The connection of offshore wind turbines to the European grid has been growing in the recent years. Many European countries are adopting this renewable energy and are increasing the number of wind power plant additions into their electrical transmission networks. Due to the phase out of conventional power plants (e.g. fossil fuel fired), new challenges are arising in terms of inertia, frequency stability, voltage stability and power quality, being the latter the main focus in the present work. It is important to study the harmonic frequencies that the wind parks are going to introduce in the electrical grid and how the grid is going to respond to this sustainable energy addition. The classical methods to identify the harmonics frequencies and to assess the stability in an electrical power system are performed by considering single-input single-output (SISO) systems. Nevertheless, when modelling a power system as a SISO system, information about the dynamics of the elements in the system is neglected. To overcome this disadvantage, a representation with more than one input and one output, a multiple-input multiple-output (MIMO) system, can be considered. The present works concerns with the development of a method for studying the harmonic frequencies of any electrical power system. Since the main elements in the grid that contribute to the creation of harmonic frequencies are the inductances and the capacitances of the transmission lines and underground cables, the present work will focus on these passive elements and it will represent the transmission lines as PI sections and the underground cables as ``fitted PI'' sections. These representations are SISO systems, because the have only a voltage signal, measured in the sending end of a transmission branch, as input; and a voltage signal, measured in the receiving end of a transmission branch, as output. Therefore, it is necessary to find an approach to build a MIMO system. This is done via a concatenation of SISO linear-time-invariant (LTI) systems to create a MIMO system. Afterwards, the MIMO system is studied with a powerful mathematical tool called the singular value decomposition that not only will give information about the harmonic frequencies in the system, but it will show it is also possible to study which input of the system is affecting the system the most and which output will be the most affected. To finish the research, a sensitivity analysis is performed with respect to the variation of the capacitances and inductances in the transmission lines and the underground cables. This analysis will evaluate possible variations in the harmonic response of the MIMO system.

The proposed method to investigate the harmonic frequencies of an electrical power system can be applied to any power system. For sake of illustration of application, two different power system models are addressed. First, to understand each step in the method a small size test system is studied. This study shows how to apply the method and illustrates how to interpret the evaluation outcomes. Subsequently, a synthetic model of the Randstad regional transmission network is used to test the method in a relatively larger system model. This case study is of great importance due to the new wind parks that are going to be connected to this region in the coming years. Therefore, the harmonic frequencies observed in the synthetic model of the Randstad region will be obtained and an assessment of which transmission line or underground cable is the most affected by the harmonics in the system will be performed.