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### Battery Parameters

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So I will start now with a very important chapter called Storage for Electrical Vehicles. Now while I do that, I want to straight away attempt to answer a question that was post to me at the end of the last lecture by a student. The question was, we had talked about efficiency for motors and controllers thus battery also have efficiency. What does it mean? First thing is when I charge battery do I lose energy? Yes, we will lose energy that will come as a charger (efficiency) inefficiency, not the battery, charger inefficiency. Where we discuss charger we will talk about the inefficiencies of that. But battery will have us after so we will have to always put in more energy then what goes into the battery.
The charge inefficiency could be 5 percent, 10 percent that much energy will be lost. In the charger finally some amount of energy that we will enter the battery. Battery inefficiency will be whether whatever is put in can I take out all of it? Well, yes or no? Remember battery also gets heated up I mentioned that. There is a internal resistance associated with the battery. So to that extent energy that has gone in part of the energy will be lost. Except the lost is very small, typically 1 percent and therefore from efficiency point of view you do not worry about it, from the heating point of view you worry about it. So that is the answer, we will get into more detail because that is discussed in detail when we do storage for electric vehicles.
I will now start talking about battery parameters. And as it was pointed out battery consists of cells. It is a cells which are put together to make a battery. Now battery pack is much more than a cell not simply assembling of cells. But yet the characteristics of cells are going to become also characteristics of battery to a large extent. So when I talk about battery parameters it may also a cell parameter. Cell parameter which gets carried into battery and there will be additional parameters for battery.
So as I pointed out what is electric vehicle? First of all is the rechargeable electric batteries. The electric batteries that we use for example in many devices I have a car key which uses a small battery. It is not a rechargeable, so I use it after it is used I throw it away, it is a onetime chargeable. Whatever it, is not even onetime charge I do not charge it, it is factory charged, it comes as a built-in charge. There can be other batteries which are you bring it without buy it without charge and you can do onetime charge and then discharge it. It is like one cycle.
Now those batteries are of very little use for electric vehicles or for a mobile phone for example or for a laptop, you want to keep on charging and discharging, charging and discharging, so they are rechargeable battery. So that is the first important thing, there are batteries which are not reachable or one time chargeable we will discard, will not talk about it in this course. After that what is the battery? Battery is basically I have been telling you it is a storage of electrical energy for the in this case for electric vehicles. So in that sense battery is like a petrol tank, petrol tank is a storage of petrol or which is energy for ICE vehicle.
Battery is a storage of electricity which is used to drive a electric vehicles. So battery is like a storage tank. A storage tank is made, petrol tank is made from aluminium and made fairly large does not cost very much, you have to ensure that there is no leakage of course but does not cost that much. Not so with the battery, battery is a complex unit, it is a storage of electricity, costs a lot, has a certain life, you will say even the petrol tank has a certain life, well its life is pretty much a life of car vehicle. Battery tank does not of, you rarely hear of a battery tank something going wrong with the battery not battery tank with petrol tank.
Now if there is accident it may crack or something but normally nothing happens. In fact, tank is design to withstand lot of pressure because you do not want petrol leaking, petrol is dangerous. Electric battery on the other hand storage of electricity is very different, its costs a lot, it is the tank is useable only for certain number of cycles, certain number amount of time, after that it is to be thrown out, replaced. So in many ways it does the same function but very different.
This was introduced in chapter 1 but I want to point out that again that electric vehicle by its very nature is 4 times more energy efficient than a petrol vehicle. And even then when I compare a petrol tank, a filled petrol tank and a filled battery, battery fully charged, electricity fully charged. Weight of a battery is 10 to 12 times higher than petrol tank and its volume is 5 to 6 times higher than petrol tank. So in fact this curve thus shows very nicely if you look at energy density kilowatt hour per liter that is in volume terms. You see the diesel and petrol are closed to 9, 9.5 kilowatt per liter. What about for lithium ion batteries? It is about 1.5 so 6 times remember, I talk to you about it and if I want to look at specific energy kilowatt hour per kg you see diesel and petrol comes to around 10-11 kilowatt hour per kg and here 0.2 probably 0.1 or 0.2 kilowatt hour per, well may be little more than that. May be a 1, something like 1 kilowatt hour per kg, no-no it is not 1, it is what 250 watt hour per kg but because of the 4 times energy efficiency it effectively becomes 1, so it is 10 to 12 times with equivalent energy. So you have to worry about this, this is a key concern difference between a petrol tank and a battery. We have discussed this in detail on what can actually happen, we will look at it. But another important aspect, while the tank is low cost petrol is expensive per kilometer. Battery is expensive electricity is inexpensive.
