Flow-based capacity calculation for prospective studies

Improving the power grid physics modeling in long-term studies.

why join artelys?

Artelys is specialized in mathematical optimization, quantitative decision-making and scientific modeling. Relying on its high level of expertise in quantitative methods, Artelys delivers efficient solutions to complex business problems. They provide services to numerous industries: Energy, Transportation, Telecommunications, Manufacturing, etc. Artelys is an international company with offices in France (Paris, Lyon, Nantes), Canada (Montréal), Belgium (Brussels), and the USA (Chicago).  

Artelys offers several products and services, including software solutions (mathematical optimization software, business specific customized and custom solutions), studies, consulting, training, etc. In particular, Artelys consultants deliver operational solutions that perform security analysis of power grids, i.e. simulations that check that the power grid will be safely operated on the short term (e.g. one day ahead). It involves performing a massive amount of power flows that evaluates the repartition of power flows on the grid from generation to loads.


Most long-term grid models are zonal, i.e. only large zones -typically the size of a country- are represented. Power transfer capacity between zones is usually modeled through simple links with limited capacity between neighboring zones. This approximation is not realistic in meshed grids (e.g. only 20% of flows between France and Italy transit through the boundary lines between the countries. The remaining loops through Germany and Switzerland but also for a significant share through Belgium, the Netherlands, Austria, and Slovenia). This is due to the second Kirchhoff law that flows are higher on low impedance paths between generation and loads.

As a result, better models have been developed. Among them, the so called “Flow-Based” models are now widely used in Europe: Based on a detailed grid representation including all network elements, individual lines capacity constraints are aggregated into linear inequalities linking country-level exchanges. As a result, the joint impact of all exchanges on each line is considered and it is possible that a line between Austria and Italy limits the exchange from France to Italy because the exchanges between Austria and Italy are already very high. This set of inequalities is defining a so called “flow-based capacity domain” that represents the domain of feasible power transfers between modelled countries.

In long term studies, the flow-based domain is computed after grid expansion, i.e. after adding new lines to the network. It allows to compute with increased precision the benefits of these new lines.

The internship will focus on the design and the implementation of a Flow-Based capacity calculation methodology using PowSyBl (a set of power system modeling tools). Once the domains will have been computed, the intern will demonstrate their use in a long-term study thanks to Artelys Crystal Super Grid.

what we are looking for

The candidate must be in his/her last year of master’s degree in computer science and/or applied mathematics and/or power systems and/or operations research.

Required skills:

  • Programming in Python
  • Linear algebra
  • Fluent in English
  • Additional relevant skills:

  • Power Systems (Power Flows and Power System Economics)
  • Mathematical optimization
  • Programming in Java
  • Python NumPy
  • Fluent in French
  • Benefits

    The intership will take place in our Paris office and may lead to a long-term job offer.


    This is your dream job? Apply now!


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