To get started, can you explain to me how battery capacity is measured?

Energy capacity (kWh) is measured by the nominal voltage (V) of the cell multiplied by the capacity of the cell coulombically (Ah). Nominal voltage is the average voltage as it expends energy across the discharge capacity of the cell. Nominal voltage is dependent on the use range for the application. The product of these numbers multiplied gives you watt-hours. Watts = Amp x Volt.

A common concern we hear when we talk about why someone chose a particular system voltage is the V=IR equation. Is there a common misconception about this?

One common misconception I often hear is that “I need this certain amount of voltage, so my x, y, or z performs well.” Essentially if the device you’re powering is a motor or electromagnetic device, it’s the percentage of copper fill you can get into that slot that will determine efficiency, continuous power, torque, continuous torque, saturation torque, and losses. Whether the slot is filled with 100 single strands of fine wire or 1 strand 100 times the size, it’s an identical electromagnetic model in the slot. If you take a slice of the wound motor stator, whether you do 10 turn winding with 10A, 1 turn with 100A, or a use a fine wire turning 100 times with 1A on it, they are all identical models of each other, and the proportion of electromagnetic field and losses are identical.

Notes for additional clarity

There is a common misconception regarding (1) inefficiencies and (2) the amount of material required for a low-voltage battery and motor versus a high-voltage system. For (1), many think that the expression “I2R loss”, also called Joule heating, indicates that the higher current (I) required by a lower voltage system to reach a specific power (P) causes more loss through the conversion of electrical to thermal energy. By Equation 1, one can see that the P is a function of both the voltage (V) and I, and V is a function of I and the resistance (R).

When it comes to thinking about inefficiencies in the system, one only needs to consider the total P output of the battery that is being put to work (i.e. powering a motor). The battery voltage does not matter in and of itself since it is the product of V and I that equals P.

An image of a motor stator with excellent slot copper fill factor can be found here.

In electric vehicles, motors function through forces generated by electromagnetic fields. Similar to the principles of a solenoid coil, a wire is wound around a motor stator creating loops that form a magnetic field as current, from the battery, which flows through the wire (Figure 1). Inefficiencies arise from losses in the magnetic flux (B), measured in units Tesla (T). For (2) by the basic principles of B, we can calculate that the same volume of wire material wound onto the solenoid is needed for any battery voltage with the same power output. Equation 1-3 show the calculations for B in a solenoid.

To demonstrate this, let’s say we have two 100kWh EV batteries with the same motor but one is a high-voltage battery while the other is a low-voltage battery. Their voltage, as well as the current when they are outputting a specific power, are listed in Table 1 below.

Table 1 - Example of two batteries with different voltages and the same power output
  • If the high-voltage battery voltage (V) is 900V, and the highest discharge current to run the motor is x Amps, then the power output is 900x = P in Watts. 
  • If the low-voltage battery voltage (V) is 100V, and the battery provides the same power as the high-voltage battery (900x Watts), then the current output is 9x Amps.

Now, let’s say that we are using these batteries to power an identical motor at an equal power output of 900x Watts. While the high-voltage battery would run a current of x Amps into the motor, the low-voltage battery would run a current of 9x Amps into the motor. For the two batteries to output the equivalent magnetic flux density (B) in the motor, the number of wire turns around the motor stator would change depending each batteries’ current (see Equation 2). The number of turns (N) is proportional to the current (Equation 4); for the high-voltage battery, n would be 1/x, while for the low-voltage battery, N would be 1/(9x); the low-voltage battery uses fewer turns to reach the equivalent magnetic flux, listed in Table 2.

Table 2 - Required N for two battery systems with the same power output but different voltages

Consider the calculation for the cross-sectional area (A) required for a wire with a specific current (I) passing through it:

For the high-voltage battery, V = 900V, so A is proportional to x/900 m2 by Equation 5. For the low-voltage battery, V = 100, so A is proportional to x/100 m2. This makes the difference in cross-sectional area (A) between this high-voltage and low-voltage battery 8x/900 m2. While the wire for A is smaller for a high-voltage battery system, this does not mean that the system uses less wire volume. In fact, because of N, the number of wire turns used to create the required B magnetic flux is the exact same volume of wire material.

