Applied Energy 306 (2022) 118140 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Novel modular multilevel converter-based five-terminal MV/LV hybrid AC/ DC microgrids with improved operation capability under unbalanced power distribution Qian Xiao a, b, Yunfei Mu a, b, Hongjie Jia a, b, Yu Jin c, *, Xiaodan Yu a, b, *, Remus Teodorescu d, Josep M. Guerrero d a Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, China Key Laboratory of Smart Energy & Information Technology of Tianjin Municipality, Tianjin 300072, China c Department of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150006, China d Department of Energy Technology, Aalborg University, Aalborg 9220, Denmark b H I G H L I G H T S • The proposed topology has a more flexible interconnection with hybrid microgrids. • The number of power switches is reduced compared with conventional MMC-based hybrid. • Improved operation capability can be obtained under unbalanced power distribution in microgrids. • A hierarchical energy control method is proposed with balanced capacitor voltages in MMC. • The microgrids can operate normally at different operation modes. A R T I C L E I N F O A B S T R A C T Keywords: Multi-terminal microgrids Hybrid AC/DC microgrids Modular multilevel converter Unbalanced power distribution Energy control Conventionally, the multilevel converter-based multi-terminal hybrid microgrids require a large number of power switches and have a limited operation capability under unbalanced power distribution in medium and low voltage (MV/LV) AC/DC microgrids. To solve this issue, this paper proposes the novel modular multilevel converter (MMC)-based five-terminal MV/LV hybrid AC/DC microgrids. The proposed hybrid microgrids realize the interconnection between the medium-voltage AC (MVAC), MVDC, low voltage AC (LVAC), and two LVDC terminals. In addition, the MVAC grid is connected to the AC terminal of MMC, and the MVDC microgrid is connected to the DC terminal of MMC through a dual active bridge (DAB) converter. Based on MMC, the compact interlinking converters are established, providing three LVDC terminals, which are connected to two LVDC microgrids and one LVAC microgrid through a DC/AC converter. Compared with the conventional MMC-based hybrid microgrids, the proposed topology can significantly reduce the number of power switches. Moreover, to overcome the control challenge of arm energy balancing in MMC and meet the requirement of different operation modes in microgrids, a hierarchical energy control method is proposed, where the low circulating currents are injected to balance the arm energy. Therefore, the system operation capability can be improved under unbal­ anced power distribution. Validation results in different conditions (power step, power reversal, and unbalanced MVAC voltages) indicate that by the proposed method, the arm energy and capacitor voltages in MMC are well balanced, and the proposed hybrid AC/DC microgrids can operate normally at different modes. * Corresponding authors. E-mail addresses: [email protected] (Q. Xiao), [email protected] (Y. Mu), [email protected] (H. Jia), [email protected] (Y. Jin), [email protected] (X. Yu), [email protected] (R. Teodorescu), [email protected] (J.M. Guerrero). https://doi.org/10.1016/j.apenergy.2021.118140 Received 29 July 2021; Received in revised form 8 October 2021; Accepted 24 October 2021 Available online 20 November 2021 0306-2619/© 2021 Elsevier Ltd. All rights reserved. Q. Xiao et al. Applied Energy 306 (2022) 118140 1. Introduction (such as wind power and PV) and energy storage systems (ESSs) into DC systems rather than AC systems [7]. On the other hand, a vast demand for DC power is raised by modern loads like variable-speed drives for elevators [8]. In addition, electric vehicles (PEVs) also appear as a crucial modern load in future DC distribution systems, and extensive novel electronic loads (such as high-quality and highly-efficient DC lighting systems) have already been integrated into modern houses. The increasing DC sources and DC loads provide a strong motivation to shift the mainstream AC microgrids to DC or hybrid microgrids. However, the widespread AC power system promotes the hybrid microgrids concept as the preferable candidate, considering its compatibility [9]. In general, the hybrid microgrids are mainly designed for lowvoltage applications, where the AC terminal is connected to the lowvoltage AC (LVAC) microgrids, and the DC terminal is connected to the low-voltage DC (LVDC) microgrids [10,11]. The AC terminal and DC terminal are interconnected by bidirectional AC/DC power converters, and the AC and DC DGs and loads can be connected to the corresponding terminal. However, to connect the medium-voltage AC (MVAC) grid, the bulky and volume-occupying line-frequency transformers are usually necessary. With the development of remote area mine sites [12] and DC electric ships [13], the medium-voltage DC (MVDC) microgrid is gaining more attention in various applications [14]. Therefore, multiple intercon­ nection schemes have been proposed to realize power conversion be­ tween the MVDC and the LVDC system [15]. In addition, with the increase of electrical power consumption, the efficiency of the power interchange can be greatly improved by the integration of the MVAC grid. Therefore, it is necessary to realize the direct power integration between the MVAC grid and MVDC microgrids through multilevel converter technology [16]. Considering the DC microgrids can better consume the renewable DGs, and the AC appliance still accounts for the major part of power loads, it is necessary to connect the MVDC terminal to the MVAC terminal in the hybrid microgrids together with LVDC and LVAC microgrids. 1.1. Backgrounds and motivation For the past two decades, the proportion of electricity in global en­ ergy consumption increase from 17% in 2000 to 22% in 2018 [1]. With the rapid growth of the economy and deterioration of the environment, gas emission reduction and carbon neutrality are becoming important global recognition [2]. The electricity, especially that generated by clean energy, is gaining much more popularity, of which the electric hybrid vehicles is a good example. It is estimated that by 2050, the growth rate of electricity consumption will reach 80% to 90% [3], and it will rapidly increase the demand for renewable clean energy [4]. The microgrid is an effective solution for the integration and con­ sumption of renewable energy. Conventionally, the AC microgrids are applied in low-voltage applications, where all distributed generations (DGs) and loads are connected to the common AC bus, such as smart buildings, military areas, and rural sectors [5,6]. However, in recent years, the DC microgrid has been drawing much attention. On the one hand, it is more economical to integrate renewable energy resources 1.2. Existing hybrid microgrids Conventionally, the grid frequency transformer is applied to realize the interconnection between the medium-voltage and low-voltage sys­ tems [17]. These transformers are usually bulky and heavy, occupying a large volume. In addition, the high-power grid-frequency transformer can be expensive [18]. Therefore, to realize flexible power conversion and meet the above interfacing requirements of the multi-terminal hybrid microgrids, multiple mainstream structures have been pro­ posed in the past decades. One of the popular topologies is motivated by the cascaded H-bridge (CHB) converter-based power electronic trans­ former (PET) [19]. This topology realizes power conversion between MVAC and LVDC terminals [20], as shown in Fig. 1. It uses a CHB converter as the main structure, where the AC output terminal of the CHB converter is connected to the MVAC grid. The dual active bridge (DAB) converters are connected to each full-bridge (FB) submodule (SM) in the CHB converter, and the output terminals of DABs are connected in parallel to increase the power rating of the LVDC microgrid. The hybrid microgrids connect the MVAC grid with the LVDC microgrid without a grid frequency transformer. Moreover, to increase the flexibility of this topology, a DC/AC converter is usually included to provide an addi­ tional terminal for the LVAC microgrid. It is noted that the LVAC grids can be integrated into the single-phase and three-phase AC grids. Therefore, the single-phase and three-phase DC/AC converters are applied individually for different AC grids. In this interconnection scheme, the power difference between LVDC and LVAC microgrids will not be influenced by the power rating of the CHB converter, and the two microgrids controllers can be designed independently. However, it lacks the interconnection flexibility for more microgrids of different voltage levels. The improved three-terminal hybrid AC/DC microgrids are pro­ posed in Fig. 2 [21]. As shown in the figure, the DAB converters are Fig. 1. The CHB-based hybrid AC/DC microgrids in [20]. Fig. 2. The CHB-based multi-terminal hybrid AC/DC microgrids in [21]. 