Multiport Energy Management System Design for a 150 kW Range-Extended Towing Vessel

Abstract

This paper proposes a multiport energy management system (EMS) and its rule-based expert control strategy for a 150 kW range-extended towing vessel (RETV). The system integrates a diesel generator system, a permanent magnet synchronous motor, a lithium battery, and supercapacitors. To verify its feasibility and effectiveness, the proposed multiport EMS was modelled and tested through MATLAB/Simulink. Simulation results demonstrate that the designed multiport EMS works efficiently under the five typical operating conditions of the 150 kW RETV. In addition, two case studies were conducted and compared to investigate the impact of the battery’s initial state of charge (SoC) on the system’s energy efficiency. It was found that an overall 85% energy efficiency can be achieved for the RETV when the initial SoC is either 75% or 15%. The battery consistently operates within the optimal SoC range of 20% to 80%, and the supercapacitors effectively meet the instantaneous high-power demand.

1. Introduction

Global warming is exacerbated by the significant carbon dioxide emissions of extensive fossil fuel use [1]. Governments worldwide have enacted the Paris Agreement to mitigate climate change, aiming to limit global warming to 1.5 °C above pre-industrial levels [2]. Transportation electrification is one of the main pathways to achieving the Paris Agreement. To improve energy efficiency, the multiport energy management system (EMS) has been researched and applied in several areas of transportation electrification, including hybrid electric vehicles and hybrid electric vessels [3,4].

The multiport EMS generally connects lithium batteries, supercapacitors, diesel generators, and electric motors through DC buses [5]. The batteries and supercapacitors are usually integrated to form a hybrid energy storage system (ESS). The ESS can drive the electric motors and supply power to other electrical equipment. It can be powered by the auxiliary power unit [6,7], which is very important as it extends the range of the vehicles or vessels. Therefore, the multiport EMS has a hybrid electric power supply system. Compared with the low efficiency of conventional diesel propulsion systems, the hybrid electric power supply system exhibits dual efficiency and stability advantages when applied to hybrid vehicles or vessels [5,8,9,10,11].

To achieve high energy efficiency, efficient EMS control strategies and optimization methods need to be investigated, such as rule-based [12,13,14] and fuzzy logic [15,16] control methods, genetic algorithms [17,18], and neural networks [19,20]. The rule-based EMS control strategy is the most effective method for commercial range-extended systems [7]. However, the design of the rules requires rich engineering experience, mathematical models, and extensive data [21]. Despite the wide application of rule-based energy management strategies in range-extended EMS, there are still opportunities for fuel and energy efficiency enhancements [22,23].

In addition to energy efficiency, several other challenges exist for developing an efficient EMS for (range-extended) hybrid electric vessels. First, the peak discharge current can significantly reduce lithium batteries’ lifespan. Second, the ESS with lithium batteries only struggles to meet the high transient power demand of the modern motors in vessels [24,25,26]. Although integrating supercapacitors can resolve these issues, this solution imposes higher requirements on the EMS control strategy and the ESS size [27]. The lithium battery should maintain within the optimal state of charge (SoC) range during operation. Insufficient SoC level will significantly reduce lithium battery efficiency and life span [28,29]. Predicted operational conditions might differ from actual conditions in SoC levels, potentially leading to SoC imbalance risks [30].

In this study, a multiport EMS was designed and modelled for a 150 kW range-extended towing vessel (RETV) by using MATLAB/Simulink. The multiport EMS included a diesel generator system, a drive system with a permanent magnet synchronous motor (PMSM) and its controller, a lithium battery, and supercapacitors. A typical operation cycle with five operation conditions was proposed for the investigated 150 kW RETV in terms of power demand. Then, a rule-based expert control strategy was proposed to control the EMS to improve the overall energy efficiency of the RETV. Experimental scenarios were designed to verify whether the proposed multiport EMS enables the RETV to balance fuel economy and battery life, and reduce the high current impact. The main contributions of this work are as follows.

• Define five typical operating conditions for a 150 kW RETV regarding the energy flow and power demand.
• Propose a rule-based expert control strategy, enabling the EMS to support various power demands.
• Construct the EMS simulation platform for the 150 kW RETV by incorporating the proposed rule-based expert control strategy.

