Three-phase power and harmonic flow

Abstract

In this chapter, a three-phase power-flow and harmonic-converter model are combined and solved using both the sequential and unified Newton's methods. Interaction between the three-phase power flow and a three-phase harmonic converter model has been solved using both decoupled and full Newton methods. The decoupled method displays good convergence if a linearising shunt is present but is slow because the Jacobian matrices need to be recalculated and factorised at every iteration. The full Newton method (with constant Jacobian), is faster and displays more robust convergence. The decoupled method is compatible with any existing three-phase power flow, including a polar fast-decoupled type. A special but simple three-phase power flow is required for the unified method as the converter model must be framed in real variables. Overall, code for the unified method is shorter and less complicated, as there is only one set of sparse storage, mismatch evaluation, convergence checking, etc. The effect of not modelling the power-flow/distortion interaction is a moderate underestimate of unbalance in the power-flow solution, and a large underestimate of distortion at low order noncharacteristic harmonics in the converter model. The AC-DC iterative algorithm can easily be extended into a general purpose model with the capability of including several AC systems, DC systems, possibly with multiple terminals in each system, and all integrated with the power-flow equations. This is essentially a software engineering task, as each half pole contributes a block to the main diagonal of the system Jacobian matrix, with diagonal matrices coupling to other harmonic sources in the same system. The main task is to code the program so as to be versatile, easy to use and modular.