Abstract
The bipolar low-voltage DC (LVDC) distribution system has become a prospective solution to better integration of renewables and improvement of system efficiency and reliability. However, it also faces the challenge of power and voltage imbalance between two poles. To solve this problem, an interface converter with bipolar asymmetrical operating capabilities is applied in this paper. The steady-state models of the bipolar LVDC distribution system equipped with this interface converter in the grid-connected mode and off-grid mode are analyzed. A control scheme based on DC offset injection at the secondary side of the interface converter is proposed, enabling the bipolar LVDC distribution system to realize the unbalanced power transfer between two poles in the grid-connected mode and maintain the inherent- pole voltage balance in the off-grid mode. Furthermore, this paper also proposes a primary-side DC offset injection control scheme according to the analysis of the magnetic circuit model, which can eliminate the DC bias flux caused by the secondary-side DC offset. Thereby, the potential core magnetic saturation and overcurrent issues can be prevented, ensuring the safety of the interface converter and distribution system. Detailed simulations based on the proposed control scheme are conducted to validate the function of power and voltage balance under the operation conditions of different DC loads.
WITH the rapid development of distributed renewable sources, energy storage, and diversified non-linear loads, the low-voltage DC (LVDC) distribution system for residential houses and commercial buildings has become an emerging alternative method to replace the conventional AC distribution system, which can realize simple control schemes, higher power conversion efficiency, higher power density, and lower cost [

Fig. 1 Structures of LVDC distribution system. (a) Unipolar configuration. (b) Bipolar configuration.
Although the unipolar configuration has been widely used in the past decades, it is becoming challenging to meet the requirements of many burgeoning applications such as data centers and electric vehicle charging stations [
1) The bipolar LVDC distribution system provides three alternative DC voltage levels, including two symmetrical positive and negative polarity voltages and a total DC-bus voltage, which can flexibly interface with renewable energy sources and diversified loads.
2) Higher reliability and power supply continuity can be achieved via this configuration under both normal and fault conditions since the poles operate independently.
3) Distribution voltage level from ground is reduced by half because the neutral line is grounded, which is safer for residents.
4) Similar to the conventional three-phase AC system, the bipolar system contains three wires, where the voltage between the positive and negative poles is analogous to the line-to-line voltage, while the voltage of one pole with respect to the neutral is analogous to the phase voltage, which contributes to improving system operation and designing the control scheme.
As illustrated in

Fig. 2 Implementation schemes for bipolar LVDC distribution system. (a) Using two sets of equipment. (b) Installing voltage balancers. (c) Employing a three-winding transformer.
Besides, DC transformers (DCTs) operate as crucial enablers for the implementation of the DC distribution system [
Hence, this paper adopts a modified DCT that evolves from the neutral point clamped (NPC) type DAB (NPC-DAB) topology as the interface converter in the bipolar LVDC distribution system. One major challenge to the bipolar system is the asymmetrical operation caused by the unequal load distribution between two poles, leading to undesirable pole power and voltage imbalance. To solve this problem, this paper proposes a control scheme based on DC offset injection at the secondary side of the NPC-DAB converter, which enables the bipolar LVDC distribution system to realize unbalanced power transfer in the grid-connected mode while operating with inherent pole voltage balancing capability in the off-grid mode. Moreover, the DC bias flux in NPC-DAB converter can be eliminated in both grid-connected and off-grid modes by controlling DC offset injection at the primary side. Compared with the implementation schemes in
The rest of this paper is organized as follows. Section II introduces the operation principles of the bipolar LVDC distribution system. Section III demonstrates the magnetic circuit with DC offset injection. Section IV presents the detailed control scheme for the bipolar LVDC distribution system. In Section V, the asymmetrical operating performance of the bipolar LVDC distribution system and the validity of the control scheme are verified by simulation results conducted in MATLAB/Simulink. Section VI concludes this paper.
The configuration of the bipolar system is shown in