So you have a very big dilemma. Battery, petrol tank therefore very little capital expenditure, comes with the car you have it or not have it, it would not make much a difference to the car cost. Battery is a high capital expenditure. Electric vehicle once you have bought the battery is only electricity costs, operation expenditure OPEX is small, OPEX for petrol vehicle is high because petrol costs are high. But this is ofcourse in India petrol cost may be low in other states where things may be different. So why is the battery costs so high? Let us understand battery.
To understand let us start looking in detail of the battery. Consider a battery 48 volt battery, you can, could have chosen another number, and let us assume a capacity of 15 kilowatt hour. This is the example one could have taken any number but just to show. Battery capacity is defined in terms of ampere hour, so you take the capacity which is 15 in this case divide it by the voltage it gives you battery ampere hour. So 15000 watt hour, 15 kilowatt hour divided by 48 it gives you approximately 300 ampere hour. So the battery is a 300 ampere hour. Remember when you buy even a pencil cell it gives you Ah or milli-ampere hour, so this is same ampere hour is the current, the voltage also has to be multiplied to get the capacity. A battery capacity is battery voltage multiplied by battery ampere hour.
So define, you must remember that battery ampere hour is not the capacity, very often you ask for a capacity and people talk about battery ampere hour but it assumes that there is a certain voltage, you have to know the voltage to really understand the capacity. There is a very important parameter and I have defined that in the past I will redefine it, state of charge tells you how much is the battery charged. What is the percentage of battery that is charged? A zero percent basically means it is totally discharged. A 100 percent means it is fully charged. So 100 percent battery or 15 kilowatt hour basically means it is a 15 kilowatt hour energy is there. And zero percent basically means a zero energy is there.
So this SoC is very important parameter we will come to that again and again. How could voltage of a battery varies with SoC? Though we have said voltage is 48 volt, it is not 48 volt. For example, when SoC is 0 the battery voltage may go down to 43 volt. When SoC is closed to 100 battery voltage may go to 56 volt. As the battery is charged its voltage keeps on going up when is discharged voltage keeps on coming down. 43 is SoC of 0, 56 is near 100 percent this you must remember and we will come to that later on. Which basically means that motor people will say I want so much voltage, well voltage will vary, it is not going to be a constant voltage, motor has to worry about these things when it designs, motor controller has to worry about it.
So for a, there is a parameter that I have been talking about, charging and discharging rates or charging and discharging at what is called C rate of a battery, C rate is somewhat called charging rate but it is also used for discharging rate, C rate of a battery. A 15 kilowatt hour battery you often talk about 1 C charge or 1 C discharge it is a 15 kilowatt hour, what does it mean? It can actually have 15 kilowatt for 1 hour, it can charge within 1 hour 15 kilowatt hour kilowatt or it can (charge) discharge for 1 hour 15 kilowatts. So 1 C charge rate, a discharge rate for 15 kilowatt hour battery is 15 kilowatt. 1 C basically means in 1 hour you can charge or discharge battery that is called 1 C. One the C rate is in some sense hours. 1C basically means 1 hour. Can discharge or charge battery from 0 percent to 100 percent in 1 hour.
