
-
Previous Article
Genetic algorithm for obstacle location-allocation problems with customer priorities
- JIMO Home
- This Issue
-
Next Article
Convergence analysis of a smoothing SAA method for a stochastic mathematical program with second-order cone complementarity constraints
Adjustable robust optimization in enabling optimal day-ahead economic dispatch of CCHP-MG considering uncertainties of wind-solar power and electric vehicle
College of Electrical Engineering, Sichuan University, Chengdu, China |
At present, electric vehicles (EVs), small-scale wind power, and solar power have been increasingly integrated into modern power system via the combined cooling heating and power based microgrid (CCHP-MG). However, inside the microgrid the uncertainties of EVs charging, wind power, and solar power significantly impact the economy of CCHP-MG operation. Therefore to improve the economy deteriorated by the uncertainties, this paper presents a two-stage adjustable robust optimization to achieve the minimal operational cost for CCHP-MG. Before the realizations of the uncertainties, the day-ahead stage as the first stage decides an operational strategy that can withstand the worst-case uncertainties. As long as the uncertainties are observed, the real-time stage as the second stage adjusts the operational units to compensate the errors caused by the day-ahead operational strategy. Due to the difficulties of the model solution, this paper further adopts the duality theory, Big-M method, and column-and-constraint generation (C & CG) decomposition to convert the model into two tractable mixed integer linear programming (MILP) problems. Further, C & CG iteration algorithm is also employed to solve the MILPs, which can ultimately provide an optimal economic day-ahead dispatch strategy capable of handling uncertainties. The experimental results demonstrate the effectiveness of the presented approach.
References:
[1] |
A. Ben-Tal, A. Goryashko, E. Guslitzer and A. Nemirovski,
Adjustable robust solutions of uncertain linear programs, Math. Program., 99 (2004), 351-376.
doi: 10.1007/s10107-003-0454-y. |
[2] |
A. Ben-Tal and A. Nemirovski,
Robust convex optimization, Math. Oper. Res., 23 (1998), 769-1024.
doi: 10.1287/moor.23.4.769. |
[3] |
C. Chen,
Simulated annealing-based optimal wind-thermal coordination scheduling, IET Generation, Transmission & Distribution, 1 (2007), 447-455.
doi: 10.1049/iet-gtd:20060208. |
[4] |
C. M. Correa-Posada and P. Sánchez-Martín,
Integrated power and natural gas model for energy adequacy in short-term operation, IEEE Transactions on Power Systems, 30 (2015), 3347-3355.
doi: 10.1109/TPWRS.2014.2372013. |
[5] |
C. Duan, L. Jiang, W. Fang and J. Liu,
Data-driven affinely adjustable distributionally robust unit commitment, IEEE Transactions on Power Systems, 33 (2018), 1385-1398.
doi: 10.1109/TPWRS.2017.2741506. |
[6] |
C. Duan, L. Jiang, W. Fang, J. Liu and S. Liu,
Data-driven distributionally robust energy-reserve-storage dispatch, IEEE Transactions on Industrial Informatics, 14 (2018), 2826-2836.
doi: 10.1109/TII.2017.2771355. |
[7] |
F. Fang, Q. H. Wang and Y. Shi,
A novel optimal operational strategy for the CCHP system based on two operating modes, IEEE Transactions on Power Systems, 27 (2012), 1032-1041.
doi: 10.1109/TPWRS.2011.2175490. |
[8] |
F. Farmani, M. Parvizimosaed, H. Monsef and A. Rahimi-Kian,
A conceptual model of a smart energy management system for a residential building equipped with CCHP system, Internat. J. Electrical Power Energy Systems, 95 (2018), 523-536.
doi: 10.1016/j.ijepes.2017.09.016. |
[9] |
H. Gao, J. Liu, L. Wang and Z. Wei,
Decentralized energy management for networked microgrids in future distribution systems, IEEE Transactions on Power Systems, 33 (2018), 3599-3610.
doi: 10.1109/TPWRS.2017.2773070. |
[10] |
W. Gu, S. Lu, Z. Wu, X. Zhang, J. Zhou, B. Zhao and J. Wang,
Residential CCHP microgrid with load aggregator: Operation mode, pricing strategy, and optimal dispatch, Appl. Energy, 205 (2017), 173-186.
doi: 10.1016/j.apenergy.2017.07.045. |
[11] |
Y. Guo, J. Xiong, S. Xu and W. Su,
Two-stage economic operation of microgrid-like electric vehicle parking deck, IEEE Transactions on Smart Grid, 7 (2016), 1703-1712.
doi: 10.1109/TSG.2015.2424912. |
[12] |
Z. Guo and X. Xiao,
Wind power assessment based on a WRF wind simulation with developed power curve modeling methods, Abstract Appl. Anal., 2014 (2014), 1-15.
doi: 10.1155/2014/941648. |
[13] |
N. Haouas and P. R. Bertrand, Wind farm power forecasting, Math. Probl. Eng., 2013 (2013), 5pp.
doi: 10.1155/2013/163565. |
[14] |
R. Hashemi,
A developed offline model for optimal operation of combined heating and cooling and power systems, IEEE Transactions on Energy Conversion, 24 (2009), 222-229.
doi: 10.1109/TEC.2008.2002330. |
[15] |
S. Jin, Z. Mao, H. Li and W. Qi, Dynamic operation management of a renewable microgrid including battery energy storage, Math. Probl. Eng., 2018 (2018), 19pp.