Fig. 3 Configuration of bipolar system.
Assuming that the positive-pole power and negative-pole power are P1 and P2, respectively, and the total power transmitted by the system is PO. When loads of the positive and negative poles are balanced, the power and voltage of the LVDC poles are equal, i.e., and . As illustrated in

Fig. 4 Operation waveform of bipolar SM under balanced load condition.
During , iL2 satisfies the following equation:
(1) |
where N is the turn ratio of the transformer; V1 is the rated DC-link voltage of the primary side; V2 is the rated output pole-to-neutral voltage of the secondary side; and the subscript L2 denotes the series inductance to transfer the electric power.
Since , can be calculated as:
(2) |
During , can be expressed as:
(3) |
Since , can be calculated as:
(4) |
is symmetrical during the positive and negative halves of the switching cycle; therefore, . The following equation can be obtained according to (1)-(4):
(5) |
satisfies the following equation based on (1), (3), and (5):
(6) |
According to (6), the average power of the positive pole, negative pole, and the total power can be calculated as:
(7) |
The LVDC voltages are fixed in the grid-connected mode since the NPC-DAB converter is connected to strong grids. If bipolar loads are balanced, the power of bipolar poles is equal (). However, the unbalanced power P between the positive and negative poles occurs when the bipolar loads are asymmetrical, affecting the power quality and even threatening the stable operation of distribution system. To transfer the unbalanced power, an analysis is conducted considering the DC offset injection at the secondary side of the NPC-DAB converter, as shown in

Fig. 5 Unbalanced power transfer between bipolar poles.

Fig. 6 Waveforms of bipolar SM with secondary-side DC offset injection.

Fig. 7 Circuit operating modes. (a) Mode 1: [t0, t1]. (b) Mode 2: [t1, t2]. (c) Mode 3: [t2, t3]. (d) Mode 4: [t3, t4]. (e) Mode 5: [t4, t5]. (f) Mode 6: [t5, t6].
When Idc2 is injected into the secondary side, the updated inductor current can be expressed as:
(8) |
With DC offset injection, the average power of the positive pole, negative pole, and the total power transmitted by the system can be calculated as:
(9) |
Considering that the bipolar system contains n SMs, the following equation can be obtained according to (9):
(10) |
From (7) and (9), the DC offset injection at the secondary side of NPC-DAB converter does not affect the total power transmitted by the bipolar system, while the unbalanced power between two poles can be transferred.
In the off-grid mode, the bipolar voltages of the LVDC side can realize inherent balance in the case of unequal loads, and the detailed explanation is given below. Assuming that the deviation of the positive-pole voltage from the rated voltage is (), the actual voltages of the positive and negative poles can be expressed as:
(11) |
Similar to the above-mentioned analysis, the inductor current satisfies the following equation:
(12) |
According to (12), can be calculated as:
(13) |
From (13), if , the variation of iL2 in a switching cycle is not 0, which does not meet the volt-second principle. When , i.e., , iL2 increases in one switching cycle. Combined with
(14) |
where IR1 and IR2 are the load currents of the positive and negative poles, respectively; IC1 and IC2 are the corresponding-pole capacitor currents; and IO1 and IO2 are the corresponding-pole output currents.
The capacitor current is zero after averaging the switching cycle according to ampere-second balance; thus, (15) can be deduced from (14) as:
(15) |
From (15), the asymmetry of the unequal load is reflected in the secondary-side inductor current, which induces a DC offset into iL2, with a value equal to the difference between the bipolar load currents. The operating conditions and power transmission model of the off-grid mode are similar to those of the grid-connected mode and thus are not discussed further in this paper.
It should be noted that the secondary-side inductor current contains a DC offset component under bipolar asymmetrical operation in both modes. The DC offset is actively injected to transfer the unbalanced power in the grid-connected mode. Besides, the DC offset is passively induced due to the difference between the bipolar load currents in the off-grid mode, which contributes to the inherent pole voltage balance. However, the DC offset in the secondary-side inductor current generates a DC bias flux in the high-frequency (HF) transformer, triggering a cascade of adverse effects. If the DC bias is accumulated to a certain degree, the iron core will encounter magnetic saturation so that the transformer no longer works in the linear region of its magnetization curve, resulting in a large excitation inrush current. This phenomenon increases the heat dissipation and the temperature of the transformer, causing the insulation aging of the transformer winding, and even thermal breakdown and fire hazard [
The magnetic flux of the transformer includes both AC and DC components, and the AC component has no influence on transformer operation. Nonetheless, DC component of the main flux caused by the DC offset current is the source of DC bias flux and must be eliminated. The magnetic flux of the primary and secondary windings can be expressed as:
(16) |
where Φ11 and Φ22 are the leakage fluxes of the primary and secondary windings, respectively; and Φ21 and Φ12 are the mutual fluxes, i.e., the main flux between the two-side windings.
The self-inductance coefficients of the primary and secondary windings can be calculated as:
(17) |
where n1 and n2 are the turn numbers of the primary and secondary windings, respectively; I1 and I2 are the corresponding winding currents; L11 and L22 are the corresponding winding leakage inductance coefficients; and LM is the mutual inductance coefficient.
The flux linkage through each winding consists of its self-inductance flux linkage and the mutual induction flux linkage, which can be calculated as:
(18) |
If Idc2 is injected into the secondary side of the transformer, the currents of the primary and secondary windings can be expressed as:
(19) |
where iac1 and iac2 are the AC currents of the primary and secondary windings, respectively.
Therefore, the magnetic flux of the primary and secondary windings can be calculated as:
(20) |
From (20), the DC offset injection of the secondary side results in a DC bias in the transformer main flux with a value equal to LMIdc2/n1. As shown in
(21) |

