Power flow modeling considering detailed constraints of the DFIGs and collector networks based on 3-layer BFS and convergence improvement

Abstract

Difficulty of power flow modeling with the doubly-fed induction generators (DFIGs) lies in: (1) Due to small capacity and large number of the DFIGs, a wind farm (WF) has many variables. The impedance level and the resistance/reactance ratio are different from those of the main system. Unified solution to the main system and the WF is impractical. The existing solutions with a few aggregated DFIGs simplify or ignore detailed constraints of the DFIGs and the collector networks (CNs). (2) The rotor voltage of the DFIG is small. The traditional flat voltage start is not suitable. Furthermore, convergence of the DFIG is related to the slip which changes with the wind speed. (3) For the DFIG at the synchronous mode with zero slip, the equivalent circuit of the DFIG with the rotor resistance and the rotor voltage divided by the slip is not valid. To solve these difficulties, a 3-layer backward/forward sweep (BFS) algorithm is newly proposed. The originalities are, (1) To facilitate power flow modeling and improve its convergence, the total system is classified into 3 layers, i.e. the DFIG, the WF with the DFIGs and the CNs, and the total system with the WFs and the main system. Each DFIG, each CN, and the main system are solved iteratively. The DFIGs and the CN are solved alternatively, interfaced by the voltages/powers at the stators. The WF and the main system are solved alternatively, interfaced by the voltages/powers at the point of common coupling. (2) To improve the convergence of the DFIG, the flat start is modified. The initial value of the rotor voltage is decided by the slip. (3) The DFIG at the synchronous speed is newly solved as a synchronous generator (SG) with the dc excitation, but the unknowns and the solution procedure are different from those of the SG. Solution to the DFIG at the synchronous mode is more accurate than the existing solution to the DFIG, since the latter ignores the power supply to the exciter. Numerical results verify the convergence improvement to the DFIG. Power flow results to IEEE RTS system with 79 DFIGs are given to show the detailed solution of each DFIG. Comparison with the existing models shows that ignoring the CNs overestimates active power of the WFs and yields optimistic judgment to var balance and voltage magnitudes of the main system. Equivalence to wind speeds will under- or overestimate the active power of the WFs.