# Less Information, Similar Performance: Comparing Machine Learning-Based Time Series of Wind Power Generation to Renewables.ninja

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- (a)
- Wind speed data were acquired, and wind speed components, i.e., the u and v variables, were interpolated from the MERRA2 grid to the actual turbine locations using LOESS regression.
- (b)
- Wind speeds were extrapolated to the corresponding turbine hub heights from the three height levels provided by MERRA2 (2, 10, and 50 m above the ground) using the logarithmic wind profile.
- (c)
- Wind speeds were converted to wind turbine power outputs by using manufacturers’ power curves.
- (d)
- An additional bias correction step for calibrating results against actual electricity generation was performed in the RN model as a post-processing step.

#### 2.1. Detailed Description of MLM

_{ij}and w

_{jk}) were estimated by minimizing the error of the network output in comparison to observations. In the chosen neural network modeling framework, the Root Mean Square Error (RMSE) is the default error measure. Error backpropagation was used to minimize the error in an iterative process (Figure 2). For the hidden layers, we tested models with layer sizes of 60 and 80 nodes. Out of these two models, the model size which resulted in better correlation, normalized root mean square error (NRMSE), and normalized mean absolute error (NMAE) was chosen for further use.

#### 2.2. Data

#### 2.2.1. Climate Input Data

#### 2.2.2. Installed Capacity and Electricity Generation Data

#### 2.3. Time Series Quality Assessment

## 3. Results

#### 3.1. Model Selection

#### 3.2. Basic Time Series Quality

#### 3.3. Diurnal Characteristics

#### 3.4. Seasonal Characteristics

#### 3.5. Durations and Frequencies of Low, High, and Extreme Values

#### 3.6. Frequencies and Ranges of Power Ramps

## 4. Discussions

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Results of a Model with a Stronger Subsetting of the Climate Data Grid Points (MLM3)

**Table A1.**Comparison of model error values for all tested models for the training and prediction dataset.

Error Metric | Network Size | MLM1 | MLM2 | MLM3 |
---|---|---|---|---|

NMAE | 60 | 0.152 | 0.144 | 0.138 |

NRMSE | 60 | 0.208 | 0.202 | 0.194 |

NMAE | 80 | 0.161 | 0.138 | 0.141 |

NRMSE | 80 | 0.220 | 0.190 | 0.194 |

#### Appendix A.2. Basic Time Series Quality of MLM3

Quality Measure | Observations | RN | MLM2 | MLM3 |
---|---|---|---|---|

Correlation | - | 0.976 | 0.975 | 0.975 |

NMAE | - | 0.152 | 0.138 | 0.138 |

NRMSE | - | 0.210 | 0.191 | 0.194 |

Variance | 0.026 | 0.030 | 0.025 | 0.024 |

Quantile | ||||

0% | 0.000 | 0.000 | −0.011 | −0.008 |

25% | 0.067 | 0.071 | 0.069 | 0.070 |

50% | 0.137 | 0.149 | 0.135 | 0.136 |

75% | 0.260 | 0.275 | 0.254 | 0.251 |

100% | 0.913 | 0.964 | 0.975 | 0.943 |

**Figure A1.**Scatterplot of modeled generation time series compared with observations (Renewables.ninja time series abbreviated as RN and machine learning model time series abbreviated as MLM2 and MLM3 versus observations on the X-axis).

**Figure A2.**Total distributions of the RN, MLM2, and MLM3 modeled time series compared with the observed total distribution (dark colored areas correspond to an accordance of the modeled and observed time series; Renewables.ninja time series abbreviated as RN and machine learning model time series abbreviated as MLM2 and MLM3).

#### Appendix A.3. Diurnal Characteristics of MLM3

**Figure A3.**Hourly deviations from observed values for RN, MLM2, and MLM3 (Renewables.ninja time series abbreviated as RN and machine learning model time series abbreviated as MLM2 and MLM3).

#### Appendix A.4. Seasonal Characteristics of MLM3

**Figure A4.**Capacity factor (CF) deviations of RN, MLM2, and MLM3 modeled time series within different CF bins for the autumn-winter and spring-summer half-year from 2010 to 2016 (Renewables.ninja time series abbreviated as RN, machine learning model time series abbreviated as MLM2 and MLM3, and n denotes the number of observations within CF bins).

#### Appendix A.5. Durations and Frequencies of Low, High, and Extreme Values of MLM3

**Table A3.**Observed and modeled (Renewables.ninja [RN] and machine learning models [MLM2 and MLM3]) CF, including frequencies, mean, and maximum durations of extremely low (<0.005), low (0.01), high (0.75), and extremely high (>0.8) generation events in consecutive hours.

