In October 2020 the UK Prime Minister pledged that “Wind farms could power every home by 2030”, as reported by the BBC. While I am certain that the Prime Minister had been well advised before making such a statement, I wondered nevertheless if the numbers stack up, whether this pledge is feasible, or overly ambitious, or simply —put in his own words — an inverted pyramid of piffle.

While my earlier article “Could Wind Farms Power Every UK Home by 2030? — Energy Analysis” looked into balancing domestic energy consumption and wind energy generation, the objective of this story is to gain an understanding on whether balancing domestic power consumption and wind power generation would be possible, hence a power analysis, i.e. looking into the details and taking the PM’s claim quite literally.

The approach taken by this story is to assume that a) the domestic power consumption for the year 2030 will be at most the sum of the current electricity consumption and an electrically equivalent third of the current natural gas consumption, totalling 200TWh/annum (see preceding story), and that b) the domestic consumption and wind power generation are in equilibrium in terms of average power or annual energy — 200TWh/annum produced, 200TWh/annum consumed, at an average power of 22.83GW (the power needed to transport about 19 DeLoreans back to the future, or in more practical terms, about 10 million electric kettles).

This story uses historical data at a high sampling rate to project domestic power consumption and wind power generation for the year 2030 and analyses the resulting instantaneous power shortfall and/or overproduction. Consequently, the amount of energy storage required over one year can be derived in order to balance domestic consumption and wind power production.

To anticipate the result, in order to realise the PM’s claim for the projected year 2030 energy storage in the order of 20TWh would be needed as an indication of the order of magnitude. This energy store could be made up of about 200 million Tesla Model X Long Range batteries (100kWh), i.e. 7 such batteries each per home for all 30 million UK homes.

Domestic Energy Consumption

While the total amount of domestic energy consumed (electricity or natural gas) can be obtained from various sources, it is more difficult to find time series of consumer data from a large enough sample.

This story is based on Domestic Energy Provider — Aggregated data, “aggregated statistics at Postcode Sector level about estimates of energy consumption (from smart meter readings) at 30-minute intervals for the year 2015 in Great Britain”, made available by the Consumer Data Research Centre (see bottom of page for project reference).

The data provided include readings of about 800k meters in the UK and were used to aggregate the data further to total domestic energy consumption as a function of time at 30-minute intervals. Given the size of the sample the time series is considered to be representative of the UK domestic power consumption profile.

Domestic Natural Gas Power Consumption

It is interesting to look at the domestic natural gas consumption over a year/day, in both time and frequency domain to see the annual/daily variation of consumption.

To start with, the following charts shows the annual domestic natural gas consumption given a large sample of gas meters with an average power of 10.695GW and a total energy of 93.688TWh (with a short measurement gap at the beginning of December):

Annual domestic natural gas consumption for a subset of UK meters.

The seasonal nature is obvious: most natural gas is used for space heating with peaks in the winter and a trough in the summer; the base load is for domestic hot water while cooking only accounts for a small proportion (UK government energy consumption). Zooming in on just one month shows some weekly patterns with the weekends sticking out (12th or 19th for instance):

Domestic natural gas consumption for a subset of UK meters in April 2015.

Zooming in even further on a single day, say April 1st shows the morning and evening peaks, like the back of a Bactrian camel:

Domestic natural gas consumption for a subset of UK meters on April 1st 2015.

Another way of looking at the data is through a frequency spectrum:

Frequency spectrum of natural gas consumption for 2015

The spectral analysis shows the pronounced frequencies:

• bin 1 = 8.389GW, i.e. the annual fluctuation, i.e. winter/summer,
• bin 365 = 2.851GW, the daily fluctuation, i.e. night /day cycle,
• bin 730 = 4.623GW, the half-daily fluctuation, i.e. morning /evening.

Note that the annual amplitude is about twice of the morning/evening amplitude. The difference in energy, however, is proportional to the period, i.e. the annual energy difference is 2*365 higher.

Domestic Electricity Power Consumption

The following charts shows the annual domestic electricity consumption given a large sample of electricity meters with an average power of 2.977GW and a total energy of 26.078TWh (with a short measurement gap at the beginning of July and December):

Annual domestic electricity consumption for a subset of UK meters.

