probabilistic forecasts of wind and solar power...
TRANSCRIPT
Probabilistic Forecasts ofWind and Solar Power GenerationHenrik Madsen1, Henrik Aalborg Nielsen2, Peder Bacher1,
Pierre Pinson1, Torben Skov Nielsen2
(1) Tech. Univ. of Denmark (DTU)
DK-2800 Lyngby
www.imm.dtu.dk/ ˜ hm
(2) ENFOR A/S
Lyngsø Alle 3
DK-2970 Hørsholm
www.enfor.dk
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 1
Outline
Wind power forecasting
Configuration example
Use of several providers of MET forecasts
Uncertainty and confidence intervals
Scenario forecasting
Examples on the use of probabilistic forecasts
Value of probabilistic forecasts
Solar power forecasting
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 2
Wind Power Forecasting - History
Our methods for probabilistic wind power forecasting have been implemented in theAnemos Wind Power Prediction SystemandWPPT
The methods have been continuously developed since 1993 - incollaboration withEnerginet.dk,Dong Energy,Vattenfall,Risø – DTU,The ANEMOS projects partners/consortium (since 2002),ENFOR (Denmark)
The methods have been used operationally for predicting wind power in Denmarksince 1996.
Anemos/WPPT is now used all over Europe, Australia, and North America.
Now in Denmark: Wind power coverson averageabout 27 pct of the system load.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 3
Prediction Performance
A typical performance measure. 13 large parks. Installed power: 1064 MW. Period: August2008 - March 2010. MET input is in all cases ECMWF. Criterion used: RMSE (notice:Power Curve model only)
Forecast horizon (hours)
Nor
mal
ized
pow
er
0.00
0.05
0.10
0.15
0 12 24 36 48
Nominal power: 1064 MW
RMSE
WPPT−PCSimple modelCommercial model 1Commercial model 2
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 4
Uncertainty and adaptivity
Errors in MET forecasts will end up in errors in wind power forecasts, but other factors leadto a need for adaptation which however leads to some uncertainties.
The total system consisting of wind farms measured online, wind turbines not measuredonline and meteorological forecasts will inevitably change over time as:
the population of wind turbines changes,
changes in unmodelled or insufficiently modelled characteristics (importantexamples: roughness and dirty blades),
changes in the NWP models.
A wind power prediction system must be able to handle these time-variations in model andsystem. An adequate forecasting system may useadaptive and recursive model estimationto handle these issues.
We started (some 20 years ago) assuming Gaussianity; but this is a very serious (wrong)assumption !
Following the initial installation the software tool will automatically calibrate the models tothe actual situation.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 5
The power curve model
The wind turbine “power curve” model,ptur = f(wtur) is extended to a wind farmmodel, pwf = f(wwf , θwf ), by introducingwind direction dependency. By introducing arepresentative area wind speed and direction itcan be further extended to cover all turbines inan entire region,par = f(war, θar).
The power curve model is defined as:
pt+k|t = f( wt+k|t, θt+k|t, k )
wherewt+k|t is forecasted wind speed, andθt+k|t is forecasted wind direction.
The characteristics of the NWP change withthe prediction horizon.
k
Wind speedWind direction
P
k
Wind speedWind direction
P
k
Wind speedWind direction
P
k
Wind speedWind direction
P
HO - Estimated power curve
Plots of the estimated power curve forthe Hollandsbjerg wind farm.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 6
Configuration Example
This configuration of Anemos PredictionSystem/WPPT is used by a large TSO.Characteristics for the installation:
A large number of wind farms andstand-alone wind turbines.
Frequent changes in the windturbine population.
Offline production data with aresolution of 15 min. is availablefor more than 99% of the windturbines in the area.
Online data for a large numberof wind farms are available. Thenumber of online wind farms in-creases quite frequently.
ModelUpscaling
predictionTotal prod.
Dynamic
Power CurveModel
Model
Offline prod.data
predictionArea prod.
NWP data
Online prod.data
predictionOnline prod.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 7
Spatio-temporal forecasting
Predictive improvement (measured inRMSE) of forecasts errors by adding thespatio-temperal module in WPPT.