doi: 10.1155/2018/5852309. |
[16] |
Y. Lee and R. Baldick,
A frequency-constrained stochastic economic dispatch model, IEEE Transactions on Power Systems, 28 (2013), 2301-2312.
doi: 10.1109/TPWRS.2012.2236108. |
[17] |
B. Li, X. Qian, J. Sun, K. L. Teo and C. Yue,
A model of distributionally robust two-stage stochastic convex programming with linear recourse, Appl. Math. Model., 58 (2018), 86-97.
doi: 10.1016/j.apm.2017.11.039. |
[18] |
B. Li, J. Sun and K. L. Teo,
A distributionally robust approach to a class of three-stage stochastic linear programs, Pac. J. Optim., 15 (2019), 219-236.
|
[19] |
B. Li, J. Sun, H. Xu and M Zhang,
A class of two-stage distributionally robust games, J. Ind. Manag. Optim., 15 (2019), 387-400.
doi: 10.3934/jimo.2018048. |
[20] |
G. Li, G. Li and M. Zhou,
Model and application of renewable energy accommodation capacity calculation considering utilization level of inter-provincial tie-line, Protection and Control of Modern Power Systems, 4 (2019), 1-1.
doi: 10.1186/s41601-019-0115-7. |
[21] |
G. Li, R. Zhang, T. Jiang, H. Chen, L. Bai, H. Cui and X. Li,
Optimal dispatch strategy for integrated energy systems with cchp and wind power, Appl. Energy, 192 (2017), 408-419.
doi: 10.1016/j.apenergy.2016.08.139. |
[22] |
G. Li, R. Zhang, T. Jiang, H. Chen, L. Bai and X. Li,
Security-constrained bi-level economic dispatch model for integrated natural gas and electricity systems considering wind power and power-to-gas process, Appl. Energy, 194 (2017), 696-704.
doi: 10.1016/j.apenergy.2016.07.077. |
[23] |
Y. Liu, Y. Liu, J. Liu, M. Li, T. Liu, G. Taylor and K. Zuo,
A MapReduce based high performance neural network in enabling fast stability assessment of power systems, Math. Probl. Eng., 2017 (2017), 1-12.
doi: 10.1155/2017/4030146. |
[24] |
Y. Liu and N. C. Nair,
A two-stage stochastic dynamic economic dispatch model considering wind uncertainty, IEEE Transactions on Sustainable Energy, 7 (2016), 819-829.
doi: 10.1109/TSTE.2015.2498614. |
[25] |
C. Marino, M. Marufuzzaman, M. Hu and M. D. Sarder,
Developing a CCHP-microgrid operation decision model under uncertainty, Comput. Industrial Eng., 115 (2018), 354-367.
doi: 10.1016/j.cie.2017.11.021. |
[26] |
M. H. Sarparandeh and M. Ehsan, Pricing of vehicle-to-grid services in a microgrid by Nash bargaining theory, Math. Probl. Eng., 2017 (2017).
doi: 10.1155/2017/1840140. |
[27] |
X. Shen, Y. Liu and Y. Liu, A multistage solution approach for dynamic reactive power optimization based on interval uncertainty, Math. Probl. Eng., 2018 (2018), 10pp.
doi: 10.1155/2018/3854812. |
[28] |
R. Shi, C. Sun, Z. Zhou, L. Zhang, and Z. Liang, A robust economic dispatch of residential microgrid with wind power and electric vehicle integration, Chinese Control and Decision Conference (CCDC), 2016, 3672–3676.
doi: 10.1109/CCDC.2016.7531621. |
[29] |
J. Soares, B. Canizes, M. A. F. Ghazvini, Z. Vale and G. K. Venayagamoorthy,
Two-stage stochastic model using benders' decomposition for large-scale energy resource management in smart grids, IEEE Transactions on Industry Appl., 53 (2017), 5905-5914.
doi: 10.1109/TIA.2017.2723339. |
[30] |
Y. Tan, Y. Cao, C. Li, Y. Li, J. Zhou and Y. Song,
A two-stage stochastic programming approach considering risk level for distribution networks operation with wind power, IEEE Systems Journal, 10 (2016), 117-126.
doi: 10.1109/JSYST.2014.2350027. |
[31] |
L. Tian, S. Shi and Z. Jia,
A statistical model for charging power demand of electric vehicles, Power System Technology, 11 (2010), 126-130.
doi: 10.13335/j.1000-3673.pst.2010.11.020. |
[32] |
T. A. Victoire and A. Jeyakumar,
Hybrid PSO–CSQP for economic dispatch with valve-point effect, Electric Power Systems Research, 71 (2004), 51-59.
doi: 10.1016/j.epsr.2003.12.017. |
[33] |
D. C. Walters and G. B. Sheble,
Genetic algorithm solution of economic dispatch with valve point loading, IEEE Transactions on Power Systems, 8 (1993), 1325-1332.
doi: 10.1109/59.260861. |
[34] |
J. Wang, J. Wang, C. Liu and and J. Ruiz,
Stochastic unit commitment with sub-hourly dispatch constraints, Appl. Energy, 105 (2013), 418-422.
doi: 10.1016/j.apenergy.2013.01.008. |
[35] |
P. Wei and Y. Liu, The integration of wind-solar-hydropower generation in enabling economic robust dispatch, Math. Probl. Eng., 2019 (2019), 12pp.
doi: 10.1155/2019/4634131. |
[36] |
H. Wu, X Hou, B. Zhao and C. Zhu,
Economical dispatch of microgrid considering plug-in electric vehicles, Automation of Electric Power Systems, 38 (2014), 77-84.
