电力负荷预测在电网削峰填谷以及平稳运行中起着重要作用。然而，电力负荷数据的非平稳性会为负荷预测带来阻碍，且现有预测方法存在着难以捕捉序列间的时空依赖关系和序列中的长距离依赖关系等问题，因此，本文将针对上述问题进行研究，主要研究内容如下：

(1)针对电力负荷数据存在非平稳性，且数据的空间相关性和时间依赖性难以捕获，导致预测精度低的问题，提出一种基于CEEMDAN和频谱时间图卷积网络的电力负荷预测方法。该方法分为两个阶段，首先通过CEEMDAN将原始数据分解为更加平稳的本征模态分量，然后使用频谱时间图卷积网络来挖掘序列的时空依赖关系。其中，为了避免误差累积，本文依据模糊熵对本征模态分量进行重构。此外，通过设计频谱时间图卷积网络并引入Timesblock，实现在频域中提取目标序列的时间模式，进行序列间的空间特征聚合。实验结果表明，相较于对比算法，在MAE、RMSE和MAPE指标上，平均改进了0.21Kwh，0.36Kwh，0.53%，验证了本文所提出的预测方法可以有效降低非平稳性对预测结果的影响，精确获取时序负荷数据的空间相关性和时间依赖性，提高预测精度。

(2)针对长时间序列负荷预测模型存在的预测精度低的问题，提出了一种改进Informer的长时间序列电力负荷预测模型。该模型在Informer框架的基础上设计了特征嵌入层，并对概率稀疏自注意力机制（ProbSparse Self-Attention）进行二次稀疏。其中，为了解决Informer在负荷预测任务上特征丰富度不足的问题，本文在特征嵌入层中进行了多特征编码和嵌入。此外，通过对键值矩阵进行二次稀疏，来降低自注意力机制的复杂度，提高预测精度。实验结果表明，相较于原Informer模型，本文模型在多个预测序列长度下，对于评价指标平均绝对误差和均方误差分别下降了6.2%-9.0%和3.3%-8.0%，且优于其他对比模型，验证了该模型能够更好地学习长时间序列电力负荷数据中的内部规律，提高预测精度。

Power load forecasting plays an important role in peak cutting, valley filling and stable operation of power grid. However, the non-stationarity of power load data will bring obstacles to load prediction, and existing forecasting methods are difficult to capture the spatiotemporal dependence between sequences and the long-distance dependence in sequences, etc. Therefore, this paper will study the above problems, and the main research contents are as follows:

(1) Aiming at the non-stationarity of power load data, and the difficulty in capturing spatial correlation and time dependence of data, resulting in low prediction accuracy, a power load prediction method based on CEEMDAN and spectral time graph convolution network is proposed. The method is divided into two stages. First, the original data is decomposed into more stable eigenmode components through CEEMDAN, and then the spectral time graph convolution network is used to mine the spatiotemporal dependence of the sequence. In order to avoid error accumulation, this paper reconstructs eigenmodal components based on fuzzy entropy. In addition, by designing a spectral time-map convolutional network and introducing Timesblock, it is realized to extract the temporal patterns of the target sequences in the frequency domain for spatial feature aggregation among the sequences.The experimental results show that compared with the comparison algorithm, the MAE, RMSE and MAPE indexes are improved by 0.21Kwh, 0.36Kwh and 0.53% on average, which proves that the prediction method proposed in this paper can effectively reduce the influence of non-stationarity on prediction results and accurately obtain the spatial correlation and time dependence of temporal load data. Improve the prediction accuracy.

(2) Aiming at the problem of low prediction accuracy of long time series load forecasting model, a long time series power load forecasting model with improved Informer is proposed.The model is designed with a feature embedding layer based on the Informer framework and a quadratic sparse ProbSparse Self-Attention. In order to solve the problem of Informer's lack of feature richness in load forecasting tasks, this paper carries out multi-feature coding and embedding in the feature embedding layer. In addition, the complexity of the self-attention mechanism is reduced and the prediction accuracy is improved by quadratic sparsity of the key-value matrix. The experimental results show that compared with the original Informer model, the average absolute error and mean square error of the evaluation index decreased by 6.2%-9.0% and 3.3%-8.0% respectively under multiple prediction series lengths, and the proposed model is superior to other comparison models, which verifies that the model can better learn the internal laws of long-term power load data. Improve the prediction accuracy.

