This paper shows the development of transmission line model, based on lumped element circuit that provides answers directly in the time and phase domain. This model is valid to represent the ideally transposed line, t...This paper shows the development of transmission line model, based on lumped element circuit that provides answers directly in the time and phase domain. This model is valid to represent the ideally transposed line, the phases of each of the small line segments are separated in their modes of propagation and the voltage and current are calculated at the modal domain. However, the conversion phase-mode-phase is inserted in the state equations which describe the currents and voltages along the line of which there is no need to know the user of the model representation of the theory in the line modal domain.展开更多
Clarke’s matrix has been applied as a phase-mode transformation matrix to three-phase transmission lines substituting the eigenvector matrices. Considering symmetrical untransposed three-phase lines, an actual symmet...Clarke’s matrix has been applied as a phase-mode transformation matrix to three-phase transmission lines substituting the eigenvector matrices. Considering symmetrical untransposed three-phase lines, an actual symmetrical three-phase line on untransposed conditions is associated with Clarke’s matrix for error and frequency scan analyses in this paper. Error analyses are calculated for the eigenvalue diagonal elements obtained from Clarke’s matrix. The eigenvalue off-diagonal elements from the Clarke’s matrix application are compared to the correspondent exact eigenvalues. Based on the characteristic impedance and propagation function values, the frequency scan analyses show that there are great differences between the Clarke’s matrix results and the exact ones, considering frequency values from 10 kHz to 1 MHz. A correction procedure is applied obtaining two new transformation matrices. These matrices lead to good approximated results when compared to the exact ones. With the correction procedure applied to Clarke’s matrix, the relative values of the eigenvalue matrix off-diagonal element obtained from Clarke’s matrix are decreased while the frequency scan results are improved. The steps of correction procedure application are detailed, investigating the influence of each step on the obtained two new phase-mode transformation matrices.展开更多
The second-order differential equations that describe the transmission line are difficult to solve due to the mutual coupling among phases and the fact that the parameters are distributed along their length. A method ...The second-order differential equations that describe the transmission line are difficult to solve due to the mutual coupling among phases and the fact that the parameters are distributed along their length. A method for the analysis of polyphase systems is the technique that decouples their phases. Thus, a system that has n phases coupled can be represented by n decoupled single-phase systems which are mathematically identical to the original system. Once obtained the n-phase circuit, it’s possible to calculate the voltages and currents at any point on the line using computational methods. The Universal Line Model (ULM) transforms the differential equations in the time domain to algebraic equations in the frequency domain, solve them and obtain the solution in the frequency domain using the inverse Laplace transform. This work will analyze the method of modal decomposition in a three-phase transmission line for the calculation of voltages and currents of the line during the energizing process.展开更多
文摘This paper shows the development of transmission line model, based on lumped element circuit that provides answers directly in the time and phase domain. This model is valid to represent the ideally transposed line, the phases of each of the small line segments are separated in their modes of propagation and the voltage and current are calculated at the modal domain. However, the conversion phase-mode-phase is inserted in the state equations which describe the currents and voltages along the line of which there is no need to know the user of the model representation of the theory in the line modal domain.
文摘Clarke’s matrix has been applied as a phase-mode transformation matrix to three-phase transmission lines substituting the eigenvector matrices. Considering symmetrical untransposed three-phase lines, an actual symmetrical three-phase line on untransposed conditions is associated with Clarke’s matrix for error and frequency scan analyses in this paper. Error analyses are calculated for the eigenvalue diagonal elements obtained from Clarke’s matrix. The eigenvalue off-diagonal elements from the Clarke’s matrix application are compared to the correspondent exact eigenvalues. Based on the characteristic impedance and propagation function values, the frequency scan analyses show that there are great differences between the Clarke’s matrix results and the exact ones, considering frequency values from 10 kHz to 1 MHz. A correction procedure is applied obtaining two new transformation matrices. These matrices lead to good approximated results when compared to the exact ones. With the correction procedure applied to Clarke’s matrix, the relative values of the eigenvalue matrix off-diagonal element obtained from Clarke’s matrix are decreased while the frequency scan results are improved. The steps of correction procedure application are detailed, investigating the influence of each step on the obtained two new phase-mode transformation matrices.
文摘The second-order differential equations that describe the transmission line are difficult to solve due to the mutual coupling among phases and the fact that the parameters are distributed along their length. A method for the analysis of polyphase systems is the technique that decouples their phases. Thus, a system that has n phases coupled can be represented by n decoupled single-phase systems which are mathematically identical to the original system. Once obtained the n-phase circuit, it’s possible to calculate the voltages and currents at any point on the line using computational methods. The Universal Line Model (ULM) transforms the differential equations in the time domain to algebraic equations in the frequency domain, solve them and obtain the solution in the frequency domain using the inverse Laplace transform. This work will analyze the method of modal decomposition in a three-phase transmission line for the calculation of voltages and currents of the line during the energizing process.
