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Mixing strings of Lithium-Ion and Lead-Acid in parallel

Mikael Claeson

Dokumenttyp: Examensarbete för Högskoleingenjörer Huvudområde: Elektroteknik

Högskolepoäng: 15 hp Termin/år: VT, 2020 Handledare: Stefan Haller Examinator: Johan Sidén

Kurskod/registreringsnummer: ETG108G

Utbildningsprogram: Elkraftingenjör, 180 hp

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Sammanfattning

Sammanfattning

Avsikten med detta exjobb har varit att testa och analysera beteendet av batteri-system där man blandar litium och bly parallellt.

Den underliggande teorin om varför batterier av olika kemier beter sig på ett visst sätt tillsammans undersöktes för att få en förståelse för testresul- taten.

Ett flertal tester gjordes med olika batterier, laster och laddare för att ve- rifiera teorin och för att upptäcka fall där systemet funkar bra och där det funkar dåligt.

Baserat på denna förståelse gjordes ett script med avsikten att hitta en punkt med en lägsta årlig kostnad. Denna kostnad jämfördes sedan med system bestående av enbart bly samt enbart litium.

Det slutgiltiga målet med scriptet var att en säljare ska kunna fylla i kända parametrar för en viss telekom-anläggning. Scriptet lägger sedan till ett litet Litium-batteri parallellt med ett konstant bly-batteri. För att sedan öka på Litium i storlek och uppskatta urladdningsdjupet för Litium och bly vid varje steg, tills dess att Li har samma storlek som bly.

En punkt för minsta kostnaden presenteras sedan tillsammans med opti-

mal storlek av Litium samt rekommenderade max-strömmar.

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Abstract

Abstract

The purpose of this survey has been to test and analyse the behaviour of battery systems mixing parallel strings of lithium and lead acid.

The underlying theory of why batteries of different chemistries behaves together was investigated in order to understand the resulting tests.

Several tests were made with different products, loads and chargers in order to confirm this theory and to discover cases where the system works good and where it works bad.

Based on this understanding a script was made in order to find a point of the least annual cost. Annual cost was then compared with systems of Lead acid only and Lithium only.

The final goal for the script was so that a salesman can input known pa- rameters for a backup site. Script is then adding a small Lithium battery in parallel with a fixed Lead acid battery and, increasing Lithium in size and estimating depth of discharge for Lithium and Lead acid at each step, until desired breakpoint.

A point of minimum system cost together with Li size is then represented

together with the recommended current limits.

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Förord

Förord

Detta examensarbete har utförts hos Incell´s R&D-avdelning i Oskars- hamn som en avslutande del av distansutbildningen högskoleingenjör El- kraft hos Mittuniversitet.

Efter 3 års studier vill jag tacka alla mina klasskamrater samt lärare vid Mittuniversitet, Umeå universitet samt Luleå Tekniska Universitet.

Jag vill tacka min företagshandledare Mats Melin för den goda handled- ningen under mitt examensarbete, samt alla tips och råd från Andreas Dunge och Ulf Heiding, samt övrig personal på Incell. Jag vill också tacka min handledare vid Mittuniversitet Stefan Haller.

Jag vill också tacka min sambo Elin, som varit ett stort stöd under hela denna period.

Mikael Claeson

Oskarshamn, Maj 2020

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Table of Contents

Table of Contents

Contents

Sammanfattning ... 1

Abstract ... 2

Förord ... 2

Table of Contents ... 2

Terminology / Notation ... 2

Acronyms / Abbreviations ... 2

1 Introduction ... 3

1.1 Background and problem motivation ... 3

1.2 Overall aim / Problem statement ... 3

1.3 Scope ... 5

1.4 Concrete and verifiable goals ... 5

2 Theory ... 6

2.1 Difference between Lead and Lithium ... 6

2.1.1 Ro and Rp for Li and LA ... 7

2.1.2 OCV curves for Li and LA ... 8

2.2 Charging and discharging states... 9

2.2.1 Charging state ... 10

2.2.2 Discharging state ... 11

2.3 Li and LA characteristics ... 12

2.3.1 LA characteristics ... 12

2.3.2 Li characteristics ... 15

3 Methodology ... 17

3.1 Lab setup ... 17

3.2 Test procedure ... 19

3.2.1 Step 1. ... 19

3.2.2 Step 2 ... 19

3.2.3 Step 3 ... 19

4 Design / Implementation ... 20

4.1 Evaluation of best suited product ... 20

4.1.1 NMC 13S ... 20

4.1.2 LFP 15S ... 20

4.1.3 NMC 14S ... 21

4.2 Safety limits and functionality ... 21

4.3 Tests and cost calculations ... 23

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Table of Contents

4.4 Current waveform and model description ... 26

4.5 Model verification ... 32

4.6 Where and how to implement the model. ... 33

5 Results ... 38

6 Discussion ... 41

6.1 Social aspects ... 41

6.2 Ethical aspect ... 42

7 Conclusions ... 43

7.1 Future work ... 43

References ... 45

Appendix A: ... 46

Appendix B: ... 52

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Terminology

Public

Terminology / Notation

Acronyms / Abbreviations

ac Annual Cost

BMS Battery Management System

CE Coulombic efficiency. Efficiency when charging.

CHG Charge

CLD Current Limiting Device

C-rate Rated DSG/CHG value.

DOD Depth Of Discharge

DSG Discharge

ECM Equivalent circuit model

EOL End of life

Energy efficiency Total energy efficiency for both CHG and DSG.

Both depending on C-rate. (Mostly DSG).

LA Lead Acid

LFP, LifePo4 Lithium iron phosphate battery

Li-ion Lithium-ion battery

OCV Open Circuit Voltage

R0(t) Time dependent total inner resistance, Ro+Rp=R0(t)

Ro Ohmic resistance

Rp Polarisation resistanc

SOC State Of Charge

SOH State Of Health

VRLA Valve Regulated Lead Acid

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1 Introduction

3

1 Introduction

1.1 Background and problem motivation

Most telecom stations today uses Lead Acid (LA) technology for battery backup.

A switch towards Lithium (Li) is happening worldwide, however LA is still the biggest market.

Li has the lowest cost/year compared to LA when installed in backup sys- tems, especially systems experiencing longer interruptions, but its higher initial cost becomes a drawback for some customers.

LA battery is cheap but has poor cyclic performances. A general telecom site, often experience shorter interruptions more frequently.

These frequent cycles wear on LA lifetime, depending on how long they are.

An option to prolong lifetime of LA would be to connect in parallel a small Li battery with good cyclic performance, with the theory that it will soak up the major part of these small interruptions, and save LA lifetime.

1.2 Overall aim / Problem statement

The overall aim for the project is to gain insight how a system mixing strings of Li and LA in parallel behaves through testing. Evaluating different scenarios with various loads and chargers.

But also which battery type in Incell’s portfolio 13S NMC, 14S NMC and 15S LFP will be best suited in a parallel system considering lifetime, safety and cost. A better knowledge regarding sizing of Li is needed as to opti- mize cost and functionality.

Backup-systems for telecom stations usually comes in 4 different setups.

1. Gridpowered including battery.

2. Gridpowered including battery and backup diesel generator.

3. Offgrid with battery and diesel generator.

4. Offgrid with diesel generator.

Number 1 in the list has the least options where cost savings can be made.

The most important save factor is that Li will be able to lower DOD

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1 Introduction

4 (Depth of Discharge) enough for LA to make a significant saving in an- nual cost. Other save factors could be less servicing for LA.

Number 2 can in the event of a site where frequent grid loss is present and LA not covering the whole interruption time before generator startup, a Li battery in parallel could prevent this and therefore save fuel costs. Correct dimensioning of Li will then both assist in DOD savings and fuel costs.

