Title: Optimised power control and balance scheme for the output parallel dual‐active‐bridge DC‐DC converters in power electronic traction transformer
Abstract: IET Power ElectronicsVolume 12, Issue 9 p. 2295-2303 Research ArticleFree Access Optimised power control and balance scheme for the output parallel dual-active-bridge DC-DC converters in power electronic traction transformer Feng An, Feng An Department of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031 People's Republic of ChinaSearch for more papers by this authorWensheng Song, Corresponding Author Wensheng Song [email protected] orcid.org/0000-0002-7447-0203 Department of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031 People's Republic of ChinaSearch for more papers by this authorKexin Yang, Kexin Yang Department of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031 People's Republic of ChinaSearch for more papers by this authorShucong Luo, Shucong Luo Department of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031 People's Republic of ChinaSearch for more papers by this authorXiaoyun Feng, Xiaoyun Feng Department of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031 People's Republic of ChinaSearch for more papers by this author Feng An, Feng An Department of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031 People's Republic of ChinaSearch for more papers by this authorWensheng Song, Corresponding Author Wensheng Song [email protected] orcid.org/0000-0002-7447-0203 Department of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031 People's Republic of ChinaSearch for more papers by this authorKexin Yang, Kexin Yang Department of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031 People's Republic of ChinaSearch for more papers by this authorShucong Luo, Shucong Luo Department of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031 People's Republic of ChinaSearch for more papers by this authorXiaoyun Feng, Xiaoyun Feng Department of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031 People's Republic of ChinaSearch for more papers by this author First published: 11 July 2019 https://doi.org/10.1049/iet-pel.2018.5056Citations: 6AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In order to achieve a comprehensive performance optimisation consisting of transmission power balance, high efficiency, and fast dynamic response for the output parallel dual-active-bridge (DAB) dc–dc converters in power electronic traction transformer, an optimised power control and balance scheme based on extended phase-shift (OPCB-EPS) control is proposed in this study. By combining current stress-optimised calculation with EPS control, the current stress of converters can be reduced significantly and the efficiency can be further improved. In addition, the desired transmission power of DAB converters is estimated on-line by introducing the virtual voltage component to enhance the dynamic response of the output voltage under the input voltage fluctuation and the load disturbance conditions. Meanwhile, the proposed OPCB-EPS scheme can realise the transmission power balance over the whole power range. Finally, a scale-down prototype of DAB dc–dc converters consisting of three cells is developed to compare the performance of the current stress optimised with dual phase-shift (CSO-DPS), current stress optimised with EPS and proposed OPCB-EPS schemes. The comparative experimental results have verified the excellent performance of OPCB-EPS scheme and the theoretical analysis in this work. 1 Introduction As an economical, convenient, eco-friendly, and massive public transportation, high-speed railway plays an important role in boosting economic development, improving environmental pollution, and promoting people living quality. The modern development of new generation high-speed trains trends toward higher speed, higher efficiency, lower running noise, lower weight, and volume. However, the bulky and low-efficiency line frequency transformer becomes one of the major obstacle to reduce energy consumption and increase the power density. Thus, power electronic traction transformers (PETT) with the salient advantages of energy saving, environmental protection, and high-power density are considered as the core equipment of next-generation high-speed trains [1-3]. At present, the most widely adopted PETT railway drive system topology [4, 5] is shown in Fig. 1, which consists of a single-phase cascaded H-bridge (CHB) converter, the output parallel dual-active-bridge (DAB) dc–dc converters [6, 7] with medium-/high-frequency transformer, a