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Final project at Essent: Improving the "Hourly Price Forward Curve"

HPFC Project

As a business unit that is acting as a center between the wholesale market for energy and the retail customers, we have to manage and price all the risks involved in incompatibilities between both. One such a risk at the power side is the lack of prices on an hourly level at the moment we sell hourly load profiles to our customers. For this purpose we generate daily an Hourly Price Forward Curve (HPFC), which should offer the best estimate for the hourly price for the next years on the moment of publication. Apart from pricing the HPFC is also used for hedge and portfolio valuations. Furthermore energy companies with conventional assets use it for plant valuations.

It is therefore an essential instrument for any serious energy company. In close cooperation with Innogy colleagues from Germany, we are currently developing an improved HPFC. Three basic approaches for developing a HPFC are:

  1. statistical model: calculation of the profile based on average calculations of historical spot price time series.
  2. fundamental model: calculation of the profile based on supply and demand curve (i.e merit order curve & load).
  3. combined model: combination of the two models to calculate the hourly profile (also known as hybrid model).

We had as basis a statistical model, which we have brought a step further by optimization techniques (minimizing deviations from quality criteria). We also partly included a fundamental model, but not looking forward, but as a correction on historical data with different asset capacity deltas as input. Regression techniques are used here. Although we have made significant steps forward, we still see ample room for improvement, as mentioned in the list below. All of these topics may be explored further by the student for his or her thesis. Some are already well defined, others need still more scoping and modelling.

  1. Improving adapted historic spot price modelling
    The model determine the sensitivity of each type of generation on the spot price, adjusts the historical generation of the relevant commodities to the current level – taking into account the development of the renewable energies and the conventional power phase-out. After that it calculates quasi-historical spot market prices using the sensitivities and the adjusted generation.
    The regressions we apply give, certainly for bigger asset deltas strange results, further improvements have to be made here. (Improving model or new model)
  2. Improving optimizing hourly factors
    The optimizations we do now are done with a certain chosen set of goal functions and restrictions.
    The forward market prices are put as restrictions and the preservation of the structure of the hourly prices as goal function. We expect that improving and fine-tuning the optimization algorithms would lead to significant improvements.
    The underlying modelling of the desired structure could be made more dynamic based on time series analytics.
  3. Improving clustering of historic spot data
    Hours in the future are matched with hours in the past with a certain method of clustering. Now this is done all static and deterministic. Making the clustering dynamic and stochastic would be a step forward.
  4. Model consistency with Simulation of hourly price
    For simulating hourly prices we use a separate temperature dependent model. To be consistent with the HPFC we would need to take care that the average of the simulations does not differ from the HPFC. This means that one or both of the models we have has to be adapted.
  5. Short term HPFC
    For the HPFC in periods nearby we should use the information of our recent history much more strong than elsewhere. How to do this is an open question yet for us. This looks like a typical time-series problem, however maybe Kalman filters can be applied in combination with recent weather actuals and forecasts.
  6. Fundamental model
    We consider a fundamental model based on forecasted future asset capacity, power demand and interconnections.
  7. Daily gas curve
    We need to make an equivalent on the gas side for the HPFC. This might be a challenge as gas has its own characteristics that need to be modelled properly, e.g. seasonal forward products and dependency on gas storages and weather.

For some background see e.g.


Innogy is one of the largest suppliers of gas and power in Europe. In addition we invest heavily in wind and solar projects. Within the Benelux, Innogy is known to the general public as Essent. We are located in Den Bosch and the office is conveniently located close to the central station (10 minute walk), and many of our employees travel by train. The thesis will be supervised by the Complex Risk department, which is the primary medium term (1-5 years ahead) modeling department within the Benelux organization. Among other things we are responsible for the modeling of the market risks of Essent.

Profile of the candidate

We are looking for a student (applied mathematics, econometrics or otherwise quantitatively oriented) with exceptional skills in mathematics and modelling. Experience with Matlab will be a strong advantage, but also knowledge of other programming languages will be beneficial.


Duration of the internship is flexible, but we are aiming for a minimum period of around 3 months.

What we offer

The student is invited to work at the office for up to 5 days per week (if he or she prefers that). Our team generally works from home on Fridays and also quite regularly on Tuesdays. The student could join the team in this pattern. Essent offers an internship fee of EUR 450 per month to all thesis students.

Contact: prof. dr. R.J. Boucherie