Distributed Control Implementation for Zonal MVDC ...

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Distributed Control Implementation for Zonal MVDC Ship Power Systems Tuyen V. Vu, Member, IEEE, David Gonsoulin, Student Member, IEEE, Dallas Perkins, Student Member, IEEE, Behnaz Papari, Student Member, IEEE, Hesan Vahedi, Member, IEEE, and Chris S. Edrington, Senior, Member, IEEE Center for Advanced Power Systems, Florida State University, Tallahassee, Florida/USA, [email protected]

Abstract—In this paper, we present a potential distributed adaptive control architecture applied to a zonal medium voltage DC (MVDC) ship power systems. The power sharing in the MVDC network among distributed generators will be presented first. Second, the active and reactive power sharing among zones in the low voltage AC (LVAC) network will be addressed. The effect of control in LVAC network on the MVDC network and vice-versa regarding power sharing and voltage stability will be investigated in this paper for the first time. Simulation results in MATLAB/Simulink and PLECS validate the promising distributed control architecture for ship power systems.

Zone6

Zone5

PCM

PMM2

IPNC 450VAC 60 Hz

ZL5

I. INTRODUCTION A. Literature Review uture all-electric ships (AES) will contain integrated power systems, where zonal MVDC and LVAC networks play an important role in increasing the ship power system efficiency and survivability [1]. The complicated power systems due to the integration of more power devices raised a concern about the system resiliency and reliability. Therefore, distributed control has been proposed in literature to handle the control issues and increase system reliability [2]-[6]. In MVDC ship systems, the DC distribution systems are required to provide power to a variety of load devices, such as propulsion motors, radars, lasers, railguns, cooling, and hotel loads. The control objectives of the distribution system are (a) to share the power as commanded by the energy system management routine and (b) to keep the DC bus voltage in the stable region [2]-[5]. To serve the zonal AC loads, LVAC power network is introduced in the integrated power node center (IPNC) to generate the low AC voltage level, which is typically rated at 450 VAC - 60 Hz. In order to improve the power demand service, multiple LVAC zones in ship systems can be interconnected; thus, each zonal load (ZL) is dually powered by two IPNC [7]. Consequently, the objectives in control of the interconnected LVAC network are active and reactive power sharing, and bus voltage and frequency stability [6]. As the interaction of the DC and AC power systems can be related to the AC/DC hybrid microgrids, there have been research on this topic [8],[9]; however, there are limited

F

Zone3

PCM

PCM

IPNC

IPNC

450VAC 60 Hz

ZL3

ZL4

ZL6

Zone2

Zone1

PGM4

PGM3

450VAC 60 Hz

PMM1

ZL1

ZL2 IPNC

IPNC PCM

Index Terms—Ship power systems, MVDC distribution systems, LVAC distribution systems, distributed control, power sharing, and voltage stability.

Zone4

PCM

IPNC EMRG

PCM

MVDC 12 kV PGM2

PGM1

Note: MTG: Main turbine generator; ATG: Auxiliary turbine generator; PCM: Power conversion module; IPNC: Integrated power node center; ZL: Zonal load; EMRG: Electromagnetic rail-gun; PMM: Propulsion motor module

Fig. 1. 12 kV MVDC – 450 V, 60Hz LVAC network.

research efforts on the interaction of MVDC and LVAC systems, especially for those applied in the ship power systems. B. Contribution of the Paper As reviewed, previous research has not investigated the mutual interaction of the LVAC and MVDC networks regarding electrical and control action in ship power systems. Therefore, in this paper, we conduct a thorough investigation on the issue. The notional MVDC system Fig. 1, leveraged from [7] is considered for control description and implementation in the following sub-sections and Sections. In Fig. 1, there are 4 gas turbine generators (PGM1 , PGM2 , PGM3 , PGM4 ) located in 6 zones to provide power to the large loads (PMM1 , PMM2 , EMRG), and AC zonal loads, ZL𝑖 (𝑖 = 1,2, … ,6), via a power conversion module connected to the 12 kV DC distribution system. Each every two zones 450 VAC interconnects and exchanges power with each other. The organization of the paper is as follows: Section II summarizes the control method for the notional ship system. The case study with simulation results are presented in Section III. The results are analyzed and discussed in Section IV to verify the effectiveness of the method. Section V concludes the achievements of the paper. II. DISTRIBUTED CONTROL METHOD In this Section, the distributed control methods for MVDC and LVAC systems are described.

