May 2008
Intermediate to advanced
340 pages
9h 41m
English
Content preview from Electrical Power System Essentials
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A.6 CIRCUIT MODELING
It is the electrical size of the structure – its size in terms of the minimum wavelength of interest in the bandwidth over which the model must be valid – that dictates the sophistication and complexity of the required model. Although this is only an approximate criterion, which is closely related to the Equations A.58 and A.96, an electromagnetic structure is said to be electrically small if its dimensions are smaller than one tenth of the smallest wavelength under consideration:
l the physical dimension [m]
λ the wavelength [m]
In the case of a steady-state analysis of the power system, only the power frequency (50 Hz or 60 Hz) is considered and the wavelength of a 50 Hz sinusoidal voltage or current equals:
λ the wave length [km]
v the speed of light ≈ 300000 [km/s]
f the frequency [Hz]
Therefore, a component, e.g. a transmission line, is ‘electrically small’ in the steady-state analysis when the dimensions are smaller than 6000/10 = 600 km. In that case, the Maxwell equations can be approximated by a quasi-static approach and the component can accurately be modeled by lumped elements. Kirchhoff's laws are then applicable to compute the voltages and currents.
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