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Effects of Wind Turbine Generators on Inter-Area Oscillations and DampingControl Design
Felipe Wilches-BernalSandia National
Christoph LacknerRensselaer Polytechnic
Joe H. ChowRensselaer Polytechnic
Juan J. Sanchez-GascaGE
Abstract
This paper analyzes the effect of wind turbineintegration (WT) on the inter-area oscillation mode of atest two-area power system. The paper uses a root-locusbased design method to propose a pair of controllers toprovide damping to the inter-area mode of the system.The controllers are selected from the best combinationof feedback signal and WT control action. One of thecontrollers uses the active power control part of the WTwhile the other uses the reactive power part. The paperanalyzes the impact that increases on the transmissionline connecting the WT to the system have on thecontrollers’ performance. Time domain simulations areprovided to evaluate the effectiveness of the controllersunder different conditions.
1. Introduction
The future grid is expected to accommodate muchhigher levels of penetration of wind and solar generationif goals such as the 50% mandate of electricity comingfrom renewables by 2030 in states like Californiaand New York are to be met [1, 2]. Because ofthis continuous introduction of renewable energy thetraditional operation of power systems is expected tochange. It is important to assess how the inclusion ofconverter-based interfaced clean energy sources, such aswind and solar, affect the dynamics of power systemstraditionally set by the swing equation governingconventional generators. In particular, studying theimpact that power electronics interfaced generation hason the small signal stability of power system is critical to
Sandia National Laboratories is a multimission laboratorymanaged and operated by National Technology and EngineeringSolutions of Sandia, LLC., a wholly owned subsidiary of HoneywellInternational, Inc., for the U.S. Department of Energy’s NationalNuclear Security Administration under contract DE-NA0003525.
This research was supported in part by the U.S. Department ofEnergy Transmission Reliability program.
This work was supported in part by the Engineering Research CenterProgram of the National Science Foundation and the Department ofEnergy under NSF Award Number EEC-1041877 and the CURENTIndustry Partnership Program.
enable its inclusion in larger quantities. Because powerelectronics have much faster responses than conventionalgeneration and can independently control active andreactive power it is of special interest to investigatehow they can help with the small signal stability of thesystem.
The effect that integrating Wind Turbine Generators(WTGs) has on inter-area oscillations have beeninvestigated in [3–8]. Most of these studies showthat wind integration increases the damping of theseoscillations. However, some works show that undercertain operating conditions the installation of windgeneration can destabilize these modes of oscillation [5,9]. Previous research has shown power electronicsinterfaced generation to be effective in damping powersystem oscillations [6, 10–14].
This paper is composed of two main parts. Thefirst studies the effect of integrating WTG in a two-areasystem representative of a transfer path continuing thework presented in [15, 16]. The second part proposesroot-locus control strategy for WTGs to damp inter-areaoscillations. The linear analysis and nonlinear simulationof wind integration presented in this paper are facilitatedby the MATLAB-based Power System Toolbox (PST)software [17] using the implemented Type-3 WTGmodel [7, 18]. The main contributions of this work canbe stated as follows:
(a) It studies the effects on the inter-area mode of thesystem of increasing wind penetration for differentpower transfer conditions. It shows that integratingWTGs in the area that is importing power may posesmall signal stability problems.
(b) It presents an investigation on how the transmissionline used to perform the installation of wind in thesystem affect its inter-area mode.
(c) It proposes two different control mechanisms forWTG to damp inter-area oscillations. One controlleractuates in the active power control of the WTGwhile the other is included in the reactive powercontrol.
(d) It studies the proper combination of measured signal
Proceedings of the 52nd Hawaii International Conference on System Sciences | 2019
URI: https://hdl.handle.net/10125/59801ISBN: 978-0-9981331-2-6(CC BY-NC-ND 4.0)
Page 3649
and point of connection of the controller within theWTG to better influence the inter-area mode of thesystem.
(e) It analyzes the effect of transmission line increaseson the proposed controllers. It shows that eventhough increases in the transmission line only affectslightly the inter-area mode of the system, the zerosof the system are heavily affected. The movementof the zeros is shown to decrease noticeably theperformance of both proposed controllers.
