using a multivariate doe method for congestion study under impacts of pevs hamed v. haghi m. a....
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Using a multivariate DOE method for congestion study under impacts of PEVs
Hamed V. HAGHIM. A. GOLKAR
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
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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 07183
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 07184
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 07185
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 07186
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 07187
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 07188
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 07189
Frankfurt (Germany), 6-9 June 2011
A very general model of a system
System
Controllable variables
Uncontrollable variables
Input(s) Output(s)
Y
X1 X2 Xn…
Z1 Z2 Zn…
Haghi – Iran – RIF Session 5 – Paper 071810
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 071811
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 071812
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 071813
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 071814
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 071815
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 071816
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 071817
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 071818
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 071819
Frankfurt (Germany), 6-9 June 2011
Copulas provide a way to create distributions that model correlated multivariate data
Multivariate DOE by frank Copula
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
Haghi – Iran – RIF Session 5 – Paper 071820
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 071821
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 071822
Frankfurt (Germany), 6-9 June 2011
Line #1Current
Line #2Current
Line #3Current
Line #4Current
Line #5Current
Scenario simulations for five practically correlated feeders
Haghi – Iran – RIF Session 5 – Paper 071823
Frankfurt (Germany), 6-9 June 2011
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
Haghi – Iran – RIF Session 5 – Paper 071824
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 071825
Frankfurt (Germany), 6-9 June 2011
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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