Wind Energy Generation: Modelling and Control

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Review This Product. Welcome to Loot. Checkout Your Cart Price. Description Details Customer Reviews With increasing concern over climate change and the security of energy supplies, wind power is emerging as an important source of electrical energy throughout the world. Modern wind turbines use advanced power electronics to provide efficient generator control and to ensure compatible operation with the power system. It also discusses how they interact with the power system and the influence of wind turbines on power system operation and stability.

Key features: Includes a comprehensive account of power electronic equipment used in wind turbines and for their grid connection. Describes enabling technologies which facilitate the connection of large-scale onshore and offshore wind farms. Provides detailed modelling and control of wind turbine systems.

Shows a number of simulations and case studies which explain the dynamic interaction between wind power and conventional generation. Review This Product No reviews yet - be the first to create one! Need help? Partners MySchool Discovery.

The text presented in this book draws together material on modelling and control of wind turbines from many sources, e. Through these programmes the authors have had the chance to interact closely with industrial partners utilities, power electronic equipment manufacturers and wind farm developers and get useful points of view on the needs and priorities of the wind energy sector concerning wind turbine generator dynamic modelling and control.

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The authors would like to thank Prof. Jim McDonald and Prof. Thanks are also given to Dr. Nolan Caliao and Mr. Piyadanai Pachanapan who assisted in the preparation of drawings, to Dr. Special thanks go to Dr. Ramtharan Gnanasambandapillai who gave permission to include material from his PhD thesis in Chapter 7.

The electricity system is viewed as being easier to transfer to low-carbon energy sources than more challenging sectors of the economy such as surface and air transport and domestic heating. Hence the use of cost-effective and reliable low-carbon electricity generation sources, in addition to demand-side measures, is becoming an important objective of energy policy in many countries EWEA, ; AWEA, Over the past few years, wind energy has shown the fastest rate of growth of any form of electricity generation with its development stimulated by concerns of national policy makers over climate change, energy diversity and security of supply.

Figure 1. This projects the growth of all renewables including wind power, up to Usually, sites are preselected based on general information of wind speeds provided by a wind atlas, which is then validated with local measurements. The local wind resource is monitored for 1 year, or more, before the project is approved and the wind turbines installed. Onshore turbine installations are frequently in upland terrain to exploit the higher wind speeds.

Offshore development, particularly of larger wind farms, generally takes place more than 5 km from land to reduce environmental impact. The advantages of offshore wind farms include reduced visual intrusion and acoustic noise impact and also lower wind turbulence with higher average wind speeds. Electricity Generation from Wind Energy 3 Table 1. In general, the areas of good wind energy resource are found far from population centres and new transmission circuits are needed to connect the wind farms into the main power grid.

For example, it is estimated that in Germany, approximately km of additional high-voltage and extra-high-voltage lines will be required over the next 10 years to connect new wind farms Deutsche Energie-Agentur GmbH, Table 1. Wind passes over the blades, generating lift and exerting a turning force. The rotating blades turn a shaft inside the nacelle, which goes into a gearbox.

The power output goes to a transformer, which converts the electricity from the generator at around V to the appropriate voltage for the power collection system, typically 33 kV. A wind turbine extracts kinetic energy from the swept area of the blades Figure 1. Although Eq. Hence, one argument for operating a wind turbine at variable rotational speed is that it is possible to operate at maximum Cp over a range of wind speeds. The power output of a wind turbine at various wind speeds is conventionally described by its power curve.

The power curve gives the steady-state electrical power output as a function of the wind speed at the hub height and is generally 0. An example of a power curve is given in Figure 1. Above rated wind speed the aerodynamic rotor is arranged to limit the mechanical power extracted from the wind and so reduce the mechanical loads on the drive train.

Then at very high wind speeds the turbine is shut down. The choice of cut-in, rated and cut-out wind speed is made by the wind turbine designer who, for typical wind conditions, will try to balance obtaining Electricity Generation from Wind Energy 7 maximum energy extraction with controlling the mechanical loads and hence the capital cost of the turbine. Power curves for existing machines can normally be obtained from the turbine manufacturer.

However, commercial designs for electricity generation have now converged to horizontal axis, three-bladed, upwind turbines. Modern electricity-generating wind turbines now use three-bladed upwind rotors, although two-bladed, and even one-bladed, rotors were used in earlier commercial turbines. Reducing the number of blades means that the rotor has to operate at a higher rotational speed in order to extract the wind energy passing through the rotor disk. Although a high rotor speed is attractive in that it reduces the gearbox ratio required, a high blade tip speed leads to increased aerodynamic noise and increased blade drag losses.

Most importantly, three-bladed rotors are visually more pleasing than other designs and so these are now always used on large electricity-generating turbines. The generator operating slip changes slightly as the operating power level changes and the rotational speed is therefore not entirely constant. Squirrel-cage induction machines consume reactive power and so it is conventional to provide power factor correction capacitors at each wind turbine.

