Archive for the ‘My House’ Category

Domestic Thermal Storage 2: Phase Change Material

July 23, 2022

Friends, this is the second of three articles in which I am comparing three different types of thermal storage.

In the last article I looked at the humble domestic hot water (DHW) cylinder, and in the next article I will look at large thermal stores. Here we will look at the use of a phase-change material (PCM) to store heat.

In practice a PCM thermal store looks like a regular ‘white goods’ metal box and is typically placed wherever the domestic hot water (DHW) cylinder would have been in a dwelling.

Click on the image for a larger version. Publicity images from the Sunamp web site demonstrating the small physical size of their PCM thermal stores.

But a PCM thermal store has a big advantage over a DHW cylinder: it is typically one third to one half the size for the same amount of thermal storage. Dimensions are typically 1 metre high, 60 cm deep and 40 cm wide.

Click on the image for a larger version. On the left-hand side is a commercial PCM thermal store. On the right-hand side is a schematic explanation of how it works. In this versions of the device, the PCM material is charged using an electrical immersion heater. In other versions it can be charged using a heat pump. In operation, cold water flowed into the device is rapidly heated and discharged.

Additionally a PCM store is cubical, and so makes use of the corners of spaces that DHW cylinders – being cylindrical – can’t use.

Functionally it works like a DHW cylinder. When a tap is opened, cold water flows into the device and is heated as it flows through pipes embedded in the hot PCM material – and hot water flows out.

However, the PCM thermal store has a trick up its sleeve. If the PCM stored heat in a substance at high temperature, then the temperature of the substance would have to be high initially – with high losses – and the storage medium would cool as heat was withdrawn.

PCM thermal stores get around this by using a material which melts – typically at around 55 °C to 60 °C.

  • Charging the PCM involves heating it up to its melting temperature, then supplying the so-called ‘latent heat’ required to change it from one ‘phase’ (a solid) to another ‘phase’ (a liquid). It is then heated further as a liquid.
  • When cold water flows through pipes embedded in the PCM, the PCM cools and freezes around the pipes. When it freezes it stays at its freezing temperature releasing its so-called ‘latent heat’ until the entire charge of of PCM has solidified.

In practice this means that one gets the benefits of a DHW cylinder in a smaller space. PCM thermal stores are particularly well-suited to smaller single-person dwellings.

PCM’s: Home experimentation

A common PCM with which you can experiment at home is candle wax.

While my wife was out at work, I put two candles into a glass container and melted them (one at a time) by putting the container in a jug of boiling water.

Click on the image for a larger version. Top-Left: Melting a candle in a jug of hot water. Right: A partially melted candle.Bottom-left: Measuring the temperature as the molten wax cooled.

When both candles were melted, I put a thermocouple into the wax, wrapped insulation around the glass vessel and then measured the temperature as the molten wax froze – i.e. changed ‘phase’ from liquid to solid (to use the technical terms). The data are shown below:

Click on the image for a larger version. The graph shows the temperature of a thermocouple embedded in 55 g of wax as it froze. Note that there is a sharp change in cooling rate when the wax starts to freeze due to the release of so-called ‘latent heat’. This allows the wax to stay above 50 °C for almost 3 hours, while if it had continued cooling at the initial rate, it would have fallen below 50 °C in under 1 hour.

What one sees is that as the molten wax cools, it looks like it will fall below 50 °C after about 50 minutes. However, once the wax starts to freeze (at about 57 °C), the cooling rate is reduced to roughly one tenth of its previous rate, and the liquid/solid mixture stays above 50 °C for around 160 minutes.

Using a very rudimentary analysis based on googled data:

  • Heat Capacity of wax ~2.5 J/g/°C – assumed the same in liquid or solid state;
  • Latent Heat of wax ~176 J/g;

…one can roughly estimate how much heat is released at temperatures above 50 °C.

Click on the image for a larger version. Analysis of cooling curve in the previous graph allows an estimate of the amount of heat released at temperatures above 50 °C. The latent heat of 55 g of wax amounts to just under 10,000 joules.

Although I had followed the golden rule of experimental physics, I still failed to anticipate just how long it would take the wax to solidify – the experiment took 4 hours and I was almost late preparing my wife’s dinner!

