Discretization of Digital Controllers Comprising Second-Order Notch Filters

Second-order notch filters (NFs) with constant coefficients are often used as part of feedback controllers in grid-connected power conversion systems to prevent unwanted harmonic content polluting the closed control loops. In practice, the value of the mains frequency resides within a certain known range rather than remaining constant. Hence, the correct selection of NF coefficients is crucial for ensuring that the desired performance is maintained within the whole expected mains frequency range. Bilinear transformation (BLT) with notch frequency prewarping is often adopted to convert an NF from a continuous to a digital form. While accurately preserving the notch frequency location, the method reduces the filter bandwidth. As a remedy, BLT with both notch frequency and damping ratio prewarping may be employed. Nevertheless, some inaccuracy remains under low sampling-to-notch frequency ratios. This technical note demonstrates that the issue may be solved by prewarping the boundary values of the expected harmonic frequency range rather than the notch frequency and/or damping factor before applying the BLT. Simulation results accurately support the presented issue and proposed solution.