Availability-Based Selection of Electricity Delivery Network in Marine Conversion Systems Using Bayesian Network Availability-Based Selection of Electricity Delivery Network in Marine Conversion Systems Using Bayesian Network

: Availability is an economically important metric used to assess the design of marine energy farms. Nowadays, three typical concepts of energy delivery network topologies have been proposed for marine energy conversion systems. Few research works assessing the availability of marine energy conversion systems have been published. Their methodology is only based upon time-consuming Monte Carlo simulations and only covers one maintenance strategy. The objective of this study is to consider different maintenance strategies and quantitatively assess the time-dependent availability of these typical energy delivery network topologies by investigating the working philosophy of these topologies and modelling the logic dependencies of them in a Bayesian network (BN). The working philosophy of each topology is investigated to obtain the logic dependencies of the units in the energy delivery network, by means of qualitative system analysis. A table-like data structure, called hierarchy, is introduced to store the information on the logic dependencies and serves as a basis for establishing the corresponding BN models. A logic gate in the hierarchy can be represented by a conditional probability table in the BN model. The availability of these topologies, as a function of time, can be estimated through the BN models. The optimal topology can be selected, based upon the time-dependent availability. Abstract: Availability is an economically important metric used to assess the design of marine energy farms. Nowadays, three typical concepts of energy delivery network topologies have been proposed for marine energy conversion systems. Few research works assessing the availability of marine energy conversion systems have been published. Their methodology is only based upon time-consuming Monte Carlo simulations and only covers one maintenance strategy. The objective of this study is to consider different maintenance strategies and quantitatively assess the time-dependent availability of these typical energy delivery network topologies by investigating the working philosophy of these topologies and modelling the logic dependencies of them in a Bayesian network (BN). The working philosophy of each topology is investigated to obtain the logic dependencies of the units in the energy delivery network, by means of qualitative system analysis. A table-like data structure, called hierarchy, is introduced to store the information on the logic dependencies and serves as a basis for establishing the corresponding BN models. A logic gate in the hierarchy can be represented by a conditional probability table in the BN model. The availability of these topologies, as a function of time, can be estimated through the BN models. The optimal topology can be selected, based upon the time-dependent availability.


Introduction
An ever-increasing demand in energy around the world has drawn the attention of entrepreneurs to clean energy resources. Marine energy, as a resource of clean energy, has seen potential to compete with the traditional fossil fuels [1][2][3]. A wide range of prototypes of converters have been invented and deployed in near-shore areas for the demonstration purposes [4,5]. According to the categorization scheme in IEC 62600-2 [6], the marine energy conversion system (MEC) represents the electrical subsystem, as shown in Figure 1. Generally, the electrical subsystem refers to the energy delivery network.

Introduction
An ever-increasing demand in energy around the world has drawn the attention of entrepreneurs to clean energy resources. Marine energy, as a resource of clean energy, has seen potential to compete with the traditional fossil fuels [1][2][3]. A wide range of prototypes of converters have been invented and deployed in near-shore areas for the demonstration purposes [4,5]. According to the categorization scheme in IEC 62600-2 [6], the marine energy conversion system (MEC) represents the electrical subsystem, as shown in Figure 1. Generally, the electrical subsystem refers to the energy delivery network. Compared to wind industry, the marine energy conversion system is a premature industry. There are very few investigations into the availability of energy delivery networks of marine energy systems. These typical research outcomes related to availability   Compared to wind industry, the marine energy conversion system is a premature industry. There are very few investigations into the availability of energy delivery networks of marine energy systems. These typical research outcomes related to availability of marine energy systems will be only reviewed to find out the gap between the available research outcomes and what can be improved in the future.

