Spatial Dynamic Wind Power Forecasting (SDWPF)

• Spatial Dynamic Wind Power Forecasting (SDWPF) is a spatio-temporal framework that leverages turbine positions and dynamic meteorological data to predict wind power output over 48 hours.
• It integrates classical statistical models and advanced neural architectures to capture both local temporal persistence and regional spatial correlations.
• The approach enhances aggregated forecasting accuracy by modeling turbine interactions, addressing data irregularities, and providing uncertainty-aware predictions.

Spatial Dynamic Wind Power Forecasting (SDWPF) denotes a spatio-temporal wind power forecasting setting in which future power output is inferred jointly from the spatial distribution of turbines or wind farms and from dynamic context factors such as meteorological variables and internal operating states. In the KDD Cup 2022 formulation, SDWPF is a multi-step, spatio-temporal forecasting task over a wind farm with 134 turbines, where historical SCADA measurements, relative positions, and contextual variables are used to predict future active power for the next 48 hours (Zhou et al., 2022).

1. Definition and conceptual scope

In the KDD Cup usage, SDWPF is “spatial” because it explicitly uses the positions of 134 turbines and their interactions within a farm, and “dynamic” because it leverages time-varying contextual variables such as wind speed, direction, ambient temperature, nacelle direction, blade pitch angles, and reactive power (Zhou et al., 2022). The spatial aspect arises from shared meteorological fields and wake effects, while the dynamic aspect arises from the continuous evolution of turbine states and environmental forcing at fine temporal resolution.

In the statistical literature, the same phrase refers to models in which a latent field evolves in time while remaining spatially correlated. A canonical formulation is the spatio-temporal AR(1) latent field

$$z(\mathbf{s},t) = \rho_2\, z(\mathbf{s}, t-1) + w(\mathbf{s},t),$$

with the innovation field $w(\mathbf{s},t)$ following a Matérn covariance over space (Lenzi et al., 2017). This formulation clarifies an important point: the spatial correlation structure can be time-invariant while the field itself is dynamic. The phrase “spatial dynamic” therefore need not imply a time-varying covariance law; it can also mean a dynamically evolving field defined on a spatial domain.

A common misconception is that spatial modeling mainly benefits individual-site prediction. Empirical evidence from wind farms in western Denmark shows that spatio-temporal models are particularly important for aggregated wind power forecasts and for spatially out-of-sample forecasts at new locations, where purely temporal models cannot borrow information from neighboring sites (Lenzi et al., 2017).

2. Canonical dataset and task formulation

The SDWPF dataset released for KDD Cup 2022 was collected from the SCADA system of a real wind farm operated by Longyuan Power Group Corp. Ltd. It contains 134 turbines, 245 days of observations, a 10-minute sampling interval, 13 columns, and 4,727,520 records (Zhou et al., 2022). Each record includes turbine ID, day index, timestamp, wind speed, relative wind direction, external temperature, internal temperature, nacelle direction, three blade pitch angles, reactive power, and active power. The forecasting target is active power $Patv$.

At time $t$, farm-level output is the sum of turbine-level active power,

$P_t = \sum_{i=1}^{134} Patv_t^{(i)}.$

The official SDWPF task is multi-step and turbine-resolved: given historical context and turbine positions, the goal is to predict future wind power generation for the next 48 hours, i.e. $288$ steps at 10-minute resolution (Zhou et al., 2022). The paper describes an input window length $L_x \le 14$ days and an output horizon $H = 288$, with tensors

$$\mathbf{X}_{t_0-L_x+1 : t_0} \in \mathbb{R}^{L_x \times N \times F}, \qquad \mathbf{Y}_{t_0+1 : t_0+H} \in \mathbb{R}^{H \times N},$$

where $N = 134$ and $w(\mathbf{s},t)$0 (Zhou et al., 2022).

The dataset also provides the relative 2D positions $w(\mathbf{s},t)$1 of all turbines in meters. These coordinates support explicit spatial modeling through pairwise distances

$w(\mathbf{s},t)$2

distance-decay weights, $w(\mathbf{s},t)$3-nearest-neighbor graphs, or learned spatial structures (Zhou et al., 2022).

Evaluation is not performed on all raw records indiscriminately. Missing, unknown, and abnormal targets are masked out. In particular, a target is treated as unknown if $w(\mathbf{s},t)$4 and $w(\mathbf{s},t)$5 m/s, or if any pitch angle exceeds $w(\mathbf{s},t)$6. A record is abnormal if $w(\mathbf{s},t)$7 or $w(\mathbf{s},t)$8. For missing, unknown, or abnormal targets, the evaluation sets the error contribution to zero (Zhou et al., 2022). This masking protocol is part of the operational definition of SDWPF and materially affects model training and offline validation.

3. Statistical formulations and probabilistic SDWPF

A classical probabilistic formulation begins with normalized wind power $w(\mathbf{s},t)$9 and applies the logit transform

$Patv$0

with inverse

$Patv$1

On the transformed scale, the observation model is Gaussian,

$Patv$2

so the spatio-temporal structure is encoded entirely in $Patv$3 (Lenzi et al., 2017).

