Auxiliary Power Supply for Medium-Voltage Modular Multilevel Converters

Transcription

1 Auxiliary Power Supply for Medium-Voltage Modular Multilevel Converters Dimosthenis Peftitsis, Michael Antivachis and Jürgen Biela LAB FOR HIGH POWER ELECTRONICS SYSTEMS, ETH Zürich URL: Keywords <<MV isolation>>, <<resonant converter>>, <<auxiliary power supply>>, <<modular multilevel converter>>, <<LLC converter>> Abstract Design considerations for a modularized auxiliary power supply suitable for variable voltage modular multilevel converters, in terms of electrical performance and isolation against high voltages, are presented. In the presented auxiliary supply, an LLC resonant converter along with several individual floated voltage sources containing high-frequency and high-voltage-isolation transformers are employed. The design process of the individual floating voltage sources is based on circuit and FEM simulations. Partial discharge measurements are also shown for the proposed high-voltage transformer design. Last but not least, electrical measurements performed on a down-scaled laboratory prototype reveal the stable and proper operation of the system at various operating points. 1 Introduction High-voltage direct current (HVDC) transmission for long distances, and from/to multiple energy sources and loads, has been a research topic of high importance during several decades. In addition to this, medium-voltage direct current (MVDC) transmission systems seem to be a promising technology in order to overcome problems associated with the alternative current (ac) transmission of electricity in decentralized power generating systems (e.g. bulky passive components etc.) [1]. Moreover, MVDC systems provide flexibility in terms of local energy distribution, while they are also preferable when it refers to fault current management compared to HVDC (i.e. lower fault currents etc.) [2, 3]. MVDC can serve as an interface between decentralized energy generation and various locally-distributed loads. In particular, collector grids for photovoltaic and off-shore wind generation systems count as two application examples where MVDC seems to be advantageous compared to the traditional ac grids (flexible control of power etc.). Moreover, the electrification of the various ac and dc load in electric ships can be efficiently done by using a MVDC distribution system on ships [3]. Thus, bulky and lossy ac transformers can be eliminated. Power electronics interfaces are vital components in order to operate such systems reliably and efficiently. Medium direct voltage test facilities are necessary in order to evaluate the performance of various components and converters. However, as the voltage level increases, there is only a narrow area of power electronics converters that are suitable for such test facilities. For testing the MV dc components, the modular multilevel converter (M2C) seems to be a very promising topology when it refers to variable medium-voltage and high-power direct voltage source used as laboratory experimental facility. In such cases, the M2C operates as bidirectional rectifier having a variable ac input voltage and supplies a variable direct output voltage (dc) to test dc loads. Such a MV 250 kva variable dc voltage source, based on the M2C concept shown in Fig. 1 is developed at ETH for testing purposes. Such a variable high-voltage lab power supply must have two features. The first one deals with current limitation under fault conditions. This can be solved by using full-bridge SMs which allow to limit the current or to turned-off completely if this is necessary. The second design feature is associated with supplying the auxiliary power to the system. The term auxiliary power supply refers to power supplies which energize the gate-drive circuits, controllers etc in each SM. Considering the modularized structure of the M2C and the floating modules, the major constraint of such a supply is to ensure that a certain isolation voltage-level exists among the individual power supplies for each SM. In addition to this, the operation of the auxiliary power supply must be independent on the operation of the M2C as such. This

