The Winter Solstice

This is was written a few days before the Winter Solstice when the day is short and the Sun is low in the sky.  It is the time of the pre-Christian festival of Yule, regardless of one's religious beliefs, this is a time of year when the spirits need lifting from the cold and damp with parties and festivals.  At present I feel a strong desire to keep warm by setting fire to something that died a few million years ago.

Most religious festivals are linked in some way to the land and climate in which they are celebrated, for example, Candlemas (Feb-2) coincides with the time the soil starts to warm after the winter and Easter marks the start of the growing season and so on.  Whilst these events were once marked in some way, we increasingly isolate ourselves from seasonal variation with central heating in winter, air conditioning in summer and strawberries in November.  This process started with the large scale use of coal at the start of the Industrial Revolution around 1750.

The graph shows the estimated clear sky irradiance over Southern England at the time of the solstices and the equinoxes.  The energy yield at each time is proportional to the area under the curve, or to put it another way, its cold in winter and warm in summer.  It is possible to do similar things with wind.

We are an urban and industrial society and there is not going to be a return to the rural idyll (if it ever existed) any time soon.  Yet understanding and appreciating the climate and economy in which we live can lead to good designs and better decisions.  The sustainable energy economy is a big challenge and it is important to realise what can be achieved.  Industrial and urban economies need continuous supply of energy, part of the base load created by street lighting, transportation, schools, hospitals, data centres, pub signs etc..  I suggest that there is little public support for a railway system powered solely by wind turbines.  Sailing ships were displaced by coal fired steamships because they could run to schedules and were big enough to accommodate all who could afford to travel.  This base load will be underpinned for the foreseeable future by fossil/nuclear generation. Within that sector of the energy economy, the key elements are conservation, management and storage, implementation of which is not helped by legacy systems.

I'm embarrassed to admit it, but some of my interest in sustainable energy was sparked by the 1970s BBC TV series "The Good Life" in which an attractive young couple unimaginably named Tom and Barbara Good, but played endearingly by Richard Briars and Felicity Kendal attempt self-sufficiency in Surrey.  Needless to say the challenge was a rich source of humour.  My wife is too well grounded to let me indulge in such fantasies so I have contented myself with a paper project to provide 1 kwh per day from renewable sources without costing the Earth.  Whilst pondering this problem, I have learnt how to mount transistors in TO 220 cases, a little about controlling them with a computer, but I'm still struggling.  My backyard almost makes us self-sufficient in garlic and provides a small supply of vegetables of the type normally discarded by supermarkets but as a source of wind and solar energy it is a sad disappointment.

The path of helium filled balloons which have escaped from young partygoers suggests that at around 500m there might be a steady wind, but the neighbours, tolerant in many ways would not accept an airborne wind turbine.  A boat on a river estuary might work, but my wife is too well grounded to let me indulge in fantasies.  The obvious solution is to buy electricity from people who generate it from wind, solar and other sustainable sources and use the grid as a delivery system.  But energy from these sources is a natural product whose availability changes with the seasons.

How do you learn about this stuff?

I first became interested in sustainable energy around 2005.  This was before the financial crisis of 2008 when environmental issues were aspirations, not perceived as costs (maybe I exaggerate).  A 2.5 kw rooftop PV installation cost between £15k and £20k and there were no feed-in-tariffs, not surprisingly there were not many to be seen.  DIY superstores were selling 1 kw wind turbines for around £1,500 (I think) and there were stories in the press expressing horror at the low yields, this was not surprising considering that rating was usually for wind speeds around 15 m/s (approx. 30 mph), whilst this is not a gale, its the sort of wind you don't feel too often (for which many of us are grateful).  I struggled to understand this stuff.

Most of my working life I've been lurking in the shadows between technology and economics.  A traditional engineering education did not include economics and the attitude towards its practitioners was illustrated by graffiti  in engineering faculty toilets above the loo roll dispenser which read "Economics degree, please take one".  However, there was an implicit understanding that there should be a link between technical performance and economic benefits, however dubious.

My perception of wind and solar energy systems is that they are conversion devices, the input is "weather" e.g. wind, sunshine, cloud etc. and the output is electricity or heat.  Attempting to understand this relationship has led to the combining bits of wood, drain pipes, Meccano and a sketchy knowledge of electronics into experiments.  I realise now that I must have been a sad disappointment to those burdened with teaching me carpentry, metal work and technical drawing, be grateful that I trained on aircraft engines and did not become a kitchen fitter.

My first attempt around 2007 was the "Solar Bucket", this consisted of three components, a small solar panel, a lead acid battery and several devices to use the energy harvest, the most useful being an early LED light.  The photo shows the panel on a winter's day.

This provided some valuable experience.  It illustrated seasonality, the effects of clouds and much more.  The battery component was originally intended as a measurement device.  I was a little slow to realise it but the battery was the important component, storage is a key element of a sustainable energy economy.  I've heard several people say things like "I want solar panels to make me independent of the energy companies" (or variations n the theme), but the Sun does not shine at night, so without storage they are as dependent on fossil/nuclear fuel as the rest of us.  I argue that investment in energy storage would give a better outcome than more rooftop PV.  As I write this I am staring at more plywood, batteries and wires designed to act as a realistic load for energy management software.

Instructive as the "Solar Bucket" was, it did not act as a resource meter.  This resulted in several attempts at making radiometers.  Initially, these used light dependent resistors and did not work, as these are successfully used in cameras and other devices, the problem was my lack of knowledge.  At some point I purchased a batch of small, flat monocrystalline PV cells for about £1 each and these work well.  The current device could be described as a shaded radiometer and for some reason it attracts the attention of dogs.  The concept is simple, a horizontally mounted cell measures global irradiance, then a shade is placed between the sun and the cell, it then measures diffuse irradiance.  Combine these two measurements with Sun-Earth geometry and you can get an estimate of the direct beam irradiance.

