Sloping Off

The clear sky performance of solar devices is reasonably easy to predict.  Man has had a good working knowledge of sun-earth geometry since the dawn of time and until scientists starting messing with decaying atoms, the sun was time.  The equations may have gained some extra terms and decimal places, but an understanding of the principles is apparent in England's Stonehenge, Mayan Temples and many other ancient world heritage sites and sundials.  Over the past few weeks I have been attempting to clean up our "Simple Clear Sky" model.  This small lump of Python code trades accuracy for simplicity, my research interest in the the effect of clouds on solar devices, whilst a solar irradiance under a clear sky follows a smooth curve, soon as a cloud gets between the sun and the earth, the curve looks like the teeth of a halloween lantern, so high accuracy is not that important.  There will be more on this model in a later post.  The code clean-up is part of a large decluttering of spreadsheets and code fragments.

When I first became interested in wind and solar energy resources, I attempted to educate myself with crude wooden constructions in the backyard.  Having gathered the photos together, I realise must have caused my neighbours some embarrassment.  Having amassed some photographic evidence of things I wish I had never started, I have none for experiments which were vaguely useful.  One of these was a 1.5 watt amorphous PV panel which was south facing, but the angle relative to the ground could be varied from zero to ninety degrees.  The objective was to see how the output of a solar panel changed with slope under an overcast sky.  A summary of the results is shown in the graph below:

There are two sets of data, one for a clear day and the other for low overcast skies.  The clear sky curve has a maxima somewhere around 50 degrees.  A reasonable estimate of the clear sky results could have been made by the Python model.  The curves of the overcast sky are more interesting.  First they "peak" when the panel is horizontal, suggesting that the irradiance is more or less evenly distributed over the hemisphere of the sky, secondly, the relationship between slope and irradiance could be approximated by a linear relationship.

Whilst my backyard is generally sheltered from the wind, a stray gust ended this experiment, the mountings of which were later used as firewood.

Later this year, I hope to have a small 20 - 30 watt solar installation working in the back yard, which hopefully will have some data logging capability which will allow a cloud sky model to be firmed-up.

Soil Temperature (A day in the life of)

I've been collecting soil temperatures from my back yard for the better part of two years, normally I do this around sunset on Sunday evening for no better reason than this is usually a pleasant time to sit in the garden and the routine provides some consistency in the data.  The link at the bottom of the page describes the process.

Recently, I found myself in the garden before sunrise (see note below).  This was an opportunity to study the variation in soil temperature during the day.  It was clear  that this could be large, on a spring the morning the ground can have a thin layer of frost and by noon it can be warm to the touch.  The graph below is for a randomly selected day at an arbitrary chosen spot, whilst the absolute values maybe suspect, it does give an indication of their variation.

At sunrise, the sky was more or less free of low cloud and the stars were visible, by noon there was scattered and broken cumulus and a few drops of rain fell but by late evening it was cool and clear again.  The most striking feature of the graph is the variation in the topsoil temperature (0.1m), maybe I missed it's low point, but this could have been 5 or 6 deg. C. by noon it was 16 deg. C, had the clouds been thinner, this might have reached 20 deg. C.  It is this part of the soil where vegetables grow in a thermally turbulent environment.  I am far from being an expert gardener, but I have learnt from the experience of losing seedlings to frost and failure to grow vegetables for winter harvesting that that the choice of crop and the timing of sowing is important.  As the depth of the measurement increases, the variation in temperature with time decreases, at 1.0m the observed range was less than 2 deg. C.

Also on graph is the air temperature from a weather station located approximately 10 km to the west.  I have attempted to collect air temperature data, but shadows from trees, the proximity of walls and our location on the side of an suburban valley make it hard to figure out what is being measured (much the same applies to the soil temperature measurements).  Comparing the soil and air temperature suggests two things.  The first is that whilst there is a correlation between air and soil temperature, the variation of the latter is much greater.  The second is more subtle and this is the complexity of the relationship.  During the morning the ground  warmed and the air followed making it reasonable to assume that there was a relationship between the two events.   However, by late evening, the air temperature started rising even though the ground was subject to radiative cooling.  At this time, the wind which had been blowing gently from the SW all day, veered to the NE, at a guess this slight rise might have been due to advection.

