# Large-Signal Stability Analysis of the Undersea Direct Current Power System for Scientific Cabled Seafloor Observatories

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## Abstract

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## Featured Application

**This technology provides a feasible approach for analyzing and improving the large-signal stability of the undersea direct current power system for scientific cabled seafloor observatories. It is of great significance for the design, construction, operation and maintenance of the cabled seafloor observatories.**

## Abstract

## 1. Introduction

## 2. The Equivalent Circuits of a Long-distance Submarine Cable

_{1}, L

_{1}and C

_{1}represent the resistance, the inductance and the capacitance of 1 km submarine cable, respectively.

_{C}is the wave impedance. γ is the propagation coefficient.

## 3. Theoretical Analysis of Undersea DC Power System Stability

#### 3.1. Steady-State Equilibrium Point

_{S}represents the output voltage of the shore station PFE. R

_{0}, L

_{0}and C

_{0}represent the resistance, inductance and capacitance of a cable segment, respectively. P

_{L}, U

_{L}and I

_{L}represent the power consumption, input voltage and input current of the undersea station, respectively, and n represents the number of submarine cable segments.

#### 3.2. Mixed Potential Function Method

_{n}and C

_{n}are diagonal arrays of branch inductance and branch capacitance, respectively. So,

_{1}and μ

_{2}must satisfy Equations (20) and (21), i.e.,

## 4. Simulation and Experiment

#### 4.1. Large-Signal Stability Simulations of a Single-Node CSO Undersea DC Power System

_{S}represents the output voltage of the source, i.e., the shore station PFE. R

_{0}, L

_{0}, and C

_{0}represent the resistance, inductance and capacitance of a cable segment, respectively. P

_{L}represents the power consumption of the CPL, i.e., the undersea station with external science payloads.

_{S}in the system is 0 V. At 0.1 s, according to experimental needs, the voltage rises from 0 V to 400 V or 350 V, and the voltage and current transient processes are generated. The simulation results are shown in Figure 8. The blue line indicates the output voltage of the shore station PFE. The green line indicates the voltage in the middle section of the submarine cable. The orange line indicates the input voltage of the undersea station. The red line indicates the output current of the shore station PFE.

#### 4.2. Large-Signal Stability Experiments of a Single-Node CSO Undersea DC Power System

_{S}represents the output voltage of the AC/DC converter. R

_{0}, L

_{0}and C

_{0}represent the resistance, inductance and capacitance of a cable segment respectively. P

_{L}represents the power consumption of the DC/DC converter with the electronic load.

#### 4.3. Large-Signal Stability Simulations of a Multi-Node CSO Undersea DC Power System

_{S}represents the output voltage of the source, i.e., the shore station PFE. R

_{0}, L

_{0}and C

_{0}represent the resistance, inductance and capacitance of a cable segment, respectively. P

_{L}represents the power consumption of the CPL4, i.e., the undersea station with external science payloads. The power consumption of the four CPLs is equal.

_{S}in the system was 0 V. At 0.1 s, according to experimental needs, the voltage rose from 0 V to 10 kV or 6 kV, and the voltage transient processes were generated.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

DC | direct current | G | conductance |

CSO | cabled seafloor observatory | R_{1} | the resistance of 1 km submarine cable |

PFE | power feeding equipment | L_{1} | the inductance of 1 km submarine cable |

MARS | Monetary Accelerated Research System | C_{1} | the capacitance of 1 km submarine cable |

OOI | Ocean Observatory Initiative | f | the characteristic frequency of the undersea DC power system |

VENUS | Victoria Experimental Network Under the Sea | ω | the angular velocity of the undersea DC power system |

NEPTUNE | North-East Pacific Time-series Underwater Networked Experiment | l | the overall length of the submarine cable |

DONET | Dense Oceanfloor Network System for Earthquakes and Tsunamis | Z_{C} | the wave impedance |

S-net | Seafloor observation network for earthquakes and tsunamis along the Japan Trench | γ | the propagation coefficient |

ESONET | European Seas Observatory Network | z | the impedance of per unit length submarine cable |

