Design and Comparison of the Performance of 12-Pulse Rectifiers for Aerospace Applications

In this paper, a conventional 12-pulse transformer unit (CTU) and an autotransformer 12-pulse transformer unit (ATU) are compared in the view of the RTCA DO-160 standard for aircraft applications. The design of the magnetic components is proposed via a coupled FEM-circuital analysis in the time domain for an 800 Hz/2 kW system. Input AC distortion, power factor, and output DC ripple are evaluated through simulations. An accurate power loss analysis is carried out, taking into account copper losses, magnetic losses, and power losses due to power switches. The reduction in the size and weight of the ATU with respect to the CTU solution is discussed, including the need for filtering systems and the standard requirements.


Introduction
Aircraft with advanced electric drives represent a green solution that can reduce fuel consumption and greenhouse gas emissions, thanks to lower weight, low maintenance, and higher conversion efficiency than mechanical, hydraulic, and pneumatic systems. This transition is possible thanks to reliable and high-efficiency power converters, which allow power loss reduction, leading to higher power density, lower weight, and lower volumes. Compliance with existing international standards guarantees the adoption of power converters with acceptable values of total harmonic distortion (THD), power factor (PF), and DC output ripple, leading to increasingly reliable systems. High-harmonic components in currents and voltages and a high ripple rate in DC output voltages may result in resonances overvoltages and other problems of electromagnetic compatibility inside the onboard electrical systems [1].
The application of a CTU as an AC-DC converter represents the most used solution, even if it may not always meet the quality standard requirements in terms of input current THD and output voltage ripple [2]. Lower current harmonic content and higher power factor are achieved by using interphase transformers and impedance-matching inductors, which, in contrast, result in increased complexity, volume, weight, and cost [3]. Moreover, these components may suffer from detuning [3][4][5][6][7][8][9]. To improve the quality standards and reduce the overall size, AC-DC converters having a higher pulse number have been proposed [1][2][3]. Recently, several authors have investigated solutions based on the use of autotransformers, indicating their possible advantages and suggesting these solutions as alternatives to the use of CTUs [10][11][12][13][14]. In the proposed autotransformer-based solution, the windings are interconnected such that the apparent power transmitted by the actual magnetic coupling is only a portion of the total apparent power [14]. The reduced apparent

Conventional 12-Pulse Unit Design
As shown in Figure 1a, the CTU was fed from a three-phase transformer with a ∆connected primary winding and two secondary windings (one is ∆ connected, and the other is Y connected). The magnetic core with the primary and secondary winding arrangement is shown in Figure 1b. Each secondary winding was connected to a three-phase, six-pulse diode bridge. The two bridges were connected in series to form a 12-pulse rectifier. The output voltage was usually connected to a DC load, such as batteries or a supercapacitor, which allowed increasing the power density, reducing weight [22]. As shown in Figure  1c, this configuration produced a 30 • phase shift between the voltage phasors of the two bridges, and this resulted in a 12-pulse per cycle output voltage [23]. The 12-pulse AC-DC converter must be suitable to operate with the desig straints shown in Table 1.  The 12-pulse AC-DC converter must be suitable to operate with the design constraints shown in Table 1. It was designed according to the following steps: (1) Design of the number of turns of the windings to achieve the desired secondary no-load voltages (2) Definition of the magnetic core cross section according to the maximum value of the working magnetic induction allowed (3) Estimation of the maximum value of the currents in the windings (4) Definition of the wire sections of the conductors (5) Calculation of the resistances and the self and mutual inductances of the windings (6) Definition of the size of the windings and the magnetic core The design procedure was recursively run, considering at that stage a linear behavior of the magnetic material.
This first stage resulted in the output characteristics shown in Table 2. The magnetic core material used in the design was a stacking iron-based Metglas ® amorphous alloy [24]. To check the previous approximated computation of the magnetic induction and that of the magnetic inductances in the magnetic coupling coefficients between the windings, a finite element analysis (FEA) was performed by using a code developed by the authors [25][26][27][28]. In particular, a 2D analysis was performed by assuming a linear behavior of the material (constant value of the magnetic permittivity, equal to the value measured at the working magnetic induction) and a current-driven formulation of the problem. A full three-phase current system was used for the excitations, and the coupling coefficient was computed by considering the effective winding geometry. The aim of this simulation was to compute both the coupling coefficient and the maximum value of the magnetic induction in real operating conditions. The mesh discretization of the magnetic core and a close-up of the air gap region are shown in Figure 2. To compute the coupling coefficient, a postprocessing of the FEA solution was performed by evaluating the linked flux in different parts of the section surrounded by the windings. The coupling coefficient   Figure 4a shows the ATU electrical circuit. It consists of a Δ-connected autotransformer with secondary windings connected to two three-phase diode bridge rectifiers; these two bridges were connected in parallel with the load. The winding representation and the voltage phasor diagram of the proposed Δ-type autotransformer are shown in Figures 4b and 4c, respectively.