Also, by applying the network voltage slowly to the generator, once energized, it brings the drive train slowly to its operating rotational speed. The drivers behind these developments are mainly the ability to comply with Grid Code connection requirements and the reduction in mechanical loads achieved with variable-speed operation. It uses a wound-rotor induction generator with slip rings to take current into or out of the rotor winding and variable-speed operation is Electricity Generation from Wind Energy 9 Wound rotor induction generator Power Converter Crowbar Figure 1.

The power converter decouples the network electrical frequency from the rotor mechanical frequency, enabling variable-speed operation of the wind turbine. A DFIG system can deliver power to the grid through the stator and rotor, while the rotor can also absorb power. This depends on the rotational speed of the generator.

If the generator operates above synchronous speed, power will be delivered from the rotor through the converters to the network, and if the generator operates below synchronous speed, then the rotor will absorb power from the network through the converters. This type of turbine may or may not include a gearbox and a wide range of electrical generator types can be employed, for example, induction, wound-rotor synchronous or permanent magnet synchronous. As all of the power from the turbine goes through the power converters, the dynamic operation of the electrical generator is effectively isolated from the power grid Akhmatov et al.

The electrical frequency of the generator may vary as the wind speed changes, while the grid frequency remains unchanged, thus allowing variable-speed operation of the wind turbine. The network-side converter can be arranged to maintain the DC bus voltage constant with torque applied to the generator controlled from the generator-side converter. Alternatively, the control philosophy can be reversed. Active power is transmitted through the converters with very little energy stored in the DC link capacitor. Hence the torque applied to the generator can be controlled by the network-side converter.

Each converter is able to generate or absorb reactive power independently. Due to these differences, wind generation interacts differently with the network and wind generation may have both local and system-wide impacts on the operation of the power system. Electricity Generation from Wind Energy 11 System-wide impacts, on the other hand, affect the behaviour of the power system as a whole. They are an inherent consequence of the utilization of wind power and cannot be attributed to individual turbines or farms UCTE, This type of generator cannot control busbar voltages by itself controlling the reactive power exchange with the network.

Variable-speed turbines have, in principle, the capability of varying the reactive power that they exchange with the grid to affect their terminal voltage. In practice, this capability depends to a large extent on the rating and the controllers of the power electronic converters. Fixed-speed turbines, in common with all directly connected spinning plant, contribute to network fault currents. Variable-speed DFIG wind turbines also contribute to network fault currents with the control system of the power electronic converters detecting the fault very quickly.

Due to the sensitivity of the power electronics to over-currents, this type of wind turbine may be quickly disconnected from the network and the crowbar activated to short-circuit the rotor windings of the wound-rotor induction generator, unless special precautions are taken to ensure Grid Code compliance. Again, this wind turbine type may also disconnect quickly in the case of a fault, if the Grid Codes do not require a Fault Ride Through capability.

The behaviour of power converter-connected wind turbines during network faults depends on the design of the power converters and the settings of their control systems. There are as yet no agreed international standards for either the fault contribution performance required of converter-connected generators or how such generators should be represented in transient stability or fault calculator simulation programs. A conservative design approach is to assume that such generators do contribute fault current when rating switchgear and other plant, but not to rely on such fault currents for protection operation.

Harmonic distortion is mainly associated with variable-speed wind turbines because these contain power electronic converters, which are an important source of high-frequency harmonic currents. It is increasingly of concern in large offshore wind farms, where the very extensive cable networks can lead to harmonic resonances and high harmonic currents caused by existing harmonic voltages already present on the power system or by the wind turbine converters.

The stored energy of the spinning mass of the rotor acts as an energy buffer. During a fault and consequent network voltage depression , they accelerate due to the imbalance between the mechanical power from the wind and the electrical power that can be supplied to the grid. When the fault is cleared, they absorb reactive power, depressing the network voltage.

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If the voltage does not recover quickly enough, the wind turbines continue to accelerate and to consume large amounts of reactive power. This eventually leads to voltage and rotor speed instability. In contrast to synchronous generators, the exciters of which increase reactive power output during low network voltages and thus support voltage recovery after a fault, squirrel-cage induction generators tend to impede voltage recovery. With variable-speed wind turbines, the sensitivity of the power electronics to over-currents caused by network voltage depressions can have serious consequences for the stability of the power system.

Such a voltage drop could be caused, for instance, by a fault in the transmission grid. To prevent this, grid companies and transmission system operators require that wind turbines have a Fault Ride Through capability and are able to withstand voltage drops of certain magnitudes and durations without tripping.

This prevents the disconnection of a large amount of wind power in the event of a remote network fault. Variable-speed wind turbines have the capability of reactive power control and may be able to support the voltage of the network to which they are connected. However, individual control of wind turbines may not be able to control the voltage at the point of connection, especially because the wind farm network is predominantly capacitive a cable network.