[1]朱俊丞,杨之乐,郭媛君,等.深度学习在电力负荷预测中的应用综述[J].郑州大学学报(工学版),2019,40(05):13-22.

[2]潘世瑶.基于集成学习与智能优化算法的LSTM短期电力负荷预测[D].中国矿业大学,2023.DOI:10.27623/d.cnki.gzkyu.2023.001047.

[3]朱莉,韩凯萍,朱春强.二次分解策略组合Informer的短期电力负荷预测方法[J].国外电子测量技术,2023,42(06):23-32.

[4]方江晓.短期风速和风电功率预测模型的研究[D].北京交通大学,2019.

[5]WANG D,LUO H,GRUNDERO,etal. Multi-step ahead electricity price forecasting using a hybrid model based on two-layer decomposition technique and BP neural net-work optimized by firefly algorithm[J].Applied Energy,2017,190:390-407.

[6]刘兴龙,刘罡,张娜,等.北方地区清洁供暖对电网负荷特性影响分析[J].电气技术,2019,20(2):57-63.

[7]肖白,聂鹏,穆钢,等.基于多级聚类分析和支持向量机的空间负荷预测方法[J].电力系统自动化,2015,39(12):56-61.

[8]李文武,石强,李丹,等.基于VMD和PSO-SVR的短期电力负荷多阶段优化预测[J].中国电力,2022,55(08):171-177.

[9]HAN L,ROMERO C E,YAO Z. Wind power forecasting based on principle component phase space reconstruction[J].Renewable Energy,2015,81:737-744.

[10]刘艳萍.风电场出力的短期预测研究[D].华北电力大学, 2023.

[11]王国彬,武晗,白杨,等.基于主成分分析降维和支持向量机回归的短期负荷预测方法研究[J].吉林电力,2020,48(04):7-10.

[12]占翔昊.基于深度学习的智能电网长期负荷预测与用电负荷检测研究[D].杭州电子科技大学,2023.DOI:10.27075/d.cnki.ghzdc.2023.000399.

[13]黄旭锐,于丰源,杨波,等.基于Transformer网络和多任务学习的园区综合能源系统电-热短期负荷预测方法[J].南方电网技术,2022:1-8.

[14]Bashir T, Haoyong C, Tahir M F, et al. Short term electricity load forecasting using hybrid prophet-LSTM model optimized by BPNN[J]. Energy Reports, 2022, 8: 1678-1686.

[15]余帆,王磊,江巧永,等.基于特征筛选的VMD-MIC-SSA-Informer短期负荷预测[J].陕西科技大学学报,2022,40(05):191-196+203.

[16]吴松梅,蒋建东,燕跃豪,等.基于VMD-PSO-多核极限学习机的短期负荷预测[J].电力系统及其自动化学报,2022,34(05):18-25.

[17]常乐.基于数据挖掘与机器学习的短期电力负荷预测研究[D].南昌大学,2023.DOI:10.27232/d.cnki.gnchu.2023.003836.

[18]王一珺,贾嵘.基于Elman和实测风速功率数据的短期风功率预测[J].高压电器,2017(9):125-129.

[19]叶瑞丽,郭志忠,刘瑞叶,等.基于小波包分解和改进 Elman神经网络的风电场风速和风电功率预测[J].电工技术学报,2017,32(21):103-111.

[20]Wei J, Chen Z, He F, et al. Short-term Load Forecasting Method Based on Daily Load Curve Clustering and SVM-WD[C]//Journal of Physics: Conference Series. IOP Publishing, 2023, 2447(1): 012007.

[21]Wang S, Deng X, Chen H, et al. A bottom-up short-term residential load forecasting approach based on appliance characteristic analysis and multi-task learning[J]. Electric Power Systems Research, 2021, 196: 107233.

[22]王士彬,何鑫,余成波,等.VMD-Stacking集成学习的多特征变量短期负荷预测模型[J].兵器装备工程学报,2024,45(02):218-224.

[23]徐先峰,赵依,刘状壮,李陇杰,卢勇.用于短期电力负荷预测的日负荷特性分类及特征集重构策略[J].电网技术,2022,46(04):1548-1556.

