Frequency analysis of generalized time-fractional telegrapher's equation

Cvetićanin, Stevan M.; Rapaić, Milan R.; Zorica, Dušan

doi:10.1109/ecctd.2017.8093252

Cited by 4 publications

(4 citation statements)

References 14 publications

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“…which proves that the magnitudes of U(x) and I(x) also follow elliptic formula. Note that, ω is the excitation frequency and parameters of a, b, and Z c are all dependent on ω, so the elliptic formula, that is Equation (18), is not only applicable for fundamental frequency, but also for harmonic frequencies. Key parameters of ellipses (focus points, semi-major axis, semi-minor axis and eccentricity) shown in Equations ( 12), ( 13), (18) are illustrated in Table 1.…”

Section: > > mentioning

confidence: 99%

“…Moreover, if the line is long enough to be a quarter length, there is always a maximum voltage or current along the line, for example for the 31th and 33rd-harmonic as discussed above. However, there can also be one the maximums even if the line is smaller than a quarter of wavelength, depending on the starting point which is based on the angle and magnitude of harmonic injection according to (18).…”

Section: From Busmentioning

confidence: 99%

“…This paper can fill this gap by analysing the distribution of harmonics along power lines that could lead to overvoltage or overcurrent problems within it. Telegrapher's equations have been early proposed in References [16][17][18] that the voltage and current spatial propagation are characterised. These equations are utilised as the basis of ellipse formulae in this paper, however, the elliptical relationship between voltage and current along the power line and the impact factors of the different shapes of ellipses have not been analysed, from which, one can obtain the relationship between peak voltage and peak current along a power line.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A study of harmonic spatial propagation along AC power lines of meshed power systems

Liu

Zhang

Silva

et al. 2022

IET Circuits, Devices & Syst

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Severe harmonics propagation in power systems may result in increased power losses and equipment damages. In this paper, an elliptic formula is derived to analyse the harmonic spatial distribution not only at the substations but also along the power lines or cables and to give a system‐wide overview of harmonic levels. It is observed that harmonic distortion along power lines can be higher than that at the busbars and the maximum amplitude of harmonic voltage and current denoted as weak positions along power lines depends on the steady‐state harmonic angle difference of voltage and current at busbars, the length of power lines, and the harmonic order. All cases are modelled in detail by analytical geometry and analysed in MATLAB. In this regard, a method to identify the weak positions in terms of maximum harmonic levels in a power system is presented, and its corresponding harmonic orders are determined. The accuracy of the model is tested using time‐domain simulations in PSCAD/EMTDC.

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Section: > > mentioning

confidence: 99%

Section: From Busmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A study of harmonic spatial propagation along AC power lines of meshed power systems

Liu

Zhang

Silva

et al. 2022

IET Circuits, Devices & Syst

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“…Here, fractional complex transform was invoked on the fractional nonlinear equations of nonlinear capacitance and applied voltage. Stevan et al [31] observed the fractional modeling of generalized time-fractional telegrapher's equation that described the transmission line. The performance frequency analysis was based on the generalization of elementary circuit in which memory effects of inductive and capacitive phenomena were achieved.…”

Section: Introductionmentioning

confidence: 99%

Analytical and fractional model for power transmission of lossy transmission line

Abro,

Atangana,

Memon

et al. 2024

International Journal of Modelling and Simulation

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A lossy transmission line can draw current from DC source if DC voltage is applied to constant resistance that's why surge impedance become uniform on lossy transmission line. This manuscript proposes the analytical and fractional modeling of lossy transmission line based on partial differential equations by employing Kirchoff's current and voltage laws via Fourier analysis. The governing equation of lossy transmission line is fractionalized by means of modern fractional differential operators. The optimal solution of voltage is investigated by means of Fourier sine and Laplace transforms subject to the imposed conditions.The investigated solutions of voltage over the transmission line have been established in terms of exponential and gamma functions. The comparative analysis of voltage over the transmission line through Caputo-Fabrizio and Atangana-Baleanu fractional operators have been presented for line losses on the conductance, resistance and inductance for the confirmation of the principle of electric power transmission.

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Frequency Characteristics of Two Topologies Representing Fractional Order Transmission Line Model

Cvetićanin

Zorica

Rapaić

2019

Circuits Syst Signal Process

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Frequency analysis of generalized time-fractional telegrapher's equation

Cited by 4 publications

References 14 publications

A study of harmonic spatial propagation along AC power lines of meshed power systems

A study of harmonic spatial propagation along AC power lines of meshed power systems

Analytical and fractional model for power transmission of lossy transmission line

Frequency Characteristics of Two Topologies Representing Fractional Order Transmission Line Model

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