I'm trying to estimate the accuracy of this device, but it suggests that the water content of the atmosphere has has a significant effect on irradiance and particularly diffuse irradiance.  There are some good models of clear sky irradiance, but some of these require data which is not readily available or are related to the climate in which the observations were made, this is an attempt to understand my own back yard.

The first radiometer was simply a PV cell shorted with a resistor, the current and therefore the irradiance was measured by measuring the voltage across the resistor with a multimeter.  For several months, I took readings with the cell horizontal with it angled at approximately 50 degrees to the horizontal.  Under a clear sky, pointing the cell in the direction of the Sun increases the output, this maximises the yield of solar devices in summer, but in winter, the English sky is often full of thick stratus cloud, on these days, the output of the PV cell was greatest in the horizontal position.  The object below was constructed to explore this further.

It consists of a light dependent resistor mounted at one end of a length of waste pipe which is mounted so that measurements can be made around the sky's hemisphere.  On an overcast day, the diffuse irradiance was equally distributed about the the sky, whilst on a clear one it was principally from the direction of the Sun.  This suggests that the yield from PV devices in an English winter might be maximised by mounting the panel horizontally.

My home is located on the western side a a valley in an area where the prevailing wind is from the south west, so we are fortunately sheltered from much bad weather.  Whilst solar is a back yard technology, observing the wind means leaving the house.  A lot of wind speed data is collected in clear open space such as airports, offshore buoys and weather balloons.  The data from these sources often relates to the flow of air over a relatively smooth surface and can have little or no relationship with the wind in nearby urban or rural environments.  In these places, the wind eddies around buildings and trees and neither the speed or direction is constant.  In this type of environment, vertical axis wind turbines offer some advantage.  I horizontal axis machine in an urban setting will often "hunt" for the wind, by the time it has aligned itself with the flow, the gust has dissipated.  I was first introduced to the Savonius design by a university friend from the Caribbean, whilst we were taught about marine, automotive and aircraft engines, simple devices for working irrigation pumps got little or no attention.  The Savonius device has two attractive features, the first is that it is not subject to the complex forces seen in other vertical designs, the second is the ease of construction.  In the West Indies they are often made by cutting a 40 gallon oil drum into two, then welding it back together so that it looks something like the model in the photo below.

A few happy days were spent cycling around the city and taking this model to the top of multi-storey car parks, to the end of breakwaters  and occasionally attracting the attention of dogs.  If you are a man wanting to attract women, borrow a puppy, if you want perfect solitude get a model wind turbine.

I did spend some time messing with a dynamometer for the Savonius model, but abandoned it when I realised that I would have little use for the data.  The Meccano tower lingered in my work room reminding me of the value of time.

What have I learnt?  The main lesson is that a sustainable energy economy is complex, its not just a case of shutting down nuclear power stations and seeding the countryside with wind turbines and putting a solar panel on every roof.  Its a blend of realistic expectations, generation, management and storage which is a large technical challenge, but so was developing the technology for nuclear power stations so we've been here before.  Also don't ignore economics, there is a belief held by some well meaning people that sustainability is above economics, one man's feed-in-tariff is another man's economic cost and this does not lead to good decision making.

Its quite possible to do a lot of experiments with limited resources.  The basic rule is to make mistakes cheaply and realise when you are wasting your time.  I put a lot of effort into a solar thermal device, this had a collector area or half a square metre, looked quite impressive but was useless for anything other than drying washing.  A series of small panels each 10 cm square cost very little and were quite instructive.

Wind is Moving Gas

A recent review of an electric car could be summarized as "This vehicle is not petrol driven".  Like a lot of things energy related, electric vehicles are not a simple swap from an old technology to a new one.  I have never owned or driven an electric vehicle so this is a framework which I might use to evaluate one, a sort of automotive lit-crit.

Most reviews of electric vehicles focus on range anxiety, at a guess this is more do with opportunities to re-charge than the distance/charge, typical numbers seem to be in the 100 - 200 km range.  I live in an area of controlled parking which is next to a railway station.  A statistically invalid survey of the parking permits of the vehicles in our road, suggests that 40% have travelled less than 1 km and that the remaining 60% have travelled less than 5 km and are parked in a garage or driveway at night.  The record shortest journey is 150 metres.  Whilst many of these vehicles are capable of crossing continents, most don't.  Whilst I have not lived in the US, I have spent a lot of time working there driving the American Dream (a.k.a. a Dodge Neon), even with a full schedule it was rare to travel more than 150 km in a day.  so with the significant exception of family holidays and trips to granny, range for many people is not an issue.

Cost is harder to deal with.  Half an hour of Googling and doing things with a pencil resulted in the following conclusions, first that electric cars are expensive to buy and secondly if charged up on-off peak electricity, cheaper to run.  What that does for my wife's 40 km commute is not obvious.

A neighbour recently described me as an "eco" because I rarely drive and prefer my bike, but I'm male and therefore lust after low slung sports cars (although my car-boot bike maybe quicker around town, sadly, beyond the city limits its not a contest).  I might drool over a Tesla.

I dispute the claims that electric vehicles produce zero emissions.  In the UK electricity is produced from a variety of sources including coal, gas, nuclear, wind and solar, last time I looked, CO2 emissions were around 0.4 to 0.5 kg/kwh for the country as a whole.  The environmental issues are at the point of generation not the car.  The fuel for electric vehicles is coal, gas, nuclear, wind and solar rather than petrol.

In the context of a sustainable energy economy, electric vehicles offer personal transportation using renewable sources such as wind and solar.  Equally important is that they are mobile storage devices.  A typical car spends 5% of its time on the road and 95% waiting to go somewhere.  Wind and solar sources produce energy at the whim of the weather and fossil/nuclear sources are most efficient at a constant load, this is why off-peak electricity maybe half the standard price.  The storage capacity of electric vehicles could be used to improve energy management as a peripatetic part of a smart grid.

At present, the case for electric vehicles is not proven, a situation made more complex by the availability of subsidies.  Subsidies are a good economic tool to bring about change, but they can also be proof of the doctrine of unforeseen consequences.

