Abstract
The management tasks of maritime grids are comprehensively reviewed in Chap. 3, then in this Chapter, various optimization models for those goals are reviewed. According to the types of decision variables, the optimization models can be classified as three main types, (1) Synthesis optimization, which refers to the optimal configuration of maritime grids, including the construction layout, electrical layout, and the system structure; (2) Design optimization or planning optimization, which refers to determine the technical characteristics of each component, such as the system capacity, and rated power; (3) Operation optimization, which refers to determine the optimal operating states for a given system (i.e., the synthesis and design are both known) under specified conditions. Three types of optimization models can be abbreviated as SynthesisDesignOperation (SDO) optimization, which is coordinated with each other to achieve the overall optimum. In this Chapter, the formulation and solution of SDO optimization for maritime grids are described. At first, the SynthesisDesignOperation (SDO) optimization of maritime grids are explained, then the typical topology of maritime grids are reviewed, then the overall compact optimization models for maritime grids are formulated. At last, the solution methods are reviewed and a decompositionbased method to solve the optimization models is described.
Keywords
 SynthesisDesignOperation (SDO)
 Formulation and solution
 Maritime grids
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4.1 SynthesisDesignOperation (SDO) Optimization
As a special energy system, the optimization of maritime grids can be considered as three levels similar to conventional landbased energy systems [1,2,3].

(1)
Synthesis optimization. Synthesis is defined as the components used in the maritime grids and their connections. Via synthesis optimization, the optimal configuration of the maritime grids can be determined. For example, the ship hull design, electrical layout, and whether to integrate a component or not. Since the synthesis optimization answers the “YesorNo” questions and therefore involves certain binary decision variables.

(2)
Design optimization or planning optimization. Design optimization is to determine the technical characteristics of components which are determined in synthesis optimization, such as the capacity and rated power. The difference between synthesis optimization and design optimization can be given by the wellknown “siting and sizing” problems. The “siting problem” determines which type of components can be used and where to install them, which belongs to the synthesis optimization. Then the “sizing problem” determines the capacities of the installed components, which belongs to the design optimization. In power system research, design optimization is often named as planning optimization.

(3)
Operation optimization. After the synthesis optimization and design optimization, the operation optimization determines the optimal operating states of each component under specified conditions. Taken the navigation speed as an example. The synthesis optimization determines the type of main engine and the design optimization determines the capacity of the main engine, then operation optimization determines the optimal loading levels to address different navigation scenarios, such as different wave and wind scenarios.
Three optimization problems are the basic problems for a maritime grid. They are abbreviated as SynthesisDesignOperation (SDO) optimization [4]. It should be noted that only energy management optimization is within the scope of this book.
Many efforts have been devoted to this field to achieve the overall optimum of maritime grids. In this Chapter, the SDO optimization of maritime grids will be comprehensively reviewed in the following, (1) topologies of maritime grids; (2) typical SDO optimization problems; (3) compact form and solution methods. Compared with other review works, this Chapter firstly points out the significance of coordination between different maritime grids in SDO optimization.
4.2 Coordination Between Maritime Grids
Maritime grids are the offspring of extensive maritime electrification, and widely existing in ships, seaports, and various ocean platforms. Conventionally, maritime grids have very limited capacities and their optimizations also have limited influences on the overall system characteristics. For example, in conventional ships, the propulsion is directly driven by the main engines and the capacity of the corresponding ship power system is much smaller than the propulsion system. However, when a ship is fully electrified, the propulsion system becomes the electric load under the ship power system, and the energy management of ship power system can determine the economic and environmental characteristics of ship. Similarly, when a seaport is fully electrified, the energy management of seaport can coordinate both the logistic and electric systems to achieve better economic and environmental benefits. In this sense, with the development of maritime electrification, the energy management of maritime grids will play an even significant role in the future.
Generally, all the electric networks installed within harbor territory can be viewed as maritime grids, which act as the interface between ocean and land. To clarify the relationship between different maritime grids, we give Fig. 4.1 to show their operating framework. There are five types of maritime grids in Fig. 4.1, (1) wind farms, and (2) island microgrids, and (3) offshore platforms, and (4) seaport microgrids and (5) ship power systems. This illustration shows that the future maritime grids will be coupled with each other, and the coordinated optimization is necessary for future maritime grids.

(1)
Offshore wind farms, can supply power to island microgrids, harbor city, offshore platforms, and seaport microgrid.