Fig. 8 Diagram for flux of transformer with DC offset injection Idc2.
The new flux of the transformer can be calculated as:
(22) |
According to (22), the relationship between Idc1 and Idc2 for DC bias removal can be obtained as:
(23) |
As shown in

Fig. 9 Diagram for flux of transformer with DC offset injections Idc1 and Idc2.
The control diagram of the bipolar LVDC distribution system in two modes is presented in

Fig. 10 Control diagram of bipolar LVDC distribution system. (a) Power control. (b) LVDC voltage control. (c) Bipolar unbalanced power control. (d) Secondary-side DC offset control in grid-connected mode. (e) Secondary-side DC offset control in off-grid mode. (f) Primary-side DC offset control. (g) Switching between constant power control and constant LVDC voltage control. (h) Control mode switching of secondary side.
(24) |
In the secondary-side DC offset injection control of the grid-connected mode, the difference between the sampled DC offset of the first SM and the reference DC offset is adjusted by the PI controller, and the outcome is used to obtain the adjustment voltage offset . In addition, Idc2,1 is used as a reference DC offset for the other SMs to achieve a balance between all SMs. Then, the normalized voltage offset is sent for comparison with the triangular carrier to produce the secondary-side switch signals for each SM, as shown in
In the off-grid mode, only the main voltage source of MV exists; therefore, the voltage of the LV side must be controlled. As shown in
As analyzed in Section III, both the grid-connected and off-grid modes should inject DC offset currents into the primary side. As illustrated in
To realize the switching between the grid-connected mode and off-grid mode, there are two aspects should be considered. One is the switching between constant power control mode and constant LVDC voltage control. The former is adopted in the grid-connected mode, while the latter is used in the off-grid mode, as shown in
To suppress the transient shock in the switching process, the feed-forward compensations of phase shift ratio and are introduced in the LVDC voltage control and power control, respectively. The other is the switching of DC offset injection control mode. For the secondary side of the converter, the DC offset is injected by the outer-loop unbalanced power control and the inner-loop DC offset injection control in the grid-connected mode, while the DC offset is generated due to the asymmetrical bipolar loads in the off-grid mode. When the system is switched to off-grid mode, the unbalanced power control and the secondary-side DC offset control are withdrawn from operation. When the system is reconnected to the grid, these two controllers require to be put into operation, as shown in
To verify the effectiveness of the proposed control scheme, a 1 MW/±375 V simulation model of the bipolar system is built in MATLAB/Simulink. In this system, NPC-DAB converter consists of 20 SMs, where the interface voltage of each SM is 1000 V at the MV side and ±375 V at the LV side. The parameters of the simulation model are listed in
Parameter | Value |
---|---|
MV-side voltage | 20 kV |
LV-side pole-to-pole voltage | 750 V(2×375 V) |
Rated power | 1 MW |
Number of SMs | 20 |
Switching frequency | 10 kHz |
Turn ratios | 8:3 |
Leakage inductor | 200 µH |
Input capacitor | 100 µF |
Output capacitor | 66 µF |
The effectiveness of the proposed control scheme in the grid-connected mode is tested in the following three working cases.
1) Case 1 (0-0.1 s): the unbalanced power is 0; therefore, no DC offset is injected into either side of the bipolar system.
2) Case 2 (0.1-0.2 s): the unbalanced power transfer requirement is -0.8PO (-0.8 MW). According to (10) and (23), the DC offset injected into the primary and secondary sides is 40 A and -106.67 A, respectively.
3) Case 3 (0.2-0.3 s): the unbalanced power transfer requirement is (0.8 MW). Similarly, the DC offset injected into the primary and secondary sides is -40 A and 106.67 A, respectively.

