Contents Introduction
With increasing attention to environmental protection around the world, great efforts have been made to find an alternative energy instead of using fossil energy in ship industry [1]. Fuel cell systems (FCS) have become a promising solution owing to their features including high energy efficiency and density, zero local emissions as well as low noise [2], [3]. FCS is proven to be more efficient than traditional diesel engines which convert fossil fuels to mechanical energy or electricity [4].
However, the wide usage of FCS is greatly limited by their disadvantages including incapability of energy storage, poor dynamic characteristics, short durability and great expense. Considering these disadvantages, a sole FCS may not be able to satisfy the transient power demand. Consequently, fuel cell hybrid power systems (FCHPS) comprising an FCS and an energy storage system (ESS) are usually adopted to make up these drawbacks [5]. One of the considerable merits of the FCHPS is that the FCS in the FCHPS is only responsible for base load instead of peak demand, which makes the FCHPS more cost-effective and energy-efficient than using the sole FCS [6]. Instead, if all the power demand of a boat is satisfied by an FCS without any auxiliary, the power capacity of the FCS has to be increased and, thus, the scale, expense and hydrogen consumption will be increased significantly [7]. Besides, an FCS is featured with slow dynamic response to changes in current, voltage and load [8], for the reason that the internal mass transfer lags actual power requirement [9]. Practically, the FCS needs to ensure a good durability with slow load dynamics [10], since load demand fluctuations may damage the FCS stack and reduce its service life by fuel starvation, flooding, membrane drying and pressure imbalance across the fuel cell membrane [11]. Therefore, the rapid load dynamics is supplied by other energy sources in the FCHPS. Furthermore, the efficiency of an FCS will be at the most desirable level under only partial load conditions [12]. Lastly, an ESS is able to restore energy. Generally, battery packs are preferred among various choices of energy storage devices of FCHPS [13], however, shipboard electric propulsion systems suffer a great deal of power fluctuations under many conditions from rotational motions of propellers and waves [14], as a result, a sole battery pack cannot satisfy the rapid variations of power and torque, and fast charging and discharging may decrease its lifetime. Therefore, an ESS combining battery and ultra-capacitor (UC) is adopted in the present study.
The performance of different components of the hybrid power system must be levered by a proper energy management system. Besides, the power flow between different power generation units should be coordinated properly to meet the power requirement of the boat. Many energy management strategies (EMSs) have been studied recently. Generally, these strategies can be clarified into three different types: rule-based, optimization-based and intelligent algorithm-based strategies. The first category is widely used in hybrid cars and ships by operating the online diesel engines at their most efficient region while adopting the ESS for leverage [15], and is proven to be able to achieve a higher economic performance than traditional PID methods [16]. Tang et al. [17] propose a wavelet transform and rule-based EMS for a fuel cell and ultra-capacitor hybrid power ship, in which the rule-based energy management strategy is used to keep the state of charges (SOC) of a UC within normal level. Another often used rule-based strategy is fuzzy logic which considers the power demand of power systems and SOC of the ESS within them. One typical example of this method is the strategy proposed for a Photovoltaic/diesel engines/batteries hybrid ship in [18], where the power distribution can be achieved by a series of IF-THEN rules based on experience and expert knowledge. Similarly, a finite state machine based energy management strategy is proposed in [19] for fuel cell/battery/ultra-capacitor powered vehicles. However, these energy management strategies do not consider the dynamic performance of energy sources and, thus, are unable to distribute the energy demand according to their dynamic characteristics.
The optimization-based strategies include two types: instantaneous optimization and dynamic optimization. Van Vu et al. [20] develop a model prediction control method to minimize a cost function. Kanellos et al. [21] develop a dynamic programming-based algorithm for a wind/PV/diesel/battery hybrid system, of which the energy management strategy is a multiple step procedure with respect to the state of charge of the battery. In [22], the authors propose a dynamic programing EMS for different hybrid propulsion structures. Interested readers can refer to [23] for more optimization-based energy management strategies. The intelligent algorithm-based strategies, such as deep reinforcement learning, are mostly applied to hybrid electric vehicles [24], [25]. In recent research work, the operation performance of fuel cells has been studied considering their dynamic performance. In [26], the authors propose an online extremum seeking algorithm-based EMS for a dual FCS/battery hybrid locomotive, which takes into consideration the dynamic performance of the FCS. In [27], an energy management strategy based on optimal equivalent consumption minimum strategy is proposed to identify the parameters of FCS in the dynamic operation process.
