Journal of Modern Power Systems and Clean Energy

ISSN 2196-5625 CN 32-1884/TK

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Power and Voltage Control Based on DC Offset Injection for Bipolar Low-voltage DC Distribution System  PDF

  • Xinyi Kong
  • Jianwen Zhang
  • Jianqiao Zhou
  • Jiajie Zang
  • Jiacheng Wang
  • Gang Shi
  • Xu Cai
the key Laboratory of Control of Power Transmission and Conversion of Ministry of Education, Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; the School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, China; the School of Mechatronic Systems Engineering, Simon Fraser University, Surrey, BC, Canada

Updated:2023-09-20

DOI:10.35833/MPCE.2022.000088

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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.

I. Introduction

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 [

1]-[4]. As shown in Fig. 1, there are two types of structures for the LVDC distribution system, i.e., the unipolar and bipolar configurations.

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 [

5]. Besides, the bipolar configuration is gradually becoming the preferred method because of the following advantages [6]-[9].

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. 1(b), the interface converter is indispensable for the interconnection of the bipolar LVDC distribution system and the medium-voltage DC (MVDC) utility grid. Three candidate implementations with bipolar DC configurations are discussed in [

10] and [11]. The first type uses two sets of equipment to provide positive and negative poles, as shown in Fig. 2(a). However, the independent operation of bipolar poles is realized by this approach at the cost of extra components with higher cost and larger footprints [12]. The other implementation adopts voltage balancers on the converter output port, as shown in Fig. 2(b). The buck-boost circuit [13], dual-buck half-bridge circuit [14], and Sepic- and Cuk-type circuits have been adopted as voltage balancers [15]. These topologies have a disadvantage of relatively high current ripple in the inductor and thus require significant filtering capacitance. Besides, all these voltage balancers require additional circuits, which still causes the problems such as extra power switches, increased cost, and higher control complexity, and it will narrow down the operation power range of the system [16], [17]. The bipolar converter can also be implemented with a three-winding transformer, as shown in Fig. 2(c). This, however, requires more semiconductors and more magnetic materials as well as much higher control complexity [18].

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 [

19], [20]. DCTs usually adopt the input-series-output-parallel (ISOP) topology, where multiple dual active bridge (DAB) cells are connected in series at the MVDC side and parallel at the LVDC side. This configuration has the advantages of high modularity, scalability, and reliability [21]-[23]. Besides, simple control scheme can be utilized in this structure. Fruitful research works have been conducted on the efficiency and reliability of the DCTs during the past decades. However, most of them are limited to unipolar LVDC distribution systems.

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 Fig. 2, the proposed embedded control system of power and voltage balance for NPC-DAB converter does not require additional circuits, thus reducing the cost of devices and footprints. Besides, it can perform good asymmetrical operation capability under the conditions of different DC loads.

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.

II. Operation Principle of Bipolar LVDC Distribution System

A. System Configuration

The configuration of the bipolar system is shown in Fig. 3, where VO1 and VO2 are the voltages of the positive and negative poles, respectively; IO1 and IO2 are the corresponding pole output currents, respectively; IC1 and IC2 are the corresponding pole capacitor currents, respectively; vi and vo are the square wave voltages of the primary and secondary windings, respectively; L2 is the series inductor to transfer the electric power; S1-S4 are the primary-side switches; Q1-Q4 are the secondary-side switches; and iL2 is the inductor current of the secondary side. An ISOP type NPC-DAB converter is applied as the interface converter, which contains multiple submodules (SMs). Each SM has the same topology, in which the primary side adopts a full-bridge circuit, and the secondary side uses an NPC circuit to form the bipolar LVDC ports. In the following discussion, a single bipolar SM is considered as an example to analyze the operation principles.

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., P1=P2 and VO1=VO2. As illustrated in Fig. 4, the operation waveforms of the bipolar SM are basically the same as those of the conventional unipolar case. Single phase-shift (SPS) modulation is adopted to control the transmission power PO by controlling the phase shift angle Φ between the primary and secondary square wave voltages. The ratio between Φ and π is defined as phase shift ratio D=Φ/π. The operation principles of forward and reverse power transmissions are similar such that only forward power transmission is analyzed in this section.

Fig. 4  Operation waveform of bipolar SM under balanced load condition.

