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8/21/2019 Grid Compatibility of Wind Generators With Hdyro-Dynamically Controled Gearbox With German Grid Codes
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P 1 3 4 7 . 2 9 t o f A u g u s t 2 0 0 8
Grid Compatibility of Wind Generators withHdyro-Dynamically Controled Gearbox withGerman Grid Codes
Draft Report
prepared for
oith Turbo Wind GmbH & Co. KG
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G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
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DIgSILENT GmbH
Heinrich-Hertz-Strasse 9
D-72810 Gomaringen
Tel.: +49 7072 9168 - 0
Fax: +49 7072 9168- 88
http://www.digsilent.de
e-mail: mail@digsilent.de
Please contact
Markus Pller
Tel.: +49-7072-9168 57
e-mail: mpoeller@digsilent.de
Prepared for:
Voi th Turbo Wind GmbH &
CoKGVothstr. 1Germany, 74564
Crailsheim
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T a b l e o f C o n t e n t s
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
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Table of ContentsTable of ContentsTable of ContentsTable of Contents
1 Introduction......................................................................................................................................... 5
2 Description of the 2 MW Wind Turbine Model including WinDrive .................................................... 6
2.1 Wind Turbine Model ...............................................................................................................................8
2.2 Voltage Controller and Excitation System..................................................................................................9
2.3 WinDrive and Drive Train Model ............................................................................................................10
2.4 WinDrive Control..................................................................................................................................12
2.5 Pitch Control and Aerodynamic Model ....................................................................................................13
3 Verification of the PowerFactoryModel............................................................................................ 15
4 Wind Farm Network........................................................................................................................... 17
4.1 Test Wind Farm with HV (110kV) Connection Point ................................................................................. 17
4.2 Test Wind Farm with MV (10kV) Connection Point...................................................................................19
5 Requirements for Connections to the Transmission (HV) Grid ........................................................ 21
5.1 Active Power Output (Section 3.3.13.3 in [1]).........................................................................................22
5.2 Reactive Power Output (Section 3.3.8 in [1])..........................................................................................22
5.3 Behaviour during Disturbances in the Network........................................................................................245.3.1 Transient Stability after Short-Circuits (section 3.3.13.5 resp. 3.3.12.1 in [1]) .......................................245.3.2 Oscillatory Stability (section 3.3.12.2 in [1]).......................................................................................25
6 Requirements for Connections to the Distribution (MV) Grid .......................................................... 29
6.1 Network Disturbances...........................................................................................................................30
6.1.1 Steady-State Voltage Changes (Section 2.3 in [2]) .............................................................................306.1.2 Voltage Change due to Switching Operations (section 2.4.1 in [2]) ......................................................306.1.3 Long-Term Flicker (Section 2.4.2 in [2]) ............................................................................................32
6.1.4 Harmonics (Section 2.4.3 in [2]) .......................................................................................................336.1.5 Commutation Voltage Drops (Section 2.4.4 in [2])..............................................................................346.1.6 Impact on Ripple Control (Section 2.4.5 in [2]) .................................................................................. 34
6.2 Behaviour of the Generator...................................................................................................................356.2.1 Transient Network Support Low-Voltage Ride-Through (Section 2.5.1.2 in [2]) ..................................356.2.2 Short-Circuit Current (Section 2.5.2 in [2]) ........................................................................................36
6.2.3 Active Power Output (Section 2.5.3 in [2]).........................................................................................366.2.4 Reactive Power Output (Section 2.5.4 in [2]) ..................................................................................... 37
7 Conclusion.......................................................................................................................................... 39
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T a b l e o f C o n t e n t s
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
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8 References ......................................................................................................................................... 40
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1111IntroductionIntroductionIntroductionIntroduction
The purpose of this study is to analyse the compatibility of the DeWind 2MW (D 8.2) wind generator, which isequipped with the Voith WinDrive system and synchronous generator with the technical requirements of therelevant BDEW connection conditions, which are:
Transmission Code 2007 [1] for wind farms with connection point at 110kV or above and
Technische Richtlinie, Erzeugungsanlagen am Mittelspannungsnetz [2]
From 2009 on, these technical requirements will also be the basis for obtaining the Systemdiensleistungsbonus,which will be introduced by the new version of the German Renewable Energy Law (EEG).
The studies have been carried out using a
50MW wind farm for connection to a HV (110kV) connection point
20MW wind farm for connection to a MV (10kV) connection point
The technical behaviour of these wind farms has been analysed for different short circuit levels at the connectionpoint and benchmarked against the relevant requirements of the technical standards.
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2222Description of the 2Description of the 2Description of the 2Description of the 2 MWMWMWMW WindWindWindWind TTTTurbineurbineurbineurbine Model including WinModel including WinModel including WinModel including WinDriveDriveDriveDrive
Based on information provided by Voith Turbo Wind (models inclusive routines based on the control software of
the wind turbine D 8.2), an updated dynamic model and routines of a wind turbine including variable dynamically-
controlled speed gearbox and directly grid-coupled synchronous generator (2 MW) is implemented in the
simulation software PowerFactory. The accuracy of the model is chosen to be suitable for analysing different
effects of power system stability problems.
The model (delivered by Voith Turbo Wind) consists of the following components, which are modelled in detail:
Synchronous generator including voltage control (VCO) and excitation system
Multi-mass shaft model
WinDrive - variable speed gearbox (simplified) including complete drive train
WinDrive and guide vane control
Speed control
Pitch angle control
Aerodynamics of the turbine model
Voith Turbo provided a Matlab model including the complete drive train and its control as well as the turbine
characteristic and pitch control. This model has been transferred to PowerFactory into a DSL model.
The Matlab model also contains a simplified generator model. PowerFactorysupports a detailed build-in generator
model, which is suitable for transient simulations and which is used during the investigation. For this model of a
2 MW wind generator with a rated voltage of 10kV a set of electrical parameters has been provided. Table 1 and
Table 2 lists the electrical parameters of the synchronous generator model including saturation. The rated
frequency of the wind farm grids is assumed to be 50 Hz in all simulations.
