Analytic models based on calculations for one repetitive day are presented for predicting the long-term performance of photovoltaic systems. For highly time-dependent loads, a general one-repetitive day simulation technique is described. For the special but practical cases of constant load distributions, simple closed-form solutions are derived for monthly solar fraction and dumped energy as functions of the important system variables. Viewing photovoltaic systems in terms of their effective "memory" enables one to predict regimes in which our analytic models should afford accurate predictions. Comparisons of model predictions and computer simulation results are presented, and include excellent agreement for many cases of practical interest. The analytic models are applicable to all solar collector types, as well as to various assumptions regarding the energy balance on assorted system components.