###### Abstract
As the share of synchronous generators diminishes and the adoption of renewable energy sources intensifies, power systems are confronted with emerging challenges marked by reduced inertia and diminished grid support capabilities [8; 9]. In recent years, there have been many major power outages caused by insufficient inertia, all of which are related to large-scale new energy access [10; 11]. For wind power transmitted via MMC-HVDC, which is studied in this paper, risks similar to those of the connected power grid exist. Firstly, since wind turbines are connected to the grid through power electronic devices, they cannot actively respond to grid frequency changes and respond to power deviations by releasing or absorbing energy, nor can they provide inertia support by releasing or absorbing energy [12]. Secondly, MMC-HVDC systems introduce a decoupling characteristic between the wind farm and the grid [13], which further reduces the overall system stability. Therefore, it is imperative to investigate a coordinated control strategy to improve the grid-supporting capability of wind farms connected via MMC-HVDC systems. Existing studies have explored improving the frequency support capability of wind turbines by modifying their control strategies. [14; 15] have designed a grid-forming control strategy for wind turbines. By simulating the characteristics of the synchronous generator, frequency-active power drop control, and voltage-reactive power drop control are realized. So, the wind turbine can provide inertia support when the frequency changes. However, these methods focus on a single turbine connected directly to the grid, making them unsuitable for wind turbines integrated with MMC-HVDC systems, in which the frequency variation information of the grid needs to be transmitted to the wind farm side. Ref. [16] proposes using communication methods to transmit grid frequency information. However, this approach is constrained by communication costs and reliability. The delay for a wind turbine to provide frequency support is typically in the range of 50 ms to 1 s [17], which is relatively long and fails to meet the rapid response requirements of inertial support. On the other hand, when a sudden grid frequency variation occurs, connected devices must provide additional active power support to reduce the rate of change of frequency (RoCoF) and set aside as much preparation time as possible for frequency regulation. However, most existing inertial support control strategies focus on a single device. Given that both offshore wind farms and MMC-HVDC transmission systems possess certain frequency regulation capabilities, it is essential to fully exploit their potential for coordinated frequency support. By combining the reserve capacity of wind farms with the energy storage capability of MMC-HVDC submodule capacitors [18; 19], the stability and operational reliability of the system can be significantly enhanced. In summary, there are the following problems in the existing research on the inertia response of wind farms transmitted by MMC-HVDC systems: 1. The inherent decoupling characteristics of power electronics impede wind turbines' ability to actively respond to grid frequency deviations; 2. Conventional communication-dependent frequency transmission methods suffer from 50 ms-1 s delays, failing to meet quickly inertial support requirements; 3. Existing control strategies lack coordinated utilization of wind farms' reserve capacity and MMC-HVDC's embedded capacitor energy storage for rapid frequency stabilization. Therefore, this paper proposes a coordination inertia support strategy for wind farms and MMC-HVDC systems without adding additional energy storage devices. First, this paper draws an analogy between the similarity of synchronous machine frequency and DC capacitor voltage and proposes a DC voltage-mapped frequency information transfer method.