Optimizing Energy Management and Case Study of Multi-Energy Coupled Supply for Green Ships

Abstract

The ship industry is currently facing numerous challenges, including rising fuel prices, limited fuel resources, and increasingly strict regulations related to energy efficiency and pollutant emissions. In this context, the adoption of green-ship wind–photovoltaic–electricity–fuel multi-energy supply systems has emerged as an efficient and clean technology that harnesses multiple energy sources. These systems have the potential to increase the utilization of renewable energy in ship operations while optimizing management practices in order to enhance overall energy efficiency. To address these challenges, this article presents a comprehensive energy supply system for ships that integrates multi-energy sources for cold–heat–electricity supply. The primary components of this system include fuel cells, photovoltaic equipment, wind turbines, electric heating pumps, electric refrigerators, thermal refrigerators, batteries, and heat storage tanks. By ensuring the safety of the system, our approach aims to minimize daily operating costs and optimize the performance of the multi-energy flow system by running scheduling models. To achieve this, our proposed system utilizes dynamic planning techniques combined with ship navigation conditions to establish an optimized management model. This model facilitates the coordinated distribution of green ship electricity, thermal energy, and cooling loads. The results of our study demonstrate that optimized management models significantly reduce economic costs and improve the stability of energy storage equipment. Specifically, through an analysis of the economic benefits of power storage and heat storage tanks, we highlight the potential for reducing fuel consumption by 6.0%, 1.5%, 1.4%, and 2.9% through the use of electric–thermal hybrid energy storage conditions.

1. Introduction

Ships play a crucial role in global trade, logistics, and tourism, making significant contributions to international commerce, maritime transportation, and the tourism industry [1]. However, ships that primarily rely on diesel engines have become major sources of air pollution and climate change worldwide [2]. In response to growing global environmental concerns, countries have implemented stricter environmental regulations, demanding the reduction of emissions, and the adoption of clean energy sources in the ship industry to promote sustainability [3].

To achieve high outputs, low levels of energy consumption, and environmentally friendly sustainable development, there is a need to transition from conventional ship energy systems, characterized by high energy consumption and pollution, to multi-energy supply ship hybrid power systems incorporating renewable energy sources [4]. The integration of renewable energy sources into hybrid power systems has been extensively explored and has shown promising results in the ship industry, serving as a key driver of transformation in the industry [5].

However, the operation of ship hybrid power systems with multi-energy supply occurs in island mode, necessitating the simultaneous fulfillment of load requirements and ensuring the safety and reliability of the energy system. Therefore, the configuration and energy management of ship energy systems have emerged as important research topics. It is crucial for researchers to consider various factors such as specific load requirements, route planning, weather conditions, and conversion efficiency between different energy sources in order to develop optimal configurations and energy management strategies for hybrid energy systems in ships.

The energy system of traditional ships comprises multiple components. The main engine serves as the core component, providing propulsion for the ship’s navigation. On the other hand, auxiliary machinery plays a secondary role by supplying electricity to support the operation of various ship equipment and systems. The fuel boiler acts as the ship’s thermal energy supply system, generating high-temperature flue gas through the combustion of ship fuel to meet the ship’s thermal energy requirements. The refrigeration unit is responsible for cooling ship equipment, providing air conditioning, and maintaining lower temperatures in cabins and the ship’s cold storage areas. To manage exhaust emissions, emission control devices are employed [6].

Nowadays, ship engines have capacities that can reach dozens of megawatts, demanding significant fuel consumption to generate sufficient power [7]. The heat reutilization rate from gasoline and marine heavy oil combustion is approximately 50% [8]. This excess heat can be effectively converted into power or utilized for refrigeration purposes. In order to enhance energy utilization efficiency, promote environmental sustainability, and achieve economic benefits in ships, researchers have explored the application of distributed cogeneration systems, commonly used on land, in the maritime context [9]. These systems adopt the concept of energy cascading, effectively and efficiently utilizing the residual heat generated by ships [10].

Wang et al. [11] proposed three ship combined cooling, heating, and power (CCHP) system schemes, namely, a traditional system, an absorption chiller-based system, and a gas turbine generator-based system. The authors conducted their research using a large cargo ship as the subject and estimated the ship’s cooling, heating, and power load demands based on actual equipment survey data. Additionally, they analyzed the thermal balance mathematical constraints of the three CCHP systems [12]. The research findings revealed that the ship CCHP system based on a gas turbine generator demonstrated superior energy-saving and energy-efficient performance [13].

Ship design has traditionally focused on reducing equipment space and weight. However, waste heat power generation technology entails complex system layouts, larger space requirements, and additional weight [14]. This poses challenges for its application on ships as it conflicts with the limited space and weight restrictions. Hence, alternative solutions need to be explored to meet ship design requirements [15,16].

