Introduction

Introduction

This technical report is a part of the joint research project 19ENG01 “Metrology for emerging PV applications” (Metro-PV) and has been developed under Work Package 2 “Determining the measurement uncertainties associated with IEC test procedures”.

The aim of this work was to gather existing knowledge on laboratory practices for uncertainty calculation associated with output power characterization and energy rating of PV modules.

This deliverable presents guidelines for calculating the measurement uncertainties related to the following IEC standards:

IEC 60891: (2021)	Photovoltaic devices - Procedures for temperature and irradiance corrections to measured I-V characteristics
IEC 60904-1: (2020)	Photovoltaic devices - Part 1: Measurement of photovoltaic current-voltage characteristics
IEC 61853-1: (2011)	Photovoltaic (PV) module performance testing and energy rating - Part 1: Irradiance and temperature performance measurements and power rating
IEC 61853-2: (2016)	Photovoltaic (PV) module performance testing and energy rating - Part 2: Spectral responsivity, incidence angle and module operating temperature measurements
IEC 61853-3: (2018)	Photovoltaic (PV) module performance testing and energy rating - Part 3: Energy rating of PV modules

Table 1: IEC standards for PV module performance measurements

Principles for PV measurement uncertainty assessment according to JCGM 100:2008

General

General principles for measurement uncertainty assessment are defined in the guidance document JCGM 100:2008 “Evaluation of measurement – Guide to the expression of uncertainty in measurement (GUM)” [1], which was prepared by the Joint Committee for Guides in Metrology (JCGM).

If a measurement variable X has X_i independent uncertainty sources, the combined standard uncertainty u_C is given by the formula

[math]\displaystyle{ u_{C} = \sqrt{\sum_{i}(u_{i})^2} }[/math] (1)

where parameters u_i are the standard uncertainties of uncertainty sources X_i, which are always related to 68% confidence level. This consideration allows to conclude that the true value of variable X lies with 68% probability in the confidence interval

[math]\displaystyle{ [ \text{measured value}-u_{C} \text{, measured value}+u_{C} ] }[/math] (2)

For industrial applications, however, a higher confidence level of 95% is commonly used. This transition is accomplished by multiplication of u_C with the coverage factor k = 2. This results in the expanded combined measurement uncertainty

[math]\displaystyle{ U=k \cdot u_{C} }[/math] (3)

where U is the Expanded measurement uncertainty, u_C is the Combined standard uncertainty, and k is the Coverage factor, k = 2 for 95% confidence level.

Note: standard uncertainties (k = 1) will be denoted by the (small) “u”, whereas expanded uncertainties (normally k = 2, but not necessarily) will be denoted by (large) “U”.

Types of uncertainty sources

For a measurement variable X, two types of uncertainty sources can be distinguished:

Type A uncertainties u_A

These are determined by statistical analysis or a series of observations. The standard uncertainty u_i of the uncertainty component X_i is given by the standard uncertainty of the mean value.

Examples for type A uncertainties are:

• Reproducibility of I-V measurements, which have been taken at different test conditions (i.e. successive days) and with electrically disconnecting and removal of the PV module from the test area of the solar simulator.

• Repeatability of I-V measurements, which have been successively taken under the same test conditions without electrically disconnecting and removal of the PV module from the test area of the solar simulator.

Note 1: The standard uncertainties for type A uncertainties are normally determined from the standard deviation of a set of measurements. The standard deviation determined from small sample sizes (in practise everything below 30 samples) should be modified to a realistic value.

Note 2: If a single measurement is performed the (expected) standard deviation (determined from a separate set of measurements) should be used as standard uncertainty.

Note 3: If several measurements are made, the (arithmetic) average of these measurements should be reported as the measurement result. The uncertainty associated with this arithmetic average is either

a) in case the standard deviation has been determined from a separate set of measurements, the standard deviation divided by the square root of the number of measurements or

b) in case the standard deviation is determined/estimated from the same set of measurements that is used to calculate the arithmetic average, that standard deviation divided by the square root of the number of measurements minus 1.

Type B uncertainties u_B

These are based on estimations or assumptions according to the experience or best practice of the test laboratory. They may also include manufacturer specifications or calibration results of measurement equipment, such as reference cells (RC). In combination with type u_B uncertainty, a probability shape must be considered to calculate the standard uncertainty u_i

• For a Gaussian distribution, the standard uncertainty u_i is the provided or estimated expanded uncertainty U_B divided by 2

Note: Care should be taken that the Xi uncertainty is related to the expanded (combined) uncertainty (k = 2).

• For rectangular shape, where all values in a Min-Max interval have (or are assumed to have) the same probability, the standard uncertainty u_i is the provided or estimated uncertainty u_B divided by [math]\displaystyle{ \sqrt{3} }[/math]

Spreadsheet for calculation of expanded measurement uncertainty

With this background, the working steps of measurement uncertainty analysis can be summarized as follows: a) Identification of uncertainty sources u_A or u_B, b) calculation of standard uncertainties u_i with consideration of probability shapes, c) calculation of the combined standard uncertainty u_C and expanded uncertainty U.

The document JCGM 100:2008 provides a standardized calculation sheet for expanded measurement uncertainty, which is shown in Table 1.

The sheet also contains so-called sensitivity factors c_i, which are unity if all uncertainty contributions u_i are expressed in the same units. Conversion of uncertainty contributions into other units will require the calculation of specific sensitivity factors, which can be a complex task.

Table 2: Standardized calculation table for expanded measurement uncertainty according to JCGM 100:2008 [1]

References

[1] Joint Committee for Guides in Metrology (JCGM), „JCGM 100, Evaluation of measurement – Guide to the expression of uncertainty in measurement (GUM)“, 2008