2 Figure 1: Circuit diagram of a phase-leg of the M2C with the resonant auxiliary power supply. means, that even if the direct voltage, V d on the output of the M2C is zero (Fig. 1), the auxiliary power must be present in order to assure that all features of the SMs are enabled (e.g. communication among the SMs, fault-detection circuits etc.). The same applies when the voltage is ramping up slowly. A concept used as auxiliary power supply, which employs a high-voltage tapped-inductor dc/dc buck converter with a high step-down ratio was proposed in [4]. In particular, the input stage of this converter is directly connected to the capacitor-tank of the module and a low voltage is supplied on the output. However, it is not a suitable solution for M2Cs operating with a wide range of input and output voltages if the auxiliary power must be present before the main power is supplied. Therefore, in this paper, an auxiliary power supply for modularized power electronics converters with input and output voltages having large variations is presented. A circuit diagram of this auxiliary power supply connected to a phase-leg of an M2C is shown in Fig. 1, while Tables I and II summarize the design parameters of the M2C and the auxiliary power supply, respectively. The main concept is based on a resonant converter which supplies power to several isolated rectifier units via transformers based on ring ferrite cores. A low-voltage design of such a converter has already been described in [5], while a high-voltage inductive power supply is shown in [6]. In the later work, however, the high-voltage design is not discussed. Table I: Design parameters of the M2C. Line-line input voltage, V in kv/50 Hz Output voltage, V d kv Submodules/phase N=30 Rated power, P 250 kva In this paper, a simple medium-voltage isolation concept for such an auxiliary power supply is presented. An overview of this systems is presented in Section 2. The isolation requirements and design procedure of the rectifier units from electrical and mechanical points-of-view are treated in details. Furthermore, design considerations of the resonant tank with respect to the isolation voltage-level (Sections 3) and leakage inductance (Sections 4) are explained. More specifically, it is shown that a trade-off between the

3 Table II: Design parameters of the auxiliary supply consisting of 30 rectifier units. Input voltage, V dc 400 V Output voltage, V out 14 V Rated power of each rectifier unit 30 W Clamped output voltage, V out,cl 28 V Range of the supplied power, P 27.5 W ±10% Switching frequency khz Resonant capacitor, C r 22 nf (Epcos B32672L8223, 9 series connected and 3 parallel branches) Turns-ratio of the transformer 2:2 Leakage inductance, L σ,1...n 660 nh Magnetizing inductance, L M,1...N 20 µh Ring core 2 x Kasche R102/65.8/15, K2006 value of the leakage inductance caused in the ring-core transformer and the isolation voltage level must be taken into account for a safe operation. It is the leakage inductance that governs the performance of the resonant tank, on the one hand, while on the other hand, the distance of the primary winding from the core must also be properly adjusted so that a non-destructive electric field is present. The detailed description of the resonant converter is shown in Section 5, while experimental results are presented in Section 6. Last but not least, conclusions are given in Section 7. 2 Auxiliary Power Supply System Figure 2: Visual illustration of a part of the rectifier units with their housing. A simplified circuit diagram of the modularized resonant power supply connected to a phase-leg of an M2C is shown in Fig. 1. It consists of a resonant converter (full-bridge converter with a resonant tank) and the rectifier units which are supplied via high-frequency transformers (T/Fs). The series resonant tank consists of a capacitor C r and the series connected primary windings of the T/Fs. In fact, each primary winding is represented by the leakage and magnetizing inductances, L σ and L M, respectively, while the T/F is assumed to be ideal. As shown in Fig. 1, the T/F T-models are series-connected constituting the inductor of the resonant tank. Fig. 2 depicts an illustration of the rectifier units. Considering that a three-phase M2C contains a number of N SMs per phase-leg, 3*N individual rectifier units are required in order to supply the auxiliary power to the converter. Each of the rectifier units is mounted on side of a SM as depicted in Fig. 2. A certain distance between the neighboring rectifier units must be kept for isolation and space-arrangement reasons. A single rectifier unit contains two stacked ring cores which are potted with a material having high permittivity, ε r = 4.5. Therefore, the electric field is pushed in the air between the primary winding

4 and the cores. Moreover, a plastic housing is used in order to mechanically fasten the potted cores on the rack with the SMs. The permittivity of the plastic housing is also higher than unity. The primary winding, on the other hand, is a two-turns winding which passes through an aluminum tube which is grounded (field-shaping tube) and through the core as well. Design considerations of the field-shaping tube in terms of shielding against electric fields and eddy current losses are presented in Section 3 and 4, respectively. In order to achieve a more uniform distribution of the magnetic field generated in the T/Fs, the returning path of the primary winding is split in two symmetrical paths as also shown in Fig. 2. Fieldshaping