The output of grid-connected PV systems is the output from the PV array less the losses in the inverter. The output from the PV array has been considered in detail in this chapter, and the performance of inverters is described in Chapter 19. As far as inverters are concerned, it is important to account for the fact that the instantaneous efficiency ny depends on the ratio between the actual power delivered to the grid PAC, and the rated power of the inverter, PIMAx. This dependence may be represented by [80]
where p = PAC/PIMAx and k0, ki1 and ki2 are parameters characteristic of the inverter defining its electrical behaviour. k0 is the quiescent power consumption, k;1 represents the losses that depend linearly on the current (voltage drop across diodes, etc.) and ki2 represents the losses that depend on the square of the current (resistive losses, etc.). These parameters can be obtained from the inverter efficiency curve. Depending on quality level, input voltage and rated power, the loss parameters of existing inverters have a spread of more than a factor of 10. As an example, k0 = 0.35,ki1 = 0.5 and ki2 = 1 correspond to very good inverters leading to 95% typical energy efficiency.
Standard methods for performance analysis of PV grid-connected plants have been introduced in the JRC Ispra Guidelines [81], extended and improved by HTA Burgdorf [82]. Global performance is appropriately described by the so-called performance ratio (PR), which is the ratio of AC energy delivered to the grid, EAC, to the energy production of an ideal, lossless PV plant with 25 °C cell temperature and the same solar irradiation. This gives a good indication of how much of the ideally available PV energy has actually been generated. It is given by
EAC
PR = Г <ft rA————— (22’89)
°y (P’a) n*
Qt ‘ ГМ
Other interesting parameters are the reference yield, Yr = Gy(fi, a)/G*, the array yield, Ya = Edc/PM, where Edc is the DC energy generated by the PV array, and the final yield, Yf = Eac/PM. All three have units of time, and allow us to distinguish between the losses due to the PV array, and the losses associated with the inverter and to the operation of the system. Capture losses, LC = Yr – Ya, are defined as the energy losses, expressed in hours per day of PV array operation at STC power output, caused by: cell temperatures higher than 25 °C, losses in wiring and protection diodes, poor module performance at low irradiance, partial shading, snow and ice coverage, module mismatch, operation of the array at a voltage other than its maximum power point, and spectral and angular losses. System losses, LS = Ya – Yf, are the losses due to inverter inefficiencies. It must be noted that PR = Yf/Yr. Again, it must be noted that Yr can be understood as equivalent to ‘sun-hours’ of full sunlight at 1 kW/m2. This way, the energy yield of the PV array is just given by the product of these ‘sun-hours’ by the PR.
Energy losses in very good PV grid-connected systems without significant shading are about LC = 15% and LS = 7%, which lead to PR & 0.78. A value of PR = 0.75 is sometimes [13] recommended for quick estimation of yearly energy production.
Example: Estimate the energy yield of a grid connected PV plant at Albuquerque, USA, having a fixed position and optimally tilted generator. The solution is:
Equation (22.89) ^ EAC/PM* = PR. GY(Popt)/G*, where GY(eopt) can be obtained by the product 365 x [column 3 x column 4 x column 8]. In this way:
GY(eopt) = 2441 kWh/m2 (or 2441 sun-hours); PR = 0.75 ^ EAC/PM* = 1831 kW h/kW. It must be mentioned that this place, with Gy (0) = 2104 kW h/m2 [365 x column 3 x column 4] is extremely fortunate, regarding solar energy availability. Because of that, tracking energy gains are very large. For example, a two-axis tracking free of shading collects up to 47% more radiation that the previously considered fix and optimally tilted surface.
Reported experimental PR values [83-86] range from 0.65 to 0.8. The main reason for PR reduction is that the actual power of installed PV arrays is sometimes below the rated power declared by the manufactures. As a representative case, Figure 22.28 describes the actual power measured by the IES-UPM at big grid-connected plants installed in Spain. The figure presents the histogram of corresponding peak power deviations (actual versus rated). Regrettably, actual power even below 90% of the rated values is still found at real installations.
Frequency (%) Arrays with P* > 100 kW
20
18
16
Deviation respect nominal power (%)
Frequency (%)
All P* IP* < 100 kW IP* > 100 kW
|
Mean = -6,1 % Mean = -6,4 % Mean = -5,6 % |
||
|
Standard deviation = 4,0 Standard deviation = 3, |
8 Standard deviation = 4,2 |
|
|
1 |
||
|
1 и 1 / |
||
0
Deviation respect nominal power (%)
Figure 22.28 Real versus rated power at big PV plants installed in Spain between 2007 and 2009. Total peak power is about 200 MW
|
Table 22.8 Power distribution of the yearly irradiation for a low and a high latitude location
|
Equation (22.89) is given in yearly terms. However, the PR is a rather general concept, so that PR values can also be obtained for any other period. It is worth noting that, mainly because dependence on solar cell temperature and shading, PR is far of being an invariant. Hence, to measure the PR during a certain period of time, for example, a month or a week, and, then, to apply the corresponding value to a longer period, for example, a year, is simply wrong.
