I've been doing a fair amount of research on wiring in the past week. It's not a simple task, figuring out what will work safely and reliably. Even now I am not absolutely confident in my decision, but at least I feel like I know what to try and what not to try.
Note: What I discuss here applies to DC and may only partially apply to AC systems.
What I found out:
I went looking for a chart saying voltage X with a maximum amperage Y requires wire Z. That doesn't really exist - mainly, because every situation is unique. There are several charts that do give you a sense of the tolerances, but please use that information carefully. A minimal list of factors that affect the accuracy of any figures you may find are as follows:
- AC vs. DC
- length of the wire
- Amps / circular mils
- Insulation rating
- The immediate environment of the wire
- Acceptable voltage drop
- Voltage rating of the wire
My questions from my last post were in regard to the chart at http://www.powerstream.com/Wire_Size.htm I was asking two main questions about main drive system wiring.
The wiring can vary on either side of the controller. Because the motor controller is just a power-converter, it takes in just as much power as it puts out. The key is that it does its input and its output over different, and varying lengths of time. The battery-side of the controller will not be handling large amperages (maybe 70 amps max for me) while the motor-side could see much higher current (limited to no more than 300 amps for 1 minute by my motor). This is most obvious at peak numbers of course, but still applicable at the continuous ratings for my components. The point is: Yes, different kinds of wire could be used to handle the different kinds of power on either side of the controller. Each wire or set of wires could be size appropriately to its own set of influencing factors. You don't have to though. You could use one size as long as it is rated for the most strenuous parts of the system. It means carrying around a little bit more weight and maybe spending a few cents more for both the wire and hardware to couple it to the battery pack, but that's about all it impacts.
As for what gauge to use, now that's kind of tough to answer. As you may know, I'm basing most of my bike on Lennon Rodger's eMoto. Naturally, I looked at his page and found that he used 4 gauge (AWG) welding cable. When I looked up the specs for 4 gauge wire on the PowerStream chart, I was confused. Firstly, there were multiple amperage ratings, but reading a bit helped. The left amperage column is called "maximum amps for chassis wiring" and the preceding paragraph explains that it is A) a conservative rating and B) for wiring in air, not bundled with other wires. Meanwhile, the "maximum amps for power transmission" column is based on the700 circular mils per amp rule.
What the heck is the 700 circular mils per amp rule?
Let me try to build up to it...
Mils does not mean millimeters. Mils means thousandths of an inch (.001 inches). Circular mils can be abbreviated CM and is used as a unit for measuring circular area, but there's a twist in the definition:
- Circular mils refers to a circular area in terms of the square having sides with length equal to the diameter of said circle.
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| Source RF Cafe |
Applying our new understanding:
The rule is talking about how much surface area is present for current to flow through. Obviously, since we're talking about circular surface areas, it is in reference to the cross-sectional area of the wires. You may find information about surface areas in regard to a wire with AC, but be careful, as that may be in reference to the longitudinal or "skin" surface area, instead of the "face" or "end" surface area of the wire which I've been describing here.
The 700 circular mils per amp rule, therefore, means that 700 CM of cross-sectional area are being taken into consideration for each amp in the wire. In other words, each amp of load adds roughly .0007 square inches to the cross-section of the wire.
Take a specific example:
PowerStream shows 1 AWG wire as being capable of carrying almost 120 amps according to 700 CM per amp rule. It shows 1 gauge as being .2893 inches in diameter. Since 1 CM is .001 inches, we can divide .2893 by .001, indicating 1 gauge wire is 289.3 mils in diameter. Using our picture and definition, we can put that in terms of CM simply by squaring it. Thus, 289.3 mils * 289.3 mils = 83694.49 squared-mils or CM. Now, we check to see how many amps we can put through a wire with that kind of cross-section by dividing it by 700 CM. 83694.49 CM / 700 CM per amp = 119.56 amps. Cool beans.
Cross-referencing our earlier statement, if each of the 120 amps adds .0007 square-inches (according to the 700 CM rule) to the wire, then the wire's cross-section has an area of .084 square-inches. The chart stated the diameter of 1 gauge as .2893 inches, so we see that .2893 inches * .2893 inches does in fact give us .08369 square-inches. Double cool. That's all without using Pi, so even though it is nice that it matches, do remember that it's not a precise measurement of the cross-sectional area.