23 months (2006-2007)
15 onshore groups
Focus here on 1-hour forecast only
Larger improvements for eastern partof the region
Needed for reliable ramp forecasting.
The EU project NORSEWinD willextend the region
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 8
Combined forecasting
A number of power forecasts areweighted together to form a newimproved power forecast.
These could come from parallelconfigurations of WPPT using NWPinputs fromdifferent METproviders or they could come fromother power prediction providers.
In addition to the improved perfor-mance also the robustness of the sys-tem is increased.
Met Office
DWD
DMI
WPPT
WPPT
WPPT
Comb Final
The example show results achieved for theTunø Knob wind farms using combinationsof up to 3 power forecasts.
Hours since 00Z
RM
S (
MW
)
5 10 15 20
5500
6000
6500
7000
7500
hir02.locmm5.24.loc
C.allC.hir02.loc.AND.mm5.24.loc
Typically an improvement on 10-15 pctin accuracy of the point prediction isseen by including more than one METprovider. Two or more MET providersimply information about uncertainty
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 9
Uncertainty estimation
In many applications it is crucial that a pre-diction tool delivers reliable estimates (prob-abilistc forecasts) of the expected uncertaintyof the wind power prediction.
We consider the following methods for esti-mating the uncertainty of the forecasted windpower production:
Ensemble based - but corrected -quantiles.
Quantile regression.
Stochastic differential equations.
The plots show raw (top) and corrected (bot-tom) uncertainty intervales based on ECMEFensembles for Tunø Knob (offshore park),29/6, 8/10, 10/10 (2003). Shown are the25%, 50%, 75%, quantiles.
Tunø Knob: Nord Pool horizons (init. 29/06/2003 12:00 (GMT), first 12h not in plan)
kW
12:00 18:00 0:00 6:00 12:00 18:00 0:00Jun 30 2003 Jul 1 2003 Jul 2 2003
020
0040
00
Tunø Knob: Nord Pool horizons (init. 08/10/2003 12:00 (GMT), first 12h not in plan)
kW
12:00 18:00 0:00 6:00 12:00 18:00 0:00Oct 9 2003 Oct 10 2003 Oct 11 2003
020
0040
00
Tunø Knob: Nord Pool horizons (init. 10/10/2003 12:00 (GMT), first 12h not in plan)
kW
12:00 18:00 0:00 6:00 12:00 18:00 0:00Oct 11 2003 Oct 12 2003 Oct 13 2003
020
0040
00
Tunø Knob: Nord Pool horizons (init. 29/06/2003 12:00 (GMT), first 12h not in plan)
kW
12:00 18:00 0:00 6:00 12:00 18:00 0:00Jun 30 2003 Jul 1 2003 Jul 2 2003
020
0040
00
Tunø Knob: Nord Pool horizons (init. 08/10/2003 12:00 (GMT), first 12h not in plan)
kW
12:00 18:00 0:00 6:00 12:00 18:00 0:00Oct 9 2003 Oct 10 2003 Oct 11 2003
020
0040
00
Tunø Knob: Nord Pool horizons (init. 10/10/2003 12:00 (GMT), first 12h not in plan)
kW
12:00 18:00 0:00 6:00 12:00 18:00 0:00Oct 11 2003 Oct 12 2003 Oct 13 2003
020
0040
00
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 10
Quantile regression
A (additive) model for each quantile:
Q(τ) = α(τ) + f1(x1; τ) + f2(x2; τ) + . . .+ fp(xp; τ)
Q(τ) Quantile offorecast error from anexisting system.
xj Variables which influence the quantiles, e.g. the wind direction.
α(τ) Intercept to be estimated from data.
fj(·; τ) Functions to be estimated from data.
Notes on quantile regression:
Parameter estimates found by minimizing a dedicated function of the
prediction errors.
The variation of the uncertainty is (partly) explained by the independent
variables.Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 11
Quantile regression - An example
Effect of variables (- the functions are approximated by Spline basis
functions):
0 1000 3000 5000
−20
000
1000
2000
pow.fc
25%
(bl
ue)
and
75%
(re
d) q
uant
iles
20 25 30 35
−20
000
1000
2000
horizon
25%
(bl
ue)
and
75%
(re
d) q
uant
iles
0 50 150 250 350
−20
000
1000
2000
wd10m
25%
(bl
ue)
and
75%
(re
d) q
uant
iles
Forecasted power has a large influence.