(f) Time domain simulation is performed to show thatWTG can be effectively used as a tool to dampinter-area oscillations and different input/outputsignal combinations can be used to achieve that goal.
2. Test System and WTG Model2.1. WTG Model
The Type-3 WTG model presented in [19, 20]and implemented in PST [18] is used in this work.The model can represent up to an entire wind powerplant and has been previously validated [21–25]. Theconverter-controlled grid interface of this type WTGallows for independent active and reactive power control.The model interacts with the grid as a controlled currentinjection. The injected current is determined by theoutputs of the active and reactive power controllers,Ipcmd and Efdcmd respectively as well as the voltage atthe point of interconnection. The current injected by theType-3 WTG model is
It =
(Ip − j
Efd
Lpp
)(cos(γ) + j sin(γ)) + j
VtLpp
(1)
where Ip and Efd correspond to the outputs of the activeand reactive power controllers after they pass through anindependent delaying stage each. Vt is the voltage atthe point where the WTG is connected and γ is a staterepresenting the PLL action of the converter [20] that isdescribed by
γ = kpllp[Vtim cos(γ)− Vtre sin(γ)] (2)
2.2. Test System
The test power system used in this paper is presentedin Fig. 1. This system corresponds to a two-area,two-machine test system that contains a dominantinter-area mode and can be interpreted as an example ofa transfer path between sparse areas that oscillate againsteach another [26]. To study the effect that positioningof wind generation has on the inter-area power swing ofthis system, WTGs are to be located independently ineach area and at the midpoint of the transfer path. Assuch three cases are considered:
• Case A – Wind integration is performed in Area 1at Bus 6. The power output of the conventionalgenerator at Bus 2 is reduced according to thedesired wind penetration.
• Case B – Wind integration is performed in Area 2at Bus 10. The power output of the conventionalgenerator at Bus 4 is reduced according to thedesired wind penetration.
• Case C – Wind integration is performed atthe transfer path’s midpoint at Bus 8. Bothconventional machines, generators at Buses 2 and4 are each reduced by half of the power producedby the WTG.
6 7 98 10 4
L17 L19
17 19
G4G2
2
Case A Case B Case C
Area 1 Area 2
12P
Figure 1: Two-area, two-machine test system used in this paper thathas a strong inter-area oscillation mode.
Note that in each case only one WTG is considered asthe idea is to see how individual WTG controls interactwith the modes of the system. In addition to the casesof WTG positioning, two scenarios regarding how thedisplacement of conventional generation is achieved areinvestigated:
• Scenario 1 – Implies a reduction on the MVAof the conventional machine displaced by windintegration according to the penetration level.
• Scenario 2 –The MVA of the conventionalmachine displaced by wind integration remainsconstant and only its power level is adjustedaccording to wind penetration.
Scenario 1 is useful to study long-term impactof wind integration when installation of new windpower plants is coupled with the decommissioning ofconventional machines. Scenario 2 is meant to representsituations when wind power plants are producing highamounts of power1 and conventional generation is keptas reserve.
1Higher than the average possibly closer to their nominal ratingbecause of strong wind.
Page 3650
3. Impact of WTG on Inter-AreaOscillations
The impact that Type-3 WTG installation has on thetest system of Fig. 1 is presented in this section.
3.1. Inter-area Mode Variations withIncreased Wind Penetration
−0.6 −0.5 −0.4 −0.3 −0.2 −0.1
3.5
4
4.5
(a) Inter-area modeS.G. Red. MVA - Export:4 pu
Real Axis
Imaginary
Axis
Case ACase BCase C
−0.5 −0.4 −0.3 −0.2 −0.1
3.2
3.3
3.4
3.5
(b) Inter-area modeS.G. Constant MVA - Export:4 pu
Real Axis
Imaginary
Axis
−0.6 −0.5 −0.4 −0.33.6
3.8
4
4.2
4.4
4.6
(c) Inter-area modeS.G. Red. MVA - Export:0 pu
Real Axis
Imaginary
Axis
Case ACase BCase C
−0.5 −0.45 −0.4 −0.35 −0.3 −0.25
3.4
3.5
3.6
(d) Inter-area modeS.G. Constant MVA - Export:0 pu
Real Axis
Imaginary
Axis
−0.6 −0.5 −0.4 −0.3 −0.2 −0.1
3.5
4
4.5
(e) Inter-area modeS.G. Red. MVA - Export:-4 pu
Real Axis
Imaginary
Axis
Case ACase BCase C
−0.4 −0.3 −0.2 −0.1
3.2
3.3
3.4
3.5
(f) Inter-area modeS.G. Constant MVA - Export:-4 pu
Real Axis
Imaginary
Axis
Figure 2: Variations in the inter-area mode of the test system withincrements in wind penetration.
