IEC Wind Turbine Type 3 (Doubly-Fed Induction Generator)

Authors: Martin Franke (Fraunhofer IEE), Luka Plavec (Fraunhofer IEE)

Reviewers: Lampros Papangelis (CRESYM)

List Of Acronyms

Context

This document refers to the IEC 61400-27-1 models which have been developed with the following specifications in mind [1]:

• Use in wind power plant models or standalone wind turbines

• Specification for generic simulation models covering most WT types

• Models address four categories of existing WT technologies (NERC nomenclature):

  • Type 1: Conventional asynchronous generators (squirrel cage)
  • Type 2: Variable rotor resistance asynchronous generators
  • Type 3: Doubly-fed induction generators (stator connected directly; rotor through converter)
  • Type 4: Synchronous generator, grid-connected via a full-size power converter

Other model considerations according to [1]:

• Include over/under frequency and voltage protection for realistic WT disconnection modeling
• Account for turbine-generator inertia and first drive train torsional mode impacts on power swings
• Phase-locked loop dynamics are not included in the models (they are modeled through a first order lag element)

The IEC 61400-27-1 [1] defines one of the most widely used series of RMS models for Wind Turbine (WT) generators, another one being the WECC model series, developed by EPRI.

The models are separated in several sub systems. The information and drawings are taken from [1] [2] [3] [4] [5] [6].

Model use, assumptions, validity domain and limitations

The controller of the generic Type 3 WT model does not represent the actual controller of the WT, which sets the references of the Rotor Side Converter (RSC) and the Grid Side Converter (GSC), but provides the current command signals to obtain an accurate response of active and reactive power, observed from the grid side.

The models are positive-sequence RMS models, hence they assume symmetrical operating conditions and neglect high-frequency dynamics. This type of models is often used in large-scale stability studies, for which it reflects the relevant phenomena. It is not a detailed physical model of the unit. Also for some stability phenomena (e.g. resonance stability) this model is not sufficient and EMT models or other approaches may be necessary.

Specifically, [1] defines the following validity domain:

• positive sequence dynamics
• transmission grid simulations
• reference value changes
• steady state voltage deviations (0.85 pu … 1.15 pu)
• phase jumps
• symmetrical faults, including short-circuits of varying impedance, where voltage can dip to close to zero (typical e.g. 0.18 pu)
• frequency disturbances, variations \(\pm\) 6 %
• electromechanical modes of synchronous generator rotor oscillations (0.2 Hz … 4 Hz)
• Typical simulation time frame: 10 s … 30 s
• Wind speed assumed to be constant during simulation time (wind speed could be included as an external condition through the available power)
• Simulation step width up to 1/4 fundamental frequency cycle (5 ms at 50 Hz), which implies that the model Bandwidth cannot be above 15 Hz.
• According to [2], the Type 3 WT model can operate with variable speed with slip values from -0.3 to +0.4.

Vice versa, [1] states that the models are not intended for the following:

• The models are not designed for long-term stability assessments.
• The models do not facilitate the exploration of sub-synchronous interaction phenomena.
• The models do not account for fluctuations due to wind speed variability over time and space, excluding factors such as turbulence, tower shadow, wind shear, and wakes.
• The models do not encompass phenomena like harmonics, flicker, or other EMC emissions outlined in the IEC 61000 series.
• Linearization for eigenvalue analysis is complex and may not be suitable for these simplified models.
• The IEC standard does not cover the details of short-circuit calculations.
• The models are not suitable for analyzing extremely weak systems, including scenarios where wind turbines operate in isolation from other synchronous generation or in cases with very low short-circuit ratios.
• The models do not incorporate negative and zero sequence components.

Wind turbine type 3

P control module

For detailed assessment of the parameters’ impact on model behaviour, see [5].

Figure 3 shows the wind turbine active power control scheme.

The control’s general behaviour is dominated by \(\omega(p)\), a lookup-table that provides the angular velocity at which the turbine should rotate when it is injecting a certain active power [6]. A possible look-up table for this system is shown in Figure 4, which is representing example values from DIgSILENT PowerFactory [7].

The power-speed-characteristic in Figure 4 has four main operating zones according to [5]:

• Zone 1: The minimum rotational speed has been reached and hence cannot decrease further due to physical (component) limits, mainly maximum slip of the converter.
• Zone 2: Between minimum rotational speed to rated rotational speed; maximum power tracking mode.
• Zone 3: Fixed at rated speed and below the rated active power. In some cases, instead of a fixed rated rotational speed, there is a linear rotational speed variation to achieve the rated rotational speed at the rated active power.
• Zone 4: Rated rotational speed and rated active power.

[!NOTE]

Dotted lines in Figure 4 imply that, for simulations, the active power reference presents a certain slope, offering more stable simulations. Under real control conditions, this look-up table has two vertical lines, as shown by the solid lines. [5]

The power-speed-characteristic’s speed reference output is then filtered (\(T_\mathrm{\omega ref}\)) to avoid sudden changes.