Three related models are central. The temporal-only baseline is

$Patv$4

with

$Patv$5

The spatio-temporal model replaces local AR structure by a spatially correlated latent field,

$Patv$6

where $Patv$7 has Matérn covariance. The combined ST+T model superposes the two:

$Patv$8

This decomposition separates local temporal persistence from regional spatio-temporal structure (Lenzi et al., 2017).

For aggregated forecasting, the capacity-weighted normalized power is

$Patv$9

and the predictive aggregate is obtained from the joint predictive distribution across all sites (Lenzi et al., 2017). This is not a cosmetic detail. If spatial covariance is ignored, the variance of the aggregate is underestimated, because

$t$0

Empirically, Model T produces aggregated predictive distributions that are too narrow and under-dispersed, whereas S-T and especially ST+T are much better calibrated (Lenzi et al., 2017).

The same study identifies the cases in which spatial dynamic modeling is most important: aggregated forecasts, spatially out-of-sample prediction at new locations, conditions with larger effective spatial range, and longer short-term horizons (Lenzi et al., 2017). These results provide a statistical baseline for later neural SDWPF systems: the central issue is not merely lower point error, but coherent multivariate uncertainty over space and time.

4. Neural architectures and learned spatial structure

Neural SDWPF systems replace or augment explicit covariance models with learned spatial operators. These operators may be fixed-graph, adaptive-graph, attention-based, neighborhood-based, hierarchical, hypergraph-based, or variable-centric. The progression across recent work shows that “spatial structure” in SDWPF is not synonymous with a single adjacency matrix.

Family	Spatial mechanism	Representative systems
Latent Gaussian spatio-temporal models	Matérn-correlated latent field with AR(1) dynamics	S-T, ST+T (Lenzi et al., 2017)
Adaptive graph neural models	Learned or adaptive graph convolution with temporal modeling	AGCRN, MTGNN (Jiang et al., 2023)
Attention-based spatial modeling	Multi-head self-attention across wind farms	STAN (Fu et al., 2019)
Local-neighborhood encoder-decoder models	$t$1-nearest-neighbor inputs and turbine embeddings	Deep Spatio-Temporal Wind Power Forecasting (Li et al., 2021)
Hierarchical spatial-temporal transformers	Parallel spatial and temporal Transformer skeletons with Contextual Fusion Blocks	HSTTN (Zhang et al., 2023)
Dynamic hypergraph models	Higher-order hyperedges and dynamic hypergraph convolution	STDHL (Dong et al., 2024)
Variable-centric dual-transformer models	Separate endogenous, exogenous static, and exogenous dynamic tokens	2DXformer (Zhang et al., 2 May 2025)

In the KDD Cup 2022 challenge, one representative graph-neural solution adopted AGCRN and MTGNN as basic models, trained AGCRN by 5-fold cross-validation, trained MTGNN directly on the training and validation sets, and ensembled the two models based on validation-set loss values (Jiang et al., 2023). This line of work treats turbines as graph nodes and learns spatial dependence through adaptive adjacency.

A different line dispenses with explicit graphs. STAN uses a multi-head self-attention mechanism to extract spatial correlations among wind farms, then captures temporal dependencies with a Sequence-to-Sequence model with a global attention mechanism (Fu et al., 2019). In another formulation, a deep encoder-decoder forecasts wind power for a target turbine using the historical wind speed of the target and its $t$2-nearest neighbors, together with turbine embeddings; this model directly predicts wind power from historical wind speed, without forecasting wind speed first and then applying a transformation (Li et al., 2021).

Long-horizon SDWPF has motivated hierarchical Transformer designs. HSTTN constructs an hourglass-shaped encoder-decoder framework with skip-connections, two parallel Transformer skeletons for temporal and spatial modeling, and Contextual Fusion Blocks that fuse complementary information from spatial and temporal features (Zhang et al., 2023). Variable-centric modeling pushes the factorization further. 2DXformer classifies inputs into exogenous static variables, exogenous dynamic variables, and endogenous variables; embeds them as variable tokens in a channel-independent manner; uses attention to capture correlations among exogenous variables; and uses a multi-layer perceptron with residual connections to model the impact of exogenous variables on endogenous variables (Zhang et al., 2 May 2025).

The most explicit challenge to pairwise graph assumptions appears in hypergraph methods. STDHL argues that higher-order spatial features among wind farms are not adequately represented by pairwise edges alone, and therefore uses a dynamic hypergraph convolutional layer together with a grouped temporal convolutional layer and a forecast decoder that maps spatio-temporal encodings to quantile results (Dong et al., 2024). Objectively, this marks a methodological divide within SDWPF: fixed pairwise graphs, adaptive graphs, attention over all nodes, and higher-order hypergraphs encode distinct assumptions about how wind fields couple turbines or farms.

