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 Topic Title: LCR Series Circuit Discharge Rate Topic Summary: Calculation of discharge time of series LCR circuit, or howlong to discharge a 100km power cable Created On: 02 May 2012 10:05 PM Status: Post and Reply Linear : Threading : Single : Branch
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 02 May 2012 10:05 PM giason Posts: 16 Joined: 19 March 2004 I am tryingto perform what I thinkshould be a relatively simple task, i.e. calculate the discharge time of a capictor in a series LCR circuit. I can happily find formula's and calculate a CR discharge rate but am unable to find the right stuff for LCR, and being fair it was 20 years ago I last used this sort of maths, and theory, in anger, and those brain cells are long gone. example cct The basics:- I have a long cable (100km) , with known LCR (and G, although I'm ignoring this) characteristics. The cable has been operating at 1000V AC and the supply (and load) is removed. I then assume the caple remains charged at 1000V as a capacitor C. With the known cable inductance L and a known resistor connected across the cable R to discharge it, how do I calculate the discharge curve allowing for the chokeing effect. I appreciate the cable has been simplified to an L C element and this is even massively simplified from the true LCRG version it should be but my rough calcs show we will not have a massive hold up time anyway so the cable model can be simplified. Either a formula or link to the correct website would be useful, please remember my brain cells are fuzzzy so the resultant answers need to be farly clear. And please don't just give an answer to the values in the example as I have to model this for other cables. 03 May 2012 10:42 AM ArthurHall Posts: 723 Joined: 25 July 2008 Is this a practical or theoretical question? If practical, close an earth switch, apply a portable earth or use the discharge stick of a pressure test set. If theoretical its a very long cable for such low voltage the leakage in the cable will dischage it very quickly also as it is AC it will depend on the point of wave that it was switched off on, I assume it is three phase, therefore you will probably have a different voltage on each phase. 03 May 2012 03:59 PM giason Posts: 16 Joined: 19 March 2004 Arthur, This is practical. Unfortunately it is not possible to earth by way of earth stick, switch etc as the system has to provide the means for controlled automatic dissipation of the charge. The application is a submarine cable between an oil / gas platform and the subsea well, which must be physically discharged when the power unit goes off line. This allows for diver and ROV safety and also electricians on the platform working on the cable joins before it goes subsea. It is accepted that the cable would naturally discharge but the forced 'controlled' discharge is required in a known given time frame, which is what I need to be able to calculate. The cable is supplied with single phase (actually a transformer output so L-L voltage applies with no earth reference). Thanks for the time looking so far though. Geof 03 May 2012 05:04 PM amillar Posts: 1833 Joined: 28 May 2002 Have you tried modelling this in Pspice? That is certainly the way I would approach it (I could probably just remember enough to do the maths but wouldn't trust myself to get it right!). There is a free version available which should be powerful enough, if you google student pspice you'll find it. It probably has a transmission line model in which might help. ------------------------- Andy Millar CEng MIET MCMIhttp://www.linkedin.com/in/millarandy 04 May 2012 01:35 PM joeduddy Posts: 4 Joined: 21 August 2002 I think you need to define the problem as a differential equation and solve it. If I remember correctly from long ago, Laplace transforms are handy tools to simplify this. 04 May 2012 03:46 PM williamjohn Posts: 178 Joined: 22 November 2010 giason The peak value between phases is 1414 volts. If the neutral is solidly earthed, the peak value to earth is 816 volts. When the cable is switched off, the voltage leaks through the capacitance and there is a distribution of the voltage through he capacitance. When the cable is then earthed to discharge it, the voltage redistributes through the capacitance and slowly drains back to earth. If the earth is removed before it has fully discharged, the voltage continues to redistribute and builds again up to a hazardous level. After a dc pressure test on an 11kv cable one mile long, I have discharged it for several minutes directly to earth. After removing the earth, the voltage quickly built up again and repeatedly drew a spark a cm long whenever the earth was next applied. Just calculating the time to discharge through the cable resistance and inductance is not enough. The voltage may still redistribute and build up again after it appears to have been fully discharged. With the cable ends such a long way apart, the cable must be earthed locally and kept connected to earth all the time that any work is done. Can anyone else comment on this. John 04 May 2012 11:11 PM JonathanHill Posts: 206 Joined: 09 September 2002 I don't believe that the voltage recovery phenomina seen on dc pressure tests occur with ac and this is supported from personal experience. ------------------------- Jonno 05 May 2012 01:22 PM williamjohn Posts: 178 Joined: 22 November 2010 Thanks Jonno Even so, I would not work on a long high voltage cable in a wet location without a local earth present all the time. Best wishes John 05 May 2012 04:25 PM JonathanHill Posts: 206 Joined: 09 September 2002 Indeed/. It's a UK requirement to ensure HV apparatus is discharged to earth after achieving isolation. Usually it's only during testing that earths are temporarily removed, with them being reinstated before removing test leads. ------------------------- Jonno
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