International audienceMost industrial processes that use electricity as a source of voltage or current, require power circuit for the control of its physical quantities. Power converters are a multi-site privileged in the control of high power systems.In this article we show that the series resonant DC/DC converter, which is a hybrid system. The SRC achieves an output DC voltage equal to n times the input voltage of the converter, the major disadvantage of this type of converter is the the stresses on the power components and Capacitor Charge Time. Furthermore, a control strategy for minimizing the no-load conduction losses is proposed and the transient behavior in case of load steps including output short-circuit is discussed based on digital simulations

Amghar, Bilal

Barbot, Jean-Pierre

Boukhetala, Djamel

Darcherif, A-Moumen

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HAL Id: hal-01092213https://hal.inria.fr/hal-01092213Submitted on 8 Dec 2014HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Modeling and control of series resonant converter forhigh voltage applicationsBilal Amghar, A-Moumen Darcherif, Jean-Pierre Barbot, Djamel BoukhetalaTo cite this version:Bilal Amghar, A-Moumen Darcherif, Jean-Pierre Barbot, Djamel Boukhetala. Modeling and control ofseries resonant converter for high voltage applications. IEEE Energycon 2014, May 2014, Dubrovnik,France. pp.216 - 221, ￿10.1109/ENERGYCON.2014.6850431￿. ￿hal-01092213￿Modeling and control of series resonant converterfor high voltage applicationsBilal Amghar 1, A- Moumen Darcherif 1, Jean-Pierre Barbot 2, Djamel Boukhetala 31 ECS-Lab 3649 EA ENSEA , EPMI, Ecole d’ingénieurs13, boulevard de l’Hautil-95092 Cergy-Pontoise , France1 b.amghar@epmi.fr,1 m.darcherif@epmi.fr,2 ECS-Lab 3649 EA ENSEA6, avenue du Ponceau 95014 Cergy-Pontoise Cedex France EPI Non-A INRIA.2 barbot@ensea.fr3 LCP, Automatic Control Department,Ecole Nationale PolytechniqueAlgiers, Algeria3 djamel.boukhetala@enp.edu.dzAbstract—Most industrial processes that use electricity as asource of voltage or current, require power circuit for the controlof its physical quantities. Power converters are a multi-siteprivileged in the control of high power systems.In this article weshow that the series resonant DC/DC converter, which is a hybridsystem. The SRC achieves an output DC voltage equal to n timesthe input voltage of the converter, the major disadvantage of thistype of converter is the the stresses on the power componentsand Capacitor Charge Time. Furthermore, a control strategy forminimizing the no-load conduction losses is proposed and thetransient behavior in case of load steps including output short-circuit is discussed based on digital simulations.Index Terms—Power converter, Petri nets, hybrid dynamicsystems, resonant converter.I. INTRODUCTIONHigh voltage dc power supplies have wide applicationrange. There are several challenging and unique issues to beaddressed while designing these power supplies. The SeriesResonant Converter (SRC) is a preferred converter topologyfor high power, high voltage power supplies. The advantagescommanded by the SRC are a good compromise over itsdisadvantages. The classical SRC is a frequency controlledconverter. Control can also be achieved by keeping the oper-ating frequency fixed but varying the duty cycle. This articlestudies the SRC for use in high voltage applications. Completesteady state analysis of the converter for operation abovethe resonant frequency is presented. Dynamic analysis of theconverter is done through numerical simulation. Interest in rep-rate operation of pulsed power systems has led to an increasein power requirements of high voltage (HV) capacitor chargingpower supplies (CCPS). The requirements for a power supplycharging the capacitor are severe The main requirements forthese applications should be as follow:- Charging voltage regulated up to few kV.- Charging time as low as few ms.