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

Considere um circuito R-L em série.
Quando a chave fecha em um momento igual a zero, ela imita um curto-circuito trifásico em uma máquina síncrona sem carga.
Dada a impedância de falta zero ou uma falha aparafusada e corrente inicial zero, o ângulo da fonte determina a tensão inicial da fonte.
A equação KVL deste circuito produz a corrente de falta assimétrica total e seus dois componentes.
A corrente de falha CA, também chamada de corrente de falha simétrica ou em estado estacionário, é uma senóide.
A corrente de deslocamento CC decai exponencialmente com uma constante de tempo como a relação indutância / resistência.
Sua magnitude varia com o ângulo da fonte, atingindo o pico quando o ângulo da fonte é igual a mais pi sobre dois.
A maior corrente de falha ocorre em um ângulo de fonte específico.
A corrente de falta assimétrica rms com deslocamento CC máximo é então calculada e simplificada substituindo a constante de tempo e o tempo em termos de ciclos e frequência.
Essa corrente é igual à corrente de falha rms AC vezes um fator de assimetria e a corrente rms diminui à medida que a tau aumenta.
Taxas de reatância para resistência mais altas produzem valores mais altos de corrente rms.

transientes de circuito série r-l

Series R&#8212;L Circuit Transients

Em um circuito resistor-indutor série (R-L), fechar o interruptor no início do período de tempo simula um curto-circuito trifásico, uma condição de falha em que todas as três fases de uma máquina síncrona descarregada são curto-circuitadas. Quando não há impedância de falha e nenhuma corrente inicial, a tensão inicial é determinada pelo ângulo de fase da tensão da fonte.


 Usar a Lei de Tensão de Kirchhoff (KVL) para analisar este circuito ajuda a determinar a corrente de falha assimétrica total, que consiste em dois componentes principais. A corrente de falha CA, também conhecida como corrente de falha simétrica ou de estado estável, segue um padrão sinusoidal. Por outro lado, a corrente de deslocamento CC diminui exponencialmente ao longo do tempo, com sua taxa de decaimento definida pela razão de indutância para resistência. A magnitude do deslocamento CC varia com o ângulo da fonte, atingindo o pico em um ângulo de fase específico da fonte.


 O cálculo da corrente de falha assimétrica RMS, incluindo o deslocamento CC máximo, envolve expressar a constante de tempo e o tempo em termos de ciclos e frequência. Essa corrente assimétrica RMS é encontrada multiplicando a corrente de falha CA RMS por um fator de assimetria. O fator de assimetria reflete a influência da corrente de deslocamento CC. À medida que a constante de tempo aumenta, a corrente RMS diminui, o que demonstra o efeito da relação indutância-resistência na corrente. Maiores relações de reatância para resistência resultam em maiores valores de corrente RMS.


 Essa análise é essencial para entender as condições de falha em circuitos elétricos e projetar sistemas para lidar com tais eventos. Ao considerar os diferentes componentes da corrente de falha e sua dependência dos parâmetros do circuito, os engenheiros podem prever e mitigar melhor os efeitos das falhas em sistemas elétricos. Esse conhecimento é essencial para garantir a confiabilidade e a segurança dos sistemas de energia.

Transientes de Circuito Série R-L

Considere um circuito R-L em série.
Quando a chave fecha em um momento igual a zero, ela imita um curto-circuito trifásico em uma máquina síncrona sem carga.
...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Symmetrical and Unsymmetrical Faults

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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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