On many occasions, the reactive power and voltage control at the point of connection of the wind farm is achieved by using reactive power compensation equipment such as static var compensators SVCs or static synchronous compensators STATCOMs. Hence, in order to respond to low network frequency, it is necessary to de-load the wind turbine leaving a margin for power increase.

A variable-speed wind turbine can be de-loaded by operating it away from the maximum power extraction curve, thus leaving a margin for frequency control. The connection codes normally focus on the point of connection between the public electricity system and the new generation. This is very important for wind farm connections, as the Grid Codes demand requirements at the point of connection of the wind farm not at the individual wind turbine generator terminals.

The grid connection requirements differ from country to country and may differ from region to region. Grid Codes also specify the steady-state operational region of a power plant in terms of active and reactive power requirements. For example, Figure 1. Almost all Grid Codes now impose the requirement that wind farms should be able to provide primary frequency response. However, with the penetration of wind generation increasing, Grid Codes now generally demand Fault Ride Through capability for wind turbines connected to transmission networks.

Grid Codes are under continual review and, as the level of wind power increases, are likely to become mode demanding. Akhmatov, V. Part 1: modelling in dynamic simulation tools, Wind Engineering, 27, — Burton, T. Summary available online at: www. Elliot, D. EWEA, Brussels. Fox, B. Heier, S. Holdsworth, L. Manwell, J. Slootweg, J. PhD thesis. Technical University of Delft. Variable-speed wind turbines decouple the rotational speed from the grid frequency through a power electronic interface. Variable-speed operation can be achieved by using any suitable combination of generator, synchronous or asynchronous, and a power electronic interface.

In FRC wind turbines, the power electronic interface is connected to the stator of the generator. In DFIG wind turbines, the power electronic interface is connected between the stator and the rotor, and allows variable-speed operation of the wind turbine by injecting a variable voltage into the rotor at slip frequency. The output of a wind farm changes constantly with wind conditions and so causes variations in the voltage at the point of connection.

This can be compensated by proper control of the power electronic converters of the wind turbine generators, within the rating and operating capability of the wind turbine generator and the converters. A reactive power compensator can also be used to improve the stability of the network to which the wind farm is connected. For large wind farms, high-voltage direct current HVDC power electronic converters may be employed to control bulk active power transfer through the DC link with independent control of reactive power both at the wind farm and to the network, as shown in Figure 2.

The soft-starter consists of six thyristors, two per phase connected in anti-parallel, as shown in Figure 2. An RC snubber circuit is connected in series across the thyristors to control the rate of change of voltage across the thyristors. Automatic transition to the off-state occurs when the device current reaches zero.

In this way, the phase current is gradually increased to the rated current. When the rated current is reached, the soft-starter is by-passed by the contactor. The two-level VSC allows the IGBTs to be connected in series, depending on the voltage rating of the device available and the supply voltage required. The basic principle of a single-phase, two-level VSC is shown in Figure 2. Therefore, each switch string must be rated for the full direct voltage, VDC. Due to the large capacitance of the DC side of the converter, the DC voltage, VDC , is more or less constant and thus the converter is known as a voltage source converter.

Three single-phase, two-level voltage source converters can be connected to the same capacitor to form a three-phase converter. Therefore, one switching function is enough to control both switches in a leg. There are a number of different switching strategies for VSCs Mohan et al. No two switches in the same leg conduct simultaneously. The six conducting switching patterns during six distinct intervals [marked as 1 to 6 in Figure 2.

With fundamental frequency switching, the switching losses are low since switching losses are proportional to the switching frequency , but the harmonic content of the output waveforms is relatively high. If the single-phase two-level circuit of Figure 2. This condition is termed over-modulation Mohan 1. As ma is increased beyond 3. This then reduces the ratings required for the converter elements and decreases the turn-on losses of the converter elements.

However, the lower-order harmonic content of the output waveform is increased Holtz, ; Taniguchi et al. Figure 2. By introducing k number of chops per half cycle into the converter output voltage Figure 2. This method has the advantage of being easier to implement than other PWM techniques and achieves similar results to regular sampled sinusoidal PWM with third harmonic added to the Power Electronics for Wind Turbines 31 reference waveform.

A single rotating vector can be used to represent three-phase voltages. This vector is called the voltage space vector which generally rotates in a two-dimension plane. In the SV-PWM technique, the sequence of the switching vectors is selected in such a way that only one leg is switched to move from one switching vector to the next. This switching sequence is achieved by arranging the adjacent active vectors and two-null vectors Boost and Ziogas, ; Holtz, The switching times of the switching vectors are calculated by equating volt-second integrals between the required voltage vector and the switching vectors.

