Energy Management Strategies for Hybrid Propulsion Ferry with Different Battery System Capacities

Abstract

The International Maritime Organization (IMO) has been continuously strengthening environmental regulations to reduce greenhouse gas emissions from ships, which has led to increased attention on hybrid ship propulsion systems combining hydrogen fuel cells and batteries. This study analyzes the energy management strategy of a hybrid ship propulsion system in relation to changes in the battery system’s energy capacity. The target vessel was set as a 500 kW-class ferry operating for 24 h, and the maximum current rate (C-rate) and effects of the equivalence factor, which are key elements of the energy management problem, in relation to changes in energy capacity were investigated. The results show that while changes in the battery system’s energy capacity do not significantly affect the optimal operating point of the hybrid ship propulsion system, they are highly influenced by the response speed of the hydrogen fuel gas supply system and fuel cells, as well as the maximum C-rate required by the battery system. Furthermore, the equivalence factor, one of the key parameters in the optimization problem, tends to vary depending on the degree of charging and discharging, as it affects the equivalent fuel consumption of the battery system.

1. Introduction

The environmental regulations of the International Maritime Organization (IMO) demand major changes in the global shipping industry. In particular, the demand for reducing greenhouse gas (GHG) emissions must be met for the successful operation of future ships. The shipping industry is responsible for a considerable portion of global GHG emissions. Accordingly, the IMO has reinforced regulations to reduce GHGs that are emitted from ships. At the Marine Environment Protection Committee (MEPC) 80th session held in July 2023, the IMO set the goal of achieving net zero by around 2050 [1] and reducing GHG emissions from ships by more than 20% by 2030 compared to 2008 and by more than 70% by 2040 as intermediate inspection indices. It also announced strategies to use low-emission and emission-free technologies or fuels for 5% to 10% of the total amount of energy used in international shipping by 2030. Eco-friendly fuel propulsion and energy production technologies are expected to be disseminated at high speed in the future.

Among various eco-friendly fuels and technologies, the hybrid ship propulsion system, which combines a hydrogen-powered fuel cell with a battery system, is deemed a promising technology that can realize carbon neutrality for the shipping industry [2,3,4,5,6]. Since fuel cells generate electricity through the electrochemical reactions of hydrogen and oxygen and emit only water as a by-product, they have attracted attention as a clean energy source with no GHG emissions. In addition, the use of the battery system as auxiliary equipment enables stable power supply even in peak load situations or when the output of the fuel cell is not sufficient. In particular, the battery system is charged under low loads and discharged when high output is required for the fuel cell to operate at its optimal point, taking into consideration the energy efficiency that varies with output fractions.

The hybrid propulsion system combines various power sources, such as fuel cells, engines, and batteries, and utilizes two or more power sources to produce the propulsion power of mobility (e.g., ships) that varies over time. As the power generation efficiency of fuel cells varies depending on the output, producing propulsion power during efficient fuel cell operation is very important for improving the energy efficiency and economic feasibility of the entire system. For this reason, the energy management system (EMS) is generally installed in the hybrid ship propulsion system. For the fuel cell and battery combined system, the EMS distributes the output of the fuel cell and battery system over time for the fuel cell to operate with optimal efficiency [7].

Studies have been actively conducted on energy management algorithms for a hybrid propulsion system combining two or more power sources for various vessels. Jung and Chang (2023) presented an EMS that can be applied to the hybrid ship propulsion system. They combined a fuel cell and battery using deep reinforcement learning algorithms for 2MW-class platform supply vessels that use liquid hydrogen as fuel, thereby comparing the performance with conventional optimization algorithms [7]. Antonopoulos et al. (2021) applied an EMS based on model predictive control methodology to hybrid power plants installed on ships [8]. Bassam et al. (2017) proposed a multi-scheme EMS that combines a state-based EMS, equivalent fuel consumption minimization strategy (ECMS), charge-depleting, charge-sustaining EMS, and classical proportional–integral controller-based EMS for passenger ships that use fuel cells, and analyzed the performance [9]. Kalikatzarakis et al. (2018) proposed an energy management algorithm for a hybrid ship propulsion system that can utilize renewable shore charging and investigated its performance for various operation profiles [10]. Research on energy management for hybrid power systems has been actively conducted in applications beyond maritime vessels. Lee and Cha (2021) determined an equivalence factor applicable to the ECMS of hybrid electric vehicles using a reinforcement learning algorithm [11]. Deng et al. (2022) proposed a twin delayed deep deterministic policy gradient-based EMS for hybrid railway vehicles and developed a stochastic training environment to simulate real driving conditions [12].