2 Q. Xiao et al. Applied Energy 306 (2022) 118140 connected to each FB SM. The DABs are divided into two groups, the output terminals of DABs in each group are connected together, forming the LVDC terminal for LVDC microgrid. The topology in Fig. 1 includes one LVDC microgrid and can be connected to one LVAC microgrid through an additional power trans­ formation stage (DC/AC converter). The topology in Fig. 2 provides two different LVDC microgrids, and it can also provide an additional LVAC terminal through an additional DC/AC converter after LVDC microgrid1 or LVDC microgrid-2. In addition, the DC/AC converter can be con­ nected to an LVDC microgrid with a closer voltage level to improve the efficiency of power conversion. However, the above CHB-based hybrid microgrids cannot integrate the MVDC microgrid. A modular multilevel converter (MMC)-based PET is analyzed in [22], where each half-bridge (HB) SM is connected to a DAB converter, and the output terminals of the DABs are paralleled connected to an LVAC microgrid through an DC/AC converter, as shown in Fig. 3. It realizes power conversion between the MVAC grid, MVDC microgrid, and LVAC microgrid, which improves the interconnection adaptability of the multi-terminal hybrid microgrids. Reference [23] analyzes the improved MMC-based hybrid AC/DC microgrids, which is shown in Fig. 4, where each SM is connected to a DAB converter. The output terminals of DAB converters are connected to an LVDC microgrid or an LVAC microgrid through DC/ AC converter. It integrates a number of LVDC and LVAC terminals, together with an MVAC terminal and an MVDC terminal. However, this topology has a great control challenge under unbalanced power distribution in microgrids, which limits its application. To improve the system operation capability under unbalanced power distribution, the MMC-based hybrid microgrids are proposed in [24], as shown in Fig. 5. The DAB converters are connected to each SM, and the output terminals of DABs in the upper arm are connected together to an LVDC microgrid. The output terminals of DABs in the lower arm are connected to another LVDC microgrid. This topology realizes the interconnection between the MVAC grid, MVDC microgrid, and two different LVDC microgrids. However, the system operation capability is still limited under unbalanced power distribution among LVDC micro­ grids. In addition, the control methods in the above papers only discuss the conditions where the microgrids operate at voltage source mode. The grid-connected operation of microgrids needs to be discussed. To further enhance the interconnection flexibility and improve the system operation capability under unbalanced power distribution in LVAC and LVDC microgrids, this paper proposes the novel MMC-based five-terminal MV/LV hybrid AC/DC microgrids and a novel energy control method. The main contributions and innovations of this paper can be listed as follows. Fig. 3. The MMC-based hybrid AC/DC microgrids in [22]. Fig. 4. The MMC-based multi-terminal hybrid AC/DC microgrids in [23]. (1) The proposed hybrid microgrids can improve the interconnection flexibility of the power system. It can realize flexible intercon­ nection and power support between the MVAC grid, MVDC microgrid, LVAC microgrid, and two LVDC microgrids. These, in return, will strengthen the mutual energy support between the different microgrids and increase the consumption of clean energy. (2) Compared with the conventional MMC-based hybrid microgrids, the proposed hybrid microgrids can significantly reduce the number of required power switches and lower the system cost for energy integration. (3) With the proposed hybrid microgrids topology and hierarchical energy control method, the required circulating current injection for arm energy balancing is lower. Therefore, the operation capability under unbalanced power distribution can be greatly improved. (4) With the proposed hierarchical energy control method, the MVDC microgrid, LVAC microgrid, and LVDC microgrids can work at different operation modes, whether the grid-connected operation mode or the voltage-source operation mode. Fig. 5. The MMC-based four-terminal hybrid AC/DC microgrids in [24]. 3 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 6. The proposed MMC-based five-terminal MV/LV hybrid AC/DC microgrids. Table 1 Advantages and disadvantages of the existing multilevel converter-based hybrid microgrids. Items Topologies Advantages Fig. 1 [20] CHB-PET-based Fig. 2 [21] CHB-based 1. No control challenge under unbalanced power distribution. Fig. 3 [22] MMC-PET-based Fig. 4 [23] MMC-based Fig. 5 [24] MMC-based 1. 2. 1. 2. 1. 2. Disadvantages 1. Realize interconnection between two different LVDC microgrids. No control challenge under unbalanced power distribution; Provide the MVDC terminal. A number of microgrids can be integrated; Provide the MVDC terminal. improved operation capability under unbalanced power distribution; MVDC microgrid is integrated The rest of the paper is organized as follows. The topology and hi­ erarchical control structure of the proposed hybrid microgrids are pre­ sented in Section 2. The proposed energy control method is introduced in detail in Section 3. Section 4 analyzes the operation capability of proposed hybrid microgrids and provides the design principle of MMC. In Section 5, the simulation model of the proposed five-terminal hybrid microgrids is established, and simulations under various conditions are conducted to validate the feasibility and advantages of the proposed operation scheme. The conclusions are listed in Section 6. 1. 2. 1. 2. 3. 1. Only two microgrids (one LVDC, one LVAC microgrid) are integrated; No MVDC terminal. Limited operation capability under unbalanced power distribution; No MVDC terminal; Limited to voltage source operation mode. Only one LVAC microgrid is integrated. 1. Highly limited operation capability under unbalanced power distribution. 1. High circulating current injection under unbalanced power distribution; 2. Limited to MVDC and LVDC voltage source operation mode. j = a, b, c; k = 1, 2, 3, 4). Four SMs and an arm inductor Larm are included in each arm. There are two arms in each phase, defined as the upper arm and the lower arm according to their position. One side of the upper and lower arms are connected together as the AC output terminal of MMC, and the other sides of the upper and lower arms are connected to the positive and the negative poles of the DC bus in MMC. The AC terminal of MMC, T1, can be directly connected to the MVAC grid through a filter inductor L, without grid-frequency transformers. The DC terminal of MMC is connected to a DAB converter, providing an MVDC terminal T2 and flexible MVDC voltage for the MVDC microgrid. To further connect the LVDC and LVAC microgrids, three groups of compact interlinking converters are established based on MMC, and they are described as follows. In the compact interlinking converters, the capacitor of each HB-SM is connected with the full-bridge high-fre­ quency transformer (FB-HFT). In the FB-HFT, the FB converter is used to provide suitable input voltage for the high-frequency transformer. The output ports of FB-HFTs in the same phase are then connected together to another FB converter, forming an LVDC terminal. The abovementioned HB-SMs, FB-HFTs, and an additional FB converter in the same phase make up the compact interlinking converters, providing an 2. The topology and control structure of the proposed hybrid AC/DC microgrids 2.1. The topology of the proposed hybrid microgrids Fig. 6 shows the topology of the proposed five-terminal MV/LV hybrid AC/DC microgrids, which is established based on MMC. MMC is composed of 24 half-bridge (HB) submodules (SMs). Each HB-SM in­ cludes two IGBTs, two parallel-connected diodes, and one capacitor, as shown in Fig. 3. The SM capacitor voltages are defined as vSMxjk (x = u, l; 4 Q. Xiao et al. Applied Energy 306 (2022) 118140 Table 2 Detailed comparisons between the proposed and the existing hybrid microgrids. Topologies N ¼ 4 Items Fig. 1 [20] CHB-PET-based Fig. 2 [21] CHB-based Fig. 3 [22] MMC-PET-based Fig. 4 [23] MMC-based Fig. 5 [24] MMC-based Fig. 6 Proposed MVDC microgrid No. of the original LV ports No. of the LV microgrids Additional power conversion Operation capability under unbalanced power IGBTs in the interlinking converters No 1 2 Yes High 144 + 4 No 2 2 No Medium 144 Yes 1 1 Yes High 240 +4 Yes 24 24 No Low 240 + 4x (x: No. of LVAC) Yes 2 2 No Medium 240 Yes 3 3 One LV DC/AC High 156 þ 14 Fig. 7. The hierarchical control structure of the proposed hybrid microgrids. hybrid microgrids, there are one MVDC terminal, one LVAC terminal, and two LVDC terminals. It has an improved operation capability under unbalanced power distribution. In addition, there are 156 IGBTs in the compact interlinking converters (including MMC, FB-HFT, and FB con­ verter), and the number of IGBTs can be greatly reduced. Based on the above analysis, the characteristics and advantages of the proposed five-terminal MV/LV hybrid AC/DC microgrids are sum­ marized as follows. LVDC terminal. Two LVDC terminals, T3 and T4, are connected to the LVDC microgrids directly. The other LVDC terminal is converted into the LVAC terminal, T5, through a DC/AC converter and then connected to an LVAC microgrid. It is noted that the two LVDC microgrids are designed with two different DC voltages, providing higher flexibility for power interchange. Each LVDC terminal provides the LVDC voltage according to the requirement of the LVDC or LVAC microgrids. By the above interconnection scheme, the MVAC grid, MVDC microgrid, LVAC microgrid, and two LVDC microgrids can be integrated, and the microgrids are supposed to operate at either the grid-connected mode or the voltage source mode. It is noted that the proposed inter­ connection scheme can be applied to both the single-phase and threephase LVAC microgrid. The energy control with a single-phase micro­ grid is more challenging due to the higher voltage ripples in the DC side. Therefore, this paper takes the single-phase LVAC microgrid as an example. (1) The proposed five-terminal hybrid microgrids provide higher flexibility for the power interchange system: The MVDC terminal can realize the power exchange with the MVDC microgrid, absorbing power from the MVDC microgrid or releasing power to the MVDC loads such as mining site and DC ship. Two different LVDC microgrids can be integrated with different DC bus volt­ ages. It can meet the variable DC voltage demands from different types of DC loads, and the power supply reliability can be improved in case of failures in the LDVC microgrids. In addition, the LVAC microgrid can also be integrated, obtaining higher compatibility for the conventional LVAC power systems. (2) Compared with the conventional hybrid microgrids, the MVAC grid can be directly connected. The bulky and expensive gridfrequency transformer is not necessary. Compared with the MMC-based hybrid microgrids [22–24], the number of power switches can be reduced, and the system cost can be lowered. (3) Compared with the conventional hybrid microgrids and the multilevel converter PET-based hybrid microgrids [20,22], the LVDC and LVAC microgrids are naturally isolated through the FBHFTs, and they can be controlled independently. Therefore, a more compact and efficient system can be obtained. (4) When the system operates under unbalanced power distribution in LVDC and LVAC microgrids, low circulating currents are injected to balance the active power. Therefore, the operation capability under unbalanced power distribution can be improved. 