three-phase inverter, and traction AC motors. Fig. 1Open in figure viewerPowerPoint Topology of train traction drive system with PETT In practical application, the transmission power unbalance problem in PETT cannot be avoided due to the circuit parameters mismatch such as storage inductance in DAB stages [8]. It can result in excessive deviation of the voltages or/and currents, bring the system into collapse and even the breakdown of power devices if there is no power balancing control solutions [9-11]. Thus, it is important and significant to balance the transmission power in PETT. In the existing literature, various power balance control strategies for the PETT system can be classified into two categories as follows [12-15]: (i) the CHB converter realises the intermediate dc voltage balancing, and the DAB converters achieve the transmission power balancing of each cell. (ii) The DAB converters control intermediate dc voltage and transmission power balancing, simultaneously. In addition, the CHB converters adopt none of balance control methods. The first category of control approaches is more flexible than the latter, while the latter is simpler. Specifically, in [12], a novel voltage and power balance control strategy based on single-phase d-q model is proposed to balance the intermediate dc voltage and the real power through the output parallel DAB modules. The control strategy is simple and intuitive, but the high-frequency inductor current sensor is necessary for each DAB module, which undoubtedly increases the system cost. In order to get rid of the inductor current sensors, a coordinating control scheme for PETT is proposed in [13], where the common duty ratio controller in the d–q coordinate for the CHB stage is used to achieve unity power factor and the feedback feed-forward controller for the DAB stage to balance the transmission power. In addition, an input and output voltage tracking control method is proposed in [14], where the intermediate dc voltages are adapted to track the output voltage of DAB converters with a constant proportion coefficient to achieve the voltage and power balance. However, it's obvious drawback is that there exists twice-grid-frequency ripple in the output voltage of DAB converters same as the intermediate dc voltage. In order to overcome the drawback, a voltage balance control strategy based on DAB dc–dc converters in PETT is proposed in [15]. The control scheme is simple and can balance the voltage and transmission power of each cell effectively. However, the dynamics and efficiency performance of the output parallel DAB converters in the above control schemes are relatively poor. Since the modulation methods for DAB converters is based on single phase-shift (SPS) control, and the power of DAB converters is adjusted only by proportional-integrator (PI) controllers. For the PETT train traction drive system shown in Fig. 1, there always exists twice-grid-frequency ripple in the dc-link voltage of CHB converters, which may cause the beat frequency phenomenon of traction motor [16, 17]. Thus, the fast dynamic response of DAB converters in PETT is necessary to face the input voltage fluctuation. In [18], the state space averaging model and the small signal model of DAB dc–dc converters are developed, and a model-based feed-forward control strategy is proposed to enhance the dynamic response. Similarly, by constructing a linearised dynamic harmonic model, a feed-forward compensation control scheme for DAB dc–dc converters is proposed in [19]. However, the harmonic model is very complex, and it is not suitable for modularisation. Meanwhile, an output voltage and current controllers of DAB converters with the double-integral sliding mode theory are designed in [20] to achieve fast dynamic response for load variations and reference changes. Furthermore, a virtual direct power control scheme based on SPS control is proposed in [21] to achieve the fast dynamic response under the input voltage fluctuation and the load disturbance conditions. However, in the traditional SPS control, power flow of the adopted DAB converters is mainly related to the storage inductor, which will lead to excessive current stress (i.e. peak current) and low efficiency when the voltage transfer ratio deviates far from one [22]. Thus, the performance of the virtual direct power control scheme combined with other optimised phase-shift modulation methods needs to be discussed and verified further. In order to reduce the current stress and improve the efficiency of DAB converters, various optimised phase-shift modulation