There is a seasonal nature in the electricity consumption: peak in the winter and a trough in the summer. Zooming in on just one month shows some weekly patterns with the weekends sticking out (12th or 19th for instance):

Domestic electricity consumption for a subset of UK meters for April 2015.

Zooming in even further on a single day, say April 1st shows a morning and a higher evening peak, possibly more due to cooking in the evening:

Domestic electricity consumption for a subset of UK meters for April 1st 2015.

The frequency spectrum reveals the periodicities:

Frequency spectrum of electricity consumption for 2015

The spectral analysis shows the pronounced frequencies:

• bin 1 = 0.526GW, i.e. the annual fluctuation, i.e. winter/summer,
• bin 365 = 1.028GW, the daily fluctuation, i.e. night /day cycle,
• bin 730 = 0.739GW, the half-daily fluctuation, i.e. morning /evening.

Note that the morning/evening amplitude is much higher than the annual amplitude and the daily amplitude, too.

Wind Power Generation

The UK’s Balancing Mechanism Reporting Service (BMRS) offers an online service to produce power generation data for various power sources or fuel types such as coal, gas, etc. Upon registration, an API can be used to download the same data over a wide period of time at a 10 minute sample interval which was used as an input into this study. Since the power consumption data was available at a 30 minute interval only the wind power data have been down-sampled to this common period.

First, let’s look at the generation power over the several years as a function of time which looks rather random apart from one annual periodicity and a steady increase over the years as more wind farms have been going online:

Wind power generation from 2016 to 2021.

Looking into a particular year, 2019, the chart shows:

Wind power generation for 2019.

Note, that the numerical integral of the power as a function of time ought to result exactly in the total energy produces over that year. In this case, the integral yields 46.43TWh which is much less than the government statistics of 64TWh. There must be different accounting taking place at the government, or the government figure relates to rated or installed power.

Zooming in on one month, the chart shows some periodicity:

Wind power generation for April 2019.

The daily power generation for a single day shows:

Wind power generation for April 1st 2019.

In order to find any pronounced periodicities the frequency analysis shows:

Wind power generation spectrum for 2019.

The first bin in this frequency plot is at one cycle per year and is of the order of 1.653GW which is about 31% of the average power. In comparison, the yearly peak for the year 2018 is about 2.294GW, and the one for the year 2020 about 2.203GW. The rest of the spectrum looks more like some coloured noise without any particular frequency, not even a daily variation.

Pledge Verification

As shown in the preceding story, Could Wind Farms Power Every UK Home by 2030? — Energy Analysis, the current domestic electricity consumption is at about 100TWh/annum and the domestic natural gas consumption at about 300TWh/annum.

Even though the trend is decreasing, the basis for this analysis is that in 2030 the energy consumption would be similar in the worst case, some decrease due to saving and insulation for instance, but an increase due to electrical car charging at home. The assumption here is that all energy from domestic natural gas (mostly used for space heating and domestic hot water) would be replaced with electricity used by heat pumps at an average efficiency of 300% .

This means that every unit of electrical energy is converted into 3 units of thermal energy (the feasibility of replacing the 20 million gas boilers in the UK within the next 9 years is a different question not addressed here).

Consequently, the projected domestic consumption of 300TWh/annum in natural gas could be met with about 100TWh/annum electrical energy instead. The grand total on the domestic electricity consumption would be about 200TWh/annum for the year 2030, or an average power of 22.83GW.

This could easily be matched with the same amount of wind energy per year as shown in the preceding story. When it comes to balancing power, the story is very different and we rely on the projection of current consumption and generation.

Power Projection to 2030

Since we don’t have either data on the power consumption nor the wind power production for 2030, some estimated power series are needed. The approach taken here is in several steps, first for domestic power consumption:

• use a sample year for which there is domestic power consumption data available, 2015 in this case from the aforementioned CDRC data,
• combine the electric power consumption and 1/3 of the natural gas power consumption as as a combined power consumption profile,
• scale the combined power consumption profile such that the accumulated energy yields the anticipated annual energy consumption of 200TWh.

Projected domestic power consumption for 2030 based on historical data.

In the same vein, obtain a projected wind power generation profile:

• use a sample year for which there is wind power generation data available, for instance the year 2019 from the aforementioned BMRS data,
• scale the wind power generation profile such that the accumulated energy yields he anticipated annual energy generation of 200TWh.

