ANALYSIS OF CONTEMPORARY METHODS FOR STEADY-STATE CALCULATION IN ELECTRICAL NETWORKS OF POWER SYSTEMS Rakhmonov I.U.1, Usmonov E.G.2, Ne'matov L.A.3
1Rakhmonov Ikromjon Usmonovich —DSc, Professor, 2Usmonov Eldor Ganievich- PhD, Prof., Tashkent State Technical University, Tashkent, Republic of Uzbekistan 3Ne'matov Laziz Alisherovich - Phd, Associate Professor, Bukhara Engineering-Technological Institute, Bukhara, Republic of Uzbekistan
Abstract: this paper provides a comprehensive analysis of existing methods for steady-state calculation in electrical networks, focusing on traditional approaches like Gauss-Seidel andNewton-Raphson, as well as modern computational techniques. The study evaluates these methods in the context of contemporary power systems, which are increasingly characterized by the integration of renewable energy sources and distributed generation. Comparative simulations demonstrate the convergence behavior and computational efficiency of the methods, highlighting their strengths and limitations. The paper concludes with a discussion on the applicability of these methods in modern power grids and suggests potential improvements to enhance their performance. Keywords: steady-state analysis, power flow, Gauss-Seidel method, Newton-Raphson method, electrical networks, renewable energy integration, distributed energy resources, computational efficiency, convergence analysis, modern power systems.
АНАЛИЗ СОВРЕМЕННЫХ МЕТОДОВ РАСЧЕТА УСТАНОВОЧНОГО СОСТОЯНИЯ В ЭЛЕКТРИЧЕСКИХ СЕТЯХ ЭНЕРГЕТИЧЕСКИХ СИСТЕМ Рахмонов И.У.1, Усмонов Э.Г.2, Неъматов Л.А.3
1Рахмонов Икромжон Усмонович - доктор технических наук, профессор, 2Усмонов Элдор Ганиевич - доктор технических наук, профессор, Ташкентский государственный технический университет, г. Ташкент, Республика Узбекистан 3Неъматов Лазиз Алишерович - кандидат технических наук, доцент, Бухарский инженерно-технологический институт, г. Бухара, Республика Узбекистан
Аннотация: в данной статье представлен комплексный анализ существующих методов расчета устойчивого состояния в электрических сетях с упором на традиционные подходы, такие как Гаусса-Зейделя и Ньютона-Рафсона, а также современные вычислительные методы. Исследование оценивает эти методы в контексте современных энергосистем, которые все больше характеризуются интеграцией возобновляемых источников энергии и распределенной генерации. Сравнительное моделирование демонстрирует поведение конвергенции и вычислительную эффективность методов, подчеркивая их сильные стороны и ограничения. Статья завершается обсуждением применимости этих методов в современных энергосетях и предлагает потенциальные улучшения для повышения их производительности.
Ключевые слова: анализ стационарного состояния, поток мощности, метод Гаусса-Зейделя, метод Ньютона-Рафсона, электрические сети, интеграция возобновляемых источников энергии, распределенные энергетические ресурсы, вычислительная эффективность, анализ конвергенции, современные энергосистемы.
UDC 621.311.12
Steady-state analysis, or load flow analysis, is crucial for the reliable operation and planning of power systems, providing key insights into voltage levels, power flows, and system losses [1, 2]. Traditional methods like Gauss-Seidel and Newton-Raphson have long been effective for conventional, centralized grids. However, the modern power grid, characterized by the integration of variable renewable energy sources, distributed energy resources, and increasing complexity, challenges these traditional approaches. This paper reviews existing methods, evaluates their effectiveness in contemporary power systems, and explores advancements in computational techniques to address the new complexities of modern grids [3].
This section introduces the fundamental equations used in steady-state power flow analysis [4, 5]. The power flow problem is generally described by the following equations: 1. Real Power Balance:
pí=ví^ vi(GH cos 8ij + Bu sin e.j)
2. Reactive Power Balance:
v
J=i
Qí = Ví^ Vj(Gíj sin 8íj - Bíj cos 8íj)
i=i
where, - Pt and Qt are the real and reactive power injections at bus i, V and V are the voltage magnitudes at buses i and j, Gy and By are the conductance and susceptance of the line between buses i and j, is the phase angle difference between buses i and \(j\).
The Gauss-Seidel method is an iterative technique used for solving systems of linear equations, particularly in power flow analysis of electrical networks. It is known for its simplicity and ease of implementation. The method works by iteratively updating the voltage at each bus in the network using the most recent values of the voltages. For each iteration, the voltage at a given bus is recalculated based on the power balance equations, while treating the other bus voltages as constants from the previous iteration.
v(k + 1) _ 1 I Pí íQí y v v(k)
v L YíjVJ
j=i,j* í
AP
AQ.
The Newton-Raphson method involves solving the linearized system of equations:
[A1A2I \A 01 \J2J22i [AVi
where/n,A2,J2i,J22 are the Jacobian matrix sub-blocks.
Discuss modern approaches like fast decoupled load flow, and machine learning-based methods. Simulation of a sample power network to demonstrate the differences in convergence between Gauss-Seidel and Newton-Raphson methods [6,7].
The Figure 1 illustrates the convergence behavior of the Gauss-Seidel and Newton-Raphson methods over successive iterations in a power flow analysis. The y-axis represents the error on a logarithmic scale, showing how much each method's solution deviates from the final steady-state solution. The x-axis represents the number of iterations.
n
Fig. 1. Convergence Comparison of Gauss-Seidel and Newton-Raphson Methods in Power Flow Analysis.
In this comparison, the Newton-Raphson method exhibits a faster rate of convergence, demonstrated by a steep decline in error within just a few iterations. In contrast, the Gauss-Seidel method converges more slowly, as shown by its gradual decline in error over iterations. This difference highlights Newton-Raphson's superior convergence speed and efficiency for power flow analysis, especially in large and complex networks, while Gauss-Seidel requires more iterations to reach a similar accuracy level. The figure effectively underscores the advantage of Newton-Raphson in achieving faster convergence, making it more suitable for modern power systems.
This paper analyzed traditional and modern methods for steady-state calculations in power systems, highlighting the strengths and limitations of the Gauss-Seidel and Newton-Raphson methods. While Newton-Raphson offers faster convergence, Gauss-Seidel is simpler but slower. The growing complexity of modern grids, with renewable integration and distributed generation, necessitates advanced techniques. Future research should focus on hybrid approaches that combine traditional methods with modern computational advancements, ensuring improved accuracy and efficiency in power flow analysis for contemporary and evolving power systems.
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