5. Evaluation protocols and benchmark systems

The official KDD Cup SDWPF score is the average of RMSE and MAE over the 48-hour horizon for each turbine,

$t$3

then summed over 134 turbines,

$t$4

and averaged over $t$5 evaluation instances (Zhou et al., 2022). The official baseline, implemented in PaddleSpatial, first aggregates active power across all turbines into a single farm-level time series,

$t$6

and then forecasts that series with a GRU. On a test set of 195 predictions, this baseline reports RMSE $t$7, MAE $t$8, overall score $t$9, and evaluation time about $P_t = \sum_{i=1}^{134} Patv_t^{(i)}.$0 seconds on a Linux machine with an Nvidia P40 GPU (Zhou et al., 2022).

Competition reports provide concrete evidence of the gains obtainable from richer SDWPF modeling. The BUAA_BIGSCity solution combines AGCRN and MTGNN and reports that its team achieves $P_t = \sum_{i=1}^{134} Patv_t^{(i)}.$1 on the test set (Jiang et al., 2023). The 88VIP solution combines a gradient boosting decision tree and a recurrent neural network, uses feature engineering, imputation techniques, offline evaluation design, and ensembling across heterogeneous forecast timescales, and reports an overall online score of $P_t = \sum_{i=1}^{134} Patv_t^{(i)}.$2 in Phase 3 (Lin et al., 2022).

Beyond the KDD benchmark, STDHL supplies a probabilistic benchmark on the GEFCom dataset. In the reported experiments, STDHL achieves MAE $P_t = \sum_{i=1}^{134} Patv_t^{(i)}.$3, RMSE $P_t = \sum_{i=1}^{134} Patv_t^{(i)}.$4, AR $P_t = \sum_{i=1}^{134} Patv_t^{(i)}.$5, PP $P_t = \sum_{i=1}^{134} Patv_t^{(i)}.$6, CRPS $P_t = \sum_{i=1}^{134} Patv_t^{(i)}.$7, and PS $P_t = \sum_{i=1}^{134} Patv_t^{(i)}.$8, outperforming PSS, Mechanism, Linear, LightGBM, DeepAR, Transformer, PatchTST, IDMDN, STSGL, STDGL, and STSHL under the stated protocol (Dong et al., 2024). This indicates that SDWPF evaluation has expanded beyond point forecasting toward multi-quantile and calibration-aware assessment.

6. Limitations, misconceptions, and research directions

A recurrent misconception is that spatial dependence can be reduced to static Euclidean proximity. The literature shows several non-equivalent alternatives: stationary Matérn covariance in latent Gaussian models, adaptive adjacency in graph neural networks, non-Euclidean self-attention across farms, $P_t = \sum_{i=1}^{134} Patv_t^{(i)}.$9-nearest-neighbor locality with turbine embeddings, and higher-order dynamic hypergraphs (Lenzi et al., 2017, Jiang et al., 2023, Fu et al., 2019, Dong et al., 2024). The modeling choice is therefore not merely computational; it encodes assumptions about whether interactions are local or global, pairwise or higher-order, static or data-adaptive.

Another misconception is that historical SCADA alone defines the full problem. The SDWPF benchmark intentionally excludes future meteorological variables, which makes the task difficult and places emphasis on temporal extrapolation from historical context (Zhou et al., 2022). A plausible implication is that benchmark-optimal models need not coincide with deployment-optimal models when Numerical Weather Prediction is available. This is consistent with statistical work that explicitly suggests incorporation of NWP-based covariates for longer horizons, and with broader forecasting taxonomies that distinguish very short-term, short-term, medium-term, long-term, and very long-term horizons as distinct methodological regimes (Lenzi et al., 2017, Dhiman et al., 2020).

Probabilistic forecasting remains a major direction. Statistical SDWPF already uses Gaussian predictive distributions on transformed power, CRPS, and reliability diagrams (Lenzi et al., 2017). For safety-critical settings, a spliced Gamma-Generalized Pareto model forecasts extreme and non-extreme wind speeds simultaneously, uses latent Gaussian structures with INLA, and supports short-term extreme and non-extreme probabilistic forecasts (Castro-Camilo et al., 2018). This suggests a natural path toward extreme-aware SDWPF: forecast wind-speed distributions, especially tail behavior, and propagate them through turbine power curves or direct probabilistic power models.

Current open problems are concrete. The SDWPF dataset contains missing, unknown, and abnormal targets that must be masked or imputed carefully (Zhou et al., 2022). Competition solutions explicitly address concept drift and heterogeneous timescales (Lin et al., 2022). Deep encoder-decoder work identifies uncertainty quantification and probabilistic forecasting as future work (Li et al., 2021). Hypergraph-based research highlights robustness under partial node corruption or missing covariates and calls for plug-and-play hypergraph modules that can flexibly adapt to varying sets of spatio-temporal covariates (Dong et al., 2024). Across the literature, the outstanding agenda is therefore not only to improve point accuracy, but to build SDWPF systems that are spatially coherent, uncertainty-aware, robust to data pathology, and extensible from turbine scale to aggregated portfolio scale.