Projected wind power generation for 2030 based on historical data.

The general assumption here is that the profiles are assumed to be similar and statistically equivalent. The objective however is to get an idea of the order of magnitude of the power and energy needed.

Power Difference in 2030

Subtracting the projected domestic power consumption from the projected wind power generation yields the instantaneous power difference, i.e. a power shortfall if more power is consumed than generated, and an excess power if more power is generated than consumed:

Projected power difference for 2030 based on historical data.

As the chart clearly shows there will be much more of a shortfall in the winter month and more an excess power in the summer month: the seasonal variation that can be expected. It is of utter interest to look at the frequency components of this power difference.

Frequency spectrum of the projected power difference for 2030 with clear peaks.

As expected, there are three frequencies standing out:

• bin 1 = 7.523GW, i.e. the annual fluctuation, i.e. winter/summer,
• bin 365 = 5.722GW, the daily fluctuation, i.e. night /day cycle,
• bin 730 = 7.653GW, the half-daily fluctuation, i.e. morning /evening.

Balancing the Power

Meeting the fluctuating consumption requirements with an intermittent power generation is only possibly by having an alternative power source, or energy store. Suppose there is such a giant energy store where the power shortfall can be drawn from and the excess power can be pushed into.

The energy contents of this giant store would be determined by the rate energy is taken out or put in; the amount of energy stored at any time can be calculated by simply integrating the power difference above. Since the energy stored cannot be negative, the integrated function needs to be shifted to only be positive as shown in the following graph.

Projected evolution of an energy store for 2030.

The required storage capacity would have to be equal to the maximum value in the previous chart, or of the order of 23.65TWh for the year 2030, which is equivalent to about 236 million Tesla Model X Long Range batteries (100kWh), i.e. 8 batteries per home for the 30 million UK homes.

Another way of obtaining the storage requirements is to look again at the power frequency spectrum: energy per bin = power at a given bin x period / π. The energy needed to allow the fluctuation is for the interesting bins:

• bin 1 = 20.976TWh, i.e. the annual fluctuation, i.e. winter/summer, or about 209 million 100kWh batteries, i.e. 7 batteries per home,
• bin 365 = 43.715GWh, the daily fluctuation, i.e. night /day cycle, or about 437,151 100kWh batteries, i.e. or a 1.5kWh battery per home,
• bin 730 = 29.234GWh, the half-daily fluctuation, i.e. morning /evening, or about 292,335 100kWh batteries, i.e. a 1kWh battery per home.

While the daily and half-daily fluctuation could be met with a combined 2.5kWh battery per home, the annual or seasonal fluctuation is a bit more challenging. In general, various measures could help in balancing power:

• consume less energy for domestic space heating in winter, e.g. by insulating buildings much better, retrofitting the current poorly insulated housing stock, and/or start building them with thermal mass on the inside and insulation on the outside, see also Changing the Face of a Country for the Sake of Energy Efficiency,
• spread the generation and consumption over a wider range and larger set of producers and consumers, respectively, e.g. importing/exporting of electric energy on a European or even global level, i.e. ideally an Ultra High Voltage DC grid backbones across the world: East-West for the daily, and North-South for the seasonal fluctuation,
• demand response to power price signals to obtain short term storage shift, e.g. heat pumps to store energy in domestic thermal stores; some energy companies such as Octopus are already offering variable pricing.

Bottom line: the total domestic energy demand is likely to be met by wind power generation in 2030; however, literally powering every UK home with wind power will not easily be possibly without significant amount of energy storage (domestic or national) and other energy balancing measures.

The figure of 23.65TWh is only indicative of the order of magnitude, i.e. we are talking about tens of TWh to get an idea of what would be required.

Future Work: there is plenty of scope for further work, for instance:

• since the calculations were done on a single sample year, both for consumption and generation, it would be interesting to take various years and build a better statistical model of both, then derive better estimates for the mean value of energy store needed as well as the associated uncertainty, e.g. as standard deviation.
• it would be interesting to create a mix of renewable energy generation, adding photovoltaic generation, then run some models with various ratios in order to see the impact on the storage needed, daily or annual.

Acknowledgement

The data for this research have been provided by the Consumer Data Research Centre, an ESRC Data Investment, under project ID CDRC 783–02, ES/L011840/1; ES/L011891/1