Decarbonising Australia's power system requires high market shares of variable renewable energy. An important policy initiative to achieve this is the establishment of Renewable Energy Zones (REZs). As renewable market share increases, curtailment within REZs is predictable. Curtailment occurs due to low utilisation rates or high peak-to-average output ratios of intermittent renewables (being ∼3:1), largely inelastic aggregate final electricity demand, and the economic limits of REZ network transfer capacity. In an open access, multi-zonal market setup, an intuitive response by policymakers may be to undertake connection reform (i.e. priority access) and underwrite storage assets to alleviate the worst effects of curtailment. Prima facie, curtailment and lines congestion may be reduced and wind and solar capacity increased through the deployment of battery storage. However, as model results in this article reveal, priority access can make multi-zonal markets more sensitive to curtailment, and competitive batteries within a REZ can aggravate congestion. Further, early entrant batteries may oversize their MW capacity and crowd-out renewables. All these cases harm welfare within a REZ. Optimally sized and coordinated ‘portfolio’ batteries alleviate congestion because they don't compete for scarce REZ transfer capacity.