The Economics of Home Solar PV

Friends, you may find this hard to believe, but someone posted something incorrect on Twitter the other day. They suggested that home installations of solar PV will soon become uneconomic.

I commented that I didn’t agree. But to my surprise, several people commented further suggesting that Home Solar was not only uneconomic, it was tantamount to theft!

At first I was bewildered: How could these people be so wrong? But then it turned out these people were economists, and so were quite un-phased by being wrong.

But after an extended exchange, I began to understand their perspective, and that is what this article is about. I still think they are wrong, but the perspective shift was interesting.

Home Solar PV: Simple Economics

The economics of home solar PV are fairly straightforward. A system of 10 panels (~£5,000) and a 5 kWh battery (~£5,000) will conservatively generate around 3,500 kWh/year of electricity which is roughly the annual usage of electricity by a household. The system will generate (on average) about 15 kWh/day in summer and perhaps just 2 kWh/day in winter depending on local shading.

Typically around 2,000 kWh will be used within the home saving (at current prices) 2,000 × 34p/kWh ~ £680/year which would otherwise have been purchased. Additionally, the extra 1,500 kWh will be exported earning a much less impressive 5p/kWh or £75 /year. So a roughly £10,000 investment has a return on investment of ~£750/year, a nominal 7.5%/year return. It’s possible to do a bit better or a bit worse depending on panel orientation and battery size.

By any conventional economic assessment, this is a reasonable investment.

Home Solar PV: Simple Carbonomics

Considering the carbon dioxide emissions avoided, the home solar PV system above might involve roughly 2,100 kg (2.1 tonnes) of embodied carbon dioxide emissions. That’s based on:

• Panels: ~400 kgCO2 per peak power (in kW) of a panel – leading to around 1.6 tonnes of emissions (Links 1, 2).
• Battery: ~100 kgCO2 per kWh of storage – leading to around 0.5 tonnes of emissions for a 5 kWh battery (Link)

Each kWh of electricity generated might avoid nominally 0.23 kgCO2 emissions. And so the system would avoid 3,500 x 0.23kg ~800 kgCO2/year. Additionally, by using the battery to avoid consumption at peak hours, the system could also help reduce grid costs and the use of ‘peaker’ plants.

This is a pretty reasonable carbon investment.

Home Solar PV: How could this not make sense?

So from an economic and carbonomic point of view, Home Solar PV systems with or without batteries definitely make sense. So what was this Twitterista going on about?

Well it turns out that they were not talking about the UK but were instead referring to (if I recall correctly) Belgium or Holland. In these countries the majority of people do not pay fixed price tariffs on their electricity. Instead they pay tariffs which change every 30 minutes depending on market conditions. In the UK this practice is not at all common.

And the situation they were referring to was the situation where there was so much solar power being made available by large solar farms, that while the sun was shining, solar power would cover the majority of electricity required. At this point, the economic market value of any extra solar generation would be zero.

This is a situation that will become increasingly possible as we expand renewable generation and the market will need to evolve to cope with this reality. But in the UK it would not make much difference. Most of the electricity generated on a rooftop is used within the home, and this avoids paying the market rate, so the savings would be unchanged. However, the price paid for exporting electricity might possibly fall to zero, but since that was only worth £75/year, it doesn’t really significantly the economics.

If consumers were exposed to market electricity prices that varied every 30 minutes through the day, then the cost of buying electricity when the Sun shone might fall to zero, and so consumers would be able to have free electricity whether or not they had a solar PV system on their home. In this situation, having a home battery would make a lot of sense because one could fill it for free!

But that is not the situation in the UK. I think it is good to have relatively fixed tariffs so that people can budget for likely electricity costs. In this way, professional traders take calculated risks for which they earn a reward. I think that is better than exposing us to the risks of a market which when under stress can become extremely volatile, and potentially bankrupt people who keep their electricity on when the system is under stress. For example, in the 2021 power crisis in Texas, in between blackouts, the price for some customers rose to $9/kWh – up from a few cents per kWh resulting in some customers facing bills of $1,000/day.

So the situation in which half-hourly market prices sometimes falls to zero is unlikely to affect the UK market directly. And even it did, people with home solar would still be getting free electricity at times when the market cost was not zero.

At the heart of this persons argument was an economic rationale that any investment in an economic activity which is sub optimal – represents a waste. This is based on a hyper-capitalistic view of society in which optimal capital deployment will result in optimal outcome. This is patently, just not in correspondence with reality.

Home Solar PV: Theft?

Theft! Surely I was dealing with an idiot here? But here is their argument.

The tariffs we pay for electricity are divided into two parts:

• a so-called ‘standing charge’ typically about £0.40/day and
• a ‘unit’ charge of typically £0.34/kWh.

Originally the idea was that this reflected the cost structure of the electricity supply industry.

• The ‘standing charge’ would pay for the costs of the electricity network that gave us the possibility of buying electricity, whether we used 1 kWh/day or 100 kWh.
• The ‘unit charge’ would pay for the extra costs – notably the fuel – used to generate every extra unit of electricity.

So with this structure, using solar PV to go ‘off grid’, I would still pay the standing charge, and so contribute my fair share to the maintenance of the electricity network.

However, standing charges are no longer just a way to pay for the fixed costs of the electricity network. They now include costs of paying for the mass failure of electricity companies in 2021/22, and elements of subsidy for ‘greener’ generation. And some elements of the unit charge actually reflect fixed costs.

So if I avoid paying for units of electricity, I am avoiding paying for some of the fixed costs of the network, and thus forcing those costs to be paid by people who can’t install solar PV. In short, by using solar PV I am stealing from the community and increasing the cost of electricity for everyone else. At this point I would understand if you wanted to just stop reading – why read words by a social reprobate like me?

Except of course that this is just nonsense. There is nothing that I – or anyone else – can do about the assignment of fixed costs to standing/unit charges. The whole mess is the combined result of weak regulation, energy industry lobbying, and government meddling. All no doubt undertaken with the aim of ‘making things better’. But if the side-effect of these historical changes is to cast someone trying to reduce carbon dioxide emissions as a thief, then I think that view is non-sense.

