Data centers are critical assets in today's digital world, supporting applications ranging from cloud computing to artificial intelligence. Their substantial energy consumption and stochasticity present challenges for sustainability and power grid operation. Long-term planning of data centers with co-located electricity generation and energy storage offers a fundamental step toward addressing these challenges, but current planning methods often overlook the influence of power imbalance on the data center's carbon footprint and operational costs. In this work, we propose a scenario-based mixed-integer stochastic optimization problem that considers intraday power imbalances to size co-located photovoltaic generation and energy storage. The framework also accounts for the life cycle assessment of the resources, their aging, the local power grid carbon intensity and the solar irradiance conditions. Using a lower bound of the intraday imbalance cost to analyze the case of three Swiss cantons, we observe significant differences in carbon and cost reduction opportunities.