EV Performance Fundamentals
Big thanks to Chris Bergsneider and Dr. Chris Bachman for many improvements to this article.
Whether you are a first year electric vehicle (EV) team, or a team member joining an experienced team, engineering maximum EV performance requires a different mindset than the conventions of internal combustion (IC) performance.
First Challenge:
Know the rules. Design within the rules.
FSAE Rules, Electrical Inspection, and Mechanical Inspection Documents
Creating a rules-legal design is worth more points than any other parameter.
If you are a first year EV team, your target is minimum viable product. Read the rules and tech inspection sheets throughout design and build. Use last year’s until the current year is released. Practice going through the entire inspection. Make the battery really easy to assemble and disassemble for inspection. Best practice is to have a designated team member responsible for every page of the inspection form, up to the maximum number of team members allowed in Tech Inspection.
Make it PASS Tech Inspection by the book.
Make it GO long enough to finish endurance.
Make it STOP enough to pass the brake test.
Make it TURN to the rules minimum radius.
Just completing that list is an immense amount of work. Building a battery and passing tech inspection is much harder than putting a restrictor on an IC powersports engine. Pay no attention to going faster, stopping harder, turning quicker, or hitting rules limits. Save that for the next car. Experience makes the second design much faster than the first.
Second Challenge:
Lithium-ion cells have finite life spans.
I think of lithium battery life like aluminum fatigue. One big event can break a cell instantly. And no matter how small, every use puts some wear on the cell. Capacity and power loss are the inevitable, eventual, cumulative effects.
Battery cells are rated by manufacturers for the number of cycles from a high state of charge (SOC) to a low state of charge and back. The amount of performance loss at the end needs to be noted, along with test cycle time and conditions. Your battery will operate under different conditions, which will affect the useful life.
Simplified equivalent cycle estimate:
Set all coefficients for the baseline data sheet cycle life = 1. All the coefficients are nonlinear, and all coefficients generally affect other coefficients. All are the most damaging at the highest and lowest State of Charge (SOC). Different chemistries will respond differently to each factor. To a much lesser degree, even different cells within the pack will respond differently.
Every time a cell is used:
Estimate the equivalent number of baseline cycles experienced.
Add this to the running total number of equivalent baseline cycles in that cell’s lifetime.
Predict the number of your cycles remaining under your usage conditions.
Change in State Of Charge (ΔSOC) coefficient
The amount of capacity used may be greater than or less than the cycle life test. Using more SOC will have a higher cycle coefficient. Using less will have a lower coefficient. For example, if a cell is attached to a charger, over time it self-discharges and the voltage drops. If the charger goes back to charging, that is a fraction of a cycle. The useful life of a cell can be noticeably reduced by sitting on a charger repeatedly turning on and off.
Reading the figure above, the best guess coefficient is the ratio of baseline_cycles / use_case_cycles. If 50% ΔSOC has the baseline coefficient of 1 and results a cycle life of 10,000, simplistically, I would say 100% ΔSOC is equivalent to 4 baseline cycles, 80% ΔSOC is equivalent to 2 baseline cycles, 20% ΔSOC is equivalent to 1/3 baseline cycles. That example number is just for that particular test of that particular cell, and it’s not even the same cell as the other graphs discussed in this article. Note the unusually high cycle life on the order of 10^4, where most other sources cited are on the order of 10^2.
Here are two schools of thought on setting the upper SOC limit:
Do not use the Constant Voltage portion of the CC-CV charge curve. This sacrifices 10%-15% of theoretical max capacity, but avoids the less efficient and more damaging area of the charging curve.
Lower the max charging voltage from the nominal 4.2V to 4.15V, or even 4.1V. This loses a similar amount of capacity, and charging takes longer, but stays further away from the higher voltages where the Lithium starts to form dendrites.
Stop discharge even further above the minimum voltage.
For example, with a nominal 3.6V cell, a good starting assumption is to never go below 3V during discharge.
Use a consistent definition for SOC
Your phone tells you 100% charge and 0% charge. This is only the capacity it is allowed to use. The battery is capable of more, but using more capacity would degrade the cells much faster. You can define SOC as nominal rated capacity, team-limited usable capacity, or estimated remaining capacity as the cell degrades. But all simulations and battery management calculations need to refer to the same thing.
It is difficult to even identify the true maximum energy capacity or remaining energy available. The limits are affected by past usage, and by real time power usage, voltage drop, and temperature. There may be a large or small change incurred by any given battery cycle.