From a wider perspective, we see that the costs of regulatory failure have been assigned to electricity bills rather than gas bills. This political choice drives people to continue to use gas for heating when using heat pumps would save the country money AND reduce carbon dioxide emissions. So by a similar argument, gas users are ‘stealing’ from electricity users.

In short, our energy supply market contains distortions. All the companies that went bust made large profits which were privatised, but their losses are now being spread over all our bills. In other words, the profits were privatised and the losses socialised: standard operating procedure in a mis-regulated monoply. This is a failure of market design and regulation and it’s not my fault!

Home Solar PV: But I’ve got no roof?

Of course if you don’t have a roof, you may feel excluded from this discourse. But by using Ripple, you can buy a fraction of a solar park, and a pro-rata share of the profits will be deducted from your energy bill.

Having previously built one wind turbine (Graig Fatha), and commenced construction of the 8-turbine Kirk Hill Wind Farm, Ripple are now (Spring 2023) looking for people to contribute money to build a solar park in Devon.

The deal is this:

• You can buy a share of the solar park from £25 to a value equivalent to 120% of annual electricity consumption priced at roughly £1/kWh.
• So if annual electricity usage is 2,900 kWh, then if you pay roughly £3,000, you will own a fraction of a solar park that will generate as many kWh as you use in a year.
• Their financial projection is summarised below:

It’s clear the projected savings are modest (~ £180/year) which for a £3,000 investment amounts to about 6%/year.

But it is interesting to compare these cost with the costs of the home solar PV system described above. The Ripple investment is cheaper per kWh generated and gives you less to worry about. For example, you don’t have to worry about pigeons. Of course, none of this is financial advice: honestly: don’t listen to me. I only care about the carbon dioxide.

Keep your eye on the carbon

If you are fortunate enough to have a few thousand pounds to invest, then putting your money into renewable energy projects either on your roof or remotely via Ripple is – in my estimation – a pretty reasonable thing to do. Whatever the location, this reduces the demand for electricity generated by gas-fired power stations and so reduces our country’s carbon dioxide emissions.

Arguments about this being unfair are – I think – spurious. We live in a society in which almost all economic activity generates a ‘trickle-up’ effect that enriches the already wealthy and in general gives rise to net carbon dioxide emissions. In this context, spending resources on renewable energy projects is amongst the least worst things we can do – and helps to build a renewable energy infrastructure from which we will all benefit.

 

Perfect Solar Days

Friends, March may have been depressingly dull, but the start of April has been upliftingly sunny. And Tuesday April 4th was a perfect solar day.

Perfect solar days are days in which the sun shines unremittingly from dawn until dusk, with not a cloud in the sky: such days are rare: Typically there are around 10 per year and I try record the solar PV generation from each one. I do this using data from the Tesla App which records solar generation every 5 minutes via a current transformer (CT) clamp on the cable from the inverters.

The graph below shows 12 perfect (or near perfect) solar days from 2021 and 2022. The days are not evenly spaced because I can’t control the weather!

Click on image for a larger versions. Graph showing the daily hour-by-hour generation for a series of near-perfect solar days in 2021 and 2022.

Attentive readers will recall that in November 2022 I had eight extra solar panels installed on the east-facing roofs of Podesta Towers (link). I had expected that these would contribute nothing to solar generation in winter, but that generation would be significant in spring, summer and autumn.

The graphs below show the generation profile for each day for which there is reasonably well-corresponding day from before the new panels were installed. As expected the new generation is very weak in December and January, but by April has grown significantly.

As expected the extra generation from the panels on the North and East is in the morning. Happily, the maximum power looks like it will peak in summer at less than 5 kW – the maximum rating of the cable between the inverters and the consumer unit.

Click on image for a larger versions. Graph showing the daily hour-by-hour generation for a series of near-perfect solar days in 2021 and 2022.

Overall

The aim of the installing the new panels was to create extra generation in the spring and summer which would hopefully be enough to keep the house off-grid for 6 months. This goal has been hampered by the dullness of March, but things seem to be returning to normal now. However the weather is still cold enough to require the heat pump to stay running for another month or so, increasing domestic consumption.

The graphs below all have a vertical axis of kWh/day and the data are smoothed to highlight trends: They compare:

• Domestic consumption and solar generation. One can see that solar generation is rising to be roughly equal to domestic consumption and should soon exceed it.
• Domestic consumption and Grid Consumption. In winter, the two are practically equal, but in spring, grid use is falling as we rely more on solar energy.
• Net Grid Consumption/Export and solar generation. As solar generation rises  we have become net exporters of electricity.

Click on image for a larger versions. Graphs variation of Daily Consumption, Daily Grid Consumption, Net Grid Consumption and Solar PV generation, all expressed in units of kW/day.

 

New Solar Panels

Friends, back at the start of September, I noted that it had been a sunny summer and I resolved to add more solar panels to the house in order to increase the solar harvest next year.

I ordered the system just a few days after writing that article and it is now being installed.

In this article I thought I would describe the new installation and how it will (hopefully) integrate with the existing installation.

Click on image for a larger version. The arrangement of the solar cells on the roof of Podesta Towers. The grey panels have been installed for two years, and the red panels were installed this week. I had hoped to fit four panels on the flat roof, but in fact I can only fit three.

The Existing Installation

The existing system was installed back in November 2020 and consists of:

• 12 Q-CELLS 340W DUO G8 panels
• A SOLIS 3.6KW 4G dual MPPT inverter

Why did I select these items? The installer recommended them and they seemed to have adequate performance. And happily, they do seem to have worked OK.

Some key features of these items are:

• 340 watts is the nominal output of a panel illuminated perfectly by sunlight with an intensity 1000 W/m^2 – this is roughly full sunlight on a UK summer day.
• Since the panels are 1.7 m x 1.03 m one can work out that around 20% of the solar energy is converted to electrical power.
• The panel is constructed as two half-panels wired in parallel, each with 60 individual solar cells.
• A silicon solar cell generates around 0.6 V so the 60 cells on a half-panel together generate around 36 V.
• Splitting the panel like this improves the panel performance when one half of the panel is shaded.
• The MPPT acronym stands for Maximum Power Point Transfer and is system for extracting maximum power from solar panels as the intensity of illumination changes.

