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Electrical Power and Energy Systems
journal homepage:www.elsevier.com/locate/ijepesHeightened state-feedback predictive control for DFIG-based wind turbines
to enhance its LVRT performance
F.E.V. Taveiros
⁎, L.S. Barros, F.B. Costa
Federal University of Rio Grande do Norte (UFRN) Natal, BrazilA R T I C L E I N F O Keywords:
Doubly fed induction generator Grid unbalances
Low voltage ride-through State-feedback Real time simulation
A B S T R A C T
This paper investigates the response to grid disturbances of the wind energy conversion system based on the doubly fed induction generator (DFIG-based WECS). It is proposed a new control termed as heightened state-feedback control structure (HSFC) with predictive behavior to regulate the rotor current loops, which is able to effectively counteract the back electromotive force surge oscillating dynamics that occur in the event of a dis-turbance in the grid voltage. The proposed method is able to mitigate oscillations in DFIG currents exempting the need to use low voltage ride-through current-modify (LVRT-CM) strategies during intermediate symmetrical and asymmetrical voltage sags or during the voltage recovery process, while provide the DFIG to contribute active and reactive current featuring bounded torque oscillations. During severe faults, the proposed structure is able to effectively track the required post-fault rotor current references as demanded by LVRT-CM, which allows the DFIG to ride-through the fault with constrained currents and torque. The proposed structure also employs a novelflux damping technique which accentuate the rotor d-axis current in order to significantly reduce stator flux settling time after faults, while the torque minimally oscillates during post-fault recovery. Real-time digital simulations and experimental results considering symmetrical and asymmetrical voltage sags due to faults show the proposed solutions advantages over classical and previous strategies.
1. Introduction
The response of DFIG-based WECS to grid disturbances is an im-portant topic nowadays, considering the steadily increasing number of installations of this type of wind generators. The transmission system operator (TSO) of several countries formulated grid codes for effective operation of grid-connected WECS, demanding the generator units to have efficient performance and robust behavior under abnormal con-ditions, such as symmetrical or asymmetrical voltage sags.
The low voltage ride-through (LVRT) feature of wind turbines is usually implemented by means of hardware intervention. The com-monly used method during a fault is to activate the crowbar bank of resistors in the rotor circuit, which will drain the excess of power and limit the generator currents. However, with increasingly stringent grid codes, the drawbacks of this method become obvious: the loss of con-trollability; the electromagnetic torque oscillations, which poses great stress on the drive train; and, the absorption of reactive power, which inhibit the voltage recovery of the grid[1]. Therefore, improvements of control strategy and performance enhancement of the LVRT feature of DFIG have been extensively studied in order to overcome these draw-backs by means of generator control.
The recent proposed solutions design special control schemes aiming to calculate the optimal rotor voltage to counteract the back electromotive force (BEMF), which significantly increases in the rotor circuit due to statorflux variations during grid disturbances, in order to keep providing the DFIG to contribute active and reactive currents to the grid, thus increasing the utilization efficiency of the rotor-side converter (RSC) output capacity. Due to the bandwidth restrictions of the conventional PI control, the DFIG is not able to effectively coun-teract oscillatory disturbances when using this strategy. Therefore, re-cent papers proposed different strategies.
In[2,3]it was proposed feedforward of transient compensation and of rotor current references derivative, respectively. However, the transient compensation depends on effective disturbance estimation whereas the rotor reference derivative only works when the reference is changing, i.e., to track oscillatory references, and consequently is not robust to external disturbances. In[2,4–17]it was proposed resonant terms in the control law, which is a well-adopted technique in grid-connected converters in order to cope with negative-sequence and transient components during grid disturbances. In [4–10,16], the PI plus a resonant term (PI-R) controller is designed and applied to the DFIG during network unbalances to counteract the negative-sequence
https://doi.org/10.1016/j.ijepes.2018.07.028
Received 1 April 2018; Received in revised form 4 July 2018; Accepted 16 July 2018
⁎Corresponding author.
E-mail addresses:filipe.taveiros@ect.ufrn.br(F.E.V. Taveiros),lsalesbarros@dee.ufrn.br(L.S. Barros),flaviocosta@ect.ufrn.br(F.B. Costa).
Electrical Power and Energy Systems 104 (2019) 943–956
0142-0615/ © 2018 Elsevier Ltd. All rights reserved.
disturbance, which oscillates at twice the synchronous frequency. In order to account for the transient component which oscillates at syn-chronous frequency, in[2,11–15,17]it was proposed the usage of the proportional-integral double-resonant (PI-R2) controller, which fea-tures resonant terms at one and two times the synchronous frequency to control the DFIG under asymmetrical faults.
Despite the widespread utilization of the PI with resonant regulators technique, only recently in[15]a concise parameter design has been proposed for the PI-R usage with grid-connected current controllers. However, no parameter design has been effectively developed for the double-resonant controller. For instance, in[17], the design of PI-R2 controller was carried out in continuous time by means of a trial and error process aided by Bode plots, and after implemented by means of continuous-to-discrete time transformation. Due to this difficulty, [5,7,18–20] moved to predictive and adaptive control approaches in order to achieve easier tuning and improved performance. Therefore, there still lacks an effective resonant controller able to track/reject oscillatory references/disturbances with comprehensive and concise parameter design.
Depending on the severity of the fault, the resulting BEMF in the rotor terminals considerably exceeds the RSC voltage output capacity. In this situation, the RSC no longer can freely control the rotor currents, but only limit its rising rate by outputting its maximum voltage[21,22], thus overcurrents are inevitable. Therefore, other recent proposals [10,17,23–31]put up a second-best objective: to suppress the over-currents. Termed as current-modify strategies, they consist in mod-ifications of rotor current reference to release certain transient, posi-tive- and negaposi-tive-sequence parcels in the event of a fault in order to reduce the required rotor voltage within RSC permissible range, while mitigate mechanic oscillations by driving the torque to zero[3,26].
For instance, in [28]it was proposed a demagnetization strategy which consists in injecting in the rotor current parcels to oppose to the transient and negative sequence components of statorflux. In[25]it was proposed a simple but effective strategy which consists in con-trolling the rotor currents to track the stator currents, which was later enhanced to be a negative fraction of the stator currents in[26]. In[29] it was proposed the inductance-simulating control in order to lower the magnetizing current. By doing so, these recently proposed techniques allow the DFIG to ride through the severe grid disturbance with bounded rotor currents and low ripple in the electromagnetic torque.
Despite the LVRT-CM techniques fulfill its main objectives, it has two major drawbacks: (i) under these strategies, the DFIG absorbs re-active power from the grid [26]; (ii) in order to generate reactive power, it is necessary to inject positive-sequence currents in the rotor reference, which produce high current references[32]and may dete-riorate the current-modify strategy performance, due to the increase of torque ripple[26]. The extraction of positive-sequence currents is also time consuming and depends on filters, which introduces delay and phase distortion[3,16]. Moreover, the required post-fault rotor currents under current-modify strategies contains AC components oscillating at grid frequency and at twice the grid frequency[3]. Therefore, in order to accomplish the LVRT feature, these techniques deeply rely on a controller capable of tracking such oscillating signals with fast response and robustness in regard to disturbance rejection, otherwise the LVRT-CM performance will be depleted.
