Hierarchical Small Signal Modeling for Multi-Functional Hybrid Energy Storage Systems Enabled by Semi-Consensus Strategy

In a hybrid energy storage (HESS), V-P droop controllers are applied to batteries, whereas supercapacitors (SCs) are governed by integral droop (ID). The coordination between V-P droop and ID assists the realization of transient power allocations among batteries and SCs. Semi-consensus distributed control strategy for the HESS further enhances its control flexibilities, which endows multi-functional operations. However, for the cyber-physical HESS wherein hardware circuits and communication infrastructures co-exist, a systematic stability analyzing architecture is lacking due to complicated couplings between cyber and physical layers. To address this issue, a hierarchical small signal modeling approach is proposed in this paper. First, nonlinear average models of converters are explicitly delineated and the corresponding small signal models are developed. Second, the control loops including V-P droops, IDs, and proportional-integral (PI) controllers are modeled and linearized as in matrix forms, in small signal sense. Third, the linearized model depicting the control dynamics of semi-consensus strategy is derived. Based on the modeling from above three levels, a holistic small signal model characterizing overall dynamic responses of HESS can be obtained, which considerably facilitates the system eigenvalue loci analyses. Then critical loading margin as well as sensitive parameters leading to instability can be identified efficiently. Time domain simulations verify the correctness of the proposed methods.