To calculate that the same volume of wire is used, first note that the length of the wire (L) wrapped around the motor stator is proportional to N. As we calculated earlier, for the high-voltage battery N = 1/x and for the low-voltage battery N = 1/(9x). Therefore, the volume of wire needed is proportional to A*L, which is 1/900 m3 for the high-voltage battery and 1/900 m3 for the low-voltage battery (see Table 3).

Table 3 - With same power output, both battery systems use the equivalent volume of wire

Note that these are the same values; the same volume of wire is required for both high-voltage and low-voltage batteries with the same motor and power requirements. This means that you can select any battery voltage for a motor power output. Any inefficiencies in the system arising from the motor are identical for the same battery power output. 

The interconnect harnessing between battery, motor controller, and motor must be sized with a proportionally thicker conductor cross sectional area. However, these are the distances in an EV design which may be configured by component placement to have very short total path lengths. This takes the total difference in harness conductor mass to under 1kg ($10.40 for copper or $3.83 for aluminum) in a well packaged system or to +10kg ($104 for copper or $38.3 for aluminum) in a system that requires significant separation between battery/inverter/motor. Aircraft with fuselage mounted batteries and motors spread far out on the ends of wings is an example where the harness conductor mass savings can be a reasonable HV use case, where the price of the additional BMS channels and more expensive HV rated fuses/pyrofuses offers system weight advantages. For powertrains in cars, motorcycles, boats, satellites, trains, drones etc., the battery can be designed with its output terminals located locally to the motor controller and motor, shortening this total high current interconnect path length distance easily below 1-2 meters total. 

So, when people see P=I2R=VI, and they see the square on the current, they may be intimidated, but they shouldn’t be. The reason why they all have identical resistive losses despite the different Amps is that the difference between a 1-turn motor and 100-turn motor is that one has 10,000 times more resistance than the other, so everything compensates and balances out from the I2R. When you go to a fatter winding with fewer turns, you get thicker at the same time you get shorter because the total series path you have to take looping the tooth is reduced. As you get shorter and you get fatter, the square root function of resistance dropping ends up being a zero-sum game.

The battery is also electrically agnostic; it’s just a range of cells. As long as you aren’t trying to get below the 3.7V nominal building block of 1 cell group, then you can adjust them into a series group to be the desired voltage. The battery pack itself is agnostic to the configuration of the cells. The motor, too, is completely agnostic as to the pattern of wires you choose to complete filling the slots. Provided you have the same amount of copper fill in the slot, you will have the same performance. This means that your motor controller is really the factor for determining what voltage makes sense for your system—design around the limitations of the switches, control, capacitors, power regulation, and filtering stage. If you have 150V parts, you can’t just run at 150V. You must run at 120V peak because, in transient conditions, it’s common to see spikes of 15-25V, so it’s critical to leave margins so as not to damage your electronics.

Can you speak about designing different battery systems according to the voltage and availability of powertrain products?

You’ll notice that there are limited options for off-the-shelf high voltage products. Every EV on the road built their own DC/DC converters, charging electronics, BMS, etc. If you’re going to integrate at that level, component availability doesn’t matter. But if you just make battery packs and want something high voltage, you’re limited to just a handful of price prohibitive offerings. Availability of powertrain products isn’t an issue in scale, but when developing prototypes, it becomes difficult.

Even with things like fuses, the arc flash energy and breaking energy and quenching plasma gets nuts. When this occurs, the higher the voltage the longer you can sustain that energy. Many fuses with HV rating in DC get derated because they were tested with equipment that doesn’t have the current delivery rate of batteries which are almost instantaneous. The current rise rate is approaching a step function towards many kA depending on the pack size. The challenge of splitting plasma joints in conductivity when the element shears becomes very complicated; this is why there are things like pyro fuses. There is the soft short potential too – low impedance bussing on lower voltage systems can clear fuse elements without drawing an arc for a long time and open contactors under load. They have a much more generous tolerance window at lower voltages. Even if you are Tesla, you still have to deal with high voltage challenges for every component and life safety touch protection.

We’ve talked about 150V DC being the borderline between what we would consider high and low-voltage systems for batteries. Why do we tend to see such high voltage ranges across EVs?