This extended experiment indicates just how much ‘latent’ heat a material can store compared with ‘sensible’ (i.e. sense-able: which can be detected with a thermometer) heat storage.

Based on the latent heat alone, 100 kg of wax – which would occupy a cube with a side of 50 cm – could store 5 kWh of thermal energy – the equivalent of a small DHW cylinder.

Commercial PCM Devices

I don’t know, but I am pretty sure that commercial PCM devices do not use wax as a storage medium.

Update: A Twitter Source tells me that the Sunamp uses “Sodium acetate tryhydrate (plus a few secret additives).”

Sunamp’s list of patents includes a variety of chemicals which can be used, but the particular chemical used and the way it is prepared is likely a trade secret. Nonetheless, I suspect their basic properties are not so different from wax.

They will have a phase change temperature ideally around 55 °C. If the phase change temperature is much higher than this, then the store will operate at too high a temperature and lose more energy. If the phase change temperature is much lower than this, then water will not be sufficiently hot when discharged.

Early models of the PCM stores were designed to be ‘charged’ electrically with a heater immersed in the PCM material. This could be powered either from the grid – ideally using off-peak electricity – or from solar PV panels. However recent versions can also be charged using a heat pump.


PCM thermal stores  represent a clever way to incorporate thermal storage in dwellings where space is at a premium. They are particularly useful in flats and households with just one or two people.

However, like all thermal storage devices, they are not perfect.

One disadvantage is that unlike a DHW cylinder, the storage medium has to ship with the device – it can’t be shipped empty. This makes the devices heavy: A PCM store equivalent to a 200 litre cylinder weighs ~ 172 kg. Of course a DHW water cylinder holding 200 litres of water would weigh more – but it can be filled and emptied in place!

Heating losses are similar to DHW cylinders – with roughly 10% of the stored energy being lost each day – and like DHW cylinders, it can be tricky to know how ‘full’ the store is because it can be difficult to work out what fraction of the PCM material is liquid or solid.

But all-in-all, the PCM thermal stores devices seem to have found a niche where they can make themselves genuinely useful.

Domestic Thermal Storage: Part 1: Hot Water

July 23, 2022

Friends, writing about the ‘Sand Battery’ fiasco the other day brought to mind smaller thermal stores that are used domestically. And so I thought it would be interesting to write about the physics of thermal storage.

But it has all got out of hand and now this this is the first of three articles over which I will compare three different types of thermal storage, one most people are familiar with, and two that are less familiar:

  • A domestic hot water tank.
    • This stores thermal energy in water which is then used directly within a household.
    • A typical Domestic Hot Water (DHW) cylinder stores between 7 kWh and 10 kWh of thermal energy.
  • A phase-change thermal storage device.
    • This stores thermal energy in the so-called ‘latent heat’ of a material which absorbs thermal energy when it is melted, and releases it at a constant temperature as the material freezes.
    • A typical Phase Change Thermal Store stores between 4 kWh and 8 kWh of thermal energy, comparable with a DHW cylinder, but requiring only approximately half the volume.
  • A Zero Emission ‘Boiler’.
    • This stores thermal energy in the heat capacity of a ‘thermal core’ – a cylinder of concrete weighing ~300 kg – which is heated to an astonishing 800 °C.
    • This can store up to 40 kWh of thermal energy.
  • A ‘big thermal store’.
    • Like a Zero Emission Boiler, but heavier – and ‘only’ heated to 500 °C.
    • This can store up to 100 kWh of thermal energy.

Click on the image for a larger version. Schematic illustration of four different types of thermal storage devices and a human being for scale.

The key role of all these devices is to separate two events:

  • The time when energy is consumed from a central resource – such as the electricity grid,
  • The time when energy is used domestically – such as when you take a shower.

Separating these events has two benefits:

  • It allows users to store thermal energy slowly but to release large amounts of thermal energy quickly – such as when you need a flow of hot water ‘instantly’.
  • It allows users to store thermal energy when it is cheap or convenient .

For each device we need to consider how it is heated (‘charged’) and how it passes on its stored heat (‘discharged’).