Using 95% SOC to 10% SOC is not a careful approach. It is a very aggressive strategy that will make all the judges take a big step back from the car. Best case, the battery will degrade quickly, limited by its worst, hottest cells. Worst case, over-discharge can short the worst, hottest cells, creating the risk of thermal runaway until they are replaced.
Resource: Chemistry of Over-Discharge
Rate of discharge / charging coefficient
Most battery cell manufacturers rate capacity and other parameters at 1C or lower. This means the battery cell is discharged over 1 hour or longer. Usually cycle life tests are charged at much less than 1C.
Reading the figure above, if 1C has the baseline coefficient of 1 and results in 80% capacity remaining after 800 cycles, simplistically, I would say 2C is equivalent to 8 baseline cycles. 80% remaining: 800 baseline / 100 use_case = Rate_coefficient = 8. That example number is just for that particular test of that particular cell, and it’s not even the same cell as the other graphs discussed in this article.
Discharging or charging a battery at a higher C-rate = higher power:
Increases heat, a function of power and efficiency
Increases energy losses from heat
Contributing to reduced energy capacity
Increases voltage drop
Increases amperage for a given power demand
Reduces the usable voltage range or charge % range
At the low end for discharging
At the high end for charging
Higher power requires more battery material available for chemical reactions.
Reduces the cycle life
Severely and immediately in some chemistries
C-rate is applied to individual cells and to whole packs as either C-rate = hours*Amperage/Ah (unitless ratio) or as C-rate = kW/kWh (a frequency of discharge or charge per hour). Both are useful ways to take instantaneous load and extrapolate total discharge or charge time.
Note for EEs: The language and thought process in this article is built around the concept of total pack energy, not Ah.
Example discharge rate characteristics, page 2. Pay attention to detail when back calculating instantaneous amperage, because rate affects voltage, amperage and capacity. Nominal values may not be consistent even for a single data sheet. For example, this cell does not deliver its rated capacity even when discharged at 1C, returning even less at 2C. Reading the on page 2 of the link, if 1C has the baseline coefficient of 1 and intercepts 3.0V at ~2600mAh, simplistically one could calculated either a lower usable energy for ΔSOC defined by 4.1V to 3.0V, or one could look at the different voltage to reach a 2600mAh discharge. The latter, by dropping to ~2.8V, is obviously much harder on the cell, suggesting:
A cause for the 2C coefficient of 8 in the different cell discussed above
Indicating that small differences in energy available may have large impacts on cell longevity
A strategy to preserve cell performance
By reducing total energy usage based at higher C-rates
By reducing C-rate at lower SOC
Cell temperature coefficient
Cells can be damaged by high temperature operation. Even the rules maximum may be stressful. At the other end, winter testing may have a very small usable window.
Example discharge temperature characteristics, page 3. If 25°C is the baseline, the cell is fairly insensitive, or even improved by running at 40°C or 60°C. On the other hand, the reduction when running at 0°C and below is even more dramatic than running at a C-rate of 2 on the page above. For this cell, it suggests again that longevity effects are much greater than the ratio of the curve values on pages 2 -3.
Required cycle life:
Consider using much gentler limits for most driving and testing. An aggressive engineering judgment call at the endurance event takes cell characterization, tracking, and predictive modeling.
Keep your cell buying budget in mind: Does the pack need to last one event only, the entire competition, an entire testing and competition season, or multiple seasons? How much performance loss can you work with? Add up all the expected events and expected testing before starting any test. Track where the battery is on the expected cycle life and degradation. Continuously update and improve the battery life and usable charge model.
In my opinion, there should be a pre-planned and calculated reason (which may include driver training) every time the team does any of the following:
Drive at full power
Fully charge the pack
If you ask the FAA, even storing a student-built prototype pack overnight at >30% is asking for trouble.
Fully cycle the pack
Any regen
Resources:
https://github.com/HVES-Battery-Testing-Consortium/LG-HG2
https://calce.umd.edu/battery-accelerated-cycle-life-testing-data
https://www.wisconsinracing.org/e-documents/
Team members, create an fsaeonline.com account:
Learning Lab, EV Workshop 2022
Learning Lab, EV Workshop 2023
Third Challenge:
Lithium-ion has low energy density.
Fuel Tank And Battery Pack Sizing, by Justin Jang
Simplified endurance energy estimate:
Number of laps * full throttle power (kW) * average throttle position (%) * laptime (hours)
= required usable capacity (kWh)
Increasing the capacity of a fuel tank is technically trivial. Battery cells come in finite sizes. Cell count in series and parallel affects capacity, voltage, and available power. A battery pack sized to complete endurance is large and heavy by comparison to a gas tank.
