Open Access

ARTICLE

A Real-Time Forecasting Framework for Non-Stationary Three-Phase Loads with Inter-Phase Dependency

Tianxiong Xiao¹, Zhi Zou¹, Hai Yan¹, Linjing Fu¹, Yifei Zhu^2,*, Lei Zhang², Xi Chen²
1 Institute of Economic and Technological Research, State Grid Huanggang Power Supply Company, Huanggang, China
2 College of Electrical Engineering & New Energy, China Three Gorges University, Yichang, China
* Corresponding Author: Yifei Zhu. Email:
(This article belongs to the Special Issue: Advances in Artificial Intelligence and Machine Learning for Next-Generation Energy Forecasting)

Energy Engineering https://doi.org/10.32604/ee.2026.083233

Received 07 April 2026; Accepted 05 June 2026; Published online 30 June 2026

Abstract

Due to the complex operating characteristics of loads in power distribution networks, three-phase loads exhibit strong non-stationarity and complex phase-to-phase coupling, thereby adversely affecting the power quality of distribution networks. However, existing decomposition-based forecasting methods usually rely on global or offline feature extraction and insufficiently consider local frequency drift, inter-phase dependency, and real-time deployment. To address these limitations, this paper proposes a causality-preserving real-time forecasting framework that integrates snow ablation optimization-assisted short-time variational mode decomposition (SAO-STVMD) with a serial gated hybrid neural network. Specifically, SAO is used to adaptively determine the key STVMD parameters, and an overlap-add rolling reconstruction strategy is introduced to suppress boundary discontinuities and reduce redundant window-wise computation. A trend–residual serial decoupling architecture is then designed to separately model slow-varying load evolution and fast-varying disturbances, while cross-phase attention (CPA) is employed to capture inter-phase dependency. In addition, a gated fusion unit is introduced as a dynamic risk trade-off mechanism rather than a pure average-error minimization module. Comparative and ablation results demonstrate the effectiveness of the proposed framework in improving forecasting accuracy under an online-compatible and causality-preserving SAO-STVMD feature-generation protocol. Additional causality audits, including prefix recomputation and future masking tests, confirm that the IMF features used at each forecasting time step are generated only from available historical observations, thereby ruling out implicit look-ahead bias in the decomposition stage. Further component-attribution analysis indicates that the dominant reduction in average forecasting error is mainly attributed to the localized STVMD decomposition stage. Under STVMD-decomposed inputs, CPA-SHNet provides additional gains by enhancing inter-phase dependency modeling. Beyond average-error performance, the gated fusion unit further serves as a conditional tail-risk mitigation mechanism, improving robustness for most high-error transient events produced by fixed additive reconstruction.

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Keywords

Three-phase load forecasting; short-time variational mode decomposition (STVMD); snow ablation optimizer (SAO); cross-phase attention (CPA); dynamic risk trade-off

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