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Electric Vehicles and the BMW i3 (60Ah & 94Ah)

David J. Bricknell

  © 2016 Brycheins Ltd All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law. For permission requests, write to the publisher, addressed “Attention: Permissions Coordinator,” at the address below. First Edition


Acknowledgements I should like to thank the BMW i3 Facebook groups, UK, USA and others, for providing the forum for discussing the usage and workings of the i3 and EVs in general. There are too many people to thank individually but the regular positive and constructive contributors are a huge help to the EV community. I should also like to thank BMW at Park Lane, London for allowing me to take the photographs of the ‘i3 internals’ used within the book and for BMW for producing such an interesting vehicle.  I have sought advice and proofing from a number of ‘experts’ and value their assistance in ironing out as many glitches as possible however all of the errors and omissions in the book are my responsibility.


Preface In 2015, after some 42 years of driving cars with internal combustion engines (ICE), I bought my first Electric Vehicle (EV). I have always been intrigued by new technology: I know electric cars were around at the end of the nineteenth century but for almost anyone alive today EVs are new technology.  I took a test drive almost as a way of deleting EVs as an option from my list of new cars but like many I was captivated by the driving experience. I ordered a car, sold my old-technology Mercedes diesel and haven’t looked back since.

go wrong; he went away, hopefully for retraining. But even as I said it I knew it wasn’t really true. I had been involved in electric propulsion systems for some time and my experience indicated that things were never quite as simple as they first seemed. 

Like many of my age, I grew up fiddling with cars and by the time I bought my first (a Morris Minor 1000) I knew what the key components and systems did, or were supposed to do anyway, and if they didn’t, I fixed them.   Later, if the car went wrong, which it rarely if ever did, then it got returned to the dealer and sorted out: no real point in ever lifting the bonnet. However, although with modern cars there are more electronics and no longer any carburetors, distributors or points, most of the key components were the same in function as in any ICE, old or new.

This book then seeks to capture the key systems and components which are different to that which you would find in an ICE car. Included are: battery, charging, cooling and heating, motors and drives, and the range extender. The key design points of the i3 components are related to the i3’s performance points and operational limits.  I don’t include chassis, suspension or interior outfit as these are not really EV specific.

So I thought I ought to find out what was really in the EV I had bought, at least to bring me up to the same level of understanding I had in 1973 when I bought my first ICE car.

This is not a ‘Haynes’ manual and nor is it a detailed technical paper but an attempt to collate and present the information relevant to understanding what is different about an EV in a way that is approachable by a wide audience with widely differing backgrounds. If sometimes the presentation is over simplified or in places over complex then you have my apologies: it’s a fine line to tread. 

So there I am at a rapid charging station answering questions from an inquisitive public about EVs (as most of us do at some time during a stop at a public charging) when in raced an RAC repair man who said ‘so what are you going to do when it breaks down’.   I responded that there’s only a battery and motor so there’s nothing really to iii


Alternating Current Air Conditioning Amp Hours Auxiliary Power Unit Advanced Vehicle Testing - Idaho National laboratory Battery Electric Vehicle BEV Extender Battery Management System California Air Resources Board Charge/discharge rate Combined Charging System Drag Coefficient x frontal Area Carbon Dioxide Cell Supervision Sensor Unit Direct Current Depth of Discharge Dynamic Stability Control Electrical Digital Machine Electronics Electrical Machine Electronics Environmental Protection Agency Electric Vehicle Global Warming Potential High Voltage HydroFlouroCarbons Hybrid Synchronous Machine Internal Combustion Engine International Electrotechnical Commission Insulated-Gate Bipolar Transistors Induction Motor



Convenience Electronics kiloWatt kiloWatt hour Lithium Cobalt Oxide Lithium Iron (Ferrous) Phosphate Lithium Ion Battery Lithium Manganese Oxide Lithium Nickel Oxide Lowest Replaceable Unit Lithium Titanate Oxide Low Voltage Maximum Continuous Rating Noise and Vibration Nickel Cobalt Aluminium New European Driving Cycle Newton metre Nickel Manganese Cobalt Nickel-Metal Hydride Permanent Magnet Synchronous Machine ReX Electrical Machine Electronics Range eXtender revolution per minute Radio Frequency Identification State of Charge State of Health Total Harmonic Distortion Three Letter Acronym Zero Emissions Vehicle

Introduction This is a book that focusses on Electric Vehicle (EV) technologies and is woven around the dynamics of the BMW i3.  It addresses those areas of EV driving that differ from those of owning and driving an Internal Combustion Engine (ICE) car.  

Motors and their power-electronic drives are the largest user of power and maximising their efficiency and minimising their weight, size and cooling requirements is very important.   As with batteries, there are competing technologies from induction (IM), wound synchronous (WSRM), permanent magnet (PMSM) and hybrid reluctance-synchronous motors (HSM) as well as a variety of power electronics suppliers.

Whilst the Dynamics covered here are of the i3, the principles are generally applicable to all EVs.  EVs are quick and fun to drive but there are boundaries on their performance imposed by the battery, by the motor and drives, and by the transmission, that are quite different in nature and characteristics to those of an ICE car.

At higher speeds and under rapid accelerations batteries and motor and their drives demand considerable amounts of cooling in order to maintain performance; it is often a surprise to EV drivers to find that they do indeed have a conventional radiator mounted at the front of the car.

The Lithium-Ion Battery (LIB) has been the single most important development that has enabled the successful introduction of EVs capable of supplanting the ICE car in the years to come. LIBs come in different shapes and sizes, with different internal chemistries, and are configured differently by the different manufacturers. 

As well as energy for cooling of the key components there is also cabin cooling. In hot climates there is air conditioning but for EVs it’s the heating requirements for colder days that is the surprise issue: unlike ICE cars, EVs don’t have enough waste heat available for free and have to generate heat as they go.  At slower speeds and in very cold weather the cabin heating energy usage can be higher than that required to propel the car.

No matter how big the battery is it is only an energy store and at some time will need to be Recharged.   The landscape of chargers, charging standards, charging speeds, different plugs, and different charging companies remains a rapidly changing ‘work in progress’. Consolidation of chargers and charging standards is beginning. A dependable and available infrastructure will be essential for the eventual replacement of ICE cars with EVs.

For the interim, whilst batteries are increasing in capacity and the charging infrastructure is developing, there is the range-extender engine.  


Dynamics EVs are fun cars to drive and the i3 is one of the best examples; it has very rapid and responsive acceleration but surprisingly a rather limited maximum speed of 94mph.  In resistance and propulsion terms an ICE vehicle with 125kW of power would be expected to achieve a maximum speed of over 140mph.  At first look, this maximum speed would seem to be a simple case of BMW adopting a single gear ratio and limiting things to the speed appropriate for a city car but this is but to scratch the surface of the challenges that come to play in designing the i3’s power and propulsion system.  An EV has sufficient torque and rpm range to need only a single-speed transmission and this is also best suited for harvesting regenerated energy. Keeping the battery discharge rate low in order to prolong battery life is important as is keeping the motor and motor drive (inverter) within their temperature limits. Both of these issues are key to higher performance and to higher continuous speeds. Range is a product of the battery capacity against the energy used for accelerating/regenerating and for sustaining speed. Battery capacity though isn’t an absolute value - it varies with cell temperature, with rate of charge and discharge, with calendar time and with the number of charge/discharge cycles.   Cabin cooling is well understood with ICE cars but for an EV the amount of energy required for cabin heating in colder climes comes as a considerable surprise to most. Cabin heating of an ICE car is essentially done using (free) waste heat whereas the EV has to generate it from its battery energy. The energy content of a tank of fuel (by volume) will vary by only a small amount as it changes temperature (~ 0.1% per oC) but this is not so with LIBs; commonly used chemistries, such as LMO-NMC, and NCA, will see a significant reduction in available energy when at or below zero oC which can then be further exacerbated by the higher C-rates of hard acceleration or high speeds. Until the battery capacity of cars increases significantly, something we’ll see in the next few years, and the availability and speed of the charging infrastructure improves, the very high energy density of fossil fuel can be very useful in extending the range of an EV.   When implemented in serial-hybrid mode (see Section 5), the BEVx will retain all of the performance characteristics of EVs so enjoyed by many.


Section 1 

Power and Speed 

The BMW i3 is a quick car with sensational acceleration for what is marketed as a ‘city-car’.

The graph opposite illustrates the power-speed curve against which the key performance limits can be overlaid. The graph shows: • The motor output power necessary to maintain vehicle speed.  Both the i3 Battery Electric Vehicle (BEV) and i3 Range Extended BEV (BEVx) curves are shown - the difference being the slightly higher drag coefficient of the BEVx and its greater weight due to the ReX.   • The electric motor maximum instantaneous power output of 125kW and its maximum continuous output power of 75kW. • The 60Ah battery instantaneous power output of 147kW (~8-C) and the battery continuous power output of 40kW (2-C). • The maximum car speed of 94mph (gear and cooling limited) and the recommended maximum continuous car speed at 1-C battery discharge of 74.5mph (60Ah) and 84mph (94Ah).

 Power-speed curve for BMW i3 overlaid with motor power and battery discharge limits


Section 2

21.6kWhrs and a net usable capacity is 18.8kWhrs. In the latest versions, 94Ah cells giving 33.2kWhrs gross capacity and 27.2kWhrs net usable.

Key Components

Cooling of battery and cabin is by refrigerant with for the BEV a heat pump for efficient heating. The condenser is mounted at the front of the car with the refrigerant-cooled compressor mounted together with the motor and drive at the rear.

BMW’s i3 BEV is a full electric Zero Emission Vehicle (ZEV) and the BEVx is a Range Extended ZEV. The BEVx has a Range eXtender (ReX) auxiliary power unit (apu) configured as a serial hybrid to deliver its performance through a 125kW electric motor independent of whether the electric is provided by the battery or by the apu.   The Hybrid Synchronous Motor (HSM) delivers a maximum instantaneous power of 125 kW and a maximum continuous output of 75kW. Maximum motor rpm is 11,400rpm equates to a speed of 94mph.  The electric motor weighs just 49kg and delivers a maximum torque of 250Nm torque. Power is transmitted through a single stage combined gearbox and differential with a reduction ratio of 9.665:1.  

Cooling of the main electrical components of motor and drives, as well as charging electronics, is by liquid glycol with heat being rejected through a conventional radiator mounted at the front of the car. 
 The Range eXtender is mounted adjacent to the motor and drive and is a 2-cylinder apu delivering up to 28kW at 5000rpm. Cooling of the ReX drives and generator is by the same liquid system as the main motor. The ReX engine will also use this circuit depending upon temperature.

Control of the electrical motor is by the Electrical Machine Electronics (EME).   The EME converts the nominal 360V Direct Current (DC) from the battery to 3-phase Alternating Current (AC) and reverses this when recuperating energy.  Maximum recuperation is 50kW, the same as the maximum charging rate. Energy for the motor comes from a battery pack consisting of eight battery modules each containing twelve Li-Ion NMC-LMO battery cells. The cells are provided by Samsung SDI and the packaging by BMW. Each cell offers 60Ah at a nominal 3.75V giving a pack capacity of 4

BEV Key Components and Systems


BEVx Key Components and Systems


Section 3

Battery Discharge Rates The high-voltage battery is a Lithium-Ion Battery (LIB) using an NMC/LMO mix for optimum energy density, power density and cycle life.   The designation "NMC/LMO mix" refers to the metals used for the cathode: it is a mix of nickel, manganese and cobalt on the one hand, and lithium manganese oxide on the other hand. Two different battery capacities are offered for the i3. Both have a single battery pack containing eight modules and each module contains 12 battery cells.  The battery pack weighs 233kg with a volume of 213 litres. One version has 60Ah at a nominal 3.75V each.   The total nominal gross battery capacity is 21.6 kWHrs (8 modules x 12 cells x 3.75v x 60 Ah) with a net, usable 18.8 kWHrs.  Maximum power discharge is 147kW at approximately 8-C discharge rate with a 40kW continuous 2-C rating.   The larger capacity battery pack has 94Ah cells at a nominal 3.68V each, giving a gross capacity of 33.2 kWhrs with 27.2 kWhrs usable.   Maximum power discharge is 230kW at approximately 8-C discharge rate with a 60kW continuous 2-C rating.   
 Battery discharge rate (C-rate) mapped against the i3 power-speed curve and the motor instantaneous power. Both 60Ah and 94Ah bands are shown. A 1-C rate equates to the recommended continuous car speed and the 2-C rate to the maximum car speed.