A not to close look at the electric vehicles on offer suggests that they "not petrol driven".  As electric vehicles are a new technology, maybe the starting point should be elsewhere.  A few times when I have been meandering through the countryside I have been overtaken by a golf buggy.  These vehicles cost around £4,000 (I think) and have been adapted for use on the Moon, so making them fit for the daily commute should not be too great a challenge.  A vehicle costing £5,000 with low running costs and a range of 200 km would be the car most people need, but maybe, not the car they want.  However, make a low slung version with good curves and you have a Sinclair C5 - Who said they were a bad idea?

Safety on the roads is an issue and the ability to survive a collision is important, once you have been in accident, this is not an academic concern.  Much as I love my bike, I am acutely aware of it's vulnerability and I nag my children to wear cycle helmets.  The city I live in is flirting with 20 mph speed limits, does a 20 mph environment offer the potential for lighter vehicles?

Postscript

After I finished this post, I saw an innovative electric trike, driven by a combination pedals and an electric motor fuelled by four lead acid batteries and a Mars bar.  I gave chase, but quickly lost contact before I could ask the owner's permission to take a photo.

Salad is a solar panel you can eat

Wind turbines and solar panels are energy conversion devices, their "fuel" is the weather prevailing at their location.  The terms we use to describe the weather also describe the energy we might expect to harvest with a given device.  If the sun is high in a clear sky, solar panels will work well, this will not be the case under a thick overcast sky in winter.  For wind, Munn's third law can be a useful guide, it states that "If you can wear a skirt or kilt without embarrassment, this might not be a good place for a turbine".

When I first became interested in sustainability, I wanted to understand the solar energy available in my back yard.  This involved spending a lot of time with a very small PV panel and cheap multimeter.  On a fine summer day, this was a pleasant task, less so when knee deep in December snow.  Builders working on a nearby roof questioned my sanity, as did my family, dog and friends.

In addition to rain sodden notes written with freezing fingers, there was also an observation of the obvious, that plants growth is related to the amount of energy they get from the sun.  In a conversation with an allotment holder I described a lettuce as a solar panel you could eat and he too doubted my sanity.  The relationship between solar energy and crop yield is well known to farmers.

Agriculture was the first solar energy business.  In many respects it is better model for wind and solar energy producers than the utility companies.  Seasonality is fundamental to farming.  Seeds have to be sown when the soil is warm and wet enough for them to germinate and crops are harvested  when the plants have done enough photosynthesis to produce something edible.  Storage is built into the system, for example the grain harvest takes place in late summer, the grain is then stored in silos and used at a more or less constant rate through the year.  This analogy can be extended to wind, the late summer harvest would be followed by higher winds around the autumn equinoxes which turned the wind mills to produce flower.

To try and understand the relationship between plant growth and solar energy, I started a crude experiment.  For a few weeks each Sunday afternoon, I sowed 5 ml of cress seeds in a shallow circular pot.  During the week I tried to ensure that it had a good supply of water.  At the end of each week I "harvested" the cress with a pair of scissors and weighed the result.  I chose cress because it will crop within the space of a week, whilst I made a point of eating the harvest, it is not a substantial meal and trips to the supermarket continued as normal.  The photos below show the difference in the plants after a "good" week and a "bad" week.

Whilst I was focussing on solar irradiance, I was aware that temperature was also important and that temperature is the result of irradiance.

During each week I made an estimate of the cumulative solar irradiance recieved cress and by the time I had used all my seeds, obtained this graph:

This exercise was not a model of experimental design and there were numerous sources of error, but a relationship between solar irradiance and cress yield emerged.

This work was done in 2011, since them I have become aware of solar irradiance data collected by satellites such as Ceres and made available as part of the NASA Earth Observation programme and at some point I want to rework the results using that type of data.

During this period, if the weather during the preceding week had been fine and sunny, Monday's lunch was either an egg and cress sandwich or some form of salad.

A slightly more detailed description of the experiment can be found at the end of this link:

The Solar Cress Experiment

A Brief History of Walls

Much of the housing in the area in which I live was built in the period 1870 to 1910.  Over the years gaps have appeared and the suburb has expanded to displace sheep from the surrounding farm land.  New houses have appeared on the lawns of grand houses, small orchards, market gardens and in a couple of places the side of a hill.  Whilst the style of building has changed, it is only in recent years that the method of construction has evolved.

The driving forces behind this evolution has been the Building Regulations and a change in the nature of home economics.  Prior to 2000, the general philosophy was to focus on capital costs, fuel for heating which is a major components of a home's operating costs was relatively cheap and a common way of getting a warm home after the arrival of North Sea Gas was to install lots of radiators.  This was not significantly different from the attitude of the Victorians who believed in the health benefits of ventilation and and whose homes needed a good supply of air to keep open fires burning, for them coal was relatively cheap.

Modern houses are built on a completely different principal, they have a higher capital cost but are intended to have much lower operating costs, not only that they are warmer.  The sketch below shows the difference between an old wall and a modern one.  For well over a century, the most houses were built with cavity walls which are just two single brick walls separated by an air gap and the inner wall finished with plaster.

Modern walls are significantly different, the outer layer of bricks might be similar, but the inner wall consists of a layer of foam insulation in front of blocks with good thermal properties and the finishing is insulated plasterboard.  In very rough numerical terms, old walls may have had U value greater than 2.0 watts per metre squared per degree C. whilst that of a modern wall will be less than 0.5.  In non-numerical terms you don't need much heating.  A proud owner of such a building I met recently did describe an alternative to a gas central heating boiler as a form of heating, but that may have been wishful thinking.  The sketches are not from the studying of Building Regulations, but the result of staring into building sites whilst walking my dog.

It is not only the construction of walls which has changed, but doors, windows, roofs.  Double glazing in sealed frames is now the standard and the thermal properties of these are significantly better than a single glazed sash window.