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the exchanged information the per-unit current reference 𝑝𝑢,𝑟𝑒𝑓 𝑝𝑢 𝑥𝐼,𝑖 and average network voltage feedback 𝑥𝑉,𝑎𝑣𝑔,𝑖 are calculated based on (1) and (2) [5].

From Energy Management Power reference 𝑟𝑒𝑓

𝑃𝑖 𝑝𝑢 𝑥𝐼,𝑗 =1

𝑁𝑗

Current Signal processing

𝑝𝑢

𝑥𝐼,𝑗 =2

𝑝𝑢 ,𝑟𝑒𝑓 𝑥𝐼,𝑖

Adaptive Current Controller

𝑟𝑒𝑓 ∆𝑣𝐼,𝑖

𝑥𝐼,𝑖 = 𝑖𝑖 𝑉 𝑟𝑒𝑓 /𝑃𝑖

𝑝𝑢

𝑝𝑢

𝑝𝑢 ,𝑟𝑒𝑓 𝑥𝑉,𝑖

Voltage Signal processing

𝑝𝑢

𝑝𝑢

𝑝𝑢

𝑗=1

𝑝𝑢

𝑤𝑉,𝑖

=1

𝑝𝑢 𝑤𝑉,𝑖

=

𝑝𝑢 𝑥𝑉,𝑎𝑣𝑔,𝑖

−

𝑝𝑢 𝑥𝑉,𝑖

𝑝𝑢

𝑝𝑢

+ ∫ ∑(𝑤𝑉,𝑗 − 𝑤𝑉,,𝑖 ).

(2) Suppose that the models that represent the relationships (a) 𝑝𝑢 between current supplying 𝑥𝐼,𝑖 and droop resistance variation 𝑝𝑢 𝑅𝑑𝐼𝑖 (𝑢𝐼𝑖 = 𝑅𝑑𝐼𝑖 ), and (b) between average bus voltage 𝑥𝑉,𝑎𝑣𝑔,𝑖 𝑗=1

𝑝𝑢 𝑥𝑉,𝑎𝑣𝑔 ,𝑖

𝑝𝑢 𝑤𝑉,𝑗 =2

𝑝𝑢

𝑁𝑗

𝑥𝑉,𝑎𝑣𝑔 ,𝑗 =2

𝑤𝑉,𝑗 =1

𝑝𝑢

𝑝𝑢 𝑥𝑉,𝑎𝑣𝑔 ,𝑖

𝑤𝑉,𝑖

𝑝𝑢

𝑁𝑗

𝑥𝑉,𝑎𝑣𝑔,𝑖 = 𝑥𝑉,𝑖 + ∫ ∑(𝑥𝑉,𝑎𝑣𝑔,𝑗 − 𝑥𝑉,𝑎𝑣𝑔,𝑖 ) + 𝑘𝑤,𝑖 ∫ 𝑤𝑉,𝑖

𝑝𝑢

𝑥𝑉,𝑎𝑣𝑔 ,𝑗 =1

(1)