Now you may not use it from 0 percent to 100 percent so to that extent it will take less time that is a different matter. But if you did go to 0 percent you can go there, there is nothing prevents you, you can go to 100 percent and if you do it at 15 kilowatt it will take 1 hour and that is the reason it is called 15 kilowatt hour battery or 1 C charge and discharge is 15 kilowatt. What about 2C rate? 2C rate means rate of charging and discharging double of 1C. 2C does not mean 2 hours, 2 C basically means half hour this is a very important, it is the double rate, it is the rate, C rate is the rate of charging and discharging, 2C means 1C is 1 hour, 2C is, 2C means it charging at half hour, it is double the rate. 2C basically means it will charge and discharge at 30 kilowatt. So therefore it will take only 30 minutes half an hour. Do not make a mistake that 2C basically means 2 hours, it is 1 by C hours, 1 by C rate hours to C rate. Similarly, 4C will means you will charge discharge in 15 minutes, it means 60 kilowatt charge and discharging. On the other hand, if you make it not 1C but 0.1 C, 0.1 C means it will take 10 hours, 0.1 C is 1.5 kilowatt charging and discharging. 0.2 C will mean 3 kilowatt charging and discharging and it will take 5 hours, so is that understood? And so for a 15 kilowatt hour battery for vehicle requires a power of 30 kilowatt you have to discharge at 2C. It is a vehicle which decides how much power is to be done, it is not the battery. Whenever battery requires 30 kilowatt you are discharging at 2C. If vehicles requires only 5 kilowatt you are discharging at one third C, C by 3.
So the vehicle or the motor requirement will (()) (17:53) at what rate you will discharge a battery. Now generally I want to point out that there is something called slow and fast charge, this is the term that is used for charging. If it is much less than a C it is slow, 0.2 C, 0.3 C even 0.5 C you can just say, it is slow. And fast is greater or equal to 1C. So a fast charger basically can be 1C that means in 1 hour you can charge from 0 to 100 percent or it can be 2 C which means half an hour you can charge or can be 4C you can charge in 15 minutes. So I have done the definitions so far depth of this charge, state of charge, so I have not done depth of discharge, state of charge of the battery, battery capacity, state of charge and then C rate of a battery, so far that is what I have done.
So I have given assignment just so that you can get familiar, a 34 kilowatt hour battery is charged at state of charge of 64 percent what is a, is at a SoC of 64 percent what is energy it contains? Or a 34 kilowatt hour battery is at 350 volt what is the capacity in Ah? A 3.5 volt battery is at 2.7 volt at a SoC of 0 percent and 4.3 where volt at SoC of 100 percent, so which is a 3.5 volt battery or a cell. It varies from 0 to 100 percent. This implies the voltage of battery lies between 3.5 plus minus delta volt, 3.5 is a nominal voltage, is a plus minus delta, what is a delta? Assuming SoC is a linear function of the voltage that is assumption, in reality that is not true. What is a SoC at 4 volt and what is a SoC when it is 64 percent? When SoC of 64 percent what is the voltage? Then I have also given you compare petrol volumetric energy density in kilowatt hour per liter and gravitational kilowatt hour per kg. Well I have given you in the diagram but take it out, coal volumetric energy density is kilowatt hour per liter and gravitational in kilowatt hour per kg. I do not the coal is there or not there I think I had given you an assignment earlier. Coal is there, so this picture gives you a very good idea.
The next important parameter I want to define for the electric vehicle is, if a battery start with a capacity C, it is a new battery, it has a capacity C. Over the time the capacity decreases, I have pointed this out several time, it decreases due to two reasons one is aging or time you leave it in the shelf it get to deteriorate, it is a slow deterioration could be 1 percent a year, could be 1.5 percent year but slowly it will deteriorate.
So, you cannot say that you will come back 7 years down the line is you will have the same capacity, no, there is a it is called aging or also called calendar life of the battery, calendar life of the battery, so you have to worry about that. Of course, however it is small so and calendar life is large so you do not have to, impact is small, so you do not have to worry as much, but you have to take that into account finally.
The second capacity decreases due to charging and discharging, every time you charge and discharge you lost a, some capacity, charge and discharge you lost a capacity that is called charge discharge cycles, number of charge discharge cycles it supports that battery will go from 100 percent capacity to 80 percent capacity, if I define 80 percent capacity is end of life, that is the effective charge discharge cycles that I can use. So, charge discharge cycles defined between 100 percent and a certain end of life, now you have to define what the end of life is, that is the number of charge discharge cycles, you can do so many charge discharge cycles is a rechargeable battery after that it is not useful and every time you are charging discharging your capacity is going down. Is that clear?
