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Parallel/Series Connection of Self-Sustained Oscillating Series-Parallel Resonant Converters H. Aigner 1 and J. Biela2 1Lorch Schweisstechnik GmbH, Im Anwender 24, 71549 Auenwald Germany, Email: [email protected] 2Laboratory for High Power Electronic Systems, ETH Zurich Physikstrasse 3, 8092 Zurich, Switzerland, Email: [email protected] „This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of ETH Zürich’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document you agree to all provisions of the copyright laws protecting it.” Parallel/Series Connection of Self-Sustained Oscillating Series-Parallel Resonant Converters H. Aigner 1 1 and J. Biela2 Lorch Schweißtechnik GmbH, Im Anwender 24, 71549 Auenwald Germany, Email: [email protected] 2 Laboratory for High Power Electronic Systems, ETH Zurich Physikstrasse 3, 8092 Zurich, Switzerland, Email: [email protected] Keywords Resonant converter, Load sharing control, Series operation Abstract In this paper, a new interconnection concept of two (or more) series-parallel resonant converter suitable for parallel/series connected inputs is proposed. With this connection method operation at a wide range of operating voltages and good semiconductor utilisation is enabled. Furthermore, the balance of the two resonant converter input voltages in case of a series connection is investigated and a method for improving the voltage balancing is presented. The proposed concept is verified by measurement results and the design of the converter/integrated transformer is discussed in detail. 1 Introduction Power electronic systems for consumer or industrial applications such as welding power supplies, often aim for an international market and therefore must be designed for a wide input voltage range. For systems with an output power higher than a few kW often a line-to-line voltage range from 208V to 460V must be considered during the design process. Besides the wide input voltage range, a high efficiency and/or a compact setup are required by the customers. There, 600V devices, which have a much better switching behaviour than 1200V devices, enable lower switching losses and/or higher switching frequencies. The high switching frequency is especially interesting for converter systems utilising magnetic devices such as DC-DC converters, since L Out I Out CS1 LS1 V DC1 I S1 + C P1 + + Gate Signals Modulation I S2 + Gate Signals A I S1 CP + CS2 LS2 Modulation VAB Gate Signals I S1 V DC2 a) B RL L Out I Out CS1 L S1 VDC1 I S2 CS2 L S2 V DC2 I S2 + C P2 b) RL Gate Signals Modulation I S2 Fig. 1: a) Series-parallel resonant converter with independent power controllers and parallel connected outputs. Due to the tolerances of the resonant tank components, the operating frequencies of the two converters are not identical in case a self sustained oscillation control is used [1] and independent controller/modulators are required for the two H-bridges. b) Proposed configuration with 1 common parallel capacitor CP , so that the two H-bridges operate at the same switching frequency and the gate signals are synchronised between the upper and the lower H-bridge. Consequently, only 1 controller/modulator is required for both converters. The input voltages VDC1 and VDC2 can be connected in parallel or in series for a) and b) due to the galvanic isolation provided by the transformer. the magnetic components shrink with increasing switching frequency resulting in a higher power density and/or a higher efficiency at a low switching frequency. To apply 600V devices also at high input voltages, a series connection of either the devices [2] or of converters [3] could be performed. At the lower input voltage it is advantageous to connect the converters/devices in parallel in order to utilise the power semiconductors better as shown in [4] for a converter system operating in a voltage range from 200VAC . . .400VAC . With the switchable configuration also a higher modularity could be achieved by utilising converter modules with a lower output power level and connect them in series and/or in parallel. In case each converter has its own control unit for controlling the voltage/current at the input and/or output, a series or a parallel connection (cf. Fig. 1a) could be relatively easily achieved [5]. In order to reduce the circuit complexity and save costs, the control could be simplified if the power inherently balances between the parallel/series connected units as shown for example in [6]. If the converters operate synchronously at the same switching frequency, only four gate signals are required to control the 8 switches of the two H-bridges at the input side (Fig. 1b). This is relatively easy to achieve with conventional DC-DC converters as forward or flyback converters, as