Competitive Intelligence has an expanded discussion of typical endurance C-rates. A quick survey of the fastest Formula Student EV cars worldwide turns up endurance times just under 1300s. Assuming the entire usable capacity is consumed, this gives an average C-rate well over 3 by the time capacity buffers and regeneration are taken into effect. Higher C-rates reduce the usable capacity compared to nominal ratings. High-power usable energy is more important than low-C maximum energy.
Study the other competitors, sort them into groups by power, energy, mass, calculate the average power over endurance.
Simplified endurance power estimate:
usable capacity (kWh) / total time (hours) = average power (kW)
The motor, controller, and battery must have a continuous power rating at least that high. Regeneration must be added to power usage for all components, and its effects must be managed for cooling and cycle life.
Fourth Challenge:
Simplify and add efficiency.
If you are considering a multi-speed gearbox on an electric racecar, the motor is not powerful enough.
The overall vehicle priorities in IC racecar design are mass, downforce, drag, power, and mu. IC FSAE teams need to simulate and validate straightline acceleration, steady state cornering, straightline braking, and slaloms if they're at the next level. For EV teams, in every calculation and test, it’s not only how fast, it’s also how much energy.
EV simulation and validation needs to map the entire speed range * traction envelope. Not just at maximum performance, because the car will not be able to run 80kW average for a 20-minute endurance. Not just at endurance performance, because it is easy for an endurance-capable car to trade farther for faster, and vice versa.
| Condition | IC - Maximum Curve | EV - Contour Plot |
|---|---|---|
| Acceleration | G vs. Speed | Energy vs. G vs. Speed |
| Cornering | G vs. Speed | Energy vs. G vs. Speed |
| Braking | G vs. Speed | Regen vs. G vs. Speed |
| Slalom | Gate vs. Speed | Energy vs. Gate vs. Speed |
Simplified efficiency estimate:
Battery efficiency (%) * controller efficiency (%) * motor efficiency (%) * drivetrain efficiency (%)
A contour map of total efficiency vs. power and motor rpm is more useful - multiply the gradients, maps, and constants on top of each other:
Battery efficiency vs power * controller map * motor map * drivetrain constant
Pay attention to the difference between battery power, controller power, motor power, and wheel power, especially for thermal management. Power * (100% - each efficiency) gives the cooling requirement for each component in Watts. (EV teams need to engineer in metric. Horsepower and inches are for marketing, tube orders, and unreliable vehicle dynamics work.) In addition to “power out divided by power in”, “how much heat in Watts is generated at a given power level?” can measure a component’s efficiency.
Efficiency is at least as important to EV racecar design as mass, downforce, drag, power, and mu. For one project I worked on, holding lap time constant, increasing vehicle mass by 1% reduced the range by 0.05 laps. Holding lap time constant, increasing the (already high) powertrain efficiency by 1% added 0.15 laps. And laps for full-size racecars are much longer than FSAE endurance laps.
As a demonstration, factor efficiency and a low estimate of full throttle power into the simplified endurance energy estimate:
Low efficiency values:
Battery (85%) * controller (94%) * motor (90%) * drivetrain (90%) =
HV powertrain efficiency = 64.7%
22 laps * ( 25 wheel kW / 64.7% efficiency) * 50% throttle * (1/60) h laptime =
Required usable capacity = 7.1kWh
Better efficiency values:
Battery (90%) * controller (99%) * motor (95%) * drivetrain (95%) =
HV powertrain efficiency = 80.4%
22 laps * ( 25 wheel kW / 80.4% efficiency) * 50% throttle * (1/60) h laptime =
Required usable capacity = 5.7kWh
Fifth Challenge:
Driving and Energy Management
Formula 1 and Le Mans have both required energy management since the early 2010s. Refueling is banned in F1, and Le Mans Prototypes are given limited fuel per lap. I count 7 instances of saving energy in the 2015 pole lap at Le Mans. They are highly strategic, and increase in lap time is minimized (quick estimate: 0.5s), while energy saved is maximized (quick estimate: 9%).
