Balancing the active power of a railway traction power substation with an sp-RPC
Abstract
The railway system is one of the safest, most efficient, and environmentally friendly means of land transport for people and goods. However, as the demand for mobility has increased, the current railway system has shown some weaknesses, requiring an increase in catenary power in order to be able to supply power to longer trains and faster locomotives, as well as to increase rail traffic. This paper proposes a control algorithm to be implemented in a sectioning post-Rail Power Conditioner (sp-RPC). The sp-RPC is connected to the neutral section between two traction power substations (TPS). With the control algorithm, it is possible to minimize the existing unbalance of the active powers of each TPS. In a regenerative braking condition, this surplus energy can be used to assist the traction of another locomotive on the existing overhead line. In this way, it is possible to increase the capacity of the overhead line. The analysis was performed with computer models using a modular multilevel converter (MMC) topology for the sp-RPC. Quantitative results for different consumption events of the locomotives and the analysis of the response to these variations are presented.
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Citation: Barros, L.A.M.; Martins, A.P.; Pinto, J.G. Balancing the Active Power of a Railway Traction Power Substation with an sp-RPC. Energies 2023,16, 3074. https://doi.org/ 10.3390/en16073074 Academic Editor: Mario Marchesoni Received: 1 March 2023 Revised: 21 March 2023 Accepted: 25 March 2023 Published: 28 March 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). energies Article Balancing the Active Power of a Railway Traction Power Substation with an sp-RPC Luis A. M. Barros 1,* , António P. Martins 2and JoséGabriel Pinto 1 1ALGORITMI Research Centre/LASI, University of Minho, 4800-058 Guimarães, Portugal 2SYSTEC Research Center, University of Porto, 4200-465 Porto, Portugal *Correspondence: lbarr[email protected] Abstract: The railway system is one of the safest, most efficient, and environmentally friendly means of land transport for people and goods. However, as the demand for mobility has increased, the current railway system has shown some weaknesses, requiring an increase in catenary power in order to be able to supply power to longer trains and faster locomotives, as well as to increase rail traffic. This paper proposes a control algorithm to be implemented in a sectioning post-Rail Power Conditioner (sp-RPC). The sp-RPC is connected to the neutral section between two traction power substations (TPS). With the control algorithm, it is possible to minimize the existing unbalance of the active powers of each TPS. In a regenerative braking condition, this surplus energy can be used to assist the traction of another locomotive on the existing overhead line. In this way, it is possible to increase the capacity of the overhead line. The analysis was performed with computer models using a modular multilevel converter (MMC) topology for the sp-RPC. Quantitative results for different consumption events of the locomotives and the analysis of the response to these variations are presented. Keywords: electric railway system; neutral section; multilevel converter; regenerative braking; sectioning post-Rail Power Conditioner 1. Introduction The constant population increase, forecasting a growth of 38%, reaching a value of 10.88 billion people in 2100 [ 1 ], as well as the migration to large urban centers, varying the current ratio from 5/10 people to 7/10 people in 2050 [ 2 ], has demonstrated the weakness of the current means of transportation. The railway system is one of the primary means of land transport for transporting people and goods. The electric railway system is energy efficient [ 3 ], environmentally friendly [ 4 ], safe [ 5 ], and capable of responding to the demand for mobility [ 3 ]. This leads to the fact that the railway system adds a distinct footprint to the economy of each country, which has encouraged investment in the railway sector. In order to meet these requirements, different countries aim to increase the speed and size of locomotives. An example is the Portuguese case that intends to increase the number of daily locomotives, speed, and size (up to 750 m). In some cases, this represents a twoto three-times increase in daily energy capacity. Furthermore, with an investment of over EUR 2 billion and over 1000 km of the line under intervention, the aim is to reduce the cost of transport (EURO/km/carriage) and increase catenary capacity (number and length of locomotives) [ 6 ]. Another example of an incentive is the European organization Shift2Rail which aims to reduce the life cycle cost of rail transport by up to 50%; double railway capacity; and increase reliability by up to 50% [ 7 , 8 ]. As it turns out, Shift2Rail is committed to making the railway system more efficient, safer, and greener, with a view to “providing, through rail research and innovation, the capabilities needed to achieve a more sustainable, cost-effective mode of transport, high performance, time-oriented, digital and competitive for Europe” [7]. Energies 2023,16, 3074. https://doi.org/10.3390/en16073074 https://www.mdpi.com/journal/energies
Energies 2023,16, 3074 2 of 22 Taking into consideration the ambitions presented as well as the predominance of the 25 kV, 50 Hz railway system, this system is analyzed to identify its weaknesses and possible improvements. In order to avoid power flow between traction power substations (TPS) due to different voltage values or phases, it is necessary to incorporate unpowered railway extensions to create isolation between TPS. These extensions are referred to as neutral sections [ 9 , 10 ]. One of the most used electrification solutions is V/Vor Scott transformers to feed the overhead lines [ 11 ]. This solution allows a better balance in the powers of each phase of the TPS. However, if there is a large unbalance in the consumption values of the locomotives in each catenary, it will accentuate the unbalance between phases of the three-phase system [ 12 ]. This problem can be mitigated by incorporating power electronics solutions such as the rail power conditioner (RPC). The RPC allows for minimizing this unbalance [ 13 – 15 ] as well as mitigating other power quality problems [ 16 ]. Furthermore, the fact that it is connected close to the TPS allows access to the different voltage and current variables instantaneously, presenting a dynamic response to any type of variation. These solutions consider each TPS as a microsystem without any interaction with adjacent TPS. In the case of a strong unbalance of the locomotives coupled to the catenaries, it will cause one TPS to operate at its maximum capacity. In contrast, the adjacent TPS operates at a percentage of its capacity. One solution to mitigate this problem is to add a power electronics converter in the neutral section in order to control the power flow between TPS [ 17 ]. Hitachi presents in [ 18 ] a solution to minimize this problem, called sectioning post-RPC (sp-RPC). The developed sp-RPC was integrated into the neutral section at Ushiku, existing between Fujishiro and Tsuchiura TPS in Japan. The sp-RPC was sized to operate with a nominal voltage of 22 kV and a nominal power of 1.3 MW for each loop. In overload mode, the sp-RPC can operate with a maximum value of 5.3 MW for a maximum period of 1 min, at more than 10 min intervals. The sp-RPC developed by Hitachi also features a static VAr compensator (SVC) functionality up to a maximum value of 1.3 MVAr. The operating values of the sp-RPC are adjusted according to the hourly forecast and the speed of the locomotives. This solution based on hourly forecast has errors that can reach 6.5% compared to the actual consumption values. This deviation is due, essentially, to delays. Nevertheless, the solution presented is exclusive to regenerative braking events. The authors of [ 19 ] present an analysis of an sp-RPC in terms of power losses using the Monte Carlo analysis. The study finds that the railway traffic, as well as the railway extension between the TPS and the neutral section, should be considered. It is intended to determine the best location for the sp-RPC in order to minimize power losses while keeping the two TPS operating at similar active powers. Regarding the semiconductor market, it is possible to see a breakthrough in the 6500 V blocking voltage barrier. In addition, in this market of high-voltage and power semiconductors, it is possible to see an increase in switching frequencies, enabling the development of more compact solutions. As an example, it can highlight the technology 4H-SiC [ 20 , 21 ] or double implanted MOSFET (DMOSFET) [ 22 ] emerging to break the 10 kV barrier. Cree presented a new SiC MOSFET for 10 kV and 240 A, featuring 116 kV/ µ s transitions during turn-on and 70 kV/ µ s during turn-off [ 23 ]. Another example is a 10 kV and 120 A MOSFET module with a half-bridge configuration for a solid-state power substation. These modules allowed configuring a switching frequency of 20 kHz, contributing to 70% less weight and 50% less volume than a 60 Hz low-frequency transformer [24]. This paper intends to contribute to the study and development of a dynamic control algorithm capable of incorporating an sp-RPC. The control algorithm is based on the average operating power of each TPS. This information is periodically sent to the sp-RPC. This paper is structured as follows: in Section 1, an introduction of the railway power systems is performed, highlighting the state-of-the-art of the RPC connected in neutral sections; in Section 2, the sp-RPC concept is realized, analyzing the possible operation modes; in Section 3, the proposed dynamic control algorithm to be integrated into sp-RPC is presented, taking into account a modular multilevel converter topology of sp-RPC to