[24]黄庭,王昕,李立学,等.基于小波-极限学习机的短期风电功率预测[J].控制工程,2018:232-236.

[25]黄炜,陈田.基于SAE与CEEMDAN-BiLSTM组合模型的短期电力负荷预测[J].计算机应用与软件,2022,39(07):52-58.

[26]李若晨,朱帆,朱永利,翟羽佳.结合受限玻尔兹曼机的递归神经网络电力系统短期负荷预测[J].电力系统保护与控制,2018,46(17):83-88.

[27]张亚超,刘开培,秦亮,等.基于聚类经验模态分解-样本熵和优化极限学习机的风电功率多步区间预测[J].电网技术,2016,40(7):2045-2051.

[28]董添.基于深度学习的电力负荷模式识别与预测方法研究[D].吉林大学,2022.DOI:10.27162/d.cnki.gjlin.2022.007916.

[29]刘成龙,高旭,曹明.基于VMD和BA优化随机森林的短期负荷预测[J].中国测试,2022,48(04):159-165.

[30]包正睿. 基于大数据分析技术的短期负荷预测方法[D].华北电力大学(北京),2019.

[31]Dat N Q, Ngoc Anh N T, Nhat Anh N, et al. Hybrid online model based multi seasonal decompose for short-term electricity load forecasting using ARIMA and online RNN[J]. Journal of Intelligent & Fuzzy Systems, 2021, 41(5): 5639-5652.

[32]Tan M, Liao C, Chen J, et al. A multi-task learning method for multi-energy load forecasting based on synthesis correlation analysis and load participation factor[J]. Applied Energy, 2023, 343: 121177.

[33]Zhang T, Zhang X, Chau T K, et al. Highly accurate peak and valley prediction short-term net load forecasting approach based on decomposition for power systems with high PV penetration[J]. Applied Energy, 2023, 333: 120641.

[34]韩爽，孟航，刘永前，等.增量处理双隐层BP神经网络风电功率预测模型[J].太阳能学报,2015,36(9):2238-2244.

[35]Wan C, Xu Z, Pinson P, etal. Optimal Prediction Intervals of Wind Power Generation[J].IEEE Transactions on Power Systems,2014,25(4):1845-1856.

[36]Wang J, Li X, Li J, et al. NGCU: A new RNN model for time-series data prediction[J]. Big Data Research, 2022, 27: 100296.

[37]Yu Y, Si X, Hu C, et al. A review of recurrent neural networks: LSTM cells and network architectures[J]. Neural computation, 2019, 31(7): 1235-1270.

[38]Staudemeyer R C, Morris E R. Understanding LSTM-a tutorial into long short-term memory recurrent neural networks[J]. arXiv preprint arXiv:1909.09586, 2019.

[39]Sherstinsky A. Fundamentals of recurrent neural network (RNN) and long short-term memory (LSTM) network[J]. Physica D: Nonlinear Phenomena, 2020, 404: 132306.

[40]Zhang Y, Liu Q, Song L. Sentence-state LSTM for text representation[J]. arXiv preprint arXiv:1805.02474, 2018.

[41]Bouktif S, Fiaz A, Ouni A, et al. Multi-sequence LSTM-RNN deep learning and metaheuristics for electric load forecasting[J]. Energies, 2020, 13(2): 391.

[42]Shi H, Xu M, Li R. Deep learning for household load forecasting—A novel pooling deep RNN[J]. IEEE Transactions on Smart Grid, 2017, 9(5): 5271-5280.

[43]Zhang Y, Li C, Jiang Y, et al. Accurate prediction of water quality in urban drainage network with integrated EMD-LSTM model[J]. Journal of Cleaner Production, 2022, 354: 131724.

[44]Dewangan F, Abdelaziz A Y, Biswal M. Load forecasting models in smart grid using smart meter information: A review[J]. Energies, 2023, 16(3): 1404.

[45]Dong PAN, Bin XU, Jun MA, et al. Short-term load forecasting based on EEMD-approximate entropy and ELM[C]//2019 IEEE Sustainable power and energy conference (iSPEC). IEEE, 2019: 1772-1775.