Optimal operating battery cell temperature is 25oC to 40oC (pre-conditioning takes approximately 3 hours before getting the temperature to about 10oC). A battery pack heater of 1kW is fitted for colder climes.   7

Section 4 


One of the ‘headline’ parameters of EVs is, for the moment at least, the achievable single-charge battery range.   Today’s (2011-2016) batteries are relatively high-cost, and high in weight and volume.  Things will change, indeed are already changing: BMW now have models with a claimed 120 mile range and 160 miles can reasonably be expected shortly.   A 200-mile (EPA) battery range is expected in the Chevy Bolt and in a Tesla 3 with both cars expected in 2017/18. An affordable 300-mile range, perhaps available by 2020, probably would ensure that range was no longer an issue when viewed against the other benefits from an EV. 

Us Environmental Protection Agency (EPA) range seems more representative of a ‘real-world’ that involves more ‘highway’ driving than the New European Driving Cycle (NEDC) figures which seems more realistic for urban driving.

The graph shows the impact of vehicle speed on range for both the 60Ah version and 94Ah versions of the i3. The dotted red line is verified by testing (and recorded by George Betak et al). The blue stars are those recorded by AVT-INL on a rolling road. The red stars are the calculated figures adjusted for 25oC. The green stars are those published on the blog.

Rolling resistance (vehicle weight and tyre efficiency) and aerodynamic resistance (CdA) are two factors which impact on vehicle efficiency. Higher vehicle speeds significantly impact on battery range.   


Range variation with ambient temperature and speed For EVs, auxiliary power for cabin heating, for initial battery heating, and for component cooling when underway, can significantly impact on range.   Ambient temperatures below 15oC and above 20oC start to demand cabin heating or cooling and as temperatures drop heating load increases until it can become the dominant power demand. There is also an impact of ambient temperature on the available battery capacity but it is often much less than that from auxiliary heating. 

Graphs opposite and below are for the 60Ah version and show range estimations against speed and ambient temperature


Section 5

towards powering the car or maintaining SOC.   When battery SOC drops very low then a number of operating profiles are used to maintain battery SOC.


The Range eXtending apu or ReX fitted to the BEVx is a BMW W20 two-cylinder engine of 647ccs.   In Europe the ReX was released at 27kW(engine output)/25.3kWe (generator output) at 4800rpm and in the USA (to meet CARB) at 25kW/23.3kWe at 4300rpm. A subsequent update in 2016 gives 28kW/26.3kWe at 5000rpm.   The internal combustion engine drives a generator having an efficiency of ~94%. The electrical energy generated by the ReX goes through the KLE (convenience charging electronics) to the EME and then either directly to the electric motor or to the battery in order to maintain State of Charge (SOC); the ReX is not intended to recharge the battery other than to maintain SOC. 

The AC output from the variable-rpm ReX electrical machine is conditioned to 330v DC by the ReX Electrical Machine Electronics (REME) at approximately 96% efficiency. 

The graph shows the operation of the ReX in the BMW i3.  Continuous operation at normal SOC is 20kW/18.8kWe at 3600rpm but at low %SOC, and in order to maintain SOC at higher vehicle speeds, a higher rpm can be used.

The BEVx is a serial hybrid EV with the ReX acting as an on-the-move energy generator; hence it impacts vehicle range and not power to the wheels. Software upgrades since 2013 have altered the operating parameters in order to improve performance.  The ReX can be started manually below a SOC of 75% (except in the USA) and, after a warm-up time, it will deliver 18.8kWe 10

Battery The Lithium-Ion Battery (LIB) has probably been the single most influential development in the reintroduction of credible electric vehicles capable of challenging the dominance of ICE power vehicles. Although first developed by Sony in 1992, it’s really been the last five years where energy density, power density, and life have come together with significant cost reductions to make LIBs the energy storage of choice for EVs.   Most consumer electronics use LIBs with a cathode of Lithium Cobalt Oxide (LCO) whereas EVs are generally adopting either Nickel Cobalt Aluminium (NCA), Lithium Manganese Oxide (LMO), Nickel Manganese Cobalt (NMC) or, an LMO-NMC mix to balance life with power density.  Heavier duty applications such as buses and trucks and marine vessels are tending towards Lithium Iron Phosphate (LFP) for longer life and for Lithium Titanate Oxide (LTO) where recharging is very frequent. LIB cells are available in different formats with cylindrical, pouch and prismatic formats being used by different manufacturers. The BMW i3 uses LMO-NMC in a hard case, prismatic-format battery cell supplied by Samsung-SDI.  The packaging into the 12-cell modules and 8-module pack is done by BMW who also add the cooling and heating system and the Battery Management System (BMS). The i3 has 60Ah and a 94Ah battery cell version available.  Both have the same cell dimensions with the 94Ah being slightly heavier. Battery capacity isn’t such an absolute value in the way that a tank of fossil fuel appears to be; the available capacity will depends upon the cell temperature and the rate of discharge.   Batteries lose capacity through life, partly due to calendar ageing and partly due to charge/discharge cycling. A Battery Management System BMS is essential for maximising range and battery life and for ensuring that the cells remain in a good State of Health (SoH). For the future, improvements in anode and cathode materials are expected to lead to increased energy storage, improved rates of charging and better cycle life. Considerable efforts are being made to introduce a solid electrolyte which would improve passive safety of the cell. 

It should be noted that tests and documents also support the nominal system voltage as 355.2V and 3.7V for the cell voltage. In this book 360V is taken as the nominal for cosistency with the bulk of official BMW documentation.

Section 1

The i3 Battery

By contrast, the Leaf uses two parallel sets of 96 seriesconnected pouch cells with each cell at 33Ah in a 2p, 96s configuration; this means that the Leaf has two parallel battery strings each providing the 360V system voltage: 96 cells x 3.75V x 33Ah = 11.88kWhr x 2 = 23.76kWhr.

BMW uses a single flat, underfloor, battery pack. Within the pack there are eight identical battery modules each containing 12 identical prismatic battery cells. Each ‘prismatic’ battery cell is rated at 60Ah at a nominal 3.75V or, for the latest model) 94Ah at 3.68V. The Lowest Replaceable Unit (LRU) is the 12-cell module: BMW exchange on a module by module basis and not on a cell by cell basis.

The Tesla S has 74 parallel sets of 96 cells in series due to the low 3.4Ah energy available from each of its small 18650 G/ NCA cylindrical cells: 96x3.6Vx3.4Ah=1.75kWhr x74=87kWhr.

The prismatic battery cells are provided by Samsung-SDI and use a Graphite anode and a NMC-LMO mix for the cathode; this enables optimum energy density, power density and cycle life. NMC-LMO mix refers to the metals used for the cathode of this cell type: It is a mix of nickel, manganese and cobalt on the one hand, and lithium manganese oxide on the other hand.   Graphite is used for the anode. (NMC is also known as NCM and other variants on the same three letter acronym (TLA) depending on the exact mix of the three metals.). The i3 has a single string of battery cells connected in series to provide a nominal system voltage of 360v.  The designation for the i3 is “1p, 96s”. This leads to 1 parallel x 96 series cells x 3.75V nominal x 60Ah giving 21.60 kWhr which is the same amount that the “Static Capacity Test” produced when tested at AVT-INEL at 1/3-C: this is the “gross” figure BMW quote in their brochures. The i3 (60Ah) has a ‘usable” battery capacity of 18.8kWhrs which matches the typical maximum DC discharge when tested on a rolling road. The ratio of usable to gross for the 60Ah is 87% (18.8/21.6) whereas with the 94Ah it’s (27.2/33.2) 82%, the reason for this difference isn’t clear.

The 12-cell, 8-module Battery Pack underneath an i3. 12

Usable battery capacity is affected by:

car speed of 70-75mph, depending upon the auxiliary power (heating and cooling mostly) demand.

• the calendar age of the cell, • its temperature - less is available at colder and temperatures, • its discharge rate - less is available at higher-discharge rates.

For the 94Ah i3, maximum ‘pulse’ power discharge from the battery is expected to be a pro-rata 230kW with a 62kW MCR. A battery pack resistive heater of 1kW is fitted to precondition the battery pack during spells of cold weather.  The pre-conditioning warms the battery cells to about 10oC, in order to maximise the usable capacity, whilst the optimal operating battery cell temperature of 20oC is reached after a short spell of driving.   

As well as using more energy when driving the car faster, rapid acceleration will also reduce the battery’s available capacity. The battery pack also contains the Battery Management (BMS) and Cell Supervision Systems – both are provided to BMW by Preh.

BMW may well offer a battery pack/module upgrade from 60Ah to 94Ah, or maybe, in the future, to 120Ah, but the likely high cost may well make this non-viable in some markets.

The 60Ah BMW i3 battery pack (8-modules of 12 cells) is 233kg with a volume of 213 litres and is packaged as one battery-pack shielded from damage from grounding by a steel plate. The 94Ah is the same dimensions but slightly increased in weight.

When batteries deteriorate beyond their useful EV life they will be repackaged as stationary energy storage systems. A further useful life of about 10-15 years can be expected: most EV suppliers seem to be following this trend. After that the battery materials can be recycled.

Contained within the battery-pack is the refrigerant cooling system that is shared with the air conditioning system. BMW is unique, for the moment, in using a refrigerant cycle (refrigerant –  R1234yf or R134a dependent on market) for cooling the battery pack. Tesla, Chevy and Ford use liquid glycol, Kia, Mitsubishi, and Nissan use forced air-cooling and VW uses passive cooling. 

Maximum ‘pulse’ power discharge from the 60Ah battery is 147kW with a 40kW Maximum Continuous Rating (MCR)   – the 40 kW MCR equates approximately to the car’s maximum speed and to a discharge rate of about 2C. The 147kW equates to a discharge rate of about 8-C and is only available for a very short period of time.  A 1C rating equates to an i3 13

Section 2

• Later software updates have made some modifications to ReX operation to ensure that more battery charge is available when required.

BMW i3 Battery Capacity For the 60Ah battery, both the i3 BEV and BEVx retain a lower 10% battery margin (~2.16kWhrs) where driving isn’t possible – dropping below this state of charge significantly reduces cell voltage and can seriously damage the battery cells. There is also a margin at the higher state of charge where the battery isn’t used.

BEVx 100% (21.6kWhrs)

100% (21.6kWhrs) BEV 100% (18.8kWhrs)

100% (18.8kWhrs)

ReX manual enabled with stop/start

6.5% (1.22kWhrs) (3.0kWhrs) 14.2%

The BEVx will have 17.6kWhrs of unrestricted driving before the ReX apu starts.

(0.92kWhrs) 4.9%

(2.16kWhrs) 10.0%

15.7% (3.4kWhrs)

3.5% (0.66kWhrs) Restricted Driving

The BEV operates as follows: • below SOC 4.9% (0.92kWh) driving is restricted.   • above that %SOC driving is unrestricted.

