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Overview of Control Systems for the Operation of DFIGs in Wind Energy Applications Roberto Cárdenas, Senior Member, IEEE, Rubén Peña, Member, IEEE, Salvador Alepuz, Senior Member, IEEE, and Greg Asher, Fellow, IEEE
Abstract—Doubly fed induction generators (DFIGs), often organized in wind parks, are the most important generators used for variable-speed wind energy generation. This paper reviews the control systems for the operation of DFIGs and brushless DFIGs in wind energy applications. Control systems for stand-alone operation, connection to balanced or unbalanced grids, sensorless control, and frequency support from DFIGs and low-voltage ride-through issues are discussed. Index Terms—Control strategies, crowbar, doubly fed induction generator (DFIG), low-voltage ride through (LVRT), reactive support, robust controller, voltage unbalance, wind turbine.
v1s v2s v0 vr vf θsl θs θr τs
Positive sequence of the stator voltage. Negative sequence of the stator voltage. Zero sequence of the stator voltage. Rotor voltage vector. GSC voltage vector. Slip angle. Position of the stator-flux vector. Rotor position. Stator time constant. I. I NTRODUCTION
N OMENCLATURE ims is ir if J ktransf Ls Lr L0 ωe ωr ωsl p ψs ψr Rs Rr s Te vs
Magnetizing current vector. Stator current vector. Rotor current vector. Grid-side converter (GSC) current vector. Rotor inertia Constant for the abc-to-d–q transformation. Stator inductance. Rotor inductance. Magnetizing inductance. Synchronous angular frequency. Rotational angular frequency. Slip frequency. Number of poles. Stator-flux vector. Rotor flux vector. Stator resistance. Rotor resistance. Slip. Electrical torque. Stator voltage vector.
Manuscript received June 19, 2012; revised October 5, 2012; accepted December 20, 2012. Date of publication January 30, 2013; date of current version February 28, 2013. This work was supported in part by the Fondo Nacional de Ciencia y Tecnología, Chile, under Contract 1110984 and Contract 1121104 and in part by the Industrial Electronics and Mechatronics Millennium Nucleus. R. Cárdenas is with the Department of Electrical Engineering, University of Chile, Santiago 837-0451, Chile (e-mail:
[email protected]). R. Peña is with the Department of Electrical Engineering, University of Concepción, Concepción 407-4580, Chile (e-mail:
[email protected]). S. Alepuz is with the Mataró School of Technology, Polytechnic University of Barcelona, 08302 Mataró, Spain (e-mail:
[email protected]). G. Asher is with the Department of Electrical and Electronic Engineering, University of Nottingham, Nottingham, NG7 2RD, U.K. (e-mail: greg.asher@ nottingham.ac.uk). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2013.2243372
T
HE DOUBLY fed induction machine (DFIM), also known as the wound-rotor or slip-ring induction machine, is an induction machine with both stator and rotor windings [1], [2]. The DFIM is nowadays widely used as a generator, particularly in variable-speed wind energy applications with a static converter connected between the stator and rotor. Currently, this topology occupies close to 50% of the wind energy market [3]. Table I shows some of the commercially available wind energy conversion systems (WECSs), with power in the range of 1.5–3 MW, which are based on doubly fed induction generators (DFIGs). In total, in Table I, there are 93 models of WECSs based on DFIGs for that power range. In Table I, “NM” stands for number of models. DFIGs are also used in higher power ranges (> 3 MW). The German company Repower manufactures two models of WECSs based on DFIGs, the model 6M with a total output power of 6150 kW and the model 5M with a total output power of 5 MW [4]. For WECSs based on DFIGs, gearboxes are required because a multipole low-speed DFIG is not technically feasible [5]. The design of a DFIG-based WECS with a one-stage gearbox was proposed in [6], but no commercial WECS has been implemented with this concept. However, even with the problems associated with a three stage (3S) gearbox, the DFIG still has some advantages when compared with other generators used in wind energy applications [3]. For instance, in [7] and [8], three generators suitable for wind energy applications are studied: a direct-drive synchronous generator (SG) (which is one of the solution offered by Enercon [9]), a direct-drive permanentmagnet generator (PMG) [10]–[14] (marketed by several companies, e.g., Vestas [13], Clipper [14], and Dewind), and a 3S-geared DFIG (see Table I). The results in terms of weight, cost, size, and losses obtained in [7] and [8] are presented in Table II. Notice that the 3S-Geared DFIG is considered the base for the comparison.
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TABLE I C OMMERCIALLY AVAILABLE WECSs IN THE R ANGE OF 1.5–3 MW BASED ON DFIGs
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One of the main reason for the popularity of DFIGs in wind energy applications is that relatively small power converters are required to control the generator. For a typical DFIG, the power converters are connected in the rotor circuit and, for restricted speed range, are rated at a fraction (usually 30%) of the machine nominal power [15]–[17]. Typically slip rings are required in order to connect the machine-side converter to the rotor. Brushless topologies are also feasible [18]–[22]. Because of the popularity of DFIGs for wind energy generation, control systems suitable for this application have been extensively investigated. Control methods for grid-connected WECSs, stand-alone systems, frequency support using DFIGs, low-voltage ride-through (LVRT) control, etc., have been presented and discussed in the literature. The aim of this paper is to give an update of the most recent trends regarding DFIG control systems. In this respect, it augments previous overview papers [23], [24]. In particular, this paper highlights the most recent issues in sensorless control of DFIGs, droop control, the application of DFIGs to microgrids, and the latest work in LVRT. This paper is organized as follows. In Section II, speed and torque control of DFIGs is discussed, and the maximum power point tracking (MPPT) control of DFIGs is also analyzed. In Section III, control of DFIGs connected to unbalanced grids is presented. Section IV addresses DFIG sensorless control methods, whereas Section V discusses frequency support using DFIGs. LVRT control is discussed in Section VI. Finally, the conclusions are presented at the end of this paper. II. S PEED AND T ORQUE C ONTROL OF DFIM A. OptiSlip of Vestas
TABLE II C OMPARISON B ETWEEN T HREE G ENERATORS P UBLISHED IN [7] AND [8]
From Table II, it is concluded that the total weight of a WECS based on a direct-drive PMG is about 4.5 times higher than that of a WECS based on a DFIG [7], [8]. The stator diameter of a direct-drive PMG is about six times that of a DFIG of similar power. Recently, the performance of the DFIG has been also compared with that of the medium-speed permanent-magnet SG (PMSG) in [8]. The medium-speed PMSG, usually coupled to a single-stage gearbox, is a relatively new topology for variable-speed wind generation (also known as the “Multibrid” concept [3]) and has been adopted by some WECS manufacturers, e.g., Vestas, Areva, and WinWinD [3].
In the past, external resistors were connected to the slip rings of wound-rotor machines in order to reduce the starting current (for motor operation) or for maximizing the electrical torque in a given operating point. The use of external resistors, at least for these applications, is now considered obsolete because better performance is obtained using power electronics as soft starters, pulsewidth-modulated (PWM) inverters, etc. However, external resistors connected to the rotor are still used in some topologies of WECSs based on wound-rotor induction machines. Vestas in its OptiSlip scheme [25]–[27] (e.g., Vestas V39– 600, V66–1.65 MW) places the resistors and electronic components (as current sensors, insulated-gate bipolar transistors (IGBTs), and part of the control hardware) mounted in the rotor, i.e., no slip rings are required. Depending on the operating point of the WECS, different ohmic values of resistors are connected to the rotor windings using the IGBT transistors. The signals for the control of the IGBTs are transmitted via an optical link from outside the rotor. This topology is designed for a slip variation of up to 10%, delivering a smoother power to the grid [25], [26], [28]. Moreover, the mechanical stresses on some parts of the wind turbines are drastically reduced [25]. A further development of the OptiSlip is the OptiSpeed scheme, which allows slip variations of about 60% [28]. The use of external resistors connected to the rotor could be augmented with pitch control in order to improve the performance of the WECS in dynamic operation, e.g., in the presence of a grid disturbance [27].
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devices in the MCs could be a problem to obtain a good performance for LVRT conditions. Further investigation about this issue is required before considering the MCs as suitable candidates for controllings DFIGs in WECSs. C. Vector Control of DFIMs
Fig. 1. Static Scherbius scheme with two back-to-back PWM VSIs.
