For transient stabilities studies, complete models of DFIG wind farms are always composed of all the wind turbine model—with the necessary detail level depending on the scope of study—and the model of the internal grid of the farm, in which the electromagnetic transients are neglected as is normal for power system simulations.
Figure 1 shows the wind farm considered in this study. It has a radial structure with 12 wind turbines in two clusters, connected to the electrical network at the same PCC. The first cluster presents 6 × 660 kW DFIG wind turbines in three branches, with two machines for each one, connected to a medium voltage (MV)/high voltage (HV) transformer (substation of the farm) and a cluster feeder to the PCC. The second one has a similar configuration but with two branches of 3 × 2 MW DFIG wind turbines on each one, connected to a common transformer and a feeder.
In the wind farm, the wind turbines are identified by three indexes: (i) the first index is the cluster, (ii) the second one represents the number of the branch in the cluster and (iii) the third one refers to the position of the wind turbine in the branch.
2.1 Wind turbine model
The DFIG wind turbine model contains the following: (i) the mechanical system: rotor and drive train and (ii) the generation system: DFIG and partial-load power converter [a bidirectional back-to-back insulated-gate bipolar transistor frequency converter with a direct current (DC) bus] and their controls. Figure 2 depicts the configuration and basic control structure of the wind turbine under study.
Some modeling assumptions, widely used in electromechanical transient simulations (fundamental frequency simulations), are considered in this paper:
- Higher harmonics of voltage and currents are neglected (fundamental frequency simulations).
- Some of the differential equations and short time constant included in the generation system model are canceled (larger time step).
- The actuator disk theory (quasi-static approach) describes the turbine behavior.
- The drive train is represented by the two-mass model.
- The stator transients are neglected in the asynchronous generator (third-order model).
- The power converter is considered ideal (internal dynamics lacks interest).
The electrical system of the wind turbine is composed of the asynchronous generator and the power converter.
As can be seen in Figure 2, the power converter consists of two converters coupled through a DC bus. The rotor side converter (RSC) enables the decoupled control of active and reactive powers acting on the rotor voltage, whereas the grid side converter (GSC) allows the power exchange with the grid. In this paper, as is normal for transient stability studies, ideal converters and constant DC bus voltage between the converters are assumed. In fact, a controlled voltage source models the RSC, in which uqr (udr) is used for controlling the rotor speed/active power (reactive power).
The control system applied to the wind turbines is the same one as that presented in. During normal operation, the aims of the control system are the following:
- Power optimization, which consists of maximizing the power extracted from the wind for a wide range of wind speeds.
- Power limitation, which is based on limiting the output power to rated power for high winds.
- Power regulation, which consists of adjusting the active or/and reactive power to a desirable set point.
To achieve these aims, the power converter must be controlled in collaboration with the blade pitch angle.
The controllers applied to the RSC are the following:
- The rotational speed controller (Figure 3(a)) controls the active power by acting on uqr. It uses the power–speed curve of the wind turbine to determine the power reference according to the rotational speed. Thus, the turbine mechanical power is maximized with below rated speed and is limited with above rated speed.
- The reactive power controller uses three control loops to define udr by using the control scheme depicted in Figure 3(b): (i) outer control loop, which controls the reactive power and determines the generation voltage reference Ug (ii)subordinated voltage control loop, which regulates idr and assures that the generation voltage is maintained between the limits while trying to reach the reactive power reference and (iii) inner control loop, which controls idr and defines udr.
Figure 3. Controllers applied to the DFIG: a) rotational speed controller, b) reactive power controller and c) pitch angle controller.
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The pitch angle controller (Figure 3(c)) is responsible for adjusting the blade pitch angle reducing the power extracted from the wind when the rotational speed increases up to the rated speed. It includes an actuator with pitch angle saturation and rate limiter.
On the other hand, the GSC provides the exchange of power to the grid with a certain power factor. It has been modeled as a controlled current source, where the direct and quadrature components of current source are calculated from the exchange power from the converter to the grid.
This wind turbine includes an external rotor resistance (Rext) coupled via the slip-rings to the generator rotor instead of the converter. This external rotor resistance works as crowbar protection so that it bypasses the RSC in case of over-current (during grid faults) and thus protecting the rotor and power converter. When the crowbar protection is switched on, the DFIG is turned into SCIG with an increased rotor resistance, and the independent controllability of active and reactive powers through the RSC gets lost. Then, the rotor voltage is defined as follows.
Since the GSC is decoupled from the rotor windings through the DC bus, it can be used to generate reactive power. All modern grid codes are required to provide a certain amount of reactive power in order to support voltage recovery. In this work, the wind turbine is required to fulfill the Spanish grid code, in which the reactive current to be provided is expressed as a function of the grid voltage. Therefore, the reactive power to be provided by the GSC during grid faults is defined from the grid voltage.
When the fault disappears, the crowbar is switched off and then the independent controllability of active and reactive powers through the RSC is recovered.
2.2 Wind farm network model and main control system
In the electrical network model of the wind farm, the electric lines and transformers are represented by constant impedances (static models), as is normal for dynamic simulations of electrical power systems.
The main control system completes the wind farm model. It tries to assure the wind farm production in a similar way to a conventional power plant, that is, controlling the power production. In this paper, the main controller presents independent proportional-integral controllers for the active and reactive powers. Figure 4 shows the main control system including a dispatch center to manage the power references to each wind turbine. The power references for each wind turbine (Pwti,ref, Qwti,ref) are computed, taking into account a proportional distribution of the available powers (Pava,i, Qava,i) and the references ordered by the system operator (Pwf,so, Qwf,so).