Energies 2023,16, 3074 3 of 22 interface with a 25 kV/50 Hz electric rail system; in Section 4, the performance of spRPC with the proposed algorithm for different locomotive power conditions is analyzed; Section 5is used for the quantitative analysis of the obtained results; Section 6is a discussion of the obtained results, presenting the conclusions. 2. sp-RPC Concept The sp-RPC is a power electronics device connected in the neutral section between two TPS. Knowing the average operating powers of each TPS, the sp-RPC can control the flow of energy between TPS in order to balance the operating powers of each TPS. In this way, overloading at a single TPS is avoided by increasing the capacity of the overhead line. Nevertheless, in the event of regenerative braking, the sp-RPC can use surplus energy to minimize the existing power consumption in the TPS. In the event of zero consumption, this surplus energy is distributed equally between the two TPS. Figure 1shows the integration of an sp-RPC in a 25 kV railway system. Energies2023,16,xFORPEERREVIEW3of23 systemsisperformed,highlightingthestate‐of‐the‐artoftheRPCconnectedinneutral sections;inSection2,thesp‐RPCconceptisrealized,analyzingthepossibleoperation modes;inSection3,theproposeddynamiccontrolalgorithmtobeintegratedintosp‐RPC ispresented,takingintoaccountamodularmultilevelconvertertopologyofsp‐RPCto interfacewitha25kV/50Hzelectricrailsystem;inSection4,theperformanceofsp‐RPC withtheproposedalgorithmfordifferentlocomotivepowerconditionsisanalyzed; Section5isusedforthequantitativeanalysisoftheobtainedresults;Section6isa discussionoftheobtainedresults,presentingtheconclusions. 2.sp‐RPCConcept Thesp‐RPCisapowerelectronicsdeviceconnectedintheneutralsectionbetween twoTPS.KnowingtheaverageoperatingpowersofeachTPS,thesp‐RPCcancontrolthe flowofenergybetweenTPSinordertobalancetheoperatingpowersofeachTPS.Inthis way,overloadingatasingleTPSisavoidedbyincreasingthecapacityoftheoverhead line.Nevertheless,intheeventofregenerativebraking,thesp‐RPCcanusesurplusenergy tominimizetheexistingpowerconsumptionintheTPS.Intheeventofzeroconsumption, thissurplusenergyisdistributedequallybetweenthetwoTPS.Figure1showsthe integrationofansp‐RPCina25kVrailwaysystem. Figure1.Electricrailwaysystemwiththeintegrationofthesp‐RPC. ThefurtherthelocomotiveisfromtheTPS,thegreaterthevoltagedropcausedby theimpedanceoftheoverheadcontactline.Inturn,intheeventofregenerativebraking, theeffectivevalueoftheoverheadcontactlinevoltagerises.Thesevariationscausedby theabovephenomenacanbeminimizedwiththesp‐RPCsinceitislocatedintheneutral section,atthefurthestpointfromtheTPS.Thiscontrolisaccomplishedbythereactive energyproducedbythesp‐RPC,capacitiveorinductive,incaseofunder‐voltageorover‐ voltage.Furthermore,byimposingamoreconstantrootmeansquare(rms)valueofthe overheadcontactlinevoltage,itispossibletomaintainanequallyconstantcurrentvalue foragivenpowerconsumption.Thisensuresamorestablepowersystem. 3.sp‐RPCProposedandOperationPrinciple Thissectionpresentstheentirestructureofthesp‐RPCforarealapplicationandthe proposedcontrolalgorithmforbalancingtheactivepowersofeachTPS.Inaddition,the othercontrolalgorithmsresponsibleforthesynchronismwiththevoltageinthecatenary, theoutputcurrentcontrol,theregulationofthedifferentdc‐linksaswellasthetechniques forthesp‐RPCarealsopresented. Power Grid 1 Catenary Rail NS A B C 220 kV Power Grid 2 220 kV A B C NS NS Power Transformer 25 kV25 kV Power Transformer 25 kV25 kV N 2 N 2 N 1 2 N 1 2 3 N 1 2 Scott BCA yx N 1 N 1 N 2 N 2 V/V BCA yx yxy x sp-RPC P PGx P PGy P spRPCx P spRPCy P trans Figure 1. Electric railway system with the integration of the sp-RPC. The further the locomotive is from the TPS, the greater the voltage drop caused by the impedance of the overhead contact line. In turn, in the event of regenerative braking, the effective value of the overhead contact line voltage rises. These variations caused by the above phenomena can be minimized with the sp-RPC since it is located in the neutral section, at the furthest point from the TPS. This control is accomplished by the reactive energy produced by the sp-RPC, capacitive or inductive, in case of under-voltage or overvoltage. Furthermore, by imposing a more constant root mean square (rms) value of the overhead contact line voltage, it is possible to maintain an equally constant current value for a given power consumption. This ensures a more stable power system. 3. sp-RPC Proposed and Operation Principle This section presents the entire structure of the sp-RPC for a real application and the proposed control algorithm for balancing the active powers of each TPS. In addition, the other control algorithms responsible for the synchronism with the voltage in the catenary, the output current control, the regulation of the different dc-links as well as the techniques for the sp-RPC are also presented. 3.1. sp-RPC Topology Considering the 25 kV on the catenary, modularity, and multilevel concepts were used. The proposed topology is shown in Figure 2. As can be seen, different submodules connected in series were used for the high-voltage ac catenary side. The low-voltage dc
Energies 2023,16, 3074 4 of 22 side of these submodules is common, which facilitates energy exchange and minimizes the complexity of the control algorithms. In order to provide isolation, the dual-active bridge (DAB) topology was integrated into each submodule. The DAB integrated in each submodule is responsible for the exchange of energy between the common dc-link and the submodule high-voltage dc-link. Nevertheless, the transformation ratio used in the high-frequency transformer of the DAB allows the creation of a common lowvoltage dc-link and a dedicated high-voltage dc-link for each submodule. In this way, the number of submodules used can be adjusted as a function of the transformation ratio. This topology features a structure similar to a solid-state transformer (SST), thus incorporating the advantages of an SST. That is, it features a low-voltage dc side and a high-voltage dc and ac side. To better understand the explanation, the power converter connected to the x-side was called spRPCx. In turn, the power electronics converter connected to the y-side was called spRPCy. Due to the modular structure, it is possible to implement redundant operating mechanisms, increasing the robustness of the system. Although it is outside the scope of this article, some protection and fault tolerance mechanisms are presented in [ 25 ]. Energies2023,16,xFORPEERREVIEW4of23 theoutputcurrentcontrol,theregulationofthedifferentdc-linksaswellasthetechniques forthesp-RPCarealsopresented. 3.1.sp‐RPCTopology Consideringthe25kVonthecatenary,modularity,andmultilevelconceptswere used.TheproposedtopologyisshowninFigure2.Ascanbeseen,differentsubmodules connectedinserieswereusedforthehigh-voltageaccatenaryside.Thelow-voltagedc sideofthesesubmodulesiscommon,whichfacilitatesenergyexchangeandminimizes thecomplexityofthecontrolalgorithms.Inordertoprovideisolation,thedual-active bridge(DAB)topologywasintegratedintoeachsubmodule.TheDABintegratedineach submoduleisresponsiblefortheexchangeofenergybetweenthecommondc-linkand thesubmodulehigh-voltagedc-link.Nevertheless,thetransformationratiousedinthe high-frequencytransformeroftheDABallowsthecreationofacommonlow-voltage dc-linkandadedicatedhigh-voltagedc-linkforeachsubmodule.Inthisway,thenumber ofsubmodulesusedcanbeadjustedasafunctionofthetransformationratio.Thistopologyfeaturesastructuresimilartoasolid-statetransformer(SST),thusincorporatingthe advantagesofanSST.Thatis,itfeaturesalow-voltagedcsideandahigh-voltagedcand acside.Tobetterunderstandtheexplanation,thepowerconverterconnectedtothex‐side wascalledspRPCx.Inturn,thepowerelectronicsconverterconnectedtothey-sidewas calledspRPCy.Duetothemodularstructure,itispossibletoimplementredundantoperatingmechanisms,increasingtherobustnessofthesystem.Althoughitisoutsidethe scopeofthisarticle,someprotectionandfaulttolerancemechanismsarepresentedin[25]. Figure2.Electricalschematicoftheproposedtopologyforthesp-RPC. Themainparametersoftheoperatingconditionsofthesp-RPCandtherestofthe