Even when the OptiSlip of Vestas has an important share of the total WECSs installed in the world (≈11% in 2008 according to [27]), the main disadvantage of this topology is in its relatively low efficiency because of the dissipation of energy in the external resistors. B. Static Scherbius Drive The Scherbius system was proposed by the German engineer Arthur Scherbius in the early years of the 20th century. The scheme allows bidirectional power flow in the rotor circuit so that operation of the machine below and above synchronous speed is possible. Several topologies have been used in this scheme [1], [2], [15], [17], [29]–[51]. The first work reported in the literature uses a topology similar to the static Kramer drive discussed in [52], but with the rotor diode bridge replaced by a current-fed (naturally commutated) dc-link converter [32], [44], [46], [53]. Another early topology of the Scherbius drive uses a cycloconverter connected between the stator and the rotor [43], [50], [54], However, the current-fed converters and the cycloconverters produce high harmonic content in the rotor current, which are reflected in the stator due to the transformer action of the machine. The disadvantages of the naturally commutated converters can be overcome by the use of two PWM voltage-fed currentregulated inverters connected back to back in the rotor circuit [15], [17], [29]–[31], [33], [35]–[42], [45], [47]–[49], [51], [55]. The scheme is shown in Fig. 1. This topology allows: • bidirectional power flow with operation below and above synchronous speed with the speed range restricted only by the rotor voltage rating of the DFIG; • operation at synchronous speed with dc injected into the rotor, with the rotor-side inverter operating in chopping mode; • low distortion stator, rotor, and supply currents; • independent control of the torque and rotor excitation; • control of the displacement factor between the voltage and the current in the GSC and, hence, control over the system power factor. The application of direct frequency power converters, namely matrix converters (MCs), and indirect MCs (IMCs) has been proposed as an alternative to the back-to-back voltage source inverter (VSI) topology shown in Fig. 1 [56], [57]. These topologies are all-silicon solutions for ac–ac conversion with sinusoidal input and output currents without using passive components in the dc link. However, the lack of energy storage
The vector control technique developed for squirrel-cage induction machines [1], [58] can be extended to DFIMs [15]. Usually, in a cage induction machine fed by an inverter connected to the stator, the stator currents are controlled using a d–q rotating frame aligned with the rotor flux. By analogy, in DFIMs, the rotor is fed by an inverter; therefore, the rotor currents are usually controlled using a rotating frame aligned with the stator flux [15], [16]. Under this scheme, the electrical torque is proportional to the q-axis rotor current. Because the stator is connected to the utility in grid-connected applications, the d-axis rotor current can be used to regulate the reactive power flow in the machine. In wind energy applications, MPPT is usually carried out by controlling the machine electrical torque [15], [41], [55]. This is discussed in Section II-G. The machine equations for a DFIG in a d–q synchronous frame orientated along the stator flux are as follows [1], [15]: ⎤ ψds ⎢ ψqs ⎥ ⎦= ⎣ ψdr ψqr vds = vqs
⎤⎡ ⎤ ids Ls 0 L0 0 ⎢ 0 Ls 0 L0 ⎥ ⎢ iqs ⎥ ⎦⎣ ⎦ ⎣ L0 0 Lr 0 idr 0 L0 0 Lr iqr d ψds Rs 0 ids + iqs 0 Rs dt ψqs 0 −ωe ψds + ωe 0 ψqs d ψdr Rr 0 idr vdr = + 0 Rr vqr iqr dt ψqr 0 −ωsl ψdr + ωsl 0 ψqr p Te = ktransf L0 (iqs idr − ids iqr ) 2
⎡
⎡
(1)
(2)
(3) (4)
where subscripts d and q denote direct and quadrature components referred to the synchronous rotating frame, respectively; and subscripts r and s denote stator or rotor quantities, respectively. ψ s = L0 · ims is the stator flux, where ims is known as the magnetizing current. The field orientation for machine variable transformation uses slip angle θsl derived from the position of the statorflux vector θs and the rotor position θr (see [15] and [16]) as follows: θsl = θs − θr .
(5)
The position of the stator-flux vector θs can be obtained from the stator-flux α–β components as
ψβs θs = tan−1 . (6) ψαs
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Fig. 3. Voltage vectors and stator and rotor fluxes.
Fig. 2.
dynamic performance of the controlled currents is similar, but in this case, the d-axis and q-axis stator current components are proportional to the stator active and reactive power [30]. Standard modulation techniques could be used to provide the PWM patterns to the rotor-side converter (RSC)/GSC [63]– [65]. For parallel connection of power converters, shifting of the PWM patterns could be implemented in order to reduce the total harmonic distortion [64].
Control schematic of a DFIG.
An alternative to (6) is to use a phase-locked loop (PLL) [59] to obtain θs . The α–β components of the stator flux can be calculated from the stator voltages and currents as ψαs = (vαs − Rs iαs ) dt (7) ψβs = (vβs − Rs iβs ) dt. The expression in (7) requires an integrator. However, in practical implementations, a pure integrator can be replaced by a low-pass filter or a bandpass filter (BPF) used as a modified integrator to block the dc component of the measured voltages and currents [60], [61]. The BPF is typically designed with a cutoff frequency of 0.1 to 1 Hz. Because the stator voltages and currents are 50-Hz signals, the performance deterioration from integral action is negligible [61]. The control schematic is shown in Fig. 2, where E is the converter dc-link voltage, and the superscript “∗ ” denotes a demand value. When the orientation along the stator flux is correct, the electrical torque is given by Te = ktransf
p L20 ims Iqr = kt1 ims iqr 2 Ls
(8)
with the torque constant kt1 = ktransf pL20 /Ls . The stator magnetizing current ims = ψds /L0 is practically constant in gridconnected applications. Under flux orientation conditions, the magnetizing current can be provided: 1) entirely from the stator with ird = 0; 2) entirely from the rotor with isd = 0; or 3) a combination of magnetizing currents supplied from both the stator and the rotor. This degree of freedom regarding the reactive power flow in the machine can lead to an optimization problem, where losses in the machine and ratings of the rotorside and the line-side converters need to be considered [41], [62]. The electrical torque is proportional to irq , and the reactive power in the machine can be regulated by acting upon ird . Vector control schemes can also be implemented using a reference frame oriented along the stator voltage vector and controlling the stator currents instead of the rotor currents. The
D. DTC of DFIM The direct torque control (DTC) technique [66], widely applied to squirrel-cage induction machines, has also been used to control the electrical torque in the DFIM because of the good dynamic performance that it achieved [31], [39], [40], [45], [67]–[69]. ABB has developed a low-voltage power converter to control a DFIM for wind power applications using this technique [70]. A two-level voltage-fed inverter can impose six active vectors and two zero vectors at the machine rotor terminals, as shown in Fig. 3(a). These voltage vectors, when applied for time interval Δt, produce changes in the rotor flux vector both in magnitude and phase with respect to the stator-flux vector (see also Fig. 3). It can be shown that the electrical torque is proportional to the cross product of the stator and rotor flux vectors, i.e., Te = kt ψs ⊗ ψr = kt |ψs ||ψr | sin δ
(9)
where kt is a constant dependent on the machine parameters. Assuming grid-connected operation, the stator-flux magnitude is practically constant. Therefore, the rotor flux vector can be changed by applying different rotor voltages via the RSC. From (9), this produces changes in the electrical torque (and generated reactive power). Depending on the position of the rotor and for a desired change in the electrical torque and rotor flux magnitude, there is an optimum voltage vector to be applied to the machine [2], [45]. In order to implement the DTC strategy, it is necessary to know the rotor flux vector in magnitude and angle, and the electrical torque. The rotor flux can be obtained using (1) with the stator and rotor currents referred to the α–β reference frame affixed to the rotor, i.e.,
2 + ψ2 |ψr | = ψαr βr ψr2 = L0 irαs + Lr iαr ; ψβr = L0 irβs + Lr iβr ∠ψr = tan−1 (ψβr /ψαr )
(10)
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Fig. 4. DTC for DFIM.
where irαs and irβs are the α–β components of the stator current referred to the rotor frame. The electrical torque can be obtained as Te = kt2 (ψαr iβr − ψβr iαr )
(11)
where kt2 is dependent on the α–β transformation being used. The control diagram of a standard DTC strategy is shown in Fig. 4. E. DPC Applied to DFIMs The direct power control (DPC) technique was proposed about 15 years ago for controlling three-phase PWM rectifiers [71]–[73]. It follows the same philosophy of DTC, but it also looks at the effect of the stator and rotor fluxes upon the stator active and reactive power. It can be shown that stator active power is proportional to the rotor flux component perpendicular to the stator flux where the stator reactive power is proportional to the rotor flux component aligned with the stator flux [44]. The approach can be extended to DFIMs [29], [42], [45], [49], [51], [74]. A DPC strategy minimizing the use of zero voltage vectors is presented in [49]. When using DTC at low rotational speed, zero voltage vectors are more frequently applied to the machine terminals causing a flux reduction because of the stator resistance. In DFIMs, the equivalent situation is the operation near or at synchronous speed where the rotor voltage applied to the machine is low. Operation at or near synchronous speed is not uncommon when the machine is used in variablespeed WECSs. The operation principle is to control directly the stator active and reactive power by applying the proper voltage vector in the machine rotor. The stator power can be calculated as Pe = ktransf (vαs iαs + vβs iβs ) Qe = ktransf (−vαs iβs + vβs iαs ).
(12)
The error between the reference active and reactive power and the calculated active and reactive power in the machine are processed by hysteresis controllers. Schemes employing both two-level and three-level hysteresis controllers have been reported in the literature [45], [49]. The implementation of the strategy needs the α–β rotor flux vector position within six predefined sectors in the rotor coordinates in order to determine the optimal rotor voltage vector to apply to the machine. Because the rotor flux vector position needs to be known, the standard
Fig. 5.
DPC scheme as reported in [49].