A study on the effect that increments of windpenetration has on the inter-area oscillation of the testsystem is presented in this section. The study is carriedout with variations of wind penetration from 0% to43% of the total power production. The three differentcases of positioning of wind integration along with the2 scenarios of displacement of conventional generationoutlined in Section 2.2 are considered. In addition, theanalysis is performed at three different power transferconditions: 400 MW (4 pu) export, no power exchange,and 400 MW (4 pu) import.
Fig. 2 shows the variations in the inter-area mode ofthe system for the 18 different configurations describedabove. The results in Figs. 2 (a),(c),(e) show themovement of the inter-area oscillation for Scenario 1where the MVA of the displaced conventional machine isrescaled. The results in Figs. 2 (b),(d),(f) correspond toScenario 2 of synchronous machine displacement. Thethree rows on Fig. 2 correspond to the result for thethree different power transfer conditions. The resultsof increasing wind penetration presented in Fig. 2 show
0.1 0.2 0.3 0.4
0.1
0.2
0.3
0.4
0.5
(a) KTEfd = ∂Te/∂Efd
S.G. Red. MVA - Export:4 pu
Wind Penetration
Case ACase BCase C
0.1 0.2 0.3 0.4
0
0.02
0.04
(b) KTEfd = ∂Te/∂Efd
S.G. Constant MVA - Export:4 pu
Wind Penetration
0.1 0.2 0.3 0.4
0.1
0.2
0.3
0.4
(c) KTEfd = ∂Te/∂Efd
S.G. Red. MVA - Export:0 pu
Wind Penetration
Case ACase BCase C
0.1 0.2 0.3 0.4
−0.01
0
0.01
0.02
0.03
(d) KTEfd = ∂Te/∂Efd
S.G. Constant MVA - Export:0 pu
Wind Penetration
0.1 0.2 0.3 0.4
0.1
0.2
0.3
0.4
0.5
(e) KTEfd = ∂Te/∂Efd
S.G. Red. MVA - Export:-4 pu
Wind Penetration
Case ACase BCase C
0.1 0.2 0.3 0.4
0
0.02
0.04
(f) KTEfd = ∂Te/∂Efd
S.G. Constant MVA - Export:-4 pu
Wind Penetration
Figure 3: Electrical modal torque of the system as affected by thereactive power current command of the WTG.
that:
• For the cases when installing WTGs causes areduction in the MVA rating of the displacedconventional machine (Figs. 2(a),(c),(e)), anincrease in wind penetration leads to an increasein both, synchronizing and damping torques.
• For cases A and B of wind integration positioningwith small penetration (green line in Figs. 2(a) andblue line in Figs. 2(c)) it can be noted that thedamping control is initially reduced before it isincreased. That is for smaller wind penetrationconditions the loading condition of the systemaffects the impact of wind integration on thedamping torque.
• The conditions presented in Figs. 2(b), (f),(cases of Scenario 1 for constant MVA rating inthe displaced conventional generator) show thatinstalling WTGs in the area that is importingpower reduces the value of the damping andsynchronizing torques of the inter-area mode ofthe system.
Fig. 3 shows the sensitivity KTEfd as a function ofincrements in wind penetration. This sensitivity isfound from the linearized model using KTEfd =∂Te/∂Efdcmd and a more detailed derivation can befound in [15]. The cases considered in this analysis
Page 3651
correspond to the same ones considered for the studyin Fig. 2. These results indicate that higher values ofKTEfd have a destabilizing effect on the damping torqueof the mode. They are also aligned with results inprevious work [4, 5]. As discussed in [15] the differencebetween the two conventional machine displacementscenarios can be attributed to differences in the inertiapresent on the system.
