Name: transmission line power limits and loadability
Uploaded: 2024-11-21T14:54:26.000Z
Duration: 1 min 23 s
Channel: JoVE

損失の多いラインの最大電力フローは、フェーザ形式のABCDパラメータを使用して導き出されます。
送信側と受信側の電圧と電流の間のマトリックス関係によって、受信側と受信側の電流が決定され、受信側に供給される複雑な電力が計算されます。
これにより、受電側に供給される実電力と無効電力が導き出されます。
ロスレスラインに値を代入すると、有効電力の方程式が単純化されます。
理論上の最大有効電力または定常状態の安定限界は、位相角が総直列インピーダンス角と等しいときに発生します。
ただし、リアクタンスよりも直列インピーダンスが高いと、最大有効電力が減少します。
実際には、電力線は、定格端子電圧と90度の角変位に基づく理論上の最大電力を供給しません。
実際のライン負荷可能性曲線は、0.95 以下の電圧降下制限と 30 度から 35 度の最大角変位に基づく理論上の定常状態の安定限界の下にプロットされます。
25 km 未満の短線の場合、負荷性は、電圧降下や安定性ではなく、導体または端末機器の定格の熱定格によって制限されます。

最大電力潮流と線路負荷能力

損失伝送線路の最大電力潮流は、位相器形式の ABCD パラメータを使用して導出されます。これらのパラメータは、送信端と受信端の電圧と電流の間に行列関係を作成し、受信端の電流を決定できるようにします。この関係により、受信端に供給される複素電力の計算が容易になり、そこから有効電力と無効電力の成分が導出されます。

<img alt="Equation1" src="/files/ftp_upload/16148/16148_Equation%201.svg" style="height: 36px;">

<img alt="Equation2" src="/files/ftp_upload/16148/16148_Equation%202.svg" style="height: 36px;">

無損失線路の場合、簡略化により実電力の計算が効率化されます。

<img alt="Equation3" src="/files/ftp_upload/16148/16148_Equation%203.svg" style="height: 36px;">

理論上の最大有効電力、または定常安定性の限界は、送信端電圧と受信端電圧間の位相角が合計直列インピーダンス角に等しいときに発生します。

<img alt="Equation4" src="/files/ftp_upload/16148/16148_Equation%204.svg" style="height: 36px;">

ただし、直列インピーダンスがリアクタンスを超えると、供給される最大有効電力は減少します。

実際のシナリオでは、定格端子電圧と 90 度の角度変位に基づく制限により、電力線は理論上の最大電力を供給しません。その代わりに、理論上における定常安定性の限界の下にプロットされた実際の線路負荷曲線は、0.95 以下の電圧降下限界と 30 ～ 35 度の最大角度変位を考慮します。これらの実際の制約により、許容可能な電圧レベルを維持し、不安定性を回避するために角度変位を制限することで、電力システムの信頼性の高い動作が保証されます。

通常 25 km 未満の短い伝送線路の場合、負荷能力は電圧降下や安定性の問題ではなく、導体または端末機器の熱定格によって制限されます。これらの熱制限により、高電流条件下で機器が過熱して損傷や故障につながることがなくなります。

要約すると、インピーダンス特性、電圧制限、熱定格などの理論的および実際的な考慮事項は、伝送線路の最大電力潮流および線路負荷能力に影響します。これらの要素を管理することは、電力システムの安全で効率的な運用に不可欠です。

損失の多いラインの最大電力フローは、フェーザ形式のABCDパラメータを使用して導き出されます。
送信側と受信側の行列関係 ...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Steady-State Transmission Lines and Power Flows

定常状態の送電線と電力潮流

steady-state-transmission-lines-and-power-flows

KEY TERMS AND CONCEPTS

主要用語および概念

Maximum Power Flow and Line Loadability

transmission line power limits and loadability

Transmission line power limits and loadability depend on voltage, angle, and line impedance. For lossy transmission lines, ABCD parameters in phasor form are used to relate sending-end and receiving-end voltages and currents. This matrix relation makes it possible to find the receiving-end current and then calculate the complex power delivered to the load.

