Introduction to Battery Analysis

Economic and financial analysis of batteries in terms of providing storage and ancillary services is introduced on this web page. Storage and battery adds complexity to economic analysis because you must make some evaluation of the value of benefits from use of the energy when batteries are discharged compared to the costs of charging the batteries and paying for the fixed cost of the batteries. This valuation of discharging batteries less the cost of charging and paying for fixed costs of batteries must be considered over the time period of the battery cycle — almost always on an hour by hour basis.  This is complicated by the fact that in electricity analysis, batteries (or hydro plants with storage or other technologies) provide two sources of value — (1) storage over a cycle and (2) ancillary services.  The first source of value, storage, is to move energy from low cost periods to expensive periods with charging and discharging which is what happens when you charge your phone or laptop.  The second service provided by batteries (or storage hydro) is to back-up the value of servicing sudden and foreseen changes in demand (balancing costs and ancillary services).

Other than evaluating the hour by hour charging and discharging from batteries there are many factors  that make battery analysis somewhat more difficult than the evaluation of dispatchable or non-dispatchable technologies. These factors include degradation rates of batteries, the round-trip efficiency of batteries during a charging cycle, the minimum depth of discharge and the lifetime of batteries as measured by the number of cycles. This is on top of the central question regarding how to measure the size of batteries which could be measured by the capacity or the energy. Because of all of these factors, evaluation of the costs and benefits from storage and/or measuring the levelised cost of electricity with storage could seem pretty intimidating. On this webpage I try to show how you can simplify the analysis or at least manage it and then I discuss alternative ways of evaluating the cost and benefit of batteries without some kind of fancy dispatch software.  I understand that politicians, Elon Musk and other people can become emotional about whether batteries can solve many problems in the world and I do not want to get into this debate. I am only trying to work through an objective analysis.

Battery Parameters

The diagram below of a water tower illustrates the issue of capacity storage and energy. In determining how much storage or ancillary service you need, should you use:

  • The maximum amount of electricity that can be sent to the battery or drawn from the battery at any instant, measured in kW.
  • The maximum amount of energy that you can take from the battery – the discharge — over a cycle (e.g. a day) measured in kW x time of discharge or kWh.  This is also the amp hours Ah multiplied by the volts divided by 1000.
  • The maximum amount of energy that you can send to the battery over a cycle – the charge – measured again in kWh.

In the diagram below, the capacity is measured by how much stuff (water or energy) that can be moved through the pipe.  This should be measured in an instant, but we can measure this over the course of an hour.  This is the kW of a battery.  The amount of energy that can be discharged or charged (there is no round trip efficiency from evaporation in the storage tank) is measured by the size of the tank, which can in turn be a multiple of the size of the maximum hourly storage.

The implication of this diagram in a cost and benefit analysis of batteries is that the amount of capacity may be measured in terms of kW or in terms of kWh or in terms of kW and kWh.  If the capacity is measured in kWh and the cost is measured in terms of money per kWh, the cost is measured in terms of kWh of charge or kWh of discharge (not the kWh of charge).  The difference between the cost in terms of kWh of charge and kWh of discharge is driven by the round trip efficiency.  Unlike me (who couldn’t grasp the different measurements of capacity) you should understand that round trip efficiency is related to energy — kWh — and not kW.

I had to look up whether, when cost is stated in terms of USD/kWh, the kWh is the discharge or the charging energy.  Apparently it is the useful charging energy as demonstrated by the quote below.  The amount of watts discussed in the quote below is presumably the amount produced at direct current (DC) rather than alternating current.

The cost, capacity and operating characteristics of different battery technologies are illustrated in the table below taken from Lazard which is very different from the presentation of battery suppliers.  Note that at the top of the table, the capacity is expressed in terms of both MW and MWh. The cost of the project is measured in terms of either USD/kWh – DC (without specifying whether the kWh is discharge or charge) and/or in terms of USD/kW.  At the bottom of the table, there is an item called the efficiency of the storage technology which presumably means the round trip efficiency of the battery.  The duration is expressed in hours, but it should really be labeled the duration in hours at maximum discharge.

When battery information is provided by suppliers, the information may look something like the excerpt below which is from a small home solar system.  Note that the capacity is not recorded and the kWh is also not there.  But you can see the battery capacity in terms of mAh.  If you look on the internet you can see that an mAh is equal to 1/1000 Ah.  Further you can find out that a kWh= Ah x V/1000 or Wh – Ah x V.  This means in the example below that the battery capacity in terms of watt hours is 12 x 3.3 or 39.6Wh. This amount of energy is presumably the amount of energy discharged.  The PV maximum power point is presumably the amount of solar at standard testing conditions (STC) that includes 1000 Watts of solar energy and 25 degrees.

I hope this demonstrates that when you are evaluating the costs and benefits of battery storage versus other possible strategies such as diesel or co-generation back-up that you should understand how many hours of storage that you need.  This all means that when you set-up your assumptions for a cost and benefit analysis of energy storage from batteries, the parameters should be specified carefully and include: (1) the amount of capacity that can be used for charging as measured in kW for one hour DC; (2) the amount of discharge storage as measured in hours at the maximum discharge rate; (3) the amount of kWh discharge required; (4) the round trip efficiency; (5) the inverter losses; (6) the maximum depth of discharge; (7) the cost per kWh of the battery; (8) the degradation rate of the battery; and (9) the lifetime of the battery as measured in cycles or in years.

