Harmonic Resonance Mode Analysis and Application for Offshore Wind Power Plants
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- Institutt for elkraftteknikk 
This thesis is centred around a form of resonance analysis for power systems known as Harmonic Resonance Mode Analysis (HRMA). It is a form of eigenvalue analysis and has some parallels to the modal analysis commonly associated with small signal stability. Modes in small signal stability analysis characterise the transient response of the system to a small disturbance, and are identified from the state matrix of the linearised state space description. Modes in HRMA characterise the parallel resonances of a power system, and are identified from the admittance matrix. Participation factors, which are derived from eigenvectors of the admittance matrix at resonance frequencies, indicate the observability of modes in the impedance measured at individual buses. In addition, sensitivity indices quantify the change in amplitude and frequency of modes when parameters are adjusted in the admittance matrix. A part of this thesis is dedicated to replicating HRMA results found in published papers. By validating published results for two different test cases, the computer implementation for carrying out the analysis is verified. Obtained results are generally consistent with those in published papers. Some critical considerations in implementation of HRMA are identified and discussed, perhaps the most important of which is the issue of modal switching. HRMA is also used to investigate resonances in a system modelled on the real offshore wind power plant of Anholt in Denmark. HRMA is based on the nodal admittance matrix, and power system components are modelled as equivalent admittances. Non-linearities and frequency dependencies can be included more easily than in a state space representation. Examining the impact of non-linear components in the admittance matrix on HRMA results is a central contribution from this thesis. The sensitivity of results with respect to degree of aggregation of the wind power plant model is also investigated. Modern wind turbines are connected to power systems via full-scale frequency converters. Such converters can be modelled for harmonic analyses as equivalent impedances which are determined primarily from the converter current control loops. An equivalent impedance representing the grid-side converter of a wind turbine generator as seen from the grid is derived, and later such impedances are incorporated in the HRMA. The resonance modes in the investigated large offshore wind power plant are sensitive to modelling of wind turbine main circuit components such as shunt harmonic filters, step-up transformers and main reactors. Suitable modelling of these electrical components is therefore important for obtaining reliable result from HRMA. Moreover, the resonance modes are highly dependent on the number of turbines in operation.