# Control of a doubly-Fed induction generator for wind energy conversion systems.

CONTROL OF A DOUBLY-FED INDUCTION GENERATOR FOR WIND ENERGYCONVERSION SYSTEMS.
Abstract
This paper deals with a variable speed device to produce electrical energy on a power network,
based on a doubly-fed induction machine used in generating mode (DFIG). This device is intended
to equip nacelles of wind turbines. First, a mathematical model of the machine written in an
appropriate d-q reference frame is established to investigate simulations. In order to control the
power flowing between the stator of the DFIG and the power network, a control law is synthesized
using two types of controllers : PI and RST. Their respective performances are compared in terms
of power reference tracking, response to sudden speed variations, sensitivity to perturbations and
robustness against machine parameters variations.overcome this problem, a converter, which must be
dimensioned for the totality of the power exchanged,
can be placed between the stator and the network. In
order to enable variable speed operations with a lower
rated power converter, doubly-fed induction generator
(DFIG) can be used as shown on Fig. 1. The stator is
directly connected to the grid and the rotor is fed to
magnetize the machine.
In this paper, the control of electrical power
exchanged between the stator of the DFIG and the
power network by controlling independently the
torque (consequently the active power) and the
reactive power is presented [2]. Several investigations
have been developed in this direction using
cycloconverters as converters and classical
proportional-integral regulators [3-5]. In our case,
after modeling the DFIG and choosing the appropriate
d-q reference frame, active and reactive powers are
controlled using respectively Integral-Proportional
(PI) and an RST controller based on pole placement
theory. Their performances are compared in terms of
reference tracking, sensitivity to perturbations and
robustness against machine's parameters variations.

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Instructor Dr. NGUYEN HUU PHUC WIND ENERGY CONVERSION SYSTEM, GENERATORS & MAXIMUM POWER OPERATION Renewable Energy * TABLE OF CONTENTS * 1.1. Power in the Wind Pw is the power in the wind (watts) ρ is the air density (kg/m3) A is the cross-sectional area through which the wind passes (m2), also called rotor’s blade swept area. v = wind speed to A (m/s) * 1. WIND ENERGY IN GENERAL 1.2. Power extracted from the Wind The actual power extracted by the rotor blades PRotor is equal to the difference in kinetic energy between the upwind and downwind air flows. Making assumption that the velocity of the wind through the plane of the rotor is just the average of the upwind and downwind speeds, then write v = upstream wind speed. vd = downstream wind speed * 1. WIND ENERGY IN GENERAL 1.3. Maximum Rotor Efficiency (Cp) Let define the ratio of downstream to upstream wind speed to be λ, then Which has solution, To find the maximum possible rotor efficiency, we simply take the derivative with respect to λ and set it equal to zero: * 1. WIND ENERGY IN GENERAL Rotor Efficiency (Cp) This conclusion, that the maximum theoretical efficiency of a rotor is 59.3%, as called the Betz’ law. * 1.3. Maximum Rotor Efficiency (Cp) 1. WIND ENERGY IN GENERAL Maximum Rotor Efficiency, For a given wind speed, rotor efficiency is a function of the rate at which the rotor turns. If the rotor turns too slowly, the efficiency drops off since the blades are letting too much wind pass by unaffected. If the rotor turns too fast, efficiency is reduced as the turbulence caused by one blade increasingly affects the blade that follows. The usual way to illustrate rotor efficiency is to present it as a function of its tip-speed ratio, 1.4. Tip-Speed-Ratio (TSR) * 1. WIND ENERGY IN GENERAL Rotors with fewer blades reach their optimum efficiency at higher rotational speeds. * 1.4. Tip-Speed-Ratio (TSR) 1. WIND ENERGY IN GENERAL The maximum rotor efficiency Cp is achieved at a particular TSR, which is specific to the aerodynamic design of a given turbine. The wind power system design must optimize the annual energy capture at a given site. The only operating mode for extracting the maximum energy is to vary the turbine speed with varying wind speed such that at all times the TSR is continuously equal to that required for the maximum power coefficient Cp. The theory and field experience indicates that the variable speed operation yields 20-30% more energy than with the fixed speed operation. 