(2)
Island microgrids, are islanded microgrids that are away from the main grid, which uses renewable energy and generators to supply the load.

(3)
Seaport microgrid, is a gridconnected microgrid in an electrified seaport, which uses electricity to drive the port cranes and providing coldironing power to the berthedin ships. Various renewable energy sources can be integrated into a seaport and excess electricity can sell to the main grid of harbor city.

(4)
Offshore platforms, are islanded microgrids with many types of construction missions, such as fuel drilling, or underground cable construction. It should be noted that, offshore platforms may be connected with the islands and harbor city by underground pipes.

(5)
Ship power systems. The ships can navigate between the islands, offshore platforms, and seaport to transfer fuel or other cargos. For example, the fuel produced by the offshore platform can be supplied to seaport by ships. It should be noted that, ships have different types, such the containers, cargo ships and the ferries for passenagers.
4.3 Topologies of Maritime Grids
Different types of maritime grids work in different conditions. For example, the notation of “CCOHR(TEMP)+” in the American Bureau of Shipping (ABS) is for the ships which are working under lowtemperature environment. “HR” is the emergency operating hours in the lowtemperature environment (18 or 36 h). “TEMP” is the design service temperature, and “+” means that there is additional equipment for the crew for training in lowtemperature [5]. The notation of “DPS” is for the dynamic position system of ships, which represents the ship has an automatic control system to maintain the position and heading at sea without external aid under specified conditions [5]. For the seaports, various equipment should be invested to serve the containers, cargo ships, or cruise ships, and so on, such as the port cranes to serve the containers, and the coldironing equipment for the berthedin ships. The above designs are all determined by the synthesis optimization of ships.
With full electrification, maritime grids are multienergy networks that use the electrical network as the backbone to supply various service networks, such as fuel flow network, thermal flow network, and water flow network [6]. In this sense, the synthesis optimization of maritime grids is mainly determining the topologies to achieve better performance. As two main representatives, the ship power system and the seaport microgrid are described in detail in this section.
4.3.1 Topologies of Ship Power Systems
For the ship power system, ABS has “R1”, “R1S”, “R2”, “R2S” standards [5]. “R” is shorted for redundancy, “1” or “2” indicates the single/multiple sets of propellers and steering systems. “S” means the propulsion machines are located in separate compartments for emergency cases. Therefore, “R2S” represents the ships that have multiple sets of propeller and steering system, and the propulsion machines are located in separate compartments. Among the above standards, “ABSR2” is a conventional standard for the commercial ships under ABS, which means the ship power system can fully restore the serviceability when single failure. Figures 4.2, 4.3, 4.4, 4.5, 4.6 and 4.7 give some examples which follow the “ABSR2” standard or above.
Ferries are small or mediumsized ships for passenager transportation, often using AC power supply with 690 V, which can carry hundreds to thousands of people, with a roundtrip distance of tens of kilometers. For example, the world’s first allelectric ferry, named as “Ampere”, has been equipped with 2.6 MWh power batteries, reducing the use of 1 million liters diesel every year [7]. A typical illustration is shown in Fig. 4.2.
Cruise ships are large tourist ships that can carry thousands or even tens of thousands of people for several weeks, shown in Fig. 4.3. It usually uses the 11 kV AC power supply and is equipped with 4 or 6 generators. The cruise ship has many restaurants, playgrounds, cinemas, casinos, etc., which uses 440 V lowvoltage power supply. Due to the huge volume of cruise ships, the rated power of a single thruster can reach 20 MW. The total propulsion power of the Royal Caribbean’s “Ocean Charm” is 97 MW [8].
Offshore construction ships are usually used for oceangoing operations, such as dredgers, oildrilling, and fiber optic cable laying ships. Such ships require good maneuverability, so they need propulsion systems with huge capacities, especially for the thrusters to meet ship steering and Uturn. A typical illustration is shown in Fig. 4.4.
Cold chain transportation ships usually transfer refrigerated containers and store all kinds of fresh food. This type of ship needs to provide a large amount of refrigeration load during navigation [9]. In Fig. 4.5, the refrigeration load is supplied by 440 V AC power.
LNG ships are mainly used to transport LNG. Unlike the cold chain transportation ships in Fig. 4.5, LNG ships do not directly supply refrigeration load, but mainly use the vaporization process of LNG to maintain Temperature (−163 °C), and the vaporized natural gas is recovered through a reliquefaction device. This type of ship usually uses the 11 kV AC power supply [10]. Generally, this type of ships usually has a displacement of more than 100,000 tons, and the propellers need to be driven by several motors at the same time to ensure the maneuverability of the ship.