3.2. Inter-area Mode Variations with WTGConnecting Transmission Line
Hitherto, the installation of WTG in the systemis made through a substation transformer and atransmission line (TL) that connects it to Bus 6, 10 or8 for Cases A, B or C respectively. In this sectionthe effects of increasing the reactance of the TL thatconnects the WTG to the system are assessed. Thereactance was varied from 0 to 0.11 pu which isequivalent to a transmission line length from 0 to 110km. The loading condition for the analysis was an importof 400 MW in Area 1 from Area 2. Fig. 4 shows themovement of the inter-area oscillation of the system forall the cases and scenarios of Section 2.2. These resultscan be described as follows:
• For all the cases of wind positioning whenthe MVA rating of the displaced machine isreduced (Scenario 1) there is a decrease of thesynchronizing torque as the WTG reactance isincreased.
• The damping torque increases for Case A which isthe area that is importing power. For cases B andC there is a minor decrease in the damping torque.
• For Scenario 2 when the MVA rating of thedisplaced synchronous generator remains constantthere is a reduced effect on how the mode isaffected for Cases A and B with respect to thosecases in Scenario 1. However the trends are thesame, a reduction on the synchronizing torque forboth cases and an increase in the damping torquefor Case B and reduction of it for case A. For caseC the effect in Scenario 2 is similar to Scenario 1,which represents a considerable reduction in bothdamping and synchronizing torques.
4. WTG Damping Control Design
This section presents a systematic approach to designan inter-area oscillation damping controller for WTGs.The presented approach analyzes a set of signals todetermine the most suitable one to use as a feedbackinput for the controller. The considered signals are asfollows:
−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1
3.4
3.5
3.6
3.7
3.8
Inter-area mode
S.G. Reduced MVA
Real Axis
Imaginary
Axis
Case ACase BCase C
−0.3 −0.2 −0.1 0
3
3.1
3.2
3.3
3.4
3.5
Inter-area mode
S.G. Constant MVA
Real Axis
Imaginary
Axis
Case ACase BCase C
Figure 4: Inter-area mode variations with increases in the reactancethat connects the WTG to the system.
• Frequency at the point of interconnection of theWTG.
• Voltage magnitude at the point of interconnectionof the WTG.
• Magnitude of the current flowing from Area 1 toArea 2, measured on one of the lines connectingBuses 7 and 8.
• Active power flow from Area 1 to Area 2,measured on one of the lines connecting Buses 7and 8.
In combination to the feedback signal selection,this work evaluates the proper place to integrate thecontroller within the WTG to enhance its ability toinfluence the power oscillation. Three different WTGpoints of action considered are:
• Adding a signal Pordsig to Pord right before theoutput of the active power control of the WTG asseen in Fig. 5.
• Adding a signal Psetsig at the active power setpointcontrol of the WTG as observed in Fig. 5. It shouldbe noted that this action implies the WTG activepower output is curtailed or the WTG is spillingwind and has the ability to increase it’s activepower output.
• Including a signal QQsig inside the WTG reactivepower control as shown in Fig. 5.
The power system loading condition selected toperform the controller design is when 4 pu of realpower are being imported by Area 1 and the WTG isinstalled in Area 1 (case A). The WTG displacing halfof the conventional generation in the area but the MVArating of the substituted machine is retained. This casewas chosen because this is one where wind integrationcreates a destabilizing effect for the power oscillation ofthe system.
Page 3652
�������������
� ����
Σ
Σ
Σ
+
−
+
−
+
+
−
Wind powermodel
f(·) reference speed
Turbine/Generator Model
Pitch angle control
Pitch angle compensator
Torque Control
Active power
delay and limiter
×ordP
gω
wv
siggP
θ
ordP
setlfP
refω
gω
._
.Σ
ordsigP
tV
cmdpI
+
setsigP
siggP
Figure 5: Schematic diagram of the active power control of the WTGmodel.
