Dynamic Power Flow Tracing in Urban Rail Transit Based on Circuit Theory and State Variable Method

A prerequisite for regenerative braking energy recovery in urban rail transit is to clarify how power flows between sources and loads in the system. Different from power flow calculation, which focuses on specific voltage and current values of each branch, power flow tracing emphasizes the contributions of sources to a specific load (upstream tracing) and the corresponding dual problem (downstream tracing). Considering the time-varying characteristics of urban rail transit, a dynamic current tracing approach based on circuit theory and the state variable method is proposed to describe the current distribution relationship between sources and loads. Thereafter, by applying fundamental circuit laws, the disaggregation result of current is straightforwardly extended to power tracing, and thus the power share that each source provides to each load (and the dual problem) can be determined. A rigorous mathematical proof is given for the derivation of tracing coefficients. Finally, a case study is implemented to verify the applicability of the proposed method. Through power flow tracing, the quantified and intuitive description of the current and power distribution relationship between sources and loads is demonstrated, which can provide a theoretical basis for future research on the optimal design and coordinated control of various braking energy recovery devices.