Whilst messing with the soil temperature data, I took the opportunity to update the graphs of Sunday sunset data (it maybe a few days before the website is updated).  The graph for the 1m is shown below:

This graph also contains significant variation.  The winter of 2012/13 was long and cold (maybe not extreme cold, but cold for a long time) which was due to a cold air mass from continental Europe.  Last winter (2013/14) was mild, but marked by wet and windy storms blowing in from the Atlantic.  During January and February the mainstream media was full of pictures of flooding and wind damage, but by April, they were free to return to party political gossip.  This contrast between the two winters is apparent in the soil temperatures, this year they are up to 5 deg. C higher than last year.

Description of the data collection process

This link describes the data collection process and the page is periodically updated with data as it becomes available:

Soil Temperature

Bloggers Note

The drinking habits of my dog are not good.  Whilst he has an adequate supply of clean water he is drawn to ponds, puddles and worse (much, much worse). Normally his digestive system copes with this abuse, but at 04:00 on Tuesday, it failed to do so dramatically.  By 05:00 it was clear that frequent trips to the garden lay ahead, so to offset my irritation and boredom, I set up the soil temperature measuring equipment and produced the graph above.  Should anyone be interested, the dog has made a full recovery and the next rain shower should restore the lawn to its former state..  I am still making up the lost sleep.

Solar Energy in Winter

Solar PV is the most accessible of the sustainable technologies.  Unlike wind turbines which are relatively expensive and require carefully selected locations to be effective, solar panels are relatively cheap and can be located in backyards, fields and roofs.  The downside of solar PV is that it does not work well in an English winter and not at all at night.

Under a clear sky, the ideal mounting for a PV panel is on a tracker device which keeps it pointed at the sun, however, this type of device is expensive and a common solution is to place them on a south facing frame tilted according the latitude of the installation.  This approach will maximise the yield over the period of a year allowing the panel to take advantage of the clear or sparsely clouded skies of summer.

Treat the comments below with caution as they are based on two experiments using  basic measuring devices and I have not yet hat the opportunity to test the ideas with a PV panel.  The hypothesis is that the yield of a PV panel may by higher in winter if it is mounted horizontally.  I'm contemplating some further work for next winter with a project which attempts to maximise the use of wind and solar power, but at the time of writing, no decision has been made.

The first experiment was conducted in 2010.  The equipment was crude, it consisted of a light dependent resistor (LDR) mounted at one end of a short length of waste pipe, this was mounted on some woodwork which allowed it to take readings around the hemisphere of the sky.  The calibration of the LDR was in Lux and whilst this was not ideal, the objective was to observe relative intensities, so units were not too important.

On occasional trips to the Science Museum, I'm inspired by the well crafted instruments and the neatly written notebooks of observations.  These are things I aspire to, this particular device was used as firewood after it had produced a few graphs.  The link below gives a slightly more detailed description of the exercise, but the graphics below show the extremes.

The first graph shows measurements made under a clear sky.

Obviously, the maximum irradiance is mainly direct and at a maximum in the direction of the sun.  Under an overcast sky, this is not the case.

In this case, the irradiance is diffuse and more or less evenly distributed around the hemisphere, albeit at a much lower intensity than under a clear sky.

The second experiment took place during the winter of 2010/11.  The equipment used was the first attempt at a solar radiometer.  Whilst the device did produce some informative data, it also taught the lesson that simplicity, reliability and repeatability should be the design objectives.  The procedure was stand in the back yard with the improvised radiometer around noon and take two observations, the first with the instrument in the horizontal position, then with it inclined to the same angle as the pitch of our roof.  The absolute magnitude of the irradiance was probably dubious, but the presented as ratios is informative.  The graph shows the distribution of the ratio of the irradiance of the horizontal surface to that of the sloped one broken down by cloud cover.

The results show two peaks.  the left one in the colours of a clear or moderately clouded sky shows that the irradiance of the horizontal surface is less than the sloped one.  More interestingly, this is reversed under an overcast sky in which case the irradiance of the horizontal surface is greater, albeit at a much lower level.