During [t0, t1], iL2 satisfies the following equation:

iL2t=iL2t0+V2-V1/NL2t-t0 (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 t1-t0=1-DT/2, iL2t1 can be calculated as:

iL2t1=iL2t0+V2-V1/NL21-DT2 (2)

During [t1, t3], iL2 can be expressed as:

iL2t=iL2t1+V2+V1/NL2t-t1 (3)

Since t3-t1=DT/2, iL2t3 can be calculated as:

iL2t3=iL2t1+V2+V1/NL2DT2 (4)

iL2 is symmetrical during the positive and negative halves of the switching cycle; therefore, iL2t3=-iL2t0. The following equation can be obtained according to (1)-(4):

iL2t2=-2V1/NDT+V1/NT-V2T4L2 (5)

iL2 satisfies the following equation based on (1), (3), and (5):

iL2=2V1/NDT-V1/NT+V2T4L2+V1/N-V2L2t-t0t0t<t12V1/NDT+V1/NT+V2T4L2+V1/N+V2L2t-t0t1t<t3 (6)

According to (6), the average power of the positive pole, negative pole, and the total power can be calculated as:

P1=-V21Tt0t3iL2tdt=V1V2T4NL2D1-DP2=V21Tt3t6iL2tdt=V1V2T4NL2D1-DPO=P1+P2=V1V2T2NL2D1-D (7)

B. Steady-state Model of Grid-connected Mode

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 (P1=P2=0.5PO). However, the unbalanced power ΔP 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. By adjusting the duty ratio of Q1-Q4, the DC offset Idc2 can be injected into the secondary side. According to different directions of power transmission and DC offset injection, there are four operating conditions: ① PO>0, Idc2>0; ② PO>0, Idc2<0; ③ PO<0, Idc2>0; and ④ PO<0, Idc2<0. This paper takes the first operating condition as an example to establish the steady-state model of the grid-connected mode. The waveforms of bipolar SM with secondary-side DC offset injection are shown in Fig. 6.

Fig. 5  Unbalanced power transfer between bipolar poles.

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

Figure 7 illustrates the circuit operating modes with secondary-side DC offset injection during a switching period, where the red line shows the current flow. Modes 1 and 4 charge the positive and negative poles, respectively, for the same duration. In addition, the duration of Mode 3, which discharges the positive pole, is longer than that of Mode 2, which charges the positive pole. Moreover, the duration of Mode 5, which charges the negative pole, is longer than that of Mode 6, which discharges the negative pole. Therefore, by injecting a positive Idc2 into the secondary side, more power is distributed to the negative pole to regulate the unbalanced bipolar power. The dead time of the switch is ignored to conduct a simple analysis.

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 iL2' can be expressed as:

iL2't=iL2t+Idc2 (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:

P1=-V21Tt0t3iL2'tdt=V1V2T4NL2D1-D-V2Idc22P2=V21Tt3t6iL2'tdt=V1V2T4NL2D1-D+V2Idc22PO=P1+P2=V1V2T2NL2D1-D (9)

Considering that the bipolar system contains n SMs, the following equation can be obtained according to (9):

ΔP=nP2-P1=nV2Idc2 (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.

C. Steady-state Model of Off-grid Mode

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 ΔV (ΔV0), the actual voltages of the positive and negative poles can be expressed as:

VO1=V2+ΔVVO2=V2-ΔV (11)

Similar to the above-mentioned analysis, the inductor current satisfies the following equation:

iL2t=iL2t0+VO1-V1/NL2t-t0=iL2t0+ΔVL2t-t0        tt0,t1iL2t1+VO1+V1/NL2t-t1=iL2t0+2V2+ΔVL2t-t1-iL2t3                                  tt1,t3 (12)

According to (12), iL2t6 can be calculated as:

iL2t6=iL2t0+ΔVL2TiL2t0 (13)

From (13), if ΔV0, the variation of iL2 in a switching cycle is not 0, which does not meet the volt-second principle. When ΔV>0, i.e., VO1>VO2, iL2 increases in one switching cycle. Combined with Fig. 3, it indicates that the discharge current of the positive pole will increase, while the charge current of the negative pole will increase. As a result, the bipolar poles can return to the same voltage value, which means that the bipolar system has inherent pole voltage balancing capability under asymmetrical operation. Due to the inherent bipolar voltage balance, the asymmetry of bipolar loads is reflected in the secondary-side inductor current. According to Kirchhoff’s current law, iL2 satisfies the following equation:

iL2=IO2-IO1=IC2+IR2-IC1-IR1 (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:

0TiL2dt=IR2-IR1=Idc2 (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 [

24], [25]. Therefore, it is necessary to eliminate DC bias flux in the transformer. The method of DC bias flux removal is analyzed in further detail below.