The last case is the warship which has multiple parallel buses (4 buses in Fig. 4.7) [9]. Four buses are backups to each other to ensure the survivability of warships on the battlefield.
In the future, with the development of allelectric ship, there will be more advanced topology designs for ship power systems, and the AC ship power system will be gradually replaced by the DC ship power system, which has larger capacities and more functionalities.
4.3.2 Topologies of Seaport Microgrids
Typically, the structure of seaport microgrid is similar to a landbased distribution network, which has (1) the main loop primary distribution network; (2) secondary loopislands distribution network; and (3) tertiary distribution systems at specified voltage levels [11]. Figure 4.8 shows the structure of a seaport microgrid [12]. The main difference is the seaport has multiple redundant switches to ensure the power supply to critical loads, such as various port cranes and refrigeration.
With the electrification of seaport, seaport is required to provide more services to the berthedin ships, such as the coldironing power. Additionally, the electrification of transferring vehicles is also another trend, which requires seaport to provide adequate charging facilities. Furthermore, harbor territory usually has much more plentiful renewable energy resources compared with inland, and the renewable generation integration into seaport to improve the energy efficiency is therefore a promising trend in the synthesis optimization of seaport microgrid. In this sense, the synthesis optimization of seaport microgrid can be viewed as an expansion planning problem. Ref. [13] analyzes the impact of coldironing power on the seaport and Ref. [14] analyzes the impact of renewable generation integration.
In the future, the seaport microgrid will become a multienergy microgrid that involves electricity, thermal power, fossil fuel, and even water flow supply [6]. To clearly show the future operating framework, we redraw Figs. 1.17 as 4.9. Different energy systems should be coordinately planned for an overall optimum.
4.3.3 Topologies of Other Maritime Grids
Besides the above two main representatives of maritime grids, i.e., ship power system and seaport microgrid, there still exist many other types of maritime grids, such as the island power system, drilling platform, or offshore oilfield. In this section, an island power system is shown in Fig. 4.10 as a representative [15].
At first, a power plant acts as the main power source of an island power system, and various renewable energy sources are integrated into this system, such as wind power and photovoltaic power. Additionally, several energy storage stations are used to improve the reliability.
4.4 SynthesisDesignOperation Optimization of Maritime Grids
4.4.1 Synthesis Optimization for Maritime Grids
There are currently lots of research on the synthesis optimization of maritime grids. Here we give three cases to show their effects.
(1) Graph theorybased ship power system expansion
Nowadays, full electrification of ships is first implemented in Warships [16, 17] and may further expand to commercial applications [9]. As we know, ships may face various failures when navigation, such as malicious attacks on warships and component failures. To improve the resilience of a ship power system, Ref. [18] has proposed a graph theorybased ship power system expansion method to determine the optimal transmission line expansion strategy. The process is briefly described as follows.
Figure 4.11 gives a graph topology of an allelectric ship [19]. There are 22 buses and 29 lines in this graph. 4 generators are employed as the main power sources. 8 loads are classified as weapon load, propulsion load, radar load, control center, and hotel load according to the significance. The proposed model is to determine which lines should be installed for better resilience.
The proposed model has two objectives, (1) the weighted maximum flow from the generations to the loads, which is defined as (4.1), (2) Graph algebraic connectivity represented by the second smallest eigenvalue of Laplacian matrix.
where \( {\text{WSMF}} \) is the defined weighted maximum flow index; \( gn,ln \) are the index set for generations and loads; \( MF_{gn,ln} \) is the maximum flow from the generations to the loads. The defined \( {\text{WSMF}} \) represents the maximum transmission capacity to the loads and can be acting as an important index to measure the resilience of ship power system.
In the case study, the proposed method is compared with the method of minimizing adding lines cost (MCR) [20]. The comparing results are shown in Table 4.1, and the simulation results bring two conclusions, (1) proper transmission line expansion can improve the resilience of ship power system; (2) the maxflow index is a useful index to measure the resilience of ship power system. From Table 4.1, the proposed model can reduce around 50% attacking scenarios which lead to load shedding.
