Comportamiento General Desarrollo a Escala Humana
2.2 Desarrollo Comunitario
Assessment models can be used to supervise the performance of the solar power plants. As proposed in (Mart´ınez Marchena I, 2014), evaluation parameters can be implemented easily as performance indexes: daily final yield and daily enegy balances (daily energy produced and daily energy forecasted).
The daily final yield, Yf,day, is defined as the useful output energy of the PV
per kWp installed:
Yf,day =
Eday
PST C
7.2. ASSESSING PHOTOVOLTAIC FACILITIES 127 where PST Cis the nominal power of the installed photovoltaic array at standard
test conditions (1 kM/m2 of solar irradiance and 25°cell temperature).
The useful daily output energy or daily energy supplied by a solar power plant is defined as: Eday = Z day PAC(t)d(t) ≈ n X j=1 PACj ∆t (7.2)
where n is the number of measurements along the day and PACj are the recorded values of the power generated at the inverter output.
The proposal is to assess photovoltaic facilities in two phases. In the first phase, the evaluation is done by comparing the values obtained for the daily final yield and the useful daily output energy when they are estimated using two different methods. On the one hand, these values are estimated directly using the recorded values in the inverter. In the other hand, these parameters are estimated using a model for the performance of photovoltaic plant and the forecasted values of hourly global radiation. In this phase only daily values are compared. Taking into account the results of this comparison, a second phase could be activated in order to compare hourly values.
7.2.1
Models for estimating the performance of a PV sys-
tem
As it has been reported previously, see for instance Ayompe et al. (2011), the inverter power output has a linear relationship with solar irradiance if it is not considered the effect of the temperature. This fact can be observed in Fig. 7.2.
We propose to include this effect in the model that allows to estimate the hourly energy generated at the output of the inverter (Eh∗) as an extension of the estimation of the power generated (PAC∗ ), according to the expression:
Eh∗ = Eh,ST C
G∗h,β
1000(1 + γ(Th,mod− 25))GL (7.3) where, G∗h,β is the forecasted hourly global radiation on the surface of the modules, β is the inclination of the modules, γ is the temperature coefficient of
128 7. MONITORING PV PLANTS
Figure 7.2: Instantaneous values of solar radiation and photovoltaic power
Pm, Th,mod is the mean hourly module temperature and GL is the global losses
coefficient of the system. Eq.7.3 is obtained from the expression proposed by Osterwald (1986) considering hourly values. The proposed expression includes not only the losses produced by the temperature but also other losses (soiling, spectral losses and so on).
The predictions of hourly global radiation on the surface of the modules are estimated in the following way:
1. Forecasting the hourly global radiation values on horizontal surface with the model proposed in Chapter 6.2.2 and meteorological variables recorded by weather agencies.
2. Obtaining the values of direct, diffuse and reflected hourly global radiation on horizontal surface.
3. Obtaining the values of global radiation on the surface of the modules.
The results obtained with this model can be used for estimating the daily energy supplied to the grid, Eday∗ , which is calculated using the expression 7.4:
7.2. ASSESSING PHOTOVOLTAIC FACILITIES 129 Eday∗ = Z day PAC∗ (t)d(t) ≈ n X j=1 Eh∗(j) (7.4)
where n is the number of hours for a day.
The proper operation of plants can be evaluated by comparing the values of Eday∗ with the values of daily energy produced, Eday, obtained with Eq.7.2.
Similarly, for detecting problems in plants operation the value of daily final yield, Eq.7.1, has been compared to the estimated daily final yield, Yf,day∗ , calcu- lated with the expression 7.5:
Yf,day∗ = E
∗ day
PST C
(7.5)
7.2.2
Statistical models for assessing solar plants
With the estimated values described in the previous section and the corre- sponding measured values, the system is capable of checking the performance of the plants by using the methodology described in (Mart´ınez Marchena I, 2014). The mean values of previously described parameters for photovoltaic solar plants of the same technology (modules and inverters) has been estimated as the standard deviation of them. For evaluating the operation of each plant, a statistical anal- ysis of the differences between the values of estimated parameters and measured parameters is implemented. Thus, for each new recorded or calculated value of some parameter X and its corresponding estimation, X∗, at hour i the difference among them is analyzed according to the criteria (significance level 5%):
d(i)X = X(i)− X∗(i);
if d(i)X ∈ [−1.96ˆ/ σ, +1.96ˆσ] then mark (i), (7.6)
where ˆσ is the sample standard deviation of X. All the marked values (i ) will indicate problems of operation.
130 7. MONITORING PV PLANTS Ed∗(i), the criteria is as follows:
d(i)P AC = E (i) d − E ∗(i) d ; if d(i)P
AC ∈ [−1.96ˆ/ σ, +1.96ˆσ] then mark (i),
(7.7)
For the daily final yield, Yf,day, the expression used to decide if there is any
operation problem taking into account the expression Eq.7.6 particularized for this parameter is the following:
d(i)Y f,day = Y (i) f,day− Y ∗(i) f,day; if d(i)Y
f,day ∈ [−1.96ˆ/ σ, +1.96ˆσ] then mark (i),
(7.8)
Fig. 7.3 shows the algorithm description for the daily assessment of a PV plant. Recorded measures are used as input and estimated measures are calculated from these inputs. Then a test is performed to check if the difference between measured and estimated daily yield is statistically significant. If these values are statistically equals (for a specified significance level) the algorithm ends without detecting problems, while if they are different, each hourly value obtained from recorded power values is compared with the corresponding estimated and if the difference is statistically significant, the corresponding hour is marked. The algorithm ends with operational problems detected and the marked hours are returned.