Maths - behind the scenes / Maths in the society / Maths is fun / PhD / Weather

Money blowing in the wind

I bet you’re not looking forward to receiving your monthly electricity bills. Can you predict how much you’ll be charged this time? Short answer: assume that more than you’d be willing to pay. Long answer: spend a couple of years studying how electricity prices evolve in time. Yes, that’s exactly what my PhD is about.

Power markets are surprisingly complicated. Trading energy is a relatively new idea, increasingly important because of the gradual liberalisation of the EU electricity industry. Not only do market rules in various countries differ significantly, but relevant laws change frequently. Therefore if you’re interested in any details, please don’t rely solely on my article, but refer to the website of the appropriate market (eg. European Power Exchange).

From the mathematical point of view, modelling any financial processes is an extremely difficult task. Stock values change in unpredictable ways, they also strongly depend on political events and human behaviour. Because of that, financial mathematics attracts increasing numbers of mathematicians with different backgrounds. Actually, not only mathematicians. For example, a building block for many financial models is a so-called Brownian motion, first used by physicists to describe chaotic movement of particles. The tools we can use are limited only by our imagination!

Energy markets are problematic, as they behave differently than traditional stock exchanges, so we have to come up with completely new ideas to model them. The main difference is that the supply and demand for electricity must always match. Storing electricity is almost impossible, in the best case very expensive, so we cannot produce (or buy) more and leave it for later. On the other hand, the supply is inelastic, because industry and citizens require a specific amount of power for their regular activities. You don’t like blackouts, do you? And they happen exactly as a result of a significant imbalance in the energy market.

Thankfully many people work very hard (this is how I like to think about myself) to make sure that you don’t have to dig out these candles too often. Mathematical models help producers decide how much energy to generate and traders to buy and sell its appropriate amounts. Most of trading takes place in electricity markets.

Two main types of contracts are traded. First, spot contracts (traded at noon) oblige producers to deliver a specified amount of energy for 24 hours, from midnight of the following day. Second, one can also trade futures contracts for a specified delivery period: a week, a month or a year. For example, if a producer signs a “2 months ahead” contract today (June 2017), she or he would have to deliver the electricity between 01/08/2017 and 31/08/2017.

However, predicting the prices so far in the future is a difficult task. We don’t know the general state of economy or if Donald T. decides to build a *huge* bridge from New York to the Moon (which would require a lot of power, I guess). And, what interests me most, what the weather will be.

Weather conditions significantly influence electricity prices, both the demand and supply. In countries like the UK or Germany, in general the demand is higher in cold months, when we need to heat our houses and offices, as well as use more light due to shorter days. In warmer places, also in the summer a lot of energy is needed for air-conditioning. On the other hand, renewable energy production strongly relies on the weather. We can’t generate wind energy without wind!

This is why in my models I have to take into account weather forecasts. As you know, they’re pretty useless a few weeks in advance, not to mention a few years. Therefore the models need to account for uncertainty related to these forecasts.

You might wonder if these factors really matter. They actually do! Now many markets even allow the prices to be negative, which means that we get paid for the electricity usage. It happens rather rarely, so you won’t even notice. However, it’s interesting to note that almost all negative prices are observed in early morning hours after a windy night. This means that a high level of wind energy generation, combined with a low demand (most factories are closed at night, we also tend to sleep), can significantly decrease electricity prices.

In other words, the chance for a lower electricity bill is literally blowing in the wind.

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