complex voltage drop question

[gashmore]

The project: Install 12VDC 3 Watt Low voltage LED pathway lights, one every 20', along a 420' boardwalk through a mangrove forest. There are 24 lights and to minimize taps in the main line they will be installed in groups of 3 with one light at the tap, one light 20 feet behind and one 20 feet ahead. Taps will be 60 feet apart.

I am assuming that the full 72 watt load in the first 60' will cause significantly more voltage drop that the 9 watts in the last 60' so I treated the setup as 7 separate segments and calculated the voltage drop for each segment with the input voltage being the reduced voltage from the previous segment and the wattage being what remains to be powered. Assuming this logic is correct, an input voltage of 13.8V and #8 AWG copper will result in voltage at the end of right at 12V. A total of 13% drop.

First question: Is my methodology reasonable?

Second, will the LED lights at the first tap be able to handle the 13.8V or do I need to add some resistance to bring the voltage down?

 

[Lucien Nunes]

Thanks @pc1966.

Obviously if there is a long run of feeder between the power brick and the start of the boardwalk, the 40.5V can be adjusted up to compensate. Actually I omitted to add in the drop in the local wiring of each LED group. If we still assume this to be #20, carrying 0.25A over 80 feet of conductor (there and back 20 feet either side of the tap point) it adds 10 * 0.25A * 80 = 200mV extra needed at launch, or 66mV lower at each LED. TBH that kind of difference will be lost in the noise, not least of which is the temperature coefficient of resistance of the main run of cable.

40.7V is not actually a very convenient launch voltage because it is slightly beyond the range of a 36V PSU with 10% adjustment range. Some will adjust over a wider range though and even launching at 39.6V only robs the LEDs of 0.36V. If the lights will accept AC, I would recommend it as electrolytic corrosion is less severe. In that case it would be a question of finding the right primary and secondary tappings, allowing for regulation. Optionally, decrease the voltage drop by upgrading to #14AWG.

 

[gashmore]

Having restored a 70 year old Hammerlund receiver, I understand the problem of electrolytics. Traco is hard to find this side of the pond but found a couple of similar converters. Marine grade wire and potting compound should make a solid package. Running at less than 20% of capacity heat should not be a problem.

 

[Lucien Nunes]

But what do you think about the series groups without converters?

 

[gashmore]

But what do you think about the series groups without converters?

That's what I am looking at now. It seems that most of these 12V nominal LED landscape lamps have internal power regulation that can accept 12 to 24V DC or AC which eliminates wiring in series but does open up some possibilities for the 3 wire solution. What about running some 12/3 for the supply line then parallel 3 watt 12W to 24V lamps every 20 feet coming back.

 

[Lucien Nunes]

If they will accept 24V AC then they can handle a peak voltage of 24 * sqrt(2) = 34V and would probably be OK on 34V DC, but we should not assume this and it would probably invalidate the warranty.

Assuming the light output is independent of voltage, which it should be, it is better to distribute positive and negative from the supply end as uniformity of voltage drop is no longer important. If using 12/3, parallel two of the conductors subject to code. I would think it's acceptable since either conductor will carry the very low short-circuit current alone, and by being paralleled at each tap point the total short-circuit loop resistance from just one side of one severed conductor anywhere will barely exceed the resistance at the end point.

Launch at 24V. Resistance of #12 = 1.6mΩ / foot, one leg single conductor, other leg two in parallel. Aim for similar loss percentage as before, so assume voltage at lights >22V and all lights at midpoint. Total current 63/22=2.9A
Drop = 420 * 1.6 * 3/4 * 2.9 = 1.46V
Cable power loss 1.46 * 2.9 = 4.2W

Those numbers are based on DC. For optimum corrosion resistance, it is better to use AC. However, depending on the exact configuration of the integral LED driver circuits, the power factor might be significantly below unity due to limited conduction angle of the input rectifier. Therefore, the peak current and hence RMS drop in the cable might be higher than we have allowed for.

Anyhow, 24V and 12/3 is probably the way to go, thanks to the inbuilt voltage regulation in the lights. You could maybe even use 14/3.

 

[gashmore]

Think it is time to prototype. Ordered a few samples of 12v-24v lamps. One dedicated to a surgical examination and the others measured under various power conditions.
Thanks to all. Will report back my findings.

 

[gashmore]

Bought a set of 4 12v to 24v LED fixtures to test. Circuitry is encased in potting compound in the bottom of the housing.
On the test bench, powered by a variable voltage DC bench power supply and a LUX meter the LED output was a steady 200 LUX at 6" on axis throughout a voltage range of 12.2 to 24V. Output dropped to 190 lux at 12V and substantially less at 11V. Current remained between 3.01 and 3.11 Watts throughout the range. Under AC power the output remained the same 200Lux and 3 to 3.14 watts throughout the range. Oscilloscope showed 60Hz at the LED chip so apparently no rectification in the circuit.
One sacrificial unit was tested for over voltage. Noticeable increase in brightness above 24 volts and I let the smoke out after 30 seconds at 28V.

Looks like I can expect reasonably constant output to the end of 400' of 12/2 fed at 24v AC or DC.
Again, Thanks to all.