The required voltage vector Vs is generated by using the adjacent active switching vectors V1 , V2 and the null vectors V0 and V7. The magnitude of the required voltage vector is assumed to be constant during the switching period, Ts. If the actual current is more positive than the upper hysteresis level, then the converter is switched such that the current is reduced and vice versa Brod and Novotny, One advantage of this control is its ease of implementation.

Table 2. This arrangement decouples the wind turbine from the AC grid, thus allowing variable-speed operation of the wind turbine. This will ensure the power transfer between the DC link and the grid if incoming power is not transferred to the grid, then the DC link voltage will increase. In variable-speed wind turbines, the frequency of the reference sinusoidal waveform Vref in Figure 2.

Therefore, the frequency of the output voltage of the VSC contains a component at the frequency of the generated voltage, referred to as the fundamental and also higher-order harmonics. The magnitude of the VSC output voltage can be controlled by changing the amplitude modulation index and the phase angle can be controlled by controlling the phase angle of Vref with respect to the generated voltage.

As the wind turbine generator can be represented by a voltage behind a reactance Kundur, , the generator-side connection of the VSC can be represented by the equivalent circuit shown in Figure 2. Hence Eqs 2. Similarly, as the other VSC is connected to the grid via a reactor or via a transformer, the power transfer between that VSC and the grid can also be described using the same principle. For example, by maintaining the DC link voltage constant, it is possible to make sure that the generated power is transferred to the grid.

The main advantages of using back-to-back VSCs include the following: a it is a well-established technology and has been used in machine drive-based applications for many years; b many manufacturers produce components especially designed for this type of converter; and c the decoupling of the two VSCs through a capacitor allows separate control of the two converters.

References Boost, M. Bowes, S. Brod, D. Buja, G. Holtz, J.

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Kundur, P. Lindberg, L. PhD Thesis. Royal Institute of Technology, Stockholm. Mohan, N. Patel, H. Taniguchi, K. Van der Broeck, H. The armature has a concentrated three-phase winding as shown in Figure 3. Even though in this chapter the dynamic equations are derived for a salient-pole generator, they are equally true for a round-rotor generator. Further, stator windings are also arranged to help produce a sinusoidal voltage waveform. Hence, for modelling purposes, the only difference is in the parameter values due to the different physical constructions.

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As shown in Figure 3. This representation is often used for steady-state studies of electrical machines. Therefore, for dynamic studies the electrical machine model is based on a two-phase representation. Therefore, this three-coil structure fed with direct current and rotating at synchronous speed can be used as an analogue for the stator of a synchronous generator. From Eqs 3. When deriving these equations it was assumed that the three-phase currents are balanced. The voltage equations Eqs 3. However an additional term of speed is present in these equations.

Dividing Eq. Table 3. Similarly, all the other equations in Table 3. When the synchronous generator carries unbalanced currents, the zero sequence current component, i 0s , should also be considered. Under such conditions, in addition to the equations given in Table 3. From Eq. In the case of salient-pole generators, damper bars are set into the pole faces as shown in Figure 3. In the case of cylindrical-pole generators, the coil wedges shown in Figure 3.

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The currents in the damper windings can be resolved into two components. The circulating damping current under a pole forms the d axis damping current; fkq q-axis d-axis fkq ikQ fkd fkd ikD is ax q- 48 37 ikQ Rotor surface In the generator model shown in Figure 3. Although the same basic representation can be used for both salient-pole and cylindrical-pole generators, the circuit parameters representing the damper windings are widely different. The synchronous generator equations in the dq domain are summarized in Table 3.

The stator voltage equations Eqs 3. The following 52 Wind Energy Generation: Modelling and Control differential equations are directly derived and 3. Loads connected to the power system have different characteristics and vary continuously in time. In order to operate the power system within the limits required voltage and frequency and in order to maintain the stability of the system in case of a disturbance, large generators are controlled individually and collectively. The different controls associated with a synchronous generator are shown in Figure 3.

Under heavy-load conditions, both the transmission system and the loads absorb reactive power and the synchronous generators need to inject reactive power into the network. Under light-load conditions, the capacitive behaviour of the transmission lines can become dominant and under such conditions it is desirable for synchronous generators to absorb reactive power. The variations in reactive power demand on a synchronous generator can be accommodated by adjusting its excitation voltage.

The excitation system performs the basic function of automatic voltage regulation. It also performs the protective functions required to operate the machine and other equipment System level signals Generating unit control Prime mover control Shaft power Excitation control Field Current Generator Voltage Speed Electric power Figure 3. A block diagram of an excitation system is shown in Figure 3.

If the generator terminal voltage falls due to increased reactive power demand, the change in voltage is detected and a signal is fed into the exciter to produce an increase in excitation voltage. The generator reactive power output is thereby increased and the terminal voltage is returned close to its initial value. The exciter may be a DC generator on small set sizes. Static excitation systems are also widely used. The necessity of employing slip rings and avoiding the associated maintenance requirement can be removed by employing brushless-excitation systems.

