Two-stage stochastic model to invest in distributed generation considering the long-term uncertainties Articles uri icon

publication date

  • September 2021

start page

  • 5694

end page

  • 5705


  • 18


  • 14

Electronic International Standard Serial Number (EISSN)

  • 1996-1073


  • This paper used different risk management indicators applied to the investment optimization performed by consumers in Distributed Generation (DG). The objective function is the total cost incurred by the consumer including the energy and capacity payments, the savings, and the revenues from the installation of DG, alongside the operation and maintenance (O&M) and investment costs. Probability density function (PDF) was used to model the price volatility in the long-term. The mathematical model uses a two-stage stochastic approach: investment and operational stages. The investment decisions are included in the first stage and which do not change with the scenarios of the uncertainty. The operation variables are in the second stage and, therefore, take different values with every realization. Three risk indicators were used to assess the uncertainty risk: Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR), and Expected Value (EV). The results showed the importance of migration from deterministic models to stochastic ones and, most importantly, the understanding of the ramifications of every risk indicator.


  • Electronics
  • Mechanical Engineering


  • distributed generation; energy markets; energy trading; mix-integer linear programming; two-stage stochastic programming