Considering that Li is able to hold a higher charge than LA at 54.5V float voltage, it may show that for adding interruption time before a certain voltage threshold point, this could be a good choice.

Number 3 is a system with lower generator lifetime. A Li battery in par- allel may help to reduce startups prolonging generator lifetime, while also increase lifetime of LA. Fuel cost should theoretically be about the same.

If there is a site where the load is not constant and may go in to sleep mode then Li could contribute as to float charging LA, keeping it from self-discharging too quickly, also resulting in fewer generator startups.

Number 4 is a system which will make a large difference in costs if adding batteries. This is because the generator will now be able to run in its opti- mum rpm range while charging batteries, and being able to shut down in between.

Less fuel consumption is an important factor, not only considering fuel cost but also the risk of theft.

There are software on the market that can optimize these type of systems.

One of these are called HOMER Energy, and it takes into account weather models, discount rates, future fuel costs, load cycles and more. [1]

However by contacting Aleph Baumbach, Senior Energy Engineer at HOMER through email, I was told that when HOMER is subjected to two different chemistries, software is choosing either/or. Not both together in the same battery bank. [7]

Final goal would be that through understanding and testing, try to de-

velop a model that with basic inputs, replicates the current waveform for

a mixed system. With that model the DOD of Li and LA can be estimated,

and therefore it is possible to calculate and to find a point of least annual

cost.

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1 Introduction

5

1.3 Scope

The study has its focus on testing different setups and does not depend on battery modelling such as the electric Equivalent Circuit Model (ECM- model) because of its complexity.

Instead the current waveform for Li and LA is estimated, where several assumptions are made from previous testing and theory.

This model will likely never be as precise as an ECM-model, however it will hopefully give enough certainty in estimating DOD in a mixed sys- tem. Without the need to develop two ECM-models.

Developing an ECM-model require measured 𝑂𝐶𝑉(𝑆𝑂𝐶) (𝑂𝑝𝑒𝑛 𝐶𝑖𝑟𝑐𝑢𝑖𝑡 𝑉𝑜𝑙𝑡𝑎𝑔𝑒(𝑆𝑡𝑎𝑡𝑒 𝑂𝑓 𝐶ℎ𝑎𝑟𝑔𝑒)) data and HPPC (Hybrid Pulse Power Characterization) to catch the dynamic response over the entire SOC range [2]. Matlab/Simulink offer some methods to do this type of simulation. Some Python scripts could also be found online.

A question is if it is good practice using an ECM-model for this purpose.

For every iteration increasing Li in size, a simulation must be done calcu- lating a new DOD for Li and LA. It may take a long time for script to execute.

1.4 Concrete and verifiable goals

The goal was to evaluate if there is a technical and economical possibility to use Li as a performance-enhancer in a LA-system.

Testing has shown that with the right combination of load, charger and fraction between Li and LA there are cost savings to be made.

A conclusion was made that selling new combined systems is a possibil- ity. However the cost savings is not huge compared to LA only, and there- fore, main objective if possible would be to motivate the consumer to go full Li directly. If a customer still wants LA, it is possible to sell a fraction Li in parallel to prolong LA lifetime and lower annual cost. In this way the customer will be introduced and familiar to Incell products.

Adding Li in systems with LA + grid + generator, big savings can be done

by adding Li in parallel by prolonging interruption time. Adding Li in-

stead of LA is more favorable because of the higher potential and extra

capacity for Li when charged at float voltage.

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2 Theory

6

2 Theory

2.1 Difference between Lead and Lithium

To understand the difference in behaviour for Li and LA it is necessary to introduce the ECM-model.

The ECM-model is not a replica for the electrochemical processes in the battery. It is a simplified construction, consisting of the ohmic voltage drops, and the polarisation voltage drop.

Ohmic voltage drops is represented with a resistance 𝑅𝑜 and can be seen as heat losses. When pulse discharging a battery for 2s, the voltage drop occurring can be seen as an approximation of 𝑅𝑜.

Polarisation resistance 𝑅𝑝 is connected in parallel with a Capacitor 𝐶𝑝 and can be seen as a time-based resistance that is an effect due to charge trans- fer inside the battery. When modelling heat losses, 𝑅𝑝 is often not in- cluded.

For a more accurate model, 2 pairs of 𝑅𝑝,𝐶𝑝 branches are often para- metrized, representing a short time constant and a long time constant.

Relaxation to true OCV can take between 15-30 min. That is why if you want to sample 𝑆𝑂𝐶(𝑂𝐶𝑉), battery must rest for a period first.

A way to collect 𝑆𝑂𝐶(𝑂𝐶𝑉) data could be to do a long discharge at a very low C-rate.

The ECM model works just the same applying current from the opposite direction, as when charging. [2]

A simple simulation was made to explain the behaviour over the whole

course, rest - discharge - rest – charge - rest. Note that in this simulation

there is no change in 𝑂𝐶𝑉(𝑆𝑂𝐶) as in a real simulation including a sam-

pled change in SOC for each step.

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2 Theory

7

Figure 2.1.1: Rest-Discharge-Rest-Charge-Rest.

As seen in figure 2.1, the combined voltage drop 𝑅𝑜 + 𝑅𝑝 after some time could be even more simplified as 𝑅0(𝑡) = 𝑅𝑜 + 𝑅𝑝. [2]

2.1.1 Ro and Rp for Li and LA

When comparing Li and LA for equal size, looking in datasheets Li has often a little bit lower 𝑅𝑜.

However LA is known for a high voltage drop when exposed to a load.

This has to do with the polarization effect that is due to charge transfer inside the battery [2]. 𝑅𝑝 for LA is larger than 𝑅𝑝 for Li, which is con- firmed in later testing.

This also means in charge mode that to charge LA, you would need a higher voltage to keep current flowing into the battery. A LA battery charged at 54.5V will rest around 52V 100% SOC when charger is off.

Same charge voltage for Li will top up the battery all the way to 54.5V and when charger is disconnected, the voltage will only drop from a charge voltage of 4.2𝑉/𝑐𝑒𝑙𝑙 down to 4.185𝑉/𝑐𝑒𝑙𝑙 (ICR18650 @ 25℃), re- sulting in a higher potential for Li [5].

This so called float voltage is always present when charging lead, which

contributes to guarantee that Li has the highest potential at 54.5V.

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2 Theory

8 The reason that LA is kept at a constant float voltage at 2.25𝑉/𝑐𝑒𝑙𝑙 is to keep the battery at full charge compensating for self-discharge. For Li, self-discharge is very low but for LA, it is necessary to include. [3]

Figure 2.1.2: Self-discharge in LA represented as Self_dsg.

2.1.2 OCV curves for Li and LA

Even though connected in parallel they share the same voltage, estima- tions can be made of how the batteries will behave together by looking at their respective OCV-curves.

Figure 2.1.3: 𝑂𝐶𝑉(𝑆𝑂𝐶) curves for the evaluated battery-types [3], [4].

Below is the equation created for calculating 𝑆𝑂𝐶

14𝑆

(𝑂𝐶𝑉).

𝑆𝑂𝐶(𝑜𝑐𝑣) = −161681 + 16372.9 ∗ 𝑜𝑐𝑣 − 659.641 ∗ 𝑜𝑐𝑣2+ 13.2154 ∗ 𝑜𝑐𝑣3− 0.131669 ∗ 𝑜𝑐𝑣4 + 0.000522175 ∗ 𝑜𝑐𝑣5 (2.1.1)

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2 Theory

9 When looking at figure 2.1.3, some conclusions can be made of which bat- tery would be the most suited. Since charging voltage varies with tem- perature at a rate of 2.5 𝑚𝑉/𝑐𝑒𝑙𝑙/°𝐶 from midpoint 2.27𝑉/𝑐𝑒𝑙𝑙 at 20°C, at 0°𝐶 a system charge voltage would be 𝑈

𝑐ℎ𝑎𝑟𝑔𝑒

(0°𝐶) = 55.7𝑉. [3]

Neither NMC 13S or LFP15S products will reach this point of charge due to high voltage shutoff, and therefore never maximize the benefits of this high float voltage.