As the PowerFactorygenerator model has a different behaviour in comparison to the simplified Matlab model,
both models have been compared by open loop tests. The verification of the model is shown in the next chapter.
All data has been provided by Voith Turbo GmbH & Co. KG.
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Table 1: Parameter Definition of the Synchronous Generator Models
Parameter Description Unit GeneratorSr Rated Mechanical Power kVA 2222
Ur Rated Voltage kV 10
cos(phi) Rated Power Factor 0.9
Pr Rated Mechanical Power kW 2000
n Nominal Speed rpm 1500
fel Nominal Frequency Hz 50
pz No of Pole Pairs 2
ra stator resistance p.u. 0.0076
xl stator leakage reactance p.u. 0.072
xd (total) d-axis synchronous reactance p.u. 1.52
xq (total) q-axis synchronous reactance p.u. 0.996x'd (total) d-axis transient reactance p.u. 0.152
x''d (total) d-axis subtransient reactance p.u. 0.116
x''q (total) q-axis subtransient reactance p.u. 0.192
Td d-axis open circuit transient time constant S 0.208
Td d-axis open circuit subtransient time
constant
S 0.022
Tq q-axis open circuit subtransient time
constant
S 0.011
Jgen Rotor Inertia kg m 109.0223
Ta Acceleration Time Constant (rated to Pr) s 1.36968
Table 2: No-load Saturation Curve Parameters
Terminal Voltage Unit Value Field Current Unit Value
V0 pu 0 Ifd0 pu 0
V1 pu 0.5 Ifd1 pu 0.45
V2 pu 0.75 Ifd2 pu 0.69
V3 pu 1. Ifd3 pu 1
V4 pu 1.15 Ifd4 pu 1.37
V5 pu 1.25 Ifd5 pu 1.95
Table 3: Operation Points from the Capability Diagram at u=1p.u.
P / MW cos() Q/Sr / p.u. Q / Mvar
2.000.9
(overexcited)0.436 0.969
2.000.9
(underexcited)-0.436 -0.969
0.000.0
(overexcited)0.710 1.578
0.000.0
(underexcited)-0.580 -1.289
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2.12.12.12.1Wind Turbine ModelWind Turbine ModelWind Turbine ModelWind Turbine Model
Frame Wind-Turbine:
Pitch AdjustElmPit*
Pitch ControlElmPit*
beta_soll
TurbineElmTur*
vw
VCOElmVco*
WinDrive CtrlElmComp*
SyncParallel
SyncEnable
Shaft/GearboxElmComp*
M_Abtrieb
Generator
ElmSym*
Frame Wind-Turbine:
beta_soll
M_
Blatt3
M_
Blatt2
M_
Blatt1
omega_rotor
beta_ist
u
Pact
ve
pt
GVP_Start
speed_Gen
WinDriveSpeed
Href
DIgSILENT
Figure 1: Schematic Block Diagram of the Voith Wind Turbine Model
Voith Turbo GmbH provided an updated model of the mechanical part including gearbox, clutches and mass-shaft
models as well as the WinDrive control in form of a Matlab Simulink model including a set of parameter for a
50 Hz turbine. The model represents a simplified representation of the WinDrive model, which is suitable for
analyzing system stability aspects.
This model is implemented in the simulation software PowerFactoryusing block diagrams and the internal
simulation language DSL. A benchmark of the PowerFactorymodel against the original Matlab model has been
carried out to verify the model used for further studies.
Figure 1 shows the schematic structure of the model including synchronous generator, excitations system and
drive train. Turbine aerodynamics and pitch controller are not included in the model because it can be assumed,
that wind speed and thus turbine power is constant during the simulation time.
The results of the model verification are described and shown in chapter 3.
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2.22.22.22.2Voltage Controller and Excitation SystemVoltage Controller and Excitation SystemVoltage Controller and Excitation SystemVoltage Controller and Excitation System
vco_ESAC5A: 1992 IEEE Type AC5A Excitation System
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Se(efd)E1,Se1,E2,Se2
KKe
[1/sTTe
_sTb_/(1+sTa)Kf,Tf1
(1+sTb)/(1+sTa)Tf2,Tf3
{K/(1+sT)}Ka,Ta
Vrmax
Vrmin
1/(1+sT)Tr
vco_ESAC5A: 1992 IEEE Type AC5A Excitation System
1
0
ustab
duo1
duosduodu
us
uek
vx
uerrs
usetp
uru
DIgSILENT
Figure 2: Schematic Block Diagram of the Voltage Controller Model (VCO) ESAC5A
Table 4: Parameter Definition of the Voltage Controller
Parameter Description Unit Values
Tr Measurement Delay s 0.01
Ka Controller Gain p.u. 40
Ta Controller Time Constant s 0.1
Ke Excitor Constant p.u. 1
Te Excitor Time Constant s 0.2
Kf Stabilization Path Gain p.u. 0.05
Tf1 Stabilization Path 1th Time Constant s 0.35
Tf2 Stabilization Path 2th Time Constant s 0.1
Tf3 Stabilization Path 3th Time Constant s 0
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Parameter Description Unit Values
E1 Saturation Factor 1 p.u. 1.96Se1 Saturation Factor 2 p.u. 1.06
E2 Saturation Factor 3 p.u. 1.47
Se2 Saturation Factor 4 p.u. 0.71
Vrmin Controller Minimum Output p.u. 0
Vrmax Controller Maximum Output p.u. 10
2.32.32.32.3WinDrive and Drive Train ModelWinDrive and Drive Train ModelWinDrive and Drive Train ModelWinDrive and Drive Train Model
Triebstrang Frame:
Shaft HSC-VBKElmSha*
n_Gen
0
1
0
1
2
HSCElmHsc*
0
1
2
0
1
2
33
AntriebElmAnt*
0
1
0
1
SampleHold*
0
1Clock
*
Hydr_AntriebElmHyd*
RotorElmRot*
0
1
2
3
Triebstrang Frame:
1
0
1
2 0
2
5
3
4GVP_Start
Href
speed_Gen
pt
M_Abtrieb
omega_Abtrieb
omega_Nabe
M_
Hauptwelle
M_Blatt3
M_Blatt2
M_Blatt1
n_WD_in
M
_Antrieb
ome
ga_
Antrieb
cl
H_soll H
DIgSILENT
Figure 3: Schematic Block Diagram of the Multi-Mass Shaft Model of the Voith Wind Turbine including WinDrive
Figure 3 shows the block diagram of the complete drive train including WinDrive. This model represents the
mechanical spring-mass system of the shaft system of the rotor and of the shaft between generator and
WinDrive. In PowerFactory, the generator inertia is integrated in the synchronous machine model and is
therefore not modelled separately.