Building an additional loop to the AVR control allows the voltage at a remote point on the network to be controlled. The load compensator has adjustable resistance and reactance that simulates the impedance between the generator terminals and the point at which the voltage is being effectively controlled.

Using this impedance and the measured current, the voltage drop is computed and added to the terminal voltage. The commonly used auxiliary stabilizing signals to control the excitation are shaft speed, terminal frequency and power. If, for example, the network load increases, then this imposes increased torques on the generators, which causes them to decelerate.

Wind Energy Generation: Modelling and Control

The resulting decrease in speed is detected by the governor of each regulating prime mover and used to increase its power output. The change in power produced in an individual generator is determined by the droop setting of its governor. At the steady state, all the generators of the network operate at the same frequency and this frequency determines the operating speeds of the individual generator prime movers. Hence, following a network load increase, the network frequency will fall until the sum of the power output changes that it produces in the regulating generators matches the change in the network load.

The basic elements of a governor power control loop are shown in a block diagram in Figure 3. By changing the load reference set point, Pref , the generator governor characteristics Figure 3. In other words, it shifts the characteristic vertically. References Fitzgerald, A. Jr and Umans, S. Hindmarsh, J. Krause, P. Wood, A. The rotor circuits have three distributed windings, ar, br and cr. The slip is positive if the rotor runs below the synchronous speed and negative if it runs above the synchronous speed Kundur, ; Krause et al. The rotor of an induction machine may be one of two types: the squirrel-cage rotor and the wound rotor.

In use, the squirrel cage adopts the current pattern and pole distribution of the stator, enabling a basic rotor to be used for machines with differing pole numbers. However, for analysis purposes a squirrel-cage rotor may be treated as a symmetrical, short circuited star-connected three-phase winding. This winding is usually star connected with the ends of the winding brought out to three slip-rings, enabling external circuits to be added to the rotor for control purposes. As can be seen in Eq. For simple analysis of torque—slip relationships, the equivalent circuit of Figure 4.

At standstill the speed is zero and the slip, s, is equal to 1 per unit pu. Between zero and synchronous speed, the machine performs as a motor. Beyond synchronous speed, the machine performs as a generator. Figure 4. One way of controlling the rotor resistance and therefore the slip and speed of the generator , is to use a wound rotor connected to external variable resistors through brushes and slip-rings.

The rotor resistance is then adjusted by means of electronic equipment. Therefore, if the generator is not disconnected from the network in an appropriate time, it can accelerate to an unstable condition. Following a voltage drop, the machine moves to point Y, at which point the machine speeds up because the mechanical torque is higher than the electrical torque.

The generator typically operates at V line—line and transmits power via vertical pendant cables to a switchboard and local transformer usually located in the tower base. As induction generators always consume reactive power, capacitor banks are employed to provide the reactive power consumption of the FSIG and improve the power factor. An anti-parallel thyristor soft-start unit is used to energize the generator once its operating speed is reached.

Energy capture can be increased by varying the rotational speed with the wind speed so that the turbine is always running at optimum tip-speed ratio. Two-speed operation is relatively expensive to implement if separate generators are used for each speed of turbine rotation. Either generators with differing numbers of poles may be connected to gearbox output shafts rotating at the same speed or generators with the same number of poles are connected to output shafts rotating at different speeds.

The rating of the generator for low-speed operation would normally be much less than the turbine rating. Fixed-speed Induction Generator FSIG -based Wind Turbines 63 The development of induction generators with two sets of windings allows the number of poles within a single generator to be varied by connecting them together in different ways, a technique known as pole amplitude modulation PAM Eastham and Balchin ; Rajaraman, Alternatively, two independent windings may be placed on the same stator. Generators of this type are available which can be switched between four- and six-pole operation, giving a speed ratio of 1.

Above rated, however, control of the resistance effectively allows the air-gap torque to be controlled and the slip speed to vary, so that behaviour is then similar to that of a variable-speed system. Slip-rings can be avoided by mounting the variable resistors and control circuitry on the generator rotor. An advantage of mounting these externally via slip-rings is that it is then easier to dissipate the extra heat which is generated above rated and which may otherwise be a limiting factor at large sizes.

It is known that reactive power does not contribute to direct energy conversion. The current associated with it, the reactive current, however, causes losses in the supply and in the machine. Due to the large amount of reactive power drawn from the network, the voltage across the transmission line drops. The voltage at the point of connection with the network decreases as the slip increases. In the synchronous reference frame, all the coils are then stationary and thus inductances are constant. The constant T 0 is the per unit transient open-circuit time constant of the induction machine and in this form it is expressed in radians.

The reduced order equations presented above are also applicable with time t and the time constant T 0 expressed in seconds. This equation is of major importance in power 68 Wind Energy Generation: Modelling and Control system stability analysis as it describes the effect of any mismatch between the electromagnetic torque and the mechanical torque of the machine. Equation 4. The differential terms representing the stator transients are then neglected. Neglecting these corresponds to ignoring the DC component in the stator transient current.