doi: 10.7500/AEPS20130911002. |
[37] |
T. Wu, Q. Yang, Z. Bao and W. Yan,
Coordinated energy dispatching in microgrid with wind power generation and plug-in electric vehicles, IEEE Transactions on Smart Grid, 4 (2013), 1453-1463.
doi: 10.1109/TSG.2013.2268870. |
[38] |
W. Wu, J. Chen, B. Zhang and H. Sun,
A robust wind power optimization method for look-ahead power dispatch, IEEE Transactions on Sustainable Energy, 5 (2014), 507-515.
doi: 10.1109/TSTE.2013.2294467. |
[39] |
Y. Xiang, J. Liu and Y. Liu,
Robust energy management of microgrid with uncertain renewable generation and load, IEEE Transactions on Smart Grid, 7 (2016), 1034-1043.
doi: 10.1109/TSG.2014.2385801. |
[40] |
L. Xie, Y. Gu, X. Zhu and M. G. Genton,
Short-term spatio-temporal wind power forecast in robust look-ahead power system dispatch, IEEE Transactions on Smart Grid, 5 (2014), 511-520.
doi: 10.1109/TSG.2013.2282300. |
[41] |
P. Xiong, P. Jirutitijaroen and C. Singh,
A distributionally robust optimization model for unit commitment considering uncertain wind power generation, IEEE Transactions on Power Systems, 32 (2017), 39-49.
doi: 10.1109/TPWRS.2016.2544795. |
[42] |
P. Xiong and C. Singh,
Distributionally robust optimization for energy and reserve toward a low-carbon electricity market, Electric Power Systems Res., 149 (2017), 137-145.
doi: 10.1016/j.epsr.2017.04.008. |
[43] |
Y. Yang, Practical robust optimization method for unit commitment of a system with integrated wind resource, Math. Probl. Eng., 2017 (2017), 13pp.
doi: 10.1155/2017/5208290. |
[44] |
J. Yu, Q. Feng, Y. Li and J. Cao, Stochastic optimal dispatch of virtual power plant considering correlation of distributed generations, Math. Probl. Eng., 2015 (2015).
doi: 10.1155/2015/135673. |
[45] |
B. Zeng and L. Zhao,
Solving two-stage robust optimization problems using a column-and-constraint generation method, Oper. Res. Lett., 41 (2013), 457-461.
doi: 10.1016/j.orl.2013.05.003. |
[46] |
Y. Zhang, J. Meng, B. Guo and T. Zhang, An improved dispatch strategy of a grid-connected hybrid energy system with high penetration level of renewable energy, Math. Probl. Eng., 2014 (2014), 18pp.
doi: 10.1155/2014/602063. |
[47] |
Y. Zhao, C. Li, M. Zhao, S. Xu, H. Gao and L. Song, Model design on emergency power supply of electric vehicle, Math. Probl. Eng., 2017 (2017), 6pp.
doi: 10.1155/2017/9697051. |
show all references
References:
[1] |
A. Ben-Tal, A. Goryashko, E. Guslitzer and A. Nemirovski,
Adjustable robust solutions of uncertain linear programs, Math. Program., 99 (2004), 351-376.
doi: 10.1007/s10107-003-0454-y. |
[2] |
A. Ben-Tal and A. Nemirovski,
Robust convex optimization, Math. Oper. Res., 23 (1998), 769-1024.
doi: 10.1287/moor.23.4.769. |
[3] |
C. Chen,
Simulated annealing-based optimal wind-thermal coordination scheduling, IET Generation, Transmission & Distribution, 1 (2007), 447-455.
doi: 10.1049/iet-gtd:20060208. |
[4] |
C. M. Correa-Posada and P. Sánchez-Martín,
Integrated power and natural gas model for energy adequacy in short-term operation, IEEE Transactions on Power Systems, 30 (2015), 3347-3355.
doi: 10.1109/TPWRS.2014.2372013. |
[5] |
C. Duan, L. Jiang, W. Fang and J. Liu,
Data-driven affinely adjustable distributionally robust unit commitment, IEEE Transactions on Power Systems, 33 (2018), 1385-1398.
doi: 10.1109/TPWRS.2017.2741506. |
[6] |
C. Duan, L. Jiang, W. Fang, J. Liu and S. Liu,
Data-driven distributionally robust energy-reserve-storage dispatch, IEEE Transactions on Industrial Informatics, 14 (2018), 2826-2836.
doi: 10.1109/TII.2017.2771355. |
[7] |
F. Fang, Q. H. Wang and Y. Shi,
A novel optimal operational strategy for the CCHP system based on two operating modes, IEEE Transactions on Power Systems, 27 (2012), 1032-1041.
doi: 10.1109/TPWRS.2011.2175490. |
[8] |
F. Farmani, M. Parvizimosaed, H. Monsef and A. Rahimi-Kian,
A conceptual model of a smart energy management system for a residential building equipped with CCHP system, Internat. J. Electrical Power Energy Systems, 95 (2018), 523-536.
doi: 10.1016/j.ijepes.2017.09.016. |
[9] |
H. Gao, J. Liu, L. Wang and Z. Wei,
Decentralized energy management for networked microgrids in future distribution systems, IEEE Transactions on Power Systems, 33 (2018), 3599-3610.
