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".