Electricity demand is increasingly difficult to predict due the uncertain timing and scale of future electrification, data center consumption, and electrolytic hydrogen adoption. This poses a new source of risk for power system planning. Though planners are often risk-averse, energy system modeling commonly takes a risk-neutral perspective. Here, we consider the implications of risk aversion concerning demand uncertainty for the optimal planning of power systems surrounding the North Sea. This region is both facing considerable demand uncertainty and expected to see substantial new investment in electricity generation capacity. In our exploratory experiments, optimal risk-averse planning under demand uncertainty features a higher share of renewable and storage investment by 2040, our planning horizon, compared to risk-neutral planning. As a result, risk-averse planning also leads to lower expected CO2 emissions in our case study. Overall, our results suggest that renewables and storage can provide a hedge against demand uncertainty.