There are many parts to this answer. To start, there tends to be a no man’s land between 150V and 300V. There’s a gap in which silicon MOSFET controller devices and IGBTs are poorly suited. IGBT is poorly suited because the percentage of forward voltage drops as a pair of 1.7V diodes in series for 3.4V drop. In a 100V system, you have a 3.4V percentage loss at all loads, even light cruise. For this reason, you don’t see IGBT used in cells until 350V because at around that range it becomes a 1% loss. In a MOSFET, you have Rds-on resistance between drain to source in the on state with the gate. This means resistive loss can approach zero in a MOSFET from the aspect that at cruise load, there is roughly no voltage drop across the MOSFET. As you go into heavy current loads, there won’t be some fixed tax in forward voltage; there will just be proportional heating to the amount of current you’re pulling. This gap in electrical switching materials is why you don’t see 200V vehicles. You see 48V or 110V, but then generally nothing until about 300V. From a silicon switching perspective, 100V and 150V switching parts are similar in the amount of power they can switch for a given amount of losses. One of those options has a lower cost. Of course, there are some exceptions.

SiCFETS are capable of switching HV without a forward voltage loss to conduct. Currently, they have a cost penalty due to the costs in working with SiC materials over Si materials. SiCFETs have a much faster switching time than Silicon, which causes increased EMC-related noise potential. SiCFETs also are an increased challenge to share current evenly due to practical layout inductance.

Another common argument I hear for designing a HV system over LV is the cost due to thicker wires. Do you have a comment on cost conceptions?

At the time of filming this, copper is $10.58 per kg and aluminum is $3.80 per kg. For example, I made two cables with ring terminals of the same length, but different gauges, weighing in at 45g and 130g, respectively. I simulated a system pulling 100kW from the motor controller. The copper at 28s is 96¢ and there is a BMS intrinsic cost of ~$40 for cell management. In the lighter cable system, there is a BMS intrinsic cost of ~$120 for managing 96s cells because the chips need to be put into series. These chips can also be difficult to procure due to global supply chain shortages.

If you have the ability to package your battery near the inverter and the inverter near the motor, then the bus length can be very short. If you do a sloppy job or have a challenging application like certain kinds of electric aircrafts, and you have 4ft of cable, copper is $8.63 for 28s and $2.88 for 96s. The cost difference is $5.75 in copper to be 28s from 96s, but the BMS difference is around $70 cheaper. The battery and motor are agnostic to voltage. However, the motor controller is sensitive to voltage and operates in different ranges, so there are cabling differences. People may be concerned with reducing the cost of the harnessing, but the additional overhead from the BMS savings makes up for it. Plus, you have the added advantage of human safety.

But it does seem as though there is a weight cost?

In an EV, for most applications, you can package the powertrain system in a short distance, so the difference in mass is only proportional to the length the cables have to span. As your difference in packaging height gets tighter, the cost difference becomes negligible. Even most airplanes can be low voltage as they don’t have the propeller separated from the battery.

Based on what you’re saying about these wires, it sounds like a low voltage system could work for a variety of applications.

That’s right. From high powered to low powered, it doesn’t matter how much energy the system has. It just depends on how far your energy storage system is from the source of use in the application. LV can very likely improve cost, safety, and longevity. There are always exceptions where people need to have the battery 100ft from the motor controller. Still, low voltage would have been appropriate, cost-saving, and an improvement in efficiency for most situations that we have encountered.

Another common piece of feedback I get is about charging methods: “I need a HV system for quick charging.” Is it true you need higher voltage to charge faster?

It’s up to the ampacity of the cabling. From a power electronics perspective at the charger, it couldn’t care less if it’s 500V or 50V; it is how the transformer’s magnetics are wound, the size of the busbar, and the capacitors that make the difference. You pay per kW for DC charge infrastructure. There are a lot of infrastructures that only support 350A. If you’re a 100V system, that means you’re getting 35kW charging, which isn’t that great. If you look at a system like the Tesla supercharger, we have measured our own charge current at over 740A into that charge connecter, at which point the 100V system has a 74kW charge rate, which is pretty good. That is faster than most existing companies DC fast charging options. Therefore, there is no need for a giant connector or an impractical to make connector because this is from the same existing Tesla supercharger connector. The beauty is that the existing supercharger connector uses a pair of 12mm RADSOK pins. It’s only using 1 pair for 740A. If you made a 100V system that charged at the same speeds as the Tesla supercharger, with a 3 pair of those pins in parallel, you would have a charge connector which you could package really small, with higher mate insertion and higher extraction force on the connector. Your cable would be stiffer to manipulate, but it would still work fine in that situation.

Are you suggesting a new kind of connector?

