Research on Synchronverter-Based Regenerative Braking Energy Feedback System of Urban Rail Transit

energies

Article Research on Synchronverter-Based Regenerative Braking Energy Feedback System of Urban Rail Transit

Shuting Li 1, Songrong Wu 1, Shiqiang Xiang 2, Yabo Zhang 3, Josep M. Guerrero 4,* and Juan C. Vasquez 4

1 Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University, Chengdu 611756, China; [email protected] (S.L.); [email protected] (S.W.) 2 China Railway Eryuan Engineering Group Co., Ltd. (CREEC), Chengdu 610031, China; [email protected] 3 The 13th Research Institute of China Electronic Technology Group Corporation, Shijiazhuang 050051, China; [email protected] 4 Center for Research on Microgrids (CROM), Department of Energy Technology, Aalborg University, 9220 Aalborg, Denmark; [email protected] * Correspondence: [email protected]

Received: 26 July 2020; Accepted: 24 August 2020; Published: 26 August 2020

Abstract: Generally running with frequent braking over short distances, the urban rail transit train generates great quantities of regenerative braking energy (RBE). The RBE feedback system can effectively recycle RBE and give it back to the AC grid. However, the lack of damp and inertia of generators makes conventional PWM RBE feedback system more sensitive to power fluctuations. To address this issue, a synchronverter-based RBE feedback system of urban rail transit is designed in this paper. First, the structure of the feedback system is presented. Then, the synchronverter-based control strategy with greater flexibility and higher stability is fully discussed. Furthermore, the parameter design of the system is analyzed in detail. Finally, simulation results and experimental results are provided to show the good dynamic performance of the system. Using this synchronverter-based approach, the system supplies traction power to the traction network when the train accelerates and gives the RBE back to the AC grid when the train brakes, in light of the variation of the DC bus voltage. Moreover, the system can be self-synchronized with the AC grid and make corresponding power management on the basis of changes in the voltage amplitude as well as the frequency of the grid. In this sense, the RBE feedback system becomes more flexible, effective and robust.

Keywords: synchronverter; regenerative braking energy; energy feedback; grid power regulation

1. Introduction Urban rail transit tends to be more eﬃcient, ﬂexible and energy saving. In light of the trend, subways have gradually become the mainstream in urban rail transit [1–3]. Subways generally run with frequent braking over short distances, thus can generate a large amount of regenerative braking energy (RBE), nearly 30–55% of the traction power [4,5]. A fraction of this part of energy can be absorbed by adjacent trains, while most of it will be left and consequently increase the DC bus voltage, which greatly disturbs the operation of the trains [6–11]. To cope with the problem, resistors are set in traction substations to consume RBE and accordingly suppress the increase of the DC bus voltage. Nevertheless, in this way, RBE is simply dissipated into the

Energies 2020, 13, 4418; doi:10.3390/en13174418 www.mdpi.com/journal/energies Energies 2020, 13, 4418 2 of 23 air in the form of heat, thus needs to consume extra energy to supply the temperature control equipment to cool the air, which is contrary to the demand of energy conservation. In addition, the in-station resistors cabinet needs to be placed separately, which increases the difficulty of site configuration [12]. However, if RBE could be recycled, it would not only supply for auxiliary equipment in the metro station but also feed the AC grid for reuse. In this sense, many RBE recycle approaches are developed to recycle the regenerative braking energy. In general, the energy recycle approaches can be divided into energy storage methods and inverter feedback methods, according to the direction of the energy transmission. The former can quickly stabilize the DC bus voltage by setting energy storage equipment on the DC side to absorb RBE, such as super capacitors and flywheels, which can also suppress fluctuations of line voltage and optimize the energy cost. However, there are some drawbacks that limit the application of these energy storage methods. For instance, because of its bulky volume and insufficient capacity, existing supercapacitor equipment is not suitable to operate in a small area or for a long time. Moreover, flywheel storage equipment has not been applied in force due to its low energy density and high self-discharge rate. Both are limited by installation constraints as well as interoperability issues [13,14]. Another possibility to recycle RBE is to feedback RBE to the AC grid for reuse. When the train brakes and the DC bus voltage exceeds the threshold value, RBE of the train obtained from the traction power network is fed back to the 35-kV AC grid through the high-power three-phase PWM inverter. The droop control method is generally applied in this approach to avoid circulating currents among converters and communication between units. In this way, stable frequency and voltage of the system can be obtained by active power–frequency (P-f) droop control and reactive power–voltage (Q-V) droop control, simulating the primary droop characteristic of the motor. However, when the conventional droop control is applied to nonlinear loads system, harmonic problems and imbalance between the active power and reactive power are inevitable [15]. Moreover, the load-dependent frequency deviation problem also affects its dynamic performance. For instance, at the moment of grid-connection, this deviation will result in a loss of synchronization. The virtual synchronous generator is developed to cope with the problem. This concept, first proposed by the Vertical Sync (VSYNC) project in Europe, adds the virtual inertia and damping to the conventional droop control and shows a better dynamic performance. Significant efforts have been done to develop the virtual synchronous generator. The existing virtual synchronous generators can be divided into current types and voltage types. At present, two current control schemes have been proposed: Virtual Synchronous Generator (VSG) proposed by The University of Leuven in Belgium and Virtual Synchronous Machine (VISMA) proposed by The Technical University of Lauxtal in Germany [16]. VSG, composed of a three-phase half-bridge inverter, a LCL filter and an ideal DC voltage source for energy storage, effectively improves the system frequency stability. Nevertheless, the simulation degree of excitation regulation mechanism of the synchronous generator is insufficient, leaving a gap between the algorithm and the principle of practical synchronous generator. VISMA indirectly constructs the synchronous generator model by directly controlling the inductance current of the AC side filter, thus simulating the characteristics of primary frequency modulation and primary voltage regulation [17]. However, the control accuracy of VISMA is easily affected by filter inductances. There are mainly two schemes for voltage-controlled virtual synchronous generator technology, the virtual inertial frequency control proposed by Iravani [18] and the synchronverter proposed by Zhong [19,20]. By using the virtual inertial frequency control, the inverter has the same moment of inertia and primary frequency modulation characteristics as the conventional synchronous generator. However, the simulation degree is insufficient. The synchronverter, the closest to the operation mechanism of the practical synchronous generator, does not need additional synchronization units, thus can synchronize with the grid smoothly. The synchronverter has been widely used in wind power generation, solar power generation, static reactive power compensation, motor speed regulation and other aspects [21–24]. However, the dynamic performance of the synchronverter is greatly affected by control parameters. Only a few works give a whole parameter design method of the overall control. Energies 2020, 13, x FOR PEER REVIEW 3 of 23

Energies 2020, 13, 4418 3 of 23 In this paper, a synchronverter-based RBE feedback system of urban rail transit is designed to supply traction power network with traction energy when the train accelerates and give RBE back to the ACInEnergies this grid paper,2020 when, 13, x a FOR synchronverter-basedthe PEER train REVIEW brakes. Moreover, RBE feedback the parameter system of urbandesign rail method transit of is designedthe3 ofoverall 23 to supplysynchronverter traction powercontrol network is researched with traction in detail. energy The rest when of this the trainpaper accelerates is organized and as give follows. RBE back In Section to the AC2, the grid structure whenIn this the of paper, trainthe RBEa brakes. synchronverter-based feedback Moreover, system the isRBE parameter pres feedbackented, design systemthe control method of urban strategy of rail the transit overall of the is synchronvertersystemdesigned is to fully controldiscussedsupply is researched and traction the operation power in detail. network characteristics The restwithof traction this at paper differentenergy is when organized mode the trainare as analyzed. follows.accelerates In In and Section Section give 2RBE, 3, the theback structure system to the AC grid when the train brakes. Moreover, the parameter design method of the overall ofcapacity the RBE and feedback the controller system parameters is presented, are designed the control in strategydetail. Inof Section the system 4, the system is fully performance discussed and is synchronverter control is researched in detail. The rest of this paper is organized as follows. In Section the operation characteristics at different mode are analyzed. In Section3, the system capacity and verified2, theby simulationsstructure of the and RBE experiments. feedback system The conclusionis presented, is the presented control strategy in Section of the 5. system is fully the controllerdiscussed parameters and the operation are designed characteristics in detail. at different In Section mode4, theare systemanalyzed. performance In Section 3, the is verified system by simulations2. Overallcapacity Design and and experiments. the of controllerSynchronverter-Based Theparameters conclusion are designedRegenerative is presented in detail. inBraking SectionIn Section Energy5. 4, the Feedbacksystem performance System is verified by simulations and experiments. The conclusion is presented in Section 5. 2.2.1. Overall Structure Design of the ofSystem Synchronverter-Based Regenerative Braking Energy Feedback System 2. Overall Design of Synchronverter-Based Regenerative Braking Energy Feedback System 2.1. StructureThe conventional of the System RBE feedback system is shown in Figure 1a. Composed of the contact rail and return2.1. rail, Structure the DC of thetraction System network supplies power for the train in operation. When the train accelerates,The conventional the DC bus RBEvoltage feedback decreases, system the isener showngy from in Figure the 351 a.kV ComposedAC grid is ofrectified the contact through rail a The conventional RBE feedback system is shown in Figure 1a. Composed of the contact rail and and24-pulse return rectifier, rail, the feeding DC traction the DC network traction supplies network power of urban for rail the traintransit. in When operation. the train When brakes, the train the return rail, the DC traction network supplies power for the train in operation. When the train accelerates,DC bus voltage the DCrises bus and voltage exceeds decreases, the threshold the energy value, from and theRBE 35 of kV the AC train grid obtained is rectified from through the DC a 24-pulseaccelerates, rectifier, the feeding DC bus the voltage DC traction decreases, network the ener ofgy urban from rail the transit.35 kV AC When grid theis rectified train brakes, through the a DC side is24-pulse fed back rectifier, to the feedingAC grid the through DC traction the hinetworkgh-power of urban three-phase rail transit. PWM When inverter the train [25]. brakes, Compared the bus voltage rises and exceeds the threshold value, and RBE of the train obtained from the DC side is with theDC conventionalbus voltage rises RBE and feedback exceeds system,the threshold the rect valuifiere, and and RBE inverter of the functiontrain obtained can befrom realized the DC with fed back to the AC grid through the high-power three-phase PWM inverter [25]. Compared with the the sameside equipmentis fed back toin the the AC synchronverter-based grid through the high-power RBE feedback three-phase system, PWM as inverter shown [25]. in Figure Compared 1b. The conventionalsystemwith operates the RBEconventional in feedback both rectifying RBE system, feedback mode the system, rectifier and in theverter and rect inverter ifiermode, and autonomously functioninverter function can be supplies realizedcan be realized traction with the with energy same equipmentto the theDC sameside in and theequipment synchronverter-basedfeeds the in the RBE synchronverter-based back to the RBE AC feedback grid. RBE In addition,feedback system, system, asthe shown system as shown in can Figure be in self-synchronized Figure1b. The 1b. systemThe operateswith thesystem ingrid both operates and rectifying make in both appropriate mode rectifying and inverterresponsesmode and mode, inonverter the autonomously basismode, of autonomously changes supplies in the supplies traction voltage traction energy amplitude energy to the and DC sidefrequency andto the feeds of DC the theside grid.RBE and feeds back the to theRBE AC back grid. to the In AC addition, grid. In addition, the system the cansystem be self-synchronizedcan be self-synchronized with the grid andwith make the grid appropriate and make responsesappropriate on responses the basis on of the changes basis of in changes the voltage in the amplitudevoltage amplitude and frequency and of thefrequency grid. of the grid.