So, this becomes an important parameter. So, battery life is 80 percent or 70 percent of C it may be termed end of life, I had defined that, implying that battery will no longer be useful for EV, it does not mean the battery has gone it has still 70 percent capacity or 85 80 percent capacity you can still use it for something else. For a 15 kilowatt hour end of life if it is 80 percent that means a 12 kilowatt hour is end of life, if it is a 70 percent end of life it is a 10.5 kilowatt hour end of life, I am again pointing out these batteries can no longer be used for EV’s as the range decreases to 80 percent or 70 percent. But it can be considered for what is called for other applications often called second life of the battery, for example, I do not have a weight or volume constraint and I do not have a range issue if I use it as a power back up in my office, so I can always take that battery out and use it for power backup. Typically, from 80 percent to around 50 percent you can have a second life.
But remember the battery does not behave as well in the second life as in the first life. First life 100 percent to 80 percent pays very well after that it pays all right from 80 percent to 50 percent, but that can be the second life, beyond 50 percent battery behaviour become erratic, not that it cannot be used, could I not use a storage up till it goes to 30 percent? Yes, but you never know at it may certainly fail at 40 percent. So, generally it does not work as a good battery, reliability itself goes down beyond 50 percent.
So, battery design for certain capacity as I told you voltage into ampere-hour this is something that I had already done capacity is a product of voltage and ampere hour, depth of discharge I had talked about, for long life the batteries never fully emptied, you leave certain energy, this is something that I had done in the previous chapter, usable energy is X percent or 85 percent of the total capacity and that comes from depth of discharge. Also battery reduces with each charge discharge cycle, when battery reaches certain end of life, let us say y percent of initial capacity, range gets proportionately reduced, so battery life of for EV is over and it needs placement and therefore if it is 80 percent end of life and 85 0.85 85 percent depth of discharge the battery at end of life usable batteries as low as 0.68 C. Keep this in mind this is a slide that I had borrowed from previous chapter and brought it here to just define it again.
Second life for the battery, once the battery reaches 70 to 80 percent of the initial capacity it can be used for fixed storage, weight is not a constraint, volume is not a constraint, like UPS or inverter or grid storage. Electric vehicle is always constrained in terms of size and weight and whereas fixed storage is not. So, you will not like using electric vehicles because it has a limited size and weight possible and it is giving you a low range, as I told you battery can be used to up to 50 percent capacity, number of cycles from 80 percent to 50 percent, well it will depend on the cells used, but roughly could be similar to a 100 percent to 80 percent, maybe less. What do you do after its second life? When you as a pointed as you can continue to use it, instead of 50 percent can use it 40 percent or 30 percent, but if it becomes unreliable you do not want to use it, because when you need it power it will not give you power, so then a very important task that you can actually do is what is called recycling, particularly well for all batteries but for lithium ion particular, you can recycle the battery. What do you mean? You take the battery and extract the raw materials.
Now, when you extract the raw material it is a dirty job. So, is it going to give you harmful gases? Will it give you liquid which is will not know where to dispose? Will it give you solid which will be a problematic in disposal? These are called effluents, whenever you recycle you recover the material and then there is effluent, the whole idea is in today’s world we will have to do the recycling process with what is called zero effluent, no solid, no liquid, no gaseous effluent. You actually convert it back into usable material, that is a ideal recycling and fortunately there are people who are shown that this can be done for lithium ion batteries.
A lithium ion batteries are not there just for electric vehicles, it is the same batteries which is there in every cell phone, it is there in laptops and today you can start recycling. And the batteries in cell phone and laptops are too small you cannot even use it for fixed storage, for office and things like that. For electric vehicles a large, if it is a 15 kilowatt hour battery you can use it, the batteries in cell phones and laptops are much smaller, so it generally goes straight for recycling, so recycling industry will start first with laptop and cell phone batteries, over time electric vehicle batteries. This is something that I wanted to get your picture.