Capacitive compensation is provided on the generator terminals. The electrical torque output of the FSIG follows the new torque reference after a short transient period. It is seen that the speed of the FSIG also decreases as the mechanical input torque decreases. In both cases the voltage dip is sustained for a period of ms. As Vinf drops the electrical torque of the generator, Te , decreases but recovers to its initial value. However, the generator continually accelerates while the voltage is low. During the fault the generator overspeeds and the terminal voltage starts to reduce further as more reactive Wind Energy Generation: Modelling and Control 1.

However, when the fault is cleared the generator and the network recover stability. The responses in Figure 4. When the stator transients are neglected, the FSIG responses contain only the fundamental frequency component. These oscillations are also present in the responses of the terminal voltage and torque of the generator as shown in Figure 4.

The system is unstable for a fault that lasts longer than ms runaway. If the fault remains longer, the system loses stability, as illustrated in Figure 4. Eastham, J. Rajaraman, K. Tande, J. Thiringer, T. It uses a wound-rotor induction generator with slip-rings to transmit current between the converter and the rotor windings and variable-speed operation is obtained by injecting a controllable voltage into the rotor at the desired slip frequency Holdsworth et al.

The variable-frequency rotor supply from the converter enables the rotor mechanical speed to be decoupled from the synchronous frequency of the electrical network, thereby allowing variable-speed operation of the wind turbine. A DFIG wind turbine can transmit power to the network through both the generator stator and the converters. When the generator operates in super-synchronous mode, power will be delivered from the rotor through the converters to the network, and when the generator operates in sub-synchronous mode, the rotor will absorb power from the network through the converters.

These two modes of operation are illustrated in Figure 5. The equivalent circuit of Figure 5. The torque—slip curves for the DFIG can be calculated from the approximate equivalent circuit model using the following equations Hindmarsh, An example where rotor injection is used to drive the machine into sub- and super-synchronous speeds is given in Figure 5. With a negative injected voltage vr , the speed of the machine will increase to super-synchronous operation as shown by curve 1. To reduce the speed of the machine to sub-synchronous operation, a positive voltage vr is applied; the torque—slip characteristic for this case is illustrated by curve 2.

At sub synchronous speed point B in Figure 5. Rearranging terms in Eq 5. Mechanical and other restrictions limit the maximum slip and a practical speed range may be between 0. This vector diagram provides an understanding of the way in which the machine is controlled and it can be readily employed for control design purposes. The bold font notation is used to represent a vector. Hence, since the magnitude of the internal voltage, E g , varies only slightly, the magnitude of the rotor voltage is approximately proportional to the slip magnitude.

Further, for sub-synchronous operation where slip, s, is positive, V r is approximately in-phase with the internal voltage vector E g and Doubly Fed Induction Generator DFIG -based Wind Turbines 83 for super-synchronous operation, where s is negative, the two voltage vectors are approximately in anti-phase Figure 5.

One control scheme, implemented by a number of manufacturers and modelled in this chapter, uses the rotor-side converter to provide torque control together with terminal voltage or power factor PF control for the overall system, while the network-side converter controls the DC link voltage. In some applications, the network-side converter is used to provide reactive power. The aim of the control strategy is to extract maximum power from the wind. A typical wind turbine characteristic with the optimal power extraction—speed curve plotted to intersect the Cp max points for each wind speed is shown in Figure 5.

The complete generator torque—speed characteristic, which is applied for the controller model is shown in Figure 5. For optimal power extraction, the torque—speed curve is characterized by Eq. This is between points B and C. Within this operating range, during low to medium wind speeds, the maximum possible energy can then be extracted from the turbine. Due to power converter ratings, it is not practical to maintain optimum power extraction over all wind speeds.

Therefore, for very low wind speeds the model operates at almost constant rotational speed A—B. The rotational speed is also often limited by aerodynamic noise constraints, at which point the controller allows the torque to increase, at essentially constant speed C—D until rated torque. If the wind speed increases further to exceed the turbine torque rating, the control objective follows D—E, where the electromagnetic torque is constant.

When the system reaches point E, pitch regulation takes over from the torque control to limit aerodynamic input power. For very high wind speeds, the pitch control will regulate the input power until the wind speed shutdown limit is reached. The rotor current is split into two orthogonal components, d and q. The q component of the current is used to regulate the torque and the d component is used to regulate power factor or terminal voltage.

For convenience, this controller is termed PVdq control in this book. Given a rotor speed measurement, the reference torque provided by the wind turbine characteristic for maximum power extraction Figure 5. The rotor voltage vqr required to operate at the reference torque set point is obtained through a PI controller and the summation of a compensation term to minimize cross-coupling between speed and voltage control loops. Using the expressions for the voltage behind a transient reactance, ed and eq [Eqs 4. A block diagram of this control scheme is shown in Figure 5.