Considering the constrained high-power WECS scenario where: (a) the grid code demands the generator to remain connected in the pre-sence of severe faults during a specific time; (b) the control sampling frequency and the converter switching frequency are limited; and, (c) the DC bus voltage is designed for regular operation and, therefore, the back-to-back converter is not able to synthesize very large voltages, this paper proposes a new control, termed as Heightened State-Feedback Predictive Control Structure, in order to: (i) effectively track LVRT-CM strategies post-fault current references during severe grid faults; (ii) overcome the need for a current-modify technique during intermediate symmetrical and asymmetrical faults while provide the DFIG to
contribute active and reactive current; (iii) fast and effectively suppress the grid frequency-related oscillations in current and torque wave-forms; (iv) bound stator and rotor currents to safe limits; and (v) damp the stator flux and reduce its settling time after the fault featuring minimal torque ripple. Throughout this paper the aforementioned fea-tures will be referred as LVRT objectives (i)–(v).
Realistic real-time simulations and experimental results of a DFIG system under actual faults presented in this paper properly validated the proposed HSFC structure capability to fulfill LVRT objectives (ii)–(v), and also pointed out its advantages over the classical PI and PI-R2 controllers to accomplish LVRT objectives (i) and (iv).
2. DFIG-based WECS under grid disturbances
In this section the DFIG behavior in the event of symmetrical and asymmetrical faults is analyzed, and how the control may compensate the generator to ride through these disturbances.
Apart from the normal operation of the wind turbine, the designed control must undertake problematic situations derived from grid vol-tage disturbances, such as unbalanced operation in weak grids or fault events. One of the most frequently occurring disturbance is a voltage sag, which often causes disconnections of the wind turbines if appro-priate counter-measures are not applied.Fig. 1presents a resumed ty-pical diagram of a wind farm integrated in the power system. The oc-currence of a fault at any point in the distribution (69 kV line) or transmission (230 kV line) networks inevitably results in voltage sags in one or more phases at the point of common connection (PCC) of the wind farm, which in the case is the 690 V bar, and it is also possible that there is a voltage increase in the phases that did not suffer from the fault, depending on the type and location, which can be propagated to remote points in the network [32]. Most faults that occur in power systems are transitory, however, even those which last for a few hun-dred milliseconds may force disconnections of the wind turbines [33,34]. In order to ride-through the distorted voltage scenario pro-viding LVRT objectives (i)–(v), the generator must keep some level of controllability.
The greater the penetration of renewable sources, the greater the energy deficit in the eventual disconnection of the generating units and, therefore, the greater the concern of the network operators. Consequently, grid codes address explicit fault behavior in time to de-termine whether or not the generator unit is allowed to disconnect. Fig. 2 depicts the LVRT regulation of the TSO grid codes of Brazil, Canada, Germany and The United States. Any sag in the voltage wa-veform that remains above the depicted reference curves should be supported in full by the WECS, that is, the turbine is not allowed to disconnect from the power system. The Brazilian code is the least de-manding regarding the level of the sag, allowing the turbines dis-connect if the voltage in the PCC falls below 20%, unlike the other countries, which require that the turbines remain connected even with the voltage in the PCC falling to 0%, for at least 150 ms as is the case of Germany and Canada, as high as to 625 ms, as is the case in the USA.
However, stay connected during such conditions is a technological challenge for the wind turbine control due to high levels of voltages, currents and mechanical vibration that may develop in the generator during and after a fault in the grid. The influence of the stator voltage
on the statorflux is the key to understand the processes inside the DFIG during a fault. The rotor circuit dynamics is described by
+ → + → =→− ⎛ ⎝ ⎜ → + →⎞ ⎠ ⎟ R jω σL i σL d i dt v L L dλ dt jω λ ( r sr r) r r r r m , s s sr s rotor circuit BEMF (1)
in which Rr and Lr are the rotor resistance and inductance;Ls is the stator inductance;Lmis the mutual inductance; vr and ir are the rotor voltage and current; λsis the statorflux; ωsris the slip speed and σ is the leakage factor given byσ= −1 Lm2/(L Ls r).
Eq.(1)highlights the distinctiveness of terms in the rotor equation: the first part denotes the rotor circuit dynamics, represented by the voltage drop due to the rotor resistance Rrand the transient dynamics due to the leaked coupled inductance σLr; whereas the second part denotes the electric potential difference between the rotor voltage→vr and the BEMF induced in the rotor by the statorflux, which represents the disturbance from the control point of view[3,26].
Control of DFIG is usually carried out in the statorflux synchronous reference frame (SRF), which means that the positive-sequence voltage, current, and flux all become DC values in steady-state, whereas the negative-sequence components, which are present during asymmetrical voltage disturbances, appear as ripples which oscillates at twice the synchronous frequency [7]. Therefore, in steady state and normal (balanced) conditions, the statorflux assumes the grid rotational fre-quency, and becomes constant in amplitude. Consequently, the deri-vative part in(1)is zero. During a disturbance in the electrical network, however, the equilibrium established in the statorflux is undone and, therefore, there are variations in the flux and consequently in the BEMF.
The statorflux, for its part, is a function of the stator voltage and the rotor current, whose dynamics are given by[34,35]
⎜ ⎟ → + ⎛ ⎝ + ⎞ ⎠ → =→+ → d dtλ R L jω λ v L R L i , s s s s s m s s r (2) whereRs is the stator resistance,vs is the stator voltage and ω is the reference frame rotating speed, which for now it is assumed the sta-tionary reference frame ( =ω 0) for simplicity of the analysis. During a fault, according to the symmetrical components theory, the stator vol-tage would consist of the sum of the resulting positive-, negative- and zero-sequence components. However, the DFIG generators in the wind farm are usually connected to the PCC by means of Y/Δ transformers (as illustrated in Fig. 1), which isolate the zero-sequence component. Therefore, the voltage in the stator side of the transformer consists generally of the positive sequence→vsP and the negative sequence→vsN components[34], in other words, the inputs to the statorflux ODE in
the stationary reference frame are given by[35] →v =→v +→v =V e +V e− ,
s sP sN sP jω ts sN jω ts (3)
in whichVsP and VsN are the positive and negative sequence phasor magnitude andωsis the stator voltage frequency. The statorflux solu-tion from(2)may now be obtained as[34,35]
→ =→ + + + − − λ λ e jωV e jωV , s sn jω t τ s sP jω t τ s sN 1 1 s s s s (4)
in whichτs=L Rs/ sis the stator time constant and →
λsnis the naturalflux, which in the fault inception has initial value Ψ that depends on the stator voltage value previous to the fault as well as the new voltage value[34,35]. The naturalflux initial value also depends on the fault inception angle[32]. From this value, the naturalflux evolves with the post-fault rotor current according to[32]
→ = − → + → d dtλ R Lλ L L i, sn s s sn m s r (5) which will represent a term that decays exponentially from Ψ with the stator time constant and another term that is a function of the rotor current. By rotating(4)to the SRF and performing few simplifications, the BEMF dynamics in the statorflux reference may be generally ap-proximated by[3,26,29,32,36]
≈sV + −s V e− −j −s ω λ e→ −
BEMF sP (2 ) sN j ω t2 s (1 ) s sn jω ts, (6)
in which s is the slip factor.