methods are reported, including dual phase-shift (DPS) control, extended phase-shift (EPS) control, and triple phase-shift (TPS) control. In TPS control, three controllable degrees can be utilised to achieve the optimised operation of DAB converters. Thus, TPS control can achieve a wider range of optimisation compared with DPS and EPS controls. Specifically, a particle swarm optimisation strategy with TPS control based on the unified phasor analysis is proposed in [23] to improve the efficiency of DAB converters. Meanwhile, a current stress optimisation and soft-switching operation of DAB converters with TPS control are proposed in [24]. This scheme can lead to the minimum current stress with the desired transmission power and voltage conversion ratio in the whole load range, and the full soft-switching operation can be achieved simultaneously. However, the above-optimised schemes are relatively complicated, so it is difficult to implement in the multiple DAB modules. For the DPS and EPS controls, many optimised schemes have been discussed for the single DAB converter. In [25], an optimised operating control scheme based on DPS control for DAB converters is proposed to achieve the current stress optimisation. Although the scheme can reduce the current stress and improve the efficiency significantly, the optimised phase-shift ratios are obtained through off-line look-up tables due to its complexity. Furthermore, a current stress optimised with DPS (CSO-DPS) control strategy is proposed in [26] to realise the minimum current stress optimisation on-line. However, the calculated process and on-line logic judgment of this control scheme are a little complex. In order to further improve the efficiency of DAB converters, current stress optimised with EPS (CSO-EPS) control is proposed in [27]. However, the adopted EPS modulation method is not comprehensive and only one phase-shift ratios condition is considered, which results in the obtained current stress under EPS control is not minimum. In addition, the CSO-EPS control scheme is not suitable to be extended to cascaded structures to balance the transmission power, because the storage inductance is not introduced into the calculating process of the optimised phase-shift ratios based on PI controller. For the output parallel DAB converters in PETT, the control scheme should be as simple as possible besides achieving the transmission balance, the dynamic and efficiency performance improvement. However, throughout the existing literatures, the optimised scheme that is suitable for the output parallel DAB converters in PETT is rarely reported. In order to balance the transmission power, improve the efficiency, and enhance the dynamic response for the output parallel DAB dc–dc converters in PETT, an optimised power control and balance scheme based on EPS (OPCB-EPS) is proposed in this paper. First, the EPS control method is depicted entirely, and the current stress optimised calculation under EPS control is derived to improve the efficiency of DAB converters. Then, the desired transmission power estimation on-line is introduced to enhance the dynamic response of output voltage. Subsequently, a comprehensive description of the proposed OPCB-EPS scheme is presented, and the transmission power balance of output parallel DAB dc–dc converters in the OPCB-EPS scheme is analysed. Finally, a comprehensive experimental performance comparison of the proposed scheme with the other control solutions is shown. The rest of the paper is organised as the following: in Section 2, the EPS control details are introduced. The CSO-EPS is presented in Section 3. Subsequently, the comprehensive description of the OPCB-EPS scheme is shown in Section 4. In Section 5, the theoretic analysis and the proposed scheme are verified by the experimental comparison of CSO-DPS [26], CSO-EPS [27], and OPCB-EPS schemes. Finally, the work is concluded in Section 6. 