One of the challenges of sustainable energy is managing seasonal variation.  In the case of solar energy, the irradiance is determined by sun-earth geometry with the clear sky irradiance in January being less than 20% of that in July and the increased frequency of overcast skies in winter reduces this still further.  Horizontal mounting might increase the winter yield, but by how much is not clear.  I am currently working on a cloud sky computer model which might allow the concept to be explored.

Timing is everything

A common measure of sustainability is the percentage of energy generated from renewable resources such as wind, solar, tidal, hydro, bio-mass etc.  Often the time period on which this statistic is estimated is a year.  Equally important is the timing of supply and demand.  The classic example is solar generation, the graph below illustrates the demand for electricity on a typical spring day and the solar irradiance available to contribute to meeting it, a similar graph could be drawn for wind and the time period extended to include seasonal variations.

The two ways of meeting the overnight demand are storage and alternative means of generation.  Most energy economies are evolving to adapt to diverse means of generation.  At the present time it is hard to make a good case for storage as most energy economies can absorb what wind and solar installations can offer them and frequently, they are given priority when working out how to meet demand.  In general, there are few surpluses of energy which can be accumulated in a storage system, even if such a system is available.  I don't have a handle on the relative risks and economics of utility scale storage and generation, but at a guess, maintaining a fossil/nuclear generating capability is the "low" risk option.  The approach makes wind and solar sources incremental parts of the energy mix which need backing up with an equivalent amount of conventional capacity.

The case for storage is that it is a step towards sustainability.  At its most basic, the harvest from solar panels during the day can be stored and used to keep the lights on after dark.  Within the arid regions towards the equator, where there a clear skies and relatively small seasonal variations, this could be a workable scenario.  In the temperate regions, more complex system are needed with a mix of solar and wind.  Solar works well in summer, but the winter yields are low, wind works better in winter and on some days neither produce very much.

I'm currently messing with a very small scale storage project in which a small computer attempts to keep itself alive by "buying" sustainable energy, this could be done as a computer similar (which is happening as a parallel task), but the having some hardware, makes it both fun (other relevant words are frustrating and expensive) and more instructive than a bunch of numbers from a computer programme.  There in one economic nicety, you can attempt to use off-peak electricity which is approx. 7p/kwh where possible in preference to normal daytime rates which are close to 20p/kwh.  If you used this approach to ensure that a high proportion of the electricity you use was from renewable resources, you would have some capital and operating costs beyond those normally associated with turning the lights on.

Living next to a railway station used by commuters, I've become aware that there are an increasing number of electric cars around, typically, these are priced at around £20k after a £5k government subsidy.  Apart from their high cost, electric vehicles charged by off-peak electricity are an attractive concept, in effect they are storage on wheels.  An interesting policy study would be the  effect of providing similar support for including storage into homes and offices.

Clouds and Irradiance - A Simple Model

Simulating the performance of a solar energy system requires a model for solar irradiance.  Solar irradiance is a function of Sun-Earth geometry and atmospheric conditions of which cloud cover is the most significant.  On a typical summer day in the south of England  there will be a few or scattered cumulus clouds which might reduce the global horizontal irradiance to 80% of its clear sky level, whilst in winter a thick layer of stratus can reduce this to 10 - 20%.

As with everything else on this blog, this is unreviewed work-in-progress and should be treated with caution.  This is post is a simplified description of a project, it is planned to compile a more detailed account of the work at a later date.

The basis of the model is the attenuation of clear sky irradiance caused by the presence of clouds, this is described by a variable called the clear sky factor (CSF) which is defined as:

The graph below was compiled from data collected around noon in June 2011 illustrates the variation in CSF with cloud cover.  for the clear sky it constant at 1.00, for overcast conditions it is more or less constant at approximately 0.15.  On a day of scattered cumulus cloud the CSF fluctuated widely, the low levels recorded when the cloud passed between the measuring device and the sun, the CSF was close to that of the overcast sky, during the period of transition between cloud and clear sky, the CSF exceeded 1.0 due to an increase in diffuse irradiance, this might be called the cloud fringe effect. 

For air mass values in the range 1.2 to 6.0, CSF appears to be more or less independent of air mass which is allows a model of solar irradiance to be based simply on an estimate of clear sky irradiance and a description of the cloud cover.

