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Low Earth Orbit
Lighting & Electrical
Correct feeder cable for distro
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<blockquote data-quote="Rob Timmerman" data-source="post: 217853" data-attributes="member: 172"><p>An induction heater isn't going to heat anything that doesn't allow current to flow, because the "induction" in that device is "induced [eddy] current", and not "inductance (the tendency of an electrical conductor to resist the change of current)".</p><p></p><p>Only the resistive (real) component of the impedance dissipates power (Joule's Law). But the reactive (imaginary) component of the impedance affects the current flow, and the resistive losses go as I^2R. So if you go from a resistor to a device that has that resistor in series with a perfect inductor (no resistive component to the impedance), your power dissipation at DC doesn't change but your power dissipation with AC goes up with frequency.</p><p></p><p>If we look at ~100' of feeder formed into a perfectly stacked coil 36" in diameter (10 turns, so a 10" tall stack), we get an inductance of 124uH. Reactance is omega*L, so 2*pi*f*L. At 60hz, this is about 50 miliohms. DC resistance of 4/0 copper is about 5 miliohms for that same 100'. So the the impedance of coil has gone up by about an order of magnitude at 60hz vs. DC. However, it is worth noting that the same 100' piece of 4/0 would have an inductance of about 50uH if not coiled, so 20 milliohms instead of 50 at 60hz.</p><p></p><p>Let's assume a purely resistive load (the case of a constant power load will be a bit worse, but is much more obnoxious to calculate) of 0.5 ohms (28.8kW, about 240A) and 120V into the feeder. This creates a voltage divider of 55 miliohms through the feeder and 500 miliohms through the load for the coiled case, and 20 miliohms through the feeder and 500 miliohms through the load for the straight cable case. Current in the coiled case is 216A, and 230A in the straight cable case. Ohmic losses are 233W for the coiled cable case, and 264W in the straight cable case, a difference of about 13% with the coiled cable actually being lower loss with a resisitive load (again, a constant power load will have different results, likely higher for the coiled cable case, but similar degree of difference).</p><p></p><p>So not a huge difference, and a difference that is probably less than the variability in contact resistance of all the connectors in the system (your terminal screws are all torqued to the manufacturer's specifications, and there's no oxidation on any of your connectors, right?). Of course, this all assumes that there's nothing ferromagnetic nearby to dissipate power via eddy currents, so coiling around steel stage legs will give you different results.</p></blockquote><p></p>
[QUOTE="Rob Timmerman, post: 217853, member: 172"] An induction heater isn't going to heat anything that doesn't allow current to flow, because the "induction" in that device is "induced [eddy] current", and not "inductance (the tendency of an electrical conductor to resist the change of current)". Only the resistive (real) component of the impedance dissipates power (Joule's Law). But the reactive (imaginary) component of the impedance affects the current flow, and the resistive losses go as I^2R. So if you go from a resistor to a device that has that resistor in series with a perfect inductor (no resistive component to the impedance), your power dissipation at DC doesn't change but your power dissipation with AC goes up with frequency. If we look at ~100' of feeder formed into a perfectly stacked coil 36" in diameter (10 turns, so a 10" tall stack), we get an inductance of 124uH. Reactance is omega*L, so 2*pi*f*L. At 60hz, this is about 50 miliohms. DC resistance of 4/0 copper is about 5 miliohms for that same 100'. So the the impedance of coil has gone up by about an order of magnitude at 60hz vs. DC. However, it is worth noting that the same 100' piece of 4/0 would have an inductance of about 50uH if not coiled, so 20 milliohms instead of 50 at 60hz. Let's assume a purely resistive load (the case of a constant power load will be a bit worse, but is much more obnoxious to calculate) of 0.5 ohms (28.8kW, about 240A) and 120V into the feeder. This creates a voltage divider of 55 miliohms through the feeder and 500 miliohms through the load for the coiled case, and 20 miliohms through the feeder and 500 miliohms through the load for the straight cable case. Current in the coiled case is 216A, and 230A in the straight cable case. Ohmic losses are 233W for the coiled cable case, and 264W in the straight cable case, a difference of about 13% with the coiled cable actually being lower loss with a resisitive load (again, a constant power load will have different results, likely higher for the coiled cable case, but similar degree of difference). So not a huge difference, and a difference that is probably less than the variability in contact resistance of all the connectors in the system (your terminal screws are all torqued to the manufacturer's specifications, and there's no oxidation on any of your connectors, right?). Of course, this all assumes that there's nothing ferromagnetic nearby to dissipate power via eddy currents, so coiling around steel stage legs will give you different results. [/QUOTE]
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Correct feeder cable for distro
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