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Using a multivariate DOE method for congestion study under impacts of PEVs

This paper explores a multivariate design of experiments (DOE) approach to study the impacts of plug-in electric vehicles (PEVs) on congestion within electrical distribution networks. It emphasizes the importance of timely network development decisions to prevent congestion and economically unviable outcomes. Employing generalized linear models (GLMs) and the Frank Copula technique, we analyze the probabilistic assignment of PEVs across various configurations and scenarios. Our findings aim to contribute to effective planning in accommodating increased PEV adoption while minimizing congestion risks.

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Using a multivariate DOE method for congestion study under impacts of PEVs

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

  2. Main Topics • 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

  3. General Outline • 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 Haghi – Iran – RIF Session 5 – Paper 0718

  4. General Outline • 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 Haghi – Iran – RIF Session 5 – Paper 0718

  5. General Outline • 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 Haghi – Iran – RIF Session 5 – Paper 0718

  6. General Outline • 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 Haghi – Iran – RIF Session 5 – Paper 0718

  7. General Outline • 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 Haghi – Iran – RIF Session 5 – Paper 0718

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

  9. Main Topics • 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

  10. A very general model of a system Haghi – Iran – RIF Session 5 – Paper 0718

  11. A very general model of PEV behavior • Controllable variables • Modern tariff structures • charging start time • Uncontrollable variables • battery’s state of charge • charging start time • location Haghi – Iran – RIF Session 5 – Paper 0718

  12. A very general model of PEV behavior • 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 Haghi – Iran – RIF Session 5 – Paper 0718

  13. Design of Experiment (DOE) Technique • 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 Haghi – Iran – RIF Session 5 – Paper 0718

  14. Design of Experiment (DOE) Technique • 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 Haghi – Iran – RIF Session 5 – Paper 0718

  15. DOE of PEVs • A probabilistic model should be fitted the system response • Here, the generalized linear model (GLM) is used Haghi – Iran – RIF Session 5 – Paper 0718

  16. Main Topics • 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

  17. Generalized linear model (GLM) • 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 Haghi – Iran – RIF Session 5 – Paper 0718

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

  19. Main Topics • 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

  20. Multivariate DOE by frank Copula • Copulas provide a way to create distributions that model correlated multivariate data Haghi – Iran – RIF Session 5 – Paper 0718

  21. Main Topics • 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

  22. Congestion study • 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 Haghi – Iran – RIF Session 5 – Paper 0718

  23. Scenario simulations for five practically correlated feeders Haghi – Iran – RIF Session 5 – Paper 0718

  24. Rank Correlation Coefficients Together with Confidence Measures (P-values) for five practically correlated feeders Haghi – Iran – RIF Session 5 – Paper 0718

  25. Conclusions • 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 Haghi – Iran – RIF Session 5 – Paper 0718

  26. Thank You! 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

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