27.6
Capacitancia: línea monofásica y trifásica
En los sistemas de energía eléctrica, comprender la capacitancia de las líneas de transmisión es fundamental para un funcionamiento eficiente.
Líneas…
Considere una línea de transmisión monofásica de dos hilos con igual espaciado de fase energizada por una fuente de voltaje. Un conductor lleva una carga uniforme y su contraparte tiene una carga negativa igual. Aplicando la fórmula para el voltaje entre conductores y sustituyendo los radios de los cilindros, se calcula la capacitancia para una línea de un metro.
Para las líneas alimentadas por un transformador de derivación central conectado a tierra, se obtiene el voltaje entre cada conductor y tierra y la capacitancia de cualquiera de las líneas al neutro conectado a tierra.
Estas capacitancias se representan en representaciones de circuitos específicos.
A continuación, considere una línea trifásica con el mismo espaciado de fase, sin tener en cuenta los efectos de tierra y conductor neutro.
Para determinar la capacitancia de secuencia positiva, se supone que la suma de las cargas de secuencia positiva es cero.
Ahora, se calcula el voltaje entre los conductores, seguido de la sustitución de los radios.
Recordando las ecuaciones de voltaje para voltajes de secuencia positiva balanceados, sumándolos, sustituyendo las expresiones de voltaje, y la relación de carga da la capacitancia a neutro por longitud de línea.
Los mismos resultados se aplican a las tres fases debido a la simetría, pero para una operación trifásica equilibrada, solo se considera una fase.
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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.