From the complex power, the real and reactive power components can be determined. For a lossless line, the equations become simpler, and the real power calculation is easier to handle. The theoretical maximum real power, also called the steady-state stability limit, occurs when the phase angle between the sending-end and receiving-end voltages equals the total series impedance angle.

If the series impedance is larger than the reactance, the maximum real power that can be delivered drops. In real power systems, lines usually do not operate at this theoretical limit. The practical line loadability curve stays below the stability limit because it must respect rated terminal voltages and a 90-degree angular displacement limit.

This practical curve also uses a voltage-drop limit of 0.95 or less and a maximum angular displacement of about 30 to 35 degrees. These limits help keep voltage levels acceptable and reduce the risk of instability. For short transmission lines, usually under 25 kilometers, loadability is not set by voltage drop or stability. Instead, the main limit is thermal rating, which keeps the conductor and terminal equipment from overheating under high current.

Transmission Line Power Limits and Loadability

transmission-line-power-limits-and-loadability

transmission-line differential equations

Modeling Voltage and Current on Transmission Lines

Transmission lines carry electric power, and their resistance, inductance, and capacitance are spread out along the line. Because these properties are distributed per unit length, voltage and current change as they move from one end of the line to the other. Differential equations are used to describe that variation. A line-section model helps show how this works. In the model, a small length, Δx, is used to represent the line. Voltage V(x) and current i(x) are measured from the receiving end.

lossless lines

Lossless Lines and Voltage Behavior

Lossless transmission lines in electrical engineering are described by a purely imaginary propagation constant and a resistive characteristic impedance. Their ABCD parameters show an equivalent pi circuit with an imaginary series impedance and a shunt admittance. When the product of beta and line length is less than pi, the line has inductive series impedance and capacitive shunt admittance, which keeps it lossless. Wavelength is the physical length over which voltage or current phase changes...

maximum power flow and line loadability

Transmission line power limits and loadability depend on voltage, angle, and line impedance. For lossy transmission lines, ABCD parameters in phasor form are used to relate sending-end and receiving-end voltages and currents. This matrix relation makes it possible to find the receiving-end current and then calculate the complex power delivered to the load. From the complex power, the real and reactive power components can be determined. For a lossless line, the equations become simpler, and...

the power flow problem and solution

Power Flow Analysis in Electric Networks

Power flow analysis helps determine how real and reactive power move through an electric network. It uses the system’s single-line diagram, which shows the buses, transmission lines, transformers, and loads. The analysis focuses on balanced three-phase steady-state operation. Each bus in the system has four key variables: voltage magnitude V k, phase angle δ k, real power P k, and reactive power Q k. Two of these four variables are treated as inputs. The power flow program solves for the...

control of power flow

Voltage and Reactive Power Control

Voltage and reactive power control help keep a power system stable and efficient. In this topic, generator settings, switched equipment, and transformer taps work together to guide how power moves through the network. A generator can be modeled with a Thevenin equivalent circuit under balanced steady-state conditions. The main terms are terminal voltage Vt, excitation voltage Eg, power angle δ, and positive-sequence synchronous reactance Xg. From this model, the generator current and the...

fast decoupled and dc powerflow

Power Flow Shortcuts for Grid Contingencies

Fast decoupled power flow and DC power flow give engineers faster ways to study a power system during contingencies such as generator outages or transmission line failures. These methods help operators get quick power flow solutions, which is important for real-time system adjustments. Fast decoupled power flow simplifies the Jacobian matrix, the set of equations used in power flow calculations, by neglecting some elements. The method drops J2 and J3 and assumes voltage magnitudes stay close...

key terms and concepts

Learn how ABCD parameters, voltage limits, stability, and thermal ratings set maximum power flow and loadability in transmission lines.

Transmission Line Power Limits and Loadability | 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

Transmission Line Power Limits and Loadability

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