aluminum tubes also also used for the returning paths of the primary winding. These tubes, as well as, the tube which passes through the cores are mechanically fastened on the top and bottom of the whole construction. Thus, the primary winding can be properly adjusted so that the distance between the primary winding and the cores will be kept constant. Therefore, no mechanical support of the primary winding is required on each rectifier unit, where there is only air between the field-shielding tube and the cores. Moreover, it must be noted that taking into account the range of the switching frequencies where the resonant converter is aimed to operate, the primary winding consists of a litz wire. The creepage distance between the field-shaping tube and the secondary winding on each rectifier unit is approximately equal to 75 mm. According to DIN EN /VDE 0110 standard, this distance is adequately long to ensure a safe operation with a peak voltage of 22.5 kv. In Fig. 2, a cross-section of a single rectifier unit is also depicted, where the arrangement of the two stacked ring cores is shown. From this figure, it can be seen that a distance of approximately 5 mm exists between the cores and the inner walls of the plastic housing. This has intentionally been done in order to leave space for the potting of the cores. Moreover, notches are also designed on the plastic housing, so that there is adequate space for the secondary winding to enfold the ring cores. The reason of using two stacked ring cores in each rectifier unit is the reduction of the core losses. A more detailed analysis of the electrical design of the converter, resonant tank and rectifier units is given in Section 5. 3 High-Voltage Design Considerations In order to evaluate the requirements for isolation between the primary and secondary windings, a 3D finite-element-method (FEM) simulation of the electric field distribution was performed. From the design inputs of the M2C, the maximum direct voltage that the isolation must withstand is equal to 22.5 kv. This is derived as follows. The corresponding voltage level equals 22.5 kv, which is defined as 35/2 kv (maximum output voltage V d = 35 kv divided by two arms per phase-leg) plus 5 kv direct voltage offset. It must be noted that the worst case voltage of the primary winding equals 0 V, so that the voltage difference is the highest possible. All in all, the high-voltage design must be done considering a voltage difference between the SM and primary winding which equals 22.5 kv. Thus, the simulation was performed by assuming the worst case in terms of voltage difference between the primary winding and rectifier units. For simplicity, in the 3D FEM simulation model, only 3 rectifier units were considered. In particular, these are considered to be connected to the SMs placed closer to the mid-point of the M2C. The permittivity of the potting material is equal to ε r =4.5, while the aluminum field-shaping tube has an outer and inner diameters of 20 mm and 18 mm, respectively. A top view of the electric field distribution between the primary and secondary windings in the rectifier unit connected to the mid-point of the M2C is shown in Fig. 3. Taking into account that there is only air between the aluminum grounded tube and the outer wall of the potting, the electric field must not exceed 2.4 MV/m [7]. From Fig. 3, it is clear that the electric field in the area between the potting and the field-shaping tube is kept lower than the electric breakdown field of the air. The effect of displacing the field-shaping metallic tube far from the center of the rectifier unit has also been investigated. In particular, the field-shaping tube was moved further from the secondary windings, as indicated with the red arrow in Figs. 3 and 4a, at steps of 1 mm. Based on the results of the 3D FEM simulations, the peak electric fields between the primary winding and the wall of the housing and between the primary and secondary winding were extracted. Fig. 4b shows the variation of the two aforementioned peak electric fields as a function of the tube displacement for various diameters of the tube. It is observed that the minimum peak electric field (2.05 MV/m) is obtained when a field-shaping tube having a diameter of 20 mm is placed in the center of the ring core. Other positions and diameters of the tube result in higher electric field as shown in Fig. 4b. In addition to these constraints, a crucial characteristic of the potting is associated with being free from air-bubbles. 4 Parasitic components of the auxiliary power supply If the concept of the presented modularized supply is carefully examined two major challenges must be addressed. The first one is associated with the leakage inductance. In particular, the leakage inductance depends on the geometry of the core and the distance of the primary winding from the core. The closer the winding is mounted on the core, the lower the leakage inductance that is obtained. A close placement

