download PDF

Abstract

Simulation of electric load is one of the most difficult modeling problems of operating condition of the electric power system. It is stipulated by a large number and a variety of electrical loads and their erratic behavior. The considerable share of loads cannot be described with sufficient accuracy by typical characteristics. To refine and actualize them, special staged field tests are carried out in power systems. This does not completely solve the problem. It is impossible to cover all loads in all possible states with such experiments. The purpose of the work is to develop a method for determining the static load model of electric power systems by voltage. The determination is made by mathematical processing of the data of steady-state observation over the parameters of an electrical mode. The method is based on the developed mathematical model considering probability nature of changes in the load power and the supply network voltage as well as the correlations between them. There are two such correlations. Changing the load power caused by a voltage variation. And also a voltage variation at the supply point caused by the change in the load power. The first correlation reflects the natural static load model. The second correlation reflects the "network response". Taking into account the "network reaction" is necessary when processing data from the steady-state measurement. The difference of the proposed method is usage of laws of probability distribution instead of the measured values. This makes it possible to use the method in combination with cluster analysis methods. In these methods, the measurement results are presented in the form of a Gaussian mixture. The proposed method can be used to automate the process of determining the static load models according to the measurements without conducting staged field tests. This will make it possible to cover all the telemetered nodes of load in all possible states in the future.

Keywords

Electric power system, static load model, steady-state measurements, cluster analysis, network response, system of random variables, covariance matrix, dispersion ellipse.

Aleksey V. Pankratov

h.D. (Engineering), Head of Tomsk Representative Office, System Operator of the United Power System, JSC, Tomsk, Russia. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID: https://orcid.org/0000-0001-8176-1925.

Alexander K. Zhuykov

Undergraduate Student, Power and Electrical Engineering Department, National Research Tomsk Polytechnic University, Tomsk, Russia. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID: https://orcid.org/0000-0001-5333-1661.

Alena A. Shuvalova

Post-Graduate student, Power Engineering Faculty, Polzunov Altai State Technical University, Barnaul, Russia. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID: https://orcid.org/0000-0003-0104-1085.

Vladimir I. Polishchuk

D.Sc. (Engineering), Professor, Dean, Power Engineering Faculty, Polzunov Altai State Technical University, Barnaul, Russia. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID: https://orcid.org/0000-0001-8100-4406.

1. Gurevich Yu.E, Libova L.E., Khachatryan E.A. Ustichivost nagruzki elektricheskikh system [Load stability of electrical systems], Moscow, Energoizdat Publ., 1981, 209 p. (In Russian)

2. Nigamatullin R.M. alculation of a Share of the Load Regulat-ing Effect in the Distribution Busbar Voltage Deviation. Vest-nik Magnitogorskogo gosudarstvennogo tekhnicheskogo uni-versiteta im. G.I. Nosova [Vestnik of Nosov Magnitogorsk State Technical University], 2020, vol. 18, no. 4, pp. 65-70. doi: 10.18503/1995-2732-2020-18-4-65-70. (In Russian)

3. Gazizova O.V., Nigamatullin R.M. Evaluation of The Effect of Static Load Characteristics on The Level of Frequency During Separate Operations with The Grid. Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya: Energetika [Bulletin of the South Ural State University. Series "Power Engineering"], 2020, vol. 20, no. 4, pp. 54–63. doi: 10.14529/power200406. (In Russian)

4. Gurevich Yu.E., Libova L.E. Primenenie matematicheskikh modeley elektricheskoy nagruzki v raschetakh ustoichivosti energosistem i nadezhnosti elektrosnabzheniya promyshlen-nikh potrebiteley [Application of mathematical models of electric load in calculations of power systems and reliability of power supply to industrial consumers]. Moscow, ELEX_KM Publ., 2008, 246 p. (In Russian)

5. Kondrashov M.A., Kondrashova A.Yu. Software for identifying the actual static load characteristics by the voltage of large consumers. Prikladnaya informatika [Journal of Applied Informatics], 2018, vol. 13, no. 5(77), pp. 44–50. (In Russian)

6. Tavlintsev A.S. Razvitie metodov identifikacii staticheskih harakteristik kompleksnogo uzla nagruzki. Kand. Diss. [De-velopment of methods for identifying the static characteristics of a complex load node: Kand. Diss.], Ekaterinburg, 2018. 172 p.