The remainder of this paper is organized as follows. Section 2 introduces the components and their models for the investigated 150 kW RETV. Section 3 details the RETV operating conditions for an operation cycle and the proposed rule-based expert control strategy. Section 4 details the simulation of the multiport EMS to verify the proposed expert control strategy, followed by the conclusion.

2. EMS Model for RETV

Figure 1 depicts the multiport EMS topology for the 150 kW RETV. In the topology, the diesel generator system was the primary power source to supply the RETV. The rest included a PMSM, a battery, and supercapacitors. The battery and supercapacitors were combined as the ESS. The diesel generator’s output was rectified (by a rectifier) and connected to the ESS through the DC bus, and it was then supplied to the PMSM.

The models of the components are described in the following subsections.

2.1. Diesel Generator System Model

The output of the diesel generator was converted to DC via a three-phase controlled bridge-type rectifier, which then supplied the PMSM through the DC bus. The three-phase controlled bridge rectifier has wide application in medium- and high-power scenarios due to its small output voltage ripple, high pulse frequency, high-side power factor, and fast dynamic response [31]. As shown in Figure 2, the rectifier consisted of a common cathode group (VT₁, VT₃, and VT₅) and a common anode group (VT₂, VT₄, and VT₆). A three-phase Phase-Locked Loop (PLL) was integrated to ensure synchronization between the rectifier and the diesel generator [31]. The parameters of the diesel generator system and three-phase PLL are listed in

Table 1. Parameters of the diesel generator system and three-phase PLL.

Parameters	Value
PLL minimum frequency	45 Hz
PLL initial phase angle	0 degree
PLL initial frequency	50 Hz
Diesel generator system configuration	Yg
Diesel generator system three-phase voltage	380 V
Diesel generator system frequency	50 Hz
Diesel generator system initial phase angle	0 degree

.

2.2. ESS Model

2.2.1. Lithium Battery Model

The charging and discharging process of the lithium battery involves complex electrochemical reactions [32]. This study adopted the equivalent circuit model to describe the battery’s characteristics [33,34]. It used an internal resistance model to explain the battery’s charge and discharge processes.

Discharge $\left(i>0\right)$:

$$f_1\left(it, i^{*}, i , Exp\right)=E_0-K·\frac{Q}{Q-it}·i^{*}-K·\frac{Q}{Q-it}·it+{Laplace}^{-1}\left(\frac{Exp\left(s\right)}{Sel\left(s\right)}·0\right)$$

(1)

Charge $\left(i<0\right)$:

$$f_2\left(it, i^{*}, i, Exp\right)=E_0-K·\frac{Q}{Q-it}·i^{*}-K·\frac{Q}{Q-it}·it+{Laplace}^{-1}\left(\frac{Exp\left(s\right)}{Sel\left(s\right)}·\frac{1}{s}\right)$$

(2)

where

$E_0$ is the battery’s constant voltage;

$Exp\left(s\right)$ is the battery’s exponential area characteristic;

$K$ is the battery’s polarity constant;

$i^{*}$ is the battery’s low-frequency current characteristics;

$it$ is the battery’s extraction capacity;

$Q$ is the battery’s maximum battery capacity.

2.2.2. Supercapacitor Model

In this study, the carbon-based electric double-layer supercapacitors were chosen to form the EMS for the investigated RETV. Due to its safety, maturity, and cost-effectiveness, carbon-based electric double-layer supercapacitors are widely used in practical engineering applications [35]. The first-order RC model was been selected to represent it in this study. The output voltage of the supercapacitor can be expressed as

$$V_{SC}=\frac{N_S{Q}_{T}d}{N_p{N}_e\epsilon {\epsilon }_0{A}_i}+\frac{2N_e{N}_{S}RT}{F}{sinh}^{-1}\left(\frac{Q_T}{N_p{N_e}^2{A}_i\sqrt{8RT\epsilon {\epsilon }_{0}c}}\right)-R_{SC}·i_{SC}$$

(3)

$$Q_T=\int i_{SC}dt$$

(4)

where

$A_i$ is the cross-sectional area of the electrode and electrolyte of the supercapacitor;