4.1. General Concepts
The control approach taken in this paper requiresa linearized representation of the power system in thefollowing state-space form
x = Ax+Bzzu, y = Cxxx (3)
obtained at an equilibrium point which corresponds tothe power system loadflow.
Since different measured signals and points of actionof the controller are being considered different inputand ouput matrices are calculated to that end. Inparticular, three different input matrices BQQ, BPset,BPord are computed to consider the three differentpoints of connection of the controller mentioned earlier.Similarly, four output matrices, Cf , CV, CIl, CP areobtained to account for the different feedback signalselection. As such any combination of one input matrixBzz with any output matrix Cxx yields a different systemHxx,zz(s) to analyze. Note that any particular system isdescribed by 47 states out of which 17 correspond to theWTG.
Based on the close relationship between root-locusanalysis and phase compensator design presented in [27–30] for PSS tuning, this paper will use root-locusdiagrams for the controller design. In the proposedapproach, the angle of departure of the inter-areaoscillation is determined. Because the idea is to createan increase in damping torque, the proposed controllerwould require the inter-area mode to move towards theLHP as seen in Fig. 6.
The controller structure utilized in this work isdepicted in Fig. 7 and is similar to the structure ofPSSs included in conventional generation. Because thecontroller needs to be inactive for steady state it has awashout filter (derivative action). In addition, it containstwo lead-lag compensator stages to move the departureof the mode in the direction of increased damping torque.
σ
jω
Increase in
damping torque
Increase in
synchronizing
torque
depφDesired
Figure 6: Controller design objective: increase the damping torque ofthe Inter-Area Mode.
w
w
1
sT
sT+
3
4
1
1
sT
sT
+
+
1
2
1
1
sT
sT
+
+p
KΣ+ −ref
y
xx
y
xx
u
Figure 7: Proposed controller structure. A two-stage lead lagcompensator with a washout filter.
4.2. WTG Active and Reactive Power Controls
Fig. 5 shows a schematic of the active power controlof the Type-3 WTG [19] whose output is the activecurrent injection Ipcmd. Note that the active powercontrol is regulated by three individual PI controllers asfollows
Pitch Control: Gcont(s) = Kpp +Kip
s= 150 +
25
s(4)
Pitch Comp.: Gcomp(s) = Kpc +Kic
s= 3 +
30
s(5)
Torque Control: Gtorq(s) = Kptrq +Kitrq
s= 3 +
0.6
s(6)
1
1r
sT+
refV
regV 1
Nf
1v
pvK
sT+
ivK
s
1
1c
sT+Σ
− + +
+Σ
+ −
gQ
cmdQ
qik
s
vik
s
cmdfdE
tV
Σ Σ
QsigQ
+
cmdfdE&r
V&
cmdQ&
2s&
4s&
3s&
Figure 8: Schematic diagram of the reactive power control of the WTGmodel.
Fig. 8 illustrates the reactive power control of theType-3 WTG [19]. Note that for this study the reactivepower control of the WTG is set to control the voltage
Page 3653
magnitude at the bus the WTG is connected to. Hence,this voltage signal corresponds to Vreg. This functionis called WindCONTROL and is a simplified version ofthe supervisory reactive power control of the entire windfarm [19].
4.3. Control Design
The control approach previously described is used forall combinations of input-output signals. Fig. 9 showsdifferent root-locus plots of the test system Hxx,zz(s)for all 12 combinations of input/output signals. Theseplots correspond to the power system with a specific pairof input and output signals as determined by the Bzz
and Cxx matrices respectively. Because the correctionof the departure angle comes only from the two stagelead-lag compensator, these plots also include the actionof the washout filter. Columns in Fig. 9 determinethe measured (output) signal while its rows correspondto the place to locate the controller in the WTG. Thepresence of zeros near the inter-area mode make someof the input/output signal combinations not suitable forthe proposed controller. This situation however couldbe overcome by using multiple input signals to thecontroller [31] and robust control which are beyond thescope of this paper.