Autotransformer 12-Pulse Unit Design
The transformer phase-shifting angle was equal to 30°, the winding configuration of the ATU resulted in the lowest apparent power rating [3], and the size of the magnetic component reduced [10] under this condition. As described in [12,29], the proposed autotransformer achieved the simplest winding configuration when the angle was 30° (±15°). To produce a 30° phase shift between the two sets of secondary windings, the winding turn ratio should be   Figure 4a shows the ATU electrical circuit. It consists of a Δ-connected autotransformer with secondary windings connected to two three-phase diode bridge rectifiers; these two bridges were connected in parallel with the load. The winding representation and the voltage phasor diagram of the proposed Δ-type autotransformer are shown in Figures 4b and 4c, respectively.

Autotransformer 12-Pulse Unit Design
The transformer phase-shifting angle was equal to 30°, the winding configuration of the ATU resulted in the lowest apparent power rating [3], and the size of the magnetic component reduced [10] under this condition. As described in [12,29], the proposed autotransformer achieved the simplest winding configuration when the angle was 30° (±15°). To produce a 30° phase shift between the two sets of secondary windings, the winding turn ratio should be   Figure 4a shows the ATU electrical circuit. It consists of a ∆-connected autotransformer with secondary windings connected to two three-phase diode bridge rectifiers; these two bridges were connected in parallel with the load. The winding representation and the voltage phasor diagram of the proposed ∆-type autotransformer are shown in Figure 4b,c, respectively.

Autotransformer 12-Pulse Unit Design
The transformer phase-shifting angle was equal to 30 • , the winding configuration of the ATU resulted in the lowest apparent power rating [3], and the size of the magnetic component reduced [10] under this condition. As described in [12,29], the proposed autotransformer achieved the simplest winding configuration when the angle was 30 • (±15 • ). To produce a 30 • phase shift between the two sets of secondary windings, the winding turn ratio should be The phasors of the voltages produced by the autotransformer VA 1, VB 1 , and VC 1 were at +15° with respect to the supply voltages VR, VS, and VT, while the other set of the phasors of the voltages VA 2, VB 2 , and VC2 were at −15° with respect to supply voltages, resulting in a 12-pulse rectification [9,30,31]. The magnitudes of the secondary line voltages (VA 1, VB 1, and VC 1 and (VA2, VB 2, and VC2) should be equal to each other to result in a symmetrical system and to reduce the ripple in output DC voltage .   The phasors of the voltages produced by the autotransformer V A1 , V B1 , and V C1 were at +15 • with respect to the supply voltages V R , V S , and V T , while the other set of the phasors of the voltages V A2 , V B2 , and V C2 were at −15 • with respect to supply voltages, resulting in a 12-pulse rectification [9,30,31]. The magnitudes of the secondary line voltages (V A1 , V B1 , and V C1 and (V A2 , V B2 , and V C2 ) should be equal to each other to result in a symmetrical system and to reduce the ripple in output DC voltage . A two-step design of the ATU, requiring the same procedure described in the previous section for the CTU, was carried out. The final parameters of the designed ATU device are reported in Table 3. According to the previous FEA, a coupling coefficient of k ps = 0.98 between the primary and the secondary and a coupling coefficient k ss = 0.96 between the two secondaries were estimated.
An additional filter constituted by ∆-connected capacitors was added to the system to reduce the input current THD. The IEEE 1531-2003 standard [20] was used to size the capacitors. To determine the value of each capacitor, the required reactive power for the system Q was first determined through the simulation and then the capacitance was calculated according to [33] where f is the fundamental frequency of the current, V i is the RMS value of the line voltage, and Q is the required reactive power. By using the power measurements Matlab's block, a reactive power Q of about 1700 VAR was estimated, leading to a filtering capacitor C f = 13 µF. To reduce the THD, three filtering capacitors ∆-connected with a value C f =25 µF were finally chosen.

