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Frontiers in Energy

ISSN 2095-1701

ISSN 2095-1698(Online)

CN 11-6017/TK

Postal Subscription Code 80-972

2018 Impact Factor: 1.701

Front. Energy    2014, Vol. 8 Issue (2) : 192-200    https://doi.org/10.1007/s11708-014-0306-x
RESEARCH ARTICLE
A solution to stochastic unit commitment problem for a wind-thermal system coordination
B. SARAVANAN(),Shreya MISHRA,Debrupa NAG
School of Electrical Engineering, VIT University, Vellore 632014, India
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Abstract

Unit commitment (UC) problem is one of the most important decision making problems in power system. In this paper the UC problem is solved by considering it as a real time problem by adding stochasticity in the generation side because of wind-thermal co-ordination system as well as stochasticity in the load side by incorporating the randomness of the load. The most important issue that needs to be addressed is the achievement of an economic unit commitment solution after solving UC as a real time problem. This paper proposes a hybrid approach to solve the stochastic unit commitment problem considering the volatile nature of wind and formulating the UC problem as a chance constrained problem in which the load is met with high probability over the entire time period.

Keywords unit commitment (UC)      randomness      wind generation      univariate      chance constrained     
Corresponding Author(s): B. SARAVANAN   
Issue Date: 19 May 2014
 Cite this article:   
B. SARAVANAN,Shreya MISHRA,Debrupa NAG. A solution to stochastic unit commitment problem for a wind-thermal system coordination[J]. Front. Energy, 2014, 8(2): 192-200.
 URL:  
https://academic.hep.com.cn/fie/EN/10.1007/s11708-014-0306-x
https://academic.hep.com.cn/fie/EN/Y2014/V8/I2/192
Fig.1  Flowchart
Unit 1Unit 2Unit 3Unit 4Unit 5Unit 6Unit 7Unit 8Unit 9Unit 10
Pimax/MW4554551301301628085555555
Pimin/MW1501502020252025101010
ai1000970700680450370480660665670
bi16.1917.2616.6016.5019.7022.2627.7425.9227.2727.79
ci0.000480.000310.0020.002110.003980.007120.000790.004130.002220.00173
Up time8855633111
Down time8855633111
Hot start cost/$45005000550560900170260303030
Cold start cost/$900010000110011201800340520606060
Cold start time5544422000
Initial state88-5-5-6-3-3-1-1-1
Tab.1  Input data for the 10 unit thermal system [9]
Hour
123456789101112
Demand70075085095010001100115012001300140014501500
Hour
131415161718192021222324
Demand1400130012001050100011001200140013001100900800
Tab.2  Load data for 24 h [9] (Case 1)
Hour
123456789101112
Wind/MW162162151168161144168168148113114125
Hour
131415161718192021222324
Wind/MW1421489672424253637479102131
Tab.3  Available wind data for 24 h [11]
HourUnit 1Unit 2Unit 3Unit 4Unit 5Unit 6Unit 7Unit 8Unit 9Unit 10Operating costStartup costTotal cost
1110000000010919.96010919.96
2110000000011749.28011749.28
3111100000014977.16111016087.16
4111110000016895.7290017795.72
5111110000017860.28017860.28
6111110000019877.38019877.38
7111111000020810.4134021150.41
8111111000021685.5021685.5
9111111000023764.94023764.94
10111111100026988.652027508.6
11111111110028703.456028763.45
12111111110029558.16029558.16
13111111000025732.38025732.38
14111110000023317.74023317.74
15111110000022504.43022504.43
16111100000019753.34019753.34
17111100000019411.28019411.28
18111101000021698.3217021868.32
19111101100023940.752024460.7
20111101111130157.646030217.64
21111101100025346.69025346.69
22110100000019880.81019880.81
23110100000015987.52015987.52
24110000000013143.73013143.73
504665.43680508345.4
Tab.4  UC schedule for Case 1
HourUnit1Unit2Unit3Unit4Unit5Unit6Unit7Unit8Unit9Unit10Wind available /MWTotal gen/MWDemand /MW
138815000000000162700700
243815000000000162750750
3454.5415036.1358.32000000151850850
4454.8115068.1484.032500000168950950
