A Battery Discharge Regulator With a Low- Output Current Ripple of an Electrical Power System in a Geostationary Satellite

The conventional Weinberg converter, owing to its high efficiency, continuous input and output current, and the soft switching of its switches and diodes, is essentially utilized in battery discharge regulators (BDR) – components that make up the overall electrical power system for geostationary satellites. However, this converter faces a crucial drawback in that the output current ripple is considerably high during the commutating operation of its output diodes. Consequently, the output root mean square (RMS) current and output voltage ripple are large. This may directly influence the lifetime and overall capacitance of the bus capacitors, ultimately affecting the longevity and size of the geostationary satellite. Therefore, reducing the BDR’s output current ripple is essential in designing a geostationary satellite’s electrical power system. As a result, this paper proposes an improved Weinberg converter to reduce the output current ripple and output voltage ripple. Specifically, the proposed converter not only has a lower output current and voltage ripples compared to the conventional converter but also reduces the magnetizing current offset of the coupled inductor. Furthermore, similar to the conventional converter, it is capable of soft switching operation of all switches and achieving high efficiency without the reverse recovery problem of diodes. Overall, the proposed converter is verified with experimental results from a 750 W-rated prototype.


I. INTRODUCTION
In recent times, the satellite-data service market has grown significantly. As a result, satellite development projects, which have previously been led by government agencies, are currently being led by private companies [1], [2]. Consequently, there is a gradual increase in the demand for satellites with various missions. In general, geostationary satellites are used for various missions such as weather observation, navigation, and communication. More so, as the mission of satellites becomes more diversified and advanced, a better-quality and higher-capacity power system is required, which may increase the satellite's weight [3], [4], [5], [6], [7], [8], [9], [10]. Therefore, a lightweight and high-power density power system for geostationary satellites is essential to reduce launch costs while satisfying the increasing power demand [11]. Interestingly, several studies have been conducted to achieve the miniaturization, lightweight, and high power density of geostationary satellites [12], [13], [14], [15], [16], [17], [18]. In particular, for the miniaturization and lightweight of geostationary satellites, it is necessary to reduce the weight of the electrical power system among the subsystems that make up the geostationary satellite. In general, the electrical power system of geostationary satellites is primarily designed with a regulated bus that maintains a constant bus voltage for a stable power supply [19], [20]. More specifically, the bus voltage is precisely and stably controlled by the power-conditioning unit (PCU) that makes up the electrical power system. Fig. 1 shows the sequential switching shunt regulator (S3R) and the battery discharge regulator (BDR) topology for the regulated bus voltage in geostationary satellites [21]. As shown in Fig. 1, the PCU consists of an S3R, a BDR, a power control unit, and a bus capacitor [22], [23]. The PCU receives the electric power generated from the solar array during the sun period, supplies the electrical power needed for the bus, and charges the battery. However, since there is no electric power generated from the solar array during the eclipse period, the energy stored in the battery is supplied to the bus by the BDR. Further, to maintain the bus voltage as stable power with a small ripple, multiple-bus capacitors are required. Therefore, the miniaturization of the electrical power system may be performed by reducing the large volume of bus capacitors contained in the PCU.
Furthermore, the bus capacitor in the PCU is connected to the output of the BDR, and the bus voltage is higher than the battery voltage, which is the input of the BDR. Thus, a stepup converter is used to implement the BDR. One of the various step-up converters, the conventional Weinberg converter, is shown in Fig. 2(a) and is mainly used in the BDRs for geostationary satellites due to its various advantages listed below [24], [25], [26], [27].
• Due to the leakage inductance, the soft switching operation of the semiconductor device is possible, thereby achieving high efficiency.
• The input and output currents are continuous, resulting in less stress on the battery and bus capacitor. 58100 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
• The operating frequency is twice the switching frequency, allowing for the size reduction of the magnetic components.
• Since the voltage across all switches can be clamped to the output voltage, the voltage stresses on the switches are not high and thus, a snubber is unnecessary. As described above, the conventional Weinberg converter has several advantages. However, as shown in Fig. 2(b), it has a few drawbacks -when all the switches are turned off, the output current rises rapidly, causing the output current ripple to increase significantly. Besides, this not only greatly increases the root mean square (RMS) current flowing through the output capacitor, but also increases the ripple of the output voltage. Moreover, these problems become more severe as the load current increases. Therefore, to solve these problems, a large number of output capacitors are required, which may consequently increase the volume and weight of the geostationary satellite.
Hence, to address the above-mentioned issues, an improved Weinberg converter is proposed as shown in Fig. 3. Precisely, the proposed converter has a similar topology structure to the conventional converter, but employs a small output inductor L o and small link capacitor C link . Consequently, it does not face serious output current ripple issues with the help of the inductor L o when all switches are turned off. Further, unlike the conventional converter, it can maintain a constant level of output current and voltage ripple regardless of the load current, which can significantly reduce the number of output capacitors. Additionally, the proposed converter can reduce the magnetic core size of the coupled inductor because the magnetizing inductor current of the coupled inductor decreases as much as the load current. Moreover, the leakage inductors of the proposed converter can not only prevent the reverse recovery problems of all diodes but also reduce the turn-on loss of all switches through the guarantee of soft switching. Therefore, the proposed converter is advantageous for high efficiency and low noise.
Meanwhile, the D clamp shown in Fig. 3 is inserted to clamp the voltage ringing of the diode D o3 to the output voltage. However, it is ignored in the mode analysis and detailed analysis because it does not have a significant effect on the converter's operation.