Fig. 11 Simulation results of grid-connected mode. (a) Unbalanced power. (b) DC offset at primary and secondary sides. (c) Total power transmitted by system, positive-pole power, and negative-pole power. (d) Voltages and currents of bipolar SM at primary and secondary sides.
The following three working cases are designed to verify the validity of the proposed control scheme in the off-grid mode.
1) Case 4 ( s): total power is transmitted in the forward direction. The bipolar power load is symmetrical at 0.4PO (0.4 MW).
2) Case 5 ( s): total power is transmitted in the forward direction. The power load of the positive pole decreases to 0, while the power load of the negative pole steps up to 0.8PO (0.8 MW), respectively. According to (10), a 106.67 A DC offset appears at the secondary side. According to (23), the DC offset injected into the primary side should be -40 A.
3) Case 6 ( s): total power is transmitted in the reverse direction. The power load of positive and negative poles is 0 and -0.8PO (-0.8 MW), respectively. Similarly, the secondary-side current exhibits a -106.67 A DC offset, whereas the DC offset injected into the primary side should be 40 A.

Fig. 12 Simulation results of off-grid mode. (a) Voltage of LVDC side. (b) DC offset at primary and secondary sides. (c) Total power transmitted by system, positive-pole power and negative-pole power. (d) Voltages and currents of bipolar SM at primary and secondary sides.
A simulation of switching between the grid-connected mode and off-grid mode is built to highlight the feasibility of the proposed control scheme in practice. The working conditions are as follows.
1) Case 7 (0-0.05 s): the system operates in the grid-connected mode. The unbalanced power is 0; therefore, no DC offset is injected into either side of the bipolar system.
2) Case 8 (0.05-0.10 s): the system operates in the grid-connected mode. The unbalanced power transfer requirement is 0.2PO (0.2 MW). The DC offsets injected into the primary and secondary sides are -10 A and 26.67 A, respectively.
3) Case 9 (0.10-0.15 s): the system operates in the off-grid mode. The loads of positive and negative poles are (0.2 MW) and (0.6 MW), respectively. The secondary-side current exhibits a 53.33 A DC offset due to the asymmetrical loads, whereas the DC offset injected into the primary side should be -20 A.