CF Ranges | Observations | RN | MLM2 | MLM3 |
---|---|---|---|---|

CF < 0.005 | ||||

Frequency | 102 | 430 | 238 | 248 |

Mean Duration | 3.19 | 4.62 | 3.50 | 3.70 |

Max Duration | 10 | 14 | 10 | 15 |

CF < 0.01 | ||||

Frequency | 509 | 748 | 341 | 283 |

Mean Duration | 2.98 | 2.60 | 1.91 | 1.78 |

Max Duration | 25 | 12 | 5 | 7 |

CF > 0.75 | ||||

Frequency | 204 | 356 | 225 | 187 |

Mean Duration | 3.46 | 3.10 | 3.41 | 3.46 |

Max Duration | 13 | 18 | 15 | 21 |

CF > 0.8 | ||||

Frequency | 121 | 471 | 125 | 115 |

Mean Duration | 7.56 | 9.24 | 5.21 | 7.19 |

Max Duration | 35 | 33 | 21 | 17 |

#### Appendix A.6. Frequencies and Ranges of Power Ramps of MLM3

**Table A4.**Minimum, maximum, and mean of negative and positive capacity factor (CF) ramps within different time frames and frequency of highly positive and negative CF ramps.

Time Frame | Observations | RN | MLM2 | MLM3 |
---|---|---|---|---|

1 h | ||||

Min | −0.66 | −0.11 | −0.13 | −0.11 |

Neg. Mean | −0.012 | −0.013 | −0.012 | −0.012 |

Neg. Freq | 31,313 | 32,243 | 31,132 | 31,308 |

Pos. Mean | 0.013 | 0.014 | 0.013 | 0.012 |

Pos. Freq | 30,054 | 29,124 | 30,235 | 30,059 |

Max | 0.50 | 0.16 | 0.14 | 0.15 |

Frequency < −0.2 | 1 | 0 | 0 | 0 |

Frequency > 0.2 | 1 | 0 | 0 | 0 |

3 h | ||||

Min | −0.67 | −0.28 | −0.33 | −0.30 |

Neg. Mean | −0.022 | −0.024 | −0.022 | −0.022 |

Neg. Freq | 94,293 | 96,677 | 94,091 | 94,389 |

Pos. Mean | 0.023 | 0.027 | 0.023 | 0.023 |

Pos. Freq | 89,805 | 87,421 | 90,007 | 89,709 |

Max | 0.50 | 0.30 | 0.31 | 0.32 |

Frequency < −0.2 | 75 | 71 | 61 | 69 |

Frequency > 0.2 | 92 | 181 | 93 | 79 |

6 h | ||||

Min | −0.67 | −0.46 | −0.50 | −0.47 |

Neg. Mean | −0.035 | −0.038 | −0.034 | −0.034 |

Neg. Freq | 188,949 | 192,660 | 188,749 | 189,180 |

Pos. Mean | 0.037 | 0.042 | 0.036 | 0.036 |

Pos. Freq | 179,238 | 175,527 | 179,438 | 179,007 |

Max | 0.51 | 0.50 | 0.47 | 0.47 |

Frequency < −0.2 | 1616 | 2140 | 1736 | 1682 |

Frequency > 0.2 | 1846 | 2921 | 1860 | 1687 |

12 h | ||||

Min | −0.68 | −0.60 | −0.64 | −0.62 |

Neg. Mean | −0.054 | −0.059 | −0.053 | −0.052 |

Neg. Freq | 376,200 | 380,753 | 376,127 | 377,137 |

Pos. Mean | 0.056 | 0.064 | 0.055 | 0.055 |

Pos. Freq | 360,138 | 355,585 | 360,211 | 359,201 |

Max | 0.62 | 0.67 | 0.68 | 0.63 |

Frequency < −0.2 | 14,185 | 18,009 | 14,245 | 13,396 |

Frequency > 0.2 | 14,680 | 19,194 | 14,237 | 13,580 |

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**Figure 1.**Comparison of the necessary modeling steps for deriving wind power output with the RN and the MLM approach indicated with letters a, b, c, d (Renewables.ninja abbreviated as RN, machine learning model abbreviated as MLM, own figure).

**Figure 3.**Training (yellow) and prediction (green) iterations P1–P4. In each iteration, model parameters are trained, and the associated prediction period is predicted with the neural network. All green periods are combined to form one 7 years timeseries.

**Figure 4.**MERRA2 grid points selected for MLM input datasets (grid points only used as MLM1 inputs depicted in blue, input grid points used for MLM1 as well as MLM2 depicted in yellow, inputs used for all three models displayed in red).

**Figure 5.**Scatterplot of modeled generation time series compared with observations (Renewables.ninja time series abbreviated as RN and machine learning model time series abbreviated as MLM1 and MLM2 versus observations on the X-axis).