Li et al. [17] conducted research on cruise ships, specifically addressing thermal energy demand issues. They proposed an onboard trigeneration system that combines the CCHP system with the electrical, thermal, and cooling demands of cruise ships. A comparative analysis of engine-based and gas turbine-based CCHP systems revealed substantial improvements in system space occupancy and pollutant emissions for the gas turbine-based system despite increased fuel consumption [18]. This study provided innovative solutions that allowed cruise ships to meet their thermal energy demands and offered environmental benefits.

Fuel cells and renewable energy sources are widely employed in ship CCHP systems [19]. You et al. [20] investigated and developed a comprehensive energy system based on hydrogen fuel. Their system utilized solid-oxide fuel cells (SOFCs) powered by liquefied hydrogen fuel as the core, combined with a steam production cycle. The study evaluated the energy and exergy performance of the SOFC, refrigeration cycle, and ship propulsion engine system. It also assessed the effects of SOFC and hydrogen fuel engines on reducing greenhouse gas emissions through case studies [21]. The system exhibited significant environmental benefits due to the utilization of clean energy sources.

Yan et al. [22] established a ship CCHP system and discovered that increasing the internal combustion engine capacity could enhance the system’s economic benefits, while they found that increasing the gas turbine capacity could reduce the system’s space occupancy. However, due to lower economic viability and larger space requirements, renewable energy sources were not chosen as the primary power units in the optimization model, which prioritized economic feasibility and space occupancy.

Research and development into operation strategies and energy management aspects for ship CCHP systems have started relatively late. This is primarily due to the complexity of the CCHP system’s composition, which involves the intricate coupling and conversion processes of multiple forms of energy, making energy management highly complex. Therefore, determining the system’s operation strategies is crucial for achieving effective energy management.

In traditional onshore CCHP systems, basic operation strategies and optimized operation strategies are employed [23]. The basic operation strategies include an electricity-driven cooling/heating strategy, a cooling-/heating-driven electricity strategy, and a hybrid operation strategy [24]. These strategies adjust the fuel supply to the power unit or purchase additional electricity based on the electricity demand or cooling/heating demand on the demand side. The hybrid operation strategy allows the system to flexibly switch between different strategies by setting threshold values [25]. However, while the basic operation strategies are simple and practical, they also come with energy losses.

To address these issues, numerous scholars have conducted research into CCHP systems, considering major equipment such as gas turbines, waste heat boilers, absorption chillers and boilers, and compression refrigeration machines [26]. Among the various study techniques available, it is preferable to analyze the configuration and operation strategies of CCHP systems using the optimization objective function of “lifecycle annual cost”. However, it is not suitable to simply apply the “heating-driven electricity” or “electricity-driven heating” approaches used on land to a ship’s isolated energy system configuration [27]. It is necessary to consider the ship’s dynamic operation or various demand profiles over multiple days and allocate energy proportionally based on the specific equipment’s energy supply capabilities to achieve the optimal configuration of a ship’s multi-energy supply system.

The operation optimization strategies used for multi-energy supply aim to solve single- or multi-objective models, using optimization algorithms to obtain optimal energy management strategies for energy systems. Researchers have designed various distributed CCHP systems based on multi-energy complementarity [28]. They have established mathematical models that include equipment energy systems, pressure networks, and terminal loads [29]. To obtain the optimal energy management strategies, nonlinear optimization models have been constructed, incorporating dynamic programming, the optimization of objective functions, and constraints. Additionally, intelligent optimization algorithms have been employed to derive the optimal solutions to these issues [30]. These related studies have also verified the effectiveness of the obtained operation strategies at reducing the system’s operating costs.

Furthermore, some papers have addressed the challenge of mismatched power generation capacity and cooling/heating/electricity load demands in CCHP systems. These are issues that make efficient operational control difficult to achieve. Innovative solutions have been proposed by designing CCHP systems with thermal and cold storage devices to achieve proactive operation optimization strategies and multi-objective energy management methods [31]. In these studies, multi-objective optimization energy management models are established, considering primary energy utilization, carbon emissions, and operating costs. Multi-objective optimization algorithms are utilized to obtain the Pareto optimal solution set. The results of these studies demonstrate that the use of novel proactive operation optimization strategies and multi-objective energy management methods significantly improves the primary energy utilization, environmental benefits, and economic benefits of CCHP systems [32]. These innovative approaches provide new pathways for the operation optimization and energy management of CCHP systems.

