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Frontiers in Energy

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Front Energ    2013, Vol. 7 Issue (3) : 333-341    https://doi.org/10.1007/s11708-013-0259-5
RESEARCH ARTICLE
Unit commitment using dynamic programming–an exhaustive working of both classical and stochastic approach
Balasubramaniyan SARAVANAN1(), Surbhi SIKRI1, K. S. SWARUP2, D. P. KOTHARI3
1. School of Electrical Engineering, VIT University, Vellore 632014, India; 2. Department of Electrical Science, IIT Madras, Chennai 600036, India; 3. JB Group of Institutions, Hyderabad, 500075, India
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Abstract

In the present electricity market, where renewable energy power plants have been included in the power systems, there is a lot of unpredictability in the demand and generation. There are many conventional and evolutionary programming techniques used for solving the unit commitment (UC) problem. Dynamic programming (DP) is a conventional algorithm used to solve the deterministic problem. In this paper DP is used to solve the stochastic model of UC problem. The stochastic modeling for load and generation side has been formulated using an approximate state decision approach. The programs were developed in a MATLAB environment and were extensively tested for a four-unit eight-hour system. The results obtained from these techniques were validated with the available literature and outcome was good. The commitment is in such a way that the total cost is minimal. The novelty of this paper lies in the fact that DP is used for solving the stochastic UC problem.
Keywords unit commitment (UC)      deterministic      stochastic      dynamic programming (DP)      optimization      state diagram     
Corresponding Author(s): SARAVANAN Balasubramaniyan,Email:bsaravanan@vit.ac.in   
Issue Date: 05 September 2013
 Cite this article:   
Balasubramaniyan SARAVANAN,Surbhi SIKRI,K. S. SWARUP, et al. Unit commitment using dynamic programming–an exhaustive working of both classical and stochastic approach[J]. Front Energ, 2013, 7(3): 333-341.
 URL:  
https://academic.hep.com.cn/fie/EN/10.1007/s11708-013-0259-5
https://academic.hep.com.cn/fie/EN/Y2013/V7/I3/333
Fig.1  Flowchart for forward DP
Fig.2  Block diagram for DP algorithm
ParameterUnit 1Unit 2Unit 3Unit 4
Pmax /MW8025030060
Pmin/MW25607520
No load cost/($·h-1)213585.62684.74252
Full load avg cost /($·MW-1·h-1)23.5420.3419.7428.00
Min up time/h4551
Min down time/h2341
Initial conditions-5886
Hot start cost/$1501705000
Cold start cost/$35040011000.02
Cold start hour4550
Tab.1  Input system data
Hour
12345678
Pload/MW450530600540400280290500
Tab.2  Load data
UnitInc cost/($·MW-1·h-1)Pmin/MWPmax/MWHour
12345678
Unit 120.877258000000000
Unit 218.006025015023025024010000200
Unit 317.4675300300300300300300280290300
Unit 423.802060005000000
Load/MW450530600540400280290500
Hourly cost/$920810648124501082883085574574810108
Total cost at the end of 8 hours/$73274
Tab.3  Load distribution data for generator (deterministic)
Hour
12345678
Unit 100000000
Unit 211111001
Unit 311111111
Unit 400100000
Tab.4  Unit combination schedule
UnitInc cost/($·MW-1·h-1)Pmin/MWPmax/MWHour
12345678
Unit 120.8772580000000062
Unit 218.00602502402501801386000250
Unit 317.4675300300300300300290200272300
Unit 423.8020600585000000
Load/MW540608480438350200272612
Hourly cost/$10828126419748899274144177543412516
Total cost at the end of 8 hours/$72500
Tab.5  Load distribution after stochasticity on load side
Hour
12345678
Unit 100000001
Unit 211111001
Unit 311111111
Unit 401000000
Tab.6  Unit combination schedule
UnitInc cost/($·MW-1·h-1)Pmin/MWPmax/MWHour
12345678
Unit 120.8772580050806000020
Unit 218.0060250250250250250250250250250
Unit 317.46752302002302302301503040230
Unit 423.802060004000000
Load/MW450530600540400280290500
Hourly cost/$926211043128731125183896270645010434
Total cost at the end of 8 hours/$76402
Tab.7  Load distribution after stochasticity on generation side
Hour
12345678
Unit 101110001
Unit 211111001
Unit 311111111
Unit 400100000
Tab.8  Unit combination schedule
UnitInc cost/($·MW-1·h-1)Pmin/MWPmax/MWHour
12345678
Unit 120.877258060800000080
Unit 218.0060250250250250250250200197250
Unit 37.4675230230230230188100075230
Unit 43.8020600480000052
Load/MW540608480438350200272612
Hourly cost/$11251130639786905375164186612613158
Total cost at the end of 8 hours/$75133
Tab.9  Load distribution after stochasticity on both load and generation side
Hour
12345678
Unit 111000001
Unit 211111111
Unit 311111011
Unit 401000001
Tab.10  Unit combination schedule
Fig.3  Optimal solution obtained by DP algorithm without considering up and downtime constraints
Fig.4  Optimal solution obtained by DP algorithm when uncertainty is on the load side
Fig.5  Optimal solution obtained by DP algorithm when uncertainty is on the generation side, without considering up and downtime constraints
CaseWithout uptime and downtime constraintsWith uptime and downtime constraints
Classical approach$73274$74110
Stochastic approach on load side$72500$73336
Stochastic approach on generation side$76402**
Stochastic approach on load and generation side$75133**
Tab.11  Validation of result
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