In the history of metrology, ideas concerning problems of current importance, as well as methods of their solution, have qualitatively changed more than once. Such changes are caused by new requirements for industry and society at each stage of development. These changes were taken into account in the revision of metrological legislative acts and regulations [1] .

Systematic effects are the most critical issue in measurement, especially in the metrological field, since their effect on the measured values and on the resulting total uncertainty are often dominant. In this respect, and considered the use of PV systems for electric power generation, it is necessary metrological suitability of the equipment used in the tests [2] .

The main purpose of this paper is to attest to the quality of the measurements carried out during the performance tests of the Sunflower prototype, evaluating the uncertainty of measurements collected through the measurements equipment, such as DDM (digital multi meter) [3] [4] .

The assessment begins with a brief introduction to the concept of basic greatness and influence. The third chapter introduces the boundary conditions during the period of measurements, detailed description of the measurements performed with the Sunflower prototype. The fourth chapter introduces all the components and assessment of uncertainty in measurement of electrical current and voltage, and, in the fifth chapter introduces the assessment of uncertainty in measurement of electrical power. Finally in the sixth chapter an analysis of conclusion is introduced, highlighting the applicability of method used.

In the PV panels, the electricity transduction occurs through the photon effect and greatest power converted, expressed in watts. It is known that electric power can be expressed in various ways, but most commonly is treated [5] .

where the voltage is expressed in volts, current in ampere and the angle is the electric discrepancy between voltage and current. When it is to resistive impedance, the reactances are despicable and the angle is approximately zero and Equation (1) results in [5] .

In this way, the voltage and electric current are the values of influence on measurement and metrological evaluation of power [5] [6] . It is essential to determine the correlation between the three variables,

because the measurements of voltage and electrical current, were performed directly with DMM. The power was not obtained from direct measurements, was obtained, indirectly, by use of Equation (2), full details of the locations and conditions of the tests performed in sunflower prototype are introduced in the paper [3] [4] .

The measurements carried out on the Sunflower prototype, voltage and electrical current, were performed in the tracking and static mode, will be adopted the following notation conventions, as follows: voltage tracking mode, voltage static mode, electric current tracking mode, electric current static mode. Figure 1 and Figure 2, demonstrate the Sunflower prototype and PV panels, in the field test [3] [4] .

The measurements of voltage and electric current were performed from 06:00 am to 06:00 pm at intervals of 10 and 10 minutes, during 5 days. Figure 3 introduce to the graph of voltage measurement, for both, tracking and static mode, during 12 hours in 5 days [3] [4] .

Figure 4, introduce to the graph of electric current measurement, for both, tracking and static mode, from 06:00 am to 06:00 pm at intervals of 10 and 10 minutes, during 12 hours in 5 days [3] [4] .

The measurements of voltage and electric current were practically constant, with low oscillation, over the period from 7:10 am to 04:00 pm, other data (outliers) were discarded at the discretion of standardization, expressed by Equation (3) [7] - [9] .

where is the average value of the measurements and is the standard deviation of measurements. In this way, the values considered “outliers” resulted in the, it may be presented as zero or negative [7] - [9] .

The expression of measurement uncertainty of a quantity takes into account, several components of uncertainty, which are classified, such as, “A” and “B”. Basically, the difference is in the evaluation of statistical reasoning of components of uncertainty [1] [2] . As mentioned, both the voltage and electric current was measured directly through DMMs, soon, the values can be expressed by Equations (4a) and (4b) [9] [10] .

In order to facilitate theoretical exposure, considers the generic notation, express by Equation (5) [7] - [9] .

where,. The value, expresses the arithmetic average of greatness or, which can be express by Equation (6) [7] - [9] .

where is the set of n measured values using a DMM. The portion from Equation (5), represents the expanded uncertainty and can be express by Equation (7) [7] - [9] .

where refers to the coverage factor obtained from [10] , to a level of confidence of 95.45% and refers to the combined uncertainty, calculated by quadratic combination of all measurement uncertainty components. Equation (8) illustrates the portions of component [7] - [9] .