(a) (a) (b()b )

FigureFigure 1. The 1. RBEThe RBE feedback feedback systems: systems: ( a )( athe ) the structure structure of of thethe conventionalconventionalonal RBE RBE feedback feedback system; system; and and ((b)) thethe( b structurestructure) the structure ofof thethe of proposed proposedthe proposed RBERBE RBE feedbackfeedback feedback system.system. system.

The RBERBEThe feedbackRBEfeedback feedback systemsystem system consists consists consists of of a of maina amain main circuit, circ circuit,uit, a transformer, a transformer, an an energyan energy energy storage storage storage module module module and aand master a andmaster controller, a master controller, controller, as illustrated as illustrated as illustrated in Figure in inFigure 2Figure. The 2. energy2. The The energy energy storage storagestorage module module module is connected is isconnected connected in parallelin parallel in parallel with with the DC traction network, and the master controller generates drive signals to control the main thewith DC the traction DC traction network, network, and the and master the master controller controller generates generates drive signalsdrive signals to control to control the main the circuit. main circuit. The energy storage module is designed as an auxiliary module to further maintain the stability The energy storage module is designed as an auxiliary module to further maintain the stability of the circuit.of The the energyDC bus voltage.storage module is designed as an auxiliary module to further maintain the stability DCof the bus DC voltage. bus voltage.

Figure 2. The diagram of the proposed RBE feedback system.

EnergiesEnergies 20202020,, 13,, x 4418 FOR PEER REVIEW 44 of of 23 23 EnergiesEnergies 20202020,, 1313,, xx FORFOR PEERPEER REVIEWREVIEW 44 ofof 2323 The main circuit consists of a DC traction network, a three-phase bi-directional converter, an The main circuit consists of a DC traction network, a three-phase bi-directional converter, an isolatingTheThe transformer mainmain circuitcircuit and consistsconsists an AC ofof agrid,a DCDC as tractiontraction shown network,netw in Figureork, aa three-phase3.three-phase The filter bi-directionalcapacitorbi-directional Cdc in converter,converter, Figure 3 ananis isolating transformer and an AC grid, as shown in Figure 3. The filter capacitor Cdcdc in Figure 3 is designedisolatingisolating transformertotransformer suppress andtheand harmonic anan ACAC grid,grid, components asas shownshown inonin FigureFigurethe DC3 .3. side, The The filter andfilter the capacitor capacitor AC side CCdc LCL inin FigureFigure filter 3 can3 is is perfectlydesigneddesigned weaken to toto suppress suppresssuppress the thehigh-order thethe harmonic harmonicharmonic harmonics components componentscomponents of onthe the ouonon tputDC thethe side, currentDCDC andside,side, [26]. the andand AC The thethe side inverter ACAC LCL sideside filter side LCLLCL can inductance filterfilter perfectly cancan perfectly weaken the high-order harmonics of the output current [26]. The inverter side inductance Lweakenperfectlys of the theLCL weaken high-order filter isthe used high-order harmonics to suppress ofharmonics the the output curren of current thet ripple output [26 produced]. current The inverter by [26]. power sideThe inductanceelectronicinverter side switches.Ls inductanceof the LCLThe Lss of the LCL filter is used to suppress the current ripple produced by power electronic switches. The grid-sidefilterL of isthe used LCLfilter to filter suppressinductance is used the toL currentg suppressof the ripple LCL the filter producedcurren furthert ripple by powerweakens produced electronic the by alternating power switches. electronic current The grid-side switches. ripple filterand The grid-side filter inductance Lgg of the LCL filter further weakens the alternating current ripple and limitsinductancegrid-side the impulsefilterLg of inductance the current LCL filter atL theof further themoment LCL weakens filterof grid thefurther-connection alternating weakens [27–29]. current the alternating rippleThe isolating and current limits transformer the ripple impulse and is appliedcurrentlimitslimits thethe atfor theimpulse impulseelectrical moment currentcurrent isolation of grid-connection atat andthethe momentmomentvoltage [ boost27 ofof– 29gridgrid ].of-connection The-connection the isolatingconverter [27–29].[27–29]. transformer output TheThe voltage. isolatingisolating is applied To further transformertransformer for electrical ensure isis theisolationappliedapplied stability forfor and ofelectricalelectrical voltage the DC boostbusisolationisolation voltage, of the andand converteran voltagevoltage energy boost boost outputstorage ofof voltage. modulethethe converterconverter Tois desi further gnedoutputoutput ensure for voltage.voltage. auxiliary the stability ToTo energy furtherfurther of storage, the ensureensure DC whichbusthethe stabilitystability voltage, consists ofof an thetheof energy anDCDC accumulator busbus storage voltage,voltage, module anandan energyenergy isa designedBuck/Boost storagestorage for module moduleDC-DC auxiliary isis converter, desidesi energygnedgned storage, forforas auxiliaryshownauxiliary which in energy energyFigure consists storage, storage,4. ofThe an doubleaccumulatorwhichwhich consistsclosed-loopconsists and ofof a an Buckancontrol accumulatoraccumulator/Boost algorithms DC-DC andand converter,applied aa Buck/BoostBuck/Boost in as the shown chargingDC-DCDC-DC in Figure converter, converter,and4 discharging. The as doubleas shownshown mode closed-loop inin ofFigureFigure the controlenergy 4.4. TheThe storagealgorithmsdoubledouble moduleclosed-loopclosed-loop applied are inshown controlcontrol the charging in algorithmsalgorithms Figure and 5. dischargingappliedapplied inin thethe mode chargingcharging of the andand energy dischargingdischarging storage module modemode ofof are thethe shown energyenergy in Figurestoragestorage5 . modulemodule areare shownshown inin FigureFigure 5.5.

Figure 3. The main circuit of the synchronverter-based RBE feedback system. FigureFigure 3.3. TheThe main main circuitcircuit ofof thethe synchronverter-basedsynchronvesynchronverter-basedrter-based RBERBERBE feedbackfeedbackfeedback system.system.system.

Figure 4. The energy storage module of the RBE feedback system. FigureFigure 4.4. TheThe energyenergy storagestorage modulemodule ofof thethe RBERBE feedbackfeedback system.system.

FigureFigure 5. 5. TheThe double double closed-loop closed-loop controller. controller. FigureFigure 5.5. TheThe doubledouble closed-loopclosed-loop controller.controller.

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The lack of damp and inertia of generators makesmakes the conventional PWM RBE feedback system more sensitivesensitive to to power power ﬂuctuations fluctuations [15 [15].]. By By using using the the synchronverter, synchronverter, the systemthe system can synchronizecan synchronize with thewith grid the autonomously grid autonomously and participate and participate in the management in the management of the grid. Moreover,of the grid. the synchronverterMoreover, the cansynchronverter make corresponding can make adjustmentscorresponding according adjustments to the according changes ofto gridthe changes frequency of grid and frequency voltage under and normalvoltage andunder abnormal normal and conditions, abnormal thus conditions, presents thus good presents dynamic good performance. dynamic performance. Hence, the controller Hence, the in thiscontroller paper in is this based paper on the is based synchronverter, on the synchronvert as showner, in Figureas shown6, generating in Figure the6, generating control instruction the controle andinstruction the PWM e and signal the PWM of each signal IGBT of of each the converter.IGBT of the converter.