these could be operated at the same switching frequency and the switching transients of the converters could be synchronised [6, 7]. In welding applications a series-parallel resonant converter is very advantageous since it enables to raise the output voltage for ignition, is short-circuit proof at the output, offers soft switching condition and allows the possibility to utilise the transformer parasitics as resonant elements [8, 9]. These converters can be operated with a self-sustained oscillation as described in [1] and shortly explained in section 2. With this control method the switching frequency directly depends on the component values in the resonant tank, which could have relatively high tolerances. Consequently, a common control of the switching devices in the two H-bridges is not possible with the configuration shown in Fig. 1a) and balancing the output power of the parallel/series connected converter requires an additional control. These limitations can be overcome with the proposed series connection of the resonant tank as shown in Fig. 1b), where the parallel capacitor Cp is used in both circuits and only one output rectifier is required. There, the secondary windings are connected in series, so that the current in the two primary sides is inherently synchronised and balanced as will be shown below. With this circuit, the control by self-sustained oscillation could be directly applied and the two H-bridges require only one control unit. Instead of series connecting the primary sides as shown in Fig. 1b), a parallel connection as shown in Fig. 3a) could also be utilised, which is advantageous at low mains voltages. Because the operation of the proposed circuit connection is closely related to the operation mode, in section 2 the operation principle of the series parallel resonant converter based on the self sustained oscillation is discussed briefly. Thereafter, the operation of the series or parallel connected converters is explained. There also combining the two transformers in one magnetic component is discussed. Furthermore, the influence of component tolerances on the load sharing is investigated. In section 3 a prototype system and measurement results validating the proposed concept are presented. 2 Operating Principle In the following, the operating principle of the resonant converter is shortly explained as it significantly influences the proposed connection of the DC-DC converters Fig. 1b). The operation is based on the self-sustained oscillation above the resonance frequency of the resonant tank as proposed in [1]. There, one leg switches always at the zero crossing of the primary current IS flowing through the series capacitor as shown in Fig. 2a), so that this leg operates at zero current switching (ZCS) condition and could preferably be realised with IGBTs [9, 10] thus lowering system costs. By shifting the turn off instant of the IGBTs to shortly before or after the zero crossing of current IS the losses can be minimised for the chosen IGBT. In the second leg, the switches always have to turn off a current. In case MOSFETs are used, the current rapidly commutates to the relatively large output capacitance of the (Super-Junction) MOSFETs and zero voltage switching (ZVS) conditions are achieved. Consequently, the switching losses in both legs are very low. IGBTs are not well suited for the second leg due to their tail current, which would result in turn off losses in spite of the ”ZVS”-condition. The resonant oscillation in the resonant tank depends on the load and also on the component VAB IS VDC ZVS CS1 LS1 VDC1 + ZCS IS LM1 LÓut IOut + Gate Signals IR IOut CS2 LS2 VDC2 IS2 + VCp Tp/2 a) b) CṔ RĹ LM2 Gate Signals Modulation IS2 Fig. 2: a) Waveforms for a series-parallel resonant converter operated on the principle of the self sustained oscillation presented in [1]. VAB is the output voltage of the H-bridge, IS the current in the series capacitor CS , IR the current in sum of the current in the two rectifier diodes and VCp . b) Series connection of the two the series-parallel resonant converter at the primary side, where the transformers are neglected and the load side is transferred to the primary (indicated by the ’). Due to the missing galvanic isolation of the transformer, the two input capacitors CDC1 and CDC2 are separated. For simplicity, the leakage inductance of the transformer is neglected. values CS and LS . Consequently, two series-parallel resonant converters utilising self-sustained oscillation for control usually do not operate at the same switching frequency, even if they are connected to the same load, due to the resonant tank tolerances. Therefore, a direct parallel/series connection as proposed in [5] for phase-shift full-bridge converter could not directly applied for the considered resonant converters. 