In this article we will look at how a domestic hot water (DHW) cylinder works and in the following articles we will look at how Phase Change Material Stores works and how Zero Emission Boilers and big thermal stores work.

Domestic Hot Water (DHW) Cylinder

When I first heard a DHW cylinder described a ‘thermal store’, I was initially confused. I had always considered them as storing water!

In the other thermal stores, heat is first stored in a material, and subsequently transferred to circulating water or DHW only when it is required. In a DHW cylinder the storage material is the water which will itself later emerge from a tap.

The amount of stored thermal energy can be estimated as the product of:

  • The volume of water in the tank
  • The heat capacity of water in the tank (4,200 J/°C/litre)
  • The difference between the storage temperature and the charging temperature.

For a 200 litre tank storing water at 55 °C which has been heated from 20 °C this amounts to ~29 MJ or 8.2 kWh.

One can store more energy in a cylinder of a given size by storing water at a higher temperature: at 75 °C the stored energy in the cylinder above would be 12.8 kWh. To prevent discharge of scaldingly hot water, a blending valve would be used on the top of the cylinder and set to (say) 50 °C.

Click on the image for a larger version. Schematic illustration of the structure of a DHW cylinder showing the internal coil for heating the stored water. On the right is a manufacturer’s illustration of the coils within their cylinder.

A DHW cylinder can be charged in one of several ways.

  • In the simplest way, an electrical heater immersed in the water heats the water directly. A 3 kW heater can charge a 200 litre cylinder to 55 °C in just under 3 hours. The heater could be powered by either grid or from excess solar PV.
  • Alternatively, hot water heated by a gas boiler or a heat pump can be flowed through a coil inside the cylinder, passing on its heat to the stored water. The rate of heating in this method will generally be slower than using an immersion heater.

Discharging the cylinder is simple: one opens a tap and the mains water pressure forces water out of the top of the cylinder replacing it with cold water at the bottom.

The rate of discharge of thermal energy is given by the product of:

  • The discharge flow rate (litres/second)
  • The heat capacity of water in the tank (4,200 J/°C/litre)
  • The difference between the storage temperature and the charging temperature.

So if 10 litres of water at 50 °C is discharged per minute, thermal energy is being released at a rate of 21 kW. This is a very high rate of energy use.

‘Combination boilers’ can provide this very high heating rate, but only at the cost of releasing (at the specified flow rate) around 0.1 kg of CO2 for each minute of operation.


One of the difficulties with a DHW cylinder is that natural convection within the cylinder causes the hot water to rise to the top. And the stratification within the cylinder can be very dramatic.

Since most cylinders have only a single thermometer somewhere in the middle of the cylinder, even after reading the thermometer it is difficult to know how much heat is currently stored in the cylinder.

Additionally since the heating coil or immersion heater is typically in the lower third of the cylinder, practically the whole cylinder must be re-heated before any sufficiently hot water is available at the top of the cylinder – which typically takes several hours.

Some modern cylinders made by the Mixergy company exploit the stratification by heating the water from the top and then carefully mixing it with the colder water below.

These computer-controlled cylinders can give a reasonable estimate of the state of charge of the cylinder, and also allow rapid heating of small volumes of water at the top of the cylinder. However, I don’t understand precisely how the technology works.

Update: This video gives a clear – if rather glossy – explanation of how the system works. It turns out that Robert Llewelyn was given one as part of a research study!

Click on the image for a larger version. The water in a conventional DHW cylinder is hotter at the top but the temperature gradient from top to bottom is not well-defined. More modern computer-controlled cylinders from the Mixergy company can precisely control the location of the temperature gradient.

Heat Losses 

A DHW cylinder holding 200 litres is typically 1 metre high with a diameter of 50 cm and insulated with 50 mm thick layer of polyurethane foam with a typical thermal conductivity of 0.025 W/°C/m.

Click on the image for a larger version. Heat losses from a DHW cylinder are typically 10% of the stored energy per day.

For a cylinder at 55 °C, this leads to a heat loss of roughly 35 watts, or 0.85 kWh/day. i.e. the cylinder loses about 10% of its stored energy per day.

