**Introduction**

Solar PV module is the biggest cost component of the PV plant capex. Depending on the module cost its percentage varies 50-55% of total plant capex. The module is priced as Rs./Wp or $/Wp. It is, therefore, important for the buyers to ensure that they get the exact wattage that they have paid for. However, determination of total wattage received by the buyer is fraught with the measurement uncertainty. Needless to say, all measurement gauges have measurement uncertainty and measurement of module wattage is, therefore, no exception. The impact of receiving wattages lower than the aggregate sum of nameplate module wattages not only has the consequence of paying more upfront than the contract value, but the life-time generation and revenue loss. It is estimated that receipt of 0.1% lower wattage in 100 MWp capacity entails loss of Rs.59 lacs or 5.9 million on NPV basis at a conservative generation estimate of 1.6 mn units/MWp, tariff of Rs.2.5/unit, yearly degradation of 0.4%, module price of Rs.18/Wp and discount rate of 8%. In addition, it may be mentioned that most modules come with positive wattage tolerance and nil negative tolerance. In case, the OEMs specification sheet gives a positive tolerance of 3% then the engineer responsible for estimating the annual energy yield considers one-quarter of it i.e., -0.75% as the module quality gain in place of loss in the PVsyst yield simulation. In a situation where the received wattage is lower than the plant capacity considered for PVsyst analysis, the problem gets compounded because of module quality gain assumption.

**Measurement System**

The wattage of the module is measured under Standard Test Condition (STC) as per IEC 60904 standard using a Sun Simulator and more commonly known as Flash Tester. STC condition means testing of modules at AM1.5 spectral irradiance, 25oC device temperature and 1000 W/m2 irradiance. The test method is generally known as flash test. This involves a light source whose spectrum closely matches with that of sun and gives off desired irradiance of 1000 W/m2 while the cell temperature of module is maintained at 25oC. For any variance in cell temperature, a correction is applied to the measured power, basis temperature coefficient of power for the module under test. Generally, Xenon lamp is used as a light source. However, depending on how closely the spectrum of Xenon lamp matches to the Sun, uniformity of irradiance over the module area and temporal stability, the flash testers are categorized in different classes, namely, A+, A, B and C. For ready reference, the values of various parameters for different flash testers are given in table 1.

Table 1: Solar Simulator classification based on characterizing parameters

A+ simulator is in the 300-1200 nm (1 nm=10-9 m), whereas all others are in the wavelength range of 400-1100 nm. In industry, mainly AAA simulators are used having a measurement uncertainty of ±3%. Total uncertainty is the square root of the sum of squares of various sensors uncertainty, such as xenon lamp, temperature, ammeter and voltmeter, etc. The major uncertainty is contributed by the light source as ammeter, voltmeter and temperature sensors have very low level of uncertainty. ±3% uncertainty means that the true value of the module wattage lies within a band of ±3% of the measured value. For example, if the measured wattage of module is 300 Wp and flash tester has a measurement uncertainty of ±3% then the true module wattage may lie in the range of 291-309 Wp. The accuracy of the flash tester is ascertained by frequent calibration using a module which is traceable to a gold standard. It is expected that flash tester is calibrated at least once per shift. The precision of the flash tester is ensured by a Standard Operating Procedure (SOP). SOP helps in reducing the variance in module wattage, if the test is performed multiple times on the same module. However, calibration and SOP cannot help in reducing the uncertainty which is intrinsic to the gauge.

In the above backdrop of gauge uncertainty, one must satisfy oneself that the total wattage received is not lower than what one paid for. Most module manufacturers offer nil negative power tolerance and 3% positive tolerance. If the measurement system itself has an uncertainty of 3%, how can one be sure of having received the right wattage. The manufacturers normally provide flash test data of all modules, and the values are always more than the rated wattage of modules. So, if one adds up wattage of all modules without considering the measurement uncertainty, one will always get total wattage more than the wattage obtained by simple multiplication of nominal power rating of module with number of modules. In a situation like this there are no simple answers, and one must resort to statistical analysis of flash test data.

