Abstract：In large-scale offshore wind power flexible high-voltage direct-current (HVDC) transmission systems, the transmission distance of AC/DC submarine cables is long, and the mutual inductance between AC/DC cables is significant. The influence of time delay, frequency dependence, and mutual inductance characteristics on the system's small-signal stability cannot be ignored. At present, the cable equivalent model does not account for frequency-dependent and mutual inductance characteristics, nor does it rely on historical data and convolution calculations, which makes it difficult to use for analytical modeling and small-signal stability analysis. Therefore, this paper proposes a cable equivalent model comprising differential- and common-mode RLC circuits with compensation current sources. Through phase-mode transformation and RLC equivalent circuits, the proposed model can accurately simulate the frequency-dependent, time-delay, and mutual-inductance characteristics of AC/DC cables. Firstly, based on the per-unit-length frequency-dependent impedance data in the phase-domain frequency- dependent model, this paper employs the vector fitting method to determine the topology and parameters of a single π-type circuit with multiple RL branches. The distribution and delay characteristics of single cables are simulated by cascading multiple π-type circuits. Secondly, based on the phase-mode transformation, the voltage-current relationship of the AC/DC cable ports, accounting for mutual inductance, is derived. The cable mutual-inductance equivalent circuit, based on the differential/common-mode RLC circuit and a compensation current source, is established. The equivalent circuit of the AC/DC cable, accounting for mutual inductance characteristics and the modular small-signal model of wind power, is derived. Finally, the small-signal dynamic characteristics and stability of the proposed model and the real cable are compared in PSCAD/EMTDC. The small-signal characteristics indicate that the relative root-mean-square error (RRMSE) of the proposed multi-RL parallel-branch multi-π cascade model is less than 2%. In contrast, the single-RL branch multi-π cascade model exhibits a higher RRMSE. Besides, the system based on the non-mutual inductance equivalent circuit exhibits noticeable errors in its small-signal dynamic characteristics compared with the real cable system. In contrast, the mutual inductance equivalent circuit closely matches the behavior of a real cable system. For the mutual-inductance-based equivalent model, the RRMSE of the small-signal responses is less than 1.5%. Finally, the small-signal stability of the wind power transmission system via VSC-HVDC is analyzed using an eigenvalue-based method by considering models with and without mutual inductance. The stability analysis results indicate that incorporating mutual inductance can accurately characterize the real system's stability. The following conclusions can be drawn from the simulation analysis. (1) The single-cable equivalent model using a multi-RL branch multi-π cascaded circuit provides a more accurate description of cable dynamic characteristics than traditional single-RL branch multi-π cascaded models. (2) Accounting for mutual inductance is essential for accurately describing the steady-state and transient performance of the AC/DC cable. (3) Mutual inductance exists between cables in proximity, significantly affecting broadband impedance characteristics. Consequently, ignoring mutual inductance leads to deviations in system dynamic behavior and may result in misjudgments in stability analysis.
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2026, Vol. 41 