The quotation suggested that I might reasonably expect 3,780 kWh of generation each year and this year we look on track to exceed that. Last year we generated only 3,517 kWh.

Click on image for a larger version. Cumulative generation from the existing solar panels in 2021 and 2022. The dotted blue lines are based on the expected output according the installer’s initial calculation.

This first installation was done quickly to take advantage of the fact we had scaffolding around the house for the external wall insulation. Because of this, we couldn’t wait six weeks for permission for a larger installation from the local Distribution Network Operator (DNO): these are the people who manage the local electricity networks.

So I opted for a standard installation (for which no permission is required) with a maximum output of 3.6 kW peak and we used the best sites available. I resolved to learn what I could about solar power, and after two years, I feel I served my apprenticeship.

The New Installation

To move beyond the standard system one needs to apply to the DNO, a process that takes about 6 weeks and which was thankfully handled on my behalf by the installer.

My aim was to get as much solar PV on the roof as I could – while not making the house look horrible! For that reason, we avoided using a patchwork of panels across the roof – sacrificing some performance for aesthetics.

Since the best sites had been taken by the first installation – I simply went with what was available.

I had noticed during the summer that in the mornings the Sun rises well north of east, and the east-facing roof of Podesta Towers was in full sun up until solar midday. Similarly, the flat roof was more or less un-shadowed over the same period.

My performance calculations using the excellent Easy PV site were very similar to the suggested performance from the installer.

• The 5 panels on the east-facing roof will hopefully generate ~1,300 kWh/year
  • The panels are tilted at ~ 40° and face roughly ~ 20° north of east.
• The 3 panels on the flat roof – might generate ~900 kWh/year
  • The panels are tilted at ~ 12° but face roughly 20° east of south –

This would correspond to 2,200 kWh/year, an additional 60% of generation bringing the total close to 6,000 kWh/year. If actual performance gets anywhere close to this I would be delighted.

To put these figures in perspective, we can compare them with household consumption.

• Last year the house used ~5,400 kWh –
• Roughly 3500 kWh of that (~65%) was for day-to-day household ‘stuff’
• Roughly 1,900 kWh of that (~35%) was used for the heat pump.
• The heat pump operated with an average COP of 3.6 to deliver 6,800 kWh of heat.

So the enlarged system will hopefully generate more electricity than we use in a year. Sadly the peak of generation (in May or June) is quite out of phase with the peak of demand (in January or February). But nonetheless, it’s a milestone of sorts.

The new system consists of:

• 8 JA SOLAR 390W MONO solar panels.
• A SOLIS SOL-3.6-S6-DT-DC inverter.

Again, I just accepted the installer’s recommended suggestions.

The Panels.

The new panels are similar to the old ones: the 390 W nominal peak output of the new panels is larger than the 340 W peak of the previous panels simply because the new panels are larger. The efficiency remains around 20%.

Each panel consists of two half-panels, each with 9 rows of 6 rectangular half-cells.

Click on image for a larger version.

When illuminated, each individual cell generates a voltage between 0.5 V and 0.7 V between the top of the cell (the part you can see) and the bottom of the cell (that is at the back of the panel).

Fine aluminium wires cover the top of the cell to collect the generated electrons, and the wires then connect the top of one cell to the underside of the neighbouring cell so that their generated voltages add together. In each half-panel, 54 cells in series generate a voltage ~ 36 V at a current of roughly 5 amps.

Click on image for a larger version. Top: Illustration of the way in which sunlight generates a voltage between the bottom and the top (illuminated) surface of the cell. Right: The fine wires collect electrons generated from within the silicon. The filigree wiring pattern is optimised to collect as many photo-electrons as possible, while not blocking the sunlight. Left: Details of the wiring showing the top surface of the lower scale is connected to the underside of the neighbouring cell.

The two half panels are wired together in parallel so that the peak output of the whole panel is ~ 36 V at a current of roughly 10 amps.

Panels which are similarly illuminated are wired in series in a so-called ‘string’. In this installation, the 5 panels on the east-facing roof are wired in one string and the 3 panels on the flat roof are wired in another.

The inverter design has two independent inputs and the DC currents from the two ‘strings’ are combined to create an AC current at 220 V.

This arrangement works excellently when all cells in a panel and all panels in a string are illuminated similarly. But if one cell in a panel is shaded, then not only does that cell not generate a current, its electrical resistance increases dramatically, and this can restrict the current which is able to flow through the whole string of which it is a part. Fortunately, clever electrical tricks can minimise the shading problem as explained in this excellent video.

Peak Power.

One aspect of the installation which concerns me is whether all the electrical circuits can cope with the sheer amount of power this system might generate.

To estimate this, I downloaded generation data from 22 June this year, a day which was nearly perfect for solar generation: close to the solstice and almost completely cloudless. This data is shown in red on the graph below.

I then made guesstimates of the generation from the two new strings:

• I guessed the 5-panels on the east-facing roof would begin generating earlier in the day and reach maximum power (5 x 390 W = 1,950 W) just before solar noon (1:00 p.m. BST). This is shown as a green dotted line.
• I guessed the 3-panels on the flat roof would generate roughly symmetrically around solar noon (1:00 p.m. BST) with a maximum power of 3 x 390 W = 1,170 W. This is shown as a blue dotted line.

Click on image for a larger version. Graph comparing a perfect midsummer generating day with the existing system (red curve) with the likely generation from the expanded system (purple curve). See text for details.

Altogether (dotted purple line) the total power could potentially exceed 5 kW – a worryingly high power level.

Summary.

Friends, as usual, I have gone on for too long. But this is a significant – and possibly final – step in the house refurbishment.

It offers the possibility of being off-grid for 6 months a year and of generating more electricity than the household consumes (averaged over a year). I think these are significant upgrades.

The cost is not completely clear yet, but looks like it will be just under £5,000. This is more than the initial system (£4,200 in November 2020) but this seems reasonable given the extra scaffolding required.

As I write, the panels are installed but the internal electrical wiring is not complete – but hopefully that will be done soon!

And if you have read this far, thank you! Please allow me to reward you with a video of the installation.

