## 2 Methodology for Selection of Studies
### Eligibility and Inclusion of Screened Manuscripts  
The Eligibility and Inclusion phase is vital in refining the selection process to ensure that only the most relevant and high-quality studies were included in this systematic review. Each of the 182 articles was carefully assessed through an in-depth full-text evaluation, utilizing a detailed three-level Likert scale based on the following criteria specifically tailored to the objectives of this investigation:  
1. Eligibility Criterion 1--Alignment with Research Objectives: This criterion evaluates how well this study aligns with the research scope, particularly its focus on hierarchical, multi-agent, or robust optimization approaches in energy management within P2P frameworks. Studies addressing the role of electric machines in DES or their integration with RES are prioritized (Scoring: 1--Peripheral, 2--Related, 3--Highly Relevant). 2. Eligibility Criterion 2--Methodological Rigor: This criterion assesses the robustness and appropriateness of this study's methodology, including experimental setups, simulation models, validation frameworks, and the overall clarity of the research process. The methods must provide sufficient evidence to support the study's findings (Scoring: 1--Needs Improvement, 2--Acceptable, 3--Strong). 3. Eligibility Criterion 3--Originality and Innovation: This criterion evaluates the novelty of the proposed strategies or frameworks in this study. This includes innovative approaches to multi-agent optimization, robust control mechanisms, or the role of electric machines (e.g., SiC- or GaN-based technologies) in enhancing energy efficiency and reliability in P2P systems (Scoring: 1--Minor, 2--Moderate, 3--Major). 4. Eligibility Criterion 4--Data Quality and Analysis: This criterion measures the reliability, reproducibility, and depth of the data analysis presented in this study. High-scoring studies provide detailed, well-documented datasets and analyses, including energy flow modeling, the machine performance, or system-level optimization outcomes in P2P environments (Scoring: 1--Satisfactory, 2--Good, 3--Excellent). 5. Eligibility Criterion 5--Impact and Contribution to the Field: This criterion evaluates this study's potential contribution to advancing knowledge in the domain of distributed energy management. High-impact studies are those that propose transformative insights, address significant challenges, or establish new benchmarks in energy management and electric machine applications measured by the number of citations (Scoring: 1--Low impact, 2--Moderate impact, 3--High impact). The Eligibility and Inclusion phase marked a critical step in refining the dataset, ensuring that only the most relevant, methodologically robust, and innovative studies were selected for synthesis. Two independent researchers conducted a thorough full-text evaluation of the 182 articles identified during the screening phase. To minimize bias, discrepancies in the evaluations were resolved through discussion and consensus. The threshold for inclusion was set at 12 out of 16 points, striking a balance between selectivity and inclusivity. This threshold was carefully chosen to ensure that selected studies met the high standards of relevance, rigor, and innovation required for the systematic review, while remaining inclusive enough to capture valuable contributions. Figure 3 presents an excerpt from the verification matrix completed by reviewers to evaluate each article fully. As can be evidenced in Figure 3, out of the 182 articles evaluated, 94 studies (51.6%) met or exceeded the threshold of 12 points and were included in the final dataset for synthesis. These articles demonstrated a strong alignment with the review's objectives, provided robust methodological approaches, and contributed innovative and impactful findings to the field. Studies that did not meet the threshold were not dismissed as inherently poor or lacking merit. Instead, their exclusion reflects the need to focus on works most pertinent to the specific objectives of this systematic review.