This loss rate increases if the water is heated to a higher temperature. For a cylinder at 75 °C the loss rate is ~ 55 watts or 1.32 kWh/day – again, about 10% of its stored energy per day.

The only way to reduce the heat loss is to apply either better insulation (which is expensive) or to apply a thicker layer, which makes the cylinder larger.


A DHW cylinder holding 200 litres is a simple way to store hot water for use around the house.

In the context of renewable energy, it allows a heat pump with a COP of 2.5 to use perhaps 1.5 kW of electricity for 2 hours (3 kWh) to fully charge a cylinder with ~8.5 kWh of thermal energy. This can then be discharged at 10 litres per minute i.e. releasing stored energy at a rate of 21 kW.

The downsides of a DHW cylinder, (large size, 10% leakage per day, unknown temperature gradient within the tank) are generally considered acceptable.

But there are alternatives and we will look at one of these in the next article.

Our Climate Crisis: Bringing it all back home

July 12, 2022

Friends, I have just returned from a holiday on the South Coast in the ancient town of Winchelsea.

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It was a lovely break, but it was not all crazy golf and castles. I also took a day off to come back to London to give a talk to some 6th formers about climate change.

I thought that possibly some other people might be interested in the presentation and so the other day I sat down in front of my television and talked my way through the slides.

The school presentation was 45 minutes long, but given the liberty of time, the video version is  slightly longer.

In the first half of the talk – video 1 (23 minutes long) – I look at the nature of our climate crisis and the urgency of the need for action. I thought the presentation of the effect of carbon dioxide in the atmosphere was quite novel – unusual when covering something I have talked about so many times. But writing the slides I was shocked again at just how bleak our situation is.

In the second half of the talk – video 2 (35 minutes long) – I explain how the way in which we use energy in our homes gives rise to carbon dioxide emissions – typically more than 3 tonnes per household. I then point out that thankfully we have the technology to reduce emissions dramatically without any loss in quality of life. And I conclude by pointing out that throughout their lives there will be many career opportunities for these teenagers to take part in the grand challenge of limiting the damage from Climate Change.

Powerpoint File

Powerpoint File  (50 Mb!)

Video 1

Video 2



“Off-Grid” or Not “Off-Grid”? That is the question.

May 26, 2022

Friends, it’s May, and slightly later than last year, our house is now ‘Off-Grid’.

Click on image for a larger version. Graph shows the daily household consumption of electricity (kWh) since the March 2021. Also shown is the amount of electricity drawn from the grid (kWh). Both quantities are averaged over ± 1 week.

By ‘Off-Grid‘ I mean that the combination of…

  • 15 kWh/day of solar electricity, and
  • 13.5 kWh of battery storage in our Powerwall,

…is enough to allow us to…

  • consume 10 ± 2 kWh/day of electricity and
  • export on average 6 kWh/day

…without having to draw any electricity from the grid. Almost


On the graph above it looks like in this happy situation, we draw zero electricity from the grid.

However, if one looks closely one can see that electricity usage is low, but not quite exactly zero.

The figure below shows half-hourly electricity usage (watts) over 4 consecutive days in May. This data was acquired using the highly pleasing Powershaper software.

Click on image for a larger version. Chart showing electricity used by the Tesla Powerwall throughout 4 consecutive days in May 2022. Averaged over half-hour periods through the day, the Powerwall draws around 1 watt, but occasionally draws as much as 20 watts. Over a day it adds up to less than 0.1 kWh costing between 1 and 2 pence.

I don’t know why the Powerwall is doing with this: it typically has a battery filled which electricity which it could use!

My guess is that it uses the grid to help it meet transient demands. I suspect that if we could look more closely then we would see that rather than consuming 1 watt continuously, it would instead be consuming no power most of the time, but then occasionally it would a draw a kilowatt or so for just a second or so.

The software that controls the battery does have a ‘True’ Off-grid mode which apparently would isolate the house completely from the grid. But in honesty, I have been too scared to push the button!

Being ‘practically off-grid is enough of an adventure for me.

Update: 26 May 2022

The 9-minute video below explains the effect I am describing with admirable simplicity.