DPC approach requires, as the standard DTC strategy, stator and rotor current measurements. However, it is claimed in [71]– [73] that DPC is less dependent of the machine parameters. In order to reduce the strategy parameter dependence, alternative schemes have been used. A strategy based on the statorflux position, which is referred to the rotor, and the effect of the different voltage vectors upon the stator active and reactive power is presented in [44]; therefore only stator voltage and currents are measured. A schematic of this strategy reported in [49] is shown in Fig. 5. Another strategy to estimate the rotor flux position is presented in [40], where an adaptive mechanism based on the effect of voltage vectors upon the reactive power variation is presented. However, the strategy requires a rather high sampling frequency. Again, only the stator current and voltages need to be measured in order to implement the DPC. The control schemes presented in Section II-D–F have been very well documented in the literature. The strategies provide good overall performance, but it is not straightforward to establish the superiority of one over the others. A fair comparison would have to include dynamic-state and steadystate performances, current ripple content, and losses in the converters. The vector control approach is based on the machine model and is more parameter dependent: the implementation complexity might be higher; currents, voltages, and position need to be measured (although implementation without encoder is feasible); and the current control dynamics are reasonable with no high sampling frequency. On the other hand, DTC implementation is simpler, even if it is a model-based approach, and is less dependent on machine parameters: high torque dynamics can be achieved, but higher nonconstant switching frequencies are typical; a higher current ripple is expected, higher bandwidth of current and voltage sensors are needed and rotor position needs also to be measured. Finally, DPC could be even simpler to implement: good power dynamics can be achieved with high variable switching frequency; a higher current ripple is usual and higher bandwidth of current and voltage sensors are also needed, but rotor position does not need to be measured. If MPPT is considered, speed measurement/estimation is typically required for any of the control strategies discussed earlier. The MPPT implementation is straightforward for DTC and vector control approaches because the electrical torque
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Fig. 6. Locus for the maximum aerodynamic efficiency, in the power-speed plane, for a typical variable-speed wind turbine.
is directly or indirectly controlled. However, DPC controls only the stator power, and MPPT requires regulation of the total power supplied to the grid or isolated load. Therefore, the rotor power has to be considered, and this increases the implementation complexity of the MPPT algorithm. Fig. 7. Some simple control system for MPPT in DFIG-based WECSs. (a) Control system of (13) and (14), as discussed in [77] and [78]. (b) Control system of (15), as discussed in [55] and [84].
F. Control of the GSC The objective of the line-side converter or the GSC in the topology depicted in Fig. 1 is to permit the active power flow, regulating the dc-link voltage to a constant level. Close-tounity power factor operation is usual, but it is also possible to control the reactive power flow between the converter and the stator/grid. A vector control approach is normally used [15], [55], with a reference frame oriented along the grid-voltage vector, enabling independent control of the active and reactive power flowing between the grid and the GSC. The grid-side PWM converter is current regulated, with the d-axis current regulating the dc-link voltage and the q-axis current regulating the reactive power. Alternatively, DPC can be also applied to the control of the GSC, leading also to a decoupled control of the active and reactive power flows in the converter [29], [71]–[73]. G. MPPT Control For a typical variable-speed wind turbine, the locus of the maximum aerodynamic efficiency corresponds to a cubic line relating the power captured with the rotational speed [75]–[81]. This is shown in Fig. 6. The optimal power Popt is related to the rotational speed of the blades by the following nonlinear function: Popt = kopt ωr3
(13)
where kopt is a function of the parameters of the WECS, e.g., gearbox size, blade radius, blade profile, etc. Two types of MPPT algorithms have been reported in the literature, i.e., the speed control and torque control of the electrical generator for maximum aerodynamic efficiency [82], [83]. For the MPPT algorithms based on speed control, the generator rotational speed is regulated to drive the WECS to the point of maximum aerodynamic efficiency. Further discussion of MPPT methods based on speed control is considered outside the scope of this paper and the interested reader is referred elsewhere [82], [83].
For the MPPT algorithms based on torque control, the quadrature current i∗qr is regulated to drive the WECS to the point of optimal power capture. As discussed in [77] and [78] to drive the WECS to the point of maximum aerodynamic efficiency, the electrical torque could be controlled as Te∗ = kopt ωr2 .
(14)
Using (8) and (14), the quadrature reference current i∗qr can be calculated as i∗qr =
kopt 2 ω . kt1 ims r
(15)
If the machine parameters are correctly identified, the simple control strategy of (15) can be used to drive the WECS to the point of maximum aerodynamic efficiency. The control system based on (15) is shown in Fig. 7(a). The rotational speed of the generator is used as the input of a lookup table (or nonlinear function), where (15) is stored. Current i∗qr is obtained at the lookup table output and is used as the reference of the quadrature current control loop. Another alternative is to implement optimal power tracking using an additional control loop. This strategy has been reported in [55] and [84]. The control system calculates the power reference Pe∗ using a lookup table, where the optimal power as a function of the rotational speed is stored [see Fig. 7(b)]. From Pe∗ , the rotor torque current is calculated as ∗ ∗ iqr = Kp (Pe − Pe ) + ki (Pe∗ − Pe ) dt (16) where kp and ki are the proportional and integral constants of the proportional–integral (PI) controller. Pe is the electrical power supplied by the DFIG to the grid, which is measured by the voltage and current transducers. The control system shown in Fig. 7(b) requires nested control loops with the bandwidth of the outer loop being a fraction of the internal current iqr loop.
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Fig. 8. DFIG feeding a stand-alone load.
The main advantage of the control strategy of (16) [and Fig. 7(b)] is that the errors in the machine parameter estimation, e.g., kt1 and ims in (15), are compensated by the PI controller. On the other hand, the relationship between the torque rotor current and power Pe is dependent on the rotational speed, and some compensation strategy, for instance gain scheduling control, could be required to maintain a good dynamic response in the whole operating range. Here, only two simple control strategies have been explained. However, other power tracking methodologies (as the speed-control-based MPPT algorithms discussed in [77] and [85]–[87]) e.g., perturbation and observation, wind speed observers, etc., can be applied to WECSs based on DFIGs. III. C ONTROL S YSTEMS FOR THE C ONNECTION OF DFIG S TO U NBALANCED S YSTEMS A WECS may be installed in remote rural areas, where weak grids with unbalanced voltages are not uncommon [42], [88]– [90]. Moreover, in stand-alone applications, the DFIGs can feed unbalanced and islanded loads [91]–[95]. As reported in [89], [90], and [96]–[99], induction machines are particularly sensitive to unbalanced operation since localized heating can occur in the stator, and the lifetime of the machine can be severely affected. Furthermore, negativesequence currents in the machine produce pulsations in the electrical torque, increasing the acoustic noise and reducing the life span of the gearbox, blade assembly, and other components of a typical WECS [88], [91], [92], [100]. For the control of DFIGs operating in unbalanced systems, control algorithms based on counterrotating synchronous d–q axes [89], [91], [92], [98], [101], resonant control [95], [102], [103], predictive control [93], [104], [105], sliding control [106], and DPC [29], [42] have been proposed in the literature. A. Control of a DFIG Feeding a Stand-Alone Unbalanced Load Fig. 8 shows a DFIG feeding a stand-alone load. The DFIG stator and the load are star-connected with the neutral points connected, to provide a path for the circulation of zerosequence currents. A four-leg grid-side inverter can be also used to supply zero-sequence signals to a star-connected linear/ nonlinear unbalanced load [107]–[109]. The initial excitation for the system start up could be provided by a battery bank (not shown in the figure). The battery could be kept charged afterward using the energy flow in the dc link. Another possibility is to use a bank capacitor in the stator for the self-excitation of the machine, generating the
Fig. 9.
Control system discussed in [91].
required stator voltage. Then, the control strategy of the lineside converter or, in this case, the stator-side converter, could regulate the required dc-link voltage. To compensate the load unbalance, the GSC and/or the RSC can be used. For instance, in [91] and [92], the use of the GSC to compensate the load unbalance is proposed. The control system discussed in [91] is shown in Fig. 9. (Only the GSC control system is shown.) The positive-sequence vector control system is oriented along the stator voltage vector. Because of the unbalance, a PLL is implemented to calculate the stator voltage angle θv [59]. From +θv and −θv , the currents can be referred to two synchronous d-axis and q-axis rotating at +ωe and −ωe , respectively. Doubly frequency components are produced when the positive/negative-sequence currents are referred to the d-axis and the q-axis rotating in the opposite direction. As shown in Fig. 9, notch filters are used to eliminate these high-frequency components [89], [91], [92], [98], [101]. + − − The output of theses filters are the currents i+ df , iqf , idf , and iqf . The control systems for the front-end positive-sequence cur+ rents i+ df and iqf are entirely conventional (see Fig. 9, and [91] and [92]). Current i+ df regulates the dc-link voltage E, and + current iqf regulates the reactive power supplied to the load. The front-end negative-sequence currents are regulated to − − − i−∗ = −i = − i + i (17) dqf dqL dqs dqf . Therefore, the negative-sequence current demand is a function of the load negative-sequence current. In the steady state, when − − i− dqf = −idqL , stator current idqs = 0 [see (17)], and the torque pulsations are eliminated.
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Fig. 11. DFIG feeding an unbalanced grid.
is controlled to eliminate the negative-sequence currents from the stator of the DFIG. B. Control of a DFIG Feeding an Unbalanced Grid Fig. 10. Experimental results corresponding to the control system discussed in Fig. 9. (a) Negative-sequence currents. (b) Stator and rotor unfiltered currents referred to the d–q positive-sequence axes.