The energy management strategies proposed through previous studies can be applied to efficiently produce power for the target system based on various optimization and machine learning algorithms. Meanwhile, despite the application of the same energy management algorithm, the power distribution strategy and power generation efficiency of the entire propulsion system may vary depending on the energy capacity of the battery system that assists the operation of the fuel cell. However, studies that analyze the optimal operation strategy of the hybrid ship propulsion system according to the energy capacity of the battery system are few.

Therefore, in this study, the energy management strategy of the hybrid ship propulsion system that combines proton-exchange membrane fuel cell (PEMFC) and battery systems was analyzed according to the energy capacity of the battery system. A 500 kW-class ferry was set as the target ship for the installation of this system, and calculations were performed for the operation profile of the ship. In addition, sensitivity analysis was conducted to determine the changes in major parameters that constitute the energy management algorithm. The contents of the manuscript are organized as follows. Section 2 introduces the model description of the PEMFC and battery systems. Section 3 discusses the energy management algorithm, which is based on sequential quadratic programming (SQP). Section 4 presents the results and discussion, and Section 5 summarizes the main conclusions of this study.

2. Model Description

2.1. Target Ship: Hybrid Propulsion Ferry

In this study, a 500 kW-class ferry was set as the target ship to which the hybrid ship propulsion system was applied. A ferry is a ship that carries passengers, cargo, and vehicles between two ports. The size, shape, and propulsion power of the ship vary depending on the cargo type and ship route. Figure 1 shows a typical load profile of a ferry [13]. In many sections, the propulsion power rapidly changes over time during operation, indicating that the hybrid ship propulsion system can effectively produce power. It should be noted that the power demand of the ferry assumed in this study may vary depending on the vessel’s operating environment and conditions. However, the operational scenario presented in Figure 1 was established considering the primary operational modes of a ferry in actual service.

In this study, the specifications of the fuel cell and battery systems were assumed to use the load profile as shown in Figure 1, based on which an optimal power split was performed. The total mass of the hybrid propulsion ferry is considered to be significantly larger than that of the battery system. Accordingly, it was assumed that the propulsion power would remain relatively unaffected by the energy capacity of the installed battery system.

2.2. Proton-Exchange Membrane Fuel Cell (PEMFC)

A PEMFC is a device that produces electricity using hydrogen as fuel. It uses polymer electrolyte membranes to move the protons of hydrogen between electrodes. As electrons travel through the external circuit, they produce electricity. In this process, protons combine with air or oxygen to produce water. Therefore, when power is produced by supplying hydrogen to a PEMFC, power is produced in an eco-friendly manner without discharging GHGs other than water.

Other benefits of PEMFCs include high reaction speed and low operating temperature [14]. A PEMFC exhibits fast start-up and can easily respond to immediate load fluctuations because it operates at a lower temperature compared to other fuel cells that operate at higher temperature (e.g., solid oxide fuel cell, molten carbonate fuel cell, etc.). This makes PEMFCs applicable in various fields, such as electric vehicles and large power generation systems. However, since PEMFCs do not have a short response time for load changes compared to traditional power sources like internal combustion engines, they are typically operated in combination with an energy storage system such as a battery system. This configuration allows the system to discharge power when there is a deficit and to recharge when there is surplus energy. Also, the platinum catalysts and polymer electrolyte membranes contained in PEMFCs cause durability problems and complicate the hydrogen fuel supply. Therefore, PEMFCs require high costs, which requires improvement through research and development in the future [15].