𝑗=1

𝑝𝑢 𝑥𝐼,𝑖

𝑟𝑒𝑓

𝑝𝑢

𝑝𝑢,𝑟𝑒𝑓

𝑥𝐼,𝑖

1 𝑝𝑢 = ∑ 𝑥𝐼,𝑗 . 𝑁𝑗

Adaptive Voltage Controller

𝑟𝑒𝑓 ∆𝑣𝑉,𝑖

𝑝𝑢

𝑥𝑉,𝑖 = 𝑣𝑖 /𝑉 𝑟𝑒𝑓

𝑟𝑒𝑓

𝑣𝑖

𝑖𝑖

𝑝𝑢

𝑝𝑢

𝑥̇ 𝐼,𝑖 = 𝑎𝐼𝑖 𝑥𝐼,𝑖 + 𝑏𝐼𝑖 𝑢𝐼𝑖 𝑝𝑢

𝑝𝑢

𝑥̇ 𝑉,𝑎𝑣𝑔,𝑖 = 𝑎𝑉𝑖 𝑥𝑉,𝑎𝑣𝑔,𝑖 + 𝑏𝑉𝑖 𝑢𝑉𝑖 ,

(3) Utilize the model reference adaptive control presented in [2] to control the system (3). Fig. 3 shows the adaptation mechanism 𝑟𝑒𝑓 for updating the control input 𝑢 (𝑢𝐼𝑖 = 𝑅𝑑𝐼𝑖 and 𝑢𝑉𝑖 = ∆𝑣𝑉,𝑖 ) based on Lyapunov stability criteria. The following reference models are applied:

PGM Fig. 2. Distributed control for 1 power generation module (PGM).

Reference model (Control requirements)

𝑝𝑢

𝑝𝑢,𝑟𝑒𝑓

𝑝𝑢

𝑥̇ 𝐼𝑚,𝑖 = 𝑎𝐼𝑚𝑖 𝑥𝐼𝑚,𝑖 + 𝑏𝐼𝑚𝑖 𝑥𝐼,𝑖 +

𝑟𝑒𝑓

and PGM terminal voltage variation ∆𝑣𝑉,𝑖 (𝑢𝑉𝑖 = ∆𝑣𝑉,𝑖 ) can be approximated as the following first-order systems:

𝑟𝑒𝑓 ∆𝑣𝑖 = 𝑟𝑒𝑓 𝑟𝑒𝑓 ∆𝑣𝐼,𝑖 + ∆𝑣𝑉,𝑖

𝑝𝑢

𝑝𝑢

𝑝𝑢

− 𝑙𝐼𝑖 (𝑥𝐼,𝑖 − 𝑥𝐼𝑚,𝑖 )

𝑝𝑢

𝑝𝑢,𝑟𝑒𝑓

𝑥̇ 𝑉𝑚,𝑎𝑣𝑔,𝑖 = 𝑎𝑉𝑚𝑖 𝑥𝑉𝑚,𝑎𝑣𝑔,𝑖 + 𝑏𝑉𝑚𝑖 𝑥𝑉,𝑖 𝑝𝑢 𝑝𝑢 − 𝑙𝑉𝑖 (𝑥𝑉,𝑎𝑣𝑔,𝑖 − 𝑥𝑉𝑚,𝑎𝑣𝑔,𝑖 ),

+

+

DC system (Unknown system paramters)

Adaptation mechanism (Identify the control parameter u based on Lyapunov)

(4) where the subscript ‘m’ indicates the reference model states or 𝑟𝑒𝑓 𝑟𝑒𝑓 parameters. Thus, the voltage outputs ∆𝑣𝐼,𝑖 and ∆𝑣𝑉,𝑖 are updated based on (5) and (6) [2]. The combined voltage 𝑟𝑒𝑓 𝑟𝑒𝑓 𝑟𝑒𝑓 reference changed ∆𝑣𝑖 = ∆𝑣𝐼,𝑖 + ∆𝑣𝑉,𝑖 will be applied to the respective PGM for desired current sharing and nominal bus voltage operation. 𝑟𝑒𝑓

Fig. 3. Model reference adaptive control algorithm for unknown system.

A. Distributed Adaptive Control for MVDC Network To share the power proportionally among generators and keep the bus voltage at the nominal level, the distributed control system in [2] is utilized. As shown in Fig. 2, there are two adaptive control loops set up on top of each power generation module (PGM). Local control of each PGM sends the current and voltage information (𝑣𝑖 ,𝑖𝑖 ) to their distributed controller for 𝑝𝑢 𝑝𝑢 the per-unit information (𝑥𝑉,𝑖 , 𝑥𝐼,𝑖 ) calculation based on the 𝑟𝑒𝑓

rated voltage 𝑉 𝑟𝑒𝑓 and rated power reference 𝑃𝑖 received from the energy management routine. In the control structure, there 2 neighbors are considered for one control node. 𝑝𝑢 Information regarding the per-unit current state (𝑥𝐼,𝑖 ) and per𝑝𝑢 𝑝𝑢 unit voltage states (𝑥𝑉,𝑎𝑣𝑔,𝑖 , 𝑤𝑉,𝑎𝑣𝑔,𝑖 ) of a control node 𝑖 is exchanged with its neighbors 𝑗 in the control network. Based on

