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A method for solving a probabilistic power flow that deals with the uncertainties of (i) wind generation, (ii) load and (iii) generation availability in power systems is proposed. Dependence between random variables has been considered. The method is based on the properties of cumulants of random variables. Cornish-Fisher expansion series are used to obtain the cumulative distribution function (CDF) of the output variables. Multimodal CDF are obtained by convolutions, whose number has been minimised in order to decrease the computation requirements.
References
-
-
1)
-
Miranda, V., Saraiva, J.T.: `Fuzzy modelling of power system optimal power flow', Proc. Power Industry Computer Application Conference, 1991, Baltimore, USA.
-
2)
-
N.D. Hatziargyriou ,
T.S. Karakatsanis ,
M. Papadopoulos
.
Probabilistic load flow in distribution systems containing dispersed wind power generation.
IEEE Trans. Power. Syst.
,
159 -
165
-
3)
-
G. Verbic ,
C.A. Cañizares
.
Probabilistic optimal power flow in electricity markets based on a two point estimate method.
IEEE Trans. Power Syst.
,
1883 -
1893
-
4)
-
H. Cramer
.
(1946)
Numerical methods of statistics.
-
5)
-
R.N. Allan ,
A.M.L. Da Silva ,
R.C. Burchett
.
Evaluation methods and accuracy in probabilistic load flow solutions.
IEEE Trans. Power Appl. Syst.
,
2539 -
2546
-
6)
-
P. McCullagh
.
(1987)
Tensor methods in statistics.
-
7)
-
A. Papoulis
.
(1991)
Probability, random variables and stochastic processes.
-
8)
-
Usaola, J.: `Probabilistic load flow with wind production uncertainty using cumulants and Cornish-Fisher expansion', Proceedings of the 2008 Power System Computation Conference, July 2008, Glasgow, UK.
-
9)
-
C.-L. Su
.
Probabilistic load-flow computation using point estimate method.
IEEE Trans. Power Syst.
,
4 ,
1843 -
1851
-
10)
-
P. Zhang ,
T. Lee
.
Probabilistic load flow computation using the method of combined cumulants and Gram-Charlier expansion.
IEEE Trans. Power Syst.
,
676 -
682
-
11)
-
A. Stuart ,
J.K. Ord
.
(1994)
Kendall's advanced theory of statistics.
-
12)
-
E.A. Cornish ,
R.A. Fisher
.
Moments and cumulants in the specification of distributions.
Revue de l'Institut Inter. Statis.
,
307 -
320
-
13)
-
S.R. Jaschke
.
The Cornish-Fisher-expansion in the context of delta-gamma-normal approximations.
-
14)
-
S. Blinnikov ,
R. Moessner
.
Expansions for nearly Gaussian distributions.
Astron. Astrophys. Suppl. Ser.
,
193 -
205
-
15)
-
L.A. Sanabria ,
T.S. Dillon
.
Power system reliability assessment suitable for a deregulated system via the method of cumulants.
Electric Power Energy Syst.
,
203 -
211
-
16)
-
Z. Hu ,
X. Wang
.
A probabilistic load flow method considering branch outages.
IEEE Trans. Power Syst.
,
507 -
514
-
17)
-
A. Schellenberg ,
W. Rosehart ,
J. Aguado
.
A cumulant-based probabilistic optimal power flow (P-OPF) with gaussian and gamma distributions.
IEEE Trans. Power. Syst.
,
773 -
781
-
18)
-
Papaefthymiou, G.: `Integration of stochastic generation in power systems', 2007, PhD, University of Delft.
-
19)
-
J.E. Gentle
.
(2003)
Random number generation and Monte Carlo methods.
-
20)
-
A. Fabbri ,
T. Gomez San Roman ,
J. Rivier ,
V.H. Mendez Quezada
.
Assessment of the cost associated with wind generation prediction errors in a liberalized electricity market.
IEEE Trans. Power Syst.
,
3 ,
1440 -
1446
-
21)
-
A.M. Leite da Silva ,
V.L. Arienti ,
R.N. Allan
.
Probabilistic load flow considering dependence between input nodal powers.
IEEE Trans. Power. Appl. Syst.
,
1524 -
1530
-
22)
-
B. Borkowska
.
Probabilistic load flow.
IEEE Trans. Power Appl. Syst.
,
752 -
759
-
23)
-
A.M. Leite da Silva ,
S.M.P. Ribeiro ,
V.L. Arienti ,
R.N. Allan ,
M.B. De Couto Filho
.
Probabilistic load flow techinques applied to power system expansion planning.
IEEE Trans. Power Syst.
,
1047 -
1053
-
24)
-
J.F. Dopazo
.
Stochastic load flow.
IEEE Trans. Power Appl. Syst.
,
299 -
309
-
25)
-
A.M. Leite da Silva ,
V.L. Arianti
.
Probabilistic load flow by a multilinear simulation algorithm.
IEE Proc.
,
276 -
282
-
26)
-
Kariniotakis, G.: `Evaluation of advanced wind power forecasting models – results of the Anemos project', Proceedings of the EWEC, 2006, Athens.
-
27)
-
Power Systems Test Case Archive. [Online]. Available at: http://www.ee.washington.edu/research/pstca.
-
28)
-
W.D. Tian ,
D. Sutanto ,
Y.B. Lee ,
H.R. Outhred
.
Cumulant based probabilistic power system simulation using Laguerre polynomials.
IEEE Trans. Energy Convers.
,
567 -
574
-
29)
-
J.M. Morales ,
J. Perez-Ruiz
.
Point estimate schemes to solve the probabilistic power flow.
IEEE Trans., Power Syst.
,
4 ,
1594 -
1601
-
30)
-
U. Focken ,
M. Lange ,
K. Moennich ,
H.P. Waldl ,
H.G. Beyer ,
A. Luig
.
Short-term prediction of the aggregated power output of wind farms – a statistical analysis of the reduction of the prediction error by spatial smoothing effects.
J. Wind Eng. Ind. Aerodyn.
,
231 -
246
-
31)
-
G.W. Hill ,
A.W. Davis
.
Generalized asymptotic expansions of Cornish-Fisher type.
Ann. Math. Stat.
,
4 ,
1264 -
1273
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