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The model of the actual WinDrive hydrodynamic gearbox is shown in Figure 4.
HSC WinDrive Model:
H_inc
0
1
rad/s -> rpm
WinDrivez_Hohlrad_UG,z_Sonne_UG,J_Tr..
0
1
2
3
0
1
2
-1
Nue
abs_min_omega_Pumpe
0
1
Torque ConverterT_Wandler,rho_Oel,D_Prof..
0
1
2
0
1
HSC WinDrive Model:
1
0
2
1
2
0
3GVP_Start
n_WD_in
M_Abtrieb_negM_Abtrieb
M_Pu
mpeM
_Turbine
H
omega_Abtrieb
M_Antrieb
omega_Antrieb
omega_T
urbine
nue
DIgSILE
NT
Figure 4: Schematic Block Diagram of the WinDrive Model
The parameter sets of all components are provided by Voith Turbo GmbH. The parameters are taken from the
Matlab model WinDrive_Tauschmaschine_Cuxhaven_Data_Rev08. They are not listed here in detail.
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2.42.42.42.4WinDrive ControlWinDrive ControlWinDrive ControlWinDrive Control
WinDriveCtrl Frame:
FDelta CalcElmFDe*
Signal VorfilterungElmSig*
0
1
0
1
2
RotorkennlinieElmRot*
0
1
2
SyncParallel
ElmSyn*
0
1
2
3
4
SyncModeElmSyn*
S yn cE na bl e 0
1
VerschliffElmVer*
SyncParallel
0
1
2
3
SubSysElmSub*
TVSActive
SyncEnable
0
1
2
WinDriveCtrl Frame:
0
1
2
1
0GVP_Start
Psoll
H_
vorst
Href
speed_Gen FDelta
Pact
WinDriveSpeed H_Netzbetrieb
Pcurr_KPP
n_WD_in_slow
n_WD_in_fast
GVP
H_
Sync
DIgSILENT
Figure 5: Schematic Block Diagram of the WinDrive Control
The WinDrive controller is providing the guide vane position (GVC or Href) to the mechanical WinDrive model.
As a feedback the speed of the WinDrive WinDriveSpeed is used.
The parameter sets of all components are provided by Voith Turbo GmbH. The parameters are taken from the
Matlab model WinDrive_Tauschmaschine_Cuxhaven_Data_Rev08. They are not listed here in detail.
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2.52.52.52.5Pitch Control and Aerodynamic ModelPitch Control and Aerodynamic ModelPitch Control and Aerodynamic ModelPitch Control and Aerodynamic Model
Pitch Control:
-Selectn_rotor_nenn,n_ec..
rad/s -> rpm
Schaltbedingungn_eck,beta_grenz
0
1
D_pitchD_pitch
0
1
Rotor Speed CtrlP_pitch_pos,P_pit..
90
0
Limiter
90
0
Pitch Control:
1
0betadn pitch_soll
n_rotor_soll
Schaltbedingung
dbeta
beta_ist
n_rotoromega_rotor
beta_soll
DIgSILENT
Figure 6: Schematic Block Diagram of the Pitch Controller
Pitch Adjustment:
- -
RateOfChangeLim0.001
max_beschl..
Limiter
max_geschw..
KKVrea..
1/s1/sDelaypitch_Totzeit
Kpitch..
Pitch Adjustment:
dbetabeta2 beta_istyi5yi3yi2yi1yidbeta2beta_soll
DIgSILENT
Figure 7: Schematic Block Diagram of the Pitch Adjustment
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Table 5: Parameter Definition of the Pitch Control and Adjustment
Parameter Description Unit Valuesmax_beschleunigung_pitch Maximale
Blattwinkelverstellbeschleunigung
deg/s 60
max_geschwindigkeit_pitch Maximale
Blattwinkelverstellgeschwindigkeit
deg/s 5.5
pitch_Totzeit Totzeit des Reglers s 0.05
pitch_amplification_factor Reglerverstrkung p.u. 13
KVreal_pitch Kehrwert der Verzugszeit 1/s 10
maximum_pitch_adjustment_speed deg/s 9.5
n_rotor_nenn 1/min 18.6
n_eck 1/min 18.193
beta_grenz deg 3P_pitch_pos deg/rpm 5
P_pitch_neg deg/rpm 6
I_pitch_pos deg/rpm/s 0.5
I_pitch_neg deg/rpm/s 2
D_pitch 5.7
Table 6: Parameter Definition of the Turbine Model
Parameter Description Unit Values
R Rotor Radius m 40.15
rho_luft Density of Air Kg/m 1.225
cp cp-lambda-Characteristic see Matlab model
Pitch angle control and turbine aerodynamics are not taken into account during the analysis of the steady-state
as well as transient and oscillatory stability aspects. Due to large time constants, these models their influence the
simulations can be neglected.
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3333Verification of theVerification of theVerification of theVerification of the PowerFactoryPowerFactoryPowerFactoryPowerFactoryModelModelModelModel
In this chapter the model of the Voith wind turbine, which is implemented by DIgSILENT GmbH in the simulation
software PowerFactory, is verified by comparing the results of a simulation with the results obtained with the
corresponding Matlab model.
