OBTAINING PROBABILITY DISTRIBUTION LAWS OF POWER SYSTEM STEADY-STATE MODE PARAMETERS
DOI:
https://doi.org/10.14529/power200305Keywords:
ELECTRIC POWER SYSTEM, STEADY-STATE MODE, PROBABILITY DISTRIBUTION LAW, RANDOM VARIABLE, QUANTILE, FUNCTIONAL DEPENDENCYAbstract
Stable operation of electrical power systems is one of the crucial issues in the power industry. Current volumes of electricity consumption cause the need to constantly increase the generated capacity, repeatedly modifying and complicating the original circuit. In addition to this, given the current trend towards the use of digital power systems and renewable energy sources, more and more uncertainties difficult to predict by standard mathematical methods appear. Events in the power system are deterministic, i.e. random. Thus, it is difficult to fully assess the system stability, voltage levels, currents, or possible power losses. Finding the probability distribution laws can give us an understanding of all the possible states in which an object can exist. Obtaining them is complicated by the difficulty of accounting for all the correlations between the random arguments of the source data. These laws are necessary to determine the optimal operating modes, the possibility of solving the problem of determining the optimal renewable energy sources installation locations and the required amount of generated energy in a non-deterministic way. The purpose of this article is to test the developed SIBD method for obtaining the full probabilistic characteristics. This method, unlike the Monte Carlo methods, does not use a random sample of initial data, but completely covers the studied functional dependence. The problem was solved using the provisions of probability theory and mathematical statistics, numerical optimization methods in particular. The MATLAB Matpower application package was also used to solve technical computing problems.
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Prognoz razvitiya energetiki mira i Rossii do 2040 goda [Forecast of energy development in the world and
Russia until 2040], INEI RAN, ATs, 2014.
Azmy A., Erlich I. Impact of distributed generation on the stability of electrical power system. IEEE Power
Engineering Society General Meeting, 2005, vol. 2, pp. 1056–1063. DOI: 10.1109/pes.2005.1489354
Voropaj N.I., Efimov D.N. [Requirements for emergency control of electric power plants taking into account changes in the conditions for their development and functioning]. Nadezhnost' liberalizovannyh sistem
jenergetiki [Reliability of liberalized energy systems]. Novosibirsk, Nauka Publ., 2004, pp. 74–84. (in Russ.)
Ve el’ E.S. Teoriya veroyatnostey: ucheb. dlya vuzov [Probability Theory: Proc. for Universities].
Moscow, Vyssh. shk. Publ., 1999. 576 p.
Andronov A.M., Kopytov E.A., Gringlaz L.YA. Teoriya veroyatnostey i matematicheskaya statistika
[Theory of Probability and Mathematical Statistics]. St. Petersburg, Piter Publ., 2004. 461 p.
Genz A. Numerical Computation of the Multivariate Normal Probabilities. Journal of Computational and
Graphical Statistics, 1992, vol. 1, pp. 141–150. DOI: 10.2307/1390838
Ufa R., Andreev M., Ruban N., Suvorov A., Gusev A., Razzhivin I., Askarov A., Bay Y., Kievets A.,
Lozinova N., Suslova O. The hybrid model of VSC. Electrical Engineering, 2019, vol. 101, pp. 11–18. DOI:
1007/s00202-018-00752-y
Mila vić J. Pr babili i abili y a aly i : The way rward r abili y a aly i u ai able p wer
systems. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences,
, vol. 2100, pp. 1–22. DOI: 10.1098/rsta.2016.0296
Chung C.Y., Chan K.W., Huazhang H. Quasi-Monte Carlo based probabilistic small signal stability analysis for power systems with plug-in electric vehicle and wind power integration. IEEE Transactions on Power Systems, 2013, vol. 28, pp. 3335– 343. DOI: 10.1109/tpwrs.2013.2254505
Hong HP. An efficient point estimate method for probabilistic analysis. Reliability Engineering & System
Safety, 1998, vol. 59, pp. 261–267. DOI: 10.1016/s0951-8320(97)00071-9
Karimishad A. Probabilistic transient stability assessment using two-point estimate method. Proceedings
of the 8th International Conference on Advances in Power System Control, Operation and Management (APSCOM
, 2009, pp. 1–36. DOI: 10.1049/cp.2009.1748
LI W. Risk assessment of power systems: models, methods, and applications. Wiley-IEEE Press Publ.,
560 p.
Hsu J. Multiple Comparisons: Theory and Methods. London, Chapman and Hall Publ, 1996. 277 p.
Bay Y.D. The Selection of Interval Boundaries of Input and Output Data Method for Obtaining
Complete Probabilistic Characteristics. MATEC Web of Conferences, 2017, vol. 141, pp. 1–4. DOI:
1051/matecconf/201714101037
Venikov V.A. et al. Elektroenergeticheskiye sistemy v primerakh i zadachakh [Electric Power Systems
Examples and Tasks]. Moscow, Energoatomizdat Publ., 1983. 504 p.
Shvedov A.S. Teoriya veroyatnostey i matematicheskaya statistika [Theory of Probability and Mathematical Statistics]. Moscow, Izd. dom GU-VShE Publ., 2005. 254 p.
Rodgers J.L., Nicewander W.A. Thirteen Ways to Look at the Correlation Coefficient. The American Statistician, 1988, vol. 42, no. 1, pp. 59–66.
Bay Y., Razzhivin I., Kievets A., Askarov A., Rudnik V. Obtaining probabilistic characteristics of electrical quantities and their imbalances. Electrotehnica, Electronica, Automatica (EEA), 2019, vol. 67, pp. 73–80.
DOI: 10.46904/eea.20.68.3.1108004
IEEE 14 Bus Power Flow Test Case. Available at: https://egriddata.org/dataset/ieee-14-bus-power-flowtest-case (accessed 29.04.2020).
Matpower Documentation. Available at: https://matpower.org/doc/ (accessed 12.04.2020).
Suresh V. Comparison of solvers performance for load flow analysis. Transactions on Environment and
Electrical Engineering, 2019, vol. 1, pp. 363–378.
Ehsan M., Aien M., Soroudi A. A probabilistic modeling of photovoltaic modules and wind power
generation impact on distribution networks. IEEE Systems Journal, 2012, vol. 6, pp. 254–259. DOI:
1109/jsyst.2011.2162994