As someone interested in the concept of a "sustainable energy economy", I am sometimes puzzled by focus on energy generation.  I occasionally do a non-scientific survey of the contents of "science and environmental" sections of the media.  The stories range from the bizarre such as "Wind Turbine catches fire in Gale", "Planning permission application for new solar park", "Minister declares offshore wind farm open" and similar.  Only rarely is there an article on conservation or storage.  Its not hard to see why, few journalists or politicians can make much of a house brick, LED light or boiler controls.  Apart from a famous photo of Winston Churchill building a wall, I can't remember any interesting picture of an MP gazing lovingly at a brick.

Postscript

Shortly after I posted this, I heard a news report stating that during the prolonged winter of 2012/13 there had been 30,000 excess deaths (meaning more than normal) and that many of  these were due to old people living in cold homes.  In part, this is due to the way homes were constructed when energy was relatively cheap and plentiful.  Now that this is no longer the case, many homes, especially those of pensioners on low incomes are underheated.  Whilst I don't want to dismiss the value of retro-fitted insulation, in many cases a modest expenditure only makes the house less cold, not warm and does not cut energy bills.  Over a very long period, many thermal disasters will fall down or be demolished, but that will not do much for the generation currently living in them.  It would help if policy makers understood the problem and not ranted on about the imperfect working of the domestic energy market.

Gas Prices - A Family History

I'm peeling away 110 years of interior decorating events in our home's main bedroom. At one point, the floor and walls were dark green, which may have seemed like a good idea at the time.  The locks on the door are were installed by someone with an unhealthy interest in privacy.  Maybe because of these locks, the door was once broken down, I suspect by a jealous lover.  Below the floorboards are three generations of electrical wiring and some plumbing described by a plumbers' merchant as "old school" which may have been installed in the 1970's.  Amongst the filth are the butts of a few "Woodies" and the remains of a fag packet.  The original fireplace was broken up with the skilled use of a 4lb club hammer and the hole blocked up. After a morning of bizarre behaviour I managed to recover a hand painted tile from the debris.  The piping for the original gas lighting appears to be more or less intact, although the fittings have long since disappeared.

There is a subtle harmony in the layout of the room. The bed was positioned to make the most of the early morning sun, the coal fire would have warmed the feet.  The gas lights on either side of the bed are perfectly placed for a book at bed time.  Maybe there was once a dressing table lit by the other gas light where the lady of the house did her makeup and needlework, a hint of her perfume remains.

Electricity was present in the house when it was completed in 1901, not for use as heat or light, but for signalling.  The three main bedrooms had bell pushes which probably connected to an indicator board in what was then the kitchen.  The house is neither large nor grand, but there may have been a live-in cook and this poor woman may have had to provide room service, but she did have the warmest room in the house to work in. The lead-acid batteries which powered this system would have been charged by one of the local shops.

The bedroom illustrates the roles of electricity, gas and coal in the Edwardian energy economy.  More than a century later we use these differently.   Gas is now the principal domestic fuel and its price is increasingly becoming a cause for concern.  The graph of domestic gas price below was compiled from from a collection of family documents:

This graph spans the period from 1928 to 2013.  I am attempting to fill in the gaps, but anecdotal evidence suggests that gas prices fell slowly in real terms during the period 1950 to 2000.

The conversion from money-of-the-day to 2011-money is based on the UK government's Composite Price Index, the attraction of this scheme being the availability of a long time series (one version extends back to 1750).

At the start of the 20th Century, gas was mainly used for lighting.  Coal was the principal domestic fuel for cooking and burning in open fires. The gas came from gas works, often located close to town centres and near a railway line. The economy of gas works was based on a combination of the sale of gas for lighting and coke for heating. By the 1920's gas stoves were rapidly replacing solid fuel ranges.  Simultaneously electricity was displacing gas as the energy source for lighting. Electricity was a much more versatile fuel than gas, it could be used for cooking, lighting, appliances and heating.  The relatively high cost of electricity limited the popularity of electric fires. By 1939, many houses were using electricity for lighting and appliances, gas for cooking and coal or coke for heating.

During the war years, domestic energy consumption declined. Coal was often difficult to obtain, the blackout discouraged the use of lighting and many men and women were away from home either working in the factories, on the land or serving in the forces.  After the war, the availability of energy for domestic consumption increased as war production ceased and the lights were turned on again and houses became warmer.

 In the 1950s, electricity was produced in increasingly larger power stations and distributed by a national grid. Gas was still produced and distributed locally, it was not until large volumes of natural gas were discovered in the Southern North Sea that a national gas distribution network was established.  The North Sea reserves stimulated a "dash-for-gas" and the role of gas in the energy economy changed significantly.

 By 1980 gas had more or less displaced coal as a domestic fuel. This transition was driven by a combination of low cost and convenience.  Anecdotal evidence suggests that domestic heating costs dropped with North Sea gas but there were two other driving forces.  Not least was the ease of  use. Whilst the occasional coal fire is pleasant, heating a house with coal is a labour intensive process requiring coal to be carried, grates to be cleaned and ash to be dumped. Also, for many years fog and smog in urban areas had been a public health problem and the advent of smokeless zones in towns discouraged the burning of coal.

The availability of low cost gas lead to its increased use as fuel for electricity generation.  By the beginning of the 20th century, the UK was ceasing to be self-sufficient in natural gas and imports either by pipeline from Europe or as LNG from the Arabian Gulf and elsewhere have been increasing.  The result of this is that the gas price is now set by international markets.

Soil Temperatures - Update

This is an update of a post published on 02-Aug-2013 which describes the hole in the ground used to collect soil temperatures.  I now have just over a little more than one year's data which makes it possible to look for patterns in the data and do a year-on-year comparison.  I started this project in August 2012 just as the ground was starting to cool after the summer.  The full data set is shown below:

The same general patter is present in the Autumn of 2013 as it was in 2012 with the topsoil cooling more quickly than the sub soil.  The maximum values of topsoil temperature were observed in July when there were several weeks of clear sky when the Sun was high in the sky.  The lows were towards then end of long winter when it was April before Earth and Englishman felt warm in the garden.