The mathematical model of a PEMFC can be applied to analyze and predict the electrochemical properties and performance of the cell. The output voltage of a PEMFC is calculated by subtracting voltage losses from the theoretical voltage that can be obtained through the Nernst equation in Equation (1). Voltage losses are divided into activation, ohmic, and concentration losses.

$$V_{cell}=E_{rev}-{\eta }_{act}-{\eta }_{ohmic}-{\eta }_{conc}$$

(1)

Referring to the results of modeling performance based on Equation (1) in previous studies, related to hybrid ship propulsion systems for fast and efficient optimization calculations, a reference table was created [2,3,7,16]. By modeling the electrochemical reactions through Equation (1), it is possible to calculate the voltage that varies with the current flowing inside the fuel cell. In particular, when calculating the three loss terms aside from the theoretically determined reversible voltage, incorporating parameters related to the actual PEMFC product allows for accurately simulating the performance of that specific product. Subsequently, the performance curve was approximated according to the output of the PEMFC through the table and used for optimal power split.

2.3. Lithium-Ion Battery

A lithium-ion battery is a secondary battery that uses the principle that as lithium ions move between the anode (graphite or carbon materials) and cathode (lithium metal oxide), the cell is repeatedly charged and discharged. Lithium ions move from the cathode to the anode during charging and from the anode to the cathode during discharge, with the discharging electrons supplying electricity. Since lithium-ion batteries have high energy density compared to other battery technologies, they have been widely used in industries where weight reduction is important, such as electric vehicles and electricity-powered ships.

The dynamic characteristics of lithium-ion batteries can be interpreted through an equivalent circuit model (ECM) that is expressed using electrical circuit elements [17,18]. An ECM typically consists of voltage sources, resistors, and capacitors. A voltage source represents the open-circuit voltage of the lithium-ion battery, which varies depending on the state of charge (SOC). A resistor refers to the electrical resistance loss that occurs inside the battery, and the voltage drops during charging and discharging. A capacitor indicates the capacity of the battery, and mainly reflects the dynamic response characteristics of the battery.

In this study, a two-dimensional reference table was created for the SOC, and the cell temperature based on the charging and discharging efficiency of the battery system was calculated through an ECM with two resistors, one capacitor, and one voltage source, which was used for optimal power split [2,3,7,19]. Assuming that the operating temperature is maintained at 20 °C through heat management of the battery system, the change in energy capacity is reflected in optimization calculations based on the contents described in the next section.

3. Energy Management Algorithm

In this study, for the propulsion power of the ship that changes over time, the ECMS problem was defined and optimal power split was performed using the sequential quadratic programming (SQP) algorithm, which is applicable to nonlinear constrained optimization problems, whereby the nonlinear optimization problem is repeatedly linearized to gradually find the optimal solution by solving quadratic programming problems at each iterative step [7,20].

The objective function and constraints of the ECMS problem for optimal power split are defined as follows. The objective function to minimize is the consumption of hydrogen supplied for power generation by the fuel cell at each time point. In summary, the role of the energy management algorithm is to determine how to allocate the outputs of the PEMFC and the battery in response to the vessel’s time-varying propulsion power demands, thereby minimizing the fuel consumption over the vessel’s operation. In addition, at all time points, the propulsion power of the ship must be produced by the fuel cell and battery. In other words, when the output of the PEMFC is lower than the required propulsion power of the vessel, power must be discharged from the battery. Conversely, when the PEMFC output exceeds the propulsion power, the surplus power should be charged into the battery. The SOC represents the state of charge of the battery, indicating its current charged energy level. It varies depending on the output power of the battery system. In this instance, the output of the PEMFC must fall within the set of minimum and maximum output.

$$Min{\dot{m}}_{H2}\left(P_{FC}\left(t\right)\right)$$

(2)

$$P_{FC}\left(t\right)+P_{BAT}\left(t\right)=P_{Required}\left(t\right)for\forall t\in [0,t_{final}]$$

(3)

$$SOC\left(t+1\right)=SOC\left(t\right)-{\displaystyle \frac{P_{BAT}\left(t\right)\times \mathsf{\Delta }t}{E_{BAT}}}$$

(4)

$$P_{FC,min}\le P_{FC}\left(t\right)\le P_{FC,max}for\forall t\in [0,t_{final}]$$

(5)

The problem of power distribution under the current ship and system conditions without knowing the propulsion power of the ship can be classified as an online energy management problem [21]. When an algorithm for an online EMS is created, it should be prepared for unknown ship propulsion power. Therefore, equivalent hydrogen consumption is calculated based on the output and SOC of the battery system using Equation (6), and is reflected in the overall hydrogen consumption in optimization.