The effect of horizon is of less importance.
Some increased uncertainty for Westerly winds.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 12
Example: Probabilistic forecasts
5 10 15 20 25 30 35 40 450
10
20
30
40
50
60
70
80
90
100
look−ahead time [hours]
pow
er [%
of P
n]
90%80%70%60%50%40%30%20%10%pred.meas.
Notice how the confidence intervals varies ...
But the correlation in forecasts errors is not described so far.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 13
Correlation structure of forecast errors
It is important to model theinterdependence structureof the prediction errors.
An example of interdependence covariance matrix:
5 10 15 20 25 30 35 40
5
10
15
20
25
30
35
40
horizon [h]
horiz
on[h
]
−0.2
0
0.2
0.4
0.6
0.8
1
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 14
Correct (top) and naive (bottom) scenarios%
of in
stalle
d ca
pacit
y
0 24 48 72 96 120 144
020
4060
8010
0
hours
100% 90% 80% 70% 60% 50% 40% 30% 20% 10%100% 90% 80% 70% 60% 50% 40% 30% 20% 10%
% o
f insta
lled
capa
city
0 24 48 72 96 120 144
020
4060
8010
0
hours
100% 90% 80% 70% 60% 50% 40% 30% 20% 10%100% 90% 80% 70% 60% 50% 40% 30% 20% 10%
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 15
Use of Stoch. Diff. Equations
The state equation describes the future wind power production
dxt =− θ(ut) · (xt − pt|0)dt+
2√
θ(ut)α(ut)pt|0(1− pt|0)xt · (1− xt)dwt,
with α(ut) ∈ (0, 1), and the observation equation
yh =xth|0 + eh,
whereh ∈ {1, 2, ..., 48}, th = k, eh ∼ N(0, s2), x0 = “observed power at t=0”, and
pt|0 point forecast byWPPT (Wind Power Prediction Tool)
ut input vector (heret andpt|0)
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 16
Examples of using SDEs
Time
Pow
er
0.0
0.2
0.4
0.6
0.8
1.0
0 12 24 36 48
April 22. 2001, 12h May 19. 2001, 12h
May 5. 2003, 18h
0 12 24 36 48
0.0
0.2
0.4
0.6
0.8
1.0October 22. 2002, 00h
0.0
0.2
0.4
0.6
0.8
1.0
Obs. pt|0 pSDE
Use of SDEs provides a possibility for a joint description ofboth non-symmetricalconditional densities as well as the interdependence of theforecasts.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 17
SDE approach – Correlation structures
Time
Tim
e
12
24
36
48
12 24 36 48
April 22. 2001, 12h May 19. 2001, 12h
May 5. 2003, 18h
12 24 36 48
12
24
36
48October 22. 2002, 00h
0.0
0.2
0.4
0.6
0.8
1.0
Use of SDEs provides a possibility to model eg. time varying and wind power dependentcorrelation structures.SDEs provide a perfect framework forcombined wind and solar power forecasting.Today both theAnemos Prediction PlatformandWPPT provide operations forecasts ofboth wind and solar power production.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 18
Type of forecasts required
Point forecasts (normal forecasts); a single value for each time point in the future.Sometimes with simple error bands.
Probabilistic or quantile forecasts; the full conditional distribution for each timepoint in the future.
Scenarios; probabilistic correct scenarios of the future wind power production.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 19
Value of knowing the uncertainties
Case study: A 15 MW wind farm in the Dutch electricity market,prices andmeasurements from the entire year 2002.
From a phd thesis by Pierre Pinson (2006).
The costs are due to the imbalance penalties on the regulation market.
Value of an advanced method for point forecasting:The regulation costs arediminished by nearly 38 pct.compared to the costs of using the persistanceforecasts.
Added value of reliable uncertainties:A further decrease of regulation costs – up to39 pct.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 20
Stochastic Portfolio Optimization
Example on the use of quantiles for optimization (From Emil Sokoler)
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 21
Wind power – asymmetrical penalties
The revenue from trading a specific hour on NordPool can be expressed as
PS × Bid +
{
PD × (Actual− Bid) if Actual > BidPU × (Actual− Bid) if Actual < Bid
PS is the spot price andPD/PU is the down/up reg. price.
