摘要： 针对电力负荷序列非平稳性强、多尺度波动显著、周期信息难以稳定建模且在多步预测中易出现衰减与相位偏移，以及温度、湿度、电价等外生变量与负荷间耦合复杂的问题，本文提出一种基于时频特征融合与多周期残差耦合的短期负荷预测方法（time-frequency fusion and periodic residual coupling，TFF-PRC），旨在提升模型对负荷序列长期趋势、局部波动和周期规律的联合表征能力，同时增强多变量场景下外生信息的有效利用，从而提高不同预测步长下的预测精度与稳定性。现有深度学习方法多依赖时域建模或全局依赖建模，对低频趋势、高频扰动及显式周期信息利用不足；同时，多变量建模中过早混合外生变量易引入冗余噪声，完全通道独立又会削弱有效交互。为此，本文从时频协同建模、多周期残差补偿和负荷中心通道交互三个方面构建预测框架。首先，在时域采用移动平均分解提取趋势和季节成分，在频域通过多层离散小波变换（discrete wavelet transform，DWT）获取低频近似分量及多尺度高频细节分量。通过定向融合机制，低频增强趋势，高频增强季节，使频域信息以残差形式参与时域成分构造，从而强化模型对长期趋势和局部扰动的刻画能力。随后，增强后的趋势与季节分量分别输入通道独立的时序切片特征提取网络，利用卷积捕捉局部模式，并通过多层LSTM建模长短期依赖，以获得稳定、纯净的高维表示。针对多步预测中周期衰减和相位偏移问题，本文基于快速傅里叶变换（fast Fourier transform，FFT）识别负荷序列主导周期，提取与预测区间相位对齐的历史同期负荷片段，并通过样本级自适应加权生成周期补偿特征，以残差形式增强主干预测结果。随后，负荷中心通道交互模块以负荷为查询中心，通过查询-键-值机制选择性聚合温度、湿度、电价等外生变量信息，在保留多变量建模能力的同时有效抑制通道间噪声干扰。本文在澳大利亚新南威尔士州（New South Wales，NSW）和西班牙（Spain）两个公开电力负荷数据集上进行实验验证，输入窗口48时间步，预测未来1、2、24和48时间步。相比于主流基线模型，TFF-PRC在NSW数据集MAE平均降低11.03%~20.11%，RMSE平均降低11.41%~18.53%；在Spain数据集MAE平均降低3.99%~5.23%，RMSE平均降低4.05%~4.10%，表明模型具有良好的泛化能力。消融实验显示，移除TFF、PRC或LCA模块后，MAE分别上升7.54%、10.63%和7.00%，RMSE分别上升7.03%、8.18%和8.10%，验证了各模块对预测性能的贡献。综上，TFF-PRC通过时频定向融合、多周期残差耦合及负荷中心通道交互，有效

Abstract: Aiming at the problems that electric load series are highly non-stationary, exhibit significant multi-scale fluctuations, and that periodic information is difficult to model stably and is prone to attenuation and phase shift in multi-step forecasting, as well as the complex coupling relationships between exogenous variables such as temperature, humidity, electricity price and load, this paper proposes a short-term load forecasting method based on time-frequency fusion and periodic residual coupling (TFF-PRC). The proposed method aims to improve the joint representation capability of the model for long-term trends, local fluctuations and periodic patterns of load series, while enhancing the effective utilization of exogenous information in multivariate scenarios, thereby improving forecasting accuracy and stability under different prediction horizons. Existing deep learning methods mainly rely on time-domain modeling or global dependency modeling, and often fail to fully exploit low-frequency trends, high-frequency disturbances and explicit periodic information. Meanwhile, in multivariate modeling, premature mixing of exogenous variables may introduce redundant noise, whereas complete channel independence may weaken effective interactions. Therefore, this paper constructs the forecasting framework from three aspects: time-frequency collaborative modeling, multi-period residual compensation and load-centered channel interaction.First, in the time domain, moving average decomposition is adopted to extract the trend and seasonal components. In the frequency domain, multi-level discrete wavelet transform (DWT) is employed to obtain the low-frequency approximation component and multi-scale high-frequency detail components. Through a directional fusion mechanism, the low-frequency information is used to enhance the trend component, while the high-frequency information is used to enhance the seasonal component. In this way, frequency-domain information participates in the construction of time-domain components in a residual manner, thereby strengthening the model’s ability to characterize long-term trends and local disturbances. Subsequently, the enhanced trend and seasonal components are separately fed into a channel-independent temporal patch feature extraction network. Convolution is used to capture local patterns, and multi-layer LSTM is employed to model long- and short-term dependencies, so as to obtain stable and clean high-dimensional representations.To address periodic attenuation and phase shift in multi-step forecasting, the proposed method identifies the dominant periods of load series based on fast Fourier transform (FFT), extracts historical load segments that are phase-aligned with the prediction interval, and generates periodic compensation features through sample-level adaptive weighting. These features are then incorporated into the backbone forecasting results in a residual form. Furthermore, the load-centered channel interaction module takes load as the query center and selectively aggregates information from exogenous variables such as temperature, humidity and electricity price through the query-key-value mechanism. This design preserves the multivariate modeling capability while effectively suppressing noise interference among channels.Experiments are conducted on two public electric load datasets, namely New South Wales (NSW), Australia, and Spain. The input window is set to 48 time steps, and the forecasting horizons are set to 1, 2, 24 and 48 time steps. Compared with mainstream baseline models, TFF-PRC reduces the average MAE by 11.03%~20.11% and the average RMSE by 11.41%~18.53% on the NSW dataset. On the Spain dataset, the average MAE is reduced by 3.99%~5.23%, and the average RMSE is reduced by 4.05%~4.10%, indicating that the proposed model has good generalization capability. Ablation experiments show that after removing the TFF, PRC or LCA module, MAE increases by 7.54%, 10.63% and 7.00%, respectively, while RMSE increases by 7.03%, 8.18% and 8.10%, respectively, verifying the contribution of each module to forecasting performance.In summary, TFF-PRC effectively alleviates non-stationary fluctuations, periodic attenuation and multivariate noise interference through time-frequency directional fusion, multi-period residual coupling and load-centered channel interaction. The proposed method achieves high accuracy and stability across different datasets and forecasting horizons.