© The Institution of Engineering and Technology
A probabilistic load flow (PLF) method based on the sparse polynomial chaos expansion (PCE) is presented here. Previous studies have shown that the generalised polynomial chaos expansion (gPCE) is promising for estimating the probability statistics and distributions of load flow outputs. However, it suffers the problem of curse-of-dimensionality in high-dimensional applications. Here, the compressive sensing technique is applied into the gPCE-based scheme, from which the sparse PCE is built as the surrogate model to perform the PLF in an accurate and efficient manner. The dependence among random input variables is also taken into consideration by making use of the Copula theory. Consequently, the proposed method is able to handle the correlated uncertainties of high-dimensionality and alleviate the computational effort as of popular methods. Finally, the feasibility and the effectiveness of the proposed method are validated by the case studies of two standard test systems.
References
-
-
1)
-
1. REN21: ‘Renewables 2016: global status report’ (, 2016), pp. 26–38.
-
2)
-
2. McCalley, J., Asgarpoor, S., Bertling, L., et al: ‘Probabilistic security assessment for power system operations’. IEEE Power Engineering Society General Meeting, Denver, CO, USA, June 2004, pp. 212–220.
-
3)
-
3. Kirschen, D.S., Jayaweera, D.: ‘Comparison of risk-based and deterministic security assessments’, IET Gener. Transm. Distrib., 2007, 1, (4), pp. 527–533.
-
4)
-
4. Borkowska, B.: ‘Probabilistic load flow computation using Copula and Latin hypercube sampling’, IEEE Trans. Power Appar. Syst., 1974, PAS-93, (3), pp. 752–759.
-
5)
-
5. Hajian, M., Rosehart, W.D., Zareipour, H.: ‘Probabilistic power flow by Monte Carlo simulation with Latin supercube sampling’, IEEE Trans. Power Syst., 2013, 28, (2), pp. 1550–1559.
-
6)
-
6. Cai, D., Shi, D., Chen, J.: ‘Probabilistic load flow computation with polynomial normal transformation and Latin hypercube sampling’, IET Gener. Transm. Distrib., 2013, 7, (5), pp. 474–482.
-
7)
-
7. Villanueva, D., Pazos, J.L., Feijóo, A.: ‘Probabilistic load flow including wind power generation’, IEEE Trans. Power Syst., 2011, 26, (3), pp. 1659–1667.
-
8)
-
8. Usaola, J.: ‘Probabilistic load flow in systems with wind generation’, IET Gener. Transm. Distrib., 2009, 3, (12), pp. 1031–1041.
-
9)
-
9. Su, C.-L.: ‘Probabilistic load-flow computation using point estimate method’, IEEE Trans. Power Syst., 2005, 20, (4), pp. 1843–1851.
-
10)
-
10. Tang, J., Ni, F., Ponci, F., et al: ‘Dimension-adaptive sparse grid interpolation for uncertainty quantification in modern power systems: probabilistic power flow’, IEEE Trans. Power Syst., 2016, 31, (2), pp. 907–919.
-
11)
-
11. Ren, Z., Li, W., Billinton, R., et al: ‘Probabilistic power flow analysis based on the stochastic response surface method’, IEEE Trans. Power Syst., 2016, 31, (3), pp. 2307–2315.
-
12)
-
12. Wu, H., Zhou, Y., Dong, S., et al: ‘Probabilistic load flow based on generalized polynomial chaos’, IEEE Trans. Power Syst., 2017, 32, (1), pp. 820–821.
-
13)
-
13. Ni, F., Nguyen, P.H., Cobben, J.F.G.: ‘Basis-adaptive sparse polynomial chaos expansion for probabilistic power flow’, IEEE Trans. Power Syst., 2017, 32, (1), pp. 694–704.
-
14)
-
14. Xiu, D., Karniadakis, G.E.: ‘The Wiener-Askey polynomial chaos for stochastic differential equations’, SIAM J. Sci. Comput., 2002, 24, (2), pp. 619–644.
-
15)
-
15. Isukapalli, S.S, Roy, A., Georgopoulos, P.G.: ‘Stochastic response surface methods (SRSMs) for uncertainty propagation: application to environmental and biological systems’, Risk Anal., 1998, 18, (3), pp. 351–363.