In normal (balanced) conditions, there is only positive-sequence in the stator voltage. Therefore, the BEMF is solely proportional to the stator voltage by a factor that is given by the slip speed. Since the DFIG operates with slipping between±30%, the maximum amplitude of BEMF is 30% of the grid voltage. However, if a symmetrical fault occurs, it will cause a change in the statorflux level, therefore, the BEMF will present a constant parcel and the naturalflux parcel, which oscillates at frequencyωs with initial amplitude equal to(1−s ω) sΨ, while decays exponentially with time constantτs. On the other hand, if the fault is asymmetrical, in addition to the constant parcel and theωsfrequency parcel, there is also the parcel which oscillates at frequency2ωs with amplitude equal to(2−s V) sN caused by the negative-sequence voltage. Therefore, during symmetrical and asymmetrical faults, the SRF vari-ables, which are constant in normal operation, are disturbed by am-plified parcels with impulsive and oscillatory behavior. In the above analysis, all the rotor variables have been referred to the stator side. The real BEMF experienced by the rotor should take into account the transformation ratio and the frequency conversion between the stator and rotor windings, given by[34]
′ = s
K
BEMF BEMF ,
sr (7)
in whichBEMF′is the real voltage in the rotor side and Ksris the stator-to-rotor turns ratio, which is usually a fraction between 1/3 and 1/2 in order to reduce the current rating in the RSC. Therefore, the real BEMF in the rotor side is amplified from two to three times.
Table 1 summarizes normalized values of positive and negative sequence voltages and initialflux in the event of phase to neutral, phase Fig. 2. LVRT required performance listed in grid codes of Brazil, Canada,
Germany and USA.
Table 1
Normalized values of voltages and initialflux.
Fault Positive Sequence
(VsP) Negative Sequence (VsN) Natural Flux (Ψ) Phase to neutral 1−p/3 p/3 0 to p2 /3 Phase to phase 1−p/2 p/2 0 to p Two phase to neutral − p 1 2 /3 p/3 p/3to p Three phase 1−p 0 p
to phase, two phase to neutral and three phase faults[32], where p is the percentage depth of the voltage sag. UsingΨ=p/2, Ksr=0.426and the values fromTable 1, and assuming no currentflowing through the rotor for simplicity,Fig. 3(a) presents the BEMF levels as seen from the rotor circuit during a single-phase voltage as a function of the sag depth and the rotor slip, whereasFig. 3(b) presents it evaluated for different slip values as a function of time and sag depth.
Fig. 3indicates that the severity of the fault is directly proportional to the depth of the sag and to the generator speed, considering the slip from s=0.3 to −0.3. The RSC DC-bus voltage is often designed to output from 1.2 to 1.5 pu maximum voltage in respect to the stator voltage. For instance, in a 690 V system, the DC-bus voltage is usually between 1200 and 1500 V. During faults, the RSC should not only match the BEMF voltage, but also exceed its level in order to fully control the rotor currents. Therefore, it is possible to define a full control boundary (FCB) encompassed between the 1.0 pu and 1.5 pu contour lines inFig. 3(a), in which any voltage sag that lies below this boundary the RSC will feature at least 0.2–0.5 pu remaining voltage to overcome the BEMF. For voltage sags above the FCB, the full control is no longer possible during all times, but only during short periods where the BEMF sinusoid instantaneous value is less or equal to 1 pu, as il-lustrated inFig. 3(b). During the periods where the BEMF exceeds this level, the RSC controller outputs the maximum voltage just in order to limit the current rising rate[21]. For voltage sags above the FCB it is encouraged the use of LVRT-CM strategies in order to reduce the re-quired rotor voltage within RSC permissible range[3,21,25,26,29].
Even voltage sags below the FCB represent difficult technological challenges for WECS control, since the disturbances still feature high levels and highly oscillatory behavior. Moreover, such disturbances may last for a long period after the fault clearance, since the statorflux slowly evolves to steady-state value, specially in high-power generators where the stator time constant ranges between 0.8 and 2.5 s, which means that the statorflux will take roughly four times this period to settle, which is much longer thant the average duration of a voltage dip [32]. During this settling period, the statorflux heavily oscillates which reflects ripple in the electromagnetic torque. This is further convoluted by unpermissive grid codes demanding the turbine to remain connected in the event of such faults and to contribute reactive current to assist the grid voltage to recover.
This paper proposes the HSFC structure as a solution for WECS control to accomplish LVRT objectives (i)-(v), as follows:
1. During the fault:
In order to fulfill objectives (i) and (iii) the proposed structure will be formulated on top of the general form of the post-fault reference
signals in conjunction with the general form of the disturbance present during symmetrical and asymmetrical faults; in order to fulfill objectives (ii) and (iv) the proposed structure will be designed toward achieving the fastest control action considering hig-power WECS switching and sampling constraints, therefore the process is fully carried out in discrete time;
2. After the fault:
In order to fulfill objective (v), the proposed structure will employ a novel flux damping technique which accentuate the rotor d-axis current in order to significantly reduce stator flux settling time after faults, while the torque minimally oscillates during post-fault re-covery.
3. The proposed heightened state-feedback control
In order to describe the realization of the proposed HSFC technique, a number of definitions are necessary. Defining the rotor state vector as
= + = x i L σL Lλ and x i , rd rd m r s s rq rq (8) the DFIG synchronous reference frame model represented in state space is given by = + + = + x x v i x A B B d C D d ̇ r r r r r 1 1 (9) where = ⎡ ⎣ ⎤ ⎦ = ⎡⎣⎢ ⎤ ⎦ ⎥ = ⎡⎣ ⎤⎦ x xx i i v i v v , , r rd rq r rd rq r rd rq , and (10) The state space system in(9) and (10)is actually formed by three inputs and two outputs: the rotor currentir is the output, the rotor voltage vr and the stator flux λs are the inputs. However, from the control point of view, as the controller only acts on the rotor voltage, it becomes clear that the disturbance d is the statorflux λs. The proposed HFSC main goals are: (i) to offset BEMF disturbances in the current control loop, which may contain a constant parcel, and oscillating Fig. 3. BEMF levels as seen from the rotor circuit during a single-phase voltage sag: (a) as a function of the sag depth and the rotor slip; and (b) evaluated for different slip values as a function of time and sag depth.
parcels of frequencyωsand2ωs, as previously reasoned; and (ii) to track the rotor current set point reference which consists of a constant parcel, and may also contain one of the aforementioned oscillating parcels, as it is the case when using LVRT-CM techniques. Therefore, it carries out an internal model (IM) of the general form of the reference to track and the disturbance to reject. In other words, the disturbance d is modeled as
= + + + +
d c0 c1sin(ω ts ϕ1) c2sin(2ω ts ϕ2), (11) where c0,c c ϕ1, 2, 1andϕ2are unknown variables of the disturbance. The rotor direct and quadrature axis referencesi∗
rdqare modeled with the same characteristic equation
= + + + +
∗
irdq c3 c4sin(ω ts ϕ3) c5sin(2ω ts ϕ4), (12) where c3, c4, c5, ϕ3 andϕ4 are unknown variables of the rotor re-ference.
