1. Introduction
Since ancient times, mankind has never given up on the exploration of the ocean, and the tools for observing the ocean have been constantly innovating, such as the scientific cabled seafloor observatories (CSOs). It is an emerging means of ocean observation that collects continuous real-time data over long periods by laying a regional observing system on the ocean floor.
Since 2006, more and more scientific CSOs have been established around the world for oceanography research, e.g., MARS (Monetary Accelerated Research System) [
1], OOI (Ocean Observatory Initiative) [
2], ALOHA cabled observatory [
3], VENUS (Victoria Experimental Network Under the Sea) [
4], NEPTUNE (North-East Pacific Time-series Underwater Networked Experiment) [
5], DONET (Dense Oceanfloor Network System for Earthquakes and Tsunamis) [
6], S-net (Seafloor observation network for earthquakes and tsunamis along the Japan Trench) [
7], ESONET (European Seas Observatory Network) [
8], Xiaoqushan seafloor observatory [
9] and MACHO (Marine Cable Hosted Observatory) [
10]. Moreover, the East China Sea (ECS) and the South China Sea (SCS) experimental observatories were built in 2015 and 2016, respectively. In 2017, the Chinese national scientific seafloor observatory (CNSSO) was launched to realize the long-term observation of the complex processes operating within the oceans.
In typical scientific CSOs, the shore station converts the alternating current (AC) power from the terrestrial electrical grid into the direct current (DC) power, rated up to −10 kV and delivers it to the undersea stations through backbone cables, branching units (BUs) and spur cables, as shown in
Figure 1 [
11]. A DC/DC converter is installed in each undersea station, converting −10 kV DC power from the spur cable into 375 V DC power for scientific instrument interface modules (SIIMs). The SIIMs convert 375 V DC power into DC power under 48 V required by science instruments (SIs). In this way, the long-distance electrical power transmission and conversion for undersea distributed science payloads are completed.
An undersea DC power system of scientific CSO has a large-scale DC distributed power system (DPS) that contains many cascaded power electronic converters, connected by hundreds to thousands of kilometers of submarine cables [
12]. Each point of load (POL) converter, installed in undersea stations, acts as a constant power load (CPL), and the distributed parameter characteristics of long-distance submarine cables greatly affect the stability of the undersea DC power system [
12,
13,
14,
15]. In the event of instability, the undersea DC power system will oscillate, or even collapse, especially under large disturbance conditions. Because of the harsh subsea environment, CSOs have low accessibility and are very expensive to construct and repair, time-consuming and labor-intensive. Therefore, the stability of the CSO undersea DC power system must be analyzed during design and operation.
At present, there is less stability analysis of the undersea DC power system of CSOs worldwide. In 2006, Dr. Lu analyzed the stability of the NEPTUNE observatory power system, but it was lacking in simulation and experimental verification [
12]. At present, the stability has been studied in small-scale DC DPSs, e.g., space stations, aircraft, ships and electric vehicles [
15,
16,
17,
18,
19]. Compared to these DC DPSs, the undersea DC power system of scientific CSOs are more complicated, mainly because of the long-distance submarine cables.
This paper focuses on the large-signal stability of the CSO undersea DC power system, which is a high-order nonlinear system. Large-signal stability means that the power system can go back to its original equilibrium state or transition to a new equilibrium state, after encountering a large disturbance during normal operating conditions [
20]. For second or lower-order nonlinear systems, large-signal stability analysis can use the phase plane method [
19]. For higher-order nonlinear systems, large-signal stability analysis can be performed by the Lyapunov direct method [
20], the key of which is to construct a suitable Lyapunov function. Various approaches have been proposed to produce Lyapunov functions, e.g., the Brayton–Moser mixed potential function method [
21,
22], the Takagi–Sugeno multi-modeling method [
23], genetic algorithm methods [
24] and the reverse trajectory tracking method [
25]. The literature [
26] compares the above several methods. The Takagi–Sugeno multi-modeling method uses multiple linear models to fit nonlinear models, and is not suitable for higher-order nonlinear systems. The Brayton–Moser mixed potential function method needs to find the voltage and current potential functions, which is conservative. The genetic algorithm method requires an artificial neural network toolbox and selects appropriate parameters. The reverse trajectory tracking method can only be represented by an image, and the analytical expression cannot be obtained. In this paper, the mixed potential function method is applied to consider the effect of long-distance submarine cables on the power system large-signal stability, and the equivalent circuits of a long-distance submarine cable are built. Based on this, the equivalent topology model of a single-node CSO undersea DC power system is established. Considering the characteristics of long-distance submarine cables, the large-signal stability of the single-node CSO undersea DC power system is analyzed by the mixed potential function method, and the large-signal stability criterion is obtained. The large-signal stability criterion is verified by computer simulations and experiments, and the factors affecting the large-signal stability of the CSO undersea DC power system are analyzed by simulations and experiments, which is of great significance to the design, operation and future development of the CSO undersea DC power system.
