Power Flow in a Multi-Frequency HVac and HVdc System: Formulation, Solution, and Validation

This paper proposes a novel power flow formulation and solution algorithm for a generalized large-scale interconnected transmission system encompassing multi-frequency HVac and HVdc grids having arbitrary numbers of buses, topologies, and operating frequencies. Back-to-back and ac/dc voltage-source converters are employed to interconnect and control the voltage and power interchange between two power grids operating at different frequencies. The power Flow formulation is based on a steady-state model of back-to-back and ac/dc converters operated in centralized and distributed droop control strategies. Each power grid is represented by a set of nonlinear power balance equations. These equations are solved simultaneously using a unified power flow algorithm, taking into account generator and converter limits. It is shown that the solution convergence is achieved rapidly despite the system size, topology, and converter control strategies. The efficacy and accuracy of the proposed steady-state solution algorithm are demonstrated by comparing the numerical solution to the one obtained by time-domain electromagnetic models of multi-frequency HVac and HVdc transmission systems with fully controllable back-to-back and ac/dc converters. The results obtained by using the proposed algorithm and the time-domain simulation are practically identical.