First Winter with a Heat Pump

April 27, 2022

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.

Could you heat your house with a hairdryer?

April 12, 2022

Click the image for a larger version. The graph shows the average electrical power (in kW) used by our heat pump to keep the 164 square metres of Podesta Towers at approximately 20.5 °C throughout the winter.  Also shown is the typical power used by a hairdryer on typical high, medium and low powers.

Friends, a chance remark on the internet intrigued me.

Someone commented that their heat pump was heating their house using less power than a hairdryer. Could that really be true?

Looking it up (link), I found that a hair dryer actually uses rather more power than I had supposed: somewhere between 850 watts (0.85 kW) and 1850 watts (1.85 kW) depending on its power setting.

I then looked up week-by-week data for our heat pump at Podesta Towers.

And slightly to my surprise I found that even in the coldest weeks, the average electrical power used by the heat pump was less than 800 watts (0.8 kW) i.e. we were heating our house with less electricity than it takes to run a hairdryer – on its lowest setting! And that includes re-heating the hot water tank each day!

So why didn’t I just buy a hairdryer?

Why? Because a hairdryer – even on full power – could not heat my house.

The wonder and fascination of heat pumps is that they don’t just squander the electricity they consume: they use it to scavenge heat from the outside air and even on the coldest days they can deliver many times more heat energy into the house than the electrical energy they consume.

The ratio of the heat energy they deliver to the electrical energy they consume is called the Coefficient of Performance (COP) and for my heat pump the average COP since installation is 3.6.

In other words the heat pump has delivered more energy than two hairdryers on full power while consuming less energy a single hair dryer on low power.


The graph below shows the COP evaluated week-by-week and the average value since August 2021.

Click the image for a larger version. The graph shows the average coefficient of performance (COP) week-by-week since installation in August 2021. Also shown in the average coefficient of performance (COP) since installation, also known as the Seasonal Coefficient of Performance (SCOP).

The low average values in the autumn are because the heat pump is only delivering domestic hot water at 55 °C and is not heating the house at all.

During this time, the 20 watts of electrical power that the heat pump’s computer consumes (0.5 kWh/day) represents a significant fraction of the energy delivered.

In contrast, in winter the heat pump is delivering more than 20 kWh of heat energy per day and the consumption by the heat pumps’ control circuitry is less than 3% of the heat energy delivered.


I found this juxtaposition intriguing. 

A hair dryer is a simple device – a hand-held fan heater – and a heat pump is a much more complex machine.

But comparing them just by their electrical consumption highlights the awesome power of heat pumps.

March 2022

April 8, 2022

Friends, Spring is springing, and our first winter with a heat pump is ending.

Overall, it has been phenomenally successful. All the parts of our refurbishment have played their part.

  • The triple-glazing and external wall insulation have reduced the heating power required to heat the house.
  • The solar panels continued to deliver ~5% of our electricity requirements even in December.
  • The battery (a 13.5 kWh Tesla Powerwall) allowed us to download cheap electricity at night and use it to heat the house during the day.
  • The heat pump kept the house warm and delivered hot water, with an average Coefficient of Performance of around 3.5.

In this article I will be looking at figures for the month of March 2022.

When the heating season is a little more over than it is at present, I will write about the winter as a whole.

Solar PV and Battery

Click image for a larger version. This is on the notice board outside my house.

I have put a notice on the front of the house to advertise how little we are spending on heating and running the house. Excluding the standing charges, we spent just £14.34 heating the house and running all the electrical items in the house.

In honesty, I am embarrassed to disclose how little I am spending on fuel bills. I am embarrassed because of the suffering and anxiety that so many people will be feeling now as prices rise.

Nonetheless, when it comes to communicating the wonder of a well-insulated home powered by solar, talking about money is one way to communicate more viscerally than using kilowatt-hours and kilograms of carbon dioxide.

Energy Flows

Click image for a larger version. This graphic shows my best estimate of the energy flows around my house. There are two sources of electricity: the grid and the solar PV system. During the hours when grid electricity is cheap, the grid supplies the house directly and charges the battery. Solar PV supplies the house directly, then if household demand is met, it charges the battery, and if the battery is full, it exports electricity. My analysis suggests that the battery is only 87% efficient i.e. 13% of the energy is lost in the process of charging and discharging the battery.