In abc coordinates, the total voltage demand for the front-end converter is obtained as (see Fig. 9) + − + vabc . vabc = vabc
(18)
Fig. 10 shows the performance of the control system depicted in Fig. 9 for negative-sequence current compensation under variable-speed stand-alone operation (see [92]). The load consists of three unbalanced resistors connected to phases a, b, and c, respectively (see Fig. 8). The rotational speed is varied from ≈1350 to ≈1650 rpm to illustrate the performance at variable speed (from below to above synchronous speed). Before t ≈ 1.25 s, the compensation system is not operating, and the stator current has a negative-sequence component [see Fig. 10(a)]. In t ≈ 1.25 s, the compensation is enabled, and the − − stator current i− dqs is driven to zero. For t > 1.5 s, idqL ≈ idqf , and the negative-sequence currents are eliminated from the machine stator. Notice that the term “unfiltered” indicates that the displayed currents have not been filtered by the notch filters shown in Fig. 9. There are other publications where control of a stand-alone unbalanced load is discussed. For instance, the control system discussed in [94] uses the RSC to regulate a balanced load voltage. In this study, the control system is tested with nonlinear loads and the authors claim a good performance. However, the main disadvantage of [94] is that the rotor current reference has negative-sequence components, and a relatively large dc-link voltage could be required to regulate these components. Predictive control systems for DFIGs feeding unbalanced stand-alone loads are discussed in [93] and [105]. In this case, the voltage vector that minimizes a cost function is identified and applied to the RSC. The control discussed in [93] and [105] use only the RSC to compensate the unbalances in the standalone load. To the best of our knowledge, the only publication reporting the use of both the RSC and GSC to compensate the load unbalance in a stand-alone DFIG is [95]. In this case, a d–q control system augmented with a resonant controller (implemented in the synchronous rotating frame) is proposed. The RSC is controlled to regulate a balanced load voltage, whereas the GSC
Fig. 11 shows a DFIG feeding an unbalanced grid. In this case, the aim of the control system is no longer to regulate the grid voltage. The control approach shown here can be useful to meet the LVRT requirements, as will be discussed in Section VI. For unbalanced conditions, neglecting the zerosequence components in the system, the stator and current voltage vectors can be written as [98], [103] v s = v1s ejωe t + v2s e−jωe t
(19)
is = i1s ejωe t+φ1s + i2s e−jωe t+φ2s .
(20)
The voltage and current vectors at the output of the GSC (see Fig. 11) can be written as v f = v1f ejωe t+φ1f + v2f e−jωe t+φ2f
(21)
if = i1f ejωe t+φ3f + i2f e−jωe t+φ4f
(22)
where the subscripts “1” and “2” are used to indicate signals of positive and negative sequences, respectively. Angles ∅if and ∅is indicate a phase angle shift with respect to the stator voltage angle. The active and reactive power supplied by the DFIG to the grid can be calculated from [29], [42], [103] (23) S = ktransf v f icf + v s ics . In (23), the superscript c is used to indicate the complex conjugate operator. It is relatively simple to show that the active power and reactive power of (23) have three terms: the mean value, a term proportional to sin(2ωe t), and a term proportional to cos(2ωe t) [98], [101], [102], [110]. This can be written as P = Pavg + Psin(2ωe t) + Pcos(2ωe t)
(24)
Q = Qavg + Qsin(2ωe t) + Qcos(2ωe t).
(25)
Using (19)–(25), several control targets for the operation of DFIGs in unbalanced grids can be defined [29], [42], [98], [101], [103], [110]. For instance, in [103], one of the following control targets is proposed: • To eliminate the oscillations in the total active power output from the overall system, i.e., Psin(2ωe t) + Pcos(2ωe t) in (24);
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• To reduce the oscillation in the total reactive power supplied to the network, i.e., Qsin(2ωe t) + Qcos(2ωe t) = 0 in (25). • To supply a grid current with no negative-sequence component, i.e., i2s e−jωe t+φ2s + i2f e−jωe t+φ4f = 0 [see (20) and (22)]. Each power converter has four degrees of freedom allowing the independent regulation of the α–β (or d–q) components of the negative and positive-sequence output currents. In some papers related to the control of DFIGs connected to unbalanced systems, only one of the converters is used. For instance, in [6], the GSC is used to compensate the negative-sequence current of the load. On the other hand, in [29], [42], [88], [89], [94], and [99], only the RSC is used to compensate the grid unbalance. DPC [29], [42] and d–q control are proposed in these publications to compensate the grid unbalance, injecting negative-sequence currents in the rotor. In recent papers, the control of both the GSC and the RSC has been proposed to compensate the grid unbalance. This has the advantage that additional degrees of freedom are introduced in the control system by using two power converters, and more control targets can be achieved [98], [101]–[103], [111], [112]. IV. S ENSORLESS C ONTROL OF DFIGs The DFIG can be used as a variable-speed generator in standalone and grid-connected applications [95], [113]–[116]. In both cases, the use of sensorless vector control is desirable because position encoders or speed transducers have many drawbacks in terms of maintenance, cost, robustness, and cabling between the speed sensor and controller [78]. There are several sensorless methods reported in the literature. In this paper, they are classified as open-loop sensorless methods, model reference adaptive system (MRAS) observers, and other sensorless methods. Most of the sensorless control methods reported here have been applied to conventional vector control of DFIGs (see Section II-C). However, sensorless schemes can also be applied to the control methods discussed in Section II-D and E.
Fig. 12.
Block diagram of a typical MRAS observer.
In (26) and (27), irs is the rotor current vector referred to the stator, and (irα + jirβ ) is the measured rotor current in α–β coordinates. Using (26) and (27), an estimation of the slip angle is obtained as (28) θˆsl = tan−1 (irβ /irα ) − tan−1 isrβ /isrα . Using (28) in (5), an estimation of rotor position angle is derived. Open-loop methods are not only based on estimation of the DFIG rotor current vector. In [122], an observer based on the magnetizing current derived from the rotor and stator equations of the machine is proposed, although only simulation results were presented, and no methodology was proposed for the observer modeling and design. In [123], a rotor-fluxbased sensorless scheme is proposed, where the rotor flux is obtained by integrating the rotor back electromotive force. This sensorless method has poor performance when the machine is operating around the synchronous speed because the rotor is excited with low frequency voltages. Therefore, the rotor flux cannot be accurately estimated by integrating the rotor voltages. In the open-loop methods, the rotational speed is obtained via differentiation of the estimated slip angle of (28), which can amplify the high frequency noise. Moreover, for the open-loop methods reported in the literature, issues of observer modeling, observer bandwidth, and design methodology for the whole sensorless system are not discussed. B. Sensorless Method Based on MRASs
A. Open-Loop Sensorless Methods Most of the early work in sensorless control of DFIGs is based on open-loop methods, where the estimated and measured rotor currents are compared in order to derive the rotor position [117]–[121]. For instance, the rotor current referred to the stator can be estimated using the stator flux and the stator current as [121] ˆιsr =
(ψ s − Ls ˆιs ) L0
.
(26)
The measured rotor current can be referred to the stator using isr = (irα + jirβ )e−jθsl where the slip angle is defined in (5).
(27)
The MRAS was first introduced for sensorless control of cage induction machines in [124]. In this publication, the observer design is discussed, and a small-signal model is proposed. Most of the MRAS observers proposed in the literature for cage induction machines are based on rotor flux estimation. The application of MRAS observers for sensorless control of DFIGs was first reported in [125] and [126]. However, in these papers, only simulations were presented for a DFIM operating at very low rotational speed. Issues such as observer dynamics, control design procedure, sensorless accuracy, and sensitivity to machine parameter variations were not addressed. Further publications discussing the application of MRAS observers for sensorless control of DFIGs were presented in [127] and [128]. In the general case, an MRAS observer is based on two models [61], [77], [124], [129]–[134]: a reference model and an adaptive model (see Fig. 12). The estimated speed and rotor position are used to adjust the adaptive model, driving the error
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Fig. 14. Sensorless control of a grid-connected DFIG using a stator-fluxbased MRAS observer. Notice that the control system is unstable when the rotor magnetizing current idr0 is driven to zero. Fig. 13. (a) Stator-flux-based MRAS observer proposed in [127]. (b) Smallsignal model corresponding to the stator-flux MRAS observer.
ε to zero. This error is usually defined as the cross product ˆ. between reference vector x and derived estimated vector x Mathematically, this can be written as ε=x ˆ d xq − xd x ˆq = |x||ˆ x| sin(θε )
(29)
where θε is the phase angle between the vectors (ˆ x, x). In [115], the small-signal model, machine parameter sensitivity, and the design procedure of a stator-flux MRAS observer were presented (i.e., x = ψ s ). In this case, the reference model and the adaptive model are obtained, respectively, as (30) ψ s = (v s − Rs is )dt ˆ ψˆs = Ls is + L0 ir ej θr .
