Calculating heat output from current
I found the formula for this but was still having trouble grasping it conceptually, but I just realized something.
A few weeks ago I was talking to some mechanical and electrical engineers about combined heat and power. Combined heat and power, aka co-generation or co-gen, is generating electricity on site, usually by burning natural gas, and using the waste heat to heat your buildings, domestic hot water, or some other process.
All of the mechanical guys were saying what a great system it is, and amongst our reasons for this is minimizing voltage drop by generating electricity on site. The electrical guy disagreed, saying that voltage drop is negligible and the grid system is not flawed (although the generation systems certainly are).
Now I realize that the part that I wasn't understanding about the inefficiencies of the grid and the part I was not understanding about this problem are one in the same. The heat generated by electrical current, which represents the energy wasted through voltage drop, depends on current only, not voltage. So when power is transmitted at high voltage, since the current is therefore low, so is the heat dissipation, and so is the wasted energy.
Say you needed to transmit 100,000 VA from point A to point B. If you were to transmit it at 100V, the energy wasted through heat dissipation would be proportional to the 1,000A current. If you were to step up the voltage to 100,000V, the current would only be 1A and the wasted energy would be proportional to 1A. Because heat generation depends on current ONLY, not voltage.