To view the electricity supply in our society as just sockets mounted in our walls with a constant voltage output is far from the truth. In reality, the power system supplying the electricity or the grid, is the most complex man-made dynamical system there is. It demands severe control and safety measures to ensure a reliable supply of electric power. Throughout the world, incidents of widespread power grid failures have been continuously reported. The state where electricity delivery to customers is terminated by a disturbance is called a blackout. From a state of seemingly stable operating conditions, the grid can fast derail into an uncontrollable state due to cascading failures. Transmission lines become automatically disconnected due to power flow redirections and parts of the grid become isolated and islands are formed. An islanded sub-grid incapable of maintaining safe operation conditions experiences a blackout. A widespread blackout is a rare, but an extremely costly and hazardous event for society. During recent years, many methods to prevent these kinds of events have been suggested. Controlled islanding has been a commonly suggested strategy to save the entire grid or parts of the grid from a blackout. Controlled islanding is a strategy of emergency control of a power grid, in which the grid is intentionally split into a set of islanded subgrids for avoiding an entire collapse. The key point in the strategy is to determine appropriate separation boundaries, i.e. the set of transmission lines separating the grid into two or more isolated parts. The power grid exhibits highly nonlinear response in the case of large failures. Therefore, this thesis proposes a new controlled islanding method for power grids based on the nonlinear Koopman Mode Analysis (KMA). The KMA is a new analyzing technique of nonlinear dynamics based on the so-called Koopman operator. Based on sampled data following a disturbance, KMA is used to identify suitable partitions of the grid. The KMA-based islanding method is numerically investigated with two well-known test systems proposed by the Institute of Electrical and Electronics Engineers (IEEE). By simulations of controlled islanding in the test system, it is demonstrated that the grid’s response following a fault can be improved with the proposed method. The proposed method is compared to a method of partitioning power grids based on spectral graph theory which captures the structural properties of a network. It is shown that the intrinsic structural properties of a grid characterized by spectral graph theory are also captured by the KMA. This is shown both by numerical simulations and a theoretical analysis.