As the Matlab model is using a simplified synchronous generator and no network model, the verification is carried
out using an open-loop test of the model in Matlab and in PowerFactory. To do this the results from the Matlab
simulation are fed as input signals into the PowerFactorymodel. These signals are the generator speed
n_Generator and the electrical power P_Gen. The output signals of the different blocks of both models are
then checked to be identical and thus to verify the dynamic response of the models.
The simulation is performed in PowerFactoryand Matlab using the following sequence:
Initialising the model with all rotational speed equal to zero.
The model is settling to a steady-state operation point at Pgen = 0 MW.
Start of a ramp onto the blade torques M_Blatt1, M_Blatt2 and M_Blatt3 at t=50 s, where the value is
increased linearly from 0 Nm to 330000 Nm with a gradient of 20000 Nm/s.
This will in turn increase the electrical power to a value of Pgen = 1.8 MW.
The simulations are carried out for a simulation time of 100 s. A fixed time step of 2 ms is used for bothsimulations. The results of both the PowerFactoryand Matlab are shown in the plots on the next pages. The
following variables of the models are visualised:
Drive train:
the rotational speed omegaAntrieband the torque MAntriebas well as omegaAbtrieband the torque MAbtrieb.
rotational speed of the generator omegaGenand the set point for the guide vane control Hsolland H.
torque of the main shaft MHauptwelleand the rotational speeds omegaHauptgetriebeand omegaRotor.
WinDrive control:
WinDrive speed and outputs of the signal input filter.
Outputs of the rotor characteristics Psolland Hvorstresp. Hgefiltert
Guide vane control setpoint and output MNetzbetrieb, GVP and Href
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The plots for the verification are shown in Annex 1. The results from the PowerFactorysimulations are shown in
red (solid curve) and the results from Matlab are shown in blue (dashed curve).
The plots show that both simulations match very well. The model implemented into PowerFactoryshows in the
mechanical part as well as in the different control modes identical behaviour compared to the Matlab model. Thus
the model can be used to be integrated into a detailed wind farm grid, to analyse the realistic behaviour of the
wind turbines during disturbances and faults in the network.
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
G r i d C o d e s
- 1 7 -
4444Wind FarmWind FarmWind FarmWind Farm NetworkNetworkNetworkNetwork
For analysing the compatibility of the Voith wind turbine concept to the German requirements for the connection
to high voltage (HV) [1] and medium voltage (MV) [2] networks, the behaviour of a complete wind farm is
investigated.
The behaviour of the wind turbines with directly grid-coupled synchronous generators and variable speed gearbox
is analyzed on the basis of typical wind farm layouts, which are described in this chapter.
4.14.14.14.1TestTestTestTest Wind FarmWind FarmWind FarmWind Farm with HV (with HV (with HV (with HV (110kV) Connection Point110kV) Connection Point110kV) Connection Point110kV) Connection Point
The steady-state and dynamic performance of a wind farm is analyzed based on a wind farm layout with a totalrated power of 50 MW and a nominal frequency of 50 Hz. The wind generators are arranged in 5 strands each
connecting 5 wind turbines with a rating of 2 MW each. Each generator has a rated voltage of 10 kV, which
corresponds to the wind farm internal voltage level. The wind farm is connected to the 110kV connection point by
a 10kV/110kV step-up transformer.
The distances between the turbines on a strand are assumed to be 500 m. The different strands are 1000 m
apart. The wind farm configuration is shown in Figure 8.
There are three different cable types used in the wind farm network. All cables are XLPE cables with a rated
voltage of 10 kV and the laying procedure is in a flat formation (row). The cable types used and wind farm
topology applied have been agreed with Voith Turbo. The cables are selected based on thermal considerations.For the connection of each strand to the main substation, two parallel cable systems (6x240RM) are used. Cable
data is based on the DIN/IEC standard and is taken from reference [3], the data is listed in Table 7.
Table 7: Characteristic Values of the used IEC Standard Cables [3]
Cable TypeUr
kV
Ir
kA
Sr
MVA
R1
/km
R0
/km
X1
/km
X0
/km
C1=C0
F/km
N2XS2Y 1x240RM
6/10kV ir10 0.546 9.77 0.0754 0.701 0.180 0.293 0.456
N2XS2Y 1x70RM
6/10kV ir10 0.303 5.25 0.286 1.087 0.215 0.555 0.283
NA2XS2Y 1x240RM6/10kV ir 10 0.453 7.85 0.125 0.751 0.180 0.293 0.456
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
G r i d C o d e s
- 1 9 -
The electrical parameters of the step-up transformers with tap changer are listed in Table 8.
Table 8: Characteristic Values of the Wind Farm Transformer
Transformer Type Sr / MVA uk / % uk0 / % Copper Losses
/ kW
ukr0 / %
110 / 10 kV YNd5 60 10 10 200 0.333
Tap Changer Add. Volt
per tap / %
Min. Pos Max. Pos.
1.5 -10 10
For all investigated cases strong wind conditions are assumed, e.g. all wind generators are operating above
nominal wind speed, thus all generators are providing rated active power of 2 MW. The total power output of the
farm is about 50 MW. The power factor at the PCC is controlled to 0 Mvar in steady-state.
The results from the load-flow calculation for the base case are shown in Annex 2.
4.24.24.24.2Test Wind Farm with MV (10kV) Connection PointTest Wind Farm with MV (10kV) Connection PointTest Wind Farm with MV (10kV) Connection PointTest Wind Farm with MV (10kV) Connection Point
The German requirements for the connection to the medium voltage (MV) network are tested using a smaller
wind farm with Voith wind generator technology. The wind farm is connected directly to the 10kV distribution
network, without any step-up transformer.
The performance of the directly grid-coupled synchronous generators with variable speed gearbox with a rated
power output of 2 MW is analyzed and the compatibility with the requirements in the Mittelspannungsrichtlinie
2008 [2] is shown.