doi: 10.1109/TPWRS.2017.2773070. |
[10] |
W. Gu, S. Lu, Z. Wu, X. Zhang, J. Zhou, B. Zhao and J. Wang,
Residential CCHP microgrid with load aggregator: Operation mode, pricing strategy, and optimal dispatch, Appl. Energy, 205 (2017), 173-186.
doi: 10.1016/j.apenergy.2017.07.045. |
[11] |
Y. Guo, J. Xiong, S. Xu and W. Su,
Two-stage economic operation of microgrid-like electric vehicle parking deck, IEEE Transactions on Smart Grid, 7 (2016), 1703-1712.
doi: 10.1109/TSG.2015.2424912. |
[12] |
Z. Guo and X. Xiao,
Wind power assessment based on a WRF wind simulation with developed power curve modeling methods, Abstract Appl. Anal., 2014 (2014), 1-15.
doi: 10.1155/2014/941648. |
[13] |
N. Haouas and P. R. Bertrand, Wind farm power forecasting, Math. Probl. Eng., 2013 (2013), 5pp.
doi: 10.1155/2013/163565. |
[14] |
R. Hashemi,
A developed offline model for optimal operation of combined heating and cooling and power systems, IEEE Transactions on Energy Conversion, 24 (2009), 222-229.
doi: 10.1109/TEC.2008.2002330. |
[15] |
S. Jin, Z. Mao, H. Li and W. Qi, Dynamic operation management of a renewable microgrid including battery energy storage, Math. Probl. Eng., 2018 (2018), 19pp.
doi: 10.1155/2018/5852309. |
[16] |
Y. Lee and R. Baldick,
A frequency-constrained stochastic economic dispatch model, IEEE Transactions on Power Systems, 28 (2013), 2301-2312.
doi: 10.1109/TPWRS.2012.2236108. |
[17] |
B. Li, X. Qian, J. Sun, K. L. Teo and C. Yue,
A model of distributionally robust two-stage stochastic convex programming with linear recourse, Appl. Math. Model., 58 (2018), 86-97.
doi: 10.1016/j.apm.2017.11.039. |
[18] |
B. Li, J. Sun and K. L. Teo,
A distributionally robust approach to a class of three-stage stochastic linear programs, Pac. J. Optim., 15 (2019), 219-236.
|
[19] |
B. Li, J. Sun, H. Xu and M Zhang,
A class of two-stage distributionally robust games, J. Ind. Manag. Optim., 15 (2019), 387-400.
doi: 10.3934/jimo.2018048. |
[20] |
G. Li, G. Li and M. Zhou,
Model and application of renewable energy accommodation capacity calculation considering utilization level of inter-provincial tie-line, Protection and Control of Modern Power Systems, 4 (2019), 1-1.
doi: 10.1186/s41601-019-0115-7. |
[21] |
G. Li, R. Zhang, T. Jiang, H. Chen, L. Bai, H. Cui and X. Li,
Optimal dispatch strategy for integrated energy systems with cchp and wind power, Appl. Energy, 192 (2017), 408-419.
doi: 10.1016/j.apenergy.2016.08.139. |
[22] |
G. Li, R. Zhang, T. Jiang, H. Chen, L. Bai and X. Li,
Security-constrained bi-level economic dispatch model for integrated natural gas and electricity systems considering wind power and power-to-gas process, Appl. Energy, 194 (2017), 696-704.
doi: 10.1016/j.apenergy.2016.07.077. |
[23] |
Y. Liu, Y. Liu, J. Liu, M. Li, T. Liu, G. Taylor and K. Zuo,
A MapReduce based high performance neural network in enabling fast stability assessment of power systems, Math. Probl. Eng., 2017 (2017), 1-12.
doi: 10.1155/2017/4030146. |
[24] |
Y. Liu and N. C. Nair,
A two-stage stochastic dynamic economic dispatch model considering wind uncertainty, IEEE Transactions on Sustainable Energy, 7 (2016), 819-829.
doi: 10.1109/TSTE.2015.2498614. |
[25] |
C. Marino, M. Marufuzzaman, M. Hu and M. D. Sarder,
Developing a CCHP-microgrid operation decision model under uncertainty, Comput. Industrial Eng., 115 (2018), 354-367.
doi: 10.1016/j.cie.2017.11.021. |
[26] |
M. H. Sarparandeh and M. Ehsan, Pricing of vehicle-to-grid services in a microgrid by Nash bargaining theory, Math. Probl. Eng., 2017 (2017).
doi: 10.1155/2017/1840140. |
[27] |
X. Shen, Y. Liu and Y. Liu, A multistage solution approach for dynamic reactive power optimization based on interval uncertainty, Math. Probl. Eng., 2018 (2018), 10pp.
doi: 10.1155/2018/3854812. |
[28] |
R. Shi, C. Sun, Z. Zhou, L. Zhang, and Z. Liang, A robust economic dispatch of residential microgrid with wind power and electric vehicle integration, Chinese Control and Decision Conference (CCDC), 2016, 3672–3676.
doi: 10.1109/CCDC.2016.7531621. |
[29] |
J. Soares, B. Canizes, M. A. F. Ghazvini, Z. Vale and G. K. Venayagamoorthy,
Two-stage stochastic model using benders' decomposition for large-scale energy resource management in smart grids, IEEE Transactions on Industry Appl., 53 (2017), 5905-5914.
doi: 10.1109/TIA.2017.2723339. |
[30] |
Y. Tan, Y. Cao, C. Li, Y. Li, J. Zhou and Y. Song,
A two-stage stochastic programming approach considering risk level for distribution networks operation with wind power, IEEE Systems Journal, 10 (2016), 117-126.