DP −  Tm 1 θ 1 θ − Js s

Te Formulas of Q e、Q、Te e

M f if i

Figure 6. Mathematical model of the synchronous generator. Figure 6. Mathematical model of the synchronous generator. According to the characteristics of the synchronous generator (SG), the rotor angle relative to the According to the characteristics of the synchronous generator (SG), the rotor angle relative to the a-phase stator winding of the SG is θ. iabc is defined as the three-phase stator current of the SG and Rs a-phase stator winding of the SG is θ. iabc is defined as the three-phase stator current of the SG and Rs and Ls are the resistance and inductance of the stator winding, respectively [15]. When defined as: and Ls are the resistance and inductance of the stator winding, respectively [15]. When defined as:      sinsinθ 𝜃   ⎧  ⎡ ⎤  sin θe =  sin (θ 2π2𝜋)   ⎪  ⎢sin(𝜃3 − )⎥  sin 𝜃= − 4π 3   ⎪  sin⎢ (θ ) ⎥  − 34𝜋 (1)  ⎪  ⎢ ⎥   ⎣sin(𝜃cos θ − )⎦   2π3   cos θe =  cos (θ )  (1)  ⎨  cos− 𝜃3    ⎡ ( 4π ) ⎤ ⎪ cos θ 32𝜋 ⎢cos(𝜃− − )⎥ ⎪cos 𝜃 = ⎢ 3 ⎥ the reverse electromotive force e = [e e ⎪e ]T, generated⎢ by4𝜋 rotor⎥ motion in stator windings, can be a b c cos(𝜃 − ) expressed as follows: ⎩ ⎣ 3 ⎦ . the reverse electromotive force e = [ea eb ec]eT,= generatedMfifθ sin θeby rotor motion in stator windings, can (2)be expressed as follows: where Mf is the maximum mutual inductance between the excitation winding and the three-phase stator winding and if is the field current of the𝑒=𝑀 rotor.f𝑖f𝜃 The 𝑠𝑖𝑛 SG 𝜃 needs to follow: (2) where Mf is the maximum mutual inductance.. 1 between the. excitation winding and the three-phase θ = (Tm Te DPθ) (3) stator winding and if is the field current of theJ rotor.− The− SG needs to follow: 1 where Tm is the mechanical torque, Te is the𝜃 = electromagnetic(𝑇 −𝑇 −𝐷 torque,𝜃) J is the moment of inertia and D(3)P 𝐽 m e is the damping coefficient. Assuming that the number of pole-pairs is 1, the electromagnetic torque Te canwhere be T calculatedm is the mechanical as: torque, Te is the electromagnetic torque, J is the moment of inertia and DP is the damping coefficient. Assuming that theT enumber= Mfif (ofi, pole-pairs sin θe) is 1, the electromagnetic torque Te can(4) be calculated as: According to the electromagnetic transient relationship, the output active power is expressed as: 𝑇 =𝑀𝑖 (𝑖, sin𝜃) . (4) P = M i θ(i, sin θe) (5) According to the electromagnetic transient frelationf ship, the output active power is expressed as:

𝑃=𝑀𝑖𝜃(𝑖, sin𝜃) (5) Moreover, the output reactive power is expressed as:

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EnergiesMoreover, 2020, 13, x FOR the PEER output REVIEW reactive power is expressed as: 6 of 23

. Q = M i θ(i , cos θe) (6) 𝑄=−𝑀− f f𝑖𝜃(𝑖, cos𝜃) (6) AccordingAccording to thethe mathematicalmathematical model model of of the the SG, SG, the masterthe master controller controller of the of RBE the feedback RBE feedback system systemcan be obtained.can be obtained. The speciﬁc The specific control contro strategyl strategy is discussed is discussed in Section in Section 2.2. 2.2.

2.2.2.2. Control Control Strategy Strategy of of the the System System

2.2.1.2.2.1. Overall Overall Control Control Strategy Strategy TheThe overall overall control control strategy strategy is is presented presented in in Figure Figure 77.. Before Before the grid-connection, the the amplitude, amplitude, frequencyfrequency and and phase of the output controlcontrol instructioninstructione eare are supposed supposed to to be be synchronized synchronized with with those those of ofthe the AC AC grid grid voltage voltage [30 [30].]. The TheV setVsetis is the the rated rated DC DC bus bus voltage, voltage,V Vutut//Vlt isis the the upper/lower upper/lower threshold threshold valuevalue of of the traction network voltage, futut/f/ltf ltisis the the upper/lower upper/lower threshold threshold value value of of the the power power grid grid frequencyfrequency and and vvutut/v/vltlt isis the the upper/lower upper/lower threshold threshold value value of of the the AC AC side side voltage. voltage.

FigureFigure 7. 7. OverallOverall control control strategy strategy of of the the master master controller. controller.

2.2.2.2.2.2. Rectifier Rectifier Control Control TheThe rectifier rectifier controller controller is is shown shown in in Figure Figure 88,, which consists of a self-synchronizationself-synchronization unit, a PP--ff controlcontrol loop, loop, a a QQ--VV controlcontrol loop loop and and a a DC DC bus bus voltage voltage loop. loop. The The difference difference value value between between the the voltage voltage V and the reference voltage Vset is fed into the PI controller to determine the compensation value of Vdcdc and the reference voltage Vset is fed into the PI controller to determine the compensation value of thethe traction traction energy. energy. Due to the reverse of the stator current, the mechanical motion equation of the rectifier controller is represented as: . . d(θ θn) . . J − = Te D (θ θn) Tm, (7) dt − P − − . where the J is the virtual moment of inertia, θ is the angular frequency of the output control instruction . e, θn is the rated angular frequency of the power grid, Te is the virtual electromagnetic torque, DP is the P-f control coefficient of the controller and Tm is the virtual mechanical torque.

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Figure 8. RectifierRectiﬁer control control strategy of the master controller.

DueThe virtualto the reverse mechanical of the torque stator Tcurrent,m of the the rectifier mechan controllerical motion can equation be expressed of the as: rectifier controller is represented as: 1 Tm = (kpv + kiv s )(Vset Vdc), Vdc Vlt (8) 𝑑𝜃 −𝜃 − ≤ 𝐽 =𝑇 −𝐷𝜃 −𝜃 −𝑇, (7) According to the P-f control loop, the𝑑𝑡 grid frequency can be regulated as: where the J is the virtual moment of inertia, θ is the angular frequency of the output control . 1 . . instruction e, θ is the rated angularθ = frequency[D (θr of θthe) + powerTe T mgrid,], Te is the virtual electromagnetic (9) n Js P − − torque, DP is the P-f control coefficient of the controller and Tm is the virtual mechanical torque. . The virtual mechanical torque Tm of the rectifier controller can be expressed as: where θr is the reference value of the grid angular frequency. Hence, the frequency droop control can be realized through the coefficient DP, and the phase1 θ of the voltage e can be controlled by the angular . 𝑇 = (𝑘 +𝑘 )(𝑉 −𝑉), 𝑉 ≤𝑉 (8) frequency θ. The coefficient DP can be defined as:𝑠 According to the P-f control loop, the grid frequency can be regulated as: ∆T 1 DP = . , (10) 𝜃 = [𝐷 𝜃 −−𝜃∆θ+𝑇 −𝑇 ], (9) 𝐽𝑠 . . . . where ∆T is the torque variation and ∆ is the difference value between and . The greater is ∆ , where θr is the reference value of the θgrid angular frequency. Hence, theθ frequencyθr droop controlθ canthe greaterbe realized is ∆T through, which regulatesthe coefficient the controller DP, and the output phase frequency. θ of the voltage e can be controlled by the angularIn thisfrequency paper, θ before . The coefficient all switches DP of can the be converter defined as: are switched on, the control instruction is supposed to be synchronized with the transformer primary side phase voltage v . As shown in Δ𝑇 pg Figure8, a PI control loop plus a virtual current𝐷 =− control, loop can form a self-synchronization unit.(10) . Δ𝜃 The reference angle frequency θr, generated by the PI controller, makes the difference between the . . where ΔT is the torque variation and Δθ is the difference value between θ and θr. The greater is controller output angle frequency θ and the reference value θr gradually approach zero, thus keeping Δθ , the greater is ΔT, which regulates the controller output frequency. . the controller frequency consistent with the grid frequency. The reference angular frequency θr can be In this paper, before all switches of the converter are switched on, the control instruction is expressed as: supposed to be synchronized with the. transformer. primary1 side phase voltage vpg. As shown in θr = θn (k + k )∆T (11) Figure 8, a PI control loop plus a virtual current− controlpf if sloop can form a self-synchronization unit. The reference angle frequencyθ , generated by the PI controller, makes the difference between the During the self-synchronization,r the current i is 0 and the controller cannot generate the virtual controller output angle frequency θ and the reference value θr gradually approach zero, thus electromagnetic torque Te. Consequently, the virtual current is is fed into the Q-V control loop to keeping the controller frequency consistent with the grid frequency. The reference angular frequency generate T , realizing the voltage synchronization. In this sense, the virtual current is expressed as: e θr can be expressed as: 1 1 𝜃is ==𝜃 −(𝑘(e +𝑘vpg),)Δ𝑇 (11) (12) Ls + R − 𝑠 whereDuringL is the the virtual self-synchronization, inductance and R theis thecurrent virtual i is resistance. 0 and the Onlycontroller when cannot the virtual generate current thei svirtualdrops electromagneticto 0 can the converter torque be T connectede. Consequently, to the power the virtual grid. current is is fed into the Q-V control loop to generate Te, realizing the voltage synchronization. In this sense, the virtual current is expressed as:

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1 𝑖 = (𝑒 − 𝑣 ), (12) 𝐿𝑠 +𝑅 Energies 2020, 13, 4418 8 of 23 where L is the virtual inductance and R is the virtual resistance. Only when the virtual current is drops to 0 can the converter be connected to the power grid. InIn thethe grid-connectedgrid-connected rectiﬁcationrectification mode,mode, thethe practicalpractical gridgrid currentcurrent ii isis usedused forfor control.control. ItIt isis importantimportant toto noticenotice that that the the direction direction of of the the input input grid grid current currenti in i in the the rectiﬁer rectifier controller controller is oppositeis opposite to theto the direction direction of the of the current currentiabc iniabc Figure in Figure8. The 8. referenceThe reference directions directions of T eof, P Tande, P Qandare Q consistent are consistent with thosewith those in the in inverter the inverter mode, mode, for the for sake the ofsake analysis. of analysis.

2.2.3.2.2.3. Inverter Control TheThe inverterinverter controllercontroller isis shownshown inin FigureFigure9 9,, which which is is mainly mainly composed composed of of a a PP--ff controlcontrol loop,loop, aa QQ--VV controlcontrol looploop andand aa self-synchronizationself-synchronization unit.unit. The inverter controller can not onlyonly feedfeed RBERBE intointo thethe grid,grid, butbut alsoalso regulateregulate thethe activeactive powerpower andand thethe reactivereactive powerpower ofof thethe grid.grid.

Figure 9.9. Inverter control strategy ofof thethe mastermaster controller.controller.

TheThe mechanicalmechanical motionmotion equationequation ofof thethe inverterinverter controllercontroller isis representedrepresented as:as: . . 𝑑𝜃 −𝜃 . . d𝐽(θ θn) =𝑇 −𝐷 𝜃 −𝜃 −𝑇 (13) J − = Tm D (θ θn) Te (13) dt𝑑𝑡 − P − − Similar to the rectifier controller, a DC bus voltage loop is introduced to determine the amount Similar to the rectiﬁer controller, a DC bus voltage loop is introduced to determine the amount of of RBE. When the train brakes, the DC bus voltage Vdc rises, Tm is determined by the variation of the RBE. When the train brakes, the DC bus voltage Vdc rises, Tm is determined by the variation of the Vdc. When Vdc is in the threshold range and Tm is determined by a set value Pset/ωn. In this sense, the Vdc. When Vdc is in the threshold range and Tm is determined by a set value Pset/ωn. In this sense, virtual mechanical torque Tm can be calculated as: the virtual mechanical torque Tm can be calculated as: 1 (𝑘 +𝑘 )(𝑉 −𝑉 ) 𝑉 ≥𝑉  ⎧ 1 , (kpv + kiv )(𝑠Vdc Vset), Vdc Vut Tm = s (14) Tm =  𝑃 − ≥ (14)  ⎨ Pset , , V 𝑉< <𝑉V <<𝑉V ωn lt dc ut ⎩ 𝜔

UnderUnder regenerativeregenerative brakingbraking ofof thethe train,train, thethe DCDC busbus voltagevoltageV Vdcdc rises and RBE is fedfed backback toto thethe ACAC gridgrid accordingly.accordingly. WhenWhen thethe gridgrid frequencyfrequency changes,changes, thethe inverterinverter controllercontroller startsstarts thethe P-fP-f controlcontrol loop.loop. When the grid voltagevoltage changes,changes, thethe inverterinverter controllercontroller startsstarts thethe QQ-V-V control loop.loop.

3. Parameter Design of the System

3.1. System Capacity Design To determine the system capacity, the traction calculation of the train operation and the DC bus voltage should be carried out ﬁrst. According to the traction power supply standard [31], the rated line voltage of the AC side is 35 kV, the rated input voltage of the DC side is 1500 V and the output frequency of the system is 50 Hz 0.5%. For the sake of convenience, assume that the train is in AW2 ± full-loaded condition without mechanical braking and the traction power can be 100% converted to Energies 2020, 13, x FOR PEER REVIEW 9 of 23

3. Parameter Design of the System

3.1. System Capacity Design To determine the system capacity, the traction calculation of the train operation and the DC bus voltage should be carried out first. According to the traction power supply standard [31], the rated line voltage of the AC side is 35 kV, the rated input voltage of the DC side is 1500 V and the output frequency of the system is 50 Hz ± 0.5%. For the sake of convenience, assume that the train is in EnergiesAW2 2020full-loaded, 13, 4418 condition without mechanical braking and the traction power can be 9100% of 23 converted to kinetic energy [32–35]; then, the traction calculation can be operated according to the kineticparameters energy in [Table32–35 1.]; then, the traction calculation can be operated according to the parameters in Table1. Table 1. Parameters of the traction calculation. Table 1. ParametersParameter of the traction calculation.Value Rated DCParameter bus voltage Vdc Value1500 V Distance between stations s 3800 m Rated DC bus voltage Vdc 1500 V MaximumDistance betweenspeed of stations the trains v 380080 km/h m MaximumMaximum braking speed force of the of train the trainv Z 80320 km/ hkN MaximumWeight braking of the force train of the Mtrain Z 320300 kN t Weight of the train M 300 t Alex number of the train n 24 Alex number of the train n 24 CarriageCarriage number number of thethe train trainN N(4M2T) (4M2T) 6 6 FrontFront area area of thethe train trainA A 1010 m2 m2

Piecewise linearizing the traction–velocity curve of the subway in [36], the function of the Piecewise linearizing the traction–velocity curve of the subway in [36], the function of the traction traction T can be approximately expressed as: T can be approximately expressed as: 40  370000, 0<𝑣≤  v 40 3.6 𝑇= 370000, 0 < 3.6 (15) T =  40 ≤ 80 (15)  −23400𝑣23400v + 630000, + 630000,40 < v<𝑣<< 80 − 3.63.6 3.6 3.6 wherewhere thethe unitunit ofof thethe velocityvelocityv vis is m m/s./s. Then,Then, thethe so-calledso-called DavisDavis equationequation [[37]37] isis appliedapplied toto calculatecalculate thethe resistanceresistance of of the the train train during during operation, operation, which which can can be be calculated calculated as: as: 𝑅 = 6.4 × 𝑀 + 130 × 𝑛 + 0.14 × 𝑀 × 𝑣 + [0.046 + 0.0065 ×(𝑁−1)] 𝐴 ×𝑣 (16) R = 6.4 M + 130 n + 0.14 M v + [0.046 + 0.0065 (N 1)] A v2 (16) × × × × × − × × Assuming that the train is running with the fastest traction strategy and brakes at maximum brakingAssuming force, the that dynamic the train curves is running of the with running the fastestcan be tractionobtained, strategy as shown and in brakes Figure at 10. maximum In Figure braking10, the urban force, therail dynamictrain starts curves to run of at the a variable running acceleration can be obtained, at 0 s as in shown the process in Figure of running 10. In Figure between 10, thetwo urban stations. rail trainAfter starts reaching to run the at maximum a variable running acceleration speed at 0at s about in the process25 s, the of train running runs betweenat a uniform two stations.speed. At After 170 reachings, the train the starts maximum to brake running with th speede maximum at about braking 25 s, the force train until runs it at stops. a uniform During speed. the Atoperation, 170 s, the the train maximum starts to traction brake with power the maximumis 3 MW and braking the maximum force until braking it stops. power During is the5.5 MW. operation, the maximum traction power is 3 MW and the maximum braking power is 5.5 MW.

(a) (b)

Figure 10. Cont. Energies 2020, 13, x FOR PEER REVIEW 10 of 23 EnergiesEnergies2020 2020, 13, 13, 4418, x FOR PEER REVIEW 1010 of of 23 23

((c)) ((d))

((e))

FigureFigure 10.10. TractionTraction calculation calculation results results of th ofe train thetrain during during running running process: process: (a)) speed–timespeed–time (a) speed–time curve;curve; ((b)) curve;distance–time (b) distance–time curve; (c)) acceleration–timeacceleration–time curve; (c) acceleration–time curve;curve; ((d)) current–timecurrent–time curve; (d curve;)curve; current–time andand ((e)) activeactive curve; power–timepower–time and (e) active curve.curve. power–time curve. When a train runs between two stations, the starting station and the terminal station are each a tractiontractionWhen substationsubstation a train runs [4].[4]. between EstablishEstablish two twotwo stations, tractiontraction the subssubs startingtationstationsstation asas twotwoand nodes,nodes, the thethe terminal traintrain asas station anan idealideal are eachcurrentcurrent a tractionsource, substationthe position [4 ].of Establish the train twoas a traction node and substations the DC traction as two nodes,network the as train a time-varying as an ideal currentresistive source,network. the According position of to the the train Nodal as avoltage node and equation, the DC the traction voltage network for two as traction a time-varying substations resistive can be network.obtained, According as shown in to Figure the Nodal 11. In voltage Figure equation, 11, we can the see voltage that the for peak two value traction of the substations traction network can be obtained,voltage is as 1620 shown V; the in Figurevoltage 11 variation. In Figure accounts 11, we for can 8% see of that the the rated peak voltage. value of the traction network voltage is 1620 V; the voltage variation accounts for 8% of the rated voltage.