Since one of the constraints is the low sampling and switching fre-quency, a controller to track such signal and reject such disturbance would require a large bandwidth, which is often not possible using classic controllers. Moreover, the design in continuous time and further implementation by continuous-to-discrete time transformation may not produce comparable results. Therefore, the HSFC design is fully carried out in discrete time. The state space system equation in (9) is re-presented in discrete time as
= + + = + + x x v i x F G G d C D d , . r k r k r k k r k r k k [ 1] [ ] [ ] 1 [ ] [ ] [ ] 1 [ ] (13)
The generic disturbance and reference functions in (11) and (12)are concisely described in discrete time by the set of difference equations
∑
+ = + = + − dk α d 0, n n k n [ 5] 1 5 [ 5 ] (14)∑
+ = + ∗ = + − ∗ ir k αi 0, n n r k n [ 5] 1 5 [ 5 ] (15) whereα1…α5are the difference equation coefficients with sampling time Ts, given by = − + − = + + + = − = − = − α ω T ω T α ω T ω T ω T α α α α α 2(cos( ) cos(2 )) 1;2(2cos( ) cos(2 ) cos(3 ) 1);
; ; and 1. s s s s s s s s s s 1 2 3 2 4 1 5 (16)
Either due to the disturbance or due to the reference, the generic difference equation description in(14)and in(15)is also present in the control error, which is given by
= −∗
e[ ]k ir k[ ] ir k[ ], (17)
wheree[ ]k =[erd k[ ] erq k[ ] T] . Replacing(17)in(15), results in
∑
∑
+ = + + = + − + = + − ek α e i α i . n n r k n r k n n r k n [ 5] 1 5 [ 5 ] [ 5] 1 5 [ 5 ] (18) Defining the error space state vector as∊[ ]k =[e[ ]k e[k+1] e[k+2] e[k+3] e[k+4]] ,T (19) and the rotor current dynamics state as
∑
= + + = + − i i ξk r k α , n n r k n [ ] [ 5] 1 5 [ 5 ] (20) and similarly defining the error space control input as the rotor voltage dynamics∑
= + + = + − v v μk r k α , n n r k n [ ] [ 5] 1 5 [ 5 ] (21) yields the heightened error-state-space system:⎡ ⎣ ⎢ ∊ ⎤ ⎦ ⎥= ⎡ ⎣ ⎢ ⎤ ⎦ ⎥⎡ ⎣ ⎢ ∊ ⎤ ⎦ ⎥+ ⎡⎣ ⎤⎦ + + 0 0 ξ β F ξ G μ Γ , k k k k k [ 1] [ 1] [ ] [ ] [ ] (22) (23) The heightened error-state-space system closed-loop dynamics is governed by the rotor voltage dynamics, which is the error space con-trol input, formed by means of feedback of the error space state vector ∊ and the rotor current dynamics stateξ:
= − ⎡ ⎣ ⎢ ∊ ⎤ ⎦ ⎥ K μ ξk , k [ ] [ ] (24)
whereK=[K5 K4 K3 K2 K1 Kξ]is the error-and-state feedback gain vector. The error-state-space system in(22)can be given arbitrary dy-namics if it is controllable. On account of the pair (Γ, ) is in the con-β
trollable canonical form and given the plant system F G( , ) is con-trollable, then the error space system in(22)is controllable. The gain vector may be calculated by means of a pole placement technique or a cost function minimizing method, such as the linear quadratic regulator (LQR).
Combining(20),(21)and(24)the heightened state-feedback con-trol law is established as
= + = − + u u e v u K i G C Γ , , c k c k c k r k c c k ξ r k [ 1] [ ] [ ] [ ] [ ] [ ] (25) where = = = + + + + u u u u u u G G G G G G C [ ] , [ ] , [1 0 0 0 0], c k dq k dq k dq k dq k dq k c c c c c c c [ ] [ ] [ 1] [ 2] [ 3] [ 4] T ,1 ,2 ,3 ,4 ,5T (26) and = − = − = − + − + = − + − − + + = − + − + + − − − − + + + G K G K α K G K α K α K K α G K α K α K α K α α K K α K α G K α K α K α K α α K α K α α K α α K α K K α K α K α , , 2 , 3 2 2 . c c c c c ,1 1 ,2 1 1 2 ,3 1 12 2 1 3 1 2 ,4 1 13 2 12 3 1 1 2 1 4 2 2 1 3 ,5 1 14 2 13 3 12 1 2 12 4 1 2 2 1 1 3 1 1 22 5 3 2 2 3 1 4 (27) The control law in(25) sets up a high-order state-feedback con-troller (which entitles the proposed technique), comprised by the cur-rent feedback regulator and the error regulator. The former accounts for instantaneous state-feedback of rotor current, whereas the latter works in a predictive loop of the control input based on the coefficients of the generic difference equation in the matrix Γ, subsequently updated on each control step as a function of the control error weighted by the matrixGc.
Matrices F G, andG1 of the discrete-time DFIG synchronous re-ference frame model are obtained using continuous to discrete time conversion techniques. The forward rectangular rule is used for the sake of simplicity, however, any technique can be used. The forward rec-tangular rule is given by
′ ≈ + − x t x x T ( ) k k. s [ 1] [ ] (28) Applying(28)in(9) and (10), matrices F G, andG1become
(29) The cross coupling between direct and quadrature axis components of rotor currents can be seen as rooted in one or more of the parcels of the disturbance d, which makes the feed-forward unnecessary. Therefore, the detached state space model for the rotor direct and quadrature currents is
= +
+
irdq k[ 1] Firdq k[ ] Gvrdq k[ ], (30)
(31) Replacing(31)in(22)andC=1 in(23)results in a 5th order error feedback predictive controller associated with a state-feedback rotor current regulator as depicted inFig. 4, which represents the proposed HSFC technique for the DFIG-based WECS control. The proposed structure was designed to attain LVRT objectives (i)–(iv) during faults, by means of effectively suppressing a disturbance given by(11)or even by accurately following the set point provided by a current-modify LVRT technique in the form of(12).
After the disturbance in the grid voltage is cleared, the statorflux will slowly evolve toward settling back into the normal level. During the set-tling period after the fault, the statorflux strongly oscillates, which reflects on the machine torque, even if the rotor currents are well controlled to constant levels. In order to overcome this problem and to accomplish LVRT objective (v), the proposed HSFC structure features a novel post-faultflux feedback damping technique which is now presented.
