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This paper addresses a detailed design of a wind power plant and turbine slope voltage control in the presence of communication delays for a wide short-circuit ratio range operation. The implemented voltage control scheme is based upon the secondary voltage control concept, which offers fast response to grid disturbances, despite the communication delays, i.e., this concept is based on a primary voltage control, located in the wind turbine, which follows an external voltage reference sent by a central controller, called secondary voltage control, which is controlling the voltage at the point of connection with the grid. The performance has been tested using PSCAD/EMTDC program. The plant layout used in the simulations is based on an installed wind power plant, composed of 23 doubly fed generator wind turbines. The resulting performance is evaluated using a compilation of grid code voltage control requirements. The results show that fast response to grid disturbances can be achieved using the secondary voltage control scheme, and the fulfillment of the design requirements can be extended for a wide range of short-circuit ratios.