Due to the high inherent uncertainty of renewable energy, probabilistic day-ahead wind power forecasting is crucial for modeling and controlling the uncertainty of renewable energy smart grids in smart cities. However, the accuracy and reliability of high-resolution day-ahead wind power forecasting are constrained by unreliable local weather prediction and incomplete power generation data. This article proposes a physics-informed artificial intelligence (AI) surrogates method to augment the incomplete dataset and quantify its uncertainty to improve wind power forecasting performance. The incomplete dataset, built with numerical weather prediction data, historical wind power generation, and weather factors data, is augmented based on generative adversarial networks. After augmentation, the enriched data is then fed into a multiple AI surrogates model constructed by two extreme learning machine networks to train the forecasting model for wind power. Therefore, the forecasting models’ accuracy and generalization ability are improved by mining the implicit physics information from the incomplete dataset. An incomplete dataset gathered from a wind farm in North China, containing only 15 days of weather and wind power generation data with missing points caused by occasional shutdowns, is utilized to verify the proposed method’s performance. Compared with other probabilistic forecasting methods, the proposed method shows better accuracy and probabilistic performance on the same incomplete dataset, which highlights its potential for more flexible and sensitive maintenance of smart grids in smart cities.

As renewable energy like wind, photovoltaic and tidal power are increasingly incorporated into smart grids, the stochastic and uncertainty features of which brought additional challenges to the electricity market and energy system [

There are two main difficulties in day-ahead probability forecasting of wind power. First, unlike conventional power plants, many wind farms, especially the smart wind grids around smart cities, are newly built, with limited historical power generation data [

Two kinds of improved forecasting approaches can be conducted to tackle the generalization difficulty: physics-based and data-driven methods [

Physics-informed neural networks (PINN) were first named by Raissi et al. [

Informed by the literature review (See

A multiple AI surrogates regression structure for day-ahead wind power probabilistic forecasting with an incomplete dataset, which infused the physics information from NWP and weather monitoring data to enhance forecasting accuracy was built.

A data augmentation method based on two kinds of GAN corresponding to the multi-surrogate model, improving the model’s generalization ability, and supporting quantifying the uncertainty propagation was created.

The proposed method’s forecasting and uncertainty quantification abilities were benchmarked by applying it to a real case dataset from a wind farm together with conventional methods.

The rest of this paper is organized as follows.

The uncertainty of wind power generation has many aspects, from stochastic weather factors to inconsistent efficiency of wind turbines. Research works for wind power forecasting can be classified through the materials that are used to quantify the uncertainty: the regression methods based on physics information from NWP data or simulation and the autoregression method based on monitored wind speed and power data.

Physics-based methods are generally powered by numerical weather prediction (NWP) data and computational fluid dynamics (CFD) simulation. Che et al. [

Data-driven methods utilize statistical or artificial intelligence (AI) based models to predict future power generation with historical and online monitoring data [

Meanwhile, incorporating physical information and neural networks (NN) to enrich the generalization ability is also a growing field in wind power forecasting. Wu et al. [

An extreme learning machine is a single hidden layer feedforward neural network (SLFN) [

The output function of a single layer ELM with

Owing to the high training speed and adaptability for non-linear activation functions, the ELM has been deterministically and probabilistically applied to wind speed and power forecasting [

Since the GAN was first introduced in 2014 [

The objective function of GAN has many forms, in which the Wasserstein distance based function (i.e., Earth–Mover distance),

Traditional wind power forecasting using NWP mainly conducts the regression from NWP features to wind power directly. However, this kind of regression ignored the prediction error within the NWP itself. That is, the regression model is founded on an unreliable prediction of physics factors rather than the real physics factors, so the robustness of NWP constrains its forecasting accuracy.

From the viewpoint of probability theory, the probabilistic forecasting of wind power generation with physics information from NWP data is a classic Bayesian inference problem. Taking the physics information of NWP as the prior knowledge and the real weather factors as the posterior stochastic variables, the generated wind power is then predicted by the regression inference of the posterior weather factors. A Bayesian network can be built to describe the forecasting process, as shown in

In

In which,

The NWP contains multiple weather features, from wind speed at a different height to the radiation of various wavelengths. However, in most practice scenarios, not all features of the weather in NWP are necessary for wind power forecasting since some are irrelevant to wind power. He et al. [

In which,

In which, the

Despite the ELM’s good generalization ability, it still needs enough samples to train the regression model. However, incomplete samples remain a problem in most day-ahead wind power forecasting tasks. Therefore, WGAN, as a data augmentation solution, is introduced to overcome the incomplete sample problem and enhance ELM training.