It is possible to represent(2)in the statorflux SRF(ω=ωs)and to rewrite it in a state-space dq representation as
= + +
λ λ I v i
d
dt s Af s 2 s Bf r, (32) whereλs=[λsd λsq] ,T vs=[vsd vsq] ,T I2is the 2x2 identity matrix and
(33) The representation in (32) is a 4-input-2-output dynamic system in which the outputs are the stator dq-fluxes, whereas the inputs are the stator dq-voltages and the rotor dq-currents. This system features very poorly damped poles at s= −R Ls/ s±jωs. The stator voltage is in-tangible as a control input, however, the rotor currents may contribute, by means of state-feedback, to damp the statorflux and consequently
the torque much faster than what would be normal[37–39]. The ap-propriate full state-feedback would drag the system poles more to the left of the complex plane, therefore, theflux settling is damped faster. However, if it is injected into the rotor current a contribution in order to damp the statorflux faster, that could result in high current references and could even worsen the oscillation in torque waveform [39], since the torque is proportional to the q-axis current. In order to overcome this problem and still damp the statorflux, the novelty of the proposed HSFCflux damping technique is to perform full state-feedback of the statorflux, however, accentuating the damping contribution in the rotor current d-axis. In this fashion, most of the oscillation and amplitude level required to damp the stator flux more quickly is transferred to the d-axis current, while the q-axis current also con-tributes to damping but minimally oscillates. The proposed flux damping technique embedded in the HSFC structure is therefore termed as rotor current d-axisflux damping (d-FD).
In order to accentuate the damping contribution in the rotor d-axis current, theflux feedback gain matrixKλis calculated by means of the well-known LQR, which minimizes the cost function
∫
= λ λ +i i J N( sTQ R )dt, s r r 0 T (34) in which Q and R are symmetric positive-definite weighting matrices. It is not in the scope of this paper to introduce the LQR in detail, which is already a widely know technique. However, the introduction of the Q an R matrices is important because they underlie the relative im-portance of the various states and inputs[40].Matrices Q and R to be used in the proposed HSFC with d-FDflux damping are given by
= ⎡ ⎣ ⎤⎦ = ⎡⎣ ⎤⎦ Q R I 10 Λ 0 0 Λ and 1 1 0 0 4 , r2 (35)
whereIr is the rated rotor current and Λ is the rated statorflux cal-culated based on the rated stator voltage asΛ= V ωs/ s. The different factors 1 and 4 in R will produce the desired accentuation in the rotor d-axis current feedback contribution (the lower the number the higher the accentuation). The values in these matrices were obtained empirically and produced good results for the cases tested. However, it may be changed in order to be adequate for different systems.
With the gains calculated from the LQR using the given Q and R matrices, the damping contributioniλdqto be injected in the rotor cur-rent reference is calculated as
⎡ ⎣ ⎢ ⎤ ⎦ ⎥= ⎡⎣⎢ ⎤ ⎦ ⎥ ⎡ ⎣ ⎢ − − ⎤ ⎦ ⎥ ∗ ∗ i i K K K K λ λ λ λ , λd λq λ λ λ λ sd sd sq sq 11 12 21 22 (36) in which λ∗
sd is the reference level for the statorflux, which can be calculated neglecting the small rotor resistance as[9]
= ∗ λ v ω, sd sq s (37) and ideally λ∗ =0
sq . The d-FD is employed as a part of the proposed HSFC structure in order to damp the statorflux after the fault clearance in order to drive the DFIG for the steady-state regime more quickly. Therefore, it does not work all the times. Instead, it should be activated whenever the fault detection method acknowledges the fault clearance. The full HSFC structure is illustrated inFig. 4.
4. Performance assessment
In order to verify the validity of the proposed method to accomplish LVRT objectives (i)-(v), two studies are carried out and presented in this session: (i) real-time hardware-in-the-loop digital simulations of a high-power DFIG-based WECS, in which the DFIG model runs in a FPGA-based simulation at 100 kHz, while the controllers are implemented in a real-time processor; and, (ii) experimental verification by means of a small-scale DFIG-based WECS test bench. The high-power simulation system parameters were obtained to realistic resemble the features and limits of a comercially-available WECS, namely the 2 MW Vestas V90 VCS [41]. The parameters of the simulation and experimental test bench systems are presented inTable 3.
The studies are carried out considering the constrained scenario, that is: (i) the back-to-back converter is able to synthesize a voltage that is only 1.5 times the PCC peak voltage; (ii) the switching and sampling frequencies are set to 2 kHz; and, (iii) the generator is generating the rated power at negative rated slip, which provokes the highest levels of back electromotive force in the case of a fault. The system is then subject to severe and intermediate voltage sags in the PCC. For sim-plicity, the voltage divider model shown inFig. 5is used to formulate the voltage sag conditions in the wind farm PCC[34], just before the elevating substation, in whichVsrepresents the pre-fault stator voltage, Zsand Zf represent the source impedance and the fault load impedance, respectively, where the latter is adjusted in the simulations in order to obtain the desired sag level.
The proposed HSFC is compared in the simulations and experiments with the conventional PI controller and the recently adopted PI-R2 controller, and as a LVRT-CM strategy, it is used the current reversely tracking control (CRTC) due to its simplicity and outstanding features. The PI-R2 and CRTC techniques are briefly described in the sections below. After, the gain design process is given in detail. Finally, the si-mulation and experiment results are presented and assessed.
4.1. current-modify LVRT technique
The CRTC was recently proposed in[26]and is used in this paper as the LVRT-CM strategy during severe faults above the FCB. During a fault, the CRTC switches the rotor current references to track the stator currents as
→
= − →
∗
ir k ir s, (38)
wherekr is the tracking coefficient. If the rotor current properly track the reference in(38), the stator and rotor currents can be solved as → = − → → = − − → i k i i k k i 1 and , s L L r sm r L r L r sm s m s m (39)
where→ism=→λ Ls/ m is the stator magnetizing current. As indicated in (39), the rotor and stator currents are uniquely determined bykr, which under appropriate values, the amplitudes of rotor current and voltage can be constrained within the RSC permissible ranges. For more details, see[26].
4.2. Proportional-integral-resonant control
The PI-R2 controller features resonant terms at frequenciesωsand ω
2 s, and was recently used to control the DFIG under symmetrical and asymmetrical faults[3,17]. The transfer function of PI-R2 is given as
= + + + + + − C s K K s K s s ω K s s ω ( ) 4 , p i s s PI R2 2 R1 2 R2 2 2 (40) whereKpis the proportional gain,Kiis the integrative gain,KR1andKR2 are the gain of resonant terms with frequencyωsand2ωs, respectively.
4.3. Controller design process
The compared controllers feature different structure: the conven-tional PI is afirst order controller, the PI-R2 is a fifth order controller and the proposed HSFC is a sixth order controller. In order to compare the controllers performance in the same scale, they were designed to attain similar dynamic closed-loop response to step input. To achieve this,firstly the HSFC and PI controllers are designed to attain the sired characteristics. Unfortunately there is no concise parameter de-sign procedure for the PI-R2 controller, therefore, the dede-signed is made by trial and error until similar dynamic characteristics are found for the three compared controllers.