- The capability of withstanding short circuit conditions. HighVoltage power of the required level is generally not availablein the raw form. A suitable HV generating equipment hasto be used to convert the low voltage available from theutility supply, on board generators or battery pack to therequired voltage level. The HV dc was obtained by rectifyingthe stepped up voltage using either vacuum tubes or otherelectromechanical devices [4]. These were not only large butalso difficult to control, inefficient and unreliable. Modern HVpower generators are solid state having high frequency designsand provide superior performance and control. The first sectionof this paper is devoted to the modeling of the converter with astudy of cell switching. A reconfiguration of the control switchis proposed in response to a variation between the currentbranches, close control by Petri nets is one of the solutions bestsuited to this type of system [6]. Finally the results simulationare presented to validate the theoretical results.II. THE RESONANT DC/DC CONVERTER MODELIn Figure 1 we show a simplified nonlinear circuit repre-senting the series resonant DC/DC power converter.The SRC (Fig. 1) is a constant frequency, duty ratio con-trolled converter. The fixed switching frequency of the SRC isan advantage over the variable switching frequency operationof the classical SRC. The duty ratio is varied through phasemodulation [5]. Conduction of switches on the leading legof the inverter (T11, T12) is phase shifted with respect to theconduction of switches on the lagging leg (T21, T22) resultingin a quasi-square excitationA direct computation shows that the controlled nonlin-ear differential equations modelling the circuit are givenby[4],[5],[1].Fig. 1. Principle of series resonance converter (SRC).Lrdidt = −Rs i− v −mvosign(i) + E(t)Crdvdt = iCodvodt = mabs(i)−voR − Io(1)where v and i are, respectively, the series capacitor voltageand the inductor current in the resonant series tank, while vois the output capacitor voltage feeding both the load R andthe sink current Io which, for simplicity, we assume to be ofvalue zero m is transformation ratio. E(t) is a control inputsignal (usually taken as a periodic square wave of variableamplitude and frequency), even though for design purposesthe amplitude is considered fixed leaving the frequency asthe only control variable. Which is usually restricted to takevalues in the discrete set −Vdc, Vdc where Vdc is a fixed givenconstant[4],[5].The SRC is, therefore, equivalent to an RsLrCr circuitsupplied by two alternating square voltages vAB (generatedby the action of the switches Q1,Q2, Q3 and Q4) with anamplitude equal to the input voltage, and voltage Vdc, aspresented in Fig. 2.Fig. 2. Series Resonant DC-DC Converter equivalent circuit.The resonant inductor (Lr) and resonant capacitor (Cr) arein series. The resonant tank and the load act as a voltagedivider DC gain is always lower than 1 (maximum gainhappens at the resonant frequency). The impedance of resonanttank can be changed by varying the frequency of drivingvoltage (E(t)).Fig. 3. DC Gain Caracteristic of Series Resonant DC-DC Converter.Let X ∈ Rn be the continuous space of the inverter statesand let Q ∈ {q1, q2, , qm} be a finite set of discrete states.In case of the inverter from Fig. 1 and the control strategypresented below, n = 3 and m = 5. The continuous statespace specifies the possible values of the continuous states forall switching configurations q ∈ Q of the converter. For eachq ∈ Q the continuous dynamics can be modeled by differentialequations of the form[8],[10]:ẋ = f(x, q, t)y = h(x, q, t)(2)The states of the circuit from Fig.1 are: x(t) =[i, v, vo]T. The discrete states of the system are defined by the statesof the two-quadrant switches T11, T12, T21 and T22. There areseveral possible strategies for the control of the inverter fromFig.1.The converter has four modes of operation defined by thefour combinations of the values of the two power suppliesFig.4.Table I identifies the operation modes and the correspondentconducting switches and generated voltages.Config 1 2vAB +Vdc −VdcuLC +Vdc − vp −Rsi −Vdc − vp −RsiSwitch Q1, Q2 D3, D4Config 3 4vAB −Vdc +VdcuLC −Vdc + vp −Rsi +Vdc + vp −RsiSwitch Q3, Q4 D1, D2Fig. 4. The five configurations status of the inverter.III. HYBRID CONTROL OF SERIES RESONANT CONVERTERBASED ON PETRI NETSA. First caseDynamical systems are usually continuous or discrete orboth. Dynamical Systems Continuous (SDC) have variableswhose behavior continuous in time (voltage, current, speed,torque ....). They are often modeled by differential equationsor equations of state and transfer functions. For discretedynamical systems (SDS), the space of output variables isa discrete set of Boolean value (state opening closing of aswitch, number of switches open closed in a simultaneousstatic converter, number of pulses for controlling switches).Systems including both continuous characteristics anddiscrete are called hybrid dynamic systems. In a verysimplified one SDH has two sub sets, a continuous block, ablock discrete:- The continuous block symbolizes the dynamic evolution ofthe state continue in our case the RLC resonant circuit andHV transformer.