III. Magnetic Circuit with DC Offset Injection

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:

Ф1=Ф11+Ф21Ф2=Ф22+Ф12 (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:

L1=n1Ф11I1+n1n2n2Ф21I1=L11+n1n2LML2=n2Ф22I2+n2n1n1Ф12I2=L22+n2n1LM (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:

Ψ1=L1I1+LMI2Ψ2=L2I2+LMI1 (18)

If Idc2 is injected into the secondary side of the transformer, the currents of the primary and secondary windings can be expressed as:

Ι1=iac1Ι2=iac2+Ιdc2 (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:

Ф1=Ψ1/n1=L11n1iac1Ф11+LMn2iac1+LMn1iac2+LMn1Ιdc2Ф21Ф2=Ψ2/n2=L22n2iac2+L22n2Idc2Ф22+LMn2iac1+LMn1iac2+LMn1Ιdc2Ф12 (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 Fig. 8, Фac and Фdc are the AC and DC components of the main flux of the transformer, respectively. To eliminate the DC bias in the main flux caused by Idc2, the compensated DC offset Idc1 should be injected into the primary side. Then, the currents of the primary and secondary windings can be expressed as:

Ι1=iac1+Idc1Ι2=iac2+Ιdc2 (21)

Fig. 8  Diagram for flux of transformer with DC offset injection Idc2.

The new flux of the transformer can be calculated as:

Ф1=L11n1iac1+L11n1Idc1Ф11+LMn2iac1+LMn1iac2+LMn2Idc1+LMn1Ιdc2Ф21Ф2=L22n2iac2+L22n2Idc2Ф22+LMn2iac1+LMn1iac2+LMn2Idc1+LMn1Ιdc2Ф12 (22)

According to (22), the relationship between Idc1 and Idc2 for DC bias removal can be obtained as:

Idc1=-n2n1Idc2 (23)

As shown in Fig. 9, by injecting Idc1 into the primary side based on the value of Idc2, the DC component in the main flux of transformer is eliminated, thus preventing the transformer from magnetic saturation.

Fig. 9  Diagram for flux of transformer with DC offset injections Idc1 and Idc2.

IV. Control Strategy

The control diagram of the bipolar LVDC distribution system in two modes is presented in Fig. 10. In the grid-connected mode, since NPC-DAB converter interconnects the strong DC grids, it is controlled as a power source to manage the power flow between the MV and LV sides. The difference between the power PO and the reference power PO,ref is adjusted by the PI controller, and the outcome is used to obtain the adjustment phase shift ratio D for each SM, as shown in Fig. 10(a). According to (10), ΔP between bipolar poles can be controlled by adjusting Idc2. In the bipolar unbalanced power control, the PI controller takes the difference between the sampled ΔP and reference ΔPref, and the outcome becomes a reference current value Idc2,1,ref for the DC offset injection controller, as shown in Fig. 10(c). The sampled ΔP can be obtained by calculating the integral of voltages and currents of bipolar poles in one switching cycle as:

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.

ΔP=P2-P1=1T0TVO2IO2t-VO1IO1tdt (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 Idc2,1 and the reference DC offset Idc2,1,ref is adjusted by the PI controller, and the outcome is used to obtain the adjustment voltage offset vo,1. 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 Fig. 10(d), where Qk,n denotes the switch signal of the kth switch of the SM n of the secondary side.

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 Fig. 10(b), the difference between the total voltage of bipolar poles VO and the reference total voltage VO,ref is adjusted by the PI controller, and the outcome is used to obtain D for each SM. The secondary-side DC offset injection control is similar to that of the grid-connected mode, as shown in Fig. 10(e), but the remarkable thing is that the reference DC offset is produced by asymmetrical loads of bipolar poles according to (15).