 

 

Another talk about reducing CO2 emissions

Friends, this week I visited Brighton to give a talk to their Café Scientifique on reducing carbon dioxide emissions from one’s home.

I spent absolutely ages getting the Powerpoint slides ready, but tragically, on the night, the projector didn’t work and I had to ad lib and just mime the key slides!

So yesterday I sat down with my phone and recorded the presentation in two parts – links below.

Because there was no audience the presentation is a little dull – but at least I get to show people the slides!

If you would like, you can download the slides here. It’s a 40 Mb file (!) but feel free to share or steal anything you like!

Presentation#1

The first part of the presentation is 22 minutes long and considers exactly why it is that Earth’s surface temperature is so sensitive to carbon dioxide in the atmosphere.

When I went out chatting to the public recently (1, 2), this was something that people just didn’t seem to understand.

Presentation#2

The second part of the presentation is 26 minutes long and involves a consideration of how we can reduce carbon dioxide emissions both collectively and personally.

Most people don’t have the resources to do very much, but absolutely everyone can help by just talking with friends and family about the reality of what we are facing.

For those that do have the resources, the presentation outlines how installing  a heat pump, and using solar PV panels and a battery can make a big difference  to personal CO2 emissions.

Warning

These videos are unscripted! Consequently, I may inadvertently fail to speak with the level of exactitude to which I would normally aspire: please accept my apologies in advance.

First Winter with a Heat Pump

Friends, our first winter with a heat pump is over.

Last week:

• I switched off the space heating, and…
• I changed the heating cycle for domestic hot water (DHW) from night-time (using cheap-rate electricity) to day-time (using free solar electricity).

From now until the end of July, I am hopeful that we will be substantially off-grid.

Let me explain…

No Space Heating 

The figure below shows the temperatures relevant to our heating system for the week commencing Saturday 9th April.

The week started cold, with overnight temperatures close to 0 °C and daytime temperatures peaking at 12 °C.

But the week ended with much warmer temperatures, and even in the absence of any heating flow, the household temperature rose above 21 °C. At this point I decided to switch off the space heating. You can see this on the monitoring data below.

Up to the 15th April, the heat pump would operate each evening – you can see this because radiator temperatures oscillated overnight as the heating circuit struggled to deliver a very low heating power.

From the 16th April – with the space-heating off – you can see the radiator temperatures simply fell after the DHW water heating cycle.

Click image for a larger version. Graph showing four temperatures during the week beginning 9th April 2022. The upper graph shows the temperature of radiator flow and the domestic hot water (DHW). The lower graph shows the internal and external temperatures. In the colder weather at the start of the week, the radiator flow temperatures cycled on and off. In the warmer temperatures at the end of the week, heating stopped automatically. On 16th April I switched the space heating circuit off.

Heating DHW during the day 

The next graph shows the same data for the following week. Now there is no space-heating in the house, but the insulation is good enough that household temperature does not fall very much overnight.

On the 20th April I switched from heating the domestic hot water at night (using cheap rate electricity) to heating during the afternoon (using electricity generated using solar PV).

My plan was that by 2:00 p.m., the battery would be substantially re-charged, and heating the hot water at that time would:

1. Minimise exports to the grid and maximise self-use of solar-generated electricity.
2. Heat the domestic hot water using air that was ~ 10 °C hotter than it would be at night – improving the efficiency of the heat pump.

Click image for a larger version. Graph showing four temperatures during the week beginning 16th April 2022. The upper graph shows the temperature of radiator flow and the domestic hot water (DHW). The lower graph shows the internal and external temperatures. The radiator flow was switched off. On 20th April I switched from heating the domestic hot water at night to heating during the day.

One can see that household temperature has fallen a little during the week, but only to around 19 °C, which feels quite ‘spring-like’ in the sunshine.

The big picture 

The graph below shows:

1. The amount of electricity used by the household
2. The amount of electricity drawn from the grid

It covers the whole of 2021 and the start of 2022 up to today (almost) the end of April. The graphs show running averages over ± 2 weeks.

Click image for a larger version. Graph showing the amount of electricity used by the household each day (kWh/day) and the amount of electricity drawn from the grid each day (kWh/day). Over the 8 months of the winter heating season, 27% was supplied by solar generated electricity.

The 4 kWp solar PV system was installed in November 2020 and was just beginning to make a noticeable difference to our electricity consumption in the spring of 2021.

In March 2021 we installed the Powerwall and immediately dropped off the grid for just over 2 months! In mid-summer we had a run of very poor solar days and we began to draw from the grid again.

In July 2021 we installed a heat pump and this extra load (for DHW) coupled with the decline in solar generation caused us to need to draw a few kWh from the grid each day.

Over the 8 month heating season from the start of August to the end of April, the household used 4,226 kWh of electricity for all the normal activities (~ 2,200 kWh) plus heating using the heat pump (~2,000 kWh). Over this period the heat pump delivered just over 7,000 kWh of heat for a seasonally averaged COP of around 3.5.

However, even in this winter season, only 3,067 kWh were drawn from the grid – mostly at low cost. The balance (27%) was solar generated.

Summer and Winter Settings

The optimal strategy for the Powerwall is now becoming clear.

In the Winter season, daily consumption can reach 25 kWh/day and solar generation is only ~ 2 kWh day. So in this season:

• We operate the household from the grid during the off-peak hours.
• We time heavy loads (dishwashing, tumble drying and DHW heating) to take place in the off peak hours.
• We buy electricity from the grid to fill the battery (13.5 kWh) with cheap rate electricity – and then run the household from the battery for as long as possible. Typically we would need to draw full price electricity from the grid only late in the day.

Click image for a larger version. Images showing the time of day that we have drawn power from the grid (kW) in half-hour periods through the day. Each image shows the average for one month. The graph was assembled using data from the fabulous Powershaper software (link).

In the ‘summer’ season, daily household consumption is ~11 kWh and average solar generation is typically 15 kWh/day. So given that the battery has 13.5 kWh of storage, we can still stay ‘off-grid’ even during a periods of two or three dull days.

So during this period

• We switch the battery from ‘time-based’ mode to ‘self-powered’ mode.
• We time heavy loads (dishwashing, tumble drying and DHW heating) to take place in the afternoon.