[!NOTE]

The time constant \(T_\mathrm{\omega ref}\) can be set to a very high value to enforce a fixed reference rotational speed during the simulation, which can be a desired operational mode. [5]

The filtered speed reference \(\omega_\mathrm{ref}\) is subtracted from the measured angular velocity \(\omega_\text{gen}\) (generator speed) or \(\omega_\mathrm{WTR}\) (turbine speed), depending on the mode \(M_\mathrm{\omega Tqpi}\) to get the speed error \(\omega_\mathrm{err}\). The measured speed can be filtered by the first order lag element with time constant \(T_\mathrm{\omega filtp3}\).

Since \(\omega_\mathrm{gen}\) comes from the mechanical module which only models the drive train resonant frequency, this first order lag is intended as a filter for only this oscillation. Since it is a low pass, it won’t be able to efficiently filter that resonance from the signal. Alternatively, by setting \(M_\mathrm{\omega Tqpi}=\mathrm{true}\), the rotor speed \(\omega_\mathrm{WTR}\) can be used instead of the generator speed, which acts as a simpler way to determine a filtered value of \(\omega_\mathrm{gen}\) [5].

The speed error \(\omega_\mathrm{err}\) is then given to the Torque PI controller (Figure 5), which outputs the electromagnetic torque reference \(\tau_\mathrm{out}\) [6].

Another input to the torque PI subsystem (see Torque PI block) is the maximum electromagnetic torque \(\tau_\mathrm{emax}\). It is determined by calculating a torque value from [5]:

• The reference power value \(p_\mathrm{WTref}\), during voltage dips optionally scaled down by the terminal voltage \(u_\mathrm{WTC}\) (if \(M_\mathrm{pUscale}=\mathrm{true}\))
• And a rotational speed, either the turbine rotor speed \(\omega_\mathrm{WTR}\) (if \(M_\mathrm{\omega Tmax}=\mathrm{false}\)) or the speed reference value \(\omega_\mathrm{ref}\) (if \(M_\mathrm{\omega Tmax}=\mathrm{true}\)).

After the torque PI controller, the electromagnetic torque reference \(\tau_\mathrm{out}\) is multiplied by the generator’s rotational speed \(\omega_\mathrm{gen}\) to obtain a power reference [6].

To obtain the active current command \(i_\mathrm{pcmd}\), \(p_\mathrm{ord}\) is divided by the measured voltage \(u_\mathrm{WTCfilt}\).

To the active power order \(p_\mathrm{ord}\) an additional component from the Drive Train Damping (DTD) system is added. Physically, the DTD provides an electrical torque that accounts for natural damping by considering speed differences between both low and high speed shafts (either side of the gearbox) [5]. It is modeled through a second-order transfer function as shown towards the bottom right of Figure 3:

As mentioned above, in this model the DTD is represented by an active power component, not a torque. The transfer function outputs an oscillating electrical power that has an efficient damping effect [5] (for parameters see Table 1).

Torque PI block

In Figure 5 the Torque PI Block can be seen. It acts as a PI-controller and is a subsystem of the active power control in Figure 3 [6].

For the calculation of the speed error input \(\omega_\mathrm{err}\) and the maximum electromagnetic torque input \(\tau_\mathrm{emax}\), see Section 4.1.

Proportional and integral parts of the controller

The proportional controller part is realized by \(K_\mathrm{Pp}\).

The integral part of the controller output is the minimum of the following two signals [6]:

• The output of the integral controller \(K_\mathrm{Ip}/K_\mathrm{Pp}\)
• A torque value increasing as a ramp with rising rate \(\mathrm{d}\tau_\mathrm{max}\), which can be used to control the mechanical stress or to meet grid code requirements. This is set to \(\tau_\mathrm{reset}\) when a low voltage fault occurs and ramps upwards after the fault.

Behavior during low voltage faults

The Delay Flag block takes a boolean value \(F_\mathrm{i}\) as input. If \(F_\mathrm{i}\) steps to 1, the integer output \(F_\mathrm{o}\) is 1 and a timer starts to run. As soon as \(F_\mathrm{i}\) steps back to 0, \(F_\mathrm{o}\) steps to 2 if the timer has not reached \(T_\mathrm{DVS}\). Once the timer reaches \(T_\mathrm{DVS}\), \(F_\mathrm{o}\) steps back to 0. [1]

The delay flag block is used to implement the following fault signals:

• \(F_\mathrm{reset}\) is true during a volage dip (\(u_\mathrm{WTC} < u_\mathrm{pdip}\)) as well as during and \(T_\mathrm{DVS}\) after a deep voltage dip (\(u_\mathrm{WTC} < u_\mathrm{DVS}\)).
• \(F_\mathrm{freeze\,I}\) is true during a voltage dip (\(u_\mathrm{WTC} < u_\mathrm{pdip}\))

These fault signals have the following functions:

• \(F_\mathrm{reset}\), while true,
  • resets and holds both integrators at \(\tau_\mathrm{reset}\) (see below); for the \(K_\mathrm{Ip}/K_\mathrm{Pp}\)-integrator this can be prevented by setting \(M_\mathrm{pUVRT} = \mathrm{false}\).
  • sets the speed error \(\omega_\mathrm{err}\), i.e. the input to the proportional controller part \(K_\mathrm{Pp}\), to zero
  • changes the upper ramp rate limit of \(\tau_\mathrm{reset}\) to \(\mathrm{d}\tau_\mathrm{maxUVRT}\) (usually set to zero, preventing \(\tau_\mathrm{reset}\) from inceasing during fault) [6]
• \(F_\mathrm{freeze\,I}\) freezes the integral controller part (\(K_\mathrm{Ip}/K_\mathrm{Pp}\)) while true.

