Abstract
The uncertainty of wind speed may lead to the deviation and change of wind power output, which influences the stability of wind farm. Therefore, in this paper, a probability box (p-box) based uncertain power flow model for wind power is proposed, which initially introduces p-box to power flow calculation. A probabilistic interval power flow model with both probability and interval is established. Firstly, the drift interval of wind speed is obtained and its p-box model is established by analyzing the distribution of wind speed. Secondly, the wind power output p-box is derived from the wind speed p-box based on the relationship between wind power output and wind speed, then the p-box of wind power output is discretized and introduced into the power flow equation to obtain the power flow p-box model. Finally, Newton–Raphson method is used to solve the power flow p-box model. Experiments on data collected from a wind farm (running standard IEEE30-bus test system) in Inner Mongolia demonstrate that our method is more effective and accurate than the traditional Monte Carlo simulation (MCS) and classical interval power flow (IPF) method.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
1. Kumar, SR, Kumar, D, Kumar, P. Fuzzy modelling of system behavior for risk and reliability analysis. Int J Syst Sci 2008;39:563–81. https://doi.org/10.1080/00207720701717708.Suche in Google Scholar
2. Utkin, LV, Destercke, S. Computing expectations with continuous p-box: univariate case. Int J Approx Reason 2009;50:778–98. https://doi.org/10.1016/j.ijar.2009.02.004.Suche in Google Scholar
3. Aughenbaugh, JM, Herrmann, JW. International management for estimating system reliability using imprecise probabilities and precise Bayesian updating. Int J Reliab Saf 2009;3:35–6. https://doi.org/10.1504/ijrs.2009.026834.Suche in Google Scholar
4. Bijwe, PR, Viswanadha Raju, GK. Fuzzy distribution power flow for weakly meshed systems. IEEE Trans Power Syst 2006;21:1645–52. https://doi.org/10.1109/tpwrs.2006.881138.Suche in Google Scholar
5. Matos Manuel, A, Gouveia Eduardo, M. The fuzzy power flow revisited. IEEE Trans Power Syst 2008;23:213–8. https://doi.org/10.1109/tpwrs.2007.913686.Suche in Google Scholar
6. Cortes-Carmona, M, Palma-Behnke, R, Jimenes-Estevez, G. Fuzzy arithmetic for the DC load flow. IEEE Trans Power Syst 2010;25:206–14. https://doi.org/10.1109/tpwrs.2009.2030350.Suche in Google Scholar
7. Soleimanpour, N, Mohammadi, M. Probabilistic load flow by using nonparametric density estimators. IEEE Trans Power Syst 2013;28:3747–55. https://doi.org/10.1109/tpwrs.2013.2258409.Suche in Google Scholar
8. Ran, XH, Miao, SH. Three-phase probabilistic load flow for power system with correlated wind, photovoltaic and load. IET Gener Transm Distrib 2016;10:3093–101. https://doi.org/10.1049/iet-gtd.2016.0424.Suche in Google Scholar
9. Xu, Y, Hu, Z, Mili, L, Korkali, M, Chen, X. Probabilistic power-flow calculation based on a novel Gaussian process emulator. IEEE Trans Power Syst 2020;35:3278–81. https://doi.org/10.1109/TPWRS.2020.2983603.Suche in Google Scholar
10. Xu, C, Gu, W, Gao, F, Song, X, Meng, X, Fan, M. Improved affine arithmetic based optimisation model for interval power flow analysis. IET Gener Transm Distrib 2016;10:3910–8. https://doi.org/10.1049/iet-gtd.2016.0601.Suche in Google Scholar
11. Zhang, C, Chen, H, Ngan, H, Yang, P, Hua, D. A mixed interval power flow analysis under rectangular and polar coordinate system. IEEE Trans Power Syst 2017;32:1422–9. https://doi.org/10.1109/TPWRS.2016.2583503.Suche in Google Scholar
12. Lin, C, Chen, Y, Bie, Z. A fuzzy probabilistic power flow method based on fuzzy copula model. 2018 IEEE Electrical Power and Energy Conference (EPEC), Toronto, ON, 2018, 1–6. https://doi.org/10.1109/EPEC.2018.8598309.Suche in Google Scholar
13. Aghili, SJ, Saghafi, H, Hajian-Hoseinabadi, H. Uncertainty analysis using fuzzy transformation method: an application in power-flow studies. IEEE Trans Power Syst 2020;35:42–52. https://doi.org/10.1109/tpwrs.2019.2929712.Suche in Google Scholar
14. Gao, YH, Wang, C. Probabilistic load flow calculation of distribution system including wind farms based on total probability formula. Proc CSEE 2015;35:327–34 (in Chinese).Suche in Google Scholar
15. Zio, E, Delfanti, M, Giorgi, L, Olivieri, V, Sansavini, G. Monte Carlo simulation-based probabilistic assessment of DG penetration in medium voltage distribution networks. Int J Electr Power Energy Syst 2015;64:852–60. https://doi.org/10.1016/j.ijepes.2014.08.004.Suche in Google Scholar
16. Ruiz-Rodriguez, FJ, Hernáandez, JC, Jurado, F. Voltage unbalance assessment in secondary radial distribution networks with single-phase photovoltaic systems. Int J Electr Power Energy Syst 2015;64:646–54. https://doi.org/10.1016/j.ijepes.2014.07.071.Suche in Google Scholar