We will get to the next important thing how do you make a battery pack, battery pack is used is made using battery cells, these are lithium ion cells and life of a battery pack is very much related to life of a cells like of those cells, what will later on show you if one cell fails battery may become unusable, it depends on how the battery is designed or its capacity can considerably come down, we will later on talk about what is called serial and parallel.
So, depending on what cell is failure you may either completely battery becomes useless or its capacity can considerably come down, we will discuss this later on, its voltage can come down which may make it unusable. So, we have to understand the life of a cell to understand the life of a battery and therefore let me start with the life of cell. Cycle life of battery is a fundamental parameter, it comes from its chemistry and it comes from the cell manufacturer you cannot improve that, if cell has a certain life you can only do worse than that, at best you can reach the battery pack will have the same life as the cell life. It depends on battery chemistry and exactly the process used by the manufacturer and it actually depends on a number of factors, such as charge rated, C rate, all battery cells depending on the charge rate and discharge rate the C rate that use it impacts the life of the battery. Most cells are such that if use higher C rate for charging or discharging the battery life will be significantly deteriorated, if you use lower C rate the battery life will not be impacted much.
So, therefore in general you will say slow charging is good, any fast charging is bad, but now there will be different cells which will be able to withstand fast charging up to a certain extent, that we will get into that. Invariably all cells, the temperature for charging and discharging matters, as well as storage temperature. But storage temperature you can more control, charging and discharging temperature you may not be able to control, you are going driving in India temperature goes to 48 degrees centigrade, What happens to cell temperature? Well, you can cool the battery, but if you cool the battery the energy part of the energy of this battery itself will be used to cool, so and it is costly. If you do not, whatever the ambient temperature is directly going to impact you, so temperature ideal temperature is 25 degrees centigrade as we will look at later on, higher temperature is bad for the battery and cells, lower temperature is bad for the battery and cells. We will look into that details.
Depth of discharge, remember that I have been talking about I will not like to use the battery beyond a certain depth of discharge, if I try to charge it full or if I try to discharge it full it impacts a life of the battery, if you leave something on the top, leave something on the bottom, batteries likes it. So, as I pointed out about 85 percent is generally used sometime 90 percent depends again on the battery chemistry and what the manufacturer gives you. To that extend capacity goes for a toss but life goes up. So, as I pointed out most lithium-ion battery functions best when its temperature is 25 degree centigrade, at 30 it behaves slightly poorer, 35 poorer, above 35 starts deteriorating rapidly. At 20 behaves alright slightly poorer, 15 slightly poorer, 10 you have to start worrying deteriorating fast, in fact if you make it much lower temperature battery stops working. Ideal charge rate discharge rate is 0.1 C, 10 hours for charging, 10 hours for discharging, well 5 hours also is okay.
Any attempt to charge or discharge a battery faster than that impacts battery life. How much it impacts? Depends on the kind of cells. Ideal depth of discharged is about 70 percent, you leave 10 percent with the bottom and do not go above 80 percent, but that will mean 30 percent capacity loss, so you do not use it and you find depends again on cell maybe 5 percentage enough in the bottom, maybe 10 percentage is enough on the top.
Factors affecting battery cell life, a lithium-ion battery manufacturer may tell you that I am giving you a battery cell which lasts for 1000 cycles, but they will always define, that the 1000 cycles is charging at C by 2 rate, discharged at maximum 1 C rate and always at 25 degree centigrade with 85 percent depth of discharge. These numbers will vary, but life cycles by a manufacturer is defined like this, as you deviate from that there 1000 cycles will start reducing.
For example, if you take 1000 cycle charged at C by 2 rate, what happens if you charge at 2 C rate? We will be surprised, sometimes it will not give you more than 250 cycles. If you do not get a full details, very often you have to conduct measurement to figure out all this, in our lab you do detailed characterization. So, rate of charging discharging higher C rate always decreases, so this is a very rough curve, so if you see it has a decent number of cycles at low C rate, as it goes up either charging or discharging the number of cycles goes down like anything.