The WGAN can learn the original data distribution and generate realistic synthetic data to augment it. Nevertheless, a conventional WGAN can only deal with non-series data since it cannot capture the intrinsic time-varying patterns of the time-series data. Hence, a WWGAN was proposed to improve the data augmentation ability with time-series data. WWGAN incorporates the WGAN into a recurrent neural network (RNN) structure, which adaptively learns time-series data’s arbitrary distribution and implicit pattern, clusters the same pattern into adjacent groups by a threshold calculated with the Wasserstein distance, and then generates the augmentation model for each group. The structure of WWGAN is shown in

As shown in

The main difference between WGAN and WWGAN is that WGAN can learn the correlation between multi-dimensional data while learning the distribution features of the data. However, it cannot capture the time series patterns of the data. WWGAN can capture the distribution and time series patterns of the data. However, because its learning algorithm needs to call four deep neural networks, it lacks the ability to efficiently deal with multi-dimensional data correlation. Therefore, WGAN can effectively augment multi-dimensional non-series data but cannot effectively augment time-series data. In contrast, WWGAN can effectively augment low-dimensional time-series data but is less efficient when dealing with multi-dimensional data.

With both WGAN and WWGAN, either the non-series regression training sample or the time-series input sample for forecasting can be augmented. Yet, this kind of augmentation is non-directional. WGAN cannot specifically augment the fewer or missing features in the incomplete dataset; instead, it augments every feature from the distribution. Hence, the augmented dataset is still imbalanced, and different features have different proportions in the dataset, which is not conducive to training the network’s generalization ability [

After clustering and resampling the augmented data, a training dataset with balanced features can be built to enhance the training efficiency of ELM and improve its generalization ability.

Based on the above Bayesian network architecture and the incomplete data augmentation method, the physics-informed AI surrogates model can be constructed, as shown in

There are two ELM-based AI surrogates in the model. The first surrogate forms a response surface from the NWP factors to the SFs to model and quantify the uncertainty that lies in the day-ahead weather prediction. The second surrogate models the regression of SFs to wind power, which quantifies the uncertainty within the wind power generation process. Utilizing both AI surrogates to solve the inference problems between Bayesian network layers, the physics information and its uncertainty are better modeled in the probabilistic forecasting model. Due to the multiple AI surrogates within the model, the training and forecasting (testing) datasets for each AI surrogate are listed in

Surrogate | Types | Form | Input features (X) | Labels/Output features (Y) |
---|---|---|---|---|

First AI surrogate | Training | Discrete features | Historical NWP data | Observed SF records |

Forecasting | Time series | Day-ahead NWP data | Day-ahead SF estimation | |

Second AI surrogate | Training | Discrete features | Observed SF records | Wind power generation records |

Forecasting | Time series | Day-ahead SF estimation | Wind power forecasting |

Step 1: Data Preprocessing.

Step 2: Build the training set and test set of the first surrogate and the training set of the second surrogate.

Step 3: Augment and resample the training set of the first surrogate, then train the first surrogate.

Step 4: Augment the test set of the first surrogate and use the test set to get the output.

Step 5: Train the second surrogate.

Step 6: Take the output of the first surrogate as the test set to obtain the output of the second surrogate, that is, the wind power forecasting result.

The framework of the proposed method is shown in the flowchart in

Due to the training data for the second surrogate being sampled from observed records, the data can be directly fed into ELM with

However, the time-series forecasting data need to be augmented by the WWGAN to quantify the uncertainty of forecasting results. After that, the augmented forecasting data

In order to examine the forecasting ability with an incomplete dataset, the raw dataset is built from 15 days of weather monitoring and wind power generation data from a wind farm in North China, the installed capacity of which is 17.29 MW, and this area’s corresponding day-ahead NWP data. The period of the raw data is from 2016-2-19 00:00:00 to 2016-3-4 23:45:00 with a time resolution of 15 min. The first 14 days’ data are used as the training period to predict the last day’s wind power generation, i.e., the wind power from 2016-3-4 00:00:00 to 2016-3-4 23:45:00. With a resolution of 15 min, there should be 96 sets of data points per day, and the training period should contain 1344 sets of samples. However, due to grid control, shutdowns, missing data, and other issues, the actual monitored amount of wind power generation data within the training period is 1318, which limits the training dataset to the same size. After aligning the NWP data, weather monitoring data, and the wind power generation data with coincident time indexes, the raw data are normalized to 0∼20 with the min-max normalization method.