5 Figure 3: Top-view of the 3D FEM simulation results of the electric field distribution in the rectifier unit using field-shaping tubes having 20 mm of diameter. (a) Figure 4: (a) Schematic drawing shown the displacement of the field-shaping tube showing the paths for the two electric fields examined and (b) peak electric field between the primary winding and the core and between the primary and secondary windings for various positions of the field-shaping metallic tube. (b) of the primary winding, however, will reduce the isolation distance between the primary winding and the rectifier units. This counts as the second design challenge of the presented concept. It must be noted that, under normal operation, maximum isolation voltage for the rectifier units equals 22.5 kv. The expected leakage inductance caused in each rectifier unit, was estimated using 3D FEM simulations. In particular, the same geometry of 3 rectifier units, as in the case of electric field simulations, was considered. A current excitation was provided in the primary winding which passes through the ring cores, while half of this current was assumed to flow through each of the primary winding returning paths. Moreover, it is assumed that the total magnetic flux in the ferrite cores equals zero (equal Ampereturns in both primary and secondary windings). Taking into account these simulation inputs, the leakage inductance, L σ, in each rectifier unit was estimated by integrating the magnetic energy. Fig. 5a shows the leakage magnetic field in the area between the primary winding and the ferrite cores for the aforementioned geometry consisting of 3 rectifier units. Based on the simulation results, it is found that the leakage inductance on the primary side for the aforementioned geometry is L σ,fem = 3.7 µh. Hence, an average L σ,fem,av per rectifier unit is assumed to be equal to 3.7/3=1.23 µh. In order to verify the 3D FEM simulation results, a measurement of L σ was also performed. The stack of 3 rectifier units which is shown in Fig. 2 was built. Fig. 5b shows the equivalent circuit of the 3 rectifier units that is used for measuring the leakage inductances. In particular, the secondary windings of the rectifier units were short-circuited, while the leakage inductance was measured on the primary winding (between points A and B shown in Fig. 5b). From these measurements, the total leakage inductance of 3 rectifier units was found to be L σ,m = 3.96 µh, which gives an average L σ,m,av = 1.32 µh per rectifier unit. A deviation of approximately 7% is observed between the value for L σ obtained from FEM simulations

6 A I p L σ1 L σ1 :N 2 L M1 I N p 2 L σ2 L σ2 :N 2 L M2 I N p 2 L σ3 L σ3 :N 2 (a) B L M3 (b) I N p 2 Figure 5: (a) 3D FEM simulation results of the leakage field caused in the primary winding and (b) Test circuit for measuring the leakage field caused in the primary winding. and lab measurements. Taking into account the T/F T-model circuits shown in Fig. 5b, the values for L σ1,l σ2 and L σ1 can be obtained. It should be noted that in the circuit shown, the leakage inductances are reflected in the primary side of the T/Fs, whereas the T/Fs are considered to be ideal. The corresponding values for the leakage inductances are L σ1 = L σ2 = L σ3 = 1.32/2 = 0.66 µh. These values are taken into account for the calculations presented in Section 5 regarding the electrical performance of the converter. Moreover, the total magnetizing inductance of the 3 rectifier units was also measured by keeping the secondary windings open-circuited. It was found that the total magnetizing inductance equals approximately 60 µh, which, on average, corresponds to average values of L M1 = L M2 = L M3 =20µH. A further design constraint is related to the induced eddy currents in the metallic field-shaping tube. An additional design requirement is, therefore, associated with suppressing the induced eddy currents on the metallic tube. The effect of the metallic tube thickness on the induced eddy currents was also investigated. Using the geometry shown above, the effect of the induced eddy currents on the fieldshaping metallic tubes was studies by means of 3D FEM simulations. The outer and inner diameters of the examined field-shaping tube are equal to 20 mm and 18 mm, respectively, while the height of the tube was set to 270 mm. It must also be noted that for the current excitation in the 3D FEM simulation model, a current source of 6 A peak-peak current at a frequency of 60 khz was used. Under these values the worst-case operation of the converter with 30 rectifier units at rated conditions is expected. Fig. 6 illustrates the 3D FEM simulation results for the induced eddy currents. Based on the FEM simulation results, the