FigureFigure 11. 11.Traction Traction network network voltage voltage of of two two traction traction substations substations [38 [38].].

Energies 2020, 13, 4418 11 of 23

On the basis of above traction calculation results, the capacity of the synchronverter-based RBE system of urban rail transit is designed to be 10 MVA, the maximum variation of traction network voltage is 150 V and a traction network voltage variation of 120 V corresponds to an active power variation of 6 MW.

3.2. Parameter Design of the Master Controller Taking the case of the inverter controller, the parameters of the controller can be designed based on above traction calculation results. The voltage fluctuation of the traction network does not exceed 10%, the frequency fluctuation of the grid does not exceed 0.5% and the voltage fluctuation of the grid does not exceed 10%.

3.2.1. Parameter Design of the P-f Control Loop Firstly, the small signal model of the P-f control loop in Figure9 is established as follows:

 ˆ  Tm = Tm0 + Tm   Te = Te0 + Tˆ e   ω = ω + ωˆ (17)  n  ˆ  δ = δn + δ   P = P0 + Pˆ where δ is the phase diﬀerence between the converter output voltage and the grid voltage. At the steady state, the phase of the AC side voltage is approximately equal to that of the grid voltage, thus sin δ0 = δ0. Ignoring the secondary disturbance term [39,40], the small signal expression can be represented as:   Pˆ = Tˆ ω  m m n  ˆ ˆ ˆ  P = Teωn + Te0ωˆ Teωn  dωˆ ≈  J = Tˆ m Tˆ e DPωˆ (18)  dt − −  dδˆ =  dt ωˆ  3E V  ˆ 0 pg ˆ P = X δ where E0 is the steady-state value of the controller output voltage e and X is the total impedance of the AC side of the converter. Using the Laplace transformation, the closed-loop transfer function of the P-f control loop can be obtained:

Pˆ 3E0Vpg ω 2 G (s) = = = n (19) f 2 2 2 Pˆm JXωns + DPXωns + 3E0Vpg s + 2ζωns + ωn

The natural oscillation angular frequency ωs and the damping ratio ζ can be calculated as:  q  3E0Vpg  ωs =  JXωn  q (20)  ζ = D ωnX  2 3JE0Vpg

When the natural oscillation angular frequency ωs is 150 rad/s, the damping ratio ζ is 1 and the impedance X is 0.005, the moment of inertia J can be 16. The P-f droop coeﬃcient DP can be calculated as: ∆T ∆P Dp = . = (21) − 2π fn 2π∆ f ∆θ · For the P-f control loop, a 0.5% change in the grid frequency corresponds to a 100% change in the active power. Energies 2020, 13, 4418 12 of 23

Energies 2020, 13, x FOR PEER REVIEW 12 of 23 3.2.2. Parameter Design of the DC Bus Voltage Control Loop 3.2.2. Parameter Design of the DC Bus Voltage Control Loop The active power of the DC side can be approximately equal to the active power of the AC side The active power of the DC side can be approximately equal to the active power of the AC side when the eﬀect of the parasitic resistance of the converter is ignored. In this sense, the synchronverter when the effect of the parasitic resistance of the converter is ignored. In this sense, the synchronverter output active power P can be calculated as: output active power P can be calculated as: V dV dc𝑉 𝑑𝑉dc P =𝑃=𝑉Vdc( ( + +𝐶Cdc ),), (22) Req dt (22) 𝑅 𝑑𝑡 wherewhereR Reqeqis is the the equivalent equivalent resistance resistance of of the the AC AC side side and andC Cdcdc isis thethe ﬁlterfilter capacitance capacitance ofofthe the DC DC side. side. TheThe small small signal signal expression expression of of the the output output active active power powerP Pis is represented represented as: as: 2Vˆ 2𝑉 dVˆ𝑑𝑉 ˆ 𝑃 =𝑉(dc +𝐶 dc ) (23) P = Vdc0( 𝑅 + Cdc 𝑑𝑡) (23) Req dt Using the Laplace transformation, combined with the P-f control loop transfer function, the transfer Using the Laplace transformation, combined with the P-f control loop transfer function, the transfer function of the DC bus voltage control loop can be obtained: function of the DC bus voltage control loop can be obtained: 𝜔𝑅𝑘 𝑘 ω R k k ( 𝑠+1) (𝑘 +𝑘)𝜔𝜔2 𝑅 n2𝑉eqi p 𝑘 𝐺 (𝑠) = (kp + k )ωnωs Req = 2V ( s + 1) (24) i dc0 ki 𝑅 𝐶 Gv(s) = 𝑠(𝑠 +2𝜁𝜔𝑠+𝜔 )𝑉(𝑅𝐶𝑠= + 2) 𝑠 𝑠 (24) s(s2 + 2ζω s + ω 2)V (R Cs + 2) 𝑠[(s 2) +2𝜁s +1](ReqC 𝑠+1) s s dc0 eq s[( 𝜔) + 2ζ 𝜔+ 1]( 2s + 1) ωs ωs 2 From Equation (24), we can see that the amplitude–frequency characteristic curve of the DC bus From Equation (24), we can see that the amplitude–frequency characteristic curve of the DC bus voltage control loop transfer function has three transition frequencies: 2/ReqC, ki/kp and ωs. Based on voltage control loop transfer function has three transition frequencies: 2/ReqC, ki/kp and ωs. Based on above parameter design, we can determine that 2/ReqC is less than 1 and ki/kp, the reciprocal of the above parameter design, we can determine that 2/ReqC is less than 1 and ki/kp, the reciprocal of the integration time, is generally greater than 1. In this sense, the bode plot of the DC bus voltage loop integration time, is generally greater than 1. In this sense, the bode plot of the DC bus voltage loop transfer function [41] can be obtained, as depicted in Figure 12. transfer function [41] can be obtained, as depicted in Figure 12.

20lgA(ω)/dB ω R k 20lg( s eq i ) -20dB/dec 2Vdc0

-40dB/dec

-20dB/dec ω ω 2 ki c s ω/(rad/s)

ReqC kp -60dB/dec

Figure 12. The amplitude–frequency characteristic curve of the DC bus voltage control loop Figure 12. The amplitude–frequency characteristic curve of the DC bus voltage control loop transfer transfer function. function.

The cut-oﬀ frequency ωc is the angular frequency corresponding to the intersection point of the The cut-off frequency ωc is the angular frequency corresponding to the intersection point of the curve and the 0dB line, as shown in Figure 12, which means ki/kp < ωc < ωs. At the point of the cut-oﬀ curve and the 0dB line, as shown in Figure 12, which means ki/kp < ωc < ωs. At the point of the cut-off frequency ωc, A(ω) is 1. Moreover, assuming ki/kp is r, the PI control parameters of the DC bus voltage frequency ωc, A(ω) is 1. Moreover, assuming ki/kp is r, the PI control parameters of the DC bus voltage loop are calculated as: loop are calculated as:  r 4  2 ωc 2 2 2 2 2 2  Vdc0ωc ωs + 2 2ωc +4ζ ωc (4+Req Cdc ωc ) ⎧  𝜔ωs −  k𝑉i = 𝜔 𝜔 + −2𝜔 +4𝜁 𝜔 (4+𝑅 𝐶 𝜔 ) ⎪  𝜔 ω ω R √r2+1 , (25) ⎪  s n eq  kir 𝑘=k = p ωc , (25) ⎨ 𝜔𝜔𝑅√𝑟 +1 ⎪ 𝑘 𝑟 where Vdc0 is 1500 V, ω⎪n𝑘is= 100π and ωc is less than twice of the power frequency [19]. If ωc is 100π, ωs ⎩ 𝜔 is 150 rad/s, ζ is 1 and r is 4, kpcan be 50 and ki can be 720.

where Vdc0 is 1500 V, ωn is 100π and ωc is less than twice of the power frequency [19]. If ωc is 100π, ωs is 150 rad/s, ζ is 1 and r is 4, kp can be 50 and ki can be 720.

