A residual-function-inspired method for constructing explicit expressions of Brayton-type pumped thermal electricity storage performance: a case study on maximum round-trip efficiency

Performance evaluation of Brayton-type pumped thermal electricity storage (PTES) systems needs to cover a high-dimensional combination space with broad parameter ranges, formed by system configurations, working fluids, operating parameters, modeling assumptions, and other factors. Existing ideal-system analytical methods are compact and broadly applicable, but their idealized assumptions lead to non-negligible deviations from real-system performance. Real-system case studies can provide accurate results, but high-dimensional parameter exploration is computationally expensive, and quantitative relationships obtained from individual cases are difficult to generalize. Data-driven methods can reduce the computational burden, but the resulting models often lack explicit physical constraints and clear physical interpretability. To address this problem, a method inspired by the thermodynamic residual-function concept is proposed for constructing explicit performance expressions for complex, strongly coupled thermodynamic systems. Using the maximum round-trip efficiency (RTE) as an example, the method is demonstrated for both non-recuperated and recuperated Brayton-type PTES configurations. It combines an ideal analytical upper bound that captures the dominant physical trend with a physics-guided explicit correction-factor expression for non-ideal deviations. Validation is performed using a dual-test-set strategy combining interpolation and extrapolation. In the interpolation tests, the mean absolute percentage errors (MAPEs) of maximum RTE prediction for the four working fluids range from 1.79% to 3.11% for the non-recuperated configuration and from 2.08% to 4.10% for the recuperated configuration. In the extrapolation tests, the corresponding MAPEs range from 2.74% to 4.29% for the non-recuperated configuration, while remaining below 5% for the recuperated configuration after excluding extreme boundary cases with maximum RTE below 5%. At the application stage, the explicit expressions reduce the runtime of a single evaluation by 99.40%–99.96% compared with real-system case calculations. The proposed method supports rapid performance evaluation and optimization of Brayton-type PTES systems and other strongly coupled thermodynamic systems.