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 Fig. 10(f), the sampled secondary-side DC offset Idc2,k (k=1,2,3,4) multiplied by -n2/n1 is used as the reference primary-side DC offset Idc1,k,ref, which ensures DC bias flux elimination of each SM. The outcome of the PI controller is the adjustment voltage offset vi,k, which is normalized and sent to pulse width modulation (PWM) to produce the primary-side switch signals for each SM. Sk,n denotes the switch signal of the kth (k=1,2,3,4) switch of the SM n at the primary side.

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 Fig. 10(g). When the system is switched from the grid-connected mode 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 are required to be put into operation.

To suppress the transient shock in the switching process, the feed-forward compensations of phase shift ratio Dref1 and Dref2 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 Fig. 10(h). For the primary side of the converter, whether it is in grid-connected mode or off-grid mode, the corresponding DC offset requires to be actively injected to prevent the transformer from DC bias flux. Therefore, the primary-side DC offset injection control does not require switching.

V. Simulation Results

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 Table I.

TABLE I  Parameters of Simulation Model
ParameterValue
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 0.8PO (0.8 MW). Similarly, the DC offset injected into the primary and secondary sides is -40 A and 106.67 A, respectively.

Figure 11 shows the simulation results of the grid-connected mode. As shown in Fig. 11(a), the transferred unbalanced power changes from 0 to -0.8 MW at t=0.1 s, and it steps up to 0.8 MW at t=0.2 s, which agrees with the set value. As shown in Fig. 11(b), Idc1 injected into the primary side rises from 0 to 40 A at t=0.1 s and then reaches -40 A at t=0.2 s. For the secondary side, Idc2 alternates from 0 to -106.67 A at t=0.1 s and then steps up to 106.67 A at t=0.2 s, which agrees with the theoretical analysis in Section III. As shown in Fig. 11(c), the total transmission power of the system remains the same when the bipolar-pole power changes. In the meantime, the power of the positive and negative poles can be controlled accurately under different working cases. As shown in Fig. 11(d), the inductor currents of the primary and secondary sides change according to the injected DC offset under different working cases, which realizes unbalanced power transfer and DC bias flux elimination.

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 (0-0.1 s): total power is transmitted in the forward direction. The bipolar power load is symmetrical at 0.4PO (0.4 MW).

2) Case 5 (0.1-0.2 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 (0.2-0.3 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.

Figure 12 shows the simulation results of the off-grid mode. As shown in Fig. 12(a), the total bipolar voltage remains the same when bipolar loads change, which verifies the effectiveness of voltage control at the LVDC side. In addition, the voltages of the positive and negative poles can remain balanced under different working cases, verifying the inherent-pole voltage balancing capability. From Fig. 12(b), Idc1 changes from 0 to -40 A at t=0.1 s and then steps up to 40 A at t=0.2 s. Idc2 increases from 0 to 106.67 A at t=0.1 s and then reaches -106.67 A at t=0.2 s, which agrees with the theoretical analysis in Section III. As shown in Fig. 12(c), when the power load of the positive and negative poles changes, the total transmission power varies accordingly, and the system remains stable during forward and reverse power transmissions. As shown in Fig. 12(d), the inductor currents at the primary and secondary sides vary according to the DC offset under different working cases, which realizes asymmetrical operation and DC bias flux elimination.

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 0.2PO (0.2 MW) and 0.6PO (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.

Figure 13 shows the simulation results of switching from grid-connected mode to off-grid mode. As shown in Fig. 13(a), the unbalanced power between two poles changes from 0 to 0.2 MW at t=0.05 s, and it steps up to 0.4 MW at t=0.1 s, which agrees with the working conditions. As shown in Fig. 13(b), the total bipolar voltage remains the same when the operation mode switches, and the bipolar-pole voltages remain balanced after mode switching. From Fig. 13(c), Idc1 injected into the primary side alternates from 0 to -10 A at t=0.05 s and then reaches -20 A at t=0.1 s. For the secondary side, Idc2 changes from 0 to 26.67 A at t=0.05 s and then steps up to 53.33 A at t=0.1 s, which agrees with the theoretical analysis in Section III. As shown in Fig. 13(d), the total transmission power of the system remains the same before and after mode switching. In the meantime, the positive-pole power and negative-pole power change according to the injected DC offset and bipolar loads in various operation modes.

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 Fig. 13(e), the inductor currents at the primary and secondary sides change according to the injected DC offset under different working cases, which realizes steady asymmetrical operation before and after mode switching.

VI. Conclusion

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.

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