Unbalanced voltage faults: the impact on structural loads of doubly fed asynchronous generator wind...

WIND ENERGY

Wind Energ. 2014; 17:1123–1135

Published online 13 June 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/we.1621

RESEARCH ARTICLE

Unbalanced voltage faults: the impact on structuralloads of doubly fed asynchronous generatorwind turbinesBraulio Barahona, Nicolaos A. Cutululis, Anca D. Hansen and Poul Sørensen

DTU Wind Energy, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark

ABSTRACT

This paper investigates the impact that unbalanced voltage faults have on wind turbine structural loads. In such cases,electromagnetic torque oscillations occur at two times the supply voltage frequency. The objectives of this work are toquantify wind turbine structural loads induced by unbalanced voltage faults relative to those during normal operation; andto evaluate the potential for reducing structural loads with the control of the generator. The method applied is integrateddynamic analysis. Namely, dynamic analysis with models that consider the most important aeroelastic, electrical, andcontrol dynamics in an integrated simulation environment based on an aeroelastic code (HAWC2) and software for con-trol design (Matlab/Simulink). In the present analysis, 1 Hz equivalent loads are used to compare fatigue loads, whereasmaximum–minimum values are used to compare extreme loads. A control concept based on resonant filters demonstratesreduction of the structural loads (shaft torsion and tower top side-to-side moment) induced by an unbalanced voltagefault. Copyright © 2013 John Wiley & Sons, Ltd.

KEYWORDS

unbalanced voltage fault; wind turbine loads; integrated dynamic analysis; DFIG; resonant damping control; resonant filters;1 Hz equivalent loads; HAWC2; Simulink; integrated design; wind turbine modeling

Correspondence

Braulio Barahona, DTU Wind Energy, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark.E-mail: [email protected]

Received 9 February 2012; Revised 12 November 2012; Accepted 13 March 2013

1. INTRODUCTION

Some power system conditions may have significant impact on structural loads of wind turbines and on the performanceand reliability of wind turbine components. In the literature, there are several publications investigating the impact onwind turbine loads due to balanced voltage faults. For example studies,1–6 analyze the time response of structural loads ofwind turbines due to balanced faults of supply voltage. Such investigations show that the shaft torsion, tower side-to-side(fixed speed1,3 and variable speed wind turbines2,4,5), and blade flap moments (fixed speed wind turbines that pitches theblades3) can be qualitatively affected by a voltage fault. In Hansen et al.,6 a computational approach to quantify the loadsimposed on wind turbines during a fault ride-through operation is proposed and demonstrated for the study case of a fixedspeed wind turbine. The conclusion in Hansen et al.6 is that neither fatigue nor ultimate loads induced by balanced faultson tower and blades are large enough to condition a given wind turbine lifetime design verification, meaning that a givenfixed-speed active stall wind turbine design would not be challenged by balanced faults nor fault ride-through requirementsbecause other load cases considered in certification standards are more demanding. The focus of this work is on the impactthat unbalanced voltage faults may have on wind turbine structural loads; this is studied by means of an integrated dynamicanalysis approach.

The case of wind turbines operating under unbalanced supply voltage has been investigated mainly from an electricalperspective. For example, in the literature,7–24 the electromagnetic torque oscillations produced by unbalanced supplyvoltage are shown to be significant. This paper follows an integrated dynamic analysis to estimate the impact of an unbal-anced fault of supply voltage on the structural loads of a 2 MW DFIG (i.e., doubly fed asynchronous generator) windturbine. It also demonstrates a control concept to reduce wind turbine structural loads during such faults. The impact that

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Analysis of unbalanced voltage fault’s impact on structural loads B. Barahona et al.

unbalanced voltage faults can have on structural loads is measured in terms of 1 Hz equivalent loads and maximum–minimum values relative to those during normal operation. Aeroelastic, electrical, and control dynamics that capturethe fundamental phenomena relevant to the present study are modeled in an integrated simulation environment basedon HAWC2 and Matlab/Simulink (MathWorks (Natick, Massachusetts)).

The article is organized as follows. The rest of the introduction explains the torque oscillations due to unbalanced volt-age, reviews the control of DFIG generators under unbalanced voltage supply, and describes 1 Hz equivalent loads. Theintegrated simulation environment and its models are then described in Section 2. An integrated dynamic analysis of theunbalanced voltage fault on the wind turbine loads is performed through a set of simulations. Results are presented anddiscussed in Section 3. Conclusions are presented in Section 4.