4.3.1. Proposed HSFC design
The gain design process of the proposed HSFC is now shown in detail for the high-power WECS, and can be done for the experiment system similarly. Firstly it will be designed the gains of the controller itself, and secondly the d-FD statorflux feedback gains. Since the goal is to compare with other controllers, in place of using a cost function minimizing technique such as the LQR, the poles are chosen based on a prototype in order to provide a settling time characteristic close to
=
Tst 20ms, which is one cycle for the 50 Hz system. The poles were chosen based on the one-second settling 6th order prototype as
= − ± − ± − ±
s [ 4.217 7.530j 6.261 4.402j 7.121 1.454 ],j
which are translated to discrete-time domain with the desired settling time according to the matched pole discretization method given by
= z es , T T k s st st (41)
in whichkstis a factor to adjust the settling time due to the presence of zeros in the closed-loop system, which was chosen as kst=1. 54. Therefore the chosen discrete poles are
= ± ± ±
z [0.815 0.24j 0.775 0.13j 0.759 0.04 ].j (42) Theαcoefficients which describes the generic internal model of the disturbance and reference function are calculated from (16) using
=
Ts 500μs andωs=100πrad/s as
= − − −
α [ 4.878 9.635 9.635 4.878 1.000], (43)
which are replaced in the Γ matrix in(22) and (23).
The DFIG parameters presented in Table 3 are replaced in (31) which results in
= =
F 0.9956 and G 1.6815, (44)
which is then replaced in(22) and (23). Once the heightened error-state-space system matrices pair
⎡ ⎣ ⎢ ⎤⎦⎥ ⎡⎣ ⎤⎦ β F G Γ 0 , 0 A B 1x5 5x1 h h
is numerically formed, the gains can be obtained straight forward using pole placement techniques, which are well implemented in modern numerical computation software, e.g. Octave, Scilab, Matlab. For in-stance, the following command syntax used in Matlab software ≫ place(Ah, Bh, z)
will result in the following gain vector
= − −
K [0.261 1.062 1.645 1.148 0.306 0.699].
WithK andα, theGc matrix which weights the error and updates the predictive loop is readily computed as from(26) to (27)
= −
Gc [0.306 0.341 0.363 0.372 0.365] .T
WithΓ,Gc, andKξ, the HSFC controller for the 2 MW simulation system is now fully assembled as described in(25)and illustrated inFig. 4, and is now ready to be implemented in a digital processor.
The design of the d-FDflux feedback gains is also straightforward using numerical computation software. Replacing the DFIG parameters presented in Table 3 in (33) and (35), and running the following command in Matlab software
≫ lqr(Af, Bf, Q, R) (45)
results in the followingflux feedback gain matrix = ⎡ ⎣ − − ⎤⎦ K 4537.076 31.574 7.894 1134.659 . λ (46)
4.4. Conventional PI and PI-R2 controllers design
The PI was designed in the conventional manner whereas the PI-R2 was designed by means of a trial and error process aided by Bode plots and step response graphs. Both controllers were designed in order to achieve dynamic response to step input as close as possible to that of the proposed HSFC. The calculated gains and dynamic features ob-tained from the comparative design are presented inTable 2.
4.5. High-power WECS real-time digital simulations
The case scenario of these studies is the machine working with rated slips= −0.12, generatingPs=1.0pu of active power andQ=0.0 pu of reactive power. When t=0, it becomes subject to symmetrical and asymmetrical faults, in which the voltage of the affected phases reduces to0.2pu. After 200 ms, the fault is cleared. It is assumed that a real-time fault detection and classification method is used in order to change the current references during the disturbance. The detection time of such methods is usually one to two cycles [42]. Therefore, in order to ac-count for a realistic delay, the current references are changed only 20 ms after the disturbance start and represents the fault detection
method acknowledgment. Similarly, the fault detection method ac-knowledges the normal operation 20 ms after the disturbance end. During the fault, the DFIG current references are modified according to the CRTC strategy described in Section4.1, with the tracking coefficient set tokr=0.8. It is evaluated the performance of the rotor-side control and the grid-side control. It should be noted that the grid-side control employed is the conventional PI. Moreover, in order to better clarify the improvements brought about the overall WECS control by the proposed HSFC, it was not employed in the simulations any kind of external protection, such as the crowbar or the braking-chopper that is used when the DC-bus exceeds its maximum allowed voltage.
4.5.1. Asymmetrical faults
Fig. 6 details the performance of the proposed HSFC structure compared to the classical PI and the PI-R2 controllers during a single phase voltage sag. In the fault inception, the stator flux, which was constant at 1.0 pu, starts to oscillate strongly atωsand2ωsfrequencies, that is, 50 and 100 Hz. As a result, the BEMF, which is proportional to theflux derivative, reach very high levels in the rotor circuit, which far exceeds the DC-bus output capacity. Therefore, the rotor references are changed to the CRTC method. However, as discussed previously, the classical PI controller cannot track the CRTC reference signals during the fault. The dq-axis rotor current references contain 50 Hz and 100 Hz components, for which the classical controller output presents sustained error in phase and magnitude. As indicated in previous works [4–16,2,17]the conventional PI does not make optimal usage of the DC-bus voltage as it can be seen in the provided results. As a con-sequence, the action of the CRTC method is compromised, and sig-nificant oscillations appear in the system currents and electromagnetic torque, resulting in over 2.5 pu peaks in stator and rotor currents. The torque presents average 1.5 pu ripple with peaks reaching up 3.0 pu in the beginning of the fault. These oscillations are further reflected in power waveforms, in which the oscillations between generating and absorbing may be considered unacceptable. Since the torque is driven to average zero by the CRTC strategy, the rotor speed inevitably rises from 1.12 pu to 1.15 pu in a very short time. The high torque ripple and the speed increase represent a great mechanical stress. A critical mo-ment is after the fault clearance. At this time, the statorflux decayed to almost 0.5 pu. When the fault clears, the statorflux slowly evolves to the rated value. As a result, during this period the oscillations last in flux, torque, currents, power and even the DC-link voltage waveforms for several seconds after the fault clearance. Regarding the PI-R2 and the proposed HSFC methods, the rotor currents correctly track its re-ference. As a result, the torque oscillations are acutely diminished while the torque is driven to zero and the stator and rotor currents are ef-fectively suppressed close to 1 pu. Furthermore, after the fault clear-ance, the system is compelled to the nominal operation point much faster. However, compared to the PI-R2 method, the rotor currents tracking performance is much superior under the proposed HSFC method, which provided lower peaks in the currents and less ripple in the electromagnetic torque transient while driven to zero. In spite of the conventional PI strategy, after the fault clearance the system under the
Table 2
Controllers gains and step response performance for the simulation and experimental systems. Simulation System
Gains Rise Time Settling Time Overshoot
PI Kp=0.209 Ki=37.556 1.50 ms 17.0 ms 15.7 %
PI-R2 Kp=0.521 Ki=37.556 KR1=89.958 KR2=97.699 0.50 ms 23.5 ms 21.6 %
HSFC K5=0.261 K4= −1.062 K3=1.645K2= −1.148 K1=0.306 Kξ=0.699 0.53 ms 22.5 ms 29.2 %
Experimental System HSFC K5=0.537 K4= −1.753 K3=2.064K2= −1.011 K1=0.163 Kξ=9.797
PI-R2 strategy was able to keep the rotor currents in the provided constant levels. However, as discussed previously the stator flux re-mains oscillating toward a slow settling. This oscillation reflects in the torque, which presented sustained ripple close to 1 pu. On the other hand, the system under the proposed HSFC control emploeyd its d-FD feature, which provided additional injection in the rotor current re-ferences in order to damp the statorflux, specially in the d-axis current, which briefly reach a maximum of 1.7 pu and fastly decays to the provided constant reference after theflux settling. As a result, the re-active power present some oscillations while the flux is settling, whereas the torque presents minimal ripple. In this fashion, the stator flux is rapidly damped and the system under the proposed HSFC control settles in the rated performance long before the other controllers.