LFP also has the disadvantage of having a steep dip in OCV voltage from 100-90% SOC. This will probably result in an early overtake in discharge current for LA. An interesting question is how a system would behave with 16S or 17S LFP, since the flat curve may give very good result.

15 cells are the maximum number of cells in series for Incell BMS, so this situation will not be evaluated further.

NMC 14S has a maximum voltage of 58.8V which allows for good mar- gins. A negative aspect is that full capacity is not utilized, but at the same time it benefits from not being charged at maximum voltage, which in- creases lifetime.

2.2 Charging and discharging states

At first basic specifications of different battery products was added in a table for easy access.

Figure 2.2.1: Basic specifications table for different Incell Li battery products.

Below possible charging and discharging states are evaluated.

Resting state is not evaluated, because it is not a normal state in real life applications where grid is present. The only thing that happens when resting is that batteries will charge/discharge each other to equilibrium, and after that LA will self-discharge itself and Li down to low voltage cutoff.

Resting state may be present when there is an off-grid solution, where the

load is not constant and goes into sleep mode.

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2 Theory

10 2.2.1 Charging state

When both LA and Li are kept in parallel, batteries will share the same potential, but not necessary the same OCV. High difference in OCV can create large currents flowing between batteries.

But thanks to Incell patented built-in CLD (Current Limiting Device), harmful charge currents for Li can be avoided.

If there is a large difference in OCV creating large currents flowing from Li to LA, from LA point of view, high charging currents is not optimal, but it is no safety risk [3]. If these discharge currents are too high for lith- ium, battery will shut off and won’t reactivate until rail voltage is less than 2V below battery voltage.

When charging is applied, due to its smaller 𝑅0(𝑡), Li will take the first charge. Since Li have a lower SOC because of its head start in discharging, (unless both batteries are fully depleted), this will also contribute to lith- ium being charged first. Note that Li taking the first charge or discharge might not be true if there is a very small fraction of Li.

To avoid that LA charges Li creating an unnecessary waste of lifetime, a charger should be chosen so that it can handle the max charge current for Li. This is in order to avoid not creating a possible moment where for example:

Li max charge current is 50A, and max charger current is 20A. If Li is ab- sorbing a charge of 40A in that moment, LA will contribute with 20A of current flowing to Li, which should be avoided in an efficient system.

Lab testing will evaluate these situations.

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2 Theory

11 2.2.2 Discharging state

During discharging the most important factor is that Li is rated to handle the full load by itself without tripping its safety systems.

A roughly expected discharge current waveform could be seen as an X, where Li will take ¾ of discharged Ah from zero to x-meetpoint, and after that point LA will take ¾ of discharge Ah from 0.5 to end of capacity.

Figure 2.2.2: Roughly expected current waveform at equal size Li and LA.

This type of X-shape discharge form may be seen at equal size Li and LA.

As the capacity of LA increases, x-meetpoint will move to the left.

Also as LA increases, combined resistance 𝑅0(𝑡) for LA will decrease, re- sulting in that Li and LA discharge curves will meet at an higher voltage potential point. This will also contribute to x-meeting point moving left, creating a current waveform looking more like figure 2.2.3. Discharge rates is also a factor.

-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Current

Mixed system discharged Wh

Current waveform

Li LA

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2 Theory

12

Figure 2.2.3: Roughly expected current waveform at greater size LA than Li.

Lab testing will evaluate these situations, and ideas can be formed to im- prove the dimensionless model in figure 2.2.2.

2.3 Li and LA characteristics

2.3.1 LA characteristics

LA capacity is highly affected by discharge rates and temperature.

Figure 2.3.1: Capacity for LA at different C-rating. 10h representing 0.1C and 1h 1C. [3]

-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0

0 0.2 0.4 0.6 0.8 1

Current

Mixed system discharged Wh

Current waveform

Li LA

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2 Theory

13 A modified graph including equation 𝑐𝑎𝑝%(𝐶

𝑟𝑎𝑡𝑒

) was made for use in calculations later.

Figure 2.3.2: Available capacity for LA at different C-rating, transformed x-axis.

Figure 2.3.3: LA capacity at different temperatures. RequiredAh=Ahcap/corr.factor. [3]

Lifetime tables was not found for the specific batteries used in test but

was collected from an Elsevier article [5], which evaluated lifetime of dif-

ferent LA batteries.

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2 Theory

14 A lifetime model called VRLAB1 was chosen which represented a VRLA (Valve Regulated Lead Acid) battery, which also had an 𝑐𝑦𝑐𝑙𝑒𝑠(𝑡𝑒𝑚𝑝) function very similar to the one in FIAMM Engineering guide.

Figure 2.3.4: Lifetime equation for VRLAB1 cycles(DOD). [3]

Figure 2.3.5: Lifetime equation temperature correction for VRLAB1, very similar to FIAMM. [3]

Figure 2.3.6: Lifetime equation combined for VRLAB1. [3]

Calendar life is generally no more than 5 years for LA, where EOL (end

of life) is often specified as 70% capacity left.

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2 Theory

15 2.3.2 Li characteristics

Li capacity is less affected by discharge rates. A discharge rate up to 1C will not affect battery capacity, as most Li battery are rated at 1C for 1h.

While LA often brands their battery capacity at 0.1C for 10h.

Figure 2.3.7: Available capacity for Li at different C-ratings. [4]

However discharge at lower temperature is contributing to a lower ca- pacity.

Figure 2.3.8: Capacity at different temperatures for Li. [5]

Lithium has better cycles(DOD) capacity than LA. Below is a graph from

Incell marketing department.

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2 Theory

16

Figure 2.3.9: Cycles(DOD) for Li NMC batteries

Below is the equation created for calculating 𝑐𝑦𝑐𝑙𝑒𝑠

𝑁𝑀𝐶

(𝐷𝑂𝐷).

𝑐𝑦𝑐𝑙𝑒𝑠𝑁𝑀𝐶(𝐷𝑂𝐷) = 151438 − 1.47529 ∗ 106∗ 𝐷𝑂𝐷 + 7.41678 ∗ 106∗ 𝐷𝑂𝐷2− 2.14086 ∗ 107∗ 𝐷𝑂𝐷3+ 3.68167 ∗ 107∗ 𝐷𝑂𝐷4− 3.7225 ∗ 107∗ 𝐷𝑂𝐷5+ 2.04022 ∗ 107∗ 𝐷𝑂𝐷6− 4.67221 ∗ 106∗ 𝐷𝑂𝐷7 (2.3.1)

No similar data or function for 𝑐𝑦𝑐𝑙𝑒𝑠(𝑡𝑒𝑚𝑝) correction was found for Li.

Calendar life is generally no more than 15 years for Li, where EOL (end

of life) is often specified as 70% capacity left.

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3 Methodology

17

3 Methodology

3.1 Lab setup

A lab test setup was made with following equipment.

• Variable power load capable of 15kW.

• 1 𝑚

3

water container together with a water pump circulating cool- ing water for the variable load, making the load capable of running with 15kW power for appr. 4h heating water container with +50deg.

• A charger station with current limiting feature. Capable of charg- ing at 75kW, however input current is limited due to a 16A fuse in- house. In reality max charging ca 11 kW.