1.1. Torque oscillations due to unbalanced voltage

The assumption of balanced voltages and symmetric circuit parameters makes it possible to analyze multi-phase circuitsby means of single-phase equivalent circuits. For example, voltages in a balanced three-phase circuit are typically repre-sented by a set of three phasors of equal magnitude, displaced 120 degrees from each other (i.e., a balanced set of phasors).The case of unbalanced voltages is typically addressed by transforming the unbalanced set of phasors to three sets ofbalanced phasors (i.e., positive, negative, and zero sequences) by using Fortescue’s theory of symmetrical components.25

An analysis of three-phase circuits under unbalanced conditions includes therefore positive, negative, and zero sequences.However, when an unbalance voltage fault occurs somewhere in a power system, the voltage at the terminals of a typicalDFIG wind turbine does not include a zero sequence because of the connection (D-Y) of the step-up transformer.7 Further-more, generator stator circuit and power converter normally do not have a neutral conductor, and therefore zero sequencedisappears.9

Technically speaking, unbalanced faults can be phase-to-phase, single phase-to-ground, or two phase-to-ground. Allof them will ultimately induce a negative sequence voltage. Therefore in this work, to demonstrate the control conceptand evaluate the impact on structural loads, a single phase-to-ground fault with a severity that does not activate electricalprotection devices is chosen as the simulation scenario (further described in Section 3.1).

According to Petersson,9 negative sequence supply voltage induces oscillations of fluxes, DC-link voltage and grid-filtercurrent at twice the supply voltage frequency. However, DC-link voltage and grid-filter current oscillations stem ultimatelyfrom oscillations of generator fluxes and can be taken care off by the grid-side converter (GSC). The main issue for mechan-ical and structural components are flux oscillations that give rise to electromagnetic torque oscillations. As intuitive resultfrom the literature,7–21,26 such torque oscillations will increase mechanical stress or even damage wind turbine compo-nents. Therefore, in this work, aeroelastic, electrical, and control dynamics are included to estimate the impact of unbalancevoltage faults on structural loads and evaluate the reduction of structural loads with generator control.

1.2. Review of control techniques

In Brekken and Mohan,8 torque and reactive power oscillations induced by unbalanced voltage supply are reduced byadding feedback compensation terms of rotor and stator currents to rotor-side converter (RSC) current control references.Control of RSC by using vector control and flux-linkage observers during an unbalanced voltage fault is demonstrated withsimulations in Xiang et al.11 In Brekken and Mohan,12 torque and reactive power measurements are compensated and fedback to RSC voltage references. The compensation is carried out with a resonant filter and lead compensation (i.e., resonantdamping control—RDC). Reduction of torque and reactive power oscillations is shown with experiments and simulations.An RSC current control based on negative and positive sequence decomposition is shown by Xu and Wang.13 Based onanalytical results, Xu and Wang state that the voltage rating of RSC has to be increased to control the negative sequencecurrent. The worst condition is at high rotor speed and large voltage unbalance.13 Different techniques for coordinated con-trol of RSC and GSC during unbalanced supply voltage are presented in the literature.14–24 For example, a proportionalresonant control is used in Hu et al.,19 whereas a proportional integral plus resonant (PI-R) control is applied in Hu andHe,20 both relaying on resonant filters that are formulated as second order systems with low damping ratio � (i.e., (4)).This formulation is common in control of inverters, for example, proportional resonant control in Teodorescu et al.27 isused for current/voltage control of grid connected inverters with advantages over conventional PI control such as reducedcomputational effort and selective harmonic compensation. Other example of resonant filters is Brekken and Mohan,12

where filters are formulated as second order filters with a high quality factor Q (i.e., (3)). Either formulation results in asystem that resonates at a given frequency when Q is high or � is low (i.e., 2� D 1=Q).