-
16)
-
16. Crestaux, T., Le Maitre, O., Martinez, J.M.: ‘Polynomial chaos expansion for sensitivity analysis’, Reliab. Eng. Syst. Saf., 2009, 94, (7), pp. 1161–1172.
-
17)
-
17. Blatman, G., Sudret, B.: ‘Adaptive sparse polynomial chaos expansion based on least angle regression’, J. Comput. Phys., 2011, 230, (6), pp. 2345–2367.
-
18)
-
18. Xiu, D.: ‘Numerical methods for stochastic computations: a spectral method approach’ (Princeton University Press, Princeton, NJ, USA, 2010).
-
19)
-
19. Candes, E.J., Wakin, M.B.: ‘An introduction to compressive sampling’, IEEE Signal Proc. Mag., 2008, 25, (2), pp. 21–30.
-
20)
-
20. Dai, W., Milenkovic, O.: ‘Subspace pursuit for compressive sensing signal reconstruction’, IEEE Trans. Inf. Theory, 2009, 55, (5), pp. 2230–2249.
-
21)
-
21. Chen, Y.C., Dominguez-Garcia, A.D., Sauer, P.W.: ‘A sparse representation approach to online estimation of power system distribution factors’, IEEE Trans. Power Syst., 2015, 30, (4), pp. 1727–1738.
-
22)
-
22. Sargsyan, K., Safta, C., Najm, H.N., et al: ‘Dimensionality reduction for complex models via Bayesian compressive sensing’, Int. J. Uncertain. Quantif., 2014, 4, (1), pp. 63–93.
-
23)
-
23. Li, X., Cao, J., Du, D.: ‘Probabilistic optimal power flow for power systems considering wind uncertainty and load correlation’, Neurocomputing, 2015, 148, pp. 240–247.
-
24)
-
24. Papaefthymiou, G., Kurowicka, D.: ‘Using Copulas for modeling stochastic dependence in power system uncertainty analysis’, IEEE Trans. Power Syst., 2009, 24, (1), pp. 40–49.
-
25)
-
25. Zhou, T., Narayan, A., Xiu, D.: ‘Weighted discrete least-squares polynomial approximation using randomized quadratures’, J. Comput. Phys., 2015, 298, pp. 787–800.
-
26)
-
26. Hans, C.: ‘Bayesian lasso regression’, Biometrika, 2009, 96, (4), pp. 835–845.
-
27)
-
27. Tropp, J.: ‘Greed is good: algorithmic results for sparse approximation’, IEEE Trans. Inf. Theory, 2004, 50, (10), pp. 2231–2242.
-
28)
-
28. Zimmerman, R.D., Murillo-Sanchez, C.E., Thomas, R.J.: ‘MATPOWER: steady-state operations, planning and analysis tools for power systems research and education’, IEEE Trans. Power Syst., 2011, 26, (1), pp. 12–19.
-
29)
-
29. Bludszuweit, H., Dominguez-Navarro, J.A., Llombart, A.: ‘A statistical analysis of wind power forecast error’, IEEE Trans. Power Syst., 2008, 23, (3), pp. 983–991.
-
30)
-
30. Chen, Y., Wen, J., Cheng, S.: ‘Probabilistic load flow method based on Nataf transformation and Latin hypercube sampling’, IEEE Trans. Sustain. Energy, 2013, 4, (2), pp. 294–301.
-
31)
-
31. Cai, D., Shi, D., Chen, J.: ‘Probabilistic load flow computation using Copula and Latin hypercube sampling’, IET Gener. Transm. Distrib., 2014, 8, (9), pp. 1539–1549.
-
32)
-
32. Hampton, J., Doostan, A.: ‘Compressive sampling of polynomial chaos expansions: convergence analysis and sampling strategies’, J. Comput. Phys., 2015, 280, pp. 363–386.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-gtd.2017.0859
Related content
content/journals/10.1049/iet-gtd.2017.0859
pub_keyword,iet_inspecKeyword,pub_concept
6
6