(31)
The estimated rotor position angle θˆr is used to drive the error of (29) to zero. The implementation of the stator-flux MRAS observer is shown in Fig. 13(a), and the small-signal model corresponding to this observer is shown in Fig. 13(b). As shown, the gain of the feedforward path is dependent on the magnetizing current idr0 . Therefore, if the DFIG is operating in a grid-connected application and if the magnetizing current required for the generator is entirely supplied from the grid, then the rotational speed cannot be tracked by the observer. The experimental result depicted in Fig. 14 further corroborate the small-signal model in Fig. 13(b) [133]. The DFIG is a sensorless vector controlled using a stator-flux MRAS observer; when t = 23 s, the magnetizing rotor current ird0 is driven to zero and the system becomes unstable because tracking of the rotor position angle and rotational speed is lost. In [61], [136] a rotor current MRAS observer (RCMO) is proposed, which is appropriate for grid-connected and standalone operation for most of the DFIG operating range. In this case, the reference “model” is simply the measured rotor current. The adaptive model is derived from (26) and can be written as ˆιr =
(ψ s − Ls ˆιs ) L0
ˆ
ej θsl .
(32)
Fig. 15. (a) RCMO presented in [61]. (b) Small-signal of the RCMO presented in [61].
A detailed description of the RCMO, including the methodology required to synchronize the DFIG to the grid, the smallsignal model, and the control algorithm used for catching the speed on the fly, is presented in [61]. The implementation of the RCMO is shown in Fig. 15(a). Fig. 15(b) shows a linearized model of an RCMO, which is used to design the PI controller in Fig. 15(a). Experimental results obtained with a DFIG vector controlled using a sensorless scheme based on an RCMO are shown in Fig. 16. Fig. 16(a) shows the performance of the control system used to synchronize the DFIG to the electrical grid before the grid-connected generation is started. Notice that, in t = 20 s, the power switch is closed, and the DFIG stator is connected to the grid. Fig. 16(b) shows the experimental results obtained for speed catching on the fly with sensorless control using the RCMO. These experimental results are fully discussed in [61] and [136]. From the small-signal model in Fig. 15(b), it is concluded that the gain of the feedforward path is only affected by the magnitude of the rotor current vector, which is not zero in the typical operation range. Therefore, unlike the stator-flux MRAS observer, the RCMO can be applied to sensorless control of DFIG when the machine is grid connected and entirely magnetized from the stator. In fact, the RCMO can be applied to standalone and grid-connected application. In addition, as presented in Fig. 16(a), sensorless vector control of the DFIG using an RCMO is appropriate to synchronize the DFIG to the grid.
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in [139] show that the variation in the stator inductance can be compensated when the proposed adaptive algorithm is properly designed. A new sensorless control topology, which is also based on the MRAS observer, is presented in [131] and [135]. The proposed observer is called the torque-based MRAS observer (TBMO) and uses a different methodology for estimating the rotor current vector. Assuming that the vector control system is orientated along the stator flux, then the torque and flux components of the rotor current vector can be calculated as irq =
ˆ s Te ˆ s |ψ ⊗ is | L L s = ˆ 0 |ψ | ˆ 0 |ψ | L L s s
ird = Fig. 16. Experimental results discussed in [61] and [136] corresponding to the operation of a RCMO. (a) Synchronization to the grid. (b) Speed catching on the fly.
Considering that the RCMO is able to operate in most of the conditions required, i.e., grid-connected operation, stand-alone operation, etc. [133], it is considered that the MRAS observer has the best overall performance among the three sensorless topologies discussed in that publication. A variation of the RCMO is presented in [132]. Because the error of (29) is a nonlinear function, in [132], it is proposed to calculate the error using ε = tan−1 ([ˆιr ⊗ ir ]/[ˆιr .ir ])
(33)
where ˆιr ⊗ ir represents the cross product between the rotor current and that estimated using a Luenbenger observer [132], [137], [138]. On the other hand, ˆιr · ir represents the inner product between both currents. The use of (33) as normalized error, instead of (29), has the advantage of producing a linear model, where the error is proportional to the phase shift angle between (ˆι) and (ir ), instead of being proportional to the nonlinear function sin(θε ) [see (29)]. This simplifies the design of the PI controller in Figs. 13 and 15, enhancing dynamic performance across the operating range. The performance of the MRAS observers reported in the literature depends strongly on the correct identification of the inductances of the DFIM. In particular, the implementation of the RCMO requires the correct identification of the magnetizing and stator inductances [61], [133], [136], [139]. For gridconnected operation of DFIGs, the stator voltage can fluctuate about ±10% of its nominal value, changing the level of magnetic saturation in the machine. Therefore, the magnetizing, stator and rotor inductances are subjected to variations. In order to maintain the tracking of the rotor position angle, even in the presence of grid-voltage fluctuations, adaptive tuning of the stator inductance is proposed in [139]. This algorithm is based on the fact that the magnitude values of the estimated rotor current and that measured by the transducers are equal when the machine parameters are correctly tuned, i.e., when |ir | = |ˆιr |; ˆ s , and L0 = L ˆ 0 (|ˆι|) is the rotor current vector estithen, Ls = L mated from (32) (see [61]). The experimental results discussed
i2rα + i2rβ − i2rq
(34)
1/2 .
(35)
The d–q components of the rotor currents calculated using (34) and (35) are the reference model of the MRAS observer. Note that the torque and flux rotor currents of (34) and (35) can be calculated from the α–β components of the stator flux and measured stator/rotor currents. According to [135], the main advantage of the proposed TBMO is that (34) and (35) can be used directly as feedback signals of the control system, increasing the dynamic response and improving the stability of the whole system. Note that (34) and (35) are not affected by errors in the rotor position angle. C. Other Sensorless Methods for DFIMs Sensorless control of DFIGs based on PLLs is proposed in [141]–[143]. As discussed in [124], the operating principle of PLLs is similar to MRAS observers because the error of (29) and (33) are driven to zero when the phase shift between the estimated vector and the reference vector is null. Therefore, the sensorless observers of [141]–[143] have a similar performance to those reported in [133]. However, some issues, such as the design of the PI controller located in the PLL system and the bandwidth of the rotor position observer, are not addressed in [141] and [142]. Sensorless control of DFIMs is also discussed in the paper reported in [144]–[147]. In [146] and [147], a rotor position observer similar to the RCMO of [61] is discussed. The PI controller (see Figs. 13–15) is replaced by a hysteresis controller. The authors claim that this controller improves the performance of the observer because the design of the hysteresis controller does not require good knowledge of the plant parameters. However, as it is well known, controllers based on hysteresis may produce signals of variable frequency at its output. Therefore, some knowledge of the plant is usually required in order to maintain this frequency inside a given operating range. In [144] and [145], a rotor position observer, which is based on the air-gap active and reactive power, is proposed. This algorithm has some similarities to the TBMO reported in [135] because the torque and flux components of the rotor current are calculated using the α−β components of the measured voltage and currents without requiring an estimation of the
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rotor position angle. Assuming a stator-flux orientation, the d−q components of the rotor current can be calculated as ˆιdr =
Pg Qg ˆι = |v s − Rs is | qr |v s − Rs is |
(36)
where Pg and Qg are the power transferred across the air gap. The current estimated using (36) are used in a RCMO in order to estimate the rotor position angle. It is claimed in [144] and [145] that the main advantage is that the calculation of the stator-flux vector is not required in the vector control system. However, in order to calculate Pg and Qg , an estimation of the iron losses and magnetizing reactive power is required [144]. This can produce some errors, particularly when the DFIM is operating with light loads. Sensorless control of DFIMs can be also achieved using signal injection [148]. This methodology is relatively well known for cage induction machines [149]. However, to the best of our knowledge, sensorless control of DFIMs using signal injection has only been discussed in [148]. The operating principle is that the DFIM is a transformer in which the relative position between the primary and secondary winding changes as the rotor rotates. Therefore, if a high-frequency signal is injected into the rotor, the phase of the corresponding signal in the stator has a component that is dependent on the rotor position angle. The main advantage of this method is high robustness against variation in the machine parameters. However, experimental validation of this method has not been reported, and injection of high-frequency signals in the DFIG rotor is not simple to achieve in relatively large machines, such as the ones used for wind power generation. To the best of our knowledge, the performance of the reviewed sensorless methods has not been studied for operation in unbalanced grids or when the DFIG is feeding a stand-alone unbalanced load of linear/nonlinear nature. Moreover, sensorless control of DFIGs during LVRT conditions has not been addressed in the literature. Further research in these subjects is required. V. F REQUENCY S UPPORT U SING DFIGs As wind power penetration increases, the fluctuating behavior of the wind velocity has more impact on the grid frequency. Wind energy penetration may increase during periods of low loads, e.g., in the night. In this case, grid-frequency fluctuations above the maximum allowed by the grid codes can be produced [150]–[152] if conventional MPPT is used to control the power generated. In some countries, such as China [153], [154], about 27% of the yearly wind energy is curtailed because most wind farms are operating using MPPT control without frequency regulation [153]. In the past, the control used was based on disconnecting part of the wind farm. Now, modern control methods based on droop control and inertia emulation are preferred [155]. Grid connection requirements (GCRs) are introducing regulations to establish grid-frequency support from wind turbines [156]. For instance, according to the E-ON GCR [157], when the frequency exceeds the value of 50.2 Hz, wind farms must reduce their active power with a gradient of 40% of the available
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power per hertz, with a ramp rate of 10% of the grid connection capacity per minute. A more detailed description about the GCRs is found in Section VI-A. There are several publications related to the subject of gridfrequency support using wind energy systems [153]–[155], [158]–[170]. Most of the proposed methods use the kinetic energy stored in the wind turbine rotating mass to provide additional power to the system in case of grid-frequency variation. In power systems, inertia constant H is used instead of inertia J. Constant H is defined as [155] H=
Jωr2 Ek = S S
(37)
where S is the nominal apparent power of the WECS, and Ek is the kinetic energy stored in the rotating blades. As shown in (37), H is equal to the time that a WECS can supply the nominal power using the kinetic energy stored in the rotor. The inertia constants for WECSs are in the range of 2–6 s, whereas H for a typical power system generator is in the range of 2–9 s [155]. Frequency support is usually accomplished using inertia emulation and/or droop control. The output power of the DFIG is controlled as a function of the grid frequency, i.e., ∗ = Prefω + Kd (fgrid − fref ) + Kei Pout
d(fgrid ) dt
(38)
where Prefω represents the output power demand for normal steady-state operation of the power system when the grid frequency fgrid is equal to the reference frequency. This power demand might be obtained, for instance, from a lookup table, where a relationship between the rotational speed and the demanded output power is stored. The second term Kd (fgrid − fref ) represents the droop power. In a typical system, when the power is unbalanced, (e.g., there is more or less consumption than power generation) the grid frequency changes. In this case, the DFIG output power is increased/decreased in order to support the generation. The last term Kei (d(fgrid )/dt) corresponds to the inertia emulation. In this case, the power demand is varied according to the rate of change of the grid frequency. This component emulates the inertia response of a conventional synchronous machine. ∗ is regAssuming stator-flux regulation, reference power Pout ulated using the quadrature rotor current in a DFIG, which is controlled by the RSC. To implement (38), the variable-speed WECS must have a power reserve. Depending on the operating point, a combination of speed control and pitch control has been used to maintain this reserve [153], [166]–[169]. In [79], the operating range is divided into low-, medium-, and high-wind-speed sectors. At low wind speed (e.g., 0 < V < V3 in Fig. 17), the steady-state system is operating at a suboptimal power line, for instance, at 90% of the maximum power curve shown in Fig. 17. When the frequency decreases below fref , the generated power is increased by decreasing the rotational speed until the maximum power point is reached (located in the curve Pout = Kopt ωr3 ). If the grid frequency increases above fref , the captured power is reduced by increasing the rotational speed. At medium wind speed (e.g., V3 < V < V5 in Fig. 17), a combination of speed control and pitch control is used. When
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Fig. 17. Optimal and suboptimal power curve for the control strategy proposed in [79].