$c$ is the supercapacitor molar concentration;

$r$ is the supercapacitor molecular radius;

$F$ is the Faraday constant;

$i_{SC}$ is the supercapacitor current;

$V_{SC}$ is the supercapacitor voltage;

$R_{SC}$ is the supercapacitor resistance;

$N_e$ is the electrode layers;

$N_A$ is the Avogadro constant;

$N_p$ is the number of supercapacitors connected in parallel;

$N_S$ is the total resistance of the number of supercapacitors in series;

$Q_T$ is the charge;

$R$ is the ideal gas constant;

$d$ is the molecular radius;

$T$ is the operating temperature;

$\epsilon$ is the permittivity of the material;

${\epsilon }_0$ is the permittivity of free space.

The parameters of the proposed ESS are listed in

Table 2. Parameters of the ESS.

Parameters	Value
Lithium battery’s nominal voltage	600 V
Lithium battery’s rated capacity	1000 Ah
Lithium battery’s initial state of charge	75%/15%
Supercapacitors’ rated capacitance	700 F
Supercapacitors’ rated voltage	700 V
Supercapacitors’ initial state of charge	100%
Supercapacitors’ number of series capacitors	200
Supercapacitors’ number of parallel capacitors	5

.

2.2.3. Bidirectional Buck–Boost Converter Model

The bidirectional DC–DC converter is the conversion device between DC voltages. As shown in Figure 3, it can enable bidirectional energy transfer while maintaining the voltage polarity on both the input and output sides.

A non-isolated bidirectional buck–boost DC–DC converter was employed for the multiport EMS. This type of converter facilitates bidirectional power flow and voltage adjustment catering to ESS [36]. The non-isolated DC–DC converter had a simple structure and a small volume because there was no isolation transformer. It can realize highly efficient bidirectional power conversion in the ESS composed of battery and supercapacitors [37,38].

According to the current flow directions, the converter mainly worked in buck and boost modes. As shown in Figure 4, the $U_1$ was connected to the lithium battery that supplied power to the external load. The load was connected in parallel with the output capacitor $C_2$, and the positive pole of the output voltage $U_2$ was downward. In this case, $S_1$ was the main switching tube and $S_2$ was the synchronous switching tube. Assuming $D_1$ is the duty cycle of $S_1$, $T=1/f_S$ is the switching period, where $f_S$ is the switching frequency, and $L$ is the inductance of the inductor $L_1$.

The working principle of the boost mode can be explained as follows.

First, when $0<t<D_{1}T$, the switch $S_1$ is turned on, and the switch $S_2$ is turned off. The inductor voltage $U_L=U_1,$ and the inductor current is

$$i_L\left(t\right)=\frac{1}{L}{\int }_0^t{U}_L\mathrm{d}t+i_L\left(0\right)=\frac{U_L}{L}t+i_L\left(0\right)$$

(5)

Bringing $t=D_{1}T$ into the Equation (6), the peak value of the AC component of the inductor current is obtained as

$$\Delta i_L=i_L\left(D_{1}T\right)-i_L\left(0\right)=\frac{U_L{D}_1}{f_{S}L}$$

(6)

where the drain-source voltage is 0 for the switch S₁ ($U_{DS1}=0$), the drain-source current is I_L ($I_{D1}=I_L$), the drain-source voltage is $U_1+U_2 \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{c}\mathrm{h} S_2$ ($U_{DS2}=U_1+U_2$), and the drain-source current is 0 ($I_{D2}=0$).

Second, when $D_{1}T<t<T$, the switch $S_1$ is turned off and $S_2$ is turned on. The inductor voltage $U_L$ = $-U_2$, and the inductor current is

$$i_L\left(t\right)=-\frac{U_2}{L}\left(t-D_{1}T\right)+i_L\left(D_{1}T\right)$$

(7)

Other relevant voltages and current values are as follows.

$$\Delta i_L=i_L\left(D_{1}T\right)-i_L\left(0\right)=\frac{U_2\left(1-D_1\right)}{f_{S}L}$$

(8)

$$U_{DS1}=U_1+U_2, I_{D1}=0, U_{DS2}=0, I_{D2}=I_L$$

The ideal DC voltage conversion ratio in the discharge state is

$$M_U=\frac{U_2}{U_1}=\frac{D_1}{1-D_1}$$

(9)

Figure 5 shows an equivalent circuit diagram for the bidirectional DC–DC buck–boost converter in buck mode. As shown, $S_2$ was the main switch, $S_1$ was used as the synchronous switch, and $D_2$ was the duty ratio of $S_2$. $U_2$ charged the lithium battery pack in this case.