Energies 2020, 13, 4418 13 of 23

3.2.3.Energies Parameter 2020, 13, x DesignFOR PEER of REVIEW the Q-V Control Loop 13 of 23

3.2.3.For Parameter the Q-V control Design loop, of the a 0.5%Q-V Control change inLoop the grid phase voltage amplitude corresponds to a 100% change in the reactive power. According to the reactive power compensation demand, the maximum For the Q-V control loop, a 0.5% change in the grid phase voltage amplitude corresponds to a Q Q V D reactive100% change power variationin the reactive∆ of power. the system According is 6 MW. to Thethe reactive- droop power coe ﬃcompensationcient Q is: demand, the maximum reactive power variation ΔQ of the system∆Q is 6 MW. The Q-V droop coefficient DQ is: D = , (26) Q ∆∆𝑄V 𝐷 = , (26) ∆𝑉 where ∆V is the variation of the primary side phase voltage Vpgm of the transformer, which is selected where ΔV is the variation of the primary side phase voltage Vpgm of the transformer, which is selected to be less than 10% of the Vpgm. In addition, the gain K is calculated as: to be less than 10% of the Vpgm. In addition, the gain K is calculated as:

K =𝐾=𝜔ωnD𝐷Qτ𝜏v,, (27) (27)

where τv is the time constant of the Q-V control. The response speed of the system voltage inner loop where τv is the time constant of the Q-V control. The response speed of the system voltage inner loop control circuit is related to the gain K. The smaller is K, the faster is the response speed of the system. control circuit is related to the gain K. The smaller is K, the faster is the response speed of the system. 4. Results and Discussion 4. Results and Discussion

4.1.4.1. Simulation Simulation Results Results Based on the simulation model, the dynamic response of the RBE feedback system under grid Based on the simulation model, the dynamic response of the RBE feedback system under grid normal and abnormal conditions were verified, with the parameters shown in Table 2. normal and abnormal conditions were veriﬁed, with the parameters shown in Table2.

Table 2. Parameters of the simulation. Table 2. Parameters of the simulation. Parameter Value Parameter Value Parameter Value Parameter Value Parameter Value Parameter Value Cdc 40 μF Rdc 0.03 Ω Ls 0.02 mH Lg Cdc 0.015mH40 µF RRs dc 0.030.005Ω Ω Ls Rg 0.02 mH 0.004 Ω L 0.015mH R 0.005 Ω R 0.004 Ω C g 127 μF Rc s 1000 Ω g R 0.002 Ω µ C 127 F Rc 1000 Ω 4 R 0.002 Ω 4 L 0.002mH DP 1.62 × 104 DQ 4 9.8 × 10 L 0.002mH DP 1.62 10 DQ 9.8 10 J 16.21 K 6.16× × 106 6 kpf × 6 5 × 10−6 J 16.21 K 6.16 10 kpf 5 10− kif 5 × 10−5 5 kpv ×50 kiv × 650 kif 5 10− kpv 50 kiv 650 ut × ut lt V Vut 1550 V1550 V f f ut 50.0550.05 Hz Hz f lt f 49.95 Hz49.95 Hz vut vut 36 kV36 kV vltv lt 3434 kV kV Vb Vb 1200 V 1200 V Rb Rb 0.03 Ω0.03 Ω LgL g 0.0150.015 mH mH Rg Rg 0.004 Ω 0.004 Ω L 0.1 mH C 68 µF k 100 Lb b 0.1 mH Cb b 68 μF pv kpv 100 Kiv 1200 kpi 1 Kii 120 Kiv 1200 kpi 1 Kii 120

4.1.1.4.1.1. Simulation Simulation under under Grid Grid Normal Normal ConditionCondition InIn the the islanded islanded mode, mode, the the system system isis inin self-synchronization.self-synchronization. The The circuit circuit breaker breaker is isswitched switched on onat at 2 s.2 Thes. The system system output output frequency frequencyf ,f, outputoutput activeactive power PP andand output output reactive reactive power power Q Qareare shown shown in in FigureFigure 13 13..

(a)

Figure 13. Cont.

Energies 2020, 13, 4418 14 of 23 Energies 2020,, 13,, xx FORFOR PEERPEER REVIEWREVIEW 14 of 23

((b))

((c))

FigureFigure 13. 13.The The outputoutput frequency,frequency, output output active active power power an andd output output reactive reactive power power of the of system the system in inislandedislanded islanded modemode mode andand and grid-connectedgrid-connected grid-connected mode:mode: mode: ((a)) outputoutput (a) output frequencyfrequency frequency ff;; ((b)) outputoutputf ;(b) activeactive output powerpower active P;; and powerand ((c)) P; andoutput (c) output reactive reactive power power Q.. Q.

AtAt the the time time of of grid grid connection, connection, the the variationvariation of the output output frequency frequency ff,, f output,output output activeactive active powerpower power P andandP and outputoutput reactive reactive power powerQ Qare are all all far far less less than than thethe ratedrated value, as as shown shown in in Figure Figure 13, 13 having, having little little impact impact onon the the grid. grid. Moreover, Moreover, the the regulation regulation speedspeed ofof thethe sy systemstem is is less less than than 0.1s, 0.1s, and and the the output output frequency frequency ff,, f, active power P andand reactivereactive powerpower Q are all restored in 0.1s. The phase voltage vaa andand phasephase currentcurrent iiaa active power P and reactive power Q are all restored in 0.1 s. The phase voltage va and phase current ia ofof the the AC AC side side with with harmonic harmonic analysis analysis areare shownshown inin Figure 14.14.14. AsAs As shownshown shown inin in FigureFigure Figure 14a,b,14a,b, 14a,b, thethe the outputoutput output AC side phase voltage basically remains unchanged at 2 s, and the rms value of output AC side phase ACAC side side phase phase voltage voltage basically basically remains remains unchangedunchanged at 2 s, and the the rms rms value value of of output output AC AC side side phase phase current rises from 0 to 85A, far less than the rated primary side phase current of the transformer current rises from 0 to 85 A, far less than the rated primary side phase current of the transformer (7697.8A),(7697.8A), whichwhich showsshows thethe smoothsmooth grgrid-connectionid-connection ofof thethe system.system. AsAs shownshown inin FigureFigure 14c,d,14c,d, thethe totaltotal (7697.8A), which shows the smooth grid-connection of the system. As shown in Figure 14c,d, the total THD of the voltage injected into the AC grid is 0.03% and the total THD of the current is 1.14%, both THD of the voltage injected into the AC grid is 0.03% and the total THD of the current is 1.14%, both less lessless thanthan 5%,5%, whichwhich meetsmeets thethe GB/TGB/T 14549–199314549–1993 public power grid harmonic standard. than 5%, which meets the GB/T 14549–1993 public power grid harmonic standard.

((a))

((b))

Figure 14. Cont. Energies 2020, 13, 4418 15 of 23 EnergiesEnergies 2020 2020, 13, ,13 x ,FOR x FOR PEER PEER REVIEW REVIEW 15 15of 23of 23

(c) (d) (c) (d) FigureFigure 14. 14.Simulation Simulation results results of of the the AC AC side side voltage voltage and and the the current current in in the the self-synchronization: self-synchronization: ( a()a) the Figure 14. Simulation results of the AC side voltage and the current in the self-synchronization: (a) outputthe outputa-phase a-phase voltage voltageva;(b )v thea; (b output) the outputa-phase a-phase current currentia;(c) harmonicia; (c) harmonic analysis analysis result result of the of output the the output a-phase voltage va; (b) the output a-phase current ia; (c) harmonic analysis result of the a-phaseoutput voltage a-phasev avoltage; and ( dv)a; harmonicand (d) harmonic analysis analysis result ofresult the outputof the outputa-phase a-phase current currentia. ia. output a-phase voltage va; and (d) harmonic analysis result of the output a-phase current ia. SimulationSimulation conditions conditions in in grid-connected grid-connected mode:mode: • Simulation conditions in grid-connected mode: Self-synchronization:Self-synchronization: The The system system startsstarts toto makemake self-synchronization with with the the grid grid atat 0 s. 0 s. •• • Self-synchronization:Traction: The train accelerates The system at starts3 s, and to th makee traction self-synchronization network voltage dropswith the to 1380grid V.at 0 s. Traction: The train accelerates at 3 s, and the traction network voltage drops to 1380 V. •• • Traction:RBE feedback: The train The accelerates train starts at to 3 brake s, and at th 9e s, traction and the networktraction network voltage risesdrops to to 1620 1380 V. V. RBE feedback: The train starts to brake at 9 s, and the traction network rises to 1620 V. •• • RBEQ- feedback:V control: GridThe trainline voltage starts to rms brake value at drops9 s, and to 33the.25 traction kV at 15 network s and rises rises to to35 1620kV at V. 18 s. • • Q-V control: Grid line voltage rms value drops to 33.25 kV at 15 s and rises to 35 kV at 18 s. • Q-VP- control:f control: Grid The gridline frequencyvoltage rms rises value to 50.05 drops Hz to at 33 21.25 s. kV at 15 s and rises to 35 kV at 18 s. • P-f control: The grid frequency rises to 50.05 Hz at 21 s. • P-fAs control: shown The in Figure grid frequency 15, the train rises accelerates to 50.05 Hzat 3 at s, 21the s. DC bus voltage drops and the controller worksAsAs shown shown in the tractionin in Figure Figure mode, 15,15, the thus train the acceleratestraction networ at at 3 3 k s, voltage the DC is bus restored voltage to 1500 drops V andin 3 thes. Then, controller the workstrain in brakes thethe tractiontraction at 9 s, the mode, mode, traction thus thus network the the traction traction voltage network networ rises and voltagek voltage the system is restoredis restored works to in 1500 to the 1500 VRBE in V 3feedback in s. Then,3 s. Then, mode, the train the trainbrakesthus brakes atthe 9 traction s, at the 9 s, traction the network traction network voltage network voltage is restored voltage rises to ri and 1500ses theand V again system the system inworks 3 s. Asworksin shown the in RBE the in Figure RBE feedback feedback 16, when mode, mode, the thus thusthetrain traction the accelerates, traction network network the voltage grid voltage supplies is restored is 6restored MW to traction 1500 to 1500 V againenergy V again in for 3 s. thein As 3 traction s. shown As shown network. in Figure in Figure When 16, when 16,the whentrain the trainis the under regenerative braking at 9 s, the DC traction network feeds 6 MW RBE back to the AC grid. trainaccelerates, accelerates, the grid the suppliesgrid supplies 6 MW 6 tractionMW traction energy energy for the for traction the traction network. network. When When the train the is train under is When the amplitude of the grid line voltage drops by 5% at 15 s, the output reactive power rises by underregenerative regenerative braking braking at 9 s, theat 9 DC s, tractionthe DC traction network network feeds 6 MW feeds RBE 6 MW back RBE to the back AC to grid. the WhenAC grid. the 50%, that is the reactive power needed of the AC grid is compensated by the DC side. When the grid Whenamplitude the amplitude of the grid of line the voltage grid line drops voltage by 5% drops at 15 by s, 5% the at output 15 s, reactivethe output power reactive rises power by 50%, rises that by is line voltage rises to 35 kV at 18 s, the output reactive power drops 3 Mvar accordingly. When the grid 50%,the reactive that is the power reactive needed power of the needed AC grid of the is compensated AC grid is compensated by the DC side. by the When DC theside. grid When line the voltage grid frequency rises by 0.1% at 21 s, the system frequency is synchronized to 50.05 Hz in a few seconds rises to 35 kV at 18 s, the output reactive power drops 3 Mvar accordingly. When the grid frequency lineand voltage the output rises to active 35 kV power at 18 s,rises the byoutput 20%, reactive which me powerans the drops excess 3 Mvar active accordingly. power of the When AC grid the gridis rises by 0.1% at 21 s, the system frequency is synchronized to 50.05 Hz in a few seconds and the output frequencytransmitted rises to by the 0.1% DC side.at 21 In s, this the way,system the frequepowerncy of the is gridsynchronized can be regulated. to 50.05 Hz in a few seconds andactive the power output rises active by 20%,power which rises means by 20%, the which excess me activeans the power excess of the active AC gridpower is transmittedof the AC grid to the is transmittedDC side. In thisto the way, DC the side. power In this of way, the grid the canpower be regulated.of the grid can be regulated.

