Extended Gersgorin Theorem-Based Parameter Feasible Domain to Prevent Harmonic Resonance in Power Grid

Harmonic resonance may cause abnormal operation and even damage of power facilities, further threatening normal and safe operation of power systems. For renewable energy generations, controlled loads and parallel reactive power compensating equipment, their operating statuses can vary frequently. Therefore, the parameters of equivalent fundamental and harmonic admittance/impedance of these components exist in uncertainty, which will change the elements and eigenvalues of harmonic network admittance matrix. Consequently, harmonic resonance in power grid is becoming increasingly more complex. Hence, intense research about prevention and suppression of harmonic resonance, particularly the parameter feasible domain (PFD) which can keep away from harmonic resonance, are needed. For rapid online evaluation of PFD, a novel method without time-consuming pointwise precise eigenvalue computations is proposed. By analyzing the singularity of harmonic network admittance matrix, the explicit sufficient condition that the matrix elements should meet to prevent harmonic resonance is derived by the extended Gersgorin theorem. Further, via the non-uniqueness of similar transformation matrix (STM), a strategy to determine the appropriate STM is proposed to minimize the conservation of the obtained PFD. Eventually, the availability and advantages in computation efficiency and conservation of the method, are demonstrated through four different scale benchmarks.