To sum up, these EMSs put their emphasis on the whole system but fail to capture the dynamic characteristics of individual power generation units. Although there might be some research works that consider the dynamic performance of energy sources, they are either with simple rules and applied to simple shipboard hybrid power system structures, e.g., Ref. [17], or applied to electric vehicles, e.g., Ref. [28]. The application of such energy management strategies in hybrid ships remains to be discussed. Therefore, in this paper, an EMS is proposed for a hybrid ship considering the dynamic response of each power source to load changes. The main contributions are summarized as follows:
A hybrid power system that contains FCS, batteries and UC is proposed for a small cruise ship. The proposed hybrid power system can achieve zero emissions;
A wavelet transform (WT) and fuzzy logic-based EMS is proposed to allocate power requirement to each power source. The WT is used to decouple the power demand into high and low frequencies, and the low frequency power is shared by the FCS and batteries due to their relatively poor dynamic performance whereas the high-frequency power is supplied by the UC considering its high power density and fast response to pulse power and fluctuations. Then, fuzzy logic is used to maintain the SOC of the ESS within safe level;
The proposed EMS is validated on a simulated hybrid power system in MATLAB/Simulink and is proven to be able to improve the energy efficiency and extend the life cycle of fuel cells and batteries by reducing their fast and sharp response.
The remainder of this paper is organized as follows. In Section II, the fuel cell/battery/UC hybrid power system of a boat is introduced. Then, the wavelet transform and fuzzy logic-based EMS is proposed in Section III, after which the simulation results are presented and analyzed in Section IV. Finally, in Section V, the whole work is concluded and future work is discussed.
Hybrid Power Systems
In this part, we introduce the FCHPS. The propulsion system of the considered boat is presented in Figure 1, in which the blue lines represent information flow and the red lines stand for power flow. The boat has three energy sources connected to a common switchboard: FCS, batteries and UC. The FCS is connected to the switchboard via a unidirectional boost DC/DC converter, by which the output voltage of the FCS is increased to a same standard level. The power flow from the FCS to the common bus is unidirectional since it cannot store energy. On the contrary, the battery and the UC can not only supply power to the boat but also store energy from the FCS. Therefore, they form the ESS of the hybrid power system and are connected to the common switchboard via bidirectional convertors. When the battery and UC supply power to the boat, their output voltages are increased to the standard voltage level by the DC/DC convertors. Conversely, when the SOCs of the battery and UC are low, they can draw energy from the common switchboard via the DC/DC convertor and get recharged by the FCS. The load demand of the boat includes two parts: service and propulsion load. Service load includes lighting, entertainment and electrical equipments whereas propulsion load drives the boat forward and is the main load of the boat. The typical application of the hybrid power system is a cruise ship in a lake or river, because the hybrid power system is featured with zero emission and, thus, is environmentally friendly.
Generally, several kinds of fuel cells can be defined according to their electrolytes, among which the polymer electrolyte membrane fuel cell (PEMFC) is the most promising one due to its relatively small scale, light weight, and easy access of construction [29], [30]. Hence, a PEMFC is adopted in our simulation in the following sections. Besides, we adopt Li-ion batteries in the hybrid power system because of the high energy and power density [31]. In the simulation, we assume that the rated and maximum power of the fuel cell is 2000 W and 3000 W, respectively. The operating temperature is 55 Celsius degree and the nominal supply pressure of fuel and air is 1.5 bar and 1 bar, respectively. The fuel cell model is set to operate in an efficiency of 62%. The output voltage of the fuel cell is boosted to 380 V by the DC/DC converter, which is the same as that of the common DC bus.
The energy generation and power distribution are managed by the energy management system. At each time slot, real-time power requirement, the SOC of the ESS and the output of each energy source are collected and transmitted to the energy management system. Then, the power demand is split to each energy source according to the proposed energy management strategy, which is embedded in the energy management system. The main objectives of the EMS are:
to satisfy the real-time power requirement of the boat;
to split the power requirement to energy sources properly according to their dynamic characteristics;
to protect the ESS from overcharging and over-discharging;
Energy Management Strategies for the Hybrid Power System
In the present study, the wavelet transform and fuzzy logic-based EMS is proposed to decouple and split the power demand, and maintain the SOC of the ESS within normal level. Firstly, an original power signal can be decomposed into several components at different positions and scales by wavelet transform. The given power signal can be decoupled in both time and frequency domains. In the present study, we decouple the power demand of the hybrid power ship into two parts with different frequencies and split each part to specific energy sources according to their dynamic characteristics. Fuzzy logic is capable of solving complex nonlinear systems with the merits of desirable robustness and good real-time performance [32]. Therefore, in the proposed strategy, fuzzy logic is adopted to protect both the battery and UC from overcharging or over-discharging.
