Using 470v as a full battery and 100uH as motor phase-phase inductance with 15khz pwmRe: Calculating controller power input capacitance
Postby HighHopes » Wed Jan 01, 2014 5:09 pm
hi Njay, in reply to your PM i thought i would post more thorough explanation here for further discussion with forum.
When evaluating components it’s really important to consider the application, design requirements and the technology involved.
Application:
we are not calculating ripple current for a DC/DC converter but a 3-phase VSI inerter. there is a big difference here.. the inverter has bEMF due to motor load which fights the bus voltage and so limits the current ripple at high RPM (a good thing), the frequency on the DC bus is 2xfsw because not one phase leg switching but two, phase shifted.
The input supply is from a battery NOT a rectified AC so there is no reason to ask our DC Link cap to perform filter function, so those calculations can be ignored (i.e. not limiting factor) unless you have an EMI requirement to meet. The failure modes are different, expectations are different.
Design Requirements:
it could be that cost is the #1 design requirement, ahead of functional, ahead of reliability. it could be EMI if you have a specific need to keep this minimized, it could be long life, could be anything. but it helps to have it clear in your mind what your priorities are and in what order because this will help guide discussions especially those that have trade-offs (engineering is all about trade-offs).
Technology:
Electrolytic caps are low cost which makes them attractive for first consideration. It will be interesting to see if, at the end of the evaluation, if they are still considered cheap(er) than other technology. Electrolytics have high ESR/ESL so the limiting factor in the design is how much heat is generated due to ripple current because the capacitor life is cut in half for ever 5degC rise and so the calculation tends towards how many caps in parallel are required to share ripple current rather than how much total uF cap value would be appropriate for desired ripple voltage. This is a significant statement... due to cost requirement, what is being said is that the DC link capacitor uF value cannot be chosen optimally for the application. So straight off we recognize not to have an optimal solution and thus we keep this in mind to look closely at what we must pay for in order to have benefit of low cost electrolytics… there are always trade-offs.
The other dielectric to consider for DC link cap in VSI application is Metalized Polypropelene Film due to its low ESR/ESL and self healing properties which makes is vastly superior. I'll make the argument that it is CHEAPER solution too.
on personal note, i only ever used Polypropelene or other custom made specials for DC link cap in VSI application. i have no experience with electrolytic.
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Re: Calculating controller power input capacitance
Postby HighHopes » Wed Jan 01, 2014 5:11 pm
For electrolytic Caps, ripple current is the deciding factor in establishing DC link capacitance value which depends on battery voltage, phase inductance and duty cycle. The maximum ripple occurs when the bus voltage is lowest allowable (battery near discharged) and duty cycle is 50%. Thus we can eliminate two variable in the equation by setting d = 0.5 (worse case). The phase inductance is also fixed because your motor is pre-selected (how did you get 2.64uH?, that is incredibly low value). Let’s assume phase inductance is accurate, then likely 20kHz switching frequency is too low for such a motor because control bandwidth requirement will be high. To get high control bandwidth probably 100kHz would be more appropriate but good luck keeping the MOSFET power dissipation low.
Battery voltage also fixed due to design requirement so.. we just go ahead and calculate ripple current delta_I:
Ripple Current:
delta_I = d*(1-d)*Vbus/(f*L)
delta_I = 0.5*(1-0.5)*72V/(100kHz*2.64uH)
delta_I = 69App or 49Arms
So how many parallel electrolytic capacitors are needed? Let’s say we arbitrarily chose Panasonic TS-ED series because the advertising for this cap makes us think it is useful for inverter application. So, assuming 60degC ambient max, looks like we would need about 5 x 560uF caps (digikey price of 5*$2.75 = $13.75). That’s ~2.5mF .. wow.. that’s a lot. Now, the next person could argue, just use ONE 560uF to achieve desired voltage ripple could be used; hooks it up turns it ON and it works so says “see you wasted money buying five”. But what is the temperature rise of the capacitor when it is presented with 49Arms and what is the life expectancy?
