Relations between two-port parameters

The aim of the work is to derive a steady state PQ-diagram for a variable speed wind turbine equipped with a Doubly Fed Induction Generator. Firstly, the dependency between optimal rotor speed and wind speed is presented. Secondly, the limitations in reactive power production, caused by the rotor current, the rotor voltage and the stator current are derived. Thirdly, the influence of switching from D to Y coupling of the stator is investigated. Finally, a complete PQ diagram for a wind turbine is plotted. It is concluded that the limiting factor regarding reactive power production will typically be the rotor current limit, and that the limit for reactive power absorption will be the stator current limit. Further, it is concluded that the rotor voltage will only have a limiting effect at high positive and negative slips, but near the limitation, the reactive power capability is very sensitive to small changes in the slip.The reactive power capability of a wind farm depends a lot on the capability of the wind turbines, although the impact of the grid should also be considered in a PQ diagram for the whole wind farm. The reactive power capability of the wind turbines depends on the type or concept for grid connection of the wind turbines.The first generation of commercial grid connected wind turbines in the 1980s was dominated by the fixed speed concept using squirrel cage induction generator, which was soon supplemented with a capacitor bank for reactive power compensation. Through the 1990s, different types of variable speed concepts became an increasing share of the market. According to Hansen et al., 2 the doubly fed induction generator (DFIG) concept was the most successful variable speed concept with more than 45% market share in 2002.For the synchronous generator, the boundaries defined by the field current limitation, the armature current limitation and the mechanical power limitation can easily be calculated from the ratings and the reactances. This is typically presented in a so-called PQ diagram. 3 A similar description of a DFIG is not found in textbooks. The scope of this paper is the reactive power capability of a DFIG, taking into account the influence of a typical speed control of a wind turbine. Other concepts are not considered here, and the impact of the grid including the step-up transformer is not included.The advantage of the DFIG concept is mainly that variable speed control is obtained with a minimum of power converter capacity. The connection of the main electrical components is shown in Figure 1, based on the description of a commercial wind turbine in Bolik. 4 The DFIG exchanges power with the grid through the stator windings as well as the rotor windings. The main part of the power passes from the generator through the stator into the grid, whereas only a fraction of the power is passed from the rotor windings through the power converter. Besides, a star-delta switch is used to increase the speed control interval as discussed below.To characterize the DFIG, the rotor speed should be taken...

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“…The power taken out through the rotor converter can be calculated by inserting the expression for V r in equation (9).…”

Section: Rotor Current As Limitationmentioning

confidence: 99%

“…The theory of two-port matrices is described in Johnstone and Deane. 9 As a basis for the derivations, the Z matrix is used. The Z matrix has been constructed per inspection from the equivalent circuit in…”

Section: Appendix C: Derivation Of Two-port Matrices For the Dfigmentioning

confidence: 99%

Reactive power capability of a wind turbine with doubly fed induction generator

Lund¹,

Sørensen²,

2007

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“…In the literature, it is the admittance structure (2) that is usually considered for voltage-controlled SSFR modeling of the synchronous machine [10], [11], [13]. For the present paper, the structure of interest is the hybrid parameter model (3) which can be written in the transfer function matrix form (5).…”

Section: ) Inverse Hybrid Parametersmentioning

confidence: 99%

“…where the relationships between various reactances of (11) are given in the appendix. (11) and (12) can be formulated into compact matrix equations for stator and rotor quantities respectively, as defined in (13), (14).…”

Section: )mentioning

confidence: 99%

Two-port circuits based hybrid model of synchronous machine

Wamkeue

Bensaker

2005

IEEE International Conference on Electric Machines and Drives, 2005.

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The paper introduces the so-called hybrid state model of a synchronous machine based on the superposition principle of the two-port representation of d-axis (two-port circuits) and the single-port structure of q-axis equivalent circuits. The detailed formulation of the hybrid state model is developed in terms of the equivalent-circuit parameters of the machine. Analytical expressions of terminal voltages and the field current following the decrement tests are derived. A practical application of the model for the load rejection test analysis is investigated. Comparisons are made between simulation results and actual data obtained from a laboratory machine to assess the efficacy of the proposed synchronous generator framework analysis.

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“…A complete list of the relations between two-port parameters (Johnstone and Deane 1991) has been published. It was thought that a useful complement would be a list of matrix equations which can be used to calculate any parameter matrix from any other matrix, and this paper presents such a list.…”

Section: Introductionmentioning

confidence: 99%