Impact of battery characteristics on off grid system cost

Overview
Research pertaining to Battery development and costs.

Research
It has become apparent that battery characteristics can substantially impact total system cost in an off grid power supply system. This should be quantified so we know ahead of time what the different characteristics will give. I will focus on solar only for now.

These include:

This is effected by the useable capacity of a battery. lead acid batteries can't be discharged below a certain fraction of their "rated" capacity, well they can but will be seriously damaged. So assume they can't and derate their capacity accordingly,(to 80% of rated capacity is about right). Nife and Zn-Br are fine with deepest discharge.
 * Capital cost/kWh

=Round trip charge/discharge energy efficiency= To keep this relatively easy to manage let's assume a fixed round trip efficiency of: 65% for nife (the increase over time in the efficiency has not been verified yet) 75% to 80% (reported actual test values) for zinc bromine (theoretical max is 82%) let's say 79% 70% for lead acid (92% at lower charge levels, but in the high charge regimes where solar off grid systems spend a lot of their time it is very low, only in the 50% range. References indicate real world efficiency in off grid solar use comes to about 70%)

=Self discharge rate= Let's assume this is an exponential decay, with the loss rate proportional with the current amount of energy the battery is effectively storing (the amount we can extract from it).

Nife: 35% per month (real world figures for commercial batts from nickel-iron-battery.com are 30 to 40% probably temperature and contaminants the main deciding factor, need to check the changhong batts probably says in the brochure)

Zinc bromine: need to check, significant depends on the separator a lot. From the sandia development doc it looks quite high. About 1% per hour or so, improved to 0.5% with better separators. It is a result of the bromine diffusing across the separator mostly, with a bit due to shunt currents. As long as the battery is being charged or discharged, this would occur with microporous separators. If it is not being used the bromine catholyte tank of a flow battery can be disconnected, and the bromine present in the flow module will still diffuse across over time, but that is a pretty small amount (less than 50 ml of catholyte very roughly for a 200 watt module just to give an idea, and you get around 2.25 mol of Br2)

LA: need to check, pretty low but significant

=Failure modes and timing thereof=

this includes "lifetime" but it is clear that the exact details of the failure mode has a large impact so this is a large category that includes other failure modes that may not be the same as total battery failure right at the end of the 10 year life or whatever. It also matters which mode is the limiting factor, of course.

Since the useage patterns are probably about the same it is most convenient and accurate to talk about the chronological time here rather than charge/discharge cycles.

Nife: More information needed to know exactly but probably it is nosedive-failure after the mfgr recommended lifetimes, gradual loss increase in internal resistance and capacity loss before then. Overhaul would be needed and the amount of money the dead battery could be sold for would be less than the materials cost as substantial reprocessing is needed. Sources say 3500 charge discharge cycles with a pocket plate type. The most reliable information for lifetime indicates probably about 10.5 years or so (marketing material says 20 in some cases but I think that is likely a lie as they inflate the figures for LA to 5-7 years, for which there is a lot of other sources that say that is wrong, 3 to 4 is more like it).

LA: Slow capacity loss and increase in internal resistance due to plate sulfation and loss of material from the plates.

Zinc bromine: Not clear exactly, commercial batteries probably loss of activity at the bromine electrode causing higher internal resistance, and/or destruction of the plastic parts, causing increased self discharge as the cell separator degrades. Capacity is likely fairly constant. Mfgrs say 5 to 20 year "life", most sources indicate 2000 charge/discharge cycles. yes, looks about right after reading the sandia load leveling doc. Failure mode is increased internal resistance due to changes in the electrodes.

The first two are working against nife and the third is in our favor.

NiFe, Zinc-bromine and LA should be compared for a unit-sized 1 kW system.

=System costs for the different systems=

This is a financial calculation only for now, and the information can be considered part of a whole later. Solar, ignoring the inverter etc. just talking about the batteries and array, which I don't think would change which winners though would change the margin by which they win a bit.

I plan on producing a time-step simulator in Calc preferrably or if I have to Excel. This will include information imported from the System advisor model software from sandia labs to determine the net output of th solar array in the first column.

The objective function gives a large number of points for when adequate performance is obtained and an order of magnitude less points for when the cost goes down, with a function that rewards for lower system prices.

User input sections : demand pattern solar array input column, amounts refer to the BOTTOM of the hour, i.e. th amount of energy that has been collected in the hour of concern. battery price, per kWh of useable capacity battery efficiency battery self discharge rate in percent per month The batterey failure mode is something that may benefit from more detailed treatment, but for now assume it is a set percent fraction of capital investment lost each year, i.e. a negative interest rate. Net tnterest rate that would have earned on the money if had invested it elsewhere, should be interest rate of index funds minus inflation. solar array cost in $/kWh

Optimizer controllable cells: the quantity of battery, in kWh storage capacity at the beginning. the size of the solar array.