II. OPERATIONAL PRINCIPLES
The proposed converter operates alternately with two switches (M 1 and M 2 ) having the same duty cycle D. In addition, for convenient analysis of the proposed converter's operation, the following assumptions are made.
• The turn ratio of the transformer is N T 1 :N T 2 = 1:1 and the magnetizing inductor of the transformer is large enough to be ignored.
• The transformer leakage inductor is represented by L k1 , which is the lumped leakage inductor reflected on the left-hand side of the transformer.
• The turn ratio of the coupled inductor is N L1 :N L2 = 1:1, and the magnetizing inductor is represented by L m . • The leakage inductor of the coupled inductor is represented by L k2 , which is the lumped leakage inductor reflected on the N L1 side.
• The two switches (M 1 and M 2 ) and three output diodes (D o1 , D o2 , and D o3 ) are ideal.
• The link capacitor C link and output capacitor C o are large enough to be considered as voltage sources V link and V o , respectively.
• Since the average voltages across the inductors are zero, the voltage V link is equal to V o at steady-state. As shown in Fig. 4, the proposed converter operates in eight modes according to the state of the switches and diodes. Assuming that L o is sufficiently larger than L k1 /4 and L k2 /2, the equivalent circuits from mode 1 to mode 4 of the proposed converter are shown in Fig. 5. In addition, Fig. 6 shows the operation key waveforms of the proposed converter. Moreover, the voltage applied to each component and the current flowing through it are shown in Fig. 3.

Mode 1 [t 1 -t 2 ]:
This mode begins when the commutation between D o2 and D o3 ends at t 1 , and D o3 is turned off. In this mode, v L1 (= v L2 ) applied to the coupled inductor can be derived as follows from Fig. 5 and v Do3 can be expressed as follows:   v Using (1) -(4), the currents flowing through L m , L k1 , and L o can be determined as follows: i In this mode, since D o3 is blocked, i Lk2 is equal to i Lm .

Mode 2 [t 2 -t 3 ]:
When M 1 is turned off at t 2 , v ds1 increases from zero to V link = V o . When v ds1 reaches V link = V o , D o1 is turned on and commutation between D o1 , D o2 , and D o3 starts. In addition, v L1 (= v L2 ) can be derived as follows from Fig. 5 Assuming that 4L m in (9) is sufficiently larger than L k1 ||L k2 , v L1 can be simplified as Using the previously derived voltages (9) -(12), the currents flowing through L m , L k1 , L k2 , and L o can be expressed 58102 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  as follows: i Furthermore, since i Lm = i Lk2 in the previous mode, i Lm (t 2 ) = i Lk2 (t 2 ). In addition, i Do3 = i Lm -i Lk2 according to Kirchhoff's current law (KCL). Therefore, i Do3 gradually increases according to (9) and (12). Meanwhile, i Lk1 (= i Do1 = i Do2 ) gradually decreases according to (11). Consequently, the commutation between D o1 , D o2 , and D o3 starts. When i Do1 and i Do2 reach zero, the diode commutation operation ends; and D o1 and D o2 are blocked. Moreover, since D o1 and D o2 are softly turned off, there is no reverse recovery problem for D o1 and D o2 . Especially in this mode, unlike the conventional converter, the proposed converter does not significantly increase the output current ripple due to the output inductor L o .