Considering the current development status and challenges faced by energy systems, a comprehensive literature review reveals the necessity and significance of energy scheduling and management. However, it remains uncertain whether existing methods can be directly applied to ship-based island multi-energy supply systems and effectively meet cooling, heating, and electricity demands during ship operations. Therefore, building upon the existing literature review, this paper introduces a novel ship-based integrated multi-energy supply system that incorporates wind, solar, electricity, and fuel sources, with a specific focus placed on providing cooling, heating, and electricity. The novelty of the approach lies in the evaluation and adaptation of existing methods to address the unique requirements of ship-based energy systems. To accomplish this, the safety of the system is prioritized, and an effort is made to minimize daily operating costs, including fuel costs, operational expenses, and maintenance costs. The performance of this multi-energy system is investigated through the development of an energy management model.

In Section 2, a modular model of ship cooling, heating, and electricity supply is presented. This model encompasses ship power supply equipment (such as SOFCs, photovoltaic devices, and wind turbines), ship heating equipment (including waste heat from SOFCs and electric heat pumps), ship cooling equipment (including electric refrigeration and waste heat refrigeration), and ship energy storage equipment (electric and thermal storage tanks). Furthermore, in Section 3, the focus is on the energy management operation strategy of the integrated cooling, heating, and electricity system. State variables, state transition equations, system constraints, decision variables, and objective functions are defined for the multi-energy model. Optimal operation strategies are derived based on the balancing characteristics and demands of the multi-energy supply system, as well as its economic objectives. To demonstrate the practical applicability of our approach, Section 4 presents a case study on energy management for an actual ship. A comparative analysis of energy management results is conducted for three operating scenarios: mixed-electric and thermal energy storage, electric energy storage only, and thermal energy storage only. This analysis allows for the assessment of the performance of our proposed model in comparison to existing methods and enables researchers to determine their applicability to ship-based energy systems.

2. Multi-Energy Coupled Supply System for Green Ships

2.1. System Architecture Description

Figure 1 illustrates the schematic diagram of a ship-based multi-energy coupling supply system. The multi-energy part consists of energy/fuel output, power output, and energy storage, integrating the power characteristics and operational modes of different components. This system considers the power characteristics and operational states of different devices, visually demonstrating the multi-energy conversion relationships between the devices and meeting the cooling, heating, and electricity demands of ship operations. The energy system prioritizes the use of photovoltaic devices, wind turbines, and SOFCs to meet the electricity demand, while the energy storage devices store electricity to provide supplementary supply when needed. To meet the heating and refrigeration loads, the system utilizes electric heat pumps, thermal energy storage devices, and waste heat generated during the operation of SOFCs. For cooling loads, the system employs electric refrigeration machines and waste heat refrigeration machines. Through this multi-energy system architecture, the ship can maximize the utilization of renewable energy, efficiently utilize different energy devices, achieve multi-energy conversion, and manage energy effectively in order to meet the cooling, heating, and electricity demands of ship operations.

2.2. Multi-Energy Flow Models

Wind power generation can be integrated with a ship’s electrical grid system to provide power for large bulk carriers and other types of ships, partially replacing or reducing the use of diesel generators. Ships have expansive surface areas and spacious areas that can accommodate large-scale solar photovoltaic panels, enabling the efficient operation of photovoltaic systems. Ships can utilize both solar photovoltaic systems and wind power generation systems to complement each other. With the help of inverters, electrical energy can be stored in batteries. The stored energy can meet the daily production and domestic electricity demands of ships, providing a sustainable power supply. This paper does not cover specific wind power and photovoltaic devices, but focuses on the concept of energy management and the total amount of energy converted. Therefore, the designed methods of energy production from wind power and photovoltaic systems for ships are denoted as P_w and P_p, respectively.

As the main energy device of new-energy ships, SOFC can directly use fuels such as hydrogen, natural gas, methanol, and other fuels during navigation. At the same time, thermal energy can be generated at high temperatures via electrochemical reactions to achieve thermal power supply. For energy management calculations, the thermal efficiency in the SOFC model changes with the output power. At present, the experience relationship between the chemical reaction output power and the thermal power of the chemical reaction output in the literature is as follows [33]:

$$\begin{array}{l}\frac{{\eta }_e}{{\eta }_{e,r}}=1.042-0.0405\frac{P_{f,r}}{P_f}\\ \frac{{\eta }_t}{{\eta }_{t,r}}=0.2477\frac{P_f}{P_{f,r}}+0.8326-0.0757\frac{P_{f,r}}{P_f}\\ H_f=P_f\frac{{\eta }_t}{{\eta }_e}\end{array}$$

(1)

where P_f is the output power of SOFCs, η_e and η_t are SOFC’s electrical efficiency and thermal efficiency, respectively, and r represents the rated work conditions. The corresponding output thermal power H_f can be calculated through the principle of energy balance.