Out of the 12 possible controller combinationstwo controllers were selected. The first acts in the
reactive power control of the WTG and uses the currentmagnitude as measured signal GQQ,Il while the secondacts in the WTG active power setpoint using the busfrequency as feedback signal. The constants for thedesigned controllers are stated in Table 1. Fig. 10shows a root-locus plot for these two controllers. Theseplots shows that the angle of departure is effectivelynear 180° as intended and are used to select theappropriate proportional constant Kp. Fig. 11 shows thecorresponding Bode plots to the Root Loci in Fig. 10.The frequency range of interest is from 0.1 Hz to 1 Hzbecause it is where inter-area oscillations occur. TheGain Margins of the the GPset,f and GQQ,Il controllers,respectively, is determined as 27.08 and 19.96 dB.
Table 1: Designed Controllers Constants
Controller T1 [s] T2 [s] Kppupu
GQQ,Il 1.1358 0.0824 0.4GPset,f 5.6613 0.0165 18
This design was then evaluated when the WTG isconnected to the system through a transmission line (TL)of different lengths. When increasing the length of theTL both controllers (GPSet,f and GQQ,Il) become lesseffective. Because the connection between the WTGand the system becomes weaker it is also reasonable to
Figure 9: Root-loci for all possible combinations of input output signals.
Page 3654
-3 -2.5 -2 -1.5 -1 -0.5 0 0.50
2
4
6
(a)
-3 -2.5 -2 -1.5 -1 -0.5 0 0.50
2
4
6
(b)
Figure 10: Root-loci for the two selected controllers: (a) GQQ,Il, (b)GPset,f .
10-1
100
101
-80
-60
-40
-20
0
20
10-1
100
101
-200
0
200
(a)
10-1
100
101
-100
0
100
10-1
100
101
-600
-400
-200
0
200
(b)
Figure 11: Bode plots for the two selected controllers: (a) GQQ,Il, (b)GPset,f .
expect the controller to be less effective.Fig. 12 shows the zeros and the inter-area mode of
the system as the TL increases from 0 to 100 km forthe GPSet,f controller. For this same TL increase, theinter-area oscillation is slightly changed a result that isexpected because the TL only connects the WTG to thesystem and does not significantly alter the characteristicsof the inter-area tie line. By adjusting the controller timeconstants for optimal damping, the root-locus will resultin the inter-area mode moving to the same zero for all TLlengths. Fig. 12 shows the movement of the dominantzero as the TL length increases; it shows that this zeroapproaches the inter-area mode of the system.
-2 -1.5 -1 -0.5 0 0.50
2
4
6
(a)
-1 -0.5 0 0.50
2
4
6
(b)
Figure 12: Zeros and Inter area mode with increasing TL length with:(a) GQQ,Il, (b) GPset,f .
Similarly, Fig. 12b shows the zero and inter areamovement of the GQQ,Il controller. The poles of thesystem are the same as in the case of the GPSet,f
controller. Although the zeros of the system differ asimilar pattern emerges: The significant zero associatedwith the inter-area mode moves closer to the inter area
mode as the TL length is increased. This indicates thatboth controllers become less effective with TL increases.Note that this effect is the result of having a zeromoving towards the right hand plane and attracting theinter-area mode towards it for increases in the controllergain. Fig. 13b and Fig. 13a show the root-locus of theinter-area mode for each controller at 0, 50 and 100 kmTL length. These results show that the controllers are notable to significantly improve damping on the inter-areamode for the case of 100 km TL. In the 50km TL caseboth controllers are capable of damping the inter-areamode better than the 100 km case. However, the effectsof the controller and TL increases on the other modesof the system have to be considered. Fig. 14 showsthe complete root locus for the case with a 100 km TL.Fig. 15 shows the corresponding Bode plots with thesame frequency range of interest as in Fig. 11. Fromthe bode plots and the Gain Margin can be determinedas 21.67 dB and 25.29 dB for the GPset,f and GQQ,Il
controller respectively. To take into account all themodes of the system as well as important nonlinearphenomena, Section 5.2 presents time domain simulationresults of the implemented controllers and analyzes theirperformance.
-2 -1.5 -1 -0.5 0 0.50
2
4
6
(a)
-2 -1.5 -1 -0.5 0 0.50
2
4
6
(b)
Figure 13: Root-loci for Controller design at different length TL for:(a) GQQ,Il, (b) GPset,f .