1.5. Importance of Variable Rotor Speeds * 1. WIND ENERGY IN GENERAL 1.5. Importance of Variable Rotor Speeds * 1. WIND ENERGY IN GENERAL * 1.5. Importance of Variable Rotor Speeds 1. WIND ENERGY IN GENERAL 1.6. Idealized Wind Turbine Power Curve The most important technical information for a specific wind turbine is the power curve, which shows the relationship between wind speed and generator electrical output. A somewhat idealized power curve is shown below. * 1. WIND ENERGY IN GENERAL Cut-in Wind Speed: Low-speed winds may not have enough power to overcome friction in the drive train of the turbine. The cut-in wind speed VC is the minimum needed to generate net power. * 1.6. Idealized Wind Turbine Power Curve 1. WIND ENERGY IN GENERAL Rated Wind Speed: As velocity increases above the VC, the power delivered by the generator tends to rise as the cube of wind speed. When winds reach the rated wind speed VR, the generator is delivering as much power as it is designed for. Above VR, must shed some of the wind’s power or else the generator may be damaged. * 1.6. Idealized Wind Turbine Power Curve 1. WIND ENERGY IN GENERAL Cut-out Wind Speed: At some point the wind is so strong that there is real danger to the wind turbine. At this wind speed VF, called the cut-out wind speed, the machine must be shut down. Above VF , output power obviously is zero. * 1.6. Idealized Wind Turbine Power Curve 1. WIND ENERGY IN GENERAL Advantages of Fixed and Variable Speed Systems * 1. WIND ENERGY IN GENERAL 1.7. Speed Control for Maximum Power Multiple Gearboxes: Some wind turbines have two gearboxes with separate generators attached to each. Pole-Changing Generators: If we could change the number of poles, we could allow the wind turbine to have several operating speeds. Variable-Slip Induction Generators * 1. WIND ENERGY IN GENERAL 2. WIND TURBINE GENERATORS * * 2. WIND TURBINE GENERATORS 2.1. DC Generators DC generator needs DC current to produce a magnetic field to excite, hence requires brushes and slip ring. The sliding contacts result in low reliability and high maintenance cost. Advantage is extremely easy speed control. Use in a limited number of wind power installations of small capacity, particularly where electricity can be locally used in the DC form, expected to the ratings below one hundred kW. * 2. WIND TURBINE GENERATORS 2.2. Synchronous Generators (SG) SGs are forced to spin at a precise rotational speed determined by the number of poles and the frequency needed for the power lines. Very small SG can create the needed magnetic field with a permanent magnet rotor. Almost all wind turbines that use SG create the field by running direct current. * 2. WIND TURBINE GENERATORS The SG uses DC current for excitation creates 2 complications: DC current has to be provided, which usually means that a rectifying circuit is needed to convert AC from the grid into DC. The DC current needs to make it onto the spinning rotor, means that slip rings and brushes on the rotor shaft are needed. Replacing brushes and cleaning up slip rings adds up to the maintenance cost, especially with offshore wind turbines. * 2.2. Synchronous Generators (SG) 2. WIND TURBINE GENERATORS The SG has an advantage, when used in the grid-connected system, it does not require the reactive power from the grid resulting in a better quality of power at the grid interface and more pronounced when the wind farm is connected to a small capacity grid using long low voltage lines. The machine works at a constant speed related to the fixed frequency, so it is not well suited for variable-speed operation in the wind plants. * 2.2. Synchronous Generators (SG) 2. WIND TURBINE GENERATORS The machine works as a motor during start-up toward synchronous speed and as a generator when the wind picks up sufficient to force the generator shaft to exceed synchronous speed. 2.3. Induction Generators (IG) * 2. WIND TURBINE GENERATORS The key advantage of asynchronous induction generators is that their rotors do not require the exciter, brushes and slip rings that are needed by most SG. They do this by creating the necessary magnetic field in the stator rather than the rotor. This means that they are less complicated and lower cost and require less maintenance. The disadvantages of both the DC and SGs are eliminated in the induction generator. * 2.3. Induction Generators (IG) 2. WIND TURBINE GENERATORS An added bonus with IG is they can cushion the shocks caused by fast changes in wind speed. When the wind speed suddenly changes, the slip increases or decreases accordingly, which helps absorb the shock to the mechanical components of the wind turbine during gusty wind conditions. * 2.3. Induction Generators (IG) 2. WIND TURBINE GENERATORS The machine is either self-excited or externally excited. A self-excited generator is to create a resonance condition between the inherent inductance of the field windings in the stator and the external capacitors that have been added in parallel forming a electronic oscillators. * 2.3. Induction Generators (IG) 2. WIND TURBINE GENERATORS For economy and reliability, induction generator is used extensively in small and large wind farms. The machine is available in numerous power ratings up to several megawatts capacity. For grid-connected inductance generators, the slip is normally maintained