This paper proposes a quasi-steady-state modeling approach for an approximation of long-term frequency dynamics in power systems. A specific phenomenon of concern is an onset of frequency swings during load/generation imbalance scenarios. The effects of system voltage characteristics, system inertia, and, more importantly, damping controllers are explained and quantified using the described quasi-steady-state models. Application of the methodology to a 14-generator benchmark system demonstrates that described models are suitable for simulation of different disturbance scenarios that can trigger frequency instability. Moreover, linearization of the proposed models can provide convenient means for impact assessment and coordinated design of damping controllers. To demonstrate this, coordinated tuning of multiband power system stabilizers to improve frequency dynamics has been performed and validated through nonlinear simulations using a commercial transient stability software.Index Terms-Frequency dynamics, frequency stability, multiband power system stabilizer, oscillation damping, quasi-steadystate models.