Electromechanical Transient Modeling of ModularMultilevel Converter based HVDC NetworkShuyao Wang

GEIRI North AmericaSan Jose, CA, USA

The University of TennesseeKnoxville, TN, USAswang67@vols.utk.edu

Xiaoying ZhaoGEIRI North AmericaSan Jose, CA, USA

xiaoying.zhao@geirina.net

Feng XueNARI Group Corporation

Nanjing, Chinaxue-feng@sgepri.sgcc.com.cn

Wei LiNARI Group Corporation

Nanjing, Chinaliwei10@sgepri.sgcc.com.cn

Huimin PengNARI Group Corporation

Nanjing, Chinapenghuimin@sgepri.sgcc.com.cn

Di ShiGEIRI North AmericaSan Jose, CA, USA

di.shi@geirina.net

Siqi WangGEIRI North AmericaSan Jose, CA, USA

siqi.wang@geirina.net

Zhiwei WangGEIRI North AmericaSan Jose, CA, USA

zhiwei.wang@geirina.net

Abstract—The electromechanical model of modular multilevelconverter (MMC) based high voltage dc (HVDC) transmissionnetwork in transient stability (TS) simulator is proposed inthis paper based on the MMC average arm model and thesubmodule (SM) equivalent capacitance approach. The accuracyof the TS model is verified by comparing the simulation resultswith that of the PSCAD/EMTDC model subject to different gridcontingencies, including the controller reference step change, theremote three-phase ground fault and the close three-phase groundfault.

Index Terms—electromechanical modeling, DSAtool, MMC-HVDC, PSCAD/EMTDC, transient stability

I. INTRODUCTION

The high voltage dc (HVDC) transmission system has beenregarded as a highly efficient alternative for bulk transmissionof electrical power over a long distance. Among which thepower electronic (PE) based HVDC configuration, such as thevoltage source converter (VSC) based HVDC, has been widelyaccepted due to its distinguishing characteristics, e.g., flexiblecontrol of power flow direction, less reactive power injectionto the grid, and black start capability [1]–[4]. In recent years,the number of modular multilevel converter (MMC) basedHVDC projects has been increasing worldwide considering itsadvantages over VSC-HVDC, including high scalability, lowerswitching loss, smaller harmonic filtering burden, etc. Theintegration of MMC-HVDC into the conventional ac networkwill affect transient stability (TS) of the system, and thereforeit is of great necessity to investigate the dynamic performanceof such systems.

The MMC-HVDC system, as many other PE based facili-ties, has been modeled and analyzed in electromagnetic tran-sient (EMT) simulators, such as PSCAD/EMTDC. EMT sim-ulation models can accurately specify fast switching dynamics

This work is funded by SGCC Science and Technology Program andNARI Group under Project Research on Electromagnetic Transient SimulationTechnology for Large-scale MMC-HVDC Systems.

of PE devices and the high control bandwidth of correspondingregulators [5], [6] with a short simulation time step, which istypically selected as 0.05 ms. However, it is computationallyprohibited to study the large-scale transmission network withMMC-HVDC systems in the EMT simulator for a considerableperiod of time.

Compared with the EMT simulation, the TS simulationfocuses on the electromechanical transients and oscillationsbetween 0.1 ∼ 3 Hz neglecting system unbalance, and thesimulation time step is usually selected as around 5 ms.Therefore, a TS simulator can process a large-scale networkwith thousands of buses in a relatively short time. The com-monly used commercial positive sequence TS simulation toolsinclude GE PSLF, Simens PIT PSS/E, PowerWorld Simulator,and PowerTech Labs TSAT (Transient Security AssessmentTool) [7].

Therefore, it is of importance to develop models of MMC-HVDC systems for transient stability studies in the context ofthe large-scale power network, which emphasizes the relativelyslow dynamics of PE components. The electromechanicalmodels of PE based power facilities have been investigated inexisting studies [8]–[11]. However, the MMC-HVDC modelapplied in commercial TS simulators has not been sufficientlystudied to the best of the authors’ knowledge. Specifically, theTS model created in PowerTech Labs TSAT is not available.