within a range of (1 – 2%). By purposely adding variable resistance to the rotor, the amount of slip can range up to around 10%. * 2.3. Induction Generators (IG) 2. WIND TURBINE GENERATORS 2.4. Doubly Fed Induction Generator (DFIG) In this approach, the wind turbine is allowed to spin at whatever speed that is needed to deliver the maximum amount of power thanks to the convertors that are needed to control on the rotor itself. Variable frequency ac from the generator is rectified and converted into DC, this DC is then sent to an inverter that converts it back to ac, but this time with a steady 50- or 60-Hz frequency. * 2. WIND TURBINE GENERATORS In addition to higher annual energy production, variable-speed wind turbines have an advantage of greatly minimizing the wear and tear on the whole system caused by rapidly changing wind speeds. When gusts of wind hit the turbine, rather than having a burst of torque hit the blades, drive shaft, gearbox and blades merely speed up, thereby reducing stresses. Moreover, some of that extra energy in gusts can be captured. * 2.4. Doubly Fed Induction Generator (DFIG) 2. WIND TURBINE GENERATORS Principle of the doubly-fed induction generator * 2.4. Doubly Fed Induction Generator (DFIG) 2. WIND TURBINE GENERATORS The back-to-back converter consists of two converters, namely machine-side converter (MSC) and grid-side converter (GSC) are connected “back-to-back”. Between the two converters a dc-link capacitor is placed as energy storage in order to keep the voltage variations (or ripple) in the dc-link voltage small. MCS it is possible to control the torque or the speed of the DFIG and also the power factor at the stator terminals, while the main objective for the GSC is to keep the dc-link voltage constant. 2.4. Doubly Fed Induction Generator (DFIG) * 2. WIND TURBINE GENERATORS Equivalent Circuit of the Doubly-Fed Induction Generator The equivalent circuit of the doubly-fed induction generator with inclusion of the magnetizing losses can be seen as above. This equivalent circuit is valid for steady-state calculations. If the rotor voltage, Vr is short circuited, the equivalent circuit for the DFIG becomes the ordinary equivalent circuit for a cage bar induction machine. * 2.4. Doubly Fed Induction Generator (DFIG) 2. WIND TURBINE GENERATORS The air-gap flux, stator flux and rotor flux are defined as Equivalent Circuit of the Doubly-Fed Induction Generator * 2.4. Doubly Fed Induction Generator (DFIG) 2. WIND TURBINE GENERATORS Equivalent Circuit of the Doubly-Fed Induction Generator * 2.4. Doubly Fed Induction Generator (DFIG) 2. WIND TURBINE GENERATORS The stator apparent power Ss and rotor apparent power Sr can be found as which can be rewritten as The stator and rotor power can be determined as * 2.4. Doubly Fed Induction Generator (DFIG) 2. WIND TURBINE GENERATORS Power Flow of DFIG The mechanical power divides between the stator and rotor circuits and it is dependent on the slip. The rotor power is approximately minus the stator power times the slip: * 2.4. Doubly Fed Induction Generator (DFIG) 2. WIND TURBINE GENERATORS Therefore, the rotor converter can be rated as a fraction of the rated power of the DFIG. * * 3. WIND ENERGY CONVERSION CONFIGURATIONS 3.1. Fixed Speed Wind Turbine For the fixed-speed wind turbine the IG is directly connected to the electrical grid. The rotor speed of the fixed-speed wind turbine is in principle determined by a gearbox and the pole-pair number of the generator. The fixed-speed wind turbine system has often two fixed speeds, which is accomplished by using two generators with different ratings and pole pairs. This leads to increased aerodynamic capture as well as reduced magnetizing losses at low wind speeds. * 3. WIND ENERGY CONVERSION CONFIGURATIONS It is observed that the machine operates as generator at super-synchronous speeds and as motor at sub-synchronous speeds. In both cases, the slip also represents the fraction of the mechanical power that is dissipated by the rotor resistance. Thus, large slip implies low efficiency. Consequently, SCIG work in normal operation with very low slip, typically around 2%. * 3.1. Fixed Speed Wind Turbine 3. WIND ENERGY CONVERSION CONFIGURATIONS With US and fS are fixed, so there is no active control on the generator. Although very simple and reliable, this configuration does not allow active control of the energy capture. In addition, the stiff connection to the AC grid provides negligible damping at the vibration modes of the drive-train. * 3.1. Fixed Speed Wind Turbine 3. WIND ENERGY CONVERSION CONFIGURATIONS 3.2. Variable Speed Wind Turbine The system consists of a wind turbine equipped with a converter connected to the stator of the generator. The generator could either be a cage IG or a SG. The gearbox is designed so that maximum rotor speed corresponds to rated speed of the generator. * 3. WIND ENERGY CONVERSION CONFIGURATIONS SG or permanent magnet SG can be