∆𝑣𝐼,𝑖 = −𝑅𝑑𝐼𝑖 𝑖𝑖 ̅ 𝑇 𝜙𝐼𝑖 𝑅𝑑𝐼𝑖 = 𝜃𝐼𝑖 ̅ = −𝛾𝐼𝑖 𝑠𝑔𝑛(𝑏𝐼𝑖 )𝜙𝐼𝑖 𝑒𝐼𝑖 , (5) 𝜃̇𝐼𝑖 ̅ = [𝜃𝐼𝑖 𝑘𝐼𝑖 ]𝑇 , 𝜙𝐼𝑖 = where 𝑅𝑑𝐼𝑖 is the virtual resistance, 𝜃𝐼𝑖 𝑝𝑢 𝑝𝑢 𝑝𝑢,𝑟𝑒𝑓 𝑇 𝑝𝑢 [𝑥𝐼,𝑖 ] , 𝛾𝐼𝑖 > 0, and 𝑒𝐼,𝑖 = 𝑥𝐼,𝑖 − 𝑥𝐼𝑚,𝑖 . 𝑥𝐼,𝑖 𝑟𝑒𝑓 ̅ 𝑇 𝜙𝑉𝑖 ∆𝑣𝑉,𝑖 = 𝜃𝑉𝑖

̅ = −𝛾𝑉𝑖 𝑠𝑔𝑛(𝑏𝑉𝑖 )𝜙𝑉𝑖 𝑒𝑉𝑖 , 𝜃̇𝑉𝑖 𝑝𝑢 ̅ = [𝜃𝑉𝑖 𝑘𝑉𝑖 ]𝑇 , 𝜙𝑉𝑖 = [𝑥𝑉,𝑎𝑣𝑔,𝑖 where 𝜃𝑉𝑖 𝑝𝑢 𝑝𝑢 and 𝑒𝑉𝑖 = 𝑥𝑉,𝑎𝑣𝑔,𝑖 − 𝑥𝑉𝑚,𝑎𝑣𝑔,𝑖 .

(6) 𝑝𝑢,𝑟𝑒𝑓 𝑇 𝑥𝑉,𝑖 ] ,

𝛾𝑉𝑖 > 0,

B. Distributed Control for LVAC Network The distributed control for interconnection among interconnected zones is leveraged from the work done in [6] and [10]. The detailed algorithm for the inverter in each IPNC is detailed in Fig. 7. The local control of IPNC sends the per-unit

3

𝑟𝑒𝑓

𝑉𝑖,𝐴𝐶

𝑉0,𝐴𝐶

𝑉𝑖,𝐴𝐶 𝑉𝑖,𝐴𝐶 + 𝑉𝑗 ,𝐴𝐶

𝑁𝑗 ,𝐴𝐶 𝑉𝑗 ,𝐴𝐶 𝑉𝑖,𝐴𝐶,𝑎𝑣𝑔 − 𝑗

𝑁𝑗 𝑗

𝑟𝑒𝑓

𝑄𝑖

𝑄𝑗

𝐺𝐶𝑄 (𝑠) −

𝑁𝑗 ,𝐴𝐶

−

𝑟𝑒𝑓

𝑃𝑖 𝑃𝑖 𝑃𝑗

⍵𝑖 ⍵𝑗

𝑁𝑗 ,𝐴𝐶 𝑗

⍵𝑖 +

𝑁𝑗 ,𝐴𝐶 𝑗

⍵𝑗

𝐺𝐶𝑃 (𝑠) −

⍵𝑖,𝑎𝑣𝑔 −

Unit

𝑃𝑖

PGM1 rated power

25

MW

⍵𝑗

PGM2 rated power

25

MW

𝑟𝑒𝑓

PGM3 rated power

25

MW

PGM4 rated power

25

MW

−

𝑟𝑒𝑓

𝑁𝑗

Value

𝑉𝑖,𝐴𝐶

𝑉𝑝 𝑠𝑖𝑛(𝜔𝑡 + 𝜃)