This year and last year 

Last year (2021), as soon as we installed the Tesla Powerwall battery, we dropped off-grid within days.

But this year (2022) we have an additional daily electrical load. Now we are heating DHW electrically with a heat pump which requires ~ 1.5 kWh/day.

Nonetheless, I hope it will be possible to remain substantially ‘off-grid’ for the next few months. Time will tell.

A Year of Solar Energy

Friends, it’s just coming up to the anniversary of the installation of solar photo-voltaic (PV) panels at Podesta Towers in Teddington. So I thought it might be interesting to see what a year of generation has brought.

First I’ll describe the installation; then explain what I expected (or at least hoped for); and then outline what has actually happened together with a discussion of the role of our domestic battery.

And finally I’ll remind you – and myself – of how solar panels fit into to my efforts to reduce carbon dioxide.

But in case you’re short of time, here are the salient points.

• 12 solar panels generated just over 3500 kWh of electricity which is close to last year’s total domestic consumption ~3700 kWh.
• This will have avoided emission of ~0.8 tonnes of carbon dioxide this year.
• On the sunniest days the system generated ~25 kWh/day and in mid-winter average generation was ~ 2kWh/day which compares with around 10 kWh/day of non-heating electrical use.
• When used with a battery, we were substantially off-grid for around 4 months.

1. The Installation

I described the installation in some detail here, but briefly it consists of 12 panels from Q-Cells, each 1.0 m x 1.7 m in size with a nominal generating power of around 340 W. I think this year’s versions are already more powerful!

Click for a larger image. Google Maps view of my home showing the shape and orientation of the available roofs. And photographs before and after the installation.

The installation cost £4,230 pounds which did not include the cost of scaffolding which was already up on the house at that point.

I chose Q-cells panels because I liked their completely black appearance; they seemed adequately specified; they were readily available; and they were cheap – around £130/panel if I recall correctly.

I later found out that they have pleasingly low embodied carbon dioxide, less than 1.6 tonnes for this installation, and so the embodied carbon dioxide payback time will be around 2 years. Q-cells also score highly for the not producing toxic waste.

2. What did I hope for?

The quotation from local installer GreenCap Energy included an estimate of the expected output – 3780 kWh/year.

But rather than trust the installer I downloaded data from an EU project that cleverly allows one to estimate how a particular solar installation with an arbitrary location and orientation would have performed hour-by-hour over the entire period from 2005 to 2016. This data suggested I might reasonably expect 3847 ± 173 kWh/year.

Click for a larger image. Estimates from an EU re-analysis project of what my solar panels WOULD have generated over the years 2005 to 2016. Year-to-Year variability appears to be about 5%.

I then averaged these 11 years of hour-by-hour data to yield my estimate for the expected monthly performance. They are shown as yellow dots on the graph below.

Click for a larger image. Expected generation in kWh per day. The yellow dots are the monthly averages of the estimated generation from 2005 to 2016. The green dotted line is a crude guess based on a ‘sine-squared’ function. The red dotted line shows our typical average daily electricity consumption ~10.5 kWh/day.

One feature of the simulated data is that the peak generation is expected to occur from April to July – a range which is not centrally arranged around the longest day (June 21st).

3. What happened?

Solar generation was broadly in line – but a little lower – than expectations. But the day-to-day and week-to-week variability was much greater than I had appreciated.

This variability makes it hard to plot readable graphs because they look chaotic! So let me introduce the data one stage at a time.

Looking at the monthly averages (below) we see that most months were close to expectations, but April was especially sunny, and August was a bit disappointing. So far, November has been a brighter than normal. Please note, the December data is from December 2020, because the data from December 2021 is not yet available.

Click for a larger image. Comparison of monthly averages of actual solar generation (green dots) with expected generation in kWh per day. (yellow dots). The black error bars show the standard deviation of that months daily data.

Now let’s additionally plot the daily data.

Click for a larger image. Similar to the graph above but now additionally showing the actual daily solar generation (kWh/day)

A few features of the daily data are really quite remarkable.

• Firstly, the day-to-day variability is large. This means that the solar generation on a given day is almost no indication of the likely generation on the next day.
• Secondly, the peak generation of around 25 kWh/day can occur in either April or July despite the substantial differences in day length and solar path.
• Thirdly, even in mid-summer there can be runs of several utterly miserable days with very little solar generation.

If we average the daily data over a week, (see below) then we still see variability – deviations from the nominally-expected generation – which deviate from the expected generation consistently over periods of up to 3 weeks

Click for a larger image. Similar to the graph above but now additionally showing the ±3 day average of the generation as pink or purple lines.

Another way to look at the data which emphasises the trend more strongly than the variability, is to show cumulative generation through the year.

Click for a larger image. Cumulative generation (kWh) shown as a blue line against nominal expected generation.

Actual generation (just over 3500 kWh) is about 8% lower than I expected, but I am not especially surprised.

It could be that 2021 was a ‘a bit dull’ over the summer months when most generation takes place, or because I had incorrectly allowed for losses at the inverter – which converts DC electricity into AC mains electricity.

Battery

The PV panels were installed in November last year and to our surprise they immediately made a measurable difference – reducing our use of electricity from the grid by around 2 units per day.

Click image for a larger version. Daily electricity usage (from a smart meter) before and after solar panel installation.

However, it was not till our battery was installed in March 2021 that the transformational power of solar became apparent. Within a couple of days, the household went ‘off-grid’ and remained off-grid for around 80 days.

Click image for a larger version. Daily electricity usage (from a smart meter) since solar panel installation. Install the panels led to a small reduction in grid use. Consumption rose over Christmas. Consumption began to fall as we entered spring, and then fell to zero once we installed the battery. As we enter Autumn and Winter grid consumption is rising because since July we are using electricity to power a heat pump which heats the house and provides hot water. The bold green line shows the daily consumption averaged over ± 1 week.

As we enter autumn and winter, the solar cells still contribute significantly – 48% of our electricity in October was solar. But generation will be just around 2 kWh/day through November, December and January.

Since July, the ASHP installation has been using ~1.5 kWh of electricity a day to provide ~4 kWh of domestic hot water.