designed with multiple poles which implies that there is no need for a gearbox. Since this “full power” converter-generator system, which is commonly used for other applications rather than wind turbines, one advantage with this system is its well developed and robust control. In practice, the converter is rated up to 120% of nominal generator power. This is the main drawback of this scheme. * 3.2. Variable Speed Wind Turbine 3. WIND ENERGY CONVERSION CONFIGURATIONS The system consists of a wind turbine with DFIG, meaning that the stator is directly connected to the grid while the rotor winding is connected via slip rings to a converter. With a limited variable speed range of ±30% of synchronous speed, the DFIG is considered to be an interesting solution. * 3.3. Variable Speed Wind Turbine equipped with DFIG 3. WIND ENERGY CONVERSION CONFIGURATIONS 3.3. Variable Speed Wind Turbine equipped with DFIG This system have recently become very popular as generators for variable speed wind turbines, mainly due to the fact that the power electronic converter only has to handle a fraction (20–30%) of the total power. Therefore, the losses in the power electronic converter can be reduced, compared to a system where the converter has to handle the total power. In addition, the cost of the converter becomes lower. * 3. WIND ENERGY CONVERSION CONFIGURATIONS This scheme enables independent control of active and reactive power. The main drawback is the increased complexity of the DFIG, which is due to the presence of rotor windings, slip rings and brushes. * 3.3. Variable Speed Wind Turbine with DFIG 3. WIND ENERGY CONVERSION CONFIGURATIONS There also exists a variant of the DFIG method that uses controllable external rotor resistances (compare to slip power recovery). Some of the drawbacks of this method are that energy is unnecessary dissipated in the external rotor resistances and that it is not possible to control the reactive power. * 3.3. Variable Speed Wind Turbine with DFIG 3. WIND ENERGY CONVERSION CONFIGURATIONS * 4. PERFORMANCE OF WIND ENERGY CONVERSION SYSTEMS In order to make the comparison as fair as possible the base assumption used in this work is that the maximum (average) shaft torque of the wind turbine systems used should be the same. The following systems are included in the comparison: 4.1. TOTAL POWER LOSSES The following losses are taken into account: * 4. PERFORMANCE OF WIND ENERGY CONVERSION SYSTEMS * Aerodynamic Losses The turbine power as a function of wind speed both for the fixed speed and variable speed systems. The power is given in percent of maximum shaft power. The solid line corresponds to the variable speed systems (VSIG & DFIG) and the two-speed system (FSIG 2). The dotted line corresponds to a fixed-speed system (FSIG 1) 4. PERFORMANCE OF WIND ENERGY CONVERSION SYSTEMS * Gearbox Losses η is the gear mesh losses constant and ξ is a friction constant. 4. PERFORMANCE OF WIND ENERGY CONVERSION SYSTEMS * Induction Generator Losses 4. PERFORMANCE OF WIND ENERGY CONVERSION SYSTEMS * Converter Losses 4. PERFORMANCE OF WIND ENERGY CONVERSION SYSTEMS The losses are given in percent of maximum shaft power * TOTAL LOSSES Aerodynamic, generator, converter, gearbox losses 4. PERFORMANCE OF WIND ENERGY CONVERSION SYSTEMS 4.2. ENERGY PRODUCTION The base assumption that all WT systems have the same average maximum shaft torque and the same mean upper rotor speed. The produced power together with the various loss components for an average wind speed of 6 m/s are presented for the various systems. * 4. PERFORMANCE OF WIND ENERGY CONVERSION SYSTEMS * 4.3. ENERGY EFFICIENCY As a function of the average wind speed 4. PERFORMANCE OF WIND ENERGY CONVERSION SYSTEMS * 5.MAXIMUM POWER OPERATION * 5.MAXIMUM POWER OPERATION Operating the wind turbine at a constant TSP corresponding to the maximum power point at all times can generate 20 – 30% more electricity per year. A possible scheme used with the variable speed operation is Constant Tip-Speed Ratio Scheme * 5.MAXIMUM POWER OPERATION This scheme is based on the fact that the maximum energy is extracted when the optimum tip-speed ratio is maintained constantly at all wind speeds. The optimum TSR is a characteristic of the given wind turbine. This optimum value is stored as the reference TSR in the control computer. The wind speed is continuously measured and compared with the blade tip speed. The error signal is then fed to the control system, which changes the turbine speed to minimize the error. At this time the rotor must be operating at the reference TSR generating the maximum power. Constant Tip-Speed Ratio Scheme * 5.MAXIMUM POWER OPERATION This scheme has a disadvantage of requiring the local wind speed measurements, which could have significant error particularly in a large wind farm with shadow effects. Constant Tip-Speed Ratio Scheme * Thanks VERY MUCH for attention! *

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