Lift-and-project MVEE based convex hull for robust SCED with wind power integration using historical data-driven modeling approach


The MVEE based convex hull is employed to cover the multiple scenarios to address the spatial correlation.

An adjustable robust SCED model over the MVEE based convex hull is set up, leading to a second order cone programming problem.

An inactive constraint reduction strategy is developed to further reduce the computational complexity of the proposed model.


This paper presents an adjustable robust security constrained economic dispatch (SCED) model with wind power uncertainties. First, the scenario based adjustable robust SCED model is presented. It considers multiple scenarios from historical data as well as the spatial correlation among wind farms. Then, the proposed SCED model becomes an optimization problem with a large amount of constraints which is skillfully solved using a lift-and-project minimum volume enclosing ellipsoid (MVEE) based convex hull. Furthermore, the proposed model is transformed into a second order cone programming (SOCP) model by the use of participation factors to generate adjustable generation outputs and thus guarantee the energy balance. In order to further reduce the computational complexity, the inactive constraints reduction strategy is proposed to quickly eliminate inactive SOC security constraints before solving the model. Numerical results of IEEE 14-bus and 118-bus test systems as well as the practical Polish power systems with several wind farms show that the proposed model can achieve better economies. Moreover, more than 82% of security constraints are identified as inactive in various cases of the simulation, and the proposed inactive constraints reduction strategy is promising for improving the computational performance.


  • Security constrained economic dispatch (SCED);
  • Minimum volume enclosing ellipsoid (MVEE);
  • Second order cone programming (SOCP);
  • Robust optimization;
  • Inactive constraint reduction

Be the first to comment

Leave a Reply

Your email address will not be published.