1.3. 1 Hz equivalent loads

To compare the impact on fatigue loads due to unbalanced voltage faults between normal operation and fault operation, a1 Hz equivalent load is calculated for each case and normalized with respect to a base case. By definition, a sinusoidal load

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B. Barahona et al. Analysis of unbalanced voltage fault’s impact on structural loads

with 1 cycle per s is a 1 Hz equivalent load. The concepts of equivalent damage and equivalent load applied to wind turbinefatigue loads are addressed in the literature.28–32 The equivalent load So given by (1), used in this work is that definedby Mouzakis et al.30 So represents a constant load amplitude that, for a chosen equivalent number of cycles Neq, wouldproduce the same damage as a load spectrum with ni cycles for Fi load amplitudes. ni and Fi are calculated by usinga rainflow counting algorithm33 that relies on a linear accumulation of damage (Palmgren–Miner rule). m is the slope ofthe material cyclic stress to cycles-to-failure (SN curve). Representative values for materials that would mainly constituteshaft, blades, tower top (TT), and tower bottom (TB) were used according to Downey.34

So D

1

Neq

XiDn

niFmi

! 1m

(1)

2. INTEGRATED DYNAMIC ANALYSIS

Given the demanding operating conditions that wind turbines are expected to meet nowadays, an integrated designand analysis approach, which combines different research areas for wind turbines, has become extremely relevantduring the last few years. For example, the dynamic response of a floating wind turbine prototype was analyzedin Skaare et al.35 by using a simulation tool specialized in dynamic response of marine structures coupled to theaeroelastic code HAWC2. This section describes the simulation platform and models used in this work for integrateddynamic analysis.

The analysis described in the present article is performed by using a simulation platform, which integrates two differ-ent simulation tools: an aeroelastic code (HAWC2) and software for control design (Matlab/Simulink). Technical detailsrelated to the coupling and the implementation of these two software can be found in the literature.36,37 HAWC2 andMatlab/Simulink are both kept as stand alone applications, which exchange data through a TCP/IP interface every timestep. In this manner, it is possible to take advantage of Simulink capabilities to solve algebraic differential equations andthe various implicit and explicit numerical integration routines.

A generic model for 2 MW DFIG wind turbines, including the most important aeroelastic, structural, electrical, and con-trol dynamics, is simulated in the integrated platform HAWC2-Matlab/Simulink. The boundary of the system is—in theaeroelastic side—the wind field and—in the electrical side—the voltage at the generator stator terminals and the DC-linkvoltage. Figure 1 shows a block diagram representing submodels of the generic wind turbine model and the correspondinginterface variables. Namely, the block HAWC2 that represents the aeroelastic model further described in Section 2.1, inter-faces with Asynchronous Machine and Blade angle control blocks. The aeroelastic model (i) gets generator electromagnetictorque Tem from a dynamic model of an asynchronous generator and blade pitch angle �ba from a blade angle control; and(ii) outputs low-speed shaft speed !lss to the asynchronous generator model and the blade angle control. On the otherhand, the Asynchronous Machine, RSC control and Blade angle control blocks further, described in Section 2.2), representthe models of electrical generator, RSC control, and blade pitch angle control respectively. The electrical generator getsas inputs the stator terminals voltage vdqs and interfaces with the RSC control by means of the rotor vdqr voltage, totalactive power Ptot, stator reactive power Qs, and rotor current idqr as shown in Figure 1. The inputs to RSC control are DC-link voltage Vdc. Meanwhile, the blade angle control interfaces with HAWC2 low-speed shaft speed !lss and blade pitchangle �ba.

Figure 1. Illustration of integrated dynamic analysis model consisting of asynchronous generator, RSC control, and blade pitchangle control that are simulated in Simulink; and aeroelastic subsystems that are simulated in HAWC2 (that includes wind field,

aerodynamics, and multibody formulation of wind turbine structure and low speed shaft).

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2.1. HAWC2

Larsen TJ, Hansen AM, “How 2 HAWC2, the user’s manual,” Technical Report, Risø-R-1597(ver. 4-3)(EN), ISBN 978-87-550-3583-6, April 2012. The structural subsystems are represented by bodies, each of which is modeled with Timoshenkothree-dimensional beam elements, each beam has six degrees-of-freedom. The model used for this study is a generichorizontal axis, 2 MW wind turbine with rotor diameter and tower height of 80 m, which comprises three blades (eachone with 10 beam elements), low-speed shaft (three beam elements), and tower (10 beam elements). Bodies have a setof algebraic equations (i.e., constraints) that relate its movements and forces to those of other bodies. Constraints aresolved together with the equations of motion (second order, non-linear differential equations). The gearbox and high-speedshaft are considered rigid. Therefore, variables that interface structural to electrical/control models at the low-speed shaft(i.e., rotational speed of the low-speed shaft, generator electromagnetic torque as shown in Figure 1) are scaled by thegear ratio.