The reset value \(\tau_\mathrm{reset}\) is the minimum value of:

• The measured voltage (during fault) multiplied by factor \(\tau_\mathrm{uscale}\)
• The output \(\tau_\mathrm{I}\) of the integrator itself
• \[u_\mathrm{TChook} + 1\]

\(\tau_\mathrm{uscale}\) can be used to alter the power injection behaviour during fault and also the starting point for power recovery after post-fault. For example, setting it to zero results in zero power injection during fault. Higher values increase power injection, until the current limitation system begins to act. See [6] for further details.

When \(F_\mathrm{reset}\) returns to false, the proportional controller \(K_\mathrm{Pp}\) will work again as before the fault. The integral controller will increase from \(\tau_\mathrm{reset}\) to steady-state, with a maximum rate dictated by \(\mathrm{d}\tau_\mathrm{max}\) [6].

Variable limits integrator with set/reset and freeze

The integrators used in the Torque PI model in Figure 5 need variable limits, set/reset and freeze functionalities. A suggestion for the implementation is shown below and the description follows thereafter.

model IntegratorVariableLimitsContinuousSetFreeze "Integrator with limited value of output (variable limits), set/reset and freeze"
    parameter Boolean DefaultLimitMax = true "If limitMin > limitMax : if true, y = limitMax, if false, y = limitMin";
    parameter Real K = 1 "Integrator gain";
    parameter Real LimitMax0 "Initial value of upper limit";
    parameter Real LimitMin0 "Initial value of lower limit";
    parameter Boolean ReinitWhenResetIsReleased = true "true: integrator state gets reinitialized to 'set' when 'reset' turns false. false: integrator state gets reinitialized to 'set' when 'reset' turns true.";
    parameter Real tDer = 1e-3 "Time constant of derivative filter for limits in s";
    parameter Real TolInput = 1e-5 "Tolerance on limit crossing for integrator input";
    parameter Real TolOutput = 1e-5 "Tolerance on limit crossing for integrator output";
    parameter Real LimitDeadband = 0.001 "Deadband for detecting a limit crossing of the integrator's state";
    Real w(start = Y0) "Integrator state variable";
    parameter Real Y0 = 0 "Initial or guess value of output (must be in the limits limitMin .. limitMax)";

    Real kFreezeMax "Freeze coefficient for upper limit";
    Real kFreezeMin "Freeze coefficient for lower limit";
    Real derLimitMax "Filtered derivative of upper limit of output";
    Real derLimitMin "Filtered derivative of lower limit of output";
    Modelica.Blocks.Interfaces.BooleanInput freeze "Optional connector of freeze signal";
    Modelica.Blocks.Interfaces.RealInput limitMax "Connector of Real input signal used as maximum of output y";
    Modelica.Blocks.Interfaces.RealInput limitMin "Connector of Real input signal used as minimum of output y";
    Modelica.Blocks.Interfaces.BooleanInput reset "Optional connector of reset signal";
    Modelica.Blocks.Interfaces.RealInput set "Optional connector of set signal";
equation
    
    ////////// reset or freeze: keep input = 0
    if freeze or reset then
        v = 0;
    else
        v = K * u;
    end if;
    
    ////////// reset: reinit integrator's state when set becomes false (or true, depending on ReinitWhenResetIsReleases)
    when if ReinitWhenResetIsReleased then not reset else reset then
      reinit(w, set);
    end when;
    
    ////////// integrator with limits
    derLimitMax = der(limitMax);
    derLimitMin = der(limitMin);
    kFreezeMax = 1 / 4 * (1 + tanh((w - limitMax) / TolOutput)) * (1 + tanh((v - derLimitMax) / TolInput));
    kFreezeMin = 1 / 4 * (1 + tanh((limitMin - w) / TolOutput)) * (1 + tanh((derLimitMin - v) / TolInput));
    der(w) = derLimitMax * kFreezeMax + derLimitMin * kFreezeMin + v * (1 - kFreezeMax - kFreezeMin);
    
    ////////// apply limit or set to output
    if limitMin > limitMax and DefaultLimitMax then
        y = limitMax;
    elseif limitMin > limitMax then
        y = limitMin;
    elseif w > limitMax+LimitDeadband then
        y = limitMax;
    elseif w < limitMin-LimitDeadband then
        y = limitMin;
    elseif reset then
        y = set;
    else
        y = w;
    end if;
end IntegratorVariableLimitsContinuousSetFreeze;

This blocks computes w as integral of the input u multiplied by the gain K, with v = K * u. If the integral reaches a given upper limit limitMax or lower limit limitMin, the integration is halted and only restarted if the input drives the integral away from the bounds.

This freeze is imposed through two coefficients kFreezeMax and kFreezeMin, each defined by a continuous expression involving the hyperbolic tangent, the integrator input v, the integrator output w, the limit limitMax or limitMin and its filtered derivative derLimitMax or derLimitMin.

The parameters TolInput and TolOutput determine the width of the transition zone from one domain to another.

The output y is the result of the limitation of w by both variable limits.

