A.4.6 Arc absorbers in the exhaust flow
6
In some switchgear designs the exhaust of gas is cooled down by arc absorbers. These are composed e.g. of 7
several layers of fine-meshed grids or other obstacles either metallic or insulating in the path of the exhausted gas. 8
These devices absorb some fraction of the energy of the out flowing gas, however, may also reduce the effective 9
cross-section of the pressure relief area. In this case the gas remains longer in the compartment and might carry 10
more arc energy into the installation room than without arc absorber counteracting the cooling effect. The effect of 11
such arc absorbers can be implemented in the equations of the models by a reduced area of the relief opening and 12
a concurrent cooling factor reducing the energy transported from the arc compartment into the exhaust 13
compartment. The cooling effect per mesh is however limited to several percent of the energy flow and does not 14
linearly increase with the number of consecutive meshes [AiF2011]. 15
A.4.7 Speed of relief opening device
16
Heavy relief flaps as used sometimes for air insulated switchgear, do not open instantaneously. The time 17
dependent increase of the opening area can be calculated from the acceleration of the plate having a certain mass 18
under the force determined by the scalar product of gas pressure and area of the relief opening. These flaps are 19
often hinged on one side so that the force on the plate is reduced in time during the opening. The simulation of its 20
motion together with the determination of the momentary opening area is most often not considered. In principle, 21
the speed of the plate can be calculated by integrating the acceleration of the plate over time. For the light burst 22
plates in SF6 insulated switchgear, this effect is of minor importance, since the full opening area is achieved almost
23
instantaneously. 24
A.4.8 Temperature dependent gas data
1
The basic pressure calculation method is based on a gas model called “classical ideal gas”, i.e. the gas particles 2
are considered as being dimensionless with their mass being concentrated in points. Collisions are only elastic and 3
the gas properties like the specific heat capacities are constant. 4
A considerable improvement is already obtained, when the gas properties are based on the “ideal gas” model. In 5
this case the gas still consists of dimensionless mass-carrying particles, however, e.g. dissociation and ionisation is 6
considered by the number of particles changing with temperature. Thus, the gas properties (specific heats, sound 7
velocity etc.) are no longer constant but depend on temperature, and also the mole numbers change with 8
temperature. The ideal gas law is still valid. Considering this gas model, the equations in Chapter 2 become much 9
more complex. 10
Some enhanced pressure calculation methods are based on real gas data. In this case the gas particles are no 11
longer regarded as concentrated points but have a certain volume so that interactions between particles exist like 12
dipole forces. The properties of real gases depend not only on their composition, but also on chemical reactions, 13
temperature and pressure. The generation of these data is time consuming. That is why they are collected once in 14
multidimensional tables and retrieved during the pressure calculation method. 15
The specific heat capacity of SF6 increases by more than a factor of 10 around a temperature of 2000 K caused by
16
collision induced dissociation of molecules. A similar anomaly is observed for N2 at a temperature of 6000 K. The
17
temperature and pressure dependence of the heat capacity and the corresponding adiabatic index can be 18
introduced into the equations by analytic approximations of the heat capacity at constant volume during the time 19
steps of calculation. This approach is permitted as long as the temperature in the volume is uniform allowing for a 20
thermodynamic equilibrium of all molecule fractions. This might no longer be true for rapidly flowing gas in the 21
exhaust. 22
The inclusion of temperature dependent heat capacities involve a lot of modifications of the equations, which are 23
not easy to implement into the basic model and therefore are not discussed in detail here. 24
A.5 Summary
25
A detailed description of the equations, which are used for the basic model, is given. The equations are based on 26
the ideal gas law, conservation of mass and energy. The reader can use these equations to develop his own 27
software. It is described how to calculate the initial conditions as well as temperature and pressure change for each 28
time step. The code may be used to recalculate the examples given in Chapter 2. 29
Further on equations are given to enhance the basic model. Enhancements consider density dependent 𝑘𝑝-factor, 30
exothermic reaction energy, pressure dependent arc voltage, mixing of gas in compartments, metal evaporation 31
and ablation of insulators, arc absorbers in the exhaust flow, speed of relief opening device, and temperature 32
dependent gas data. 33
34 35
REFERENCES: 1
[AiF2011]: Jan Christoph Kahlen, G. Pietsch: “Reduzierung der Druckbeanspruchung elektrischer Anlagen im 2
Störlichtbogenfall”, Schlussbericht, AiF-Forschungsvereinigung, 2011. 3
[Anantavanich2010]: K. Anantavanich: “Calculation of Pressure Rise in Electrical Installations due to Internal Arcs 4
Considering SF6-Air Mixtures and Arc Energy Absorbers”, Aachener Beiträge zur Hochspannungstechnik, Band 5
14, ISBN 3861306778, Dissertation, RWTH Aachen University, 2010. 6
[Bjørtuft2005]: T. Bjørtuft, O. Granhaug, S. Hagen, J. H. Kuhlefelt, G. Salge, P. K. Skryten, S. Stangherlin. “Internal 7
arc fault testing of gas insulated metal enclosed MV switchgear”. CIRED 2005 proceedings. Turin, 6-9 June 2005. 8
[Dullni1994]: E. Dullni, M. Schumacher, G. Pietsch, “Pressure rise in a switchroom due to an internal arc in a 9
switchboard”, 6th Int. Symposium on Short Circuit Currents in Power Systems, Liege, 1994. 10
[Friberg1999]: G. Friberg und G. Pietsch: “Calculation of pressure rise due to arcing faults”, IEEE Transactions on 11
Power Delivery, Vol. 14(2): S. 365-370, 1999. 12
[Hochhaus1985]: H. Hochhaus, „Untersuchung der Wechselwirkungen zwischen Schaltlichtbögen und Isolierstoff- 13
wänden“ (“Investigation of the interaction between switching arcs and insulating walls“), PhD Thesis in German, 14
Technical University Braunschweig, 1985. 15
[Zhang2002]: Xiang Zhang: “Modellierung der Auswirkungen von Störlichtbögen in elektrischen Anlagen”, Ph.D 16
Dissertation, RWTH Aachen, 2002. 17