Table 1 List of symbols and definitions used in the mathematical modeling section.
Symbol | Description | Unit/meaning |
|---|---|---|
\(W^{(\tau )}_{\kappa }\) | True wind power at site \(\kappa\) and time \(\tau\) | MW |
\(\hat{W}^{(\tau )}_{\kappa }\) | Predicted wind power output | MW |
\(\chi ^{(\tau )}_{\kappa }\) | Input feature vector (meteorological and turbine data) | – |
\(\phi ^{(\tau -1)}_{\kappa }\) | Lagged feature embedding from previous step | – |
\(\nu ^{(\tau -2)}_{\kappa }\) | Volatility or uncertainty estimator at lag 2 | – |
\(R^{(\tau )}_{\kappa }\) | Predicted rank order of site \(\kappa\) at time \(\tau\) | Ordinal index |
\(\pi ^{(\tau )}_{\kappa }\) | Ground-truth ranking probability distribution | – |
\(\mathcal {L}^{(\tau )}_{\text {MSE}}\) | Mean squared error loss component | \(\hbox {MW}^2\) |
\(\mathcal {L}^{(\tau )}_{\text {rank}}\) | Listwise ranking loss term | Dimensionless |
\(\mathcal {L}^{(\tau )}_{\text {temp}}\) | Temporal rank deviation penalty | Dimensionless |
\(\alpha , \beta , \gamma\) | Weighting coefficients for composite loss terms | – |
\(W^{\max }_{\kappa }\) | Rated power capacity of wind turbine/farm | MW |
\(\delta _{\text {smooth}}\) | Threshold for rank curvature smoothness | – |
\(\varepsilon _{\text {spread}}\) | Minimum quantile spread to prevent overconfidence | MW |
N | Total number of sites in the forecasting system | – |
T | Total number of forecasting horizons | – |
B | Training batch set of samples | – |
\(\eta ^{(k)}\) | Learning rate at iteration k | – |
\(\Theta , \Phi , \Xi\) | Trainable parameter sets of the model | – |
\(\lambda\) | Regularization coefficient for weight decay | – |
\(R_{\text {reg}}\) | \(\ell _2\) regularization term for complexity control | – |
\(NDCG(\tau )\) | Normalized discounted cumulative gain metric | Dimensionless |
TRSI | Temporal rank stability index | Dimensionless |
\(q_{\kappa }, k_{\upsilon }, v_{\upsilon }\) | Query, key, and value vectors in attention mechanism | – |
\(\alpha ^{(\tau )}_{\kappa \rightarrow \upsilon }\) | Attention coefficient between site \(\kappa\) and \(\upsilon\) | – |
\(c^{(\tau )}_{\kappa }\) | Context vector aggregated by attention weights | – |
\(\sigma (\cdot )\) | Activation function (e.g., sigmoid, ReLU) | – |
\(\zeta ^{(\tau )}_{\kappa }\) | Time-aware feature embedding | – |
\(\Psi _{\text {final}}\) | Unified evaluation metric (Eq. 27) | Dimensionless |