5. Simulations Results
This section presents time simulations results of theinter-area oscillation damping controllers of Section 4.
The test-system in Fig. 1 is selected to performthis analysis which is based on the following event: athree-phase short circuit to ground that lasts 0.1 s isapplied to Bus 7 without changing the topology of thesystem once it is cleared.
The following two cases were considered whenconnecting the WTGs:
• The WTG is directly connected to the systemusing a step up transformer with X = 0.15puin the machine base. This corresponds to a HighVoltage connection of the WTG.
• The WTG is connected to the system througha 100 km transmission line (in addition to a
Page 3655
-3 -2.5 -2 -1.5 -1 -0.5 0 0.50
2
4
6
(a)
-3 -2.5 -2 -1.5 -1 -0.5 0 0.50
2
4
6
(b)
-3 -2.5 -2 -1.5 -1 -0.5 0 0.50
2
4
6
(c)
-3 -2.5 -2 -1.5 -1 -0.5 0 0.50
2
4
6
(d)
Figure 14: Root-loci for the two selected controllers with a long TLconnecting the WTG to the system.
10-1
100
101
-50
0
50
10-1
100
101
-300
-200
-100
0
100
(a)
10-1
100
101
-100
-50
0
50
10-1
100
101
-300
-200
-100
0
100
(b)
Figure 15: Bode plots for the two selected controllers with a long TLconnecting the WTG to the system: (a) GQQ,Il, (b) GPset,f .
similar transformer as in the previous case). Thiscorresponds to a WTG located in a area with aweak grid connection.
5.1. High Voltage Connection
Four cases were considered: (i) a Type-3 WTGis installed in Area 1 producing around half of thetotal power in the area with the displaced conventionalgeneration retaining the same MVA rating, (ii) similar tocase (i) but including the GPset,f controller of Section 4to the WTG, (iii) similar to case (i) but including theGQQ,Il controller of Section 4 to the WTG and (iv) ano wind case for comparison.
Fig. 16 shows the results of the system for the cases(i)-(iv) just presented when Area 1 is importing 4 pu ofreal power as the loading condition of the system. Theno wind case in these results show that the system has aninter-area mode that is excited by the applied fault anddamped by the PSSs installed in conventional generatorsG2 and G4. They show that integrating wind in the areathat is importing power (Area 1, Case A) reduces thedamping of the power swing. They also show that when
including any of the controllers (GPset,f , GQQ,Il) theinter-area oscillation is effectively damped as intended.Results in Fig. 16 (c) show that the controller GPset,f
makes the pitch angle responsive to the power swings.This result is expected because this controller is placedin the active power control loop of the WTG that is alsoresponsible for managing the blade pitch. However itshould be noted that this controller would be completelyeffective when the pitch angle has room for action (i.e.,when the WTG is spilling some power). On the otherhand, the controller GQQ,Il does not affect the pitchangle, it mainly affects the reactive power injection ofthe WTG which is reflected in the voltage behavior atBus 6 as seen in Fig. 16 (b).
0 2 4 6 8 10-198
-196
-194
-192
-190
-188
-186
(a)
0 2 4 6 8 10
2
3
4
5
6
(b)
0 2 4 6 8 10
1.01
1.015
1.02
1.025
1.03
1.035
1.04
(c)
0 2 4 6 8 101.02
1.025
1.03
1.035
1.04
(d)
Figure 16: Plots for the case 4 pu of power is imported to Area 1. Thefollowing signals are presented for the different WTG control cases:(a) Power flow in line connecting Bus 7 and 8; (b) WTG pitch angle;(c) voltage at Bus 6; (d) voltage at Bus 10.
In addition, the two controllers were tested in adifferent power loading condition when Area 1 isexporting about 4 pu to Area 2 and the results arepresented in Fig. 17. These results show that bothcontrollers are again effective in damping the inter-areaoscillation2. Note that for this case of power transferwind integration in Area 1 also increases the dampingof the power swing, a situation expected from the resultsoutlined in Section 3.