2.2. The characteristics of the proposed hybrid microgrids The conventional hybrid microgrids are usually designed based on the grid-frequency transformers, which are applied to connect the MVAC grid with the low-voltage microgrids. These transformers are usually bulky and volume-occupying, and the price could be high for high-power applications. The multilevel converter (CHB converter or MMC)-based hybrid microgrids usually lack interconnection flexibility or have a limited operation capability under unbalanced power distri­ bution in microgrids, especially among the LVDC and LVAC microgrids. The advantage and disadvantages of the existing hybrid microgrids are demonstrated in Table 1. More detailed comparisons with the proposed hybrid microgrids are shown in Table 2. For the CHB-PET-based hybrid microgrids in [20], and the CHB-based hybrid microgrids in [21], there is no MVDC terminal, and there are two low-voltage microgrids. In addition, there are 144 IGBTs in the CHB and DAB converters. For the MMC-PET-based hybrid microgrids [22] and the MMC-based hybrid microgrids in [23] and [24], there is an MVDC terminal in the system. In addition, there are 240 IGBTs in the MMC and DAB converters. How­ ever, the 24 low-voltage microgrids in [23] lead to a limited operation capability under unbalanced power distribution. For the proposed 2.3. The control challenges in the proposed system Although the proposed five-terminal hybrid microgrids have the 5 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 8. The overall diagram of the converters control. above advantages, the following control challenges still exist, especially under unbalanced power distribution in LVDC and LVAC microgrids. control method is proposed in this paper. To obtain fast dynamic response and symmetric MVAC currents, the power management layer is designed with feedforward power regulation and references genera­ tions. To realize balancing control in MMC, the circulating currents are injected to balance arm energy, and the modulation reference in each SM is adjusted to balance the individual capacitor voltages. To realize different modes of operation, system controllers for the microgrids are designed individually. (1) The system is supposed to have a fast dynamic response under power step or power reversal changes in microgrids, and sym­ metric MVAC currents are expected in the MVAC grid, even under unbalanced MVAC grid voltages. (2) The arm energy and HB-SM capacitor voltages in MMC are sup­ posed to maintain balanced, and the voltages in the microgrids are supposed to stabilize at the rated values, even under unbal­ anced power distribution in the LVDC and the LVAC microgrids. (3) The MVDC microgrid, LVDC microgrids, and LVAC microgrid should be able to work at different operation modes, either the grid-connected mode or the voltage-source mode. 2.4. The hierarchical control structure The hierarchical structure of the proposed control method is shown in Fig. 7, which includes the power management and the converters control. The power management in this paper features the operation mode selection (the grid-connected operation mode or voltage source operation Therefore, to realize the above control targets, a hierarchical energy 6 Q. Xiao et al. Applied Energy 306 (2022) 118140 mode) and the control reference calculation. It is designed to provide a faster dynamic response through feedforward control in the proposed five-terminal hybrid microgrids. Firstly, it receives information from the load dispatching center, including the operation modes and the trans­ mitted power references of the MVDC microgrid, two LVDC microgrids, and LVAC microgrid (P*MVDC, P*LVDC1, P*LVDC2, and P*LVAC). Then, to obtain a faster response and avoid voltage and current surge during the operation condition changes in microgrids, references of the AC output currents (i*gj) and the DC component of the circulating currents (i*dca, i*dcb, i*dcc) are calculated based on the power distribution in the hybrid microgrids. The converters control includes the power control in the MMC, FBHFTs, FB converters, and DAB converters. For the MMC control, it re­ ceives AC output current references and DC circulating current refer­ ences. In addition, the internal arm energy and SM capacitor voltage also need to be controlled in the MMC. For MVDC microgrid and LVDC microgrids, the interlinking converters are controlled to generate the specific power (P*MVDC, P*LVDC1, P*LVDC2) or rated DC voltage according to their references (V*MVDC, V*LVDC1, V*LVDC2). For LVAC microgrid, the interlinking converters of the DC side are controlled to generate the DC voltage according to their references (V*LVAC_DC), and the DC/AC con­ verter is controlled to generate the specific AC power (P*LVAC) or rated voltage according to its reference value (V*LVAC). fluctuation during power step. 3. The proposed hierarchical energy control method Req = R + Rarm /2, Leq = L + Larm /2 3.2. Modeling and control of MMC 1) MMC modeling To realize the precise control of MMC, the simplified control model of MMC is analyzed, which can be divided into the AC control loop and the DC control loop. The AC control loop controls the output current, and the DC control loop controls the circulating current [25]. For the AC control loop, the control model can be expressed as ⎧ dij ⎪ ⎪ ⎨ Req ij + Leq = uj − vgj dt (4) ⎪ u − uuj ⎪ ⎩ ij = iuj − ilj , uj = lj 2 where ij (j = a, b, c) is the output current of MMC; iuj and ilj are the arm current of the upper and lower arms; vgj is the grid voltage; uuj and ulj are the output voltages of the upper and lower arms; uj is the equivalent output voltage of MMC. Leq and Req are the equivalent inductance and the equivalent resistance in the AC control loop, which can be expressed as For the DC control loop, the control model can be expressed as ⎧ dicirj ⎪ ⎪ = Vdc − ulj − uuj = − 2ucirj ⎨ 2Rarm icirj + 2Larm dt (6) ⎪ (iuj + ilj ) ⎪ ⎩ , icirj = 2 The power management (power regulation and reference genera­ tion) in Fig. 7 is discussed in Section 3.1. The overall diagram of the converters control is shown in Fig. 8. It introduces the control principles of the interlinking converters, including the MMC, the DAB converter in the MVDC microgrid, the FB-HFTs, and FB converters in the LVDC microgrids, the FB-HFTs, FB converter, and DC/AC converters in the LVAC microgrids. More details are as follow. where icirj is the circulating current; Vdc is the DC voltage of the MMC; ucirj is the voltage reference for the circulating current controller. With the above control model, the MMC controller can be designed. 3.1. Power management 2) MMC control To realize the power regulation and obtain a faster dynamic response in the hybrid microgrids, the power references of each interlinking converter need to be calculated. Based on the information from the central load dispatching center, the operation mode and transferred active and reactive power references of each interlinking converter can be obtained. For MMC, the active power can be calculated by the operation con­ dition of each microgrid, while the reactive power references will be provided by the MVAC grid. With the positive active power defined as from MMC to the MVAC grid, or from MMC to the microgrids, the power references can be expressed as P*MVAC = − P*MVDC − P*LVDC1 − P*LVDC2 − P*LVAC (5) The overall control diagram of the MMC is shown in Fig. 8(a) and Fig. 8(b), which includes the AC output current control and the DC circulating current control. For the AC output current control, references of the active and reactive currents are calculated firstly, based on the power references and the sum of all capacitor voltages. In the proposed five-terminal hybrid microgrids, the reactive current reference of MMC is deter­ mined by the requirement of the MVAC grid. The active current refer­ ence is decided by both the system power regulation and the sum capacitor voltages in MMC. It is noted that the reference calculated by system power regulation works as the feedforward control component. In Fig. 8(a), the sum of all capacitor voltages in MMC are realized by absorbing or releasing active currents from the MVAC grid. Therefore, the active and the reactive current references can be expressed as ( ) ⎧ ) 2P* KiAC1_MMC ( ⎪ ⎪ i*d = MVAC + KpAC1_MMC + vSMsum − 24v*SM ⎪ ⎨ 3Vg s (7) ⎪ ⎪ 2Q*MVAC ⎪ * ⎩ iq = 3Vg (1) Supposing the AC output currents of MMC are symmetric, the active AC power flow in each phase can be expressed as / (2) P*ACa = P*ACb = P*ACc = P*MVAC 3 With the calculated power references and active power flow in each microgrid, the DC component of the circulating currents can be derived as )/ ( P* P* ⎧ * idca = − MVAC − MVDC + P*LVDC1 Vdc ⎪ ⎪ 3 3 ⎪ ⎪ ⎪ ⎪ ⎪ )/ ( ⎨ P* P* (3) Vdc i*dcb = − MVAC − MVDC + P*LVDC2 ⎪ 3 3 ⎪ ⎪ ⎪ ⎪ ⎪ )/ ( ⎪ ⎩ * P* P* Vdc idcc = − MVAC − MVDC + P*LVAC 3 3 where KpAC1_MMC and KiAC1_MMC are the control parameters of the proportional-integral (PI) controller; vSMujk and vSMljk are the capacitor voltages in the upper arm and the lower arm; v*SM is the capacitor voltage reference; vSMsum is the sum of all capacitor voltages in MMC. j=a,b,c; ∑ vSMsum = ( vSMujk + vSMljk ) (8) k=1,..N; Then, the AC output current controller is designed to control the AC Thus, the references of MMC can be calculated to reduce the power 7 Q. Xiao et al. Applied Energy 306 (2022) 118140 ⎧ * icirj ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ i*cirj ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ dc 1st ( ) ) KiDC1_MMC (vSMsum KpDC1_MMC + − vSMuj − vSMlj s 3 ( ) ) KiDC2_MMC ( = KpDC2 MMC + 0 − vSMlj + vSMuj cosθj s ( ) ) KiDC3_MMC ( * i*dc = KpDC3 MMC + Vdc − Vdc s = (11) where Vdc and V*dc are the DC voltage of MMC and its reference value; vSMuj and vSMlj are the sum capacitor voltage in the upper and lower arms; θj is the phase angle of each phase; KpDC1_MMC, KiDC1_MMC, KpDC2_MMC, KiDC2_MMC, KpDC3_MMC, and KiDC3_MMC are the PI control pa­ rameters of the arm voltage controller. ⎧ j=a,b,c; ∑ ⎪ ⎪ vSMuj = vSMujk ⎪ ⎨ Fig. 9. The arm output voltage reference calculation and modulation scheme. k=1,..N; j=a,b,c; ⎪ ∑ ⎪ ⎪ ⎩ vSMlj = vSMljk (12) k=1,..N; With the calculated circulating current references, the capacitor voltages can be balanced between each arm. In addition, the capacitor voltage balancing within each arm can be realized by modulation reference modification in each SM. The circulating current control is designed to track the circulating current reference and suppress the inherent second-order circulating current in MMC. Therefore, the PIR circulating current