GHI was chosen as a measure of irradiance because it is the most commonly collected form of irradiance data.  A basic measuring device is simply a small horizontally mounted PV cell.  Clear sky irradiance is influenced by factors such a aerosols and water vapour, whilst there are some excellent models which take these into account, for most locations little is known about the state of the atmosphere at a specific time, especially when clouds are present in the sky.  After some experimentation, a correlation developed by the Meinells which requires only air mass as an input was found to produce a reasonable estimate of Direct Normal Irradiance (DNI).  GHI is a combination of direct normal irradiance and diffuse horizontal irradiance (DHI), as no equivalent formula to the Meinell one could be found for diffuse irradiance, one was derived from local observations using a simple shaded radiometer, this latter formula is subject to revision as more data becomes available.

In the south of England, the "economic" range of air mass is approximately 1.2 to 6.0, for these values the plane parallel formula for Air Mass produces a workable estimate and offers some computational convenience.  This simplification may not be appropriate for regions such as Arizona where there is significant DNI at much higher values of air mass.

The formulas used for the estimated clear sky GHI are:

The most readily available source of cloud cover, apart from looking upwards to the sky, is the METAR reports used in aviation.  These include a description of the sky, if one or more layers of cloud are present, there will be a description of its base height and extent, e.g. SCT040 means scattered cloud at 4,000 feet.  A basic description of the extents is is shown below:

• FEW - up to 2 octas
• SCaTtered - 3 - 4 octas
• BroKeN - 5 - 7 octas
• OVerCast - 8 octas, no blue sky visible

The widespread use of these description made them a logical choice for use as the basis of a model.

One way of creating a model it use distributions of CSF for a given cloud extent.  The graphs below are summaries of the effect of low cloud (less than 6,000 feet) in a maritime temperate climate, also known as Sussex of Cfb in the Koppen system of climate classification.  The distributions for few, scattered and broken cloud are typically bimodal.  the low mode describes the CSF when the sun is obscured by cloud and the high mode is the interval of clear sky between the passage of clouds.

When there are only a few clouds in the sky, the average value of CSF is around 0.8 and there is a greater probability of high values of CSF (i.e. the overall attenuation is small).

As the extent of the cloud increases, the average value of CSF falls for scattered clouds and the probability of CSF being either high or low is approximately equal.  This is consistent with the definition of scattered cloud which is that up to half the sky contains cloud.

 Part of the definition of broken cloud is that there is at least some blue sky visible even though most of the sky is full of cloud, this is reflected in the summary graph.

There is no blue sky visible under an overcast sky and the distribution is unimodal and the mean is low.

These summaries are over  simplifications designed to allow a simple model.  Other factors which are important are the height of the equivalent summaries  cloud, high cloud are significantly different and the values of CSF much greater.  The model as currently configured, simply takes the highest, and most dense layer, which effectively assumes a simple sky, often the sky is complex, especially during the passage of fronts.  Part of the work in progress is to determine the variation in attenuation between climates, for example the nature of solar irradiance in the desert regions of Arizona, are significantly different from those on the south coast of England.

I'd like to call this research.....

But its also having fun with a kite.

The kite was given to me as a Christmas present by my son (aged 23 at the time, him not me).  It's a small kite which fits easily into a pocket and would be ideal for business people.  One can imagine herding the participants of a meeting into the car park and sending the kite aloft.  Then point upwards and exclaim "that's were we should be", followed by a profound silence and the sensible one saying "shall we go back inside now?".

Despite a complete lack of electronics and telemetry, the kite gives an insight into the the nature of wind at heights between 5 and 25 metres (maybe higher, I replaced the original string with a longer one and its still climbing).  Last Saturday when the wind was blowing 3 - 4 m/s, I took the kite to two different locations.  The first was a beach where the wind was coming in off the sea and the second was a public park in an urban area a mile or so north of the seafront.  The behaviour of the kite was significantly different at each site.

On the beach, the kite effortlessly took to the air and was stable at a height of 5m and the trailing streamers had no difficulty in keeping it head up to the wind.  Once the string was fully unwound, the kite sat comfortably in the sky, maybe with the odd flutter, but I was able to hook the handle on to the bike and take the photo at the top of the page.  After half an hour, I felt guilty about bringing it back to Earth.