Therefore a wind farm is used based on a wind farm layout with a total rated power of 20 MW at a nominal
frequency of 50 Hz. The generators are arranged in 2 strands each connecting 5 wind turbines with a rating of
2 MW each. Each generator has a rated voltage of 10 kV. This layout and electrical components used are identical
to two of the 5 strands from the 50 MW wind farm described in the previous section for the connection to a HV
network.
Figure 9 shows the wind farm grid used for the calculations including cable types and lengths.
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
G r i d C o d e s
- 2 0 -
Voith
DIgSILENT
PowerFactory 14.0.506
Wind Farm Layout
Voith Wind Turbine ModellingConnection to MV Network
Project: P1347
Graphic: WF Grid Docu
Date: 8/7/2008
Annex:
bb_S210.00 kV
bb_S110.00 kV
bb_WP_LV10.00 kV
bb_S2G510.00 kV
bb_S2G110.00 kV
bb_S2G210.00 kV
bb_S2G310.00 kV
bb_S2G410.00 kV
bb_S1G510.00 kV
bb_S1G410.00 kV
bb_S1G310.00 kV
bb_S1G210.00 kV
bb_S1G110.00 kV
cb_
WP_
S1
NA2XS2Y1x240RM6/10kVir
0.5
0km
cb_
WP_
S1
NA2XS2Y1x240RM6/10kVir
0.5
0km
X_
S1
X_
S1
X_
S2
X_
S2
G~S2G5
HVWI804D_W
DG81
G~S1G5
HVWI804D_W
DG81
G~S2G4
HVWI804D_W
DG81
G~S1G4
HVWI804D_W
DG81
G~S2G3
HVWI804D_W
DG81
G~S1G3
HVWI804D_W
DG81
G~S2G2
HVWI804D_W
DG81
G~S1G2
HVWI804D_W
DG81
G~S2G1
HVWI804D_W
DG81
G~S1G1
HVWI804D_W
DG81
cb_
S2_
G4G5
N2XS2Y1x70RM6/10kVir
0.5
0km
cb_
S2_
G4G5
N2XS2Y1x70RM6/10kVir
0.5
0km
cb_
S1_
G4G5
N2XS2Y1x70RM6/10kVir
0.5
0km
cb_
S1_
G4G5
N2XS2Y1x70RM6/10kVir
0.5
0km
cb_
S2_
G3G4
N2XS2Y1x70RM6/10kVir
0.5
0km
cb_
S2_
G3G4
N2XS2Y1x70RM6/10kVir
0.5
0km
cb_
S1_
G3G4
N2XS2Y1x70RM6/10kVir
0.5
0km
cb_
S1_
G3G4
N2XS2Y1x70RM6/10kVir
0.5
0km
cb_
S2_G
2G3
N2XS2Y1x240RM6/10kVir
0.5
0km
cb_
S2_G
2G3
N2XS2Y1x240RM6/10kVir
0.5
0km
cb_
S1_G
2G3
N2XS2Y1x240RM6/10kVir
0.5
0km
cb_
S1_G
2G3
N2XS2Y1x240RM6/10kVir
0.5
0km
cb_
S2_
G1G2
N2XS2Y1x240RM6/10kVir
0.5
0km
cb_
S2_
G1G2
N2XS2Y1x240RM6/10kVir
0.5
0km
cb_
S1_
G1G2
N2XS2Y1x240RM6/10kVir
0.5
0km
cb_
S1_
G1G2
N2XS2Y1x240RM6/10kVir
0.5
0km
110kV Netz
cb_
WP_
S2
NA2XS2Y1x240RM6/10kVir
1.5
0km
cb_
WP_
S2
NA2XS2Y1x240RM6/10kVir
1.5
0km
DIgSILENT
Figure 9: Wind Farm Layout for Connection to MV-Network
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
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G r i d C o d e s
- 2 1 -
5555Requirements for Connections to the Transmission (HV) GridRequirements for Connections to the Transmission (HV) GridRequirements for Connections to the Transmission (HV) GridRequirements for Connections to the Transmission (HV) Grid
For the connection of power plants to the transmission network level in Germany, the German grid code
TransmissionCode 2007 [1] published by the VDN e.V. Verband Deutscher Netzbetreiber defines the technical
requirements for the generators. In this chapter the different requirements are analysed and the compatibility of
the wind turbine concept using a hydro-dynamically controlled gearbox (WinDrive) is investigated. The
corresponding calculations and simulations are described and the results are shown.
The layout of the wind farm with 25 x 2 MW wind turbines is shown in the previous chapter. The wind farm is
connected to the transmission grid at the 110 kV voltage level. Each wind turbine is modelled in detail, as
described in section 2.
For assessing the dynamic behaviour of the turbines under different network configurations, three different short-circuit levels at the point of common coupling (PCC) have been assumed:
Strong network: Sk=1000 MVA (SCR=20)
Weak network: Sk=300 MVA (SCR=6)
Very weak network: Sk=200 MVA (SCR=4)
In a previous study the behaviour of the wind generators during different wind scenarios has been analysed. As a
result of the simulation it can be concluded, that the strong wind scenario (wind speeds larger than nominal wind
speed) is the worst case regarding the stability and fault ride-through of the turbines. Thus all calculations have
been performed assuming full power output of 2 MW of all wind generators.
For several of short circuit levels at the connection point, the following stability aspects have to be analysed
according to the TransmissionCode 2007, section 3.3.13 Requirements upon generating units using renewable
energy sources [1]:
Active power output
Reactive power output
Behaviour during network disturbances
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
G r i d C o d e s
- 2 2 -
5.15.15.15.1Active Power OutputActive Power OutputActive Power OutputActive Power Output (Section(Section(Section(Section 3.3.13.3 in [1])3.3.13.3 in [1])3.3.13.3 in [1])3.3.13.3 in [1])
Section 3.3.13.3 describes the requirements of the grid code regarding the active power output of the wind
power plant with regard to deviations of the network frequency from its nominal value.