railwaysystemarepresentedinTable1.TheaveragenominalpowerforthespRPCx, PspRPCx,andthespRPCy,PspRPCyof2.5MW,wasconsideredforthedevelopedsimulationmodel.Regardingthedc-link,anominalvoltageof1kVwasconsideredonthe commondc-link,vdc,andavoltageof7kVonthededicateddc-linkofeachsubmodule, DAB_y6 DAB_y5 DAB_y4 DAB_y3 DAB_y2 DAB_y1 Sy2 Sy1 Sy3 Sy4 C y1 Sy6 Sy5 Sy7 Sy8 C y2 Sy10 Sy9 Sy11 Sy12 C y3 Sy14 Sy13 Sy15 Sy16 C y4 Sy18 Sy17 Sy19 Sy20 C y5 Sy22 Sy21 Sy23 Sy24 C y6 Sx70 Sx69 Sx71 Sx72 Sx66 Sx65 Sx67 Sx68 Sx22 Sx21 Sx23 Sx24 Sx62 Sx61 Sx63 Sx64 Sx58 Sx57 Sx59 Sx60 Sx18 Sx17 Sx19 Sx20 Sx54 Sx53 Sx55 Sx56 Sx50 Sx49 Sx51 Sx52 Sx14 Sx13 Sx15 Sx16 Sx46 Sx45 Sx47 Sx48 Sx42 Sx41 Sx43 Sx44 Sx10 Sx9 Sx11 Sx12 Sx38 Sx37 Sx39 Sx40 Sx34 Sx33 Sx35 Sx36 Sx6 Sx5 Sx7 Sx8 Sx30 Sx29 Sx31 Sx32 Sx26 Sx25 Sx27 Sx28 Sx2 Sx1 Sx3 Sx4 v dc C x1 C x2 C x3 C x4 C x5 C x6 Sy71 Sy72 Sy63 Sy64 Sy55 Sy56 Sy47 Sy48 Sy39 Sy40 Sy31 Sy32 Sy70 Sy69 Sy62 Sy61 Sy54 Sy53 Sy46 Sy45 Sy38 Sy37 Sy30 Sy29 Sy66 Sy65 Sy67 Sy68 Sy58 Sy57 Sy59 Sy60 Sy50 Sy49 Sy51 Sy52 Sy42 Sy41 Sy43 Sy44 Sy34 Sy33 Sy35 Sy36 Sy26 Sy25 Sy27 Sy28 v dc_y5 v dc_y4 v dc_y3 v dc_y2 v dc_y1 v dc_y6 v dc_x6 v dc_x5 v dc_x4 v dc_x3 v dc_x2 v dc_x1 vspRPCy vspRPCx N:1 T x1 N:1 T x2 N:1 T x3 N:1 T x4 N:1 T x5 N:1 T x6 1:N T y1 1:N T y2 1:N T y3 1:N T y4 1:N T y5 1:N T y6 C 1 spRPCx Submodule_x6 spRPCy voutx vouty Submodule_x5 Submodule_x4 Submodule_x3 Submodule_x2 Submodule_x1 LspRPCx LspRPCy Figure 2. Electrical schematic of the proposed topology for the sp-RPC. The main parameters of the operating conditions of the sp-RPC and the rest of the railway system are presented in Table 1. The average nominal power for the spRPCx, PspRPCx, and the spRPCy, PspRPCy of 2.5 MW, was considered for the developed simulation model. Regarding the dc-link, a nominal voltage of 1 kV was considered on the common dc-link, v dc , and a voltage of 7 kV on the dedicated dc-link of each submodule, v dc_xk , and v dc_yk ,k being the number of the submodule of the x-side or y-side. The value of 1 kV was defined in order to obtain a voltage value on the low-voltage common dc-link. In this way, it would be easier to integrate a solar photovoltaic system and an energy storage system with a lower voltage interface.
Energies 2023,16, 3074 5 of 22 Table 1. Main parameters of the topology. Variable Nominal Unit Nominal active power for the sp-RPC Psp_RPCx,Psp_RPCy 2.5 MW Common dc-Link nominal voltage Vdc 1 kV Nominal voltage on the dedicated dc-links of the sp-RPC V dc _ x1 ,V dc _ x2 ,V dc _ x3 ,V dc _ x4 ,V dc _ x5 ,V dc _ x6 , Vdc_y1,Vdc_y2,Vdc_y3,Vdc_y4,Vdc_y5,Vdc_y67 kV Catenary nominal voltage vPGx,vPGy 25 kV sp-RPC output nominal current ispRPCx,ispRPCy 100 A Communication frequency between TPS and the sp-RPC fs_PG 5 Hz Sampling frequency for the sp-RPC fs50 kHz Switching frequency for the ac side fsw_spRPC 1 kHz Switching frequency for the DAB fsw_spRPC_DAB 1 kHz Moreover, as it is a common dc-link with different power converters connected, it needs high-capacity capacitors, being in the market solutions with a nominal voltage value close to 1 kV. In addition, the sp-RPC was also designed to allow a simple interface of a solar photovoltaic (PV) system as well as a battery energy storage system (BESS). Considering the legislation regarding the maximum limits of a solar photovoltaic system, the 1 kV dc-link was considered a reference value for the realization of the interface with the solar PV and the BESS by using simple non-isolated dc-dc converters topologies. In this way, it is possible to implement power converters, without isolation maintaining a low difference between the voltage levels of the solar PV system or BESS and the common dc-link voltage. Regarding the high-voltage dc-link in each submodule, the 7 kV value was defined considering the number of submodules and the peak value of the catenary voltage. A modulation index of around 80% was also considered. The communication between the two TPS and the sp-RPC is performed at 5 Hz. For the local variables, the sp-RPC is performed at a sampling frequency of 50 kHz. In turn, a switching frequency of 1 kHz was implemented for each submodule of spRPCx and spRPCy, considering the DAB and the cascaded full-bridge on the ac side. Table 2shows some of the values considered for the different components that compose the simulation model of the sp-RPC topology based on SST. The simulation model was developed with the PSIM v9.1 software. The simulations were run on a computer with an i7-8700, 3.2 GHz processor, and 24 GB of RAM, featuring a simulation time of 154 min. The integration time was 1 µ s, generating data files with 3.9 GB. Table 2. Main parameters of the electric components used on the sp-RPC topology based on SST. Variable Value Unit Line impedance inductors LPGzx,LPGzy,LspRPCzx,LspRPCzx,2.5 (250 #1) mH (mΩ) Coupling inductor LspRPCx,LspRPCy 50 (10 #1) mH (mΩ) Capacitance on the dc-link C1200 (10 #1) mF (mΩ) Capacitance on the dc-link Cx1,Cx2,Cx3,Cx4,Cx5,Cx6, Cy1,Cy2,Cy3,Cy4,Cy5,Cy6 10 (10 #1) mF (mΩ) #1 Considered as internal series resistance for each component. Equation (1) was used to determine the coupling inductors, L spRPCx and L spRPCy , of the sp-RPC with the catenary [ 26 ]. Determining L spRPCk , with kbeing equal to xor ydepending on the xor yside, requires taking into account the voltage on the dc-link of each submodule.
Energies 2023,16, 3074 6 of 22 Being a cascaded converter with 13 levels, the inductor current ripple comes from the transition between adjacent levels with 7000 V (V dc_k ) on the V dc . Additionally, considering six submodules with a switching frequency of 1 kHz with a unipolar modulation at the output of each full-bridge, the resulting output frequency of the sp-RPC is 12 kHz (f sw ). Finally, a 3% ripple in the inductor ( ∆ i spRPCk ) was considered, obtaining a minimum value in the coil of 48.6 mH. This value was rounded off to 50 mH LspRPCk =Vdc_k 4∆ispRPCk fsw,[being kequal to xor y], (1) Equation (2) was used to size the capacitors in each submodule [ 27 ]. The value of α (=0) represents the operating power factor, v spRPCk (25,000 V) the rated voltage of the sp-RPC at the point of connection to the catenary, and i spRPCk (100 A) the maximum rated current of the sp-RPC. In turn, ω (2 π 50 rad/s) relates the frequency of the catenary voltage, N(6) is the number of submodules, V dc (7000 V) is the voltage at the dc-link of each submodule, and the desired voltage ripple is defined by ∆ v dc (20 V peak to peak). The value obtained was 9.5 mF and was adjusted to 10 mF. The capacitor C 1 was adjusted with the aid of the simulation results until the best response was obtained. Ck=(1−α)vspRPCkispRPCk ωNVdc∆vdc ,[being kequal to xor y], (2) 3.2. Sp-RPC Control Algorithm For the correct functioning of the sp-RPC, it is necessary to constantly monitor the different variables of the system. The sp-RPC controller has real-time access to the local variables and the active power in each TPS in intervals of 0.2 s (f S_PG = 5 Hz). Due to the inherent concept, the sp-RPC will have to conciliate the instantaneous monitoring of the operating variables of the power electronic converters, with periodic monitoring, caused by the time delay of sending information, of the active powers of each TPS. In this way, throughout this topic, all the implemented algorithms are presented in order to provide a continuous operation of the sp-RPC. This topic starts by analyzing the different variables to be controlled, the interaction between different control algorithms, the determination of the reference values for each power electronics converter, and the control signals for the power semiconductors. Figure 3shows a simplified electrical schematic of the proposed topology for integrating a full scale sp-RPC. In the represented electrical diagram, it is possible to verify not only the constitution of each power electronics converter but also the measurement points of the different variables, currents, and voltages. For the correct operation of sp-RPC, the entire algorithm must present a given sequence of data processing, as well as identify the interaction of variables between different blocks of data processing. Figure 4shows the main implemented control algorithms, highlighting the input and output variables. Nevertheless, it is possible to verify a sequence of data processing, starting with the acquisition of instantaneous voltage and current values from different points of the sp-RPC, going through to determine the average values of both voltage and power required. Then, based on the combination of average and instantaneous values with specific control functions, it is possible to determine the reference operating powers for each sp-RPC side, the spRPCx and spRPCy. These values are later used to adjust the control signals in order to minimize operating errors compared to the reference values.