Mode 3 [t 3 -t 4 ]:
Since D o1 and D o2 are blocked in this mode, i Lk1 is zero, and the input current flows through D o3 . Additionally, the energy stored in L m is transferred to the output. From Fig. 5 Therefore, according to (17), v Lk2 and v Lo can be expressed as follows: v Based on the previously derived (17) - (19), the current flowing through L m , L k2 , and L o can be expressed as follows: Like the previous mode, i Do3 = i Lm -i Lk2 , and mode 3 ends when M 2 is turned on.

Mode 4 [t 4 -t 5 ]:
When M 2 is turned on at t 4 , the current flows through the transformer. Therefore, D o1 conducts and v ds1 and v Do2 are clamped to . Therefore, the voltages across L k1 , L k2 , and L o are as follows. v

VOLUME 11, 2023
From previously derived (23) - (26), the currents flowing through L m , L k1 , L k2 , and L o are as follows: In this mode, i Do1 is equal to i Lk1 , and i Do3 = i Lm -i Lk2 by KCL. Therefore, since i Do1 gradually increases and i Do3 gradually decreases according to (27), (29), and (30), the commutation between D o1 and D o3 starts. Additionally, since i ds2 is equal to i Lk1 in this mode and i Lk1 was zero in the previous mode. Therefore, i ds2 gradually increases from zero due to L k1 and L k2 as shown in (28). Consequently, soft switching operation of M 2 is possible, such that the turn-on loss can be considerably reduced. In mode 8, M 1 can be turned on with the soft switching operation, which is similar to how M 2 operates. Therefore, the turn-on loss of M 1 can be considerably reduced. Further, since this mode ends when i Do3 reaches zero, there is no reverse recovery problem for D o3 .
Since the operations of modes 5 through 8 are similar to those of modes 1 through 4, a detailed operation analysis is omitted here. The operation of the proposed converter is repeated from mode 1 to mode 8 as one switching cycle.

III. ANALYSIS OF THE PROPOSED CONVERTER A. VOLTAGE CONVERSION RATIO
To derive the voltage conversion ratio of the proposed converter, applying KVL to the outermost loop in Fig. 7 Since the average voltage across the inductor is zero at steady-state, the average voltage < v Do3 > of D o3 is as follows: As shown in Fig. 6, D o3 conducts for a duration of (1-2D) T s +2T CM (on) within one switching cycle. Therefore, from (5), < v Do3 > is determined as follows: From (31) and (32), the effective duty ratio D eff and the voltage conversion ratio can be obtained as follows: For reference, since the conventional converter operates identically to the proposed converter, its voltage conversion ratio and effective duty cycle are the same as those of the proposed converter.

