Nonlinear optimization for optimal power flow problems
 

Economic dispatch relates to the operation of generation facilities to produce energy at the lowest cost to reliably satisfy consumers' demands, taking into account any operational limits of generation and transmission facilities. There were 22,126 TWh of electric energy generated world-wide in 2011, according to the International Energy Association and it is forecasted to grow by 70% to 37,000 TWh in 2030. The global production cost is around 500$bn, hence if one were able to optimize the energy generation even by a small fraction, this would lead to substantial savings in terms of absolute expenses.

The optimal power flow problem is one example of an industry decision optimization problem which can be cast as a nonconvex quadratically-constrained quadratic program. There are a great variety of relaxations and heuristic solution methods available to solve the optimal power flow. Such methods find locally optimal solutions or stationary points and are not guaranteed to find a global optimum. In this project we use semidefinite programming and non-linear programming tools to find tight bounds and under some conditions global optimal solutions for the problem. Additionally, we improve the computational performance of our methods by exploiting the structure of the problem which allows us to target real-world instances. DRL collaborates with transmission system operators to implement these approaches to real large-scale optimal power flow problems.

The main idea of the proposed approach is to solve the optimal power flow problem using strong and efficient convexifications of the quadratic formulation. In the one approach, we tighten the relaxation of the quadratic program by adding valid inequalities in an iterative fashion to improve the quality of the solution at each stage. In another approach, we exploit the structure of the optimal power flow problem by using sparsity. We exploit two cases of sparsity: the sparsity of the energy network as well as the sparsity of the relaxation of the quadratic program. Both methods result in better solutions that be found more efficiently. The methodology we propose is extendible to variety of network optimization problems:  Pressure management in urban water networks, transportation in gas network, planning in supply-chain networks.

Bissan Ghaddar Jakub Marecek Martin Mevissen Joe Naoum-Sawaya Nicole Taheri
Challenge
Solution
Benefits

Extraction structure

nonlinear optimisation

Cut generation

cut generation

Journal and conference publications

Conference presentations

  1. X. Kuang, L. Zuluaga, B. Ghaddar, and J. Naoum-Sawaya. Approximating the ACOPF problem with a hierarchy of SOCP problems, accepted in IEEE PES General Meeting, Denver, Colorado, 2015.
  2. B. Ghaddar, J. Marecek, and M. Mevissen. Optimal Power Flow as a Polynomial Optimization Problem, accepted in IEEE Transactions on Power Systems, 2015
  1. B. Ghaddar, J. Marecek, and M. Mevissen. Tractable Relaxations of Polynomial Optimization Problems Applied to Optimal Power Flow, PGMO-COST Workshop on Validation and Software, Ecole Polytechnique, Paris, France, 2014.
  2. M. Mevissen, Sparse Polynomial Optimization for Urban Distribution Networks, Workshop on Mathematical Models and Methods for Energy Optimization, Budapest, Hungary, 2014.
  3. B. Ghaddar, J. Marecek, and M. Mevissen. Tractable Relaxations and Stronger Convexifications for Urban Networks, 20th Conference of the International Federation of Operational Research Societies, Barcelona, Spain, 2014.
  4. J. Marecek. Computational Semidefinite Programming in Polynomial Optimisation in Power Systems, IBM-RTE Workshop on Semidefinite Programming for Optimal Power Flow Problems, Dublin, Ireland, 2014.
  5. M. Mevissen. Sparse SDP relaxations and applications to industrial decision problems, IBM-RTE Workshop on Semidefinite Programming for Optimal Power Flow Problems, Dublin, Ireland, 2014.
  6. B. Ghaddar. Tractable Relaxations and Stronger Convexifications for OPF, IBM-RTE Workshop on Semidefinite Programming for Optimal Power Flow Problems, Dublin, Ireland, 2014.
  7. J. Marecek, T. McCoy, and M. Mevissen. Polynomial optimisation in power systems at IBM Research, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 2013.