(2) Renewable generation expansion for Houston port
As the main interfaces between the ocean and inland, the environmental behaviors of seaports are always the concerns of the maritime industry [6]. With the electrification of seaports, massive renewable generation expansion in seaport has become reality. Ref. [14] proposes a model for the renewable generation planning and defines (1) smart energy index and (2) smart environmental index to measure the behaviors of seaports. The relevant parts with renewable energy integration are shown as follows.
where \( SEgI_{RPG} \) and \( SEnI_{RPG} \) are the relevant parts of renewable power generation in smart energy index and smart environmental index; \( RS_{RPG} \), \( RS_{MG} \) are the energy consumption ratios from renewable power generation and the main grid; \( P_{RPG} \) and \( P_{MG} \) are the power from renewable power generation and the main grid; \( { \Pr }_{outage} \) is the outage percentage of the main grid; \( RS_{T}^{max} \) is the goal value of total renewable power generation within the seaport; \( EM \) is the average gas emission of unit power; \( EM_{T}^{max} \) is the goal value of total gas emission.
With the above two defined indexes, seaport can select a proper capacity of renewable power generation to achieve various economic and environmental management targets. The case study has shown that the gas mission of seaport can reduce more than 50% by the optimization of the proposed method, which can be a reference for future research.
(3) Structural optimization of an offshore oilfield power system
The ship power system and seaport microgrid are two main types of maritime grids, and there also exist various other maritime grids. The offshore oilfield power system is one representative that is studied by Ref. [15]. An offshore oilfield power system to be optimized is shown in Fig. 4.12a.
An offshore oilfield power system generally consists of an island and many drilling platforms. The island acting as the power source and a proper network structure should be planned to achieve (1) acceptable economic cost; (2) acceptable environmental behavior; and (3) acceptable reliability level. After solving the formulated model, the optimized structure is shown as Fig. 4.12b.
Practically, the drilling platforms may be away from an island. Therefore a more general case is the island is replaced by the mobile power plant. The mobile power system can move with the drilling platform when the mission is finished.
4.4.2 Design and Operation Optimization for Maritime Grids
In this section, two cases are given to show the effects of design and operation optimization for maritime grids.
(1) Multiagent energy management for a large port
Reference [21] proposes an energy management method based on a multiagent system for a large electrified port. The agents in a port are shown in Fig. 4.13. The energy management process is simplified as follows.
The overall port is under the control of the port manager agent (PM/A). PM/A aggregates the load demand within the port and communicates with the upper grid to determine the electricity price. The other agents include the pluggedin EV agent (PEV/A), which determines the charging/discharging of transferring vehicles, and the reefers agent (R/A), which determines the load demand of reefer containers, and shoreside power agent (SSP/A), which determines the coldironing power for each berthedin ship. PEV/A, R/A, and SSP/A optimally dispatch the load demand of local agents (each component, such as one EV, or one reefer container) and then update with the PM/A. The overall process can be shown in the following Fig. 4.14.
PM/A sends electricity price to each agent (PEV/A, R/A, SSP/A), then each agent calculates its own optimal power demand plan and sends signals to each local agent of components. Each local agent determines if the load demand plan can be achieved. Then the “Yes/No” signals are sent back to PEV/A, R/A, and SSP/A. If all the local agents can achieve the optimal load demand, the total load demand under this agent will be sent to the PM/A. If not, the agent, i.e., PEV/A, R/A, SSP/A, will recalculate the optimal load demand based on updated system conditions. This process will be repeated until convergence. This method has proved to be efficient and accurate in a realworld large electrified port. However, as an important part, the energy consumed by the port cranes are not considered in this research.
(2) Sizing of the shipboard gas capture system
We have mentioned the gas capture system in Chap. 1. Here we redraw Fig. 1.11 to show the process of Ref. [22]. When the gas capture system is integrated into ships, the gas emission will be absorbed into storage and not emitted to the atmosphere. Before the wide usage of clean fuel, the gas capture technologies are viewed as feasible transition routes to control the gas emission.
Currently, the sulfur emission capture is the most mature technology among all the available technologies [23]. Lots of commercial applications have been implemented to meet the “2020 sulfur limit” [24]. The capture of carbon emission is a mature technology in landbased applications, but it still has many obstacles to be used in ships, such as the installment space, energy requirement, and so on. Other gas capture technologies, such as nitrogen capture and particle capture are all under investigation to find feasible implementations (Fig. 4.15).
The gas capture system integration will bring two problems, (1) what is the capacity of the gas capture system? and (2) what is the capacity of additional power sources to supply the gas capture system?