• Several batteries from Incell to be tested plus 4*48V 100Ah LA bat- teries from Fiamm and Leoch.

• Keysight logging equipment.

• 4 current sensors measuring LA, Li, CHG, and DSG currents.

• System voltage measurement.

• Ambient temperature.

Table 3.1.1: Battery list.

Battery ref. Product name Identification Note

Li NMC 13S 100Ah SLB-100-x-1 Gen5 NMC 13S Li LFP 15S 100Ah SLB48-100-x-5 Gen5 LFP 15S

Li NMC 14S 100 Ah SP48-33-100-SC 14S 33J

483310SC0198 19010001

Max dsg 60A.

Li NMC 14S 44Ah SP48-22-44-C 14S 44Ah CLD

Unknown

Bat Lead1 4x FIAMM 12FIT101 12FIT101 48V 100Ah

Bat Lead2 4x FIAMM 12FIT101 12FIT101 48V 100Ah

Bat Lead3 4x Leoch LPF12-100A LPF12-100A 48V 100Ah Bat Lead4 4x Leoch LPF12-100A LPF12-100A 48V 100Ah

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3 Methodology

18

Table 3.1.2: Equipment list.

Equipment Product name Identification Note

Load In-house design Op- Amp based CP-control.

Water cooled transistor-bank.

15000W adj.Load Water cooled Charger Emerson R48-5800e

M800D ACU controller

Cabinet Cabinet, stackable up to 75 kW charge.

Logger Keysight 34970A 34901A Mux module

Including software.

3*Amp Sensor LEM LA Series LA305-S +-500A , Hall Effect

Current Shunt 250A 60mV Load CP-control and

logging load current.

Figure 3.1.1: Test setup

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3 Methodology

19

3.2 Test procedure

Measurements were made for several combinations in a 3-step test pro- gram.

1. Evaluation of best suited product.

2. Evaluation regarding safety limits and functionality.

3. Testing to collect sufficiently amount of data in able to understand how different setups behave and to help create a model that repli- cates the process in a way, that a script can be made that optimizes a system for least annual cost.

3.2.1 Step 1.

First tests were made with all 3 battery products NMC13S, NMC14S and LFP15S to evaluate the most suited battery. Testing was made with dif- ferent loads and charge currents. Based on several inputs the best suited battery was chosen for step 2.

3.2.2 Step 2

An evaluation was made regarding safety and functionality based on the assumptions made earlier in theory. Any problems that could occur was noted and design demands were stated of how to minimize these occa- sions.

3.2.3 Step 3

Testing was made to understand the behaviour when changing the amount of Li compared to LA, having a fixed load and fixed charge. These results was then imported to excel where calculations was made to eval- uate system cost and DOD for Li and LA at all points of discharged Wh.

A pattern was assumed of how the current waveform for Li and LA was

affected by changing the ratio between Li and LA and the amplitude of

load. The appearance of the waveform was also considered with the op-

tion to change the linear function in figure 2.2.2 into a more realistically

shaped function.

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4 Design / Implementation

20

4 Design / Implementation

4.1 Evaluation of best suited product

4.1.1 NMC 13S

Since NMC 13S is not able to benefit from higher charge voltages than 54.5V, it was excluded as the most suited battery. NMC13S behaved a bit differently, where Li and LA tends to share current at the end of dis- charge. At this test, Li never jumped out of CLD-mode during charging, due to that several slow-regulated Emerson chargers was connected to- gether creating a big current spike.

Figure 4.1.1: Test NMC 13S.

4.1.2 LFP 15S

One test was performed with LFP15S. LFP took merely no current at start, even lower than expected.

At 13000s or 3.6h Li takes over discharging in a surprisingly short in-

stance. This is not an electrochemical effect but is due to that charge-FET

is turned on at -20A in the bidirectional mosfet switch. Before that, current

is flowing through charge-FET body diode. A bit later load is turned off

and charging is started.

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4 Design / Implementation

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Figure 4.1.2: Test LFP15S.

4.1.3 NMC 14S

14S was considered as the most suited battery. More tests for this product was then made which can be found at part 4.3, tests and cost calculations.

4.2 Safety limits and functionality

The most important factor is that Li should be able to handle the maxi- mum current of a system. To be on the safe side, this could be calculated as:

𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 =

𝐿𝑜𝑤 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑑𝑖𝑠𝑐𝑜𝑛𝑛𝑒𝑐𝑡 𝑀𝑎𝑥 𝑊𝐿𝑜𝑎𝑑

(4.2.1)

One aspect when designing for an efficient system is to avoid that LA is

charging Li. Below is an example showing this phenomenon.

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4 Design / Implementation

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Figure 4.2.1: Charging in different steps.

At step 1 neither load or charger is present, only illustrating that LA is charging Li. In reality, load is always present.

At step 2, charger is activated at 20A, but due to the charger’s slow regu- lation and great current spike, Li has gone into overcharge current shut- down. Zooming in it can be seen that Li is going into CLD-mode for a very short while, where LA is charged with 13A and Li charged at 7A CLD-limit.

At step 3, Li tests to disconnect CLD and the current overshoot from charger is no longer that large so that an overcharge current state will occur. Now the charge limit for Li is 50A and the charger limit is 20A.

For the rest of period 3 LA is now charging Li with the additional current.

At step 4 this is avoided by raising the charge current to 50A. Graph shows 44A but its only due to slow/poor charger regulation.

At step 5 charging is raised to 70A but shortly after Li goes into CLD-

mode. There is a Li shutdown at 5200s that is due to a large charge spike

when CLD is disconnecting. These spikes were later mostly avoided by

using only the required amount of chargers.

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4 Design / Implementation

23 The conclusion is that for an efficient system there is a need to dimension the charger so that it can handle max charge current for Li. In real world this would mean that charger should be able to handle:

𝑟𝑒𝑞. 𝑐ℎ𝑎𝑟𝑔𝑒𝑟 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 = 𝑚𝑎𝑥 𝑐ℎ𝑎𝑟𝑔𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝐿𝑖 + 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝐿𝑜𝑎𝑑

(4.2.2)

If the charger is greater than required, Li will likely go into CLD-mode for a period. User then must be aware that charging is limited to 6-12A, which will result in a longer charging time for Li.

4.3 Tests and cost calculations

NMC 14S was chosen as the most suited product and several compara- ble tests were performed with different ratios of Li and LA. These tests were made with the same load and charger setup.

From these tests following calculations was added to the graphing sheets.

𝐷𝑂𝐷

𝐿𝑖

=

𝐿𝑖𝑊ℎ𝑑𝑠𝑔

𝐿𝑖𝑊ℎ𝑐𝑎𝑝

𝐷𝑂𝐷

𝐿𝐴

=

𝐿𝐴𝑊ℎ𝑑𝑠𝑔

𝐿𝐴𝑊ℎ𝑐𝑎𝑝

(4.3.1)

𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑠𝑡

𝐿𝐴

=

𝑐𝑜𝑠𝑡𝐿𝐴𝑏𝑎𝑡

𝑐𝑦𝑐𝑙𝑒𝑠𝐿𝐴(𝐷𝑂𝐷)

∗ 𝑐𝑦𝑐𝑙𝑒𝑠/𝑦𝑒𝑎𝑟

(4.3.2)

𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑠𝑡

𝐿𝑖𝐿𝐴

= 𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑠𝑡

𝐿𝐴

+ 𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑠𝑡

𝐿𝑖

(4.3.3)

Before evaluating results, lifetime should be observed in order to see that an unrealistically high lifetime is not seen.