B. COMMUTATION TIME
As shown in Fig. 6, the currents flowing through D o1 and D o2 gradually decrease while the current flowing through D o3 gradually increases during T CM (off ) . In addition, the current flowing through D o1 gradually increases while the current flowing through D o3 gradually decreases during T CM (on) . From the i Lk1 waveform shown in Fig. 6, T CM (off ) can be expressed as follows: where v Lk1 (t 2 -t 3 ) represents the voltage applied to L k1 during mode 2. As shown in Fig. 4(a), i Lk1 is equal to i ds1 during the time interval t 1 -t 2 . Assuming an ideal circuit, the average current I ds1 flowing through M 1 is 0.
Moreover, as shown in Fig. 6, assuming that the average cur- can be derived as follows: where v Lk1 (t 1 -t 2 ) represents the voltage applied to L k1 during mode 1. Since i Lk1 (t 2 ) = i ds1 (t 2 ), T CM (off ) can be determined from (35) and (36) as follows: 58104 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. More so, T CM (on) can be determined from the i Lk1 waveform shown in Fig. 6 as follows: where v Lk1 (t 4 -t 5 ) represents the voltage applied to L k1 during mode 4. From (2), (10), and (38), T CM (on) can be expressed as follows: For reference, since the operation of the conventional converter is similar to that of the proposed converter, the T CM (off ) and T CM (on) of the two converters are the same under the condition of the same leakage and magnetizing inductances. converters. As shown in Fig. 8(a), the average magnetizing current of the coupled inductor in the conventional converter is 2I ds -2I Do +2I o according to KCL. Meanwhile, the proposed converter shown in Fig. 8(b) has an average magnetizing current of 2I ds -2I Do + I o , which is smaller than that of the conventional converter. Therefore, if the two converters have the same magnetizing inductance for the coupled inductor, the peak current of the magnetizing inductor in the proposed converter can be lower than that in the conventional converter. As a result, the core size of the coupled inductor in the proposed converter can be further reduced compared to that of the conventional converter.
In comparison to the conventional converter, although the proposed converter is added to a small output inductor, the average magnetizing current of the coupled inductor is reduced by the amount of the load current. Therefore, the core size of the coupled inductor for the proposed converter can be smaller than that of the conventional converter. Additionally, since the average current flowing through output inductor is I o and the output current ripple is small, a small size core can be used for the output inductor.

D. OUTPUT CURRENT AND VOLTAGE RIPPLE
Figs. 9 and 10 show the output current and voltage ripples of the proposed and conventional converters, respectively. Specifically, the output current of the proposed converter is the same as i Lo . Assuming that the T CM (on) is negligibly short compared to D eff T s , the output current ripple of the proposed converter is as follows: As shown in (40), the output current ripple of the proposed converter is independent of the load current and is determined by the output inductor L o . Therefore, the output current ripple can be freely adjusted with the value of L o . Meanwhile, since the conventional converter operates similarly to the proposed converter, the output current ripple of the conventional con-  verter can be obtained from Fig. 10 as follows: As shown in (41), the output current ripple of the conventional converter is not only very large but also increases as the load increases. Therefore, there is a limit to reducing the output current ripple by increasing the inductances of L m , L k1 , and L k2 . Meanwhile, for analysis of the output voltage ripple of the two converters shown in Figs. 9 and 10, it is assumed that the current variation during T CM (on) is very small and negligible. From Fig. 9 and (40), the output voltage ripple v o_prop of the proposed converter is derived as follows: Meanwhile, assuming that the output capacitor C o is charged only during the time from t 2 to t 3 when the output current rises significantly as shown in Fig. 10, the output voltage ripple v o_conv of the conventional converter can be derived as follows: As shown in (42), v o_prop can be reduced by L o and is determined by inductances L m , L k1 , and L k2 . Additionally, v o_prop is independent of the load current. In contrast, as shown in (43), v o_conv is affected by the inductances of L m , L k1 , and L k2 , but their influences are not significant. Instead, v o_conv strongly depends on the load current and increases proportionally. Fig. 11 shows the output current ripple of the conventional and proposed converters according to the input voltage.  To compare the output current ripple of the two converters, it is assumed that the leakage inductance L k1 of the transformer is 0.3 uH; the magnetizing inductance L m of the coupled inductor is 2.625 uH; and the leakage inductance L k2 is 10 % of L m . Additionally, the output inductor L o of the proposed converter is selected as 5.08 uH. As for selecting the values of L o and L m presented here, it is discussed in detail in Section IV. As shown in Fig. 11, the largest output current ripple of both converters can be observed when the input voltage is in the middle range. Moreover, it can be seen that the output current ripple of the conventional converter is about four times larger than that of the proposed converter in all input voltage ranges. Fig. 12 shows the output current ripple of the two converters according to the load current at an input voltage of 36 V, where the output current ripple is the largest. As shown in Fig. 12, the output current ripple of the conventional converter increases significantly as the load current increases. Meanwhile, the output current ripple of the proposed converter is constant and is determined by the output inductor L o regardless of the load current. Therefore, the proposed converter can have a very low and constant output current ripple regardless of the load current, unlike the conventional converter. Moreover, the difference between the output current ripple of the two converters becomes much larger as the load increases. As a result, the proposed converter can greatly reduce the number of output capacitors.   Fig. 13, the output voltage ripple of the proposed converter is almost independent of L m , whereas that of the conventional converter depends on L m and is smallest when L m = 1.5 uH. Therefore, since L m is not related to the output voltage ripple of the proposed converter, the L m of the proposed converter can be designed focusing only on efficiency. Meanwhile, the L m of the conventional converter must be designed considering both output voltage ripple and efficiency; hence, it is difficult to derive an optimal L m .

