Name: generator rotor motion and the swing equation
Uploaded: 2024-11-21T14:54:38.000Z
Duration: 1 min 21 s
Channel: JoVE

스윙 방정식(Swing Equation)은 3상 동기 발전기와 같은 발전 장치의 역학을 이해하는 데 중요합니다.
뉴턴의 제2법칙을 통해 회전자 운동을 설명하며 관성, 각가속도, 기계 및 전기 토크와 같은 요소를 통합합니다.
정상 상태에서 기계적인 것이 전기 토크와 같을 때 회전자 가속도와 가속 토크는 0이 되어 일정한 회전자 속도 또는 동기 속도를 유지합니다.
기계적 토크가 전기 토크를 초과할 때 로터 속도가 증가하고 그렇지 않으면 감소합니다.
동기식으로 회전하는 기준축을 기준으로 로터 위치를 측정하는 것이 고정식 회전축보다 더 편리합니다.
또한 단위당 전력으로 작업하면 정규화된 H 상수를 사용하는 것과 마찬가지로 계산이 단순화됩니다.
비선형 2차 미분 방정식인 단위당 스윙 방정식은 과도 안정성 연구에 필수적입니다.
이는 전력과 회전자 속도의 가변적인 특성을 고려합니다. 계산의 편의를 위해 두 개의 1계 미분 방정식으로 다시 작성됩니다.
스윙 방정식은 풍력 터빈 발전기의 로터 역학을 예측하는 데에도 사용됩니다.

스윙 방정식

The Swing Equation

스윙 방정식은 전력 시스템 역학에서 기본적인 도구로, 특히 3상 동기 발전기와 같은 발전 장치의 동작을 분석하는 데 유용합니다. 이 방정식은 뉴턴의 제2 법칙을 발전기의 회전자에 적용하여 관성, 각가속도, 기계적 토크와 전기적 토크 간의 상호 작용과 같은 요소를 포괄하여 도출되었습니다.

정상 상태 작동에서 발전기에 공급되는 기계적 토크(T_m)는 생성된 전기 토크(T_e)에 의해 균형을 이룹니다. 이 균형은 회전자의 각 가속도와 가속 토크(T_a)가 0이므로 일정한 회전자 속도 또는 동기 속도가 유지됨을 의미합니다. 이 균형에서 벗어나는 것은 T_m이 T_e를 초과하여 회전자 속도가 증가하거나 T_e가 T_m을 초과하여 회전자 속도가 감소할 때 발생합니다.

로터 위치(δ)는 일반적으로 고정된 축이 아닌 동기적으로 회전하는 기준 축을 기준으로 측정되므로 더 간단한 분석이 가능합니다. 또한, 전력을 나타내는 단위당(p.u.) 시스템을 사용하면 정규화된 관성 상수(H)를 사용하는 것과 마찬가지로 계산이 간소화됩니다. 비선형 2차 미분 방정식인 단위당 스윙 방정식은 다음과 같습니다.

<img alt="Equation1" src="/files/ftp_upload/16034/16034_PT%20Equation_1.svg" style="height: 36px;">

여기서 δ는 로터 각도이고, ω_syn은 동기 각속도이며, H는 정규화된 관성 상수입니다. 이 방정식은 과도 안정성 연구에 핵심이 되며, 전력과 로터 속도의 가변적 특성을 다룹니다.

계산의 편의를 위해 Swing 방정식은 종종 두 개의 1차 미분 방정식으로 재구성됩니다.

<img alt="Equation2" src="/files/ftp_upload/16034/16034_PT%20Equation_2.svg" style="height: 100px;">

이러한 변환을 통해 보다 효율적인 수치 적분과 시뮬레이션이 가능해졌습니다.

스윙 방정식의 역할은 풍속에 따라 기계적 토크가 변하는 풍력 터빈 발전기와 같이 변동 조건에서 로터 역학을 예측하는 데까지 확장됩니다. 이러한 역학을 정확하게 예측하는 것은 그리드 안정성을 유지하고 일시적인 교란이 시스템 불안정성이나 고장으로 이어지지 않도록 하는 데 매우 중요합니다. 따라서 스윙 방정식을 이해하고 적용하는 것은 현대 전력 시스템의 안정적인 작동과 제어에 필수적입니다.

스윙 방정식(Swing Equation)은 3상 동기 발전기와 같은 발전 장치의 역학을 이해하는 데 중요합니다.
그것은 로터 움직임을 설명합니다 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Transient Stability and System Controls

과도 안정도 및 계통 제어

KEY TERMS AND CONCEPTS

핵심 용어 및 개념

generator rotor motion and the swing equation

Generator rotor motion is described by the Swing Equation in power system dynamics. It is used to study generating units such as three-phase synchronous generators. The equation comes from Newton’s second law applied to the generator rotor. It links inertia, angular acceleration, and the balance between mechanical and electrical torques.