ReX auto enabled with stop/start


Sta)c Capacity Test

17.6 kWhrs unrestricted before ReX

75% (14.1kWhrs)

Usable Capacity

The BEV has a net usable capacity of 18.8kWhrs of which 17.9kWhrs is available before entering restricted driving and a further 0.92kWhrs of restricted driving.

17.9 kWhrs Unrestricted Driving

Sta)c Capacity Test

BaIery Only

1.9% stop/start disabled 0.4% Restricted driving ReX start reserve

Driving not possible

10.0% (2.16kWhrs)

The BEVx operates as follows: • 0.4% (75Wh) relative SOC is reserved to enable ReX start. • Between 0.4% and 1.9% (357Wh) driving is restricted.   • Between 1.9% and 3.5% (660Wh) driving is unrestricted but ReX stop/start is disabled.   • Between 3.5% and 6.5% ReX is automatically enabled stop-start enabled – driving is unrestricted.   • Above 6.5% and below 75% SOC Rex can be manually selected (except USA).

The 60Ah battery showing capacity from the Static Capacity Test and the usable capacity based on the maximum battery discharge test as well as margins and typical cell voltage for both BEV and BEVx.


Section 3

A graph of the preconditioning process shows packets of heating being applied and this then being allowed to soak through before the next heating input.   LIBs have a high thermal mass and are slow to warm and to cool; too much heat too quickly will lead to physical cell distortion.

Preconditioning of battery Low cell temperatures reduce available capacity and available power, and can impact on battery life. BMW offers battery pre-conditioning as standard now although originally it was an option - pre-conditioning is advantageous in any market where ambient temperatures are likely to be around 0oC at any time of the year. Of the LIB chemistries only LTO is relatively immune to low temperature degradation.    

The charging process itself will also cause battery heating synchronising battery charging to coincide with departure time can be the most energy efficient solution.

For the i3, preconditioning of the battery takes approximately 3 hours to raise the battery cell temperature to 10oC and takes around 0.5 to 1kWhrs of energy; driving the car will cause battery chemical reactions to take place ensuring that the cell temperature increases further towards the optimum.  

Typical preconditioning power and energy usage showing the early discrete packages of energy applied to heat the battery and then to let it soak through.

The precondition process when setting a ‘departure time’ requires 3-hours to implement and the i3 need to be plugged in to at least a 220V/10A supply.  The final part of the pre-con process is cabin heating and this can take a further 0.5kWhr maybe up to 3kWhrs of energy with peaks of 5kW power in very cold conditions but for shorter periods of time.  The car takes the power directly from the charging socket and will top it up with battery power should cabin heating demand higher power than is available.  This means that you may have less than 100% battery SOC on departure unless your charger can provide at least 7kW.

Battery pre-con offers a benefit for performance and for battery capacity but it’s pre-conditioning of the cabin interior temperature, done in the final 30 minutes of ‘departure-set’ pre-con, that can offer the greatest benefit to range. On the i3, pre-con without setting ‘departure’ just implements cabin heating.


Section 4

Battery Types

NMH batteries were used in recent early EVs as well as the now ubiquitous Toyota Prius but all of the latest generation EVs now adopt LIBs in one form or another.

By the turn of the 20th century about a third of all cars were electric powered. Batteries for these vehicles were LeadAcid which were heavy and slow to recharge but the cars were very easy to drive. Improvements in the internal combustion engine (ICE) led to electric car developments halting until the relatively recent development of the Lithium Ion Battery (LIB).  

Lithium is the lightest metal, and the third lightest element; it also has the lowest reduction potential and hence the highest possible cell potential (voltage).   Lithium-Ion Batteries have an anode, a cathode, a separator, and an electrolyte.   A LIB works by passing lithium ions between the electrodes through an electrolyte solution.   As lithium ions move from the anode to the cathode it generates power.  For recharging, the lithium ions move from the cathode to the anode.

Sony introduced the first Lithium Ion cell in 1992 for use in consumer electronics and it has since displaced many other battery types due to its high cell voltage and its high energy and power density.

 Typical Li-Ion battery showing the current, electron and Ion flow during charging and discharging. The Anode is most often Graphite (except LTO) and the Cathode of a mixed metal (NMC, LMO, NCA, etc.). Varying the anode/cathode composition leads to different battery characteristics.

Lithium Ion Batteries can be significantly smaller and lighter than other rechargeable battery technologies and, importantly, have a much higher nominal cell voltage. 

Section 5 

Li-Ion Battery Chemistry 

• Graphite/Lithium Cobalt Oxide LCO is used in most consumer electronics. It has a good cycle life and energy density but poor power density.   It is expensive and has a higher likelihood of thermal runaway.   • Graphite/Lithium Manganese Oxide LMO is a safer alternative to LCO but it has a lower cycle life.  Nissan’s early Leaf used LMO batteries. • Graphite/LMO-NMC where LMO is mixed with Lithium Nickel Cobalt Manganese Oxide NMC   - LMO provides the high current boost for acceleration with the NMC providing the longer endurance.   NMC suffers significant capacity loss and performance below zero OC.   Most EV manufacturers, including BMW, use NMC-LMO. • Graphite/Lithium Nickel Cobalt Aluminium Oxide NCA offers a high energy density, a good power density and a long life but has more potential for thermal runaway.  NCA’s power density is exploited to the full in the Tesla ‘Ludicrous’ and ‘Insane’ modes of rapid acceleration. • Graphite/Lithium Iron Phosphate LFP has excellent safety and good cycle life but has lower energy and power density as well as a lower cell voltage (3.2V).   It is a favoured technology for ‘longduration between charges’ bus and coaches and for marine ferries that can charge only once per day.   • Lithium Titanate Oxide/Graphite LTO use a titanate metal anode and graphite cathode (unlike the other LIB variants) giving it a very fast charge rate, due to the very high surface area of the titanate anode. LTO offers a wide operating temperature and a very high cycle life but a low energy density and a low cell voltage leading to a high initial battery cost.   LTO is considered very safe and is gaining favour for buses and ferries that are configured to charge very frequently (every hour or sometimes even more frequently).

The principal LIB designations are: LCO, NCA, LMO, NMC, and LFP - these refer to the cathode composition. LTO is the other significant designation. All apart from LTO use a metal or mixed-metal cathode and a graphite anode; LTO uses a metal (titanate) anode and a graphite cathode. For EVs the following spider diagram shows each battery chemistry against five key parameters (5 is best, 1 is worst): • Energy Density – how much energy (WHrs) in a specific space and/or weight. • Power Density – how quickly the energy can be released. • Life – how many times it can be cycled. • Cost – largest number is least expensive. • Safety – likelihood of a thermal runaway. 

Information from ‘The Battery University’. 17

Section 6


Battery Formats Three shapes of LIBs are used in current EVs with each having their own strengths: 

The 85kWHr Tesla Model S uses 7,104 of the 18650 format NCA cells in its battery pack. Photo courtesy of Oleg Alexandrov (cc-by-sa-3.0)

• cylindrical, as with the 18650 shape used by Tesla with its Panasonic battery cells.   The cylindrical battery is like a Swiss-roll of positive electrode, separator, negative electrode and separator rolled up.   Tesla are the principal EV proponent of cylindrical cells although the configuration has widespread usage outside of EVs.   Today’s cells are 3.1 and 3.4Ah and the next generation of cells is expected to be 20700 at up to 4.9Ah. 

Samsung’s SDI Prismatic can be seen within the LRU 12cell module and the battery pack. Photo courtesy of Rudolph Simon (CCA)

• Prismatic, used by many EVs, including BMW, the prismatic cell uses layers of anode, separator, cathode, separator, etc., within a hard aluminium case.   The electrodes and separators are wound, as a flattened spiral, or stacked as sheets giving a lower density pack size than the cylindrical arrangement. Significantly less cells are used in prismatic battery packs as the cell Amp-hours are much greater than the cylindrical cell e.g. Samsung SDI has 26, 28, 60, 94, and 120Ah available.

 The Nissan Leaf showing the LRU cell modules packaged into a complete battery pack. Each cell module contains four pouch cells. Photo courtesy of Tennen-Gas (cc-by-sa-3.0)

• Pouch, used by Nissan and Renault and by the new Bolt, allows a very flat and thin installation.  The electrodes and electrolyte are packaged in a foil envelope that is then packed into a module and the modules stacked within the overall battery pack.


Section 7

Leaf with cells of just over half the energy (Ah) of the i3 reaches system voltage with the same number of cells but needs twice as many in order to provide the required system energy. Tesla uses the 18650 cylindrical cells; it needs 96 cells in series to reach system voltage and 74 in parallel to reach battery energy capacity.

Pack configurations Within the battery pack the cells can be connected in series, in parallel or in a combination of both. • Serial connection determines the battery pack voltage – add the voltages of each cell together. • Parallel connection adds the current of the batteries together but holds to the cell voltage. Different combinations of serial and parallel connections are used by EV manufacturers.

Parallel connection of multiple series connected battery cells is required when the current available from individual cells is insufficient for the required power or series connecting more than 96 cells would lead to too high a system voltage.

Clearly the building blocks of each cell will impact on the configuration of the battery pack.   The i3 uses all cells in series in order to reach the required system voltage.   The

For light commercial vehicles and for marine installations system voltages are more often greater than 700V with some exceeding one kV 19

Section 8

may well encourage longer and faster road trips incurring higher-C-rates and probably higher DODs.

Battery Life

The Rate of Discharge (C-Rate) affects battery life as the chemical processes that take place during discharge will be less complete the more rapid it occurs.

Battery Life is a combination of Calendar life and Cycle life: Calendar Life is influenced by temperature and time. Cell resistance increases with elapsed time, due to a build up of a passivation layer of unwanted chemicals on the anode; the speed with which resistance increases is greater at higher temperatures.   Cycle life is normally described as the number of complete charge and discharge cycles it can sustain before its nominal 80% capacity is exceeded.   One cycle is a complete charge and discharge.   Five partial 20% charge and discharges is equal to one cycle.   Battery life reduces with increasing number of cycles.

% Ba=ery Capacity

Cycle life varies with varying electrode chemistries and with rate and Depth of Discharge (DOD): the amount of active chemicals transformed during charge and discharge is broadly proportional to the DOD. For the same EV, the DOD per cell is lower on larger capacity battery packs.  For the i3 with ~ 80 mile range per charge, 1000 full cycles corresponds to 80,000 – 118,000 miles which at an average 10,000 to 12,000 miles per annum equates to about eight years.   For the Mk2’s 94Ah battery pack, on the same usage cycle, life can be expected to be significantly longer albeit the larger battery capacity














Cell Amp hours

Chart showing the typical relationship between Depth of Discharge and number of cycles for different rates of discharge.

42.0 -

12,000 24,000 36,000 48,000 60,000 72,000 84,000 96,000 Miles

 Chart showing battery capacity reduction on i3 fleet of four cars - tested by AVT-INL.


Chemical reactions within the battery cell are affected by cell voltage and battery temperature:

Temperature of Operation - The hotter the battery, the faster the internal chemical reactions will be.   Higher temperatures will mean higher power but also a shorter life. As a rule of thumb, for every increase of 10oC it doubles the rate of chemical reactions i.e. an hour at 30oC equals 2hours at 20oC.  Temperature impacts on both cycle life and c a l e n d a r l i f e .

Cell Voltage - Once all the available chemical reactions within a cell have been completed and it has reached its upper cell voltage, then forcing more energy into a cell will cause it to heat up whilst producing irreversible chemical reactions that will damage the cell.   Similar irreversible reactions occur when discharging the cell below its lower voltage limit. 