2.2. Models and controls in Matlab/Simulink

The models and controls implemented in Matlab/Simulink are described in the following.

2.2.1. Blade pitch angle control.The angles of the blades in the HAWC2 model, are controlled by a deterministic adaptive control, implemented in

Matlab according to Hansen and Michalke38. A block diagram is shown in Figure 2. It consists of a PI regulator witha scheduled gain; which acts on the error of a speed reference !ref and filtered value of the low-speed shaft speed !lss.The schedule of the gain is designed to compensate nonlinear aerodynamic characteristics.38 The servo motors thatrotate the blades are represented by a first order system, whose time constant is given by Tservo; with limits to mini-mum and maximum blade pitch angle; and with limits to the rate of change of the blade pitch angle as indicated bythe block d

dt�ba. Maximum blade pitch angle rate is shown to be important to prevent over-speeding during a supply

voltage fault.38

2.2.2. Generator system.A typical DFIG configuration consists of a wound rotor induction generator with the stator windings connected to the

electrical network and with the rotor windings connected to a back-to-back partial scale power converter. The back-to-back converter consists of two independent controlled voltage source converters (RSC and GSC) connected to a commondc-bus. It is normally rated to 30% of the wind turbine rated power. The terminals of the generator stator are connectedto the electrical network through a step-up transformer (i.e., vdqs in Figure 1). It is assumed that the power controlledby the RSC can be transferred to the electrical network and that the voltage in the dc-link Vdc is kept practically con-stant. These simplifications are reasonable as long as reactive power requirements do not limit the capacity of RSC todamp torque oscillations. That is the case in this present work, where the machine is not required to provide reactivepower (i.e., Qref D 0). Furthermore, generic parameters of a megawatt DFIG machine with stator to rotor turns ratio 1:1are used.

2.2.2.1. Electrical generator model. The classical full-order dynamic model of an asynchronous machine wasimplemented with flux linkages � as state variables. In state-space form, it can be expressed by (2). The system matrix Mis composed of machine parameters (Rs, Rr, Ls, Lr, Lm), speed of stator (!se), and rotor (!se �!re) dq-frame.

Figure 2. Blade pitch angle control.


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2.2.2.2. RSC control. The RSC control during normal operation is shown in Figure 3(a). This is the classical vectorcontrol oriented with the stator flux and implemented as PI cascade. The inner loops of the cascade are fast current controlloops, where the q-axis controls active power, whereas the d -axis controls reactive power. The slower outer loops calcu-late current references based on the active and reactive power set-points (Pref, Qref), measurements of total active powerPtot D Ps C Pr and stator reactive power Qs, respectively. Tuning of the overall control of the wind turbine is carried outwith the response to a step change of wind speed around the nominal wind speed (12 m/s).

2.2.3. Resonant damping control.The RDC is implemented in the RSC with the principal objective of reducing electromagnetic torque fluctuations due

to unbalanced faults, thereby minimizing wind turbine structural loads. RDC in this work consists of the normal operationcontrol shown in Figure 3(a), resonant filters for damping at specific frequencies and switches to keep the set points forcurrent control loops practically constant during and shortly after the unbalanced faults. The q-axis cascade loop of theRDC is shown in Figure 3(b). The d -axis cascade loop (not shown) has the same structure as that in Figure 3(b) withQref, Qs, idr, Fd.s/, Cd.s/, vdr, vc�

d , and Qos instead of Pref, Ptot, iqr, Fq.s/, Cq.s/, vqr, vc�

q , and P .!m/. The objective ofresonant filters Cq.s/, Cd.s/ is to damp Tem, Qs oscillations at 100 Hz during and partly after an unbalanced fault, whileFq.s/, Fd.s/ damp oscillations at 50 Hz of iqr, idr after the fault once the control of the outer loop is back to normal.

