# Category Photovoltaics for Rural Development in Latin America: A Quarter Century of Lessons Learned

## Sensitivity analysis

The sensitivity analysis consists in performing several simulation runs by oscillating each parameter according to a sinusoid over its range of interest. Analyzing the spectrum (Fourier transform or power spectral density) of the output, identification of the most influential factors can be easily derived (Mara, 2000); (Mara et al., 2000); (Mara, 2002).

The proposed FAST method (Fast Fourier Amplitude Transform) uses a sinusoidal sampling of parameters around their base value, each parameter having its own frequency, the variation being applied to a simulation on the other as shown in fig. 12...

## Empirical validation

In order to improve the PV model, a comparison has been made between measurements and simulation data (see fig. 11) for the case of the PV panel with a confined air layer. In previous articles, the ISOLAB code has already been validated in many cases by comparisons with other building simulation codes, as well as experimental validations. This comparisons can show advantages and disadvantages of the model. In figures presented below, the main temperatures are compared for the previous cell.

 Fig. 11. Temperatures of the PV installation with a confined air layer.

For the temperatures obtained for the body of the cell, a good agreement is obtained, the average difference of temperature being weak, of the order of 1°C...

## Validation

2.6 Overview

Building simulation codes are useful to point out the energetic behaviour of a building as a function of given inputs. The steps involved in this process depend on a mathematical model, which is considered a global model because it involves several so-called elementary models (conductive, convective, radiative, etc.). Therefore the validation procedure will involve verifying not only the elementary models, but also their coupling, as the building model can be seen as the coupling of a given combination of elementary models.

For several years a common international validation methodology has been developed, which, among others, has led to Anglo-French cooperation...

## Data acquisition sensors and errors

The data measured in this experiment are inside surface temperatures of walls and roof, air temperatures, and heat flux through each roofs (see fig 10). The global error of these measurement equipments (sensors and data acquisition system) is about one degree Celsius (±1°C) for the temperature and ±10% for the heat flux (Miranville, 2002). The last study made with this equipment dating for one year, it was necessary to calibrate the equipment. This was done by running a calibration procedure consisting in determining the calibration coefficient allowing the correct inter-comparison of the response of the cells.

## Experimentation of BIPV

2.5 A dedicated experimental platform

In order to apply the preceding combined methodology, a dedicated experimental platform was set up, in field environment. It is indeed very important to be able to determine the physical behaviour of the whole building equipped with the BIPV or the BAPV, under realistic conditions. For this, the experimental platform includes several cells, facing north, and fully instrumented. A meteorological station is also integrated, to allow the measurement of the climatic conditions of the location. The cells are of two types. A large scale test cell, named LGI, is used to represent typical conditions of a real building and its thermal response. Four other cells (ISOTEST cells) are installed on the platform, reduced size and dedicated to the
simultaneous comparis...

## Derivation of the problem

The « ray tracing » method is a model that can describe radiative exchanges in semitransparent mediums. In this work, the model was inspired of Robert Siegel works (Siegel, 1992). This model consists on a net radiative balance of fluxes at each layer of material. As its name suggests, a ray of light will be followed and dispatched every time it will meet a new material surface (see Fig 4). With each new surface it encounters, the ray will be divided into three parts until meeting an opaque layer: the flux absorbed by the layer
encountered, the flux transmitted through this layer, and the flux reflected by this layer to the layer where the ray comes from. These phenomena are reproduced until encounter an opaque layer (the layer N where т > 0 on Fig. 4).

A system describing radiative flux ...

## Thermal phenomena and assumptions

The walls are modelled layer by layer. The goal is to find the energy transfer across the solar system and its coupling with the building, it is not necessary to model finely phenomena. In addition, the coupling of the wall model with the PV will be done with an existing code, named ISOLAB (Miranville, 2003). This code models each type of walls in the same manner, by reducing the thermal problem at the scale of the material layer.

ISOLAB is a building simulation code able to predict the heat and mass transfer in buildings according to a nodal 1D description of the building and its corresponding thermo-physical and geometrical parameters...