4.5.2. Symmetrical fault
Fig. 7 details the performance of the proposed HSFC structure compared to the classical PI and the PI-R2 controllers during the three phase voltage sag. Differently from the asymmetrical faults, the stator flux presented only the 50 Hz component with an exponential decay, which well agrees with the results presented in Section2. The rotor current references provided by the CRTC strategy therefore shows only 50 Hz component along with a transient component. However, it does not represent any relief for the conventional PI controller to ride through the fault. Since the CRTC was impaired due to the ineffective
tracking of the current references, high levels of stator and rotor cur-rents are drawn in this case. During the fault, the excess of power in-evitably reached the back-to-back converters. Due to the converters current restriction, it was not possible to deliver this power to the grid in the required rate, which caused a severe increase in the DC-bus voltage. In this case, it would be unavoidably necessary to fire the crowbar circuit or the braking-chopper in order to protect the devices. After the fault clearance, the statorflux presented the highest levels of oscillation, which propagated to all other system variables. It can be stated that the recovery after the fault using the classical controller presented unacceptable results. The PI-R2 and proposed HSFC con-trollers, on the other hand, were able to successfully track the CRTC references. As a result, the currents are constrained close to 1 pu during the fault the electromagnetic torque is driven to zero with low ripple. However, the excessive increase in the DC-bus voltage is also shown in the results of the system under the PI-R2 control, and the external protection should then be activated. Conversely, the system under the proposed HSFC control did not present overvoltage in the DC-bus, which is consequence of the superior reference tracking that led to the smallest current levels during the fault. After the fault, the system under PI-R2 control also presented high levels offlux and torque oscillations. Conversely, similar to the asymmetrical fault case, the proposed HSFC employed its d-FD feature which provided with rotor references injec-tion in order to allow fast damping of the stator flux. As discussed
í 0 0 Rotor Currents (pu) Active and Reactive Power (pu) (0 Torque (pu) Stator Currents (pu) í 0 í 0 í 0 í 0 Rotor dq Currents (pu) Rotor dq Voltages (pu) PI PI-R2 HSFC 0 í 0 0 0 0 0 0 0 í 0 Time (s) 0 0 0 0 0 0 Time (s) 0 0 0 0 0 0 Time (s) Stator Voltages (pu) Stator Flux (pu) DC Bus Voltage (pu) Generator Speed (pu) d-FD d-FD d-FD
Fig. 6. Real-time simulation comparison of low-voltage ride through performance of the classical PI, PI-R2 and proposed HSFC during 80% voltage sag due to a single phase-to-ground fault at the 2 MW WECS using the CRTC current-modify strategy.
previously, since the d-axis current performs most of the damping contribution, the DFIG system was able to fastly return to steady con-ditions with minimal torque ripple.
4.6. Intermediate voltage sags
One drawback characteristic of the current-modify LVRT techniques is that the DFIG absorbs some reactive power from the grid whenever some residual voltage remains in the PCC, which is considerably often the case. In order to generate reactive power, it is necessary a trade-off with torque oscillations in some level [26]. This is accomplished by injecting positive-sequence currents in the references, which is not ef-fective for the reasons discussed previously. Therefore, if the inter-mediate voltage sag lies below the FCB illustrated inFig. 3, the HSFC is proposed as a solution to ride through the fault with constant references relying only in the disturbance rejection feature of the proposed HSFC structure. In this fashion, since the SRF is usually oriented by the phase-locked loop (PLL) with negative-sequence rejection feature[2,32], by controlling the rotor current to constant levels the DFIG will feature positive-sequence only currents. Moreover, the freedom to set the cur-rent references allow for reactive curcur-rent contribution, which is a de-mand of grid codes, and to provide some active current to the grid, depending on the sag level.
In order to accomplish for reactive current contribution, the rotor
d-axis current reference is switched forird∗ =1pu while the q-axis current reference is switched toi∗ =0.5
rq pu.Fig. 8presents the real-time si-mulation performance of the HSFC structure applied to the 2 MW system during the event of intermediate symmetrical and asymmetrical faults. Again the fault detection method delay is about 20 ms, after what the current references are switched to the indicated values. In all three cases the HSFC structure was able to keep the rotor currents in the given constant levels without oscillations, which further upholds its robust-ness against the disturbance in the form of(11). The electromagnetic torque waveform exhibited bounded oscillations, with average ripple of 0.5 pu in the asymmetrical faults and 0.7 pu in the symmetrical fault, however, with the advantageous average level of 0.5 pu thanks to the active current. The power waveforms exhibited low ripple around average values different from zero. Despite in the symmetrical fault the results were similar, the electromagnetic torque oscillation level may be considered unacceptable. In this case, it would be more advantageous to use proposed HSFC with the LVRT-CM strategy.
4.7. Small-scale WECS experiment
The scheme of the small-scale WECS test bench used in this paper is presented inFig. 9. The 1.5 kW rated wound rotor induction machine is directly coupled to a 1 kW rated DC motor. The latter performs the role of wind turbine emulation, being exclusively driven by a thyristor
í 0 0 Rotor Currents (pu) Active and Reactive Power (pu) (0 Torque (pu) Stator Currents (pu) í 0 í 0 í 0 í 0 Rotor dq Currents (pu) Rotor dq Voltages (pu) PI PI-R2 HSFC í 0 0 0 0 0 0 0 í 0 Time (s) 0 0 0 0 0 0 Time (s) 0 0 0 0 0 0 Time (s) Stator Voltages (pu) Stator Flux (pu) DC Bus Voltage (pu) Generator Speed (pu) d-FD d-FD d-FD
Fig. 7. Real-time simulation comparison of low-voltage ride through performance of the classical PI, PI-R2 and proposed HSFC during 80% voltage sag due to a three phase fault at the 2 MW WECS using the CRTC current-modify strategy.
rectifier PLC according to the references produced by the real-time si-mulation of the turbine[43]. The system is controlled by means of the Single-board Reconfigurable Input–Output (sb-RIO) system from Na-tional Instruments. Voltage, current and other waveforms are acquired
and recorded in a supervisory system developed in LabVIEW platform. The disturbances are generated by means of connecting a high-power load to one or more phases of the grid, for a given amount of time.