The graphic above describes the energy flows in the house.

On a typical day:

  • Between 00:30 and 04:30 the house runs on cheap grid electricity, and we time the dishwasher and hot water heating to run over this period. The grid also charges the battery.
  • After 04:30 the battery runs the household and is then re-charged during daylight hours by whatever solar PV is available.
    • If the battery charge reaches 100%, then solar PV is exported.
    • If the battery discharges to 0%, then we run off full price grid electricity.

Analysing the data from the Tesla App, it looks like the battery returns 87% of the charge delivered to it. The system is specified to have a charge/discharge efficiency of 90%. I suspect that extra losses arise from the energy the battery uses to maintain its own condition.

The figure below shows the average pattern of grid use during the month. The majority of electricity is used during the cheap rate period and only a small fraction of full-price electricity is required on days when solar PV generation is insufficient to keep the battery topped up.

Click image for a larger version. This graphic shows the time of day at which the house drew electricity from the grid in March 2022. The vast majority of the electricity was consumed at night to (a) charge the battery and (b) directly operate timed loads such as the dishwasher, washing machine, and heat pump domestic hot water cycle.

Heat Pump

Click image for a larger version. Graph showing internal and external temperatures, and the temperature of water flowing in the radiators during the month of March. Data were collected every 2 minutes. The radiator flow temperature data has been smoothed. It is clear the system operates well to keep the internal temperature constant even as the external temperature varies

The average external temperature was 9.3 °C, but the month started very cold, and then later there were some exceptionally warm days (with cold nights).

The weather compensation adjusted the flow temperature in the radiators to keep the internal temperature at a comfortable average of 21.1 °C

The monthly averaged Coefficient of Performance was 3.75 which is rather more than I had hoped for.


When we installed the battery in March 2021, we immediately dropped of the grid for 90 days: this felt astonishing. But back then then our heating was with gas.

Now our heating and hot water systems are electrical and this adds to the daily load.

As the year progresses, Solar PV generation is growing and heating demand is falling. At some point I hope we will again be able to reduce grid use to zero for an extended period – but it will definitely not be as long as last year.

It was interesting to arrive at a figure for the battery storage efficiency. The figure of 87% was lower than I had hoped for, but since the battery is saving us so much money, it seems churlish to complain!



What Size Heat Pump Do I Need? A Rule of Thumb

April 5, 2022

Friends, a few weeks ago I wrote four articles about using the idea of Heating Degree Days to make simple calculations about heat losses from one’s home.

  • Article 1 was an introduction to the idea of Heating Degree Days as a general measure of the heating demand from a dwelling.
  • Article 2 explained how and why the idea of Heating Degree Days works.
  • Article 3 looked at the variability of Heating Degree Days across the UK, at locations around London, and from year to year.
  • Article 4 introduced some rules of thumb for estimating the Heat Transfer Coefficient for a dwelling and the size of heat pump it requires.

The Rule of Thumb for Heat Pump Sizing is dramatically simple:

The video above is about using these ‘Rules of Thumb’.

I feel these rules could be helpful to both heat pump installers and their clients.

The Powerpoint slides (.pptx) I use in the presentation can be found here.






Analysis of 16 years of Solar PV data.

March 16, 2022

A friend from North London kindly allowed me to analyse the data they had collected on the performance of their solar PV installation over the last 16 years.

What an opportunity to discover how solar PV panels behave over the long term!

Let me tell you what I found:

The System

Installed in July 2006, the system consisted of 16 Sanyo PV panels, each 0.88 m x 1.32 m with a nominal peak output of 210 W. This implies the panels output was initially ~180 watts per square metre.

They were installed on two adjacent roofs with a tilt of about 30° and facing 25° East of South and with no nearby trees or shading structures on the horizon other than their neighbour’s house.

The data set consisted of roughly 700 readings of the solar generation meter, most of them taken weekly but with a couple of gaps for a few months, and few points that were clearly in error. Rather than try to be sophisticated, I simply omitted points that were obviously in error.

