Embed Size (px)
Citation preview
Aalborg Universitet
Fault Modeling of Grid-forming Converters using Dynamic Phasor Theory
Zhang, Qi; Liu, Dong; Chen, Zhe
Published in:2021 IEEE IAS Industrial and Commercial Power System Asia
DOI (link to publication from Publisher):10.1109/ICPSAsia52756.2021.9621633
Creative Commons LicenseCC BY 4.0
Publication date:2021
Document VersionAccepted author manuscript, peer reviewed version
Link to publication from Aalborg University
Citation for published version (APA):Zhang, Q., Liu, D., & Chen, Z. (2021). Fault Modeling of Grid-forming Converters using Dynamic Phasor Theory.In 2021 IEEE IAS Industrial and Commercial Power System Asia (pp. 1011-1016). IEEE.https://doi.org/10.1109/ICPSAsia52756.2021.9621633
General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
- Users may download and print one copy of any publication from the public portal for the purpose of private study or research. - You may not further distribute the material or use it for any profit-making activity or commercial gain - You may freely distribute the URL identifying the publication in the public portal -
Take down policyIf you believe that this document breaches copyright please contact us at [email protected] providing details, and we will remove access tothe work immediately and investigate your claim.
Downloaded from vbn.aau.dk on: February 04, 2022
Fault Modeling of Grid-forming Converters usingDynamic Phasor Theory
Qi ZhangDepartment of Energy Technology
Aalborg UniversityAalborg, Denmark
Dong LiuDepartment of Energy Technology
Aalborg UniversityAalborg, Denmark
Zhe ChenDepartment of Energy Technology
Aalborg UniversityAalborg, Denmark
Abstract—It has been pointed out in recent years that grid-following and grid-supporting converters are harmful to thestability of the power system, and grid-forming converters (GFM)are becoming to be the most promising grid-connected convertersfor the integration of renewable energy. Nevertheless, the devel-opment of GFM converters challenges the fault analysis of thepower system because GFM converters have a totally differentfault response with that of the grid-supporting, grid-followingconverter, and the synchronous generator. The fault modelingof GFM converters is a foundation to overcome this issue, soit should be investigated firstly. However, this topic is rarelydiscussed in the previous literature. In order to fill this researchgap, this paper proposes a fault modelling method for GFMconverters based on the dynamic phasor theory. The dynamicphasor model of GFM converters can provide an effectiveinterface to the power system analysis. Thus, the proposed modelis outstanding because of its ability to analyze the interactionbetween converters and the power system in the fault analysis.To verify the correctness of the proposed model, a 12 MVAgrid-forming converter is established in MATLAB/Simulink. Thesimulation results show that the proposed model can almostperfectly handle the fault analysis of the grid-forming converter.
Index Terms—Fault modeling, grid-forming converter, renew-able energy, dynamic phasor theory.
I. INTRODUCTION
Grid-connected converters as the interface equipment ofrenewable energy generations push the modern power sys-tem into power electronics dominated systems (PEDS) [1].In comparison with traditional synchronous generators, thedisparate fault response of grid-connected converters resultsin new fault conditions to the operation and protection ofPEDS [2]. Thus, it brings a new challenge to the fault analysistheory and the protection system design because the traditionalfault analysis for synchronous generators is not applicable forthat of grid-connected converters. Therefore, the traditionalfault analysis theory should be further expanded to handlethe challenge caused by new fault conditions caused by grid-connected converters.
Generally, based on the control strategies, grid-connectedconverters can be divided into three classes: grid-forming(GFM), grid-supporting (GST), and grid-following (GFL) con-verters. For GST and GFL converters, they work under a
This Project is funded by China Scholarship Council and the Departmentof Energy Technology, Aalborg University.
stable voltage provided by the power grid and are normallycontrolled as a PQ node in the power system, so the interactionbetween these converters and the grid is weak. In contrast,GFM converters are designed to support the voltage of thegrid, which means that the interaction between converters andthe grid are strong. Consequently, GFL and GST convertersare widely used in the power system at the beginning ofdevelopment of renewable energy integration. However, inrecent years, some studies has pointed out that, the GST andGFL converter are harmful to the stability of the power system,especially for the weak grid [1], [2], [6]. Under this content,the GFM converter is becoming the most promising candidatefor the renewable energy integration of power system. Forthe widespread deployment of the GFM converter, it is verycritical to grasp the fault behavior, fault response, and the faultcharacteristics.