Illustrative voltage for cell discharge for different cell chemistries. NMC, NCA and LMO taken from AVT-INL testing. LTO and LFP from The Battery University.

Batteries have an optimum operating temperature.  Operating outside of this can lead to life and performance degradation.  


Battery usable capacity varies with cell temperature and discharge rate (C-Rate). The battery C-Rate is a term expressing how quickly the battery is discharging energy compared to the total battery capacity per hour.   For the i3 the 60Ah has a 1/3-C rate of approximately 20kWhrs per hour and 20kW delivers about 70mph.   The battery is capable of releasing 147kW or a short-term pulse discharge C-Rate of almost 8-C. For the 94Ah the 1C rate is pro-rata increased. Lithium-Ion cells show a reduction in cell voltage as the cells discharge.   The rate at which the cell voltage reduces is affected by the rate at which the discharge occurs – higher rates of power will more rapidly reduce the cell voltage which in turn reduces the capacity of the cell. As the internal battery cell temperature drops, due to ambient temperature, the usable battery capacity reduces. This means that some of the energy charged into the battery cannot be accessed.   
 For the EV LIB the above graph illustrates the ‘full’ battery (max cell voltage) reducing as cell temperature falls – around 10% loss from 30oC to 0oC.  More dramatic, however, is the effect of discharge rate at lower temperatures where high discharge rates (rapid acceleration) will reduce the battery capacity substantially.

The i3 offers two strategies for protecting against the impact of lower cell temperatures  • preconditioning of the battery to 10oC, usually taking up to three hours due to the high thermal mass of the cells. • power restriction, that can be seen on the i3’s horseshoe power display where several of the upper bars can be greyed out. 



Section 9

During charging the strongest cell will reach full first, leaving the weakest short of charge whilst during discharge the weakest cell is depleted first and sets the minimum battery pack charge – this will mean continually reduced battery capacity if not addressed.

Battery Management The EV battery pack requires a Battery Management System BMS and a Cell Supervision Sensor Unit CSSU. Preh, based in Bad Neustadt in Germany, supply both units to the i3. The BMS ensures that a uniform charge is provided to the HV battery. It measures the: • system voltage,  • current flowing into or out,  • individual cell voltages and temperatures, and  • calculates the State of Charge (SOC) and • calculates the State of Health (SOH).

Passive cell balancing will, once the battery is charged, identify the lowest cell voltage and burn the other cells extra energy off through a resistor until all cells are equal and then charge all of them up to full again.   This takes a little while to do and is best done once cell voltages have settled. It can be wasteful of energy but it is simple to do.   Active cell balancing can be done whilst the cells are charging or discharging but the ability to balance reduces as charge or discharge rate goes up.  Those cells with a higher voltage are ‘paused’ briefly to allow the others to catch up. This method is ‘lossless’ but the BMS to manage this and the extra connections to remove cells from charging can be complex. 

The CSSU monitors every battery cell (96 for the i3) for cell voltage and temperature (cells differ due to manufacturing tolerances and ageing) and communicates with the BMS to adjust the charging and balance the cells for optimum performance.

The State of Charge for an EV is the % battery capacity compared to the usable battery capacity:   SOC for a LIB varies with cell temperature, the rate of charge and discharge, and the time between charges.

Lithium Ion batteries typically have a nominal cell voltage of 3.6 to 3.75V and a maximum cell voltage of between 4.1 and 4.2V. Connecting 96 cells in series gives a nominal system voltage of 345 - 360v and a maximum of ~ 400V.  Ensuring that the 96 cells in series are balanced in order to avoid overcharging individual cells and to maximise battery capacity is a challenge: cells at the beginning of life have normal manufacturing variation and through life the imbalance can worsen if not managed.  

Measuring a battery’s SOC to an accuracy necessary for an EV is quite difficult. The i3 uses a AS8510 battery sensor within a Preh CSSU and BMS.  The BMS measures current to an accuracy of ±0.5% and voltage to an accuracy of better than ±0.1%.


Charging Charging (and re-charging on-route or at a destination) is something entirely new to most drivers and, as with all newly introduced technologies, there are a myriad of different charging plugs, charging rates, charging companies and charging standards. This section looks at the principles of charging, rates of charge and discharge, charging efficiency, the effects of charging on the battery (including heating and battery life), and State of Charge (SOC) (how it’s measured and what it means). The national charger infrastructure is rapidly developing and expanding but with so many different charging companies and cost models being introduced it’s confusing for the EV driver. There are too many different RFID cards and apps to trigger charging, and to pay for time or energy from the charger.  This will no doubt improve but it needs to do so quickly because the number of plug-in vehicles is increasing rapidly. The latest models with larger capacity battery packs are being introduced without any similar increase in rapid charging power meaning that, whilst the number of times charging is needed on route is less, the time spent for each charge is more - this needs to be addressed at both the charger and on the vehicle. With a typical daily mileage of around 25 miles most EV drivers will most often charge the battery at home from their 230V domestic supply (UK and EU).   For trips further from home EVs will need either to recharge from 50kW rapid chargers or at destinations from a mix of 3kW and 7.4kW chargers.



BMW i3 on a Mode 3 charger. Home charging, whilst not essential to EV ownership, is the perfect solution for EVs and is where around 80-90% of all battery charging is likely to be done.

Mode 4 charging at an on-route CCS. Rapid chargers are essential for timely longer journeys.


Section 1

During the constant current phase the charging current is at the maximum that the charger can provide, subject to any other maximum imposed by the manufacturer. Power will increase as voltage increases until the cell voltage nears its maximum after which the charger switches to a constant voltage mode.   During the constant voltage phase, the current will decrease gradually until, at pre-determined minimum current cut-off point, full-charge is reached and the charge is abruptly stopped.

Charging Li-Ion Batteries The charging rate for Lithium Ion Batteries (LIBs) is affected by how quickly the chemical reactions can take place within the cell and this is influenced by: • the rate of chemical reaction of the electrode with the electrolyte,  • the speed at which the electrode surface can move on to the next chemical reaction, • the speed with which Lithium Ions can be inserted into the host electrode. 

These three processes are temperature dependent with colder batteries requiring a longer time both to charge and to discharge: • too rapid a discharge can lead to cracking or crystal growth in the electrodes. • too rapid a charge will force too much current through the battery which can result in surplus ions being deposited irreversibly on the anode in the form of lithium metal (lithium plating).   
 This chart shows a characteristic LIB charging profile.

EVs, including the BMW i3, carefully control the rate of charge and discharge.   LIBs adopt a constant-current / constant-voltage charge system and hence any charging system must be able to monitor and control both current and voltage: LIBs can be damaged if the upper voltage limit is exceeded.   


Section 2 The i3 is supplied with a Mode 2 cable, 13A/3kW 3-pin charging cable with a Type 2 (Mennekes) vehicle connector. Charging with this cable takes around 8 – 12 hours from empty to full. Mode 2 can also be used at 7.4kW/32A with an BS EN 60309-2 industrial plug and socket.       

Charging Modes The EV battery pack is always charged with Direct Current (DC) with the conversion from Alternating Current (AC) to DC being done either in the EV or on the off-car charger.

Mode 3 Either 230V 1-phase (up to 16.1kW/70A) or 400V 3-phase  (up to 44kW/63A) supply is used from a dedicated EV charging station either installed at home or on route. The control, communication and protection functions are all integrated into the charge point with the charger device (AC-DC rectifier) being in the vehicle.   Most EV drivers have a Mode 3 domestic charge point installed at 32A/7.4kW.  

In Europe, the modes of charging for EVs are defined in IEC 61851 and plugs, sockets, connectors and cable assemblies are defined in IEC 62196. In Modes 1, 2, and 3 the conversion from AC to DC is done within the vehicle – for the i3 this is the KLE (consumer electronics unit) at 13A and using both the KLE and Electrical Machine Electronics (EME) at 32A. In Mode 4, the conversion of AC to DC is done in the off-car charging unit and bypasses the AC/DC rectifiers in the vehicle – this minimises both the size of the on-car AC/DC rectifiers and the impact on the on-board vehicle’s cooling system.

The charge cable can be separate or tethered as a user option. Charging time at 32A is around 2 – 3 hours.

Mode 1 (up to 16A per phase) is not used by BMW i3 because of the lack of communication between the vehicle and the voltage supply.

The Renault Zoe and Kangoo make use of the 43kW Rapid A/C charger with the AC-DC rectifier in the vehicle.  The use of such a large rectifier leads to rather slow charging from a domestic 7kW single phase supply and Renault will be phasing out the 43kW option soon in favour of a lower rated but more efficient (at lower power) AC-DC charger; to cover rapid charging Renault will adopt DC CCS.

Mode 2 (up to 32A per phase) is used from a non-dedicated power supply such as a domestic power socket.  The control and protection device is integrated into the charging cable and the charger (AC-DC rectifier) is in the vehicle. 27

Mode 4 DC Charging. Mode 4 is a dedicated DC rapid charging from an external charger specified for 200-450V up to 240kW/400A.  Three systems are currently in use: 

In the USA, the CCS Combo is specified at up to 600VDC up to 150A/90kW (or 200A/125kW) and AC at 250V up to 32A/13kW.  In Europe, the CCS Combo is specified at up to 850VDC and up to 200A/170kW and AC at single-phase 230V/70A and three-phase 400V/63A/43kW.

CHAdeMO – developed by Nissan and Mitsubishi in 2010 (together with Tokyo Electric Power Company and Fuji Heavy Industries) with Toyota joining the standard later. CHAdeMO can deliver up to 50kW and 120A at up to 500V DC. An 150kW version has been recently announced for 2017. 


CCS system – developed by the majority of European and US car manufacturers and supported by SAE and ACEA with the aim of developing a single and open global standard. CCS combines single and three-phase AC charging up to 43kW as well as DC charging up to 200kW with up to 350kW possible in the future.   Most DC CCS chargers found today offer a range of power with 20, 44, 48 or 50kW more often found but 100kW units are available. i3 Modes of charge

Tesla has a dedicated Supercharger network that can charge at powers up to 120kW. It uses twelve of the 10kW Model-S AC/DC rectifiers to deliver the high power at DC.

Mode 4 CCS Charging Plug 28

DC charging time depends upon battery size and charging power. Today’s chargers are usually 44kW continuous but higher power chargers are expected in the future and indeed are essential as battery pack size increases to deliver greater range.


Section 3 

Common Connectors AC & DC AC SAE J1772 is used in North America and in Japan.   Capable of 80A / 120V-240V AC / <19.2kW.

SAE J1772 DC CCS Combo 1 used in North America and Japan Capable of 200A / 200-600V DC / <125kW (max current).

(Photo Michael Hicks CCA-2)

(Illustration CCA-sharealike)

IEC 62196-2 or Mennekes is used in Europe on single and three-phase Capable of 63A / 230-400V AC / <43kW (max current).

EU DC CCS Combo 2 used in Europe (BMW, Chysler, Daimler, Ford, General Motors, Volvo, and VW Group.) Capable of 200A / 200-850V DC / <170kW (max current).

GB/T 20234.2-2011 AC is used in China Capable of 32A / 220-400V AC / <14kW (max current)

Tesla – proprietary single and three-phase <250A / <500V DC / <125kW (Photo Dr Kludge CCA-2)

DC CHAdeMO Yazaki (Nissan, Toyota, and other Japanese manufacturers.) 120A / 500V DC / <60kW (max current). 

(Photo C-CarTom CCA By-SA 3.0)

GB/T 20234.3-2011 DC is used in China Capable of 250A / 400-750V DC / <187.5kW (max current) 


Section 4

The KLE is rated up to 50kW for both charging and for regeneration - the EME provides the bi-directional motordrive inverter for this.  