So far, weather at the end of Autumn has been milder than in 2012 and the subsoil temperatures are two to three degrees higher than last year.  The topsoil more or less follows the air temperature but, it's variation is increased by radiative heating and cooling can lead to loss or moisture and frost respectively.

The observations from the last month illustrate the complexity of the heating and cooling processes.  During the weekend of 13-Oct,  average air temperatures had fallen to below 10 deg. C (cold air from mainland Europe?) and the topsoil temperature fell below that of the subsoil.  A week later, average air temperature rose to more than 15 degrees (warm air from the Atlantic?) and the situation was reversed, the topsoil was warmer than the subsoil.  In addition to air movements (note to self, try and look at a weather map each day and see what's happening), there would also have been radiative cooling and heating.

After a year, the ritual of poking a wire down a hole in the back yard at dusk on Sundays is well established, data on this web page is periodically updated:

Brighton Webs - Soil Temperature

Energy Storage and Vegas Values

Energy storage is the buffer between supply and demand.  Wind and solar sources are weather dependent systems whilst home and work life tends to follow a more or less predictable routine.  Whilst the ancient mariner or miller might have taken a duvet day when the wind was not blowing, the office worker is expected to be at his/her desk when the weather outside is fair or foul.  Storage is a key component in renewable energy systems.

Monte Carlo simulation is one way to explore the interaction between supply, demand and storage.  The concept is simple, you throw random events as a mathematical model and see how it behaves, whilst this may sound abstract, its more than a bit like real life.  The name was comes from the roulette wheels in the casinos of Monte Carlo in the 19th century, in a fair and decent world, these devices are true random number generators.  If the technique was being named today, it might be called Vegas Values.

The example is based on a simplistic model of a system with three components, a small wind turbine, battery storage and a load. The example has been set up such that the average supply and demand are both 1 kwh.day, however, the distribution of  the supply and demand are different, and it is probable that on any given day, supply and demand will not balance. There could be large demand for energy on a calm day or little demand on a windy one. The inclusion of storage in the form of a battery helps match supply and demand. In this example, we want to understand the effect on system reliability for different amounts of storage.

Over a given 30 day month, the wind turbine produces an average of 1 kwh/day, this supply is assumed to be a triangular distribution with a minimum of 0, a  mode of 0.5 and maximum of 2.5 kwh. This supplies a 100% efficient battery, the capacity of which subject of the simulation. The model was run with storage capacities ranging from zero (no storage) to 10 kwh. The load is also 1 kwh/day and also modelled as a triangular distribution, the minimum, mode and maximum values are 0.5,1.0 and 1.5 respectively. The system "fails"; when the battery cannot supply the load. The parameter of interest is the number of days per month the system fails, which can also be expressed at the probability of the system not failing during the month.

The core of the model is shown in the flow chart:

This is a very simplistic model, so a single function is used to return a triangularly distributed random number, the arguments being the minimum, mode and maximum values. The Python code for this simulation can be found on our website. The principal variable is "storagesize" which is the capacity of the battery in kwh. The output of the program was used to create the graph below.

This simplistic model of a hypothetical system suggests that increasing storage reduces the probability of system failure but at the amount of storage increases, the law of diminishing returns set in.

Related Material

Monte Carlo Simulation

Triangular Distribution

The Clear Sky

The starting point was a statement of the obvious.  Clouds affect the performance of solar energy systems and this can be summarised as "clear sky, good"  and "overcast sky: bad".  The problem was how to quantify this, a convenient descriptor is something that might be called the clear sky factor (reduced to CSF) which is defined as:

For this concept to be useful it is necessary to have a definition and an estimate of the clear sky irradiance.  There are well developed models which can provide good estimates of clear sky irradiance, but they require some knowledge of the state of the atmosphere, whilst such data is provided by satellites such as Ceres and weather balloons, it can be hard to relate this data to a casual observation.  Another approach is to use a correlation for a given location, a good example of this is the work the Meinels in the Mojave Desert in the 1960s.

Comment

This is a discussion of work in progress and is a development of a previous post on the diffuse fraction and should be treated with similar caution.

Correlation

The Meinel's formula produces an estimate of direct normal irradiance for a given value of air mass:

The solar constant is approximately 1370 watts/m2, it varies during the year due to the elliptical nature of the Earth's orbit around the Sun.  The form of the equation is well suited to its application and whilst I was defeated in an attempt to work out the least squares equation, it is possible work with it using the Solver add-in for MS Excel.

I had found that a crude piece of equipment (described in the post on diffuse fraction) can provide an insight into the way irradiance changes with the state of the sky.  I became curious to know if the data collected by this device could be used to provide a correlation in the form of the Meinel formula which reflects the local climate and possibly produce an estimate of diffuse irradiance.

Clear skies are rare in England, out of approximately 100 observations, only a few were taken under a completely cloudless sky.  Typically the day will start clear, but by noon, some clouds will have formed.  Whilst the equipment is simple, the method of operation does ensure you observe the sky and this provides partial compensation for the lack of sophistication.

First Attempt

The equipment provides an estimate of global horizontal and diffuse horizontal irradiance and if the time of the observation is recorded correctly, the zenith angle can be calculated from Sun-Earth geometry and this in turn can be used to calculate the plane parallel air mass.  A combination of these bits of information provides an estimate of the direct normal irradiance:

A plot of the result to date is shown below:

The graph shows two things, the first is wide spread in the range of values for DNI for a given air mass.  Most of the low values were observed when there was some cloud present in the sky, even though the sky was clear in the direction of the Sun, quite often whilst the sky appeared to be clear, satellite images suggest that there was some cirrus present within a few kilometres.  A secondary objective was to compare my description of the sky with those from metar reports from a nearby airfield, in general, there was reasonable agreement on the extent of cover (I do not attempt to estimate height).  Many airfields only report low level cloud because that has the greatest influence on aircraft movements, thus a report which suggests a clear sky does not take into account any high level cloud which has the effect of increasing diffuse irradiance and increasing the diffuse fraction.  Secondly, the upper limits of direct normal irradiance with low values of diffuse fraction were close to the values predicted by the Meinel formula.  As the diffuse fraction increases with air mass, some selection of data points, possibly using satellite images as a guide, might yield some clear sky data points at high air masses.