Application of RTCA DO-160G Standard Tests
From RTCA DO-160G, the equipment intended for use on aircraft electrical systems where the primary power is supplied through an AC system with a frequency in the range of 360-800 Hz was designated as A(WF). Regarding the DC side, if the output was 270 V, the systems were designated with the letter D. Therefore, the systems studied in this paper were classified as A(WF)-D. This information is required to properly select tests that must be performed on the rectifiers to check the required compliance of the system. In addition to the tests required from RTCA DO-160G, an accurate evaluation of the conversion efficiency of the system was carried out, properly analyzing the power losses.
During the analysis, a line inductance L s = 0.1 mH was assumed to be connected in series to the three-phase voltage sources to take into account the electrical power supply system upstream of the device.
The same diode was used in the CTU and ATU rectifiers, with a forward voltage V F = 0.6 V and a conduction resistance r ON = 0.1 Ω. The performance of each rectifier was evaluated for three different load resistances, R L1 = 37 Ω, R L2 = 74 Ω, and R L3 = 148 Ω, called here heavy load, intermediate load, and light load resistances, respectively, which represent, approximatively, a working condition at 100%, 50%, and 20% of the nominal power, respectively. These working conditions are summarized in Table 4. 37 Ω Intermediate load resistance R L2 74 Ω Light load resistance R L3 148 Ω As requested from the RTCA DO-160G standard, the following parameters must be evaluated.
The output voltage ripple ∆V o was evaluated under the three different operating conditions and calculated as The total harmonic distortion (THD) of the input current was calculated as where I 1 is the amplitude of the fundamental current harmonic and I 2 , I 3 , . . . , I N are the amplitudes of the second, third, . . . , N-th current harmonic, respectively. The power factor (PF) was also evaluated by using where ϕ 1 is the displacement angle between the fundamental components of the input current and voltage. Another parameter of primary importance is the AC-DC conversion efficiency. As known, it can be calculated as η = P o /P i with P o = V o ·I o and P i = P o + P loss .
The power losses can be assumed to be constituted by two main contributions as where P D is the loss due to the rectifier and it is strictly related to the characteristics of the diodes. It can be calculated as where I D,RMS and I D,AVG are the RSM and average current flowing through the diode, respectively. The average and RMS value of the current were calculated on Simulink, measuring the current flowing through each diode and then computing the power loss using Equation (7). P TRF is the transformer power loss and can be divided into two contributions where P Cu is the ohmic loss due to the copper windings and is calculated as Energies 2021, 14, 6312 9 of 23 while P Core is the magnetic core loss given by From the datasheet of the Metglas ® alloy 2605SA1, the values of the parameters for this material were α = 1.51, β = 1.74, and C m = 6.5 [25].

AC Current Distortion Test
In this section, the AC current distortion for both the CTU and the ATU are evaluated by using the procedure provided by the RTCA DO-160 standard.
This test must be performed for AC equipment with a maximum power consumption larger than 35 VA. The first 40th harmonics are required to satisfy the individual current harmonic limits, as shown in Table 5. From the RTCA DO-160G standard, the current distortion must be evaluated under two operating conditions: When the circuit is supplied with a voltage waveform with THD V < 1.25%. In this case, the equipment will not demand harmonic current components above the limits shown in Table 5. B.
When the circuit is supplied with a distorted voltage waveform THD V > 1.25%. The equipment will not demand a harmonic current greater than 1.25% above the limits already specified in Table 5 for every 1% of distortion in the corresponding individual voltage harmonic.
The two waveforms used to perform test A and test B are shown in Figure 5a,b, respectively. In particular, test A was simulated assuming a three-phase voltage with THD V = 0%, while test B was simulated assuming THD V = 10% with equal RMS values of the third, fifth, and seventh harmonics. Next are summarized the results obtained for the simulated tests on both the CTU and the ATU.