Third, when $0<t<D_{2}T$, switch $S_2$ is turned on and $S_1$ is turned off. The inductor voltage $U_L=U_2$, and the inductor current is

$$i_L\left(t\right)=\frac{U_2}{L}t+i_L\left(0\right)$$

(10)

Bringing $t=D_{2}T$ into Equation (11), the peak-to-peak value of the AC component of the inductor current is obtained as

$$\Delta i_L=\frac{U_L{D}_2}{f_{S}L}$$

(11)

where the drain-source voltage is 0 ($U_{DS2}=0)$ for the switch $S_2$, the drain-source current is $I_{D2}=I_L$, the drain-source voltage is $D_{DS1}=U_1+U_2$ for the switch $S_1$, and the drain-source current is $I_{D1}=0$.

Finally, when $D_{2}T<t<T$, the switch $S_2$ is turned off and $S_1$ is turned on. The inductor voltage $U_L$ = $-U_1$, and the inductor current is

$$i_L\left(t\right)=-\frac{U_1}{L}\left(t-D_{2}T\right)+i_L\left(D_{2}T\right)$$

(12)

Other relevant voltages and current values are as follows.

$$\Delta i_L=i_L\left(D_{2}T\right)-i_L\left(0\right)=\frac{U_1\left(1-D_2\right)}{f_{S}L}$$

(13)

$$U_{DS2}=U_1+U_2, I_{D2}=0, U_{DS1}=0, I_{D1}=I_L$$

The ideal DC voltage conversion ratio in the charge state is

$$M_U=\frac{U_1}{U_2}=\frac{D_2}{1-D_2}.$$

(14)

The control strategy for the bidirectional DC–DC converter was based on EMS power distribution. For example, when the converter works in the discharge mode, a discharge current should be output and maintained by Proportional Integral (PI) controllers. The overall control logic is shown in Figure 6. The parameters for the bidirectional DC–DC buck–boost converter are tabulated in

Table 3. Parameters of the bidirectional DC–DC buck–boost converter.

Parameters	Value
Converter internal resistance	1 × 10−3 Ω
Converter snubber resistance	1 × 105 Ω
Converter snubber capacitance	inf
Proportional factor of lithium battery PI controller	0.1
Integral factor of lithium battery PI controller	0.05
Proportional factor of supercapacitors PI controller	0.3
Integral factor of supercapacitors PI controller	0.02

.

2.3. PMSM Control Model

PMSMs have gained popularity in marine propulsion due to their high efficiency and power density [39,40]. PMSMs leverage vector control for efficient operation. Implementing this control technique involves transitioning from a three-phase system (abc) to a two-phase quadrature system (dq), to state the mathematical models of PMSMs [41,42]. Figure 7 shows a block diagram for the vector control of PMSMs. Three PI controllers were used to achieve speed and current adjustment. Their parameters are listed in

Table 4. Parameters of the PI controller for vector control of PMSMs.

Parameters	Value
Speed loop P	0.2
Speed loop I	100
Speed loop saturation	−3000, 3000
q axis current loop proportional factor	40
q axis current loop integral factor	50
q axis current loop saturation	−500, 500
d axis current loop proportional factor	20
d axis current loop integral factor	5
d axis current loop saturation	−500, 500

.

3. Rule-Based Expert Control Strategy for the EMS of RETV

The EMS manages the power distribution between the ESS and the diesel generator system during operation, aiming to maximize the benefits of the lithium battery and supercapacitors. The rule-based expert control strategy was formulated to adjust the lithium battery’s discharge process. This strategy reduces the high current impact on the lithium battery, compensates for sudden power demands with supercapacitors, and maintains the ESS in optimal condition during charging and discharging cycles.

