# Calculating heat generated by resistance wire on 3 phase current

I am designing a heating element consisting of resistance wires coiled around a tube to heat water flowing in the tube. All three heating elements (loads) will have the same resistance and will be connected in delta. I want to control the heat output by varying the voltage to the loads by using a variable transformer. I did some calculations to ensure that the design will work as expected. I would appreciate it if people who know better could tell me whether the procedure I employed to calculate the heat generated, as provided below, is correct.

a) I have access to a three phase 250 V, 30 A electricity. I understand these are line voltage and line current. So the phase current would be 17.34 A, and the total power available would be 13 kW.

b) I want a total of 4.8 kW heating power, so 1.6 kW on each load

c) I know the wire diameter and length I need. Hence, for the given wire material, I know the resistance of each heating element.

Here is where the calculations start.

d) In an excel sheet, I list out a range of voltages (from 100 to 300, say), and for each I divide the phase power (total power/3) by the voltage to find maximum current available (assuming no losses).

e) Then for each leg/load, I find the calculated current by dividing the voltage across it by its resistance.

f) Whichever step (d or e) gives lower value for the current, I take that as the actual current flowing through the load, and I calculate the heat generated by each leg/load as I^2*R.

g) Finally, when I find the correct combination that generates the heat required (1.6 kW), I assume that the other two loads are generating the same amount of heat for a total of the desired 4.8 kW.

So my question is, is this the right way to calculate the heat generated. Also, is it appropriate to isolate each leg/load and perform calculations on it alone, as I have done here.

• Why are you using a variable transformer rather than using a 3-phase solid-state relay to do "dimming" or variable duty cycle? The latter would be far more compact and cheaper unless you happen to have a three-phase variable transformer to hand. Sep 10, 2019 at 20:24
• Transformer was the first idea I had (not an electrical guy!). Then I came across SCR. In fact, I am currently evaluating which one would be better if the cost difference is not very high. Sep 10, 2019 at 20:26
• @SineNomine mains voltage is very dangerous, potential deadly. Three phase is even more dangerous. If you are “not an electrical guy” it’s best to use a solution that has already been designed and safety tested. Sep 10, 2019 at 22:12
• "Then for each leg/load, I find the calculated current by dividing the voltage across it by its resistance." - yes, but.. how do you know what the resistance is? Sep 10, 2019 at 23:02
• I think you would eventually get to a reasonable result with your dedication. However there is a lot of past experience in the trade that you may be missing. Insulation, water and protection come to mind. My first suggestion would be to see how others have done what you plan to do (in line water heaters) and carefully consider if you can achieve the same level of reliability and safety for less money. google.com/… Sep 11, 2019 at 9:11

Power is voltage squared divided by resistance. That is the easy way to calculate the required resistance.

Calculating one leg is sufficient for 3-phase balance systems.

The easy and inexpensive way to regulate the heat is to turn the power on and off. That is all that is necessary in a lot of applications. If necessary, you can use solid state relays to turn power on and off cycle by cycle.

• Thanks Charles. As far as heat regulation goes, are you suggesting that using an SCR or an SSR is more effective than using a transformer? Sep 11, 2019 at 14:12
• A variable transformer is a simple manually-adjustable method, but likely to be a lot more expensive than SCRs, SSRs or electromechanical contactors. The latter three can be easily used with an automatic control system. SCRs control voltage on a sub-cycle basis. They require a gate-drive circuit that is synchronized with the voltage waveform. SSRs can allow one cycle or multiple cycles to pass or simply connect to a thermostat for on/off control. Electromechanical contactors can be easily turned on and off with a thermostat. Heating applications rarely need more than simple on/off control.
– user80875
Sep 11, 2019 at 14:37
• You could check the cost of electromechanical vs. solid state relays. SSRs are quiet, non-sparking and not subject to mechanical wear out. The thermal time constant or on/off frequency is a factor to consider.
– user80875
Sep 11, 2019 at 14:46
• I had looked at the cost of automatic variable transformers and SCRs, and looked like the prices are similar. Same with size. Regardless, because of their silent(er) operation and the ability to control the firing more finely, I think I will choose between SSR and SCR. Currently looking into that. I appreciate your help. Sep 11, 2019 at 14:57