controller can be designed based on [26]. ) ( ucirj = i*cirj − icirj × ( ) KiDC4_MMC KR1_MMC ω0 s 2KR2_MMC ω0 s KpDC4_MMC + + 2 + 2 2 2 s s + ω0 s + ω0 s + 2ω0 s + (2ω0 ) where ω0 is the grid angular frequency. In this paper, the grid frequency is 50 Hz, and ω0 = 100π; KpDC4_MMC, KiDC4_MMC, KR1_MMC, and KR2_MMC are the PI and resonant control parameters of the circulating current controller. Fig. 10. Transmission power model of DAB. 3) Arm output voltage reference calculation and modulation output current of MMC according to their references. Decoupled PI controllers are applied in the dq coordinate, and the final output voltage references in the dq coordinate can be expressed as ( ) ⎧ ) KiAC2_MMC ( * ⎪ u = K + id − id − ωLeq iq + vgd d pAC2_MMC ⎪ ⎨ s (9) ( ) ) ⎪ ⎪ KiAC2_MMC ( * ⎩u = K iq − iq + ωLeq id + vgq q pAC2 MMC + s The modulation scheme is designed to realize arm output voltage generation and SM capacitor voltage balancing. The detailed modula­ tion scheme is shown in Fig. 9. The carrier phase-shifted (CPS) pulse width modulation (PWM) technique is applied in this paper. With the calculated voltage references uj and ucirj, the arm output voltage references in the upper and lower arms can be derived as ⎧ Vdc ⎪ ⎪ − uj + ucirj ⎨ uuj = 2 (14) ⎪ ⎪ ⎩ ulj = Vdc + uj + ucirj 2 where ud and uq are the AC output voltage references of the MMC; KpAC2_MMC and KiAC2_MMC are the control parameters of the AC output current controller; id and iq are d-axis and q-axis components of the AC output currents in MMC; i*d and i*q are the reference values of id and iq; vgd and vgq are d-axis and q-axis components of the MVAC grid voltages. For the circulating current control, their references can be calculated based on the power regulation layer control and the arm capacitor voltages. i*cirj = i*cirj dc + i*dcj + i*cirj 1st + i*dc (13) For individual voltage balancing, the SM modulation references are modified with an additional adjustment to the arm modulation refer­ ences. According to [27], the final modulation signals can be expressed as ⎧ uxjk = uxj + sgn(ixj )⋅Kpind (v*SM − vSMxjk ) ⎪ ⎨ (15) ⎪ ⎩ v* = Vdc (x = u, l; j = a, b, c; k = 1, 2, 3, 4) SM 4 (10) where i*cirj_dc is the DC component reference used to balance the capacitor voltages between each phase; i*cirj_1st is the reference of the fundamental frequency component used to balance the capacitor volt­ ages between the upper and lower arms; i*dcj is the feedforward component reference generated by power regulation in Fig. 7; i*dc is the DC component reference used to control the DC voltage of MMC. They can be further expressed as where uxj is the arm modulation reference; uxjk is the final modulation reference of each SM; Kpind is the control parameter of the proportional controller; ixj is the arm current. The sgn function can be described as ⎧ ⎨ 1, ixj > 0 0, ixj = 0 sgn(ixj ) = (16) ⎩ − 1, ixj < 0 8 Q. Xiao et al. Applied Energy 306 (2022) 118140 In this paper, the dual active bridge (DAB) converter is used as the DC/DC converter for the MVDC microgrid, and the single phase-shift control method is applied to the DAB converter. When the MVDC microgrid operates in grid-connected mode, the input and output voltages of the interlinking DAB converter are fixed and clamped by the MVDC bus of MMC and the MVDC grid. Therefore, the main control target of this operation mode is to control the active power flow between the input port and the output port. For a conven­ tional DAB controller, the transferred active power can be illustrated in Fig. 10. In Fig. 10, nT is the transformation ratio; VHV is the input DC voltage of DAB; VLV is the output DC voltage of DAB; fs is the switching frequency of DAB; Lp is the power transferring inductor of DAB; PDAB is the transferred power of DAB; D is the phase shift angle. More detailed information can be found in [28]. It is noted that the maximum trans­ ferred power of the MVDC microgrid can be expressed as Fig. 11. The control principle of DAB. PDABmax = nT VHV VLV 8fs Lp (17) Equation (17) indicates that the maximum transferred power of DAB depends on the power transferring inductor. Therefore, the power transferring inductor should be carefully designed to meet the power transmission requirement of the DAB converter. Usually, when the DAB reaches its rated power, the phase shift angle D should be designed at about 0.3 to 0.45 [29]. According to Fig. 10, the transferred power of DAB is decided by the phase-shift angle D, and the phase shift angle is positive correlation or negative correlation under each quarter operation range. In this paper, only the shadowed area in Fig. 10 is utilized [30], where D ∈ [-0.5, 0.5]. Therefore, the phase shift angle is in positive correlation to the trans­ ferred power of DAB. The PI controller can thus be applied to control the transferred active power in DAB. With the feedforward component of the phase-shift angle, the MVDC microgrid acquires a faster dynamic response and smaller fluctuation during the power step. The phase-shift angle can be derived by the following control equation. ( ) ( ) ) Ki1_MVDC ( * DMVDC = FMVDC P*MVDC + Kp1_MVDC + PMVDC − PMVDC s (18) where DMVDC is the phase shift angle of the MVDC microgrid; FMVDC(P*MVDC) is the power function of transferred power to describe Fig. 10; Kp1_MVDC and Ki1_MVDC are the control parameters of the trans­ ferred power controller in the MVDC microgrid. Therefore, the DAB converter in the MVDC microgrid can be controlled under the grid-connected operation mode. Fig. 12. The operation region of the proposed hybrid microgrids under different MVAC power. (a) The operation region under hMVAC = 1. (b) The operation region under hMVAC = 0.5. (c) The operation region under hMVAC = 0. (d) The operation region under hMVAC = -0.5. (e) The operation region under hMVAC = -1. 2) Voltage source operation mode When the MVDC microgrid works in the voltage source operation mode, the control target of the interlinking converter is the MVDC output voltage. Under this condition, the phase shift angle can be calculated based on the MVDC output voltage. ( ) ) Ki2 MVDC ( * DMVDC = Kp2 MVDC + (19) VMVDC − VMVDC s When the MVDC output voltage is lower than its reference value, the phase shift angle of DAB increases. When the MVDC output voltage is higher than its reference value, the phase shift angle decreases. With the derived phase shift angle, the MVDC output voltage can be controlled. Based on the above analysis, the output signal of DAB can be shown in Fig. 11, where Ts is the switching period; uHV is the input voltage waveform of the transformer; uLV is the output voltage waveform of the transformer; D is the phase shift angle. Fig. 13. The current waveform of the upper arm in phase a. 3.3. MVDC microgrid control The MVDC microgrid is designed to operate under two modes, the grid-connected operation mode, and the voltage source operation mode. In this paper, the two operation modes are discussed individually. 1) MVDC grid-connected operation mode 9 Q. Xiao et al. Applied Energy 306 (2022) 118140 Table 3 Simulation parameters. Table 4 Control parameters of the proposed hierarchical control method. Table 5 Simulation scenarios under normal operation. Scenarios 1 2 3 4 5 Time 0 s ~ 0.5 s 0.5 s ~ 1.0 s 1.0 s ~ 1.5 s 1.5 s ~ 2.0 s 2.0 s ~ 2.5 s MVAC grid voltage Balanced Balanced Balanced 0.5 sag in phase C 0.5 sag in phase C MVDC LVDC-1 LVDC-2 grid-connected voltage source grid-connected 300 kW 300 kW 300 kW 300 kW − 300 kW 50 kW 100 kW 100 kW 100 kW 100 kW 50 kW 50 kW 100 kW 100 kW 100 kW 3.4. LVDC microgrid-1 and LVDC microgrid-2 control LVAC grid-connected 100 kW 100 kW 100 kW 100 kW 100 kW connected to HB SM, and they are parallel-connected to a FB con­ verter of the LVDC microgrid. Therefore, the rated power of each FBHFT is one-eighth of the rated power in the LVDC microgrid. Corre­ spondingly, the power transferring inductor can be selected based on the The control principle of the LVDC microgrids is similar to that in the MVDC microgrid. However, it is noticed that there are eight FB-HFTs 10 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 14. Simulation results of the modular multilevel converter from scenario 1 to scenario 2 with a single-phase LVAC microgrid. rated power of each FB-HFT. In addition, to make sure the equal power distribution in these FB-HFTs and the connected HB SMs, their switching signals are assigned with the same PWM signal of 50% duty cycle. Then, the switching signals of the output FB converter can be derived based on the calculated phase shift angle in different operation modes. microgrid-2; FLVDC1,2(P*LVDC1,2/8) is the power function of transferred power in LVDC microgrid-1 or LVDC microgrid-2; Kp1_LVDC and Ki1_LVDC are the control parameters of the transferred power controller in LVDC microgrids; PLVDC1,2 and P*LVDC1,2 are the transferred power in LVDC microgrid-1 or LVDC microgrid-2 and its reference value. Based on equation (20), the phase shift angle of the output FB con­ verter in LVDC microgrid-1 or LVDC microgrid-2 can be calculated. 1) LVDC grid-connected operation mode When the LVDC microgrid works in grid-connected operation mode, the phase shift angle can be calculated based on the transferred active power reference. ( * ) ( ) ) PLVDC1,2 Ki1 LVDC ( * DLVDC1,2 =FLVDC1,2 + Kp1 LVDC + PLVDC1,2 − PLVDC1,2 8 s (20) 2) Voltage source operation mode When the LVDC microgrid works in the voltage source operation mode, the control target of the interlinking converter is the LVDC output voltage. Under this condition, the phase shift angle can be calculated based on the LVDC output voltage. ( ) ) Ki2_LVDC ( * DLVDC1,2 = Kp2_LVDC + (21) VMVDC1,2 − VMVDC1,2 s where DLVDC1,2 is the phase shift angle of LVDC microgrid-1 or LVDC 11 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 15. Simulation results of the LVDC microgrids and single-phase LVAC microgrid from scenario 1 to scenario 2. where VLVDC1,2 and V*LVDC1,2 are the output voltage in LVDC-1 or LVDC2 microgrid and its reference value; Kp2_LVDC and Ki2_LVDC are the control parameters of the output voltage controller in LVDC microgrids. The control principle under voltage source operation mode is similar to that in the MVDC microgrid, and it will not be further discussed. ( DLVAC = KpDC LVAC + KiDC ) LVAC s ( * VDC LVAC − VDC ) LVAC (22) where DLVDC is the phase shift angle of the FB converter in the LVAC microgrid; KpDC_LVAC and KiDC_LVAC are the control parameters of the DC bus voltage controller in the LVAC microgrid; VDC_LVAC and V*DC_LVAC are the DC bus voltage in the LVAC microgrid and its reference value. Then, the DC/AC converter can be controlled according to its oper­ ation mode. 3.5. LVAC microgrid control For the LVAC microgrid, there is a single-phase DC/AC interlinking converter connected to the FB output converter. For the FB-HFTs and FB converter, the control target is to regulate the DC output voltage to the rated value. The control method and the switching signal distribution are the same as the LVDC microgrids, where the FB-HFTs share the same PWM signal with a 50% duty cycle to obtain equal power among the FBHFTs and their connected HB SMs. The phase shift angle of the FB converter is calculated based on the DC bus voltage in the LVAC microgrid interlinking converter. 