3.1. Statement of 150 kW RETV Operation Conditions

A typical driving cycle of the RETV can have five operation stages: start-up, before cruise, cruise, towing, and end towing. The details are explained as follows.

3.1.1. Start-Up

At this stage, the RETV requires a large power demand, and the lithium battery is the primary power source. Supercapacitors are the backup power source to balance the increased power demand and reduce lithium battery loss. Charging is processed depending on the SoC level. The energy flow of the start-up process is shown in Figure 8.

3.1.2. Before Cruise

The RETV operates at a fixed speed (lower than the peak speed) before the cruise as it normally waits for future instructions after start-up. The battery drives the RETV to the required speed at this stage. The diesel generator system does not contribute due to low power efficiency in this condition. The supercapacitors do not work because there is no sudden power change. Charging may occur depending on the SoC level. The energy flow of the EMS before the cruise stage is shown in Figure 9.

3.1.3. Cruise

In the cruise stage, the RETV reaches and maintains peak speed with rated power. The diesel generator system is active at this stage as it can provide constant power at high speed [43,44,45]. When the operating speed exceeds 87% of its peak rotating speed, the RETV is regarded as working in the cruise stage. Since the battery performs poorly when discharging in the high-power demand period, the diesel generator system directly drives the PMSM alone [46,47]. Supercapacitors address sudden power demand while transitioning to peak speed with rated power. The battery and supercapacitors may be charged due to their SoC levels. The energy flow of the EMS under cruise is shown in Figure 10.

3.1.4. Towing

When the RETV is towing, its cruising speed is reduced compared with the peak speed. Due to the reduced power demand, the lithium battery is the energy source. The lithium battery and supercapacitors may be charged due to their SoC levels. The energy flow of the EMS under towing is shown in Figure 11.

3.1.5. End Towing

At this stage, the rotor speed will be higher than the synchronous speed, and the generated reverse power charges the battery and supercapacitors. The energy flow of the EMS under end towing is shown in Figure 12.

3.2. Expert Control Strategy for the EMS

The EMS control target is to distribute power between the ESS and the diesel generator system. By monitoring the SoC level of the ESS, charging can be dynamically adjusted to meet the PMSM’s power demands. As the ESS design combines the battery and supercapacitors, the EMS’s rule-based expert control strategy is complex, as each component can be either charged or discharged.

The operating conditions of the RETV are relatively fixed, making it suitable for the rule-based expert control strategy. The logical threshold control decomposes the RETV’s different operation stages into control parameters, providing a tailored control strategy for each stage to ensure comprehensive energy management.

According to the analysis of the operation stages, we set the PMSM power demand $P_t$, and lithium battery ${\mathrm{S}\mathrm{o}\mathrm{C}}_b$ as the threshold values. Operating the lithium battery at low SoC accelerates aging. To optimize the battery’s lifespan, we set the upper and lower thresholds of ${\mathrm{S}\mathrm{o}\mathrm{C}}_b$ as 0.9 (${\mathrm{S}\mathrm{o}\mathrm{C}}_{bMAX}$) and 0.2 (${\mathrm{S}\mathrm{o}\mathrm{C}}_{bMIN}$), respectively. When $P_t$ was greater than the rated output power of the battery, the diesel generator system was used as the compensation power supply to supply the extra power demand. The control logic flowchart is shown in Figure 13. The specific rules were as follows:

• When $P_t>0$ and ${\mathrm{S}\mathrm{o}\mathrm{C}}_b$ > ${\mathrm{S}\mathrm{o}\mathrm{C}}_{bMIN}$
  • If the rotating speed of the PMSM was not fixed in the high-speed range (beyond 87% of its peak speed), the lithium battery and supercapacitors could supply the RETV.
  • If the rotating speed was fixed in the high-speed range, the diesel generator system supplied the PMSM.
  • If the rotating speed of the PMSM was not fixed and was less than 87% of its peak speed, the lithium battery and supercapacitors supplied the RETV for various power demands.
  • If the rotating speed was fixed and was less than 87% of its peak speed, only the lithium battery supported the RETV.
• When $P_t>0$ and ${\mathrm{S}\mathrm{o}\mathrm{C}}_b$ < ${\mathrm{S}\mathrm{o}\mathrm{C}}_{bMIN}$
  • As the lithium battery and supercapacitors could not supply the RETV in this operation stage, the diesel generator system joined in and compensated for power. The lithium battery and supercapacitors were charged if necessary.
• When $P_t<0$ and ${\mathrm{S}\mathrm{o}\mathrm{C}}_b$ < ${\mathrm{S}\mathrm{o}\mathrm{C}}_{bMAX}$
  • The RETV worked under the end towing stage. The PMSM acted as a reverse power generator. The lithium battery and supercapacitors were charged in this case.
• When $P_t<0 \mathrm{a}\mathrm{n}\mathrm{d}$ ${\mathrm{S}\mathrm{o}\mathrm{C}}_b$ > ${\mathrm{S}\mathrm{o}\mathrm{C}}_{bMAX}$
  • The braking resistor consumed the negative power.

3.3. The Analysis of PMSM Reverse Generation

When the PMSM rotor rotated in the same direction, the rotor speed exceeded the stator magnetic field speed due to inertia, which resulted in the PMSM entering a regenerative power generation state. The power generated by the asynchronous PMSM was returned to the DC link of the inverter through the six freewheeling diodes of the inverter (IGBT). Reverse power generation in the RETV occurred at the end of towing. Large inertia retained from descending from higher speeds caused the rotor to rotate faster than its synchronous speed. Additionally, the water resistance and external torque generated by the physically connected towing object contributed to this phenomenon.

3.4. PMSM Load Design

The RETV’s power demand was calculated based on different operation stages. The calculated power demand was the product of the PMSM speed and torque, as shown in

Table 5. PMSM speed and torque demand value sheet.

Time (s)	RPM (r/min)	Torque (Nm)
0	0	0
1	0	0
1.25	42	218
1.50	85	437
2.00	170	873
3.00	340	1747
4.00	416	2800
5.00	416	2800
6.00	416	2800
7.00	478	3000
8.00	478	3000
9.00	478	3000
10.00	478	3000
10.50	424	2750
11.00	370	2500
12.00	370	2500
13.00	370	2500
14.00	370	2500
15.00	210	0
16.00	50	−2500
17.00	50	−2500
18.00	50	−2500
19.00	50	−2500
19.50	25	−2500

. To shorten the simulation time, the time of an operation cycle was set at 20 s. The reference speed and torque demand of the PMSM are shown in Figure 14 and Figure 15, respectively.

4. Simulation

4.1. PMSM Load Simulation

PMSM speed and torque demands were simulated over an operation cycle. The powergui was set as Discrete with a sampling time of 1 × 10⁻⁵ in Matlab/Simulink. Due to the static resistance (viscous resistance or frictional resistance) generated by the relative movement of the RETV and the sea surface, additional energy was consumed to resist the irregular motion of the sea-surface waves. The PMSM power fluctuations were limited to within 5%. The units for the PMSM speed, torque, and power were set as rad/s, Nm, and kW, respectively, to unify and clearly show the results. The results depicted in Figure 16 and Figure 17 illustrate the comparison between the designed and simulated speed, torque, and power. These figures demonstrate that the PMSM load simulations are consistent with engineering reality.

4.2. Simulation of ESS

Three case studies, as shown below, were simulated and analyzed for the ESS.

• Case 1: ESS with a satisfied initial battery condition (75% SoC).
• Case 2: ESS with the lithium battery only and satisfied initial battery condition (75% SoC).
• Case 3: ESS with an unsatisfied initial battery condition (15% SoC).

4.2.1. Case 1: ESS with a Satisfied Initial Battery Condition (75% SoC)

Figure 18a shows the required output power of the PMSM (P_PMSM) and the power provided by the battery (P_LB), supercapacitors (P_SC), and diesel generator (P_EG) by using the proposed EMS in this case. In the simulation, the battery’s initial SoC was set as 75%.

Table 6. Power data for case 1.