The factor refers to the sensitivity coefficients of each portion of the combined uncertainty with respect to the measured. When this value is unknown, considers the worst case, which is unitary. The represents the “” portions of uncertainty components, which are express by Equation (9) [7] - [9] .

where:

Ø , component type “A”, related to measurements carried out;

Ø , component type “B”, related to the percentage of the output as read on the DMM and the offset from the DMM, in accordance with the manufacturer’s specifications;

Ø , component type “B”, related to the resolution of the DMM;

Ø , component type “B”, related the manufacturer specification of the PV cell;

Ø , component type “B”, related to the resolution of the PV cell.

The component is express by Equation (10).

The components and are obtained by specifications contained, respectively, in the manuals of the DMM and manufacturers of PV cells, whose distributions are rectangular [11] . The components and

are obtained, respectively, of the resolutions of the DMM and PV cells, whose distributions also are rectangular. Table 1, contains the values of each component, both for voltage and electrical current and both the operating modes, tracking and static [12] [13] .

Once calculated the components of uncertainty and the combined uncertainty of each of the variables, both for tracking and static mode, the next step is to calculate the effective degrees of liberty, by Equation (11) [12] .

In this present value, analysis will depend, primarily, of the component in all 4 scenarios analysed (VTracking, Itracking, Vstatic, Istatic). Therefore, Table 2, presented the values obtained for, , , , and, finally, the expression of measurement uncertainty for the situations mentioned.

The algebraic expression that relates voltage and current is express by Equation (2) and the electric power values were determined by calculations involving the quantities and. In this scenario, for the determination of electric power values related to values of correlated quantities, it is necessary the use of covariance resource for determining the uncertainty of measurement of electrical power. The following Equation (12) expresses the cal- culation for correlated quantities [7] [13] .

Measurement uncertainties are estimated for both Ptracking (correlates Vtracking and Itracking) and Pstatic (correlates Vstatic and Istatic). It is considered the experimental average and the experimental standard deviation to express the uncertainties of electrical power from the PV panel. Table 3 presented the average values ob- tained for power electrical, the correlation coefficients, the combined uncertainties, the factors included and their uncertainties.

The metrological analysis of the Sunflower Prototype, method presented in this paper concerns the specific data of the measurements carried out during the performance tests. The methodology, presented in the paper, for testing and describing the metrological properties of the measurements collected though the measurements equipment’s, and introducing methods to minimize uncertainties of measurement equipment in the PV systems. The determination of the distribution for an output quantity, using the propagation of distributions, through a DDM, proved to be appropriate. The concepts of probability theory provide a unique, self-consistent method for quantitative reasoning given incomplete information. In the case of measurement data evaluation, they permit the rigorous treatment of non-linear measurement models that, for particular reasons, cannot validly be linearized.

It is possible to decrease the measurement uncertainty through the following factors:

・ Decrease the time interval considered as representative measurements carried out, taking into account only the 4 hours of greater solar intensity, which would imply in the range of measured from 30 to 35 values. This reduced of the sample space would allow them to be used the methods of Dixon, Cochran and Grubbs to determining the outliers;

・ Using DMMs with 5½ or 6½ digit, to decrease the component type A of measurement uncertainty and even the component type B, concerning the resolution of the instrument.

The powers (Ptracking and Pstatic) were not measures, were obtained through calculations performed with the measures of V and I, which makes the measurement uncertainty of power be calculated through correlation of variables. It is possible to decrease the uncertainty of measurement of power, replacing the indirect for direct methodology, i.e. made using energy meters or wattímetros.

The authors would like to thank The Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), The Department of Communications (DECOM), The Faculty of Electrical Engineering and Computing (FEEC) and The State University of Campinas (Unicamp), for their support in the development this research.