1) LVAC grid-connected operation mode As mentioned before, the LVAC grid can be categorized into the single-phase AC grid or the three-phase AC grid. Therefore, when the LVAC microgrid operates in grid-connected mode, the control strategy should be designed individually. This paper mainly focuses on the single-phase AC grid application. However, to keep the uniform control 12 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 16. Simulation results of the modular multilevel converter from scenario 2 to scenario 3 with a single-phase LVAC microgrid. structure and simplify the controller design process, this paper uses the decoupled PI controller in the virtual dq frame to control the DC/AC controller. Firstly, the active power and reactive power required by the AC microgrid are used to calculate the active and reactive current references as ⎧ 3P*LVAC * ⎪ ⎪ ⎪ idLVAC = 2V , ⎨ g ⎪ ⎪ 3Q*LVAC ⎪ ⎩ i* qLVAC = 2Vg The AC output current can be further transformed into virtual dq frame as { idLVAC = iαLVAC cos(ωt) + iβLVAC sin(ωt) (25) iqLVAC = − iαLVAC sin(ωt) + iβLVAC cos(ωt) With the calculated output currents in the virtual dq frame, the conventional decoupled PI controllers are used to control the active and reactive currents, which can be expressed as ( ) ⎧ ) KiAC_LVAC ( * ⎪ idLVAC − idLVAC − ωLac iqLVAC + vdLVAC ⎪ udLVAC = KpAC_LVAC + ⎨ s ( ) ) ⎪ ⎪ KiAC_LVAC ( * ⎩u iqLVAC − iqLVAC + ωLac idLVAC + vqLVAC qLVAC = KpAC LVAC + s (26) (23) Then, the single-phase AC output current can be transformed into αβ frame as ( ) T iαLVAC = iLVAC (t), iβLVAC = iLVAC t − (24) 4 where udLVAC and uqLVAC are output voltage references of the DC/AC converter on the virtual d-axis and q-axis; KpAC_LVAC and KiAC_LVAC are the 13 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 17. Simulation results of the LVDC microgrids and single-phase LVAC microgrid from scenario 2 to scenario 3. control parameters of the AC output current controller in LVAC micro­ grid; Lac is the AC filter inductor in the LVAC microgrid; idLVAC and iqLVAC are virtual d-axis and q-axis components of the AC output currents in LVAC microgrid; i*dLVAC and i*qLVAC are the reference values of idLVAC and iqLVAC; vdLVAC and vqLVAC are the LVAC grid voltages on the virtual daxis and q-axis, which can also be calculated based on the trans­ formation for virtual dq frame as shown in (24) and (25). Next, the output voltage references in the virtual dq frame are transformed back into αβ frame { uαLVAC = udLVAC cos(ωt) − uqLVAC sin(ωt) (27) uβLVAC = udLVAC sin(ωt) + uqLVAC cos(ωt) If the LVAC microgrid operates in the voltage source mode, the output voltage of the DC/AC converter is fixed. In this circumstance, only a modulation scheme is required in the single-phase DC/AC con­ verter. Therefore, with the output voltage reference uLVAC, the final PWM signals of the single-phase DC/AC converter can be obtained. 4. Discussion In this section, the operation region of the proposed hybrid micro­ grids is analyzed, and it is compared with the other MMC-based topol­ ogies. Then, the design principle of MMC is discussed The voltage reference in the α-axis, uαLVAC, will be the final modu­ lation reference of the single-phase DC/AC converter, as shown in Fig. 8. More detailed information can be found in [31], and it will not be further discussed in this paper. 2) Voltage source operation mode 4.1. Operation region analysis of the proposed hybrid microgrids In the proposed five-terminal hybrid microgrids, each microgrid is designed based on its rated power. Supposing the rated MVAC power is PratedMVAC; the rated MVDC power is PratedMVDC; the rated LVDC-1 power 14 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 18. Simulation results of the modular multilevel converter from scenario 3 to scenario 4 with a single-phase LVAC microgrid. is PratedLVDC1; the rated LVDC-2 power is PratedLVDC2; the rated LVAC power is PratedLVAC. Here, the maximum system power is defined as Pmax, the rated power of each microgrid in this paper can be configured as { ⃒ rated ⃒ ⃒ rated ⃒ ⃒ = ⃒P ⃒ = HMV Pmax ⃒P ⃒ rated ⃒MVAC⃒ rated MVDC ⃒ ⃒ rated ⃒ (28) ⃒P ⃒ = ⃒P ⃒ = ⃒P ⃒ = HLV Pmax LVDC1 LVDC2 PMVDC = − PMVAC − PLVDC1 − PLVDC2 − PLVAC (30) The above operation equation can be further expressed as hMVDC Pmax = − (hMVAC + hLVDC1 + hLVDC2 + hLVAC )Pmax (31) where hMVDC is the operating power coefficient of the MVDC microgrid; hMVAC is the operating power coefficient of the MVAC grid; hLVDC1 is the operating power coefficient of LVDC microgrid-1; hLVDC2 is the operating power coefficient of LVDC microgrid-2; hLVAC is the operating power coefficient of LVAC microgrid. It is noted that the power flow in each microgrid can be either pos­ itive or negative, and the above parameters meet the following constraint { ∀(hMVDC , hMVAC ) ∈ [ − HMV , HMV ] (32) ∀(hLVDC1 , hLVDC2 , hLVAC ) ∈ [ − HLV , HLV ] LVAC where HMV and HLV are the rated power coefficients for the mediumvoltage and low-voltage microgrids. They are supposed to meet the following constraints { HMV ∈ [0, 1] (29) HLV ∈ [0, 1] Usually, HMV and HLV are selected based on the operation data of the microgrids. In this paper, they are designed as HMV = 1 and HLV = 0.5 for simplicity. Then, the operating power of the MVDC microgrid should be 15 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 19. Simulation results of the LVDC microgrids and single-phase LVAC microgrid from scenario 3 to scenario 4. When the MVAC grid operates at the different power conditions, equation (31) can be further expressed as hMVDC = − (hMVAC + hLVDC1 + hLVDC2 + hLVAC ) microgrid is zero, hMVAC = 0, the operation region of the low-voltage microgrids reaches its maximum boundary. (33) 4.2. Operation capability comparisons under unbalanced power distribution Based on the rated power of MVDC, LVDC, and LVAC microgrid, hMVDC, hLVDC1, hLVDC2, and hMVAC should meet hMVDC ∈ [-1, 1] and ∀(hLVDC1, hLVDC2, hMVAC) ∈ [-0.5, 0.5]. The operation region of the lowvoltage microgrids under different MVAC power can be shown in Fig. 12. As shown in Fig. 12, if the operating powers of the MVAC grid are opposite, the low-voltage microgrids have the same operation region but in the opposite direction. When the absolute operating power of the MVAC grid is equal to its rated value, hMVAC = 1 or hMVAC = -1, the LV microgrids have the smallest operation region. When the absolute operating power of the MVAC microgrid is half of its rated value, hMVAC = 0.5 or hMVAC = -0.5, the operation region of the low-voltage micro­ grids grows higher. When the absolute operating power of the MVAC The operation ability under unbalanced distributed power is compared between the proposed hybrid microgrids and two other topologies. For the hybrid microgrids in Fig. 4, each SM in MMC is connected to a DC microgrid through a DAB converter. In this topology, the main re­ striction for unbalanced power distribution is the modulation differ­ ences (or the maximum transferred power) between two SMs in the same arm. Supposing the amplitude of the MVAC grid is Iac, and the active power flows among the three phases are asymmetry (which means the injected circulating currents should be 0). Taking two SMs in the upper arm in phase a as examples, the arm current can be expressed as 16 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 20. Simulation results of the modular multilevel converter from scenario 4 to scenario 5 with a single-phase LVAC microgrid. iua = iga Iac = − cosθ 2 2 Usually, the modulation references should be within the linear modulation region. Therefore, the maximum transferred power between two SMs can be expressed as ( ) 0.5Vdc − Vg Iac (37) ΔPmaxMG = max(PSMm − PSMn ) = 2 (34) Supposing the voltage drops across the inductors and the circulating current control references are small enough to be neglected, the arm modulation references will be approximted to 1 vga u*ua = − 2 Vdc (35) where Vg is the amplitude of the MVAC grid voltage. The maximum transferred power can be further expressed as If the microgrids connected to the mth and nth SM consume the largest and the smallest active power, the average active power flow in SMm and SMn can be expressed as ( ∫ )/ ⎧ udc ⎪ ⎪ PSMm = T u*uam iua dt ⎪ ⎨ 4 (36) ( ∫ )/ ⎪ ⎪ udc ⎪ ⎩ PSMn = T u*uan iua dt 4 ΔPmaxMG1 = max(PSMm − PSMn ) = (1 − m)Vdc Iac 4 (38) where m is the modulation index in MMC. For the hybrid microgrids in Fig. 5, the restriction for the unbalanced power distribution is the circulating current injection. Supposing the maximum injected circulating current is Icir_max, the maximum power exchange between the upper and lower arms can be expressed as 17 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 21. Simulation results of the LVDC microgrids and single-phase LVAC microgrid from scenario 4 to scenario 5. ∫ ΔPmaxarm = (vga Icir max cosθ)dt T = Vg Icir 2 max = mVdc Icir 4 max twice the rated AC output current, which means the maximum ampli­ tude of the circulating current can be higher than Iac. (39) For the proposed hybrid microgrids, the maximum transferred power between two LVDC microgrids can be expressed as ΔPmaxMG2 = 3ΔPmaxarm 3Vg Icir = 2 max 3mVdc Icir = 4 max Icir max , icirb = − Icir max , icirc =0 (40) ΔPmaxMG3 = 2Vdc Icir max max > ΔPmaxMG2 = > ΔPmaxMG1 = 3mVdc Icir 4 (1 − m)Vdc Iac 4 max (44) Therefore, the proposed hybrid microgrids have improved operation capability under unbalanced power distribution in the AC/DC microgrids. (41) On this condition, the maximum transferred power should be ΔPmaxMG3 = 2Vdc Icir (43) > Iac The modulation index m is usually selected from 0.85 to 1. Comparing the equations in (38, 40), and (42), it is obvious that For the proposed hybrid microgrids in Fig. 6, if the maximum circulating current injection is Icir_max, the maximum transferred power between two low-voltage microgrids appears when the circulating cur­ rent injection references are icira = Icir max (42) According to [32], the rated current of the power module is about 18 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 22. Simulation results of the modular multilevel converter from scenario 3 to additional 10 kW negative-sequence active power in the three-phase LVAC microgrid. 