2.1 Series/Parallel Connection In order to overcome the limitations presented in the previous section, the circuit as shown in Fig. 1b) is proposed in this paper [11]. There, the parallel capacitor CP is used by both resonant converters. Replacing the transformers, the simplified circuit shown in Fig. 2a)b) results, where the input capacitors providing VDC1 and VDC2 are separated as the galvanic isolation of the transformer is not included any more in the equivalent circuit. There, it could be seen that the two H-bridges and the two resonant tanks are connected in series, so that the resonant current IS must flow through both resonant tanks and both H-bridges if the magnetising current is neglected in a first approximation. Consequently, the operating frequencies as well as the zero crossings of the resonant current of the two converters are inherently synchronised and the H-bridges can be simply controlled by a single controller. This controller only requires one resonant current IS1 or IS2 for controlling the circuit and synchronously triggers the respective switches of the two H-bridges. With the galvanic isolation provided by the transformer, the input voltages can be connected in series or in parallel. In case of a parallel connection as shown in Fig. 3a), which is suitable for low mains voltages, the two converter input voltages are inherently equal VDC1 = VDC2 and due to the equal resonant tank currents IS1 ≈ IS2 the power transferred by each converter is also equal. In case of a series connection as shown in Fig. 3b) the input current IDC of the two resonant Table I: Difference of VDC1 and VDC2 in dependence of the component tolerances for two converters, that are connected in series at the input. LS1 = LS2 LS1 ±5% CS1 ±5% LM 1 ±5% LS1 & CS1 ±5% LS1 & CS1 & LM 1 ±5% Fig. 3b) Fig. 4a) Fig. 4b) Voltage Difference VDC1−VDC2 ≈ 0V ≈ 0V ≈ 0V ≈ 50V ≈ 10V ≈ 1.4V ≈ 24V ≈ 4.5V ≈ 0.4V ≈ 40V ≈ 7.5V ≈ 0.6V ≈ 60V ≈ 11.5V ≈ 1.8V ≈V ≈V ≈ 2.4V C S1 LS1 VDC1 + VDC IDC1 CDC1 IS1 IS L Out IOut CP VDC1 + VDC + RL a) I DC2 C DC2 IS1 VDC2 + b) L Out IOut IS CP + IDC IHB2 I S2 CS1 LS1 IDC1 C S2 L S2 VDC2 + I HB1 I DC RL CS2 L S2 IS2 I DC2 Fig. 3: a) Parallel connection of the two the series-parallel resonant converter at the primary side. Due to the identical resonant tank currents, which are determined by the secondary side current that is identical for both converters due to the output series connection, the transferred power is the same for both converters. b) Series connection of the two resonant converters at the primary side. The current IDC from the input voltage source VDC flows through both DC capacitors CDC1 and CDC2 due to the series connection. converters from the DC voltage source VDC is the same. Neglecting the magnetising current and/or magnetising inductance of the two transformers in a first step, the two resonant tank currents IS1 and IS2 must be the same since the secondaries of the two transformers are connected in series so that secondary currents of the two transformers are identical. Since the switches of the two H-bridges are triggered synchronously, the input currents of the two H-bridges IHB1 and IHB2 are equal. Consequently, the charging/discharging currents of the DC-link capacitors IDC1 and IDC2 are identical and with identical capacitance values CDC1 = CDC2 , the two converter input voltages VDC1 and VDC2 are equal. If CDC1 6= CDC2 , slightly unbalanced converter input voltages result VDC1/VDC2 ≈ C2/C1 . In case the resonant tank component values are not exactly identical due to tolerances, only the voltage drop across the resonant tank elements de-/increases if the magnetising inductance is neglected. Still, the currents in the resonant tanks IS1 and IS2 are identical as they are determined by the secondary current, so that the input voltages are still balanced even for not identical CS1 /CS2 and LS1 /LS2 if magnetising inductances are neglected. Considering the magnetising inductance with unidentical resonant tank component values, results in an unequal voltage drop across the magnetising inductances, since the voltage drop across the resonant tank is not equal (assuming at the beginning: VDC1 = VDC2 ). Therefore, the magnetising currents are also not equal, resulting in slightly different resonant tank currents IS1 and IS2 and consequently slightly different H-bridge input currents IHB1 and IHB2 . This leads to a decreasing converter input voltage of those converter, which has a higher input current. Due to the phase shift of the resonant tank voltage with respect to H-bridge output voltage VAB and the synchronisation of VAB to the zero crossing of the resonant current IS1 and/or IS2 as shown in Fig. 2a), the phase of the magnetising current is usually shifted by more than 90◦ and less than 270◦ with respect to the secondary current IS . Consequently, the amplitude of the resonant tank current slightly decreases with an increasing magnetising current. The reduced resonant current results in a slightly smaller input current of the H-bridge/discharge current of the input capacitor and consequently in a slightly increasing input voltage of the H-bridge. The increasing input voltage of the H-bridge leads to an increasing magnetising current, so that in total the input voltages are not stable and balanced any more. These considerations are true for an ideal converter with linear inductances/transformers (without saturation/hysteresis) and ideal switches (without loses or parasitic output capacitances). In the real circuit with parasitics and nonlinear effects, the losses of the resonant converter are dependent on the DC input voltage and usually increase with increasing voltage. For example the nonlinear behaviour and the hysteresis of the magnetising inductance result in higher losses with increasing voltage. Also the parasitic output capacitances of the switches, which are used to achieve ZVS in case of the MOSFETs, result in slightly higher losses with increasing voltage due to the increased circulating reactive power and non-ideal switches/conductors. In case of the IGBTs, which switch at zero current or close to zero current, the parasitic output capacitances must be dis-/charged directly via the switch and result in input voltage dependent switching losses. Because of these voltage dependent losses, the unbalance of the two input voltages VDC1 and VDC2 is limited to relatively small values – usually in the range of a few 10V as could be seen in + CDC1 L Out IOut CS1 LS1 VDC1 B A CP + C DC1 L BA1 VDC + Coupling VDC2 CS2 LS2 + CDC2 LBA2 a) CP A NB VDC2 + CDC2 B ΦB VDC RL LOut IOut CS1 LS1 VDC1 NB RB + RL CS2 LS2 b) Fig. 4: a) Extension of the proposed series connected resonant converters shown in Fig. 3b) by two coupled inductors LBA1 and LBA2 for voltage balancing, which reduce the unbalance of the input voltage in case of tolerances of the resonant components. b) An improved balancing circuit based on a small three winding transformer. The windings on the outer legs have the same number of turns NB and the winding in the middle leg is connected to a balancing resistor. the second column of Table I – and the two resonant converters can be operated safely also for a series connection at the input if the resonant tank component tolerances are not too large. For improving the balancing of the input voltages and increasing the robustness of the input series connection, a coupled inductor could be added to the circuit as shown in Fig. 4a). If both resonant tank currents IS1 and IS2 are identical, the coupled inductors have no influence on the circuit. They are like a 1:1 transformer with identical primary and secondary current, so the core is not magnetised in the ideal case (IS1 = IS2 ). In case of unequal currents IS1 and IS2 , the coupled inductors result in an induced voltage, which tries to make the two currents IS1 and IS2 equal and therefore also tries to balance the input voltages VDC1 and VDC2 . This could be nicely seen in the third column of Table I, where the input voltage unbalance is shown for the converter system with additional inductors LBA1 and LBA2 , which is much smaller than the voltage unbalance of the original circuit. However, for achieving a tight balancing in the range of a few volts even in case of larger component values tolerances, relatively large inductance values for the coupled inductors are required. Due to the high peak value of the resonant tank current ISν , this results in large cores for the coupled inductors and relatively high additional costs. A more compact and cheaper solution is shown in Fig. 4b), which achieves a similar performance as the coupled inductors as could be seen in the right column of Table I, but requires a much smaller additional magnetic core. The balancing circuit consists of a core with two windings with NB turns, which are for example wound around the outer legs of an E-Core. Each of these windings is connected in parallel to one of the primary windings of the two transformers. The third winding is wound around the middle leg of the E-core and is connected to a resistor RB . The number of turns of this winding is adjusted to the resistance value of RB and is not critical - here it is chosen to have also NB turns. In normal operation, i.e. all the component values have no tolerances and VDC1 = VDC2 , the two windings on the outer legs generate the same flux linkage amplitude but with opposite direction. Thus, the flux generated by the left winding must also flow through the right winding and no flux is flowing through the middle leg and no voltage is induced in the