CTU Current Distortion Evaluation
The input currents ia when the system was supplied with the voltage shown in Figure  5a,b are shown in Figure 6 a,b, respectively.  Next are summarized the results obtained for the simulated tests on both the CTU and the ATU.

CTU Current Distortion Evaluation
The input currents i a when the system was supplied with the voltage shown in Figure 5a,b are shown in Figure 6a,b, respectively. Next are summarized the results obtained for the simulated tests on both the CTU and the ATU.

CTU Current Distortion Evaluation
The input currents ia when the system was supplied with the voltage shown in Figure  5a,b are shown in Figure 6 a,b, respectively.  The CTU harmonic current components under tests A and B are summarized in Table 6. The amplitude of the primary harmonic (order H 1 in the table) at f = 800 Hz was I H1 = 8.4 A. Each harmonic value was expressed as a percentage of the amplitude of the primary harmonic. As can be seen from Table 6, the simulation indicated that the limits of the standards were respected for both tests A and B.
Therefore, it was indicated by the simulation results that the designed CTU complies with the current harmonic limits.

ATU Current Distortion Evaluation
The ATU harmonic current components under tests A and B are summarized in Table 7. The amplitude of the primary harmonic (order H 1 ) at f = 800 Hz was I H1 = 9.6 A. Each higher-order harmonic was expressed as a percentage of the amplitude of the primary harmonic. As can be seen from Table 6, the simulations that indicated the limits of the standards were respected for both tests A and B.
The input currents i a when the system was supplied with the voltage shown in Figure 5a,b are shown in Figure 7a,b, respectively.
In addition, for the ATU, the test simulations indicated that the input current harmonic content allows satisfying the standard limits. The input currents ia when the system was supplied with the voltage shown in Figure  5a,b are shown in Figure 7a,b, respectively. In addition, for the ATU, the test simulations indicated that the input current harmonic content allows satisfying the standard limits.

AC Power Factor Test
Another test required by RTCA DO-160G is the AC power factor test. The power factor, defined as in Equation (5), will be equal to or higher than the values listed in Table  8.

AC Power Factor Test
Another test required by RTCA DO-160G is the AC power factor test. The power factor, defined as in Equation (5), will be equal to or higher than the values listed in Table 8. Since the proposed 12-pulse rectifiers were characterized by a 2 kW nominal load power and they were seen as ohmic-inductive loads by the source, a lagging power factor PF > 0.8 was required to comply with the standard requirement.

CTU Power Factor Test Results
The THD of the line currents and the PF computed under different load conditions are summarized in Table 9.
The simulations indicated that the PF was always higher than the limit defined by the standard PF > 0.8 for all the load conditions examined. The presence of resistive-inductive loads seemed to not affect the converter behavior.

ATU Power Factor Test Results
The THD of the input line current and the PF values, calculated in analogy with the case of the CTU, are summarized in Table 10. In addition, for the ATU case, the PF computed was always higher than the limits specified by the standard, and it can be concluded that both AC-DC converters comply with the standard requirements.

DC Current Ripple Test
The output voltage of a 12-pulse rectifier is characterized by a DC component plus a fundamental AC component with a frequency 12 times higher than that of the AC line, plus higher-order harmonics. The RTCA DO-160G standard establishes amplitude limits for different frequency contents. Thus, the harmonic content of the output voltage was analyzed to evaluate whether the two converters meet the standard limits.

CTU Output Voltage Ripple Results
The waveforms of the output voltage computed under nominal conditions are shown in Figure 8.
To evaluate whether the standard limits are respected, the first 20 voltage harmonics (fundamental frequency f 0 = 800 Hz) were evaluated at different load levels, as shown in Table 11. To evaluate whether the standard limits are respected, the first 20 voltage harmonics (fundamental frequency f0 = 800 Hz) were evaluated at different load levels, as shown in Table 11.   Table 12. Simulated results indicated that the voltage amplitudes values were only marginally affected by the load, even when it was ohmic-inductive.

