Name: fault current in a series r-l circuit
Uploaded: 2024-11-21T14:54:30.000Z
Duration: 1 min 22 s
Channel: JoVE

Si consideri un circuito in serie R-L.
Quando l'interruttore si chiude a un tempo pari a zero, imita un cortocircuito trifase in una macchina sincrona scarica.
Data un'impedenza di guasto pari a zero o un guasto imbullonato e una corrente iniziale pari a zero, l'angolo della sorgente determina la tensione iniziale della sorgente.
L'equazione KVL di questo circuito produce la corrente di guasto asimmetrica totale e le sue due componenti.
La corrente di guasto CA, chiamata anche corrente di guasto simmetrica o stazionaria, è una sinusoide.
La corrente di offset CC decade esponenzialmente con una costante di tempo come rapporto induttanza/resistenza.
La sua grandezza varia con l'angolo della sorgente, raggiungendo il picco quando l'angolo della sorgente è uguale a theta più pi su due.
La corrente di guasto più grande si verifica a un angolo di sorgente specifico.
La corrente di guasto asimmetrica rms con offset c.c. massimo viene quindi calcolata e semplificata sostituendo la costante di tempo e il tempo in termini di cicli e frequenza.
Questa corrente è uguale alla corrente di guasto c.a. rms moltiplicata per un fattore di asimmetria e la corrente efficace diminuisce all'aumentare della tau.
Rapporti reattanza / resistenza più elevati producono valori più elevati di corrente rms.

transitori del circuito di serie r-l

Series R&#8212;L Circuit Transients

In un circuito di serie resistore-induttore (R-L), la chiusura dell'interruttore all'inizio del periodo di tempo simula un cortocircuito trifase, ovvero una condizione di guasto in cui tutte e tre le fasi di una macchina sincrona scarica sono in cortocircuito. Quando non c'è impedenza di guasto e nessuna corrente iniziale, la tensione iniziale è determinata dall'angolo di fase della tensione sorgente.

Utilizzando la legge di tensione di Kirchhoff (KVL) per analizzare questo circuito si determina la corrente di guasto asimmetrica totale, che è formata da due componenti principali. La corrente di guasto CA, nota anche come corrente di guasto simmetrica o in stato stazionario, segue un andamento sinusoidale. D'altro canto, la corrente di offset CC diminuisce esponenzialmente nel tempo, con il suo tasso di decadimento definito dal rapporto tra l’induttanza e la resistenza. L'entità dell'offset CC varia con l'angolo della sorgente, raggiungendo il picco ad un angolo di fase specifico di quest’ultima.

Il calcolo della corrente di guasto asimmetrica RMS, incluso l'offset DC massimo, comporta l'espressione della costante di tempo e del tempo in termini di cicli e frequenza. Questa corrente asimmetrica RMS si trova moltiplicando la corrente di guasto AC RMS per un fattore di asimmetria. Il fattore di asimmetria riflette l'influenza della corrente di offset DC. All'aumentare della costante di tempo, la corrente RMS diminuisce, questo dimostra l'effetto del rapporto induttanza-resistenza sulla corrente. Rapporti più elevati tra la reattanza e la resistenza determinano valori di corrente RMS più elevati.

Quest’analisi è essenziale per comprendere le condizioni di guasto nei circuiti elettrici e per progettare dei sistemi per gestire tali eventi. Considerando le diverse componenti della corrente di guasto e la loro dipendenza dai parametri del circuito, gli ingegneri possono prevedere e mitigare meglio gli effetti dei guasti nei sistemi elettrici. Questa conoscenza è fondamentale per garantire l'affidabilità e la sicurezza dei sistemi di alimentazione.

Transitori del circuito di serie R-L

Si consideri un circuito in serie R-L.
Quando l'interruttore si chiude a un tempo pari a zero, imita un cortocircuito trifase in una macchina sincrona scarica.
...

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

Symmetrical and Unsymmetrical Faults

Guasti simmetrici e asimmetrici

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

fault current in a series r-l circuit

A series resistor-inductor, or R-L, circuit can model a three-phase short circuit when the switch closes at the start of the time period. In this fault condition, all three phases of an unloaded synchronous machine are short-circuited. With no fault impedance and no initial current, the starting voltage depends on the source voltage phase angle.

Kirchhoff's Voltage Law, or KVL, is used to analyze the circuit and find the total asymmetrical fault current. This current has two parts. The AC fault current, also called the symmetrical or steady-state fault current, follows a sinusoidal pattern. The DC offset current is the other part, and it decays exponentially with time. Its decay rate depends on the inductance-to-resistance ratio.