As the foundation of the fault analysis theory, fault modelingof grid elements aims to provide simple and correct modelsto analyze the fault response of grid elements. Comparedwith traditional synchronous generators, fault responses ofgrid-connected converters are more complicated because ofthe fast-response control and the deficiency in over-currentcapability [1], [3], which makes the development of the faultanalysis model of GFL and GST more sophisticated. Becauseof the widespread usage in power system, the fault analysismodel of GFL and GST converters have been discussed andproposed in previous studies. However, the fault modeling ofGFM converters is rarely discussed, and the fault analysismodel of GFM converters is becoming a critical topic withthe increasing amount of GFM converters connected to thegrid.
In order to fill the research gap, this paper proposes thefault analysis model of GFM by using the dynamic phasors.Firstly, the V/F droop control strategy of GFM converters isoverviewed. Secondly, the state-space dynamic phasor modelof GFM converters is derived, in which the time-domain state-space model is established firstly and then the time-domainmodel is transformed into the dynamic phasor model.
Gio
PCC
ZgZlL
C v
i
V/F droop vio
V*ω*P* Q*
abc/dq
Vref ωo
Vdref Vqref
voltagecontroller
vd
vq
id*
iq*current
controller
abc/dq
id iq
io ωo
dq/abc
vcd
vcq
SVPWMmodulation
vcabc
PWM
sign
al
Fig. 1: The typical topology and the V/F control structure ofthe grid-forming converter.
powercalculation
vdvqiodioq
s+ωc
ωc
s+ωc
ωc
P
Q
ω*-mp(P-P*)
V*-mq(Q-Q*)
ωo
Vo
Fig. 2: The block diagram of the V/F droop controller.
II. FAULT MODELING OF GRID-FORMING CONVERTERS
A. Overview of the GFM and its control structure
The typical topology and general V/F droop control struc-ture of GFM are shown in Fig. 1. The DC source andtransformer of the grid-forming converter are assumed as idealones because the impact of them on the fault analysis can beignored. Typically, the control system contains three parts: V/Fdroop based power controller, the voltage controller, and thecurrent controller. The current controller controls the three-phase current flowing through the inductor labeled as i in Fig.1, and the voltage controller is responsible for controlling theoutput voltage of GFM on the connection-port labeled as v.The output active and reactive power of GFM are controlledby the V/F droop controller and the reference input of thevoltage controller is generated by the V/F droop controller.The block diagram of the V/F droop controller is shown inFig. 2. Based on the structure of the V/F droop controller, theamplitude of the reference voltage Vo and the power angle φof GFM can be expressed as (1).
Vo = V ∗ −mq(Q−Q∗)
φ =
∫2π(ω∗ −mp(P − P ∗))dt
(1)
where: mp,mq are the droop coefficient of the droop con-troller.
B. Fault modeling of the GFM
The block diagram of the voltage and current controlleris shown in Fig. 3. Take outputs of four PI controllers asstate variables of the voltage and current controller, which are
ωL
PI
ωL
PI
ωC
PI
ωC
PI
iod
ioq
iq
id
idref
iqref
vd
vq
vcd
vcq
vd
vq
vdref
vqref
xvd
xvq
xid
xiq
Voltage controller
kcp,kci
kcp,kci
kvp,kvi
kvp,kvi
Current controller
Fig. 3: The block diagram of the voltage and current controller.Note: the state-variables are labeled by red fond with arectangle background, and the parameters of PI controller arelabeled by red font.
represented by xvd, xvq, xid, xiq , and labeled by red font witha rectangle background in Fig. 3. Subscripts v, i denote thestates in the voltage and current controller, and subscripts d, qrepresent DQ components.
xvdq = [xvd, xvq]
T
xidq = [xid, xiq]T (2)
Define the input and output of the voltage controller as:
vdqref = [vdref , vqref ]T
vdq = [vd, vq]T
idq = [id, iq]T
iodq = [iod, ioq]T
idqref = [idref , iqref ]T
(3)
Based on the structure of the voltage controller, the state-space model of the voltage controller can be obtained as (4).By the similar way, the model of the current controller can beobtained as (5).
xvdq = B1vdqref +B2vdq
idqref = C1xvdq +D1vdqref +D2vdq +D3iodq(4)
xidq = B1idqref +B2idq
vcdq = C2xidq +D4idqref +D5idq +D3vdq
(5)
where:
B1 = diag(1, 1),B2 = −diag(1, 1)C1 = diag(kvi, kvi),C2 = diag(kci, kci)
D1 = diag(kvp, kvp),D3 = diag(1, 1), D4 = diag(kcp, kcp)
D2 =
[−Kvp −ωCωC −Kvp
],D5 =
[−Kcp −ωLωL −Kcp
](6)
ωL
ωL
ωC
ωC
vcd
vq
xLd
xLq
Ls+R1
Ls+R1
Cs1
Cs1
xCd
xCq
vcq
vd
id
iq
iod
ioq
vd
vq
Fig. 4: The block diagram of the LC power filter.Note: the state-variables are labeled by red fond with arectangle background.