4.3. Design of the MMC expressed as With the confirmed rated power in each microgrid, the MMC can be designed accordingly. Taking the upper arm in phase a as an example, the arm current should be i*ua = (− i*ua = i*a * +i 2 cira (45) P*MVAC P*MVDC − + P*LVDC1 )/Vdc 3 3 (47) Considering Vg < 0.5Vdc, the upper arm current waveform in phase a can be shown in Fig. 13. Therefore, it can be concluded that the maximum arm current should be about When the system is in stable operation condition, the circulating current only includes the DC component in equation (3) i*cira = i*dca = (− 1 1 1 0.5 cosωt + + + )Pmax 3Vg 3Vdc 3Vdc Vdc i*ua max 1 7 =( + )Pmax 3Vg 6Vdc (48) The capacity of the arm current should be designed based on this result. In addition, the maximum power flow of each SM is expressed as (46) The maximum power flow in phase a should include the condition when hMVAC = -1, hMVADC = -1, hLVDC1 = 0.5. Supposing only active power are transferred in the MVAC grid, the arm current can be P*SM max = Pmax Vdc 1 7 + ) ( 3Vg 6Vdc N With the above analysis, the MMC can be designed. 19 (49) Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 23. Simulation results of the LVDC microgrids and three-phase LVAC microgrid from scenario 3 to additional 10 kW negative-sequence active power in the LVAC microgrid. [24]. Table 6 Simulation scenarios under system fault. Fault type Fault time Fault conditions Figure number Fault 1 Fault 2 Fault 3 0.5 s 0.5 s 0.5 s MVDC microgrid fault LVDC microgrid-1 fault LVAC microgrid fault Fig. 24 and Fig. 25 Fig. 26 and Fig. 27 Fig. 28 and Fig. 29 5.1. Operation of the proposed scheme with single-phase LVAC microgid To verify the effectiveness of the proposed hybrid microgrids and the hierarchical energy control method, a series of simulations are con­ ducted, and the simulation scenarios are listed in Table 5. The simulation results of the proposed hybrid microgrids from operation scenario 1 to operation scenario 2 are shown in Fig. 14 and Fig. 15. The active power of LVDC-microgrid-1 increases from 50 kW to 100 kW at 0.5 s under this operation condition. Fig. 14 shows the waveforms of the MMC. The MVAC grid voltages are shown in Fig. 14(a), whose amplitudes are about 2450 V. The am­ plitudes of MVAC output currents increase from about 136 A to about 150 A at 0.5 s, as shown in Fig. 14(b). The circulating currents of MMC are shown in Fig. 14(c). From 0.3 s to 0.5 s, the active power of LVDC 5. Simulation results To verify the effectiveness of the proposed hybrid microgrids and energy control method, the five-terminal MV/LV hybrid AC/DC micro­ grids are built in the MATLAB/SIMULINK simulation environment. The simulation model is established based on the proposed topology in Fig. 6. The circuit parameters are given in Table 3, and the control pa­ rameters are given in Table 4. These parameters are selected based on 20 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 24. Simulation results of the modular multilevel converter under fault type 1. microgrid-1 and LVDC microgrid-2 are the same, and the circulating currents in phase a and phase b are the same. When the power step oc­ curs, the active powers in LVDC microgrid-1 and LVAC microgrid are the same, and the circulating currents in phase a and phase c are the same. The three-phase SM capacitor voltages are shown in Fig. 14(d) to Fig. 14 (f), where the average values remain stable at about 1500 V. The voltage and current of the DC side are shown in Fig. 14(g) and Fig. 14(h), which are about 6 kV and 50 A. Fig. 15 shows the waveforms of the microgrids. The MVDC microgrid voltage and current are 5 kV and 60 A, as shown in Fig. 15(a) and Fig. 15 (b). The voltage of LVDC microgrid-1 is stable at 1 kV, and its current increase from 50 A to 100 A at 0.5 s, as shown in Fig. 15(c) and Fig. 15 (d). The voltage and current of LVDC microgrid-2 are stable at 750 V and about 66.7 A, as shown in Fig. 15(e) and Fig. 15(f). Fig. 15(g) and Fig. 15 (h) show the DC side voltage and current of the LVAC microgrid, where the voltage stabilizes at about 750 V and the current stabilizes at about 133.3 A. Fig. 15(i) and Fig. 15(j) show the AC voltage and output current of the LVAC microgrid, where the amplitude of the voltage is about 311 V and the amplitude of the current is about 643 A. It indicates that the active power of the LVAC microgrid remains at about 100 kW during the whole operation condition. The above results verify the effectiveness of the proposed hybrid microgrids and the hierarchical control method under power increase in the voltage source operation mode in LVDC microgrid-1. The simulation results of the proposed hybrid microgrids from operation scenario 2 to operation scenario 3 are shown in Fig. 16 and Fig. 17. The active power of LVDC-microgrid-2 increases from 50 kW to 100 kW at 1.0 s under this operation condition. The waveforms of MMC are shown in Fig. 16. The MVAC grid volt­ ages are shown in Fig. 16(a), the amplitudes of which are about 2450 V. The amplitudes of MVAC output currents increase from about 150 A to about 163 A at 1.0 s in Fig. 16(b). The circulating currents of MMC are shown in Fig. 16(c). From 0.8 s to 1.0 s, the active power flows of LVDC microgrid-1 and LVAC microgrid are the same, and the circulating 21 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 25. Simulation results of the hybrid AC/DC microgrids under fault type 1. currents in phase a and phase c are the same. After 1.0 s, the active power in LVDC microgrid-2 becomes the same as the other microgrids, and the circulating currents in the three phases are the same. The SM capacitor voltages in three phases are shown in Fig. 16(d) to Fig. 16(f), where the average values remain at about 1500 V. The DC side voltage and current of MMC are shown in Fig. 16(g) and Fig. 16(h), and their values are about 6 kV and 50 A. The waveforms of the microgrids are shown in Fig. 17. The MVDC microgrid voltage and current are 5 kV and 60 A as shown in Fig. 17(a) and Fig. 17(b). The voltage of LVDC microgrid-1 is stable at 1 kV, and its current is stable at 100 A, as shown in Fig. 17(c) and Fig. 17(d). The voltage of LVDC microgrid-2 stabilizes at 750 V, and its current increases from about 66.7 A to about 133.3 A, as shown in Fig. 17(e) and Fig. 17 (f). Fig. 17(g) and Fig. 17(h) show the DC side voltage and current of the LVAC microgrid, where the voltage stabilizes at about 750 V and the current current stabilizes at about 133.3 A. Fig. 17(i) and Fig. 17(j) show the AC voltage and output current of the LVAC microgrid, where the amplitude of the voltage is about 311 V and the amplitude of the current is about 643 A. It indicates that the active power of the LVAC microgrid remains at about 100 kW during the whole operation condition. The above simulation results verify the effectiveness of the proposed hybrid microgrids and the hierarchical control method under power increase in grid-connected operation mode in LVDC microgrid-2. The simulation results of the proposed hybrid microgrids from operation scenario 3 to operation scenario 4 are shown in Fig. 18 and Fig. 19. The grid voltage in phase c drops by about 50% at 1.5 s under this operation condition. Fig. 18 shows the waveforms of the MMC. The MVAC grid voltages are shown in Fig. 18(a), and their amplitudes are about 2450 V. The amplitudes of MVAC output currents increase from about 163 A to about 195.6 A at 1.5 s in Fig. 18(b), due to the voltage drop in phase c. The circulating currents of MMC are shown in Fig. 18(c). From 1.3 s to 1.5 s, the active powers in the LVDC and LVAC microgrids are the same, and the circulating currents are also the same. At 1.5 s, the voltage drop 22 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 26. Simulation results of the modular multilevel converter under fault type 2. occurs in phase c, and the circulating current in phase c becomes different from those in other phases. The SM capacitor voltages in three phases are shown in Fig. 18(d) to Fig. 18(f), where the average values are about 1500 V, but they witness some fluctuation during the dynamic transition process. The DC side voltage and current are about 6 kV and 50 A, as shown in Fig. 18(g) and Fig. 18(h). The waveforms of the microgrids are shown in Fig. 19. The MVDC microgrid voltage and current are about 5 kV and 60 A as shown in Fig. 19(a) and Fig. 19(b). The voltage of LVDC microgrid-1 is stable at 1 kV, and its current is stable at 100 A, as shown in Fig. 19(c) and Fig. 19 (d). The voltage of LVDC microgrid-2 is stable at 750 V, and its current is stable at about 133.3 A, as shown in Fig. 19(e) and Fig. 19(f). Fig. 19(g) and Fig. 19(h) show the DC side voltage and current of the LVAC microgrid, where the voltage stabilizes at about 750 V and the current stabilizes at about 133.3 A. Fig. 19(i) and Fig. 19(j) show the AC voltage and output current of the LVAC microgrid, where the amplitude of the voltage is about 311 V and the amplitude of the current is about 643 A. It indicates that the active power of the LVAC microgrid remains at about 100 kW during the whole operation condition. The above simulation results verify the effectiveness of the proposed hybrid microgrids and the hierarchical control method under unbalanced grid voltage operation conditions. The simulation results of the proposed hybrid microgrids from operation scenario 4 to operation scenario 5 are shown in Fig. 20 and Fig. 21. The operation power in MVDC reverse at 2.0 s under this condition. Fig. 20 shows the waveforms of the MMC. The MVAC grid voltages are shown in Fig. 20(a), the amplitudes of which are about 2450 V. The amplitudes of MVAC output currents decrease from about 195 A to 0 at 2.0 s in Fig. 20(b) due to the balanced power