In this paper, the point-to-point MMC-HVDC electrome-chanical model is developed in TSAT. The proposed MMC-HVDC model is derived based on the MMC average modelwhich can reflect the electromechanical transients of theMMC-HVDC. Meanwhile, the MMC-HVDC model specifiesthe vector control which includes the power regulation and acgrid voltage support. The TSAT in DSATools is selected asthe TS simulator since the MMC-HVDC model can be easilycustomized by the User-Defined Model (UDM) editor includedin the TSAT standard package [12].

The paper is organized as follows: Part II introduces the

MMC circuit topology and the general modeling approach.Part III explains the realization of the MMC-HVDC modelin the TS simulator, including the MMC average model, thecontroller model, and the model representation in the phasordomain. Part IV presents the simulation verification of theMMC-HVDC electromechanical model considering varioustesting conditions, and conclusions are drawn in section V.

II. MMC-HVDC MODELING CONSIDERINGELECTROMECHANICAL TRANSIENTS

As illustrated in Fig. 1, the point to point MMC-HVDCnetwork connects two remote ac grids through dc transmissioncables. The vector control based on the Parker Transformationis commonly used to regulate the energy balance and providegrid support, which is similar to the VSC-HVDC controller.

Fig. 1. MMC-HVDC electrical connection with ac network.

The MMC topology diagram is illustrated in Fig. 2. Thereare N submodules (SM) in each MMC phase arm, wherethe half-bridge dc-dc converter is the most frequently usedSM configuration. The arm inductance Larm and the armresistance Rarm are placed in each phase arm for current spikesuppression. The MMC EMT dynamics have been widelystudied and simulated using the commercial EMT simulatorswhere the PE switching characteristics and sophisticated con-troller are fully considered [13], [14].

Fig. 2. Three-phase MMC circuit topology with half-bridge dc-dcconverter as SM.

According to the existing studies [9], [15]–[19], the MMC-HVDC electromechanical model is divided into the following3 parts :

• The ac side dynamic model, which includes the point ofcommon coupling (PCC), the decoupling inductance, and

the equivalent MMC ac model which is usually specifiedas an equivalent voltage source as illustrated in Fig. 3.

Fig. 3. Equivalent MMC-HVDC circuit: ac side.

• The dc side dynamic model, which specifies the dynamicperformance of the dc transmission network, includes theequivalent dc link capacitor, the effect of the arm induc-tance/ resistance, and the dc transmission line capacitor.

Fig. 4. Equivalent MMC-HVDC circuit: dc side.

• The dynamic controller model, which combines the acand dc side model. The vector control is the most com-monly used control algorithm in the MMC-HVDC, whichcan be basically divided as: 1) the outer control loopwhich is designed according to the particular applicationrequirement, e.g. regulate the power flow, support theterminal bus voltage; 2) the inner current control loopwhich closely follows the reference current in dq axis byregulating the MMC output voltage.

In this paper, the developed MMC-HVDC model is alsoclassified into three parts as above, details of which arediscussed in section III.

III. MMC-HVDC REALIZATION IN TSAT

As explained in section II, the MMC-HVDC fast dynamicshave to be simplified to guarantee only the electromechanicaltransients are included in the TS simulator. The MMC-HVDCdynamic equivalent modeling approaches are explained asfollows:

A. MMC SM Capacitor Equivalent Method based on the ArmAverage Model

It can be observed in Fig. 2 that the MMC configurationis similar to that of the two-level VSC except that the MMCshould consider the voltage balance of each SM capacitor andthe circulating current suppression in each phase leg. In orderto simplify the MMC model, the voltage across each SM isassumed to be equal and the circulating current is assumed tobe well suppressed. The MMC Arm Average Model (AAM) isproposed in [18], [20] based on the aforementioned assump-tions. Due to the simplicity and good dynamic performanceconsidering the fundamental frequency of the ac network,the AAM has been widely used in related studies, includingthe MMC stability analysis, impedance modeling, controllerdesign, etc.

