On possibilistic and probabilistic uncertainty assessment of power flow problem: A review and a new approach Morteza Aien a,b,n , Masoud Rashidinejad b,c , Mahmud Fotuhi-Firuzabad d,1 a Energy Department, Graduate University of Advanced Technology, Kerman, Iran b Energy & Industry Commission of Kerman Chamber of Commerce, Industry, Mines & Agriculture, Iran c Electrical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran d Center of Excellence in Power System Management & Control (CEPSMC), Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran article info Article history: Received 29 June 2013 Received in revised form 30 April 2014 Accepted 18 May 2014 Available online 12 June 2014 Keywords: Probabilistic uncertainty modeling Possibilistic uncertainty modeling Uncertain power flow Unscented Transformation abstract As energy resource planning associated with environmental consideration are getting more and more challenging all around the world, the penetration of distributed energy resources (DERs) mainly those harvesting renewable energies (REs) ascend with an unprecedented rate. This fact causes new uncertainties to the power system context; ergo, the uncertainty analysis of the system performance seems necessary. In general, uncertainties in any engineering system study can be represented probabilistically or possibilistically. When sufficient historical data of the system variables is not available, a probability density function (PDF) might not be defined, while they must be represented in another manner i.e. possibilistically. When some of system uncertain variables are probabilistic and some are possibilistic, neither the conventional pure probabilistic nor pure possibilistic methods can be implemented. Hence, a combined solution methodology is needed. This paper proposes a new analytical probabilistic- possibilistic tool for the power flow uncertainty assessment. The proposed methodology is based upon the evidence theory and joint propagation of possibilistic and probabilistic uncertainties. This possibilistic–probabilistic formulation is solved in an uncertain power flow (UPF) study problem. & 2014 Elsevier Ltd. All rights reserved. Contents 1. Introduction ........................................................................................................ 884 2. Power flow (PF) problem ............................................................................................. 885 2.1. PF formulation ................................................................................................ 885 2.2. Uncertain power flow formulation ................................................................................ 886 3. Probabilistic uncertainty modeling ...................................................................................... 886 3.1. Simulation based probabilistic methods ............................................................................ 886 3.2. Analytical probabilistic methods .................................................................................. 886 3.3. Unscented Transformation (UT) method ........................................................................... 886 4. Possibilistic uncertainty modeling ...................................................................................... 887 4.1. Possibility theory .............................................................................................. 887 4.2. α-Cut method................................................................................................. 887 4.3. Defuzzification ................................................................................................ 888 5. Uncertainty in the PF problem ......................................................................................... 888 5.1. Uncertain parameters .......................................................................................... 888 5.2. Uncertainty modeling .......................................................................................... 888 6. Evidence theory and joint possibilistic–probabilistic uncertainty modeling...................................................... 889 6.1. Basic idea .................................................................................................... 889 6.2. Algorithm for joint propagation of probabilistic and possibilistic uncertainties............................................. 889 Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/rser Renewable and Sustainable Energy Reviews http://dx.doi.org/10.1016/j.rser.2014.05.063 1364-0321/& 2014 Elsevier Ltd. All rights reserved. n Corresponding author at: Kerman Chamber of Commerce, Jomhori Eslami Blvd., Kerman, Iran. Postal code: 761 965 3498. Tel./fax: +98 341 2458394. E-mail address: morteza_aien@yahoo.com (M. Aien). 1 Fellow member, IEEE. Renewable and Sustainable Energy Reviews 37 (2014) 883–895