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# AC Ah vs. DC Ah

#### maverick3n1

##### Member
So I just purchased my Tesla Model 3 Performance (75kwh battery). Unfortunately, I pulled a brain fart when I originally calculated my power costs as I was just thinking KW to KW. I completely spaced on the fact that the batteries are DC, not AC.

So my question is, at 240v AC, how many amp hours will it take to charge this 75AH DC battery from completely empty to 100%, considering the voltages are different, and there is power loss in the conversion from AC to DC, factors of which I do not know the efficiency of, or voltage of the DC packs. I'm trying to calculate what it actually truly costs me per DC Kwh. I'm guessing one DC Kwh takes 1.5 AC Kwh approx, so a total of 112.5 Kwh of 240v AC, but not positive.

#### mongo

##### Well-Known Member
So I just purchased my Tesla Model 3 Performance (75kwh battery). Unfortunately, I pulled a brain fart when I originally calculated my power costs as I was just thinking KW to KW. I completely spaced on the fact that the batteries are DC, not AC.

So my question is, at 240v AC, how many amp hours will it take to charge this 75AH DC battery from completely empty to 100%, considering the voltages are different, and there is power loss in the conversion from AC to DC, factors of which I do not know the efficiency of, or voltage of the DC packs. I'm trying to calculate what it actually truly costs me per DC Kwh. I'm guessing one DC Kwh takes 1.5 AC Kwh approx, so a total of 112.5 Kwh of 240v AC, but not positive.

1.5 implies a chare efficiency of only 67%, it's much better than that. I think the EPA testing includes wall to road efficency, but it should be >90% for battery and >90% for the charger putting you at >80% efficiency charging, or 1.25 AC power to DC.
This thread calls out 83% from wall to plug
Model 3 Charging Efficiency

#### maverick3n1

##### Member
Mongo, 1.5 is my guess because you're charging at 240v AC while I believe the battery is around 360v.. so if you had 0% loss, or 100% efficiency, and AC converted to DC volt for volt and amp for amp, You're only charging at 2/3rd the voltage of the battery. Thus it'd take 1.5 amps of 240vAC to make 1 amp of 360vDC. That said, AC and DC do not directly correlate that way, and there is loss in the conversion. This is why I asked the question.

#### mongo

##### Well-Known Member
Mongo, 1.5 is my guess because you're charging at 240v AC while I believe the battery is around 360v.. so if you had 0% loss, or 100% efficiency, and AC converted to DC volt for volt and amp for amp, You're only charging at 2/3rd the voltage of the battery. Thus it'd take 1.5 amps of 240vAC to make 1 amp of 360vDC. That said, AC and DC do not directly correlate that way, and there is loss in the conversion. This is why I asked the question.

Sure, if you want to talk Amps in vs amps out, however you mentioned kWh, which only depends on efficency.
I'm guessing one DC Kwh takes 1.5 AC Kwh approx, so a total of 112.5 Kwh of 240v AC, but not positive.

1 AC kWh in is 0.83 kWh (or so) into the pack. Or 1 DC kWh per 1.2 AC kWh.

• Rocky_H

#### maverick3n1

##### Member
Sure, if you want to talk Amps in vs amps out, however you mentioned kWh, which only depends on efficency.

1 AC kWh in is 0.83 kWh (or so) into the pack. Or 1 DC kWh per 1.2 AC kWh.
Is this 100% accurate, or estimated/hearsay? Would love to know the exact conversion. I've also heard that 120v doesn't deliver nearly the efficiency as 240v.

#### mongo

##### Well-Known Member
Is this 100% accurate, or estimated/hearsay? Would love to know the exact conversion. I've also heard that 120v doesn't deliver nearly the efficiency as 240v.
The link at the end of post #2 goes to the discussion thread.
The 120V efficiency issue is due to the amount of power that the car uses while charging that does not go into charging. Basically, there is a fixed amount of power needed to run the car while charging that gets subtracted from the wall power.
If (for extreme example) the car uses 100W when charging, and you provide 200W, then charging could only be 50% efficient. If you provided 400W, then you could hit up to 75%, 1kW:90%.
120V @ 12 Amp = 1.44kW max input, wheras 240A @ 24 Amp = 5.76kW, so that base load is a much lesser portion of the power available.

#### ewoodrick

##### Well-Known Member
A kW is a kW, a kWh is a kWh
A W is V " A
Amps don't mean much without the voltage

A kWh is a unit similar to a gallon.

• Rocky_H

#### Rocky_H

##### Well-Known Member
You are creating more confusion with trying to think in terms of amp hours and voltage conversions. It's much easier to just think of the amounts of energy in kilowatt hours, and about a 90% efficiency level to get it into the car.

#### maverick3n1

##### Member
Can't believe I overlooked that.. I'm so used to batteries being rated in Ah, I was thinking it was 75Ah, not 75kw. Big difference.

• mongo

#### Rocky_H

##### Well-Known Member
Can't believe I overlooked that.. I'm so used to batteries being rated in Ah, I was thinking it was 75Ah, not 75kw. Big difference.
I've always thought the thing of battery energy capacity being measured in amp hours was kind of confusing, because it's incomplete information. Let's say you have two batteries, and one has 500 amp hours capacity and the other has 700 amp hours. Oh, the 700 amp hours one is more energy, right? Not necessarily. It may be a 1.5 volt battery compared to a 24 volt battery. That amp hours terminology has to also know the voltage level of the battery.

And not "75kw". That is the much more common units mistake that is all over electric car forums. Kilowatts is power, which is energy per second. So to get energy, it's power times time: kilowatt hours.

#### mongo

##### Well-Known Member
I've always thought the thing of battery energy capacity being measured in amp hours was kind of confusing, because it's incomplete information. Let's say you have two batteries, and one has 500 amp hours capacity and the other has 700 amp hours. Oh, the 700 amp hours one is more energy, right? Not necessarily. It may be a 1.5 volt battery compared to a 24 volt battery. That amp hours terminology has to also know the voltage level of the battery.

And not "75kw". That is the much more common units mistake that is all over electric car forums. Kilowatts is power, which is energy per second. So to get energy, it's power times time: kilowatt hours.
It (Ah) is usually used to compare batteries of the same voltage/ type. Loads are usually described by current draw, so if you are operating in the same voltage domain, it is fairly useful.

It is also critical in dealing with battery monitoring systems because the electrochemical reations are based purely on Ah (current flow) and not the battery voltage at that moment (Wh). Though the voltage is critical in terms of limits.

#### MD-2000

##### Member
Is the difference between AC and DC related to RMS (root mean square) value? The AC is a wave, not steady value, so the actual power is the integral of the absolute value of the wave function. The RMS power of a sine wave is .707 of its peak.

#### mongo

##### Well-Known Member
Is the difference between AC and DC related to RMS (root mean square) value? The AC is a wave, not steady value, so the actual power is the integral of the absolute value of the wave function. The RMS power of a sine wave is .707 of its peak.

Interesting question. It is not the main factor.

AC voltage is usually given in volts RMS (120V house power has a peak around 160). The power is going through a switching converter where power-out=power-in*efficency and power=volts*amps on each side. Since RMS is the equivalent heating power (V^2/R), it doesn't quite match. Rather, the average voltage, 0.6367 times peak, does. Then you need to factor in the average current vs RMS.
Dealing in power is easier. 100W in 94W out, 94% efficiency. 100 V at 1 A in, 47V at 2 Amp out.
(Then there is the power factor side of things...)