⍵0

−

𝑃𝑖𝑟𝑒𝑓

𝑃𝑗

𝑉𝑝

𝑉0,𝐴𝐶

𝑄𝑖

Parameter

𝑄𝑖

𝐺𝐶𝑉 (𝑠)

1 + 𝑁𝑗 ,𝐴𝐶

𝑄𝑖 𝑄𝑗

TABLE I 12 KV MVDC SHIP SYSTEM PARAMETERS.

To neighbors

From neighbors

TABLE II ADAPTIVE CONTROL PARAMETERS

⍵

Symbol

𝐺𝐶⍵ (𝑠)

1 + 𝑁𝑗 𝑟𝑒𝑓

𝑖𝑖,𝐴𝐶

⍵0

𝐿𝑣𝑖𝑟

𝜔𝑓 𝑠 𝑠 + 𝜔𝑓 𝑟𝑒𝑓

𝑉𝑖,𝐴𝐶

IPNC

Fig. 4. Distributed control for interconnected LVAC distribution system.

information regarding the bus voltage (𝑉𝑖,𝐴𝐶 ), frequency (⍵𝑖 ), active power (𝑃𝑖 ), and reactive power (𝑄𝑖 ) to the distributed controller. The distributed controller 𝑖 also needs to exchange this information with its neighbors (𝑗, 𝑗 = 1,2, …, 𝑁𝑗,𝐴𝐶 ). The information received is processed for the average bus voltage (𝑉𝑖,𝐴𝐶,𝑎𝑣𝑔 ), average frequency (⍵𝑖,𝑎𝑣𝑔 ), active power reference 𝑟𝑒𝑓 𝑟𝑒𝑓 (𝑃𝑖 ), and reactive power reference (𝑄𝑖 ). The PI controllers 𝐺𝐶𝑉 (𝑠), 𝐺𝐶⍵ (𝑠), 𝐺𝐶𝑃 (𝑠), 𝐺𝐶𝑄 (𝑠) are required to regulate the power sharing, bus voltage, and system frequency via generating change in the Inverter reference terminal voltage (𝑉𝑝 𝑠𝑖𝑛(𝜔𝑡 + 𝜃) ). The virtual impedance is 𝐿𝑣𝑖𝑟 with low pass filter is included to guarantee the initial system stability if the inverters of IPNC are not synchronized. III. CASE STUDY AND RESULTS In this paper, a notional 12 kV - 100 MW MVDC system is taken for the simulation validation. The power information of PGM of the MVDC network shown in TABLE I. In this MVDC network, there are six zones providing power to devices including propulsion motors (PMM), an electro-magnetic railgun, and multiple hotel loads ZL. Adaptive controller parameters are shown in TABLE II. The initial virtual resistance of each PGM is set to 𝑅𝑑0 = 0.5 𝛺. The control time step of each node is 𝑇𝑠 = 1 𝑚𝑠. In the LVAC network, each inverter in IPNC, which is rated at 1 MVA generates a 450V60Hz at the terminal. The following scenario is as follows for system control verification:  From time t = 00 – 15 s: - PGM shared the current at the 𝐼PGM1 : 𝐼PGM2 : 𝐼PGM3 : 𝐼PGM4 = 1: 1: 1: 1.

