The energy demand of cities is highly influenced by urban planning parameters such as urban density and land use. These parameters are mostly determined during early stages of planning. The effects of these parameters on the energy performance of districts is rarely incorporated into the conventional planning processes. This paper studies the relationship between urban planning parameters and energy systems of an urban area. For this, we used a Mixed Integer Linear Programming (MILP) formulation to identify trade-offs between urban density, land use and share of renewable energy sources (RES). The model is applied to a real case study of urban planning in Singapore. The optimization results give quantified implications of how to determine the mix of land use and density that simultaneously ensure a certain degree of penetration of RES in the area. The results show that when the required share of RES increases from 20% to 70%, the maximum achievable density (floor area ratio) decreases from 11.6 to 2.9 with purely residential land use. While maximizing the self-consumption of electricity produced by PV panels, the resulting mixtures of land uses are more diverse. These results provide urban planners with constraints that can shape their ideas from the perspective of energy performance.