Energies 2023,16, 3074 7 of 22 Energies2023,16,xFORPEERREVIEW7of23 Figure3.Simplifiedschematicoftheproposedtopologyforthesp‐RPC,highlightingthe measurementpointsforthevariablesinvolvedinthecontrolalgorithms. Forthecorrectoperationofsp‐RPC,theentirealgorithmmustpresentagiven sequenceofdataprocessing,aswellasidentifytheinteractionofvariablesbetween differentblocksofdataprocessing.Figure4showsthemainimplementedcontrol algorithms,highlightingtheinputandoutputvariables.Nevertheless,itispossibleto verifyasequenceofdataprocessing,startingwiththeacquisitionofinstantaneousvoltage andcurrentvaluesfromdifferentpointsofthesp‐RPC,goingthroughtodeterminethe averagevaluesofbothvoltageandpowerrequired.Then,basedonthecombinationof averageandinstantaneousvalueswithspecificcontrolfunctions,itispossibleto determinethereferenceoperatingpowersforeachsp‐RPCside,thespRPCxandspRPCy. Thesevaluesarelaterusedtoadjustthecontrolsignalsinordertominimizeoperating errorscomparedtothereferencevalues. Forthecorrectfunctioningoftheimplementedalgorithm,itisnecessarytoinitially determinetheaveragevoltageandpowervalues.Thisway,thecontrolalgorithm Alg_Vdc_Avgdeterminestheaveragevaluesofthevoltagesinthedc‐linksthatcompose thesp‐RPC.Inturn,thecontrolalgorithmAlg_Power_Avgisresponsibleforperforming thecommunicationbetweentheTPSandprovidingtheaverageoperatingpowerofeach one.Finally,asthelastcontrolblockfortheinputvariables,thephase‐lockedloop(PLL) controlalgorithm,Alg_PLL,isresponsibleforsynchronizingthesp‐RPCwiththe fundamentalcomponentofeachvoltagecatenary. Oncealltheinstantaneousinputvariableshavebeenprocessed,itisnecessaryto definetheoperatingreferencevaluesforeachpowerelectronicsconverter.Inthisway, basedontheAlg_Vdc_Regfunction,onestartsbydeterminingtheregulatingpowerin ordertokeepthevoltagesofthedc‐linksregulated.Thesumoftheregulatingpowers Preg_spRPCxforthespRPCxandPreg_spRPCyforthespRPCy,arelaterusedinthecontrol algorithmAlg_Balance.Thisblock,Alg_Balance,isresponsibleformanagingand determiningthereferenceactivepowervaluesforthedifferentpowerelectronics converters. dc ac ac dc dc ac dc ac ac dc dc ac dc ac ac dc dc ac dc ac ac dc dc ac dc ac ac dc dc ac dc ac ac dc dc ac v dc_y1 vdc spRPCx spRPCy L PGzx v PGx i PGx L PGzy v PGy i PGy PGy v spRPCx v spRPCy i spRPCy i spRPCx NS L spRPCzy L spRPCzx PG x dc ac ac dc dc ac dc ac ac dc dc ac dc ac ac dc dc ac dc ac ac dc dc ac dc ac ac dc dc ac dc ac ac dc dc ac v dc_x6 v dc_x5 v dc_x4 v dc_x3 v dc_x2 v dc_x1 v dc_y2 v dc_y3 v dc_y4 v dc_y5 v dc_y6 v outy v outx DABy DABx L spRPCx L spRPCy Figure 3. Simplified schematic of the proposed topology for the sp-RPC, highlighting the measurement points for the variables involved in the control algorithms. Energies2023,16,xFORPEERREVIEW8of23 Figure4.Blockdiagramofallthecontrolalgorithmsimplementedfortheproposedsp-RPC. Oncealltheoperatingreferencevalueshavebeendetermined,itisnecessarytoactivatethedifferentpowersemiconductorsthatcomposethepowerelectronicsconverters basedonthemodulationtechniqueused.FortheSST,thecontrolisdonebythephaseshifttechnique,withthecontrolalgorithmAlg_Phase_Shift_DABxresponsibleforgeneratingthephaseanglesforeachSSTthatconstitutesthespRPCx.Atthesametime,the Alg_Phase_Shift_DAByisresponsibleforgeneratingthephaseanglesforeachSSTthat constitutesthespRPCy.Thesevaluesarelaterusedforthedirectdriveofsemiconductors Sx25toSx72ofspRPCxandSy25toSy72ofspRPCy.Forthepowerconvertersconnected tothecatenary,apredictivecontrolalgorithmisusedinordertodetermineamodulation waveforthepulsewidthmodulation(PWM)signals.Inthisway,theAlg_Predic‐ tive_spRPCxfunctionisresponsibleforgeneratingamodulatingwavevMod_spRPCx, whileAlg_Preditice_spRPCyisresponsibleforgeneratingamodulatingwave vMod_spRPCy.ThesemodulatingwavesarelatercomparedwithcarrierwavesfortheactivationofsemiconductorsSx1toSx24ofspRPCxandsemiconductorsSy1toSy24of spRPCy.Itshouldbementionedthatinordertoimposeabetterpowerbalancebetween submodules,thephase-shiftcarrierPWMtechniquewasimplemented. Figure5showsthesimplifiedflowdiagramoftheimplementedalgorithm.Afterthe startoftheoperation,theoperatingconditionsofthetwoTPSmustbechecked.After acquiringPPGxandPPGy,thenextstepinvolvesdeterminingthereferenceactivepower PspRPCx*andPspRPCy*.ThisdeterminationisbasedonEquations(5)and(6),explainedinthe nexttopic.Next,thesevaluesareusedtodeterminetheispRPCx*andispRPCy*operatingcurrents(basedonEquations(7)and(8),alsoexplainedinthefollowingtopic).Oncethis sequenceiscomplete,itischeckedifanupdatedvaluehasbeenreceivedintheTPSoperatingpower.Ifso,theaveragevaluesoftheTPSareupdated,repeatingtheentireprocess. Otherwise,thevaluesofPPGxandPPGyaremaintained,updatingPspRPCx*andPsRPCy*only basedontheinstantaneousoperationvaluesofsp-RPC. PWM for the dc-ac of the spRPCx Alg_Power_Avg v spRPCx v spRPCy i spRPCx i spRPCy P spRPCx P spRPCy Alg_Balance P PGx P PGy P spRPCx P spRPCy P reg P spRPCx * P spRPCy * Alg_Predictive_ spRPCx p spRPCx * i PGx v Mod_spRPCx S x1 S x24 ….. Alg_Vdc_Avg v dc V dc v dc_x1 V dc_x1 v dc_x2 V dc_x2 v dc_x3 V dc_x3 v dc_x4 V dc_x4 v dc_x5 V dc_x5 v dc_x6 V dc_x6 v dc_y1 V dc_y1 v dc_y2 V dc_y2 v dc_y3 V dc_y3 v dc_y4 V dc_y4 v dc_y5 V dc_y5 v dc_y6 V dc_y6 Ppg_Delay P PGy P PGx P PGx P PGy v spRPCx v spRPCy v PLLx V PLLx v PLLy V PLLy Alg_PLL P reg_spRPCx P reg_spRPCy Alg_Vdc_Reg V dc V dc_x1 V dc_x2 V dc_x3 V dc_x4 V dc_x5 V dc_x6 V dc_y1 V dc_y2 V dc_y3 V dc_y4 V dc_y5 V dc_y6 P reg P reg_spRPCx_x1 PWM for the DAB of the spRPCx Alg_Phase_Shift_DABx p spRPCx * S x25 S x72 ….. α x1 α x6 ….. p DABx1 p DABx2 p DABx3 p DABx4 p DABx5 p DABx6 p DABy1 p DABy2 p DABy3 p DABy4 p DABy5 p DABy6 P DABx1 P DABx2 P DABx3 P DABx4 P DABx5 P DABx6 P DABy1 P DABy2 P DABy3 P DABy4 P DABy5 P DABy6 P DABx1 P DABx6 P reg_spRPCx PWM for the DAB of the spRPCy p spRPCy * S y25 S y72 ….. α y1 α y6 ….. P reg_spRPCy v PLLx V PLLx PWM for the dc-ac of the spRPCy Alg_Predictive_ spRPCy p spRPCy * i PGy v Mod_spRPCy S y1 S y24 ….. v PLLy V PLLy P reg_spRPCx_x6 ... P reg_spRPCx_y1 P reg_spRPCx_y6 ... P reg_spRPCx_x1 P reg_spRPCx_x6 ... P reg_spRPCx P reg_spRPCx_y1 P reg_spRPCx_y6 ... P reg_spRPCy ... ... P reg_spRPCx_y1 P reg_spRPCx_y6 P DABx1 P DABx6 ... ... P reg_spRPCx_y1 P reg_spRPCx_y6 Alg_Phase_Shift_DABx Figure 4. Block diagram of all the control algorithms implemented for the proposed sp-RPC. For the correct functioning of the implemented algorithm, it is necessary to initially determine the average voltage and power values. This way, the control algorithm Alg_Vdc_Avg determines the average values of the voltages in the dc-links that compose the sp-RPC. In turn, the control algorithm Alg_Power_Avg is responsible for performing the communication between the TPS and providing the average operating power of each one. Finally, as the last control block for the input variables, the phase-locked loop (PLL) control algorithm, Alg_PLL, is responsible for synchronizing the sp-RPC with the fundamental component of each voltage catenary.
