In order to evaluate the performance of the PV emulator, developed according to the previously described design constraints, a simulation analysis is carried out. It exploits the association of Matlab/Simulink® environment and PLECS® (Piecewise Linear Electrical Circuit Simulation for Simulink) toolbox.
As specified in Chap. 5, PLECS® allows an actual plant, for example a power electronic circuit, to be implemented, as subsystem, while the related control is developed using standard Simulink® blocks. Its main advantage is the very short simulation time.
As for the considered application, the DC/DC buck converter has been built using PLECS® libraries, while the control algorithm has been implemented in Simulink® and directly interfaced to the circuit-based simulation model.
Figure 8.18 shows the whole implemented model, including the PV model, the DC/DC converter, and the pole placement controller.
It can be noted that, at the beginning of simulation, a constant value of reference voltage is given to the controller in an open loop mode to avoid handling high voltage error signals. This constant voltage is indicated as Vstart; after a short transient of 0.02 s the closed-loop operation is enabled.
The PV model implementation is done using the form V = f(I), to obtain the voltage reference for the DC/DC converter.
In order to correctly reproduce partial shading conditions, the whole PV model is represented as the composition of the single module models. In particular, each module is considered with its own temperature and solar irradiance.
Fig. 8.20 Circuit scheme of the DC/DC converter implemented in PLECS®
In this way, the PV plant behavior is implemented by summing the voltages of each module and the currents of parallel connected assemblies. Moreover, with reference to a single assembly, as shown in Fig. 8.16, if the current is greater than the short-circuit current of a module, the module output voltage is set to the threshold voltage of the bypass diode (Vg), otherwise the voltage is obtained by the model. This approach allows the PV assembly to be accurately analyzed under partial shading conditions.
The above described rules are summed up on the flow chart drawn in Fig. 8.19.
Figure 8.20 illustrates the PLECS® model of the DC/DC buck converter; it encompasses the output filter and its parasitic parameters. In particular, the load is
Fig. 8.22 Representation of the assembly under partial shading condition
realized by two series connected resistors where a switch, parallel connected to one of them, is used to impose a sudden variation of the load.
The PLECS® model has two inputs and three outputs. The inputs are the switching command for the IGBT, modeled as an ideal switch, and the command for the switch used to obtain the load step transition. The outputs give the inductor current, used to assess the continuous conduction mode, the output voltage, and the output current of the PV emulator.
The scheme shown in Fig. 8.18 is conceived for testing the PV emulator behavior with step load transitions and constant solar irradiance.
Other testing conditions are obviously possible, for example, step transitions of irradiance or load/irradiance variations according to a chosen profile.
The pole placement controller block is shown in detail in Fig. 8.21.
It should be observed that the values of the three gains g1, g2, and g3 are calculated according to Eq. (8.37). This calculation is done by a MATLAB® script, run before operating the PV emulator for tests.
As an example, the static I-V characteristics of a PV assembly are determined both under uniform solar irradiance of 950 W/m2 and under the partial shading condition represented in Fig. 8.22. This condition is given by two modules with an irradiance of 950 W/m2, two modules with an irradiance of 650 W/m2, and the last two with an irradiance of 250 W/m2. The obtained I-V curves are shown in Fig. 8.23.
The following tests are carried out:
• Test #1: step load transition with constant solar irradiance;
• Test #2: irradiance step transition with constant load resistance.
In Test #1 solar irradiance is set equal to 550 W/m2, while the load is switched between an initial value of 50 X, nearly corresponding to the MPP, to a final value of 75 X. Due to this transition, the operating point goes from P1 to P2 on the I-V curve corresponding to G = 550 W/m2, as illustrated in Fig. 8.24. Here, it can be noted that the sudden variation of the load resistance produces an initial quasivertical trajectory in which the operating point jumps from the straight line corresponding to the load resistance of 50 X to the straight line corresponding to the final resistance load of 75 X. Then it continues toward the final point remaining on the same line. The slight deviations from points P1 and P2 exhibited in the operating point locus are due to the switching operation of the emulator.
Fig. 8.25 Current and voltage transition, corresponding to Test #1, versus time
p3 = — 2я100 rad/s
• p3 = —2n500 rad/s
• p3 = —2P2000 rad/s
while the complex conjugate pair of poles remains unchanged.
The voltage transition has been observed in all cases, whose corresponding time domain waveforms are given in Fig. 8.27.
It is possible to observe that the first choice implies an over-damped response with a slower dynamics.
The second choice leads to an over-damped behavior and a faster dynamics. Finally, with the third choice, additional oscillations appear.
In Test #2 the load resistance is kept constant and equal to 50 X, while a step variation of the solar irradiance from 550 to 950 W/m2 is imposed.
In this case, the trajectory of the operating point goes from the I-V curve corresponding to 550 W/m2 to the I-V curve corresponding to 950 W/m2, remaining on the straight line imposed by the load resistance.
This trajectory is shown in Fig. 8.28, where the slight deviations from points p and P2 exhibited in the operating point locus are due to the switching operation of the emulator.
The voltage and current transitions in Test #2, versus time, are plotted in Fig. 8.29.
A zoom of these transitions is drawn in Fig. 8.30, where, differently from Test #1, it can be noted both the current and voltage variations follow practically the same variation trend with a rise time of about 10 ms.
Fig. 8.31 Principle block diagram of the PV emulator