Now (November) the ASHP is providing space heating within the house, and in the coldest weather (~0°C) I expect  this will require an additional 15 kWh/day of electricity to provide ~50 kWh/day of heating. Most of this electrical energy will be downloaded at cheap rates overnight.

Summary

The PV and battery system has been installed to reduce carbon dioxide emissions from the house. They are the part of a suite of measures to reduce heating demand, eliminate gas use, electrify heating and increase the use of renewable energy.

Together they have dramatically reduced the running costs of the house.

The graph below shows expected household carbon dioxide emissions (not including consumption or travel) over the period up to 2040.

Click image for a larger version. Anticipated household carbon dioxide emissions (not including consumption or travel) over the period up to 2040. The red line shows what would have happened if I had made no changes. The green line shows the expected outcome.

In the short term, all the actions I have taken have made things worse!

The embodied carbon dioxide in the solar panels, insulation, batteries, and heat pump amounts to ~11.5 tonnes, and this ‘debt’ will not be re-paid until the end of 2023.

I would love to add more solar panels, but I am resolved to hold off until my existing carbon dioxide debt is re-paid.

Overall, I hope you can see that the solar panels are central to the plan to reduce anticipated emissions by 60 tonnes by 2040

 

Battery Day: First Results

Me and my new Tesla. This unit contains 13.5 kWh of battery storage along with a climate control system to optimise battery life. We have placed it in the porch so that (when visits are allowed again) everyone who visits will know about it!

Last September, Tesla held their ‘Battery Day‘ during which they unveiled their road map towards cheaper, better, batteries.

Not to be outdone, last Monday VW held their own ‘Battery Day‘ during which they unveiled their road map towards cheaper, better, batteries.

And last Thursday was my own battery day, when Stuart and Jozsef from The Little Green Energy Company came and installed a Tesla Powerwall 2 at Podesta Towers in Teddington. I was (and still am) ridiculously excited.

I am still evaluating it – obviously – but here are a couple of notes.

How it works

The system has two components. An intelligent ‘gateway’ that monitors loads and supplies, and a climate-controlled battery storage unit.

Click for a larger version. The left-hand graphic shows how AC power enters our house, and how DC power generated by solar panels is linked to the grid. When the Solar PV is sufficient ,power is exported to the grid. The right-hand graphic shows how the TESLA ‘gateway’ device monitors the solar PV, domestic loads and battery status and intelligently decides what to do.

The gateway (and the battery) are electrically situated between the electricity meter and all the loads and power sources in the house. So all energy enters or leaves the battery module as AC (alternating current) power.

But its internal batteries must be supplied with DC (direct current).

This makes it ideal for storing power from the AC grid, but less than ideal for storing the DC current generated by solar PV panels.

One might have expected that a device designed to store solar power might intrinsically operate using DC and indeed, some battery systems – positioned between the solar PV and the inverter – do this.

So the choice to place the Powerwall™ where it is, is a compromise between the extra functionality this location offers – it can back up the entire house – and the inefficiency of storing solar PV which is first converted to AC by the inverter, and then re-converted back to DC by the Powerwall. The support document states that the conversion from AC to DC and back to AC has 90% round-trip efficiency.

The photograph below shows the gateway installed under the stairs in our house.

Click for a larger version. The Tesla ‘Gateway’ installed in our house. The unit is positioned in between the electricity meter and all the domestic loads. The black conduit leads under the floor to the battery which is installed in the porch.

Control

The system is controlled by an app which is – frankly – mesmerising. It shows how electrical power flows between:

• the grid,
• the battery,
• our home, and
• our solar panels

Click for a larger version. Screenshots from the app at various times yesterday.

There is less room to adjust the parameters of the system than I had anticipated. This appears to be because, in exchange for a guarantee that the battery will retain at least 80% capacity (10.8 kWh) after 10 years, one is required to relinquish detailed control to the Tesla Brain.

Through a built in network connection, the device is in constant touch with Tesla who monitor its performance and can detect if it is abused in some way. I am not sure how I feel about that – but then guaranteed long-term performance is certainly worth something.

One feature of this relinquishing of detailed control concerns ‘time-of-use’ tariffs. I anticipate that – especially in winter – I will need to charge the battery overnight on cheap rate electricity.

The system supports this mode of operation but is not yet operational. Apparently it needs to study the patterns of household use for 48 hours before being enabled.

When operational, one gives the system general instructions and then allows it to choose when, and by how much, to charge. There is for example no way to force the battery to charge to 100% on command.

In practice I suspect it will be fine, but at the moment it still feels a little weird.

Performance on Day#1

The simplest way to show how the Powerwall™ works is by looking at the data which the ‘App’ makes available.

The first graph shows the household demand through the day. It’s fascinating to look at this data which has 5 minute and 0.1 kW resolution. The metrologist in me would like more – but in honesty, this is enough to understand what is happening.

Click for a larger graph. See text for details.

Now we can look to see how that demand was met. Overnight, we relied mainly on the grid.

Click for a larger graph. See text for details.

The battery could have supplied this overnight electricity, but it had been set to hold a reserve of 16% of its capacity (~2 kWh) in case we required backup after a power cut. We have lowered that setting now because, thankfully, power cuts are rare in Teddington. The battery drew power from the grid overnight in two short periods to maintain this reserve.

Additionally, at the end of a sunny day in which the solar PV filled the battery, there was brief period where we returned electricity to the grid.

During the day – which was very sunny 🙂 – the household electricity demand was met by the electricity from the solar panels.

Click for a larger graph. See text for details.

Without the battery, most of this 16.91 kWh of electricity would have been sent to the grid. But now only a tiny fraction was returned to the grid, most of it being captured by the battery – see below.

Click for a larger graph. See text for details.

The graph above shows the battery maintaining its reserve charge at night, and then charging from the solar PV during the day. At peaks of household demand, the charging is paused. At around 16:00, the battery was briefly full, and shortly thereafter it began discharging to meet household demand.

As I write this at 1:00 p.m. on the day after the day shown (a rather dull day 😦 ), the battery is 56% full and charging.

The graph below shows all the above curves together.

Click for a larger graph. See text for details.

Overall

The Powerwall system is an object of wonder. It is beautifully engineered and miraculous in its simplicity.

