## The costs of storing energy in batteries

The cost of storing energy in batteries is getting less as this report shows, quoting a figure of about \$135/kWh for the cost of storage in 2020. That’s about £100/kWh.

Nissan Leaf replacement battery
In the US, a 30 kWh replacement battery costs about \$4000, about £3000. That’s £100/kWh – about the same as the Bloomberg figure.

The real cost of storage – 1 the battery cost of storing energy
What you are buying for £100/kWh is the ability to store energy. But that ability to store decreases with time. Even with the most careful charging and discharging, a battery can be expected to lose 20% of its capacity after 1000 cycles and 40% after 2000 cycles. For a rough cost of storing each kWh, let’s assume we get a total of 2000 cycles and the average capacity is 70% of the original capacity.

For a £100 battery storing 1 kWh new, it stores an average of 0.7 kWh for 2000 cycles, which is 1400 kWh. Therefore cost per kWh stored is £100/1400 = 7.1p.
Your £100 battery, if it is very carefully charged and discharged, will cost you 7p for each kWh that you store.

2 – the inefficiency cost of storing energy
You don’t get 1 kWh out of a battery for every kWh that you put in. That’s because the process of charging and discharging involve current flowing through resistance, hence energy loss. And the chemical changes caused by charging and discharging waste energy.
If you charge a battery slowly, then its efficiency can be over 90%. If you charge or discharge quickly (say in one of those motorway fast chargers) the efficiency can be as low as 70%. A reasonable figure for the overall charge/discharge efficiency is around 85%. This means that there is a loss of 15% of the energy you put into a battery.
Even if you charge at a low night-time rate of around 13 p/kWh (see below), you lose 15% of that. That is about 2 p/kWh. It’s 3 p/kWh if you charge at a daytime rate.
The total cost of storing energy in a battery is the battery cost plus the inefficiency cost, ie 7p + 2p = 9 p/kWh.

Domestic electricity costs
The current Octopus tariff which, with an Economy 7, tariff quotes a night rate of 13.24p and a day rate of 20.25p. That’s a difference of 7p per kWh.

But remember, every time you store a kWh in a battery, that process costs you 9p. You may think that you are paying only 13p a kWh to charge your car battery, but the battery storage costs bump that up to 22p/kWh. And if you charge you car during the day, or at a place that does not have cheap night rate electricity, it is costing you 30p per kWh.

Tesla Powerwall
For reference, a Tesla Powerwall costs £9,810 including VAT for a UK domestic installation. It has a capacity of 13.5 kWh – over £700/kWh, albeit in a nice box with battery management equipment. That’s 7 times as much as our batteries above. So the storage costs of a Tesla Powerwall are 7 times as much, which is 50p/kWh. But it’s obvious that Tesla make loads on the Powerwall and the Powerwall could be sold for significantly less than the current prices.

## There’s nothing we can do about the spread of Covid. 1: the argument from mechanism.

The null hypothesis
Once Covid has spread significantly among a population, normal lockdown actions have no significant effect on the spread of the disease.

Definitions of significant and normal
By ‘spread significantly’ I mean the sort of spread that was observable in most countries, the UK in particular, well before there was a general awareness of the presence of the virus, say in January 2020.
By ‘normal lockdown actions’ I mean those that were applied generally in the UK.
By ‘no significant effect on spread’ I mean no effect that could not reasonably be regarded as a statistical fluctuation.
Another way of stating the null hypothesis is ‘by the time we know we have Covid, there is nothing we can do about it.’

Reasons for the null hypothesis
There is an excellent paper, the Routes of Transmission of the Influenza Virus, published by the Department of Heath. Summarising relevant content and applying it to Covid one sees the following.

1. Scientists have tried to transmit viruses by contact with surfaces (fomites). But their best attempts to do so have failed. This accords with the lack of evidence for the fomite transmission of Covid. So all our washing supermarket trolleys, prohibiting trying clothes on in shops and cleaning chairs has likely done nothing to restrict the transmission of Covid and has been a waste of time. As the Nature article quoted is titled, Why are we still deep cleaning?

2. Respiratory viruses are transmitted by personal contact. The evidence for this is good. This is easy to stop. We’ve stopped it and Covid has still spread. From this we conclude that Covid spreads by means other than fomites and personal contact.

3. There is no doubt that respiratory viruses are transmitted by droplets. But droplets fall to the ground in a few feet. In any case, droplets are readily stopped by the upper respiratory tract and do not penetrate deeply into the lungs, where the body is more susceptible to infections. In any case, we’ve massively restricted the transmission by droplets by stopping stopped sneezing and coughing in public and the wearing of masks. Even so, Covid has spread. So there must be a mechanism other than fomite, personal contact and droplet that transmits Covid.

4. The final mechanism for transmission of respiratory viruses is aerosols, about which there is some knowledge, but there are clear limits to our knowledge. So far as the evidence pre-covid about influenza is concerned, the Department for Health paper referred above states:
i) There is good evidence for aerosol transmission between animals, despite lack of research about transmission between humans.
ii) Lower doses seem to be needed with aerosols into the lung compared with virus drops into the nose.
iii) Resulting illness from aerosol inoculation seems more severe.
iv) Though there is no good quality epidemiological data to support transmission via aerosols, even long-range transmission cannot be ruled out and and short-range aerosol transmission may be significant.

As the Nature article already quoted states, ‘As evidence has accumulated over the course of the pandemic, scientific understanding about the virus has changed. Studies and investigations of outbreaks all point to the majority of transmissions occurring as a result of infected people spewing out large droplets and small particles called aerosols when they cough, talk or breathe.