With 2.5mF of electrolytic capacitor there is no need to calculate the voltage ripple, for sure it is acceptable. But anyway, we will check
Voltage Ripple:
I=C*dV/dt
We know current expected from cap is the ripple current previously calculated 49Arms.
Have to integrate both sides to get delta_V (at 50% duty), some math magic and:
delta_V = Vbattery/(32*L*C*f^2)
delta_V = 72/(32*2.64uH*2.5mF*100k^2) <-- Note that Vbattery should have been the fully charged pack value
delta_V = 0.03Vpp or about 0.05%.
Wow.. really exceeded any reasonable requirement for bus voltage ripple.
Still at cost of $13.75, seems attractive. But such large DC link capacitance comes with other draw backs that need solutions which cost money (inrush, cap bleed for safety, replacement every 5 years and all of these things are sized for the 2.5mF cap!).
* added note to use fully charged pack value when assessing voltage ripple
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Re: Calculating controller power input capacitance
Postby HighHopes » Wed Jan 01, 2014 5:14 pm
For polypropylene film capacitors (proper choice dielectric for VSI application) the situation is different because ripple current rating tends to be at least 10x that of electrolytic. So we skip ahead to determine the voltage ripple allowable first and then second check current ripple (heating). Seems we are just swapping around order of events but don’t miss how important this is. It means we can select DC link capacitor based on energy balance rather than heating limits which is optimal method.
We assume an allowable voltage ripple, for VSI application tends to be 3 to 5%; I always used 5% unless told otherwise.
Voltage Ripple:
delta_V = Vbattery/(32*L*C*f^2) rearrange, solve for C
C=Vbattery/(32*L*delta_V*f^2) delta_V = 5%*72 = 3.6V
C=72/(32*2.64uH*3.6*100k^2) <-- Note that Vbattery should have been the fully charged pack value
C = 24uF.
For part number Panasonic EZPE series 50uF, cost is $15. Current ripple rating on this part is 16Arms at 10kHz. Assuming this cap has at least same multiplying factor as electrolytic for ambient temp of 60C (multiplier 2.2) and switching frequency of 100kHz (multiplier 1.5) then 16Arms * 1.5*2.2 = 52.8Arms > 49Arms. Good!
Ya… quite a bit smaller than 2.5mF! So you save money on packaging, time to install. Also the same inrush limiter, safety discharge is sized now for much smaller cap. And replacement ever 20years..
Oh, and did I mention that because of the much lower self inductance, and tighter overall bus-bar packaging, the voltage spikes will be less which is always desirable.
so.. which solution is cheaper?
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Re: Calculating controller power input capacitance
Postby HighHopes » Wed Jan 01, 2014 5:14 pm
Other factors:
So the above considers capacitor dielectric & capacity to suit application and argument made that polypropylene is not an expensive solution. Now we must consider some other application specific factors that may (or may not) influence your decision on cap size.
Load dynamics:
If you have high acceleration then the cap may be asked to supply some of that current for first instant.
Regenerative breaking:
Depends on how fast your battery can take the energy, if the regenerative energy comes faster then the cap will take it raising the voltage. May need big cap to handle this, or, electronics to dissipate excess energy, or reduce ability to regenerate (slower deceleration).
BLDC/Induction:
BLDC motors have magnets so no need to ask inverter to supply magnetic field (medium through which torque is transferred to rotor). But, for induction motor this current (Id) comes from inverter since the machine has no magnets. It is not possible for the battery to supply reactive energy so it all comes from the cap meaning the capacity has to be about 15% higher.
Stiff bus during fault detection:
If your gate drive or phase current sensor has some sort of fault current shut-down, then the cap must supply the fault current for as long as it takes for system to detect fault and tell MOSFET to open. 10uS? The bus voltage is not allowed to drop more than 20% during this time or else fault shut down may not work properly.