distribution between MVDC, LVDC, and LVAC microgrids. The circulating currents of MMC are shown in Fig. 20(c). From 1.8 s to 2.0 s, the circulating current in phase c is higher than those in other phases due to the voltage sag in phase c. At 2.0 s, the internal power flows between MVDC, LVDC, and 23 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 27. Simulation results of the hybrid AC/DC microgrids under fault type 2. LVAC microgrids become balanced, and the transferred power in the MVAC grid becomes 0. Therefore the circulating currents in three phases become balanced again even under unbalanced MVAC grid voltages. The SM capacitor voltages in three phases are shown in Fig. 20(d) to Fig. 20(f), where the average values remain at about 1500 V. However, the capacitor voltage ripples drop significantly due to the reduced MVAC output currents. The DC side voltage is shown in Fig. 20(g), the value of which is about 6 kV. The DC circulating current reverses from 50 A to − 50 A at 2.0 s, as shown in Fig. 20(h). Fig. 21 shows the waveforms of the microgrids. The MVDC microgrid voltage is 5 kV, and its current reverses from 60 A to − 60 A as shown in Fig. 21(a) and Fig. 21(b). The voltage and current of LVDC microgrid-1 are stable at 1 kV and 100 A, as shown in Fig. 21(c) and Fig. 21(d). The voltage of LVDC microgrid-2 is stable at 750 V, and its current is stable at about 133.3 A, as shown in Fig. 21(e) and Fig. 21(f). Fig. 21(g) and Fig. 21(h) show the DC side voltage and current of the LVAC microgrid, where the voltage stabilizes at about 750 V and the current stabilizes at about 133.3 A. Fig. 21(i) and Fig. 21(j) show the AC voltage and output current of the LVAC microgrid, where the amplitude of the voltage is about 311 V and the amplitude of the current is about 643 A. It indicates that the active power of the LVAC microgrid remains at about 100 kW during the whole operation condition. The above simulation results verify the effectiveness of the proposed hybrid microgrids and the hi­ erarchical control method under power reverse operation conditions in the MVDC microgrid. 5.2. Feasibility verification of the proposed scheme with three-phase LVAC microgrid To verify the feasibility of the proposed system interconnection scheme and its hierarchical control method, the simulation is further verified with the three-phase LVAC microgrid. It should be mentioned that the control for the three-phase LVAC microgrid should be the same control structure in the dq frame, as discussed in [33]. 24 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 28. Simulation results of the modular multilevel converter under fault type 3. The hybrid microgrids are integrated with a three-phase LVAC microgrid. Firstly, before 0.5 s, the system operates in scenario 3 in Table III. Then, at about 0.5 s, 10 kW additional negative-sequence active power is injected in the three-phase LVAC microgrid. In this operation condition, the grid voltage is balanced; the active power of the MVDC microgrid is 300 kW; the active power of the two LVDC micro­ grids is 100 kW. The simulation results are shown in Fig. 22 and Fig. 23. Fig. 22 shows the waveforms of the MMC. The MVAC grid voltages are shown in Fig. 22(a), and their amplitudes are about 2450 V. The amplitudes of MVAC output currents are about 163 A before 0.5 s, as shown in Fig. 22(b). The amplitudes only increase slightly when the negative-sequence active power is injected in the LVAC microgrid. The circulating currents of MMC are shown in Fig. 22(c). Since the active power of LVDC microgrid-1, LVDC microgrid-2, and LVAC microgrid are almost the same, the circulating currents in the three phases are also almost the same. The SM capacitor voltages in three phases are shown in Fig. 22(d) to Fig. 22(f), where the average values remain stable at about 1500 V during the whole operation process. The voltage and current of the DC side are shown in Fig. 22(g) and Fig. 22(h), which are about 6 kV and 50 A. Fig. 23 shows the waveforms of the microgrids. The MVDC microgrid voltage and current are 5 kV and 60 A, as shown in Fig. 23(a) and Fig. 23 (b). The voltage of LVDC microgrid-1 is stable at 1 kV, and its current stabilizes at about 100 A, as shown in Fig. 23(c) and Fig. 23(d). The voltage and current of LVDC microgrid-2 are stable at 750 V and about 66.7 A, as shown in Fig. 23(e) and Fig. 23(f). Fig. 23(g) and Fig. 23(h) show the DC side voltage and current of the LVAC microgrid. During the whole operation process, the average value of the DC side voltage sta­ bilizes at about 750 V, and the average value of the DC current stabilizes at about 133.3 A. However, when the negative-sequence active power is injected, both the voltage and the current begin to fluctuate. Fig. 23(i) shows the voltages of the LVAC microgrid, where the amplitudes are about 311 V. Fig. 23(j) shows the output currents of the LVAC microgrid. Before 0.5 s, the amplitudes of the currents are about 214 A. After 0.5 s, 25 Q. Xiao et al. Applied Energy 306 (2022) 118140 Fig. 29. Simulation results of the hybrid AC/DC microgrids under fault type 3. the amplitude in phase a increases to about 237 A, and the amplitudes in phase b and phase c decrease to about 202 A. The above results verify the effectiveness of the feasibility of the proposed scheme with a three-phase LVAC microgrid. are shown in Fig. 24(a), and their amplitudes are about 2450 V. The amplitudes of the output currents are about 163 A before the fault oc­ curs, as shown in Fig. 24(b). When the fault occurs, the amplitudes of output currents decrease to about 81 A. The circulating currents of the MMC are shown in Fig. 24(c). When the fault occurs, the circulating current values decrease to 0 due to the disconnection of the MVDC microgrid. The three-phase SM capacitor voltages are shown in Fig. 24 (d) to Fig. 24(f), where the average values remain stable at about 1500 V. However, when the fault occurs, the capacitor voltage ripples tend to decrease due to the reduced active power exchange. The voltage of the DC side is shown in Fig. 24(g), and the value stabilizes at about 6 kV. The current of the DC side is shown in Fig. 24(h), which decreases from about 50 A to 0 when the fault occurs. The waveforms of the microgrids are shown in Fig. 25. The MVDC microgrid voltage is shown in Fig. 25(a), and the value remains stable at about 5 kV. The MVDC microgrid current is shown in Fig. 25(b), which decreases from about 60 A to 0 when the fault occurs. The voltage of 5.3. Operation ability under system fault The fault ride-through operation ability is important to improve the system’s reliability. The internal SM fault will be solved by the internal control strategy of the interlinking converter. Therefore, this paper only discusses the external fault condition. The open circuit and short circuit fault are two different common faults. It is noted that no matter the open circuit fault or the short circuit fault, the microgrid will be disconnected from the system. The fault operation conditions are listed in Table 6. The simulation results under fault type 1 (MVDC microgrid fault) are shown in Fig. 24 and Fig. 25. Fig. 24 shows the waveforms of the MMC. The MVAC grid voltages 26 Q. Xiao et al. Applied Energy 306 (2022) 118140 LVDC microgrid-1 is stable at 1 kV, and its current stabilizes at about 100 A, as shown in Fig. 25(c) and Fig. 25(d). The voltage and current of LVDC microgrid-2 are stable at 750 V and about 133.3 A, as shown in Fig. 25(e) and Fig. 25(f). Fig. 25(g) and Fig. 25(h) show the DC side voltage and current of the LVAC microgrid, where the voltage stabilizes at about 750 V and the current stabilize at about 133.3 A. Fig. 25(i) and Fig. 25(j) show the AC voltage and output current of the LVAC micro­ grid, where the amplitude of the voltage is about 311 V and the amplitude of the current is about 643 A. It indicates that the active power of the LVAC microgrid remains at about 100 kW. The above re­ sults verify the effectiveness of the operation ability of the proposed scheme under MVDC microgrid fault. The simulation results under fault type 2 (LVDC microgrid-1 fault) are shown in Fig. 26 and Fig. 27. Fig. 26 shows the waveforms of the MMC. The MVAC grid voltages are shown in Fig. 26(a), and their amplitudes are about 2450 V. When fault occurs, the amplitudes of the output currents decrease from about 163 A to about 136 A, as shown in Fig. 26(b). The circulating currents of the MMC are shown in Fig. 26(c). When the fault occurs, the circulating currents in phase a decrease due to the reduced active power. The threephase SM capacitor voltages are shown in Fig. 26(d) to Fig. 26(f), where the average values remain stable at about 1500 V. However, when the fault occurs, the capacitor voltages fluctuate in phase a. The voltage and current of the DC side are shown in Fig. 26(g) and Fig. 26(h), which are stable at about 6 kV and 50 A. The waveforms of the microgrids are shown in Fig. 27. The MVDC microgrid voltage and current are about 5 kV and 60 A, as shown in Fig. 27(a) and Fig. 27(b). The voltage of LVDC microgrid-1 is stable at 1 kV, as shown in Fig. 27(c). However, its current decreases from about 100 A to 0 due to the disconnection of LVDC microgrid-1, as shown in Fig. 27(d). The voltage and current of LVDC microgrid-2 are stable at 750 V and about 133.3 A, as shown in Fig. 27(e) and Fig. 27(f). Fig. 27(g) and Fig. 27(h) show the DC side voltage and current of the LVAC microgrid, where the voltage stabilizes at about 750 V and the current stabilizes at about 133.3 A. Fig. 27(i) and Fig. 27(j) show the AC voltage and output current of the LVAC microgrid, where the amplitude of the voltage is about 311 V and the amplitude of the current is about 643 A. It indicates that the active power of the LVAC microgrid remains at about 100 kW. The above results verify the effectiveness of the operation ability of the proposed scheme under LVDC microgrid-1 fault. The simulation results under fault type 3 (LVAC microgrid fault) are shown in Fig. 28 and Fig. 29. Fig. 28 shows the waveforms of the MMC. The MVAC grid voltages are shown in Fig. 28(a), and their amplitudes are about 2450 V. When the fault occurs, the amplitudes of the output currents decrease from about 163 A to about 136 A, as shown in Fig. 28(b). The circulating currents of the MMC are shown in Fig. 28(c). When the fault occurs, the circulating current in phase c decreases due to the reduced active power. The three-phase SM capacitor voltages are shown in Fig. 28(d) to Fig. 28 (f), where the average values remain stable at about 1500 V. However, when the fault occurs, the capacitor voltages fluctuate in phase c. The voltage and current of the DC side are shown in Fig. 28(g) and Fig. 28(h), which are stable at about 6 kV and 50 A. The waveforms of the microgrids are shown in Fig. 29. The MVDC microgrid voltage and current are about 5 kV and 60 A, as shown in Fig. 29(a) and Fig. 29(b). The voltage of LVDC microgrid-1 is stable at 1 kV, and its current stabilizes at about 100 A, as shown in Fig. 29(c) and Fig. 29(d). The voltage and current of LVDC microgrid-2 are stable at 750 V and about 133.3 A, as shown in Fig. 29(e) and Fig. 29(f). Fig. 29(g) and Fig. 29(h) show the DC side voltage and current of the LVAC microgrid, where the voltage stabilizes at about 750 V, but the current decreases from about 133.3 A to 0 when the fault occurs. Fig. 29(i) and Fig. 29(j) show the AC voltage and output current of the LVAC micro­ grid, where the amplitude of the voltage is about 311 V, but the amplitude of the current decreases from about 643 A to 0 when the fault occurs. The above results verify the effectiveness of the operation ability of the proposed scheme under LVAC microgrid fault. 