At the time of writing, there is not enough data to attempt a correlation, but the work to date suggests that one may be possible.

Diffuse Fraction

Whist making these observations is pleasant task involving walking or cycling in the sunshine, it can be frustrating when the data yield is small, especially at the start or end of the day. The graph below shows the temperature, dew point, diffuse fraction and sky state for the 01-May of this year.

Around nine, in the morning, the sky appeared to be hazy, but clear, as the morning progressed a few small cumulus clouds passed across the sky, it was only around noon, that the sky was "clear".

The wind, my mobile and the Space Shuttle

Last week's post was about the fluctuations in wind and solar with time.  The week is an attempt to understand how wind speed varies with location.  What might be called a reference for wind speed in our area is the METAR reports from an airfield approximately 10 km to the west, Most of the time, this is upper limit of the wind speed which will be found in the wider town and country where the variations are significant. This is can be seen in the observations from personal weather stations on the Weather Underground, these are a valuable source of data, but as many of them are located in urban areas it is difficult to separate out the effects of terrain from rooftops.

The research plan was simple, go for a walk in the countryside with a wind speed meter and record the location of the readings using the GPS on my mobile phone.  As an aside, if you want perfect isolation from your fellow man, simply wander around with a clipboard and a measuring device and no one will come near you, this also works with sheep.  After several days locked in mortal combat with VB.net I managed to plot the results of the expedition on Google Earth together with contours derived from data made available from the Space Shuttle's SRTM mission.  I would like to express my appreciation of the openness of NASA and NOAA for placing fascinating datasets in the public domain, apart from hikes and cycle rides most of my knowledge of renewable energy comes from studying this material.

The results of the first attempt are shown in the screenshot from Google Earth:

The colour gradient chosen for the contours makes the valleys yellowish and the ridges reddish.  The numbers by the placemarks are the ratio of the observed wind speed to that of the nearest source of METAR reports.  On this occasion, the wind was blowing more or less steadily at 5 m/s from the south west.

The direction of travel was from South to North.  The first couple of kilometres were along a main road through an urban area where trees were rustling, but the wind speed meter was not registering, thus the wind speed was probably less than 2.5 m/s.    The next stage was along a ridge leading to the crest of The Downs, the start of this was sheltered wna the wind was approximately 4 m/s and turbulent, however, once on crest of the ridge the wind was steady at around 5 m/s.  The route had been chosen to include an descent into a valley through which runs a four lane highway but which is crossed a convenient bridge where a track goes up the eastern side.  During this stretch, the trees were rustling, but the wind speed meter was lifeless.  Once on the crest of The Downs, the wind was back to 5 m/s.  Carrying on to the North takes you down a steep scarp leasing to the relatively smooth Low Weald where only a gentle breeze was experienced.

Whilst this approach is simplistic, it does provide an insight into the relationship between wind speed and terrain.  I will test the tolerance of the local sheep population with some more hikes.

The Fickle Wind and Shifting Sun

The energy input to wind and solar devices

Wind turbines and solar panels are energy conversion devices.  The input to these systems is not constant, it changes with the seasons, the weather and the time of day.

Comment 
   
This work has not been reviewed, thus it should be treated as a discussion not a description.

Wind

Wind is the result of uneven heating of the Earth's surface, in addition to climate, the airflow over any given location will be influenced by terrain. There can be significant variation in the wind experienced by places only a few kilometres apart. Whilst wind is often described in terms of velocity and direction of travel, it can be useful to consider it in terms of  power. The wind power available for conversion by a turbine is related to the cube of its velocity.

Power = area * density * velocity³ / 2

A small increase in wind speed represents a large increase in energy, for example wind blowing  at 8 m/s has more than twice the energy than at 6 m/s.

By setting the area equal to 1 square metre and approximating the density of air to 1.2 kg/m3 and  converting the units to kw, the formula reduces to:

Power = 1.2 * Velocity³ / 2000

Comparisons based on this formula should be treated with caution. The density of  air falls with increasing altitude, for example it is close to 1.0 around 1,500m. The height of the observation above ground also has an influence, for a few  hundred metres above the surface, the wind speed increases with height above ground as the effect of friction reduces. The power of a wind turbine is substantially less the value given by this formula as only a fraction of the energy is extracted.  The fraction of the energy extracted at any given time is known as the  coefficient of performance, typically this is in the range 0.1 to 0.4 and may vary according to the wind speed.

If enough data is available, then estimates of power (the rate of doing work) can  be used to make an estimate of the wind energy passing over the point of observation during a given time period.  The graphs below are are based on a randomly selected location and are an estimate of the wind energy by month, day and hour.

The first graph shows the cumulative wind energy broken down by month, In this example, there is significant seasonal variation, this may vary with climate.  In Western Europe peaks in wind energy often cluster around the equinoxes.  However, in general, there is some correlation between  the periods of peak wind energy and the demand for electricity which also peaks in winter.

Breaking the same dataset down by day shows that wind energy tends to be packaged in pulses a few days apart.

This pattern is present in many sets of observations.  This pattern of supply makes it necessary to have either an element of buffer storage in the system or an alternative that provides an adequate supply of  energy in during the periods of relatively low output.

Many areas have a pattern of diurnal variation, In coastal areas this can be caused by the different      heating/cooling behavior of land and sea with the direction and intensity changing with night and day.

These short term fluctuations emphasise the need for storage or alternative means of generation which can respond quickly to changes in supply and demand.

Solar

The principal variation in solar irradiance comes from Sun-Earth geometry.  The Earth's axis is inclined relative to its orbital plane, in the Northern hemisphere the pole is inclined towards the Sun in summer and away from it in winter and each day the Earth rotates about its own axis. As a result the solar irradiance varies during the day, and seasonal variations are related to latitude.