doi: 10.1109/JSYST.2014.2350027. |
[31] |
L. Tian, S. Shi and Z. Jia,
A statistical model for charging power demand of electric vehicles, Power System Technology, 11 (2010), 126-130.
doi: 10.13335/j.1000-3673.pst.2010.11.020. |
[32] |
T. A. Victoire and A. Jeyakumar,
Hybrid PSO–CSQP for economic dispatch with valve-point effect, Electric Power Systems Research, 71 (2004), 51-59.
doi: 10.1016/j.epsr.2003.12.017. |
[33] |
D. C. Walters and G. B. Sheble,
Genetic algorithm solution of economic dispatch with valve point loading, IEEE Transactions on Power Systems, 8 (1993), 1325-1332.
doi: 10.1109/59.260861. |
[34] |
J. Wang, J. Wang, C. Liu and and J. Ruiz,
Stochastic unit commitment with sub-hourly dispatch constraints, Appl. Energy, 105 (2013), 418-422.
doi: 10.1016/j.apenergy.2013.01.008. |
[35] |
P. Wei and Y. Liu, The integration of wind-solar-hydropower generation in enabling economic robust dispatch, Math. Probl. Eng., 2019 (2019), 12pp.
doi: 10.1155/2019/4634131. |
[36] |
H. Wu, X Hou, B. Zhao and C. Zhu,
Economical dispatch of microgrid considering plug-in electric vehicles, Automation of Electric Power Systems, 38 (2014), 77-84.
doi: 10.7500/AEPS20130911002. |
[37] |
T. Wu, Q. Yang, Z. Bao and W. Yan,
Coordinated energy dispatching in microgrid with wind power generation and plug-in electric vehicles, IEEE Transactions on Smart Grid, 4 (2013), 1453-1463.
doi: 10.1109/TSG.2013.2268870. |
[38] |
W. Wu, J. Chen, B. Zhang and H. Sun,
A robust wind power optimization method for look-ahead power dispatch, IEEE Transactions on Sustainable Energy, 5 (2014), 507-515.
doi: 10.1109/TSTE.2013.2294467. |
[39] |
Y. Xiang, J. Liu and Y. Liu,
Robust energy management of microgrid with uncertain renewable generation and load, IEEE Transactions on Smart Grid, 7 (2016), 1034-1043.
doi: 10.1109/TSG.2014.2385801. |
[40] |
L. Xie, Y. Gu, X. Zhu and M. G. Genton,
Short-term spatio-temporal wind power forecast in robust look-ahead power system dispatch, IEEE Transactions on Smart Grid, 5 (2014), 511-520.
doi: 10.1109/TSG.2013.2282300. |
[41] |
P. Xiong, P. Jirutitijaroen and C. Singh,
A distributionally robust optimization model for unit commitment considering uncertain wind power generation, IEEE Transactions on Power Systems, 32 (2017), 39-49.
doi: 10.1109/TPWRS.2016.2544795. |
[42] |
P. Xiong and C. Singh,
Distributionally robust optimization for energy and reserve toward a low-carbon electricity market, Electric Power Systems Res., 149 (2017), 137-145.
doi: 10.1016/j.epsr.2017.04.008. |
[43] |
Y. Yang, Practical robust optimization method for unit commitment of a system with integrated wind resource, Math. Probl. Eng., 2017 (2017), 13pp.
doi: 10.1155/2017/5208290. |
[44] |
J. Yu, Q. Feng, Y. Li and J. Cao, Stochastic optimal dispatch of virtual power plant considering correlation of distributed generations, Math. Probl. Eng., 2015 (2015).
doi: 10.1155/2015/135673. |
[45] |
B. Zeng and L. Zhao,
Solving two-stage robust optimization problems using a column-and-constraint generation method, Oper. Res. Lett., 41 (2013), 457-461.
doi: 10.1016/j.orl.2013.05.003. |
[46] |
Y. Zhang, J. Meng, B. Guo and T. Zhang, An improved dispatch strategy of a grid-connected hybrid energy system with high penetration level of renewable energy, Math. Probl. Eng., 2014 (2014), 18pp.
doi: 10.1155/2014/602063. |
[47] |
Y. Zhao, C. Li, M. Zhao, S. Xu, H. Gao and L. Song, Model design on emergency power supply of electric vehicle, Math. Probl. Eng., 2017 (2017), 6pp.