The ship’s thermal pump technology operates through the heating cycle of a working quality, and the heat in the low-temperature heat source is transferred to a high-temperature environment to realize the transmission and conversion of energy. A water source heat pump is a common type of pump possessed by ships. It uses seawater as a heat source or cold source, and passes the thermal energy to the air conditioner and heating system of the ship through the heat exchanger. The efficiency model is as follows:

$$H_h=P_h{\eta }_h$$

(2)

where H_h, P_h and η_h are, respectively, the electric power consumed by the electric heat pump, the thermal power generated and its heating efficiency.

Electric refrigeration and thermal refrigeration are widely used on ships to provide a cooling effect. The difference is that the relevant refrigeration machine, which ensures that the temperature of the equipment, cabin and relevant ship cold storage is appropriate, and that the ship, comfort and food preservation needs of passengers are met, is driven by electricity or waste heat. Their efficiency model of energy balance is

$$\begin{array}{l}{R}_{er}=P_{er}{\eta }_{er}\\ R_{tr}=H_{tr}{\eta }_{tr}\end{array}$$

(3)

where R, P and η are, respectively, refrigeration power, electric power consumed and refrigeration efficiency. The subscripts er and tr refer to electrical refrigeration and thermal refrigeration, respectively.

Batteries, as electrical energy storage devices, enable load valley recovery. This load-shifting strategy helps to reduce peak-to-valley differences in the ship’s energy system and improves energy utilization efficiency. Moreover, ship energy system equipment often generates significant waste heat. To fully harness these waste heat energy sources, heat storage tanks can be employed to store and recycle waste heat. Heat storage tanks convert the waste heat generated by equipment into usable thermal energy, supplying hot and cold load demands as needed. This approach not only enhances energy utilization efficiency and reduces energy waste but also lowers the ship’s energy costs. Definition B represents the percentage of energy currently stored by the battery and can be used to measure the battery’s power level. S can be defined as representing the stored heat of a heat storage device.

$$\begin{array}{l}{B}_{k+1}=B_k-\frac{E_c}{E_{\max }}\\ S_{k+1}=S_k-\frac{T_c}{T_{\max }}\end{array}$$

(4)

where E_max and T_max are, respectively, the maximum electrical storage capacity of the battery and the maximum thermal storage capacity of the heat storage tank. Subscript c indicates battery discharge/storage or heat storage/discharge in heat storage tank. By leveraging the energy storage capacity of batteries to balance loads and utilize waste heat from heat storage tanks, ship energy systems can flexibly and efficiently manage power and thermal resources.

3. Energy Management for Multi-Energy Coupled Supplying

3.1. Energy Management Strategy

The operating strategy of a multi-energy supply system is essential for the performance and energy utilization rate of the ship.

(1)

Electric energy management: The primary power supply is the solid-oxide fuel cell (SOFC), complemented by renewable energy sources like solar photovoltaic and wind power. Optimal power management is achieved by considering the power load demand and energy availability. Excess electricity is used to charge the battery. During power shortages, the battery discharges to meet the ship’s power load demand.

(2)

Thermal energy management: The main heating pump serves as the primary heating device. Its thermal energy is utilized to fulfill the ship’s thermal load demand and meet the thermal energy requirements of the thermal refrigeration unit. Additionally, residual heat generated during SOFC runtime can be recycled to supplement thermal energy needs and efficiently fill the heat storage equipment. When the electric heating pump cannot meet the heat load demand, adjusting the operation of thermal refrigeration units and increasing the energy consumption of electrostatic refrigerators can reduce the reliance on thermal energy.

(3)

Cold load management: The focus is on optimizing the collaborative operation of multiple equipment and maximizing cold load demand. By coordinating the operation of electric refrigeration units and thermal refrigeration units based on the ship’s thermal load and electric load requirements, the system ensures efficient cooling. When there is low thermal load demand and high electric load demand, electric refrigeration units are preferred for refrigeration. Conversely, in cases of high thermal load demand and low-power load demand, thermal cooling units are utilized.

Coordinating the use of electricity, thermal energy, and cold energy can optimize the ship’s energy supply system, reduce operating costs, and improve energy utilization efficiency.

3.2. Energy Management Model

To implement the aforementioned energy management strategies, the ship’s operation process is divided into 24 decision stages corresponding to each hour with the aim of minimizing economic costs. In this context, the following elements are defined: state variables, state transition equations, and decision variables. The energy management model finally achieves the optimization of energy distribution and maximizes economic benefits. The computational architecture and workflow depicted in Figure 2 provide a visual representation of the energy management process. It outlines the data flow, decision-making procedures, and feedback loops within the system. This framework enables the efficient calculation of optimal strategies for each decision stage, ensuring effective energy management throughout the ship’s operation.

