Xu Andy Sun

Multistage Stochastic Unit Commitment Using Stochastic Dual Dynamic Integer Programming

  • Shabbir Ahmed
  • Xu Andy Sun
  • Jikai Zou
    • Categories Applications - Science and Engineering, Stochastic Programming Tags , ,

    Unit commitment (UC) is a key operational problem in power systems used to determine an optimal daily or weekly generation commitment schedule. Incorporating uncertainty in this already difficult mixed integer optimization problem introduces significant computational challenges. Most existing stochastic UC models consider either a two-stage decision structure, where the commitment schedule for the entire planning … Read more

    Matrix Minor Reformulation and SOCP-based Spatial Branch-and-Cut Method for the AC Optimal Power Flow Problem

  • Santanu S. Dey
  • Burak Kocuk
  • Xu Andy Sun
    • Categories Applications - Science and Engineering, Global Optimization Applications Tags , , ,

    Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining near optimal primal solutions as well as high quality dual bounds for this non-convex program, presents a major … Read more

    Stochastic Dual Dynamic Integer Programming

  • Shabbir Ahmed
  • Xu Andy Sun
  • Jikai Zou
    • Categories Dynamic Programming, Integer Programming, Stochastic Programming Tags , , ,

    Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely challenging problems. A common formulation for these problems is a dynamic programming formulation involving nested cost-to-go functions. In the linear setting, the cost-to-go functions are convex polyhedral, and decomposition algorithms, such as nested Benders’ decomposition and … Read more

    Multistage Robust Unit Commitment with Dynamic Uncertainty Sets and Energy Storage

  • Alvaro Lorca
  • Xu Andy Sun
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , , ,

    The deep penetration of wind and solar power is a critical component of the future power grid. However, the intermittency and stochasticity of these renewable resources bring significant challenges to the reliable and economic operation of power systems. Motivated by these challenges, we present a multistage adaptive robust optimization model for the unit commitment (UC) … Read more

    New Formulation and Strong MISOCP Relaxations for AC Optimal Transmission Switching Problem

  • Santanu S. Dey
  • Burak Kocuk
  • Xu Andy Sun
    • Categories Applications - Science and Engineering, Global Optimization, Integer Programming Tags , , , , ,

    As the modern transmission control and relay technologies evolve, transmission line switching has become an important option in power system operators’ toolkits to reduce operational cost and improve system reliability. Most recent research has relied on the DC approximation of the power flow model in the optimal transmission switching problem. However, it is known that … Read more

    Strong SOCP Relaxations for the Optimal Power Flow Problem

  • Santanu S. Dey
  • Burak Kocuk
  • Xu Andy Sun
    • Categories Applications - Science and Engineering, Global Optimization, Nonlinear Optimization Tags , , ,

    This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in … Read more

    Partially Adaptive Stochastic Optimization for Electric Power Generation Expansion Planning

  • Shabbir Ahmed
  • Xu Andy Sun
  • Jikai Zou
    • Categories Stochastic Programming Tags , ,

    Electric Power Generation Expansion Planning (GEP) is the problem of determining an optimal construction and generation plan of both new and existing electric power plants to meet future electricity demand. We consider a stochastic optimization approach for this capacity expansion problem under demand and fuel price uncertainty. In a two-stage stochastic optimization model for GEP, … Read more

    A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching

  • Santanu S. Dey
  • Hyemin Jeon
  • Burak Kocuk
  • Jeff Linderoth
  • James R. Luedtke
  • Xu Andy Sun
    • Categories Applications - Science and Engineering, Integer Programming Tags , ,

    It is well-known that optimizing network topology by switching on and off transmission lines improves the efficiency of power delivery in electrical networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that the U.S. should “encourage, as appropriate, the deployment of advanced transmission technologies” including “optimized transmission line configurations”. As such, … Read more

    Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow

  • Santanu S. Dey
  • Burak Kocuk
  • Xu Andy Sun
    • Categories Global Optimization Tags , , ,

    It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load over-satisfaction. In this paper, we investigate the situation where generation lower bounds are present. We show that even for a … Read more

    Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind

  • Alvaro Lorca
  • Xu Andy Sun
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , ,

    The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in today’s power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. … Read more