statistical modelling for inclusion of wind generation in industrial … · 2015-09-20 · durham...
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Durham University
Statistical modelling for inclusion of windgeneration in industrial adequacy studies
Amy Wilson
Durham University
July 2015
Durham University
Table of Contents
1 Introduction
2 National grid projectCorrelation between demand and windStatistical model for windResults
3 EPRI project
4 Conclusion
Durham University
Introduction
Contents
1 Introduction
2 National grid projectCorrelation between demand and windStatistical model for windResults
3 EPRI project
4 Conclusion
Durham University
Introduction
Wind generation and capacity adequacy
Increasing wind generation in energy systems - will the wind bethere when we need it?
2000
4000
6000
8000
1000
0
Wind at peak demand
Time
Win
d ge
nera
tion
(MW
)
Durham University
Introduction
Wind generation and capacity adequacy
Current capacity adequacy methods assume conventionalgeneration at a given time is independent of the demand at thattime. Holds for wind generation?
0 2000 4000 6000 8000 10000 120000.00
000
0.00
015
Wind distribution
Wind generation
Den
sity
0 2000 4000 6000 8000 10000 120000.00
000
0.00
015
Wind distribution − high demand
Wind generation
Den
sity
Durham University
Introduction
Wind generation and capacity adequacy
Model for amount of available wind at a given demand level isrequired.
Hindcast? Insufficient data at low wind/high demand times.
Independence? Doesn’t hold.
Durham University
Introduction
Current methodology
Non-sequential approach:
Does not use a stochastic process to model conventionalgeneration (also often variable generation).
Instead, distribution of conventional generation estimated at arandom point in time (so averaged over all time periods).
Sufficient for expected value indices.
Durham University
Introduction
Non-sequential vs. sequential
Ideal situation - full sequential joint model for demand,conventional generation and variable generation.
Accounts for correlations through time,
Model extra aspects of the system such as time to repair,
Allows for interdependencies that change through time,
More complete picture of capacity adequacy - probabilitydistribution for size of shortfall.
Problem: this would be a very large project.
Durham University
Introduction
Projects
Two projects:
National grid consultancy - expand on current methodologyfor the inclusion of wind generation in GB capacity adequacyassessment.
Non-sequential,Nine years of demand data (rescaled to 2014/15 scenario), 28years of temperature and wind speed data (wind generationdata obtained by combining wind speed data with 2014/15scenario).
EPRI project - pilot project for investigating probabilisticmethods for including variable generation (VG) when assessingcapacity adequacy and highlight further research requirements.Three years of data from four regions: BPA, Duke, NVP, WY.
Durham University
National grid project
Contents
1 Introduction
2 National grid projectCorrelation between demand and windStatistical model for windResults
3 EPRI project
4 Conclusion
Durham University
National grid project
Correlation between demand and wind
Correlation - non-sequential
Demand and wind correlated through time - both haveseasonal patterns over year and over day.
Correlated through temperature?
Investigated presence of correlation beyond temperature andseasonal patterns.
Regression model for peak daily demand, conditional on dayof week, temperature, days since GMT,(days since GMT)2 (based on model used internally byNational Grid).
Tested whether inclusion of wind speed at time of peakdaily demand necessary.
Durham University
National grid project
Correlation between demand and wind
Correlation - non-sequential
Wind speed termstatisticallysignificant(significance likelyto beoverestimated), butonly raised R2 from91.4% to 91.8%.
Impact on residualsonly seen at highwind speeds - notimportant forcapacity adequacy.
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5 10 15 20
−30
00−
1000
010
0020
0030
00
Wind Speed (knots)
Res
idua
ls−
no W
S
Durham University
National grid project
Statistical model for wind
Statistical model for wind
Peak demand and wind approximately independent at lowwind speeds (i.e. times of system stress), conditional on timeand temperature.
So model wind generation conditional on time andtemperature (not demand).
Regression model for wind generation conditional on:temperature (non-linear terms included to allow fordifferences at high and low temperatures), days since GMT,(days since GMT)2, hour and year.
Logistic transformation of wind generation to improve fit.
Random year term added to incorporate weather patternsthat change between years (year ∼ N(0, σ2)).
Durham University
National grid project
Statistical model for wind
Is temperature necessary?
And large improvement in model fit summary statistics.
Durham University
National grid project
Statistical model for wind
Risks of independence assumption
Durham University
National grid project
Results
Estimating the LOLE
Use model to estimate LOLE:
P(Dt − Yt > Xt),
Dt =demand (time t), Yt =wind (time t), Xt =conventionalgeneration.For each t over period of data
Take demand and temperature as in historical data (demandrescaled),
Sample wind generation conditional on this demand andtemperature,
Estimate P(Dt − Yt > Xt) from conventional generationdistribution.
Durham University
National grid project
Results
LOLE results
Year LOLE(hours per year)
2005–06 0.452010–11 3.122013–14 0.13
Table: LOLE estimates conditional on one year’s demand/temp profile.
Method LOLE Lower bound Upper bound(hours per year) (90% interval) (90% interval)
Temperature as 1.15 0.52 1.95proxy for demand
Hindcast 0.68 0.31 1.17
Table: LOLE estimates over whole dataset
Durham University
EPRI project
Contents
1 Introduction
2 National grid projectCorrelation between demand and windStatistical model for windResults
3 EPRI project
4 Conclusion
Durham University
EPRI project
Demand/wind correlation - sequential
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−500 0 500
−15
000
1000
BPA
Demand (MW)
VG
(M
W)
r=−0.133
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−2000 −1000 0 1000 2000
−40
000
2000
Duke
Demand (MW)
VG
(M
W)
r=−0.00316
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−800 −400 0 200 400 600
−20
00
100
NVP
Demand (MW)
VG
(M
W)
r=0.0927
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−40 −20 0 20 40
−20
000
2000
WY
Demand (MW)
VG
(M
W)
r=−0.0160
Sequential model accounting for time and temperature.
Durham University
EPRI project
Technical challenges
Sequential model for wind needs improving - not stationary,
Seasonal effects over day, year. Diurnal effects changethrough year,
Link with historical demand, or model demand (difficult),
Need sequential model for conventional generation.
Durham University
Conclusion
Contents
1 Introduction
2 National grid projectCorrelation between demand and windStatistical model for windResults
3 EPRI project
4 Conclusion
Durham University
Conclusion
Conclusion
Wind generation not independent of demand (time,temperature, more?),
Inadequate data for accurate hindcast estimates,
Statistical model for wind generation developed - modelsdependence on time and temperature,
Sequential approach?
Durham University
Conclusion
With thanks to:
Chris Dent,
Stan Zachary,
National Grid,
EPRI and EPRI project partners.