Firstly, the objective function is defined. The key to a multi-energy supply system is to rationally arrange and manage the energy and to maximize the operation economy of the ship. The model takes the daily operation cost of the ship energy system as the objective function F of optimization, including fuel cost and operation and maintenance cost [34].

$$\begin{array}{l}{F}_k=C_f+C_o\\ C_f=\frac{P_{{}_f}^k\cdot \Delta }{{\eta }_f^k{\varphi }_f}{m}_f\\ C_o={\displaystyle \sum _i{\displaystyle \sum _k{\gamma }_i}}\cdot P_{i,k}\end{array}$$

(5)

where C_f and C_o are, respectively, shipping fuel cost and the operation and maintenance cost of each piece of equipment in the ships. ∆, ϕ and m_f are defined as calculating step size, calorific value of fuel and unit fuel cost, respectively. γ is the operation of different equipment and maintenance costs, and P_i,k is the output power of each device at time k.

In the operation and optimization of energy management strategy, it is necessary to divide the decision-making stage reasonably and solve the sub-problems to achieve the optimal distribution of multiple energy sources and maximize the economic benefits. The state transition equation and decision variables are the key elements in the discrete state space of a policy:

$$\begin{array}{l}{x}_{k+1}=f\left(x_k,u_k\right)\\ x_k=\left[B_k,S_k\right]\\ u_k=\left[P_f^k,P_h^k,H_{tr}^k\right]\end{array}$$

(6)

where x_k is a state variable that reflects the operational status of key components, and the decision sequence u_k schedules the allocation of energy to key components every hour to determine state transitions.

The electrical, thermal, and cooling energy balance of the ship’s multi-energy supply system are:

$$\begin{array}{l}{P}_f+P_w+P_p=P_l+P_h+P_{er}\\ H_f+H_h+T_c=H_l+H_{tr}\\ R_{tr}+R_{er}=R_l\end{array}$$

(7)

where P_l, H_l, C_l are, respectively, the electrical, thermal, and cooling loads required by the ship during its voyage.

$$\begin{array}{l}{P}_{f,\min }\le P_f\le P_{f,\max }\\ P_{h,\min }\le P_h\le P_{h,\max }\\ P_{er,\min }\le P_{er}\le P_{er,\max }\\ H_{tr,\min }\le P_{tr}\le P_{tr,\max }\end{array}$$

(8)

Subscripts max and min are used to represent the upper and lower power limits for fuel cells (P_f,max, P_f,min), heat pumps (P_h,max, P_h,min), electric refrigeration (P_er,max, P_er,min), and thermal refrigeration (H_tr,max, H_tr,min) in order to monitor power status points for the safe operation of the equipment.

$$\begin{array}{l}{B}_{k,\min }\le B_k\le B_{k,\max },\hspace{1em}\hspace{1em}k=1,2,\dots ,24\\ S_{k,\min }\le S_k\le S_{k,\max },\hspace{1em}\hspace{1em}k=1,2,\dots ,24\end{array}$$

(9)

The operating constraints and terminal boundary conditions of the battery B_k and the heat storage tank S_k at each time period k are defined, respectively, and their initial values are set to 0.5, realizing the energy storage balance at the beginning of the 24 h energy management cycle.

4. Case Study of Ships Energy Management

4.1. Ship Operation Case Description

The conditions for a suitable case caused us to select a cruise ship to and from Dalian Port and Qingdao Port, China as the research object. The cruise ship is 105 m long, 28 m wide, 18 m high, and the total tonnage is 24,882 tons. Every day at 4 pm, the cruise ship departs from the port of Dalian, sails to the Bohai Sea, and stays in the Bohai Sea for one night. Subsequently, it arrives in Qingdao Port in the early morning and returns to Dalian Port at 2 pm.

The demand for shipping, as well as thermal and cold load, varies with season and operation time. Figure 3 illustrates the load, photovoltaic power generation, and wind power generation data obtained during a single day of sailing on the cruise ship in the summer. In the summer season, the cold load reaches its peak among the four seasons, with an average of 734 kW, and the peak period occurs between 10:00–17:00. The average thermal load is 382 kW, and the average power load is 812 kW. The increased load during summer presents various challenges and tests that better reflect the complexity and reality of the problem. It enables the discovery of energy-saving potential and facilitates the observation and measurement of energy-saving effects.