Table 2 shows a summary of the inter-area modefor the different cases of wind integration and controllerimplementation in combination with the two powertransfer conditions for a WTG with high Voltageconnection.
5.2. Low Voltage Connection
The same four cases as in the high voltage connectioncase were considered in the low voltage connection case
2The gain of the controller for GQQ,Il has to be multiplied by -1.
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0 2 4 6 8 10
200
205
210
215
220
225
(a)
0 2 4 6 8 10
1
2
3
4
5
6
(b)
0 2 4 6 8 10
1.025
1.03
1.035
1.04
1.045
(c)
0 2 4 6 8 10
1.005
1.01
1.015
1.02
1.025
(d)
Figure 17: Plots for the case 4 pu of power is imported to Area 2. Thefollowing signals are presented for the different WTG control cases:(a) Power flow in line connecting Bus 7 and 8; (b) WTG pitch angle;(c) voltage at Bus 6; (d) voltage at Bus 10.
Table 2: Inter-area mode with controllers
Case P12 = −4 pu P12 = 4 pu
No wind -0.11 + 3.39j -0.13 + 3.39j25% Wind (Case A) -0.03 + 3.27j -0.42 + 3.39j
25% W. (C. A) – GPset,f -0.59 + 3.36j -0.65 + 3.61i25% W. (C. A) – GQQ,Il -0.34 + 3.28j -1.24 + 3.00i
where the TL length is set to 100 km. Because thedifference is the connection of the WTG, case (iv) whichdoes not contain a WTG yields exactly the same resultsas in the previous section.
Fig. 18 shows the results of the system for cases(i)-(iv) when Area 1 is importing 4 pu of real power.Fig. 18 (c) shows that integrating wind in the areathat is importing power (Area 1, Case A) reduces thedamping of the power swing, even if the WTG isconnected through a long TL. It also shows that anyof the controllers (GPset,f , GQQ,Il) designed for a lowvoltage connection improves the inter-area oscillationdamping to some degree.
Table 3 shows a summary of the inter-area mode forthe different cases of controller implementation for aWTG connected to the system through a 100km TL.
6. Conclusions and Future Work
This paper analyses the impact that integrating windhas on the inter-area oscillation of a test system. Itpresents a comprehensive study as to how this mode isaffected by: (i) increased wind penetration for differentWTG locations and (ii) increases in the reactance of thetransmission line connecting the WTG to the system.
0 2 4 6 8 10-198
-196
-194
-192
-190
-188
-186
(a)
0 2 4 6 8 10
3.5
4
4.5
5
(b)
0 2 4 6 8 10
1
1.01
1.02
1.03
(c)
0 2 4 6 8 10
1.02
1.025
1.03
1.035
1.04
(d)
Figure 18: Plots for the case 4 pu of power is imported to Area 1 whenthe TL length is 100 km. The following signals are presented for thedifferent WTG control cases: (a) Power flow in line connecting Bus 7and 8; (b) WTG pitch angle; (c) voltage at Bus 6; (d) voltage at Bus 10.
Table 3: Inter-area mode with controllers for the system with WTGconnected through 100km TL
Case P12 = 4 pu
No wind -0.1133 + 3.33868j25% Wind (Case A) -0.0958 + 3.2159j
25% W. (C. A) – GPset,f -0.1160 + 3.2545j25% W. (C. A) – GQQ,Il -0.3651 + 3.2878j
The paper shows that even though integrating windintegration in general increases the damping of theinter-area mode, it could potentially destabilize it whenwind is installed in the area that imports power.
The paper then introduces a root-locus approachto design a two-stage lead lag controller for WTG todamp the inter-area oscillation of the system. Usingthis approach, two different controllers one actingin the active power control and the other in thereactive power structure of the WTG are designed andimplemented. The paper then analyzes the effect on thecontroller performance of increases in the reactance ofthe transmission line that connects the WTG to the grid.Time domain simulation is used to test the performanceof these controllers. These simulations show that windcan be effectively used to enhance the damping of theinter-area oscillations in power systems.
Future work will include designing a controller usingmore advanced multi-variable control techniques to dealwith the zeros that appear near the inter-area mode whenonly SISO controllers are considered.
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