Newton relaxation algorithms for simulating large power systems

Three methods based on Newton relaxation for simulating large power systems are developed. Large systems are partitioned into smaller subsystems using partition points called cut-nodes. The Newton relaxation algorithm is used to update the variables on the cut-nodes depending on the difference of power flow or the voltages of adjacent cutnodes. Hence, there are two nested iteration loops. Three methods are developed. Method I, the Newton voltage relaxation, utilizes power residuals and adjusts voltages between each pair of adjacent cut-nodes on two adjacent blocks, Method II, the Newton power relaxation, employ, voltage residuals, and cut-node power is adjusted. Method III, called fast decoupled relaxation, uses the imaginary part of the bus admittance (bus susceptance) matrix in place of Jacobian matrices