The bid maximising the expected revenue is the followingquantile
E[PS ]− E[PD]
E[PU ]− E[PD]
in the conditional distribution of the future wind power production.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 22
Wind power – asymmetrical penalties
It is difficult to know the regulation prices at the day ahead level – research intoforecasting is ongoing.
The expression for the quantile is concerned with expected values of the prices – justgetting these somewhat right will increase the revenue.
A simple tracking ofCD andCU is a starting point.
The bids maximizing the revenue during the period September 2009 to March2010:
Qua
ntile
0.0
0.4
0.8
2009−09−01 2009−11−01 2010−01−01 2010−03−01
Monthly averages Operational tracking
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 23
Balancing wind by varying other production
Correct
Storage (hours of full wind prod.)
Den
sity
−10 −5 0 5 10
0.00
0.10
0.20
0.30
Naive
Storage (hours of full wind prod.)
Den
sity
−10 −5 0 5 10
0.00
0.10
0.20
0.30
(Illustrative example based on 50 day ahead scenarios as in the situation considered before)
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 24
Use of scenarios - Examples
Ramp forecasting; probabilities oframp events
Calculation of required storage asa function of horison (possibly ob-tained by varying hydro power pro-duction). Also show is the proba-bility that this storage will be suffi-cient.
Pro
babi
lity
of 1
0%, 2
h up
−re
gula
tion
even
t (%
)
h0 5 10 15 20 25 30 35
010
2030
0 5 10 15 20 25 30 35
−10
−5
05
Ene
rgy
stor
ed (
h of
full
prod
uctio
n)
100% 99%
98% 95%
90% 80%
70% 60%
50% 40%
30% 20%
10%100% 99%
98% 95%
90% 80%
70% 60%
50% 40%
30% 20%
10%
h
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 25
Solar Power Forecasting
Same principles as for wind power ....
Developed for grid connected PV-systems mainly installed on rooftops
Average of output from 21 PV systems in small village (Brædstrup) in DK
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 26
Method
Based on readings from the systems and weather forecasts
Two-step method
Step One: Transformation to atmospheric transmittanceτ with statistical clear skymodel (see below). Step Two: A dynamic model (see paper).
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 27
Example of hourly forecasts
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 28
Conclusions
The forecasting models must beadaptive (in order to taken changes of dust onblades, changes roughness, etc., into account).
Reliable estimates of theforecast accuracyis very important (check the reliability byeg. reliability diagrams).
Reliable probabilistic forecasts are important to gain thefull economical value.
Usemore than a single MET provider for delivering the input to the prediction tool– this improves the accuracy of wind power forecasts with 10-15 pct.
Estimates of thecorrelation in forecasts errors important.
Forecasts of ’cross dependencies’ between load, prices, wind and solar power areimportant.
Probabilistic forecasts are very important for asymmetric cost functions.
Probabilistic forecasts can provideanswersfor questions likeWhat is the probability that this storage is large enough forthe next 5 hours?What is the probability of an increase in wind power production of more that 50pct over the next two hours?What is the probability of a down-regulation due to wind power on more than xGW within the next 4 hours.
The same conclusions hold for our tools foreg. solar power forecasting.Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 29
Some references
H. Madsen:Time Series Analysis, Chapman and Hall, 392 pp, 2008.
H. Madsen and P. Thyregod:Introduction to General and Generalized Linear Models, Chapman
and Hall, 320 pp., 2011.
P. Pinson and H. Madsen:Forecasting Wind Power Generation: From Statistical Framework to
Practical Aspects. New book in progress - will be available 2012.
T.S. Nielsen, A. Joensen, H. Madsen, L. Landberg, G. Giebel:A New Reference for Predicting
Wind Power, Wind Energy, Vol. 1, pp. 29-34, 1999.
H.Aa. Nielsen, H. Madsen:A generalization of some classical time series tools, Computational
Statistics and Data Analysis, Vol. 37, pp. 13-31, 2001.