Intuitively, wind speed is the most obvious factor affecting wind power generation. However, in the day-ahead wind power forecasting scenario, the error of the NWP wind speed itself cannot be ignored. If only wind speed is used as a regression factor, it may cause a significant error in the final prediction result. As Han et al. [

Rank | Weather factors | Abbreviation | MIQ |
---|---|---|---|

1 | Wind speed at 70 m height | ws70 | 1.0000 |

2 | Mean sea level pressure | mslp | 1.2750 |

3 | Temperature | T | 2.4698 |

4 | Wind speed at 100 m height | ws100 | 1.5318 |

5 | Wind speed at 30 m height | ws30 | 1.2623 |

6 | Wind direction at 70 m height | direction70 | 1.4087 |

7 | Sensible heat flux | senf | 1.4117 |

8 | Temperature at 2 m height | T2m | 1.3554 |

9 | Relative humidity at 2 m height | RH2m | 1.2242 |

10 | Wind direction at 30 m height | direction 30 | 0.6249 |

11 | Wind direction at 10 m height | direction 10 | 0.4397 |

12 | Wind direction at 100 m height | direction 100 | 0.5829 |

Since the main job of the first surrogate is to calibrate the prediction results of NWP to make it closer to the real weather features, therefore, the first surrogate does not focus on the time series features of the data but on the relationship between different weather features, so it does not need to use WWGAN to augment it but uses WGAN. The raw training datasets

Parameters | Value | Parameters | Value |
---|---|---|---|

Order of input data | 10 | Batch size | 60 |

Hidden size | 27 | Learning rate | 0.001 |

Number of hidden layers | 10 | 5 |

Dataset

Parameters | Value | Parameters | Value |
---|---|---|---|

Order of input data | 1 | Batch size | 6 |

Hidden size | 42 | Learning rate | 0.0001 |

Number of hidden layers | 3 | 0.2 | |

Slice size | 12 | Threshold for WWGAN | 0.2 |

With the prepared datasets, the training process of these two AI surrogates designed by ELM is convenient. The hidden nodes of the ELM for both surrogates are set to 14, and the training epoch set to 10,000. The output weights are the average of results from these 10,000 epochs to improve the robustness.

The first surrogate contains three sub-surrogates that are trained with

Abbreviation | Indicator | Equation |
---|---|---|

MAE | Mean Absolute Error | |

RMSE | Root Mean Square Error | |

RSS | Residual Sum of Squares | |

PICP | Prediction Interval Coverage Probability | |

ACE | Average Coverage Error | |

PINAW | Prediction Interval Normalized Average Width |

ws70 | mslp | T | |||||||
---|---|---|---|---|---|---|---|---|---|

Not augmented | Mean | Original NWP | Not augmented | Mean | Original NWP | Not augmented | Mean | Original NWP | |

RMSE | 1.9334 | 1.8313 | 3.3036 | 0.5812 | 0.7454 | 1.0961 | 1.4822 | 1.5372 | 5.2035 |

MAE | 1.5737 | 1.5206 | 2.8288 | 0.4880 | 0.5996 | 0.9749 | 1.2092 | 1.2684 | 3.9593 |

RSS | 358.8472 | 321.9585 | 1047.7269 | 32.4295 | 53.3361 | 115.3353 | 210.9015 | 226.8560 | 2599.3187 |

The second AI surrogate is trained with

When training is completed, the outputs from the first surrogate were used as inputs to produce the probabilistic forecasting result for wind power. After denormalization, the forecasting results from 2016-3-4 00:00:00 to 2016-3-4 23:45:00 are shown in

Indicator | RMSE | MAE | SSE | PICP | ACE | PINAW |
---|---|---|---|---|---|---|

Value | 1.3011 | 1.0064 | 162.5204 | 0.9583 | 0.0083 | 0.6036 |

In order to evaluate the forecasting effect of the proposed method, three mainstream wind power forecasting methods are selected as benchmarks, the ELM-based method [

Datasets | Approaches | RMSE | MAE | RSS | PICP | ACE | PINAW |
---|---|---|---|---|---|---|---|