doi: 10.1155/2017/9697051. |









C & CG Iteration Algorithm |
Step 1 (Initialization): Set an initial scenario |
Step 2 (Solve MP): Input the scenario set |
Step 3 (Solve SP): Input |
Step 4 (Check Convergence): If |
C & CG Iteration Algorithm |
Step 1 (Initialization): Set an initial scenario |
Step 2 (Solve MP): Input the scenario set |
Step 3 (Solve SP): Input |
Step 4 (Check Convergence): If |
CG | $P^{min}$ | $P^{max}$ | $R^{Up}$ | $R^{Dn}$ | $a$ | $b$ | $\lambda^{Up}$ | $\lambda^{Dn}$ |
(kW) | (kW) | (kW/min) | (kW/min) | ($/kWh) | ($/kWh) | ($/kWh) | ($/kWh) | |
MT | 50 | 550 | 6 | 6 | 0.67 | 0 | 2.5 | 1.5 |
FC | 50 | 240 | 2 | 2 | 0.60 | 0 | 2.5 | 1.5 |
EB | 20 | 500 | 5 | 4 | - | - | 0.5 | 0.5 |
CG | $P^{min}$ | $P^{max}$ | $R^{Up}$ | $R^{Dn}$ | $a$ | $b$ | $\lambda^{Up}$ | $\lambda^{Dn}$ |
(kW) | (kW) | (kW/min) | (kW/min) | ($/kWh) | ($/kWh) | ($/kWh) | ($/kWh) | |
MT | 50 | 550 | 6 | 6 | 0.67 | 0 | 2.5 | 1.5 |
FC | 50 | 240 | 2 | 2 | 0.60 | 0 | 2.5 | 1.5 |
EB | 20 | 500 | 5 | 4 | - | - | 0.5 | 0.5 |
$\lambda_{Wind}$ ($/kWh) | $\lambda_{Solar}$ ($/kWh) | $\lambda_{Load}$ ($/kWh) |
0.536 | 0.536 | 5 |
$\lambda_{Wind}$ ($/kWh) | $\lambda_{Solar}$ ($/kWh) | $\lambda_{Load}$ ($/kWh) |
0.536 | 0.536 | 5 |
Hour | Day-ahead stage | Real-time stage | |||
$\lambda_{Buy}^{DA}$ | $\lambda_{Sell}^{DA}$ | $\lambda_{Buy}^{RT}$ | $\lambda_{Sell}^{RT}$ | ||
($/kWh) | ($/kWh) | ($/kWh) | ($/kWh) | ||
(00:00-08:00) | 1.35 | 1.04 | 2.70 | 0.11 | |
(08:00-09:00, 12:00-19:00) | 0.90 | 0.69 | 1.80 | 0.07 | |
(09:00-12:00, 19:00-24:00) | 0.50 | 0.39 | 1.00 | 0.04 |
Hour | Day-ahead stage | Real-time stage | |||
$\lambda_{Buy}^{DA}$ | $\lambda_{Sell}^{DA}$ | $\lambda_{Buy}^{RT}$ | $\lambda_{Sell}^{RT}$ | ||
($/kWh) | ($/kWh) | ($/kWh) | ($/kWh) | ||
(00:00-08:00) | 1.35 | 1.04 | 2.70 | 0.11 | |
(08:00-09:00, 12:00-19:00) | 0.90 | 0.69 | 1.80 | 0.07 | |
(09:00-12:00, 19:00-24:00) | 0.50 | 0.39 | 1.00 | 0.04 |
$P_{Cha}^{min}/P_{Cha}^{max}$ | $P_{Dis}^{min}/P_{Dis}^{max}$ | $\eta_{ESS}^{Cha}/\eta_{ESS}^{Dis}$ | $\delta_{ESS}$ | $E_{ESS}^{max}$ | $E_{ESS}^{min}$ | $E_{ESS}(0)$ |
(kW) | (kW) | (kWh) | (kWh) | (kWh) | ||
0/200 | 0/200 | 0.9/0.9 | 0.001 | 480 | 120 | 120 |
$P_{Cha}^{min}/P_{Cha}^{max}$ | $P_{Dis}^{min}/P_{Dis}^{max}$ | $\eta_{ESS}^{Cha}/\eta_{ESS}^{Dis}$ | $\delta_{ESS}$ | $E_{ESS}^{max}$ | $E_{ESS}^{min}$ | $E_{ESS}(0)$ |
(kW) | (kW) | (kWh) | (kWh) | (kWh) | ||
0/200 | 0/200 | 0.9/0.9 | 0.001 | 480 | 120 | 120 |
$Q_{Cha}^{min}/Q_{Cha}^{max}$ | $Q_{Dis}^{min}/Q_{Dis}^{max}$ | $\eta_{HSS}^{Cha}/\eta_{HSS}^{Dis}$ | $\delta_{HSS}$ | $E_{HSS}^{max}$ | $E_{HSS}^{min}$ | $E_{HSS}(0)$ |
(kW) | (kW) | (kWh) | (kWh) | (kWh) | ||
0/200 | 0/200 | 0.9/0.9 | 0.01 | 600 | 0 | 0 |
$Q_{Cha}^{min}/Q_{Cha}^{max}$ | $Q_{Dis}^{min}/Q_{Dis}^{max}$ | $\eta_{HSS}^{Cha}/\eta_{HSS}^{Dis}$ | $\delta_{HSS}$ | $E_{HSS}^{max}$ | $E_{HSS}^{min}$ | $E_{HSS}(0)$ |
(kW) | (kW) | (kWh) | (kWh) | (kWh) | ||
0/200 | 0/200 | 0.9/0.9 | 0.01 | 600 | 0 | 0 |
Method | Time (s) | Day-ahead Cost($) | Expected | Actual ($) | |||
$C_{MT}$ | $C_{FC}$ | $C_{DA}$ | Cost ($) | RT | SUM | ||
D-DED | 6.52 | 5422.48 | 2251.42 | 5972.69 | 5972.69 | 613.25 | 6585.95 |
S-DED | 1695.69 | 5336.95 | 2099.66 | 6011.19 | 6449.07 | 566.70 | 6577.90 |
R-DED | 6.92 | 5425.33 | 1146.89 | 6503.61 | 10916.15 | 457.79 | 6961.91 |
A-DED | 8.37 | 5422.83 | 1796.67 | 6203.84 | 8305.34 | 367.47 | 6571.81 |
Method | Time (s) | Day-ahead Cost($) | Expected | Actual ($) | |||
$C_{MT}$ | $C_{FC}$ | $C_{DA}$ | Cost ($) | RT | SUM | ||
D-DED | 6.52 | 5422.48 | 2251.42 | 5972.69 | 5972.69 | 613.25 | 6585.95 |
S-DED | 1695.69 | 5336.95 | 2099.66 | 6011.19 | 6449.07 | 566.70 | 6577.90 |