Combine (4) and (5), the time-domain state-space model ofthe controller can be obtained, which is shown in (7).
p
[xvdq
xidq
]= Actr
[xvdq
xidq
]+Bctr
vdqref
vdq
iodqidq
vcdq = Cctr
[xvdq
xidq
]+Dctr
vdqref
vdq
iodqidq
(7)
Actr =
[0 0C1 0
],Bctr =
[B1 B2 0 0D1 D2 B1 B2
]Cctr = [D4C1] ,Dctr = [D1D4, D3 + D2D4, D4, D5]
where p is the differential operator. The block diagram of themodel of the power filter is shown in Fig. 4. Define states vari-ables of the inductor and the capacitor as xLd, xLq, xCd, xCq ,which are labeled in Fig. 4, and define the output of the LCpower filter as vdq, idq:
xLdq = [xLd, xLq]
T
xCdq = [xCd, xCq]T
vdq = [vd, vq]T
idq = [id, iq]T
Based on the voltage-current relationship of inductors andcapacitors, the time-domain model of the inductor and capac-itor can be obtained as shown in (8) and (9).
xLdq = AL1xLdq +BL1vcdq +BL2vdq
idq = CL1xLdq
(8)
xCdq = AC1xCdq +BC1idq +BC2iodq
vdq = CC1xCdq
(9)
where:
AL1 =
−RL ω
−ω −RL
,AC1 =
[0 ω−ω 0
]BL1 = diag(1, 1),BL2 = −diag(1, 1)BC1 = diag(1, 1),BC2 = −diag(1, 1)
CL1 =
1
L0
01
L
,CC1 =
1
C0
01
C
Combine (8) and (9), the time-domain state-space model of
the power filter can be obtained, which can be expressed as(10).
p
[xLdq
xCdq
]= Aplt
[xLdq
xCdq
]+Bplt
[vcdq
iodq
][
idqvdq
]= Cplt
[xLdq
xCdq
] (10)
where:
Aplt =
[AL1 CC1
CL1 AC1
],Bplt =
[BL1 00 BC2
]Cplt =
[CL1 00 CC1
]
According to the dynamic phasor theory [13], the dynamicphasor model of one three-phase voltage or current variablehas a relationship with the DQ components, which can beexpressed as (11).
xph =1
2(xd + jxq)e
−jπ2 (11)
where xph is the dynamic phasor model of a three-phasevoltage or current, and xd, xq are their DQ components.
Combine (7) with (10), the time-domain state-space modelof GFM can be obtained, and then the model can be trans-formed into the dynamic phasor model of GFM, based on therelationship defined as (11). The dynamic phasor model ofGFM is expressed as (12).
p
〈xv〉1〈xi〉1〈xL〉1〈xC〉1
= Aph
〈xv〉1〈xi〉1〈xL〉1〈xC〉1
+Bph
[〈Vref 〉1〈io〉1
]
[〈v〉1〈i〉1
]= Cph
〈xv〉1〈xi〉1〈xL〉1〈xC〉1
(12)
Gioabc
voabc
Z1 Z2
GridLoad
Fig. 5: The structure of the simulated test system.
TABLE I: Parameters of simulation model
Parameters Values
Grid voltage 25 kVZ1 (positive sequence) 0.1273 + j2.9333 Ω
Z1 (negative sequence) 3.864 + j12.964 Ω
Z2 (positive sequence) 0.6365 + j14.6665 Ω
Z2 (negative sequence) 19.32 + j64.820 Ω
Load 6 MWRated Power of GFM 12 MVAVoltage of DC source 10 kV
System frequency 50 HzResistance of the power filter 60 mΩ
Inductance of the power filter 4.2 mHCapacitance of the filter 220 uF
Cutoff frequency of current controller 1 kHz
where: 〈xv〉1 , 〈xi〉1 , 〈xL〉1 , 〈xC〉1 , 〈Vref 〉1 , 〈io〉1 , 〈v〉1 , 〈i〉1are transformed from xvdq, xidq, xLdq, xLdq, vdqref , iodq ,vdq, idq respectively, based on (11). And:
Aph =
0 0 0 − 1
C
kvi 0 − 1
L−kvpC
+ jω
kcpkvi kci −kcp +R
L−kcpkvp
C+ jkcpω
0 01
L−jω
Bph =
1 0kvp 1
kcpkvp kcp0 −1
,Cph =
0 0 01
C
0 01
L0
The voltage frequency droop controller endows the GFM
converter with a grid-supporting function. The amplitude andpower angle generated by the V/F droop controller give theGFM converter the reference to control the output active andreactive power. Thus, compared with the slack bus, the powerphase angle of the GFM converter is φ, and then the outputvoltage voph and current ioph of the GFM converter can beexpressed as (13).