Introduction on Typical Energy Network Topologies
The typical energy delivery network topologies are three typical design solutions in an EU-sponsored project, i.e., DTOceanPlus. This project aims to design tools for the selection, development, deployment and assessment of ocean energy systems. Three typical energy delivery network topologies refer to Radial, Star and Direct [10]. Graphical examples of these energy delivery network topologies are shown in Figures 2-4, respectively. The symbols in the brackets represent the labels of the nodes in the BN models.
The notations in Figures 2-4 are explained as follows: • "AC" represents array cable; • "Connection" represents either: a connector in the case of a fixed device or an umbilical and its connectors for floating devices; • "CP" represents the collection point. There are six devices in these network topologies for the demonstration purpose; • "EC" represents the export cable.
A connection refers to a connector connecting an array cable and a device (or called marine energy converter). An array cable refers to a cable connecting different devices or a device and a connection point. An export cable refers to a cable transmitting the power from an array to the on-shore terminal.
A collection point acts as a hub or a substation, or both. Each collection point could be a switchgear, transformer, or power quality/conditioning equipment. Two typical collection point solutions may be on the free water surface or mounted on the seabed.

Bayesian Network Formulation
This section mainly describes the key aspects for assessing the availability using Bayesian networks, with the focus on improvements of the BN models compared to that used in [12]. The key aspects include: • Bayesian network structure for the system: Calculate the current availability of the system given the current state of the basic components; • Dynamic Bayesian network for calculation of time-dependent availability; • Implementing repairs through decision rules.

Bayesian Network Structure for the System
The aim of this step is to establish a logic Bayesian network model for the calculation of the system availability based on the current state of the basic components. The logic dependencies of the units identified through qualitative system analysis can provide enough information to establish this part of the BN model. A logic gate in the hierarchy can be represented by a conditional probability table in the BN model. In most engineering applications, the 'gate' can be either 'OR', 'AND' or 'k/N' (also called vote gate in some textbooks). With no loss of generality, the nodes underneath the gate are called input, and the node above it is called output. 'OR' means that if any input to the gate fails, the output fails. 'AND' means that if all the inputs to the gate fail, the output fails. 'k/N' means that if either k out of N inputs fail, the output fails. Here we will exploit the logic relations to estimate the availability.
The system availability is 100% if energy from all N devices in the system is transmitted to the terminal; if energy from n components is transmitted, the availability is n/N. In Figures 2-4, the relations between the basic components in the systems are illustrated. All nodes for basic components have two states: 0-faulty, or 1-healthy. The system availability is calculated based on the node T0 which have N + 1 states, and indicates the number of devices for which energy is transmitted to the terminal. To establish a Bayesian network for assessment of the system availability, it is convenient to define sub-assemblies. For sub-assemblies, the state correspond to the number of devices for which energy is transmitted. For example, a sub-assembly with three connected devices have four possible states: 0, 1, 2, 3, as defined in Table 1. The Bayesian network structure is defined in terms of the hierarchy of the nodes. As an example we will consider a simple structure with three basic components, X1, X2 and X3. X1 and X2 both have a device connected. They are connected in parallel, and together they form the sub-assembly T1. This corresponds to an 'AND' gate. For AND gates, the number of working devices of the parents are added together to get the number of working units. Sub-assembly T1 and component X3 are connected in series, which correspond to an 'OR' gate. For OR gates, the number of working units of the child is zero if it is zero for any of the parents. In Section 4, the actual hierarchies will be shown.

Dynamic Bayesian Network Models
With the aim of investigating the time-dependent availability, the dynamic BN model will be used in this study. The concept, time slice, should be introduced. The continuous design lifetime is split into some discretized time intervals for which the probabilities of different states of the energy delivery network topology are assessed. Each of these time intervals is called a time slice, which could refer to 1 day, 1 week, 1 month, 1 year, etc.

Conditional Probability Tables
In this section, how to define temporal condition probabilities will be presented. Initially, all the basic components are in healthy state, which means the state of the temporal clone of the nodes representing the basic components is 1.
The temporal conditional probabilities depend upon the state of the energy delivery network in the previous time slice and the pre-chosen decision rule. With the aim of taking into account these effects, a temporal clone of the node representing the energy delivery network and a node representing the repair option should be created. The node representing the repair option has two states, namely '0'-no repair; or '1'-repair. The state of the node representing the repair option depends upon the state of the energy delivery network in the previous time slice.
With no loss of generality, a single basic component, R1, is used to demonstrate how to define the temporal conditional probabilities. The time to failure (TTF) of the basic component k is assumed to follow the exponential distribution, with a constant failure rate of λ k . ∆t denotes the time interval between two time slices. The subscripts i and i + 1 represent two consecutive time slices.
If no repair is required between two consecutive time slices, the conditional probabilities are given as follows: If repair is required between two consecutive time slices, the conditional probabilities are given as follows: The decision rules can be implemented through a repair node in the BN model. This repair node is a child of the node representing the energy delivery network. The state of this system node in time slice i determines that of the repair node in time slice i + 1. See Supplementary Materials for the CPTs of the repair node.

