A Retained-Port MIMO Dynamic Equivalent of IBR-Dominated Distribution Networks for Multi-PCC Transmission Studies

초록

Distribution systems tied to the transmission grid at several points of common coupling (PCCs) exchange currents through shared feeder paths, so a disturbance at one PCC alters currents at the others- coupling that single-port and independent per-PCC equivalents cannot represent. This paper proposes a topology-embedded retained-port (TERP) multi-input/multi-output dynamic equivalent that preserves the prescribed external-PCC channels and their full cross-PCC block structure. Internal feeder coordinates are eliminated first, resource and controller dynamics are closed through the resulting topology operator, and balanced truncation is applied only after the boundary transfer is assembled, so reduction leaves the terminal channels intact. On a modified two-PCC CIGRE benchmark, a 63-state realization reduces to 12 states with five inputs and four outputs. Status-specific templates are evaluated before each study without run-time feeder reconstruction or access to internal DSO data. A fitted equilibrium-current map initializes each template consistently with the transmission base case. In a 1,848-trajectory electromagnetic-transient campaign with proportional vector current limiting, the 1,344 voltage events spanning [-90, +30]% give mean and maximum trajectory errors of 0.0188 and 0.0823. Of the 504 common-frequency events, the 336 within +/- 0.6 Hz give 0.0277 and 0.0550; the remaining 168 form a stress set where error arises from linearization rather than order reduction. Removing the cross blocks raises that voltage-event mean to 0.635, confirming that these channels carry a first-order share of the boundary response. The retained transfer also yields PCC-resolved inertia-like, damping-like, and matrix-valued Q-V coefficients.

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