Electrical power has become an important design constraint in high-performance computing (HPC) systems. On future HPC machines, power is likely to be a budgeted resource and thus managed dynamically. Power management software needs to reliably measure application performance at runtime in order to respond effectively to changes in application behavior. Execution time tells us little about how the science in the application is progressing toward an application-defined end goal. To the best of our knowledge, no study has defined or categorized online application progress in the context of power management. Based on semi-structured interviews with HPC application-specialists, we define an online notion of progress — an application-specific metric that can be monitored at runtime to provide a sense of the rate at which application science is being performed. Using instrumentation, we characterize and categorize the progress of various production scientific applications and benchmarks. We propose a model of the impact of dynamic power capping on application progress. By experimental evaluation, we show that our model accurately captures the general behavior of the progress of different classes of applications under a power cap. We believe that such a model is an important first step toward the design of more dynamic power management policies for HPC systems.