Switches are implemented as indicated in Figure 3(b). Notice that both switches use the same signals to change state.One of them is used to switch the process variable (i.e., Ptot to P .!m/) that is fed back to the outer control loop. This is toavoid that the oscillations induced by the unbalanced fault are fed back into the outer loop and passed on to the set pointfor current control loop. The active and reactive power will show 100 Hz oscillations that are generally hard to controlor minimize without decomposition of positive and negative sequences. Namely, in Figure 3(b), the process variable isswitched from Ptot to P .!m/ when the voltage unbalance factor VUF is different than one. It is switched back to Ptot whenVUF D 1 and when the sampled damping term vc�

q is within the values ˙V clim. Ptot is the total active power calculated

from current and voltage measurements, whereas P .!m/ is the total active power calculated from the design table of powerversus speed. Analogously, in the d -axis loop (not shown), the process variable is switched from Qs to Qo

s is the statorreactive power calculated from current and voltage measurements, and Qo

s is the value of Qs before the fault. Therefore,the set points for current control loops are kept nearly constant during an unbalanced fault and until the damping termsvc�

q , vc�d are relatively small. Moreover, the other switch in Figure 3(b) indicates that once the control is back to normal,

the input to Fq.s/ is switched to iqr, thereby adding a term to the error of q-axis current control loop that effectively damps50 Hz oscillations. The same is carried out in the d -axis current control loop with the input to Fd.s/ switched from 0 to idr.

(b)(a)

Figure 3. Generator control (RSC).


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As mentioned, the objective of the resonant filters is to damp electromagnetic torque, reactive power, and current fluc-tuations. The resonant filters Cq.s/ and Cd.s/ in (3) are aimed at damping electromagnetic torque Tem and reactive powerQs oscillations respectively. The filters Fq.s/ and Fd.s/ in (4) are aimed at reducing current oscillations. The formulationof the damper Cda.s/ is that of a second order filter with a high quality factor Q as in Brekken and Mohan.12 However, toavoid introducing other phases to the system, no further phase compensation is added. The only implication being that thegain margin is reduced. The natural frequency of dampers !da is equal to twice the supply voltage frequency (i.e., 100 Hz).The resonant filter FR.s/ in (4) is formulated as a second order system with low damping ratio �R and natural frequency!R equal to the supply voltage frequency (i.e., 50 Hz).

Cq.s/DH1 �Cda.s/ and Cd.s/DH2 �Cda.s/ (3)

Cda.s/Ds

s2C !daQ sC!2da

Fq.s/DKRq �FR.s/ and Fd.s/DKRd �FR.s/ (4)

FR.s/Ds

s2C 2�R!RsC!2R

3. SIMULATION RESULTS

Three simulation cases are considered to estimate the relative impact of an unbalance voltage fault on structural loads. Thedynamic response of control variables, structural loads, and electrical variables is discussed in Section 3.1. The influenceof turbulence intensity and load reduction potential using RDC is discussed in Section 3.2.

The simulation cases are (i) the operation under normal conditions without any fault of the supply voltage, which is thebase case, referred to as normal; (ii) the case when an unbalanced voltage fault occurs and the RDC is applied, which isnamed damper; and (iii) the case when an unbalanced voltage fault occurs, and no special control to damp the oscillationsis used, in the following named unctrl.fault.

3.1. Dynamic response

The dynamic response of a 2 MW DFIG wind turbine model (described in Section 2) to an unbalance voltage fault at ratedoperation with constant wind speed is analyzed in the following. An unbalanced voltage fault in the power system, seen atthe terminals of a wind turbine generator as a single-line-to-ground fault, is emulated by dropping the voltage magnitudeof one phase to 70% of its nominal value for 600 ms. The corresponding three-phase and dq voltages at the generatorterminals are shown in Figure 4 during the instant that the fault occurs t D 90 s. At t D 90:6 s the fault is cleared, and thevoltage restored. Electrical and structural signals are shown in Figure 5 and Figure 6 respectively.

Let us first look at Figure 5, it shows the dynamic response of the electrical signals for the three cases: damper,unctrl.fault, and normal. Figure 5(b) is a zoom of Figure 5(a) at the instant that the fault is cleared when the volt-age goes back to normal and RDC switches back to Ptot, Qs, iqr, idr. On the top plots of Figure 5, the response of the RSCcontrol (i.e., vdr and vqr) to the fault is shown in terms of the magnitude of rotor voltage jVrj and the controlled variables(i.e., idr and iqr) by means of the magnitude of rotor current jIrj. The total active power Ptot and stator reactive power Qsare shown in the bottom plots. Similarly, structural loads in Figure 6 show the response of the wind turbine structure to

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Figure 4. Voltage at stator terminals at start of unbalanced fault.


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in solid thin line (unctrl.fault).

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Figure 6. Structural loads from top to bottom: shaft torsion, tower bottom (TB) and tower top (TT) side-to-side moment. In eachplot, normal operation with dash-dot (normal), unbalanced fault with RDC in solid thick (damper), and unbalanced fault with normal

control in solid thin line (unctrl.fault).