The screenshot below illustrates the set-up of assumptions for a solar project, a battery project, a diesel project and a mini-hydro project.  I start with the capacity as measured in DC kW.  But please note that for economic analysis, the capacity is just a benchmark number that is used to measure cost.  The value of electricity comes from the ability to switch on your lights, to charge your phone battery, to watch television or the use an air conditioner for your dog.  This product is measured in kWh rather than kW.  The second input is for the amount of storage hours which only applies to the battery option.  To be a little more precise, this should be termed the discharge storage hours rather than the storage hours.  In the context of the water storage diagram, it is the amount of hours of discharge after pretending that there is some evaporation in the storage tank.  I have included a whole section below on alternative ways to compute the storage hours from a uses of energy (load) and sources of energy (solar, battery and other production).

A summary of battery characteristics is included in the website below.

Battery Sizing Analysis – Computation of Storage Hours Required and Necessity of Direct or Indirect Hour by Hour Analysis

The cost of a battery depends on how much storage is necessary as the cost of batteries are primarily a function of the amount of storage and expressed in kWh (although the cost does appear to change as a function of capacity).  For some battery uses such as provision of ancillary services and support for uncertainty, capacity measured in kW rather than energy is the issue and there is a need to move power suddenly and quickly to the grid.  For other battery uses, the value of storage is to move power from one period to another.  Value in this circumstance depends on the discharged energy during the cycle measured in kWh. The classic example of this is to move power that is produced by solar during the day to lighting requirements that occur at night.  The key point that I am sorry that I will repeat is that the cost of a battery depends on an hour by hour analysis. There are a few different ways to evaluate the number of storage hours required for discharge.  I have tried to discuss these different methods of measuring the size of the battery required.  Each of these requires and hour by hour analysis and each should consider uncertainty in both the solar pattern and the uncertainty in demand.  Analysis of uncertainty in demand and solar production is discussed in the microgrid page

Case 1: Battery to Support Solar Given the Size of Solar

You need the shape

I begin by pretending that we know how many hours of storage are needed relative to the maximum load that must be served by the battery.  For example if there are 8 hours of flat sunlight and then 8 hours of street lighting demand, the amount of the storage must be eight hours.  On the other hand, if the load is a refrigerator.  In this case, the assume that the refrigerator uses the same energy throughout the day. If the solar was constant for 12 hours (not at all realistic), then the storage capacity would be less.  Finally, pretend that there was a usage — say air conditioners — that have a similar profile as the solar itself.  In this case the battery capacity would be less.  To illustrate this I have made a few simple examples.

The values created by storage depend on the manner in which demand occurs over time and optimal capacity and storage of batteries should be considered in an analysis.

The notion of using kWh instead of kW as the basis for cost can easily create confusion at first as the cost depends on the amount of storage in a battery per cycle (like the hours of storage on your phone or laptop).  Rather than presenting a bunch of fancy graphs I attempt to walk you through storage analysis using carrying charge rates and spreadsheets that tabulate charging and discharging of batteries in different situations.  I have put together examples of when to use kW or kWh in analysis of batteries in the slides below.

Power Point Slides that Work Through Analytical Issues Associated with Batteries Including Analysis with kWh Instead of kW

Incorporating Storage and Batteries into Basic LCOE Analysis

First, compute the storage necessary.  This is illustrated in the screenshot below.

Lazard case for cost of battery and other characteristics.  Need capital cost, O&M cost and some operating parameters just like anything else.

The screenshot below illustrates a positive case.

Excel File that includes LCOE Analysis of Storage together with Battery Storage and Flexible Carrying Charge Analysis

A couple of extreme pictures from the power point slides illustrate the problem.  In the first case illustrated in the screenshot below, an extreme situation where there is only one hour of solar power during the day is assumed.  Here, there is no need for storage that exceeds the capacity of the battery because all of the battery capacity (kW) must be used in the one hour to put energy into the battery.  Paying for multiple hours of storage over (kWh) above the capacity of the battery would be a complete waste of money.  Here you should only look at cost per kW and not cost per kWh.

In a second case, there are many hours of solar power which can be “pushed” into the battery and there are many hours of required load that do not occur until after the sun has come down.  In this second case, the amount of storage over and above capacity makes a big difference and it is the cost per kW – hour of storage that matters.  This case is illustrated on the diagram below.  In this diagram a battery that could store four times as much capacity and have 1,000 kWh of storage would be much more valuable than a battery that had only 250 kW of storage.

Currently, there is a lot of BS surrounding discussion of the value of batteries ranging from the Paypal ripoff man (Elon Musk) to suggesting that the levelised value of storage means anything at all. Another B.S. is shown in a publication by Imperial College on the confusing notion of the levelised cost of storage. In this file, the cost per kWh and the cost per kW of the Lithium-ion battery is about the same even though there is 8 hour of discharge.

