**4.Application of Modelling to Distribution System Analysis**

The application of simulation techniques to the analysis of overcurrent protection for telecommunications DC power systems is a complex task. The typical distribution system contains many elements, of which the fuse is but one non-linear device. The major power system components can be modelled to provide good correlation between simulated and measured results in an exchange environment, however many of the component models require further development to accurately represent their transient behaviour. This section briefly discusses the inadequacies of component models presently applied to distribution system analysis.

**Battery Model** : The battery is typically modelled by a constant voltage source and parasitic series resistance and inductance. Short circuit battery currents have been shown to remain constant over a short time duration (up to 10ms) but to have reduced significantly for a duration exceeding a few seconds, due mainly to diffusion polarisation. This effect could be modelled by a current-time dependent resistor using **ABM**.

Battery impedance measuring equipment is now readily available, allowing simple direct measurements to be made of parasitic resistance and inductance on a battery string, rather than using manufacturers’ specifications for resistance and physical geometry for inductance.

**Bus Bar Model** : Bus bar is made of rectangular copper section, and typically connects the rectifier and battery components of a central power system to the exchange equipment distribution cubicles. The bus has both positive and negative conductors which run in parallel at little separation.

We have found that the practical application of many ‘inductance formulae’ give significant errors when applied to bus bars. However Schering provides a graph of inductance curves that shows very good correlation with measurements made by Cher and Bryant on typical sized exchange bus bars.

**Distribution Cable Model** ; Distribution cable is typically used to connect exchange equipment placed in racks with the power system distribution cubicles. The cables are typically run in close proximity to each other over a significant portion of their length, introducing mutual inductance effects between separate feeds.

Some exchange architectures common the earth potential cable of each feed at both the distribution cubicle end and the equipment load end. This significantly lowers both the parasitic resistance and inductance values of the earth potential cable.

**Inductor Model** : The parasitic inductance associated with any power system component displays real world high frequency losses, however a simulated inductor only obeys the equation v= L di/dt. High levels of di/dt can be generated when a fault closes a low-impedance loop around either a battery or a large capacitor, or when a fuse subsequently opens the loop. This can occur for example, with faults close to capacitors placed in the distribution cubicles or in the equipment racks.

Significant errors in the simulated levels for voltage spikes developed across inductors can therefore occur whenever high di/dt levels exist, unless the inductor model includes high frequency

effects.

**5.Conclusion**

This article has reported on the development of a fuse model for SPICE derived software using analogue switch and analogue behavioural modelling (ABM) functions. The fuse model can also be used to represent the operation of circuit breakers.

The fuse model has been validated against measured results from a fuse operating in a test circuit under conditions typically existing in a high-ohmic distribution (HOD) feed of a telecommunications exchange. The inadequacies of other component models applied to the analysis of DC distribution systems has been discussed.

In summary, the use of accurate component models will allow the benefits of computer aided design (CAD) to be applied to the design and analysis of over-current protection for telecommunication DC power systems.

References

[1] D.P.Reid and D.S.McGinn, `Short circuits on low voltage D.C. distribution facilities’, in Proceedings of the Conference INTELEC, 1978, pp.368-373.

[2] S.Muroyama, K.Sakakibara and T.Yamashita, `Transient voltage analysis of DC power distribution systems’, in Proceedings of the Conference INTELEC, 1983, pp.315-321.

[3] E.S.Lee and A.S.Herbert, `Fault isolation within power distribution systems’, in Proceedings of the Conference INTELEC, 1991, pp.74-79.

[4] T.Robbins and G.Newhouse, `Models for over-current protection analysis of DC distribution systems’, Telecom Australia: Telecom Research Laboratories Report, 1993.

[5] S.Okazaki, S.Higuchi, NKubota and S.Takahashi, `Measurement of short circuit current for low internal resistance batteries’, Journal of Applied Electrochemistry, Vol. 16, pp.513-516, 1986.

[6] H.Schering, `The inductivity of two straight parallel conductors with equal rectangular cross sections’, ETZ-A, (Elektrotechnische Zeitschrift. Ausgabe A. West Germany), 10th May 1954, pp.335-338.

[7] R.Cher and J.Bryant, `The inductance of busbars of rectangular cross-section’, Australian Postmaster-General’s Department: Research Laboratory Report No.4139, February 1956.

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