Name: power-system stability in multi-machine networks
Uploaded: 2024-11-21T14:54:38.000Z
Duration: 1 min 25 s
Channel: JoVE

En un sistema de alimentación de N-bus con máquinas síncronas M, las cargas se modelan como admitancias constantes y se formulan ecuaciones nodales de red.
La matriz de admitancia se divide para incluir las admitancias de carga y las impedancias invertidas del generador.
Con voltajes de máquina conocidos, la ecuación de voltaje de bus se resuelve para encontrar las corrientes de la máquina y la potencia eléctrica.
El análisis de estabilidad transitoria requiere resolver ecuaciones de oscilación para máquinas y ecuaciones de flujo de potencia para la red.
Primero, ejecute un programa de flujo de energía previo a la falla para determinar los voltajes iniciales del bus, las corrientes de la máquina y las salidas eléctricas.
Establezca las salidas de potencia mecánica iguales a las salidas eléctricas e inicialice la frecuencia a la frecuencia angular síncrona.
A continuación, calcule las admitancias de carga, los voltajes internos de la máquina y la matriz de admitancia del bus de flujo de potencia.
Ajuste la matriz de admitancia para eventos como operaciones de conmutación, cambios de carga o fallas.
En cada paso de tiempo t más delta t, calcule la potencia eléctrica de la máquina, los ángulos de potencia y las velocidades.
Repita este proceso hasta alcanzar el horizonte de tiempo deseado, asegurándose de que el tamaño del paso equilibre la precisión de la solución y el tiempo de cálculo.

modelo simplificado de máquina síncrona

El análisis de estabilidad de múltiples máquinas es fundamental para comprender la dinámica y la estabilidad de los sistemas de potencia con múltiples máquinas sincrónicas. El objetivo es resolver las ecuaciones de oscilación para una red de M máquinas conectadas a un sistema de potencia de N buses.

Al analizar el sistema, las ecuaciones nodales representan la relación entre las tensiones de bus, las tensiones de máquina y las corrientes de máquina. La ecuación nodal viene dada por:

<img alt="Equation1" src="/files/ftp_upload/16170/16170_PT_Equation_1.svg" style="height: 44px;">

V es el vector N de tensiones de bus, E es el vector M de tensiones de máquina, I es el vector M de corrientes de máquina. Y11, Y12, Y21 e Y22 son matrices de admitancia N×N, N×M, M×N y M×M, respectivamente. Las ecuaciones se pueden desacoplar como:

<img alt="Equation2" src="/files/ftp_upload/16170/16170_PT_Equation_2.svg" style="height: 28px;">

Suponiendo que se conoce E, la primera ecuación se puede resolver iterativamente para V utilizando métodos como la eliminación de Gauss o Gauss-Seidel. Una vez que se calcula V, se puede obtener I a partir de la segunda ecuación.

La potencia eléctrica real de salida de la máquina n es:

<img alt="Equation3" src="/files/ftp_upload/16170/16170_PT_Equation_3.svg" style="height: 16px;">

El procedimiento de cálculo de estabilidad transitoria implica resolver iterativamente las ecuaciones de oscilación y las ecuaciones de flujo de potencia:

<ul style="padding-left: 35px; list-style-type: disc;">
	<li>Determinar las tensiones iniciales del bus V_k, las corrientes de la máquina I_n y las potencias de salida pan.</li>
	<li>Calcule E_n.</li>
	<li>Modifique Y_11 y calcule Y_22 y Y_12.</li>
	<li>Inicializar t=0.</li>
	<li>Determinar si hay operaciones de conmutación o cambios de carga.</li>
	<li>Calcular las potencias eléctricas de la máquina en el instante t.</li>
	<li>Utilice estimaciones iniciales para calcular los ángulos de potencia δ y las velocidades de la máquina ω en el momento t+Δt.</li>
	<li>Refinar las estimaciones de potencias eléctricas en el tiempo t+Δt.</li>
	<li>Finalizar los ángulos de potencia δ y las velocidades de la máquina ω en el tiempo t+Δt.</li>
	<li>Incrementa el tiempo y repite los pasos hasta el final de la simulación.</li>
	<li>La selección precisa del paso de tiempo es esencial para evitar la inestabilidad en la integración numérica.</li>
</ul>

Siguiendo estos pasos y utilizando las ecuaciones proporcionadas, los ingenieros pueden analizar la estabilidad transitoria de sistemas de energía de múltiples máquinas y garantizar un funcionamiento confiable en diversas condiciones.

Modelo simplificado de máquina síncrona

En un sistema de alimentación de N-bus con máquinas síncronas M, las cargas se modelan como admitancias constantes y se formulan ecuaciones nodales de red.
El...

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

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 is the N-vector of bus voltages, E is the M-vector of machine voltages, and I is the M-vector of machine currents. The admittance matrices Y11, Y12, Y21, and Y22 describe the connections between buses and machines.

These equations can be separated into two parts. If E is known, the first equation can be solved iteratively for V using Gauss elimination or Gauss-Seidel methods. After V is found, I can be calculated from the second equation. The real electrical power output of machine n is then determined from these values.

Transient stability is computed by stepping through time and solving the swing equations together with the power flow equations. The procedure starts with initial bus voltages Vk, machine currents In, and power outputs pan. Next, En is computed, Y11 is modified, and Y22 and Y12 are calculated. Time begins at t = 0, and the model checks for switching operations or load changes.

At each time step, the machine electrical powers are calculated at time t. Initial estimates are then used to find the power angles δ and machine speeds ω at time t + Δt. The electrical powers are refined at t + Δt, and the final values of δ and ω are obtained. The process repeats until the simulation ends.

Choosing a proper time step is important because it helps prevent numerical instability in the integration. With these equations and steps, engineers can analyze transient stability in multimachine power systems and judge how reliably the network will operate under changing conditions.

Power-System Stability in Multi-Machine Networks

power-system-stability-in-multi-machine-networks

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

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 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 multi-machine power systems use nodal equations, swing equations, and time-step simulation to test transient stability after switching or load changes.

Power-System Stability in Multi-Machine Networks | 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

Power-System Stability in Multi-Machine Networks

Description

Transcript

Tags