ratio

of

QUANTITY

Values

𝑎𝑚𝑉𝑖

Voltage reference model parameter

-10

𝑏𝑚𝑉𝑖

Voltage reference model parameter

-10

𝑎𝑚𝐼𝑖

Current reference model parameter

-100

𝑏𝑚𝐼𝑖

Current reference model parameter

-100

𝛾𝑉𝑖

Voltage adaptation gain

-1000

𝛾𝐼𝑖

Current adaptation gain

-1000

𝑙𝑉𝑖

Voltage feedback gain

-1000

𝑙𝐼𝑖

Current feedback gain

-1000

TABLE III LVAC CONTROL PARAMETERS

Symbol

QUANTITY

Values

𝑘𝑝,𝑉

Voltage control proportional gain

0

𝑘𝑖,𝑉

Voltage control integral gain

5

𝑘𝑝,𝑃

Active power control proportional gain

0.003

𝑘𝑖,𝑃

Active power control integral gain

0.001

𝑘𝑝,𝑄

Reactive power control proportional gain

0.015

𝑘𝑖,𝑄

Reactive power control integral gain

1

𝑘𝑝,⍵

Frequency control proportional gain

0

𝑘𝑖,⍵

Frequency control integral gain

1

𝐿𝑣𝑖𝑟

Virtual impedance (mH)

0.2

- Initially, the loading condition was as 𝐼PMM1 = 833 A, 𝐼PMM2 = 833 A, and 𝐼EMRG = 0 A. - At t = 5 s, the inverter of IPNC changed power consumption from 480 kW – 45 kVA to 960 kW – 103 kVA. - At t = 10 s, PMM modules changed the power consumption as 𝐼PMM1 and 𝐼PMM2 each ramped up the power at 120 A/s.  From time t = 15 – 50 s: - PGM changed the current sharing ratio to 𝐼𝑃𝐺𝑀1 : 𝐼𝑃𝐺𝑀2 : 𝐼𝑃𝐺𝑀3 : 𝐼𝑃𝐺𝑀4 = 2: 2: 1: 1. - IPMM1 and IPMM2 continued to ramp up the power at 120 A/s to settle at 2040 A. - At t = 30 s, EMRG is fired with a pulse of 1 s - 20 MW pulse every 6 s

4

Fig. 5. MVDC current profile of gas generators. (a) Increase Zonal load power by 2.88 MW, (b) Change current sharing ratio among generators, (c) Activate 20 MW – 1s period EMRG, (d) Fail one gas generator (PGM4), (e) 20 MW EMRG with three remaining generators.

Fig. 6. MVDC voltage profile of gas generators. (a) Increase Zonal load power by 2.88 MW, (b) Change current sharing ratio among generators, (c) Activate 20 MW – 1s period EMRG, (d) Fail one gas generator (PGM4), (e) 20 MW EMRG with three remaining generators.

- At t = 40 s, PGM4 failed and was disconnected from the bus. The controller of PGM4 also stopped exchanging information with its neighbors. The results showing the responses in the MVDC network for the previous cases are shown in Fig. 5 and Fig. 6, and the responses of LVAC network for zone 1 and zone 2 are shown in Fig. 7

IV. DISCUSSION Fig. 5a shows that the current sharing ratio was well maintained at the predefined ratio as each PGM changed the current supplying from 480 A to 540 A without an overshoot. The bus voltages dropped by 2% and then are recovered to the nominal value after 0.3 s (Fig. 6a). At 15 s, as the current sharing change the ratio, there was an a 45% overshoot in the current response before reaching to the

5

(a)

(b)

(c)

(d)

