Synthetic Generation of Solar States for Smart Grid: A Multiple Segment Markov Chain Apptoach

The use of photovoltaic (PV) sources is becoming very popular in smart grid for their ecological benefits, with higher scalability and utilization for local generation and delivery. PV can also potentially avoid the energy losses that are normally associated with long-range grid distribution. The increased penetration of solar panels, however, has introduced a need for solar energy models that are capable of producing realistic synthetic data with small error margins. Such models, for instance, can be used to design the appropriate size of energy storage devices or to determine the maximum charging rate of a PV-powered electric vehicle (EV) charging station. In this regard, this paper proposes a stochastic model for solar generation using a Markov chain approach. Based on real data, it is first shown that the solar states are inter-dependent, and thus suitable for modeling using a Markov model. Then, the probabilities of transition between states are shown to be heterogeneous over different time segments. A model is proposed that captures the intertemporal dependency of solar irradiance through segmentation of the Markov chain across different times of the day. In the studied model, different state transition matrices are constructed for different time segments, which the proposed algorithm then uses to generate the solar states for different times of the day. Numerical examples are provided to show the effectiveness of the proposed synthetic generator.