actual eddy-current losses, in the case of 30 rectifier units, were found to be W. 5 Design of the Resonant Converter Apart from the HV isolation and parasitic components issues, the electric performance of the resonant converter must carefully be studied. In particular, the operating range of the resonant converter must be such that it is able to supply an output power equal to the rated power. An additional design constraint of such a converter deals with supplying a constant output voltage also for changing output power. This can be achieved for a constant switching frequency, f sw if the resonant tank is properly designed. As already shown in Section 4, the leakage inductance is high so that to be considered in the design process of the resonant converter. This is due to the fact that both L σ and L M are basically determined by the HV isolation requirements of the rectifier units (distance of the primary winding from the cores, space requirements, etc.). Therefore, the examined resonant converter is of the LLC type [8], as it is also shown in the schematic diagram in Fig. 1. In the LLC resonant converter, three passive elements are contained: the leakage and magnetizing inductances, L σ and L M, respectively and the resonant capacitor, C r. Thus, two resonant frequencies exist. A unity gain, which is independent on the load variations, is expected at the series- Figure 6: 3D FEM simulation results of the eddy current induced on the field-shaping metallic tubes.

7 resonant frequency: f 0 = 1/(2 π (N L σ C r )). On the contrary, the pole-resonant frequency is given by: f p = 1/(2 π (N (L σ + L M ) C r )). Under no-load conditions, the peak resonance appear at f p, while as the load increases the peak resonance moves to frequencies closer to f 0. The design process of the resonant converter is based on the flowchart shown in Fig. 7. The most crucial design constraint deals with assuring the HV isolation between the primary winding of the T/Fs and the cores. Along with this, a proper range for the switching frequencies and a suitable value for the capacitor C r must also be chosen. In particular, these two are the only independent parameters which can be tuned so that the system will operate within the design requirements Taking into account the flowchart in Fig. 7, the HV isolation requirements count as the starting design criterion which dictates the core selection (i.e. core size) and the value of the leakage and magnetizing inductances (L σ and L M ). Based on these design inputs and also considering the input voltage of the resonant converter, V dc and the constraints for the output voltage, V out and the supplied power to each rectifier unit, P sm, the resonant capacitor C r and the switching frequency, f sw can be properly chosen. In addition to this, the turns-ratio, n of the T/Fs might also be adjusted if it is necessary. All in all, the three independent design parameters that can be adjusted are the resonant capacitor, C r, the switching frequency, f sw and the turns-ratio, n. A further crucial design requirement is associated with the power losses generated in the cores. These losses depend on the core size and material, the operating switching frequency and the magnetic flux density, B. In this specific design case, it is only the two latter parameters that can be properly adjusted. However, the choice of f sw is mainly governed by the desired performance of the resonant tank. It is, therefore, the reduction of B which can result in lower core losses. Considering the space limitation in terms of height in the rectifier units, B that corresponds to a specific operating point can be reduced by stacking two ring cores in each rectifier unit. In addition to this, the voltage across the leakage and magnetizing inductances are governed by the operating point of the resonant converter, so that I LM can only be reduced by means of increasing L M. This is basically the reason that the primary winding consists of two turns. Along with this, lower magnetizing current is also associated with lower reactive power drawn from the power source. The values for L M and L σ, as those have been measured on the examined rectifier units geometry, are shown in Table II. Considering the values for L M and L σ, several iterations using different values of C r, f sw and n have been performed in order to reach an output voltage, V out, having the lowest possible variations as the output load is changed. This counts as the last design constraint shown in Fig. 7. The design parameters of the resonant tank are summarized in Table II. It must be noted that for the calculations a separate resonant tank is assumed to be connected on each phase-leg of the M2C. In other words, only N=30 rectifier units are supplied by each separate resonant tank. Furthermore, in order to meet the operating voltage and