As with other cases of energy and finance problems my hope is that you can use information to calculate values yourself and do not rely on either confusing graphs of meaningless statistics nor statements from famous people. To to this for batteries I suggest that you first make a few fundamental cost and benefit calculations and then try to simulate the value of batteries  in the context of an island (if you are fancy you can call this a microgrid) where the only choices for energy generation are solar and diesel. This is and and a retail rate analysis is presented on later pages of the website. To establish such a micro-grid simulation I include discussion of how to collect real world data on items including the cost of batteries and other storage; the cost of operating diesel power plants; the potential future price of diesel fuel; and the economics of solar power with batteries in a micro-grid.  I demonstrate how you can make your own analysis of batteries and storage and how the analysis of batteries and storage depend on load shapes and the value of power during different time periods.  You can download files with the analysis by clicking on the two buttons below.

File with Analysis of Batteries in Microgrid Case with Comparison of Diesel, Solar and Battery in Alternative Scenarios

File with Analysis of Retail Rates that Evaluates Different Scenarios with Batteries and Solar Power

In addition to evaluating the value of batteries in a micro-grid and retail situation, I present the value of storage and ancillary services using merchant prices in later webpages.  Ultimately, the value of batteries in merchant markets depend on analogous issues to the factors that drive the mirco-grid analysis.  This is loads during different times that converts to differences between on-peak and off-peak prices as well as the fuel costs that are behind the variation between on-peak and off-peak prices.

General Discussion of Batteries and Storage

A dispatchable plant (e.g. a peaking plant) has some measure of capacity that measures the output of the plant in any instant. The input to the plant in any instant (measured in MMBTU or Kcal or Giga Joules or even kWh) is also delivered at a single point in time.  There are generally no constraints on the storage of inputs that limit a dispatchable plant from operating. For a battery, the output can only be delivered over time, if that the battery has storage. This issue of storage makes batteries not comparable to dispatchable plants such as peaking plants. For example, if the battery has a capacity output that can produce 1 kW, that 1 kW may be produced for 8 hours producing an output of 8 kWh. Alternatively it may have less storage and produce power only for one hour producing 1 kWh.

The amount of output from the battery contrasts with the amount of electricity that is used to “push power” into storage. This amount of power at any instant is like the amount of energy that is delivered to an electricity plant and can be measured with standard units of capacity such as kW.

Some people have explained to me that batteries are like a water tower that stores and releases water. The amount of water that is pushed up is measured in kW at any instant. It takes time to charge the battery. The discharge of stored energy also has a time element. This makes measurement and benchmarking of the cost of a battery somewhat more complicated than for a typical electricity plant.

For example, one would not express the cost per capacity of a peaking plant as the cost per delivering five hours of electricity. One expresses the number as the Euro or USD relative to the amount of capacity — in kW — that can be delivered at an instant. For batteries, the standard is to measure the cost of the battery relative to the kWh discharge. If we are on an island and we need power at night, we can pay for it with a diesel plant that is benchmarked on a per kW basis. If we want to use a battery instead (which is very difficult) we would have to pay for many batteries with no storage or a lot more for a battery with storage. Without arguing about whether this idea of using kWh instead of kW is a good or a bad benchmark, we should understand that the benchmark is different for a battery than for a standard plant. Further, the output may be able to be produced very quickly for frequency regulation, spinning reserve or voltage regulation (discussed below). I have tried to explain these things a bit in the video below.


Batteries as Capacity and Differences between Batteries and Other Peaking Capacity

One way to think about batteries is to compare the discharge from a battery to the generation from a peaking plant such as an open cycle plant or a diesel plant on a large system with a lot of baseload plants. The peaking plant can be switched on during peak periods to meet large increases in demand. Indeed, a load duration can be used to demonstrate that it is efficient to have peaking plants on a system. A battery could be used in the same way if it is charged-up during off-peak periods and then discharged during peak periods. There are, however important differences between a battery and a gas-fired peaking plant.

First, the battery has limited discharge driven by the storage capability of the battery. For example, if the battery has a storage a discharge period (modelling as duration) as four hours, but really hot weather drives up demand all day from early in the morning to sundown, then the battery is not as useful as the peaking plant in providing capacity. On the other hand, as long as the peaking plant can provide energy using natural gas from a pipeline system, then the gas-fired unit does not have this limitation. Economic analysis cannot simply label something as the “levelised cost of storage” without taking account of this limitation.

Second, the source of energy from the battery is electricity itself rather than natural gas. This means the battery can use solar power and move it around. A natural gas plant on the other hand must of course use natural gas. In our island example, if there is sunlight during the day and we need power at night to read books, the battery can move solar power to the evening. The natural gas plant cannot do this.

Batteries and Ancillary Services

One of the pages below works through the benefits batteries provide in terms of ancillary services.  There are many ancillary services, meaning things that a power plant or a battery can provide other than providing energy that turns on the lights.  People like to make this very complicated and seem to suggest that these services that do not turn on any lights are more valuable than the energy itself.  Some of these services are called frequency support, regulation support, black start capability, and what I think is the most important which is spinning reserve. Many of these problems arise from variation in loads or renewable energy.