IV. DESIGN OF OPTIMAL PARAMETERS A. LOSS ANALYSIS FOR OPTIMAL PARAMETERS
Since high efficiency is essential to reduce the size and volume of the BDR, a loss analysis scheme for selecting optimal parameters is presented here.
The efficiency of the proposed converter is mainly determined by the losses of switches, diodes, and magnetic components. Since the soft switching operation is guaranteed during the turn-on transients, the turn-on losses of the switches are negligible. Additionally, the equations for analyzing the loss of each component are summarized in Table 1, and the coefficients for the transformer core loss are given in Table 2.
When calculating the switch loss in Table 1, t f and R ds(on) represent the turn-off switching time and on-resistance of the switches (M 1 and M 2 ), respectively. Additionally, R eff _NT 1 , R eff _NT 2 , R eff _NL1 , R eff _NL2 , and R eff _NLo represent the effective wire resistances considering the AC losses of the transformer, coupled inductor, and output inductor. The other symbols used in Table 1 have previously been defined in the nomenclature. For the worst-case loss analysis, the switching frequency f sw is set to 100 kHz; the number of turns of the transformer (N T 1 = N T 2 ) is fixed at 5; the load condition is full load (I o = 15 A), the output voltage is 50 V, and the input voltage is set to a minimum voltage of 30 V. Besides, the transformer uses the PQ2625 ferrite core of the PL-7 material, and the coupled and output inductors use the CH234125 powder core of a high-flux material.  Based on the specifications listed above, the total converter loss according to the number of turns of the coupled inductor N L1 (= N L2 ) and output inductor (N Lo ) are shown in Fig. 14. As shown in Fig 14, the total loss is the smallest at N Lo = 5 and tends to increase as N Lo increases, except for N Lo = 3. Although the total loss at N Lo = 5 is the smallest, there is no significant difference from the loss at N Lo = 7. Therefore, N Lo = 7 is more suitable considering the output current ripple. Meanwhile, Fig. 14 shows that the total converter loss is the largest when N L1 (= N L2 ) = 2 and is almost the same when N L1 (= N L2 ) ≥ 3.    Fig. 15, when N L1 (= N L2 ) = 5, not only are the core loss and copper loss most similar, but the total loss is also the smallest. Therefore, N L1 (= N L2 ) has an optimal value at 5.
Based on the N Lo = 7 and N L1 (= N L2 ) = 5 determined above, Fig. 16 shows the total converter loss according to N T 1 (= N T 2 ). As shown in Fig. 16, the total loss is smallest at N T 1 (= N T 2 ) = 5. Therefore, N T 1 (= N T 2 ) has an optimal value at 5.

B. LEAKAGE INDUCTANCES FOR SOFT SWITCHING
As described in Section II, the soft switching operation of switches M 1 and M 2 in the proposed converter is achieved with the help of leakage inductances L k1 and L k2 . However, if the T CM (off ) shown in Fig. 6 becomes greater than (0.5-D) T s , the current flowing through the transformer may not drop to zero before the next switching operation occurs, resulting in a hard-switching operation. Therefore, to ensure the soft switching operation for all switches, the following conditions must be met: From (37) and (44), Fig. 17 shows the range of the leakage inductances L k1 and L k2 to ensure the soft switching operation of all switches under worst-case conditions -an input voltage of 30 V and a full load of 750 W. As shown in Fig. 17, if L k1  and L k2 become too large, it is unfavorable to soft switching. Therefore, it is advantageous for L k1 and L k2 to be smaller for soft switching operations.