Although the over-bar notation to identify per unit quantities has been omitted, all the variables shown in the block diagram are in per unit. To obtain the required value of the rotor voltage in the q-axis, v qr , a compensation term is added to the PI compensator to minimize the cross-coupling between torque and voltage control loops. Although reactive power injection can also be obtained from the network-side converter, for DFIG voltage control schemes the rotor-side converter is likely to be preferred to the network-side converter.

This is the main reason why the rotor-side converter is the preferred option to provide the machine requirements for reactive power. The control action for terminal voltage or power factor control is derived as follows Holdsworth et al. The total reactive power is also divided into Qmag and Qgen.

Hence Eq. To obtain this, from Eq. In this case, the compensation term is derived from the equation of the rotor voltage in the d-axis. All variables shown in Figure 5. The operation of the rotor-side converter with regard to the terminal voltage or power factor control is entirely dependent upon the requirements or the preferred operation of the system.

Therefore, the voltage at the terminals will be reduced resulting from the reactive power absorbed by the machine. To implement this strategy, the rotor current reference, shown in Figure 5. This strategy has the advantage of providing low interaction between the power and voltage control loop and enhanced system damping and voltage recovery following faults.

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It comprises two distinct loops, one to control the terminal voltage and the other to control the power output of the generator. In the following discussion and examples, E g has been selected as control vector. Both the voltage and power control loops employ PI controllers, with the provision of additional lead—lag compensation in the case of the voltage loop to ensure suitable margins of loop stability.

PI control with additional lead—lag compensation is employed to provide appropriate speed of response and stability margins in the individual loops. The rotor voltage vector, V r , is then transformed from its polar coordinates to rectangular dq coordinates vdr and vqr and used by the PWM generators to control the switching operation of the rotor-side converter. Typical control parameters and transfer functions can be found in Appendix D. In this case, the large lumped turbine, shaft and generator rotor inertia dominates the dynamic control performance of the DFIG.

The responses for this operation are shown in Figure 5. Initially, the electrical torque output increases sharply due to the action of the torque controller, which tries to follow the new torque reference value.

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The results are shown without crowbar protection. Due to the fault, the electrical torque of the generator falls to zero and therefore the machine starts to speed up. During the fault, the terminal voltage drops to approximately 0. When the fault is cleared after ms, the system recovers stability and the voltage recovers the pre-fault state with a fast and smooth response. Crowbar protection is not in operation Figure 5.

Without crowbar protection, the maximum value that the rotor current can reach during the fault is then just limited by the DFIG and power network parameters. References Anaya-Lara, O. Ekanayake, J. Hughes, F. This chapter describes the main components and features of these technologies and presents results from recent studies conducted on their dynamic modelling and control design.

This type of wind turbine may or may not have a gearbox and a wide range of electrical generator types such as asynchronous, conventional synchronous and permanent magnet can be employed. Hence the electrical frequency of the generator may vary as the wind speed changes, while the network frequency remains unchanged, permitting variable-speed operation. The rating of the power converter in this wind turbine corresponds to the rated power of the generator.

The power converter can be arranged in various ways. In the direct-drive arrangement, the turbine and generator rotors are mounted on the same shaft without a gearbox and the generator is specially designed for low-speed operation with a large number of poles. The synchronous generators of direct-drive turbines tend to be very large due to the large number of poles.

However, if the turbine includes a gearbox typically a single-stage gearbox with low ratio , then a smaller generator with a smaller number of poles can be employed Akhmatov et al. The turbine speed is much lower than the generator speed, typically between 20 and 60 rpm.

Therefore, in a conventional wind turbine, a gearbox is used between the turbine and the generator. An alternative is to use a generator for very low speeds. The generator can then be directly connected to the turbine shaft. The drive trains of a conventional wind turbine and one with a direct-driven generator are shown schematically in Figure 6. There are two main reasons for using direct-driven generators in wind turbine systems.

Direct-driven generators are favoured for some applications due to reduction in losses in the drive train and less noise Grauers, The most important difference between conventional and direct-driven wind turbine generators is that the low speed of the direct-driven generator makes a very high-rated torque necessary. This is an important difference, since the size Gear a Generator rpm Generator 32 rpm b Figure 6. A direct-driven generator for a kW, 30 rpm wind turbine has the same rated torque as a 50 MW, rpm steam-turbine generator.

To decrease the weight of the rotor and stator yokes and to keep the end-winding losses small, direct-driven generators are also usually designed with a small pole pitch. Such excitation may be obtained by means of either a current-carrying winding or permanent magnets PMs. The wound-rotor synchronous machine has a very desirable feature compared with its PM counterpart, namely an adjustable excitation current and, consequently, control of its output voltage independent of load current. This feature explains why most constant-speed, grid-connected hydro and turbo generators use wound rotors instead of PM-excited rotors.