If the “upper” limit is smaller than the “lower” one, the output y is ruled by the parameter DefaultLimitMax: y is equal to either limitMax or limitMin.

set/reset

The integrator’s output is forced to the value of set while reset=true, as it is descibed in [1].

When reset returns to false (=falling edge), the integrator’s state is reinitialized to set to resume integration without a jump discontinuity (change ReinitWhenResetIsReleased to false to reinitialize at a rising edge instead).

freeze

If boolean input is set to true, the derivative of the state variable is set to zero.

Parameters

Typical values were gathered from the DIgSILENT PowerFactory [7] implementation of the model.

[!NOTE]

According to [1], using rotor speed instead of generator speed (by setting \(M_\mathrm{\omega Tqpi} = true\)) is an easy way to filter the speed measurement.

Table 2: Typical values for lookup table \(\omega(p)\), based on [7] implementation

Variables

Inputs

Outputs

Equations & algorithm

\(\omega_{\mathrm{DTD}} = \sqrt{k_{\mathrm{drt}} \left( \frac{1}{2 \cdot H_{\mathrm{WTR}}} + \frac{1}{2 \cdot H_{\mathrm{gen}}} \right)} \qquad(1)\)

(parameters from mechanical module)

Initial equations

For the used initialization helper variables, see Operating point and initialization helpers

The lookup-table \(\mathbf{\omega}(p)\) is the same as described in Figure 4.

\(x_\mathrm{pord\,0} = P_\mathrm{ord\,0} \qquad(2)\)

\(x_\mathrm{DTD1\,0} = x_\mathrm{DTD2\,0} = 0 \text{ (make sure to obtain steady zero output)} \qquad(3)\)

\(x_\mathrm{\omega ref\,0} = \mathbf{\omega}(P_\mathrm{0}) \qquad(4)\)

\(x_\mathrm{\omega filtp3\,0} = \omega_0 \qquad(5)\)

\(x_\mathrm{dprefmax\,0} = P_\mathrm{WTRef\,0} \qquad(6)\)

\(x_\mathrm{\tau reset\,0} = \begin{cases} U_\mathrm{0} \cdot \tau_\mathrm{uscale}, & \text{if } U_\mathrm{0} \cdot \tau_\mathrm{uscale} < P_\mathrm{ord\,0}/\omega_0\\ P_\mathrm{ord\,0}/\omega_0, & \mathrm{otherwise} \end{cases} \qquad(7)\)

\(x_\mathrm{d\tau max\,0} = \tau_\mathrm{emax\,0} \qquad(8)\)

\(\tau_\mathrm{emax\,0} = \begin{cases} P_\mathrm{WTRef\,0} / \mathbf{\omega}(P_\mathrm{0}),& \text{if } M_\mathrm{\omega T max}\\ P_\mathrm{WTRef\,0} / \omega_0, & \mathrm{otherwise} \end{cases} \qquad(9)\)

\(x_\mathrm{KIpKPp\,0} = \begin{cases} \tau_\mathrm{emax\,0},& \text{if } P_\mathrm{ord\,0}/\omega_0 > \tau_\mathrm{emax\,0}\\ \tau_\mathrm{emin},& \text{if } P_\mathrm{ord\,0}/\omega_0 < \tau_\mathrm{emin}\\ P_\mathrm{ord\,0}/\omega_0, & \mathrm{otherwise} \end{cases} \qquad(10)\)

Q control module

The WT Q Control Module consists of a normal path and a fast reactive current injection path, which acts during and some time after an event (voltage drop or rise). There are multiple possible operating modes for each path, described in detail in [8].

Depending on the mode, \(x_\mathrm{WTref}\) can be a voltage or reactive power setpoint.

The available control modes are listed in Table 5 and Table 6. The following descriptions have been based on [8] and [1].

For example in mode 1, the normal path consists of two cascaded Proportional-Integral (PI) controllers. The first one (reactive power controller) controls reactive power by generating a voltage reference for the second controller (voltage controller), which then generates the reactive current command \(i_\mathrm{qbasehook}\). Input and output limitations are applied.

During faults, the fast injection path adds an additional component to the q-axis current which is computed based on the voltage deviation \(\Delta u\), a dead-band and droop (gain \(K_\mathrm{qv}\)).

Special attention must be paid to the reactive current signs in [1], as they seem to be inconsistent [8]. In the fast injection path, \(u_\mathrm{WTC}\) voltage drop leads to \(\Delta u < 0\), resulting in \(i_\mathrm{qvhook} < 0\). This behavior is opposite to the normal path. To solve this, the fast injection path’s sign can be inverted, as has been done in Figure 6 (red -1 block).

Parameters

Variables:

Inputs

Outputs

Initial equations

For the used initialization helper variables, see Operating point and initialization helpers

\(x_\mathrm{Iu\,0} = x_\mathrm{qord\,0} = Q_\mathrm{ord\,0}/U_\mathrm{0} \qquad(11)\)

\(x_\mathrm{Iq\,0} = U_\mathrm{0} \qquad(12)\)

\(x_\mathrm{uss\,0} = 0 \qquad(13)\)

Q limitation

The Q limitation module consists of a set of lookup-tables that determine the maximum and minimum reactive power that can be supplied by the WT depending on active power and voltage. It can be used to implement the generator’s capability curve.