Intermediate outputs:

These refer to the present state of the system at the bottom of the hour unless stated otherwise. Flux events occur ath the bottom of the hour.

self discharge per hour SDPH F1

The energy-stored-in battery column. The sum of last hours amount plus the last hour's I (negative I indicatees withdrawal), or 0 =, whivhever is more (should never end up negative if all done right) G

The amount of energy from the array minus the amount the user demands, both in this hour. If positive, the amount is multiplied by the battery efficiency and then stored (limited by battery capacity) at the bottom of the hour, which the energy stored in the battery cell of the suceeding hour will reflect. If negative it represents demand on the battery, H

The amount of energy that goes into (+)or comes out (-) of the battery. If H is positive, should be H*round trip efficiency, or the amount of storage room left in the battery, whichever is less. If H is negative, H minus (F1*G)  or the battery capacity of the last hour multiplied by negative one, whichever is less. I

Amount of energy from array that gets wasted. The if H is positive, H minus storage capacity of the battery/round trip efficiency, or 0, whichever is more. K

Total energy delivered to user. Sum of amount withdrawn from battery(if I is negative, I*-1, otherwise 0) and the amount from the array. L

Sucess column, each cell is the ratio of what the system supplied to the user and what the user wanted. Should not end up more than one at any time if al ldone right. M

sum of all success cells. 365 indicates adequate performance. N1

State info, inputs are always from the previous hour, current value refers to the bottom of th ehour. flux information, info is from the current one, values refer to the bottom of the hour but immediatel before the state values:

Optimize for: The total system cost with adequate performance after 1 year The total system cost WAP after 5 years total system cost WAP after 10 years

The objective function gives a large number of points for when adequate performance is obtained and an order of magnitude less points for when the cost goes down, with a function that rewards for lower system prices

then put these in a 3 by 3 table, 3 columns for the dif systems including net price and quantity of the parts and 3 rows for dif timeframes

we can also use this or something like it to decide on the cost which the batteries should be sold for, in order to cost the same after say 5 years as LA would, thus ensuring that a large impact is acheived in the marketplace.

Calculations
Nife batteries are relatively inefficient. To decide on how important an impact this has on cost let's do some reckoning:

The Efficiency compensated equivalent cost needs to be estimated calculated for various batteries, I define this as the effective cost per Wh of battery in a solar power system:

Basically we need to know how much energy the battery wastes, and the find the cost of that and add that to the sticker price of the battery.

It's the total energy that needs to be withdrawn from the socket by the user plus the energy wasted by the battery, which is the total energy the array needs to supply, divided by the array cost per unit energy, minus what the cost woudl be if the battery was 100% efficient.

Es=Wh that must be delivered/day to socket Ea= Wh delivered per day by the solar array/watt of array EFb= Efficiency of battery charge/discharge overall Cc=cost of collector, in $/watt. Fsib=fraction of the energy that gets to the socket that had to be stored in the battery

Cb= cost of battery per Wh of storage

ECc=efficiency compensated cost per Wh of battery Cabbi=Total cost added by battery inefficiency

Cabbi=((Es+(((Fsib*Es)/EFb)-Fsib*Es))*Cc/Ea)-Cc*Es/Ea

then (Cabbi/(Fsib*Es))+Cb=ECc

Cost added per Wh of battery storage needed by the system, plus cost of battery per Wh.

So if Es=1000Wh Ea= 5Wh/watt EFb= 0.65 Cc= $2/watt Fsib= 0.5

Cb= $0.2

Cabbi=((1000+(((0.5*1000)/0.65)-0.5*1000))*2/5)-2*1000/5

Cabbi=507.69-400 =107.69

(107.69/0.5*1000)+0.2= 0.415

It more than doubles the effective cost of the battery for Nife. Lithium iron phosphate batteries are already available at $0.4 per watt, but only 80-90 percent efficiency they are only just inferior according to wikipedia (might be higher, remember hearing it was, should check battery handbook) search ebay for "thundersky lithium". And they have cycle durability in the same range as nife :http://evolveelectrics.com/Thunder%20Sky%20Lithium%20Batteries.html

But if the cost of the nife batteries was $0.1 per Wh then we'd be ahead of the game even with the low efficiency. Plus the cost of collectors is going to go down, probably a lot faster than the cost of batteries. Indeed the cost of batteries may well increase substantially, especially lithium batteries, due to market fluctuations or the cost of materials, especially lithium which is coming into huge demand. With zinc bromide we might get the best of both worlds, producing an exceptionally cheap system.