A Probabilistic Method for Optimal Power Systems Planning with Wind Generators

  • Maryam Dadkhah
  • Bala Venkatesh
Conference paper


Radial Distribution Systems (RDS) connect a large number of renewable generators that are inherently uncertain. From being unidirectional power flow systems, RDS now enable bi-directional power flow. Depending upon availability of power from renewables, they receive or feed power to the connected transmission system. RDS optimal power flow (OPF), is an important tool in this new era for utilities, to minimize losses and operate efficiently. With large scale integration of wind generators to distribution systems, they must be appropriately represented using probabilistic models capturing their intermittent nature in these OPF algorithms. This paper proposes characterizing the solution of a Probabilistic Optimal Power Flow (P-OPF) for RDS using the Cumulant Method. This method makes it possible to linearly relate the probabilistic parameters of renewables at the optimal solution point to the state of the RDS. To assess the accuracy of the proposed P-OPF Cumulant Method, wind generators and system probabilistic data are incorporated in a 33-bus and 129-bus test system. The results are compared with those of Monte Carlo simulations (MCS). It is shown that the proposed method possesses high degree of accuracy, is significantly faster and more practical than an MCS approach.


Cumulant method Optimal power flow Radial distribution systems Reactive power optimization Stochastic optimization Wind energy 



Financial Support: This work was supported in part by the NSERC Discovery and Wind Energy Strategic Network grants to Bala Venkatesh.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Centre for Urban EnergyRyerson UniversityTorontoCanada

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