It transforms the utility of the solar PV allowing me (rather than electricity companies) to benefit from the investments I have made.

I will post more about the performance in terms of cost, electricity and carbon dioxide when I have more data.

But for the moment I will just thank Jozsef and Stuart from The Little Green Energy Company for their professionalism and attention to detail. And ‘No’. I am not being paid to say that – quite the opposite!

Stuart and Jozsef from The Little Green Energy Company. You can’t see it, but they assure me they were both smiling. Click for a larger version

 

Domestic Batteries: Purchase decisions and realistic models

Friends, earlier this week I ordered a Tesla PowerWall 2 from the charming people at The Little Green Energy Company (TLGEC). They have given me a nominal installation date in late March 2021 and I will be sure to keep you updated.

So in my excitement I wrote another article about using batteries – and you can read it at length below. But AFTER I had spent hours calculating and graphing , I realised something very obvious but very profound.

• The triple-glazing and external wall insulation have been ‘green’ investments. They avoid the need to burn fossil fuels.
• The solar panels have been a ‘green’ investment. They produce low-carbon electricity.
• The heat pump (when I install it) will be a ‘green’ investment. It will avoid the need to burn gas to heat the house.
• But the battery is a financial investment. It will actually use extra electricity! However, it will lower the cost to me personally of making the ‘green’ investments.

My aim is to transition away from burning gas by using a heat pump. This switch requires me to use more electricity each year and without the financial savings that a battery yields this would be punitive.

More battery modelling: but using a climate re-analysis database!

I chose TLGEC over other installers because of their willingness – and ability – to answer tricky questions. And in one of their answers they gave me a jewel of link to this EU funded site with useful information about solar PV.

The site can be used like others to estimate the monthly generation from a solar PV installation. But unlike other sites the predictions are based on actual solar data over the period 2005-2016.

And uniquely – by using climate re-analysis –  it is possible to download this data for any location on Earth (!) to simulate hour-by-hour how a particular installation of panels would respond at any time during that period.

Click for a larger image. This web portal is available here.

This has enabled me to create models simulating the interaction of solar panels with a domestic battery similar to those I made previously. But instead of:

• a minute-by minute model of a single day using simulated solar data,

I can now make…

• an hour-by-hour model of an entire year using actual solar data.

Crucially this incorporates real-world (hour-to-hour and day-to day) variability which is one of the difficulties in trying to optimise the use of a battery.

The Model 

The Excel™ model (Solar Time Series Analysis 2005 – 2016 for Blog) is based (unsurprisingly) on a Tesla Powerwall 2 with 13.5 kWh of storage, but that can be changed in the file. Please note – this is not a simple model and is set up just for my panels in Teddington! If you want to use it for your site you will need to download data from the web portal above and place it in the spreadsheet.

The model has the following ‘features’ (default values shown in brackets)

1. The electrical demand can have separate daily peak (1 kW) and off-peak (0.5 kW) values.
2. The overnight charging rate can be changed (3 kW)
3. The fractional filling of the battery in the morning can be changed seasonally between a summer value (100%) and a winter value (100%).
4. The range of the ‘summer’ and ‘winter’ seasons can be defined (summer runs from day 60 to day 300)

The model evaluates:

• The state of the charge of the battery hour-by-hour through the year,
• The amount of peak and off-peak electricity which must be purchased to meet the required demand.
• The amount of solar generation and the amount used on site, or exported.
• The costs of different strategies.

One shortcoming of the model is that the 1-hour step is too long and so in some situations the model appears to overfill or underfill the battery. However I think the uncertainty this adds is relatively small.

The Parameters

I set the model to run with data both from individual years and from the average behaviour of all 12 years of data.

The demand I modelled was 0.5 kW overnight and 1 kW during the day. This is more than our house uses at present but is in line with the demand I expect when I install a heat pump to replace the gas boiler.

The model calculates the amount of electricity bought from the grid in both peak and off-peak periods and evaluates the fraction of demand met by solar electricity, and the cost.

I then investigated how different settings for the morning filling of the battery affected:

• the amount of electricity bought from the grid (peak and off-peak) over the year,
• the fraction of demand met by solar electricity,
• the cost.

Typical Runs

The graph below shows the simulated State of Charge (SoC) of the battery during days 1 to 30 of the year 2016 i.e. January 2016.

Click for a larger view.

The graph shows daily overnight charging of the battery to 100% in the morning. The 1-hour time resolution of the simulation makes it appear the battery does not quite completely fill up, but it gets close.

The 1 kW daytime load then drains the battery completely on most days – the SoC reaches zero – and so some full price electricity must be bought.

However, there are a few days (e.g. days 7 & 8 and days 13 to 16) even in January in which strong sunlight fills the battery sufficiently that it lasts to the end of the day. These would typically be cold, crisp, clear winter days.

To indicate the variability, the equivalent graph for the year 2011 is shown below.

Click for a larger view.

But if we plot the average data from 2005 to 2016 we see it has a different character from that for individual years. Instead of the 3 or 4 bright sunny days, we have – on average – a little bit of sunshine on many more days.

Click for a larger view.

This difference between individual years and their average is important in this case, because it the intermittency of solar generation that makes a battery useful, and it is the irregularity of solar generation in any one year that makes it hard to optimise the use of a battery.

A whole year of averaged data is shown in the graph below. I have used average data to illustrate the general characteristics of the behaviour of the battery.

Click for a larger view.

In this graph the battery is charged each night to 100% SoC. In the winter it discharges through the day and the SoC reaches zero before the end of the day, requiring full price grid electricity to tide the household over to the end of the day and the start of cheap electricity.

But between days 60 and 300 there is enough solar generation – on average – such that the battery does not ever fully discharge at the end of each day. Thus in this period is not really necessary to fully charge the battery overnight.

The graph below shows the effect of only charging the battery to 70% in the mornings over this ‘summer’ period.

Click for a larger view.

The result of this is that less night-time electricity is used, and less electricity is exported. Consequently, the ‘self-use’ of solar electricity increases. However, there are now a few more occasions during the ‘summer’ when the  SoC reaches zero before the end of the day i.e. where full price electricity must be bought.