The experimental test consists of producing a situation where the
í 0 0 0.5 Rotor Currents (pu) Active and Reactive Power (pu) E.M. Torque (pu) Stator Currents (pu) í 0 í 0 í 0 0 Rotor dq Currents (pu) Rotor dq Voltages (pu)
Single-phase Fault Two-phase Fault Three-phase fault
0.8 . . . . 0 0 0. 0. 0.3 0. 0.5 í 0 Time (s) 0 0. 0. 0.3 0. 0.5 Time (s) 0 0. 0. 0.3 0. 0.5 Time Stator Voltages (pu) Stator Flux (pu) DC Bus Voltage (pu) Generator Speed (pu)
Fig. 8. HSFC low-voltage ride through real-time simulation results without the usage of current-modify techniques during 40% symmetrical and asymmetrical voltage sags with rotor direct current switched to 1 pu and quadrature current switched to 0.5 pu.
proposed HSFC operates without a current-modify LVRT strategy, and the current references are adjusted to constant values during symme-trical and asymmesymme-trical faults in order to generate reactive power. Prior to the fault, the system was generating 1.0 pu of active power and 0.0 pu of reactive power, the generator speed was 1.2 pu(s= −0.2)and the rotor current set points wereird∗ =2andirq∗ =1. During the fault, after the fault detection method acknowledgment, the references were switched toi∗ =3
rd andirq∗ =0. The results are presented inFig. 10. Due to the realistic way the faults were generated, high depth sags were not possible for safety and practical reasons. In the single phase fault, the affected phase dropped to 0.5 pu while the other phases increased to 1.25 pu, which further aggravated the unbalance. In the two phase fault, one of the affected phases dropped to 0.75 pu, whilst the other dropped to 0.9 pu. The unaffected phase increased to 1.25 pu. Finally in the three phase case, there were a small drop in the three phases be-tween 0.85 and 0.9 pu.
In both symmetrical and asymmetrical faults the proposed HSFC structure was able to fast and effectively control the rotor currents to new set points in spite of the high disturbances provoked by the BEMF, aggravated due to the high speed of the generator and the depth of the sag. As a result, the electromagnetic torque together with the active power were quickly driven to zero with minimal oscillations. In addi-tion, the system effectively generated 1.0 pu of reactive power in the interim of the fault. In similar fashion, the system is promptly directed to nominal conditions after the fault clearance. In the asymmetrical faults, which presented the highest depth of sags, the stator currents were effectively bounded below 2 pu. In the symmetrical fault, in spite of the shallow sag, the system presented the highest peaks of 3 pu in the stator currents during thefirst moments of the fault and after the fault clearance.
The DC bus voltage is also shown in order to demonstrate that the fault ride-trough performance of the proposed HSFC structure was able to minimally stress the DC bus, which often presents increase or re-duction in its voltage during a fault, indicating high powerflowing through the converters. In the experiments, the grid side control was able to keep the DC bus voltage with a maximum of 4% ripple.
4.8. General assessment
The presented simulation and experimental results demonstrated the capability of the proposed structure to (i) effectively track the re-ferences provided by the CRTC current-modify LVRT strategy, which allowed the DFIG to ride-through severe faults featuring low torque ripple and bounded currents; and (ii) control the DFIG rotor currents to constant levels during symmetrical and asymmetrical intermediate faults, which permitted the generator to still contribute reactive current while riding through the fault featuring bounded positive-sequence currents; minimal oscillations in power waveforms; and bounded ripple in electromagnetic torque waveform. After the fault clearance, the d-FD feature embedded in the proposed HSFC proved able to fastly damp the stator flux and drive the generator to steady conditions faster than usual.
Despite the wind speed variation was not taken into account in the results, the proposed HSFC was formulated using the same internal-model approach presented in[44]in addition to the dynamics of the general disturbance model present during voltage sags. Therefore, a superior performance of the proposed HSFC is expected also during wind gusts or turbulence conditions.
In spite of the high order of the proposed technique, its im-plementation is very simple and demands low processing time. Fig. 10. Experimental results of HSFC low-voltage ride through without the usage of current-modify techniques during symmetrical and asymmetrical voltage sags with rotor direct current switched to 3 pu.
Moreover, the design process is well determined and concise. The perceptive disadvantages are due to direct feedback of rotor currents, which account for the more quantity of noise in the dq-voltage wave-forms of the proposed HSFC; and due to the torque ripple that exists under constant references control in the intermediate sag case, however with bounded peaks.
5. Conclusion
This paper proposed the Heightened State-Feedback Control struc-ture as a solution for the DFIG-based wind energy conversion system to remain connected to the grid during severe and intermediate symme-trical and asymmesymme-trical faults, featuring bounded currents, minimal oscillation in power and electromagnetic torque waveforms while contributing reactive power. The proposed structure was implemented in hardware and tested by means of real-time hardware-in-the-loop digital simulations and experimental results, based on the specifications of a commercially-available high-power rated WECS.
The proposed HSFC was formulated on top of the general form of the post-fault reference signals in conjunction with the general form of
the disturbance present during symmetrical and asymmetrical faults, and also employs a novelflux damping technique which is able to drive the generator to steady conditions after the fault faster than usual. Its design process is well determined and concise. An important feature achieved by the proposed technique and highlighted in this paper is the capability to ride through the intermediate voltage scenario featuring the DFIG currents constrained in permissible levels, with low torque oscillations and still contributing reactive current, as required by most demanding grid codes. Due to the its tracking and disturbance-rejection capabilities, the proposed HSFC presents superior performance com-pared to the classical proportional-integral and double-resonant con-trollers. Therefore, the proposed control structure may also be used as a control solution to support the current-modify LVRT strategies to pro-vide the DFIG to ride-through severe faults.
Acknowledgement
This work was supported by the Brazilian National Research Council (CNPq).
Appendix A
The parameters of the DFIG-based WECS used in the simulations and the experiments are presented in the following Table.
Table 3
DFIG-based WECS parameters.
Parameter Simulation System Experimental System
Rated Power 2 MW 1 kW
Electrical Frequency 50 Hz 60 Hz
Rated stator voltage 690 V 220 V
Pairs of Poles 2 2
Rated power factor 0.96 0.96
Rated slip −0.12 −0.2
Rated RPM 1680 2160
Stator resistance 2.65 mΩ 0.993Ω
Stator leakage inductance 168.7μH 2.86 mH
Rotor resistance 2.63 mΩ 0.877Ω
Rotor leakage inductance 133.7μH 6.97 mH
Magnetizing inductance 5.48 mH 86.3 mH
Stator/rotor turns ratio 0.426 1.0
DC-link rated voltage 1500 V 450 V
Converter switching frequency 2000 Hz 2000 Hz
DC-link capacitor 22.5 mF 470μF
Base Values
Stator power 1785.6 kW 833.3 W
Stator voltage (line-line,RMS) 690 V 220 V
Stator current (phase, peak) 2200 A 3.22 A
(at rated slip and PF = 0.96)
Rotor power 214.4 kW 166.7 W
Rotor voltage (line-line RMS) 194.5 V 44 V
Rotor current (phase, peak) 900 A 3.1 A
(at rated slip and PF = 1)
Max. converter output voltage 1060 V 318 V
(line-line,RMS)