Decision Rules
For the energy transfer subsystem composed of M converters, the decision rules can be defined from the perspective of effective energy production. A decision rule pre-defines which maintenance activities should be taken when a certain amount of devices shut down.
It is assumed that there is a threshold ratio of the full energy production, k. A maintenance team should be dispatched to repair the damaged components when the monitored energy production is less than k% of the full energy production. Figure 5 demonstrates which activity should be done in which decision rule for which failure scenario. For example, it is required in Decision Rule 2 that if two out of M devices malfunction, namely the energy loss is (200/M)%, the damaged components causing such an energy loss should be repaired as soon as possible.
Energies 2021, 14, x FOR PEER REVIEW 6 of pre-defines which maintenance activities should be taken when a certain amount of d vices shut down. It is assumed that there is a threshold ratio of the full energy production, k. maintenance team should be dispatched to repair the damaged components when th monitored energy production is less than k% of the full energy production. Figure demonstrates which activity should be done in which decision rule for which failur scenario. For example, it is required in Decision Rule 2 that if two out of M devices ma function, namely the energy loss is (200/M)%, the damaged components causing such a energy loss should be repaired as soon as possible.

Network Topologies
Three typical energy delivery network topologies in the project DTOceanPlus, wit the sketches shown in Figures 2-4, are used for this case study. Due to no tailor-mad reliability database for marine energy converters, the failure rates of the basic compo nents can be referred to a generic database for electrical components in other industri applications [13,14] and also should be subject to engineering judgement. The failur rates to be used are given in Table 2.

Network Topologies
Three typical energy delivery network topologies in the project DTOceanPlus, with the sketches shown in Figures 2-4, are used for this case study. Due to no tailor-made reliability database for marine energy converters, the failure rates of the basic components can be referred to a generic database for electrical components in other industrial applications [13,14] and also should be subject to engineering judgement. The failure rates to be used are given in Table 2.

Logic Dependencies of the Topologies
The logic dependencies are defined in a table-like data format. The advantages are: • the system structure and the interrelationship between units at different level can be clearly represented without a long description. • such a data structure is self-explanatory and can be easily implemented in computer code.
Besides the table-formatted hierarchy, the interrelationship between units on the topmost level in the hierarchy will be briefly interpreted with text for each topology in the following sub-sections.
The hierarchies of the Radial, Star, and Direct topology are defined in Tables 3-5