𝐿𝑖𝑓𝑒𝑡𝑖𝑚𝑒

𝐿𝐴

=

𝑐𝑦𝑐𝑙𝑒𝑠𝐿𝐴(𝐷𝑂𝐷)

𝑐𝑦𝑐𝑙𝑒𝑠/𝑦𝑒𝑎𝑟

𝐿𝑖𝑓𝑒𝑡𝑖𝑚𝑒

𝐿𝑖

=

𝑐𝑦𝑐𝑙𝑒𝑠𝐿𝑖(𝐷𝑂𝐷)

𝑐𝑦𝑐𝑙𝑒𝑠/𝑦𝑒𝑎𝑟

(4.3.4)

In the following graphing sheets lifetime is not plotted because of lack of space.

Since all calculations in following sheets are based on the same fraction

Li and LA from lab testing, the only conclusion from annual cost you can

make is that a very short discharge will not give an advantage for the

mixed system regarding annual cost.

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24 This is because LA has a low initial cost, and its lifetime is not drastically changed by short Wh discharges.

However as discharged Wh gets larger, the mixed system has an ad- vantage over LA only. Li has the lowest annual cost over all periods of discharged Wh.

Figure 4.3.1: Ratio 44/100. It can be seen that when a low ratio of Li is present, Li will not display the expected current waveform. LA is taking the first instant discharge since it has a lower 𝑅𝑜 than Li when several batteries are paralleled together. After a period, Li is taking the most discharge due to its lower 𝑅0(𝑡). A bit later LA is back and discharging more than Li again until end of discharge.

A conclusion from figure 4.3.1 can be made that with a smaller fraction of

Li, the desired function of Li taking the first discharge is no more substan-

tial.

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4 Design / Implementation

25

Figure 4.3.2: Ratio 100/400. At a ratio of 0.25 the expected waveform can be seen. Cost calculations shows that if this system would only experience short interruptions of less than 1000Wh (20min, 3000W), there would be minor economic benefit of installing an extra 100Ah Li in parallel. Conclusion is that small interruptions where a large LA battery is installed, cost savings will not be especially reduced.

Figure 4.3.3: Ratio 100/200.

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Figure 4.3.4: Ratio 100/100.

The expected x-shape was seen for 𝐿𝑖/𝐿𝐴 ratios between 0.25-1 according to tests. When batteries are reaching a DOD of about 50-60%, the current shape tend to be more unstable until end of discharge.

The reason that Li and LA cost comparison calculations are only halfway, is because both are based on LA Wh capacity.

4.4 Current waveform and model description

As a start a dimensionless model could be based on a linear function as in figure 4.2.

The span 0-1 over the x-axis could be seen as the whole discharge period.

This could be divided so that 0-0.5 is seen as Wh discharged before cur- rents meet at crossing point. 0.5-1 is seen as Wh discharged after crossing point.

A current waveform could be implemented as a function or a combina-

tion of two different functions. These functions could also be changed

depending on the fraction of 𝐿𝑖/𝐿𝐴 or other factors as load size.

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Figure 4.4.1: Example of two different “0-1” functions and its inverse.

Function chosen to start with was f(x)=1-x, as a simple function can help to understand the results at first. An evaluation of the model will later prove if the result is close to reality.

At first properties of the waveform are set accordingly, (starting with a low Li Wh capacity and a constant LA Wh capacity) :

𝐿𝑖

𝑊ℎ𝑐𝑎𝑝𝑐𝑜𝑟𝑟

= 𝑆𝑂𝐶

𝐿𝑖

(𝑐ℎ𝑎𝑟𝑔𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒) ∗ 𝐿𝑖

𝑊ℎ𝑐𝑎𝑝

(4.4.1)

𝐿𝐴

𝑊ℎ𝑐𝑎𝑝𝑐𝑜𝑟𝑟

= 𝑐𝑎𝑝

𝑓𝑎𝑐𝑡𝑜𝑟

(𝐶

𝑟𝑎𝑡𝑒

) ∗ 𝐿𝐴

𝑊ℎ𝑐𝑎𝑝

(4.4.2)

𝑡𝑜𝑡𝑎𝑙 𝑊ℎ = 𝐿𝑖

𝑊ℎ𝑐𝑎𝑝𝑐𝑜𝑟𝑟

+ 𝐿𝐴

𝑊ℎ𝑐𝑎𝑝𝑐𝑜𝑟𝑟

(4.4.3)

A voltage point where currents meet are then calculated with a function

based on the ratio of 𝐿𝑖/𝐿𝐴. Where system voltage values are taken from

actual tests at the ratios of 0.25, 0.5 and 1 at 3000W load.

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Figure 4.4.2: Voltage at 𝑥𝑝𝑜𝑖𝑛𝑡(𝑟𝑎𝑡𝑖𝑜 𝐿𝑖/𝐿𝐴).

This function is in real world not linear and may later be improved with some more data.

This crossing point is also correlated according to the voltage drop that will occur with higher loads. A function was made estimating 𝑅0(𝑊ℎ

𝑐𝑎𝑝

), based on a 𝑅0 of 16.9 mΩ for a 100Ah NMC 14S39P battery. 𝑅0 is divided by 2 when doubling capacity in parallel.

Figure 4.4.3: 𝑅0(𝐿𝑖𝑊ℎ𝑐𝑎𝑝)

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29 Both these functions could later be slightly altered, in order to improve the model. It would be preferred if function in figure 4.4.2 was based on a very low C-rate, but this would imply time-consuming tests.

Next step in script will be to calculate the amount of Li discharged before the x-point.

𝑈

𝑙𝑜𝑎𝑑

= 𝑈

𝑟𝑎𝑖𝑙

= 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑎𝑡 𝑥

𝑝𝑜𝑖𝑛𝑡

(𝑟𝑎𝑡𝑖𝑜 𝐿𝑖/𝐿𝐴)

(4.4.3)

𝐼 =

𝑊𝐿𝑜𝑎𝑑

𝑈𝑟𝑎𝑖𝑙

1

2

(4.4.4)

𝑈

𝑟𝑎𝑖𝑙

= 𝑂𝐶𝑉 − 𝐼 ∗ 𝑅0(𝑊ℎ𝑐𝑎𝑝) → 𝑂𝐶𝑉 = 𝑈

𝑟𝑎𝑖𝑙

+ 𝐼 ∗ 𝑅0(𝑊ℎ𝑐𝑎𝑝)

(4.4.5)

𝐿𝑖𝑊ℎ

𝑏𝑒𝑓𝑜𝑟𝑒𝑋

= (𝑆𝑂𝐶

𝑂𝐶𝑉14𝑆

(𝑐ℎ𝑎𝑟𝑔𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒) − 𝑆𝑂𝐶

𝑂𝐶𝑉14𝑆

(𝑈

𝑟𝑎𝑖𝑙

+ 𝐼 ∗ 𝑅0(𝑊ℎ𝑐𝑎𝑝) ) ∗ 𝐿𝑖𝑊ℎ

𝑐𝑎𝑝

(4.4.6)

When function 𝑓(𝑥) = 1 − 𝑥 is used, 𝑊ℎ

𝑏𝑒𝑓𝑜𝑟𝑒𝑋

is calculated as:

𝑊ℎ

𝑏𝑒𝑓𝑜𝑟𝑒𝑋

=

𝐿𝑖𝑊ℎ𝑏𝑒𝑓𝑜𝑟𝑒𝑋

0.75

(4.4.7)

Enough parameters are now known to define how the waveform will look like.

If the interruption discharge is less than 𝑊ℎ

𝑏𝑒𝑓𝑜𝑟𝑒𝑋

, script is calculating the integral of the area in the figure below. The amount of area calculated is depending of a point where the discharge ends between 0-0.5.