Parameters

Variables

Inputs

Outputs

Current limitation

The current limitation acts after the P and Q controls as shown in Figure 2. The priority between active and reactive current can be set by \(M_\mathrm{qpri}\). Outside FRT, P-Priority is always active regardless of \(M_\mathrm{qpri}\).

Current is limited to the maximum admissible current \(i_\mathrm{max}\). During FRT there is a separate maximum current value \(i_\mathrm{maxdip}\).

In addition to \(i_\mathrm{max}\), Voltage Dependent Limits (VDL) are defined for active and reactive current components through the look-up tables \(\mathbf{i_\mathrm{pmax}}(u_\mathrm{WT})\) and \(\mathbf{i_\mathrm{qmax}}(u_\mathrm{WT})\).

The current limitation contains an additional high-voltage current limit logic (Kpqu-logic), which limits voltage-supporting reactive current injection when voltage is already high (parameters \(u_\mathrm{pqumax}\), \(K_\mathrm{pqu}\)).

The following Figure 9 shows a python inspired pseudo-code implementation of the the current limitation as shown in [8].

M_DFSLim,imax_hook,iqmax_hook = (0,0,0)
if F_FRT == 1:
    i_maxset = i_maxdip
else: 
    i_maxset = i_max
# P Priority
if (M_qpri == 0) or (F_FRT == 0):
    i_pmax = i_pmaxVDL(u_WTCfilt)
    
    i_qlimit = min(
        i_qmaxVDL(u_WTCfilt),
        sqrt(max(0,
            i_maxset**2 - min(
                i_pcmd, 
                i_pmaxVDL(u_WTCfilt))**2) 
    ))
    i_qmin = -i_qlimit
    i_qmax = K_pqulogic(i_qlimit)
# Q Priority
else: 
    i_qlimit = i_qmaxVDL(u_WTCfilt)
    
    i_qmin = -i_qlimit
    i_qmax = K_pqulogic(i_qlimit)
    i_pmax = min(
        i_pmaxVDL(u_WTCfilt),
        sqrt(max(0,
            i_maxset**2 - min(
                abs(i_qcmd), 
                i_qmaxVDL(u_WTCfilt))**2)
    ))

Parameters

Variables

Inputs

Outputs

Mechanical module

Two-mass model to represent drive train oscillations (mass oscillations between generator rotor and WT rotor).

Parameters

Variables

Inputs

Outputs

Initial equations

For the used initialization helper variables, see Operating point and initialization helpers

\(x_\mathrm{WTR\,0} = x_\mathrm{gen\,0} = \omega_0 \qquad(14)\)

\(x_\mathrm{drt\,0} = P_\mathrm{ag\,0} / \omega_0 \qquad(15)\)

Two-dimensional aerodynamic module

The two-dimensional aerodynamic module is shown in Figure 11. \(\theta_0\) represents the rated pitch angle (refers to the angle at which the turbine blades are positioned to achieve maximum power output at a specific wind speed).

The rated pitch angle \(\theta_0\) is subtracted from the actual wind turbine pitch angle \(\theta\) to obtain \(\Delta\theta\). The pitch angle difference \(\Delta\theta\) is then multiplied by \(\mathrm{d}p_{\theta}\) to compute \(\Delta p_\mathrm{\theta}\), the change of aerodynamic power depending on the pitch angle change [3]. \(\mathrm{d}p_{\theta}\) is the the aerodynamic power partial derivative with respect to \(\theta\).

\(\Delta p_\mathrm{\theta}\) is typically negative because \(\mathrm{d}p_{\theta}<0\) and represents power redution because of pitch angle change. It is then added to the available power \(p_\mathrm{avail}\), which depends on wind speed.

To get the speed-dependent component \(\Delta p_\mathrm{\omega}\), first \(\Delta\omega\) is calculated from the wind turbine’s reference speed \(\omega_\mathrm{0}\) and the actual speed \(\omega_\mathrm{WTR}\). \(\Delta\omega\) is then multiplied by \(\mathrm{d}p_\mathrm{\omega}\), the aerodynamic power partial derivative with respect to \(\omega\).

\(\mathrm{d}p_\mathrm{\omega}\) is itself dependent on the pitch angle \(\theta\), so it is calculated from \(\theta\), \(\mathrm{d}p_\mathrm{\omega\theta}\) and \(\mathrm{d}p_\mathrm{\omega0}\), where \(\mathrm{d}p_\mathrm{\omega\theta}\) is the pitch-dependency of \(\mathrm{d}p_\mathrm{\omega}\). \(\mathrm{d}p_{\omega0}\) is the constant term of \(\mathrm{d}p_{\omega}\) and depends on the wind speed.

The resulting change \(\Delta p_\mathrm{\omega}\) of aerodynamic power depending on rotor speed is added to \(p_\mathrm{avail}\) as well, resulting in the wind turbine aerodynamic power \(p_\mathrm{aero}\) [3].

Parameters

Typical values were gathered from the DIgSILENT PowerFactory [7] implementation of the model.

[!NOTE]

According to [1], for \(0 < p_\mathrm{avail} < 1\) the pitch angle should be zero. It should be greater than zero if \(p_\mathrm{avail} = 1\) or if the initial value of \(p_\mathrm{aero}\) is less than \(p_\mathrm{avail}\).

