Grid-tied inverter simulation and analysis

A program for simulation and analysis of the output stage in grid-connected systems. Considering an grid-tied system consisting of a half-bridge voltage source inverter (VSI) and an output LCL filter, it allows evaluating the operation of such electronic device for high-frequency switching and under different load conditions.

The program contains the following file types:

• MATLAB scripts for general settings and controller design
• Simulink implementation for digital-control simulation
• PSIM implementation for power-electronics simulation

Main file named as 'run_grid_tied.m'.

Current regulation

The current regulator in grid-connected inverters aims to maintain the current injected to grid at quality levels accepted by standards such as IEEE 1547. One solution for designing such output-current regulators are controllers based on the internal model principle (IMP), which in case of grid-tied inverters yield to the multi-resonant and repetitive controllers.

Consider a closed-loop in the form

employing a proportional-multiple-resonant (PMR) controller with transfer function

$$C(s) = \frac{u_v(s)}{e(s)} = k_{e} +\sum_{i=1,3,\dots}^{h}\frac{k_{{2i-1}} +k_{{2i}}s}{s^{2} +2\xi_{i}\omega_{r_i} s +\omega_{r_i}^{2}}$$

where $k_{e}$, $k_{{2i-1}}$, and $k_{{2i}}$ are gains to be determined, $\xi_{i}$ is the damping factor of the $i$-th resonant mode and $\omega_{r_i}$ the $i$-th multiple of the fundamental frequency $\omega_0$.

An appropriate design of $C(s)$, considering a sufficient number of resonant modes, results in grid-tied controllers allowing to perfectly follow a sinusoidal current reference and its harmonic frequencies when supplying non-linear loads.

The control law shown can be rewritten as

$$u(t) = Kx_{a}(t)$$

where $x_{a}(t) = [x'(t)\ x_{r}'(t)]' \in \mathbb{R}^{3+2h}$ is the augmented state where $x(t) = [i_L(t)\ v_c(t)\ i_o(t)]'$, $x_r(t)$ contains the resonant states and

$$K = [k_{c}\quad k_{v}\quad k_{g}\quad k_{1}\quad k_{2}\quad \cdots\quad k_{2h-1}\quad k_{2h}].$$