As already discussed, we are aware of droplets and our measures to control droplet spread are well understood and well implemented. What we now know is that aerosol transmission is an important mechanism for transmission and, since we have implemented methods that markedly reduce, possibly largely eliminate other forms of transmission, we realise that aerosol transmission is sufficiently able to spread Covid that, even if we eliminate other transmission methods, Covid still spreads.

The scientific consensus is now that Covid is airborne and spread effectively by aerosols. Here are some references.

Coronavirus drifts through the air in microscopic droplets – here’s the science of infectious aerosols

Aerosols, Droplets, and Airborne Spread: Everything you could possibly want to know

Aerosol transmission of SARS-CoV-2? Evidence, prevention and control

A quick google reveals many further sources showing that Covid is airborne.

How can we stop the spread of aerosols?
Those of us who live near farms on which various forms of muck is spread as fertiliser, know that everyone downwind smells the much that has been spread. Those who live near landfill sites are also used to the smells of decomposing which are produced. If you visit Burton, you smell Marmite, a bi-product of the brewing there. And there is no way to stop airborne smells.

In the same way it is not possible to stop airborne viruses. They spread around like smells and we all encounter the viruses.

Likely not at all. See for example Our findings indicate that surgical masks can efficaciously reduce the emission of influenza virus particles into the environment in respiratory droplets, but not in aerosols and a host of other easily available references.

The null hypothesis
Once Covid has spread significantly among a population, normal lockdown actions have no significant effect on the spread of the disease.

So, once it’s around, there’s nothing we can do to stop the spread of Covid? That’s pretty much the case. California locked down hard: Florida didn’t. Death rates were similar in the two states. There is similar evidence from comparing a whole range of states in the US and seeing that their various lockdown policies made not difference.

But if you don’t like what I have written, prove me wrong. Show any situation in which lockdown action has had any significant effect. After all, that’s how science proceeds: one makes a null hypothesis and invites others to prove one wrong. One doesn’t bumble along saying ‘wearing masks helps’ if one has no evidence that they do so.

## UK Covid mortality update April 2021

We are so used to seeing Covid daily death figures in the following format:

In fact such figures mean nothing at all unless the figures are a) seen in the context of general death figures and b) corrected for those who would have died at similar times had Covid not been around.

The only way to get any grips on both a) and b) is to consider the Age Standardised Mortality (ASM) figures which are now conveniently available. These figures are deaths per 100,000 of a European standard population, something not very different from that of the UK. The average ASM is about 1000, per 100,000. Since the UK has a population of about 68 million, that’s 680 lots of 100,000, which means that we have on average 680 x 1000 = 680,000 deaths per year.

Here are the raw ASM figures from the above source.

The red line is based on extrapolated figures assuming that the depression of the monthly figures of 13% below the 5-year history continues from May to August 2021.

The mortality figures show significant spikes of short duration due to Covid peaks. But these peaks are also associated with significant lows, well below historical averages. For instance, the April 2021 mortality figure was 13% below a five year average for that month. This is an extraordinarily low figure. It suggests that the death rate, in April 2021, may well have been reduced because of some deaths in both the Spring of 2020 as well as the winter season of 2020/2021.

We can make more sense of the pattern of mortality by averaging it over a number of months, in this case over 3 months.

In this graph I have extrapolated assuming that the reduction in deaths in May-August 2021 is 9% below the 5 year previous figure average, a less optimistic extrapolation than the current rate of 13% down.

The 12-month averages are, of course, annual figures, shifting in starting point as we go along the x-axis.

Again the ASM varies around 1000 per 100,000 but is noticeably stable. Mortality dropped in the years up to 2009. Since then it has remained fairly constant, averaging 988 per 100,000. More noticeable are the distinctly good years, 933 in 2014 and 907 in 2019, both of which years have increases in mortality in the subsequent years. There are good reasons to expect good years to be followed by bad years and vice versa. Two-year (24-month) mortality figures average these adjacent years, showing the overall trend.

Before we look at an amplified version of this graph, the first thing we should notice is its remarkable steadiness, hovering just under 1000 deaths per 100,000. Particularly noticeable is the unusual low in February-March 2020. There had been no significant respiratory deaths yet that winter and very few the previous year, leaving very many vulnerable people still alive.

This graph shows clearly the falling mortality before 2014, its remarkable steadiness from 2014 to 2018 at about 980 per 100,000, a sudden dip late in 2019 and then the rises already referred to.

To make any estimate of ‘deaths due to Covid’ one needs a good grasp of what should be regarded as ‘normal’. A figure of 975 from both the graph and the ASM figures is a reasonable guess at what might be an average and therefore ‘expected’ annual UK ASM.

In June 2020, at the end of the first Covid winter (containing the very mild first part of the winter season and the rapid rise due to covid), the ASM for that year was 1020 per 100,000, which is 45 per 100,000 above our average, representing an 30,600 extra deaths.

Using our extrapolation figure which expects deaths in May and June to be 9% below those for a previous 5-year period (whereas they are currently running 13% below) the 20-21 winter season will end in June 2021 with an annual mortality of 981, which is 6 per 100,000 more than recent averages. This corresponds to an extra 4080 deaths.

Putting these figures together, it seems that a realistic figure for the total number of Covid deaths over the two winter seasons, Jul 2019 – Jun 2021, have been about 35,000 for two years, an average of 17,000 extra deaths per year.

These figures show, as did the graph of 2-year average mortality, that despite the sad deaths of some, the actual effect of death rate from Covid has been very mild indeed. In a city like Preston or Bath, with 100,000 people, normally 975 would die every year. The effect of Covid over 2 winter seasons has been to increase the number of deaths by about 25 per year to 1000.
17 over 80’s, all but one with pre-existing conditions.
7 of age 60-79, all with pre-existing conditions.
1 person under 60 also with pre-existing conditions.