## Markov Models to Analyze Photovoltaic System Reliability and Performance

**Sairaj Dhople with adviser A. DomÃnguez-GarcÃa**

Markov reliability models to estimate photovoltaic (PV) system reliability are derived and integrated with reward models to quantify system performance. The proposed framework is illustrated in Figure 19. The states in the Markov chain (i and j) correspond to operational or failed components. Each state is characterized by a performance level (Ïi and Ïj). A numerical solution to the steady-state distribution Ï€ of the ergodic Markov chain and its sensitivity to system parameters (Ï‰1 = Î»i, Ï‰2 = Î¼j) can be derived from a QR factorization and the group inverse of the transition matrix that describes the reliability model. The steady-state distribution is tied to system performance Îž through the reward rates (Îž = Ï€ Ï).

The proposed framework establishes the mathematical basis to analyze the reliability and performance of PV systems. By choosing the reward vector to represent power ratings of different states, the performance metric obtained is an expected system power rating.

This research is partially supported by the Grainger Center for Electric Machinery and Electromechanics.