2 Analysis of EPS control In the PETT shown in Fig. 1, the output parallel DAB dc–dc converters can be equivalent to the input independent output parallel connection when the CHB converter plays the role of balancing intermediate dc voltage [15]. In addition, the equivalent circuit composed of N DAB cells is shown in Fig. 2, where is the input voltage of the ith DAB cell; Cgi and Cfi are the input and output capacitors of the ith DAB cell; Li is the storage inductor of the ith DAB cell; and are the equivalent ac output voltages of two H-bridges located on the primary and secondary sides of the medium-/high-frequency transformer; ioi is the output current of the ith DAB cell; Uo represents the output voltage; R is the load resistance; io is the load current; and n is the turn ratio of each transformer. Fig. 2Open in figure viewerPowerPoint Equivalent input independent output parallel connection of DAB dc–dc converters in PETT In the CSO-EPS control scheme [27], there are two controllable phase-shift ratios: one is defined as the phase-shift ratio between S1 and S4 (S4 ahead of S1), and the other one is defined as the phase-shift ratio between S1 and S5 (S1 ahead of S5). However, the phase of ac output voltage Uab in the primary H-bridge is always leading that of ac output voltage Ucd in the secondary H-bridge under the definition of phase-shift ratios. Thus, the CSO-EPS control scheme is not comprehensive and not all the phase-shift ratio combinations are included, which makes the obtained current stress not the minimum in EPS control. In order to describe the EPS control entirely, the two controllable phase-shift ratios are redefined. Taking the ith DAB cell as an example, Di1 is defined as the inner phase-shift ratio between S1 and S4 (S1 ahead of S4), and Di2 is defined as the outer phase-shift ratio between S1 and S5 (S1 ahead of S5). Thus, the waveforms of voltage and current for the ith DAB dc–dc converter in EPS control can be divided into two conditions: 0 ≤ Di1 ≤ Di2 ≤ 1 and 0 ≤ Di2 ≤ Di1 ≤ 1. Fig. 3 shows the main curves of switching sequences, voltage, and current for the ith DAB cell in EPS control, where is the inductor current of the ith DAB cell and Ts represents a switching cycle. Meanwhile, in order to suppress the output voltage ripple and reduce the volume of the output capacitor, the phase-shift angle between the ac output voltage of primary H-bridge in each DAB cell is set as 360°/N [12]. Fig. 3Open in figure viewerPowerPoint Main curves of switching sequences, voltage, and current for the i-th DAB cell in EPS control (a) Switching sequences, (b) The waveforms of voltage and current in 0 ≤ Di1 ≤ Di2 ≤ 1, (c) The waveforms of voltage and current in 0 ≤ Di2 ≤ Di1 ≤ 1 Obviously, the EPS control scheme in Fig. 3 is more comprehensive compared to the traditional EPS control [27], which only consists of one of the cases (Fig. 3b). In addition, the average transmission power and the current stress of the ith DAB cell in a switching cycle under EPS control can be expressed as follows: (1)The voltage transfer ratio of the ith DAB cell is defined as and we assume ki ≤ 1 in this paper; the other condition ki>1 can be analysed similarly. Combining Fig. 3 with (1), the average transmission power of the ith DAB cell in EPS control can be derived as (2)where f = 1/Ts represents the switching frequency. In addition, the current stress of the ith DAB cell in EPS control can be derived as (3)In order to simplify analysis and calculation, the unified average transmission power and current stress of the ith DAB cell can be defined as (4)where and are the maximum transmission power and the maximum average input current of the ith DAB cell in EPS control, i.e. (5)Based on (2)–(5), the unified average transmission power and current stress of the ith DAB cell in EPS control can be expressed as (6) 3 Current stress optimised calculation in EPS control In order to seek the optimal phase-shift ratios combination to reduce the current stress and improve the efficiency in EPS control under the desired transmission power for the output parallel DAB dc–dc converters, the Lagrange multiplier method (LMM) is adopted. LMM is one of the most widely used optimisation method to solve the extreme optimisation problem with the equivalent constraint, and the simple expression relationship between inner phase-shift ratio and outer phase-shift ratio can be obtained to achieve the minimum current stress control with LMM. First, the Lagrangian function Ei can be defined to establish the connection between the current stress and the transmission power for the ith DAB cell with EPS control as (7)where Ei is the Lagrangian function; λ is the Lagrangian multiplier; and p* is the unified desired transmission power of the ith DAB cell. Then, the relationship between outer phase-shift ratio Di1 and inner phase-shift ratio Di2 can be described by LMM, (8)Substituting (6) and (7) in (8), the relationship between phase-shift ratios Di1 and Di2 can be deduced as (9)Thus, the minimum current stress optimisation in EPS control can be achieved when the relationship between outer and inner phase-shift ratios of the ith DAB cell meets the expression in (9). Furthermore, combining (6) and (9), the optimised phase-shift