Name: transient stability in synchronous generators
Uploaded: 2024-11-21T14:54:38.000Z
Duration: 1 min 30 s
Channel: JoVE

Synchronous Machine Model은 과도 안정성 연구에서 매우 중요합니다.
이는 직접 축 뒤에 일정한 내부 전압이 있고, 균형 잡힌 3상 포지티브 시퀀스 조건, 일정한 여기 및 손실이나 포화가 없는 과도 리액턴스를 가진 동기 기계를 나타냅니다.
여기에서 각 발전기는 전송선, 변압기, 부하 및 시스템 리액턴스 뒤에 있는 무한 버스로 표시되는 기타 기계로 구성된 시스템에 연결됩니다.
그리드 또는 무한 버스에 일정한 전압 크기, 위상 및 주파수로 연결된 동기식 발전기를 생각해 보십시오. 그 힘은 기계 동력 각도의 사인파 함수입니다.
과도 상태 동안, 내부 및 버스 전압은 전력 계산을 위해 일정하게 간주됩니다.
동일 면적 기준은 기계적 동력에서 단계 변화가 발생할 때 사용됩니다. 로터는 관성으로 인해 가속되어 기계적 및 전기적 손실로 인한 댐핑으로 인해 안정화되기 전에 최종 정상 상태 지점을 초과합니다.
동일 면적 기준은 무한 버스에 연결된 단일 기계 또는 상호 연결된 두 기계에 적용됩니다.
다중 기계 시스템의 경우, 각 기계의 비선형 스윙 방정식은 안정성과 최대 출력 각도를 결정하기 위해 수치 적분을 사용하여 해결됩니다.

단순화된 동기식 기계 모델

Simplified Synchronous Machine Model

동기 기계 모델은 전력 시스템의 과도 안정성을 분석하고 보장하는 데 기본적인 도구입니다. 이 모델은 균형 잡힌 3상 양성 시퀀스 조건에서 동기 기계의 표현을 단순화하여 일정한 여기를 가정하고 손실과 포화를 무시합니다. 이 모델은 특히 과도 이벤트 중에 전력망에 연결된 동기 발전기의 동작을 이해하는 데 중요합니다.

이 모델에서 각 발전기는 송전선, 변압기, 부하 및 기타 기계를 포함하는 시스템에 연결되며, 이 모든 것은 시스템 리액턴스 뒤에 있는 무한 버스로 표현됩니다. 무한 버스 개념은 일정한 전압 크기, 위상 및 주파수를 가정하여 시스템 안정성 분석을 위한 기준점으로 사용합니다.

그리드에 연결된 동기 발전기를 고려할 때, 그 출력 전력은 기계의 전력 각도(δ)의 사인 함수입니다. 이 관계는 다음과 같이 표현됩니다.

<img alt="Equation1" src="/files/ftp_upload/16169/16169_PT_Equation_001.svg" style="height: 50px;">

여기서 V_bus는 버스 전압이고, E^’는 발전기의 내부 전압이며, X_eq는 리액턴스입니다. 과도 이벤트 동안 내부 전압 E과 버스 전압 V는 일정하게 유지된다고 가정하여 전력 계산을 간소화합니다.

동일 면적 기준은 기계적 전력의 급격한 변화에 따른 시스템의 안정성을 평가하는 데 사용되는 그래픽 방법입니다. 단계적 변화가 발생하면 동기식 기계의 회전자는 관성으로 인해 가속되어 기계적 및 전기적 손실의 감쇠 효과를 통해 안정화되기 전에 최종 정상 상태 위치를 초과합니다. 이 기준은 가속 전력(기계적 전력에서 전기적 전력을 뺀 값)을 나타내는 면적이 시스템이 안정적인 작동 지점으로 돌아가려면 감속 전력을 나타내는 면적과 같아야 한다고 명시합니다.

동일 면적 기준은 무한 버스에 연결된 단일 기계나 두 개의 상호 연결된 기계를 분석하는 데 특히 유용합니다. 더 복잡한 다중 기계 시스템의 경우 과도 안정성 분석에는 수치 적분 기술을 사용하여 각 기계의 비선형 스윙 방정식을 풀어야 합니다. 이 접근 방식은 여러 발전기 간의 상호 작용을 고려하고 각 발전기가 유지할 수 있는 전체 시스템 안정성과 최대 전력 각도를 결정합니다.

요약하자면, 동기식 기계 모델은 등면적 기준과 수치적 적분 방법으로 보완되어 전력 시스템의 과도 안정성을 분석하고 보장하기 위한 견고한 프레임워크를 제공합니다. 이러한 개념을 이해하는 것은 특히 교란과 다양한 작동 조건에 직면했을 때 그리드 안정성을 유지하는 데 필수적입니다.

Synchronous Machine Model은 과도 안정성 연구에서 매우 중요합니다.
그것은 뒤에 일정한 내부 전압이 있는 동기 기계를 나타냅니다 ...

Education

JoVE Core

Electrical Engineering

Unit 1

Transient Stability and System Controls

KEY TERMS AND CONCEPTS

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 represented by an infinite bus behind a system reactance. An infinite bus has constant voltage magnitude, phase, and frequency, so it serves as a stable reference for analysis.

For a synchronous generator connected to the grid, output power changes with the machine power angle, δ. The power follows a sinusoidal relationship with the bus voltage, the internal generator voltage E', and the equivalent reactance Xeq. During transient events, the internal voltage E and the bus voltage V are treated as constant, which simplifies the power calculation.

The Equal-Area Criterion is a graphical way to test stability after a sudden change in mechanical power. When a step change occurs, the rotor accelerates because of its inertia. It may overshoot its final steady-state position before damping from mechanical and electrical losses brings it back.

The criterion says the accelerating area, which is the difference between mechanical power and electrical power, must equal the decelerating area for the system to return to a stable operating point. This method is especially useful for a single machine connected to an infinite bus or for two interconnected machines. For more complex multi-machine systems, engineers solve each generator's nonlinear swing equation with numerical integration methods.

These calculations account for how multiple generators interact and help determine overall system stability. They also show the maximum power angle each generator can sustain. Together, the synchronous machine model, the Equal-Area Criterion, and numerical integration provide a practical framework for studying transient stability in power grids.

Transient Stability in Synchronous Generators

transient-stability-in-synchronous-generators

the swing equation

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...

simplified synchronous machine model

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

Explore how the synchronous machine model, infinite bus, and Equal-Area Criterion are used to study transient stability in power systems and grid behavior.

Transient Stability in Synchronous Generators | 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

Transient Stability in Synchronous Generators

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