Energies 2023,16, 3074 8 of 22 Once all the instantaneous input variables have been processed, it is necessary to define the operating reference values for each power electronics converter. In this way, based on the Alg_Vdc_Reg function, one starts by determining the regulating power in order to keep the voltages of the dc-links regulated. The sum of the regulating powers Preg_spRPCx for the spRPCx and Preg_spRPCy for the spRPCy, are later used in the control algorithm Alg_Balance. This block, Alg_Balance, is responsible for managing and determining the reference active power values for the different power electronics converters. Once all the operating reference values have been determined, it is necessary to activate the different power semiconductors that compose the power electronics converters based on the modulation technique used. For the SST, the control is done by the phase-shift technique, with the control algorithm Alg_Phase_Shift_DABx responsible for generating the phase angles for each SST that constitutes the spRPCx. At the same time, the Alg_Phase_Shift_DABy is responsible for generating the phase angles for each SST that constitutes the spRPCy. These values are later used for the direct drive of semiconductors Sx25 to Sx72 of spRPCx and Sy25 to Sy72 of spRPCy. For the power converters connected to the catenary, a predictive control algorithm is used in order to determine a modulation wave for the pulse width modulation (PWM) signals. In this way, the Alg_Predictive_spRPCx function is responsible for generating a modulating wave vMod_spRPCx, while Alg_Preditice_spRPCy is responsible for generating a modulating wave vMod_spRPCy. These modulating waves are later compared with carrier waves for the activation of semiconductors Sx1 to Sx24 of spRPCx and semiconductors Sy1 to Sy24 of spRPCy. It should be mentioned that in order to impose a better power balance between submodules, the phase-shift carrier PWM technique was implemented. Figure 5shows the simplified flow diagram of the implemented algorithm. After the start of the operation, the operating conditions of the two TPS must be checked. After acquiring P PGx and P PGy , the next step involves determining the reference active power P spRPCx * and P spRPCy *. This determination is based on Equations (6) and (7), explained in the next topic. Next, these values are used to determine the i spRPCx * and i spRPCy * operating currents (based on Equations (8) and (9), also explained in the following topic). Once this sequence is complete, it is checked if an updated value has been received in the TPS operating power. If so, the average values of the TPS are updated, repeating the entire process. Otherwise, the values of P PGx and P PGy are maintained, updating P spRPCx * and PsRPCy* only based on the instantaneous operation values of sp-RPC. Energies2023,16,xFORPEERREVIEW9of23 Figure5.Simplifiedflowchartofthesp-RPCcontrolalgorithm. 3.2.1.Dynamicsp-RPCControl Inthistopic,theconstitutionoftheAlg_Balancecontrolblockispresentedbelow.For thecorrectfunctioningofthesystemdynamically,itisnecessarytocontinuouslyacquire theactivepowervaluesoneachsideoftheTPS.ThatistheaveragevalueoftheTPSon thex-side,PPGx,andthey-side,PPGy.DuetothedistancefromtheTPStothesp-RPC,these parametersareupdatedperiodically.Inthisway,thedeterminationoftheaveragevalue oftheoperatingpowerbetweenthetwoTPS,Pavg,representedinEquation(2),isaffected bythetimeofsendingthisinformation(200ms). 𝑃 𝑃 𝑃 /2 , 2 OncethePavgvaluehasbeendetermined,itisnecessarytodeterminethedesired energytransferbetweenTPSandPtrans.Thatis,ifitisintendedtoabsorbenergyfromthe TPSonthex‐sideandinjectitintothey‐sideorviceversa.Forthis,Equation(3)isnecessarytodeterminetheactivepowerofthespRPConthey-side,PspRPCy.ByaddingPPGyto PspRPCyandsubtractingthevalueofPavg,itispossibletoverifytheintendedenergyflow.If apositiveresultisobtained,thepowerflowiscarriedoutfromthex-sideTPStotheysideTPS.Otherwise,theenergyflowiscarriedoutintheoppositeway. 𝑃 𝑃 𝑃 𝑃 ,(3) OncethePtransvalueisdetermined,itremainstodefinetheaverageoperatingpowers forspRPCxandspRPCy,PspRPCx*andPspRPCy*,respectively.Equation(4)determinesthe valueofPspRPCx*,whileEquation(5)isusedforthePspRPCy*. 𝑃∗𝑃 ,(4) 𝑃∗𝑃 , (5) Thesevaluespresentedarelimitedtothemaximumandminimumvaluesdesiredfor theoperatingpowersofeachpowerconverter,spRPCx,andspRPCy.However,itisstill necessarytoconsidertheregulatingpowersdeterminedinordertokeepthevoltagesat alldc-linksregulated.Pregrepresentstheregulatingpowertokeepthecommondc-link regulated.Inturn,Preg_spRPCxrepresentstheregulatingpowertokeepallthededicated dc-linksofthespRPCx,whilePreg_spRPCyrepresentstheregulatingpowertokeepallthededicateddc-linksofthespRPCy.Thedeterminationoftheseregulatingpowersisanalyzed Start Determine P PGx , P PGy Determine P spRPCx* , P spRPCy* [Equation (6) and (7)] Determine i spRPCx* , i spRPCy* [Equation (8) and (9)] New TPS information? NoYes Figure 5. Simplified flowchart of the sp-RPC control algorithm.