If you could start from scratch, this would be a great foundation to start from a connector capable of 3 Tesla pins and 2200A. A 110V system with 220kW charging would be a dream. That would be a plausible solution for fast charging. Interestingly, a lot of existing infrastructure for motor and controller chargers is based around 1980’s era industrial VFD drive technology. It was groundbreaking at the time, but they ran these voltages based on industry 480 3-phase and IGBT switching range optimized for 800-1200V spikes. This is the voltage range used today in cars, but that range was selected at a time when you were looking to mount your industrial equipment in different locations around your factory. If you wanted to get a MW from point to point, hundreds of yards away, then 480 3-phase was a great option that could easily carry all the power you needed long distances with minimal cabling losses. This enabled a bunch of inverter and drive parts, existing high current IGBT, and modules built around this technology for this application. But it wasn’t designed for a battery-powered vehicle. Whenever MOSFET technology gets lower RDS on resistance, the ideal operating voltage for an electric vehicle drops. IGBTs have the same intrinsic forward voltage they have had since the 80’s due to the properties of silicon, but for MOSFETs, every time silicon lithography etching can make finer resolve structures and surface features, or the MOSFET can have higher conductivity per unit area, this is why we see MOSFET’s continue to drop in RDS on resistance.

Does voltage have anything to do with cooling the battery?

No – just the C rate of the pack. Say you have a 100kWh pack in your car - if you discharge at 100kW, you’re burdening your pack at a 1C rate of discharge load. Whether this 100kWh pack was one huge series string or one huge parallel-group, if you pulled 100kW from it, it would produce identical heat per cell. What is different is that when you have high current density and high current bussing, your possibility of imbalance in current in balance are magnified. Your bussing design needs to allow symmetrical sharing of current in a validated current path to ensure that you don’t have bussing hot spots from non-uniform current density, which can be difficult to see with your eyes.

Feedback we commonly get is that “Everyone is doing high voltage, so we need to do it too.” There is a sentiment that people are more afraid of high current than high voltage because they feel high current is inherently not safe.

A dozen years ago, I had the same misconception. I’m almost embarrassed to admit this, but I wanted to build a 600V electric bicycle with small RC hobby packs. I would have done it had there been controller technology that was cost-effective and sized correctly. But this was my own misconception, even with EE training. When you initially consider the rule of I2R, then smaller A numbers = good. It’s an easy mistake to make. But 25+ EV builds later, I like to design them 16s – 20s.

So you are more concerned about voltage than current? What’s the difference between taking a high current shock or a high voltage shock?

Your skins dielectric potential prevents you from being able to take high current when you’re at lower voltages. The only way you can take high current is by touching high voltage. That’s the paradox. When humans take high current that stops their heart, it’s when they are 30-100mA range. But the cool news is that your skin’s resistance is generally protective up to 90-120V DC. With that voltage, you may feel a small current path and the tickle and may be uncomfortable, but it would be nothing imposing dangerous stress on your heart or respiratory system. They say touch-safe is below 60V, but even then, they are a little conservative, I think, having touched 120Vdc hundreds of times without much discomfort. I have unfortunately touched over 200V and luckily survived to tell the tale. That voltage causes your ribs to displace, tears your muscles and is extremely uncomfortable. Not great. I reevaluated my personal safety rules in high voltage applications after having a shock from over 200V.

That’s the danger of having high voltage systems. Life safety is obviously very important, and industries take steps with that in mind. But there is an insidious danger when it comes to high voltage – dielectrics, adhesives, and coatings break down under electrostatic stress and time. If you don’t validate your materials under voltage stress, you’ll get to find out when you build your pack if they last under voltage stress. You may say, ‘I measured the resistance on this adhesive joint, and its 100 MΩ.’ Often times it is not even as good as this, but the crazy thing is that even 100 MΩ with 1V is 6.23/1013 electrons – that is hundreds of trillions of electrons flowing across your insulator. This electron flow drives the breakdown of the dielectrics. It’s what carries metal ions through it. When testing through the base plates, you must run each polarity orientation between the materials and the interface because there is only one polarity that migrates towards a breakdown. One is pulling aluminum up, and one is trying to pull Nickel from the can.

There are a lot of things to consider when designing a high voltage system.

Absolutely. Let’s say you go with 500-1000V – everywhere you have a sharp edge on a conductor, the air breaks down spontaneously from electrostatic field forces. These make reactive species to break down plastics and dielectrics. Even when it isn’t breaking the air down, it’s inside your plastics imposing stress that drives decomposition with time. This is something I felt the most let down about from my training. They treat dielectrics as though it is an unimportant insulator you can ignore. It’s not. Polymer science is a weird one. We are lucky to have Bryan, our in-house polymer expert, on our team.