middle winding. If the two voltages at the primary side of the transformers are different, the flux linkages generated by the two windings are not equal any more and the difference between the two fluxes must flow via the middle leg, which induces some voltage in the middle winding. The induced voltage in the middle winding results in a current flow in RB that causes losses. These losses are fed from the primary transformer voltage, which has a higher amplitude and therefore generates a higher flux, as the surplus flux of this voltage flows via the middle leg. Due to the losses the increase of the primary voltage and/or input DC voltage VDCν is limited. For the considered specifications (cf. Table III), the additional losses are at most 5W for a worst case situation with component tolerances of ±5%. By adapting the number of turns of the winding on the middle leg, the winding on the middle leg could also be connected to some auxiliary supply to reuse the power. However, the amount of transferred energy depends on the component value tolerances and in case of ideal components no power is transferred. For the balancing circuit an E19/8/5 is sufficient in case of NB = 30. With a custom core with a larger area on the outer legs and a smaller middle leg, the balancing circuit could be made even more compact since the flux in the middle leg is quite small. Remark: As explained in section 2 the operation of the converter is synchronised to the zero crossing of the resonant current. With the proposed setup only one control unit/modulator is used, which is synchronised on one of the two resonant currents IS1 or IS2 . In the case of equal resonant currents, it does not make a difference, which of the two resonant currents is chosen. However, due to the influence of the magnetising current, there is a small difference in amplitude and phase of IS1 and IS2 in the case component tolerances are included in the considerations. This could result in slightly different operation. For example one resonant current has its zero crossing slightly after the rising/falling edge of VAB . Usually, this small effect does not have an influence on the system performance and could be neglected. 2.2 Component Selection For determining the component values of the resonant tank, a fundamental frequency analysis as presented in [12] or [13] is performed for the equivalent circuit shown in Fig. 5. There, the load and the parallel capacitor are split in two parts, as the outputs of the two resonant converters are connected in series. The components are furthermore transferred to the primary side of the transformer by multiplying the inductor and the resistor by (NP /NS )2 and the capacitors by (NS /NP )2 . CS VDC + 2 L´Out 2 LS 2 C´P CS + 2C´Out RĹ 2 VDC + 2 LS IS,Eq 2 C´P R´AC b) a) Fig. 5: a) Equivalent circuit for the series connected series-parallel resonant converters shown in Fig. 3b), where the elements of the resonant tank result in the same operating frequency and duty cycle, so with this simplified circuit the design of the resonant converter could be performed. b) By replacing the output rectifier and the load by the resistor RAC as proposed in [12], a linear circuit results and a relatively simple fundamental frequency analysis could be performed. Table II: Considered design parameters for the equivalent resonant converter shown in Fig. 5. Output Power PO Input Voltage VDCν Load Characteristic Output Current IO 2.8kW 250V 20V + 0.04Ω 200A @ VO =28V This simplified circuit is designed for providing half of the required output power at half of the input DC voltage VDC at the nominal operating point. The load resistance for the considered welding application is determined with the model of a welding arc, which usually is a voltage source of 20V in series with a 40mΩ resistance (refer to Table II). Additionally, a voltage drop of 2V for the rectifier diodes and the interconnections is considered, so that the total output voltage VOut of the converter is 30V at nominal current and RL = (20V + 0.04ΩIN + 2V )/IN . In order to obtain a linear circuit the rectifier and the output filter plus load resistance are replaced by an equivalent 2 2 load resistance RAC = π N /16 RL as shown in Fig. 5b). There, N is the transformer turns ratio NP /NS and is given by the truncated value of N = 16/π 2 VDC/VOut . As the output current is relatively high, a very low number of secondary turns is chosen – in this case NS = 1. The operating frequency of the converter is chosen to be approximately 100kHz. To safely achieve ZVS conditions, the resonance frequency fLs Cs , resulting for a short circuited output (i.e. CP is inactive), is chosen to be 80kHz in order to have a safety margin. The quality factor at nominal output power of the resonant tank including equivalent load resistance is chosen to be QN = 2, so that the transfer ratio of the resonant tank is 1. With these assumptions the series inductance and capacitance can be determined by LS = QN RAC 2πfLs Cs and 1 . 