Online photovoltaic array hot-spot Bayesian diagnostics from streaming string-level electric data

Abstract

We report on a physics-based suite of machine-learning algorithms which performs online, real-time photovoltaic-array incipient hot-spot diagnostics and prognostics, using as input panel-string electrical sensor data. These data consist of module-string currents and voltages and their instantaneous (filtered) rates of change, acquired via a combination of analog and digital sensors. Our diagnostics algorithms comprise thermal and electrical System ID stages, augmented by a Bayesian MAP (Maximum A posteriori Probability) inference engine utilizing a simplified stochastic, spline-based integrated plant model in the optical, electrical and thermal domains. Our (path-integral, physics-based) MAP inference engine detects incipient hot-spots; attributes them to the most likely proximate- and underlying causes (such as shading or dust-deposition patterns, direct heating, inherent mismatches or circuit failures); and renders quantitative estimates of the most likely culpable environmental factor (e.g. a time-varying shading pattern). The same simplified plant model is periodically used to prognosticate the likely future evolution of the incipient hot spot. Our diagnostics and prognostics algorithms can be applied to simulated and/or empirical data (the latter from our roof-top PV lab at Carnegie Mellon). The algorithms leverage changes in estimated conductances in different regions of the electrical state-space, and at different granularities (cells, panels, strings and full array). It take into account temperature coefficients, ohmic- and optical heating, and (optionally) inherent electrical mismatches. Our algorithm suite requires as input neither temperature sensors, nor sub-panel electrical data, nor load sweeps; even pyranometer data is optional. The only necessary sensor data are string electrical data at the actual instantaneous in-operation external load (either with or without a perturb-and-observe MPPT control procedure). Digitized measurements of the low-pass-filtered time derivatives of these currents are useful, but if not available they can be replaced with numerical differentiation. However, occasional voltage sweeps — augmented with pyranometer, thermal and intra-panel (bypass diode voltage) data from our heavily instrumented PV array — along with online astronomical and meteorological data and artificially induced shading patterns — are used to validate our algorithms and to improve the baseline System ID parameters estimation.