In steady-state operation, the mechanical torque supplied to the generator is equal to the electrical torque produced by the generator. When these torques match, the rotor has no angular acceleration. The accelerating torque is also zero, and the rotor keeps a constant speed called synchronous speed.

If the balance changes, the rotor speed changes too. When mechanical torque is greater than electrical torque, the rotor speeds up. When electrical torque is greater than mechanical torque, the rotor slows down. The rotor angle, written as δ, is measured relative to a synchronously rotating reference axis instead of a fixed stationary axis. This makes the analysis easier.

The Swing Equation is often written in the per-unit system, or p.u., which simplifies power calculations. It also uses the normalized inertia constant H. In this form, the Swing Equation is a nonlinear second-order differential equation. It is important for transient stability studies because both electrical power and rotor speed can change with time.

For numerical work, the equation is often rewritten as two first-order differential equations. This form is easier to integrate and simulate on a computer. The same ideas also help predict rotor behavior when mechanical torque varies, such as in wind turbine generators as wind speed changes. These calculations support grid stability and help prevent transient disturbances from causing system instability or failure.

Generator Rotor Motion and the Swing Equation

generator-rotor-motion-and-the-swing-equation

the swing equation

Generator rotor motion is described by the Swing Equation in power system dynamics. It is used to study generating units such as three-phase synchronous generators. The equation comes from Newton’s second law applied to the generator rotor. It links inertia, angular acceleration, and the balance between mechanical and electrical torques. In steady-state operation, the mechanical torque supplied to the generator is equal to the electrical torque produced by the generator. When these torques...

simplified synchronous machine model

Transient Stability in Synchronous Generators

The synchronous machine model helps students analyze transient stability in power systems. It represents a synchronous generator under balanced three-phase positive-sequence conditions. The model assumes constant excitation and ignores losses and saturation. These simplifications make it easier to study how a generator behaves during a disturbance. In this setup, the generator is connected to a network of transmission lines, transformers, loads, and other machines. That larger system is often...

multimachine stability

Power-System Stability in Multi-Machine Networks

Power-system stability in multi-machine networks focuses on how several synchronous machines behave as they stay connected to an N-bus power system. The analysis solves the swing equations for the machines and tracks how the network responds when conditions change. It is used to study transient stability, which is the system’s ability to stay in step after a disturbance. The network is written with nodal equations that link bus voltages, machine voltages, and machine currents. In this model, V...

wind turbine machine models

Wind Turbine Types and Generator Control

Wind turbine machine models are used to study how wind turbines behave in transient stability analysis. In this setting, induction machines and synchronous machines are the main model types. Induction machines are common because they are simple and reliable. Induction machines work through the rotating magnetic field made by the stator and rotor. A key term is slip, which is the difference between synchronous speed and rotor speed relative to synchronous speed. Slip is zero at synchronous...

generator voltage control

Voltage Regulation in Generators and Wind Turbines

Generator voltage regulation helps keep synchronous generators and wind turbines working stably. Older systems use a DC generator driven by the rotor to supply DC power to the rotor field winding. That power is passed through slip rings and brushes. Newer systems use static exciters or brushless exciters. A static exciter rectifies AC power from the generator terminals and sends DC power directly to the rotor. A brushless exciter uses an inverted synchronous generator, takes AC power from...

turbine-governor control

How Turbine Governors Stabilize Power Output

Turbine-governor control helps keep generator frequency and rotor speed stable when electrical load changes. It does this by matching turbine mechanical power with the power demand on the system. In a power grid, that balance is important for steady operation. Turbine-generator units also store kinetic energy because their parts are rotating. When load increases, that stored energy is released to help meet the demand. At first, electrical torque rises while mechanical torque stays nearly...

load-frequency control

Load-frequency control in power grids

Load-frequency control keeps a power grid stable when electrical demand changes. It helps keep system frequency and power flow within acceptable limits. Turbine-governor control reduces rotor speed changes after a load shift, but a steady-state frequency error can still remain when the turbine-governor reference setting does not change. In an interconnected power system, each area agrees to export or import a scheduled amount of power through tie-lines, which are the transmission lines that...

key terms and concepts

Learn how the Swing Equation describes generator rotor motion, torque balance, synchronous speed, and grid stability using the per-unit system.

Generator Rotor Motion and the Swing Equation | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Generator Rotor Motion and the Swing Equation

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