The wind generator must disconnect, if the network frequency is outside the range of 47.5 Hz to 51.5 Hz. If the
frequency increases above 50.2 Hz, the active power output has to be reduced linearly. Also the transmission
system operator must be able to reduce the active power output using of the complete wind farm in emergency
cases. This ability has to be implemented into the control of the turbine to comply with the requirements.
5.25.25.25.2Reactive Power OutputReactive Power OutputReactive Power OutputReactive Power Output (Section 3.3.8 in [1])(Section 3.3.8 in [1])(Section 3.3.8 in [1])(Section 3.3.8 in [1])
The requirements concerning the output of reactive power and voltage control at the PCC is similar for
conventional power plants and for generators using renewable energy sources in section 3.3.8 in [1].
Three different figures 3.3a to 3.3c are defining requirements for the steady-state reactive power support of the
plant to the network at the PCC. The values of reactive power output at rated active power are depending on the
voltage at the PCC. The TSO can then select one of the variants relevant for its network.
Figure 10 shows the different curves of the reactive power output in p.u. depending on the voltage at the PCC,
where the dashed curves indicate the requirements according to [1].
The reactive power output capability of the wind farm has been tested using a series of load-flow calculations.
The voltage at the PCC is set by the external network and the individual generators are controlled to providemaximum and minimum reactive power output according to the capability diagram (see also Table 3 in a previous
chapter). It is then checked, if the reactive power value at the PCC is matching or exceeding the requirements.
Because the requirements according to section 3.3.8 of the TC2007 [1] can be seen as requirements for slow
reactive power control, it is assumed that the required reactive range must be covered in the time frame of
minutes, hence with the support of the on load tap changer of the step-up transformer and possible with the
support of mechanically switched capacitor banks. It can further be assumed that the range of the on load tap
changer of the 10kV/110kV is able to maintain the voltage at the 10kV main bus bar at around nominal voltage.
As a resulting curve the reactive power capability of the wind farm with the generators at maximum and at
minimum reactive power output is shown in Figure 10 as a red solid curve. It can be seen, that the wind farmexceeds the required reactive power range for underexcited operation (consumption of reactive power at PCC),
whereas the maximum requirements are not met for overexcited operation (support of reactive power at PCC).
The reason for this are reactive losses in the wind farm internal distribution network and reactive losses of the
10kV/110kV step-up transformer, which are not covered by the synchronous generators having a rated power
factor of only 0.9.
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
G r i d C o d e s
- 2 3 -
80
90
100
110
120
130
140
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Figure 3.3b
Figure 3.3a
Figure 3.3c
Q_WP / pu
overexcitedunderexcited
Figure 10: Requirements according to [1] and Capability of Wind Farm for Steady-State Reactive Power Support
at P=PN.
In this case two solutions are possible:
A generator with high reactive power range (and therefore higher rated apparent power) should be
used. Instead of using a generator with a rated power factor of 0.9, a generator with rated power factor
of 0.85 or even 0.8 should be used for compensating reactive losses in the wind farm internal network
and the 10kV/110kV step-up transformer.
The resulting curve is shown in Figure 11 as a solid violet curve. It can be seen, that all three dashed
curves from [1] are inside the capability curve.
An additional capacitor can be added at the main MV bus bar of the wind farm for shifting the complete
reactive capability curve. In this example a 7 Mvar capacitor has been added at the 10 kV substation. The
yellow curve in Figure 11 shows that the wind farm meets all reactive power requirements according to
[1].
Depending on requirements during partial load, the capacitor bank must be switchable with differentsteps.
Option 1, using a generator with larger reactive power range, will be the more cost effective solution in
most wind farm projects. It is therefore recommended to reconsider the size of the standard generator
and possible go towards a generator with larger MVA rating, at least for projects with HV connection
point.
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
G r i d C o d e s
- 2 4 -
80
90
100
110
120
130
140
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Figure 3.3b
Figure 3.3aFigure 3.3cQ_WP / puQ_(pf=0.85) / puQ_WP_Cap / pu
overexcitedunderexcited
Figure 11: Requirements and Capability of Wind Farm for Steady-State Reactive Power Support.
5.35.35.35.3Behaviour duringBehaviour duringBehaviour duringBehaviour during DDDDisturbances in theisturbances in theisturbances in theisturbances in the NNNNetworketworketworketworkThe grid code is dividing the generating units using renewable energy sources into two types:
Type 1: a synchronous generator directly connected to the network.
Type 2: any other generator technology.
The turbine using the Voith WinDrive technology is applying a synchronous generator directly coupled to the
network. Thus for analysing the behaviour of the wind farm after disturbances, the requirements for generators
of type 1 has to be applied. These requirements are listed under section 3.3.12 in [1].
5.3.15.3.15.3.15.3.1Transient StabilityTransient StabilityTransient StabilityTransient Stability after Shortafter Shortafter Shortafter Short----CiCiCiCircuitsrcuitsrcuitsrcuits (section 3.3.13.5 resp. 3.3.12.1 in [1])(section 3.3.13.5 resp. 3.3.12.1 in [1])(section 3.3.13.5 resp. 3.3.12.1 in [1])(section 3.3.13.5 resp. 3.3.12.1 in [1])Most grid codes require that generators stay connected in the case of network faults (low-voltage ride-through
capability, LVRT). It is of particular importance to transmission system operators, that wind farms stay connected
in case of faults at major transmission levels leading to a voltage depression in a wide area, which could lead to a
major loss of wind generation if wind farms were not equipped with LVRT-capability. Therefore, LVRT-capability is
a definite requirement for all larger wind farms.
The main issue of synchronous generators with direct grid connection (without power electronics converters) is
their ability to remain in synchronism during and after major voltage sags. The corresponding effect is named
Transient Stability in literature. The main parameters influencing transient stability are:
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
G r i d C o d e s
- 2 5 -
Rotor inertia/turbine power during the fault.
Depth of the voltage sag.
Duration of the voltage sag.
Short circuit impedance of the grid to which the generators are connected.
