Generator Models

The generator characteristics must be provided if either the rigid or flexible shaft drive train model is specified. Three types of generator model are available:

A directly connected Fixed Speed Induction Generator model (for constant speed turbines),
A Variable Speed Generator model (for variable speed turbines), and
A variable slip generator model (providing limited range variable speed above rated)

In each case the generator torque response is represented by a first order lag. In addition, a custom / an external generator model may be interfaced to Bladed via the Generator DLL interface. This enables an external electrical dynamic model to be coupled to the Bladed turbine model. This is useful for calculations of terminal voltage variations and flicker, active and reactive power variations, and response to network voltage and frequency transients, which wind turbines are generally required to ride through without shutting down.

Fixed speed induction generator

This model represents an induction generator directly connected to the grid. Its characteristics are defined by the slip slope \(h\) and the short-circuit transient time constant \(\tau\). The air-gap or generator reaction torque \(Q\) is then defined by the following differential equation:

\[ \begin{equation} \dot{\bscalar{Q}} = \frac{1}{\bscalar{\tau}} \left(\bscalar{h} (\bscalar{\omega} - \bscalar{\omega}_0) - \bscalar{Q} \right) \label{eq:fixedSpeedInductionLag} \end{equation} \]

where \(\bscalar{\omega}\) is the actual generator speed and \(\omega_0\) is the generator synchronous or no-load speed.

The slip slope is calculated as

\[ \begin{equation} h = \frac{\bscalar{P}_r}{\bscalar{\varepsilon} \bscalar{\omega}_r (\bscalar{\omega}_r - \bscalar{\omega_0}) } \label{eq:slipSlope} \end{equation} \]

where \(\bscalar{\omega}_r\) is the generator speed at rated power output \(P_r\), given by \(\bscalar{\omega}_r = \bscalar{\omega}_0 (1 + \bscalar{S}/100)\) where \(\bscalar{S}\) is the rated slip in \(\%\), and \(\bscalar{\varepsilon}\) is the full load efficiency of the generator.

Variable speed generator

This model should be used for a variable speed turbine incorporating a frequency converter to decouple the generator speed from the grid frequency. The variable speed drive, consisting of both the generator and frequency converter, is modelled as a whole. A modern variable speed drive is capable of accepting a torque demand and responding to this within a very short time to give the desired torque at the generator air-gap, irrespective of the generator speed (as long as it is within specified limits). A first order lag model is provided for this response:

\[ \begin{equation} \bscalar{Q}_g = \frac{\bscalar{Q}_d}{1 + \bscalar{\tau}_e \bscalar{s}} \label{eq:varSpeedLag} \end{equation} \]

where \(\bscalar{Q}_d\) is the demanded torque, \(\bscalar{Q}_g\) is the air-gap torque, and \(\bscalar{\tau}_e\) is the time constant of the first order lag. Note that the use of a small time constant may result in slower simulations. If the time constant is very small, specifying a zero time constant will speed up the simulations, without much effect on accuracy.

A variable speed turbine requires a controller to generate an appropriate torque demand, such that the turbine speed is regulated appropriately. Details of the control models which are available with Bladed can be found in power production control.

The minimum and maximum generator torque must be specified. Motoring may occur if a negative minimum torque is specified.

The phase angle between current and voltage is specified assuming that both active and reactive power flows into the network are being controlled with the same time constant as the torque and the frequency converter controller is programmed to maintain constant power factor. The active power is the electrical power output by the generator \(P_{elec}\). The power factor can be specified by the user \(P_{factor}\). The reactive power \(P_{reactive}\) is computed as

\[ \begin{equation} P_{reactive} = \tan ( \arccos(P_{factor})) P_{elec}. \end{equation} \]

Note

If \(P_{factor} = 1/\sqrt{2}\) then \(P_{reactive} = P_{elec}\). It is recommended to use a value of \(P_{factor} > 1/\sqrt{2}\) so the reactive power does not exceed the electrical power (active power) output by the generator.

Variable slip generator

A variable slip generator is essentially an induction generator with a variable resistance in series with the rotor circuit (Bossanyi, 1991) and (Pedersen, 1995). Below rated power, it acts just like a fixed speed induction generator, so the same parameters are required as described in fixed speed Induction Generator.

Above rated, the variable slip generator uses a fast-switching controller to regulate the rotor current, and hence the air-gap torque, so the generator behaves just like a variable speed system, albeit with a limited speed range. Therefore, the same parameters as for a variable speed system must also be supplied as described in Variable Speed Generator, except for the phase angle since power factor control is not available in this case.

Drive Train Damper

An option for drive train damping feedback is provided. This represents additional functionality which may be available in the frequency converter controller which adds a term derived from measured generator speed onto the incoming torque demand. This term is defined as a transfer function acting on the measured speed. The transfer function is supplied as a ratio of polynomials in the Laplace operator, \(s\). Thus, the equation for the air-gap torque \(\bscalar{Q}_g\) becomes

\[ \begin{equation} \bscalar{Q}_g = \frac{\bscalar{Q}_d}{1 + \bscalar{\tau}_e s} + \frac{\bscalar{a}_0 + \bscalar{a}_1 \bscalar{s} + \cdots + \bscalar{a}_8 \bscalar{s}^8}{\bscalar{b}_0 + \bscalar{b}_1 s + \cdots + \bscalar{b}_8 \bscalar{s}^8} \label{eq:generatorTransferFunction} \end{equation} \]

where the coefficients \(\bscalar{a}_i\), \(\bscalar{b}_i\) for \(\bscalar{i}=0,\ldots,8\) need to be defined by the user. The transfer function would normally be a tuned bandpass filter designed to provide some damping for drive train torsional vibrations, which in the case of variable speed operation may otherwise be very lightly damped, sometimes causing severe gearbox loads.