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.

Summary A novel scheme based on the complex atom transform (CAT) for detection of subsynchronous oscillations (SSO) is proposed in this paper. SSO components and the fundamental are closely spaced in frequency domain causing the possibility of aliasing. Some conventional SSO detection methods share the problems of low mode resolution and slow dynamic response. The CAT has flexible window in time–frequency domain. By adjusting the window of the CAT, the scheme can achieve high multi‐mode resolution, desirable accuracy and fast dynamic response when analyzing multi‐mode SSO waveforms to facilitate multi‐mode SSO suppression. First step of the scheme is to use the CAT to obtain oscillation frequencies and envelope curves of SSO waveforms. The least squares (LS) method is then deployed to measure initial oscillation amplitude and damping ratio from the envelope curve. The effectiveness and correctness of the proposed scheme are verified with simulations using both an artificially generated signal and the IEEE First Benchmark Model. Compared with the conventional methods, such as the continuous wavelet transform (CWT), the scheme has higher mode resolution, more desirable accuracy and faster dynamic response. In addition, the scheme is simple and the computation burden is low; thus, it is easy to be implemented for online application. Moreover, the CAT‐based scheme can also be used for synchrophasor measurements; hence, the scheme can be integrated into phasor measurement units (PMU), which are installed in generator terminals. Copyright © 2013 John Wiley & Sons, Ltd.

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