The onboard equipment responsible for energy supply and consumption includes SOFCs, electric heat pumps, electric refrigeration, thermal refrigeration, batteries, and heat storage tanks, as well as photovoltaic and wind power systems.

Table 1. Some selected technical data.

Items	Imputed Cost [35,36]	Maximum	Minimum	Efficiency or Capacity
SOFCs	0.2 $/kWh	2500 kW	500 kW	52%
Electric heat pump	0.02 $/kWh	600 kW	0 kW	2
Electric refrigeration	0.02 $/kWh	720 kW	0 kW	1.5
Thermal refrigeration	0.02 $/kWh	800 kW	0 kW	1.5
Battery	0.09 $/kWh	0.9	0.2	1300 kWh
Heat storage tank	0.003 $/kWh	1	0	1900 kWh
Photovoltaic power	0.008 $/kWh	-	-	-
Wind power	0.07 $/kWh	-	-	-

provides the relevant parameters required for calculating energy management strategies, such as unit costs and equipment operating limits.

4.2. Energy Management Results Analysis

The case study examines three distinct scenarios to evaluate the economic performance of the ship’s multi-energy supply system and emphasize its operational advantages.

(1)

Hybrid heat and power storage for case 1: This configuration is commonly employed in ships with diverse energy demands. It is well-suited for optimizing energy utilization and efficiently meeting both power and thermal load requirements.

(2)

Power storage, only for case 2: Some ships, particularly those engaged in short-distance navigation or with low power demands, may rely solely on power storage systems. This scenario is also applicable to pure electric ships or those dependent on independent energy systems.

(3)

Heat storage, only for case 3: Certain ships, especially those requiring substantial thermal energy, such as those equipped with heating equipment, may exclusively rely on heat storage systems.

To compare the economic performance of the ship’s multi-energy supply system and highlight the economic benefits derived from its operation, we analyze the battery storage and heat storage tanks under three different operating conditions. Case 1: In this scenario, we analyze and optimize the combined operation of battery storage and heat storage to achieve an optimal balance between power and thermal energy requirements. Case 2: This scenario focuses exclusively on analyzing and optimizing the operation of the battery storage system. Case 3: Here, our analysis and optimization efforts concentrate on the operation of the heat storage system alone.

By developing tailored energy management strategies for these three operating conditions, we can assess and improve the economic performance of the ship’s multi-energy supply system. This analysis aims to provide valuable insights into the cost-effectiveness and efficiency of the system and ultimately offers to support sustainable and economical energy utilization in ship operations. The comparison of economic indicators among these three cases allows us to evaluate the financial aspects of the system and identify any potential improvements.

The energy management results for case 1, which incorporates hybrid power and heat storage, are presented in Figure 4. The ship’s electrical demand is primarily met by the solid-oxide fuel cell (SOFC), which has a total power output of 19,154 kW. Additionally, the wind power system contributes 2905 kW, and the solar power system provides 1340 kW. The battery storage has a total power capacity of 1440 kW and a discharge power of 1430 kW. To meet the ship’s high electrical demand, the SOFC operates at a high-power state and simultaneously generates a significant amount of heat.

The ship’s thermal demand is mainly supplied by the waste heat from the SOFC, with a total heat supply of 13,171 kW. The electric heat pump further contributes 7798 kW of thermal power, and the heat storage tank has a thermal storage capacity of 1116 kW, with a heat release power of 1147 kW. The cooling demand of the ship is entirely satisfied by the absorption refrigeration units, which have cooling capacities of 17,760 kW. Since the SOFC operation provides both electrical and thermal energy, the compression refrigeration units are not in operation. This ensures an ample supply of waste heat, improving the overall cost-effectiveness of the system.

These results demonstrate that the hybrid power and heat storage system effectively meet the ship’s electrical, thermal, and cooling demands. The integration of the SOFC, wind power, solar power, battery storage, and heat storage components optimizes energy utilization, enhancing the economic viability and sustainability of the ship’s energy system.

During the nighttime navigation phase from 1:00 to 7:00, during which the ship operates at lower loads, the power supply is primarily used for onboard lighting and essential equipment. The thermal load is relatively low during this time, and the heat storage tank helps to reduce the electrical demand on the equipment. The SOFC operates at its minimum power output. The excess power generated by the SOFC and wind power is used to charge the battery. However, from 4:00 to 7:00, the ship’s engines may start running to preheat for subsequent high-load operations. The thermal load continues to increase while the electrical load remains low. During this period, the battery discharges to support part of the electrical load, and the SOFC operates at a lower power level. The heat storage tank depletes its thermal storage capacity temporarily, resulting in a lack of waste heat storage.

