In this paper, we introduce a model representing the key characteristics of high frequency variations of solar irradiance and photovoltaic (PV) power production based on Clear Sky Index (CSI) data. The model is suitable for data-driven decision-making in electrical distribution grids, e.g., descriptive/predictive analyses, optimization, and numerical simulation. We concentrate on solar irradiance data since the power production of a PV system strongly correlates with solar irradiance at the site location. The solar irradiance is not constant due to the Earth’s orbit and irradiance absorption/scattering from the clouds. To simulate the operation of a PV system with one-minute resolution for a specific coordinate, we have to use a model based on the CSI of the solar irradiance data, capturing the uncertainties caused by cloud movements. The proposed model is based on clustering the days of each year into groups of days, e.g., (i) cloudy, (ii) intermittent cloudy, and (iii) clear sky. The CSI data of each group are divided into bins of magnitudes and the transition probabilities among the bins are identified to deliver a Markov Chain (MC) model to track the intraday weather condition variations. The proposed model is tested on the measurements of two PV systems located at two different climatic regions: (a) Yverdon-les-Bains, Switzerland; and (b) Oahu, Hawaii, USA. The model is compared with a previously published N-state MC model and the performance of the proposed model is elaborated.