Forecasting Daily Solar Energy Production Using Robust Regression - - PowerPoint PPT Presentation

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Forecasting Daily Solar Energy Production Using Robust Regression - - PowerPoint PPT Presentation

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Forecasting Daily Solar Energy Production Using Robust Regression Techniques Gilles Louppe (@glouppe) Peter Prettenhofer (@pprett) Universit e de Li` ege, Belgium Graz University of Technology, Austria Problem statement Goal Short-term

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Forecasting Daily Solar Energy Production Using Robust Regression Techniques

Gilles Louppe (@glouppe)

Universit´ e de Li` ege, Belgium

Peter Prettenhofer (@pprett)

Graz University of Technology, Austria

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Problem statement

Goal

Short-term forecasting of daily solar energy production based on weather forecasts from numerical weather prediction (NWP) models.

Challenges

◮ High volatility

rapidly changing weather conditions

◮ Noisy response

hardware failure

◮ Noisy inputs

inaccuracy of NWP model

Apr 04 1998 Apr 18 1998 May 02 1998 May 16 1998 May 30 1998 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1e7

Solar energy production in April/May 1998

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Data

Solar energy production

◮ 98 Oklahoma Mesonet

sites

◮ Total incoming solar

energy in Jm−2

◮ Time period : 1994 -

2007

Courtesy : Dr. Amy McGovern

Numerical weather prediction

◮ NOAA/NCEP GEFS Reforecast, 5 forecasts per day ◮ Ensemble comprises 11 members (one control) ◮ 15 measurements (temp, humidity, upward radiative flux, ...)

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Overview of our approach

Interpolation

(Kriging)

Feature engineering

Learning

(Gradient Tree Boosting)

  • 1. Interpolation of meteorological measurements from GEFS

grid points onto Mesonet sites ;

  • 2. Construction of new variables from the measurement

estimates ;

  • 3. Forecasting of daily energy production using Gradient

Boosted Regression Trees, on the basis of the local measurement estimates.

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Kriging

Goal : Estimate meteorological variables (temperature, humidity, ...) locally at all Mesonet sites. For each day d, period h and type f of meteorological measurement :

  • 1. Build a local learning set

Ldhf = {(xi = (lati, loni, elevationi), yi = midhf )}, where midhf is the average value (over the ensemble) of measurements midhf of type f , at GEFS location i, day d and period h ;

  • 2. Learn a Gaussian Process from Ldhf , for predicting

measurements from coordinates ;

(Fitting is perfomed using nuggets to account for noise in the measurements.)

  • 3. Predict measurement estimates

mjdhf at Mesonet stations j from their coordinates.

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Feature engineering

Goal : Build a learning set L from the measurement estimates.

  • 1. Concatenate the estimates at all periods h and for all types f ,

for each Mesonet station j and day d : L = {(xjd = ( mjdh1f1, mjdh1f2, ...), yjd = pjd)} where pjd is the energy production at Mesonet station j and day d.

  • 2. Extend inputs xjd with engineered features :

◮ Solar features (delta between sunrise and sunset) ◮ Temporal features (day of year, month) ◮ Spatial features (latitude, longitude, elevation) ◮ Non-linear combinations of measurement estimates ◮ Daily mean estimates ◮ Variance of the measurement estimates, as produced by the

Gaussian Processes

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Predicting energy production

Goal : Predict daily energy production at Mesonet sites.

  • 1. Learn a model using Gradient Boosted Regression Trees

(sklearn.ensemble.GradientBoostingRegressor), predicting output y from inputs x ;

◮ Use the Least Absolute Deviation loss for robustness ; ◮ Optimize hyper-parameters on an internal validation set ;

  • 2. For further robustness, repeat Step 1 several times (using

different random seeds) and aggregate the predictions of all models.

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Results

Evaluation

◮ Held-out data from 2008 - 2012. ◮ Mean Absolute Error (MAE) as metric :

MAE = 1 JD

J

  • j=1

D

  • d=1

|pjd − ˆ pjd|

Results

Method Heldout-Score [MAE] ∆ [%] GMM 4019469.94 46.19% Spline Interp. 2611293.30 17.17% Kriging + GBRT 2162799.74

  • Best

2107588.17

  • 2.62%
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Error analysis

2001 2002 2003 2004 2005 2006 2007 0.0 0.2 0.4 0.6 0.8 1.0 1.21e7

Daily MAE

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 doy 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1e8

Day-of-year MAE ae

1 2 3 4 5 6 7 8 9 10 11 12 month 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1e8

Monthly MAE ae

9 36 46 72 22 6 30 35 63 75 96 3 12 4 78 39 48 18 37 66 34 60 77 55 64 97 11 8 81 58 69 51 67 13 88 71 92 42 79 20 76 26 90 65 56 21 16 5 41 86 29 27 28 44 17 53 40 61 73 7 10 38 23 14 52 68 32 84 50 54 2 83 1 33 91 57 62 15 49 82 87 70 89 47 80 19 31 43 74 45 95 59 93 25 85 94 24 stid 500000 1000000 1500000 2000000 2500000

Station MAE

104 102 100 98 96 94 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5

Station MAE (spatial correlation)

0.800 0.825 0.850 0.875 0.900 0.925 0.950 0.975 1.000

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Conclusions

✓ Competitive results (4th position) ; ✓ Robust approach at all steps of the pipeline ; ✗ Including additional data from nearest GEFS grid points might have further improved our results. Questions ? g.louppe|peter.prettenhofer@gmail.com

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Kriging illustration