Click image for a larger version. The ‘cleaned up’ data set.

Annual Analysis

One of things I was most anxious to search for was evidence of a year-on-year decline. The annual results are shown below:

Click image for a larger version. Graph of the Annual Output (kWh) of a North London PV system from 2006 to 2021. The dotted line is a linear fit to the data showing a systematic year-on-year decline in output.

It’s clear that there is a systematic year-on-year decline. If we re-plot the data to express this as a percentage we can compare it with what we might expect.

Click image for a larger version. The same data as in the previous graph but expressed as a fraction of the average output over the years 2007 and 2008. The dotted line is a linear fit to the data showing a systematic year-on-year decline in output.

This decline is – sadly – inevitable, arising as I understand it from atomic defects created in the silicon cells by exposure to the UV radiation in sunlight. These defects trap electrons which would otherwise reach an external contact if the crystal had been undamaged.

A decline of 6.1% per decade (0.61% per year) is quite competitive. Older panels showed higher declines (link) and more modern cells claim better performance, but not much better.

For example a 2020 Q-Cells Duo panel (link) specifies 0.54%/year decline for up to 10 years,  i.e. 5.4% per decade.

Click image for a larger version. Extract from a Q-cells data sheet showing expected decline in panel output over 25 years.


In addition to a linear decline in output the data also shows significant year-to-year variability. I wondered whether this variability arose from the natural variability of available sunshine, or some other factor.

To check this I exploited the EU Photovoltaic Geographical Information System (a.k.a. a ‘Sunshine Database’) which allows the calculation of the output of PV cells at any point in Europe or Africa over the period 2005 to 2016.

I had previously used this database to model the year-to-year variability of sunshine in West London when I was planning a battery installation.

To see if this was the cause of the year-to-year variability I plotted two quantities on the same graph:

  • The so-called ‘residuals’ of the fit to the data in the second graph above.
  • The variability of EU-database data.

The results are shown below.

Click image for a larger version. The variability of the North London PV data and the natural variability of sunshine as retro-dicted by the EU sunshine database

It is clear that in the years for which the two datasets overlap they agree well, suggesting that the variability observed is not due to some other poorly understood factor.


My North London friend had one final question. Would they avoid more carbon dioxide emissions if they upgraded to modern panels?

To answer this I made two models:

  • The first model assumed that they did not upgrade and the existing panels were used to out to 2050.
  • The second model assumed they were replaced in 2022 with panels which operated with an efficiency of around 200 W/m^2 at peak illumination. This is about 20% more than the panels currently generate.

I assumed that the new panels would embody around 2 tonnes of CO2 emissions because Q-cells suggest their latest panels embody 400 kgCO2 per kWp.

I then assumed that 50% of the generated electricity was exported and 50% used domestically. As the grid currently functions:

  • Exported electricity reduces gas-fired generation which emits 450 gCO2/kWhe.
  • Domestic use avoids consumption of grid electricity with a carbon intensity of around 220 gCO2/kWhe in 2022.

Based on these assumptions, there is small advantage to replacing the panels, but this would not be realised until 2035.

Click image for a larger version. Does it make carbon-sense to replace existing PV cells with new more efficient cells?

One can model variations of these parameters, but the basic result is not affected: the carbon advantage is marginal.

My friend would help the climate more effectively by allocating his capital expenditure to something which might have more impact on CO2 emissions, perhaps buying shares in a wind farm?

But the result that really struck me from this modelling was how great the solar panels were in the first place!

Installed in 2006 and given minimal maintenance, it looks like the existing cells will avoid almost 30 tonnes of CO2 emissions by 2050. Not many technologies can achieve results like that as easily as that.

Heating Degree Days:3: How do they vary?

March 15, 2022

Friends, having read the previous two posts (1, 2) about Heating Degree Days, you may be wondering.

  • How carefully do I need to be in choosing the baseline temperature?
  • How do heating degree days vary around the UK?
  • How do heating degree days vary from year-to-year?

If you were wondering things, then the text below should provide the answers you seek.

Seek on!

