# ГОЛОМОРФНОЕ ПОГРУЖЕНИЕ КАК АНАЛИТИЧЕСКИЙ МЕТОД РАСЧЕТА ЭЛЕКТРИЧЕСКИХ СЕТЕЙ НЕФТЯНЫХ И ГАЗОВЫХ МЕСТОРОЖДЕНИЙ

Translated title of the contribution: Holomorphic embedding as analytical technique for calculating electric grids of oil and gas deposits

Yusup N. Isaev, Dmitry A. Kabalin

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

## Abstract

In order to ensure the required level of reliable operation of oil production, it is necessary to pay attention to the operating conditions of the power system. This is important if we take into account that for oil and gas extraction the powerful sources of energy that significantly affect the mode of operation of the power grid are needed. In this case, the urgent task is to calculate the steady-state modes of the oil production electric network. The calculations of the established modes are of great practical importance to ensure efficient and safe management of the operating modes of oil and gas enterprises, and are important in the design of electrical networks for oil and gas enterprises. However, the application of classical iterative methods for calculating steady-state regimes, such as the Gauss-Seidel and Newton-Raphson methods, does not always allow finding the right solution, since the convergence of these methods depends on initial conditions. The method is based on the Padé approximation and the perturbation method. The paper demonstrates the disadvantages and the advantages of the proposed method over the well-known Gauss-Seidel and Newton-Raphson iteration method and the examples of solving the problems of electric power chains. The problems of sustainability are considered. The aim of the research is to apply the analytical method of holomorphic embedding to calculate two and three nodal energy schemes; compare the capabilities of the method with other alternative methods; investigate the limitations of the holomorphic embedding method and show the area of its work. Methods: Taylor expansion, analytic continuation, solving algebraic equations by the recurrent method, infinite fractions. Results. The authors gave the examples of using the holomorphic embedding method for two and three PQ nodal circuits, and showed the shortcomings of the holomorphic embedding method. The holomorphic embedding method is compared with alternative methods. Conclusions. The analytical method of holomorphic embedding has several advantages: physical visibility; the simplicity of the algorithmic implementation consisting in recurrence relations for the coefficients of the expansion of the desired function in a Taylor series. The function laid out in a series is holomorphic, which allows analytic continuation of a function to obtain the desired accuracy of solution.

Translated title of the contribution Holomorphic embedding as analytical technique for calculating electric grids of oil and gas deposits Russian 115-125 11 Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering 331 4 https://doi.org/10.18799/24131830/2020/4/2599 Published - 2020

## ASJC Scopus subject areas

• Materials Science (miscellaneous)
• Fuel Technology
• Geotechnical Engineering and Engineering Geology
• Waste Management and Disposal
• Economic Geology
• Management, Monitoring, Policy and Law