Table 1. Parameters for optimization problem.

Parameters	Value
Operation time ($t_{final}$)	24 h
Minimum SOC (${SOC}_{min}$)	0.2
Maximum SOC (${SOC}_{max}$)	0.8
Reference SOC (${SOC}_{ref}$)	0.5
Minimum output of PEMFC ($P_{FC,min}$)	0 kW
Maximum output of PEMFC ($P_{FC,max}$)	520 kW
Equivalence factor ($\mu$)	0.3, 0.5, 0.7
Power coefficient for SOC ($p$)	1
Potential energy output of PEMFC (${\eta }_{FC,min}$)	22.05 kWh/kg

shows the parameters required for optimal power split and equivalent hydrogen consumption. Among the parameters listed in Table 1, the operation time, minimum output of PEMFC, and maximum output of PEMFC are assumed values based on the propulsion system of a 500 kW-class ferry. Additionally, the minimum SOC, maximum SOC, and reference SOC can vary depending on the technical characteristics of the battery system provided by manufacturers.

The parameters that determine equivalent hydrogen consumption are the equivalence factor and the power coefficient. The equivalence factor measures the proportion of hydrogen flow, converted based on the output of the battery system, relative to the output of the PEMFC. Additionally, the power coefficient is a factor that sets the penalty imposed on the converted hydrogen flow when the SOC of the battery system deviates from the reference value over time, typically assigned values of 1 or 3.

$${\dot{m}}_{H2,BAT}(t)={\displaystyle \frac{\mu }{{\eta }_{FC,min}}}\times P_{BAT}\left(t\right)\times {\{1-{\displaystyle \frac{SOC\left(t\right)-{SOC}_{ref}}{0.5\left({SOC}_{max}-{SOC}_{min}\right)}}\}}^p$$

(6)

One of the important measures for ensuring the operational stability of the battery system is the C-rate [22,23,24]. The C-rate is the ratio of the output of the battery system to its energy capacity. For example, 0.5C, 1C, and 2C indicate discharging or charging by the total energy capacity of the battery system for two hours, one hour, and 30 min, respectively. In this study, Equation (7) was used to examine the maximum C-rate according to the energy capacity of the battery system.

$$C_{rate,max}={\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}\left\{\left|P_{BAT}\left(t\right)\right|\right\}}{E_{BAT}}}for\forall t\in [0,t_{final}]$$

(7)

In addition, simulation cases were defined in this study to analyze the sensitivity of optimal power split according to the energy capacity and equivalence factor of the battery system, as shown in

Table 2. Simulation cases for optimal power split of PEMFC and battery systems.

Case Index	Energy Capacity of Battery System	Equivalence Factor
Ref. Case	463 kWh	0.5
Case 1-1	347 kWh	0.5
Case 1-2	231 kWh	0.5
Case 1-3	116 kWh	0.5
Case 1-4	46 kWh	0.5
Case 2-1	463 kWh	0.3
Case 2-2	463 kWh	0.7

. For each case, optimization (i.e., optimal power split of PEMFC and battery systems) was performed using the aforementioned SQP algorithm. The algorithm used in the calculations can be applied to optimization-based energy management for various applications, such as vessels, vehicles, and trucks equipped with hybrid propulsion systems. This study utilized the same methodology to analyze changes in energy management strategies based on the energy capacity of the battery system, without considering variations in the optimal operating points due to changes in the methodology (i.e., the performance of different optimization algorithms).

For real-world energy system power distribution, the key parameters assumed in Table 1 must be adjusted based on the actual system specifications (e.g., design specifications, as shown in [25]). Additionally, a review of various energy management methodologies applicable to energy management is essential to identify the most efficient approach for allocating the outputs of power sources.