**Figure 6.**Total distributions of the RN, MLM1, and MLM2 modeled time series compared with the observed total distribution (dark colored areas correspond to an accordance of the modeled and observed time series; Renewables.ninja time series abbreviated as RN and machine learning model time series abbreviated as MLM1 and MLM2).

**Figure 7.**Hourly deviations from observed values for RN, MLM1, and MLM2 (Renewables.ninja time series abbreviated as RN and machine learning model time series abbreviated as MLM1 and MLM2).

**Figure 8.**Capacity factor (CF) deviations of RN, MLM1, and MLM2 modeled time series within different CF bins for the autumn-winter and spring-summer half year from 2010 to 2016 (Renewables.ninja time series abbreviated as RN, machine learning model time series abbreviated as MLM1 and MLM2, and n denotes the number of observations within CF bins).

**Figure 9.**Cumulative density of one-hour capacity factor (CF) changes for the RN, MLM1, and MLM2 modeled time series compared with observations.

**Table 1.**All variables used in the machine learning modeling (MLM) process and validation with their corresponding name, application, unit, size in MLM1, size in MLM2, size in MLM3 and source (in the size column, the multiplicator corresponds to the number of grid points used and the multiplicand to the time series length in hours from 2010 to 2016; 43 date dummy variables: 24-h, 7-day, and 12-month dummy variables).

Name | Application | Unit | MLM1 Size | MLM2 Size | MLM3 Size | Source |
---|---|---|---|---|---|---|

2 m northward wind speed (V2M) | predictor | m/s | 378 × 61,368 | 206 × 61,368 | 58 × 61,368 | MERRA2 |

10 m northward wind speed (V10M) | predictor | m/s | 378 × 61,368 | 206 × 61,368 | 58 × 61,368 | MERRA2 |

50 m northward wind speed (V50M) | predictor | m/s | 378 × 61,368 | 206 × 61,368 | 58 × 61,368 | MERRA2 |

2 m eastward wind speed (U2M) | predictor | m/s | 378 × 61,368 | 206 × 61,368 | 58 × 61,368 | MERRA2 |

10 m eastward wind speed (U10M) | predictor | m/s | 378 × 61,368 | 206 × 61,368 | 58 × 61,368 | MERRA2 |

50 m eastward wind speed (U50M) | predictor | m/s | 378 × 61,368 | 206 × 61,368 | 58 × 61,368 | MERRA2 |

date dummy variables | predictor | - | 43 × 61,368 | 43 × 61,368 | 43 × 61,368 | OPSD date sequence |

actual generation | response | capacity factor | 61,368 | 61,368 | 61,368 | OPSD |

RN generation | validation | capacity factor | 61,368 | 61,368 | 61,368 | Renewables.ninja |

MLM1 generation | validation | capacity factor | 61,368 | 61,368 | 61,368 | Neural network prediction |

MLM2 generation | validation | capacity factor | 61,368 | 61,368 | 61,368 | Neural network prediction |

MLM3 generation | validation | capacity factor | 61,368 | 61,368 | 61,368 | Neural network prediction |

**Table 2.**Comparison of model error values for MLM1 and MLM2 for the training and prediction dataset.

Error Metric | Network Size | MLM1 | MLM2 |
---|---|---|---|

NMAE | 60 | 0.152 | 0.144 |

NRMSE | 60 | 0.208 | 0.202 |

NMAE | 80 | 0.161 | 0.138 |

NRMSE | 80 | 0.220 | 0.190 |

**Table 3.**Comparison of the error metrics for Renewables.ninja (RN), the first MLM-generated time series (MLM1), and the second MLM-generated time series (MLM2).

Quality Measure | Observations | RN | MLM1 | MLM2 |
---|---|---|---|---|

Correlation | - | 0.976 | 0.970 | 0.975 |

NMAE | - | 0.152 | 0.152 | 0.138 |

NRMSE | - | 0.210 | 0.209 | 0.191 |

Variance | 0.026 | 0.030 | 0.025 | 0.025 |

Quantile | ||||

0% | 0.000 | 0.000 | −0.012 | −0.011 |

25% | 0.067 | 0.071 | 0.072 | 0.069 |

50% | 0.137 | 0.149 | 0.140 | 0.135 |

75% | 0.260 | 0.275 | 0.260 | 0.254 |

100% | 0.913 | 0.964 | 0.970 | 0.975 |

**Table 4.**Observed and modeled (Renewables.ninja [RN] and machine learning models [MLM1 and MLM2]) CF, including frequencies, mean, and maximum durations of extremely low (<0.005), low (0.01), high (0.75), and extremely high (>0.8) generation events in consecutive hours.