According to the configuration of AAM proposed in [18],the aggregated energy storage effect of all SM capacitorsis simplified into one equivalent capacitor across the dctransmission line, which is similar to the real VSC capacitorplaced between the dc and ac grid. Since the individual SMdynamic performance is out of the scope of electromechanicaltransient studies, the aggregated effect of the SM capacitorscan be equivalent to that of one capacitor connected across thedc bus [9], which is expressed as:

Ceq = 6 · CSM

NSM(1)

where Ceq represents the MMC equivalent capacitance, NSM

represents the number of SMs in each phase arm, and CSM

represents the capacitance of each SM.Therefore, the MMC is equivalent to the configuration of

VSC by this simplification approach. It should be noticedthat this equivalent method is only effective when the MMCdc link current is not regulated [18], [21], [22], otherwise,the dc link voltage is not equal to the total average voltageacross the MMC phase arm. The cases that include the dclink current controller is out of the scope of this paper. TheMMC dynamic equivalent circuit in the dq coordinates isillustrated in Fig. 5 based on this constraint, where Leq,ac,Req,ac and Leq,dc, Req,dc represent the MMC ac and dcequivalent line impedance respectively; igd and igq representthe current injection into the ac network; vgd and vgq representthe ac terminal voltage at PCC; md and mq represent theMMC modulation index.

Fig. 5. MMC dynamic equivalent circuit in dq coordinates.

B. MMC Vector Controller Model

According to Fig. 5, the ac side and dc side dynamics ofMMC-HVDC have been modeled respectively. Generally, thecontroller model is created to decide the modulation index md

and mq , linking up the ac and dc side dynamics. As mentionedin section II, the double-loop control is usually applied in theMMC-HVDC system. Generally, the dc link voltage and theactive power regulation are performed in d axis, while theac voltage amplitude and the reactive power are regulated inthe q axis. The MMC-HVDC control diagram modeled in thispaper is illustrated in Fig. 6, where the inner current loop issimplified as a first order system.

Fig. 6. MMC-HVDC vector control diagram.

The inner current loop control bandwidth is too high to becharacterized by the TS simulator. So the MMC ac currentinjection is assumed to closely follow the current reference,regarding the inner current loop dynamic as a time delay.

Fig. 7. RI and dq coordinates transformation.

C. Electrical Variables Transformation between TS and EMT

The ac terminals of an MMC-HVDC system should berepresented in the phasor domain considering the TS simulatorrequirement. Therefore, the transformation between the dq axisand the phasor domain is necessary. The phasor domain coor-dinate is illustrated in Fig. 7 by solid black line, where the realand imaginary axises are used to represent the phase angle andthe amplitude of the electrical variables. The correspondingphasor variables remain static at the steady state operatingpoint in the static RI coordinates, while the dq axis, whichis illustrated by the black dash line in Fig. 7, rotates at thefundamental frequency of the adjacent ac grid. The V andI are illustrated in Fig. 7 as an example of the voltage andcurrent in the RI coordinates. In this paper, the PCC voltagemeasured at the MMC terminal is aligned with the d axis,so the transformation between the phasor domain and the dqcoordinates is expressed as follows:

id =√I2I + I2R · cos (θ2 − θ1)

iq =√I2I + I2R · sin (θ2 − θ1)

(2)

θ1 = arctan (VI/VR)

θ2 = arctan (II/IR)(3)

IR =√i2d + i2q · cos (θ2)

II =√i2d + i2q · sin (θ2)

(4)

θd = θ2 − θ1 = arctan (id/iq)

θ2 = arctan (VI/VR) + θd(5)

where id and iq represent the current I in the dq coordinates;VR and VI represent the voltage V in the RI coordinates; IRand II represent I in the RI coordinates; θ1 and θ2 representthe V and I phase angle; θd represents the angle differencebetween θ1 and θ2.

D. MMC AC Terminal Specification

The MMC ac-terminal voltage expressed as phasor is usedto represent the MMC-HVDC performance in the TS simula-tor. The circuit diagram of the MMC ac-terminal connectedto the PCC is illustrated in Fig. 3. With the line current Idand Iq derived by the controller model in Fig. 6, the MMCterminal voltage in phasor domain is calculated as:

˙VM = VS − jXL˙IL,ref (6)

where ˙VM represents the MMC terminal voltage in phasordomain, VS represents the PCC voltage in phasor domain,XL represents the line reactance, ˙IL,ref represents the currentflowing through the transmission line derived by the controllermodel, of which the phasor expression is derived by (4), (5).