ratios can be expressed with unified transmission power pi and voltage transfer ratio ki as (10)where the power range 0 ≤ pi<(2ki − 2)/ki2 is corresponding to the phase-shift ratios condition 0 ≤ Di2 ≤ Di1 ≤ 1, and the power range (2ki − 2)/ki2 ≤ pi ≤ 1 is corresponding to the phase-shift ratios condition 0 ≤ Di1 ≤ Di2 ≤ 1. Then, substituting (10) in (6) and combining the current stress optimised scheme in traditional EPS control [27], the unified minimum current stress of the ith DAB cell in the EPS and traditional EPS control schemes can be obtained as (11)where ipi is the unified minimum current stress of the ith DAB cell in EPS control, and ipTi represents the unified minimum current stress of the ith DAB cell in the traditional EPS control. Based on (11), the relation curves of unified current stress in traditional EPS and EPS controls with respect to the unified transmission power pi and the voltage transfer ratio ki are drawn in Fig. 4. Fig. 4Open in figure viewerPowerPoint Relation curves of the unified current stress with respect to the unified transmission power and voltage transfer ratio in traditional EPS and EPS control schemes From Fig. 4, it is clear that the current stress of DAB dc–dc converters increases with the increase of unified transmission power pi and voltage transfer ratio ki. However, the current stress of DAB converters in the traditional EPS control scheme is not global minimum because only one phase-shift ratios condition is considered. Compared with the traditional EPS control scheme, the adopted EPS control scheme can further reduce the current stress and achieve the global minimal current stress of DAB converters, as all the phase-shift ratios combination is included. 4 OPCB scheme in EPS control In the existing current stress and efficiency optimised control schemes [26, 27], the PI controller is usually adopted to control part or all phase-shift ratios to boost the converters to the desired power, and the other phase-shift ratios are estimated with the unified transmission power pi and the voltage transfer ratio ki to achieve the optimised operation. It does not only sacrifice the dynamic performance of the converters to a certain extent, but also restricts the expansibility of the optimised methods for the cascaded structure to achieve the transmission power balance, because the storage inductance of each module is not introduced into the calculated process of optimised phase-shift ratios. Specifically, in CSO-EPS control scheme [27], the inner and outer phase-shift ratios of converters are obtained through PI controller, which are calculated as follows: (12)where Di is the phase-shift ratio of the ith DAB dc–dc converter in SPS control, which is obtained through the PI controller of the output voltage. It can be known that the existing CSO-EPS control scheme is implemented by searching the relationship of optimised phase-shift ratios between SPS control and EPS control. In addition, the calculation of all the optimised phase-shift ratios in CSO-EPS control scheme is only related to the phase-shift ratio Di, which is obtained through the PI controller of the output voltage, but it is not related to any circuit parameters, such as storage inductance. Thus, for the output parallel DAB dc–dc converters in PETT, the optimised phase-shift ratios Di1 and Di2 of each DAB cell are same regardless of whether the circuit parameters are matched or not, because the output voltage and obtained phase-shift ratio Di of each DAB cell are same. It indicates the existing CSO-EPS control scheme is the same as the SPS control method, which is not suitable to be extended to cascaded structures to achieve the transmission power balance. In addition, the existing CSO-DPS control scheme [26] is implemented as follows: the outer phase-shift ratio is also obtained through the PI controller of the output voltage, but the inner phase-shift ratio is estimated with the voltage transfer ratio ki and unified transmission power pi, which is related to the circuit parameters. When the voltage transfer ratio kiis close to one, the inner phase-shift ratio is close to zero, and the DPS control can be approximately equivalent to SPS control. Then, each of the DAB cells is applied with the same outer phase-shift ratio obtained from the PI controller of the output voltage. Based on (2) and (3), it can be known that the transmission power of the DAB cell with small storage inductance is larger, and the corresponding current stress is larger. Conversely, when the voltage transfer ratio ki is far from one, the inner phase-shift