## Modal analysis

Modal analysis is a mathematical tool for checking the dynamic properties of different physical systems in frequency space. It is a method of analyzing, measuring and calculating the dynamic responses of different (excited) systems. In the power system, the modal analysis procedure is now established mainly for the implementation of angular stability studies as a result of small disturbances. The question arises as to whether it is possible in the field of determining the influence of the resonant state on the propagation of harmonics across the network.

The aim is to test the possibilities of using modal analysis to study and limit resonant research in power grids.

## Reference models of LV and MV networks

Network operation with renewable generation sources and active users can be simulated on models implemented in different simulation environments. Accurate modelling and known actual operating conditions are required to accurately analyze the impacts of different consumers on the operation of a particular part of the network. Unfortunately, actual network data is not available to us in practice. It is also difficult to assess the overall impact of different technologies on the whole network, as the analyzed network may not be representative of the whole network. For this reason, the impact of technologies is often simulated on reference network models, and the results obtained can then be applied throughout the new network. To search for reference or representative networks, some machine learning methods are often used, e.g. classification. To perform the classification of networks in a group, we need a multitude of networks, which we write with different attributes or features. Examples of features include total feeder length, overhead line length, rated power of transformers, and share of resident customers. The characteristics need to be pre-processed. Sorting methods then offer us the result in the form of groups of networks that have similar properties and thus differ from networks from other groups. The representative of these groups shall mark it as a reference network covering the characteristics of the individual groups. The simulation results of the reference models are then easily extended to the entire distribution network.

## Impact of electric vehicles

The transport sector contributes a large share to global CO2 greenhouse gas emissions, so decarbonisation of this sector is in the interests of most countries around the world. In recent years, we have witnessed the accelerated replacement of internal combustion vehicles with connected electrical or hybrid vehicles. Due to the high charging power, a larger number of connected electric vehicles will affect the operation of the transmission and distribution network. Uncontrolled charging of a large number of electric vehicles can lead to overloading of network elements such as transformers and power lines and unacceptable voltage drops in the network, potentially leading to high investments to strengthen the network. The latter can be avoided by proper implementation of the smart charging concept, which allows charging to be adjusted according to the current network situation in order to reduce the number of limit violations.

When simulating the impact of charging electric vehicles on the grid, we are faced with, among other things, unknowns such as charging power, battery size, user habits and vehicle consumption. The availability of charging infrastructure, which must be appropriately spatially located and enable the carefree use of electric vehicles, will also play a very important role in facilitating the mass transition to electric vehicles.

## Distribution network state estimator

Distribution networks have been subject to new challenges in recent years, including the increased integration of distributed generation, heat pumps, the increasing share of electric vehicles and the desire to increase network flexibility. This requires increasing the awareness of the modern distribution network, which is a prerequisite for increasing its manageability.

The visibility of the system is directly related to the amount of available measurements and their accuracy. Due to various technical and economic reasons, the condition of existing meters in the system usually does not allow for adequate knowledge of the system. In such cases, an appropriate level of awareness can be achieved through the implementation of the state estimator.

The state estimator algorithm calculates, or estimates, most likely the state of the system, based on currently available network measurements and mathematical network model. The method, known in the transmission network for decades, shows promising results when used in distribution networks of various types.

The process of assessing the situation in the distribution system is basically the same as in the case of the transmission system. Despite the initial similarity, its design and implementation in the distribution network is significantly different. This is due to many differences between the two types of networks. The main challenge in the implementation of the evaluator is its robustness, which allows it to quickly and reliably assess the state of various distribution networks.