Energies 2023,16, 3074 9 of 22 3.2.1. Dynamic sp-RPC Control In this topic, the constitution of the Alg_Balance control block is presented below. For the correct functioning of the system dynamically, it is necessary to continuously acquire the active power values on each side of the TPS. That is the average value of the TPS on the x-side, P PGx , and the y-side, P PGy . Due to the distance from the TPS to the sp-RPC, these parameters are updated periodically. In this way, the determination of the average value of the operating power between the two TPS, P avg , represented in Equation (3), is affected by the time of sending this information (200 ms). Pavg =PPGx +PPGy/2, (3) Once the P av gvalue has been determined, it is necessary to determine the desired energy transfer between TPS and P trans . That is, if it is intended to absorb energy from the TPS on the x-side and inject it into the y-side or vice versa. For this, Equation (4) is necessary to determine the active power of the spRPC on the y-side, P spRPCy . By adding P PGy to P spRPCy and subtracting the value of P avg , it is possible to verify the intended energy flow. If a positive result is obtained, the power flow is carried out from the x-side TPS to the y-side TPS. Otherwise, the energy flow is carried out in the opposite way. Ptrans =−PAvg +PPGy +PspRPCy,(4) Once the P trans value is determined, it remains to define the average operating powers for spRPCx and spRPCy,P spRPCx * and P spRPCy *, respectively. Equation (5) determines the value of PspRPCx*, while Equation (6) is used for the PspRPCy*. PspRPCx ∗=−Ptrans, (5) PspRPCy ∗=Ptrans, (6) These values presented are limited to the maximum and minimum values desired for the operating powers of each power converter, spRPCx, and spRPCy. However, it is still necessary to consider the regulating powers determined in order to keep the voltages at all dc-links regulated. P reg represents the regulating power to keep the common dc-link regulated. In turn, P reg_spRPCx represents the regulating power to keep all the dedicated dc-links of the spRPCx, while P reg_spRPCy represents the regulating power to keep all the dedicated dc-links of the spRPCy. The determination of these regulating powers is analyzed in the following topic. Once limited, the portion of the regulating powers used to regulate the dc-links that constitute the full sp-RPC system, as represented in Equation (7), is subsequently added. PspRPCx ∗=PspRPCx ∗−Preg +PregspRPCx −PregspRPCy , (7) Once the reference values for the active power of P spRPCx * and P spRPCy * are set, it is necessary to determine the reference current values i spRPCx * and i spRPCy *. Equation (8) is used to determine i spRPCx *, using the values determined by the PLL control algorithm (Alg_PLL): ˆ VPLLx (the peak value) and v PLL (sinusoidal waveform with amplitude equal to 1). The factor of 2 arises from the ratio of the peak and rms value of the voltage and current values. An analogous approach is taken in Equation (9) to determine ispRPCy*. ispRPCx ∗=2×PspRPCx ∗×vPLLx ˆ VPLLx , (8) ispRPCy ∗=2×PspRPCy ∗×vPLLy ˆ VPLLy , (9)
Energies 2023,16, 3074 16 of 22 maximum value of 364.8 A, and a new unbalance appears. At instant 1.2 s, the proposed control algorithm updates the operation reference values, as can be seen with the amplitude change of the i spRPCx and i spRPCy , being able to verify that i PGx and i PGy converge again to similar amplitude values. Energies2023,16,xFORPEERREVIEW17of23 Figure14.Detailedreal-scalesimulationresultsduringthetimeintervalfrom0.3sto0.6s:(a)the voltagesoneachTPS,vPGxandvPGy,theoutputvoltagesofthespRPCxandspRPCy,vspRPCxandvspRPCy,and voltagesonthedc-linkofeachsubmodule,vdc_x1tovdc_x6,andvdc_y1tovdc_y6;(b)themultilevelvoltage ofthespRPCxandspRPCy,voutxandvouty,andthevoltageofthecommondc-linkvoltage,vdc;(c)the currentsoneachTPS,iPGxandiPGy,andtheoutputcurrentsofthesp-RPC,ispRPCxandispRPCy. Figure15.Detailedreal-scalesimulationresultsduringthetimeintervalfrom0.95sto1.25s:(a)the voltagesoneachTPS,vPGxandvPGy,theoutputvoltagesofthespRPCxandspRPCy,vspRPCxandvspRPCy,and voltagesonthedc-linkofeachsubmodule,vdc_x1tovdc_x6,andvdc_y1tovdc_y6;(b)themultilevelvoltage ofthespRPCxandspRPCy,voutxandvouty,andthevoltageofthecommondc-linkvoltage,vdc;(c)the currentsoneachTPS,iPGxandiPGy,andtheoutputcurrentsofthesp-RPC,ispRPCxandispRPCy. Figure16showstheresultduringthetimeintervalfrom1.95sto2.25s,representativeofevent(iii)inFigure13.Figure16ashowsitispossibletoverifythevoltagesofeach TPS,vPGxandvPGy,aswellasthevoltagesoneachsideofthesp-RPC,vspRPCxandvspRPCy. Moreover,itispossibletoseethatvdc_x6hasanaveragevalueof7.06kV,whilevdc_y6hasan averagevalueof6.94kVduringthisinterval.Theremainingvoltageshavesimilarvalues ofthedc-linkonthesameside.InFigure16b,themultilevelvoltagesvoutxandvoutyare 0 1000 2000 3000 4000 5000 6000 7000 – 60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) 0 200 400 600 800 1000 1200 –60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) –400 –300 –200 –100 0 100 200 300 400 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Curre nt (A) Time (s) v PGy (a) v dc_x1 … v dc_x6 v PGx v dc_y i PGx i spRPCx i spRPCy (b) (c) v spRPCy v spRPCx i PGy v outy v outx v dc_y1 … v dc_y6 v dc v dc v dc_x 0 1000 2000 3000 4000 5000 6000 7000 –60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) 0 200 400 600 800 1000 1200 –60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) –400 –300 –200 –100 0 100 200 300 400 0.95 1 1.05 1.1 1.15 1.2 1.25 Curre nt (A) Time (s) v PGy (a) v dc_x1 … v dc_x6 v PGx v dc_y i PGx i spRPCx i spRPCy (b) (c) v spRPCy v spRPCx i PGy v outy v outx v dc_y1 … v dc_y6 v dc v dc v dc_x Figure 14. Detailed real-scale simulation results during the time interval from 0.3 s to 0.6 s: (a) the voltages on each TPS, v PGx and v PGy , the output voltages of the sp RPCx and sp RPCy ,v spRPCx and v spRPCy , and voltages on the dc-link of each submodule, v dc_x1 to v dc_x6 , and v dc_y1 to v dc_y6 ; ( b ) the multilevel voltage of the spRPCx and spRPCy,v outx and v outy , and the voltage of the common dc-link voltage, v dc ; ( c ) the currents on each TPS, i PGx and i PGy , and the output currents of the sp-RPC, i spRPCx and ispRPCy. Energies2023,16,xFORPEERREVIEW17of23 Figure14.Detailedreal-scalesimulationresultsduringthetimeintervalfrom0.3sto0.6s:(a)the voltagesoneachTPS,vPGxandvPGy,theoutputvoltagesofthespRPCxandspRPCy,vspRPCxandvspRPCy,and voltagesonthedc-linkofeachsubmodule,vdc_x1tovdc_x6,andvdc_y1tovdc_y6;(b)themultilevelvoltage ofthespRPCxandspRPCy,voutxandvouty,andthevoltageofthecommondc-linkvoltage,vdc;(c)the currentsoneachTPS,iPGxandiPGy,andtheoutputcurrentsofthesp-RPC,ispRPCxandispRPCy. Figure15.Detailedreal-scalesimulationresultsduringthetimeintervalfrom0.95sto1.25s:(a)the voltagesoneachTPS,vPGxandvPGy,theoutputvoltagesofthespRPCxandspRPCy,vspRPCxandvspRPCy,and voltagesonthedc-linkofeachsubmodule,vdc_x1tovdc_x6,andvdc_y1tovdc_y6;(b)themultilevelvoltage ofthespRPCxandspRPCy,voutxandvouty,andthevoltageofthecommondc-linkvoltage,vdc;(c)the currentsoneachTPS,iPGxandiPGy,andtheoutputcurrentsofthesp-RPC,ispRPCxandispRPCy. Figure16showstheresultduringthetimeintervalfrom1.95sto2.25s,representativeofevent(iii)inFigure13.Figure16ashowsitispossibletoverifythevoltagesofeach TPS,vPGxandvPGy,aswellasthevoltagesoneachsideofthesp-RPC,vspRPCxandvspRPCy. Moreover,itispossibletoseethatvdc_x6hasanaveragevalueof7.06kV,whilevdc_y6hasan averagevalueof6.94kVduringthisinterval.Theremainingvoltageshavesimilarvalues ofthedc-linkonthesameside.InFigure16b,themultilevelvoltagesvoutxandvoutyare 0 1000 2000 3000 4000 5000 6000 7000 – 60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) 0 200 400 600 800 1000 1200 –60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) –400 –300 –200 –100 0 100 200 300 400 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Curre nt (A) Time (s) v PGy (a) v dc_x1 … v dc_x6 v PGx v dc_y i PGx i spRPCx i spRPCy (b) (c) v spRPCy v spRPCx i PGy v outy v outx v dc_y1 … v dc_y6 v dc v dc v dc_x 0 1000 2000 3000 4000 5000 6000 7000 –60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) 0 200 400 600 800 1000 1200 –60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) –400 –300 –200 –100 0 100 200 300 400 0.95 1 1.05 1.1 1.15 1.2 1.25 Curre nt (A) Time (s) v PGy (a) v dc_x1 … v dc_x6 v PGx v dc_y i PGx i spRPCx i spRPCy (b) (c) v spRPCy v spRPCx i PGy v outy v outx v dc_y1 … v dc_y6 v dc v dc v dc_x Figure 15. Detailed real-scale simulation results during the time interval from 0.95 s to 1.25 s: (a) the voltages on each TPS, v PGx and v PGy , the output voltages of the sp RPCx and sp RPCy ,v spRPCx and v spRPCy , and voltages on the dc-link of each submodule, v dc_x1 to v dc_x6 , and v dc_y1 to v dc_y6 ; ( b ) the multilevel voltage of the spRPCx and spRPCy,v outx and v outy , and the voltage of the common dc-link voltage, v dc ; ( c ) the currents on each TPS, i PGx and i PGy , and the output currents of the sp-RPC, i spRPCx and ispRPCy. Figure 16 shows the result during the time interval from 1.95 s to 2.25 s, representative of event (iii) in Figure 13. Figure 16a shows it is possible to verify the voltages of each