ratio is introduced to reduce the current stress and improve efficiency. In addition, the calculated process of the inner phase-shift ratio is related to the storage inductance, so the degree of transmission power balance under CSO-DPS control scheme is better than CSO-EPS control and SPS control schemes. In conclusion, in CSO-DPS control scheme, the closer the voltage transfer ratio ki is to one, the more terrible the unbalanced degree of transmission power is. In order to achieve the transmission power balance in the entire power range, improve the efficiency and enhance dynamic response under the input voltage fluctuation and load disturbance conditions for the output parallel DAB dc–dc converters in PETT, an OPCB-EPS is proposed. The main idea of improving the dynamic response of DAB converters in OPCB-EPS scheme is to estimate the desired transmission power. In the traditional CSO scheme, the unified transmission power of converters is calculated as follows [26], which only represent the unified output power of converters. (13)However, in practical application, the difference between the input power and the output power always exists due to the power loss. Thus, the desired transmission power P* cannot be simply expressed as the output power such as (13) or the arithmetic product of the desired output voltage Uo* and current io*. In order to compensate for the power losses, the virtual voltage component Uv is introduced, which is obtained from the PI controller of the output voltage. In addition the desired transmission power of DAB dc–dc converters can be described as (14)Meanwhile, the desired output current can be estimated on-line as (15)Substituting (15) in (14), the desired transmission power can be calculated as (16)In order to realise the transmission power balancing during the entire power range for the output parallel DAB dc–dc converters composed of N cells in PETT, the output current of each DAB cell should satisfy (17)Based on (5), (16), and (17), the unified desired transmission power of the ith DAB cell can be expressed as (18)Furthermore, the proposed OPCB-EPS scheme can be implemented as the following steps: first, the input voltage the output voltage Uo and the load current io are sampled by using the voltage/current sensors. Then, the voltage transfer ratio ki of the ith DAB cell is calculated and the unified desired transmission power pi* is estimated on-line with (18). Subsequently, the optimised phase-shift ratios in EPS control scheme can be calculated according to (10). Finally, the driving pulse signals are generated from EPS pulse modulator stage according to the obtained optimised phase-shift ratios. In addition, the block diagram of the proposed OPCB-EPS scheme for the output parallel DAB dc–dc converters in PETT is shown in Fig. 5a. Fig. 5Open in figure viewerPowerPoint Block diagram of the proposed OPCB-EPS scheme and the scale-down DAB converters with three cells experimental platform (a) Block diagram of the proposed OPCB-EPS scheme for the output parallel DAB dc–dc converters in PETT, (b) The photo of the scale-down DAB dc–dc converters with three cells experimental platform It is clear that the unified desired transmission power pi* of the ith DAB cell is always estimated according to the storage inductor Li, thus the transmission power balance can be realised in the entire power range, and the efficiency and dynamic performance of the output parallel DAB dc–dc converters can be improved, simultaneously. 5 Experiments In order to verify the effectiveness of the proposed OPCB-EPS scheme in this paper, a scale-down DAB dc–dc converters with three cells experimental platform is developed with TMS320F28335+FPGA_6SLX45 as the core digital controller. In addition, the main electrical parameters of the prototype are listed in Table 1. Table 1. Electrical parameters of the three cells DAB dc–dc converters experimental prototype Parameters Values switching frequency f = 10 kHz inductor of cell 1 L1 = 181 μH inductor of cell 2 L2 = 112 μH inductor of cell 3 L3 = 226 μH transformer voltage ratio n = 1 input-side capacitor Cg1 = Cg2 = Cg3 = 1.12 mF output-side capacitor Cf1 = Cf2 = Cf3 = 1.12 mF the resistive load R = 10/20 Ω rated power P = 1 kW A comprehensive experimental comparison consisting of CSO-DPS control scheme [26], CSO-EPS control scheme [27], and the proposed OPCB-EPS scheme is adapted in this section. The experimental test mainly includes three parts: first, the transmission power balance under the proposed OPCB-EPS scheme is verified, and then, an experimental comparison of CSO-DPS scheme, CSO-EPS scheme, and OPCB-EPS scheme is carried out with the load resistance, the input voltage, and the desired voltage step-change. Finally, the experimental comparison of current stress and efficiency with respect to the input voltage under CSO-DPS, CSO-EPS, and OPCB-EPS schemes is presented. 