capacitance requirements of the resonant capacitor, C r consists of 3 parallel-connecting branches of 9 series-connected single capacitors. The possibility to employ a common resonant tank for the whole three-phase system was also investigated. Assuming that the primary windings are series-connected, the leakage inductance becomes three times higher compared to the single-phase configuration. Thus, the corresponding value of C r must be lower (a factor of 3) in order to obtain the same resonant frequency and the range of f sw must also properly be adjusted in order to achieve the desired operation. Moreover, the turnsratio might also need to be properly adjusted in order to obtain the required output voltage and power. An additional design requirement is associated with supplying a constant output voltage, V out regardless of the delivered power, P sm. As shown in Table II, the expected operating range of the system in terms of supplied power on each rectifier unit is P sm = 27.5 ± 10% W. Figure 7: Flowchart shows the design procedure of the auxiliary power supply. Considering a fixed value for f sw, a variation in the output voltage, as P sm varies, is expected. In particular, as P sm is reduced, an slightly higher V out is expected. As will be examined in the following paragraph, the worst-case over-voltage across the output of a rectifier unit is expected when an open-circuit appears. When a SM of the M2C has a reduced auxiliary power consumption due to a failure, the output of the rectifier unit supplying this SM will be subjected to an over-voltage. Considering N rectifier units, an equivalent circuit diagram under a worst-case open-circuit (OC) condition of a single rectifier unit is shown in Fig. 8. Under the assumption of an OC on the output of one rectifier unit, the design parameters shown in Table II and N=30 the simulated output voltages, V out, of a healthy rectifier unit and the OC

8 A (N-1)L σ (N-1)L σ (N-1)L M (N-1)R ac L σ L σ B L M Figure 8: Schematic diagram of the resonant tank under a worst-case open-circuit of a single rectifier unit. The clamping circuit for over-voltages is also shown. R Z D Z T cl (a) (b) Figure 9: (a) Simulation results of the full system containing 30 rectifier units under an open-circuit condition of one rectifier unit without any clamping circuit on the outputs and (b) simulation results showing the operation of the clamping circuit against over-voltages. unit are shown in Fig. 9a. As expected, an over-voltage appears across the OC rectifier unit. The lower subplot in Fig. 9a illustrates the voltages across the primary windings of the T/Fs which correspond to the waveforms shown in the upper subplot. It is clear that the primary voltage across the OC rectifier increases, while the primary voltages of the healthy rectifier units are slightly reduced. The reason is that the sum of the voltages across the primary windings of the T/Fs is constant for a specific switching frequency. Therefore, an over-voltage protection circuit is required on the output of each rectifier unit in order to ensure a safe operation of the loads. Such a circuit might consists of a thyristor which is controlled by a zener diode having a reverse breakdown voltage slightly lower than the clamped output voltage, V out,cl = 28 V (Table II). The circuit diagram of the over-voltage protection scheme is shown in Fig. 8. When the thyristor is triggered, the output voltage of the OC rectifier unit in that circuit, which is detected by the main controller, resulting in a system shut down. In the upper subplot of Fig. 9b, the simulated clamped output voltage is shown. Potential tolerances in the parameters of the T/Fs (i.e. L m and L r ) should also be taken into account during the design process of the system. Considering a tolerance of 10% in L m and L σ of the T/Fs, simulations of the full system at the rated operating conditions were performed in order to evaluate any changes in the output voltage. In particular, L m of one T/F is reduced by 10% compared to the value given in Table II, while L m of the rest 29 T/Fs is increased by 10%. Thus, the extreme case in terms of tolerances in L m is investigated. A voltage difference of approximately 8.3% was obtained between the output voltages of the 29 units (V out = V) and the single rectifier unit (V out = 13.1 V). 6 Experimental Results In order to evaluate the performance of the presented auxiliary power supply, a down-scaled laboratory prototype was constructed. It basically consists of the full-bridge resonant converter shown in Fig. 10a which supplies three rectifier units as they are illustrated in Fig. 10b. In Fig. 10b the field-shaping tubes of the primary winding are also shown. The parameters of the full-scale system shown in Table II have been adapted to those shown in Table III. Thus, the operation of the down-scaled prototype in terms of output voltage, switching frequency and delivered power will be identical to the expected operation of the

