WIAS Preprint No. 3069, (2023)

Optimizing the economic dispatch of weakly-connected mini-grids under uncertainty using joint chance constraints


  • Ouanes, Nesrine
  • González Grandón, Tatiana
  • Heitsch, Holger
    ORCID: 0000-0002-2692-4602
  • Henrion, René
    ORCID: 0000-0001-5572-7213

2020 Mathematics Subject Classification

  • 90B06 90B25 90C15


  • Joint chance constraints, mini-grid operation, unreliable main grid, stochastic forecasting errors, spherical radial decomposition




In this paper, we deal with a renewable-powered mini-grid, connected to an unreliable main grid, in a Joint Chance Constrained (JCC) programming setting. In several rural areas in Africa with low energy access rates, grid-connected mini-grid system operators contend with four different types of uncertainties: forecasting errors of solar power and load; frequency and outages duration from the main-grid. These uncertainties pose new challenges to the classical power system's operation tasks. Three alternatives to the JCC problem are presented. In particular, we present an Individual Chance Constraint (ICC), Expected-Value Model (EVM) and a so called regular model that ignores outages and forecasting uncertainties. The JCC model has the capability to guarantee a high probability of meeting the local demand throughout an outage event by keeping appropriate reserves for Diesel generation and battery discharge. In contrast, the easier to handle ICC model guarantees such probability only individually for different time steps, resulting in a much less robust dispatch. The even simpler EVM focuses solely on average values of random variables. We illustrate the four models through a comparison of outcomes attained from a real mini-grid in Lake Victoria, Tanzania. The results show the dispatch modifications for battery and Diesel reserve planning, with the JCC model providing the most robust results, albeit with a small increase in costs.

Download Documents