Charging the i3 The BMW i3 has three options for charging – ‘slow’ and ‘fast’ (using AC) and ‘rapid’ (using DC).  Charging efficiency through the on board rectifiers is typically around 93-94%.

Time to 80% charge

Both Mode 2 and Mode 3 take in AC current from a 230V supply and convert it into DC current to charge the battery. The i3 does this through the convenience charging electronics (KLE) using one 3.7kW rectifier and passing half the current on to the Electrical Machine Electronics (EME) which has a second 3.7kW rectifier: together they provide the 7.4kW of power required for fast charging.



DC Rapid

25 min

39 min

Domestic (12A/240V)

7:45 h

9:30 h

3.7kW / 16A

5:30 h

7.30 h

7.4kW / 32A

2:5 h

3.45 h


2:45 h

11kW / 16A 3ph

BMW’s stated recharging times to 80%

The 94Ah model has now introduced three-phase charging enabling better use to be made of the 3-phase fast charging on-route network.   It does this by adding a third 3.7kW rectifier so that each now handles one of the phases.  This adds minimal weight whilst improving charging flexibility. Mode 4 allows DC charging using off-board rectifiers mounted in the charging unit; these operate at >93% efficiency.

 Charging point on BMW i3 - the top part is the Mennekes socket for mode 2 and 3 charging whilst both top and bottom sockets are for the mode 4 SC CCS charger.  Also shown is the Mode 2 13A charging cable, a tethered 32A Mode 3 and a CCS Mode 4 plug.  

In the i3, the charging socket (LIM) implements the decision to DC charge and the KLE monitors the charging process but otherwise passes the DC current straight through to the battery; this bypasses the on-board rectifiers and avoids the necessity for cooling them whilst charging.


Section 5 An illustrative charging profile for an i3 on a CCS DC charger (110A/44kW) is shown below. The current is constant up to about 60-70% with power gradually rising as system voltage rise; this yields a charge rate of about 0.68kWhrs per minute.  At maximum system voltage ~396V the current (and power) declines whilst voltage remains constant.  This reduces the charge rate to about 0.34kWhrs per minute.  After about 90% SOC the charge rate reduces again whilst the charge completes.

Charger rates Whether it’s Mode 2, 3 or 4, the charging profile is similar. This chart shows the constant-current and constant-voltage part of the charging profile for a typical ~400V EV system. What can be seen clearly is that the transition point, where the charge move from constant current to constant voltage, moves to a lower SOC% as the charger power increases. To move this transition point to a higher SOC% will require a higher system voltage. An 80%SOC is not a significant point for an i3.

 Illustrative Charge rate for BMW i3 with 18.8kWhr usable battery capacity connected to Mode 4 rapid CCS charger – 50kW peak, 44kW cont. Each charge will vary depending upon ambient conditions and battery state. In this example charging started at 20%SOC.

 Charging profiles for typical Mode 2, 3, 4 chargers. 32

Section 6

Tests on battery charging at different ambient temperatures also show a variation in charge capacity.   AVT showed a difference in battery capacity of about 15% between a battery at -6oC compared to one at 35oC

Efficiency and Temperature

The charging process itself leads to cell heating; this is true of rapid, fast and, to a lesser extent, slow charging. Hotter cells increase the chemical processes allowing faster charging. If cells get too hot then the charging process can damage the cells themselves and so it will be beneficial to cool the cells.

The efficiency of the charging process will vary between chargers and between charging modes. For Mode 2 and 3, charging utilises the on-board AC/DC rectifier; for the i3 these are optimised around 13A and 32A currents.  

Whilst no information is publicly available of cell temperature during Fast AC or Rapid DC charging of the BMW i3 battery, data is available (from AVT) on the Nissan Leaf LMO Pouch Cells.

Tests conducted by the Advanced Vehicle Testing Activity in Idaho National Laboratory showed, for the i3, an efficiency of 93-94% over the 3kW to 7.4kW range with a current Total Harmonic Distortion (THD) of 3.8% whereas below that the charge rate efficiency dropped to nearer 91% with a much higher THD of 17.6%. THD should be as low as possible excessive amounts of THD can be harmful to power system components.

Taking the Nissan Leaf (air-cooled battery and equipped with battery heating) after a ‘normal’ drive the following battery pack temperature rises were seen:  • CHAdeMo - 50kW DC charger the average pack temperature rise at the end of charging was about 6.5oC.  It could reasonably be inferred that CCS charging would lead to similar temperature increases. • Level 2 - 7kW/240v charger showed a rise in battery pack temperature of about 2.9oC by the end of each charging session. 

Mode 4 Charging depends on the rectifier efficiency in the off-board charging unit but typically this will be >93%, manufacturers’ claim. EVs can vary considerable with charger efficiency with some models being as low as 80% and some very early EVs showed charger inefficiencies as low as 65%.

These rises are not significant when considered against the change in battery pack temperature changes due to ambient conditions. 


Motors, Drives and Transmissions Electric Vehicles (EVs) are driven by electric motors and are powered by batteries or generators.  EVs can be front drive, rear drive or four wheel drive; distributing electrical power can be done more flexibly than with geared mechanical transmission. Battery weight, compared to a ‘tank’ of fossil fuel, can be quite high so it’s important that other systems are as light and compact as possible to help compensate for this.   BMW has developed the Hybrid Synchronous Machine (HSM) that provides very high power density with very high levels of performance whilst avoiding the use of rare-earth metals.   Other manufacturers use Induction Motors (IM), Wound Rotor Synchronous Machines (WRSM), or Permanent Magnet Synchronous Machines (PMSM).   The Electrical Machine Electronics (EME) is developed and produced by BMW. It contains the motor-drive inverter which is sourced from Infineon; Infineon has recently acquired International Rectifier who also provide the motor-drive inverter for Tesla.  Power is transmitted to the rear wheels through a permanently connected, fixed-ratio gear set.  In an EV there is no need for a clutch and no need of a multiple gear set: the i3 motor reaches 11,400rpm (Zoe - 11,300rpm, Tesla ~ 18,000rpm).   Gear changing would simply interrupt energy regeneration and add little useful higher speeds or faster acceleration. 


Section 1

The i3 is capable of 94mph with power from its 49kg HSM delivering a peak power of 125kW at 11,400rpm and a 30minute continuous power of 75kW (ECE R85).  The motor is liquid-glycol cooled and has a power density of 2.5kW/kg. Maximum torque is 250Nm.   The peak power of 125kW is limited to 30s bursts to avoid the possibility of the motor, electronics and battery overheating.  

The i3 Motor The i3 has a Hybrid Synchronous Machine (HSM) mounted at the rear driving the rear wheels through a single speed gearbox; there is no clutch involved.   The HSM motor is designed and built by BMW (their first electrical machine) and is driven by the BMW Electrical Machine Electronics (EME) including a motor drive inverter provided by Infineon. Configurations for motors for EVs include the following: asynchronous (Induction Motors IM), and Synchronous (Wound Rotor Synchronous Machine WRSM and Permanent Magnet Synchronous Machine PMSM), and switched and synchronous reluctance motors.   Tesla adopts an IM, Renault a WRSM and most other manufacturers adopt PMSMs. BMW use an in-house developed HSM.

The BMW electric machine with EME mounted atop. Forward of the motor is EKK scroll-type compressor for the air-conditioning, and the battery pack. Photo courtesy of Rudolf Simon (CCA).

The most widely adopted configuration is a single motor driving either the front or the rear wheels.  Some EVs use a single motor driving the front or a single motor driving the rear wheels whilst others look to have a motor per wheel.

The motor has a maximum torque of 250Nm available from standstill and hence does not need a clutch.   Maximum torque is available out to 4,775rpm after which it gradually reduces but is always more than sufficient for the required performance of the vehicle.  The motor has 6 pole-pairs in order to reduce yoke weight. Iron mass is reduced to absolute minimum through careful mechanical design. 

Universally, the requirement of the motor is to be highly compact, light-weight and very efficient throughout the rpm range, particularly at lower speeds, as well as inexpensive to manufacture and as free as possible from high cost, scarce and toxic components.  


Section 2

WRSM’s do not use rare-earth permanent magnets but can reach similar performance to a PMSM.   Renault now uses an in-house designed WRSM in its Zoe (and Fluence) having first developed a WRSM motor in collaboration with Continental.

Types of AC Electric Motors Asynchronous Motors

Permanent Magnet Synchronous Motors PMSM use permanent magnets to provide the secondary magnetic field in the rotor eliminating the induction heat losses and providing a higher efficiency than an induction motor. PMSMs are very power dense but can be expensive when rare-earth magnets are used. Most EV manufacturers use PMSMs with rare-earth permanent magnets mounted on the surface.

In the AC Induction Motor IM there is a ring of electromagnets arranged around the outside (stator) and inside that is the rotor that is made up of an axle and coils of wire.  The electromagnets in the stator are energised so that they induce a current in the rotor thereby making it rotate. IMs are widely used and relatively low cost but are not usually as compact or as efficient as other motors - IMs don’t include permanent magnets.   Tesla use IMs but adopt a copper rotor cage, rather than the more usual aluminium, in order to improve motor performance but at a cost penalty due to the higher material cost.

A PMSM with magnets mounted in the interior combines both reluctance torque and magnetic torque to improve efficiency whilst delivering a wide speed range, a high power factor, and high efficiency as well as very high power density.   BMW uses Hybrid Synchronous (Reluctance) Machines (US patent No 2012/0267977). It includes ferrous magnets rather than expensive rare-earth magnets as in other manufacturer’s motors.

Synchronous motors also have a stator providing a ring of electromagnets but instead of inducing a current in the rotor, the rotor is either wound with electromagnets excited by DC current fed from slip rings, or it has a rotor made up from permanent magnets. The synchronous motor rotates at a synchronous speed with speed control implemented by varying the supply frequency.   Synchronous machines can be used as either a motor or a generator.

Most electrical machines are radial flux (where the flux is radial from the shaft) but considerable interest is being shown axial flux (where the flux is along the shaft - think of it as a pancake style motor). designs because their form factor makes them very suitable for in-wheel hub drive. 

Wound Rotor Synchronous Machines WRSM more normally associated with very high-power low-speed applications exhibit high efficiency and a high power factor – typical usage would be the French TGV high-speed train. 

Section 3

The BMW i3 Mk1 uses an Infineon HybridPack2 automotive qualified power module designed specifically for electric vehicle applications up to continuous powers of 100kW.  

EDME, EME and Drives

The HybridPack2 module contains a ‘3-phase 6-pack configuration of Trench-Field-Stop IGBTs (Insulated-Gate Bipolar Transistors) and matching emitter controlled diodes’; maximum chip ratings are 800A/650V.  

The Electrical Digital Motor Electronics (EDME) provides the drive control integrating the throttle peddle, gear selection, Battery Management System (BMS) and Dynamic Stability Control (DSC) and turns this into a power demand from the motor via the EME.   The EDME also controls the cooling system pumps and fans, power management of LV systems and interfaces with the drivers display.  

The hybrid pack module is direct-liquid (water/glycol) cooled through a pin-fin baseplate of nickel plated copper.  The pinfin arrangement significantly contributes to the compact dimensions of the unit.

The principal purpose of the Electrical Machine Electronics (EME) is control of the electrical motor, converting the DC voltage (260V-396V) into 3-phase AC and vice versa when the motor acts as a generator.

The 2016 model BMW i3 Mk2 may well adopt Infineon’s latest lower-cost HybridPack Drive, 30% smaller with improved cooling. The new 750V faster-switching 10kHz Trench-Field-Stop IGBTs provide improved efficiency over the HybridPack2.

