590	Down	Down	Down	Down	Down	700	Down	Down
6	700	700	700	590	590	590	Down	Down	Down	Down	Down	700	Down	Down
7	700	700	700	590	590	590	Down	Down	Down	Down	Down	700	Down	Down
8	700	700	700	590	590	590	Down	Down	Down	Down	Down	700	Down	Down
9	700	700	700	590	590	590	Down	Down	Down	Down	Down	700	Down	Down
10	700	700	590	590	590	590	Down	Down	Down	Down	Down	700	Down	Down
11	590	590	590	590	590	590	Down	Down	Down	Down	Down	700	Down	Down
12	590	590	590	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down
13	590	590	590	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down
14	700	700	700	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down
15	700	700	700	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down
16	700	700	700	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down
17	700	700	700	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down
18	590	590	590	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down
19	590	590	590	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down
20	590	590	572	570	570	570	Down	Down	Down	Down	Down	Down	Down	Down
21	700	590	590	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down
22	700	590	590	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down
23	700	700	700	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down
24	700	700	700	590	590	590	Down	Down	Down	Down	Down	Down	Down	Down

	Right-bank
	Orient power				ALSTOM				HEC				UC
	15#	16#	17#	18#	19#	20#	21#	22#	23#	24#	25#	26#	UC

1	Down	Down	Down	Down	Down	Down	Down	Down	605	590	590	590	11110110100100000000001111
2	Down	Down	Down	Down	Down	Down	Down	Down	605	590	590	590	11110110100100000000001111
3	Down	Down	Down	Down	Down	Down	Down	Down	700	640	590	590	11110110100100000000001111
4	Down	Down	Down	Down	Down	Down	Down	Down	700	700	700	630	11110110100100000000001111
5	Down	Down	Down	Down	Down	700	Down	Down	700	700	700	630	11111100000100000001001111
6	Down	Down	Down	Down	Down	700	Down	Down	700	700	700	630	11111100000100000001001111
7	Down	Down	Down	Down	Down	700	Down	Down	700	700	700	630	11111100000100000001001111
8	Down	Down	Down	Down	Down	700	Down	Down	700	700	700	630	11111100000100000001001111
9	Down	Down	Down	Down	Down	700	Down	Down	700	700	700	630	11111100000100000001001111
10	700	700	Down	Down	Down	700	Down	Down	700	700	700	657	11111100000100110001001111
11	700	700	Down	700	Down	700	Down	Down	700	700	700	614	11111100000100110101001111
12	700	700	Down	700	Down	700	Down	Down	700	700	696	590	11111100000000110101001111
13	700	700	Down	700	Down	700	Down	Down	700	661	590	590	11111100000000110101001111
14	700	Down	Down	700	Down	Down	Down	Down	700	700	700	630	11111100000000100100001111
15	700	Down	700	Down	Down	Down	Down	Down	700	700	700	630	11111100000000101000001111
16	700	Down	700	Down	Down	Down	Down	Down	700	700	700	630	11111100000000101000001111
17	700	Down	700	Down	Down	Down	Down	Down	700	700	700	630	11111100000000101000001111
18	700	700	700	Down	Down	Down	Down	Down	590	590	590	590	11111100000000111000001111
19	700	700	700	700	Down	700	Down	Down	700	700	700	614	11111100000000111101001111
20	690	690	690	690	Down	590	Down	Down	590	590	590	590	11111100000000111101001111
21	700	700	700	700	Down	700	Down	Down	700	700	700	650	11111100000000111101001111
22	700	700	700	700	Down	700	Down	Down	700	700	700	650	11111100000000111101001111
23	700	700	Down	Down	Down	Down	Down	Down	700	700	700	630	11111100000000110000001111
24	700	700	Down	Down	Down	Down	Down	Down	700	700	700	630	11111100000000110000001111