6. Conclusion This paper proposes the novel MMC-based five-terminal MV/LV hybrid AC/DC microgrids. It realizes the flexible bidirectional power interchange between the MVAC grid, MVDC microgrid, LVAC microgrid, and two LVDC microgrids, providing mutual power support. To balance the arm energy and capacitor voltage in the MMC and realize different modes of operation in microgrids, a hierarchical energy control method is proposed with improved operation capability under unbalanced power distribution in MV/LV AC/DC microgrids. Based on the analysis and simulation results in this paper, the main conclusions are drawn as follows. • The proposed hybrid microgrids have a simplified structure and a greatly reduced number of power switches compared with the existing MMC-based hybrid microgrids. • The proposed hybrid microgrids possess a high operation capability under unbalanced power distribution in the MV/LV AC/DC micro­ grids due to the reduced circulating current injection. • In various conditions (including under power step, power reversal, and unbalanced MVAC grid voltages), the proposed control method can effectively balance the arm energy and the capacitor voltages in the MMC, and meet the requirement of different operation modes in microgrids. • The proposed hybrid microgrids and the hierarchical control method possess the operation ability under different system faults (MVDC microgrid fault, LVDC microgrid fault, and LVAC microgrid fault). Despite the above advantages of proposed hybrid microgrids, the wide application in practical engineering is still facing some challenges, such as the massive data communication, measurement and control signal transportation delay, optimization of system power flow, system control stability, and fault ride-through operation strategies. These challenges will be the main focus of our future research work. CRediT authorship contribution statement Qian Xiao: Conceptualization, Funding acquisition, Methodology, Project administration, Writing –original draft. Yunfei Mu: Formal analysis, Data curation, Writing – review & editing. Hongjie Jia: Data curation, Writing – review & editing. Yu Jin: Investigation, Software, Validation, Writing – review & editing. Xiaodan Yu: Resources, Visu­ alization, Writing – review & editing. Remus Teodoresc: Supervision, Writing – review & editing. Josep M. Guerrero: Supervision, Writing – review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported by the National Natural Science Foundation of China (No. 52107121, U2066213), and China Postdoctoral Science Foundation (No. 2020M680880). References [1] Najafzadeh M, Ahmadiahangar R, Husev O, Roasto I, Jalakas T, Blinov A. Recent contributions, future prospects and limitations of interlinking converter control in hybrid AC/DC microgrids. IEEE Access 2021;9:7960–84. 27 Q. Xiao et al. Applied Energy 306 (2022) 118140 [18] Zou ZX, De Carne G, Buticchi G, Liserre M. Smart transformer-fed variable frequency distribution grid. IEEE Trans Ind Electron 2018;65(1):749–59. [19] Wang X, Liu J, Ouyang S, Xu T, Meng F, Song S, et al. Control and experiment of an H-bridge-based three-phase three-stage modular power electronic transformer. IEEE Trans Power Electron 2016;31(3):2002–11. [20] Wang L, Zhang D, Wang Yi, Wu B, Athab HS. Power and voltage balance control of a novel three-phase solid-state transformer using multilevel cascaded H-bridge inverters for microgrid applications. IEEE Trans Ind Electron 2016;31(4): 3289–301. [21] Jia H, Xiao Q, He J. An improved grid current and DC capacitor voltage balancing method for three-terminal hybrid AC/DC microgrid. IEEE Trans Smart Grid 2019; 10(6):5876–88. [22] Briz F, Lopez M, Rodriguez A, Arias M. Modular power electronic transformers: modular multilevel converter versus cascaded H-bridge solutions. IEEE Ind Electron Mag 2016;10(4):6–19. [23] Lachichi A, Junyent-Ferre A, Green TC. Comparative optimization design of a modular multilevel converter tapping cells and a 2L-VSC for hybrid LVAC/DC microgrids. IEEE Trans Ind App 2019;55(3):3228–40. [24] Xiao Q, Mu Y, Jia H, Jin Yu, Hou K, Yu X, et al. Modular multilevel converter based multi-terminal hybrid AC/DC microgrid with improved energy control method. Appl Energy 2021;282:116154. https://doi.org/10.1016/j.apenergy.2020.116154. [25] Jin Y, Xiao Q, Jia H, Mu Y, Ji Y, Teodorescu R, et al. A dual-layer back-stepping control method for Lyapunov stability in modular multilevel converter based STATCOM. IEEE Trans Ind Electron; early access. [26] Sharifabadi K, Harnefors L, Nee H, Norrga S, Teodorescu R. Design, control, and application of modular multilevel converters for HVDC transmission systems. 1st ed. Hoboken, NJ, USA: Wiley; 2016. [27] Hagiwara M, Akagi H. Control and experiment of pulse width modulated modular multilevel converters. IEEE Trans Power Electron 2009;24(7):1737–46. [28] Chen L, Shao S, Xiao Q, Tarisciotti L, Wheeler PW, Dragicevic T. Model predictive control for dual-active-bridge converters supplying pulsed power loads in naval DC microgrids. IEEE Trans on Power Electron 2020;35(2):1957–66. [29] Sha D, Zhang J, Liu K. Leakage inductor current peak optimization for dualtransformer current-fed dual active bridge DC-DC converter with wide input and output voltage range. IEEE Trans on Power Electron 2020;35(6):6012–24. [30] Xiao Q, Chen L, Jin Yu, Mu Y, Cupertino AF, Jia H, et al. An improved fault-tolerant control scheme for cascaded H-bridge STATCOM with higher attainable balanced line-to-line voltages. IEEE Trans Ind Electron 2021;68(4):2784–97. [31] Riverso S, Tucci M, Vasquez JC, Guerrero JM, Ferrari-Trecate G. Stabilizing plugand-play regulators and secondary coordinated control for AC islanded microgrids with bus-connected topology. Appl Energy 2018;210:914–24. [32] Tu Q, Li Y, Liu W, Huang M, Zeng G, Du B, et al. Arm overcurrent protection and coordination in MMC-HVDC. IEEE Power Energy Soc General Meeting (PESGM) 2018:1–5. [33] Xiao Q, Wang J, Jin Yu, Chen L, Jia H, Dragicevic T, et al. A novel operation scheme for modular multilevel converter with enhanced ride-through capability of submodule faults. IEEE J Emerg Sel Topics Power Electron 2021;9(2):1258–68. [2] Ge L, Xian Y, Wang Z, Gao B, Chi F, Sun K. A GWO-GRNN based model for shortterm load forecasting of regional distribution network. CSEE J Power Energy Syst; early access. [3] Zhang X, Wang B, Gamage D, Ukil A. Model predictive and iterative learning control based hybrid control method for hybrid energy storage system. IEEE Trans Sustain Energy; early access. [4] Ma Z, Gao F, Gu X, Li N, Wu Q, Wang X, et al. Multilayer SOH equalization scheme for MMC battery energy storage system. IEEE Trans Power Electron 2020;35(12): 13514–27. [5] Som S, De S, Chakrabarti S, Sahoo S, Ghosh A. A robust controller for battery energy storage system of an islanded AC microgrid. IEEE Trans Ind Informat; early access. [6] Xing X, Li X, Gao F, Qin C, Zhang C. Improved space vector modulation technique for neutral-point voltage oscillation and common mode voltage reduction in threelevel inverter. IEEE Trans Power Electron 2019;34(9):8697–714. [7] Sahoo S, Mishra S. A distributed finite-time secondary average voltage regulation and current sharing controller for DC microgrids. IEEE Trans Smart Grid 2019;10 (1):282–92. [8] Abhinav S, Modares H, Lewis FL, Davoudi A. Resilient cooperative control of DC microgrids. IEEE Trans Smart Grid 2019;10(1):1083–5. [9] Chen S, Li P, Ji H, Yu H, Yan J, Wu J, et al. Operational flexibility of active distribution networks with the potential from data centers. Appl Energy 2021;293: 116935. https://doi.org/10.1016/j.apenergy.2021.116935. [10] Mi Y, Zhang H, Fu Y, Wang C, Loh PC, Wang P. Intelligent power sharing of DC isolated microgrid based on fuzzy sliding mode droop control. IEEE Trans Smart Grid 2019;10(3):2396–406. [11] Wang R, Sun Q, Ma D, Liu Z. The small-signal stability analysis of the droopcontrolled converter in electromagnetic timescale. IEEE Trans Sustain Energy 2019;10(3):1459–69. [12] Yuan C, Haj-ahmed MA, Illindala MS. Protection strategies for medium voltage direct current microgrid at a remote area mine site. IEEE Trans Ind Appl 2015;51 (4):2846–53. [13] Khan MMS, Faruque MO, Newaz A. Fuzzy logic based energy storage management system for MVDC power system of all electric ship. IEEE Trans Energy Convers 2017;32(2):798–809. [14] Saleh K, Hooshyar A, Saadany E. Ultra-high-speed travelling-wave-based protection scheme for medium-voltage dc microgrids. IEEE Trans Smart Grid 2019; 10(2):1440–51. [15] Liu C, Li X, Zhi Y, Cai G. New breed of solid-state transformer mainly combing hybrid cascaded multilevel converter with resonant DC-DC converters. Appl Energy 2018;210:724–36. [16] Liu W, Liu C, Lin Y, Bai K, Ma L. Interval multi-objective optimal scheduling for redundant residential microgrid with VESS. IEEE Access 2019;7:87849–65. [17] Xu T, Gao F, Hao T, Meng X, Ma Z, Zhang C, et al. Two-layer global synchronous pulse width modulation method for attenuating circulating leakage current in PV station. IEEE Trans Ind Electron 2018;65(10):8005–17. 28