Figure 15. The DC bus voltage of the system.

Figure 15. TheThe DC DC bus bus voltage voltage of of the the system. system.

EnergiesEnergies 20202020,, 1313,, 4418x FOR PEER REVIEW 16 of 23

(a)

(b)

(c)

Figure 16. The system outputsoutputs underunder gridgrid normalnormal condition:condition: (a) thethe gridgrid frequencyfrequency ffgg and thethe systemsystem output frequency f;;( (bb)) the the system system output output active active power power PP; ;and and (c (c) )the the system system output output reactive reactive power power QQ. .

Simulation conditioncondition ofof thethe energyenergy storagestorage modulemodule inin thethe islandedislanded mode:mode:

• ChargingCharging mode:mode: The traction networknetwork voltagevoltage risesrises toto 16201620 VV atat 11 s.s. • DischargingDischarging mode:mode: The traction networknetwork voltagevoltage dropsdrops toto 13801380 VV atat 33 s.s. • As shown in Figure 1717,, the tractiontraction network voltage rises to 1620 V at 11 s;s; thethe storagestorage modulemodule worksworks inin thethe chargingcharging mode,mode, absorbingabsorbing 66 MWMW activeactive power;power; and thethe tractiontraction networknetwork voltagevoltage is restoredrestored toto 1500 1500 V V after after ﬂuctuation. fluctuation. Then, Then, the tractionthe traction network network voltage voltage drops drops at 3 s; theat 3 storage s; the modulestorage worksmodule in works the discharging in the discharging mode, releasing mode, releasing 6 MW active 6 MW power; active and power; the traction and the network traction voltage network is restoredvoltage is to restored 1500 V afterto 1500 ﬂuctuation. V after fluctuation.

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(a)

(b)

Figure 17. Dynamic response of the energy storage module to variation of the DC bus voltage: ( a) the DC bus voltage; and (b)) thethe activeactive powerpower ofof thethe module.module.

Simulation condition of the energy storagestorage modulemodule inin thethe grid-connectiongrid-connection mode:mode: • • Self-synchronization mode:mode: The system starts to make self-synchronization atat 00 s.s. • • Grid-connection mode:mode: The system is connected to the grid at 2 s. • P-f control: The grid frequency rises to 50.05 Hz at 3 s. P--ff control: The The grid grid frequency frequency rises to 50.05 Hz at 3 s. • As shown in Figure 18, at 3 s, as the grid frequency fg rises, the system frequency f synchronously As shown in Figure 1818,, at 3 s, as the grid frequency ffg rises,rises, the the system system frequency frequency f synchronouslysynchronously rises to 50.05 Hz. Accordingly, the output active power Pg drops to −1.6 MW, which means the excess rises to 50.05 Hz. Accordingly, thethe output active power P drops toto −1.6 MW, which means the excess energy of the AC grid is transmitted to the DC side, and the storage− module works in the charging energy of the AC grid is transmittedtransmitted to the DC side,side, and the storagestorage module works in the charging mode, absorbing 1.6 MW active power transmitted from the AC side. mode, absorbing 1.6 MW active power transmitted from the AC side.

(a) Figure 18. Cont.

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(b) (b) Figure 18. Dynamic response of the energy storage module to variation of the grid frequency: (a) the gridFigure frequency 18. Dynamic fg and response the system of the output energy frequency storage f ;module and (b) tothe variation energy storage of the grid module frequency: active power( a) the Pgridb and frequency the system fg and andoutput the the systemactive system power output output P frequency. frequency ff;; and and ( (bb)) the the energy energy storage storage module module active active power power Pb andand the the system system output output active power P.. The simulation results of the energy storage module show that, when the system is off the grid, the energyThe simulation storage module results canof the absorb energy RBE storage of the module DC traction show show networkthat, that, when when as thean the auxiliarysystem system is is module off oﬀ thethe grid, grid,and feedthe energyenergy it back storagestorage to the DC module module traction can can absorbnetwork absorb RBE RBEwhen of of the nece the DC ssary.DC traction traction Moreover, network network when as an as the auxiliaryan system auxiliary module is connectedmodule and feedand to thefeedit back grid, it back to the to DC energythe tractionDC tractionstorage network networkmodule when canwhen necessary. provide necessary. Moreover,the Moreover,energy when needed when the systemthefor systemactive/reactive is connected is connected power to the to regulationthegrid, grid, the energythe of theenergy storage grid, withoutstorage module moduleaffectin can provideg canthe stability theprovide energy ofthe neededth eenergy DC bus for needed activevoltage./reactive for active/reactive power regulation power of regulationthe grid, without of the grid, aﬀecting without the stabilityaffecting of the the stability DC bus of voltage. the DC bus voltage. 4.1.2. Simulation under Grid Faults 4.1.2. Simulation Simulation under Grid Faults Simulation conditions: Simulation conditions: • The converter is connected to the power grid at 1 s. • The converter is connected to the power grid at 1 s. • The grid line voltage drops by 50% at 2 s and restores at 2.1 s. • The grid frequency line voltage drops drops by by 1% 50%50% at 3 atat s 22and ss andand restores restoresrestores at 3.1atat 2.1 2.1s. s.s. • • The grid frequency drops byby 1%1% atat 33 ss andand restoresrestores atat 3.13.1 s.s. • As shown in Figure 19, when the grid frequency plummets at 2 s, the system frequency drops accordingly.As shown When in Figure the grid 19,19 ,frequency when the restores grid frequencyfrequenc at 2.1 s,y plummets the system at frequency 2 s, the system is restored frequency quickly. drops The outputaccordingly. voltage When When of the the the systemgrid grid frequency frequencydrops slightly restores restores when at 2. at1 2.1thes, the s,grid thesystem voltage system frequency plummets frequency is restored at is restored3 s andquickly. restores quickly. The quicklyTheoutput output voltageafter voltage the of grid the of fault thesystem systemis cleared, drops drops whichslightly slightly shows when when a greatthe the grid fault grid voltage ride-through voltage plummets plummets capability at at 33 s sof and and the restores system. quickly after the grid fault is is cleared, cleared, which which shows shows a a great great fault fault ride-through ride-through capability capability of of the the system. system.

(a) (a) Figure 19. Cont.

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((bb))

FigureFigure 19. 19. Dynamic Dynamic response responseresponse of of the the system system toto gridgrid faults:faults: ( (aa)) the the reference reference frequency frequency ff nfn and andand the thethe system systemsystem outputoutput frequencyfrequency ff ;;f ; andand and (( b(bb))) thethe the rmsrms rms value value value of of of the the the system system systema -phasea a-phase-phase output output output voltage voltage voltageV aV Vandaa and and the the the rms rms rms value value value of oftheof the the grid grid grid voltage voltage voltageVpga V Vpgapga. . .