Now, exactly to the curve we will depend on the battery chemistry, as I pointed out when specified at C by 2 rate for charging you do 3 say battery life may be down by a factor of 5 or even more, that is the point that I want to make. So, very often people say why cannot I fast charge, well I why cannot I get a charger which can fast charge, is not a matter of charge, battery cells itself, battery pack itself, battery pack was may not be designed to take fast charging.
This is another curve which shows the same, look at this, relative capacity and as the number of cycles increases if you see if you charge or discharge, this is a cycle life for discharge rate this is discharge rate, if you discharge it a 2 amperes 2 amperes the in 500 cycle you are still left with about 95 percent of the battery, so probably it will last to 2000 cycles, before it comes to 80 percent. But, let us say that suppose you instead of 2 amperes if you do at 10 amperes, well battery life has gone to 90 percent in has gone down by 10 percent in 5 minute cycles is okay, if you do 15 ampere, then battery life is infinite cycles of battery life is over 80 percent is reached and if you do 20 amperes it is it takes only 300 cycles for battery life to become 80 percent, this is for a typical cell.
So, your life will significantly deteriorate actual value you can ask the manufacturer they will give you, they will give you something, not necessarily fully but some idea. This is a something that you must remember rate of charging and discharging, ideally do it law small, of course if you want faster rate charging-discharging you try to purchase cells which are able you to do that.
Higher temperature or lower temperature as I said effects the battery life, battery life is ideally between 20 and I will say 15 and 35, 15 and 35 it is okay, it deteriorates not as bad, but if you see even the deterioration is more at 3 C rather than 2 C and 1 C, 1 C it may handle larger temperature range and 2 C does not handle as much, 3 C it handles much less number of life cycles can go down like anything. Below 15 degree centigrade you start seeing very rapid decline and you will see that most batteries below 0 degree centigrade will not even work, at higher temperature it drops down even worse, from 35 you go to 40 45 it gets much worse. It depends again on the characteristics depend on the cell, this is for a cell which can handle 40 degree centigrade reasonably well, the cells which will not handle even 40 degrees centigrade.
This is a depth of discharge, another number of cycles if you have 80 percent very good, as you increase as you start going to 100 percent number of cycles goes down like anything, these three things you must remember is always there so you can say, what is the window in which we will operate? Will it be top SOC window with 0 percent to 85 percent? Bottom SOC window 15 percent two 100 percent? Or middle 5 percent to 90 percent? Normally this middle window is always better. Again depends on the battery chemistry, the manufacturer you can ask them, but this is what happens, extend of dependency on various parameter depends upon battery chemistry that way it is manufactured.
To sum up, what have we done so far, we have defined battery capacity, we have always said battery costs are very important we will look into it that more detail, battery life dependence on rate of charging discharging, temperature and depth of discharge, look at this, this is 1 C charge 1 C discharge and you see discharge capacity 1 C charge discharge, in 500 cycles the battery life goes down, but it looks like the battery will last for at least another 5 minutes cycles 1000 cycles. You see 2 C charge discharge, it has gone down to 300 and 3 C charge discharge do not even ask, it is going down, your battery is over, so it started with 650 cycles it going down to 100 cycles well with number of cycles sorry, the capacity went down by from 600 to almost 100. So, the if you look at 80 percent it would reach very, very rapidly.
This is important to understand with battery life. The other key parameter state of charge is always important, how much it is discharged, depth of discharge, which is same as well I have mentioned that. End of life, what is the end of life, is important, C rate we have define which is again rate of charging discharging, cycle life, what is the total cycle life? We have talked about aging, calendar life, so calendar life plus charge discharge cycle. This is what we have done so far about the first part of looking at battery. (Refer Slide Time: 24:18) And we will there is an assignment problem, it is a fairly standard problem, but it is a interesting problem in the sense that we sort of say that yes it is supposed to do at 25 degree centigrade, but what if it is operated at 30 degree centigrade? What if it is done at 35 degree centigrade? Yes, it is supposed to be charged at 0.5 C, but what happens if it is charged at somet