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unbalanced voltage fault for the three cases in study. Notice that the structural loads that are influenced the most are theones presented. Namely, from top to bottom, shaft torsion, TB, and TT side-to-side moments.

The most important observation from Figure 5 is the reduction of rotor current jIrj oscillations of damper comparedwith unctrl.fault, which reflect in the reduction of electromagnetic torque oscillations. Therefore, the reduction ofthe loading on the structure at the shaft and at the TT can be observed in Figure 6 top and bottom plots respectively.

Furthermore, from Figure 5(a), it can be seen that as the fault occurs (at t D 90 s), in the case damper, the RDC is acti-vated to reduce torque and reactive power oscillations. Therefore, the rotor voltage jVrj fluctuates more compared with thecase when there is no special control during the fault (i.e., unctrl.fault). Similarly, active power will fluctuate withlarger amplitude during the fault in damper than in unctrl.fault, because the RDC control is regulating the rotorvoltage to reduce electromagnetic torque fluctuations to ultimately reduce loads on the structure as it was just described.

Moreover, notice that after the fault (at t D 90:6 s), the RDC helps to damp oscillations induced by the sudden restorationof the stator voltage. This reduction of electromagnetic torque oscillations can be clearly seen in terms of structural loads, asthe shaft torsional moment (top plot in Figure 6) and the TT side-to-side moment (bottom plot in Figure 6) oscillations areless in damper than in unctrl.fault. Finally, observe that the TB side-to-side moment amplitude is slightly increasedin damper compared with unctrl.fault and normal. However, as it is shown in the following section, such increaseof the TB side-to-side moment amplitude is not significant in terms of equivalent loads So relative to turbulence intensity.

Overall, the RDC control shows to achieve reduction of electromagnetic torque oscillations and loading at the shaft andTT induced by unbalance voltage faults. In addition, notice that the torque oscillations induced by the unbalanced fault arenot significant at the bottom of the tower, neither at the wind turbine rotor (not shown) because they are filtered out by thetower and the low speed shaft respectively.

3.2. Quantification of load reduction

This section compares structural loads amongst the three different simulation cases, given different wind conditions andcontrol settings to quantify the possible reduction of structural loads. Comparison of loads for different wind speed turbu-lence intensities is carried out in Section 3.2.1 to ponder the influence of turbulence intensity and also to measure the loadreduction potential by using RDC. Section 3.2.2 aims at drawing similar conclusions with regards to the change of a givencontrol parameter.

3.2.1. Comparison of loads at different turbulence intensities.

3.2.1.1. Relative fatigue loads. Rainflow calculations on time series of loads (such as those shown in Figure 6)yield 1 Hz equivalent loads So according to (1), described in Section 1.3. Such So loads at different wind speed turbulenceintensities are presented in Figure 7 normalized to So value at 0 turbulence intensity. In Figure 7(a), So values are nor-malized to So of normal at 0 turbulence intensity; and in Figure 7(b) values are normalized to So of unctrl.faultat 0 turbulence intensity. Therefore, from Figure 7, conclusions can be drawn about the impact of an unbalanced fault onstructural loads relative to turbulence intensity and the control used.

It is evident that increased turbulence intensity will yield more load cycles and therefore larger So. Figure 7 illustratesthe influence of turbulence intensity on So of the shaft torsion, TB and TT side-to-side moment for normal and dampercases. Notice that the stochastic nature of So is not represented here, namely that each data point is actually one sample (atone wind turbine operating point) of a stochastic variable whose probability distribution function depends on many param-eters, mainly on wind speed distribution and coherence.30 A comprehensive statistical analysis, which is outside the scopeof this work, is however interesting when considering to evaluate the actual cost of reducing loads over lifetime. Notice alsoin Figure 7(a) that shaft torsion and TT side-to-side moment are much larger in damper than in normal. However, bearin mind that (i) the normalized 1 Hz equivalent loads So are calculated over a short time interval (60 s) to capture mainlythe cycles induced by the fault, and (ii) naturally, from the rainflow histogram (not shown here), it is observed that the vastmajority of load cycles induced by the unbalanced fault have low amplitude. These considerations let us put in perspectivethe severity of the relative fatigue loads presented in terms of So.

