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

El modelo de máquina síncrona es crucial en los estudios de estabilidad transitoria.
Representa una máquina síncrona con un voltaje interno constante detrás de su reactancia transitoria de eje directo en condiciones de secuencia positiva trifásica equilibrada, excitación constante y sin pérdidas ni saturación.
Aquí, cada generador se conecta a un sistema compuesto por líneas de transmisión, transformadores, cargas y otras máquinas representadas por un bus infinito detrás de la reactancia del sistema.
Considere un generador síncrono conectado a una red o bus infinito con magnitud, fase y frecuencia de voltaje constante. Su potencia es una función sinusoidal del ángulo de potencia de la máquina.
Durante los transitorios, los voltajes internos y de bus se consideran constantes para los cálculos de potencia.
El criterio de áreas equivalentes se utiliza cuando se produce un cambio de escalón en la potencia mecánica. El rotor acelera debido a la inercia, sobrepasando su punto final de estado estacionario antes de estabilizarse debido a la amortiguación de las pérdidas mecánicas y eléctricas.
El criterio de áreas equivalentes se aplica a una sola máquina conectada a un bus infinito o a dos máquinas interconectadas.
Para sistemas de múltiples máquinas, la ecuación de oscilación no lineal de cada máquina se resuelve mediante integración numérica para determinar la estabilidad y el ángulo de potencia máximo.

modelo simplificado de máquina síncrona

El Modelo de Máquina Sincrónica es una herramienta fundamental para analizar y asegurar la estabilidad transitoria de los sistemas de potencia. Este modelo simplifica la representación de una máquina sincrónica en condiciones de secuencia positiva trifásica equilibrada, suponiendo una excitación constante e ignorando las pérdidas y la saturación. El modelo es fundamental para comprender el comportamiento de los generadores sincrónicos conectados a una red eléctrica, en particular durante eventos transitorios.

En este modelo, cada generador está conectado a un sistema que incluye líneas de transmisión, transformadores, cargas y otras máquinas, todas representadas por un bus infinito detrás de una reactancia del sistema. El concepto de bus infinito supone una magnitud de tensión, fase y frecuencia constantes, que sirven como punto de referencia para los análisis de estabilidad del sistema.

Si consideramos un generador síncrono conectado a la red, su potencia de salida es una función sinusoidal del ángulo de potencia de la máquina (δ). Esta relación se expresa como:
<img alt="Equation1" src="/files/ftp_upload/16169/16169_PT_Equation_001.svg" style="height: 50px;">
Donde V_bus es la tensión del bus, E^’ es el voltaje interno del generador y X_eq es la reactancia. Durante eventos transitorios, se supone que el voltaje interno E y la tensión del bus V permanecen constantes, lo que simplifica los cálculos de potencia.

El criterio de áreas iguales es un método gráfico que se utiliza para evaluar la estabilidad del sistema tras un cambio repentino en la potencia mecánica. Cuando se produce un cambio brusco, el rotor de la máquina sincrónica se acelera debido a su inercia, sobrepasando su posición final de estado estable antes de estabilizarse mediante los efectos de amortiguación de las pérdidas mecánicas y eléctricas. El criterio establece que el área que representa la potencia de aceleración (potencia mecánica menos potencia eléctrica) debe ser igual al área que representa la potencia de desaceleración para que el sistema vuelva a un punto de funcionamiento estable.

El criterio de áreas iguales es particularmente útil para analizar una sola máquina conectada a un bus infinito o dos máquinas interconectadas. Para sistemas más complejos con múltiples máquinas, el análisis de estabilidad transitoria requiere resolver la ecuación de oscilación no lineal de cada máquina mediante técnicas de integración numérica. Este enfoque tiene en cuenta las interacciones entre múltiples generadores y determina la estabilidad general del sistema y el ángulo de potencia máxima que puede soportar cada generador.

En resumen, el modelo de máquina síncrona, complementado con el criterio de áreas iguales y los métodos de integración numérica, proporciona un marco sólido para analizar y garantizar la estabilidad transitoria de los sistemas de energía. Comprender estos conceptos es esencial para mantener la estabilidad de la red, especialmente frente a perturbaciones y condiciones operativas variables.

Modelo simplificado de máquina síncrona

El modelo de máquina síncrona es crucial en los estudios de estabilidad transitoria.
Representa una máquina síncrona con un voltaje interno constante ...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Transient Stability and System Controls

Estabilidad Transitoria y Controles del Sistema

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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 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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