29.1
直列R-L回路の過渡現象
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)…
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。
View the full transcript and gain access to JoVE Core videos
Q1: What are the two main components of asymmetrical fault current in an R-L circuit?
Asymmetrical fault current consists of two components: the AC fault current (also called symmetrical or steady-state fault current), which follows a sinusoidal pattern, and the DC offset current, which decays exponentially over time. The DC offset's magnitude depends on the source angle and peaks at a specific phase angle. Together, these components determine the total fault current response when a switch closes in a series R-L circuit.
Q2: How does the DC offset current decay in a series R-L circuit?
The DC offset current decays exponentially with a time constant defined by the inductance-to-resistance ratio (L/R). The rate of decay depends directly on this ratio; higher inductance relative to resistance results in slower decay. The magnitude of the DC offset varies with the source angle, peaking when the source angle equals theta plus pi over two, which determines the maximum initial offset current.
Q3: What does a series R-L circuit model when the switch closes at time zero?
When the switch closes at time zero in a series R-L circuit with zero fault impedance and zero initial current, it simulates a three phase short circuit in an unloaded synchronous machine. The source voltage phase angle determines the initial voltage at the moment of switching. This setup allows engineers to analyze fault conditions and understand how circuit parameters affect the resulting fault current behavior.
Q4: How is the RMS asymmetrical fault current calculated?
The RMS asymmetrical fault current is calculated by multiplying the RMS AC fault current by an asymmetry factor that reflects the influence of the DC offset current. The calculation expresses the time constant and time in terms of cycles and frequency. As the time constant increases, the RMS current decreases, demonstrating that higher inductance-to-resistance ratios yield higher RMS current values.
Q5: What role does Kirchhoff's Voltage Law play in fault current analysis?
Kirchhoff's Voltage Law (KVL) is applied to the series R-L circuit to determine the total asymmetrical fault current and its two components. By analyzing the voltage equation across the resistor and inductor, engineers can derive expressions for both the AC and DC offset currents. This fundamental circuit analysis technique enables prediction of fault current magnitude and behavior under different source angle conditions.
Q6: Why does the maximum fault current occur at a specific source angle?
The magnitude of the DC offset current, which significantly contributes to the total asymmetrical fault current, varies with the source angle. The DC offset peaks when the source angle equals theta plus pi over two, resulting in the largest total fault current at this specific phase angle. Understanding this relationship helps engineers predict worst-case fault scenarios and design protective systems accordingly.
Q7: How does the reactance-to-resistance ratio affect RMS fault current?
Higher reactance-to-resistance ratios result in higher RMS asymmetrical fault current values. This ratio directly influences the time constant (L/R), which governs the decay rate of the DC offset component. Since the asymmetry factor depends on this time constant, circuits with greater inductance relative to resistance produce larger and more persistent fault currents, requiring more robust protective equipment.