H. Madsen, P. Pinson, G. Kariniotakis, H.Aa. Nielsen, T.S. Nilsen: Standardizing the performance
evaluation of short-term wind prediction models, Wind Engineering, Vol. 29, pp. 475-489, 2005.
H.A. Nielsen, T.S. Nielsen, H. Madsen, S.I. Pindado, M. Jesus, M. Ignacio:Optimal Combination
of Wind Power Forecasts, Wind Energy, Vol. 10, pp. 471-482, 2007.
A. Costa, A. Crespo, J. Navarro, G. Lizcano, H. Madsen, F. Feitosa,A review on the young history
of the wind power short-term prediction, Renew. Sustain. Energy Rev., Vol. 12, pp. 1725-1744,
2008.
J.K. Møller, H. Madsen, H.Aa. Nielsen:Time Adaptive Quantile Regression, Computational
Statistics and Data Analysis, Vol. 52, pp. 1292-1303, 2008.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 30
Some references (Cont.)
P. Bacher, H. Madsen, H.Aa. Nielsen:Online Short-term Solar Power Forecasting, Solar Energy,
Vol. 83(10), pp. 1772-1783, 2009.
P. Pinson, H. Madsen:Ensemble-based probabilistic forecasting at Horns Rev. Wind Energy, Vol.
12(2), pp. 137-155 (special issue on Offshore Wind Energy),2009.
P. Pinson, H. Madsen:Adaptive modeling and forecasting of wind power fluctuations with
Markov-switching autoregressive models. Journal of Forecasting, 2010.
C.L. Vincent, G. Giebel, P. Pinson, H. Madsen:Resolving non-stationary spectral signals in wind
speed time-series using the Hilbert-Huang transform. Journal of Applied Meteorology and
Climatology, Vol. 49(2), pp. 253-267, 2010.
P. Pinson, P. McSharry, H. Madsen.Reliability diagrams for nonparametric density forecastsof
continuous variables: accounting for serial correlation. Quarterly Journal of the Royal
Meteorological Society, Vol. 136(646), pp. 77-90, 2010.
G. Reikard, P. Pinson, J. Bidlot (2011).Forecasting ocean waves - A comparison of ECMWF wave
model with time-series methods. Ocean Engineering in press.
C. Gallego, P. Pinson, H. Madsen, A. Costa, A. Cuerva (2011).Influence of local wind speed and
direction on wind power dynamics - Application to offshore very short-term forecasting. Applied
Energy, in press
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 31
Some references (Cont.)
C.L. Vincent, P. Pinson, G. Giebel (2011).Wind fluctuations over the North Sea. International
Journal of Climatology, available online
J. Tastu, P. Pinson, E. Kotwa, H.Aa. Nielsen, H. Madsen (2011). Spatio-temporal analysis and
modeling of wind power forecast errors. Wind Energy 14(1), pp. 43-60
F. Thordarson, H.Aa. Nielsen, H. Madsen, P. Pinson (2010).Conditional weighted combination of
wind power forecasts. Wind Energy 13(8), pp. 751-763
P. Pinson, G. Kariniotakis (2010). Conditional predictionintervals of wind power generation. IEEE
Transactions on Power Systems 25(4), pp. 1845-1856
P. Pinson, H.Aa. Nielsen, H. Madsen, G. Kariniotakis (2009). Skill forecasting from ensemble
predictions of wind power. Applied Energy 86(7-8), pp. 1326-1334.
P. Pinson, H.Aa. Nielsen, J.K. Moeller, H. Madsen, G. Kariniotakis (2007).Nonparametric
probabilistic forecasts of wind power: required properties and evaluation. Wind Energy 10(6), pp.
497-516.
T. Jónsson, P. Pinson (2010).On the market impact of wind energy forecasts. Energy Economics,
Vol. 32(2), pp. 313-320.
T. Jónsson, M. Zugno, H. Madsen, P. Pinson (2010).On the Market Impact of Wind Power
(Forecasts) - An Overview of the Effects of Large-scale Integration of Wind Power on the Electricity
Market. IAEE International Conference, Rio de Janeiro, Brazil.
Seminario International de Clausura del Proyecto TRES, Las Palmas 2012 – p. 32