## Abstract

To effectively solve the problems of operational dispatch control of the operating modes of the unified power system, its individual power systems and power districts, in particular, oil production power districts, it is required to carry out calculations of the established modes of electrical networks. In addition, along with the calculations of steady-state regimes, it is important to study the stability of the power grid operation. The convergence and rate of convergence of widely used iterative methods for calculating steady-state modes depend on many operating and design factors determined by the network and mode parameters, the choice of initial approximations, and the method for specifying the initial data. Therefore, the development of new methods that make it possible to calculate all steady-state regimes are of significant practical interest. One of the promising techniques is the holomorphic imbedding method. In this method, the unknown parameters of the nodes are represented in the form of holomorphic functions, which can be written in the form of power series, the coefficients of which are calculated using recurrent expressions, and the problem is reduced to finding the coefficients of the power series. In a previously published article by the authors, the method is considered for a circuit with load nodes. For a complete correct analysis of the modes of real power systems, it is necessary to show how to calculate for generating units. The paper presents recurrent expressions for calculating the unknown coefficients of the holomorphic functions of the unknown parameters of the system of steady-state equations for the load and generator nodes. The expressions obtained, in contrast to those proposed in the works of other authors, are more general. The principle of forming a matrix equation for finding unknown coefficients with the division of complex parameters into real and imaginary parts is shown. A method for obtaining converging power-law in some cases is proposed. On the example of a test power system, the advantage over the Newton–Raphson method is shown. We consider the question of evaluating the existence of a solution to the system of equations of the steady state for a multinode network based on a sigma-graph. An approach is proposed to determine the indicator of the static stability margin of the power system, based on the Fabry criterion. The aim of the research is to apply the analytical method of holomorphic imbedding to calculate an electrical circuit containing load and generator units; to evaluate the influence of the number of calculated power series coefficients on the accuracy of the obtained solution, and also to consider ways to increase the numerical accuracy of the solution, consider the question of evaluating the existence of a solution to the system of equations of the steady state for a multi-node network based on the analysis of power series. Methods: Taylor expansion, analytic continuation, Padé approximation, solving algebraic equations by the recursive method. Results. Using the example of a scheme with a poorly conditioned Jacobi matrix, in which the Newton–Raphson method does not converge from a flat start, the advantage of the holomorphic immersion method is shown. The influence of the number of members of the power series on the calculation error is shown. For the considered scheme, a graphical estimate of the existence of a solution to the system of equations is performed. Conclusions. For load and generator nodes, the unknown parameters can be represented as holomorphic functions, which can be written down as a Taylor series, the coefficients of which are calculated using recurrent expressions. Partial consideration of shunts to the ground in the diagonal elements of the matrix of successive conductances makes it possible to obtain converging power series in some cases. The considered graphical method for assessing the possibility of the regime existence allows us to make a rough estimate. Unlike classical iterative methods, an initial approximation is not specified for the holomorphic immersion method.

Translated title of the contribution | Holomorphic embedding as analytical technique for calculating electric grids of oil and gas deposits and assessing their stability |
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Original language | Russian |

Pages (from-to) | 214-228 |

Number of pages | 15 |

Journal | Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering |

Volume | 332 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2021 |

## 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