This paper quantifies the transient power losses incurred in re-synchronizing a network of generators and loads. The power system is represented using a network preserving model with loads and asynchronous generators modeled as frequency dependent power injections, which we refer to as 'first-order oscillators'. Coupling these models with the swing equations of traditional generators leads to a mixed-oscillator system. The power flows used to maintain network synchronization induce resistive (real power) losses in the system, which we quantify through an H2 norm that is shown to scale with network size. Our results also show that given a fixed network size, this H2 norm is the same for first-order, second-order and mixed-oscillator systems, provided that the damping coefficients are all equal. Therefore, if the renewable power generators being added to a power network can be controlled so that their effective dampings match those of the existing generators, they will not increase transient power losses in the system.