17. Prusty, BR, Jena, D. A spatiotemporal probabilistic model-based temperature-augmented probabilistic load flow considering PV generations. Int Trans Electr Energy Syst 2019;29:e2819. https://doi.org/10.1002/2050-7038.2819.Suche in Google Scholar
18. Chen, Y, Wen, J, Cheng, S. Probabilistic load flow method based on nataf transformation and latin hypercube sampling. IEEE Trans Sustain Energy 2013;4:294–301. https://doi.org/10.1109/tste.2012.2222680.Suche in Google Scholar
19. Ye, L, Zhang, Y, Ju, Y, Song, X, Lang, Y, Li, Q. Gaussian mixture model for probabilistic power flow calculation of system integrated wind farm. Proc CSEE 2017;37:4379–87. https://doi.org/10.13334/j.0258-8013.pcsee.161245.Suche in Google Scholar
20. Sheng, H, Wang, X. Probabilistic Power flow calculation using non-intrusive low-rank approximation method. IEEE Trans Power Syst 2019;34:3014–25. https://doi.org/10.1109/TPWRS.2019.2896219.Suche in Google Scholar
21. Ding, T, Bo, R, Li, F, Guo, Q, Sun, H, Gu, W, et al.. Interval power flow analysis using linear relaxation and optimality-based bounds tightening (OBBT) methods. IEEE Trans Power Syst 2015;30:177–88. https://doi.org/10.1109/tpwrs.2014.2316271.Suche in Google Scholar
22. Bao, H, Guo, X. Interval load flow calculation using Monte Carlo method based on stochastic space affine transformation. Power Syst Clean Energy 2019;35:33–42 (in Chinese).Suche in Google Scholar
23. Liu, B, Huang, Q, Zhao, J, Hu, W. A computational attractive interval power flow approach with correlated uncertain power injections. IEEE Trans Power Syst 2020;35:825–8. https://doi.org/10.1109/tpwrs.2019.2947779.Suche in Google Scholar
24. Mohsin, M, Rao, KVS. Estimation of Weibull distribution parameters and wind power density for wind farm site at Akal at Jaisalmer in Rajasthan. In: 2018 3rd International innovative applications of computational intelligence on power, energy and controls with their impact on humanity (CIPECH). IEEE; 2019:1–6 pp.10.1109/CIPECH.2018.8724170Suche in Google Scholar
25. Bao, H, Wei, H, Guo, X. The model and algorithm of probabilistic interval power flow considering wind power uncertainty. Proc CSEE 2017;37:5633–42 (in Chinese).Suche in Google Scholar
26. Ferson, S, Kreinovich, V, Ginzburg, L, et al.. Constructing probability boxes and Dempster Shafer structures. SAND2002-4015. Albuquerque, NM: Sandia National Laboratories; 2003.10.2172/809606Suche in Google Scholar
27. Zhang, Y. Statistical analysis for the characteristics of wind speed and electrical generation. J Nan Kai 2010;7:85–94 (in Chinese).Suche in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Editorial
- Fault location in the distribution network based on power system status estimation with smart meters data
- Research Articles
- Study on the characteristics of secondary arc current of UHV high compensation degree TCSC line under the fine-tuning mode
- Reactive power and harmonic compensation in a grid-connected photovoltaic system using fuzzy logic controller
- Enhancement of system performance using STATCOM as dynamic compensator with squirrel cage induction generator (SCIG) based microgrid
- A novel non-isolated dual-input DC-DC boost converter for hybrid electric vehicle application
- Suppression of very fast transients in 245 kV gas insulated substation
- Locational marginal price computation in radial distribution system using Self Adaptive Levy Flight based JAYA Algorithm and game theory
- Modeling of unforced demand response programs
- Probability box theory-based uncertain power flow calculation for power system with wind power
Artikel in diesem Heft
- Frontmatter
- Editorial
- Fault location in the distribution network based on power system status estimation with smart meters data
- Research Articles
- Study on the characteristics of secondary arc current of UHV high compensation degree TCSC line under the fine-tuning mode
- Reactive power and harmonic compensation in a grid-connected photovoltaic system using fuzzy logic controller
- Enhancement of system performance using STATCOM as dynamic compensator with squirrel cage induction generator (SCIG) based microgrid
- A novel non-isolated dual-input DC-DC boost converter for hybrid electric vehicle application
- Suppression of very fast transients in 245 kV gas insulated substation
- Locational marginal price computation in radial distribution system using Self Adaptive Levy Flight based JAYA Algorithm and game theory
- Modeling of unforced demand response programs
- Probability box theory-based uncertain power flow calculation for power system with wind power