A Testable Three-Layer Retained-State Framework for Intelligent Energy Systems: Metrics, Public Experimental Validation, and Cross-Scale Applications

This paper proposes a testable three-layer retained-state framework for intelligent energy systems grounded in mem-element theory. The framework distinguishes constitutive physical memory (Layer I), distributed circuit/converter memory (Layer II), and functional operational memory (Layer III) while preventing the indiscriminate classification of any history-dependent model as a mem-system. A retained variable is admissible only when it satisfies persistence, trajectory dependence, observable engineering consequence, and positive relevance beyond an instantaneous reference. Quantitative trajectory-separation, retained-state relevance, and engineering-gain indices, together with observability and falsification conditions, convert the framework from a taxonomy into a testable methodology. Layer I was partially validated using 636 experimental discharge cycles from four cells in the public NASA Ames PCoE Li-ion Battery Aging Dataset. Across 120 cycle–disjoint within-cell pairs matched at closely similar voltages, currents, temperatures, and local slopes, the median future-trajectory separation (MTS) was 0.0688, the noise-normalized separation (MNS) was 20.13, and the remaining-discharge duration differed by 150.7 s. Leave-one-battery-out prediction yielded positive retained-state relevance (MRI = 0.159 with a random-forest model; 95% bootstrap interval: 0.121–0.194). Two reduced-order cross-scale applications were then used for Layers II and III. In resonant wireless EV charging, retained-state augmentation reduced the efficiency RMSE by 29.9–32.2% and the current MAE by 27.5–27.9% in disturbed scenarios. In EV charging/V2G scheduling, history-aware operation reduced the charging cost by 3.3%, the degradation proxy by 12.0%, thermal-limit violations by 27.3%, and aggressive cycling by 17.2% while accepting lower peak reduction and V2G revenue. Same-information controls produced identical numerical outputs to the structured models by construction, showing that the framework’s novelty lies in admissibility, falsifiability, and cross-scale interpretation rather than privileged input information. The NASA study provides bounded public-experimental-data validation of Layer I; Layers II and III remain proof-of-concept demonstrations.