MACHO | Marine Cable Hosted Observatory | y | the admittance of per unit length submarine cable |

ECS | East China Sea | Z | the impedance of a submarine cable segment |

SCS | South China Sea | Y | the admittance of a submarine cable segment |

CNSSO | Chinese national scientific seafloor observatory | U_{S} | U_{S} represents the output voltage of the shore station. |

AC | alternating current | R_{0} | the resistance of a cable segment |

BU | branching unit | L_{0} | the inductance of a cable segment |

SIIM | scientific instrument interface module | C_{0} | the capacitance of a cable segment |

SI | science instrument | P_{L} | the power consumption of the undersea station |

DPS | distributed power system | U_{L} | the input voltage of the undersea station |

POL | point of load | I_{L} | the input current of the undersea station |

CPL | constant power load | n | the number of submarine cable segments |

i | current | P(i,u) | the mixed potential function |

u | voltage | −A(i) | the current potential function of some non-energy storage elements in the circuit |

t | time | B(u) | the voltage potential function of non-energy storage elements in the circuit |

μ_{1} | minimum value | D(i,u) | the energy of capacitors and part of non-energy storage elements in the circuit |

μ_{2} | minimum value | P_{u} | partial derivative of P to u |

M | matrix | P_{i} | partial derivative of P to i |

λ(M) | the eigenvalue of the matrix M | A_{ii}(i) | the second derivative test of A(i) to i |

−R_{L} | the dynamic negative impedance of the CPL | B_{uu}(u) | the second derivative test of B(u) to u |

R | resistance | L_{n} | diagonal arrays of branch inductance |

L | inductance | C_{n} | diagonal arrays of branch capacitance |

C | capacitance |

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**Figure 7.**The Saber file for the large-signal stability simulation of a single-node CSO undersea DC power system.

**Figure 8.**(

**a**) The voltage transient processes in the parameter set #1; (

**b**) the current transient processes in the parameter set #1; (

**c**) the voltage transient processes in the parameter set #2; (

**d**) the current transient processes in the parameter set #2; (

**e**) the voltage transient processes in the parameter set #3; (

**f**) the magnified view of voltage transient processes in the parameter set #3; (

**g**) the voltage transient processes in the parameter set #4; (

**h**) the voltage transient processes in the parameter set #5.

**Figure 10.**(

**a**) The voltage transient processes in the parameter set #1; (

**b**) the current transient processes in the parameter set #1; (

**c**) the voltage transient processes in the parameter set #2; (

**d**) the current transient processes in the parameter set #2; (

**e**) the voltage transient processes in the parameter set #3; (

**f**) the current transient processes in the parameter set #3; (

**g**) the voltage transient processes in the parameter set #4; (

**h**) the current transient processes in the parameter set #4; (

**i**) the voltage transient processes in the parameter set #5; (

**j**) the current transient processes in the parameter set #5.

**Figure 11.**The Saber file for the large-signal stability simulation of a multi-node CSO undersea DC power system.

Parameters | R_{1} | L_{1} | C_{1} |
---|---|---|---|

Values | 1 Ω | 0.4 mH | 0.2 μF |

**Table 2.**The comparison of the two-port network and the lumped parameter model under different cable segment lengths.

f = 1 kHz | Z (Two-Port Network) | Z (Lumped Model) | Y (Two-Port Network) | Y (Lumped Model) |
---|---|---|---|---|

l = 1 km | 1.00 + 2.51i | 1.00 + 2.51i | 1.32 × 10^{−7} + 1.26i × 10^{−3} | 1.26i × 10^{−3} |

l = 2 km | 1.99 + 5.02i | 2.00 + 5.03i | 1.06 × 10^{−6} + 2.52i × 10^{−3} | 2.51i × 10^{−3} |

l = 3 km | 2.97 + 7.51i | 3.00 + 7.54i | 3.57 × 10^{−6} + 3.78i × 10^{−3} | 3.77i × 10^{−3} |

l = 4 km | 3.93 + 9.98i | 4.00 + 10.05i | 8.51 × 10^{−6} + 5.05i × 10^{−3} | 5.03i × 10^{−3} |