The proposed WT and fuzzy logic-based EMS is presented in Figure 2. In the Figure, the power signal is decoupled into three parts by the wavelet transform, i.e., the reference powers of the PEMFC, Li-ion battery and UC. But wavelet transform does not consider the SOC of the ESS, so the reference power is not the actual power output of each power source. The fuzzy logic takes into consideration real-time power requirement of the hybrid ship, the SOC of the ESS and, then, adjust the reference power obtained from the WT. The output of the fuzzy logic is the amount of power that should be added to the reference power of the battery and UC, i.e., 
\begin{align*} P_{\text {bat}}=&P_{\text {ref-bat}} + P_{\text {fuzzy-bat}}\tag{1}\\ P_{\text {uc}}=&P_{\text {ref-uc}} + P_{\text {fuzzy-uc}}\tag{2}\end{align*}
Since the power requirement is supplied by three energy sources, the actual output of the PEMFC will change accordingly when the power output of the ESS changes. Thus, the final output of the PEMFC power can be calculated as:\begin{equation*} P_{\text {fc}} = P_{\text {ref-fc}} - P_{\text {fuzzy-bat}} - P_{\text {fuzzy-uc}}\tag{3}\end{equation*}
The proposed strategy is introduced in detail in the following subsections.
A. Wavelet Transform
The continuous wavelet transform (CWT) is defined as:\begin{equation*} CWT_{a,b} = \int _{R} x(t)\overline {\Psi _{a,b}(t)}dt = \frac {1}{\sqrt {a}}\int _{R} x(t)\overline {\Psi \left({\frac {t-b}{a}}\right)}dt\tag{4}\end{equation*}
\begin{equation*} \Psi (t)\,\,= \overline {\Psi (t)}\tag{5}\end{equation*}
However, CWT is not proper for practical scenarios. Instead, the efficient discrete wavelet transform (DWT) is preferred. The method to transform CWT to DWT is to select the scale and shift factor according to the power of two and, thus, quantity of wavelet coefficients can be reduced [33]. Thereby, the two factors will be transformed into:\begin{equation*} a = 2^{j}, \quad b = k \bullet 2^{j}; \quad (j, k) \in Z^{2}\tag{6}\end{equation*}
Therefore, the DWT is defined as:\begin{align*} \text {DWT}_{j,k} = \int _{R} x(t)\overline {\Psi _{j,k}(t)}dt = 2^{- \frac {j}{2}}\int _{R} x(t)\overline {\Psi (2^{-j}\bullet t-k)}dt \\\tag{7}\end{align*}
The Haar wavelet is chosen as the mother wavelet in the present study because of its shortest filter length in the time domain comparing with other wavelet bases [34]. The Haar wavelet can be expressed as:\begin{align*} \Psi (t) = \begin{cases} \displaystyle 1 & t\in \big[0, \frac {1}{2}\big) \\ \displaystyle -1 & t\in \big[\frac {1}{2}, 1\big) \\ \displaystyle 0 & \text {otherwise} \end{cases} \tag{8}\end{align*}
In the present study, the original power requirement signal is decoupled into two kinds according to their frequency: high transient power and average power, in which the high transient power is supplied by the UC because of its advantage in dynamic characteristics, whereas the average load is shared by the PEMFC and the Li-ion battery. To achieve this goal, we adopt a three-level Haar wavelet to decompose the power demand signal. The decomposition and reconstruction process of the three-level wavelet transform is presented in Figure 4.
