Utilizing the reactive power (var) capability of wind turbines (WTs) has become the primary method for increasing var reserves in offshore wind farms. However, current methods place an unbearable burden on outdated equipment, which requires frequent communication. Catering to this problem, an asynchronous hierarchical voltage/var (volt/var) control (AHVC) method is proposed, which is constrained by the original communication capability and topology of collector grid, and embedded in a master-slave multi-agent system with an asynchronous hierarchical control scheme. The proposed AHVC method is built on the bilinear optimal power flow (Bilinear-OPF) model with a parallel alternating direction method of multipliers (ADMM) algorithm. It resolves voltage distortion issues in high-capacitance grids by ensuring more precise var targeting across the grid, then the var burden on the static synchronous compensator (STATCOM) is reduced. Additionally, the volt/var sensitivity-based Mahalanobis norm hyperparameter setting method ensures local compensation of var sources. The proposed AHVC method achieves rapid convergence and reliable performance amid typical load volatilities of WTs. Simulation results verify the significant improvement of accuracy and voltage stability, even under challenging communication conditions.