From 8:00 to 10:00, as the ambient temperature rises and crew activities increase, the ship requires more electricity to support the operation of various pieces of equipment. During this period, the electrical load is high while the thermal load is low. The excess heat generated by the SOFC is stored in the heat storage tank.

From 11:00 to 15:00, the ship operates at a low thermal and electrical load. From 20:00 to 24:00, as the temperature drops, the ship absorbs less ambient heat, and most equipment and systems are either turned off or operate at low power. Consequently, the cooling and electrical loads are low, resulting in a reduced total heat demand. During these time slots, the energy storage devices are appropriately charged, and heat is stored to replenish the energy discharged continuously in the preceding time periods. The SOFC operates at a higher power level during these periods in order to maintain the stability of the state of charge and heat storage devices.

During the remaining time periods, the SOFC no longer provides a significant amount of power and heat. It operates at a low power level, relying on the discharge of the photovoltaic system, wind power, and batteries to compensate for insufficient electrical demand. The electric heat pump and heat storage tank are utilized to meet the thermal energy requirements. This operational strategy ensures a sufficiently reliable energy supply to meet the demand at different time periods while maximizing the advantages of renewable energy and energy storage technologies.

The energy management results for case 2, which focuses solely on battery storage, are presented in Figure 5. The primary source of power for meeting the ship’s electrical demand is the SOFC, with a total power output of 19,129 kW. The wind power system contributes 2905 kW, and the solar power system generates 1340 kW. The battery storage system has a total capacity of 1691 kW, with a discharge power of 1729 kW. Given the high electrical demand of the ship, the SOFC operates at a high power level, resulting in a significant amount of waste heat production. This waste heat is utilized to meet the ship’s thermal demand, with a total heat supply power of 13,156 kW. The electric heat pump provides an additional thermal power output of 7844 kW. The ship’s cooling demand is entirely satisfied by the thermal refrigeration system, which has a total cooling power output of 17,760 kW. The electrical refrigeration system remains inactive in this case since the SOFC operation provides both electrical and thermal energy, making the overall system more cost-effective.

These results demonstrate that the battery storage system effectively supports the ship’s electrical demand, working in conjunction with the SOFC, wind power, and solar power systems. The waste heat from the SOFC is efficiently utilized to meet the ship’s thermal demand. The integration of these components optimizes energy utilization, enhancing the economic viability and sustainability of the ship’s energy system.

Compared with operating condition 1, it is evident that the absence of a heat storage tank leads to an increase in the output of the electric heat pump. During certain time periods, the SOFC can operate at its minimum power level, relying on the photovoltaic system, wind power, and battery discharge to compensate for the insufficient electrical demand. In the absence of a heat storage tank, the thermal load is solely supplied by the SOFC and electric heat pump. To avoid wasting waste heat from the SOFC into the environment, the system prioritizes matching the thermal load. The power output of the SOFC is determined based on this premise, and it works in synergy with the photovoltaic system, wind power, and battery discharge to meet the electrical load and the power demand of the compression refrigeration system and electric heat pump.

During specific time periods, such as 6:00–8:00, 10:00, 14:00–17:00, 20:00, and 24:00, the ship’s engines and other mechanical equipment generate a significant amount of heat during operation. Therefore, the cooling system needs to operate for longer periods and with a higher level of intensity to maintain temperature stability. These operations typically do not require a substantial amount of electrical power supply. It is preferable to appropriately charge the battery during these time slots. The cumulative thermal load demand from the thermal refrigeration system increases, resulting in a higher overall thermal demand, while the contribution of the electric heat pump to the thermal load is relatively low.

The results for case 3, which only involves the heat storage tank, are presented in Figure 6. It can be observed that the ship’s electrical demand is primarily met by the SOFC, with a total power output of 19,240 kW. The power generation from wind power and photovoltaic systems remains unchanged. Due to the high electrical demand of the ship, the SOFC operates at a high-power level, generating a significant amount of heat. The ship’s thermal demand is mainly supplied by the waste heat from the SOFC, with a total heat supply power of 13,233 kW. The electric heat pump provides a heat power output of 7663 kW. The heat storage tank has a total heat storage capacity of 1425 kW, with a heat discharge power of 1405 kW. The ship’s cooling demand is primarily fulfilled by the thermal refrigeration system, with a total cooling power output of 17,575 kW. The electric refrigeration system contributes a cooling power of 185 kW.

Compared with the previous cases, the heat storage tank plays a crucial role in meeting the ship’s thermal energy demand. It effectively stores excess waste heat from the SOFC during high-power operation periods and releases it during low-power operation periods, thus ensuring a stable and reliable thermal supply. The electric heat pump and thermal refrigeration system work in conjunction with the heat storage tank to optimize thermal energy utilization and meet the ship’s cooling requirements.