2πfLs Cs QN RAC CS = (1) 100 70 90 60 80 50 20 10 a) RL=5RNom 40 30 0 50 Voltage [V] 80 RL=2RNom RL=RNom 60 50 70 40 60 50 150 20 30 200 Frequency [kHz] 250 300 20 b) 30 IS 40 RL=0.5RNom 100 70 VOut VARC 50 100 150 200 Output Current [A] 250 Resonant Current IS [A] Output Voltage [V] The parallel capacitor transferred to the primary is chosen to be CP0 = CS / 2 , so that the 2 parallel capacitor on the secondary side is CP = N / 8 CP0 . Based on these equations the component values given in Table III have been determined and the output voltage as function of operating frequency as shown in Fig. 6 results. 10 300 Fig. 6: a) Output voltage of the converter system as function of operating frequency and for 4 different load resistors. The values of the components are given in Table III. b) Output voltage of the converter system, arc voltage (20V + 0.04mΩ IL ) and current IS through the resonant tank as function of the output current. There, an operation at the resonance frequency of the resonant tank is assumed, so that the maximal possible output power/current is shown. The shown operating point is 280A at nominal input voltage enabling also full output current at reduced input voltage. 2.3 Transformer Design So far two independent transformers and a separate series inductance LS have been assumed for the two resonant converters. In a first step, the series inductance could be integrated in the transformer by increasing the leakage inductance of the transformer. This is performed by adding a defined path for the leakage flux as explained in [14], resulting in a compact and simplified converter design. In a second step, the two transformer can be combined into one magnetic device as shown in Fig. 7a). There, each primary winding encloses one core and the secondary winding encloses the middle legs of both cores, i.e. the area enclosed by the secondary winding is twice the one enclosed by the primary winding. Therefore, the transfer ratio is NP :NS × AP :AS . Such a configuration Primary Winding 1 Midpoint E55/21 Core Primary Winding 1 Secondary Path for Winding Leakage Flux Primary Winding 2 Space for Secondary Winding Bobbins Rectifier Primary Winding 2 b) a) Diodes Fig. 7: a) Transformer setup with two separate primary windings and one secondary winding enclosing both E-cores. The transformer is designed for an output current of 200A at 30V and uses E55/21 cores made of N87 material. b) View of the bobbins for the transformer, where the additional path for the leakage flux (small additional core) could be clearly seen. With the added ferrite material the leakage inductance is adjusted, so that it is equal to the desired series inductance value. Primary Winding 1 IP1 j NP RM,1 RM,2 NPIP1 NSIS R P1 IP2 j NP RM,3 RM,4 R P2 S S NPIP2 P2 j NS 1 P1 Primary Winding 2 IS Secondary Winding Midpoint NSIS IS j NS 2 S S Fig. 8: Equivalent circuit of the transformer with two primary windings on two cores and one centre tapped secondary winding enclosing both cores. is called a matrix transformer [15, 16] and offers the advantage that the length of the secondary winding could be reduced. Since the output current in the considered application is high, this allows a reduction in losses. For modelling the transformer, the equivalent circuit shown in Fig. 8 is used. It is based on magnetic reluctances (cf. e.g. [17]) and directly links the geometrical properties of the transformer to its magnetic and electrical behaviour. The two fluxes ΦP 1 and ΦP 2 generated by the two primary windings add up in the secondary winding, which is split in two parts due to the midpoint connection. The leakage inductance between the primaries and the secondary winding, which is used as series inductance for the resonant converter, is mainly defined by Rσ1 and Rσ2 , which could be calculated by p p L1ν (L1ν − Lσν ) 2 L1ν − L1ν (L1ν − Lσν ) 2 NP and RM,ν = NP . (2) Rσν = L1ν Lσν L1ν Lσν These equations can be derived with the mesh equations set up for the magnetic circuit of a three leg transformer, where one leg is used as leakage flux path and solving the equations for the fluxes in the core as discussed in [17]. Based on the flux equations the related equations for the inductances can be solved. In the considered case, the leakage flux/inductance between the two secondary windings (turns) is neglected, as it is relatively small and has little influence on the considerations performed in this paper. However, this leakage inductance could have significant influence in converters with voltage output and split secondary windings [18]. Table III: Specifications of the prototype system for