Figure 7(b) illustrates that reduction of shaft torsion and TT side-to-side moment by using RDC (damper) comparedwith using a normal control during an unbalanced fault (unctrl.fault) is very significant. However, TB side-to-sidemoment is increased when using RDC compared with the normal control case, particularly for lower turbulence intensityvalues (i.e., below 0.1). Moreover, comparing the trends of plots in Figure 7(b) to those of Figure 7(a), it can be said thatgiven an unbalanced fault, the influence of turbulence intensity on So of shaft and TT side-to-side moment is not as largeas during normal operation, whereas for TB side-to-side moment turbulence intensity has similar impact with and withoutan unbalanced fault. This supports the information from time series with 0 turbulence intensity, shown in Figure 6 and sug-gests that the potential for reducing loads at the shaft and TT side-to-side moment is the same regardless of the turbulenceintensity, whereas the negative impact of reducing such loads seen on TB side-to-side moment is mostly relevant at lowerturbulence intensities.


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1

1.5

Turb. int.0 0.1 0.2

0

0.2

0.4

0.6

0.8

1

Turb. int.

damper

unctrl. fault

(Shaft) (T.B.) (T.T.)

(a)

(b)

Figure 7. Normalized 1 Hz equivalent loads versus turbulence intensity.

The main observation from Figure 7 is that the RDC reduces about 40% the load cycles induced by an unbalancedvoltage fault on the shaft and the TT. Also relevant is the fact that although there are still significantly more load cycleswith RDC than during normal operation since their amplitude is relatively small, it is unlikely that fatigue lifetime wouldbe affected, specially for demanding site-specific design conditions.

3.2.1.2. Extreme loads. Maximum and minimum values of structural loads for the three simulation cases, underdifferent turbulence intensity values, are shown in Figure 8. Similarly, as with 1 Hz So shown previously, RDC reducesthe load range (i.e., maximum–minimum values) on shaft torsion and TT side-to-side moment. The maximum values ofshaft torsion (left plot in Figure 8) are reduced by using RDC (damper) around 25% compared with unctrl.fault.However, they are still around 15% higher than the normal operation without a fault (normal). In the case of the TTside-to-side moment (right plot in Figure 8), the maximum values in damper are reduced around 18% compared withunctrl.fault. However, those values are around 7% higher than normal. Regarding the TB side-to-side moment,shown in the middle plot in Figure 8, the load range is slightly increased—at lower turbulence intensity—in dampercompared with the other two cases; whereas at higher turbulence load ranges are essentially the same.

Let us now look at electrical signals. Maximum values of rotor voltage magnitude versus turbulence intensity areshown on the left plot in Figure 9 for the three simulation cases. Notice that to damp the oscillations, the maximummagnitude of rotor voltage jVrj in damper increases about 20%, at very low turbulence intensity, compared withthat in unctrl.fault. However, as the turbulence increases the difference between maximum jVrj in damper andunctrl.fault reduces to about 10% at 0.16 turbulence intensity. The increased control effort in damper pays out in


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0 0.08 0.16−1800

−1600

−1400

−1200

−1000

−800

−600

−400

Sha

ft [k

Nm

]

turbulence intensity0 0.08 0.16

−1000

−500

0

500

1000

1500

2000

2500

3000

3500

TB

[kN

m]

turbulence intensity

normal

damper

unctrl. fault

0 0.08 0.16700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

TT

[kN

m]


Figure 8. Comparison of maximum and minimum values of structural loads given different levels of turbulence intensity. From leftto right: shaft torsion, TB, and TT side-to-side moments. In each plot, maximum and minimum values for normal, damper, and

unctrl.fault are presented.

0 0.05 0.1 0.15 0.220

40

60

80

100

120

140


|VR|

[V

]

normal

damper

unctrl. fault

0 0.05 0.1 0.15 0.22400

2600

2800

3000

3200

3400

3600

|I R|

[A

]


Figure 9. Comparison maximum values of rotor voltage jVrj (left plot) and rotor current magnitude jIrj (right plot) given different levelsof turbulence intensity for normal, damper, and unctrl.fault.

the reduction of maximum rotor current magnitude jIrj, as it can be observed in the plot to the right of Figure 9, wheremaximum jIrj for the three cases is plotted versus turbulence intensity. The difference between maximum jIrj in damperand unctrl.fault is practically the same as the turbulence intensity increases, corresponding to about 5% reduction ofmaximum jIrj in damper compared with unctrl.fault.

