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So, guys, I hope you can explain to me how to calculate the necessary parameters for a ballast to limit the current on the primary side of a high voltage transformer.It is for a tesla coil project. To stop excessive current being drawn through the transformer's winding when the secondary is short-circuited.

Transformer specs.
Pri: 230 V/50 Hz, 2.09 A Resistance: 0.5ohm Sec: 5 kV, 80 mA

So how much inductance I need to limit the current to 2A?

Solution. The total resistance Z of a choke coil consists partially of the actual coil resistance R and partially of the inductive resistance XL in a linear relationship of the frequency f and the inductivity L as XL = 2 πf*L and Z = √ R2+XL2 The resistance of the coil R can be measured directly over the coil with an Ohm-meter but usually R hardly plays a role compared to the inductive resistance. We want to reduce the current flowing through our primary of the HV transformer to 2 A maximally at 230 VAC. This means that the choke coil must have a total resistance Z of 230/2 = 115 Ω. We measure a resistance R over the coil of 0.5 Ω than the inductive resistance must be √Z2-R2 or √((115Ω2)-(0.5Ω2)) = 114.9 Ω. The next step is to calculate the inductivity by arranging our formula into L = XL/(2*π*f)
or L = 114.9/(2*π*50) = 365 mH.

Problem. So I build a choke of the calculated value and test it out. enter image description here

But the ballast is not limiting the current of the calculated target Its 2 times higher

enter image description here I can't figure it out what's going wrong

Nano
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    Why are you wanting to limit the current? Anything wrong with a fuse or using a more powerful transformer? In other words your question is made unclear because your stated requirements are unclear. – Andy aka Sep 07 '18 at 18:00
  • Z=2 * Pi * f * L, but this sounds like an XY problem. – winny Sep 07 '18 at 18:24
  • It is for a tesla coil project. To stop excessive current being drawn through the transformer's winding when the secondary is short-circuited. – Nano Sep 07 '18 at 18:24
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    Why do you hope we *can't* explain it to you? – Transistor Sep 07 '18 at 18:25
  • Oh! I stand corrected. Compute according to the formula above. Please edit your question to include the Tesla coil and the reason. – winny Sep 07 '18 at 18:26
  • @winny Can you plz give me more explanations for the formula. – Nano Sep 07 '18 at 18:37
  • Try it yourself first and tell us where you are stuck. Here is some reading for you: https://www.allaboutcircuits.com/textbook/alternating-current/chpt-3/ac-inductor-circuits/ – winny Sep 07 '18 at 18:40
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    L=XL/(2*π*f) XL=√Z2-R2 Z=230/2=150ohm R=0.5ohm XL=114.9ohm L=0.36H – Nano Sep 07 '18 at 22:11
  • Oh! I would just go ahead and ignore the resistive part and aim for 115 ohm or 360 mH. @Sparky256 solution below would work too and goes visual indication. – winny Sep 08 '18 at 09:04
  • @winny Hey buddy just 1 more thing,how do i calculate the amperage requirement for the ballast? – Nano Sep 10 '18 at 15:46
  • Maximum peak input voltage divided by minimum impedance of the choke. – winny Sep 10 '18 at 15:56
  • 325 Volts/113.04ohm=2.8A (XL= 2πfL) ? – Nano Sep 10 '18 at 18:05
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    That sounds correct. Don’t overlook the incandescent light bulb solution with. – winny Sep 10 '18 at 22:22
  • Update: Strange. Are you saturating the core by any chance? What B do you end up with for LI=NAB? – winny Sep 22 '18 at 19:21
  • Update: Can you give me some reading material for calculating Saturation of an inductor and how to approach the problem. – Nano Sep 22 '18 at 19:49
  • I just gave you the formula :-) All values are in SI. You know the inductance, current, number of turns (hopefully) and you can easily measure the cross section area with a ruler. Oh, and you need to include @ and username, or he/she won’t be notified. – winny Sep 22 '18 at 20:00
  • You need to use incandescent lamps which have a steep non-linear response to an increase in current. Farmers use them to protect their electric fences from shorts and to limit the current so as not to burn the animals skin. High current will only be allowed to flow until the filament heats up, about 1/10th second. –  Sep 23 '18 at 03:48
  • The Zo of the transformer is the Imax/Isc *100% which is usually 10%+/-few % which is designed higher for MVA rated in order to limit Isc. So If you add impedance to the secondary, it must withstand the breakdown voltage to prevent shunted windings. so you better limit the primary side. – Tony Stewart EE75 Sep 23 '18 at 06:15
  • @ Tony EE rocketscientist I em limiting the current on the primary side. – Nano Sep 23 '18 at 11:20
  • @Nano Don’t worry about him. He jumps on anything he sees here. Any luck with the saturation calculation? – winny Sep 23 '18 at 14:10
  • @winny just for now how do I calculate the (Inductance Factor) or the (Reluctance) for my particular core? The problem is that I can't find the data sheet for my cores :( – Nano Sep 30 '18 at 17:27
  • No need! Take out your ruler, measure the core cross section area (in square meter) and apply that to IL=NAB and you are done. – winny Sep 30 '18 at 17:41
  • @winy but i need calculate (Magnetic Flux Density B = Φ / Ae) for that I need (Magnetic Flux Φ = I × L / N) and cross-sectional area, and then calculate Al is that correct sorry i em a complete noob :) – Nano Sep 30 '18 at 19:48
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    You can do that but no need since you already know your inductance (366.8 mH) and number of turns (hopefully). Cross section area with a ruler. Now you can solve IL=NAB for B. – winny Sep 30 '18 at 21:03

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You actually need a device with a non-linear response. Typically this would be a 100 watt incandescent light bulb. This would be in series with the 230 VAC power to the transformer.

If there is no arcing the current is low and the bulb is dim or not lit at all. When arcing occurs the bulb flickers and heats up, increasing resistance and limiting the current to the transformer to about 1/2 amp (with a 250 volt 100 watt bulb).

For more current simply put more lamps in parallel until you reach the maximum current you want. 2 bulbs would give you 1 amp maximum current. 4 bulbs would give you 2 amps maximum current.

You could use 200 watt bulbs but they do cost more and tend to have a short life. It depends on how many hours of arcing you want.

  • Thank you very much for your answer,I em familiar with that option. But i em simply interested with the idea of inductive ballast,and i want to learn the math behind it. – Nano Sep 23 '18 at 11:25