The size of the DC offset changes with the source angle. It reaches a maximum at a specific phase angle of the source. To calculate the RMS asymmetrical fault current, the time constant and time are written in terms of cycles and frequency. The result is found by multiplying the RMS AC fault current by an asymmetry factor.

That asymmetry factor shows how much the DC offset affects the current. As the time constant increases, the RMS current decreases. Higher reactance-to-resistance ratios produce higher RMS current values. This analysis helps explain fault conditions in electrical circuits and supports the design of systems that can handle them safely and reliably.

Fault Current in a Series R-L Circuit

series r&#8212;l circuit transients

A series resistor-inductor, or R-L, circuit can model a three-phase short circuit when the switch closes at the start of the time period. In this fault condition, all three phases of an unloaded synchronous machine are short-circuited. With no fault impedance and no initial current, the starting voltage depends on the source voltage phase angle. Kirchhoff's Voltage Law, or KVL, is used to analyze the circuit and find the total asymmetrical fault current. This current has two parts. The AC...

three-phase short circuit&#8212;unloaded synchronous machine

three-phase-short-circuitunloaded-synchronous-machine

Synchronous Machine Fault Current Decay

A three-phase short circuit on an unloaded synchronous machine shows how fault current changes over time. The AC fault current, with the DC offset removed, starts at a high value and then falls to a steady-state level in one phase of the machine. This change happens because of the magnetic flux created by the short-circuit armature currents. At first, these currents flow through high-reluctance paths. They later shift to lower-reluctance paths, which increases the armature inductance. This...

power system three-phase short circuits

Subtransient Fault Current in Power Systems

Subtransient fault current analysis in a power system uses simplified models for the main equipment. Transformers are represented by their leakage reactances. Transmission lines are modeled with equivalent series reactances, and synchronous machines are treated as constant voltage sources behind their subtransient reactances. Several elements are left out of the calculation because their effect on the immediate fault current is small or they make the model harder without changing the result...

bus impedance matrix

Three-Phase Fault Current Analysis

Three-phase fault current analysis in an N-bus power system uses the positive-sequence network and the bus impedance matrix. It helps estimate subtransient fault currents when a short circuit occurs at one bus. The method uses superposition, which means the problem is split into two circuits that are studied separately. In the first circuit, all machine voltage sources are short-circuited. Only the prefault voltage source at the faulted bus remains. The positive-sequence bus impedance matrix...

circuit breaker and fuse selection

Protective Devices in Power Systems

Circuit breakers and fuses protect electrical systems from fault current and overcurrent. They help stop damage when current rises above safe limits. Both devices are chosen based on the needs of the electrical system. A circuit breaker interrupts fault current by separating its contacts. This creates an arc, which must be extinguished by elongation, cooling, or splitting, depending on the breaker design. Breakers are grouped by operating voltage and by the arc-extinguishing medium, such as...

sequence networks of rotating machines

Generator Sequence Currents and Impedances

Generator sequence currents and impedances explain how a Y-connected synchronous generator behaves under balanced and unbalanced conditions. When the generator is grounded through a neutral impedance, it is set up to produce balanced internal phase voltages with only positive-sequence components. The source voltage therefore appears only in the positive-sequence network, and the line-to-ground voltages at the generator terminals show the sequence components of this setup. Zero-sequence current...

per-unit sequence models

Transformer Sequence Networks in Per Unit

Transformer sequence networks in per unit show how three-phase transformers respond to positive-, negative-, and zero-sequence currents. For an ideal Y-Y transformer grounded through neutral impedances, the per-unit sequence networks act much like those of a single-phase ideal transformer when the current is balanced. Balanced positive-sequence and negative-sequence currents do not create neutral current, so they do not cause voltage drops across the neutral path. Zero-sequence current behaves...

fault types

Power System Faults in Sequence Networks

Power system faults can be analyzed by moving between the phase domain and the sequence domain. This approach helps relate fault currents and voltages for three-phase bus faults and keeps the fault impedance in the model. Fault impedance is zero for a bolted fault, equal to the arc impedance for an arcing fault, and it represents the total fault impedance for a transmission-line insulator flashover. For a single line-to-ground fault from phase A to ground, the phase-domain conditions are...

key terms and concepts

Explore fault current in a series R-L circuit, including AC fault current, DC offset decay, RMS asymmetrical current, and the role of source angle.

Fault Current in a Series R-L Circuit | 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

Fault Current in a Series R-L Circuit

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