Energies 2023,16, 3074 17 of 22 TPS, v PGx and v PGy , as well as the voltages on each side of the sp-RPC, v spRPCx and v spRPCy . Moreover, it is possible to see that v dc_x6 has an average value of 7.06 kV, while v dc_y6 has an average value of 6.94 kV during this interval. The remaining voltages have similar values of the dc-link on the same side. In Figure 16b, the multilevel voltages v outx and v outy are displayed, and it is also possible to see that v dc shows an average value of 0.99 kV during this interval. Finally, by analyzing Figure 16c, it is possible to verify that until the instant 2 s, the amplitudes of i PGx and i PGy were similar, obtaining a maximum value of 81.15 A and 85.51 A, respectively. At this time, i spRPCx has a maximum value of 137 A, while i spRPCy has a maximum value of 68.61 A. However, with the locomotive on the y-side starting to accelerate, varying the P Loadx > 0, i PGx increases to a maximum amplitude value of 381 A, and a new unbalance appears. At the time instant 2.1 s, the proposed control algorithm updates the operation reference values, as can be seen with the amplitude change of the i spRPCx and i spRPCy , being able to verify that i PGx and i PGy converge again to similar amplitude values. Energies2023,16,xFORPEERREVIEW18of23 displayed,anditisalsopossibletoseethatvdcshowsanaveragevalueof0.99kVduring thisinterval.Finally,byanalyzingFigure16c,itispossibletoverifythatuntiltheinstant 2s,theamplitudesofiPGxandiPGyweresimilar,obtainingamaximumvalueof81.15Aand 85.51A,respectively.Atthistime,ispRPCxhasamaximumvalueof137A,whileispRPCyhasa maximumvalueof68.61A.However,withthelocomotiveonthey-sidestartingtoaccelerate,varyingthePLoadx>0,iPGxincreasestoamaximumamplitudevalueof381A,anda newunbalanceappears.Atthetimeinstant2.1s,theproposedcontrolalgorithmupdates theoperationreferencevalues,ascanbeseenwiththeamplitudechangeoftheispRPCxand ispRPCy,beingabletoverifythatiPGxandiPGyconvergeagaintosimilaramplitudevalues. Figure16.Detailedreal-scalesimulationresultsduringthetimeintervalfrom1.95sto2.25s:(a)the voltagesoneachTPS,vPGxandvPGy,theoutputvoltagesofthespRPCxandspRPCy,vspRPCxandvspRPCy,and voltagesonthedc-linkofeachsubmodule,vdc_x1tovdc_x6,andvdc_y1tovdc_y6;(b)themultilevelvoltage ofthespRPCxandspRPCy,voutxandvouty,andthevoltageofthecommondc-linkvoltage,vdc;(c)the currentsoneachTPS,iPGxandiPGy,andtheoutputcurrentsofthesp-RPC,ispRPCxandispRPCy. Finally,thelastresultispresentedinFigure17duringthetimeintervalfrom2.9sto 3sinFigure13,whenthesystemisinsteady-stateoperation.Figure17ashowsitispossibletoverifythevoltagesofeachTPS,vPGxandvPGy,aswellasthevoltagesoneachside ofthesp-RPC,vspRPCxandvspRPCy.Moreover,itispossibletoseethatvdc_x6hasanaverage valueof6.95kV,whilevdc_y6hasanaveragevalueof7.07kVduringthisinterval.Theremainingvoltageshavesimilarvaluesofthedc-linkonthesameside.InFigure17bthe voltagesvoutxandvoutyaredisplayed,anditisalsopossibletoseethatvdcshowsanaverage valueof1.02kVduringthisinterval.Finally,byanalyzingFigure17c,itispossibleto verifythatiPGxandiPGyhaveasimilaramplitudevalue,obtainingamaximumamplitude of146.3Aand155A,respectively.Atthistime,ispRPCxhasamaximumvalueof89.74A, whileispRPCyhasamaximumvalueof87.46A. 0 200 400 600 800 1000 1200 –60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) –400 –300 –200 –100 0 100 200 300 400 1.95 2 2.05 2.1 2.15 2.2 2.25 Current (A) Time (s) 0 1000 2000 3000 4000 5000 6000 7000 –60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) v PGy (a) v dc_x1 … v dc_x6 v PGx v dc_y i PGx i spRPCx i spRPCy (b) (c) v spRPCy v spRPCx i PGy v outy v outx v dc_y1 … v dc_y6 v dc v dc v dc_x Figure 16. Detailed real-scale simulation results during the time interval from 1.95 s to 2.25 s: (a) the voltages on each TPS, v PGx and v PGy , the output voltages of the sp RPCx and sp RPCy ,v spRPCx and v spRPCy , and voltages on the dc-link of each submodule, v dc_x1 to v dc_x6 , and v dc_y1 to v dc_y6 ; ( b ) the multilevel voltage of the spRPCx and spRPCy,v outx and v outy , and the voltage of the common dc-link voltage, v dc ; ( c ) the currents on each TPS, i PGx and i PGy , and the output currents of the sp-RPC, i spRPCx and ispRPCy. Finally, the last result is presented in Figure 17 during the time interval from 2.9 s to 3 s in Figure 13, when the system is in steady-state operation. Figure 17a shows it is possible to verify the voltages of each TPS, v PGx and v PGy , as well as the voltages on each side of the sp-RPC, v spRPCx and v spRPCy . Moreover, it is possible to see that v dc_x6 has an average value of 6.95 kV, while v dc_y6 has an average value of 7.07 kV during this interval. The remaining voltages have similar values of the dc-link on the same side. In Figure 17b the voltages v outx and v outy are displayed, and it is also possible to see that v dc shows an average value of 1.02 kV during this interval. Finally, by analyzing Figure 17c, it is possible to verify that i PGx and i PGy have a similar amplitude value, obtaining a maximum amplitude of 146.3 A and 155 A, respectively. At this time, i spRPCx has a maximum value of 89.74 A, while i spRPCy has a maximum value of 87.46 A.
Energies 2023,16, 3074 18 of 22 Energies2023,16,xFORPEERREVIEW19of23 Figure17.Detailedreal-scalesimulationresultsduringthetimeintervalfrom2.9sto3s:(a)the voltagesoneachTPS,vPGxandvPGy,theoutputvoltagesofthespRPCxandspRPCy,vspRPCxandvspRPCy,and voltagesonthedc-linkofeachsubmodule,vdc_x1tovdc_x6,andvdc_y1tovdc_y6;(b)themultilevelvoltage ofthespRPCxandspRPCy,voutxandvouty,andthevoltageofthecommondc-linkvoltage,vdc;(c)the currentsoneachTPS,iPGxandiPGy,andtheoutputcurrentsofthesp-RPC,ispRPCxandispRPCy. 5.PerformanceAnalysesofthesp-RPC Thistopicservesasacriticalanalysisanddiscussionoftheresultsobtained,presentingquantitativedataontheperformanceofthereal-scalemodeldeveloped.Thesedata essentiallyportraytheabilitytobalancetheactivepowerineachTPS. Forthequantitativeanalysis,itisnecessarytoimplementamethodologyquantifying thepercentagevalueofactivepowerunbalanceinoperationineachTPS.Oncethevalues beforeandaftertheactivationoftheimplementedcontrolalgorithmsweremeasured, withtheaidofthemethodologyimplementedin[25],itwaspossibletoquantifytheperformanceofthesp-RPC.TheequationusedisrepresentedinEquation(14).Initially,the maximumabsolutevalueofthedifferencebetweenPPGandPavgisdetermined,wherePPG representstheoperatingpowerofonesideoftheTPS,eithersidex-sideory-side,andPavg representstheaveragevalueoftheoperatingpowerofthetwoTPS.Themaximumvalue determinedisthendividedbyPavginordertodeterminetheunbalance.Finally,bymultiplyingtheresultby100,itispossibletoobtainthepercentagevalueoftheunbalance. 𝑈𝑛𝑏𝑎𝑙𝑎𝑛𝑐𝑒% 100 in %,(14) Table3showsthecurrentandvoltagermsvalues,theactivepowerofeachTPSas wellasfromeachsideofthesp-RPC,andtheunbalancevalue.Thisanalysisisperformed takingintoaccountthemomentsbeforeandafterthesp-RPCisactivated.Thus,thePPG_off variablerepresentstheaverageactivepowerbetweenthetwoTPSwhenthesp-RPCisoff, andPPG_onisusedforthesamemeasurementwhenthesp-RPCison. Table3.Currentsandvoltagesrmsvalues,andactivepowerandunbalancevaluefordifferentlocomotiveconsumptionbeforeandafterthesp-RPCbeingenabled. –400 –300 –200 –100 0 100 200 300 400 2.9 2.922.942.962.98 3 Current (A) Time (s) 0 200 400 600 800 1000 1200 –60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) 0 1000 2000 3000 4000 5000 6000 7000 –60 –40 –20 0 20 40 60 Voltage (V) Voltage (kV) v PGy (a) v dc_x1 … v dc_x6 v PGx v dc_y i PGx i spRPCx i spRPCy (b) (c) v spRPCy v spRPCx i PGy v outy v outx v dc_y1 … v dc_y6 v dc v dc v dc_x Figure 17. Detailed real-scale simulation results during the time interval from 2.9 s to 3 s: ( a ) the voltages on each TPS, v PGx and v PGy , the output voltages of the sp RPCx and sp RPCy ,v spRPCx and v spRPCy , and voltages on the dc-link of each submodule, v dc_x1 to v dc_x6 , and v dc_y1 to v dc_y6 ; ( b ) the multilevel voltage of the spRPCx and spRPCy,v outx and v outy , and the voltage of the common dc-link voltage, v dc ; ( c ) the currents on each TPS, i PGx and i PGy , and the output currents of the sp-RPC, i spRPCx and i spRPCy . 5. Performance Analyses of the sp-RPC This topic serves as a critical analysis and discussion of the results obtained, presenting quantitative data on the performance of the real-scale model developed. These data essentially portray the ability to balance the active power in each TPS. For the quantitative analysis, it is necessary to implement a methodology quantifying the percentage value of active power unbalance in operation in each TPS. Once the values before and after the activation of the implemented control algorithms were measured, with the aid of the methodology implemented in [ 25 ], it was possible to quantify the performance of the sp-RPC. The equation used is represented in Equation (15). Initially, the maximum absolute value of the difference between P PG and P avg is determined, where P PG represents the operating power of one side of the TPS, either side x-side or y-side, and P avg represents the average value of the operating power of the two TPS. The maximum value determined is then divided by P avg in order to determine the unbalance. Finally, by multiplying the result by 100, it is possible to obtain the percentage value of the unbalance. Unbalance%= PPG −Pavg Max Pavg ×100[in%], (15) Table 3shows the current and voltage rms values, the active power of each TPS as well as from each side of the sp-RPC, and the unbalance value. This analysis is performed taking into account the moments before and after the sp-RPC is activated. Thus, the P PG_off variable represents the average active power between the two TPS when the sp-RPC is off, and PPG_on is used for the same measurement when the sp-RPC is on. Analyzing the performance firstly, when the sp-RPC is off (the left side of Table 3), it is possible to verify that the side with the highest load causes a voltage drop—concluding that the greater the load, the greater the voltage drop at the connection point of sp-RPC, v spRPCx and v spRPCy . Additionally, to highlight the existing unbalance in the current values of the i PGx and i PGy . On the bottom side of Table 3, the average values of the operating powers of each TPS for different initial operating load conditions (with the sp-RPC disconnected) can be seen. Analyzing the data, it is possible to verify that the greater the difference in the value of the connected load, the greater the unbalance caused by each TPS, as expected. Nevertheless, to mention that the system unbalance varies from values of 33.3% to 169.3%.