- The block has the discrete system is discrete event receivesinternal events, external conditions, the converter is the stateof the switches of switching cells.In this work, we were interested in modeling method andcontrol systems hybrid event-based dominant the use of Petrinets. The method is illustrated in Fig.5.Fig. 5. The schematic of close-loop control of DC-DC resonant converter.The command consists of two parts, a continuous and adiscrete part. The first is based on a control loop PI controllerfor controlling the output voltage. This loop has as input theerror ev = vo−ref−vo and Iref as output current . The secondcontrol loop is modeled by a Petri net whose mission is thecurrent regulation i to value isref calculated by the PI.Figure 6 represents the Petri net control of the switches,the places P0, P1 and P2 respectively are modeling the initialstate of converter and state of the switches of cells CELL1and CELL2.This algorithm is developed in order to control the outputvoltage of system. The transition from one place to anotheris dependent on the resonant current state of converter. Theclosure of the switch of the cell (Celli) depends on the vali-dation of the transition ti0. The Petri net contol is composedof tow arcs inhibitors, their role is to prevent the presence ofmore than one token in places P1 and P2, [1],[7],[9].Depending on the current i(t) and error ei = iref − i theconverter is allowed to set in 4 configurations.The significance of all places and transition is shown inTable 1 and 2TABLE ISIGNIFICATION OF PLACESPlaces Pi DesignationsP0 Initial stateP1 The switch of the first cellP2 The switch of the second cellwith :-δv = Undulation of voltage outputFig. 6. Hybrid control of DC-DC resonant converter.Fig. 7. The Petri net control of system.TABLE IITHE TRANSITIONSTransitions Designationst01 iref > 0 and ei > δit02 iref < 0 and ei < −δit10 iref < 0 or (iref > 0 andei < δi)t20 iref > 0 or(iref < 0 and ei > −δi)-δi = Undulation of currentThe time response of system is one of the major problemsof this type of converter . Pollution of the power systemharmonics reactions is one of the other consequences of thisproblem, we will show in the simulation result the contributionof our approach on the input current and clean up the powergrid.B. Second caseIn this part of work we studied two resonant converters inparallel. The regulation consists of two parts:-Two PI regulators for regulating of output voltage.-A controller based on Petri nets for the regulation of currentsi1 and i2. the outputs of the networks Petri nets are the statesof the switches cells.The same as the first case the command consists of twoparts, a continuous and a discrete part. The first is based ona control loop PI controller for controlling the both outputsvoltages vs1 and vs2 (Fig.8) . This loop has as inputs the errores1 = vsref1 − vs1, es2 = vsref2 − vs2 and Iref1, Iref2 asoutputs current references. The second control loop is modeledby a Petri net whose mission is the currents regulation i1 andi2 respectively to value iref1 and iref2 calculated by the PI.Figure 9 represents the Petri net control of the switches,the places P0, P1, P2, P3 and P4 respectively are modelingthe initial state of converter and state of the switches of cellsCELL1, CELL2, CELL3 and CELL4.Fig. 8. DC-DC resonant converter.Fig. 9. The Petri net control of system.This algorithm is developed in order to control the outputvoltage of system. The transition from one place to anotheris dependent on the resonant current state of converter. Theclosure of the switch of the cell (Celli) depends on the vali-dation of the transition ti0. The Petri net control is composedof arcs inhibitors, their role is to prevent the presence of morethan one token in places Pi [1],[12],[3]. The significance ofall places and transition is shown in Table 3 and 4TABLE IIISIGNIFICATION OF PLACESPlaces Pi DesignationsP0 Initial stateP1 The switch of cell1P2 The switch of cell2P3 The switch of cell3P4 The switch of cell 4TABLE IVTHE TRANSITIONSTransitions Designationst01 iref1 > 0 and ei1 > δi1t02 iref1 < 0 and ei1 < −δi1t03 iref2 > 0 and ei2 > δi2t04 iref2 < 0 and ei2 < −δi2t10 iref1 < 0 or (iref1 > 0 andei1 < δi1)t20 iref1 > 0 or(iref1 < 0 and ei1 > −δi1)t30 iref2 < 0 or (iref2 > 0 andei2 < δi2)t40 iref2 > 0 or(iref2 < 0 and ei2 > −δi2)with :-δi1 = Undulation current through the first resonant