the turbine velocity reaches maximum speed, pitch control is activated to avoid overspeeds. At high wind speed, the power is regulated mainly by pitch control. In this case, the output power is controlled below the nominal value in order to maintain a power reserve, which is used when the grid frequency goes below the reference value. A control system for frequency support, also dividing the wind speed into three operating areas, is presented in [167] and [169]. The main difference to that discussed in [79] is at low wind speed; here, it is suggested to regulate the output power linearly with the rotational speed, i.e., ∗ = kωr . Pout
(39)
According to [171], smoothed power generation could be obtained when the rotational speed is linearly changed with the power. The application of variable-speed WECSs based on DFIGs for frequency and voltage regulation in microgrids and minigrids has also been discussed [159], [172]–[174]. In this case, the DFIG stator voltage is regulated according to fs = kp (P ∗ − P )
(40)
Vs = kq (Q∗ − Q)
(41)
where fs and Vs are the frequency and stator voltage of the DFIG and kp and kq are the droops. A control system similar to that proposed in [159] is shown in Fig. 18. The magnetizing current supplied from the RSC is regulated to control the stator voltage, and the stator frequency is varied according to (40). An energy storage system (ESS) is used to supply power to the grid or absorb excess power captured from the WECS. When the ESS is fully charged, pitch control is required to limit the power transferred to the grid. VI. LVRT W ITH DFIGs A. GCRs In the last two decades, the installed wind power capacity has considerably grown. At the end of 2011, the total installed wind power world capacity reached 238.5 GW [175]. At the same
Fig. 18. Control system similar to that proposed in [159] for the operation of DFIGs in microgrids.
time, wind energy penetration into the grid has significantly increased. A good example is Spain, where the average wind energy penetration has been 11%, 13.8%, and 16% in 2008, 2009, and 2010, respectively [176]–[178], although the wind power penetration can temporarily reach a much higher value, e.g., the 64% experienced on September 24, 2012 [179] in the Spanish grid. The GCRs are set by the power system operators to ensure the reliability and efficiency of the utility [156], [180]. These requirements can be divided into two main classes: steadystate or quasi-stationary operation requirements, and LVRT requirements. A review of the GCRs of several countries is presented in [156]. In steady-state or quasi-stationary operation, the requirements such as reactive and active power regulation to support the utility voltage and frequency are specified in the GCR, and have been dealt with in part in Section V. Under grid disturbances, the former GCRs allowed the disconnection of the WECSs to avoid large overcurrents. However, with the increase in the wind energy penetration, the sudden disconnection of WECSs can lead to instability of the entire power system [181], [182]. In this scenario, the power system operators have updated their GCRs, and the wind generators are required to remain connected to the grid during disturbances as it is standard for conventional generators [156], [157], [180], [183], [184]. With the current GCRs, the LVRT requirement demands wind power plants to remain connected when a grid-voltage sag occurs, thus contributing to maintaining stable network voltage and frequency by delivering active and reactive power to the grid with a specific profile depending on the grid-voltage dip depth. Hence, LVRT is probably the most challenging requirement among the GCRs, at least from the point of view of the WECS. LVRT requirements, extracted from the GCR of the utility operator E-ON [157], are shown in Figs. 19 and 20. Very similar curves are provided in the LVRT requirements of other power systems operators [156], [180], [183], [184]. When a
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Fig. 21. Machine model from the rotor side.
Fig. 19. Voltage limit curve to allow generator disconnection.
Most of the disturbances are asymmetrical. Only 12% of grid dips are symmetrical [189], [190]. As shown earlier, conventional regulation for the DFIG is achieved by controlling the rotor currents. The machine model seen from the rotor side is shown in Fig. 21 [182], [186], [188], [191], where σ = (1 − L20 /Ls Lr ). To control the rotor currents by the RSC voltage, it is useful to calculate the opencircuit rotor voltage v rr0 . Note that superscript “r” denotes the variables expressed in the rotor reference frame. Considering the Park model for the induction generator (1)–(3) and the rotor in open circuit, the expression for the stator flux is d Rs ψ = vs − ψ dt s Ls s
Fig. 20. Reactive current to be delivered to the grid under a voltage dip.
grid-voltage sag appears, the power generation plant must remain connected to the grid if the line voltage remains over the limit line 1 in Fig. 19 (region A). In certain cases, a brief disconnection is allowed if the line voltage lies between the limit-lines 1 and 2 (region B). Here, resynchronization typically within 2 s is required to ensure a minimum reactive power supply during the fault; also required is an active power increase rate of > 10% of the rated generator power per second after fault clearance [157]. A brief disconnection is always allowed in region C, where resynchronization times of more than 2 s and an active power increase following fault clearance of less than 10% of the rated power per second are also possible in exceptional cases. If the grid voltage remains low for longer than 1.5 s (region D), selective disconnection of generators depending on their condition can be carried out by the grid protection system [157], [185]. In addition, during the voltage sag, the WECS has to deliver a reactive current, specified in Fig. 20, to aid the utility in holding the grid voltage. The reactive power to be injected depends on grid-voltage reduction during the dip, the system rated current, and the reactive current given to the grid before the dip appears. B. DFIG Behavior Under Grid Fault A number of studies concerning the impact of grid faults on DFIGs have been reported. For the grid, symmetrical disturbances, particularly the deep voltage sags, can be seen as more stressing than asymmetrical disturbances since all phases are lost. However, the analysis for asymmetrical disturbances is more complex due to the appearance of negative-sequence components in the voltages and currents [3], [186]–[188]. DFIGs have low negative-sequence impedance, and small negativesequence stator voltages can lead to high stator currents [106].
(42)
where the stator voltage can be expressed as the sum of the positive (v1s ), negative (v2s ), and zero (v0 ) sequences v s = v1s ejωe t + v2s e−jωe t + v0 .