Variables

Inputs

Outputs

Pitch angle control module

The pitch angle control module is shown in Figure 12. It uses two PI controllers to control the pitch angle \(\theta\), one associated with rotor speed (\(K_\mathrm{I\omega}\), \(K_\mathrm{P\omega}\)) and one with generator power (\(K_\mathrm{Ic}\), \(K_\mathrm{Pc}\)) [2].

The outputs of both PI controllers are pitch angle setpoints (\(\theta_\mathrm{\omega}\) and \(\theta_\mathrm{c}\)). They are kept inside their respective limits (\(\theta_\mathrm{\omega min|max}\) and \(\theta_\mathrm{cmin|max}\)), similarly for the pitch angles’ rates of change.

The rotor speed and power integrators are anti-windup, which means that the integrator is blocked when the lower or upper limit of \(\theta\) are reached, until the error input changes direction. Both controller outputs are added before a low-pass filter (time constant \(T_\theta\)) is applied. The filter with limitation detection considers the pitch angle limitation \(\theta_\mathrm{min|max}\) and pitch angle rate of change \(\mathrm{d}\theta_{\mathrm{min|max}}\).

The pitch angle rate of change plays a crucial role during power system faults since it avoids overspeeding during faults by controlling how fast the aerodynamic power is reduced [2].

Since a Doubly-Fed Induction Generator (DFIG) turbine is already operating at rated rotor speed before reaching nominal wind speed, under certain conditions, the pitch (\(\theta\) > 0) could be activated even though the generated active power is lower than 1 pu. Therefore, the cross-coupling gain \(K_\mathrm{PX}\) is used to modify the signal introduced into the rotor speed error [2].

Parameters

Typical values were gathered from the DIgSILENT PowerFactory [7] implementation of the model.

Variables

Inputs

Outputs

Initial equations

For the used initialization helper variables, see Operating point and initialization helpers

For the used parameters of the aerodynamic module, see Section 4.6

\(x_\mathrm{I\omega} = x_\mathrm{\theta \omega} = x_\mathrm{\theta} = \theta_0 + (P_\mathrm{ag\,0}-p_\mathrm{avail})/\mathrm{d}p_\mathrm{\theta} \qquad(16)\)

\(x_\mathrm{Ic} = x_\mathrm{\theta c} = 0 \qquad(17)\)

Generator system type 3

Description

Two different models (3A and 3B) have been definded in the IEC [1], depending on the FRT solution implemented for the WT.

FRT implies large currents in the rotor and large power injected into the DC circuit of the converter [2]. Rotor and converter protection against high currents and voltages is realized by a DC chopper and/or an AC crowbar circuit.

A DC chopper basically keeps the DC voltage constant by dissipating energy through a switched resistor. This implies controllability of the rotor by the converter during FRT.

A crowbar circuit consists of switchable resistances between the rotor’s phases. In case of undesirably high currents in the machine rotor or high DC voltages, the crowbar switches are closed and the rotor’s windings short-circuited through the crowbar resistances. This way, overcurrents and -voltages are prevented but there is no control action by the converter on the rotor windings anymore and the generator acts like a conventional slip-ring induction machine (Type 1 machine) [4]. This leads to a delay on the delivery of voltage control functionality as well as active and reactive power transients after fault inception and fault clearance [2].

Type 3A

The Type 3A Generator System represents a DFIG. Inside the WT controls, \(i_\mathrm{p}\) and \(i_\mathrm{q}\) represent active and reactive current components. On the grid side (gs), after the reference frame rotation, this is not the case, because the voltage angle is different. Hence, the PI current controller’s output as well as the feedback of the generator system’s current need to be rotated in either direction to match the respective reference frames.

Because the stator is directly coupled to the grid in case of a DFIG, an abrupt voltage variation will cause a change in the reactive power flow. The addition/subtraction of \(u / x_\mathrm{eqv}\) is added to simulate these electromagnetic transients (related to rotor flux derivative) [2] [6].

The air-gap power \(p_\mathrm{ag}\) is an additional output of the model, which is used as an input for the mechanical model in Figure 10.

In this model a DC chopper is assumed. The model is not applicable for older DFIG systems that require a crowbar during grid faults ([3], p. 111).

Type 3B

The Type 3B Generator System models a DFIG with crowbar circuit.

In the model, as shown in Figure 14, the crowbar system is not physically modeled but instead represented by multiplying the current commands by zero for a certain period of time when the voltage module’s derivative goes beyond a certain threshold [5].