voph = 〈v〉1 ejφ
ioph = 〈io〉1 ejφ
(13)
III. SIMULATION VERIFICATION
In order to verify the correctness of the proposed model, a12 MVA GFM converter is established in MATLAB/Simulink.The structure of the test system in simulation is shown inFig. 5. The converter is connected to an infinity power system
1 1.05 1.1 1.15Time (s)
-1.5
-1
-0.5
0
0.5
1
1.5
Vol
tage
(p.u
.)
The output voltage of the GFM converter
1 1.05 1.1 1.15Time (s)
-6
-4
-2
0
2
4
6
Cur
rent
(p.u
.)
The output current of the GFM converter
simulation calculation
simulation calculation
Fig. 6: The comparison result between the simulation andcalculation when the three-phase to ground fault occurs.
through two transmission lines which are presented by Z1, Z2.In the simulation, the π-network equivalent electric circuitmodel is used for the presentation of transmission lines. Thetopology and the control system of the GFM converter areshown in Fig. 1. The average model of the three-phase H-bridge in the GFM converter is used in the simulation, sothe harmonics caused by the switching action are ignored.The detailed parameters of the simulation system are listed inTable. I. All measured voltages and currents in the simulationare per-unit based, and the base value of voltage and powerare 25 kV and 12 MVA respectively.
The four normal kinds of fault including the three-phaseto ground fault, the two-phase to ground fault, the two-phaseshort fault, and the single-phase to ground fault are analyzedby simulation and the proposed model, and the related resultof the analysis are shown in Figs. 6 - 9. The output voltage andcurrent of the GFM converter are recorded in the simulation,and they are also calculated by using the proposed model.For comparison, the simulation results are shown by the solidline, and the results calculated by the proposed model arehighlighted by the dashed line in Figs. 6 - 9.
In all cases, the fault occurs at 1s. Before the fault oc-currence, the converter works under normal conditions, inwhich the output voltage of the GFM converter is controlledto 1 p.u. and it injects rated power to the grid. After thefaults, because of the voltage controller, the output voltageof the GFM converter only has a small disturbance but theoutput current increases seriously. Obviously, in all cases,the calculated results are almost perfectly consistent withthe simulation results, which verifies the correctness of the
1 1.05 1.1 1.15Time (s)
-1.5
-1
-0.5
0
0.5
1
1.5
Vol
tage
(p.u
.)
The output voltage of the GFM converter
1 1.05 1.1 1.15Time (s)
-4
-2
0
2
4
Cur
rent
(p.u
.)
The output current of the GFM converter
simulation calculation
simulation calculation
Fig. 7: The comparison result between the simulation andcalculation when the two phase (phase B and C) to groundfault occurs.
1 1.05 1.1 1.15Time (s)
-1.5
-1
-0.5
0
0.5
1
1.5
Vol
tage
(p.u
.)
The output voltage of the GFM converter
1 1.05 1.1 1.15Time (s)
-4-3-2-101234
Cur
rent
(p.u
.)
The output current of the GFM converter
simulation calculation
simulation calculation
Fig. 8: The comparison result between the simulation andcalculation when the two phase (phase B and C) short faultoccurs.
proposed model.
1 1.05 1.1 1.15Time (s)
-1.5
-1
-0.5
0
0.5
1
1.5
Vol
tage
(p.u
.)
The output voltage of the GFM converter
1 1.05 1.1 1.15Time (s)
-2
-1
0
1
2
Cur
rent
(p.u
.)
The output current of the GFM converter
simulation calculation
simulation calculation
Fig. 9: The comparison result between the simulation andcalculation when the single phase (phase A) to ground faultoccurs.
IV. CONCLUSION
The fault response of GFM converters is different with thatof the synchronous generator and other types of grid-connectedconverters. Thus, a new fault analysis model is required forthe GFM converter. However, there is very limited researchon it. In order to fill the research gap, this paper proposes afault analysis model for the droop-controlled GFM converterbased on the dynamic phasor theory. The proposed modelhas a major advantage that the interaction between the gridand converters can be analyzed simply due to the dynamicphasor theory. Especially for the fault analysis of the large-scale power system, such advantage of the proposed modelis more obvious. The simulation result in MATLAB/Simulinkverify the correctness of the proposed model.