After the decomposition process, the original power requirement signal is decomposed into approximate power signal \begin{equation*} P_{\text {detail}} = x_{1}+x_{2}+x_{3}\tag{9}\end{equation*}
\begin{equation*} P_{\text {app}} = x_{0}\tag{10}\end{equation*}
\begin{equation*} P_{\text {ref-uc}} = P_{\text {detail}}\tag{11}\end{equation*}
\begin{align*} P_{\text {ref-fc}}=&0.6 P_{\text {app}}\tag{12}\\ P_{\text {ref-bat}}=&0.4 P_{\text {app}}\tag{13}\end{align*}
B. Fuzzy Logic
In the above Subsection, the power signal of the hybrid power system is decoupled into different parts and split to different energy sources according to their dynamic characteristics. However, another characteristic of the Li-ion battery and the UC is their SOCs. To ensure continuous and reliable operation of the hybrid power system, the components of the ESS need to be recharged when their SOCs are relatively low and discharged when their SOCs are high. In this work, we use fuzzy logic to determine when and how much to charge and discharge the ESS.
The fuzzy logic method takes the power requirement
The first step of fuzzy logic is the fuzzification of input and output variables. In the present study, the input variables are
After defining the membership functions of the input and output, another key problem is to design fuzzy rules. In the present study, fuzzy logic is a supplement of the WT regarding specific conditions. The general rules are implemented as follows:
When the power requirement is large, the power demand of the hybrid power ship is satisfied by all the three power sources regardless of the SOC of the ESS;
When the power requirement is medium, the PEMFC supply part of the power demand, and whether the power is provided by the battery, UC or both depends on their SOCs:
If the SOC of the battery is high, then most or all of the power requirement is supplied by PEMFC and Li-ion battery whereas UC only supplies little power or even is recharged;
If the SOC of the UC is high, the UC supplies more power than the reference power obtained from the WT and vice versa.
If the SOCs of both the battery and UC are low, then most of the power is supplied by the PEMFC.
When the power requirement is small, the battery and UC supply less power than the reference power from the WT, and they will be recharged by the PEMFC in most time.
The rule surfaces of the designed logic rules with regard to various input and output variables are presented in Figure 7. From Subfigures 7a and 7b, we can observe that, when the SOCs of the Li-ion battery and the UC are very small (smaller than 30%),
Results Analysis
The proposed strategy is tested and verified by a simulated hybrid power system in MATLAB/Simulink. The models of the components of the hybrid power system are the same as those in Ref. [35]. In the present study, to evaluate the performance of the proposed EMS in maintaining the SOCs of the ESS, two cases are considered, in which the initial SOCs of the Li-ion battery and the UC are different:
Case 1: the initial SOCs of the battery and UC are 90% and 60%, respectively;
Case 2: the initial SOCs of the battery and UC are 60% and 90%, respectively.
A. Wavelet Transform Results
Firstly, we look at the outputs of wavelet transform. The input of wavelet transform is the original power signal
The original power signal, which is shown in the first subfigure in Figure 8, is part of classical power requirement patterns from a passenger ship named FCS Alsterwasser in Germany [36]. It includes several working patterns including cruising, docking, stop and sailing. It should be noticed that the load verification must consider the capacity of the hydrogen tank of the FCS and the energy capacity of the ESS to enable the ship to finish the route, i.e., from one point to another point where the hydrogen tank can be refilled. We can observe that during the docking mode, the power requirement suffers from severe fluctuation, which is hard for FCS to deal with. After the decomposition of the signal by WT, we get two kinds of power signals: high-frequency signal which is split to the UC, as shown in the last Subfigure in Figure 8; and the low-frequency power, which is shared by the PEMFC and the Li-ion battery, as shown in the second and third subfigures in Figure 8, respectively. It can be observed that the power curves of the PEMFC and batteries in the Subfigures become much smooth during the docking mode, whereas the fluctuation of the reference power of UC becomes dramatic.
B. Results Analysis of Case 1
The comparison of the power requirement and the output power of the PEMFC, Li-ion battery and UC in Case 1 is shown in Figures 9–11, respectively. The red lines in these Figures represent the output power of the PEMFC, Li-ion battery and UC, respectively, whereas the blue lines stand for the power requirement. The SOC of the ESS is presented in Figure 12, in which the green line stands for the SOC of the battery whose initial value is 90%, and the blue one stands for the SOC of the UC whose initial value is 60%.
