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In Denmark, incorporation of wind power into the power system is increasing whereas power generation from the large conventional power plants is reducing. The common concern has become maintenance of reliable and stable operation of the Danish power system with a large amount of wind power - the large wind power system. At present, maintaining the voltage stability of such a large wind power system relies on strong ac connections to neighboring power systems with sufficient reactive power and voltage control and on control of central power plants in Denmark. This paper presents the results of a stability investigation carried out by the Danish transmission system operator (TSO), Energinet.dk, for the case of almost island operation of the Western Danish wind power system. The main ac lines connecting Western Denmark to the synchronous area of the Union for the Co-ordination of Transmission of Electricity (UCTE) were out of service and the wind power generation was high. The investigation has shown that the reactive power and voltage control of the domestic power plants is essential for maintaining short-term voltage stability of the Western Danish wind power system and becomes even more relevant when ac connections to the strong transmission system of the UCTE are out of service. The results presented in this paper may also be relevant for the operators of the power systems that are in island ac operation and with plans for significant commissioning of wind power - Great Britain, Ireland, Tasmania, etc.