l = 5 km | 4.87 + 12.43i | 5.00 + 12.57i | 1.67 × 10^{−5} + 6.33i × 10^{−3} | 6.28i × 10^{−3} |

l = 6 km | 5.77 + 14.84i | 6.00 + 15.08i | 2.91 × 10^{−5} + 7.61i × 10^{−3} | 7.54i × 10^{−3} |

l = 7 km | 6.64 + 17.21i | 7.00 + 17.59i | 4.66 × 10^{−5} + 8.91i × 10^{−3} | 8.80i × 10^{−3} |

l = 8 km | 7.47 + 19.54i | 8.00 + 20.11i | 7.02 × 10^{−5} + 1.00i × 10^{−}^{2} | 1.00i × 10^{−}^{2} |

l = 9 km | 8.25 + 21.81i | 9.00 + 22.62i | 1.01 × 10^{−4} + 1.10i × 10^{−}^{2} | 1.10i × 10^{−}^{2} |

l = 10 km | 8.97 + 24.03i | 10.00 + 25.13i | 1.40 × 10^{−4} + 1.30i × 10^{−}^{2} | 1.30i × 10^{−}^{2} |

Parameters | U_{S} | n | R_{0} | L_{0} | C_{0} | P_{L} |
---|---|---|---|---|---|---|

Values | 400 V | 36 | 10 Ω | 4 mH | 2 µF | 84 W |

**Table 4.**Five Saber parameter sets for large-signal stability simulation of a single-node CSO undersea DC power system.

No. | U_{S}/V | P_{L}/W | R_{0}/Ω | L_{0}/mH | C_{0}/µF |
---|---|---|---|---|---|

#1 | 400 | 84 | 10 | 4 | 2 |

#2 | 400 | 84 | 10 | 400 | 2 |

#3 | 400 | 84 | 10 | 4 | 0.0164 |

#4 | 350 | 84 | 10 | 4 | 2 |

#5 | 400 | 112 | 10 | 4 | 2 |

No. | U_{S}/V | P_{L}/W | R_{0}/Ω | L_{0}/mH | C_{0}/µF |
---|---|---|---|---|---|

#1 | 400 | 82.29 | 10.2 | 4 | 2.03 |

#2 | 400 | 82.29 | 10.5 | 400 | 2.03 |

#3 | 400 | 82.29 | 10.2 | 4 | 0.016 |

#4 | 350 | 82.29 | 10.2 | 4 | 2.03 |

#5 | 400 | 96 | 10.2 | 4 | 2.03 |

**Table 6.**Five Saber parameter sets for large-signal stability simulation of a multi-node CSO undersea DC power system.

No. | U_{S}/kV | P_{L}/kW | R_{0}/Ω | L_{0}/mH | C_{0}/µF |
---|---|---|---|---|---|

#1 | 10 | 10 | 10 | 4 | 2 |

#2 | 10 | 10 | 10 | 4000 | 2 |

#3 | 10 | 10 | 10 | 4 | 0.001 |

#4 | 6 | 10 | 10 | 4 | 2 |

#5 | 10 | 50 | 10 | 4 | 2 |

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**MDPI and ACS Style**

Jiang, Y.; Lyu, F.
Large-Signal Stability Analysis of the Undersea Direct Current Power System for Scientific Cabled Seafloor Observatories. *Appl. Sci.* **2019**, *9*, 3149.
https://doi.org/10.3390/app9153149

**AMA Style**

Jiang Y, Lyu F.
Large-Signal Stability Analysis of the Undersea Direct Current Power System for Scientific Cabled Seafloor Observatories. *Applied Sciences*. 2019; 9(15):3149.
https://doi.org/10.3390/app9153149

**Chicago/Turabian Style**

Jiang, Yamei, and Feng Lyu.
2019. "Large-Signal Stability Analysis of the Undersea Direct Current Power System for Scientific Cabled Seafloor Observatories" *Applied Sciences* 9, no. 15: 3149.
https://doi.org/10.3390/app9153149