Source impedance:
If your battery and/or cable has high source impedance then the voltage will drop as you accelerate. The cap has to take up this droop so is sized higher in proportion to source impedance and acceleration rate.
Filtering/EMI:
Generally not an issue when sourced from battery.
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ts not magic anymore if i have to derive the equations. that i need to check my lab notes to find the papers this equation came from.
Ripple Current:
1. delta_I = d*(1-d)*Vbatteri/(f*L)
how is this ?
start with common inductor equation: V = L*di/dt & integrate both sides & rearrange to get:
2. delta_I = VL*delta_t/L : VL = votlage across motor phase inductor
more discussion,
VL is when the upper mosfet turns ON it puts Vbattery across the phase inductor. but because its a motor with PWM it already had a voltage fighting the applied voltage, the motor's bEMF. so then VL = Vbattery - VbEMF. but what is bEMF voltage? it would be tempting to get crazy with the cheese wiz with more equations but we are only making a rough dimension of the capacitor so i think it is good enough to take an approximation. when the mosfet is OFF the voltage does not suddenly drop to zero, it is roughly maintained due to motor continue to spin and the voltage is roughly what the applied was so we can use bEMF = d*Vbattery. so VL = Vbattery - d*Vbattery. I should put a side note here that we could make a worse case assessment and say that the bEMF (d*Vbattery) is worse case equal to zero, i.e. when the motor is at stand still. but maybe that is a bit excessive if we think that the period of time that this occurs is small in comparison to period of time when motor is running. but perhaps not for EV application.. start/stop..start/stop.. hmm... anyway, for now i will leave it as bEMF = d*Vbattery and just accept that the capacitor is stressed when motor is starting up.
3. delta_I = (Vbattery - d*Vbattery) * delta_t/L : delta_t = mosfet ON time = d*PWM_time = d*1/PWM_frequency = d/f
4. delta_I = (Vbattery - d*Vbattery) * d/f * 1/L
5. delta_I = Vbattery*(1-d)*d/(f*L) : here you have to plot the formula of (1-d)*d to learn that peak is at d = 0.5
6. delta_I = (1-0.5)*0.5*Vbattery/(f*L)
7. delta_I = 0.25*Vbattery/(f*L)
Thanks.marcos wrote:Thumbs very up man
Ping me if you want the shunt sensor, isabellenhuete agreed to send me samples if I put their logo somewhere.
My gate driver complies with IEC61800 for working voltages of 1000Vrms and basic isolation, and its beefy power supply should be able to feed those Qg. If you are still planning to use kicad that design could be useful.
I guess you're getting a model s rear motor for this? Can't think of any other 1400 amp motor out there Well, maybe a train if you're into that.
0.7MW? That's crazy. Can't wait to see that run. Amazing they get that much through those little bonding wires. The batteries might have a hard time keeping up.Arlo1 wrote:
They are rated for 1400a at 96 degC! In my experience with field weakening you can achieve a little more DC current then the max the IGBT is rated for it self. Even 1400 amps at 410v (112s under load) you are at 574000 watts or 769hp. I feel ~1750 amps peak for 5-10 sec or so, is achievable which is 717500 watts. and likely even a little more as these are rated at 96 deg C where as the Fuji parts I am using in the CRX are rated at 80deg C
Ohbse wrote:Awesome stuff Arlo, love your work. Get that Patreon page set up - I will happily contribute.
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I added that to the allowed extension list. See if it works now.Arlo1 wrote:I will see if it lets me attach it here.
:Edit nope extension sldprt not allowed
Awesome thanksfechter wrote:I added that to the allowed extension list. See if it works now.Arlo1 wrote:I will see if it lets me attach it here.
:Edit nope extension sldprt not allowed
Lebowski wrote:I looked at Fusion 360 (as I want to get a 3D printer) but all I can seen is $25 a month subscription ? I am thinking about going the FreeCAD route...
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