Investigation of Power Grid Islanding Based on Nonlinear Koopman Modes

Abstract: To view the electricity supply in our society as just sockets mountedin our walls with a constant voltage output is far from the truth. Inreality, the power system supplying the electricity or the grid, is themost complex man-made dynamical system there is. It demands severecontrol and safety measures to ensure a reliable supply of electric power.Throughout the world, incidents of widespread power grid failures havebeen continuously reported. The state where electricity delivery to customersis terminated by a disturbance is called a blackout. From a stateof seemingly stable operating conditions, the grid can fast derail intoan uncontrollable state due to cascading failures. Transmission linesbecome automatically disconnected due to power flow redirections andparts of the grid become isolated and islands are formed. An islandedsub-grid incapable of maintaining safe operation conditions experiencesa blackout. A widespread blackout is a rare, but an extremely costlyand hazardous event for society.During recent years, many methods to prevent these kinds of eventshave been suggested. Controlled islanding has been a commonly suggestedstrategy to save the entire grid or parts of the grid from a blackout.Controlled islanding is a strategy of emergency control of a powergrid, in which the grid is intentionally split into a set of islanded subgridsfor avoiding an entire collapse. The key point in the strategy is todetermine appropriate separation boundaries, i.e. the set of transmissionlines separating the grid into two or more isolated parts.The power grid exhibits highly nonlinear response in the case oflarge failures. Therefore, this thesis proposes a new controlled islandingmethod for power grids based on the nonlinear Koopman Mode Analysis(KMA). The KMA is a new analyzing technique of nonlinear dynamicsbased on the so-called Koopman operator. Based on sampled data followinga disturbance, KMA is used to identify suitable partitions of thegrid.The KMA-based islanding method is numerically investigated withtwo well-known test systems proposed by the Institute of Electrical andElectronics Engineers (IEEE). By simulations of controlled islanding inthe test system, it is demonstrated that the grid’s response following afault can be improved with the proposed method.The proposed method is compared to a method of partitioning powergrids based on spectral graph theory which captures the structural propertiesof a network. It is shown that the intrinsic structural propertiesof a grid characterized by spectral graph theory are also captured by theKMA. This is shown both by numerical simulations and a theoreticalanalysis.