BasedBased onon aboveabove simulationsimulation results, results, when when the the traitraintrainn isis inin tractiontraction mode,mode, thethe systemsystem cancan transmittransmit thethe corresponding corresponding amount amount of ofof tracti tractiontractionon energy energy to to thethe DCDC tractiontraction nenetworknetworktwork toto compensatecompensate thethe tractiontraction networknetwork energy,energy, accordingaccording toto thethe variationvariation ofof DCDC busbubuss voltage.voltage. WhenWhen thethe traintrain isis braking,braking, RBERBE ofof thethe traintrain is is fedfed backback toto thethe ACAC grid.grid. In InIn addition, addition, the thethe aboveabove resultsresults alsoalso showshow th thatthatat the the system system has has a a goodgood gridgrid power power regulation regulation capabilitycapability andand faultfault ride-throughride-through capability.capability.

4.2.4.2. Experimental ExperimentalExperimental Results ResultsResults DueDue toto thethe restrictedrestricted experimentalexperimental laboratorylaboratory coconditions,conditions,nditions, thethe systemsystem funcfunctionfunctiontion waswas verifiedveriﬁedverified byby aa scaled-downscaled-down prototype. prototype. As AsAs shown shownshown in inin Figure FigureFigure 20, 2020,, the thethe system systemsystem model modelmodel prototype prototypeprototype is isis composed composedcomposed of ofof a aa power powerpower supply,supply, a aa DSP DSPDSP module, module,module, a driveaa drivedrive circuit, circuit,circuit, a sampling aa samplingsampling circuit circuitcircuit and a andand main aa main powermain powerpower circuit. circuit.circuit. The DC TheThe side DCDC voltage sideside voltageofvoltage the model of of the the is model model 140 V, is is and 140 140 the V, V, ratedandand the the phase rate rated voltaged phase phase ofvoltage voltage the AC of of sidethe the AC isAC 50 side side V. is is 50 50 V. V.

FigureFigure 20. 20. The The experimental experimental model modelmodel of ofof the thethe synchr synchronverter-basedsynchronverter-basedonverter-based RBE RBE feedback feedback system. system.

AsAs shown shown in in Figure Figure 2121a, 21a,a, whenwhen thethe DCDC busbus voltage voltage VV Vdcdc rises rises by by 14 14 V, V, the thethe system systemsystem works worksworks in inin the thethe RBE RBERBE feedbackfeedback mode.mode. The TheThe AC ACAC side sideside voltagevoltage VVabcabcabc isisis nearlynearly nearly constant,constant, constant, withwith with thethe the rmsrms valuevalue of of 50 50 V. V. The TheThe AC ACAC side sideside currentcurrent i iiabcabc risesrises to toto 1.51.5 A,A, whichwhich means meansmeans the thethe DC DCDC side sideside feeds feedsfeeds 225 225225 W WW RBE RBERBE back backback to toto the thethe AC ACAC side. side.side. As AsAs shown shownshown in inFigurein Figure Figure 21 21b,b, 21b, when when when the the the system system system works works works in in in the the the rectiﬁer rectifier rectifier mode, mode, mode, the the the AC AC AC side side side voltage voltage voltageV V Vabcabcabc is isis nearly nearlynearly constant, constant,constant, withwith thethe rms rmsrms value valuevalue of ofof 50 5050 V, V,V, and andand the thethe AC ACAC side sideside current currentcurrentiabc iiabcabcrises risesrises to to 1.4to 1.41.4 A. A. TheA. TheThe phase phasephase diﬀ differenceerencedifference between betweenbetween the thecurrentthe currentcurrentia and iiaa andand the the voltagethe voltagevoltageva is vva 180a isis ◦180°,180°,, which whichwhich means meansmeans the the ACthe AC sideAC sideside feeds feedsfeeds 212 212 W212 traction WW tractiontraction energy energyenergy into intointo the theDCthe DC side.DC side. side.

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((aa)) ((bb))

FigureFigure 21. 21.21. TheThe resultsresults of ofof the thethe system systemsystem bi-directional bi-directionalbi-directional ﬂow flowflow experiment: experiment:experiment: (a) the((aa)) phasethethe phasephase voltage voltagevoltage and the andand phase thethe phasecurrentphase current current of the of ACof the the side AC AC in side side the in inverterin the the inverter inverter feedback feedback feedback mode; mode; andmode; (b )and and the ( phase(bb)) the the voltagephase phase voltage voltage and the and and phase the the currentphase phase currentofcurrent the AC of of the sidethe AC AC in theside side traction in in the the traction traction mode. mode. mode.

DueDue to to the the limitation limitation of of the the experimental experimentalexperimental cond conditions,conditions,itions, the the frequency frequency and and amplitude amplitude of of the the grid grid cannotcannot be be suddenly suddenly changed. changed. InIn In thisthis this sense,sense, sense, thethe the compensationcompensation abilityability ability ofof of thethe systemsystem forfor the the active active powerpower and and reactive reactive power power of of the the grid grid was was verified veriﬁedverified by by giving giving the the active active power power and and reactive reactive power power compensationcompensation instructionsinstructions inin thethe DSP DSP program. program. AsAs As shownshown inin FigureFigure 22a, 22a,22a, whenwhen the the system system is is given given 450450 W W active active power, power, the thethe rms rmsrms value valuevalue of ofof the thethe a aa-phase-phase-phase voltage voltagevoltage v vvaaa of of the the AC AC side side remains remains constant constant and and the the rmsrms value valuevalue of ofof the the a a-phase-phase currentcurrent current ii aaia risesrises rises toto to 2.92.9 2.9 A,A, A,with with with a a a power power power factor factor factor of of of 0.95. 0.95. 0.95. The The The system system system feeds feeds feeds 413.3 413.3 413.3 W WactiveW activeactive power powerpower into intointo the the grid,the grid,grid, which whichwhich is close isis closeclose to the toto given ththee givengiven value. value.value. As shown AsAs shownshown in Figure inin Figure Figure22b, when 22b,22b, the whenwhen system thethe systemissystem given is is 450 given given Var 450 450 reactive Var Var reactive reactive power, thepower, power, rms the valuethe rms rms of value thevalue phase of of the the voltage phase phase vvoltage voltagea of the v ACvaa of of sidethe the AC remainsAC side side remains constantremains constantandconstant the rms andand value thethe rmsrms of the valuevalue phase ofof the currentthe phasephaseia rises currentcurrent to 3.1 iaia rises A,rises with toto 3.1 a3.1 power A,A, withwith factor aa powerpower of 0.06. factorfactor The system ofof 0.06.0.06. feeds TheThe system437.1system Var feeds feeds reactive 437.1 437.1 powerVar Var reactive reactive into the power power power into into grid, the the which power power is grid, grid, close which which to the is is given close close value. to to the the given given value. value.

((aa)) ((bb))

FigureFigure 22. 22. System System dynamic dynamic response: response: ( (a a)) )a aa-phase-phase-phase voltage voltage voltage and and a a-phase-phase current current of of the the AC AC side side in in active active powerpower compensation compensation mode;mode; andand ((b b)) aa-phase-phase voltage voltage andand a a-phase-phase currentcurrent ofof the the AC AC side side in in reactive reactivereactive powerpower compensation compensation mode. mode. In summary, the experimental results are consistent with the theoretical analysis done and the InIn summary,summary, thethe experimentalexperimental resultsresults areare consisteconsistentnt withwith thethe theoreticaltheoretical analysisanalysis donedone andand thethe simulation results, showing the good dynamic performance of the system. simulationsimulation results, results, showing showing the the good good dynamic dynamic performance performance of of the the system. system.

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5. Conclusions To improve the utilization of RBE of the train, a synchronverter-based RBE feedback system of urban rail transit is designed in this paper. The structure of the system is presented first, and then the control strategy is fully discussed. The synchronverter-based control proposed in this paper offers a more flexible and stable approach to give RBE back to the AC grid. Moreover, the capacity of the system is designed according to the traction calculation and the parameters of the system are analyzed in detail. The simulation and experimental results are both provided to verify the good dynamic performance of the system under grid normal condition and grid faults. By using the synchronverter-based approach, the system supplies traction power to traction network when the train accelerates and feeds RBE back into the AC grid when the train brakes, in light of the variation of the DC bus voltage, thus keeping the DC traction network constant. Moreover, the system can be self-synchronized with the grid and make corresponding response according to the variation of the grid voltage or the variation of the grid frequency. In this sense, the grid power can be easily regulated and safeguarded by the system. Furthermore, the system dynamic performance under grid faults also shows a good fault ride-through capability of the system. In addition, with the help of the energy storage module, the system is able to operate in both islanded mode and grid-connection mode. Consequently, by using the proposed synchronverter-based approach, the RBE feedback system becomes more flexible, effective and robust. The calculation accuracy of the traction energy and RBE will be improved in future work, along with the impact of inductive load of lines.

Author Contributions: Conceptualization, S.L. and S.W.; methodology and software, S.L.; validation, S.L., S.X. and Y.Z.; writing—original draft preparation, S.L.; writing—review and editing, S.W. and J.C.V.; project administration, S.W.; and resources, supervision and funding acquisition, S.W. and J.M.G. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by VILLUM FONDEN under the VILLUM Investigator Grant (No. 25920): Center for Research on Microgrids (CROM); www.crom.et.aau.dk. Acknowledgments: The authors would like to show gratitude to PCC laboratory of Southwest Jiaotong University for providing equipment and suggestions on revision. In addition, we would like to thank the three prestigious reviewers for their valuable comments that improved the quality of this paper. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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