While electricity access is lowest in developing countries, the academic literature on generation expansion planning (GEP) has been informed almost exclusively by challenges in industrialised countries. This paper presents the first multi-objective, long-term energy planning optimisation model tailored towards national power systems with little existing power infrastructure. It determines the location, type, capacity and timing of power system infrastructure additions. Specifically, three novel generalisations of standard generation planning are introduced: (1) an expansion of the demand constraints to allow for industrial and household electrification rates below 100%, (2) a minimisation of sub-national energy access inequality in conjunction with minimising system costs considering environmental constraints, and (3) an integration of distribution infrastructure, explicitly including both on-grid and off-grid electrification. Using a specifically designed solution algorithm based on the epsilon-constraint method, the model was successfully applied to the previously unexplored Ugandan national power system case. The results suggest that while it is cost-optimal to maintain highly unequal sub-national access patterns to meet Uganda's official 80% electrification target in 2040, equal access rates across all districts can be achieved by increasing discounted system cost by only 3%. High optimal shares of locationally flexible on-grid and off-grid solar energy enable cheap sub-national shifts of generation capapcity. This paper strongly challenges the Ugandan government's nuclear energy and largely grid-based electrification expansion plans. Instead, it calls for solar concentrated power as a baseload option in the future and a focus on off-grid electrification which the model selects for the majority of household connections in 2040, even in a high-demand scenario.