This paper describes a model of the 2020 Irish electricity system which was developed and solved in a mixed integer programming, unit commitment and economic dispatch tool called PLEXOS. The model includes all generators on the island of Ireland, a simplified representation of the neighbouring British system including proposed wind capacity and interconnectors between the two systems. The level of wind curtailment is determined under varying levels of three influencing factors. The first factor is the amount of offshore wind, the second is the allowed limit of system non-synchronous penetration (SNSP) and the third is inclusion or exclusion of transmission constraints. A binding constraint, resulting from the 2020 EU renewable energy targets, is that 37% of generation comes from wind. When the SNSP limit was increased from 60% to 75% there was a reduction in wind curtailment from 14% to 7%, with a further reduction when the proportion of wind capacity installed offshore was increased. Wind curtailment in the range of SNSP limit of 70-100\% is influenced primarily by the inclusion of transmission constraints. Large changes in the dispatch of conventional generators were also evident due to the imposition of SNSP limits and transmission constraints.