As can be seen in Figures 9–11, when the power requirement fluctuation is very small, i.e., at the period of 0 - 90s, 140 - 150s and 180 - 350s, the power requirement is shared by the PEMFC and the Li-ion battery, whereas the UC does not supply power to the system. It is because that the UC is only responsible for high transient power and the SOC of the Li-ion battery is relatively high. When the boat is at the docking operation mode, i.e., 90 - 140s, the power requirement suffers from dramatic fluctuations and, we can see that, the output power of the PEMFC fluctuates slower than the power requirement. Besides, the PEMFC supplies little power at the peak power periods whereas most of the power requirement is satisfied by the Li-ion battery and the UC. Specifically, the PEMFC supplies about 50% of the high-frequency power and the proposed EMS can reduce the peak power supplied by the FCS by 80%, which can be seen in Figure 9. Besides, the frequency of the output power of the UC is higher during the docking mode than that of the PEMFC and the Li-ion battery.
From Figure 12, we can see that the initial value of the SOC of the Li-ion battery starts from 90% and, then, gradually drops within an acceptable range. In Figure 10, we can see that, when the power requirement curve becomes steady after around 200s, the output power of the battery gradually decreases, and the output power of the PEMFC increases accordingly since the
C. Results Analysis of Case 2
Figures 13–16 show the simulation results in Case 2. Similar to the results in Case 1, the PEMFC and the Li-ion battery supply the main energy requirement whereas the UC satisfies the transient power when the power requirement curve is smooth. Compared with the output of the PEMFC and the Li-ion battery in Case 1 (see Figures 9 and 10), the PEMFC provides more power whereas the Li-ion battery provides less power in Case 2 due to the lower initial SOC of the battery. Therefore, the SOC of the battery does not change much and is kept between 50% and 60%, as shown in Figure 16. During around 90 to 170s, when the cruiser suffers from high-frequency load fluctuations, the FCS supplies around 400% higher than the low peak power and about 50% of the high peak power, making the output of the FCS smooth. Besides, the battery is recharged in this time period, since the power requirement is relatively small and the UC supplies most of the peak power. The value of
D. Power Sources Operating Stress Analysis
Power fluctuation is a key factor that influences the performance of power sources [37]. Inspired by Ref. [38], we present the operating stress of power sources in both Case 1 and Case 2 in Figures 17–22.
From Figures 17–19, we can observe that in Case 1, the power fluctuation of fuel cells and batteries is mainly distributed within [−200, 200], whereas the power fluctuation of UC is distributed within [−600, 800], which indicates that the operating stress of fuel cells and batteries is lower than that of UC. The results in Case 2, which are presented in Figures 20–22, are similar to those in Case 1, showing that the proposed energy management strategy can reduce the operating stress of fuel cells and batteries, and assign the high-frequency power to UC. Furthermore, it can be seen that, comparing with the results in [38], the proposed EMS in the present study can achieve a similar performance even though the FCS works in a wider range of power capacity.
Conclusion and Future Work
This paper proposes a wavelet transform and fuzzy logic-based EMS for a hybrid power cruiser. Firstly, the high transient power requirement is decomposed into different frequencies, and split to different power sources according to their dynamic performance. Then, fuzzy logic is employed to maintain the SOC of the ESS within acceptable range. In order to verify the proposed EMS, two cases are considered, in which different initial SOCs of the ESS are assumed. The proposed EMS is validated via a simulated fuel cell/battery/ultra-capacitor hybrid power system in MATLAB/Simulink. The simulation results show that, when the initial SOC of the battery is high whereas that of UC is relatively low, the proposed EMS enables the PEMFC to supply about 50% of the high frequency power and reduces the peak power supplied by the FCS by 80%. On the other hand, when the initial SOC of the battery is relatively low whereas that of UC is high, the proposed EMS enables the FCS supply around 400% higher than the low peak power and 50% of the high peak power, making the output of the FCS fairly smooth. Besides, the proposed EMS can keep the SOC of the ESS within 50% - 80%, showing that the proposed strategy is capable of dealing with power supply under various operation conditions.
In the present work, we suppose that the power requirement is known. However, the power demand of a ship might encounter many uncertainties, such as the change of the sailing environment and, thus, is difficult to predict. Therefore, in future work, we will consider a robust energy management strategy that considers the energy requirement uncertainty.
ACKNOWLEDGMENT
The authors would like to express their deepest gratitude to the anonymous reviewers for their insightful comments and questions that have helped improve the quality of this work significantly. They would also like to thank Prof. Yupeng Yuan for his suggestion in the preparation of this work.