Fig. 13 Simulation results of switching from grid-connected mode to off-grid mode. (a) Unbalanced power. (b) Voltage of LVDC side. (c) DC offset at primary and secondary sides. (d) Total power transmitted by system, positive-pole power, and negative-pole power. (e) Voltages and currents of bipolar SM at primary and secondary sides.
As shown in
In this paper, an ISOP type NPC-DAB converter suitable for a bipolar LVDC distribution system is investigated. A novel control scheme based on DC offset injection is proposed for the bipolar LVDC distribution system to achieve asymmetrical operation in the following two modes: the unbalanced power transfer in the grid-connected mode and the inherent-pole voltage balance in the off-grid mode. In the designed controlled scheme of NPC-DAB converter, the control of DC offset injection at the secondary side overcomes the limitation in DC load unbalance, which has been demonstrated in simulation results by decreasing DC load of one pole down to 0. Furthermore, the DC bias flux can be eliminated by controlling the DC offset injected into the primary side, such that the safety of the NPC-DAB converter and the distribution system can be guaranteed. The simulation results show that the proposed control scheme has valid outcome in power and voltage balance in both grid-connected and off-grid modes. Compared with the existing implementations, the bipolar distribution system facilitating with the NPC-DAB converter can present better asymmetrical operating performance with fewer power electronic devices and smaller footprints. Overall, the control scheme based on DC offset injection is prominent and economical in the bipolar LVDC distribution system.
References
A. Bharatee, P. K. Ray, and A. Ghosh, “A power management scheme for grid-connected PV integrated with hybrid energy storage system,” Journal of Modern Power Systems and Clean Energy, vol. 10, no. 4, pp. 954-963, Jul. 2022. [Baidu Scholar]
W. Wu, P. Li, B. Wang et al., “Integrated distribution management system: architecture, functions, and application in China,” Journal of Modern Power Systems and Clean Energy, vol. 10, no. 2, pp. 245-258, Mar. 2022. [Baidu Scholar]
L. Zheng, R. P. Kandula, and D. Divan, “Current-source solid-state DC transformer integrating LVDC microgrid, energy storage, and renewable energy into MVDC grid,” IEEE Transactions on Power Electronics, vol. 37, no. 1, pp. 1044-1058, Jan. 2022. [Baidu Scholar]
J. Yao, W. Chen, C. Xue et al., “An ISOP hybrid DC transformer combining multiple SRCs and DAB converters to interconnect MVDC and LVDC distribution networks,” IEEE Transactions on Power Electronics, vol. 35, no. 11, pp. 11442-11452, Nov. 2020. [Baidu Scholar]
Y. Zhang, W. Zhang, Q. Peng et al., “Impact of grid topology on pole-to-ground fault current in bipolar DC grids: mechanism and evaluation,” Journal of Modern Power Systems and Clean Energy, vol. 11, no. 2, pp. 434-445, Mar. 2023. [Baidu Scholar]
T. Jung, G. Gwon, C. Kim et al., “Voltage regulation method for voltage drop compensation and unbalance reduction in bipolar low-voltage DC distribution system,” IEEE Transactions on Power Delivery, vol. 33, no. 1, pp. 141-149, Feb. 2018. [Baidu Scholar]
S. Rivera, R. Lizana F., S. Kouro et al., “Bipolar DC power conversion: state-of-the-art and emerging technologies,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 9, no. 2, pp. 1192-1204, Apr. 2021. [Baidu Scholar]
J.-Y. Lee, H.-S. Kim, and J.-H. Jung, “Enhanced dual-active-bridge DC-DC converter for balancing bipolar voltage level of DC distribution system,” IEEE Transactions on Industrial Electronics, vol. 67, no. 12, pp. 10399-10409, Dec. 2020. [Baidu Scholar]
X. Yu, Y. Wei, Q. Jiang et al., “A novel hybrid-arm bipolar MMC topology with DC fault ride-through capability,” IEEE Transactions on Power Delivery, vol. 32, no. 3, pp. 1404-1413, Jun. 2017. [Baidu Scholar]