The synchronous generator in wind turbines is in most cases connected to the network via an electronic converter. Therefore, the advantage of controllable no-load voltage is not as critical. Wound rotors are heavier than PM rotors and typically bulkier particularly in short pole-pitch synchronous generators. Also, electrically excited synchronous generators have higher losses in the rotor windings. Although there will be some losses in the magnets caused by the circulation of eddy currents in the PM volume, they will usually be much lower than the copper losses of electrically-excited rotors.

This increase in copper losses will also increase on increasing the number of poles. Figure 6. The topology with a permanent magnet synchronous generator and a power converter system consisting of two back-to-back voltage source converters is illustrated in Figure 6. In this arrangement, the generator-side converter controls the operation of the generator and the network-side converter controls the DC link voltage by exporting active power to the network. The generator-side converter can be controlled using load angle control techniques or using vector control.

The network-side converter is commonly controlled using load angle control techniques. With reference to Figure 6. Hence Eqs 6. The reactive power transfer depends mainly on voltage magnitudes and it is transmitted from the point with higher voltage magnitude to the point with lower magnitude. The operation of the generator and the power transferred from the generator to the DC link are controlled by adjusting the magnitude and angle of the voltage at the AC terminals of the generator-side converter.

The reference value Pgref is obtained from the maximum power extraction curve Figure 5. Vt and Eg are equal in magnitude. The implementation of the load angle control scheme is shown in Figure 6. The major advantage of the load angle control is its simplicity. However, as in this technique the dynamics of the generator are not considered, it may not be very effective in controlling the generator during a transient operating condition. The test system used for the simulations is that shown in Figure 6.

The mechanical structure of the turbine is represented by a single-mass model and ideal operation of the voltage source converters is assumed. The electromagnetic torques of the non-reduced order, reduced order and steady-state generator models are given in Figure 6. It can be seen that the load angle control tracks satisfactorily the torque reference with the three models of the synchronous generator. The responses of the electrical speed and load angle are also given in Figure 6. These current oscillations are damped out by the damper windings in the generator rotor and are only present during the transient period.

The frequency of the current oscillations observed in the non-reduced order model corresponds to the operating electrical frequency of the generator.

For this particular example, the frequency of oscillation is approximately As the power converter decouples the generator from the network, these oscillations are not transferred to the network. Consequently, the reduced order model may be used as an appropriate representation of the synchronous generator when the load angle control strategy is employed and the overall performance of the variable-speed wind turbine on the power system is the main concern.

Vector Control Strategy Vector control techniques are implemented based on the dynamic model of the synchronous generator expressed in the dq frame. Additional terms are included to eliminate the cross-coupling effect as shown in Figure 6. The current reference i qsref is determined from the torque equation. The implementation of the vector control technique is shown in Figure 6. The reference value of the stator current in the q axis, i qsref , is calculated from Eq. The error between these two signals is processed by a PI controller whose output is the voltage in the q axis, v qs , required to control the generator-side converter.

To calculate the required voltage in the d axis, v ds , the reference value of the stator current in the d axis, i dsref , is compared against the actual current in the d axis, i ds , and the error between these two signals is processed by a PI controller. The reference i dsref may be assumed to be zero for the permanent magnet synchronous generator.

Dynamic Performance Assessment The performance of the vector control strategy is illustrated using the non-reduced order model of the synchronous generator. The responses of the rotor speed, active power and stator q axis current are shown in Figure 6. In the case of the vector control strategy, the transient observed in the responses is associated with the mechanical dynamics of the turbine rather than with electrical transients.

The stator current in the q axis increases from to A, which is proportional to the input torque variation. In the vector control strategy, the controller uses the measured stator currents as feedback signals. For the implementation of this control strategy, the generator model usually includes the stator transients.

To demonstrate the importance of the stator transients in the vector control, performance results are shown using the reduced order model of the synchronous generator where the stator transients are neglected. The responses of the torque and rotor speed obtained with both the non-reduced order and reduced order models are shown in Figure 6.

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This shows that in order to use the vector control technique it may be necessary to use a non-reduced representation of the synchronous generator to avoid inaccuracies such as those shown during the transient period when the reduced order model was employed. The error between these two signals is processed by a PI controller, the output of which provides the reference active power Pnetref , as shown in Figure 6. It should be noted that in a physical implementation, the actual value of the DC link voltage, VDC , is obtained from measurements via a transducer.

The inductor coupling these two sources is the reactance Xnet. To implement the load angle controller, the reference value of the reactive power, Qnetref , may be set to zero for unity power factor operation. Vector Control Strategy A block diagram of the vector control of the network-side converter is shown in Figure 6. The DC link voltage is maintained by controlling the q axis current and the network terminal voltage is controlled in the d axis.