5448.28150101.88113.83250000016110001000
6454.29245.78128.99101.91250000014411001100
7454.93226.57125.481302520000016811501150
84552721301302520000016812001200
9454.9145592.66104.412520000014813001300
10454.9845513013072.01202500011314001400
11454.96455130130111.032025100011414501450
12454.98455130130150.012025100012515001500
13455455112.6662.72123.5549.058000014214001400
14454.9745587.02130250000014813001300
15454.45364.5413013025000009612001200
16452.40268.32129.02128.240000007210501050
17454.90243.091301300000004210001000
18454.9745553.3374.6902000004211001100
19454.66406.20111.13130020250005312001200
20454.8145513013002066.4938.4927.6914.56314001400
21454.93455130130031.07250007413001300
22454.71436.2801300000007911001100
23454.86213.130130000000102900900
24454.75214.2400000000131800800
Tab.5  Economic dispatch for Case 1
Hour
123456789101112
μ1035.71832.06778.66827.79723.28876.95870.79810.08899.87850.46975.60713.67
σ9.4489.62710.96011.4358.3679.36410.07610.1319.92812.04410.46510.123
Hour
131415161718192021222324
μ890.86816.911099.55825.49943.54788.79894.74697.60859.55901.18941.85850.42
σ9.66810.4329.50510.6518.5019.22910.5888.6379.78311.1369.6949.475
Tab.6  Mean and standard deviation of load for Case 2
HourUnit 1Unit2Unit 3Unit 4Unit 5Unit 6Unit7Unit 8Unit 9Unit 10Operating costStartup costTotal fuel cost
1110000000015881.24015881.24
2111110000016024.86201018034.86
3111110000015423.49015423.49
4111110000014762.93014762.93
5111110000013202.98013202.98
6111110000015811015811
7110010000012522.54012522.54
8110010000014011.56014011.56
9110011000016949.2834017289.28
10110001000013594.18013594.18
11110001000016667.52016667.52
12110000000012389.21012389.21
13110000000014162.43014162.43
14110000000013996.18013996.18
15111100000020421.18111021531.18
16111110000016499.890017399.8
17111111000019921.6517020091.65
18111111000017334.67017334.67
19111111000018135.59018135.59
20111110000013732.3013732.3
21111110000016539.01016539.01
22111110000016962.22016962.22
23111111000018586.2217018756.22
24111111000016595.74016595.74
380127.84700384827
Tab.7  UC schedule for Case 2
HourUnit 1Unit 2Unit 3Unit 4Unit 5Unit 6Unit 7Unit 8Unit 9Unit 10Wind available/MWTotal gen /MWDemand /MW
1454.98370.9700000000162987.95987.95
2454.651504258.532500000162892.19892.19
3454.9715044.12202500000151845.09845.09
4434.201502025.302500000168822.51822.51
5345.3415020202500000161721.34721.34
6454.491503156.922500000144861.41861.41
7427.65150002500000168770.65770.65
8454.96209.60002500000168857.56857.56
9454.99331.200025200000148979.19979.19
10454.81193.04000200000113780.85780.85
11454.99369.14000200000114958.14958.14
12454.84170.7300000000125750.58750.58
13454.99272.5100000000142869.51869.51
14454.93263.0300000000148865.97865.97
15453.45307.53130125.38000000961112.361112.36
16454.9615057.0771.44250000072830.48830.48
17454.77171.771301302520000042973.55973.55
18454.8915053.9075.692520000042821.48821.48
19454.60180.520125.552520000053878.66878.66
20377.351502020250000063655.35655.35
21454.991505377.82250000074834.82834.82
22454.97155.3220130250000079864.29864.29
23454.8215091.66112.0825200000102955.57955.57
24454.841503154.5825200000131866.43866.43
Tab.8  Economic dispatch result for Case 2
MethodCost/$
LR565825
SFLA563937.70
BFOA564842
Genetic algorithm565825
Proposed hybrid algorithm518512.308
Tab.9  Validation of proposed algorithm
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[1] Balasubramaniyan SARAVANAN, Surbhi SIKRI, K. S. SWARUP, D. P. KOTHARI. Unit commitment using dynamic programming–an exhaustive working of both classical and stochastic approach[J]. Front Energ, 2013, 7(3): 333-341.
[2] B. SARAVANAN, Siddharth DAS, Surbhi SIKRI, D. P. KOTHARI. A solution to the unit commitment problem—a review[J]. Front Energ, 2013, 7(2): 223-236.
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