Multilevel converters are nowadays an enabling key in the integration of electric power into the grid as they introduce less distortion and, thus, they are more compliant with the grid standards, among other benefits. A well-known topology is the three-level Neutral-Point-Clamped (NPC) whose control requires to deal with the capacitors voltage unbalance. This paper presents a modulation approach where the injection of a common component in the modulated voltage is studied in order to achieve such voltage balance. An optimization problem that, apart from the voltage balance, aims the lowest number of commutations and can be solved very efficiently with up to five computations of the cost function is formulated. The main advantages of the proposed modulation strategy are its simplicity and its flexibility, since it is also valid for unbalanced grid conditions and, with little added complexity, for low (and even zero) power factor conditions. Simulation results under unbalanced grid conditions are provided in order to show its validity under this scenario. The strategy is evaluated and compared with a space-vector-based approach in an experimental setup, yielding similar total harmonic current distortion (4.4%), a 30% reduction in the number of commutations, and better voltage balance performance for lower power factor conditions.