From technical and economical viewpoints, an all-dc offshore wind farm (OWF) with a high-voltage direct-current (HVDC) connection, which is also known as HVDCconnected all-dc OWF, is the future trend for offshore wind energy applications. However, due to the decoupling effect of power converters, all-dc OWF cannot directly provide short-term frequency support for the onshore ac gird, that is, primary frequency response and inertia support. To address this issue, this paper presents a distributed model predictive control (DMPC) scheme for all-dc OWF. By directly suppressing the voltage deviation and the rate of change of voltage of the offshore dc collection network, this scheme indirectly decreases the frequency deviation and the rate of change of frequency (RoCoF) of the onshore ac grid. Meanwhile, the scheme ensures the stability of wind turbines in alldc OWF during the frequency events. Considering a large number of wind turbines in the OWF, the corresponding optimization problem is solved in a distributed way using the alternating direction method of multipliers (ADMM), thus reducing the computational burden. Simulations including the performance comparison with droop control validate the effectiveness of this scheme.

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Renewable energy sources have been characterized by a persistent and rapid proliferation, which has resulted in a notable reduction in grid inertia over an extended period. There is a widely held belief that the primary source of inertia within the grid stems from generation-side conventional units. However, in power consumption, a significant number of induction motors are present, which can inherently offer rotational inertia by virtue of their kinetic energy. To investigate the influence of induction motors on grid inertia, in this paper, we propose two types of models, i.e., a detailed grid model and a dynamic equivalent model that considers multiple induction motors. Specifically, the detailed grid model with multiple induction motors is first established. However, the detailed model requires the specific parameters of induction motors, which are hard to acquire in large systems. Moreover, the accuracy of the model is unsatisfactory. To fill these gaps, the dynamic equivalent model (DEM) is further proposed to emulate the detailed model. Compared with the detailed model, the proposed dynamic equivalent model is structurally simple and does not require the specific parameters of induction motors. Therefore, it is possible to apply to large systems for investigating the influence of induction motors on grid frequency dynamics. A genetic algorithm is introduced in order to figure out the parameters of the proposed dynamic equivalent model from historical frequency data. The proposed detailed model and dynamic equivalent model are evaluated on the IEEE 9-bus system in MATLAB and SimPowerSystems toolbox.