Time (s)	${\mathit{P}}_{\mathit{L}\mathit{B}}$ (kW)	${\mathit{P}}_{\mathit{S}\mathit{C}}$ (kW)	${\mathit{P}}_{\mathit{E}\mathit{G}}$ (kW)	${\mathit{P}}_{\mathit{P}\mathit{M}\mathit{S}\mathit{M}}$ (kW)
0	0	0	0	0
1	0	0	0	0
3	30	20	0	50
4	120	0	0	120
7	0	0	150	150
10.5	77	0	43	120
11	100	0	0	100
15	100	0	0	100
16	−13.3	0	0	−13.3

lists the power data for nine operating points at different times. The following analysis was conducted.

(1)

During the start up stage (0–4 s), the ESS supplied the PMSM’s power demand. Both $P_{LB}$ and $P_{SC}$ reached up to 60 kW.

(2)

Between 4–6 s, the RETV entered the before-cruise stage. The lithium battery powered the RETV with about 120 kW. The $P_{SC}$ and $P_{EG}$ remained at 0 W.

(3)

During cruise (6–10 s), the PMSM power demand initially rose, then stabilized. The supercapacitors assisted the lithium battery in meeting the surge in power demand. The diesel generator system output ramped up to 100 kW between 6–7 s, ultimately supplying 150 kW when cruising at peak speed.

(4)

In towing (10–14 s), the PMSM required a lower constant power, around 100 kW, provided by the lithium battery. The $P_{SC}$ and $P_{EG}$ remained at 0 W.

(5)

From 14 s to 20 s, the lithium battery was charged due to the reversal of the PMSM. It stabilized at 13.3 kW at 16 s.

(6)

Table 6 demonstrates the power demand successfully distributed by the EMS throughout one operation cycle. The PMSM-demanded power for one operation cycle was 0.3942 kWh, and the diesel generator system and ESS output power was 0.4415 kWh. The comprehensive energy efficiency of the EMS was approximately 85%.

Figure 18b shows the SoC curves of the lithium battery and supercapacitors in case 1. As shown, the ESS provided the power demand during start-up, so the SoC of the lithium battery was reduced during 0–6 s. The SoC of the supercapacitors also had a certain decrease during the first operation stage (0–4 s). After that, the lithium battery provided power as the operation stage switched to towing, causing the SoC of the lithium battery to drop to 74.97%. The SoC gradually increased due to reverse charging from the PMSM.

4.2.2. Case 2: ESS with the Lithium Battery Only and Satisfied Initial Battery Condition (75% SoC)

This case study compared the performance of the EMS with and without supercapacitors to show the advantages of using supercapacitors in the ESS. In this study, the capacitors were mainly used to address the sudden power demand and large discharge current. For this purpose, the results for two simulation periods (3.995–4 s and 6.837–6.841 s) were investigated. Figure 19 and Figure 20 show the battery’s discharge current waveforms and SoC curves of the two ESS systems, respectively. Please note that the hybrid ESS shown in the two figures means the ESS with both battery and supercapacitors. The following analysis was conducted:

(1)

In the period 3.995–4 s, the ESS with lithium battery only maintained a peak current of about 190 A, which was 1.9 times higher than that of the hybrid ESS (100 A).

(2)

In the period of 6.837–6.841 s, the ESS with lithium battery only maintained a peak current of about 85 A, which was 1.7 times higher than that of the hybrid ESS (50 A).

(3)

The SoC decrease rate for the ESS with lithium battery only was faster than that of the hybrid ESS before 4 s. At 4 s, the battery’s SoC of the ESS with lithium battery only dropped to 74.996%, which was slightly lower than that of the hybrid ESS (74.998%).

(4)

Both systems showed a consistent SoC decrease rate during 4–6 s. In the subsequent cruise, the sudden power demand decreased the battery’s SoC. At 7 s, the battery’s SoC of the ESS with lithium battery only fell to 74.985%, which was also lower than that of the hybrid ESS (74.988%).

Therefore, the hybrid ESS outperformed the ESS with lithium battery only in reducing the impact of sudden power demands. This indicates that the hybrid ESS has a smaller energy flow in the lithium battery. It can also be seen from the SoC curves that the energy consumed by the hybrid ESS was lower than that of the ESS with lithium battery only. It proved that the supercapacitors in the hybrid ESS allowed the battery to discharge more stably and avoided the impact of the high discharge current, so as to reduce the battery’s aging rate.