(43)
The solution for (42) is shown in (44). The zero-sequence voltage does not create flux [188], [191]. From (44), the expression for the open-circuit rotor voltage shown in Fig. 21 can be obtained, as shown in (45), which is given in the following: ψ s = ψ1s ejωe t + ψ2s e−jωe t + ψn0 e−t/τs =
v1s jωe t v2s −jωe t e + e + ψn0 e−t/τs jωe jωe L0 jsωe t L0 se + v2s (s − 2)e−j(2−s)ωe t Ls Ls
L0 1 + + jωr ψn0 e−t/τsejωr t . Ls τs
(44)
v rr0 = v1s
(45)
In normal operation, the grid voltage presents only the positive sequence, and the second and third terms in (44) and (45) are zero. However, when a grid-voltage sag appears, the flux is expressed as the sum of three components [182], [187], [188], [191]: 1) the nonhomogenous or forced flux composed by two terms corresponding to the positive- and negative-sequence stator voltages; and 2) the homogenous or natural flux. The natural flux vector does not rotate. This is a transient dc component flux that exponentially decays with time constant τs = Ls /Rs and initial value ψn0 , which depends on the type and depth of the grid-voltage sag and, in case of asymmetrical dips, on the instant of time within the grid-voltage period in which the grid disturbance occurs [182], [191]. The forced flux is the sum of the positive-sequence flux that rotates at synchronous speed and the negative-sequence flux [86]. The difference between asymmetrical and symmetrical
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TABLE III P OSITIVE , N EGATIVE , AND NATURAL F LUXES (P ER U NIT ) FOR D IFFERENT T YPES OF FAULTS [191]
voltage sags is the presence or absence of the negative-sequence voltage and flux. With respect to the rotor, as shown in (45), the open-circuit rotor voltage has three components: 1) the positive-sequence voltage rotating at sωe (the only component that is present in balanced operation); 2) the negative sequence that rotates at almost twice the synchronous speed (2 − s)ωe and that only appears when the disturbance is asymmetrical; and 3) the rotor voltage produced by the natural flux that creates an open-circuit voltage rotating at ωr . When a grid disturbance occurs, the open-circuit rotor voltage has a large transient overvoltage (mainly caused by the natural flux), which can be even greater than the stator voltage [156], [182]. Because of the transient nature of the natural flux, during symmetrical disturbances, the rotor voltages return to positive-sequence values even if the grid fault is permanent [see (45)]. During asymmetrical faults, however, the rotor voltage also has a large and permanent negative-sequence component [see (46)], and the rotor voltages are higher and more damaging than those for symmetrical grid dips [191]. Table III shows the per unit (p.u.) values of the positivesequence, negative-sequence, and natural fluxes in (44) as a function of the grid fault type and the depth of the voltage sag d in p.u. (i.e., for a three-phase voltage sag where the voltage falls from 1 to 0.2 p.u., the d value is 0.8). The natural flux value depends on the time instant within the voltage period where the fault occurs. The phase-to-phase fault presents the highest natural and negative-sequence flux, and the highest overvoltages in the rotor windings [191]. The maximum amplitude of the transient rotor voltage is given in (46) for a symmetrical fault [182]. A discussion of the maximum rotor voltage amplitude produced by an asymmetrical fault [see (47)] is reported in [99]. As shown in Table III and (44), deeper voltage sags lead to higher transient voltages, and larger dip asymmetry increases negative-sequence voltages and the maximum rotor voltages, as shown in the following, respectively: (vro_transient )max ≈
L0 (|s|(1 − d)v1s + (1 − s)dv1s ) (46) Ls
(vro_asym )max ≈
L0 |sωe | · v1s + |(s − 2)ωe | · v2s . (47) Ls ωe
Without specific control action, the rotor overvoltages produce high ac rotor currents with synchronous frequencies superposed upon the low-frequency steady-state rotor currents injected by the RSC [156], [182], [192]. The rotor overcurrent may exceed 2–3 times the nominal rotor current, which is not acceptable [192]. On the stator side, these currents appear as dc components [192], [193].
The higher rotor currents lead to rising dc-link voltage [156], [192], [194]. If the system in Fig. 1 is assumed, the GSC controller intends to regulate the dc-link voltage to its nominal value, causing a GSC overcurrent of up to 1.5 times the nominal value. Even with GSC control action, the dc-link voltage can reach values of about 2–3 times higher than the nominal dc-link voltage, beyond the limit of the dc-link capacitor [192]. The positive-sequence flux produces a similar torque behavior to that of the balanced operation, but the negative-sequence flux tends to create motoring action that results in an increase in torque pulsation at twice the synchronous frequency [89], [99], [191] and a reduction in the average torque [195]. The presence of the second harmonic in the electromagnetic torque can cause undesired mechanical oscillations, reducing the turbine life span and creating higher acoustic noise [89], [195]. During the grid disturbance, there is a mismatch between the mechanical and electromagnetic torque that leads to rotor overspeed [196]. However, this is not too significant since the rotor inertia acts as a storage system for the energy surplus, and a certain increase in speed (10%–15%) is acceptable [156]. An induction machine fed by unbalanced voltages produces unbalanced flux [191] that can lead to unexpected magnetic saturation, excessive heating, and reduced generator lifetime [195]. Moreover, it will draw unbalanced currents that will increase the grid-voltage unbalance and cause overcurrent problems [89]. Immediately after the voltage sag clearance, the sudden change in the stator voltages causes the natural flux [182] to appear again. This causes the electromagnetic torque to oscillate, causing increased stress on the turbine shaft [192]. C. Systems and Control for LVRT Compliance With DFIG As stated earlier, the grid disturbances cause rotor overcurrents and overvoltages together with a dc-link overvoltage that can lead to converter failure if no protection is included [182], [191], [192], [197]. Different protection devices are depicted in Fig. 22. Their operation and some control approaches to comply with the LVRT requirements will be discussed here. The initial solution implemented by manufacturers to protect the rotor and the converter was to short-circuit the rotor windings with the so-called crowbar and to disconnect the turbine from the grid [198], [199]. This solution is not allowed with the LVRT requirements set at the current GCRs because the WECSs do not support the utility to resume normal operation. If the RSC is sized to generate a voltage equal to the rotor overvoltages of (46) and (47), it will be able to fully control the rotor currents [182], [186], [191]. This is the best solution to deal with rotor overvoltages because it allows full control of the DFIG at all times. To achieve it, overmodulation in the RSC would be required [200], in spite of the increased rotor current harmonics. A method to design the RSC size based on the maximum rotor overvoltage and overcurrent is presented in [90]. One of the most extensive analysis of the operation limits for the RSC under grid disturbance is presented in [201], which considers the impact of limited ratings for the GSC and RSC during grid disturbances. Oversized converters allow more controllability, but the DFIG topology loses its advantages of
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Fig. 22. Rotor and converter protection devices: crowbar, dc-link chopper, ESS, and ac switch [156], [213].
the low-size power converter [182]. It is well known that the converter is sized to manage ≈30% of the total DFIG power [3], [181], [202] and is not normally rated to generate a voltage equal to the rotor overvoltages [182]. It is also noted that, for deep grid-voltage sags, the RSC oversizing is far beyond the converter steady-state ratings. Converter sizing is thus a tradeoff between the LVRT requirements and the cost, together with other protection elements such as the crowbar and the dc-link chopper. DFIGs are always equipped with a crowbar, as shown in Fig. 22, which is a device that short-circuits the rotor windings through resistors, thereby limiting the rotor voltage and providing an additional path for the rotor current [185]. Two crowbar options are available [156]. The first option is the passive crowbar implemented with a diode rectifier or two thyristors in antiparallel. This implementation requires the crowbar current to be forced to zero to deactivate the device, and full control over the crowbar deactivation is not possible. The second option is the active crowbar using IGBT switches; this allows crowbar deactivation and, consequently, faster recovery of the DFIG control. The crowbar resistance value affects the rotor and current behavior [197]. Large crowbars result in better damping of the rotor and stator overcurrents, and the torque overshoot. It also reduces the reactive power consumption. However, very large crowbars can cause current spikes upon deactivation and a high voltage at the rotor slip rings, resulting in voltage stress on the rotor windings [193], [194]. In [194], Kasem et al. suggest a crowbar resistance of 0.3 p.u. if the maximum rotor voltage is limited to 1.2 p.u. The calculation of the crowbar resistance using √ 2(vr )max ωe Ls (48) (Rcrowbar )max = 3.2Vs2 − 2(vr )2max is discussed in [193], where (vr )max is the maximum allowable rotor voltage, Ls = Ls + Lr L0 /(Lr + L0 ), and Vs is the stator voltage. Upon activation of the crowbar, the RSC can be switched off [192], [194], [203]. However, the rotor currents continue
to circulate to the converter dc-link through the freewheeling diodes of the RSC, leading to a very fast dc-link voltage increase and a possible activation of the dc-link chopper to limit the dc-link voltage value [192], [203]. During crowbar operation, rotor currents are not controlled by the RSC, and the machine acts as a single-fed induction generator with rotor resistors. The machine consumes reactive power that can contribute to deepening the grid-voltage sag [203]. The GSC must supply the grid with reactive power, as demanded by the LVRT requirements, and the reactive power to the machine [204], [205]. In [194], it is proposed to connect the GSC and the RSC in parallel, using suitable ac switches, to supply more reactive power to the grid. If the DFIG is not able to supply the reactive power support required by the GCR, dynamic VAR compensators, static VAR compensators [206], or static synchronous compensators [207]–[210] can be installed at the DFIG terminals to provide it. Other equipment, such as the dynamic voltage restorer, can also be used [211]. After the fault clearance, transient rotor overvoltages appear again, and the system experiences a disturbance similar to that of the initial fault. This would require a crowbar [or dc-link chopper activation (see Fig. 22)] for a second time [192], [194]. Unlike asymmetrical disturbances, symmetrical grid disturbances only cause transient rotor overvoltages, and the crowbar mode is active until the rotor currents die down. After this, the crowbar is disconnected, and the RSC is started again to control the rotor currents. Since the fault is still present, the active power reference is reduced to avoid overload. The DFIG can contribute to the reactive power support to the grid. Note however that reactive power support is provided by the GSC throughout the crowbar mode period [192], [204], [212]. In [214], the crowbar is disconnected when the rotor currents fall below a threshold value instead of reaching zero, reducing the crowbar mode time. The dc-link chopper [156], as shown in Fig. 22, is another protective device to keep the dc-link voltage within acceptable limits. It can concurrently operate with the crowbar [156], [192], [203]. The dc-link chopper is not essential for fault
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ride-through operation, but it increases the range of DFIG operation [192], [203]. The ESS [213], [215] connected to the dc-link absorbs the extra energy supplied to the dc link and returns it to the DFIG in normal operation. However, it significantly increases the complexity and cost of the WECS. A good performance comparison using a crowbar, a dc-link chopper, and ESS methods is found in [213]. The stator switch shown in Fig. 22, [156], [185], [216] is another device to meet the LVRT requirements. The stator is disconnected for a short period using this switch; the RSC is blocked, and the generator is demagnetized. After the RSC is restarted, the stator is reconnected, and the operation is resumed. During stator disconnection, the GSC supplies reactive power to the grid. This implementation limits the transient magnitude and duration and keeps full control over the generator during the largest part of the disturbance interval [156], [216]. As discussed earlier, there is a mismatch between the electromechanical torque and the mechanical torque in the presence of the grid disturbance. Pitch control can also be used to reduce the mechanical torque [156], [192] to avoid rotor overspeed. However, pitch control can change the blade angle at a relatively slow rate [217], which is too slow to help the system to respond to a grid fault.