The EME also receives power from the convenience charging electronics (KLE), and distributes power to the resistive heating system, the refrigerant compressor, the HV battery, as well as the DC-DC link for powering low voltage vehicle electrical systems.

Infineon are a major worldwide chipmaker based in Germany with headquarters in Munich.  They have recently acquired Tesla’s motor drive supplier International Rectifier IR.

The DC-DC link reduces the voltage from the HV Battery (260V – 396V depending upon battery SOC) to about 14V (similar to an ICE vehicle’s alternator output). The DC-DC link handles up to 2,500W of power. 

The EME is developed and supplied by BMW in Dingolfing with the motor-drive inverter provided by Infineon.


Section 4

Drive Train Efficiency BMW’s Hybrid Synchronous Machine (HSM) has a maximum efficiency of 97% and, whilst no quoted efficiencies could be found for the Infineon Inverter, a likely maximum efficiency of around 99% based on other similar inverter drives. However, as with all electrical machines and power electronics efficiency at different loads and at different rpm can vary considerably. The graph opposite shows the typical efficiency across the whole motor speed range including at low motor speeds/ vehicle speeds. Below 25mph efficiency drop quite quickly although alongside that the power required also reduces significantly. 

The broad band of efficiency reflects differing efficiencies for different load demands with higher acceleration resulting in lower efficiencies. 

Some improvements in motor-drive efficiency can be expected with later models of HybridPack inverter. 


Section 5


As Formula-E is finding out, more than one transmission gear means interrupted re-generation, something that plays against energy efficiency.

Electric motors provide full torque at low speeds, unlike an Internal Combustion Engine (ICE), and hence a singlespeed transmissions can provide the necessary performance across the vehicle operating speed range including quick and smooth acceleration from standing start. The BMW i3 has a single speed transmission with a reduction ratio of 9.665:1.   The gear is integral with the differential unit that distributes torque to each wheel.   This unit is designed, developed and produced in-house by BMW  Most drivers’ experience is with internal combustion engines, clutches and multi-speed transmission, whether manual or automatic.   This leads many to wish for an electric motor coupled to multi-speed transmissions in order to improve efficiency and to reduce the expected noise and vibration that normally accompanies high-revving ICE. There is no need for a clutch as the electric motor doesn’t turn until required and when it does it has enough torque not to stall. The motor is rotary machine and hence inherently has a lower vibration than a reciprocating machine. The blue lines map a typical five-speed ICE car.  As can be seen the electric motor can cope with the maximum gradient (around 32%, typically) that an ICE car can handle whilst still allowing the maximum speed of 94mph.  

ICEs use multi speed transmission so that the engine doesn’t stall under the extra loads arising from steep hills, particularly when pulling away – the classic driving test hillstart.  


COOLING AND HEATING Cooling and/or heating isn’t something that would feature much when discussing ICE cars but for an EV it can have a considerable impact on vehicle performance and on range.  
 Electric cars use a number of different technologies for cooling of key components including active and passive air, liquid/glycol and refrigerants. An EV’s continuous performance is critically dependent upon cooling of motor, drive electronics and battery.  
 The BMW i3 BEVx uses a resistive heating system for the cabin whilst, in addition, the BEV can also use a more efficient heat pump.  The heat pump was initially an option but from mid 2016 is now standard. A number of other manufacturers have also adopted heat pumps in order to reduce the impact of heating of the vehicle’s range. 


Section 1

New EV drivers’ often say ‘there’s something wrong with my battery’ once winter comes but the impact is more likely coming from cabin heating. Evidence of the magnitude of the demand is supported by ‘fleetcarma’s’ analysis of a number of EVs and an analysis by the Institute for Powertrains and Automotive Technology.

Range impact Depending on vehicle speed, the maximum energy demand for an electrical vehicle can come from the heating and ventilation system.

Direct sunlight will cause a significant shift in the peak range by maybe five or 10oC lower in ambient temperature, such is the thermal gain from solar energy in modern vehicles glassy cockpits. In sunny climates window tinting may be beneficial; in cooler climates keep them clear.

For an ICE car it’s been normal, since around the 1960s, to have a cabin heating system using waste heat from the internal combustion process; car-sized internal combustion engines have a rather poor efficiency with a significant amount of waste heat being rejected through the car’s radiator or redirected to cabin heating , essentially for ‘free’. This amount of ‘free’ waste heat isn’t available to the more efficient electric car.

Manufacturers of EVs are making strenuous efforts to reduce the impact of lower ambient temperatures on vehicle range including an increasing use of more efficient heat pumps and, for the future, radiant panels in the car’s interior.

Since the 2000s, in the UK, Air Conditioning A/C has become increasingly a ‘standard specification’. There is a noticeable increase in an ICE car’s fuel consumption and decrease its range (~8%-10%) when running A/C. For an EV, range will be impacted whenever a cooling A/C demand is made.   However what comes as a surprise to many first time EV drivers is the magnitude of that impact on range when heating the car interior during very cold temperatures. 

The graph opposite shows a typical reduction in range arising from the use of battery-stored energy to heat the car interior.  A typical UK Summer’s day will draw neither heat nor cooling but either side of that an impact is felt on range.

Cabin heating varies with time and propulsion power varies with speed so the slower you go the greater the impact of cabin heating will be. 41

Section 2

car. At maximum power the EKK can develop as much as 30bar in the refrigerant using up to 4.5kW at a maximum compressor speed of 8600rpm.   When the vehicle is stationary rpm is limited to 5160 in order to reduce emitted noise.

The i3 Heating and Cooling The i3 has a number of heating and cooling systems. Given the simplicity of the electric motor, the heating and cooling system is comparatively complex.

The compressor draws gaseous refrigerant into the scroll at low temperature and pressure and, after three revolutions, ejects it still as a gas but at a higher temperature and pressure. The EKK is cooled by the refrigerant.

The i3 heats and cools the battery and the car’s interior.  It cools  the motor and its motor drive inverter/rectifier, the battery charging rectifiers, and, where fitted, the ReX engine, as well as the ReX engine space.

Initially as part of the winter pack option, and now standard for the i3, is a 1kW resistive heating system for the (slow) warming up of the main battery pack.

Waste heat from these systems is not recovered in the i3 but use is made of some common systems to maximise efficiency.   EV manufactures’ may turn to using these sources of waste heat in future designs but that will likely depend on future costs and weight of the next generation of batteries as, at times, the waste heat can be low quality and small in energy terms.

Both BEV and BEVx have resistive heating – similar to a domestic immersion heater.   Three heating coils are available 0.75kW, 1.5kW and 2.25kW.   These are ‘mixed and matched’ to provide heat in various combinations in steps of 0.75kW up to a 4.5kW maximum.  

The i3 uses a refrigerant for air conditioning as do ICE cars. Where the i3 differs from other current EVs is in its use of refrigerant to cool the battery.   This is the same for both BEV and BEVx and utilises a number of tubes sitting at the bottom of the battery pack through which refrigerant is evaporated.  

Along with other EVs such as the latest Nissan Leaf and Renault Zoe, the i3 also uses the A/C compressor and refrigerant in reverse mode to deliver cabin heat – this is a heat pump.   Heat pumps, using the refrigerant cycle to deliver cabin heat, are significantly more efficient than resistive heating and, for the i3 BEV, its additional cost, weight and complexity is justified to eke out every last mile of range – BEVx owners aren’t offered the choice as range from battery and fossil fuel is already double that of the BeV.

The i3 has a scroll-type compressor for the refrigerant circuit complete with its own three-phase synchronous motor and drive inverter.   The compressor is designated EKK and is mounted adjacent to the propulsion motor at the rear of the 42

The i3 has a liquid-glycol heating circuit for circulating the heat from the heating coils into the cabin interior; a small 20W pump circulates the hot liquid through the cabin heat exchanger. The BEV with heat pump uses the same circulating liquid system and cabin heat exchanger but adds the heat pump output to the resistive heating circuit via another heat exchanger before it gets transferred to the cabin.

amplified in EcoPro mode where the response to changes in ambient temperature is slower again.

The i3 uses a highly efficient ‘auto’ cabin heating and cooling system.  ICE cars minimise the energy usage of airconditioning by recirculating the air in the cabin and minimising the fresh air bled into the system – this is the difference between a ‘climate-control’ system and a simple ‘manual’ air-conditioning compressor.   The i3 uses exactly that principle when cooling albeit it adopts a slower response to changes in solar gain or ambient temperature than is normal for an ICE car in order to further minimise energy use.

Whilst the i3 motor and its drive electronics (EME) are very efficient they are also very power-dense: waste heat removal is a key area if performance is not to be reduced. Similarly, the charging electronics (KLE) with its integral AC/ DC rectifier requires cooling whilst in use.   These three components use the same liquid glycol cooling circuit disposing of heat through a conventional front-mounted radiator with integral electric fan – a surprise to many EV drivers is that their car has a radiator and radiator fan.

The A/C button in a ICE car normally turns on or off the compressor whereas in the i3 it just isolates the cabin cooling system heat exchanger.   This is because the refrigerant compressor may be needed for battery cooling, or, in the BEV, for the heat pump.

Where a ReX is fitted the generator and its electronics are added directly to the liquid cooling circuit for the EME and motor whereas the BEVx apu ICE unit is cooled by its own liquid coolant circuit before passing its heat through a heat exchanger and on to the same radiator used by the motor and electronics. 

Where the i3 differs from ICE cars is by using the same recirculation and minimal fresh air bleed for cabin heating as well; this minimises the energy necessary to heat incoming cold fresh air.   One consequence of restricting fresh air bleed is an increase in humidity (from passengers’ normal breathing) and the i3 auto mode will use the air condition system as necessary to reduce recirculated air humidity as necessary.

The following sections will discuss the principles of refrigerant cooling and describe the compressor pump, the heat pump, battery heating and cooling, electric resistive heating, and motor and electronics cooling.

In the same way as careful and gentle driving results in the longest range so it is with the auto climate control where changes to ambient temperatures is responded to more slowly than a ‘conventional’ ICE car system.   This is 43

Section 3

compressor will still be available for use by battery cooling and/or by the heat pump.

Cabin Cooling and Heating

The i3 uses three modes - Comfort, EcoPro, and EcoPro+. EcoPro mode applies a more efficient climate control regime than comfort by further restricting the rate of temperature changes. Restrictions are also applied to seat and mirror heating. EcoPro+ deactivates cabin heating and cooling, rear window defrosting and seat heating.

The cabin climate is served by an innovative and low energy system that is new to BMW but not perhaps too dissimilar to the Efficient Dynamics principle used in other BMWs. The system uses a much higher amount of recirculated, treated air, than is usual with an ICE car: this reduces the energy normally used either to heat, cool or dehumidify the air.  

The ‘user interface’ IHKA (Integrated Automatic Heating and Air-Conditioning Unit) is similar to other IHKA’s used across the BMW range of cars.  It has a an automatic temperature selection, air flap and blower control wheel and automatic air recirculation control as well as manual overrides.

The i3 climate control system is more energy efficient because its response to changing ambient temperatures, including strong sunshine, is slower than is normally the case with ICE cars.  Just as gentle acceleration and braking is more energy efficient so gentle changes to cabin temperature are also more efficient; this can take some getting used to.

Temperature sensors are in the cabin dash air outlet and in the footwell air outlet and a sunlight/light/rain sensor is located in the rear-view mirror housing.   Rear screen heating and front seat heating is also selectable.

In Auto mode the temperature selector wheel controls the temperature by adjusting the air flap and blower, the temperature distribution of the air, and the amount of fresh air make-up used when recirculating air.  The auto mode will also use the A/C to dehumidify the air when necessary.  

