Jove
Visualize
Contact Us

Related Concept Videos

The Swing Equation01:21

The Swing Equation

1.2K
The Swing Equation is a fundamental tool in power system dynamics, especially for analyzing the behavior of generating units like three-phase synchronous generators. This equation emerges from applying Newton's second law to the rotor of a generator, encompassing factors such as inertia, angular acceleration, and the interplay between mechanical and electrical torques.
In a steady-state operation, the mechanical torque (Τm) supplied to the generator is balanced by the electrical torque (Τe)...
1.2K
The Power Flow Problem and Solution01:26

The Power Flow Problem and Solution

767
Power flow problem analysis is fundamental for determining real and reactive power flows in network components, such as transmission lines, transformers, and loads. The power system's single-line diagram provides data on the bus, transmission line, and transformer. Each bus k in the system is characterized by four key variables: voltage magnitude Vk​, phase angle δk​, real power Pk​, and reactive power Qk​. Two of these four variables are inputs, while the power flow program computes...
767
Multimachine Stability01:25

Multimachine Stability

514
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
514
Fast Decoupled and DC Powerflow01:24

Fast Decoupled and DC Powerflow

687
The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
687
Control of Power Flow01:30

Control of Power Flow

634
There are several methods to control power flow in power systems:
634
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

920
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
920

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Analytic solution to swing equations in power grids with ZIP load models.

PloS one·2023
Same author

Distributed optimal power flow.

PloS one·2021
See all related articles
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Video

Updated: Jan 3, 2026

Experimental Investigation of the Hierarchical Control in DC Microgrids Using a Real-time Simulator
06:04

Experimental Investigation of the Hierarchical Control in DC Microgrids Using a Real-time Simulator

Published on: February 14, 2025

961

Analytical solution to swing equations in power grids.

HyungSeon Oh1

  • 1Department of Electrical and Computer Engineering, United States Naval Academy, Annapolis, Maryland, United States of America.

Plos One
|November 20, 2019
PubMed
Summary
This summary is machine-generated.

Researchers derived a closed-form analytical solution for the power system swing equation. This new method accurately estimates system dynamics after faults without unphysical assumptions, improving stability assessments.

More Related Videos

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
04:35

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

Published on: July 5, 2024

2.3K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.9K

Related Experiment Videos

Last Updated: Jan 3, 2026

Experimental Investigation of the Hierarchical Control in DC Microgrids Using a Real-time Simulator
06:04

Experimental Investigation of the Hierarchical Control in DC Microgrids Using a Real-time Simulator

Published on: February 14, 2025

961
Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
04:35

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

Published on: July 5, 2024

2.3K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.9K

Area of Science:

  • Electrical Engineering
  • Applied Mathematics
  • Power Systems Analysis

Background:

  • The swing equation is a nonlinear second-order differential equation crucial for power system dynamics.
  • Existing methods for stability assessment involve computationally intensive simulations or simplified models with questionable assumptions.
  • A closed-form analytical solution for the swing equation has remained elusive due to system complexity.

Purpose of the Study:

  • To derive a closed-form analytical solution for the power system swing equation.
  • To provide a more accurate and efficient method for power system stability analysis.
  • To overcome limitations of existing computational and assumption-based approaches.

Main Methods:

  • Formulated the swing equation in the Cartesian coordinate system, deviating from conventional polar coordinate approaches.
  • Leveraged properties and operational conditions of electric power grids from existing literature.
  • Derived an analytical solution valid within a specific region.

Main Results:

  • The derived analytical solution demonstrates accurate estimation of power system dynamics post-fault.
  • Results obtained from the analytical solution show strong agreement with conventional methods.
  • The solution provides a computationally efficient alternative to digital simulations.

Conclusions:

  • A novel closed-form analytical solution for the swing equation has been successfully derived.
  • This solution offers accurate power system dynamics estimation without relying on unphysical assumptions.
  • The findings pave the way for improved and more reliable power system stability assessments.