4. Results and Discussion

Figure 2 shows the power split calculated through the optimization algorithm and SOC variation when the energy capacity of the battery system is approximately 500 kWh (i.e., the reference case). The battery system is observed to rapidly discharge or charge, to assist in the operation of PEMFC when the propulsion power of the ship rapidly increases (t = 10 h) or decreases (t = 15 h), and some power needs to be charged and discharged for efficient operation. The SOC remains between approximately 20% and 55% during the operation of the ship. The maximum output required for the battery system was calculated to be approximately 380 kW. In the future, the C-rate will be further discussed through the sensitivity analysis results for the energy capacity of the battery system.

Figure 3 shows only the output of the battery system for the optimally performing power split according to the energy capacity of the battery system. The time to assist the operation of the PEMFC decreases as energy capacity is reduced compared to the reference case, even though the operation strategy of the hybrid ship propulsion system does not significantly change as the energy capacity of the battery system decreases. In other words, for the hybrid propulsion ferry set as the target ship, the energy capacity of the battery system has no significant impact on the optimal energy management strategy and needs to be set according to the response speed of the PEMFC.

Based on the output of the battery system calculated above, the maximum C-rate of the battery system according to the energy capacity can be identified in

Table 3. Maximum C-rate for different energy capacity of battery system.

Simulation Case	Maximum C-rate
Ref. Case	0.82
Case 1-1	1.09
Case 1-2	1.52
Case 1-3	2.88
Case 1-4	6.26

. The lowest C-rate of 0.82 corresponds to an energy capacity of approximately 500 kWh, which was set as the reference case, and the maximum C-rate increases despite the reduction in energy capacity because the optimal energy management strategy does not change significantly. The maximum C-rate is 6.26 for approximately 50 kWh, which is the lowest energy capacity. Since this causes a high load for the thermal management system and is a problem related to the safety of the target system, the energy capacity of the battery system should be set considering the allowable C-rate of the battery system commercially used for mobility.

Figure 4 shows the output of the battery system for the different equivalence factor of the battery system affecting the performance of an optimization-based EMS, i.e., the equivalence factor and corresponding SOC variation. When the energy capacity of the battery system is set to the reference case, the charging and discharging power of the battery system shows different peak values over time because of the change in equivalence factor. Since an increase in equivalence factor indicates an increase in equivalent hydrogen consumption for power charging and discharging of the battery system, the absolute value of the battery system output tends to decrease despite showing the same tendency. In Case 2-1, with the lowest equivalence factor, there are sections where the minimum SOC is lower than 0.2 because the SOC penalty during operation was calculated to be low.

5. Conclusions

This study analyzed an energy management strategy according to the energy capacity of a battery system installed in a hybrid ship propulsion system applicable to a 500 kW-class ferry. Using the ECMS-based SQP algorithm for energy management, the equivalent fuel consumption of the battery system was calculated through the output of the battery system, SOC, fuel consumption of the PEMFC, equivalence factor, and power coefficient, as reflected in the optimization. A total of seven simulation cases were defined to examine the effects of changes in the energy capacity and equivalence factor. The energy capacity of the investigated battery system ranged from 46 to 463 kWh. The calculation results showed that the power split strategy of the target system during operation did not significantly change with the energy capacity of the battery system, indicating the necessity of setting the energy capacity based on the response speed of the PEMFC, hydrogen fuel gas supply system (FGSS), and maximum C-rate. In addition, the sensitivity of the equivalence factor, which significantly affects the equivalent fuel consumption of the battery system, was analyzed. As the equivalence factor changed, the equivalent fuel consumption increased or decreased, causing some changes in the maximum charging and discharging power of the battery system and the time to assist the operation of the PEMFC.

Currently, most research and development on hydrogen-fueled vessels focus on configurations of hybrid propulsion systems that combine fuel cells and battery systems. However, detailed discussions on the energy capacity of battery systems, which assist in fuel cell operation and impact the energy efficiency of the propulsion system and power plant, have not been sufficiently addressed. Therefore, the results of this study are expected to provide major insights into the design and interpretation of a hybrid ship propulsion system that uses hydrogen as fuel and combines fuel cells and batteries. The study is also expected to serve as a guideline for setting the optimal energy capacity of the battery system. However, deriving economically optimum points that consider the initial investment and operation cost of the target system as well as the cost of fuel consumption through follow-up research requires the development of a validation framework that can be generalized to various ship types so as to contribute to the successful dissemination of the hybrid ship propulsion system.