Energies 2023,16, 3074 19 of 22 Table 3. Currents and voltages rms values, and active power and unbalance value for different locomotive consumption before and after the sp-RPC being enabled. sp-RPC Disabled sp-RPC Enabled Parameters Event (i) (ii) (iii) (i) (ii) (iii) iPGx 39.97 39.97 39.97 144 56.9 102 A iPGy 245.8 155 165.4 143 63.5 104 A ispRPCx - - - 105 97 62.4 A ispRPCy - - - 100 100 61.4 A vPGx 24,992 24,992 24,994 24,983 25,004 24,987 V vPGy 24,982 25,018 24,985 24,990 25,005 24,992 V vspRPCx 24,982 24,982 24,984 24,923 25,043 24,950 V vspRPCy 24,940 25,081 24,968 25,013 25,014 25,000 V PLoadx 999 999 999 999 999 999 kW PLoady 6119 −3884 4122 6119 −3884 4122 kW PPGx 999 999 999 3612 −1419 2565 kW PPGy 6119 −3884 4122 3626 −1367 2565 kW PspRPCx - - - −2608 2424 −1564 kW PspRPCy - - - 2507 2507 1534 kW PPG_off 3559 −1442 2560 - - - kW PPG_on - - - 3619 −1393 2565 kW PPG_%inc - - - 1.7 −3.4 0.2 % Unbalance 71.9 169.3 61.0 0.19 1.86 0 % Regarding the analysis when the sp-RPC is on, this can be evaluated with the data presented on the right side of Table 3. Thus, it was possible to verify that on the side where the sp-RPC injects energy, the voltage at the coupling point increases slightly. On the other hand, on the side with the highest load coupled, the voltage drop is minimized. Nevertheless, to highlight the balancing capability of the sp-RPC, imposing similar i PGx and i PGy rms values. Analyzing the active power values, it is possible to conclude that the proposed algorithm mitigates the existing unbalance, decreasing to values below 1.86% in the existing operating conditions. Nevertheless, it was possible to verify that with the start of the operation of the sp-RPC, the average value of the power between the two TPS increased. That is, and for the case P Loadx = 999 kW and P Loady = 6119 kW, initially, the average value of the two TPS with the sp-RPC disabled, P PG_off , was 3559 kW, changing to 3619 kW when the sp-RPC was enabled, P PG_on . The start-up of the sp-RPC reflected an increase of 1.7%, P PG_%inc , in the average operating power of the two TPS. The same phenomenon occurs in the remaining operating conditions. 6. Discussion In this topic, a critical analysis of the results obtained is performed. For this, it is necessary to verify the initial operating conditions of the active powers of the TPS presented in the table. It verified the existence of operation unbalances, the largest unbalance identified by the regenerative braking event. These unbalances are reflected in different operating currents, as shown in the table. Nevertheless, the higher the current, the higher the voltage drop at the end of the overhead contact line, which is identified by the connection point of sp-RPC, v spRPCx and v spRPCy . In turn, with regenerative braking, one encounters an
Energies 2023,16, 3074 20 of 22 increase in the rms value of the overhead contact line voltages, being most evident, once again, at the end of the overhead contact line, v spRPCy . With the sp-RPC on, it is possible to impose a similar average operating power in each power TPS. This characteristic was quantified by presenting the results obtained in the table. Analyzing the first case presented, with PLoadx = 999 kW and P Loady = 6119 kW, it is possible to verify that with the sp-RPC, it was possible to decrease an unbalance from 71.9% to 0.19%. Analyzing the initial data with sp-RPC disabled, it is possible to verify an active power between the two TPS of Ppg_off = 3559 kW . When the sp-RPC starts operating, this value rises to P PG_on = 3619 kW. This increase, PPG_inc%, is due essentially to the energy losses presented by the sp-RPC. Regarding the regenerative braking event, it was also possible to minimize system unbalances by distributing the energy from regenerative braking to the two energy TPS. With this, it was also possible to impose a greater balance of voltages on the overhead contact lines. The negative value in P PG_on is due to the decrease in the average absolute value of the active powers of the two TPS due to the sp-RPC losses. In general, the overhead supply circuit can have different parameters (resistance and inductance per km, namely), and they have an impact on the voltage drop. The higher the traction load, the longer the distance from the TPS, and the lower the power factor, the higher the voltage drop. The sp-RPC has the capability of compensating this voltage drop through reactive power control (i.e., an SVC function); this will be addressed in future work together with the interface of a PV and BESS system. In the same way, when redirecting active power, the sp-RPC can increase (in some operating scenarios) the system’s overall losses, which can be an issue for infrastructure managers. 7. Conclusions This paper proposes a control algorithm integrated into a sectioning post-Rail Power Conditioner (sp-RPC) connected to a neutral section between two TPS. The proposed control algorithm presents a good dynamic response to any disturbance originated by the electric locomotives, either in a moment of acceleration or regenerative braking, maintaining a similar operating active power in the two TPS. The developed analysis was based on real-scale computational models, presenting a modular and multilevel architecture for the power electronic converters. As such, the proposed control algorithm also allows the correct balancing of the voltages at the different dc-links that compose the sp-RPC. For the sp-RPC analysis, different scenarios were considered, showing in a detailed way how the sp-RPC works in the instant of disturbance as well in steady-state. Quantitative data are also presented and analyzed. In general, it is possible to conclude that the sp-RPC manages to reduce power imbalances between neighboring TPS, contributing to the better operation of electrified railway systems. Author Contributions: Conceptualization, L.A.M.B.; formal analysis, L.A.M.B.; investigation, L.A.M.B., A.P.M. and J.G.P.; methodology, L.A.M.B. and J.G.P.; software, L.A.M.B.; supervision, A.P.M. and J.G.P.; validation, L.A.M.B. and A.P.M.; writing—original draft, L.A.M.B.; writing—review & editing, L.A.M.B., A.P.M. and J.G.P. All authors have read and agreed to the published version of the manuscript. Funding: This work has been supported by FCT—Fundação para a Ciência e Tecnologia, within the R&D Units Project Scope UIDB/00319/2020. Luis A. M. Barros is supported by the doctoral scholarship PD/BD/143006/2018, granted by the Portuguese FCT foundation. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. References 1. Future Population Growth. Available online: https://ourworldindata.org/future-population-growth (accessed on 24 March 2023). 2. Goulding, L.; Morrell, M. Future of Rail 2050; Arup Rail: London, UK, 2019; p. 60. 3. IEA—International Energy Agency. The Future of Rail: Opportunities for Energy and the Environment; IEA—International Energy Agency: Paris, France, 2019.
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