{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T21:07:28Z","timestamp":1771967248421,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,15]],"date-time":"2025-06-15T00:00:00Z","timestamp":1749945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"China Southern Power Grid Co., Ltd.","award":["030100KC23110037"],"award-info":[{"award-number":["030100KC23110037"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>State evaluation of relay protection equipment constitutes a crucial component in ensuring the stable, secure, and symmetric operation of power systems. Current methodologies predominantly encompass fuzzy-rule-based control systems and data-driven machine learning approaches. The former relies on manual experience for designing fuzzy rules and membership functions and exhibits limitations in high-dimensional data integration and analysis. The latter predominantly formulates state evaluation as a classification task, which demonstrates its ineffectiveness in identifying equipment at boundary states and faces challenges in model parameter selection. To address these limitations, this paper proposes a quantitative state evaluation method for relay protection equipment based on a two-stage artificial protozoa optimizer (two-stage APO) optimized improved Conformer (two-stage APO-IConf) model. First, we modify the Conformer architecture by replacing pre-layer normalization (Pre-LN) in residual networks with post-batch normalization (post-BN) and introducing dynamic weighting coefficients to adaptively regulate the connection strengths between the first and second feed-forward network layers, thereby enhancing the capability of the model to fit relay protection state evaluation data. Subsequently, an improved APO algorithm with two-stage optimization is developed, integrating good point set initialization and elitism preservation strategies to achieve dynamic equilibrium between global exploration and local exploitation in the Conformer hyperparameter space. Experimental validation using operational data from a substation demonstrates that the proposed model achieves a RMSE of 0.5064 and a MAE of 0.2893, representing error reductions of 33.6% and 35.0% compared to the baseline Conformer, and 9.1% and 15.2% error reductions over the improved Conformer, respectively. This methodology can provide a quantitative state evaluation and guidance for developing maintenance strategies for substations.<\/jats:p>","DOI":"10.3390\/sym17060951","type":"journal-article","created":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T04:20:23Z","timestamp":1750134023000},"page":"951","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quantitative State Evaluation Method for Relay Protection Equipment Based on Improved Conformer Optimized by Two-Stage APO"],"prefix":"10.3390","volume":"17","author":[{"given":"Yanhong","family":"Li","sequence":"first","affiliation":[{"name":"Guangzhou Power Supply Bureau of Guangdong Power Grid Co., Ltd., Guangzhou 510620, China"},{"name":"School of Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min","family":"Zhang","sequence":"additional","affiliation":[{"name":"Guangzhou Power Supply Bureau of Guangdong Power Grid Co., Ltd., Guangzhou 510620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaofan","family":"Zhang","sequence":"additional","affiliation":[{"name":"Guangzhou Power Supply Bureau of Guangdong Power Grid Co., Ltd., Guangzhou 510620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yifan","family":"Zhou","sequence":"additional","affiliation":[{"name":"NR Engineering Co., Ltd., 69 Suyuan Avenue, Nanjing 211102, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,15]]},"reference":[{"key":"ref_1","first-page":"2","article-title":"Key Scientific Issues and Theoretical Research Framework for Power Systems with High Proportion of Renewable Energy","volume":"41","author":"Kang","year":"2017","journal-title":"Autom. 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