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complex circuits - maths involved in powering up secondry unit

Postby mrsonic2013 » Sun May 25, 2014 2:52 pm


small shed 50 meters away from building which has the primary mains unit.

i want to know how i can mathematically invent a circuit which will power up a secondary unit in the shed.
i am only interested in the maths.

current = w / v

how to choose the protective device?

because there is a long distance between primary unit and secondary unit , would there be a need for an rcbo in the mains unit?

i know the calculation for volt drop. vd = mv x ib x L / 1000
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Postby ericmark » Sun May 25, 2014 11:09 pm

Most of the maths is given in the 17th Edition (BS7671:2008) much is really OTT for example I was told the max amount of cable allowed in a ring final was 106 meters and I tried to work it out for myself but because the cable is rated at 22 amp and in fact it only draws 16 amp one has to include temperature correction before one gets the true valve.

Ct = 230 + tp - (ca² Cg² - Ib²/It²)(tp - 30)/230+tp

Ct = Correction factor
tp = Max permitted operating temp
ca = Rating factor for ambient temperature
cg = Rating factor for grouping
ib = Design current for circuit
It = Tabulated current-carrying capacity of a cable

However in real terms much of this is not really required we tend not to plan any circuit right to the limits. So simple take current and look at volt drop per meter of cable being used times length so assuming lights are used then the volt drop is limited to 3% so as we go up cables sizes for 50 meters you get:-
1mm max amps 3
1.5mm max amps 4.7
2.5 mm max amps 7.6
4mm max amps 12.5
6mm max amps 19
10 mm max amps 31
16 mm max amps 49

All working on 50 meters of cable and for volt drop of 3% as to the loop impedance and use of RCD this is going to take account of the loop impedance of supply in the first place.

Where a transformer is used then loop impedance of transformer I know on one job we did transform up to 3.3kV and then back down to 230v I am not convinced it was really required not only cost of transformers but also all the hassle of safety with such high voltages.

In real terms this is only worked out in collage courses it's rarely done in real terms. If your looking at Norton's theorem and Thévenin's theorem then google them there are plenty of sites explaining how it works.

Good look I learn to pass exam then never used again.
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Postby ericmark » Thu Jun 26, 2014 2:58 am

After your post I looked at my Excel program and thought it would be better as a java script program as my new phone will not run Excel but will run java script with a HTML document. I also by doing that way was able to enlist the help of others to check if there were faults which there were and correct them.

Still working on the pages but the pages are working and I have made it so as default the inputs are maximum for a final ring. Made 4 pages to work out in different directions there are links on each one to others.

First page is at hope this helps and if you find any errors please let me know.
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Postby ericmark » Sat Jun 28, 2014 7:05 am

I now realise I missed two questions.
how to choose the protective device?

because there is a long distance between primary unit and secondary unit , would there be a need for an rcbo in the mains unit?

To answer in reverse. The RCD has a number of functions one being to disconnect the supply within a set time when there is a direct short to earth. For that job the RCD could require quite a lot of current often 300 mA with delay (S type) is selected high enough to stop it tripping with no real fault but low enough to ensure enough current will flow through an earth rod with a direct short.
However 300 mA is too high to ensure a RCD will trip before causing permanent damage to the human body so to protect personal we use a 30 mA RCD with will work within 40 ms.
Modern RCD's use electronics which require voltage to operate at the consumer unit any fault will either blow fuse or open MCB or have enough voltage to work the RCD. However at the end of a cable run a short to earth could cause the volts to drop to such an extent that the RCD would fail. So we have two types passive and active. The active type auto disconnects with voltage drop so fails safe.
We should RCD protect with 30 mA all cables hidden in walls at less than 50mm deep unless using special cable and nearly all socket outlets there are one or two exceptions.

Now onto fuse or MCB in the main the fuse protects the cable so a cable rated at 21A will have a same or lower rated fuse so 20A fuse. It will take time to blow the fuse and the permitted time varies according to type of installation and there are charts made for the fuses which are used to select one which at the impedance of the circuit will blow in the required time.

The MCB is slightly different it's two devices in one. The thermal part of the MCB is slow to operate and will trip at the amps shown on the device in the fullness of time so will protect the cable but will often not disconnect within the times laid down. So there is also a magnet device with will disconnect within 0.01 of a second but the current to operated this is far higher. We use a letter to show how much higher. B = 5 times, C = 10 times and D = 20 times so a B32 MCB will trip with the magnetic part at 160A. For this current to flow the impedance (resistance) of the circuit has to be low enough. 230/160 = 1.44 ohms so the loop impedance for that MCB will be less than 1.44 ohms.

There is some debate as to if a RCD protected circuit needs the MCB to trip with the magnetic part but since a RCBO still has the magnetic part I personally would say it does. Although on the line - neutral impedance rather than the line - earth. Since better meters measure ELI from earth to line and PSSC from line to neutral the PSSC is more useful as often a direct measurement.

All MCB's also have a maximum current they can handle often either 4.7kA or 10kA and we should test the PSSC to ensure within these limits and we should measure both line - earth and line - neutral and take highest figure. In the main line - neutral is the highest hence why meter auto selects that pair of wires on the C13 connector for the patch lead of the meter.

However not all meters do this and in the past I have made special patch leads to allow plug in testing without having to use GU10 wandering probe test leads.

The maths one hopes means when you come to the stage of testing all will pass. In the days when I was an active electrician I did make errors because of the time it takes to calculate. Boss says run 4mm there to there and I answer are you sure 4mm is big enough that's rather a long run but to say no 4mm is not big enough needs calculating and my fag packet was not big enough. As mobiles were replaced with PDA's I found I could run Excel so at last I could calculate in the field but then mobile phones started to charge to have Excel installed. Hence I moved to Java Script which will run on a browser. However Java Script has so off features for example is a = 5 and b = 6 then a + b = 56 but eval(a) + eval(b) = 11 as a result I made some errors when moving from Excel to Java Script a x b = 30 as expected so eval is not always required.

Since I am no longer working as an electrician I have not had actual figures to enter into my calculator to see if the results are correct. But I think I have found all the bugs now. Since using Java Script they can be put on the www so I could ask others to test. Reports to date seem to show they work as expected so I have extended them to work with different installation methods. Please do report any bugs found.
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