27.6
電力システムでは、伝送線路の静電容量を理解することが効率的な運用の基本となります。
単相線
電圧源によって通電される、位相間隔が等しい単相 2 線式伝送線路を考えてみましょう。一方の導体は均一な正電荷を帯び、もう一方の導体は等しい負電荷を帯びます。線路の静電容量 C は、導体間の電圧 V から算出で…
電圧源によって通電される等相間隔の単相2線式伝送線路について考えてみましょう。一方の導体は均一な電荷を持ち、そのもう一方の導体は等しい負電荷を持っています。導体間電圧の式を適用し、シリンダ半径を代入すると、1メートルのラインの静電容量が計算されます。
接地されたセンタータップトランスによって供給されるラインの場合、各導体とグランド間の電圧と、いずれかのラインから接地されたニュートラルまでの静電容量が得られます。
これらの容量は、特定の回路表現で表されます。
次に、アースと中性導体の影響を無視した、位相間隔が等しい三相線を考えます。
正のシーケンス容量を決定するために、正のシーケンス電荷の合計はゼロであると仮定します。
ここで、導体間の電圧が計算され、続いて半径を代入します。
平衡正のシーケンス電圧の電圧方程式を思い出し、それらを加算し、電圧式を代入し、電荷関係を代入すると、ラインあたりの容量-中性値の長さが得られます。
対称性により、3つのフェーズすべてに同じ結果が適用されますが、バランスの取れた3フェーズ操作では、1つのフェーズのみが考慮されます。
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Q1: How is capacitance calculated for a single-phase two-wire transmission line?
Capacitance for a single-phase two-wire transmission line is derived from the voltage between conductors carrying equal and opposite charges. The capacitance per unit length depends on the permittivity of free space, the distance between conductors, and conductor radius. For a one-meter line section, these parameters are substituted into the capacitance formula to obtain the result.
Q2: What is the role of a grounded center tap transformer in single-phase transmission line capacitance?
A grounded center tap transformer establishes a reference point for voltage measurements in single-phase lines. It allows determination of the voltage between each conductor and ground, as well as the capacitance from either line to the grounded neutral. These capacitances are then represented in circuit models to accurately reflect transmission line behavior.
Q3: Why is the sum of positive-sequence charges assumed to be zero in three-phase transmission lines?
In balanced three-phase systems, the sum of positive-sequence charges is zero due to the symmetrical nature of the three phases. This assumption simplifies the voltage calculations between conductors and enables derivation of the capacitance-to-neutral per unit length. The same capacitance result applies to all three phases because of this inherent symmetry.
Q4: How does geometric mean distance affect capacitance in three-phase transmission lines?
Geometric mean distance represents the equivalent distance between conductors in three-phase lines with equal phase spacing. This distance is used in the capacitance-to-neutral formula to account for the interaction among the three phases. Using geometric mean distance ensures accurate representation of the capacitive effects in balanced three-phase systems.
Q5: What parameters determine the capacitance of a transmission line?
Transmission line capacitance is determined by the permittivity of free space, the distance between conductors, and the conductor radius. These physical parameters are substituted into the capacitance formula to calculate the capacitance per unit length. For three-phase lines, the geometric mean distance replaces simple conductor spacing in the calculation.
Q6: How does capacitance relate to series impedances in transmission line analysis?
Capacitance is a shunt parameter that works alongside series impedances to characterize transmission line behavior. While series impedances include resistance and inductance, capacitance represents the shunt admittance effects. Together, these parameters enable complete modeling of transmission line performance and are essential for series impedances three phase line analysis.
Q7: Why is capacitance analysis important for transmission line design?
Capacitance analysis is fundamental for understanding transmission line behavior and ensuring efficient power system operation. Accurate capacitance calculations enable proper circuit modeling, voltage regulation, and reactive power management. This knowledge is critical for transmission line design considerations and reliable system performance under various operating conditions.