This process of imposing stress from an electric field that drives decomposition of plastics and dielectrics is called ionic migration. When it occurs in metallic materials, it is called electromigration.

I know you’ve been a long-term proponent of low voltage systems and that it comes from your intense history with high voltage and sharp learning curves. I want to make sure I’m asking a balanced question – do you know any concepts that successfully use DC high voltage systems?

If you have unlimited space, weight, and budget, it can be done safely. It’s a lot of unnecessary cost and will probably never match the powertrain system efficiency you can have otherwise, but it can be done, and there are some situations where it makes sense, like the above mentioned wing motors fuselage battery aircraft example. What I would love to advocate for, though, is that high voltage shouldn’t be the first place you look to, it should be the last. Maybe there is some deal-breaker that you can’t make work with lower voltage where if, for some reason, you can’t locate your energy source proximally to the place where you are using the energy. But consider this carefully because if you go low voltage, you are going to have a safer, cheaper, faster, longer-lasting system. Everything gets better - including BOM cost. Losses don’t have to increase because of low voltage. If you go to 1/4th the voltage and go to 4 times the cross-section cable, you have no loss increase.

It is the controller switches that impact powertrain system efficiency, not battery voltage.

It sounds like low voltage is thinking about the future and whether the kinds of battery systems we want to live out in the wild, as people refurbish and reuse them, are being made with that in mind. With HV, it seems plausible that wild things are going to start happening out there.

Definitely. Ironically, everyone builds high voltage packs in LV module strung together because they don’t want to work on it otherwise. Plus, it’s safe and effective for employees to move them around when there are 60-100V in the modules. Then they don’t combine them into HV assembly until it’s underneath some kind of case to encapsulate everything. This is a huge fire risk to the factories. Plenty of folks are learning hard HV and dielectric decay lessons in volume manufacturing. I remember in 2015 that Porsche said they would ship the Mission E at 800V the following year. Then the next several years came and went. The Mission E never shipped. If you want to add 5 years of project delays learning how to make HV work, that is… an option… but not the easiest, most cost-effective, or longevity-prone route.

When it comes to a battery system, what do you think Is the ideal battery system voltage.

If I was going to do a system under 2kW, I like operating around 24V. I can give you a couple of kW systems and 24V that are 98-99% efficient, cost-effective, and touch-safe. If the system is in the scooter range, maybe up to 25kW, I really like between 16s – 21s. One gets to us 80V rated MOSFETs and the other 100V rated MOSFETS. They are very close in power density and equivalent in efficiency. Up to 250kW is great for LV because, with 250kW per motor controller, you can run as many motors and/or motor controllers as you like. Most vehicles these days run multiple motor controllers, which is so convenient for LV applications due to the short wiring. Also, if we have a motor controller that does 2400 phase Amps up to 120V per wheel - say you do a 3 or 4 motor car - now you’re a low voltage system with 1000 horsepower or a 500 horsepower 2 motor system. Either way, low voltage can fill all those niches cost-effectively.

Let’s talk about stationary storage. We have seen some pretty wild designs come through with very high voltage. Any thoughts?

If you run a bunch of high voltage batteries, you will have to deal with balancing resistance with the harnesses, and they are never going to be equidistant from each other, even with radial arrays. It doesn’t package well. What Tesla has done is they run just 12s which is a 48V battery system, max. Each of these 48V systems has an isolated HV DC/DC converter, with the output at 1200V. Because it’s an isolated DC/DC, it can share current and bidirectionally charge or discharge through the same device. It also allows any system to be isolated, so, if you have a malfunction from any of the packs, you can stop charging or discharge it to a low SOC and leave it without affecting any more loss to the system than that one cell. I really like its current sharing ability and intrinsic low voltage safety. The cells themselves are going to hold your 18.5Wh of energy no matter how you arrange them. Some arrays have higher cost, failure modes, and risks associated with them.

Anything else?

When I think about the system I would personally choose to buy, I would seek out products that are lower voltage if they are similar in function. This is because, probabilistically, we will have the least trouble with those. There are fewer things to go wrong.

Below is a summary of high-voltage and low-voltage battery systems for electric vehicles.

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