S. Ouyang, J. Liu, S. Song et al., “Solid state transformer for low-voltage distribution system with DC/DC stage-controlled split-capacitor,” in Proceedings of 2019 IEEE Energy Conversion Congress and Exposition, Baltimore, USA, Sept. 2019, pp. 5805-5809. [Baidu Scholar]
N. Naseem and H. Cha, “Triple-active-bridge converter with automatic voltage balancing for bipolar DC distribution,” IEEE Transactions on Power Electronics, vol. 37, no. 7, pp. 8640-8648, Jul. 2022. [Baidu Scholar]
P. Najafi, A. H. Viki, and M. Shahparasti, “Evaluation of feasible interlinking converters in a bipolar hybrid microgrid,” Journal of Modern Power Systems and Clean Energy, vol. 8, no. 2, pp. 305-314, Mar. 2020. [Baidu Scholar]
Q. Tian, G. Zhou, L. Wang et al., “Symmetric bipolar output full-bridge four-port converter with phase-shift modulated buck-boost voltage balancer,” IEEE Transactions on Industrial Electronics, vol. 69, no. 8, pp. 8040-8054, Aug. 2022. [Baidu Scholar]
B. Li, Q. Fu, S. Mao et al., “DC/DC converter for bipolar LVDC system with integrated voltage balance capability,” IEEE Transactions on Power Electronics, vol. 36, no. 5, pp. 5415-5424, May 2021. [Baidu Scholar]
F. Wang, Z. Lei, X. Xu et al., “Topology deduction and analysis of voltage balancers for DC microgrid,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 5, no. 2, pp. 672-680, Jun. 2017. [Baidu Scholar]
M. Lee, S. Cheon, D. Choi et al., “High efficiency voltage balancing dual active bridge converter for the bipolar DC distribution system,” in Proceedings of 2021 IEEE Energy Conversion Congress and Exposition–Asia, Singapore, May 2021, pp. 86-91. [Baidu Scholar]
X. Zhang, H. Zhu, Y. Song et al., “Three-level dual-buck voltage balancer with active output voltages balancing,” IET Power Electronics, vol. 12, no. 11, pp. 1-9, Sept. 2019. [Baidu Scholar]
S. Ouyang, J. Liu, S. Song et al., “Solid state transformer for low-voltage distribution system with DC/DC stage-controlled split-capacitor,” in Proceedings of 2019 IEEE Energy Conversion Congress and Exposition, Baltimore, USA, Sept. 2019, pp. 5805-5809. [Baidu Scholar]
J. E. Huber and J. W. Kolar, “Applicability of solid-state transformers in today’s and future distribution grids,” IEEE Transactions on Smart Grid, vol. 10, no. 1, pp. 317-326, Jan. 2019. [Baidu Scholar]
S. Zhao, Y. Chen, S. Cui et al., “Three-port bidirectional operation scheme of modular-multilevel DC-DC converters interconnecting MVDC and LVDC grids,” IEEE Transactions on Power Electronics, vol. 36, no. 7, pp. 7342-7348, Jul. 2021. [Baidu Scholar]
M. Salimi, F. Radmand, and M. H. Firouz, “Dynamic modeling and closed-loop control of hybrid grid-connected renewable energy system with multi-input multi-output controller,” Journal of Modern Power Systems and Clean Energy, vol. 9, no. 1, pp. 94-103, Jan. 2021. [Baidu Scholar]
Y. Wang, Q. Song, B. Zhao et al., “Quasi-square-wave modulation of modular multilevel high-frequency DC converter for medium-voltage DC distribution application,” IEEE Transactions on Power Electronics, vol. 33, no. 9, pp. 7480-7495, Sept. 2018. [Baidu Scholar]
R. Cao, Y. Zhang, X. Liu et al., “Capacitor lifetime-based power routing of ISOP-DAB converter within comprehensive constraint,” IEEE Transactions on Industrial Electronics, vol. 69, no. 11, pp. 11283-11292, Nov. 2022. [Baidu Scholar]
J. Hu, S. Cui, S. Wang et al., “Instantaneous flux and current control for a three-phase dual-active bridge DC-DC converter,” IEEE Transactions on Power Electronics, vol. 35, no. 2, pp. 2184-2195, Feb. 2020. [Baidu Scholar]
P. Yao, X. Jiang, P. Xue et al., “Flux balancing control of ungapped nanocrystalline core-based transformer in dual three-g bridge converters,” IEEE Transactions on Power Electronics, vol. 35, no. 11, pp. 11463-11474, Nov. 2020. [Baidu Scholar]