In comparison to case 1, where the battery storage is present, it can be observed that in the absence of the battery, the output of the SOFC increases. Without the battery, the electrical demand is primarily met by the SOFC, with only a portion being compensated by the photovoltaic and wind power systems. The electric heat pump operates during specific time periods, namely 1:00–6:00, 13:00–15:00, and 18:00–20:00, utilizing excess electricity for heating and heat storage purposes.

The operation cost of the heat storage tank is relatively low, and its charging and discharging characteristics are fully utilized to enhance its economic efficiency. Therefore, the thermal load is given priority, and the SOFC operates at a higher power level, with the heat storage tank providing additional heat supply.

During certain time periods, when there is insufficient waste heat available, the thermal refrigeration system may not be able to supply sufficient power. In such cases, the electric refrigeration system is activated to compensate for the inadequate cooling power. However, the contribution of the electric refrigeration system is relatively small compared to the thermal refrigeration system.

By analyzing these different operating conditions, it becomes evident that the integration of various energy storage systems and components, such as batteries and heat storage tanks, can significantly optimize energy utilization, enhance system efficiency, and reduce operational costs in ship energy management.

From

Table 2. Comparison of economic indicators of three cases.

Items	Cf (kg)	Co ($)	Total Cost ($)
Case 1	1689.0	8726.4	70,881.6
Case 2	1800.7	8846.4	75,110.4
Case 3	1710.2	8985.6	71,920.0

, it can be observed that the integration of the heat storage tank and battery has significantly reduced economic costs in different operating conditions. When comparing operating case 2 to case 1, the integration of the heat storage tank resulted in a 6.0% cost reduction. Similarly, when comparing operating case 3 to case 1, the integration of the battery led to a reduction of approximately 1.5% in costs. These findings highlight the positive impact of introducing the heat storage tank and battery on the system’s economic efficiency.

Furthermore, the integration of the heat storage tank and battery has also positively affected fuel consumption and operation and maintenance costs. When comparing case 2 to case 1, fuel consumption and operation and maintenance costs were reduced by 6.1% and 1.4%, respectively. Similarly, when comparing operating case 3 to case 1, fuel consumption and operation and maintenance costs were reduced by 1.2% and 2.9%, respectively. These reductions not only contributed to lower greenhouse gas emissions, energy conservation, and improved air quality, but also signified a decreased overall workload for the equipment. Moreover, the effective maintenance resulting from these cost reductions extended the lifespan of the equipment, further enhancing the economic benefits of the integrated system. These economic and operational improvements underscore the significance of integrating energy storage systems and components in ship energy management and provide sustainable and cost-effective solutions.

5. Conclusions

This paper presents an energy management and economic optimization model for the multi-energy supply of ships. This is carried out with the objective of minimizing economic costs while considering energy balance, equipment safety constraints, operational constraints, and coupling characteristics among different energy sources. By optimizing the scheduling and efficiently managing the operational states and energy supply of each device, our proposed approach achieves the goal of minimizing economic costs and maximizing energy utilization efficiency.

(1)

The integration of a heat storage tank effectively prevents the waste of waste heat from the SOFC, resulting in maximum energy-saving benefits. By storing excess heat in the heat storage tank, it can be utilized for other systems or heating when needed, thereby reducing energy waste. The integration of a battery provides additional flexibility and energy-saving effects to the system, allowing the electrical refrigeration to be idle and reducing reliance on energy-intensive equipment.

(2)

Through our analysis, we have observed that the integration of heat storage devices can reduce economic costs by approximately 6.0%, fuel consumption by 6.1%, and operation and maintenance costs by 1.4%. Similarly, the integration of energy storage devices can reduce economic costs by approximately 1.5%, fuel consumption by 1.2%, and operation and maintenance costs by 2.9%. These results significantly reduce the energy consumption and operational costs of the ship while improving energy utilization efficiency.

(3)

Furthermore, the variability of hybrid energy storage on ships depends on factors such as the selected storage timing, the size, and the variation of the thermal, electrical, and cooling loads. It is important to consider these factors comprehensively based on specific circumstances. Depending on the energy demands and supply conditions, energy storage systems may require more frequent charging and discharging operations, which may slightly increase the variability of heat and electricity storage.

In conclusion, the integration of a heat storage tank and battery into the multi-energy supply system for ships contributes to maximizing energy-saving benefits, and reducing economic costs, fuel consumption, and operation and maintenance costs. It improves energy utilization efficiency and provides flexibility in managing energy supply. However, the variability of the ship’s hybrid energy storage should be carefully considered based on specific load profiles and energy requirements.