This area can then be seen as a percentage of 𝑊ℎ

𝑏𝑒𝑓𝑜𝑟𝑒𝑋

, in that way

knowing how much Li is discharged. From this DOD of both LA and Li

can be calculated including annual cost at each step.

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Figure 4.4.4: Li and LA discharge before x-point. X-axis: Mixed system discharge Wh.

𝐿𝑖𝑊ℎ

𝑑𝑠𝑔𝑏𝑒𝑓𝑜𝑟𝑒𝑋

= ∫ (1 − 𝑥) 𝑑𝑥 ∗ 𝑊ℎ𝑏𝑒𝑓𝑜𝑟𝑒𝑋 ∗ 2

𝑊ℎ𝑑𝑠𝑔 𝑊ℎ𝑏𝑒𝑓𝑜𝑟𝑒𝑋∗0.5

0

(4.4.8)

If the interruption discharge is longer than 𝑊ℎ

𝑏𝑒𝑓𝑜𝑟𝑒𝑋

, this part also needs to be calculated.

Figure 4.4.5: Li discharge after x-point. X-axis: Mixed system discharge Wh.

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31 I choose to calculate this part of Li discharged seeing the blue area as 0- 100% Li discharge after x-point.

𝐿𝑖𝑊ℎ

𝑎𝑓𝑡𝑒𝑟𝑋

= 𝐿𝑖

𝑊ℎ𝑐𝑎𝑝𝑐𝑜𝑟𝑟

− 𝐿𝑖

𝑊ℎ𝑑𝑠𝑔𝑏𝑒𝑓𝑜𝑟𝑒𝑋

(4.4.9)

𝐿𝑖𝑊ℎ

𝑑𝑠𝑔𝑎𝑓𝑡𝑒𝑟𝑋

= ∫ (1 − 𝑥) 𝑑𝑥 ∗ 𝐿𝑖𝑊ℎ

𝑎𝑓𝑡𝑒𝑟𝑋

∗ 8

𝑊ℎ𝑑𝑠𝑔−𝑊ℎ𝑏𝑒𝑓𝑜𝑟𝑒𝑋

𝑊ℎ𝑎𝑓𝑡𝑒𝑟𝑋 ∗0.5+0.5

0.5

(4.4.10)

A resulting DOD of both LA and Li is calculated including with econom- ics as annual cost, cycle cost and return of investment. Data is stored in lists for later plotting.

Script is then increasing Li in size and starts all over again until Li is as large as the user chooses.

One graph is then plotting LiLA (Litihum and LeadAcid) combined an- nual cost including DOD for Li and LA, and another is showing lifetime for Li and LA.

Code is presented in appendix A.

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4.5 Model verification

Model is compared to data for tests in figure 4.3.1 to 4.3.4. Graphs from script are presented in appendix B.

Below is a table presenting data from real tests and model prediction.

Table 4.5.1: Comparing model with real tests. Green = lab test, Blue = model.

Discharge

3000W, 2000Wh

fig. 4.4

44Ah Li 400Ah LA

fig. 4.5

100 Ah Li 400 Ah LA

fig. 4.6

100 Ah Li 200 Ah LA

fig. 4.7

100 Ah Li 100 Ah LA

DOD% Li 25.7, 24.9 24.5, 27 27.7, 31 30.5, 33 DOD% LA 7.47, 7.51 4, 3.5 6.2, 4.9 9.8, 7 Annual cost LiLA 2400, 2401 2260, 2240 1665, 1638 1400, 1338

3000W, 4000Wh -- -- -- --

DOD% Li 37.15, 34.8 36.3, 36 43.7, 45.1 51.2, 55 DOD% LA 16.56, 17 11.4, 12 18.7, 17.5 29.9, 25.5 Annual cost LiLA 4180, 4214 3660, 3668 3220, 3170 3010, 2843

3000W, 8000Wh -- -- -- --

DOD% Li No data 51.4, 49.5 64.3, 64.1 No data DOD% LA No data 28.3, 27 49.6, 49 No data Annual cost LiLA No data 7770, 7833 7330, 7331 No data

Model shows better result than expected under these inputs, with a max-

imum difference in DOD of 4.4%. Conclusion is that the model can suffi-

ciently replicate the results from tests. How well it is performing with

different setups could be evaluated by adding more lab testing.

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4.6 Where and how to implement the model.

• Site with grid + battery.

Input LA installed size at site or required backup time, average load, av- erage interruption time and interruptions/year. From model result, a de- cision can be made whether there are sufficient savings to be made to mo- tivate a Li battery in parallel. One way to decide is to look at how many years it takes to get a return of investment in Li.

𝐿𝑖𝐿𝐴

𝑟𝑜𝑖

=

𝑐𝑜𝑠𝑡𝐿𝑖𝑏𝑎𝑡

𝐿𝐴𝑎𝑙𝑜𝑛𝑒𝑎𝑐−𝐿𝑖𝐿𝐴𝑎𝑐

(4.6.1)

Another could be to calculate the percentage savings.

𝑎𝑐 𝑆𝑎𝑣𝑖𝑛𝑔𝑠 % =𝐿𝐴𝑎𝑙𝑜𝑛𝑒𝑎𝑐𝐿𝐴 −𝐿𝑖𝐿𝐴𝑎𝑐

𝑎𝑙𝑜𝑛𝑒𝑎𝑐

∗ 100

(4.6.2)

A reasonable lifetime of Li and LA must be observed at the chosen capac- ity, otherwise the cost/year calculations will not be true because of limi- tations in calendar life. In some cases with short discharge times and large LA packs, a Li lifetime under 15 years might not be seen.

An example with 30kWh LA and 1h long 5000W interruptions 6 times/day is presented below:

Figure 4.6.1: 1h long 5000W interruptions 6 times/day. In this case, simulation time is extended in order to visualize that a minimum point exists. However this point is at a very oversized Li.

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Figure 4.6.2: A li battery not greater than 10 kWh has to be chosen in this case due to a rising lifetime for LA. There is no point of extending LA lifetime more than its calendar lifetime.

Figure 4.6.3: At a 5000W load Li needs to be rated at 125A discharge current. This is not the case for a single 100Ah battery. Mounting 2pcs 100Ah may be done instead for a total 200A discharge rating.

Choosing a certain Li size, the potential savings can now be presented to

a customer. If choosing a Li battery of 10kWh, eq 4.6.2 will result in an

annual cost saving of 23%.

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• Site with grid + battery + diesel generator.

If there is a site with generator, biggest savings can be made when fuel costs can be eliminated.

For example, if a normal interruption time is 2h, after 1h LA is observed at a voltage potential where generator is started. At this moment genera- tor will run for 1h until the grid is back online.

If assuming that battery is fully charged before a grid loss event and that generator is turned on at a pre-set voltage 𝑉

𝑔𝑒𝑛

. Then following calcula- tions can be made.

