Contents
In this paper analytic relations are developed for the calculation of the shell losses in three phase arrangements with nonmagnetic enclosure, for the steady state and the short circuit conditions. The phase conductors are taken as filamentary. The losses result as Fourier series ofn terms. Parametric investigations showed that a restriction on two terms gives results of great accuracy for the steady state losses. The analytic relations for the short circuit losses calculation are cumbersome. These losses can be calculated from the steady state losses, that are given from simpler relations, by an appropriate coefficient given here from the relevant curves.
Ubersicht
In dieser Arbeit werden analytische Beziehungen zur Berechnung der Mantelverluste für Dreileiterkapselungen mit unmagnetischem Mantel im stationären Betrieb und im Kurzschlußfall entwickelt. Die Innenleiter werden als Linienleiter betrachtet (Leiterradiusr=0). Die Verluste erhält man als Fourier-Reihen mitn Gliedern. Durch Parameteruntersuchungen der Verluste im stationären Betrieb ergibt sich, daß die ersten beiden Glieder für die erforderlichen Genauigkeit ausreichend sind. Die analytischen Beziehungen für die
Kurzschlußverlust-berechnung sind umfangreich. Diese Verluste können aber aus den Verlusten im stationären Betrieb mit Hilfe eines geeigneten Faktors berechnet werden, der aus Diagrammen entnommen werden kann.
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Abbreviations
- A M :
-
vector potential at the shell
- A n ,B n :
-
Fourier coefficients
- d M :
-
shell thickness
- i :
-
instantaneous current
- I cc :
-
RMS value of the short-circuit current
- I th :
-
thermal equivalent short-time current
- K M :
-
current line density at the shell
- K Mth :
-
thermal equivalent short-time current line density
- m :
-
conductor distance from the arrangement center
- n :
-
terms of Fourier series
- p :
-
abbreviation, eq. (10)
- P′ cc :
-
short-circuit shell losses per unit length
- P′ M :
-
steady-state shell losses per unit length
- P′ M 0:
-
reference shell losses per unit length, eq. (13)
- q :
-
abbreviation, eq. (A. 2a)
- Q′:
-
thermal losses per unit length
- R :
-
resistive component of the short-circuit power system impedance
- R{imM}:
-
mean shell radius
- R′ s :
-
shell resistance per unit length
- t :
-
time
- T cc :
-
short-circuit duration
- X :
-
inductive component of the short-circuit power system impedance
- α:
-
angle; describes the instantaneous values of voltages at the moment of fault appearance
- γ:
-
angle of the short-circuit power system impedance, eq. (2)
- δ:
-
skin depth
- κ:
-
factor for the computation of short-circuit current, eq. (26)
- κ M :
-
shell conductivity
- κ′ M :
-
surface conductance of the shellκ′ M =κ M d M
- λ:
-
eigenvalue (λ=1/τ)
- μ 0 :
-
vacuum permeability (μ 0=4π×10−7H/m)
- τ:
-
time constant, eq. (3)
- ω:
-
circular system frequency
References
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Hannakam, L.: Berechnung der Verluste im Eisen-Mantel dreiphasiger Rohrleitungen. Arch. Elektrotech. 64 (1981) 37–42
Sonntag, J.: Stromärmeverluste im dreiphasigen Rohrgaskabel. Arch. Elektrotech. 63 (1981) 35–45
Hoseman G.; Tsanakas, D.: Dynamic short circuit stress of busbar structures with stiff conductors. Parametric studies and conclusion for simplified calculation methods. Electra Nr 68. (1980) 37–64
IEC Publication 865-1: Short circuit currents—Calculation of effects. Part 1: Definitions and calculation methods. Geneva: IEC, 1993
IEC Publication 909: Short circuit current calculation in three-phase ac systems. Geneva: IEC, 1988
Sonntag, J.: Einfluß der Mantelströme auf die Kurzschlußkräfte im dreiphasigen Rohrgaskabel. etzArchiv 2 H.4 (1980) 121–126
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Safigianni, A. Short circuit losses in three phase arrangements with nonmagnetic enclosure. Electrical Engineering 78, 57–62 (1994). https://doi.org/10.1007/BF01233219
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DOI: https://doi.org/10.1007/BF01233219