## 1 Introduction  
The rapid growth in DC (direct current) transmission has intensified the need for advanced insulation materials that can meet the demands of high-capacity power systems and long-distance transmission networks. In this context, thermoplastic insulation materials have emerged as promising alternatives to conventional materials like XLPE (cross-linked polyethylene) and EPR (ethylene propylene rubber) [1, 2, 3]. These materials not only exhibit higher melting points and superior thermal stability but also offer environmental benefits such as recyclability and reduced space charge accumulation, which in turn help minimize electric field distortions [4, 5, 6]. Compared to conventional insulation materials, namely, XLPE, EPR, HEPR (highly cross-linked ethylene propylene rubber), HDPE (high-density polyethylene), and LDPE (low-density polyethylene), thermoplastic insulation materials offer notable advantages in thermal and environmental performance. Their higher melting points and thermal stability support increased current capacity and improved transmission efficiency under elevated temperatures. Additionally, the absence of crosslinking enhances recyclability and lowers the risk of degradation from space charge accumulation. However, polypropylene (PP), a representative thermoplastic, is inherently rigid and lacks flexibility, which presents mechanical challenges during cable bending, laying, and installation [7,8]. Consequently, mechanical properties are not only a limitation but also a key indicator of insulation reliability. In particular, degradation in tensile strength and elongation under thermal aging critically reflects the material's performance decline. While aging diagnostics and health indices have been widely investigated for conventional AC cables using materials like XLPE and EPR, very limited research has addressed aging evaluation methods for DC-specific thermoplastic-insulated cables, especially those based on polypropylene. Given the unique mechanical rigidity of PP, which significantly affects installation and operational durability, mechanical degradation must be prioritized when evaluating its insulation performance. This study, therefore, introduces a novel framework that emphasizes mechanical behavior as the primary degradation indicator. By focusing on tensile strength and elongation, a customized Aging Condition Index (ACI) is proposed for PP-based insulation, filling a gap in the existing literature and providing a new direction for condition assessment in DC cable systems. The successful implementation of thermoplastic insulation in practical power cable systems necessitates reliable methods for evaluating long-term aging behavior. Accurate assessment of cable aging is crucial for effective asset management and reliability evaluation, where indices such as the aging index, aging condition index, and health index serve as essential metrics [9, 10, 11]. A key element in these evaluations is the determination of the aging coefficient, which serves as the foundation for establishing the aging model. Based on this model, the ACI can be defined, enabling the estimation of the remaining lifetime of the cables. This study introduces a systematic approach to calculate the aging coefficient for thermoplastic-insulated power cables. Accelerated aging experiments were conducted at controlled temperatures of 90 \({}^{\circ}\)C, 110 \({}^{\circ}\)C, and 130 \({}^{\circ}\)C for durations up to 5000 h. During these tests, critical mechanical properties, specifically tensile strength and elongation at break, were continuously monitored. The resulting experimental data were then fitted to an exponential model to extract the aging coefficient, providing a quantitative measure of performance degradation. The aging coefficient was utilized to establish the aging model, based on which a systematic process was proposed for calculating the ACI and estimating the remaining life.