The use of solar photovoltaic (PV) power has recently increased in electric distribution grids. However, the stochastic properties of solar energy, such as intermittency (i.e. the presence of a correlated high frequency of large fluctuations), can negatively affect power quality and cause grid instabilities, especially in microgrids. In this study, we differentiate the diffusive and jumpy characteristics of solar power and introduce a stochastic dynamical jump-diffusion equation to model non-gaussian PV power. Using the obtained dynamical equation, we generate new synthetic data sets with varying jump rates. Finally, we implement a straightforward filtering method, i.e. a combination of an inverter and a battery storage system to show the applicability of our proposed stochastic method.