Bollinger bands based on exponential moving average for statistical monitoring of multi-array photovoltaic systems

Monitoring the performance of a photovoltaic (PV) system when environmental parameters are not available is very diffcult. Comparing the energy datasets of the arrays belonging to the same PV plant is one strategy. If the extension of a PV plant is limited, all the arrays are subjected to the same environmental conditions. Therefore, identical arrays produce the same energy amount, whatever the solar radiation and cell temperature. This is valid for small-to medium-rated power PV plants (3-50 kWp) and, moreover, this typology of PV plants sometimes is not equipped with a meteorological sensor system. This paper presents a supervision methodology based on comparing the average energy of each array and the average energy of the whole PV plant. To detect low-intensity anomalies before they become failures, the variability of the energy produced by each array is monitored by using the Bollinger Bands (BB) method. This is a statistical tool developed in the financial field to evaluate the stock price volatility. This paper introduces two modifications in the standard BB method: the exponential moving average (EMA) instead of the simple moving average (SMA), and the size of the width of BB, set to three times the standard deviation instead of four times. Until the produced energy of each array is contained in the BB, a serious anomaly is not present. A case study based on a real operating 19.8 kWp PV plant is discussed.