With any appreciable straights, teams that master high acceleration, efficient cruise, and energy saving will be significantly faster than beginner teams that simply set a power limit. Watch Formula E onboards. EV racers need to manage energy on a corner-by-corner basis, in addition to traditional skills of sensing the limit and managing tires. Drivers have to develop a sense of how much energy is saved vs. time lost with different strategies. Strategies may include coasting, restricting top speed, throttle and brake application, reducing slip angles, drag reduction, maintaining speed instead of accelerating then braking. Energy management is closely related to battery temperature management.
Every dash display needs to provide drivers with the following information:
Laps or distance remaining
Usable battery capacity remaining
Usage rate
Choose the easiest units for drivers to process on the fly, at different points in a lap. As a driver, numbers are much better than a single LED (or less) per lap. Radioing instructions is far from optimal.
Single pedal driving might be appealing from a design and programming perspective. It’s great for street driving, nowhere near the limit. But requiring multiple control inputs for braking and corner entry will create mistakes, and drivers will not coast successfully if it doesn’t happen at a control limit.
Sixth Challenge:
Regenerative Braking
Regenerative braking should only be added when the team has a strong base in all other areas. Take everything that’s hard about electric powertrains, and do it backwards wearing high heels. Regeneration works best with:
6A. A fast car + a fast course + heavy braking
6B. High system efficiency
6C. A battery that can charge at very high C-rates
6D. Powerful motors on the front axle
6E. A braking map that changes vs. pedal pressure and vs. motor speed
6A. Fast car, fast course, heavy braking.
Roughly counting up braking time at the (unusual) 2019 Michigan course, I get around 12%. Use your team’s own recorded and simulated data to get a better number. Less potential energy budget reduces the justification for regen.
6B. High System Efficiency
If system efficiency is low, regenerative braking will not help as much as increasing efficiency, because it goes through the system in both directions
Low efficiency values:
Braking: drivetrain (90%) * motor (90%) * controller (94%)
Battery efficiency, may need to separate regen and accel: (85%)
Accelerating: controller (94%) * motor (90%) * drivetrain (90%) =
Regen system (49.3%)
A hybrid racecar with low assist power and 49% efficiency could lose more performance to the mass of the system than it would gain from the electric assist. Hybrid racecars are a great entry into regeneration. There is ~20s of braking per lap at Le Mans. A 200kW system, with 49.3% round trip efficiency, would gain 9.9s of 200kW electric assist per lap. Using the better efficiency values to get 71.8% round trip would result in 14.4s of 200kW electric assist per lap.
6C. Regen charging the battery at high C-rates.
Neither road driving nor Formula E spend 20% of the time braking, so how does regeneration account for 20% or more of their energy budget?
Regeneration power is higher than average driving power.
60 s / lap * 12% braking = 7.2s braking / lap
7.2s * 80kW regen * 70% efficiency / 25kW driving = 16.1 s / lap
16.1 s / 60 s = 26.8%
Braking longer at high regen.
7.2s * 80kW regen * 70% efficiency / 3600 s/h = 0.11 kWh / lap
15.0s * 80kW regen * 70% efficiency / 3600 s/h = 0.23 kWh / lap
80kW regen charging is very hard on a small Formula battery.
Very high C-rate = very high heat
Do not go over voltage limits per rules or cell manufacturer.
Do you start with a low enough charge to allow full regen?
Do you start with the full usable capacity?
Driver has to wait before using full regen, changing driving characteristics?
Lower regen power reduces the effect on the energy budget
6D. Powerful motors on the front axle
Regeneration increases the average RMS power during braking and acceleration due to more energy available. Adding regeneration requires higher continuous power from the battery, controller, and motor.
Getting 80kW of rear tire traction is difficult when accelerating. It is even harder to get enough rear traction for 80kW when the load is transferred to the front under braking. Due to short wheelbases, 75% or more of braking on an FSAE car could come from the front axle.
I would be interested in the levels of mass, balance, power, aero, and regen that would make Front Wheel Drive faster over an endurance than Rear Wheel Drive. My philosophy is 50::50 and identical front::rear powertrain assemblies is by far the best concept.
6E. A braking map that changes vs. pedal pressure and vs. motor speed
Longitudinal force = power / velocity, an exponential decay
kN = kW / (m/s)
Grip, with downforce, is squared with speed.
Until reaching tire load sensitivity limits.
Mind the center of vertical pressure.
Drag and acceleration shift loads rearward.
Drivers want the same level of longitudinal tire force for a given pedal pressure.
Test any proposed approaches in lap sim and a driving sim.
Blending friction braking when regeneration >= traction reduces the energy recovered.
The car must lock all four wheels during the brake test.
T.3.1.6 bans brake-by-wire.
Good luck.