**Data Analytics**

Module manufacturer shares the flash test data of all modules. If the ordered quantity is large, then the module manufacturing is spread over multiple shifts and possibly for many days. In manufacturing there are common cause and special cause variations. Common causes such intrinsic variability in cell quality and other bill of materials will produce modules of wattage which will have a gaussian distribution. However, special causes may produce modules of wattages predominantly either in lower or higher wattage bin. Thus, by plotting the histogram of module wattage in a lot and comparing it with a lot of similar size produced at different time one can judge the stability of the process. In this context it is pertinent to invoke the concept of process capability index (Cpk). Cpk is defined as:

Here, mean is the average module wattage of either one container or a lot or that of entire lot and σ is the standard deviation. If the measurement uncertainty is more than the standard deviation of the module lot, then higher of the two is taken as σ. The LSL and USL are the lower specification limit and upper specification limit, respectively. The specification limits are generally defined by the purchaser. Let us say that the buyer agrees to purchase modules of 320 Wp nominal wattage and the supply agreement mandates nil negative tolerance and +3% positive tolerance, then the LSL and USL are 320 Wp and 329.6 Wp, respectively. Cpk denotes the process performance and ideally shall be greater than 1. However, in this case because measurement system uncertainty overrides product variability, it is not possible to comment on the process. To comment on the product or process variability, the gauge variability shall be lower than the process variability.

Assuming that the mean wattage of the modules in a Lot is normally distributed, one can find out the probability of number of modules having wattages above the USL and the probability of number of modules having wattages below LSL. For this estimation one has to use the Z-table, where Z is defined as:

Thus, the area between the mean module wattage and USL (329.6 Wp) can be estimated using a standard deviation of 3, the measurement uncertainty. After calculating the Z value one can find out the total area between mean and USL by looking up the Z table. Since 50% area of a gaussian curve is on either side of the mean, subtracting the area so calculated from 50% gives the % modules having wattage above USL or 329.6 Wp. Similarly, one can estimate the area of the curve below 320 Wp. If the area above the 329.6 Wp outweighs are below 320 Wp then one can be reasonably confident of having received total wattage not below the contracted wattage. This is illustrated with the help of a case history. This assumes that module wattage has a Gaussian distribution.

**Case History**

A developer placed order for 25.1 MWp modules of 320 Wp. The agreement with the vendor was 100% 320 Wp modules with nil negative and 3% positive tolerance. The purchase agreement mentioned 3% measurement uncertainty of the measuring system. The modules were supplied in 5 lots. The flash test data for all modules (total 78544 Nos.) was provided basis which the average wattage and standard deviation of wattage for each lot was estimated and same is given in table 2.

Table 2: Snapshot of the supplied modules

Randomly one of the containers containing 632 modules was selected and histogram of module wattage was plotted, shown in the fig.1. The histogram is skewed towards the lower wattage.

Fig. 1: Flash test wattage of 320 Wp nameplate 632 nos. modules contained in single Container.

Likewise, the average wattage of each container was calculated, and histogram of average wattage was plotted, shown in fig.2. It can be seen that there is no uniform trend in module wattage mean of various containers in each lot.

Fig.2: Histogram of module wattage mean of containers in various lots

The histogram of all mean wattage of all containers is finally plotted in fig 3. This also does not show an expected ideal gaussian distribution despite sample size being large. The total number of modules is 78544 nos. shipped in 125 containers. The average wattage of all the containers combined is 323.97 Wp with a standard deviation of 1.7 Wp. 58.4% containers have the mean module wattage higher than 323.7 Wp

Fig.3: Histogram of mean module wattage of 125 containers having 78544 nos. modules

**Conclusions**

Using the mean wattage of each lot and for the entire lot, the percentages of modules within the specified range i.e., 320-329.6 Wp as well as below 320 Wp and above 329.6 Wp was estimated to ascertain that total wattage received was not below the contracted quantity. The summary of calculation is given in table 3

Table 3 Summary of module wattage distribution

From the table it is evident that percentage of modules above 329.6 Wp far outweigh than the module percentage below 320 Wp. However, it may be mentioned that here is assumption is that module wattages are normally distributed about the mean value. Furthermore, the nominal wattage of entire module lot of 78544 nos works out to be 25.13 MWp. However, considering the mean wattage of each container, the estimated wattage is 25.45 MWp i.e., 1.24% higher. In PVsyst analysis if the module tolerance is 3% positive and nil negative then the module quality loss factor is taken -0.75%, which corresponds to gain and this analysis supports the assumption.

**About Author**

**Amitabh Verma** has been associated with Renewable Industry since 2006 and, has varied experience. After having superannuated from Aditya Birla Renewables in 2022 as CEO and CTO, he worked as Advisor to Aditya Birla Renewables business for 2 years.