Planning electricity supply is important because power demand continues to increase while there is a concomitant desire to increase reliance on renewable sources. Extant research pays particular attention to highly variable, low-carbon energy sources such as wind and small-scale hydroelectric power. Models generally employ only a simple load levelling technique, ensuring that generation meets demand in every period. The current research considers the power transmission system as well as load levelling. A network model is developed to simulate the integration of highly variable non-dispatchable power into an electrical grid that relies on traditional generation sources, while remaining within the network’s operating constraints. The model minimizes a quadratic cost function over two periods of 336 hours, with periods representing low (summer) and high (winter) demand, subject to various linear constraints. The model is numerically solved using Matlab and GAMS software environments. Results indicate that, even for a grid heavily dependent on hydroelectricity, the addition of wind power can create difficulties, with system costs increasing with wind penetration, sometimes significantly.