5e). The bus voltages also exhibited a worse response with 15% overshoot and 15% undershoot. However, the system was still stable with the normal operation afterward (Fig. 6e). In the LVAC network, the equally active and reactive power sharing between zone 1 and zone 2 are maintained from 480 kW, 45 kVA to 960 kW, 103 kVA (Fig. 7a,b). The power requirement change at 5 s caused a 0.25% undershoot in the frequency response and 9% undershoot in the system voltage; however, the system frequency and system voltage were recovered to their nominal value after 0.1 s, and 1 s respectively (Fig. 7c,d). These test cases have proved the effectiveness of the distributed control algorithm for MVDC-LVAC network with a varying scenario, where high power devices are engaged in the verification process. V. CONCLUSION In this paper, we presented the design and implementation of the distributed control algorithms for MVDC and LVAC network. The effects of LVAC on the MVDC with a transient case were observed. Moreover, the effects of high power devices (PMM and EMRG) on the MVDC system were also observed with a failure case in PGM4 . The case studies and analysis validated the effectiveness of the distributed control implementation. ACKNOWLEDGEMENT This material is based upon research supported by, or in part by, the U.S. Office of Naval Research under award number N00014-16-1-2956. REFERENCES D. T. Rigterink, R. Ames, A. Gray, and N. Doerry, “Early-Stage Assessment of the Impacts of Next Generation Combat Power and Energy Systems on Navy Ships,” ASNE AMTS 2016, 2016. [2] T. V Vu, D. Perkins, F. Diaz, D. Gonsoulin, C. S. Edrington, and T. ElMezyani, “Robust adaptive droop control for DC microgrids,” Electr. Power Syst. Res., vol. 146, pp. 95–106, May 2017. [3] T. V. Vu, S. Paran, F. Diaz-Franco, T. El-Mezyani and C. S. Edrington, "An Alternative Distributed Control Architecture for Improvement in the Transient Response of DC Microgrids," in IEEE Transactions on Industrial Electronics, vol. 64, no. 1, pp. 574-584, Jan. 2017. [4] T. Dragicevic, J. M. Guerrero, and J. C. Vasquez, "A Distributed Control Strategy for Coordination of an Autonomous LVDC Microgrid Based on Power-Line Signaling," IEEE Trans. Ind. Electron., vol. 61, no. 7, pp. 3313–3326, July 2014. [5] V. Nasirian, A. Davoudi, F. L. Lewis and J. M. Guerrero, "Distributed Adaptive Droop Control for DC Distribution Systems," in IEEE Transactions on Energy Conversion, vol. 29, no. 4, pp. 944-956, Dec. 2014. [6] A. Bidram and A. Davoudi, "Hierarchical Structure of Microgrids Control System," in IEEE Transactions on Smart Grid, vol. 3, no. 4, pp. 19631976, Dec. 2012. [7] N. Doerry and J. Amy "MVDC Shipboard Power System Considerations for Electromagnetic Railguns". 6th DoD Electromagnetic Railgun Workshop, Laurel MD, Sept 15-16, 2015 (2015B). [8] X. Liu, P. Wang and P. C. Loh, "A Hybrid AC/DC Microgrid and Its Coordination Control," in IEEE Transactions on Smart Grid, vol. 2, no. 2, pp. 278-286, June 2011. [9] N. Eghtedarpour and E. Farjah, "Power Control and Management in a Hybrid AC/DC Microgrid," in IEEE Transactions on Smart Grid, vol. 5, no. 3, pp. 1494-1505, May 2014. [10] J. M. Guerrero, J. C. Vasquez, J. Matas, L. G. de Vicuna and M. Castilla, "Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization," in IEEE Transactions on Industrial Electronics, vol. 58, no. 1, pp. 158-172, Jan. 2011. [1]

Fig. 7. LVAC profiles for interconnected Zone 1 and Zone 2. (a) real power sharing,(b) reactive power sharing,(c) system frequency,(d) averaged bus voltage.

new shared current ratio in 0.4 s (Fig. 5b). The voltage recovered back to the nominal value after deviating by 1% after 0.5 s (Fig. 6b). At 30s, EMRG operated, which changed the current consumption at the same desired ratio. The currents of PGM1 and PGM2 changed from 1520 A to 2060 A, and the currents of PGM3 and PGM4 changed from 760 A to 1030 A. The overshoot and undershoot of these currents reach to 20% and 10%, respectively. Additionally, the settling time is 0.8 s (Fig. 5c). The bus voltages had a 20% overshoot and 20% undershoot and then recovered to the nominal value (Fig. 6c). Regarding the failure of PGM4 at 40 s, the current supplying of the other three PGM changed to the different supplying values as PGM1 and PGM2 supplied 1820 A, and PGM3 supplied 910 A (Fig. 5d). The bus voltages had a 10% undershoot but recovered to the nominal value after 0.8 s (Fig. 6d). Because of the failure in the PGM4 and its communication channels, the worst overshoot, which occurred in PGM3 reached to 33% although it was eliminated 0.7 s after the transient (Fig.