In this paper, the low voltage ride through and the currentlimitation of the GFM converter are not considered in theproposed model, which will be further studied in our futurework.
REFERENCES
[1] “Impact of Inverter Based Generation on Bulk Power System Dynamicsand Short-Circuit Performance,” IEEE PES Industry Technical Sup-port Task Force, PES-TR68, 2018. [online]. https://resourcecenter.ieee-pes.org/publications/technical-reports/PES TR 7-18 0068.html.
[2] G. Kou, L. Chen, P. VanSant, F. Velez-Cedeno and Y. Liu, ”FaultCharacteristics of Distributed Solar Generation,” in IEEE Transactionson Power Delivery, vol. 35, no. 2, pp. 1062-1064, April 2020, doi:10.1109/TPWRD.2019.2907462.
[3] B. Kroposki et al., “Achieving a 100% Renewable Grid: Operating Elec-tric Power Systems with Extremely High Levels of Variable RenewableEnergy,” in IEEE Power and Energy Magazine, vol. 15, no. 2, pp. 61-73,March-April 2017, doi: 10.1109/MPE.2016.2637122.
[4] J. Rocabert, A. Luna, F. Blaabjerg and P. Rodriguez, “Controlof Power Converters in AC Microgrids,” in IEEE Transactions onPower Electronics, vol. 27, no. 11, pp. 4734-4749, Nov. 2012, doi:10.1109/TPEL.2012.2199334.
[5] D. Pattabiraman, R. H. Lasseter, and T. M. Jahns, “Comparisonof Grid Following and Grid Forming Control for a High InverterPenetration Power System,” in 2018 IEEE Power and Energy So-ciety General Meeting (PESGM), 5-10 Aug. 2018, pp. 1-5, doi:10.1109/PESGM.2018.8586162.
[6] I. Kim, “Short-Circuit Analysis Models for Unbalanced Inverter-BasedDistributed Generation Sources and Loads,” in IEEE Transactionson Power Systems, vol. 34, no. 5, pp. 3515-3526, Sept. 2019, doi:10.1109/TPWRS.2019.2903552.
[7] M. A. Azzouz and A. Hooshyar, ”Dual Current Control of Inverter-Interfaced Renewable Energy Sources for Precise Phase Selection,” inIEEE Transactions on Smart Grid, vol. 10, no. 5, pp. 5092-5102, Sept.2019, doi: 10.1109/TSG.2018.2875422.
[8] T. Kauffmann et al., ”Short-Circuit Model for Type-IV Wind TurbineGenerators With Decoupled Sequence Control,” in IEEE Transactionson Power Delivery, vol. 34, no. 5, pp. 1998-2007, Oct. 2019, doi:10.1109/TPWRD.2019.2908686.
[9] W. Du et al., ”Modeling of Grid-Forming and Grid-Following Invertersfor Dynamic Simulation of Large-Scale Distribution Systems,” in IEEETransactions on Power Delivery, doi: 10.1109/TPWRD.2020.3018647.
[10] M. E. Elkhatib, W. Du, and R. H. Lasseter, ”Evaluation of In-verterbased Grid Frequency Support using Frequency-Watt and Grid-Forming PV Inverters,” in 2018 IEEE Power and Energy SocietyGeneral Meeting (PESGM), 5-10 Aug. 2018 2018, pp. 1-5, doi:10.1109/PESGM.2018.8585958.
[11] B. J. Pierre et al., ”Bulk Power System Dynamics with Varying Levelsof Synchronous Generators and Grid-Forming Power Inverters,” in the46th IEEE Photovoltaic Specialists Conference, Chicago, Illinois, USA,2019.
[12] G. Denis, T. Prevost, M. S. Debry, F. Xavier, X. Guillaud, and A.Menze, ”The Migrate project: the challenges of operating a transmis-sion grid with only inverter-based generation. A grid-forming con-trol improvement with transient current-limiting control,” IET Re-newable Power Generation, vol. 12, no. 5, pp. 523-529, 2018, doi:10.1049/ietrpg.2017.0369.
[13] S. R. Sanders, J. M. Noworolski, X. Z. Liu and G. C. Verghese,”Generalized averaging method for power conversion circuits,” in IEEETransactions on Power Electronics, vol. 6, no. 2, pp. 251-259, April1991, doi: 10.1109/63.76811