C. LEAKAGE INDUCTANCES FOR OUTPUT CURRENT RIPPLE
The output current ripple of the proposed converter is determined by inductances (L m , L k1 , L k2 , and L o ) as shown in (40).
Besides, the output current ripple decreases as the output inductance L o increases. Fig. 18 shows the output current ripple of the proposed converter according to the leakage inductances L k1 and L k2 . Here, to derive Fig. 18, assuming that L k2 is 10 % of L m , L o = 5.08 uH, P o = 750 W, and V in = 36 V. As shown in Fig. 18, the larger L k1 and smaller L k2 tend to reduce the output current ripple more. Therefore, to minimize the output current ripple, it is desirable to have a large L k1 and a small L k2 within the range that guarantees the soft switching operation of the switches.

V. EXPERIMENTAL RESULTS
To confirm the feasibility of the proposed converter, the experimental results of the conventional and proposed converters based on the specification shown in Table 3 are presented in this section. Fig. 19 shows the prototypes of the two converters and Figs. 20 and 21 present the experimental key waveforms of the two converters.
Specifically, Figs. 20(a) and (b) represent the output capacitor current ripple of the two converters according to the load current at an input voltage of 36 V, which represents the maximum output current ripple within the input voltage range. Precisely, as shown in Fig. 20(a), the output current ripple of the conventional converter is 15.4 A at 10 A load, whereas that of the proposed converter is 4.2 A at the same load. Additionally, Fig. 20(b) shows that the output current ripple of the conventional converter is 20.2A at 15 A load, while that of the proposed converter is 4.21 A at the same load. Moreover, when the load current increases from 10 A to 15 A, the output current ripple of the conventional converter increases by 4.8 A. Meanwhile, that of the proposed converter remains almost constant regardless of the load current. Therefore, the output current ripple of the proposed converter is significantly reduced compared to the conventional converter.
Meanwhile, as shown in Fig. 20(b), the RMS current flowing through the output capacitor of the conventional converter is measured as 4.65 A rms at 15 A load. Meanwhile, the output capacitor RMS current of the proposed converter is as small as 1.05 A rms , which is approximately 4.4 times smaller than that of the conventional converter. Therefore, if the same bus capacitor is used in the PCU, the reduced RMS current can reduce the stress on the bus capacitor, which may lead to an increase in the lifetime. In addition, it can be considered that the proposed converter, which has an almost constant RMS current through the output capacitor regardless of the load current, is more suitable for high-power applications. Fig. 20(c) shows the magnetizing current waveforms of the coupled inductor of the two converters, which is measured using the Math function of the oscilloscope. Precisely, the proposed converter has a peak magnetizing current of 18.5 A, whereas the conventional converter has 32 A, which is about 13.5 A higher than that of the proposed converter. Therefore, since the proposed converter has a lower peak magnetizing current of the coupled inductor than the conventional converter, a smaller OD234 core can be used in the proposed converter, whereas the conventional converter requires a larger OD270 core. Additionally, as shown in Fig. 20(d), the peak current of the output inductor used in the proposed converter is 17.11 A, which is not much different from the 18.5 A of the coupled inductor in the proposed converter. Therefore, both the output inductor and the coupled inductor of the proposed converter can use the same size OD234 magnetic core, which is smaller than that used in the conventional converter. Finally, the maximum magnetic flux density B max of the magnetic cores used in the two converters is calculated as follows: the B max of the coupled inductor used in the conventional converter is 0.317 T; the B max of the coupled inductor used in the proposed converter is 0.247 T; and the B max of the output inductor used in the proposed converter is 0.32 T. Consequently, as shown in Fig. 19, the conventional converter requires only one large magnetic core for the coupled inductor, whereas the proposed converter requires two small magnetic cores for both the coupled and output inductors.
Furthermore, Fig. 20(e) shows the output voltage ripple of the two converters at 36 V input voltage and 15 A full load. As shown in Fig. 20(e), to maintain the output voltage ripple of both converters at around 0.45 V, the conventional converter requires eleven output capacitors (C o = 24.2 uF), while the proposed converter requires only two link capacitors (C link = 8 uF) and three output capacitors (C o = 6.6 uF). Therefore, as shown in the prototypes in Fig. 19, the conventional converter uses one large-coupled inductor core and eleven output capacitors, while the proposed converter uses one small-coupled inductor core, one small-output inductor core, two link capacitors, and three output capacitors. Although the proposed converter uses an additional magnetic core for an output inductor compared to the conventional converter, the total number of capacitors required to satisfy the same output voltage ripple is significantly reduced compared to the conventional converter. Additionally, since the peak magnetizing current of all the inductors used in the proposed converter are lower than that used in the conventional converter, the smaller size magnetic core can be used in the proposed converter. Therefore, the proposed converter can reduce the overall volume and weight. Furthermore, multiple BDRs are commonly used in a parallel combination in the electrical power system of geostationary satellites to ensure   reliability and high power [28]. As a result, the proposed converter can further reduce the volume and weight of the electrical power system. Fig. 21 shows the soft switching waveforms of the switch M 1 , diode D o1 , and diode D o3 in the proposed converter at 30 V input voltage and 15 A full load, which is the worst case of soft switching operation. As shown in Figs. 21(a) and (b), D o1 and D o3 do not have reverse recovery issues because the current gradually decreases to zero before they are blocked. Further, as shown in Fig. 21(c), when M 1 is turned on, the current through M 1 gradually increases from zero because of leakage inductances. Therefore, since the overlap of voltage and current in M 1 can be minimized, switching loss can be significantly reduced. More so, since the switch M 2 and the diode D o2 operate symmetrically to M 1 and D o1 , their soft switching operation are possible. Fig. 22 represents the measured efficiencies of the proposed converter according to the load variation at input voltages of 30 V, 36 V, and 42 V, respectively. More precisely, as shown in Fig. 22, the proposed converter achieves an   (15 A), and an average efficiency of about 96.6 % for the entire load range. Specifically, this high efficiency is achieved due to the soft switching operation of the switches, the elimination of the reverse recovery problem of the diodes, and an optimal design of the magnetic components through loss analysis. Additionally, the selection of turns for the transformer, coupled inductor, and output inductor is determined through loss analysis.

