{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:44:51Z","timestamp":1760060691448,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T00:00:00Z","timestamp":1757548800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2016EEM13"],"award-info":[{"award-number":["ZR2016EEM13"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Accurate and efficient short-term load forecasting is crucial for the secure and stable operation and scheduling of power grids. Addressing the inability of traditional Transformer-based prediction models to capture symmetric correlations between different feature sequences and their susceptibility to multi-scale feature influences, this paper proposes a short-term power distribution network load forecasting model based on an enhanced Komodo Mlipir Algorithm (KMA)\u2014Multivariate Variational Mode Decomposition (MVMD)-Crossformer. Initially, the KMA is enhanced with chaotic mapping and temporal variation inertia weighting, which strengthens the symmetric exploration of the solution space. This enhanced KMA is integrated into the parameter optimization of the MVMD algorithm, facilitating the decomposition of distribution network load sequences into multiple Intrinsic Mode Function (IMF) components with symmetric periodic characteristics across different time scales. Subsequently, the Multi-variable Rapid Maximum Information Coefficient (MVRapidMIC) algorithm is employed to extract features with strong symmetric correlations to the load from weather and date characteristics, reducing redundancy while preserving key symmetric associations. Finally, a power distribution network short-term load forecasting model based on the Crossformer is constructed. Through the symmetric Dimension Segmentation (DSW) embedding layer and the Two-Stage Attention (TSA) mechanism layer with bidirectional symmetric correlation capture, the model effectively captures symmetric dependencies between different feature sequences, leading to the final load prediction outcome. Experimental results on the real power distribution network dataset show that: the Root Mean Square Error (RMSE) of the proposed model is as low as 14.7597 MW, the Mean Absolute Error (MAE) is 13.9728 MW, the Mean Absolute Percentage Error (MAPE) reaches 4.89%, and the coefficient of determination (R2) is as high as 0.9942.<\/jats:p>","DOI":"10.3390\/sym17091512","type":"journal-article","created":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T07:51:46Z","timestamp":1757577106000},"page":"1512","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Symmetry-Aware Short-Term Load Forecasting in Distribution Networks: A Synergistic Enhanced KMA-MVMD-Crossformer Framework"],"prefix":"10.3390","volume":"17","author":[{"given":"Jingfeng","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kunhua","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"You","sequence":"additional","affiliation":[{"name":"School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lan","family":"Bai","sequence":"additional","affiliation":[{"name":"Institute of Artificial Intelligence, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuolin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huiping","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haowen","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Intelligent Manufacturing, Huanghuai University, Zhumadian 463000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1109\/TSG.2024.3482361","article-title":"Response Capacity Allocation of Air Conditioners for Peak-Valley Regulation Considering In-teraction with Surrounding Microclimate","volume":"16","author":"Zhang","year":"2024","journal-title":"IEEE Trans. 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