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Using a multivariate DOE method for congestion study under impacts of PEVs Hamed V. HAGHI M. A. GOLKAR valizadeh@ieee.org K. N. Toosi University

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Frankfurt (Germany), 6-9 June 2011 General Outline Design of Experiment (DOE) Technique Generalized linear model (GLM) Multivariate DOE by frank Copula Congestion study Conclusion Haghi – Iran – RIF Session 5 – Paper 0718 Main Topics 2

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Frankfurt (Germany), 6-9 June 2011 Undertaking a partial development in the planning stage is further encouraged in ADN Proliferation of plug-in electric vehicles (PEVs) congestion may appear if a network development decision is not taken at the right time Assuming overestimated network developments may be economically unsuccessful General Outline Haghi – Iran – RIF Session 5 – Paper 0718 3

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Frankfurt (Germany), 6-9 June 2011 Evaluation of potential impacts of PEVs Probabilistic projections of both spatial and temporal diversity Monte Carlo simulation Simulations are composed of probabilistic assignment of PEVs to the distribution base case General Outline Haghi – Iran – RIF Session 5 – Paper 0718 4

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Frankfurt (Germany), 6-9 June 2011 Each PEV is randomly assigned a location, type, and daily charge profiles based on the provided pdf for each characteristic Multiple probabilistic scenarios are generated from the system and pdf There are millions of possible configurations when the chosen factors vary General Outline Haghi – Iran – RIF Session 5 – Paper 0718 5

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Frankfurt (Germany), 6-9 June 2011 Design of experiment (DOE) method To create an optimal DOE of fewer configurations chosen between the millions of possible configurations Multivariate distribution underlying a pre-chosen model General Outline Haghi – Iran – RIF Session 5 – Paper 0718 6

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Frankfurt (Germany), 6-9 June 2011 Proposed DOE method for impacts of PEVs bivariate DOE for two of the correlated variables in the randomization process PEVs location Base typical load profiles Using a Frank Copula function to create multivaraite distributional dependency General Outline Haghi – Iran – RIF Session 5 – Paper 0718 7

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Frankfurt (Germany), 6-9 June 2011 1.Modeling uncertainties (database creation) 2.Applying multivariate DOE 3.Power flow calculations on the reduced scenarios 4.Statistical analysis of the results General Outline Haghi – Iran – RIF Session 5 – Paper 0718 8

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Frankfurt (Germany), 6-9 June 2011 General Outline Design of Experiment (DOE) Technique Generalized linear model (GLM) Multivariate DOE by frank Copula Congestion study Conclusion Main Topics Haghi – Iran – RIF Session 5 – Paper 0718 9

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Frankfurt (Germany), 6-9 June 2011 A very general model of a system Haghi – Iran – RIF Session 5 – Paper 0718 10

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Frankfurt (Germany), 6-9 June 2011 Controllable variables Modern tariff structures charging start time Uncontrollable variables battery’s state of charge charging start time location A very general model of PEV behavior Haghi – Iran – RIF Session 5 – Paper 0718 11

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Frankfurt (Germany), 6-9 June 2011 designing a most informative reduced set of scenarios, all variables are better to be treated as controllable variables as well in order to have their part in the final outcome These optimally-chosen runs are more than enough to fit the model A very general model of PEV behavior Haghi – Iran – RIF Session 5 – Paper 0718 12

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Frankfurt (Germany), 6-9 June 2011 A technique to obtain and organize the maximum amount of conclusive information from minimum empirical work Efficiency getting more information from fewer experiments/data Focusing collecting only the information that is really needed Design of Experiment (DOE) Technique Haghi – Iran – RIF Session 5 – Paper 0718 13

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Frankfurt (Germany), 6-9 June 2011 The critical part is to decide which variables to change, the intervals for this variation, and the pattern of the experimental points limited resource here is the computational time required for calculating load flow for all scenarios Design of Experiment (DOE) Technique Haghi – Iran – RIF Session 5 – Paper 0718 14

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Frankfurt (Germany), 6-9 June 2011 A probabilistic model should be fitted the system response Here, the generalized linear model (GLM) is used DOE of PEVs Haghi – Iran – RIF Session 5 – Paper 0718 15

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Frankfurt (Germany), 6-9 June 2011 General Outline Design of Experiment (DOE) Technique Generalized linear model (GLM) Multivariate DOE by frank Copula Congestion study Conclusion Main Topics Haghi – Iran – RIF Session 5 – Paper 0718 16

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Frankfurt (Germany), 6-9 June 2011 A generalization of linear regression Avoids approximations such as CLT Magnitude of variance of each measurement is a function of its expected value A change/shift in the expected value of the total power demand of PEV chargers (maybe due to a shift in timing) correlates with a change in its variance Generalized linear model (GLM) Haghi – Iran – RIF Session 5 – Paper 0718 17

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Frankfurt (Germany), 6-9 June 2011 GLM consists of three elements 1.A probability distribution from the exponential family 2.A linear predictor η = Xβ. 3.A link function g such that E(Y) = μ = g-1(η) Generalized linear model (GLM) Haghi – Iran – RIF Session 5 – Paper 0718 18

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Frankfurt (Germany), 6-9 June 2011 General Outline Design of Experiment (DOE) Technique Generalized linear model (GLM) Multivariate DOE by frank Copula Congestion study Conclusion Main Topics Haghi – Iran – RIF Session 5 – Paper 0718 19

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Frankfurt (Germany), 6-9 June 2011 Copulas provide a way to create distributions that model correlated multivariate data Multivariate DOE by frank Copula Haghi – Iran – RIF Session 5 – Paper 0718 20

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Frankfurt (Germany), 6-9 June 2011 General Outline Design of Experiment (DOE) Technique Generalized linear model (GLM) Multivariate DOE by frank Copula Congestion study Conclusion Main Topics Haghi – Iran – RIF Session 5 – Paper 0718 21

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Frankfurt (Germany), 6-9 June 2011 33-bus distribution system test case The 200 configurations/ scenarios final outcome is about knowing which lines will be simultaneously congested under impacts of PEVs Congestion study Haghi – Iran – RIF Session 5 – Paper 0718 22

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Frankfurt (Germany), 6-9 June 2011 Scenario simulations for five practically correlated feeders Haghi – Iran – RIF Session 5 – Paper 0718 23

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Frankfurt (Germany), 6-9 June 2011 Rank Correlation Coefficients Together with Confidence Measures (P-values) for five practically correlated feeders Line #1Line #2Line #3Line #4Line #5 Line #1 1.0000.865 (0.045)0.172 (0.000)-0.034 (0.042)0.903 (0.057) Line #2 1.0000.227 (0.004) 0.350 (0.010)0.005 (0.000) Line #3 1.000-0.146 (0.011)0.202 (0.149) Line #4 1.0000.026 (0.000) Line #5 1.000 Haghi – Iran – RIF Session 5 – Paper 0718 24

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Frankfurt (Germany), 6-9 June 2011 Correlation analysis applicable to a database of currents in the lines Forecast which congestions are correlated Illustrate where congestions will appear in the future Planner could implement a line reinforcement which removes correlated congestions A technique to take into account the impacts of PEVs in other types of studies Conclusions Haghi – Iran – RIF Session 5 – Paper 0718 25

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Frankfurt (Germany), 6-9 June 2011 Contact: Hamed VALIZADEH HAGHI PhDc, P.Eng Faculty of Electrical and Computer Engineering K. N. Toosi University of Technology, Tehran 16315-1355, Iran +98 (21) 2793 5698 valizadeh@ieee.org Thank You! 26

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