𝐼

𝐿𝐴

= 𝑊

𝐿𝑜𝑎𝑑

/ 𝑉

𝑔𝑒𝑛

(4.6.3)

𝑉

𝑔𝑒𝑛

= 𝑂𝐶𝑉 − 𝐼

𝐿𝐴

∗ 𝑅0(𝑊ℎ

𝑐𝑎𝑝

) → 𝑂𝐶𝑉 = 𝑉

𝑔𝑒𝑛

+ 𝐼

𝐿𝐴

∗ 𝑅0(𝑊ℎ

𝑐𝑎𝑝

)

(4.6.4)

𝐿𝑎𝑊ℎ

𝑡𝑜𝑉𝑔𝑒𝑛

= (1 − 𝑆𝑂𝐶

𝐿𝐴

( 𝑉

𝑔𝑒𝑛

+ 𝐼 ∗ 𝑅0(𝑊ℎ

𝑐𝑎𝑝

) )) ∗ 𝐿𝑎𝑊ℎ𝑐𝑎𝑝

(4.6.5)

A simplified calculation could also be made:

𝐿𝑎𝑊ℎ

𝑡𝑜𝑉𝑔𝑒𝑛

= (1 − 𝑆𝑂𝐶

𝐿𝐴

(𝑉

𝑔𝑒𝑛

)) ∗ 𝐿𝑎𝑊ℎ𝑐𝑎𝑝

(4.6.6)

An example with 20kWh LA battery:

𝐿𝑎𝑊ℎ

𝑡𝑜𝑉𝑔𝑒𝑛

= (1 − 0.7 ) ∗ 20000 𝑊ℎ = 6000 𝑊ℎ

(4.6.7)

*assuming a SOC of 0.7 from previous calculations, DOD=1-SOC

If this battery is subjected to a 6000W load under 1h, how much added capacity is needed to run for 2h without generator starting?

𝑛𝑒𝑤𝐿𝐴𝑊ℎ𝑐𝑎𝑝 =

𝑑𝑒𝑖𝑟𝑒𝑑 𝑟𝑢𝑛𝑡𝑖𝑚𝑒 𝑊ℎ𝑡𝑜𝑉𝑔𝑒𝑛

𝐷𝑂𝐷𝑡𝑜𝑉𝑔𝑒𝑛

(4.6.8)

𝑛𝑒𝑤𝐿𝐴𝑊ℎ𝑐𝑎𝑝 =

12000

1−0.7

= 40000 𝑊ℎ

(4.6.9)

Instead adding lithium, how much is approximately needed to be able to

keep LA from reaching a DOD of 0.3? By using same inputs in model,

locate where DOD is 0.3 for LA, and observe Li capacity.

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Figure 4.6.4: Dimensioning a mixed system preventing LA from reaching an estimated 𝑫𝑶𝑫𝒕𝒐𝑽𝒈𝒆𝒏 .

Figure 4.6.5: Observing Li and LA lifetime at 11000Wh Li capacity.

At this point model states that required capacity is 11000 Wh for Li with

a 11 year lifetime if cycled 1000 times/year.

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4 Design / Implementation

37 Comparison data:

𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 𝑖𝑛 𝑓𝑢𝑒𝑙/𝑦𝑒𝑎𝑟 = 1000 𝑐𝑦𝑐𝑙𝑒𝑠/𝑦𝑒𝑎𝑟 ∗ 1ℎ ∗ 5𝑙𝑖𝑡𝑒𝑟/ℎ ∗ 15𝑘𝑟/𝑙𝑖𝑡𝑒𝑟 = 75000 𝑘𝑟.

(4.6.10) LA only old system: 20 kWh.

Lifetime: 1.4 years.

Annual cost: 14300 𝑘𝑟 + (75000 𝑘𝑟 𝑓𝑢𝑒𝑙) = 89300 𝑘𝑟

LA only: 40 kWh.

Lifetime 2.8 years.

Annual cost: 14380 kr.

Mixed system: Li 11kWh, LA 20 kWh.

Lifetime: Li 11 years, LA 3 years.

Annual cost: 10300 kr.

*It is assumed that you will have to change LA 3-4 times before replacing Li in this mixed system, this does not affect cost/year calculation.

*An oversizing of Li should be considered to be confident that desired interruption time is cleared.

*Mixed system model has not been verified at these inputs.

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5 Results

38

5 Results

The goal was to evaluate if there is a technical and economical possibility to use Li as a performance-enhancer in a LA system. Testing has shown that with the right combination of load, charger and fraction between Li and LA there are cost savings to be made.

A conclusion was made that selling new combined systems is a possibil- ity. However the cost savings is not huge compared to LA only, and there- fore, main objective if possible would be to motivate the consumer to go full Li directly.

If a customer wants LA, it is still possible to sell a fraction Li in parallel to prolong LA lifetime and lower annual cost. In this way the customer will be introduced and familiar to Incell products, which could result in a switch to Li the next time LA needs replacement.

Adding Li in systems with LA + grid + generator, big savings can be done by adding Li in parallel by prolonging interruption time. Adding Li in- stead of LA is more favorable because of the higher potential and extra capacity for Li when charged at float voltage.

Some basic thumb roles were for dimensioning a mixed system was pre- sented under conclusions in part 7.

A python script was made where a user can input known parameters for a telecom site. The script will then help user to find the most optimum size of Li in a mixed system, by iterating size of Li and finding a point of least annual cost.

Below is the user input screen presented:

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5 Results

39

Figure 5.1: User input screen. Below additional 2 graphs are plotted.

Figure 5.2: 20min long 4000W interruptions 8 times/day. At short discharges with a large LA battery, cost savings are small and care should be taken not to oversize Li.

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5 Results

40

Figure 5.3: Plotted lifetime results from user inputs. LA calendar lifetime limits Li size to 5 kWh.

If choosing a Li battery of 5kWh, eq 4.6.2 will result in an annual cost saving of 5.5%. Same parameters simulated but with 1h interruption time instead, resulted in following table presenting cost percentage savings.

Table 5.1: Annual cost percentage savings at 1h interruption time.

5kWh Li 10kWh Li 15kWh Li

1h interruption 17% 24.3% 25%

Annual savings up to 25% for a mixed system can be seen as a general estimation.

Script has been added in Appendix A.

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6 Discussion

41

6 Discussion

The aim was to be able to find a point where a mixed system works best and achieves the lowest annual cost. Finding a thumb role where to find this point turned out to be complicated with a lot of factors playing a part.

Therefore it felt needed to make a script that would find this point.

Interruption times and fraction between Li and LA makes a big difference in outcome, so a script that could process those factors and some others felt like it had to be made to be able to represent some usable result.

I think this was a fun challenge and the model was producing an almost accurate result. However it may not come as an surprise modelling some- thing that is based on tests, turns out to replicate these same tests.

An interesting thing would be to first improve the model with some things there was not time for. And then compare it with some new tests, or if there could be found data from larger mixed systems from real sites and compare it with those.

Overall, I think there is a market for mixed systems. For new installations, a better option is to choose full Li.

6.1 Social aspects

This work could push the switch towards lithium and replacing lead acid.

It could also motivate to prolong lifetime of existing lead acid batteries and in that way save resources.

Lead Acid batteries contain a heavily amount of toxic materials. There are well evolved procedures of how to recycle these batteries. However there is also an amount of LA batteries being shipped to third world countries where these procedures are non-existent.

Li is not recycled to the extent that LA is. However there are ongoing re-

search of how to make this process more profitable and less energy con-

suming.

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6 Discussion

42 Li is not as toxic as LA, and can actually be placed as landfill. However it is preferable to use Li as long as possible, finding new applications where used batteries can be applicable. There is large amount of effort in creat- ing Li batteries, all the way from mining to manufacturing the cells. Min- ing of Li and other rare earth metals is often located in developing coun- tries, where either working conditions or environmental consideration is less taken.

Li is either mined in open quarry’s or over large areas evaporating brines, demanding a huge amount of fresh water.

6.2 Ethical aspect

Even though no battery could be called environmentally friendly. The positive effects that battery solutions provide do make a great difference.

Battery backup can provide less fuel cost, reducing emission. Good backup-systems for telecom-sites are also from a human perspective very important. Especially since society is being more and more dependent on mobile communications.

This has been even more clear during this period of time when the corona pandemic is forcing people to use more and more mobile services.

So even if there can be found negative aspects regarding environmental

and sometimes working aspects in the process of manufacturing battery

cells, the benefit that these types of systems bring to society is paramount.

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7 Conclusions

43 P

7 Conclusions

When trying to find thumb roles when dimensioning a mixed system, without using a model, some conclusions can be made.

