Energy-Auditable Distributed Virtual Asynchronous Machine Control for Thermal-Energy-Storage-Based Virtual Energy Storage Systems

Converter-dominated power systems increasingly require flexible resources that can support frequency while preserving a physically interpretable energy trajectory. Thermal-energy-storage (TES)-based virtual energy storage systems (VESSs) can shift electrical demand within thermal-energy and comfort constraints, and have therefore attracted extensive interest. However, existing studies commonly coordinate requested or normalized power without fully connecting it to actuator execution and the electrical-to-thermal energy path. Command-level sharing cannot be directly equated with executed physical power, and controller storage cannot be combined with joule-valued hardware energy without dimensional separation. Therefore, this paper proposes a physically coupled and energy-traceable virtual asynchronous machine (VAM) control method for TES-based VESSs. First, a loss-resolved averaged model establishes the point-of-common-coupling (PCC)–converter–DC-link–actuator–TES physical chain and separates the hardware Hamiltonian from the dimensionless control Lyapunov function. Second, a neighbor-coupled marginal controller is embedded in a command–projection–execution chain so that frequency regulation and weighted sharing are evaluated using the executed service. Third, a constraint-handling mechanism combines directional headroom gating, actuator saturation and ramp limits, thermal comfort bounds, and request-inactive state reset to maintain executable trajectories under the declared constraints. Simulations under a sustained $120\mathrm{kW}$ disturbance show that primary-only control retains a $-0.08883\mathrm{Hz}$ steady-state offset, whereas the proposed nominal case restores frequency. In the constrained case, the 30 s terminal trend remains above the prescribed limit, while both terminal windows of the 60 s run satisfy the restoration criterion; the final-window mean error and dimensionless eligible-unit sharing spread are $-6.317\times {10}^{-5}\mathrm{Hz}$ and $6.564\times {10}^{-5}$, respectively. The model-internal electrical–thermal balance achieves a dimensionless relative RMS residual of $6.2361\times {10}^{-8}$. Because the PCC voltage/current pair is reconstructed from the same power source, this residual quantifies model-internal consistency rather than independent measured closure. These results demonstrate constrained frequency restoration, executed-power coordination, and energy traceability within the averaged-model scope.