CF Ranges | Observations | RN | MLM1 | MLM2 |
---|---|---|---|---|

CF < 0.005 | ||||

Frequency | 102 | 430 | 193 | 238 |

Mean Duration | 3.19 | 4.62 | 3.27 | 3.50 |

Max Duration | 10 | 14 | 10 | 10 |

CF < 0.01 | ||||

Frequency | 509 | 748 | 312 | 341 |

Mean Duration | 2.98 | 2.60 | 1.91 | 1.91 |

Max Duration | 25 | 12 | 7 | 5 |

CF > 0.75 | ||||

Frequency | 204 | 356 | 174 | 225 |

Mean Duration | 3.46 | 3.10 | 3.63 | 3.41 |

Max Duration | 13 | 18 | 22 | 15 |

CF > 0.8 | ||||

Frequency | 121 | 471 | 75 | 125 |

Mean Duration | 7.56 | 9.24 | 4.17 | 5.21 |

Max Duration | 35 | 33 | 11 | 21 |

**Table 5.**Minimum, maximum, and mean of negative and positive capacity factor (CF) ramps within different time frames and frequency of highly positive and negative CF ramps.

Time Frame | Observations | RN | MLM1 | MLM2 |
---|---|---|---|---|

1 h | ||||

Min | −0.66 | −0.11 | −0.14 | −0.13 |

Neg. Mean | −0.012 | −0.013 | −0.013 | −0.012 |

Neg. Freq | 31,313 | 32,243 | 31,070 | 31,132 |

Pos. Mean | 0.013 | 0.014 | 0.013 | 0.013 |

Pos. Freq | 30,054 | 29,124 | 30,297 | 30,235 |

Max | 0.50 | 0.16 | 0.16 | 0.14 |

Frequency < −0.2 | 1 | 0 | 0 | 0 |

Frequency > 0.2 | 1 | 0 | 0 | 0 |

3 h | ||||

Min | −0.67 | −0.28 | −0.30 | −0.33 |

Neg. Mean | −0.022 | −0.024 | −0.023 | −0.022 |

Neg. Freq | 94,293 | 96,677 | 93,587 | 94,091 |

Pos. Mean | 0.023 | 0.027 | 0.023 | 0.023 |

Pos. Freq | 89,805 | 87,421 | 90,411 | 90,007 |

Max | 0.50 | 0.30 | 0.38 | 0.31 |

Frequency < −0.2 | 75 | 71 | 84 | 61 |

Frequency > 0.2 | 92 | 181 | 85 | 93 |

6 h | ||||

Min | −0.67 | −0.46 | −0.48 | −0.50 |

Neg. Mean | −0.035 | −0.038 | −0.035 | −0.034 |

Neg. Freq | 188,949 | 192,660 | 188,102 | 188,749 |

Pos. Mean | 0.037 | 0.042 | 0.036 | 0.036 |

Pos. Freq | 179,238 | 175,527 | 180,085 | 179,438 |

Max | 0.51 | 0.50 | 0.55 | 0.47 |

Frequency < −0.2 | 1616 | 2140 | 1678 | 1736 |

Frequency > 0.2 | 1846 | 2921 | 1650 | 1860 |

12 h | ||||

Min | −0.68 | −0.60 | −0.66 | −0.64 |

Neg. Mean | −0.054 | −0.059 | −0.053 | −0.053 |

Neg. Freq | 376,200 | 380,753 | 375,262 | 376,127 |

Pos. Mean | 0.056 | 0.064 | 0.055 | 0.055 |

Pos. Freq | 360,138 | 355,585 | 361,076 | 360,211 |

Max | 0.62 | 0.67 | 0.65 | 0.68 |

Frequency < −0.2 | 14,185 | 18,009 | 13,781 | 14,245 |

Frequency > 0.2 | 14,680 | 19,194 | 13,634 | 14,237 |

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## Share and Cite

**MDPI and ACS Style**

Baumgartner, J.; Gruber, K.; Simoes, S.G.; Saint-Drenan, Y.-M.; Schmidt, J. Less Information, Similar Performance: Comparing Machine Learning-Based Time Series of Wind Power Generation to Renewables.ninja. *Energies* **2020**, *13*, 2277.
https://doi.org/10.3390/en13092277

**AMA Style**

Baumgartner J, Gruber K, Simoes SG, Saint-Drenan Y-M, Schmidt J. Less Information, Similar Performance: Comparing Machine Learning-Based Time Series of Wind Power Generation to Renewables.ninja. *Energies*. 2020; 13(9):2277.
https://doi.org/10.3390/en13092277

**Chicago/Turabian Style**

Baumgartner, Johann, Katharina Gruber, Sofia G. Simoes, Yves-Marie Saint-Drenan, and Johannes Schmidt. 2020. "Less Information, Similar Performance: Comparing Machine Learning-Based Time Series of Wind Power Generation to Renewables.ninja" *Energies* 13, no. 9: 2277.
https://doi.org/10.3390/en13092277