5.1 Transmission power balance testing With the input voltage the desired voltage Uo* = 100 V, and the load resistor R = 10 Ω, the output current waveforms of each DAB cell in the process from CSO-EPS scheme to OPCB-EPS scheme are shown in Fig. 6a. It is clear that the transmission power of each DAB dc–dc converters in CSO-EPS control scheme is unbalanced and the output current of DAB No.2 cell is obviously higher than the other DAB cells because of the adopted smaller storage inductance in the No.2 cell. Thus, the CSO-EPS control scheme is not suitable for the cascaded structure to balance the transmission power, which is in accordance with the theoretical analysis. By contrast, it can be seen that the output current of each DAB cell is equal in the proposed OPCB-EPS scheme, and it indicates the proposed OPCB-EPS can balance the transmission power effectively. Fig. 6Open in figure viewerPowerPoint Experimental waveforms of the output current of each DAB cell (a) The output current waveforms of each DAB cell in the process from CSO-EPS scheme to OPCB-EPS scheme, (b) The output current waveforms of each DAB cell in CSO-DPS scheme under the input voltage step-change, (c) The output current waveforms of each DAB cell in CSO-EPS scheme under the input voltage step-change, (d) The output current waveforms of each DAB cell in OPCB-EPS scheme under the input voltage step-change With the desired voltage Uo* = 100 V, and the load resistor R = 10 Ω, Figs. 6b–d show the output current experimental waveforms of each DAB cell under CSO-DPS, CSO-EPS, and OPCB-EPS control schemes when the input voltage steps up from 110 to 120 V and then to 130 V successively, and then steps down back to 110 V successively. For the CSO-EPS scheme (Fig. 6c), it can be seen that the transmission power of every DAB cell is always unbalanced no matter how the input voltage steps up or down. Furthermore, for the CSO-DPS scheme (Fig. 6b), when the input voltage Udc = 110 V and the voltage transfer ratio k = 1.1, the output current waveforms of each DAB cell is similar with the experimental waveforms in the CSO-EPS control scheme. However, when the input voltage Udc = 130 V and the voltage transfer ratio k = 1.3, it can be seen that the effect of transmission power balance in CSO-DPS control scheme is better than CSO-EPS control scheme, which is caused by the increase of inner phase-shift ratio with the increase of the voltage transfer ratio. For the proposed OPCB-EPS scheme, it is clear that the output current of each DAB cell is always equal when the input voltage steps change, and the transmission power balance of each DAB cell can always be achieved. 5.2 Dynamic performance testing With the input voltage and the desired voltage Uo* = 100 V, the transient experimental results with load step-change are shown in Fig. 7a, where the load resistance steps down from 20 to 10 Ω. It can be seen that the dynamic response of the output voltage in CSO-EPS scheme is the slowest, with a long settling time and large voltage fluctuation. It is because all the phase-shift ratios of DAB dc–dc converters in CSO-EPS control scheme are obtained through the PI controller of the output voltage. In CSO-DPS control scheme, the settling time of the output voltage is slightly shortened, about 266 ms, and the output voltage fluctuation is reduced significantly. The main reason is that the inner phase-shift ratio in CSO-DPS control scheme is estimated according to the unified transmission power and the voltage transfer ratio, rather than PI controller. By contrast, it is clear that the output voltage of DAB converters always keeps constant and the settling time is almost zero in the proposed OPCB-EPS control scheme. Fig. 7Open in figure viewerPowerPoint Experimental results of the output parallel DAB converters in the CSO-DPS, CSO-EPS, and OPCB-EPS schemes (a) Experimental results when the load resistance steps from 20 to 10 Ω, (b) Experimental results when the input voltage steps down from 130 to 100 V, (c) Experimental results when the desired output voltage steps from 100 to 80 V With the desired voltage Uo* = 100 V and the load resistor R = 10 Ω, Fig. 7b shows the transient experimental results with the input voltage step-change, where the input voltage steps down from 130 to 100 