At the park, things were different.  I almost pointed out to the man mowing the cricket pitch who cast disapproving looks in my direction, that what he was going to do on the grass later in the day was no less ridiculous than what I was doing but life's too short for pointless conversations.  Here the kite  struggled with turbulence up to, say, 15m and getting it airborne required many attempts, hoping that it would acquire enough upward motion to counter any downward influences.  With patience, it was possible to get the string fully extended, but the kite was never stable and was prone to twisting and each twist tied a small knot in the string.  I suggest that the number of knots in a kite string is a measure of wind turbulence.  Nor did the kite stay aloft.  Typically in urban areas, wind is not a smooth stream of air, but a series of gusts, often with significant gaps between then, it was in these gaps that the kite spiralled to the ground.  The kite suggested that conditions measured at 2m, extend upwards to at least 25m.  It was also clear that wind speed increased with height, even though the turbulence persisted.

When the next opportunity presents itself, I will take the kite into the hills to the north of the town, just because its fun.

PS - 18-Apr-2014 - I found myself on the same beach yesterday, this time the wind was coming from the NE and was blowing from the land to the sea.  The turbulence that is observable inland made it hard to get the kite airborne and once aloft, it started to drift earthwards as soon as a gust had subsided.

The Rayleigh Distribution

One of the reasons for modelling a system is to get an understanding of how it might work before you build it, the logic being that paper are spreadsheets are cheap whilst metal and earth moving are expensive.  There are many ways of doing this, one is to use historic data as the input, for example a time series of wind speed measurements, another is use some form maths/stats function to mimic the real world.  Each approach has its strengths and weaknesses.

I'm currently messing with a storage based project, some initial work was done on a computer, but to make it a bit more fun, I'm building a very small prototype which is controlled by weather reports from the internet.  This provides some insights which a purely maths and stats approach would hide, not the least of these is the economics of the process.  In a mathematical model, changing a parameter is often just a matter of editing a line of code, with a physical model, changing something usually involves a cycle ride and spending money.  This has forced some decisions on how much information is needed to drive the system and what is nice-to-have which leads to a discussion on the merits of a big budget which allows flexibility and experimentation or a small budget in which constraints may foster creativity.   Such is life at the cutting edge of R and D.

As with anything on this blog, this is unreviewed work in progress which should be treated with caution.

When I first became interested in sustainable energy systems, I found a source of data which provided the average wind speed for a given location. the figure for my backyard was 5.0 m/s (I think), this might be the case for level ground devoid of trees and houses, but it was a start.  To make an estimate of the energy that might be extracted from a stream of moving air, it is necessary have a distribution of the wind speed.  One solution is to use the Rayleigh distribution, which with the help of spreadsheet can take an average wind speed and turn it into a histogram which is an estimate of the of the number of hours per year a given wind speed will occur.  The Rayleigh distribution is a special case of the Weibull in which the shape factor is fixed at 2.0 which simplifies the process.  Both the Rayleigh and Weibull distributions can be used to model wind speed.  The relationship between the maths and the wind is empirical which simply means "it works" without a providing a causal mechanism.  This sort of model is common in science, the goals scored in a football match can follow a Poison distribution, rainfall can follow a Gamma distribution, extremes can be described with the Pareto and Gumbel distributions (amongst others).

The graph below shows the distribution of wind speed which is estimated by the Rayleigh model and observed wind speed for a selected location with an average wind speed of 5 ms/s:

In this case, there is reasonable agreement between the estimated and observed values, in part because the dataset was chosen for this reason.

As part of a project to learn about the nature of wind as an energy source, I collected data from diverse location, which I'm still studying.  The inference from this, so far, is that the Rayleigh distribution describes the wind speed distribution at an "ideal" location.  It provides a reasonable model where the terrain is flat or a plateau and also for offshore wind in locations poleward of the tropics and for upper air soundings at the 850 mb level.  It does not provice a good model where the terrain is complex or for urban areas.  In these cases, a better solution might be to use a Weibull distribution where the shape factor is in the range 1.2 to 1.8.  In these cases, the Rayleigh distribution will over estimate the energy yield.

This is a link to a more detailed description of the Rayleigh Distribution, it will be updated over the next few weeks as other work is completed.

Rayleigh Distribution