7. Dzyuba M.A., Tarasenko V.V., Korzhov A.V. Method for Determining of Voltage Steady-State Load Characteristics with Subject to The Limitation on Sensitive Parameters and Electrical Safety of Active Experiment. Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya: Energetika [Bulletin of South Ural State University. Series "Power Engineering"], 2018, vol. 18, no. 2 pp. 28-35. doi: 10.14529/power180204. (In Russian)

8. Kondrashov M.A., Popov M.G. Information exchange profiles for the task of identifying static load characteristics. Elektroenergetika glazami molodezhi: Materialy XI Mezhdunarodnoj nauchno-tekhnicheskoj konferencii ["Electric power industry through the eyes of youth". Materials of the XI International Scientific and Technical Conference.]. Stavropol, North Caucasus Federal University Publ., 2020, pp. 30-31. (In Russian)

9. Pankratov A.V., Polishchuk V.I., Batseva N.L. Experimental determination of static load characteristics of electric power systems. Vestnik Yuzhno-Uralskogo gosudarstvennogo uni-versiteta. Seriya: Energetika [Bulletin of South Ural State University. Series "Power Engineering"], 2015, vol. 15, no. 1, pp. 11-20. doi: 10.14529/power150102. (In Russian)

10. Kravchenko V.F., Nagai V.I., Burakov I.F., Zoloev B.P. Determination of Static Characteristics of Power Loads of Network Nodes Based on The Active Experiment. Izvestiya vysshih uchebnyh zavedenij. Severo-Kavkazskij region. Tekhnicheskie nauki [University News. North-Caucasian Region. Technical Sciences Series], 2015, no. 1 (182), pp. 54-59. (In Russian)

11. Khrushchev Yu.V., Pankratov A.V., Batseva N.L., Polishchuk V.I., Tavlintsev A.S. The technique for identify-ing load static characteristics based on experimental data. Izvestiya Tomskogo politekhnicheskogo universiteta [Bulletin of the Tomsk Polytechnic University], 2014, vol. 325, no. 4, pp. 164-175. (In Russian)

12. Gorbunova L.M., Portnoy M.G., Rabinovich R.S., Sovalov S.A., Timchenko V.F. Eksperimentalnye issledo-vaniya rezhimov energosistem [Experimental studies of the modes of energy systems]. Moscow, Energoatomizdat Publ., 1985, 448 p. (In Russian)

13. Konovalov Yu.S, Kugelevichus I.B. On the possibility of determining the static characteristics of the load by methods of mathematical statistics. Elektrichestvo [Electricity], 1968, no. 3, pp. 11-13. (In Russian)

14. Tavlintsev A.S., Suvorov A.A. Statistically equilibrium states of load in the problem of static load characteristics identification. Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya: Energetika [Bulletin of South Ural State University. Series "Power Engineering"], 2017, vol. 17, no. 2, pp. 23-28. doi: 10.14529/power170203. (In Russian)

15. Gurevich Yu.E., Libova L.E. On determining the characteris-tics of the load by voltage by the method of steady-state measurements. Elektrichestvo [Electricity], 1972, no. 2, pp. 21-24. (In Russian)

16. Kozlov V.A. Elektrosnabzhenie gorodov [Power supply of cities]. Moscow, Energy Publishing House, 1977, 280 p. (In Russian)

17. Stepanov V.P., Krotkov E.A., Vedernikov A.S., Gudkov A.V., Idiatulin R.F. Estimation of the values of peaks and troughs when limiting the limits of changes in the theta ordinates of electrical load graphs. Vestnik Samarskogo gosudarstvennogo tekhnicheskogo universiteta. Seriya: Tekhnicheskie nauki [Vestnik of Samara State Technical University. Technical Sciences Series], 2005, no. 37, pp. 121-127. (In Russian)

18. Petrov V.V. Limiting theorems of classical type for sums of independent random variables. Itogi nauki i tekhn. Ser. Sov-rem. probl. mat. Fundam. Napravleniya [Results of science and technology. Series: modern problems of mat. fundamental direction], 1991, vol. 81, pp. 10-38. (In Russian)

19. PonarinYa.P. Afinnaya i proektivnaya geometriya [Affine and projective geometry]. Moscow, Moscow Center for Continu-ing Mathematical Education Publ., 2009. 288 p. (In Russian)

20. Vorontsov K.V., Potapenko A.A. Modifications of the EM algorithm for probabilistic thematic modeling. Mashinnoe obuchenie i analiz dannyh [Machine learning and data analy-sis], 2013, vol. 1, no. 6, pp. 657–686. (In Russian)

21. Wentzel E.S. Teoriya veroyatnostey [Probability theory]. Moscow, High School Publ., 2001. 575 p. (In Russian)

22. Zhmylev S.A., Aliev T.I. Queuing systems with polymodal flows. Nauchno-tekhnicheskij vestnik informacionnyh tekhnologij, mekhaniki i optiki [Scientific and Technical Journal of Information Technologies, Mechanics and Optics], 2018, vol. 18, no. 3, pp. 473-478. doi: 10.17586/2226-1494-2018-18-3-473-478. (In Russian)