One mode that EV drivers won’t easily give up once they’ve had an EV is stationary cooling or heating.  On an ICE car the engine has to be running in order to either develop waste heat or to run the A/C compressor and hence preconditioning the cabin is not possible.  On a battery car the cabin can be cooled or heated prior to departure by simply activating the feature from a smart phone.   Heating or cooling will run up to 30 minutes in this mode before driving off; there is a battery drain unless one is plugged in but for many journeys this probably has little impact.

In Manual mode control of the air distribution and and the blower strength can be adjusted but the high degree of air recirculation is then lost. If Auto mode is selected then A/C will also be selected. Subsequently turning off A/C will isolate the heat exchanger that delivers cold, dry air to the cabin interior but the A/C 


Section 4 

Resistive Heating Whether the i3 is a BEV with heat pump or a BEVx the car still has electric resistive heating: the heating unit is similar to a home immersion heater using electric coils to heat a water/glycol mix which is then pumped around a circuit and into the cabin heat exchanger matrix through which air is blown to warm the cabin. The ‘immersion heater’ has three resistive coils rated at 0.75kW, 1.5kW and 2.25kW.  Any combination of the three heaters can be selected with the maximum output being 4.5kW with a granularity of 0.75kW steps.   • • • • • •

0.75 kW 1.50 kW 2.25 kW 3.00 kW (0.75+2.25) 3.75 kW (1.50+2.25) 4.50 kW (0.75+1.50+2.25)

The heater unit is bulkhead mounted at the front of the car together with the 20W circulating pump. For the BEV with heat pump the same heating circuit is used and the same electric heating ‘immersion’ is retained but an additional heat exchanger is fitted in the circuit for using the heat from the refrigeration cycle.   The heating circuit coolant then exchanges heat with the cabin heat exchanger matrix as in the non heat-pump car.



Section 5

The BMW i3 resistive heating uses around 5kW of power for 4.5kW of heat whereas using a heat pump reduces this to about 2.25kW of power for 4.5kW of heat – a 2:1 ratio.  In cooling mode the refrigerant achieves a 3:1 ratio of energy used to cooling input.

Refrigerant Circuit The refrigerant cooling and heating system uses the refrigeration cycle to cool the battery pack, cool the cabin interior, and (for the BEV) to heat the cabin interior.  

The refrigerant system uses: • a compressor, to add energy to the refrigerant making it a higher pressure gas at a hotter temperature • a condenser, to turn the higher pressure gas to a high pressure liquid thereby releasing heat • an evaporator to ‘boil’ the liquid to a gas thereby extracting heat from the the battery and/or cabin.

The refrigerant used is R-1234yf (in USA R-134a). R-1234yf has a Global Warming Potential GWP of just 4, whereas R134a (a HFC) has a GWP of 1440 and R-12 (a CFC, that is now no longer used) had a GWP of 8500. Some manufacturers are adopting CO2 (R-744) with a GWP of 1 but this comes with much higher pressures and other engineering challenges. Using refrigerants is efficient because heat is extracted when turning the refrigerant liquid into a gas and in reverse the refrigerant gives up heat when condensing from a gas to a liquid.  The normal boiling point of R1234yf is minus 29oC (R134a is minus 26oC) and, when turning the liquid refrigerant into a gas, heat will be extracted from the cabin or the battery. When used as a heat pump the heat comes from the atmosphere (similar to an air-source heat-pump) with the condensor being re-assigned as an evaporator. As the ambient temperature gets colder, the efficiency of the heat pump reduces as the temperature differential between the atmosphere and the refrigerant reduces.


Section 6

temperature from any heat or cold provided to the outside of the cell case:   this is the reason why preconditioning the battery is such a slow process and can take up to three hours to reach 10oC if an even gain in temperature throughout the cell is to be achieved.

Refrigerant cooling circuit Using the refrigerant principle the i3 cools the cabin or the battery or both using the same compressor and refrigerant. Valves divert the refrigerant to one or the other or to both depending upon the demand. Refrigerant is run through cooling tubes that form part of the base of the battery pack; the cooling tubes within the battery pack act as an evaporator expanding the high-pressure liquid refrigerant to a low-pressure gas, extracting heat from the battery to evaporate the refrigerant.   This cools the battery whilst using very little electrical energy: about 1kW of electrical energy in the compressor to 3kW of extracted heat.  The battery prismatic cells packaged within modules sit on these cooling/evaporator tubes, transferring heat through the prismatic cell case. Draining and refilling the refrigerant in this circuit is the most time consuming part of changing the battery pack. The High Voltage (HV) battery operates most efficiently between 25oC and 40oC and benefits from pre-heating if it is below 10oC and from cooling if it is likely to exceed 40oC. Battery Heating - along the outside of the cooling tubes run resistive heating wires used to heat the battery to around 10oC.  The heating system uses up to one kW.  The battery pack has a very high thermal mass and is slow to change


Section 7

As the ambient temperature drops closer to the boiling point of the refrigerant, the efficiency of the system drops markedly as the amount of heat easily extracted from the atmosphere will fall.  

BEV with heat pump When the i3 doesn’t require cooling of the battery or of the cabin, it can use the compressor, and the efficiency of a refrigerant circuit, as a heat pump to heat the cabin.   The heat pump requires only 2.25kW of power to deliver 4.5kW into the cabin whereas a resistive heating system requires 5kW to deliver 4.5kW into the cabin.  This saving in energy is directly related to the potential increase in vehicle range – maybe up to an extra 10% miles could be achieved in the right conditions. In the heat pump the condenser-role is now the heat exchanger that exchanges the heat rejected by the refrigerant with the electric resistive heating glycol circuit.   Further efficiency can be gained, provided either the battery or cabin dehumidification isn’t required. The high-pressure liquid leaving the heat exchanger can be expanded and re condensed to extract heat in what was the cabin evaporator and now can act as another condenser.  The final stage is now to use what was the condenser (when just air conditioning or battery cooling was required) to becomes an evaporator where the ambient air temperature is used to turn the liquid refrigerant into a low pressure gas.



Section 8

Heat pump in mixed mode Mixed mode allows the compressor and refrigerant to cool the battery, cool the cabin, and to heat the cabin with the same refrigerant circuit. This mode is highly efficient (and highly complex!). The same circuit is used to transfer heat via the heat exchanger into the electric heating system but the use of refrigerant cooling for the battery and cabin interior means that the secondary heat can no longer be extracted from the cabin refrigerant heat exchanger.   Instead the refrigerant used in the heat pump joins the refrigerant gas coming out of the battery and cabin heat exchangers before being returned to the compressor and then circulated through the condenser and either back to the battery and cabin interior heat exchangers or back to the heat pump circuit.   



Section 9

The engine compartment housing the ReX has its own cooling fan and the ReX internal combustion engine has its own 35litre/min liquid-glycol cooling system which, should the internal temperatures exceed 85-95 o C, uses a conventional wax thermostat to dump heat through a heat exchanger into the motor/inverter cooling system and out through the front mounted radiator.  The ReX circuit has an 80W coolant pump included.

Liquid cooling Both the HSM motor and its motor drive inverter/rectifier (EME) are highly power dense and, at 75kW continuous and 125kW peak, handle a lot of power in a very small space. This necessitates very efficient liquid cooling.  Peak power can be sustained for about 30s before overheating of the battery, motor and inverter would most likely occur. Both motor and drives are very efficient.   The electric machine mostly operating between 94-97% efficiency but at lower speeds and higher acceleration loads the efficiency can drop to as low as 80%.  Similarly whilst the IGBT based inverter will see high efficiencies at high motor rpms (high vehicle speeds), at lower motor rpm efficiencies can be expected to drop off considerably. The BMW i3 uses a 17litres/min liquid-glycol cooling circuit for the motor and inverter (EME) cooling and also includes the convenience charging electronics (KLE) in the same loop.   The cooling system consists of a conventional radiator and 400W electric fan mounted in the nose of the car.   When the i3 is a BEVx model with a ReX, cooling is required for the ReX electrical machine (generator) and the ReX inverter electronics (REME).  This is done by the same motor and drive cooling system as when a ReX isn’t fitted. 


Range Extending Engine The i3 BEVx with the Range eXtending ReX auxiliary power unit (apu) can be thought of as an i3 with approximately 40kWhr (or ~ 50kWhr in the 94Ah version) energy store. The 60Ah BEVx has 17.6kWhrs of usable energy from the battery and approximately 21.6kWhrs once converted by the ReX from the 9-litre fuel tank. The 94Ah BEVs has 26kWhr of usable battery plus the 21.6kWhr converted from the 9-litres of fuel.   
 In power terms the BMW i3 has an electric motor of 125kW and by comparison the ReX brings just 27kW (or 28kW from the 2016 models).  For a parallel-hybrid vehicle this disparity in power would be important but the i3 BEVx is a serial-hybrid.   The ReX engine shouldn’t be treated as a seemingly power limited 27kW/28kW ICE but as a 20kWhr energy store generating electricity on-the-fly.  
 This chapter sets the disparity between peak motor power and peak ReX power in context and describes why, when thinking of the ReX, it’s more useful to consider energy (kWHrs) rather than power (kW). 


Section 1 

A 21kWHr energy store 

Most other manufacturers, including some BMWs, adopt a parallel-hybrid arrangement using a smaller electric motor/ battery pack to deliver relatively low speed, short duration, journeys whilst a much larger mechanically geared internal combustion engine delivers maximum speed and acceleration from a larger fuel tank.  

The i3 BEVx ReX is a serial hybrid all-electric Battery Electric Vehicle (BEV) with a range-extending engine, sometimes described as a BEVx, a term adopted also in this book.  All performance (top speed and acceleration) is provided by the 125kW electric motor, always, and performance is not affected by whether the ReX is on or off provided that the battery charge is above 1.9% (or 360Whrs). 

For the parallel hybrid, there is a penalty in terms of performance and fuel economy for carrying around the extra weight of the electrical and battery systems and there is limited acceleration to be gained from the low-power electric motor and limited battery pulse power (approx. max pulse power ~ 40-60kW).  

If the ReX were to be 5kW or 50kW the car’s performance would still be the same and would remain the same until the battery is exhausted – see the water tank analogy.

 Range-extending Serial Hybrid.   The BMW i3 is the only example of such a configuration.


Section 2

The ReX is a variable rpm electrical machine although, for Noise and Vibration (N&V) reasons, it spends more time at 3600rpm producing 20kW/18.8kWe output.

On-the-move generator

The i3 BEVx has a 9-litre petrol tank and at 9.6kWhrs per litre and a realistic average 25% engine efficiency this equates to approximately 21.6kWHrs of energy, broadly equivalent to the i3’s installed battery pack.   At the same 3.8miles/kWHr as the 72 miles of the battery range is calculated at, this should deliver an additional range of about 82 miles - total of 154m.

The Range eXtending engine, or ReX, is a BMW W20 twocylinder engine of 647ccs based upon the twin cylinder engine that powers the c600 BMW scooter.  In the UK and Europe, the W20 produces 27kW at 4800rpm or, in the most recent model, 28kW at 5000rpm.   In the USA, the W20 is rated at 25kW at 4300rpm – one assumes to meet CARB regulations. In the c600 scooter, the engine develops 44kW at 7500rpm giving a maximum speed of 109mph.   Being a directlygeared ICE means that it has a maximum ‘sprint’ power some way above its maximum continuous power in order to enable normal acceleration through the gears; a serialhybrid generator doesn’t need this margin. The ReX W20 generator drives a variable rpm AC permanent magnet synchronous electrical machine having an efficiency of approximately 94% and giving an output power of 25.4kWe at 4800rpm (or 26.3kWe at 5000rpm).   The output from the ReX electrical machine is AC and is conditioned to 330VDC by the ReX Electrical Machine Electronics (REME); the REME has an efficiency of about 96%.   The DC output, via the KLE and EME, can then be used either to drive the main propulsion motor or to maintain the %SOC of the battery.  