ATU Output Voltage Ripple Results
In Figure 9, the output voltages for different loads are shown; the average output voltage V o avg and the ripple V o ripple are summarized in Table 13.

ATU Output Voltage Ripple Results
In Figure 9, the output voltages for different loads are shown; the average output voltage Vo avg and the ripple Vo ripple are summarized in Table 13.

Load
Vmax   The first 20 harmonics of the output voltage are reported in Table 14. The output voltage harmonic contents computed for the CTU and ATU are shown in Figure 10. Both solutions maintained the harmonic content inside the allowable standard limits.  The output voltage harmonic contents computed for the CTU and ATU are shown in Figure 10. Both solutions maintained the harmonic content inside the allowable standard limits.

Phase Unbalance Test
The RTCA DO-160G standard requires the evaluation of the effects of phase unbalances. The unbalance includes unequal voltage magnitudes at the fundamental system frequency, fundamental phase angle deviation, and unequal levels of harmonic distortion

Phase Unbalance Test
The RTCA DO-160G standard requires the evaluation of the effects of phase unbalances. The unbalance includes unequal voltage magnitudes at the fundamental system frequency, fundamental phase angle deviation, and unequal levels of harmonic distortion between the phases. A major cause of voltage unbalance is the asymmetry of the loads, if the loads are not uniformly shared among the three phases. The input voltage waveforms shown in Figure 11 has been used to reproduce the unbalanced operating condition.

CTU under Unbalanced Input Voltage
In Figure 12a, the output voltages vo computed under unbalanced voltage conditions for different loads are shown. The related output voltage ripples are indicated in Table 15. The input current computed is shown in Figure 12b. The THD of the line currents and the PF for different loads are indicated in Table 16. Simulations indicated that there is an inversely proportional relationship between the THD of the input line current and the output load power, while the power factor changed from 0.86% at 10% of the load to 0.65 at full load. Finally, Figure 12c shows that independent from the load conditions, the magnetic flux density B(t) was sinusoidal, as expected, with an RMS value BRMS = 0.58 T.

CTU under Unbalanced Input Voltage
In Figure 12a, the output voltages v o computed under unbalanced voltage conditions for different loads are shown. The related output voltage ripples are indicated in Table 15. The input current computed is shown in Figure 12b. The THD of the line currents and the PF for different loads are indicated in Table 16. Simulations indicated that there is an inversely proportional relationship between the THD of the input line current and the output load power, while the power factor changed from 0.86% at 10% of the load to 0.65 at full load. Finally, Figure 12c shows that independent from the load conditions, the magnetic flux density B(t) was sinusoidal, as expected, with an RMS value B RMS = 0.58 T.
Simulations indicated that there is an inversely proportional relationship between the THD of the input line current and the output load power, while the power factor changed from 0.86% at 10% of the load to 0.65 at full load. Finally, Figure 12c shows that independent from the load conditions, the magnetic flux density B(t) was sinusoidal, as expected, with an RMS value BRMS = 0.58 T.  Figure 13a shows the output voltages vo of the ATU computed for different loads. The average output voltage Vo avg and the ripple Vo ripple are summarized in Table 17.

Load
Vo max (V)