9 (a) (b) Figure 10: Picture of the (a) converter laboratory prototype and (b) the down-scaled rectifier units consisting of three T/Fs and field-shaping tubes with a diameter of 10 mm, which are replaced by tubes with 20 mm in the final setup. full system containing 30 rectifier units. Apart from the input voltage, V dc, which was reduced to 10% of the rated value, also the capacitor of the resonant tank, C r, was scaled to match the full system operation. In particular, C r increased by ten times in order to meet the desired performance of the down-scaled experimental system. Table III: Parameters of the down-scaled auxiliary supply consisting of 3 rectifier units. Input voltage, V dc 40 V Output voltage, V out 14 V Rated power of each rectifier unit 30 W Clamped output voltage, V out,cl 28 V Range of the supplied power, P 27.5 W ±10% Switching frequency khz Resonant capacitor, C r 220 nf Turns-ratio of the transformer 2:2 Total leakage inductance per rectifier unit, 2 L σ,1,2, µh Magnetizing inductance per rectifier unit, L M,1,2,3 20 µh Ring cores per rectifier unit 2 x Kasche R102/65.8/15, K2006 Measurements of the down-scaled experimental system employing three rectifier units were performed at various loads on the output of the rectifiers and a wide range of switching frequencies, f sw. Thus, several output voltage, V out and supplied power characteristics were obtained. Based on this data, the variation of V out at various supplied power levels for given frequencies are shown in Fig. 11. As already mentioned above, a desired operation of the system is associated with supplying a flat output voltage while the delivered power is varying at P sm = 27.5 ± 10% W and the switching frequency is kept constant. With the presented design and at a switching frequency of f sw = khz, V out is varying between V as shown in Fig. 11. Partial discharge measurements For validating the isolation design, partial discharge (PD) measurements were performed on a rectifier unit with potting. Fig. 12 shows the experimental setup for the PD measurements. The field-shaping tube having an outer diameter of 20 mm was fastened in the center of the ring cores, which will also be the case in the real setup employing 30 rectifier units. By applying a peak voltage of 22.5 kv and using the Omicron MPD600 measurement equipment, PDs were measured to be lower than 2 pc. It must also be noted that the background partial discharge is lower than 1 pc.

10 Figure 11: Measured output voltage of a single rectifier unit as a function of the supplied power for various switching frequencies. Figure 12: Picture of the partial-discharges measurement setup. 7 Conclusions A modularized auxiliary power supply suitable for energizing the drive and control circuits of modularized converters or high-voltage series connected switches is studied in terms of electrical and highvoltage isolation designs. A resonant converter and rectifier units on the output consisting of ring-corebased transformers, count as vital parts for supplying floated voltages to the SMs. It is shown that a special design effort must be made on the rectifier units in order to comply, on the one hand, with the required electrical performance, while on the other hand with the high-voltage isolation requirements. From 3D FEM simulations, as well as measurements using an impedance analyzer, the leakage and magnetizing inductances in the transformers of the rectifier units were estimated and measured, respectively, and based on these, the resonant tank was designed. Additionally, from the distribution of the electric field in the rectifier units, and by using a metallic grounded shielding of the primary winding, it is shown that for certain core and field-shaping tube geometries, high-voltage isolation with only air can be assured. A worst-case peak electric field of approximately 2.05 MV/m was expected in the air between the field-shaping tube and the ring cores. Experiments performed on a down-scaled prototype consisting of three rectifier units show that using a constant switching frequency of f sw = khz, the rectifier units can supply power in the range of P sm = 27.5 ± 10% W with a variation on the output voltage in the range of V. The sensitivity of the supplied loads at over-voltages must be carefully studied before choosing the specific operating conditions of the auxiliary power supply. However, a clamp circuit can be employed in order to clamp potential over-voltages on the rectifiers outputs. Last but not least, from partial-discharge measurements at the maximum peak voltage of 22.5 kv, partial discharges were found to be lower than 2 pc, which are not destructive for the transformers.

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