Another control approach introduces a virtual resistance in the rotor to reduce rotor overcurrents. A combination of demagnetization and virtual resistance control is found in [188]. For symmetrical dips, reduced rotor currents in comparison with [186] are reported. Operation under asymmetrical faults has not been reported. A PI controller with a resonant compensator is presented in [110], [224], and [225] for operation under distorted gridvoltage conditions. Although results seem promising, the LVRT issue is not addressed. In [226] and [227], the conventional controller used in normal operation is switched to a vector-based hysteresis current controller during grid faults. Good system performance is achieved; however, the operation limits are not specified, and there are drawbacks to the hysteresis control: higher harmonic content, higher switching frequency or, if the maximum switching frequency is limited, large error bands that produce significant low-order harmonics. Sliding control has been successfully applied to DFIG in [228] under unbalanced conditions and a harmonically distorted grid. Future application of this control method to the LVRT problem can be expected.
VII. C ONCLUSION D. Control Methods for LVRT Compliance With DFIG This subsection summarizes the control methods for LVRT compliance. The goal is to control rotor voltages and currents, to reduce the rotor overvoltages and/or overcurrents, and to avoid the crowbar activation in order to keep full DFIG control at all times to meet the LVRT requirements. However, in many cases, the crowbar activation cannot be avoided, and the crowbar mode concurrently works with the control method. Some control approaches regulate rotor and GSC currents in the positive and negative d–q reference frames [90], [98], [219]–[221] based on a positive- and negative-sequence models of the DFIG [99]. The main control goals cover the DFIG active and reactive power to meet the LVRT requirements. As discussed in Section III-B, each power converter has four degrees of freedom, allowing to include additional control goals as, for instance, the regulation of the dc-link voltage, stator current balancing, and cancelation of the oscillations in the active power, rotor current, and torque. Although crowbar activation cannot be avoided in case of severe asymmetrical faults [90], a noncrowbar method to reduce the rotor overvoltages based on injecting demagnetizing flux currents from the RSC is proposed in [33], [186], [221], and [222]. Full DFIG control is retained, but a large rotor current capacity is needed, and there is limited capability in the case of asymmetrical faults. If the crowbar is activated, the use of the demagnetizing current reduces the crowbar mode time [223]. A robust controller in the α–β stationary frame is presented in [106], claiming full control in all LVRT cases. However, the results have been obtained with an oversized converter that can accommodate rotor overvoltages and full rotor current control. With a suitable-sized converter, this control method may have some limitations.
This paper has summarized the most recent research in the field of control systems for DFIGs in wind energy applications. After reviewing the papers related to conventional control methods for DFIGs connected to balanced systems, it is concluded that vector control, typically orientated along the stator flux, is still the most adopted method for regulating the rotor currents of DFIGs. With this control methodology, decoupling of the reactive power and electrical torque is simple to achieve. However, as discussed in Section II, most of the control schemes presented in Section II-D–F can provide good overall performance. Regarding sensorless control of variable-speed DFIGs, the most popular methods are based in MRAS schemes, with the RCMO providing good performance in both stand-alone and grid-connected operation of DFIGs. The TBMO is also an interesting method for sensorless vector control, particularly because the direct and quadrature rotor currents can be directly obtained from the α–β components of the signals without resorting to transformations to a synchronous rotating axis. Concerning sensorless methods, more research can be required in some areas, particularly because the performance of the rotor position observers proposed in the literature have not been evaluated for LVRT operation. In this paper, the control systems for the operation of DFIGs connected to unbalanced grid or loads, have also been assessed. Several control targets for unbalanced operation have been proposed in the literature, e.g., to eliminate the oscillations in the total active power output from the DFIG, to reduce the oscillations in the total reactive power supplied to the network, or to supply a grid current with no negative-sequence components. To fulfill these control targets, the RSC and/or the GSC can be used. The current trend is to use both power
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converters simultaneously because more degrees of freedoms are available in this case. Control systems for ancillary services and grid-frequency support have also been discussed in this paper. In the past, DFIGs where mostly controlled for MPPT operation. Nowadays, it is expected that WECSs based on DFIGs can provide droop control and inertia emulation. This has been reviewed in this paper. Finally, in this paper, LVRT control systems for DFIGs have been discussed. The operation of the elements typically used for LVRT compliance, such as crowbars, choppers, static switches, and other elements, has been analyzed and extensively discussed in this paper.
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Roberto Cárdenas (S’95–M’97–SM’07) was born in Punta Arenas, Chile. He received the B.S. degree from the University of Magallanes, Punta Arenas, in 1988 and the M.Sc. and Ph.D. degrees from the University of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively. From 1989 to 1991 and from 1996 to 2008, he was a Lecturer with the University of Magallanes. From 1991 to 1996, he was with the Power Electronics Machines and Control Group, University of Nottingham. From 2009 to 2011, he was with the Department of Electrical Engineering, University of Santiago, Santiago, Chile. He is currently a Professor of power electronics and drives with the Department of Electrical Engineering, University of Chile, Santiago. His main research interests include the control of electrical machines, variable-speed drives, and renewable energy systems. Dr. Cárdenas was a recipient of the Best Paper Award from the IEEE T RANSACTIONS ON I NDUSTRIAL E LECTRONICS in 2005 and the “Ramon Salas Edward” Award from the Chilean Institute of Engineers in 2009.
Rubén Peña (S’95–M’97) was born in Coronel, Chile. He received the Electrical Engineering degree from the University of Concepcion, Concepcion, Chile, in 1984 and the M.Sc. and Ph.D. degrees from the University of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively. From 1985 to 2008, he was a Lecturer with the University of Magallanes, Punta Arenas, Chile. He is currently with the Department of Electrical Engineering, University of Concepción. His main research interests include the control of power electronics converters, ac drives, and renewable energy systems.
Salvador Alepuz (S’98–M’03–SM’12) was born in Barcelona, Spain. He received the M.Sc. and Ph.D. degrees in electrical and electronic engineering from the Technical University of Catalonia (UPC), Barcelona, Spain, in 1993 and 2004, respectively. Since 1994, he has been an Associate Professor with the Mataró School of Technology (Tecnocampus Mataró-Maresme), UPC, Mataró, Spain. From 2006 to 2007, he was with the Departamento de Electrónica, Universidad Técnica Federico Santa María, Valparaíso, Chile, conducting postdoctoral research. In 2009, he was a Visiting Researcher for three months with the Department of Electrical and Computer Engineering, Ryerson University, Toronto, ON, Canada. His research interests include multilevel conversion and ac power conversion applied to renewable energy systems.
Greg Asher (M’98–SM’04–F’07) received the B.Sc. and Ph.D. degrees from Bath University, Bath, U.K., in 1976. He is a Research Fellow in superconducting systems with the University of Bangor, Gwynedd, U.K. In 1984, he was appointed as a Lecturer of control with the University of Nottingham, Nottingham, U.K. In 2000, he was appointed as a Professor of electrical drives; in 2004, as a School Head with the School of Electrical and Electronic Engineering; and in 2008, as the Associate Dean for Teaching and Learning with the Faculty of Engineering, University of Nottingham. He is the author of nearly 300 research papers. He has received over £5 million in research contracts and has successfully supervised 31 Ph.D. students. His research interests include motor drive control, cover power system modeling, power microgrid control, aircraft power systems, and motor drive systems, particularly the control of ac machines. Dr. Asher was a member of the Executive Committee of the European Power Electronics Association until 2003 and the Chair of the Power Electronics Technical Committee of the IEEE Industrial Electronics Society until 2008. He is currently an Associate Editor for the IEEE Industrial Electronics Society.