Bayesian Network Models
Hugin Expert [15], used for Bayesian inference, provides an independent interface for Python to construct the BN models, which is more efficient than manual operations of drawing BNs in the Hugin graphical user interface. The dynamic BN models of the three energy delivery network topologies are shown in Figures 6-8, respectively. The arrows pointing from nodes in time slice i to the same nodes in time slice i + 1 should be drawn to explicitly represent the temporal dependencies. However, due to a large number of nodes, the readability will be unfavourably affected if too many arrows are shown on the same figure. Therefore, three overlapped boxes approximately represent the temporal dependencies. The implicit temporal clones of the nodes corresponding to the basic components can be represented by Ti.xx. "Ti" indicates the time slice i, and "xx" is the node label. In Figures 6-8, the initial temporal clones of nodes are only shown (the prefix, "T0" in front of the nodes corresponding to the basic components). The T0 in "T0.xx" is a symbol representing the initial time slice. It should be differentiated from the node T0 representing the energy delivery system. Hugin Expert [15], used for Bayesian inference, provides an independent interfac for Python to construct the BN models, which is more efficient than manual operations o drawing BNs in the Hugin graphical user interface. The dynamic BN models of the thre energy delivery network topologies are shown in Figures 6-8, respectively. The arrow pointing from nodes in time slice i to the same nodes in time slice i + 1 should be drawn t explicitly represent the temporal dependencies. However, due to a large number o nodes, the readability will be unfavourably affected if too many arrows are shown on th same figure. Therefore, three overlapped boxes approximately represent the tempora dependencies. The implicit temporal clones of the nodes corresponding to the bas components can be represented by Ti.xx. "Ti" indicates the time slice i, and "xx" is th node label. In Figures 6-8, the initial temporal clones of nodes are only shown (the prefi "T0" in front of the nodes corresponding to the basic components). The T0 in "T0.xx" is symbol representing the initial time slice. It should be differentiated from the node T representing the energy delivery system.
The criterion for choosing a time interval between slices should depend upon th actual maintenance interval adopted by the owners. As mentioned in Section 1, the ma rine energy industry is still at a pre-mature stage. However, the operating experience o the wind industry can be borrowed. Generally, wind turbine owners have both long-term and short-term maintenance plans. The short-term maintenance is usually planned on monthly basis. Therefore, the time interval between slices is one month. With considera tion of a 20-year design lifetime, there are 240 time slices in the dynamic BN model.  The criterion for choosing a time interval between slices should depend upon the actual maintenance interval adopted by the owners. As mentioned in Section 1, the marine energy industry is still at a pre-mature stage. However, the operating experience of the wind industry can be borrowed. Generally, wind turbine owners have both long-term and short-term maintenance plans. The short-term maintenance is usually planned on a monthly basis. Therefore, the time interval between slices is one month. With consideration of a 20-year design lifetime, there are 240 time slices in the dynamic BN model.

Calculation of Time-Dependent Availability
Based upon the improved BN models, the time-dependent availability has been calculated for the three network topologies (see Figures 9-11). The computational time can be significantly shortened if the improved BN model is used. For the direct and radial network topologies, it only takes around 20 s to obtain the results for all time slices. For the star topology, it takes about 15 min. The original method in [12] took about 1 h for 1000 simulations.

Calculation of Time-Dependent Availability
Based upon the improved BN models, the time-dependent availability has been calculated for the three network topologies (see Figures 9-11). The computational time can be significantly shortened if the improved BN model is used. For the direct and radial network topologies, it only takes around 20 s to obtain the results for all time slices. For the star topology, it takes about 15 min. The original method in [12] took about 1 h for 1000 simulations.

Calculation of Time-Dependent Availability
Based upon the improved BN models, the time-dependent availability has been calculated for the three network topologies (see Figures 9-11). The computational time can be significantly shortened if the improved BN model is used. For the direct and radial network topologies, it only takes around 20 s to obtain the results for all time slices. For the star topology, it takes about 15 min. The original method in [12] took about 1 h for 1000 simulations.     The generic trend shown in these figures is: • The availability remains close to 100% (greater than 99%) if Decision rule 1 is chosen; this agrees with the engineering prediction, because Decision rule 1 indicates that repair must be done immediately if any basic component fails; the energy delivery network is almost always in a fully rated state and the system availability should remain close to 100%.    The generic trend shown in these figures is: • The availability remains close to 100% (greater than 99%) if Decision rule 1 is chosen; this agrees with the engineering prediction, because Decision rule 1 indicates that repair must be done immediately if any basic component fails; the energy delivery network is almost always in a fully rated state and the system availability should remain close to 100%.   The generic trend shown in these figures is: • The availability remains close to 100% (greater than 99%) if Decision rule 1 is chosen; this agrees with the engineering prediction, because Decision rule 1 indicates that repair must be done immediately if any basic component fails; the energy delivery network is almost always in a fully rated state and the system availability should remain close to 100%. The generic trend shown in these figures is: • The availability remains close to 100% (greater than 99%) if Decision rule 1 is chosen; this agrees with the engineering prediction, because Decision rule 1 indicates that repair must be done immediately if any basic component fails; the energy delivery network is almost always in a fully rated state and the system availability should remain close to 100%.
• For the decision rules other than Decision rule 1, the mean availability decreases with decreasing rate, thus stabilizing over long time. For Decision rules 2 and 3, there is no significant difference in the system availability between these topologies. • For Decision rules 5 and 6, where more energy losses can be allowed, the availability is relatively low, because these decision rules exactly or almost correspond to a corrective maintenance strategy, respectively.
It can be observed from Figures 9 and 10 that: • For Decision rules 2 and 3, the decrease rate becomes slow after around Year 14. This indicates that these decision rules can ensure that the mean system availability stabilizes around a relatively high value in the long term.