circuit-δi2 = Undulation current through the second resonant circuitIV. SIMULATION RESULTSThe simulation results are obtained using the parameters ofconverter as follows::Rr = 2 mΩ, Ls = 24 10−6H , Lp = 150 10−6H , Cs =0.75 10−6F , Vsref = 50 10+3V , Rload = 10 Ω, Co = 10010−9F , Fo = 15 kHz and Vdc = 560 V.After application of the close control of the converter,simulation results are shown in the following figures:The Fig.10 and Fig.11 show respectively a simulation ofthe evolution of the output Vs voltage and output current is inboth control.Fig. 10. Output voltage Vs variations in both control.Fig. 11. Output current Is variations in both control.The figure Fig.12 represents the results obtained by usingth proposed control law on the converter. The result showsthe hybrid control using Petri net control regulate the outputvoltage Vs1, Vs2 and Vs in a finite time.Fig. 12. Output voltages Vs1, Vs2 and VsThe figure Fig.13 shows the evolution in Output current .Note that if the system has an imbalance current phase, thecontrol by a Petri net consumes less current wavy and this isan important factor for the electrical systems.Fig. 13. Output currents Is1, Is2 and Is .The dynamics of the output voltage is the image of thetotal current branch. The response time of the system is inthe range of 3.10−3 s. Simulation results have shown thatthe hybrid controller is efficient with respect to PI controller.The difference is in the instantaneous reaction to changes inphysical parameters of the system.V. CONCLUSIONThis work consists of a modeling and control of SeriesResonant Converter, an algorithm for controlling the switchesof the converter using Petri nets has been proposed to solvethe problem related to the time response and robustness ofcontrol. Petri nets are among the powerful tools for modelingand control of such systems which have discontinuitiesin their mathematical models. The algorithm is based onthe statements of resonant current , the resonant currentreference calculated by the PI and the configurations ofswitch cells. Finally simulation results show the convergenceof output voltage Vo to a neighborhood of the valueof the reference output voltage Vo in finite time. Theevolution of the resonant current and primary voltage oftransformer shows a remarkable performance of our approach.VI. REFERENCES[1] Bilal Amghar, Abdelmoumen Darcherif, Jean-PierreBarbotZ(TN )-Observability and control of parallel multicellchopper using Petri nets Author(s): IET Power Electronics,Volume 6, issue 4, 2013 , p. 710 - 720 Type: Article[2] B. Yang, R. Chen, and F.C. Lee, Integrated magneticfor LLC resonant converter, in Proc. IEEE-APEC 2002, Vol.1, pp. 346-351.[3] Hangseok Choi, Analysis and Design of LLC ResonantConverter with Integrated Transformer, in Proc. IEEE-APEC2007, pp. 1630-1635.[4] J. Garcia, A. J. calleja, E. L. Corominas, D. Gacio, andJ. Ribas, Electronic driver without electrolynic capacitor fordimming high brightness LEDs, in Proceeding of IECON, pp.3518-3523, Nov. 2009.[5] ST Microelectronics AN 2393: Reference design: widerange 200W L6599-based HB LLC resonant converter forLCD TV and flat panels, Aug. 2006.[6] Seong-Wha Hong, Hong-Jin Kim, Hyung-Gu Park,Joon-Sung Park, Young-Gun Pu, and Kang-Yoon Lee : ”AHigh Efficiency Controller IC for LLC Resonant Converter in0.35 µm BCD ”. Journal of Power Electronics, Vol. 11, No.3, May 2011[7] NIU Huapeng, PEI Yunqing, YANG Xu, WANG Laili,WANG Zhaoan, ”Design of High Power Density DC Bus Con-verter Based on LLC Resonant Converter with SynchronousRectifier” IPEMC 2009[8] H. Figge, T. Grote, N. Froehleke. J. Boecker and P.Ide: Paralleling of LLC resonant converter using frequencycontrolled current balancing, IEEE PESC 2008, June 2008 pp.1080 1085.[9] ST Microelectronics AN 2450: LLC resonant half-bridgeconverter design guideline, Mar. 2007.[10] B. Amghar , M. Darcherif ,J-P. Barbotl :” Observabilityanalysis for parallel muticell chopper ” .Proceedings of IEEESSD’11[11] M. M. Peretz and S. Ben-Yaakov, Digital control ofresonant converters: resolution effects on limit cycles, IEEETrans on Power Electronics, VOL. 25, NO. 6, pp. 1652-1661,Jun. 2010[12] J. Tian, J. Petzoldt, T. Reimann, M. Scherf, G. Berger,Modelling of asymmetrical pulse width modulation withfrequency tracking control using phasor transformation forhalf-bridge series resonant induction cookers, 11th EuropeanConference on Power Electronics and Applications (EPE),September, 2005, Dresden, Germany

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