The graph below shows the estimated clear sky solar irradiance over the course of the day for Southern England (approx. latitude 51 deg. N) at four times of  the year.

In winter, the air mass at solar noon is approx. 4 and the length of day is only eight hours whilst in summer, the air mass at solar noon is close to 1 and the length of the day has extended to 16 hours. At the equator, the air mass at solar noon is always close to 1 and there is little variation in the length of day. Above the Arctic circle (approx. 66.5 deg. N) there are times when the Sun does not rise in winter nor set in Summer.

Superimposed on the variations imposed by planetary motion is the influence of  atmospheric conditions, the most significant of these is the effect of clouds.  Clouds are a feature of climate, itself closely related to latitude. The height and extent graphics below illustrate the variations.  These diagrams are compiled from the height and extent of the cloud cover at solar noon.

The first is for a maritime temperate climate, such as the South of England.

Clouds limit the solar radiation reaching the Earth's surface through a combination of absorption and reflectance.  In general, low, thick overcast cloud such as stratus can attenuate irradiance by more than 80%, whilst the effects of high level cloud such as cirrus may only cause 20% attenuation.  In southern England winters  are characterized by periods of low and very low overcast skies.  In summer the general pattern consists of few, scattered or broken  cumulus, the attenuating effect of these summer clouds is less than those of winter and the overall effect is to cause fluctuations in the output of solar devices.

 A significantly different climate to that of Southern England is that of Arizona, whose height and extent diagram is shown below.

The principal difference is the much lower frequency of occurrence of low level cloud and less seasonal variation.

The effects of planetary motion and cloud cover are combined in the simulation of solar irradiance over Southern England which is shown below:

This graph is based the solar radiation received by a horizontal surface, such as a field.  In most cases the yield of solar devices is increased by tilting them towards the Sun.  Output can be further enhanced by mounting the panels on a tracking device which ensures the panels are always pointing directly at the Sun, however the extra yield must be set against the cost of the  the tracking mechanism.

The graph below shows the effect of cloud on the output of a solar device.  It was compiled from three sets of observations taken around solar noon in June 2011 each with a different cloud extent.

The solar irradiance can vary significantly over a short period of time.  Under a clear sky, the fluctuation in the level of insolation is small and the output is a function of the Earth's rotation about its xis. Similarly, under an overcast sky, the output is more or less constant, but at a much lower level than under a clear sky, in this example, the output is reduced to approximately 10% of the clear sky value. In this case, the scattered cloud was cumulus drifting across the sky at around 4,000 feet obscuring the Sun during for intervals of varying length.. The level of attenuation lies broadly between the clear and overcast skies. The observations for scattered cloud show a phenomenon which might be termed cloud fringe effect, as the edge of the cloud passes over the device, there is an increase in the diffuse irradiation causing the overall level to exceed the clear sky value.

Description of Diagrams


The core of both sets of diagrams is a database of weather and related reports.

• Cloudbase and Extent -  The diagrams are an attempt to show variation in the nature of cloud cover with climate. The diameter of the circle indicates the frequency of occurrence and those representing cloud cover are pie charts showing the proportion of the extent.   Extent is described using the descriptions  used in Metar reports, e.g.FEW (1 - 2 Octas), SCaTtered (3 - 4 Octas), BroKeN (5-7 Octas) and OVerCast (8 Octas).  Cloud is described as high, if the base is greater than 18,000 feet, low if less than 6,000 feed and very low if it is less than 1,000 feet. Only the highest, most significant layer is used in the computations. It is planned to evolve these diagrams to include more layers, the code was originally intended for use with Western Europe data where the lowest layer is frequently the most significant, however, they do not provide a full picture of the sky in monsoon areas  where the sky can be significantly more complex.

• Wind - The wind related graphs are based on SQL retrievals from a database of weather reports which were clipboarded into Excel.  Datasets where chosen which had an almost complete set of hourly observations   for a given year.  There are some anomalies in the process, but it is thought that the results give  are reasonable description of the variation in wind speed over time.

Pumped Water Storage

Pumped water systems store energy by increasing the potential energy of a mass of  water by pumping it from a lower reservoir to a higher one, then recovering that energy with a turbine when it flows back down again. The diagram below shows the  main components of a system which acts as a form of battery. During the "charge"  phase electric motors drive pumps which move water from the lower reservoir to the upper one. The energy is recovered when the water flows back to the lower reservoir and passes through turbines which drive "generators".  There are losses associated with the process, the figures quoted in Wikipedia suggest that typical efficiencies are in the range 65 - 85%.

The basic equation which describes the systems storage capacity is shown below.  The simplicity of the equation is in contrast to the construction of these of system which are often massive civil engineering projects.

The key term is the product of V and H.  For utility scale projects, the volume V is typically of the order of millions of cubic metres whilst the height, is tens or hundreds of metres.  The density of water rho is constant of at 1,000 kg/m3.  The acceleration due to gravity is also a constant at 9.81 m/s2 and the efficiency eta is a fraction less than one.  The efficiency of the Dinorwig plant in North Wales is thought to be around 75%. Q is the energy stored in Joules (1 kwh represents 3.6 MJ).

A typical urban water tower with a height of 30 metres and a storage volume of 1,000 m3 if used as a  pumped water storage system would have a capacity of approximately 50 kwh, assuming an efficiency of 60%.  However, major installations such as Dinorwig have sufficient capacity to provide some grid management capability by using electricity during off-peak periods to fill the upper reservoir and provide 1 to 3 GW of generating capacity during peak demand.