[46]Zheng H, Yuan J, Chen L. Short-term load forecasting using EMD-LSTM neural networks with a Xgboost algorithm for feature importance evaluation[J]. Energies, 2017, 10(8): 1168.

[47]Zhou F, Zhou H, Li Z, et al. Multi-step ahead short-term electricity load forecasting using VMD-TCN and error correction strategy[J]. Energies, 2022, 15(15): 5375.

[48]文昌斌,石强,郑凯新,等.基于EMD-BP模型的10 kV开关柜温度预测[J].通信电源技术,2020,37(01):73-75.DOI:10.19399/j.cnki.tpt.2020.01.025.

[49]Junior M Y, Freire R Z, Seman L O, et al. Optimized hybrid ensemble learning approaches applied to very short-term load forecasting[J]. International Journal of Electrical Power & Energy Systems, 2024, 155: 109579.

[50]Liu M, Qin H, Cao R, et al. Short-term load forecasting based on improved TCN and DenseNet[J]. IEEE Access, 2022, 10: 115945-115957.

[51]Zhang B, Wu J L, Chang P C. A multiple time series-based recurrent neural network for short-term load forecasting[J]. Soft Computing, 2018, 22: 4099-4112.

[52]Vaswani A, Shazeer N, Parmar N, et al. Attention is all you need[J]. Advances in neural information processing systems, 2017, 30.

[53] Tay Y, Dehghani M, Bahri D, et al. Efficient transformers: A survey[J]. ACM Computing Surveys, 2022, 55(6): 1-28.

[54]Wang C, Wang Y, Ding Z, et al. A transformer-based method of multienergy load forecasting in integrated energy system[J]. IEEE Transactions on Smart Grid, 2022, 13(4): 2703-2714.

[55]Zhou H, Zhang S, Peng J, et al. Informer: Beyond efficient transformer for long sequence time-series forecasting[C]//Proceedings of the AAAI conference on artificial intelligence. 2021, 35(12): 11106-11115.

[56]Peng Z, Liu H, Jia Y, et al. Attention-driven graph clustering network[C]//Proceedings of the 29th ACM international conference on multimedia. 2021: 935-943.

[57]Levie R, Monti F, Bresson X, et al. Cayleynets: Graph convolutional neural networks with complex rational spectral filters[J]. IEEE Transactions on Signal Processing, 2018, 67(1): 97-109.

[58]Zeng H, Jiang C, Lan Y, et al. Long Short-Term Fusion Spatial-Temporal Graph Convolutional Networks for Traffic Flow Forecasting[J]. Electronics, 2023, 12(1): 238.

[59]Gilmer J, Schoenholz S S, Riley P F, et al. Neural message passing for quantum chemistry[C]//International conference on machine learning. PMLR, 2017: 1263-1272.

[60]Wu H, Hu T, Liu Y, et al. Timesnet: Temporal 2d-variation modeling for general time series analysis[C]//The eleventh international conference on learning representations. 2022.

[61]Bruna J, Zaremba W, Szlam A, et al. Spectral networks and locally connected networks on graphs[J]. arXiv preprint arXiv:1312.6203, 2013.

[62]Kipf T N, Welling M. Variational graph auto-encoders[J]. arXiv preprint arXiv:1611.07308, 2016.

[63]Torres M E, Colominas M A, Schlotthauer G, et al. A complete ensemble empirical mode decomposition with adaptive noise[C]//2011 IEEE international conference on acoustics, speech and signal processing (ICASSP). IEEE, 2011: 4144-4147.

[64]Cao D, Wang Y, Duan J, et al. Spectral temporal graph neural network for multivariate time-series forecasting[J]. Advances in neural information processing systems, 2020, 33: 17766-17778.

[65]Rasouli A, Kotseruba I. Pedformer: Pedestrian behavior prediction via cross-modal attention modulation and gated multitask learning[C]//2023 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2023:9844-9851.

[66]Wang D, Chen C. Spatiotemporal Self-Attention-Based LSTNet for Multivariate Time Series Prediction[J]. International Journal of Intelligent Systems, 2023, 2023.

Kitaev N, Kaiser Ł, Levskaya A. Reformer: The efficient transformer[J]. arXiv preprint arXiv:2001.04451, 2020.