• Li is rated to handle the full load by itself without tripping its in- ternal safety systems.

• A small fraction Li less than 0.15, the desired function of Li taking the first discharge is no more substantial.

• For systems experiencing small interruptions where a large LA battery is installed, lifetime will not be drastically reduced, and therefore cost savings are limited, unless there may be over 15 in- terruptions/day.

• As the fraction of Li is larger than 0.6, it should be considered go- ing full Li instead.

• Annual savings up to 25% for a mixed system can be seen as a gen- eral estimation.

In order to predict the estimated behaviour of a mixed system, it is ad- visable to run the model with parameters from the actual site.

7.1 Future work

Make some minor improvements of model and verify it against some more data would be the closest in time.

These minor improvements may include:

• A more accurate SOC(OCV) function.

• A more accurate 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑎𝑡 𝑥

𝑝𝑜𝑖𝑛𝑡

(𝑟𝑎𝑡𝑖𝑜 𝐿𝑖/𝐿𝐴) function.

• Changes due to user requests. For example: average cycles/day instead of cycles/year, added graphs, percentage savings, calculations etc.

• Figure out how to run the script in a windows environment without a Python IDE (Integrated Development Environment) editor.

More functions that could be added is:

• Temperature dependence

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7 Conclusions

44 P

• More trustable cycles(DOD) input data for both Li and LA.

• Improved and selectable SOC(OCV) function, ICR, INR etc.

• Better interface, clearer explanations and options.

• Implement the option to choose 2 or more different interruption times including their frequency. This could be done taking the inverse of the obtained number of cycles (aging rate), adding these aging rates, and then obtaining a new lifetime. As described in referenced article [6].

• Improved current waveform functions.

• Develop a better and faster way to verify model against real data.

Calculations made in part 4.6 for a hybrid site with grid + generator + battery. These could be implemented in script or a complementing excel sheet could be made.

More test could be added, complementing ratio tests with a fixed 400Ah LA bat. There could also be more tests with different loads.

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References

45 P

References

References

[1] (). HOMER - Hybrid Renewable and Distributed Generation System De- sign Software. Available: www.homerenergy.com.

[2] L. Plett Gregory, Battery Management Systems Volume 1 - Battery Mod- eling. 2015.

[3] FIAMM Energy Technology S.p.A, Engineering Manual AGM Rev. 7.

2018.

[4] (). SPECIFICATION OF PRODUCT ICR8650-22F. Available:

http://gamma.spb.ru/media/pdf/liion-lipolymer-lifepo4-akkumulya- tory/ICR18650-22F.pdf.

[5] (). Introduction of ICR18650-22F. Available:

https://datasheetspdf.com/pdf-file/792431/Samsung/ICR18650-22F/1.

[6] T. M. Layadi et al, "Lifetime estimation tool of lead–acid batteries for hybrid power sources design," Simulation Modelling Practice and Theory, vol. 54, pp. 36-48, 2015. Available: http://dx.doi.org/10.1016/j.sim- pat.2015.03.001. DOI: 10.1016/j.simpat.2015.03.001.

[7] (). Email from Homer Energy:

”Dear Mikael,

HOMER can only use one type of chemistry per system. So if you add two types of batteries it will choose either/or, but not both together in the same battery bank.

Kind regards, Aleph Baumbach

Head of Professional Services, Lead Trainer, & Senior Energy Engineer www.homerenergy.com

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Appendix A:

46 P

Appendix A:

Below is the attached Python code. Note that code may look a bit strange here due to line breaks.

# -*- coding: utf-8 -*-

import matplotlib.pyplot as plt from math import e

from sympy import Symbol, Integral

#---FUNCTIONS---#

def cyclesDOD_VRLAB1(dod): #cycles(DOD)

cycles=12850*e**(-9.738*dod)+3210*e**(-1.4299*dod) return cycles #

def cyclesDOD_IncellNMC(DOD): #cycles(DOD)

cycles=151438 - 1.47529*10**6 * DOD + 7.41678*10**6 * DOD**2 -

2.14086*10**7 * DOD**3 + 3.68167*10**7 * DOD**4 - 3.7225*10**7 * DOD**5 + 2.04022*10**7 * DOD**6 - 4.67221*10**6 * DOD**7

return cycles

def SOCocv_14S_NMC(ocv): #OCV 40-60V (data from INR battery, tried making a function of ICR, but it was a tricky one) (INR better than a bad ICR- function) no time to fix

SOC=-161681+16372.9*ocv-659.641*ocv**2+13.2154*ocv**3-0.131669*ocv**4 + 0.000522175*ocv**5

return SOC

def xpoint_V(liWhcap, laWhcap): #returns a Voltage point where LA and Li cur- rents meet, based on tests at ratio .25 .5 1 at 3000W dsg

ratio = liWhcap/laWhcap

xpoint_V = -3.2323*ratio+51.632 # return xpoint_V

def c_rateLA(avg_loadW, laWhcap): #returns a cap_factor, scaling LA capacity as a function of C-rate.

c=avg_loadW/laWhcap

cap_factor=-0.4953*c**4 + 0.5458*c**3 - 0.3016*c**2 - 0.2179*c + 1.0233 return cap_factor

def R0_Wh(liWhcap): #based on 14S R0(Wh) r0_Wh = 86.688/liWhcap

return r0_Wh

#---Data arrays for plotting---#

arr_liWhcap = []

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Appendix A:

47 P

arr_lila_ac = [] #lithium+lead annual cost arr_lila_cc = [] #lithium+lead cycle cost arr_costLi_bat = []

arr_xp = []

arr_dodLi = []

arr_dodLA = []

arr_li_ac = [] #lithium annual cost arr_la_ac = [] #lead annual cost arr_li_lifetime = []

arr_la_lifetime = []

arr_lila_roi = [] #lithium+lead return of investment (lithium)

#---USER INPUTS---#

print("\nMixed system DOD simulator")

priceLi=3 #kr/Wh #lithium 3x dyrare enligt Jesper B priceLA=1 #kr/Wh

#BatteryType = "NMC 14S"

nom_voltage = 50.4

avg_loadW =float(input("Input average Load W: ")) #load for calculations max_load_W = avg_loadW # 1000 #check so that Li can handle max current req_break_h = float(input("Input required interruption time h: ")) #re-

quired break,interuption time h, dimensioning factor for LA

avg_break_h = float(input("Input average interruption time h: ")) #avg break,interuption time h, grid loss time

avg_cycles_year = int(input("Input average cycles/year at avg load and avg int.time: ")) #avg cycles/year @ avg load and avg int. time

max_load_W = avg_loadW #check so that Li can handle max current

sim_time=int(input("Input desired simulation time, increase LiWhcap until x*LAWhcap: ")) #(sim_time*laWhcap) #limits simulation time if liWhcap >=

sim_time*laWhcap: break

#---Process data from USER INPUTS---#

print("\n--- ---")

Li_A_dsgmax = max_load_W/40 #40V minimum voltage print("\nLi_A_dsgmax : " + str(Li_A_dsgmax))

req_Wh = avg_loadW*req_break_h #decides size of LA bat avg_Whdsg = avg_loadW*avg_break_h #avg Whdsg

liWhcap = nom_voltage*40 #starts low 50Ah rating and iterates

liWhcap_corr = (SOCocv_14S_NMC(54.5)/100)*liWhcap #starts low 44Ah rating and iterates

laWhcap=req_Wh*1.5 # normal overdim. *1.5 enligt Jesper B

#LAAhcap=laWhcap/48 #LA nom voltage = 48V

cap_factor=c_rateLA(avg_loadW, laWhcap) #see function description

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