R-DED | 6.92 | 5425.33 | 1146.89 | 6503.61 | 10916.15 | 457.79 | 6961.91 |
A-DED | 8.37 | 5422.83 | 1796.67 | 6203.84 | 8305.34 | 367.47 | 6571.81 |
Method | Day-ahead Transaction | Actual Transaction | |||||
Revenue ($) | Loss ($) | State | Revenue ($) | Loss ($) | State | ||
D-DED | 1701.19 | - | Profit | 1303.22 | - | Profit | |
S-DED | 1425.36 | - | Profit | 1051.32 | - | Profit | |
R-DED | - | 68.61 | Loss | - | 275.65 | Loss | |
A-DED | 1015.67 | - | Profit | 671.63 | - | Profit |
Method | Day-ahead Transaction | Actual Transaction | |||||
Revenue ($) | Loss ($) | State | Revenue ($) | Loss ($) | State | ||
D-DED | 1701.19 | - | Profit | 1303.22 | - | Profit | |
S-DED | 1425.36 | - | Profit | 1051.32 | - | Profit | |
R-DED | - | 68.61 | Loss | - | 275.65 | Loss | |
A-DED | 1015.67 | - | Profit | 671.63 | - | Profit |
$\Gamma $ | Iteration | Time (s) | Day-ahead Cost ($) | Expected | Actual | |||
Number | $C_{MT}$ | $C_{FC}$ | $C_{Grid}^{DA}$ | $C_{DA}$ | Cost ($) | SUM ($) | ||
4 | 1 | 17.5 | 5422.8 | 1945.8 | -1249.8 | 6118.6 | 7580.2 | 6568.5 |
8 | 2 | 28.7 | 5422.8 | 1596.3 | -715.1 | 6304.1 | 8975.5 | 6753.4 |
12 | 3 | 36.2 | 5422.8 | 1332.3 | -323.9 | 6431.6 | 9981.2 | 6880.8 |
16 | 5 | 37.1 | 5422.8 | 1237.5 | -203.4 | 6457.3 | 10594.5 | 6900.3 |
20 | 6 | 42.0 | 5422.8 | 1180.7 | -118.4 | 6485.0 | 10809.4 | 6928.3 |
$\Gamma $ | Iteration | Time (s) | Day-ahead Cost ($) | Expected | Actual | |||
Number | $C_{MT}$ | $C_{FC}$ | $C_{Grid}^{DA}$ | $C_{DA}$ | Cost ($) | SUM ($) | ||
4 | 1 | 17.5 | 5422.8 | 1945.8 | -1249.8 | 6118.6 | 7580.2 | 6568.5 |
8 | 2 | 28.7 | 5422.8 | 1596.3 | -715.1 | 6304.1 | 8975.5 | 6753.4 |
12 | 3 | 36.2 | 5422.8 | 1332.3 | -323.9 | 6431.6 | 9981.2 | 6880.8 |
16 | 5 | 37.1 | 5422.8 | 1237.5 | -203.4 | 6457.3 | 10594.5 | 6900.3 |
20 | 6 | 42.0 | 5422.8 | 1180.7 | -118.4 | 6485.0 | 10809.4 | 6928.3 |
Error | Iteration | Time | Day-ahead Cost ($) | Expected | Actual ($) | ||||
Number | (s) | $C_{MT}$ | $C_{FC}$ | $C_{Grid}^{DA}$ | $C_{DA}$ | Cost ($) | RT | SUM | |
10% | 1 | 15.3 | 5422.5 | 2098.4 | -1500.2 | 6020.2 | 7152.4 | 103.5 | 6123.7 |
20% | 3 | 36.3 | 5422.8 | 1715.5 | -914.3 | 6224.8 | 8562.3 | 235.7 | 6460.5 |
30% | 3 | 29.2 | 5422.8 | 1332.7 | -323.9 | 6431.4 | 9987.2 | 449.4 | 6880.8 |
40% | 4 | 30.3 | 5409.2 | 1050.6 | 176.8 | 6636.0 | 11425.6 | 479.9 | 7385.9 |
50% | 8 | 36.4 | 5306.4 | 937.1 | 752.9 | 6996.3 | 13021.7 | 1023.3 | 8019.6 |
Error | Iteration | Time | Day-ahead Cost ($) | Expected | Actual ($) | ||||
Number | (s) | $C_{MT}$ | $C_{FC}$ | $C_{Grid}^{DA}$ | $C_{DA}$ | Cost ($) | RT | SUM | |
10% | 1 | 15.3 | 5422.5 | 2098.4 | -1500.2 | 6020.2 | 7152.4 | 103.5 | 6123.7 |
20% | 3 | 36.3 | 5422.8 | 1715.5 | -914.3 | 6224.8 | 8562.3 | 235.7 | 6460.5 |
30% | 3 | 29.2 | 5422.8 | 1332.7 | -323.9 | 6431.4 | 9987.2 | 449.4 | 6880.8 |
40% | 4 | 30.3 | 5409.2 | 1050.6 | 176.8 | 6636.0 | 11425.6 | 479.9 | 7385.9 |
50% | 8 | 36.4 | 5306.4 | 937.1 | 752.9 | 6996.3 | 13021.7 | 1023.3 | 8019.6 |
$\eta_{MT}^{EH}$ | $\eta_{EB}^{EH}$ | $\eta_{MT}^{HC}$ | $\eta_{EB}^{HC}$ | $\eta_{HSS}^{HC}$ |
0.8 | 0.8 | 0.8 | 0.8 | 0.8 |
$\eta_{MT}^{EH}$ | $\eta_{EB}^{EH}$ | $\eta_{MT}^{HC}$ | $\eta_{EB}^{HC}$ | $\eta_{HSS}^{HC}$ |
0.8 | 0.8 | 0.8 | 0.8 | 0.8 |
[1] |
Ripeng Huang, Shaojian Qu, Xiaoguang Yang, Zhimin Liu. Multi-stage distributionally robust optimization with risk aversion. Journal of Industrial & Management Optimization, 2021, 17 (1) : 233-259. doi: 10.3934/jimo.2019109 |
[2] |
Haodong Yu, Jie Sun. Robust stochastic optimization with convex risk measures: A discretized subgradient scheme. Journal of Industrial & Management Optimization, 2021, 17 (1) : 81-99. doi: 10.3934/jimo.2019100 |
[3] |