The transmission code requires LVRT for two different types of faults at the PCC:
Solid 3-phase short-circuit with 150ms clearing time (0% remaining voltage)
3-phase short-circuit for 5s with large fault impedance (85% remaining voltage)
According to the requirements a SCR of 6 should be analysed. To assess transient stability of the turbines more
thoroughly and to get a better overview of the performance of the generator concept, simulations are carried out
for three different short-circuit levels at the 110kV connection point (PCC): Strong network: SCR=20
Weak network: SCR=6
Very weak network: SCR=4
All results of the transient simulations are shown in Annex 3. Table 9 summarizes the results.
Table 9: Results from the Simulations for the Transient Stability according to [1]
Fault Strong Network
(SCR=20)
Weak Network
(SCR=6)
Very Weak
Network (SCR=4)
3ph Short-Circuit, 0% stable stable stable3ph Short-Circuit, 85% stable stable stable
The simulations show that the wind generators are stable for all combination of faults and short-circuit levels
analysed. Even at very weak networks with a SCR of 4, the generators are remaining in synchronism after the
short-circuit. Thus in all cases the transient stability of the wind generators is ensured.
As shown in a previous study, the layout of the wind farm grid has a substantial influence on the impedances
between generator and PCC and hence on the stability of the generators. For this layout the minimum short
circuit level is Sk=180 MVA or a SCR=3.6 for a solid three-phase fault.
5.3.25.3.25.3.25.3.2Oscillatory StabilityOscillatory StabilityOscillatory StabilityOscillatory Stability (section 3.3.12.2 in [1])(section 3.3.12.2 in [1])(section 3.3.12.2 in [1])(section 3.3.12.2 in [1])After large disturbances or also after minor network disturbances as they are always present, such as changes in
the voltage due to switching of lines or other network components or load changes, oscillations between the wind
farm and the main network or oscillations between the different generators within the farm can be excited. This
can already be seen in the simulation from the last section transient stability. Especially for the very weak
network with SCR of 4 and the three-phase fault with remaining voltage of 85%, an oscillation of around 4-5 Hz
can be seen, which is damped out within 10 s.
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
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G r i d C o d e s
- 2 6 -
The effect of these oscillatory modes and their damping can be analyzed using eigenvalue analysis. Using this
analysis technique characteristic modes of a system are obtained in terms of damping and characteristic
frequency.
The behaviour of the generators and thus the damping of possible modes is depending on the operation point of
the generator. [1] requires the analysis of modes in all possible operation points of the generator within its
capability diagram. Thus for each combination of short-circuit level at the PCC (SCR=20, SCR=6, SCR=4),
different operating points of the generators are investigated:
Operation Point 1: P=PN, Q=0 Mvar (at PCC)
Operation Point 2: P=PN, Q=Qmax
Operation Point 3: P=0 MW, Q=Qmax
Operation Point 4: P=0 MW, Q=Qmin Operation Point 5: P=PN, Q=Qmin
Frequency and damping of each mode is calculated and analyzed. The results of the calculations are visualized in
Annex 3 in form of eigenvalue plots containing eigenvalues in the complex plane. Additionally the participation
factors are shown for two eigenvalues with the lowest damping. The results for these eigenvalues from the
eigenvalue analysis are summarized in Table 10 to Table 12 for all short-circuit levels at the PCC.
Table 10: Results of the Eigenvalue Analysis for SCR=20
SCR=20 Mode No. Period Frequency Damping Ratio
s Hz A1/A2
P=PN, Q=0 Mvar Mode 00576 0.183 5.47 2.750 1.654Mode 00578 0.171 5.84 4.526 2.171
P=PN, Q=Qmax Mode 00576 0.184 5.44 2.796 1.672
Mode 00578 0.174 5.76 4.568 2.212
P=0MW, Q=Qmax Mode 00507 0.190 5.27 1.539 1.339
Mode 00509 0.186 5.38 2.796 1.681
P=0MW, Q=Qmin Mode 00452 0.198 5.04 1.841 1.441
Mode 00454 0.200 5.01 2.139 1.533
P=PN, Q=Qmin Mode 00578 0.161 6.20 4.103 1.937
Mode 00626 0.178 5.62 2.406 1.535
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
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G r i d C o d e s
- 2 7 -
Table 11: Results of the Eigenvalue Analysis for SCR=6
SCR=6 Mode No. Period Frequency Damping Ratio
s Hz A1/A2
P=PN, Q=0 Mvar Mode 00575 0.171 5.84 4.524 2.171
Mode 00583 0.189 5.29 2.286 1.541
P=PN, Q=Qmax Mode 00573 0.190 5.26 2.303 1.549
Mode 00575 0.174 5.75 4.567 2.211
P=0MW, Q=Qmax Mode 00494 0.193 5.18 1.014 1.216
Mode 00496 0.186 5.38 2.796 1.681
P=0MW, Q=Qmin Mode 00454 0.198 5.05 1.564 1.363
Mode 00486 0.200 5.01 2.139 1.533
P=PN, Q=Qmin Mode 00624 0.186 5.38 2.044 1.462
Mode 00575 0.161 6.20 4.100 1.937
Table 12: Results of the Eigenvalue Analysis for SCR=4
SCR=4 Mode No. Period Frequency Damping Ratio
s Hz A1/A2
P=PN, Q=0 Mvar Mode 00574 0.171 5.84 4.524 2.171
Mode 00622 0.192 5.21 2.155 1.513
P=PN, Q=Qmax Mode 00572 0.193 5.17 2.167 1.520
Mode 00574 0.174 5.75 4.566 2.211
P=0MW, Q=Qmax Mode 00494 0.195 5.12 0.810 1.171
Mode 00496 0.186 5.38 2.796 1.681
P=0MW, Q=Qmin Mode 00453 0.198 5.05 1.416 1.324
Mode 00486 0.200 5.01 2.139 1.533
P=PN, Q=Qmin Mode 00575 0.161 6.20 4.100 1.937
Mode 00624 0.186 5.38 2.044 1.462
From the eigenvalue diagrams in Annex 3 it can be derived, that there are oscillatory modes in different
frequency ranges:
around 2.6Hz inherent mechanical mode of the drive train and low damping,
no participation of generators.
