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

The Synchronous Machine Model is crucial in transient stability studies.
It represents a synchronous machine with a constant internal voltage behind its direct axis transient reactance under balanced three-phase positive-sequence conditions, constant excitation, and no losses or saturation.
Here, each generator connects to a system composed of transmission lines, transformers, loads, and other machines represented by an infinite bus behind system reactance.
Consider a synchronous generator connected to a grid or infinite bus with constant voltage magnitude, phase, and frequency. Its power is a sinusoidal function of the machine power angle.
During transients, internal and bus voltages are considered constant for power calculations.
The Equal-Area Criterion is used when a step change occurs in mechanical power. The rotor accelerates due to inertia, overshooting its final steady-state point before stabilizing due to damping from mechanical and electrical losses.
The Equal-Area Criterion applies to a single machine connected to an infinite bus or two interconnected machines.
For multi-machine systems, each machine&#39;s nonlinear swing equation is solved using numerical integration to determine stability and maximum power angle.

vereenvoudigd synchroon machinemodel

Het Synchronous Machine Model is een fundamenteel hulpmiddel bij het analyseren en waarborgen van de transiënte stabiliteit van energiesystemen. Dit model vereenvoudigt de weergave van een synchrone machine onder gebalanceerde driefase positieve-sequentie omstandigheden, met constante excitatie en zonder verliezen of verzadiging. Het model is essentieel voor het begrijpen van het gedrag van synchrone generatoren die zijn aangesloten op een elektriciteitsnet, vooral tijdens transiënte gebeurtenissen.

In dit model is elke generator verbonden met een systeem dat transmissielijnen, transformatoren, belastingen en andere machines omvat, die allemaal worden weergegeven door een oneindige bus achter een systeemreactantie. Het oneindige busconcept gaat uit van een constante spanningsgrootte, fase en frequentie, die dienen als referentiepunt voor stabiliteitsanalyses van het systeem.

Bij het beschouwen van een synchrone generator die is aangesloten op het net, is het uitgangsvermogen een sinusvormige functie van de vermogenshoek van de machine (δ). Deze relatie wordt uitgedrukt als:

<img alt="Equation1" src="/files/ftp_upload/16169/16169_PT_Equation_001.svg" style="height: 50px;" />

Waar V_bus de busspanning is, E^’ de interne spanning van de generator is en X_eq de reactantie is. Tijdens transiënte gebeurtenissen wordt aangenomen dat de interne spanning E en de busspanning V constant blijven, wat vermogensberekeningen vereenvoudigt.

Het Equal-Area Criterion is een grafische methode die wordt gebruikt om de stabiliteit van het systeem te beoordelen na een plotselinge verandering in mechanisch vermogen. Wanneer een stapverandering optreedt, versnelt de rotor van de synchrone machine vanwege zijn traagheid, waarbij hij zijn uiteindelijke stationaire positie overschrijdt voordat hij stabiliseert door de dempende effecten van mechanische en elektrische verliezen. Het criterium stelt dat het gebied dat het versnellende vermogen vertegenwoordigt (mechanisch vermogen minus elektrisch vermogen) gelijk moet zijn aan het gebied dat het vertragende vermogen vertegenwoordigt, zodat het systeem terugkeert naar een stabiel werkpunt.

Het Equal-Area Criterion is met name handig voor het analyseren van een enkele machine die is aangesloten op een oneindige bus of twee onderling verbonden machines. Voor complexere systemen met meerdere machines vereist de transiënte stabiliteitsanalyse het oplossen van de niet-lineaire swingvergelijking van elke machine met behulp van numerieke integratietechnieken. Deze aanpak houdt rekening met de interacties tussen meerdere generatoren en bepaalt de algehele systeemstabiliteit en de maximale vermogenshoek die elke generator kan volhouden.

Samenvattend biedt het Synchronous Machine Model, aangevuld met het Equal-Area Criterion en numerieke integratiemethoden, een robuust raamwerk voor het analyseren en garanderen van de transiënte stabiliteit van energiesystemen. Het begrijpen van deze concepten is essentieel voor het handhaven van de stabiliteit van het net, met name in het geval van verstoringen en wisselende bedrijfsomstandigheden.

Vereenvoudigd synchroon machinemodel

The Synchronous Machine Model is crucial in transient stability studies.
It represents a synchronous machine with a constant internal voltage behind its ...

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Electrical Engineering

Elektrotechniek

Unit 1

Transient Stability and System Controls

Transiënte stabiliteit en systeemregelingen

KEY TERMS AND CONCEPTS

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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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