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Accelerated kriging interpolation for real-time grid frequency forecasting

Carlos Moreno-Blazquez, Filiberto Fele, Teodoro Alamo

Abstract

The integration of renewable energy sources and distributed generation in the power system calls for fast and reliable predictions of grid dynamics to achieve efficient control and ensure stability. In this work, we present a novel nonparametric data-driven prediction algorithm based on kriging interpolation, which exploits the problem's numerical structure to achieve the required computational efficiency for fast real-time forecasting. Our results enable accurate frequency prediction directly from measurements, achieving sub-second computation times. We validate our findings on a simulated distribution grid case study.

Accelerated kriging interpolation for real-time grid frequency forecasting

Abstract

The integration of renewable energy sources and distributed generation in the power system calls for fast and reliable predictions of grid dynamics to achieve efficient control and ensure stability. In this work, we present a novel nonparametric data-driven prediction algorithm based on kriging interpolation, which exploits the problem's numerical structure to achieve the required computational efficiency for fast real-time forecasting. Our results enable accurate frequency prediction directly from measurements, achieving sub-second computation times. We validate our findings on a simulated distribution grid case study.

Paper Structure

This paper contains 22 sections, 1 theorem, 36 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Universal Kriging
  3. The Universal Kriging Model and Unbiasedness Constraints
  4. Expressing Error Variance via the Semivariogram
  5. Universal Kriging Formulation
  6. Regularized Universal Kriging
  7. Efficient Numerical Solution
  8. Spectral Decomposition
  9. Numerical Challenges
  10. K-ADMM Formulation
  11. The $\nu$-Subproblem
  12. The ${\alpha}$-Subproblem
  13. The Dual Update
  14. Recovering the Solution
  15. Case Study
  16. ...and 7 more sections

Key Result

Proposition 1

Consider the optimization problem with $w>0$, $\beta\geq 0$, and $c\in \mathbb{R}$. Then, $\blacktriangleleft$$\blacktriangleleft$

Figures (8)

  • Figure 1: MATLAB's Simscape model of the proposed case study; the setup is built on the one proposed in haberle2023mimo. Chirp-PRS signals were used as reference for the IBR to generate the dataset for the kriging-based prediction.
  • Figure 2: Experimental semivariogram estimates (yellow markers) obtained by averaging pairwise semivariances within 200 distance lags, and the fitted theoretical model (red curve).
  • Figure 3: Flowchart of the online recursive prediction procedure. At time step $t$, the regressor $z(t|t)$ is initialized. For each $l=0, \dots, n_p-1$, $\mathbf{1.}$ select the nearest data cluster $\mathcal{D}_{j^*}$, $\mathbf{2.}$ apply the pre-computed whitening transformation and compute the adaptive $\ell_1$ penalties using the LU factors, $\mathbf{3.}$ run the K-ADMM solver. Finally, the obtained prediction is incorporated in the regressor used on the subsequent iteration.
  • Figure 4: Impact of the regularization $\ell_1$ on the $\lambda^*$ weights for two random query points (steps of trajectory). The top plots display the dense solutions obtained by the standard UK formulation, where the screening effect results in nonzero weights assigned to the entire cluster. The bottom plots demonstrate how the proposed K-ADMM algorithm enforces sparsity, selecting a minimal subset of approximately $50$ highly informative neighbors ($\sim 80\%$ sparsity) while suppressing spurious correlations.
  • Figure 5: Heatmap of the total error $\zeta$ (in %) over the test dataset, as a function of the autoregressive orders $n_a$ and $n_b$: the chosen configuration ($n_a=2, n_b=4$) minimizes the prediction error.
  • ...and 3 more figures

Theorems & Definitions (1)

  • Proposition 1