Integrated electromagnetic–circuit digital twin modelling for constraint-consistent optimal operation in heterogeneous multi-receiver wireless power transfer systems

Heterogeneous multi-receiver wireless power transfer (WPT) systems exhibit strong electromagnetic coupling and non-uniform load requirements, making it difficult to determine an operating point that is simultaneously feasible for all receivers and efficient at the system level. This study presents an integrated electromagnetic–circuit digital twin modelling approach that enables constraint-consistent optimal operation in single-transmitter, multi-receiver WPT systems with mixed compensation topologies. A design-stage digital twin is constructed by tightly coupling three-dimensional electromagnetic-field simulation with equivalent circuit modelling. Self- and mutual-inductance parameters are extracted from the physical coil configuration and mapped into the circuit model, allowing physics-consistent prediction of receiver delivered power and total transmission efficiency under interacting receiver conditions. The operating point is then determined by explicitly enforcing receiver-specific rated power requirements as feasibility constraints while refining system efficiency within the feasible region. The approach is demonstrated on a 1T–3R WPT case study comprising two series-compensated receivers and one parallel-compensated receiver with non-uniform rated powers. The results show that the proposed digital twin modelling enables identification of an operating condition that satisfies all receiver power constraints and improves overall efficiency. A one-dimensional parameter sweep around the obtained operating point further confirms local robustness and sensitivity characteristics, supporting the validity of the constraint-consistent optimum for heterogeneous multi-receiver configurations.