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

直列R-L回路を考えてみましょう。
スイッチがゼロに等しい時間に閉じると、無負荷の同期マシンの三相短絡を模倣します。
フォルトインピーダンスがゼロまたはボルトで固定されたフォルト、および初期電流がゼロの場合、ソース角度によって初期ソース電圧が決まります。
この回路のKVL方程式は、非対称のフォルト電流とその2つの成分の合計を算出します。
AC障害電流は、対称障害電流または定常障害電流とも呼ばれ、正弦波です。
DCオフセット電流は、インダクタンス対抵抗比として時定数で指数関数的に減衰します。
その大きさはソース角度によって異なり、ソース角度がシータプラス円周率を2にするとピークに達します。
最大の故障電流は、特定のソース角度で発生します。
次に、最大DCオフセットを持つrms非対称フォルト電流を計算し、サイクルと周波数の観点から時定数と時間を代入することにより、簡略化します。
この電流は、rms AC障害電流に非対称係数を掛けたものに等しく、rms電流はタウが増加するにつれて減少します。
リアクタンスと抵抗の比率が高いほど、rms電流の値が高くなります。

直列r-l回路の過渡現象

Series R&#8212;L Circuit Transients

直列抵抗器-インダクタ (R-L) 回路では、期間の開始時にスイッチを閉じると、無負荷同期機の 3 つの相すべてが短絡する障害状態である 3 相短絡がシミュレートされます。故障インピーダンスがなく、初期電流がない場合、初期電圧は電源電圧の位相角によって決まります。 
キルヒホッフの電圧法則 (KVL) を使用してこの回路を解析すると、2 つの主な要素で構成される非対称故障電流の合計を判定するのに役立ちます。対称故障電流または定常故障電流とも呼ばれる AC 故障電流は、正弦波パターンに従います。一方、DC オフセット電流は時間の経過とともに指数関数的に減少し、その減少率はインダクタンスと抵抗の比率によって定義されます。DC オフセットの大きさは電源角度によって変化し、電源の特定の位相角度でピークに達します。 
最大 DC オフセットを含む RMS 非対称故障電流の計算には、時定数と時間をサイクルと周波数で表すことが含まれます。この RMS 非対称電流は、RMS AC 故障電流に非対称係数を掛けて求められます。非対称係数は、DC オフセット電流の影響を反映します。時定数が増加すると、RMS 電流が減少します。これは、インダクタンスと抵抗の比率が電流に与える影響を示しています。リアクタンスと抵抗の比率が高いほど、RMS 電流値が高くなります。 
この分析は、電気回路の障害状態を理解し、そのようなイベントに対処するシステムを設計するために不可欠です。障害電流のさまざまなコンポーネントと回路パラメータへの依存性を考慮することで、エンジニアは電気システムの障害の影響をより正確に予測し、軽減することができます。この知識は、電力システムの信頼性と安全性を確保するために不可欠です。

直列R-L回路の過渡現象

直列R-L回路を考えてみましょう。
スイッチがゼロに等しい時間に閉じると、無負荷の同期マシンの三相短絡を模倣します。
...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Symmetrical and Unsymmetrical Faults

対称故障および非対称故障

KEY TERMS AND CONCEPTS

主要用語と概念

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Fault Current in a Series R-L Circuit

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