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