The remainder of the paper is divided as follows.
Section 2 introduces the equivalent circuits of a long-distance submarine cable.
Section 3 analyses the steady-state equilibrium point and the large-signal stability criterion of the CSO undersea DC power system.
Section 4 simulates and experiments on the large-signal stability of CSO undersea DC power systems.
Section 5 summarizes the conclusion and anticipates further research on this topic.
2. The Equivalent Circuits of a Long-distance Submarine Cable
In scientific CSOs, submarine electro-optic cables are used to transmit electrical power to the seafloor, and mainly consist of the insulating sheath, the composite conductor, the steel wires strand, the steel tube, the thixotropic jelly and optical fibers [
12].
According to the electrical conductivity and radius of different materials in submarine cables, the resistance, inductance and capacitance of per unit length submarine cable can be obtained by theoretical calculation, shown in
Table 1 for a typical submarine cable [
12,
27]. In
Table 1, R
1, L
1 and C
1 represent the resistance, the inductance and the capacitance of 1 km submarine cable, respectively.
The lumped parameter equivalent circuits of long-distance submarine cables are the approximation of the actual distributed characteristics within a certain range. In our studies, multiple π-type lumped parameter models are cascaded to simulate a long-distance submarine cable. The length of each cable segment represented by a π-type lumped parameter model, as shown in
Figure 2, will affect the accuracy of the equivalent circuits of a submarine cable.
The two-port network of a submarine cable can be expressed as
where
f is the characteristic frequency of the undersea DC power system,
f = 1 kHz in our study.
ω is the angular velocity of the undersea DC power system.
l is the overall length of the submarine cable.
R,
L,
G and
C are corresponding to the equivalent resistance, inductance, conductance and capacitance of the submarine cable, respectively. The insulation resistance of submarine cables is very high, so that the conductance between the copper conductor and the seawater can be negligible, that is,
G = 0.
z and
y are the impedance and admittance of per unit length submarine cable, respectively.
ZC is the wave impedance.
γ is the propagation coefficient.
When
γl << 1,
Z and
Y can be expressed approximately as
In order to study the influence of the cable segment length on the model accuracy, the two-port network model of the submarine cable is regarded to be accurate as a reference, and the π-type lumped parameter models of different cable segment lengths are taken as approximations. The comparison of the two-port network and lumped parameter model under different cable segment lengths are shown in
Table 2. When multiple π-type lumped parameter models are cascaded to simulate a long-distance submarine cable, the longer the cable segment represented by each π-type equivalent circuit, the greater the model parameter error is between the actual submarine cable characteristics and the equivalent circuits.
Computer simulation is performed by using MATLAB. The simulation file is shown in
Figure 3. The output voltage of the shore station power feeding equipment (PFE) is 10 kV, and the rising time of the output voltage is 1 ms. The length of the submarine cable is 200 km, and the load is 200 Ω.
The simulation results are shown in
Figure 4. The red line indicates the distributed parameter model of the submarine cable, closest to the actual submarine cable characteristics. The blue, orange, purple and green lines indicate the lumped parameter models of the submarine cable, formed by cascaded 200, 100, 40 and 20 π-type lumped parameter equivalent circuits, respectively. Each π-type lumped parameter model represents 1 km, 2 km, 5km or 10 km submarine cable segment.
Taking the red line as a reference, it can be seen that the differences between the blue, orange and red lines are small, and the errors are less than 0.5%. The difference between the purple and red lines is larger, and the error is about 1.5%. The difference between the green and red lines is even larger, and the error is about 6%. It shows that the shorter the submarine cable segment represented by each π-type lumped parameter equivalent circuit, the smaller the difference between the lumped and distributed parameter models, which is consistent with the results of the above theoretical analysis.