Paramaters

Type 3A

Type 3B

Variables

Inputs

Outputs

Initial equations

For the used initialization helper variables, see Operating point and initialization helpers

\(x_\mathrm{Ip} = P_\mathrm{ord\,0}/U_0 \qquad(18)\)

\(x_\mathrm{Iq} = Q_\mathrm{ord\,0}/U_0 \qquad(19)\)

\(x_\mathrm{PIp} = x_\mathrm{PIq} = 0 \qquad(20)\)

\(x_\mathrm{intp} = I_\mathrm{gs\,re\,0} + \frac{U_\mathrm{gs\,im\,0}}{X_\mathrm{eqv}} \qquad(21)\)

\(x_\mathrm{intq} = I_\mathrm{gs\,im\,0} - \frac{U_\mathrm{gs\,re\,0}}{X_\mathrm{eqv}} \qquad(22)\)

\(x_\mathrm{Tgp} = I_\mathrm{gs\,re\,0} + \frac{U_\mathrm{gs\,im\,0}}{X_\mathrm{eqv}} \qquad(23)\)

\(x_\mathrm{Tgq} = I_\mathrm{gs\,im\,0} - \frac{U_\mathrm{gs\,re\,0}}{X_\mathrm{eqv}} \qquad(24)\)

\(x_\mathrm{wo} = 0 \qquad(25)\)

Assumptions in Modelica implementation

Grid measurement module

Calculates measured values from complex grid voltage and current and grid frequency.

Parameters

Variables

Inputs

Outputs

Initial equations

For the used initialization helper variables, see Operating point and initialization helpers

\(x_\mathrm{meas\,p} = P_0 \qquad(26)\)

\(x_\mathrm{meas\,q} = Q_0 \qquad(27)\)

\(x_\mathrm{meas\,i} = \frac{\sqrt{P_0^2 + Q_0^2}}{U_0} \qquad(28)\)

\(x_\mathrm{meas\,u} = U_0 \qquad(29)\)

\(x_\mathrm{meas\,f} = x_\mathrm{meas\,df} = 0 \qquad(30)\)

Protection module

The grid protection module offers protection against both over-voltage and under-voltage, as well as over-frequency and under-frequency conditions. As desribed in [1], this time-based grid protection has specific ranges of protection levels along with associated disconnection times.

Parameters

Variables

Inputs

Outputs

Wind power plant model

The Wind Plant (WP) model includes two controllers: active power / frequency controller (Figure 19) and and reactive power / voltage control (Figure 20).

Both, the P and Q controllers, freeze their state variables during FRT.

The WP model controls one single Point of Common Coupling (PCC). According to [1] it is normally enough to use a single aggregated model for all WTs in a WP. Still, also large WP can be modeled by using multiple WT models which all get the same reference values from the WP controller.

WP P Control

The active power controller controls P as a function of frequency or external reference changes [1].

Parameters

Variables

Inputs

Outputs

Initial equations

For the used initialization helper variables, see Operating point and initialization helpers

\(x_\mathrm{WPPref} = P_\mathrm{WTRef\,0} \qquad(31)\)

\(x_\mathrm{WPIp} = (1-K_\mathrm{WppRef})P_\mathrm{WTRef\,0} \qquad(32)\)

WP Q Control

The reactive power controller can control power factor, reactive power, or voltage [1]. Reactive power capability limitations are taken into account through the limitations in the WT model (Q limitation module).

Variables

Inputs

Outputs

Initial equations

For the used initialization helper variables, see Operating point and initialization helpers

\(x_\mathrm{uqfilt} = Q_0 \qquad(33)\)

\(x_\mathrm{WPIq} = \frac{Q_\mathrm{ord\,0}}{U_0} - Q_0 \cdot K_\mathrm{WPqref} \qquad(34)\)

\(x_\mathrm{PDrefRamprate} = \frac{Q_\mathrm{ord\,0}}{U_0} \qquad(35)\)

Linear communication delay module

Parameters

Variables

Inputs

Outputs

Base values

The following base values are defined according to [1]:

\(S_\mathrm{base} = \begin{cases} P_\mathrm{WT\,n} &\mbox{(wind turbine nominal power) if referring to the wind turbine}\\ S_\mathrm{AUX\,n} &\mbox{(auxiliary nominal power) if referring to auxiliary components}\\ P_\mathrm{WP\,n} &\mbox{(plant nominal power) if referring to the wind power plant} \end{cases} \qquad(36)\)

\(U_\mathrm{base} = \begin{cases} U_\mathrm{WT\,n} &\mbox{(wind turbine nominal voltage) if referring to the wind turbine}\\ U_\mathrm{AUX\,n} &\mbox{(auxiliary nominal voltage) if referring to auxiliary components}\\ U_\mathrm{WP\,n} &\mbox{(plant nominal voltage) if referring to the wind power plant} \end{cases} \qquad(37)\)

\(I_\mathrm{base} = \dfrac{S_\mathrm{base}}{\sqrt{3}U_\mathrm{base}} \qquad(38)\)

\(Z_\mathrm{base} = \dfrac{U_\mathrm{base}^2}{S_\mathrm{base}} \qquad(39)\)

\(\Omega_\mathrm{base} = \begin{cases} \omega_\mathrm{n} &\mbox{if referring to generator}\\ \dfrac{\omega_\mathrm{n}}{n_\mathrm{gearbox}} & \mbox{if referring to wind turbine rotor} \end{cases} \qquad(40)\)

\(T_\mathrm{base} = \dfrac{P_\mathrm{WT\,n}}{\Omega_\mathrm{base}} \mbox{ (use turbine nominal power)} \qquad(41)\)

\(x_\mathrm{base} = \begin{cases} S_\mathrm{base} &\mbox{if in reactive power control mode}\\ U_\mathrm{base} &\mbox{if in voltage control mode} \end{cases} \qquad(42)\)

