Mathematical Modeling of WTGS Components

  • Zbigniew Lubosny
Part of the Power Systems book series (POWSYS)


Models of reality (objects, processes, phenomena, etc.) are usually an element of the process presented in Fig. 5.1.


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  1. 1.
    For a properly designed WTGS, within the wind turbine operating speed range, the curves showing eigenfrequencies as a function of the rotor speed should not cross. This prevents resonance self-excitation.Google Scholar
  2. 2.
    Therefore, these two values cannot be subtracted directly. When computing rotor-shaft twist, it is necessary to divide or multiply the relevant torsion angle.Google Scholar
  3. 3.
    The mean value of wind velocity at partial load is usually assumed as equal to the value which on the WTGS power characteristic p=f(v) gives the highest slope, e.g. v0=9 m/s.Google Scholar
  4. 4.
    In general, in WTGS modeling, the drive-train model described in sect.5.2 should be used.Google Scholar
  5. 5.
    In general, in WTGS modeling, the drive-train model described in sect.5.2 should be used.Google Scholar
  6. 6.
    Other types of transformation are also utilized.Google Scholar
  7. 7.
    The subscript on defines the on-state of the swich, e.g. thyristor, while the subscript off defines the off-state of the switch.Google Scholar
  8. 8.
    The network consists of conductance-type branches only (except for current and voltage sources).Google Scholar
  9. 9.
    In some types of control systems the WTGS characteristic between points 2 and 3 in Fig. 5.44 is defined by the function P = K•w with high slope (high value of coefficient K).Google Scholar
  10. 10.
    When a non-realistic step change of the wind velocity is assumed.Google Scholar
  11. 11.
    In fact, energy storage is not utilized for this purpose today.Google Scholar
  12. 12.
    Various types of WTGS utilize supervisory algorithms that can differ from that presented here. Those algorithms should be considered as examples only.Google Scholar
  13. 13.
    Taking into account the number of conditions being checked.Google Scholar
  14. 14.
    The controller reaction to a given input signal depends, of course, on the controller structure. Here, a controller with integration block is considered.Google Scholar
  15. 15.
    The control system can determine the turbine power-speed characteristics.Google Scholar
  16. 16.
    Whether the real power is proportional to the d-axis rotor current and the reactive power is proportional to the q-axis rotor current, or whether the opposite state takes place depends on the dq-reference frame definition.Google Scholar
  17. 17.
    Insuch a case, the maximum point power tracking (MPPT) scheme, based on the dp/dw=0 rule, is not utilized.Google Scholar
  18. 18.
    The generator stator winding can be (and is) switched between delta and star connection. The area of operation of the generator with the given connection is marked in Fig.5.61. The generator operation with the star connection reduces losses when the wind speed is lower, A t higher winds, when the rated power is achieved, the generator operates with delta-connected stator windings.Google Scholar
  19. 19.
    Because the power flows here in one direction only, converters with non-controlled rectifiers can be (and usually are) utilized.Google Scholar
  20. 20.
    The rated voltage of the network depends on the power system.Google Scholar
  21. 21.
    Usually, in such a type of WTGS, the power factor cos is controlled, which means that present wind turbines are not utilized for voltage control.Google Scholar
  22. 22.
    The power network is modeled by a set of algebraic equations, while the generating units (and sometime loads), FACTS and AC/DC systems are modeled by a set of differential and algebraic equations.Google Scholar
  23. 23.
    Its multi-modality is the positive feature of the multi-machine produce many more complex and difficult operating conditions (characteristic of the real system) for turbine and generator controllers than those obtainable in the single-machine system.Google Scholar
  24. 24.
    The presented controlled rectifier model described by (5.237) is a simplified model of the one defined by (5.243).Google Scholar
  25. 25.
    This assumed that s=3v I, which causes the inductive power to be positive (Q 0). When equation s=3VI is used, the inductive power becomes negative (Q 0).Coefficient 3 results from utilizing the phase-to-neutral rms voltageV.Google Scholar
  26. 26.
    That is 10kv,15kv, 20kv or 60kv, depending on the country grid type (voltage level and the WTGS location).Google Scholar
  27. 27.
    It is usually possible to make these networks closed.Google Scholar
  28. 28.
    When the feeding bus voltage value is imposed, the WTGES voltage and current can be computed iteratively by using the WTGS f(P,Q,V) characteristics.Google Scholar
  29. 29.
    Terminal voltage (and mechanical torque) is the generator model input and the current is the output. Inverse models of generator.Google Scholar
  30. 30.
    A power system model in which the dynamic elements (e.g. generators) are modeled with current as outpur and voltage as input is considered.Google Scholar
  31. 31.
    All quantities are per unit quantities.Google Scholar
  32. 32.
    For load flow computation purposes (especially for computing bulk power systems), the methods using sparse matrix techniques are widely utilized.Google Scholar
  33. 33.
    The problem can be solved also in rectangular coordinates a,b (V=Va+jvb)Google Scholar
  34. 34.
    There are set as initial in the computing procedure.Google Scholar
  35. 35.
    When the loads are modeled as constant admittances then the power P.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Zbigniew Lubosny
    • 1
  1. 1.Dept. Electrical Power SystemsGdansk University of TechnologyGdanskPoland

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