The first question is influenced by the environmental policies. For example, in 2020, IMO has launched the ever strictest sulfur limit policy, which requires to use 0.5% sulfur fuel. Then the installed gas capture system should have enough capacity to make the emitted gas has no more than 0.5% sulfur. In the future, the installed carbon capture system should also meet the global and regional carbon reduction goals. The second question is a design optimization for the ship power system. Since the original configuration of the ship does not have the gas capture system, the original generation system may not have enough capacity to supply the gas capture system. So extra power source, i.e., extra generator or energy storage, should be installed onboard. Ref. [22] formulates a sizing model to determine the above two questions. Its process is shown as the following Fig. 4.16.
4.5 Formulation and Solution of SDO Optimization
4.5.1 The Compact Form of SDO Optimization
In general terms, the compact form of SDO optimization for maritime grids can be shown as follow.
where \( f\left( {v,w,z} \right) \) is the management objective for SDO optimization, which is described in detail in Chap. 2; \( v \) is the set of decision variables for operation optimization, i.e., load factors of generators or engines, mass flow rates, pressure/temperature of streams, etc.; \( w \) is the set of decision variables for design optimization, i.e., nominal capacities of generators or engines, transmission limits of pipes or lines, etc.; \( z \) is the set of decision variables for synthesis optimization, which are generally binary variables to indicate the investment or noninvestment of each component, i.e., with 1 value for investment and with 0 for noninvestment.
For a complete SDO problem, Eq. (4.4) is under a set of constraints, including both equality and inequality constraints, to represent various limits in different scenarios.
A typical problem can involve one type, two types, or even three types of variables. For example, Refs. [1,2,3] involves three types of variable \( v,w,z \), and Ref. [22] only involves two types. Generally, the SDO problems are nonlinear and nonconvex and very hard to be solved. Various methods have been proposed in this field to solve the SDO problems. In the following, the solution methods are classified into groups and then a decompositionbased method is described in detail for its usage in Chaps 4–7.
4.5.2 Classification of the Solution Method
The main classifications for solving the SDO problems are shown in Table 4.2 with some representative references, i.e., (1) mixedinteger linear programming, and (2) constrained nonlinear programming, and (3) dynamic programming, and (4) evolutionary algorithm.
4.5.3 DecompositionBased Solution Method
In the following Chaps. 4–7, a decompositionbased solution method is proposed to solve a certain type of SDO problem, which is used in Refs. [22, 32,33,34,35,36] and belongs to the type of constrained nonlinear programming. This type of SDO problem is shown in the following compact form.
This problem belongs to the operation optimization, and \( v_{1} ,v_{2} \) are two types of operation variables, and usually belong to two different systems. For example in the navigation optimization of allelectric ships, \( v_{1} \) represents the energyrelated variables and \( v_{2} \) related to the speed variables.
In the above formulation, Eqs. (4.8), (4.10) are the constraints in two different systems. For example in the navigation optimization of allelectric ships, Eq. (4.8) is the constraint set for energy and Eq. (4.10) is the constraint set for speed, and they are related by Eq. (4.9). This is a special type of maritime grid optimization problems since the couple between two systems only lies on Eq. (4.9).
In this book, this type of problem can be solved by a decompositionbased method and divided the original model into two levels as Eqs. (4.11) and (4.12).
Equation (4.11) refers to the upper level, and in this level, decision variables \( v_{2} \) are viewed as constant variables, which are updated in the lower level, i.e., Eq. (4.12). In Eq. (4.12), \( f_{aux} \) is an auxiliary objective function, which represents a management target, such as minimization of voyage deviation, or minimization of voyage period, and so on. With the above decomposition, the original problem is decomposed into two simplified subproblems.
In literature, Refs. [22, 32,33,34,35,36] solve the energy management problem for allelectric ships. Equation (4.8) is the energyrelated constraints and Eq. (4.10) is the speedrelated constraints, and Eq. (4.9) is the speedenergy relationship, i.e., a cubic polynomial constraint. With the above decomposition, a nonlinear and nonconvex original problem is reformulated as a quadratic and linear programming problems, respectively, and therefore can be solved efficiently. In the following Chapters, this method will be used to solve various practical problems. Ref. [44] give a general method to select the parameters of this solution method.
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Fang, S., Wang, H. (2021). Formulation and Solution of Maritime Grids Optimization. In: OptimizationBased Energy Management for Multienergy Maritime Grids. Springer Series on Naval Architecture, Marine Engineering, Shipbuilding and Shipping, vol 11. Springer, Singapore. https://doi.org/10.1007/9789813367340_4
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DOI: https://doi.org/10.1007/9789813367340_4
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