Photovoltaic generator & solar array simulator

The input source has a significant effect on interfacing converter dynamics as discussed in Chapter 2. A PVG is internally a power-limited non-linear current source having both constant-current (CC) and constant-voltage (CV) like properties depending on the operating point, which implies that the dynamics of a PV interfacing converter cannot be validated solely by using a voltage or current source as the input source. Therefore, the validation should be performed using a real PVG as the input source.

If a real PVG is to be used in the converter validation process, an artificial light source providing controllable illumination should be used to guarantee the repeatability of the measurements. This can be accomplished cost-effectively in small scale but is impractical for larger systems. Therefore, a PVG is usually replaced with a power electronic substi- tute, i.e. a solar array simulator, so that the time-invariant conditions can be guaranteed in the validation process. The input sources used in the experimental measurements were Raloss SR30-36 PV module composed of 36 series-connected monocrystalline silicon cells

illuminated by an artificial light unit and Agilent E4360A solar array simulator. The purpose of this section is to validate the theoretical analysis regarding the PVG as an input source and prove the feasibility of the used solar array simulator for later usage.

In the standard test conditions (1000 W/m2 _{irradiance, 1.5 spectrum air mass, 25} ◦

C module temperature), the Raloss PV module produces short-circuit current of 1.9 A, open-circuit voltage of 21.8 V, and maximum power of 30.8 W. The module was illuminated by a fluorescent lamp unit that was able to produce an irradiance level of approximately 500 W/m2_{yielding short-circuit current of 1.0 A and open-circuit voltage}

of 19.2 V at the module temperature of approximately 45◦

C. The MPP current of the artificially-illuminated module was 0.91 A at the voltage of 15.9 V.

The measured impedances of the Raloss PV module are shown in Fig. 4.1 in open- circuit (OC) and short-circuit (SC) conditions as well as at the MPP. The dynamic resistance rpv represents the low-frequency value of the impedance, and is the most

significant variable that will have an effect on the interfacing converter dynamics as discussed earlier. The dynamic capacitance, in turn, can be approximated from the PVG impedance (Fig. 4.1) as

cpv≈

1 2πrpvf-3dB

, (4.1)

where f-3dB is the cut-off frequency of the impedance magnitude curve. Eq. (4.1) gives

a good estimate for cpv in the CCR, since rd||rsh >> rs. In the CVR, (4.1) slightly

underestimates cpv since rd||rsh and rs are in the same order of magnitude, but is still

101 102 103 104 105 106 −20 0 20 40 60 Magnitude (dB Ω ) 101 102 103 104 105 106 −90 −45 0 45 90 Phase (deg) Frequency (Hz) OC MPP OC MPP SC SC

sufficiently accurate.

The tested commercial power electronic substitute has three different modes of oper- ation: SAS, table and fixed modes. In SAS-mode, the simulator is programmed using three reference points: short circuit current and open circuit voltage as well as current and voltage at the MPP. In the table-mode, the IV-curve is represented by voltage-current pairs with a limitation that the voltage points must be ascending and the current points descending. In fixed mode, a maximum voltage is given and the simulator operates as a voltage limited current source having rectangular IV-curve characteristics.

Measured dynamic resistances and capacitances from the Raloss PV module and the Agilent solar array simulator are shown in Figs. 4.2 and 4.3. Later on in the figures, the solar array simulator at the two different operating modes will be referred to as ‘Table’ and ‘SAS’. Based on rpvof the real PVG, it can be seen that the curve has two distinct

slopes. Because rpvis presented in dBΩ, it is clear that rpvwould be best approximated

with a two-diode (i.e. double exponential) model as opposed to the single-diode model of Fig. 2.8, although the single-diode model is sufficient in most cases in power-electronic applications (Villanueva et al., 2009). The same double-exponential characteristics are also visible in Fig. 4.3, which presents the measured dynamic capacitances.

Based on Fig. 4.2, the solar array simulator produces similar double-exponential char- acteristics in respect to rpv when it is used in the table-mode. However, its dynamic

resistance in the SAS-mode is constant in the CV region as can be seen in Fig. 4.2. This indicates that the dynamic resistance of a real PVG can be emulated with higher precision by using the table mode. The operating mode of the solar array simulator does not affect the emulated dynamic capacitance as can be seen in Fig. 4.3. The capacitance of the

0 5 10 15 20 0 10 20 30 40 50 60 70 Voltage (V) Resistance (dB Ω ) PVG SAS Table

0 5 10 15 20 −30 −20 −10 0 10 20 30 Voltage (V) Capacitance (dB µ F) PVG SAS Table

Fig. 4.3: Measured dynamic capacitances.

0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Voltage (V) Current (A) SAS Table

Fig. 4.4: Solar array simulator IV-curve comparison.

solar array simulator is considerably higher (up to 30 dBµF higher) than the capacitance of the real PVG and it does not show the double-exponential characteristics.

Fig. 4.4 presents the IV-curves of solar array simulator in SAS and table-modes. It was stated earlier that the dynamic resistance in the SAS-mode is constant in the CV region. Constant dynamic resistance implies that the IV-curve is a straight line in the CV region as can be noticed from Fig. 4.4. In table-mode, the solar array simulator produces the IV-curve correctly, and thus also the dynamic resistance as was analyzed in Section 2.4. It is worth noting that a solar array simulator can produce the dynamic resistance of a PVG correctly only if the simulator produces the IV-curve correctly when

101 102 103 104 105 106 0 20 40 60 Magnitude (dB Ω ) 101 102 103 104 105 106 −90 −45 0 45 90 Phase (deg) Frequency (Hz) Table SAS PVG CC CV

Fig. 4.5: Impedance comparison.

loaded with the specific power electronic device under test.

Figs. 4.2-4.3 compared the PVG and the electronic substitute in terms of rpv and

cpv. Fig. 4.5 presents the measured PVG and solar array simulator impedances in the

CCR and CVR of the IV-curve. By considering the impedance in the CCR, the solar array simulator shows PVG-like characteristics but with a higher capacitance up to ca. 2 kHz. The impedance in the CVR correlates up to the same frequency range. After the ca. 2 kHz frequency the solar array simulator impedance does not show similar resistive- capacitive characteristics as the real PVG does. Figs. 4.1 and 4.5 show that the phase of the PVG impedance lies between ±90◦

. A solar array simulator should show similar passive-circuit-like characteristics so that it would be justified to substitute the PVG with the solar array simulator, as is the case in Fig. 4.5. The higher capacitance of the solar array simulator can affect the behavior of a converter having small input capacitor but is small enough not to affect typical single-phase PV inverters.