Pumped water is the principal grid scale storage technology.  The energy storage density is low, in the water tower example used above, the density is 20 tonnes/kwh. For small scale systems, the cost could exceed £1,000/kwh, these figures are high compared to lead/acid  batteries which might cost around £250/kwh for a similar sized system.  The main strength of pumped water is that very large quantities of energy that can be stored, much more than is possible with the various battery technologies.  Pumped storage systems are major civil engineering projects, some are based on disused quarries, others on large dams and disused mine workings are being considered for conversion. Existing systems have generating capacities similar to those of small to medium sized power stations, the buffer capacity for most grid systems is measured in hours rather
than days.

Links to other sources

• Wikipedia - Pumped Water Storage
• Wikipedia - Dinorwig Power Station
• Wikipedia - Raccoon Mountain
• Wikipedia - Guangdong

Laundry

One of the side effects of installing rooftop PV is a desire to balance generation and consumption. I know of one father who is frustrated by his daughter's use of hair straighteners.  A recent piece in "The Guardian" told of a couple who were surprised by the amount of energy used by a tumble dryer.  Proof of the doctrine of unexpected consequences is that working from home results in swapping the daily commute for domestic chores.  In an attempt to turn laundry into environmental science, I sometimes weigh the washing before hanging it out to dry and then once again when it is it back in the house.  The results of a year's bizarre behaviour are shown in the graph below:

Over the year, the average water removal is 1.5 kg/wash.  By making some assumptions about the efficiency of tumble driers, this approximates to the equivalent of 600 kwh/year, which might account for say 10 - 20% of the average household electricity consumption of 3,500 kwh/year.

Several houses in our road put their underwear on public display a couple of times each week. but there was a time when most households had a washing line and a prop to keep sheets of the ground.  To authenticate this statement, consult the works Shirley Hughes, a favourite author of bedtime stories for many children.

In the newspaper supplements which attempt to promote "eco" living, you will find adverts for rooftop solar water heaters (useful for six to eight months each year) costing around £3,000, ground source heat pumps for even larger amounts, but with the lure of RHI payments.  Washing lines and whirligigs seldom figure in these publications.  We are fortunate in having a conveniently placed railing, but if we installed a proper south facing washing line, the cost might be £100 for poles and concrete foundations, this would be an investment which would pay back in a couple of years.  Laundry is not a sexy subject, even for environmental journalists, so can the lifestyle gurus make laundry fashionable, reduce emissions and boost energy security?

Conservation is difficult for politicians, our present government has attempted to be "the greenest government ever", but it is easier to encourage wind turbines than washing lines.  Does 10 Downing Street have a whirligig?

Urban Wind

Munn's third law states that any place you can wear a kilt or a skirt without embarrassment might not be a great place to put a wind turbine.  With this in mind, I spent a few mornings cycling round a seaside town with a simple wind speed meter in an attempt to get an understanding of urban wind.

Until recently the most common source of wind speed data was weather reports from airfields. These are large open spaces and the weather station is usually located somewhere close to the point of touchdown where its data will make the greatest contribution to aircraft safety.  This is in contrast to most residential and commercial areas which are cluttered with buildings, trees and infrastructure such a bridges all of which might be crammed into hillsides and valleys. In the past few years, data from small weather stations mounted in backyards has become available.  The two sources give different impressions, typically, airfields have a average annual wind speed in roughly in the range 4 - 7 m/s, whilst backyards might experience 1 - 4 m/s.  As with all gross generalisations, there are exceptions, but my own backyard sitting on the sheltered side probably has an average of around 1 m/s based on many calm days and a few gusty ones.

Wind speed measurements are typically taken at a standard height of 10m although there are some important exceptions, for offshore buoys it is often 4 - 5 m, for offshore platforms it can be well over 100m (to assist helicopter operations).  Private weather stations can be at any height available to the owner. However, they are generally located at the base of the boundary layer which is not an ideal place to put a wind turbine.  Utility scale machines are mounted on towers, typically 100 metre tall which lift the rotor out of the turbulent and complex air flows found around roof and tree tops.  The photo shows a medium sized wind turbine mounted on a tall tower in an urban location:

However, this type of structure is not practical/acceptable in the average backyard, so wind found at approximately 10 metres is the the resource that is available to most people (subject to neighbours, town planning and building regulations which keep towns and cities safe and relations between residents harmonious).

The plan was to cycle around the town taking wind speed measurements at a variety of locations and compare them to data from a small airfield a few km to the west.  In a failed attempt to introduce an element of street theatre I took a small model of a Savonius wind turbine with me.

Whatever other merits it may possess, the Savonius design can withstand the rough handling that comes from being strapped to the back of a bike.

During seven outings I found about 20 locations where I could take measurements.  With the single exception of a curious dog, this bizarre activity attracted no attention.  The locations included the seafront and a breakwater, the roofs of multi-story car parks and my own backyard.  One days results are shown in graphic form below:

Moderate winds at the airfield are usually smooth and there is a good relationship between the wind there and that experienced on the sea front.  In these places the Savonius model would spin continuously when the wind was greater than 3 m/s.  However, in the town, suburbs and parks the wind was usually attenuated and turbulent, the graphic is a sketch of the relationship between "clear" and "urban" wind:

The rooves of car parks were the most interesting, all five locations were well above surrounding roof tops, yet in all cases, the wind was turbulent and it was rare for the Savonius model to spin continuously.  Having seen several horizontal axis wind turbines in urban locations they often appear to "hunt" for the wind then spin up and down with the gusts.  The vertical axis Savonius was usually quick to respond to gusts, however, the coefficient of performance is low.  The coefficient of performance is the fraction of the wind's energy that the turbine manages to extract.

The relationship between wind speed and power is cubic, thus a 5 m/s wind has almost five times the energy of one of 3 m/s, the relationship is complicated by variations in a turbine's coefficient to performance with wind speed.  In general, the coefficient of performance declines with increasing turbulence.

It is probable that a suburban area with low and widely spaced housing on flat land might give more encouraging results, but in a densely populated English town, small wind turbines have limited potential for generating significant amounts of energy.  The greatest potential for wind energy appears to be large turbines located offshore where average annual wind speeds are significantly higher than those onshore.  However, offshore wind is still a weather/climate dependent energy source.