Operating point and initialization helpers

Initial operating point parameters

\(\underline{u}_0 = U_0 \exp (\mathrm{j}\varphi_\mathrm{0}) \qquad(43)\)

\(\underline{i}_0 = ((P_0 + \mathrm{j}Q_0)/\underline{u}_0)^* \qquad(44)\)

\(U_\mathrm{gs\,re\,0} + \mathrm{j}U_\mathrm{gs\,im\,0} = \underline{u}_\mathrm{gs\,0} = \underline{u}_0 - \underline{Z} \cdot \underline{i}_0 \qquad(45)\)

\(I_\mathrm{gs\,re\,0} + \mathrm{j}I_\mathrm{gs\,im\,0} = \underline{i}_\mathrm{gs\,0} = \underline{i}_0 - \underline{Y} \cdot \underline{u}_\mathrm{gs\,0} \qquad(46)\)

\(P_\mathrm{ord\,0} = \begin{cases} P_\mathrm{0} & \text{for Type 3A}\\ U_\mathrm{0} \cdot ((I_\mathrm{gs\,re\,0} + \frac{U_\mathrm{gs\,im\,0}}{X_\mathrm{eqv}})\cos(\varphi_\mathrm{u\,0}) + (I_\mathrm{gs\,im\,0} - \frac{U_\mathrm{gs\,re\,0}}{X_\mathrm{eqv}})\sin(\varphi_\mathrm{u\,0})) & \text{for Type 3B} \end{cases} \qquad(47)\)

\(Q_\mathrm{ord\,0} = \begin{cases} Q_\mathrm{0} & \text{for Type 3A}\\ -U_\mathrm{0} \cdot ((I_\mathrm{gs\,re\,0} + \frac{U_\mathrm{gs\,im\,0}}{X_\mathrm{eqv}})\sin(\varphi_\mathrm{u\,0}) - (I_\mathrm{gs\,im\,0} - \frac{U_\mathrm{gs\,re\,0}}{X_\mathrm{eqv}})\cos(\varphi_\mathrm{u\,0}) &~\\ + \frac{\sqrt{U_\mathrm{gs\,re\,0}^2+U_\mathrm{gs\,im\,0}^2}}{X_\mathrm{eqv}}) & \text{for Type 3B} \end{cases} \qquad(48)\)

\(P_\mathrm{ag\,0} = \Re \left( (U_\mathrm{gs\,re\,0}+ \mathrm{j}U_\mathrm{gs\,im\,0}) \cdot (I_\mathrm{gs\,re\,0}- \mathrm{j}I_\mathrm{gs\,im\,0}) \right) \qquad(49)\)

Open questions

• It remained unclear to the authors what the torque PI input \(u_\mathrm{TChook}\) represents in the P Controller.

Open source implementations

This model has been successfully implemented in :

Table of references

[1] IEC 61400-27-1 Wind Energy Generation Systems – Part 27 – Electrical simulation models – Generic models. Jul. 2020.

[2] A. Honrubia-Escribano, E. Gómez-Lázaro, J. Fortmann, P. Sørensen, and S. Martin-Martinez, “Generic dynamic wind turbine models for power system stability analysis: A comprehensive review,” Renewable and Sustainable Energy Reviews, vol. 81, pp. 1939–1952, Jan. 2018, doi: 10.1016/j.rser.2017.06.005.

[3] J. Fortmann, Modeling of wind turbines with doubly fed generator system. Wiesbaden: Springer Vieweg,

1. doi: 10.1007/978-3-658-06882-0.

[4] J. Fortmann, S. Engelhardt, J. Kretschmann, C. Feltes, and I. Erlich, “New Generic Model of DFG-Based Wind Turbines for RMS-Type Simulation,” IEEE Transactions on Energy Conversion, vol. 29, no. 1, pp. 110–118, Mar. 2014, doi: 10.1109/TEC.2013.2287251.

[5] A. Lorenzo-Bonache, A. Honrubia-Escribano, F. Jiménez-Buendía, Á. Molina-García, and E. Gómez-Lázaro, “Generic Type 3 Wind Turbine Model Based on IEC 61400-27-1: Parameter Analysis and Transient Response under Voltage Dips,” Energies, vol. 10, no. 9, 9, p. 1441, Sep. 2017, doi: 10.3390/en10091441.

[6] A. Lorenzo-Bonache, A. Honrubia-Escribano, J. Fortmann, and E. Gómez-Lázaro, “Generic Type 3 WT models: Comparison between IEC and WECC approaches,” IET Renewable Power Generation, vol. 13, no. 7, pp. 1168–1178, 2019, doi: 10.1049/iet-rpg.2018.6098.

[7] DIgSILENT, “PowerFactory.” 2024. Available: https://www.digsilent.de/

[8] M. Franke, A. Guironnet, and C. Cardozo, “Comparing IEC and WECC Generic Dynamic Models for Type 4 Wind Turbines,” 2024.

[9] G. Tsourakis, B. M. Nomikos, and C. D. Vournas, “Contribution of Doubly Fed Wind Generators to Oscillation Damping,” IEEE Trans. Energy Convers., vol. 24, no. 3, pp. 783–791, Sep. 2009, doi: 10.1109/TEC.2009.2025330.