Dynamic graph structure and spatio-temporal representations in wind power forecasting | Science and Technology for Energy Transition (STET)

Decarbonizing Energy Systems: Smart Grid and Renewable Technologies

Open Access

Table A1

The major symbols and their definitions.

Symbol	Definition
X ∈ ℝ^N × C	Observation data matrix of wind turbines with N features and C time points.
X_t ∈ ℝ^N × 1	Wind power data vector at timestamp t, and x_i represents the i-th feature.
ϕ (·)	Nonlinear function for DSTG model fitting.
$\hat{Y} \in R^{t^{'} \times 1}$ $\widehat{Y}\in {\mathbb{R}}^{{t}^\mathrm{\prime}\times 1}$	Predicted active power values for t' time steps.
$G_{T} = (V, E, A)$ ${G}_T=(V,\mathcal{E},{A})$	Temporal graph, where V is the set of nodes, $E$ $\mathcal{E}$ is the edge set, and A is the adjacency matrix.
V ∈ ℝ^1 × N	Set of nodes representing multivariate signals.
$F_{i} \in R^{N \times F_{emmd}}$ ${{F}}_i\in {\mathbb{R}}^{N\times {F}_{\mathrm{emmd}}}$	Feature matrix for each time series variable $x_{i}$ ${x}_i$ after EEMD.
$E_{mn}$ ${\mathcal{E}}_{{mn}}$	Edge weight representing the connection between nodes z_m and z_n.
A_mn = g(z_m, z_n)	Adaptive function to determine edge connectivity based on node features.
L_gsl	Loss function for graph structure learning incorporating distance and regularization.
$I, F, O$ $\mathcal{I},\mathcal{F},\mathcal{O}$ and $H$ $\mathcal{H}$	Gates in the GAL-cell: input, forget, output gates and hidden states.
w	Trainable weight vector for GSL module.
W	Trainable matrices for different DTG layers.
$E_{t}^{G}$ ${{E}}_t^{\mathcal{G}}$	Feature matrices for the t-th graph structure.
L_mse	Mean squared error loss between true and predicted values.
L_s	Regularization terms for time smoothness.
L_total	Total loss function for model optimization.

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