We formulate and compare optimization models of investment in renewable generation using a suite of social planning models that compute optimal generation capacity investments for a hydro-dominated electricity system where inflow uncertainty results in a risk of energy shortage. The models optimize the (possibly risk-adjusted) cost of capacity expansion and operation allowing for investments in hydro, geothermal, solar, wind, and thermal plant, as well as battery storage for smoothing load profiles. A novel feature is the integration of uncertain seasonal hydroelectric energy supply and short-term variability in renewable supply in a two-stage stochastic programming framework. The models are applied to data from the New Zealand electricity system and used to estimate the costs of moving to a 100 % renewable electricity system by 2035. We also explore the outcomes obtained when applying different forms of CO2 constraint that limit respectively non-renewable capacity, non-renewable generation, and CO2 emissions on average, almost surely, or in a chance-constrained setting, and show how our models can be used to investigate the merits of a proposed pumped-hydro scheme in New Zealand’s South Island.