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Uncertainty and several competing criteria on the demand and generation sides make multi-objective optimization difficult. Selecting a model capable of resolving scheduling issues related to loads and dispersed energy sources is, therefore, essential. This study details a concept for optimizing the SPG\u2019s operating cost and pollutant emissions using renewable electricity. Renewable energy sources, such as solar photovoltaic and wind power, are inherently unpredictable and subject to change. Uncertainty around renewable energy is handled by the suggested approach via the use of a probability density function (PDF). In order to address a multi-objective optimization (MOCO) issue, the model that was built relies on a MOCO method. A benchmark model for energy management and control is used to verify the performance of the suggested model, which is a multi-objective deep reinforcement learning (DRL) method. According to the results, MOCO reduces operating costs by 15% and environmental emissions by 8%. The results show that compared to the comparison models, the proposed model achieves the aims better.<\/jats:p>","DOI":"10.1186\/s42162-025-00526-4","type":"journal-article","created":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T17:32:15Z","timestamp":1754328735000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Multi-objective optimization models for power load balancing in distributed energy systems"],"prefix":"10.1186","volume":"8","author":[{"given":"Zhuo","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuchen","family":"Luo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lei","family":"Cao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhun","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,8,4]]},"reference":[{"key":"526_CR1","doi-asserted-by":"crossref","unstructured":"Huang K, Yi Z, Xu Y, Zhou Z, Han L (2024) Operation mode and scheduling plan optimization approach for multiple balancing zones in a distribution system. 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