VI. CONCLUSION
In this paper, an improved Weinberg converter is proposed to overcome the drawbacks of the conventional Weinberg converter. More precisely, the proposed converter can significantly reduce the output current ripple compared to the conventional converter due to the output inductor. Consequently, the number of output capacitors required to satisfy the same output voltage ripple is significantly reduced compared to the conventional converter. Furthermore, the output capacitor root mean square (RMS) current of the proposed converter is much smaller than that of the conventional converter. Thus, if the same output capacitance is used in both converters, the proposed converter can reduce the burden on the output capacitor. In addition, when the load current increases, the proposed converter maintains an almost constant output current ripple. Meanwhile, the output current ripple of the conventional converter increases proportionally as the load current increases. Therefore, it can be considered that the proposed converter, which maintains an almost constant output current ripple regardless of the load current, is more suitable for high-power applications.
In contrast, compared to the conventional converter, the proposed converter requires an additional magnetic component for the output inductor. However, the proposed converter has a lower peak magnetizing current of the coupled inductor, which is approximately half as much as that of the conventional converter. Therefore, the proposed converter can prevent magnetic core saturation even at higher loads and reduce the size of the magnetic core compared to the conventional converter.
Moreover, the proposed converter was verified through a 750 W-rated prototype based on the designed optimal parameters. Specifically, the proposed converter can achieve high efficiency due to three factors: the soft switching operation of the switches, the absence of the reverse recovery problem of diodes, and the optimal design of the magnetic components through loss analysis. More precisely, the proposed converter achieves an efficiency of at least 92.9 % over the entire load range at input voltages of 30 V, 36 V, and 42 V. In addition, the proposed converter can reduce the overall weight of the conventional converter from 404 g to 392 g because the size of the magnetic components and the number of output capacitors are reduced. More so, since multiple BDRs are generally used in parallel combinations to achieve reliability, redundancy, and higher power, the weight reduction effect of the proposed converter will be more pronounced.
From these results, the proposed converter is anticipated to be suitable for high-power applications and achieve the miniaturization and weight reduction of electrical power systems for geostationary satellites, as well as reduce the satellite launch costs.

ACKNOWLEDGMENT
The preparation of this paper was aided by ChatGPT, a language model developed by OpenAI. In particular, ChatGPT played a role in refining the paper. VOLUME 11, 2023