4.2.3. Case 3: ESS with an Unsatisfied Initial Battery Condition (15% SoC)

In this case, the initial SoC of the battery was set as 15%. According to the power demand of the PMSM, the output power of the lithium battery, supercapacitors, and diesel generator system is shown in Figure 21a. The power data for several typical operation points are listed in

Table 7. Power data for case 3.

Time (s)	${\mathit{P}}_{\mathit{L}\mathit{B}}$ (kW)	${\mathit{P}}_{\mathit{S}\mathit{C}}$ (kW)	${\mathit{P}}_{\mathit{E}\mathit{G}}$ (kW)	${\mathit{P}}_{\mathit{P}\mathit{M}\mathit{S}\mathit{M}}$ (kW)
0	0	0	0	0
1	0	0	0	0
3	−170	20	200	50
4	−80	0	200	120
7	−50	0	200	150
10.5	−80	0	200	120
11	−100	0	200	100
15	0	0	0	0
16	−13.3	0	0	−13.3

. The following analysis was conducted:

(1)

During the initial stage (0–4 s), the supercapacitors and the diesel generator system supplied the PMSM. The battery was charged as its SoC dropped below 20%. The charging power diminished from 200 kW to 80 kW due to the continuous rise of the PMSM power demand.

(2)

In the before-cruise stage, the diesel generator system provided the entire power demand, simultaneously providing consistent charging to the lithium battery during 4–6 s. The charging power to the lithium battery was constant at 80 kW. The diesel generator’s output power was 200 kW.

(3)

During the cruise stage (6–10 s), the diesel generator system and supercapacitors supported the RETV until its speed peaks. After that, the diesel generator system contributed to the peak power demand (150 kW). The battery’s charging rate declined when the power was around 50 kW.

(4)

As the power demand decreased during the towing stage (10–14 s), the charging power of the lithium battery increased to 100 kW. The diesel generator system provided a total of 200 kW, of which 100 kW went to the PMSM.

(5)

In the end towing stage (after 15 s), the lithium battery received a small amount of charging power, 13.3 kW, from the PMSM until the end of the operation cycle at 20 s.

(6)

As shown in Table 7, the power demand of the PMSM in one operation cycle was 0.3742 kWh, while the diesel generator system and ESS output power was 0.4418 kWh. The comprehensive energy efficiency of the EMS was approximately 85%.

Figure 21b shows the SoC curves of the battery and supercapacitors during an operation cycle. As shown, because the lithium battery SoC continued to be below the limit (20%), it remained charged for 0–20 s. At 0–4 s, it had the highest charging power due to the lower PMSM power demand. During the working stages, with constant speed, the diesel generator system provided uniform charging power, which can be explained by the stable increase in the SoC in 6–10 s. The reduced charging power after 15 s was provided by the reverse charging of the PMSM. The performance of the supercapacitors in this case was consistent with the performance in case 1.

5. Conclusions

This paper proposed a multiport EMS with a rule-based expert control strategy for a 150 kW RETV. Three case studies were conducted to show the effectiveness and advantages of the proposed EMS. The following conclusion can be drawn:

(1)

When the initial SoC of the battery is in the satisfactory range, like 75%, the proposed EMS can effectively distribute energy among the diesel generator system, lithium battery, and supercapacitors according to the requirements of each operation stage. The simulation results for two ESSs (with and without supercapacitors) showed that the hybrid ESSs have better performance when handling sudden power demand and big battery current.

(2)

When the initial SoC of the battery is not in the satisfactory range, like 15%, the system operates normally without the battery. It was found that the diesel generator system continuously charges the battery before the PMSM reverse charging occurs. The EMS showed the flexibility to maintain operational efficiency while the battery is less than ideal and extended the battery lifespan by keeping it within its optimal SoC range.

(3)

The simulation revealed that the comprehensive energy efficiency of the designed RETV is approximately 85% under the typical operation cycle proposed in this paper.