Electricity is the main power source on which we rely to perform our everyday routines. It is used to power everything from lighting, air-conditioning, electronic devices and large industrial electro-motors. However despite its ubiquitous nature we rarely think about the underlying infrastructure that delivers electricity to our homes and offices 24-hours a day at the same precise voltage and frequency. The power grid consists of many different components which makes maintaining stable operation a difficult task.

During normal operation the power grid is subjected to a large number of disturbances. The grid operators are tasked with maintaining the stability of the power grid i.e. maintaining voltage and frequency at prescribed levels when such disturbances occur. Depending on the type of disturbance that can be small or large we differ between two types of stability: steady-state stability and transient stability. Steady-state stability is concerned with small disturbances such as small load changes and switching of less important elements in the power grid. On the other hand, transient stability is the study of power systems when they are subjected to large disturbances such as bus faults or tripping of major transmission lines. In this project we focus on transient stability.

One of the main tasks when studying transient stability is determining the critical clearing time (*t _{ccl}) for a given disturbance. The critical clearing time is the maximum duration of the disturbance when the power system is still able to return to stable operation. As an example, let us assume that a disturbance has a t_{ccl} = 0.2 s. This means that if that disturbance is not repaired within 0.2 seconds this will inevitably lead to a loss of synchronism in the power grid and eventually a blackout (List of major power outages).*

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Calculating the critical clearing time has always been an interesting and difficult problem for power grid researchers. In this project, we asses existing methods for estimating *t _{ccl} for real networks. Additionally, we work on developing new methods and comparing their performance with existing ones. Currently, we are focused on using Lyapunov energy functions as a possible solution to the problem of efficiently estimating t_ccl for large power systems.*

A precise estimate of the critical clearing times for different disturbances is very important to power grid operators and engineers. It enables them to establish requirements for switching elements, and also to identify weak points in the system. Additionally, emergency control protocols can be prepared in order to better cope with large disturbances. This could help immensely in preventing future blackouts.