2.4-3.3 Hz local wind farm modes representing oscillations of combined generator/turbine
inertias within the wind farm and of the wind farm against the network.
5-7 Hz oscillations related to generator inertia within the wind farm and of the wind farm
against the network.
30-33 Hz torsional modes of the drive trains.
45-46 Hz torsional modes of the drive trains.
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
G r i d C o d e s
- 2 8 -
These results are similar to the results derived in the previous study. An additional torsional mode at 45 Hz is
occurring, due to the more complex drive train model.
The modes at around 2.4..3.3 Hz are oscillations related to the combined inertia of generator and turbine. The
mode with lowest damping indicates the oscillation between the wind farm and the network. The local wind farm
modes representing oscillations between generators and groups of generators show higher damping. Generally all
modes are very well damped.
The lowest damped mode at around 5 Hz represents oscillations of the wind farm against the external 110 kV
network (first mode listed in Table 10 to Table 12). These oscillations show a good damping even at low short
circuit levels at the PCC, where the ratio between consecutive swings is around 1.1 to 1.4. The minimum is
reached at low power output (low wind conditions) and at weak PCCs, although the damping is still sufficient.
The other modes in the frequency range between 5..7 Hz are related to generator oscillations within the windfarm, i.e. groups of generators or strands oscillating against each other. These modes are better damped then
the wind farm mode described above. The mode with the lowest damping is the second mode listed in Table 10
to Table 12. Annex 3 also shows the participation phasor diagrams for both modes. Here it can be seen, that the
generators are oscillating against the network resp. against each other.
Oscillatory modes at higher frequencies are torsional modes of the drive trains. These oscillations are always
present in case of wind turbines. However, they are not causing any interactions between the wind generators
and are therefore not critical.
Additionally it can be concluded that oscillatory modes around frequencies of 0.5 1 Hz are not present, thus
periodically excited frequencies in this range, like the tower shadow effect, will not result in persisting oscillations.
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
G r i d C o d e s
- 2 9 -
6666RequireRequireRequireRequirements for Connections to thements for Connections to thements for Connections to thements for Connections to the DistributionDistributionDistributionDistribution (MV)(MV)(MV)(MV) GridGridGridGrid
For the connection of power plants and wind generators to the German distribution grid at medium voltage level,
the German grid code Mittelspannungsrichtlinie 2008 [2] published by the BDEW - Bundesverband der Energie-
und Wasserwirtschaft e. V. defines the technical requirements.
In this chapter the different requirements are analysed and the compatibility of the wind turbine concept using a
hydro-dynamically controlled gearbox (WinDrive) is investigated. The corresponding calculations and simulations
are described and the results are shown.
Here a wind farm with 10 x 2 MW wind generators is connected to the distribution network at 10 kV voltage level.
The generators are assumed to operate at full power output in all calculations. The wind turbine is modelled in
detail, as described in section 2. A step-up transformer for the wind generator is not needed when connecteddirectly to the 10 kV voltage level.
For the simulations three different values for the short-circuit level at the point of common coupling (PCC) have
been assumed. These values are chosen to be typical values for strong and weak MV networks:
Strong network: Sk=500 MVA SCR=25
Weak network: Sk=250 MVA SCR=12.5
Very weak network: Sk=150 MVA SCR=7.5
For all listed short circuit levels at the PCC, the following stability aspects have to be analysed according to the
Mittelspannungsrichtlinie 2008 [2]:
Network Disturbances (section 2.4):
Steady-state voltage changes.
Transient voltage changes due to switching.
Flicker.
Harmonics.
Commutation voltage drops.
Impact on ripple control.
Behaviour of the Generator (section 2.5):
Transient stability of the wind farm (behaviour during large disturbances).
Short-circuit current.
Active power output.
Reactive power output.
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P 1 3 4 7P 1 3 4 7P 1 3 4 7P 1 3 4 7
G r i d C o m p a t i b i l i t y o f W i n d G e n e r a t o r s w i t h H d y r o - D y n a m i c a l l y C o n t r o l e d G e a r b o x w i t h G e r m a n
G r i d C o d e s
- 3 0 -
6.16.16.16.1Network DisturbancesNetwork DisturbancesNetwork DisturbancesNetwork Disturbances
6.1.16.1.16.1.16.1.1SteadySteadySteadySteady----StatStatStatState Voltage Changes (Section 2.3 in [2])e Voltage Changes (Section 2.3 in [2])e Voltage Changes (Section 2.3 in [2])e Voltage Changes (Section 2.3 in [2])
The steady-state voltage change is depending on the layout of the medium voltage network, the strength of the
network (short-circuit level) and the point in the network, where the wind farm is interconnected. Also the
steady-state voltage change is not depending on the generator technology but only on the rated power of the
power plant.
Thus this issue has to be analysed for each individual wind farm project and can not investigated in combination
with a simplified network equivalent.
6.1.26.1.26.1.26.1.2Voltage Change due to Switching Operations (section 2.4.1 in [2])Voltage Change due to Switching Operations (section 2.4.1 in [2])Voltage Change due to Switching Operations (section 2.4.1 in [2])Voltage Change due to Switching Operations (section 2.4.1 in [2])Due to connection and disconnection of wind generators the maximum voltage change shall not exceed the limit
of 2%. Compared to asynchronous generators, which might use a direct start-up method having a large impact
on network voltage, the direct coupled synchronous generator uses an offline start-up method and
synchronisation devices. Thus the analysed wind turbine concept will only have a minor impact on system voltage
during switching operations.
According to [2] a simple way of estimate the maximum voltage step change is to use an approximated value
kimax, which is defined as the maximum switching current rated to nominal generator current. For synchronous
machines this factor can be assumed to be kimax=1.2. The voltage step change can then be calculated
%2)cos(
1maxmaxmax
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