The graph below shows the same partial-charging strategy (only 70% between days 60 and 300) but using data for the year 2011: notice that the irregularity is much greater than when looking at the averaged data.

Click for a larger view.

So how does one make sense of all this? I do not want to spend my entire life optimising battery charging!

Basic Results

There are too many variables to succinctly summarise the modelling results, so here I will just summarise one investigation relevant to my own situation.

Imagining that I am running a heat pump to replace the gas boiler, I have assumed overnight use at 0.5 kW and daytime use at 1.0 kW. This amounts to 21 kWh/day or 7665 kWh/year. Due to the limited time step, the model calculates annual use as 7661 kWh – which is an error of 0.05%.

Using the solar data for each individual year – and for the average of all the years – I calculated how self-use of solar power varied as I changed the state of charge (SoC) of the battery in the morning from 0% to 100%.

By ‘self-use’ I mean that the solar electricity was either used immediately at the house or stored in the battery for later use. Nominally either of these uses is ‘free’, but in reality the storage and retrieval is only around 90% efficient.

Result#1

First of all looking at solar data from each year 2005 to 2016 I calculated that on average the panels would generate 3847 kWh/year with a standard deviation of about 5%. The average value is same as is calculated from just using the average 2006-2016 datset

Click for a larger view.

The solar generation is only around half of the anticipated demand (see below). And without a battery, most of that is exported at a relatively low price (1.8 p/kWh from EDF). This benefits the planet and EDF, but means I still have to pay EDF 23.7 p/kWh for peak time electricity to operate the heat pump.

Click for a larger view.

Next – using the solar data for each individual year – and for the average of all the years – I calculated how self-use of solar electricity varied as I changed the state of charge (SoC) of the battery in the morning from 0% to 100%.

Click for a larger view. The graph shows the number of units of solar electricity (kWh) that would have been used on site.

If we pick one year (say 2014) as an example, we that in this sunnier-than-average year, charging the battery to about 30% SoC in the morning leaves plenty of capacity to store solar electricity during the day.

In a more typical year (say 2016) the optimum morning SoC is between 40% and 50%.

• Higher morning SoC results in solar generation being ‘lost’ to export.
• Lower morning SoC will give rise to earlier discharge of the battery and the use of more mains electricity.

Curiously, the optimum morning SoC for any individual year (30% to 60%) is quite different from that calculated from the average of all 12 years. This is because of reduced irregularity in the averaged data.

The difference between self-use calculated from data for individual years and the self-use calculated from the average data is even more striking if we show each year’s result as a fraction of that year’s total generation.

Click for a larger view. The graph shows the fraction of total solar generation (%) that would have been used on site for each year.

We see that we might hope to get around 90% of self-use in any individual year with a morning SoC of around 40%. This is much lower than the 98% which appears possible using averaged data.

Results: Economics 101

As I whiled away happy hours with Excel I became fascinated by different possible strategies. And I filled my head with clever calculations that I might attempt.

But then I realised that none of these strategies affects the carbon reduction I achieve by installing solar panels. This happens with or without a battery and is independent of the charging strategy I adopt!

• What these charging strategies affect is who gets the benefit!

If I export electricity at low cost (1.8 p/kWh in the case of EDF) and am then forced to buy electricity later in the day for 23.7 p/kWh (EDF) then it is EDF who gets the benefit of my investment.

Financially, the optimum strategy arises from the differences between night-time and day-time electricity, and the price paid for exports. I have illustrated this for two ‘tariffs’ below – those from EDF and those from Tesla – who have a deal with Octopus.

Click for a larger view.

If I simply bought the electricity from EDF without solar panels, then the annual cost would be just over £1600.

The solar panels should reduce this cost substantially. The investment of £4200 in the solar panels should generate a saving of around £500/year, a 12% return on investment.

The battery should lower the annual cost much further. The savings generated by this £10,000 investment should be more than £800/year.

• Using the EDF tariff, the big difference between the price of day-time and night-time electricity makes it always preferable to have a morning SoC as high as possible, thus minimising the possibility of ever having to use full-price electricity.
• Using the Tesla tariff – the morning SoC doesn’t matter because there is no time-of-day price difference, and no difference in price between imports and exports.

But using either tariff, I calculate the savings to be massive. So large in fact that I just can’t believe them! The battery should be installed in March and I will let you know how it goes!

Of course I could also lower the cost by switching from EDF. I checked with Octopus energy (link) and it listed 80 different tariffs. Eighty! Enough for 10 octopuses to each have a tariff for each leg.  I absolutely detest this confusopoly. In any case the cheapest night time price was around 11p. Hopefully with the battery I will be able to subsist mainly on EDF’s night-time tariff.

Summary

So after all that work, I realised something very obvious but very profound. As I said at the top the article:

• The triple-glazing and external wall insulation have been ‘green’ investments. They avoid the need to burn fossil fuels.
• The solar panels have been a ‘green’ investment. They produce low-carbon electricity.
• The heat pump (when I install it) will be a ‘green’ investment. It will avoid the need to burn gas to heat the house.
• But the battery is a financial investment. It will actually use extra electricity! However, it will lower the cost to me personally of making the ‘green’ investments.

Solar Power in Teddington

 

New houses being built on Railway Road, Teddington

Some new houses are being built on Railway Road, Teddington, at the back of my home on Church Road. The houses are being built  on a site which used to house garages, which themselves were put there in the place of houses destroyed by bombs in World War II. Searching on line I found this photograph which shows houses around 5 doors down from the bomb/building site. So much for the local history.

What I actually wanted to comment on was the fact these not very luxurious houses ALL have large expanses of solar panels built in.

 

Solar Panels on the roof of new houses in Teddington

Now these panels face west and this is not a superb site for solar panels. But I just wanted to comment on the fact that it is now part of normal building practice to put solar panels on new houses. Fifty years ago, when solar  panels were developed for spacecraft, only a zealot or a visionary would have suggested that this would become the orthodoxy. But it has, and we are living in that future now – where people build solar panels into modest houses in Teddington. And I mention this just to reinforce my faith that things do change. And that the world tomorrow can be different and better than the world today.  And who knows what will become the orthodoxy in 50 years from now?