using a multivariate doe method for congestion study under impacts of pevs

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

Hamed V. HAGHIM. A. GOLKAR

[email protected]

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


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



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



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



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



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



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



General Outline




Congestion study

Conclusion

Main Topics



A very general model of a system

System

Controllable variables

Uncontrollable variables

Input(s) Output(s)

Y

X1 X2 Xn…

Z1 Z2 Zn…



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



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



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




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




A probabilistic model should be fitted the system response

Here, the generalized linear model (GLM) is used

DOE of PEVs



General Outline




Congestion study

Conclusion

Main Topics



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




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)




General Outline




Congestion study

Conclusion

Main Topics



Copulas provide a way to create distributions that model correlated multivariate data


1 1 2 2 1 2[ ( ), ( ), , ( )] ( , , , )n n nC F x F x F x F x x x

1 21

1 2

( 1)( 1)( , ; ) log 1

1

u ue eC u u

e



General Outline




Congestion study

Conclusion

Main Topics



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



Line #1Current

Line #2Current

Line #3Current

Line #4Current

Line #5Current

Scenario simulations for five practically correlated feeders



Rank Correlation Coefficients Together with Confidence Measures (P-values)

for five practically correlated feeders

Line #1 Line #2 Line #3 Line #4 Line #5

Line #1 1.000 0.865 (0.045) 0.172 (0.000) -0.034 (0.042) 0.903 (0.057)

Line #2 1.000 0.227 (0.004) 0.350 (0.010) 0.005 (0.000)

Line #3 1.000 -0.146 (0.011) 0.202 (0.149)

Line #4 1.000 0.026 (0.000)

Line #5 1.000



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



Contact:Hamed VALIZADEH HAGHIPhDc, P.EngFaculty of Electrical and Computer EngineeringK. N. Toosi University of Technology, Tehran 16315-1355, Iran+98 (21) 2793 [email protected]

Thank You!

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using a multivariate doe method for congestion study under impacts of pevs

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