the parallel connected series-parallel resonant converter. Output Power PO Mains Voltage Range VN Input Voltage Range VDCν Output Voltage Range VO Output Current IO Ambient Temperature Dimensions (incl. AC/DC) Weight (incl. AC/DC/Housing) Efficiency (incl. AC/DC) Resonant Tank Transformer 2×2.8kW 208V. . .460V 254V. . .360V 20. . .100V 200A @ VO =28V 45◦ C 337x×130×211 [mm] 5.5kg ≈ 90% Ls =58µH, Cs =68nF & Cp =700nF E55/21 Cores, N87 Material Prim. 13 Turns 200×100µm litz wire Sec. 1 Turn 1470×100µm litz wire It can be seen in the equivalent circuit, that due to the parallel connection of the two magnetic circuits modelling the two primary windings, the currents in the two primary windings must be identical (for the ideal circuit) due to the balance of the voltage sources modelling the magnemotive forces (Nν Iν ). Based on the equivalent circuit shown in Fig. 5b) and the current through the resonant tank IS,Eq , the voltage across the parallel capacitor VCp could be calculated. With VCp the voltage across the transformer winding is given by VP rim = N VCp 4 with VCp = 0 1/(jωC 0 ) RAC P ILS,Eq . 0 RAC + 1/(jωCP0 ) (3) With the primary voltage, the required core area could be determined by ACore = VP rim / Bmax NP ν ω. There, Bmax is the maximal flux density in the core. 3 Measurement Results In order to verify the proposed concept a prototype system as shown in Fig. 9a) with the specifications given in Table III has been built. The commercial version of the prototype is designed for a nominal three-phase input voltage of 400V and operates with an input series connection of the two resonant converter. The prototype could be easily reconfigured to work with a input parallel connection for markets with lower mains voltages. With this system, measurements for a series connection at the input of the two converters has been performed. The results for operation at nominal power are given in Fig. 9b)-d), where Secondary Midpoint Primary Winding Zoomed View DC Link Capacitors VDC1 & VDC2 IS IOut b) Zoomed View IS c) Output is shorted VDC1 VDC2 IOut VDC1 VDC2 Output Connectors Parallel Capacitor Transformer 200A a) 240A IOut d) Fig. 9: a) Photo of the prototype system for the welding power source with a max. output current of 200A at 28V output voltage. Further specifications are given in Table III. Measurement results for two converters with the specification given in Table III, which are connected in series at the input. The operating point is IO =200A, VO =30V and VDC1 = VDC2 = 266V for b) and VDC1 = 278, VDC2 = 251V for c). In c) the two series inductances are not identical resulting in unbalanced DC input voltages. d) DC-link voltages and output current for a load step, from nominal output power (200A) to a short circuit at the output (very low output power), what is a typical condition for welding power sources. As could be seen, the DC-link voltages stay nicely balanced. measurements for approximately identical resonant tank components resulting in balanced input voltages and measurements for not identical series inductances are shown. Furthermore, measurement results for a load step from nominal output power to a short circuit at the output, which is a typical operation condition for a welding power source, are given. All the results nicely match with the predicted behaviour and show a stable operation of the two converters even in the case of tolerances. 4 Conclusion With the proposed circuit configuration series-parallel resonant converters operating with selfsustained oscillation can be operated with a series connection at the output and the possibility of a parallel or a series connection at the input. In the case of a parallel connection at the input the transferred power of the converter units balances inherently. For a series connection of the converter inputs, a new concept is proposed which also enables an automatic balancing of the transferred power. Furthermore, the integration of the two transformers of the converters into a single magnetic component and the integration of the series inductances in the transformer is explained. This allows to reduce the losses especially on the secondary side, which conducts the high output current. The proposed concept is verified by simulations and measurements on a prototype system, which nicely confirm the concept. References [1] H. Pinheiro, P. K. Jain, and G. Joos, “Self-sustained oscillating resonant converters operating above the resonant frequency,” IEEE Transactions on Power Electronics, vol. 14, no. 5, pp. 803–815, Sept. 1999. [2] J. R. Pinheiro and I. Barbi, “The three-level ZVS-PWM DC-to-DC converter,” IEEE Transactions on Power Electronics, vol. 8, no. 4, pp. 486–492, Oct. 1993. [3] I. Barbi, R. Gules, R. Redl, and N. O. 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