After all that, you should know that 700 CM per amp is a "very, very conservative" rule of thumb. Additionally, the shorter the wire, the less area you have to provide for each amp. For my bike, hopefully I'll be dealing with no more than two-foot lengths of high-power wiring. I've read that with such short distances, a rule more like 200 or 300 CM per amp is acceptable. If that's true, then we can safely use a slightly smaller wire. Given that my motor is rated for a continuous load of 125 amps, if I used the 250 CM per amp rule, 125 amps * 250 CM / amp = 31250 CM. Since 1 CM = .000001 square inches, that is .03125 square inches. The diameter of a wire with that surface area is then the square-root of .03125 square-inches, which is .17677 inches. Referencing the PowerStream chart once again, that does fall pretty close to 5 gauge, which is a reasonably accurate result considering Lennon's choice of 4 gauge.
Voltage drop:
The voltage drop along a wire depends on the resistance between the source and the load. All wire resists charge flow and this resistance reduces the amount of voltage being provided further down the circuit. It comes down to how electrons flow through the wire really, so considering water flowing through pipes can help here. The longer the wire, the more electrons there are in the way causing increased resistance. However, the wider the wire, the more electrons are available to carry the current and therefore decreased resistance. Furthermore, all materials have their own unique makeup so the exact resistivity and operating temperature of the conductor in use will definitely have an impact.
These factors are represented by the relationship R = p L / A, where R is the resistance of the wire in ohms, p (rho) is the specific electrical resistance of the conductor in ohm-meters, L is the length of the wire in meters, and A is the cross section area of the wire in square meters. Keep in mind that voltage is actually a potential difference, so L is usually twice the one-way distance between source and load so as to incorporate the losses to and from the load. Also note that temperature will affect the electrical resistivity of the metal.
The amount of voltage drop obeys V = I R, where R is the resistance of the wire in ohms, I is the load current in amps and V is the resulting voltage drop in volts. Based on that relationship, we know how voltage drop will fluctuate, given the details of the circuit. As an example, when the current flowing into or out of the controller varies, we know the voltage drop will vary. Similarly, as the wire heats and cools, it's resistivity will change, resulting in slight variances in voltage drop.
Having a larger amount of supply voltage doesn't change the resistance of the wire, nor the current drawn and therefore does not affect voltage drop. What a larger supply voltage does affect is the percent voltage drop, because it is a ratio of voltage available to the load versus source voltage. That is, if 72 Volts is supplied, and the wire causes a drop of 1 volt, then the ratio is 1/72 which is .01388. In terms of voltage loss, that's 1.38 % which, according to my reading, would usually be very acceptable.
Most of what I found on voltage drop spoke about limiting the percent voltage drop to an acceptable level. The idea is that the load device should be provided an acceptable voltage after the drop caused by the wires. Outside of that acceptable input-voltage range, you're probably sacrificing device life or efficiency or both.
Insulation:
Insulation protects a wire, but can only stand so much heat. If more heat is being generated than the insulation handle, then obviously, it will fail (melt). Apparently, most battery cable has PVC insulation. Most welding cable has rubber insulation and may handle 600 volts. Then there's locomotive-grade DLO cable which may handle 2000 volts. I looked up a few specs for battery cable available at a local auto-parts store only to find that the insulation was rated for a maximum of 60 volts. I know 72 isn't too much of a stretch, but as usual, I'd rather be safe than sorry. I'll probably go with a welding cable instead of at least 4 gauge.
Ideally, wires would be rated for some overall power, instead of just a maximum current. However, as we've seen there are a lot of factors which make that kind of rating difficult to determine. In the end, I'll probably go with two sizes of cable, for the two sides of the controller. Something like 4 or 5 gauge welding cable on the battery-side, and 3 or 4 gauge welding cable on the motor-side of the controller.
References used:
Formulas, charts, notes, and facts:
Good coverage of a lot of wiring knowledge:
Voltage drop
Wire insulation types and ratings:
http://www.wesbellwireandcable.com/PowerCable.html (awesome, detailed info for each cable type)
Discussion of calculation of heat generated by wire resistance:
Practically exhaustive chart of gauge specifications:
Car-audio speaker and amplifier wiring information:
Other news:
Hooper Imports served me well. I got my parts and they look great. I'll have to report back one more time when I get a chance to actually put them on the bike. The point is they sent exactly what I ordered, and they did so quickly, with no fuss and no issues.
