*Limit checking of measured variables in a monitored system is a method frequently used for fault detection. 3E uses it as a first step on its protocol of fault detection and diagnosis to know at which stage of a Photovoltaic plant actions need to be taken before any further deep analysis on the characteristics of the problems. Here, 3E illustrates the methodology used to apply it in their use case.*

Photovoltaic (PV) plants are energy conversion systems which convert sunlight into electricity that is fed into the public utility grid. The physical structure and the important process variables of a PV plant measured when monitoring the performance of a photovoltaic (PV) plant are illustrated in Figure 1. The input variables of the process model are: the solar irradiance in the plane of the PV array (*G _{POA}*) and the ambient temperature (

*T*). Output variables from the process model point of view are: the PV module temperature (

_{amb}*T*); the Direct Current voltage(

_{mod}*V*) and current (

_{DC}*I*) at the output of the PV array; the Alternating Current voltage (

_{DC}*V*); the power factor (

_{AC}*PF*); and the electric AC power to the grid (

*P*).

_{AC}

## Implementation

Normalized performance parameters can be derived from the previously mentioned measurements and allow to quantify the energy flow and losses through the PV array per loss type. They are:

*L _{A,I}*=

*Y*–

_{r}*Y*

_{A,}

*L _{A,T}*=

*Y*–

_{A,I}*Y*

_{A,T}*L _{A,V}* =

*Y*–

_{A,T}*Y*

_{A}with *L _{A,I}*,

*L*,

_{A,T}*L*, the conversion losses due to current, temperature and voltage, respectively and

_{A,V}*Y*,

_{r}*Y*,

_{A,I}*Y*,

_{A,T}*Y*the normalized energy yield from reference yield (based on irradiation from the sun), array yield after current losses, array yield after temperature losses and array yield after all array losses, respectively.

_{A}The main variables used for limit checking are solar irradiance in the plane of the PV array (*G _{POA}*), ambient temperature (

*T*), PV module temperature (

_{amb}*T*), DC voltage and current at the output of the PV array (

_{mod}*V*,

_{DC}*I*) and electric AC power to the grid (

_{DC}*P*). The AC voltage (

_{AC}*V*) and power factor (

_{AC}*PF*) are not used for limit checking.

For checking the operational performance over different energy conversion steps, a performance loss ratio per step is defined. This performance loss ratio is computed for a given time span, e.g., a day up to several months. It is the useful energy lost over the energy conversion step divided by the energy available, i.e. the incoming solar energy on the PV array as represented by the solar irradiance in the plane of the PV array (*G _{POA}*); all normalized to standard rating conditions of the PV array. Accordingly, the overall performance of a PV plant is described by the performance ratio (PR), i.e., 100% minus the sum of all performance losses.

In practice, we compare the performance loss ratios from measurements to model-based performance loss ratios and thresholds. The model is fed with measured values of *G _{POA}* and

*T*. The model parameters can be set from data sheet parameters of the devices in the PV plant or identified from measurements from the plant in a healthy state. Accordingly, adequate limits can be derived either from tolerances on the data sheet parameters or from choosing percentiles from the healthy plant. Both the model-based performance loss ratios and their limit values vary depending on the PV plant and the weather during the evaluation period.

_{amb}

Figure 2 illustrates this application of limit checking for a PV plant located in Belgium. The current-related array losses (‘Array (current)’) in Figure 2a by far exceed the threshold. During a thorough maintenance action after this problem was detected, several smaller PV module failures were fixed. After maintenance action, all performance loss ratios were back within their expected ranges, yielding a much higher PR of 82.9% (Figure 2b).