3.2.2. Load reduction with different control parameters.This section demonstrates the influence on 1 Hz equivalent loads So and on maximum rotor voltage magnitude jVrj

of increasing the gain H1 of Cq.s/ (in (3), Figure 3(b)). The objective is to ponder to what extend can So be reducedwithin RSC voltage limits. Simulations are performed at rated wind speed with 10% turbulence intensity. Figure 10 showsmaximum jVrj versus So of shaft torsion, TB, and TT side-to-side moment for 40 < H1 < 200.

As expected, Figure 10 shows that as H1 increases, jVrj increases and some of the structural loads are reduced. Namely,it is possible to reduce the loading on the shaft torsion and on TT with higher H1, while jVrj will increase but yet withinthe values expected over the operating range based on the DFIG design data used in this work. The operation range is


DOI: 10.1002/we


0 50 100 150 200 250 3000.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1−H

z E

q. lo

ad (

So)

ShaftTBTT

High slip,Low power

Low slip,high power

increase H1

|Vr| [V]

Figure 10. Normalized 1 Hz equivalent loads So versus maximum rotor voltage magnitude jVrj given control gain 40< H1 < 200. H1

increases from left to right. Shaft torsion represented with (gray) dashed line and triangle, TB side-to-side moment with (green) solidline and triangle, TT side-to-side with (black) dashed-dot line and rectangle. jVrj operating range is illustrated with (blue) vertical lines.

represented in Figure 10 with (blue) vertical lines: at low jVrj corresponding to low slip-high power operation and at highjVrj corresponding to high slip-low power operation. Therefore, there is margin to increase jVrj to damp oscillations. How-ever, the effectiveness of increasing H1 to reduce So of shaft and TT diminishes at higher H1, reaching a point where jVrj

continues to increase without achieving a significant reduction of So. Furthermore, loads on TB are practically insensitiveto increase of H1/jVrj.

4. CONCLUSION

The reduction of the impact that unbalanced grid faults have on wind turbine structural loads, through adequate generatorcontrol, was investigated in this paper. The most important dynamics for that purpose are modeled in a simulation environ-ment based on HAWC2 and Matlab/Simulink. Such an integrated dynamic analysis environment facilitates the simulationof electrical, aeroelastic, and control dynamics. This approach may prove relevant in the design process of modern largewind turbines, because it can help to accelerate an integral design process that aims at meeting design requirements fromdifferent engineering disciplines. Namely, the case studied in this paper demonstrated the principle of meeting a require-ment of the electrical network to stay connected during a voltage fault while minimizing the impact on the wind turbinestructure.

More specifically, the simulations presented in this article quantify the impact of electrical generator damping controlon wind turbine structural loads during an unbalanced grid fault. It was shown that an appropriate RDC of the RSC canlead to about 40% reduction of load cycles induced by an unbalanced voltage fault on the shaft torsion and TT side-to-sidemoment. The analysis of the extreme loads indicated that by using RDC, a reduction of maximum values of shaft torsionand TT side-to-side moment of about 25% and 18% respectively can be achieved. In general, the control effort in terms ofvoltage magnitude to achieve such load reduction did not exceed the design limits of the RSC.

On the other hand, the influence on the TB loads when using the RDC is marginal in comparison with the loading cyclesand the maximum loads added by wind field turbulence. Overall, it seems unlikely that lifetime of wind turbine structurewould be considerably reduced because of unbalanced voltage faults. However, this would depend on the frequency andseverity of such faults, control algorithms in place, and site-specific design conditions. Furthermore, given that the equiva-lent loads on shaft torsion and TT side-to-side moment were largely affected by unbalanced voltage faults, it is relevant tostudy further the impact of this load case on drive train components.

Next steps in these investigations are coordinated control of converters to meet diverse electrical network requirementsand reduction of structural loads. Furthermore, benchmarking of different design driving operating conditions with loadcases related to electrical network requirements would help to identify design cases.

Finally, the integrated simulation environment applied in the present article and in general, the method of dynamicanalysis integrating aeroelastic, electrical, and control models is relevant in the design of future wind turbines, as it canprovide a thorough insight into the complex interaction between large wind turbines and power systems due to grid coderequirements and future grid integration issues.

ACKNOWLEDGEMENTS

Thanks to Christian Wessels and to Ioannis Margaris for the fruitful discussions regarding the doubly fed asynchronousmachine and to Helen Markou for the discussions regarding equivalent loads.


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