Section 3

• If SOC charge is <0.7% then the ReX runs at idle up to about 12mph (7kW) and then increases gradually to 4800rpm (25kWe) at about 40mph. • The latest i3 model has the ReX run up to 5000rpm and 28kW/26kWe. • Later versions of the i3 software continue to fine tune ReX operation. • The 28kW model 2016 is assumed to follow the same operating principle but progressing to a maximum of 28kW in place of the 27kW.

ReX operation The ReX is started using the electrical machine/generator and then has a number of operating modes depending upon battery SOC. • At <6.5% SOC the ReX will be started automatically.   • The ReX can be started and stopped manually at a SOC below 75% (except in the USA, unless ‘coded’).  • Once started the ReX has a warm-up period (for catalytic converter to heat up) of about 6 minutes, depending on ambient temperature. During that time it runs at 2,200-2,400rpm (12kW) – this is the engine idle-speed. Stop/Start is inactive during the warm-up period. • Between 3.5% and 6.5% SOC the engine runs at idle between 6mph and 35mph when it increases gradually to 3600rpm at 56mph and above to provide 20kW/18.8kWe. Stop/Start is enabled and the engine stops at speeds of less than 6mph.  • Between 1.9% and 3.5% stop/start will be deactivated.   • If SOC charge is <2.5% then the ReX runs at idle up to about 35mph and then increases gradually to 4800rpm at about 64mph. • If SOC charge is <1.9%, then power is restricted  • Above 1.9% SOC the i3 performs exactly the same whether on ReX or pure battery but has the capability to deliver an additional 21.6 kWHrs of energy from the 9 litres of petrol. • If SOC charge is <1.5% then the ReX runs at idle up to about 25mph and then increases gradually to 4800rpm at about 56mph.

ReX operation against the power-speed curve for the BEVx showing the operation of the ReX at different SOC.  As can be seen from the graph, in normal operation, where battery SOC is above 3.5% and up to 56mph, the Rex maintains a margin of around 9kW or more over that required to maintain speed.  After 56mph when it levels off to provide a consistent 20kW/18.8kWe. Breakeven speed is shown as about 70mph where 18.8kWe is sufficient to maintain speed without drawing extra from the battery.

Section 4

a journey has steadied in terms of miles/kWhr, the trip computer can be used as an aid – multiply the journey miles/kWhr by 20 to give the approximate breakeven speed where the ReX can supply enough energy to propel the car and maintain battery charge.

‘Breakeven’ Speed The ReX is designed to provide a maximum power output for a steady-state speed of approximately 70mph with the battery pack providing the ‘buffer’ for extra power for uphill, and recover this energy when going downhill. This minimises the size of the required ReX engine whilst maintaining the i3’s performance.

Weight, wind and gradient are other factors affecting the breakeven speed that 18.8kWe can maintain without depleting the buffer: add more passengers and the breakeven speed is lower; similarly if driving into head winds the breakeven speed will be lower but conversely with a tail wind the breakeven speed will be higher.   Gradients (up and down hills) should broadly even themselves out over the journey but the time over which they do so may vary.   The graph shows the power-speed curve for the i3 ReX on the level (black line) and a 2% gradient uphill  (red line) and downhill (green line) either side. The latest software allows the ReX to use its maximum rpm to generate enough power to maintain the SOC; it does this by taking into account the route, the terrain and the electrical load demand. A/C and heating is the main auxiliary consumer power drain. The resistive heating can be combined to provide a maximum of 5.5kW – about the same effect as a 2% hill gradient at 75mph.

The ReX can maintain 70-75mph whilst coping with moderate hills; the BEVx uses the battery as a buffer to maintain performance from such a small generator as the load from hills varies.

Both the BEV and BEVx can go into ‘reduced power’ mode when the motor/inverter and maybe battery become overheated. The i3 will also go into such a mode if the battery SOC drops below 4.9% (BEV) and 1.9% (BEVx).

For the BEVx driver the latest driver’s display shows % SOC which can be a considerable help in judging the breakeven speed for any particular conditions, allowing a few miles to even out the ups and downs. Alternatively, once 55

Section 5

Extended journeys In the UK and Europe (and where US cars have been ‘coded’), the ReX can be turned on before the 6.5% SOC and at any SOC up to 75%.   This allows any journey to proceed at any speed and with any performance that the BEV is able to deliver whilst offering about twice the range.  The two charts below illustrate the potential (60Ah battery). If the ReX is started at 75% SOC (14kWHrs) and below, once it has idled for about 6 minutes, then it will provide a steady state 18.8kWe with the battery providing any power over and above this.  



Section 6

The ‘water-tower’ analogy An analogy for the i3 BEVx might be a water tower serving some homes. The pipe going to the houses would be, say, 125mm in case everyone turned their tap on at the same time; the average amount of water drawn by the houses though is that which could be provided by 20mm pipe.  The pipe refilling the water tower is 20mm because that will keep the water tower topped up under ‘average’ use. If everyone decided to use more water than normal for an extended period then the tank would eventually run dry and it’s the size of the pipe refilling the water tower that governs when that time will be.  For the i3 the ‘pipe going to the houses’ is the 125kW taken by the electric motor. The ‘water tower’ is the battery. The ‘pipe refilling the tower’ is the ReX at 20kW. Normal ‘water usage’ or power for the i3 would be less than 72mph and ‘abnormal’ would be sustained ‘water usage’ or power above 72mph but the time for the water tower to run out of water (or energy in the case of the i3) even at 85mph would still be a couple of hours depending on when you started the ReX (or when you started refilling the water tower) and during that time the BEVx’s performance remains exactly the same. 

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 The high voltage batteries of the BMWi3 and BMWi8  - Dipl.Ing. Florian Schoewel, Dipl-Ing. Elmar Hockgeiger BMW Group, München  
 Will your battery survive a world with fast chargers - Jeremy S. Neubauer and Eric Wood, National Renewable Energy Laboratory 




Glossary Battery – a device that delivers electrical energy from chemical energy . Battery Cell – the building block of a battery pack. Each cell contains an anode, a cathode, a separator and an electrolyte.  For Li-Ion, each cell will produce a nominal 3.6 – 3.8V.  Battery Cells can be ‘primary’ (not rechargeable) or ‘secondary’ (rechargeable).  All EV batteries are secondary. Battery Module – is a collection of battery cells and is the smallest Line Replaceable Unit LRU of the battery pack. Battery Pack – is a collection of modules with a single thermal management system.   Some EVs may have more than one pack. Capacity – Ampere-Hour (Ah) is the nominal capacity at a specified temperature and discharge rate.  For the i3 this is 60Ah and with the latest battery, 94Ah. Capacity, rated –Watt hours or kiloWatt hours is the Ampere-Hours times the nominal voltage time the number of cells.     Current, Maximum Discharge – is the maximum current that can be delivered by the battery without sustaining damage.  For the 60Ah BMW i3 this is ~ 110A.  Along with the max continuous motor power this limits the car’s continuous maximum speed. Current, Max 30-sec discharge pulse current -   is the maximum current that can be delivered in a 30-second pulse. For the BMW i3 this is ~ 400A and along with the

motor peak power (and gearing) determines the car’s maximum acceleration. Current, recommended charge current – is the current that the vessel charges at before reaching the constant voltage phase.  For the 60Ah i3 this is 110 Amps.. Battery Reversal – if a series connected set of battery cells isn’t regularly balanced the weakest cell will continue to get weaker at every charge and discharge until at some point the cell will reverse its voltage causing a complete failure, often catastrophic, of the battery pack. Battery Management System BMS – is the system, software and hardware that monitors and controls the charging and discharging of the battery and the battery temperature. Calendar Life – is the life span of the battery under storage.  It will be affected by temperature and SOC.  Together with cycle-life this determines overall battery life. C-Rate – is the battery capacity charged or discharged in one-hour. Cathode - During Charging the ions move from Cathode to Anode.   During discharge ions move from Anode to Cathode.   The Cathode material is either a lithium mixedmetal oxide (typically NMC, NCA or LMO), lithium iron phosphate, or, in the case of LTO, graphite.   Cycle Life – is the number of charge and discharge cycles at a specified Depth of Discharge DOD (normally 80% of absolute SOC) that the battery can undergo before failing to 61

meet its manufacturer’s defined end-of-life.   The i3 is expected to undergo 1000 complete cycles before its SOH falls below 70%.  BMW warrants the i3 battery for 8-years or 100,000 miles whichever is earliest.   Cycle Life is affected by temperature and C-Rate.   Together with Calendar Life this determines overall battery life. Calendar Life – is the life span of the battery under storage.  It will be affected by temperature and SOC.  Together with cycle-life this determines overall battery life. Depth of Discharge DOD – is the amount (%) of battery discharged compared to the maximum capacity of the battery. The higher the DOD, the lower the battery life. Electrolyte – the electrolyte allows the ions to move from anode to cathode and back again.  It is normally a liquid or gel of lithium salts and solvents.   Considerable interest exists in a solid electrolyte. Internal Resistance – varies with charging and discharging as well as under different operating conditions, such as CRate and temperature – hence it affects battery capacity and battery power. Increasing Internal resistance means reducing battery efficiency leading to greater battery temperature. Lithium-Polymer – uses a microporous polymer in place of the separator.  The polymer is covered by an electrolytic gel that acts as a catalyst that improves the efficiency of the chemical reaction.  Power Density – is the battery peak power (kW) per battery pack unit volume (litres).   For the i3 this is 147kW and a battery pack volume of 191 litres ~ 0.77kW/l State of Charge SOC – is an estimate of the amount of usable energy remaining in the battery.  Given that this will vary with rate of charge or discharge and cell temperature this is a difficult criteria to quantify accurately.

State of Health SOH – is a measure of the battery charge capacity compared to the charge capacity when the battery was new. Specific Energy – is a measure of the capacity of the battery (Watt hours) per battery mass (kg).   The i3 battery pack is 21.6/18.8kWhrs in 236kg ~ 92/80kWhr/kg. Specific Power – is a measure of the battery peak power (kW) per battery pack mass (kg).  For the i3 this is 147kW in 236kg ~ 0.62kW/kg. Voltage, Cut-off – is the cell voltage at ‘empty’ as determined by the supplier and monitored by the Battery Management System. Voltage, Terminal – is the voltage the battery delivers under load and will reduce with reducing battery SOC. Voltage, Nominal – is taken as the average voltage of the battery cell and is between the maximum and minimum voltage. Voltage, Open Circuit – is the no-load cell voltage Voltage, Charge – is the voltage that the cell is charged at. For a Li-Ion this increases during the constant-current charge phase, typically up to about 70%, and is steady at the constant-voltage phase allowing the charge current to gradually reduce until the battery is fully charged. 


About the Author David J. Bricknell began his engineering career as an apprentice in Her Majestyâ&#x20AC;&#x2122;s Royal Dockyard in Devonport and subsequently he studied Ship Science and Engineering at the University of Southampton. His career in the marine world involved ship repair, ship building, electronics and engineering at a number of large UK engineering companies (Vosper Thornycroft and British Aerospace) as well as consultancy at leading UK-based global engineering company, British Maritime Technology. At Rolls-Royce Ltd, David led the Naval design, power and propulsion sector, publishing over thirty technical papers around the world; the principles and technologies of power and propulsion being broadly similar across ships and vehicles. A responsibility for R&D as well as marine-wide business development provided the breadth of understanding across engines, transmissions as well as electrical machines, drives and energy storage. David continues his engineering career through his own consultancy, Brycheins Ltd.


ELectric Vehicles and the BMW i3