Reza Lotfi, Zahra Yadegari, Seyed Hossein Hosseini, Amir Hossein Khameneh, Erfan Babaee Tirkolaee, Gerhard-Wilhelm Weber. A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020158 |
[4] |
Guangbin CAI, Yang Zhao, Wanzhen Quan, Xiusheng Zhang. Design of LPV fault-tolerant controller for hypersonic vehicle based on state observer. Journal of Industrial & Management Optimization, 2021, 17 (1) : 447-465. doi: 10.3934/jimo.2019120 |
[5] |
Xiaoxiao Li, Yingjing Shi, Rui Li, Shida Cao. Energy management method for an unpowered landing. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020180 |
[6] |
Jian-Xin Guo, Xing-Long Qu. Robust control in green production management. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021011 |
[7] |
Xinfu Chen, Huiqiang Jiang, Guoqing Liu. Boundary spike of the singular limit of an energy minimizing problem. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3253-3290. doi: 10.3934/dcds.2020124 |
[8] |
Marcello D'Abbicco, Giovanni Girardi, Giséle Ruiz Goldstein, Jerome A. Goldstein, Silvia Romanelli. Equipartition of energy for nonautonomous damped wave equations. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 597-613. doi: 10.3934/dcdss.2020364 |
[9] |
Min Xi, Wenyu Sun, Jun Chen. Survey of derivative-free optimization. Numerical Algebra, Control & Optimization, 2020, 10 (4) : 537-555. doi: 10.3934/naco.2020050 |
[10] |
Li-Bin Liu, Ying Liang, Jian Zhang, Xiaobing Bao. A robust adaptive grid method for singularly perturbed Burger-Huxley equations. Electronic Research Archive, 2020, 28 (4) : 1439-1457. doi: 10.3934/era.2020076 |
[11] |
Chongyang Liu, Meijia Han, Zhaohua Gong, Kok Lay Teo. Robust parameter estimation for constrained time-delay systems with inexact measurements. Journal of Industrial & Management Optimization, 2021, 17 (1) : 317-337. doi: 10.3934/jimo.2019113 |
[12] |
Bin Wang, Lin Mu. Viscosity robust weak Galerkin finite element methods for Stokes problems. Electronic Research Archive, 2021, 29 (1) : 1881-1895. doi: 10.3934/era.2020096 |
[13] |
Luis Caffarelli, Fanghua Lin. Nonlocal heat flows preserving the L2 energy. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 49-64. doi: 10.3934/dcds.2009.23.49 |
[14] |
Dominique Chapelle, Philippe Moireau, Patrick Le Tallec. Robust filtering for joint state-parameter estimation in distributed mechanical systems. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 65-84. doi: 10.3934/dcds.2009.23.65 |
[15] |
Duy Phan, Lassi Paunonen. Finite-dimensional controllers for robust regulation of boundary control systems. Mathematical Control & Related Fields, 2021, 11 (1) : 95-117. doi: 10.3934/mcrf.2020029 |
[16] |
Paul A. Glendinning, David J. W. Simpson. A constructive approach to robust chaos using invariant manifolds and expanding cones. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020409 |
[17] |
Ningyu Sha, Lei Shi, Ming Yan. Fast algorithms for robust principal component analysis with an upper bound on the rank. Inverse Problems & Imaging, 2021, 15 (1) : 109-128. doi: 10.3934/ipi.2020067 |
[18] |
Bing Liu, Ming Zhou. Robust portfolio selection for individuals: Minimizing the probability of lifetime ruin. Journal of Industrial & Management Optimization, 2021, 17 (2) : 937-952. doi: 10.3934/jimo.2020005 |
[19] |
Lin Jiang, Song Wang. Robust multi-period and multi-objective portfolio selection. Journal of Industrial & Management Optimization, 2021, 17 (2) : 695-709. doi: 10.3934/jimo.2019130 |
[20] |
Predrag S. Stanimirović, Branislav Ivanov, Haifeng Ma, Dijana Mosić. A survey of gradient methods for solving nonlinear optimization. Electronic Research Archive, 2020, 28 (4) : 1573-1624. doi: 10.3934/era.2020115 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]