This example shows the operation of a typical transformerless photovoltaic (PV) residential system connected to the electrical utility grid.
The SPS PV array model implements a PV array built of series- and parallel-connected PV modules. It allows modeling a variety of preset PV modules available from NREL System Advisor Model (Jan. 2014) as well as a user-defined PV module. The PV array block has two inputs that allow you to supply varying sun irradiance (input Ir in W/m^2) and temperature (input T in deg. C) data.
In our example, the PV array consists of one string of 14 Trina Solar TSM-250 modules connected in series. At 25 deg. C and with a solar irradiance of 1000 W/m2, the string can produce 3500 W.
Two small capacitors, connected on the + and - terminals of the PV array, are used to model the parasitic capacitance between the PV modules and the ground.
The inverter is modeled using a PWM-controlled single-phase full-bridge IGBT module ( H-bridge). The topology of the grid-side filter is the classical LCL configuration with the inductors split equally between the line and the neutral branches.
The control system contains five major Simulink®-based subsystems:
MPPT Controller: The Maximum Power Point Tracking (MPPT) controller is based on the 'Perturb and Observe' technique. This MPPT system automatically varies the VDC reference signal of the inverter VDC regulator in order to obtain a DC voltage which will extract maximum power from the PV string.
VDC Regulator: Determine the required Id (active current) reference for the current regulator.
Current Regulator: Based on the current references Id and Iq (reactive current), the regulator determines the required reference voltages for the inverter. In our example, the Iq reference is set to zero.
PLL & Measurements: Required for synchronization and voltage/current measurements.
PWM Generator: Use the PWM bipolar modulation method to generate firing signals to the IGBTs. In our example, the PWM carrier frequency is set to 3780 Hz (63*60).
The grid is modeled using a typical pole-mounted transformer and an ideal AC source of 14.4 kVrms. The transformer 240V secondary winding is center-tapped and the central neutral wire is grounded via a small resistance Rg. The residential load (10 kW / 4 kvar @ 240 Vrms) is equally distributed between the two "hot" (120 V) terminals.
Run the simulation and observe the resulting signals on the various scopes.
The initial input irradiance to the PV array model is 250 W/m2 and the operating temperature is 25 deg. C. When steady-state is reached (around t=0.25 sec.), we get a PV voltage (Vdc_mean) of 424.5 V and the power extracted (Pdc_mean) from the array is 856 W. At t=0.4 sec, sun irradiance is rapidly ramped up from 250 W/m^2 to 750 W/m^2. Due to the MPPT operation, the control system increases the VDC reference to 434.2 V in order to extract maximum power from the PV string (2624 W). These values correspond well to the expected values. To confirm that, use the Plot button of the PV Array menu to plot the I-V and P-V characteristics of the PV string based on the manufacturer specifications.
If you look at the leakage current (Ig scope), you will notice that there are no current flowing through the stray capacitance of the PV modules. This is due to PWM method used and the filter topology. Now, if you select the PWM unipolar modulation method (using the Inverter control menu) and repeat the simulation, you will see a significant leakage current in the system.