Vo min (V)
Vo avg (V)  As in the case of the CTU, Figure 13c indicates that independent from the load conditions, the magnetic flux density B(t) was sinusoidal, as expected, with an RMS value BRMS-= 0.58 T.  Figure 14 shows the comparison between the estimated CTU and ATU conversion efficiency under different load conditions. The AC-DC conversion efficiency evaluated as in Section 3 was always higher than 95% under all the considered operating conditions  The input current is plotted in Figure 13b. The THD of the line currents and the PF for different loads are indicated in Table 18. As in the case of the CTU, Figure 13c indicates that independent from the load conditions, the magnetic flux density B(t) was sinusoidal, as expected, with an RMS value B RMS = 0.58 T. Figure 14 shows the comparison between the estimated CTU and ATU conversion efficiency under different load conditions. The AC-DC conversion efficiency evaluated as in Section 3 was always higher than 95% under all the considered operating conditions and for both the analyzed solutions. Simulations indicated that the ATU has higher efficiency than the CTU under heavy load conditions (i.e., R L = 37 Ω and R L =74 Ω), while the ATU efficiency is comparable with the CTU's under lighter load conditions (R L3 = 148 Ω).  The power loss contributions at different loads were analyzed for each converter, and results are summarized in Figure 15. The copper losses PCu, the core loss PCore, and the diode rectifier losses PD were separately computed. The three power loss contributions for the CTU are shown in Figure 15a. The core loss was the higher contribution, independent from the operating conditions. As expected, the diode loss and the winding loss decreased under a lighter load condition. The copper loss always represents the lowest contribution.

Final CTU and ATU Comparison
In Figure 15b, in analogy, the different ATU-related power loss contributions are shown. In this case, the simulations indicated that the diode losses were higher than in the case of the CTU, independent from the load condition, as expected, in consideration that the two diode bridges were in series for the ATU and in parallel for the CTU. The diode losses and winding losses decreased according to the load current. The core losses, as expected, were almost constant and independent from the different load conditions. (a) The power loss contributions at different loads were analyzed for each converter, and results are summarized in Figure 15. The copper losses P Cu , the core loss P Core , and the diode rectifier losses P D were separately computed. The three power loss contributions for the CTU are shown in Figure 15a. The core loss was the higher contribution, independent from the operating conditions. As expected, the diode loss and the winding loss decreased under a lighter load condition. The copper loss always represents the lowest contribution.
In Figure 15b, in analogy, the different ATU-related power loss contributions are shown. In this case, the simulations indicated that the diode losses were higher than in the case of the CTU, independent from the load condition, as expected, in consideration that the two diode bridges were in series for the ATU and in parallel for the CTU. The diode losses and winding losses decreased according to the load current. The core losses, as expected, were almost constant and independent from the different load conditions. In Figure 16, the comparison of the input current THDs predicted by the simulations by using the CTU and ATU is shown. Both the CTU and the ATU allowed meeting the standard requirements under the whole operating conditions, ensuring a THD lower than the threshold value THD max = 8%. Thanks to the input capacitive filter, the THD of the ATU was always lower than in the case of the CTU and <2%.  The obtained results for the two topologies are summarized in Table 19. Table 19. Summary of CTU and ATU characteristics.

Characteristic CTU ATU
Higher AC-DC conversion efficiency X Galvanic isolation X Lower input current THD X Lower output voltage ripple X Good performance without additional input capacitive filter X Good performance without additional series inductors X Lower size and weight X

Conclusions
This paper describes the design and modeling of two different AC-DC 12-pulse rectifiers, here named CTU and ATU. These devices are suitable for both terrestrial and aircraft applications. The parameters considered for the comparison of the performance of the CTU and the ATU are the conversion efficiency, output voltage, and input current THD in view of the RTCA DO-160 standard requirements. The comparison was performed by suitable numerical simulations made by a coupled FEM-circuital approach and considering variable load conditions up to the nominal power. Both pure resistive and inductiveresistive loads were considered.
Based on the simulation results, either the CTU or the ATU solutions comply with the standard requirements and limits and have a high conversion efficiency (more than 96%).
Results of the simulations indicate also that the ATU solution allows for a significant reduction in weight (more than 50% in the case study) and for an appreciable increase in efficiency (2% at nominal current) with respect to the CTU solution. However, the ATU solution needs an additional input capacitive filter, which, anyway, does not change substantially the gain in weight and size obtained and, in addition, greatly reduces the THD with respect to the case of the CTU solution and is under 2%.
Another important difference between the two topologies is that the CTU, differently from the ATU solution, allows for galvanic isolation between primary and secondary.
As future development, other 12-pulse topologies will be compared with ATU and CTU systems. The effect of the non-linearities on the magnetic core will be analyzed and techniques able to reduce copper and diode losses will be studied. Experimental validation of the obtained results will be performed.