AA4 – Energy Transition



Modelling and Optimization of Weakly Coupled Minigrids under Uncertainty

Project Heads

René Henrion, Dietmar Hömberg

Project Members

Nina Kliche

Project Duration

16.06.2022 − 15.06.2025

Located at



Ensuring access to affordable, reliable, sustainable and modern energy for all is one of the United Nations’ seventeen Sustainable Development Goals for 2030. In rural areas of African sub-Saharan countries, electrification is still at low speed. In Ethiopia for instance, 70% of the people living in re- mote rural areas have no access to electricity. As a viable solution mini-grids have emerged as the extension of the main grid can be extremely expensive and cannot even guarantee good quality of service. Mini-grids typically consist of several decentralised energy generation sources, a battery energy storage system (BESS), a backup diesel generator (DG), inverters, meters and controller units. They are either connected to or isolated from the main grid and distribute en- ergy at a community level. The mini-grid designer now must find a compromise between efficient management of resources, a low cost and high resilience.

There is a vast literature on modeling and optimization related to mini-grids which often miss involving battery degradation, which is of major importance as the battery is key component in terms of capital and operational expenditures, and the presence of uncertainty and their impact on optimal decision making. Typical sources of uncertainty are energy supply by renewables, demand of energy and unforeseen outages of the main grid. Load coverage then can only be guaranteed with a certain probability over a period of time. For that, one imposes so called joint probabilistic constraints in continuous time.

In a first step, a deterministic optimal control problem for minimizing the daily operational costs including an appropriate battery model will be set up and solved numerically. After that, the uncertainty aspects of the problem will be tackled and binary decisions for e.g. switching on/off the backup DG will be included. Eventually, a bi-level problem for the optimal design of mini-grids will be studied.

Related Publications

  • M. H. Farshbaf-Shaker, R. Henrion, and D. Hömberg. Properties of chance constraints in infinite dimensions with an application to pde constrained optimization. Set-Valued and Variational Analysis, 26(4):821–841, 2018.
  • M. Hassan Farshbaf-Shaker, Martin Gugat, Holger Heitsch, and René Henrion. Optimal neumann boundary control of a vibrating string with uncertain initial data and probabilistic terminal constraints. SIAM Journal on Control and Optimization, 58(4):2288–2311, 2020.
  • T. González Grandón, R. Henrion, and P. Pérez-Aros. Dynamic probabilistic constraints under continuous random distributions. Mathematical Programming, 196(1):1065–1096, 2022.
  • Wim van Ackooij, René Henrion, and Pedro Pérez-Aros. Generalized gradients for probabilistic/robust (probust) constraints. Optimization, 69(7- 8):1451–1479, 2020.

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