Choice of Base Temperature

Click on Image for a larger version. The graph shows annual running average of the number of heating degree days for the London St. James Park Weather station. Each curve corresponds to the number of heating degree days with a difference base-temperature. For each degree Celsius increase in the internal temperature, the heating demand increase by approximately 260 °C-days.

The choice of the base temperature is important when estimating heating demand.

The evidence in the previous article is that a ‘rule of thumb’ for choosing a base temperature is to pick a value 3.5 °C below the internal thermostat setting is probably OK.

  • 19 °C thermostat setting: use a base temperature of 15.5
  • 20 °C thermostat setting: use a base temperature of 16.5
  • 21 °C thermostat setting: use a base temperature of 17.5

Using data from St James Park in London, each 1 °C change in base temperature changes the annual degree-day estimate by roughly 260 °C-days/year. So if we estimate an average value of HDD(17.5 °C) is ~ 2,100, then turning down the thermostat by 1 °C would reduce heating demand (and hence gas consumption) by ~260/2,100 = 12.4%.

Variability over Time

Click on Image for a larger version. The graph shows annual running average of the number of heating degree days based on a 16.5 °C base temperature for London Heathrow Airport (in black). The dotted lines show the 20-year average and ± 1 standard deviation. Also shown are the monthly degree day totals (in purple) from which the annual averages are derived.

Looking at the data from Heathrow – which has a longer HDD record than most stations

  • The average number of HDD(16.5)s is 2053 °C-days/year and the standard deviation is roughly 8%.
  • The average number of HDDs(15.5)s is 1778 °C-days/year and the standard deviation is roughly 9%.

First we notice that the difference between HDD(15.5) and HDD(16.5) is 275 °C-days/year, similar to the 260 °C-days/year that we deduced from looking at the St James’s Park data.

Considering the variability, a standard deviation of 8% or 9% suggests that once in 20 years or so one might expect winters which have 16% or 18% more heating demand.

Variability with Location

The number of HDDs varies from place to place. The figure and table below show the number of HDDs based on a 16.5 °C base temperature averaged over the last 3 years.

  • A wide swathe of southern England, from Manchester southward, has heating demand within approximately 16% of the heating demand at Heathrow.
    • i.e. in the range 2,150 ± 150 °C-days/year
  • In Yorkshire, the North East, and Central Scotland, heating demand is about 25% greater than Heathrow.
    • i.e. ~ 2,500 °C-days/year

Click on Image for a larger version. The annual number of heating degree days based on a 16.5 °C base temperature for various UK locations averaged over the 3-year period from 1/3/2019 – 28/2/2022. The data are also shown as deviations from the number of HDDs(16.5 °C) at Heathrow Airport.

Click on Image for a larger version. Summary of the results in the previous figure.

In addition to large scale variations across the UK, there are smaller variations due to local factors, notably elevation and the city heating effect.

Based on the typical decline in temperature with height (typically 6.5 °C/km) then each 100 m of additional elevation would be approximately 0.65 °C colder. This will result in additional HDDs roughly equivalent to 275 x 0.65 °C or 165 °C-days/year.

To look at the urban heat island effect, I downloaded data from 4 locations around London.

Click on Image for a larger version. The annual number of heating degree days based on a 15.5 °C base temperature 4 locations around London.

Compared to data at Heathrow, there are significant changes in heating demand, with the centre of London being significantly warmer, and Gatwick Airport – just 38 km from the centre of London – being significantly colder.

Variability Summary

The heating demand at Heathrow Airport with base temperature of 16.5 °C (i.e. a likely thermostat temperature of 20 °C) is very roughly 2,000 °C-days per year.

This 2000 °C-day/year varies by typically:

  • 10% in nearby locations depending on more or less urban heating.
  • 12% to 15% per °C change in base temperature
  • -3% to + 15% over England and Wales south of the latitude of Manchester.
  • Up to 30% as far north as Aberdeen
  • Year to year variability of ±9% with occasional excursions to ±18%

So if one could not look up the number of degree days for a particular location (which one can easily at Degree Days!) one could characterise heating demand against a base temperature of 16.5 °C as likely to be within 15% of 2,300 °C-days per year almost anywhere in the  UK.

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