•
For the other decision rules, the availability decreases significantly over the design lifetime. A higher number of damaged basic components is allowed, which will definitely lower down the expected system availability.
It can be observed from Figure 11 that: • The Direct topology leads to higher mean availabilities for decision rules 4-6. This makes sense because the Direct topology resembles a parallel system, while Radial and Star topologies are more like a series of parallel systems; if more components are allowed to fail without repair, the parallel system should be able to work at a derated energy delivery level.
In the BN model, the probabilities of different states of the node T0 representing the system are calculated at each time slice. Take Decision Rule 6 for Direct topology as an example. The probabilities of different states as a function of time are shown in Figure 12. • For the decision rules other than Decision rule 1, the mean availability decrease with decreasing rate, thus stabilizing over long time. For Decision rules 2 and there is no significant difference in the system availability between these topologie • For Decision rules 5 and 6, where more energy losses can be allowed, the availabilit is relatively low, because these decision rules exactly or almost correspond to corrective maintenance strategy, respectively.
It can be observed from Figures 9 and 10 that: • For Decision rules 2 and 3, the decrease rate becomes slow after around Year 14. Th indicates that these decision rules can ensure that the mean system availability st bilizes around a relatively high value in the long term.

•
For the other decision rules, the availability decreases significantly over the desig lifetime. A higher number of damaged basic components is allowed, which w definitely lower down the expected system availability.
It can be observed from Figure 11 that: • The Direct topology leads to higher mean availabilities for decision rules 4-6. Th makes sense because the Direct topology resembles a parallel system, while Radi and Star topologies are more like a series of parallel systems; if more components a allowed to fail without repair, the parallel system should be able to work at a d rated energy delivery level.
In the BN model, the probabilities of different states of the node T0 representing th system are calculated at each time slice. Take Decision Rule 6 for Direct topology as a example. The probabilities of different states as a function of time are shown in Figure 1  From the perspective of engineering design, the predicted availability of an optim energy delivery network should exhibit a high robustness and redundancy. Basicall Direct topology gives relatively higher availability when more basic components fa (corresponding to Decision rules 4-6).

Conclusions
The improved BN model in this study can more efficiently calculate th time-dependent availability than the method used in [12]. The significant decrease computational time is due to no Monte Carlo simulation of time to failure of basic com ponents and no need to search the fault tree to determine when maintenance has to b done according the pre-chosen decision rule. Instead, a two-state repair node (state 0-n repair; or state 1-repair) is added to determine if a repair is needed in the current tim slice, based upon the state of the system node (T0) in the previous time slice. From the perspective of engineering design, the predicted availability of an optimal energy delivery network should exhibit a high robustness and redundancy. Basically, Direct topology gives relatively higher availability when more basic components fail (corresponding to Decision rules 4-6).

Conclusions
The improved BN model in this study can more efficiently calculate the time-dependent availability than the method used in [12]. The significant decrease in computational time is due to no Monte Carlo simulation of time to failure of basic components and no need to search the fault tree to determine when maintenance has to be done according the prechosen decision rule. Instead, a two-state repair node (state 0-no repair; or state 1-repair) is added to determine if a repair is needed in the current time slice, based upon the state of the system node (T0) in the previous time slice. The decision rules covering both different maintenance strategies are directly implemented in the BN model by defining the relevant CPTs of the repair node. The BN model can automatically take into account the effect of maintenance strategies on the probabilities of different availability states, then predict the time-dependent availability.
From the perspective of energy delivery efficiency and robustness, the Direct topology is optimal to give the highest availability. Based upon this improved model, future works can include: • the maintenance costs (OPEX costs) can be estimated by adding relevant nodes in the BN model; • with the combination of CAPEX and OPEX costs, the optimal design solution to the energy delivery network can be finally determined.
It should be noted that some factors affecting the maintenance costs, for example the weather window and logistic-related issues (the availability of technicians, vessels and spare parts), are not considered in this study. These factors can be integrated in the updated BN model in the future research work.