Extended affine arithmetic-based global sensitivity analysis for power flow with uncertainties

Abstract In order to quantitatively assess the impacts of input uncertainties on power flow solutions, a novel analytical variance-based global sensitivity analysis method using extended affine arithmetic was proposed in this paper. With input uncertain variables described as intervals, the power flow output models based on extended affine arithmetic were originally derived. These models are normally expressed by second-order interval response surface model, and thus the total variance of the models can be calculated analytically. Finally, we proposed a novel framework of variance decomposition based global sensitivity analysis method to clarify the components of total variance contributions. The tests on the IEEE14-bus, IEEE300–bus, 2383wp system demonstrate that extended affine arithmetic-based global sensitivity analysis method can acquire maximum relative error of total sensitivity indices is less than 4.55% and max relative error of main sensitivity indices is less than 9.1% when comparing to Monte Carlo simulation method, which is able to greatly improve the evaluation efficiency relative to Monte Carlo simulation method.

[1]  W. Ren,et al.  An interval model updating strategy using interval response surface models , 2015 .

[2]  M.A. Matos,et al.  The fuzzy power flow revisited , 2005, 2005 IEEE Russia Power Tech.

[3]  Jorge Stolfi,et al.  Affine Arithmetic: Concepts and Applications , 2004, Numerical Algorithms.

[4]  Yixin Ni,et al.  Uncertain Power Flow Analysis Based on Evidence Theory and Affine Arithmetic , 2018, IEEE Transactions on Power Systems.

[5]  Armando Martins Leite da Silva,et al.  A Method for Ranking Critical Nodes in Power Networks Including Load Uncertainties , 2016, IEEE Transactions on Power Systems.

[6]  Kazi N. Hasan,et al.  Influence of Stochastic Dependence on Small-Disturbance Stability and Ranking Uncertainties , 2018, IEEE Transactions on Power Systems.

[7]  Wanxing Sheng,et al.  An affine arithmetic-based algorithm for radial distribution system power flow with uncertainties , 2014 .

[8]  Yachao Zhang,et al.  Interval method for uncertain power flow analysis based on Taylor inclusion function , 2017 .

[9]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[10]  Wang Xiaoming,et al.  Research on modelling and solution of stochastic SCUC under AC power flow constraints , 2018 .

[11]  Boddeti Kalyan Kumar,et al.  A modified affine arithmetic-based power flow analysis for radial distribution system with uncertainty , 2019, International Journal of Electrical Power & Energy Systems.

[12]  Jovica V. Milanovic,et al.  Assessing the Applicability of Uncertainty Importance Measures for Power System Studies , 2016, IEEE Transactions on Power Systems.

[13]  Honwing Ngan,et al.  A Mixed Interval Power Flow Analysis Under Rectangular and Polar Coordinate System , 2017, IEEE Transactions on Power Systems.

[14]  B. Iooss,et al.  A Review on Global Sensitivity Analysis Methods , 2014, 1404.2405.

[15]  Chao Jiang,et al.  Interval arithmetic operations for uncertainty analysis with correlated interval variables , 2016 .

[16]  Mohammad Shahidehpour,et al.  Power System Voltage Stability Evaluation Considering Renewable Energy With Correlated Variabilities , 2018, IEEE Transactions on Power Systems.

[17]  Phuong H. Nguyen,et al.  Variance-Based Global Sensitivity Analysis for Power Systems , 2018, IEEE Transactions on Power Systems.

[18]  Jovica V. Milanović,et al.  Priority Ranking of Critical Uncertainties Affecting Small-Disturbance Stability Using Sensitivity Analysis Techniques , 2017, IEEE Transactions on Power Systems.

[19]  Julio C. Teixeira,et al.  Insertion of wind generators in electrical power systems aimed at active losses reduction using sensitivity analysis , 2016 .

[20]  Frédéric Messine,et al.  A General Reliable Quadratic Form: An Extension of Affine Arithmetic , 2006, Reliab. Comput..

[21]  Paola Annoni,et al.  Estimation of global sensitivity indices for models with dependent variables , 2012, Comput. Phys. Commun..

[22]  Alfredo Vaccaro,et al.  An Affine Arithmetic-Based Framework for Uncertain Power Flow and Optimal Power Flow Studies , 2017, IEEE Transactions on Power Systems.

[23]  Wenrui Hao,et al.  A new interpretation and validation of variance based importance measures for models with correlated inputs , 2013, Comput. Phys. Commun..

[24]  J. V. Milanovic,et al.  Ranking the Importance of Synchronous Generators for Renewable Energy Integration , 2012, IEEE Transactions on Power Systems.

[25]  Alfredo Vaccaro,et al.  An Affine Arithmetic-Based Methodology for Reliable Power Flow Analysis in the Presence of Data Uncertainty , 2010, IEEE Transactions on Power Systems.

[26]  Mohammad Mohammadi,et al.  A new approach of point estimate method for probabilistic load flow , 2013 .

[27]  Kaichao Zhang,et al.  A new framework of variance based global sensitivity analysis for models with correlated inputs , 2015 .

[28]  Zheng Yan,et al.  Probabilistic load flow calculation with quasi-Monte Carlo and multiple linear regression , 2017 .

[29]  Saltelli Andrea,et al.  Global Sensitivity Analysis: The Primer , 2008 .

[30]  Haibo He,et al.  Optimized Control of DFIG-Based Wind Generation Using Sensitivity Analysis and Particle Swarm Optimization , 2013, IEEE Transactions on Smart Grid.

[31]  N. Amjady,et al.  Application of a new sensitivity analysis framework for voltage contingency ranking , 2005, IEEE Transactions on Power Systems.

[32]  Wenrui Hao,et al.  Uncertainty importance measure for models with correlated normal variables , 2013, Reliab. Eng. Syst. Saf..

[33]  V. M. da Costa,et al.  Interval arithmetic in current injection power flow analysis , 2012 .