V. It is clear that the CSO-DPS control scheme takes a long settling time, over 300 ms. Meanwhile, the dynamic response of the output voltage under the input voltage step-change in CSO-EPS scheme is more terrible. However, the proposed OPCB-EPS control scheme can always remain the output voltage constant no matter how the input voltage steps change. With the input voltage and the load resistor R = 20 Ω, Fig. 7c shows the transient experimental results under the condition that the desired voltage Uo* steps change from 100 to 80 V. In the CSO-EPS control scheme, the transient response of the output voltage is the slowest, about 83 ms. However, the DAB converters can achieve excellent dynamic response under the CSO-DPS control scheme, and the settling time of the output voltage is about 31 ms, By contrast, the proposed OPCB-EPS control scheme can achieve the fastest dynamic response with the shortest settling time, only 19 ms. According to Fig. 7, a comprehensive experimental comparison of CSO-DPS, CSO-EPS, and OPCB-EPS control schemes can be concluded in Table 2. It is intuitive and clear that the proposed OPCB-EPS control scheme can achieve the most excellent dynamic performance among the three control schemes. Table 2. Dynamic response time of DAB converters in the CSO-DPS, CSO-EPS, and OPCB-EPS schemes Scheme Load disturbance Input voltage disturbance Desired voltage step-change CSO-DPS fast slow fast CSO-EPS slow slow slow OPCB-EPS faster fast faster 5.3 Current stress and efficiency testing With the desired voltage Uo* = 100 V and the load resistor R = 10 Ω, Fig. 8 shows the current stress and efficiency of the output parallel DAB dc–dc converters with respect to the input voltage under CSO-DPS, CSO-EPS, and OPCB-EPS control schemes, respectively. Obviously, the current stress of DAB converters increases with the increase of the input voltage (voltage transfer ratio), which leads to decrease of the efficiency. In CSO-DPS control scheme, the maximum current stress of DAB converters is up to 14.8 A, which results in the lowest efficiency of converters, about 79.1%. Compared with CSO-DPS control scheme, the CSO-EPS control scheme can reduce the current stress and improve the efficiency of the DAB converters. In addition, the maximum current stress in CSO-EPS scheme is about 11.6 A. However, the adopted EPS control in CSO-EPS scheme is not comprehensive, which result in that the minimum current stress is not the global optimal solution. By contrast, it is clear that the proposed OPCB-EPS scheme can further achieve smaller current stress and higher efficiency compared with CSO-EPS scheme. The maximum current stress of DAB converters in OPCB-EPS scheme is about 10.6 A. Meanwhile, compared to CSO-EPS control scheme, the largest efficiency improvement of DAB converters in the proposed OPCB-EPS scheme is about 3.6%. Fig. 8Open in figure viewerPowerPoint Experimental waveforms of current stress and efficiency with respect to the input voltage under CSO-DPS, CSO-EPS, and OPCB-EPS control schemes (a) Current stress, (b) Efficiency 6 Conclusion An optimised OPCB-EPS for the output parallel DAB dc–dc converters in PETT is proposed to achieve the efficiency and dynamic performance improvement, and transmission power balance. By introducing the current stress optimised calculation and desired transmission power estimation on-line in EPS control, the efficiency and the dynamic response of the output voltage under the input voltage fluctuation and the load disturbance conditions can be improved at the same time. From a comprehensive experimental comparison of CSO-DPS, CSO-EPS, and the proposed OPCB-EPS control schemes, the salient features of OPCB-EPS scheme can be summarised as: (1) Compared with CSO-DPS and CSO-EPS control schemes, the proposed OPCB-EPS scheme can achieve the transmission power balance over the whole power range for the output parallel DAB dc–dc converters in PETT. (2) The proposed OPCB-EPS scheme realises the excellent dynamic performance under the input voltage fluctuation and the load disturbance conditions. The output voltage always keeps constant and the settling time is almost zero. (3) The proposed OPCB-EPS scheme can achieve the minimum current stress optimisation for DAB converters in EPS control, and the efficiency of converters can be further improved compared to CSO-DPS and CSO-EPS control schemes. 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Publication Year: 2019
Publication Date: 2019-07-11
Language: en
Type: article
Indexed In: ['crossref']
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