IV. MMC-HVDC MODEL BENCHMARK

The MMC-HVDC model is created in TS simulator basedon the modeling process expressed in section II, and the accu-racy of the electromechanical model is verified in this section.As illustrated in Fig. 8, the MMC-HVDC model is integratedinto the IEEE 3-machine 9-bus transmission network betweenBus 6 and 4. Bus 10 and 11, which are directly connectedto the MMC terminals, are created additionally and locatedadjacent to Bus 4 and 6 respectively. The right-side MMCterminal is regarded as the rectifier, while the left-side one isregarded as the inverter as illustrated in Fig. 1.

Fig. 8. MMC-HVDC model integrated into the IEEE 3-machine 9-bussystem.

The detailed EMT model of the aforementioned networkunder study has also been developed in the PSCAD/EMTDC

Fig. 9. MMC model subject to the reference step change.

to evaluate the accuracy of the TS model. The step response,the remote three-phase ground fault and the close three-phaseground fault are simulated and analyzed respectively in thefollowing subsections.

A. Controller Reference Step Response

The TSAT model is built based on the average model inFig. 5 and the control model in Fig. 6. The step responseis performed on the electromechanical model characterizing astep change of the controller reference to evaluate the model’sdynamic response subject to the small system disturbance.Four independent simulation cases are illustrated in Fig. 9,including the decrease of MMC power reference Pref , Qref ,the increase of ac terminal voltage Vac, and the increase of dclink voltage Vdc. In each case, the controlled variable referenceexperiences a step change at t = 3 s respectively while the otherreferences remain constant. In Fig. 9, red curves representthe simulation results in PSCAD while blue curves representthose in the TS simulator. It can be observed in Fig. 9 thatthe electromechanical model simulation results show a goodagreement with the PSCAD model at the reference value stepresponse.

B. Ground Fault Remote from the MMC Terminal

A three-phase ground fault at Bus 8 is applied to evaluatethe performance of the model during grid contingency. Theground fault occurs at t = 3 s and lasts for 0.1 s. Both the MMCac side and dc side performance are evaluated, where thefollowing variables are recorded respectively: the active powerconsumption P and the voltage at two MMC ac terminal busesVac, the dc link voltage at two dc transmission line terminalsVdc. Simulation results are illustrated in Fig. 10. It can beconcluded that the ac side performance of the MMC TSATmodel achieves a good match with that of the PSCAD model.Regarding the dc link voltage, the dynamic performance before

(a) MMC rectifier side: Response to ground fault. (b) MMC inverter side: Response to ground fault.

Fig. 10. MMC model subject to the three-phase ground fault at Bus 8: active power, dc link voltage, ac terminal voltage.

and during the fault shows a better match than the performanceafter the fault. The high-frequency oscillation at dc link voltagecannot be observed in the simulation results from TS simulator.

C. Ground Fault Close to the MMC Terminal

In this case, a three-phase ground fault at Bus 4 is applied tothe testing network. Compared with the last case, the groundfault is closer to the MMC terminal, so the impact on theMMC-HVDC is more severe. The low-voltage ride-throughcontrol is applied to the MMC at Bus 10 to withstand thelow terminal voltage. The ground fault occurs at t = 3 sand lasts for 0.1 s. The simulation results are illustrated inFig. 11. Compared with the PSCAD simulation results, it isobserved that the performance of the MMC electromechanicalmodel achieves a relative good match with that of the accuratemodel before and during the fault. After the fault is cleared,the ac terminal voltage raised back faster than that of thePSCAD model, which also leads to the mismatch in the activepower. However, TSAT simulation results after 3.3 s show agood agreement with the EMT simulation results, indicatingrelatively accurate dynamic performance.

V. CONCLUSION

This paper proposes an electromechanical model for MMC-HVDC system in the widely used commercial TS simulatorTSAT. The MMC-HVDC analytical model is created basedon the MMC AAM and the equivalent dc link capacitor,and meanwhile realized in TSAT by using the UDM editorwhich can customize the dynamic performance of the HVDCpower converters. The accuracy of the TSAT model has been

evaluated by comparing the simulation results with those ofthe PSCAD/EMTDC model subject to different grid contin-gencies, including the controller reference step change and thethree-phase ground fault. According to the simulation results,the MMC-HVDC model developed in TSAT can accuratelyreflect the dynamic performance regarding the electromechan-ical transients when the HVDC network is subject to bothsmall grid disturbances or grid contingencies.

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