Representation of synchronous machines using constant-parameter voltage-behind-reactance (VBR) formulations improves accuracy and numerical efficiency of power systems transient simulation programs. This paper extends the VBR representation to the rotor circuit and presents two new formulations that achieve direct constant-parameter interfacing of the rotor and stator terminals with arbitrary external networks. In the first model, the entire machine is represented by constant RL branches that have algebraic coupling among the circuit variables. In the second model, all damper windings are implemented in state-space form to increase the numerical efficiency, while the stator and field windings are provided as constant-parameter circuits. The proposed models are validated against the commonly used and some state-of-the-art alternative models using a single machine with a simplified ac excitation system. Computer studies demonstrate the improved accuracy and efficiency of the proposed models when external rotor circuitry is considered.Index Terms-AC machines, interfacing circuit, power system modeling, power system simulation, synchronous machine, voltage-behind-reactance model.
NOMENCLATUREThroughout this paper, matrix and vector quantities are represented by boldface characters (e.g., v abcs ), and scalar quantities are in italics (e.g., i f d ). All variables are assumed to be referred to the stator side using the appropriate turns ratio. The q-axis is 90°ahead of the d-axis [1]. Similar naming convention for the machine variables as in [1] is used here. The rotor reference frame is assumed, but the superscript "r" is omitted. The main machine quantities are listed as follows. L lf d Field winding leakage inductance. L lk dj , j = 1 . . . N Direct-axis rotor damper winding leakage inductances. L lk q j , j = 1 . . . M Quadrature-axis rotor damper winding leakage inductances.
L lsStator winding leakage inductance. L m q , L m d Quadrature-and direct-axis magnetizing inductances. pHeaviside's operator (differentiation with respect to time or d/dt when t is time).
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