Train and test with NWP | 2.185 | 1.7852 | 458.3373 | 0.9375 | −0.0125 | 0.5802 | |

2.8727 | 2.4293 | 792.2321 | 0.6563 | −0.2937 | 0.5935 | ||

1.9922 | 1.5746 | 380.9975 | 0.8958 | −0.0542 | 0.5803 | ||

2.5376 | 2.0856 | 618.1598 | 1 | 0.0500 | 1.3316 | ||

Train and test with real weather factors | 1.7403 | 1.3481 | 290.7432 | 0.9271 | −0.0229 | 0.5867 | |

1.4448 | 1.0504 | 200.4038 | 0.9688 | 0.0188 | 0.6536 | ||

1.6471 | 1.1957 | 260.4523 | 0.9583 | 0.0083 | 0.6275 | ||

1.9258 | 1.4671 | 356.0313 | 0.9688 | 0.0188 | 0.8365 | ||

Train with real weather factors test with NWP | 2.0315 | 1.5807 | 396.1728 | 0.9271 | −0.0229 | 0.589 | |

5.3081 | 4.4806 | 2704.8980 | 0.3958 | −0.5542 | 0.6140 | ||

3.9384 | 3.1374 | 1489.0836 | 0.6354 | −0.3146 | 0.6408 | ||

5.5735 | 4.7552 | 2982.1671 | 0.4167 | −0.5333 | 0.8371 | ||

In

Variable | Type | RMSE |
---|---|---|

ws70 | Calibrated NWP | 2.1062 |

Original NWP | 3.3036 | |

mslp | Calibrated NWP | 1.0904 |

Original NWP | 1.0961 | |

T | Calibrated NWP | 1.6475 |

Original NWP | 5.2035 | |

Wind power | Calibrated NWP prediction | 2.1547 |

Original NWP prediction | 3.7056 |

Note that the proposed method exceeds the approaches trained and tested with real weather factors, as shown in

In order to further verify the effect of the proposed method on a smaller data set, the training set is reduced to half. Only the data from 2016-2-26 to 2016-3-3 are used as training data. Employ the proposed method to build surrogates and predict the wind power generation in 2016-3-4. The training and testing process remains unchanged; the results are shown in

This article aims at the operation and management of renewable energy smart grids for smart cities and buildings. A physics-informed AI surrogates method for probabilistic forecasting of wind power generation is introduced to tackle the insufficient generalization ability of high-resolution day-ahead forecasting caused by incomplete datasets. The proposed method is able to mine the implicit physical information in NWP data by employing small sample augmentation algorithms based on GAN, then train the forecasting model with a multiple AI surrogates structure constructed with ELM. Thus, the uncertainty within the NWP data and wind power generation are modeled and quantified. Compared with conventional probabilistic forecasting methods, the proposed method improves in these three aspects:

Compared with conventional methods, the proposed method improves the accuracy and probability forecasting performance of day-ahead wind power generation forecasting, tested on a certain incomplete dataset of a particular wind power farm.

Through incomplete data augmentation, the proposed method enhances the training effect and generalization ability of the prediction model on the one hand and, on the other hand, provides a more extensive data basis for quantifying the uncertainty of the prediction results. This characteristic makes it applicable for relatively small datasets with missing, discontinuous, and abnormal data. Therefore, considering the fluctuating nature of renewable energy, the proposed method’s prospects in modeling and controlling renewable energy smart grids are apparent.

The prediction model constructed by multiple AI surrogates enables the wind power prediction model trained on real weather factors to provide accurate wind power prediction with NWP data. Therefore, it is possible to calibrate the prediction model in real-time through the weather and wind power data monitored online to ensure its prediction ability, which is meaningful for the power generation simulation tasks in the digital twin of smart cities.

Average coverage error

Artificial intelligence

Computational fluid dynamics

Confidence intervals

Convolutional neural network and long short-term memory

Direct quantile regression

Extreme learning machines

Generative adversarial network

Mean absolute error

Mutual information quotient

Neural networks

Numerical weather prediction

Probability density function

Prediction interval

Prediction interval coverage probability

Prediction interval normalized average width

Physics-informed neural networks

Root mean square error

Recurrent neural network

Residual sum of squares

Selected factors

Single hidden layer feedforward neural network

Variational mode decomposition

Wasserstein generative adversarial network

Weather research forecasting

Worm Wasserstein generative adversarial network

This work was funded by the

The authors declare that they have no conflicts of interest to report regarding the present study.