Weather files

One of the main input data used for the simulation of a PV system is the weather file containing the irradiance data. For calculation time reasons, the weather files used cover no more than one year, and give different values such as temperatures, irradiance, and precipitation on an hourly basis. The way to summarize weather characteristics in a one-year file depends on the purpose of the weather file. For example, it can be constructed for representing a typical year – like TMY (Typical Meteorological Year), IWEC (International Weather for Energy Calculations) and CWEC (Canadian Weather for Energy Calculations) files – which thus reduces the presence of extreme conditions in the data (Wilcox & Marion, 2008). Therefore, this type of file should not be used in a case of worst-conditions sizing. Note that TMY files were developed by the NREL based on the algorithm created by Sandia National Laboratories, and this algorithm became a standard also used in IWEC and CWEC construction (CWEC, 2016 ; Figure 1.2: General inputs and models used in a PVPS modeling process Skeiker, 2007). On the opposite, special data can be built for representing extreme weather condition on one year, but these weather are not as common. (Nik & Arfvidsson, 2017) Even before being processed in a one-year data, the data can be obtained by different means, yielding different biases in the final result.

Three main families of data gathering strategies can be drawn: direct measurement, which are usually processed in Typical Year (TY) weather files; space interpolation, which uses the measurement files of the closest locations around to interpolate the weather of the considered place; and satellite observation, which relies on some indicators measured by meteorological satellites like the clearness index to infer the irradiance on the ground level (Al-Mofeez, Numan, Alshaibani, & Al-Maziad, 2012 ; Kumar & Umanand, 2005). (Monteoliva, Villalba, & Pattini, 2017) studied three TY weather files coming from either satellites or ground stations measurements for the region of Mendoza in Argentina. They found that the mean yearly Global Horizontal Irradiance (GHI) could vary up to 8.3% between the data and could vary up to 15% in the case of Direct Normal Irradiance (DNI) and Diffuse Horizontal Irradiance (DHI) taken aside.

(Remund, 2008) processed the same analysis between data coming from ground measurements and from space interpolation given by the software Meteonorm. He found that the relative error on GHI values was comprised between 3.1% and 11%. For DHI and DNI, the mean relative errors were respectively 7.3% and 5.4%. (Skeiker, 2007) ran a similar analysis by comparing TY weather files constructed from the same weather data records but with different algorithms. The researcher found that different algorithms could induce a relative difference between each other up to 8% for GHI data. Eventually it is stated that the algorithm inducing the smallest relative error is the one from Sandia National Laboratories. (Kou, Klein, & Beckman, 1998) compared the throughput of a PVPS according to two hourly weather files, one coming from measured data (TY weather data) and the other generated from clearness index following a procedure proposed in the first edition of (Duffie & Beckman, 2013). It is found that the Root Mean Square Error (RMSE) in flow rate output between the two simulations ranges only from 3 to 6%. Nevertheless, this fairly good relative difference has to be considered with care because the authors used a pump model which was found to introduce important uncertainties as discussed in 1.2.3.1. In this same research work, the use of monthly averaged weather data is shown not to be suitable for PVPS simulation as it can widely underestimate the total volume pumped. Previously discussed results are gathered in Table 1.1.

Empirical approaches

These approaches consist in fitting curves for the existing pump data, and then to use these curves to interpolate and extrapolate extra points. Therefore, the pump data must be complete enough to ensure a correct curve fitting. This complete data can be given by the manufacturer of the pump or can be obtained by some tests run on the pump prior to the modeling or sizing. As the manufacturer rarely give enough data, except some companies like (SunPumps, s.d.), the researchers have to carry out tests on the pump before the study in most cases (Hadj Arab, Benghanem, & Chenlo, 2006 ; Hamidat & Benyoucef, 2008 ; Jafar, 2000). Once the pump data is complete enough, the following approaches can be applied. A typical pump datasheet can be found in Figure 1.6. It contains the flow rate Q and the current I drawn for different voltage and for different head. In total, it gives a certain amount of points (TDH, V, I, Q) that can be used later. In Figure 1.6, three voltages and seven heads are given, resulting in 21 points (TDH, V, I, Q).

a. Kou’s model (Kou et al., 1998) determine the function V=f1 (I, TDH) and Q=f2 (V, TDH) from manufacturer’s data. To obtain these two functions, they fit the data with a 3rd order polynomial with cross terms. The resulting multivariate polynomial functions f1 and f2 have the form of equation 1.6.1.6) As the functions f1 and f2 are third order polynomials on I and TDH, it means that the pump data needs to provide information for at least four different voltages and heads, and needs to have a total of at least 16 points (TDH, I, V, Q) in order to yield a correct curve fit. Jahnig (Jahnig D., Klein S.A., & Beckman W.A., 1998) investigated this model for validation. He found a significant discrepancy between expected flow rates and measured flow rates. The relative error is around 20-40% for high irradiance and could even be infinite for irradiance levels below 550W/m2. The authors explain the difference by incorrect data given by the pump manufacturer, but the author did not investigate the model with corrected pump data, so it is not possible to decorrelate the error from the model and the error from the incorrect pump data. It is also stated that at least 10% of the discrepancy comes from the four parameters singlediode model used for PV prediction. As this single-diode model is now outdated, some improvements could be expected with Kou & al.’s model. The same model is used later by (Martiré, Glaize, Joubert, & Rouvière, 2008) for modeling f2 only. In their paper, the authors fit an affinity law in order to get an algebraic equation more convenient to use. Equation f1 is useless in this case as the electric power is processed through a MPPT. Indeed, it is considered that the electric power is always maximised. The resulting relative errors between predicted and measured flow rates are about 15% in the morning, and stabilize around 5% during the day, at the time the pump operates in steady state.

b. Hadj Arab’s model Hadj Arab (Hadj Arab et al., 2006) and Djoudi Gherbi (Djoudi Gherbi, Hadj Arab, & Salhi, 2017) propose another empirical model for modeling the pumps. Even though their research relies on data obtained by tests made on the pump in their laboratory, it can also be used on manufacturer’s data if the data set is complete enough. This model proposes to use a linear equation for I-V curve of pump, corresponding to f1: 𝐼 = 𝑎 + 𝑏 ∗ 𝑉 (1.7) The flow rate Q is dependent on voltage V through a quadratic equation, corresponding to f2: 𝑄 = 𝑐 + 𝑑 ∗ 𝑉 + 𝑒 ∗ 𝑉􀬶 Eventually, all coefficients a, b, c, d, e are dependent on TDH following either a quadratic (Hadj Arab et al., 2006) or cubic equation (Djoudi Gherbi et al., 2017):  (1.9) In order to apply the model to a pump, the data requires at least three voltages and four different heads, for a total of at least 12 points (TDH, P, Q) and 8 points (TDH, I, V), or 12 points (TDH, I, V, Q). The model has been tested by the researchers on two centrifugal and two positive displacement pumps. When considering a quadratic equation for the variation of the coefficients with head, the relative error between model and measures remains below 14% for all heads on centrifugal pumps, and below 5% for positive displacement ones. When the input data of the model is reduced to the minimum of nine points, the model still manages to fit the measurements, adding only a maximum of 5% to the relative error. When considering a cubic equation for the variation of the coefficients, the relative error diminishes below 10% for all heads on centrifugal pumps and remains below 4% for positive displacement pumps. In this case the input data needs to be complete, as a higher order of polynomial regression obviously requires more data points for the fitting.