Energy Saving in Ship Central Cooling Systems: IMC-Tuned PID with Feedforward Control

Abstract

This study examines the energy savings in a ship’s central cooling system using feedforward control with IMC (Internal Model Control)-based PID tuning. A central cooling system is essential for maintaining the temperature of the engine and other major machinery, thereby improving the overall energy efficiency. The seawater pump in the central cooling system consumes a relatively large amount of power, which makes efficient operation essential. This study compared the power consumption of variable-speed seawater pumps based on actual operational data from a ship. By incorporating a feedforward PI controller into the IMC-based PI-PID controller combinations, this study simulated energy savings. The results indicate that the proposed controller combined with the feedforward PI controller reduces the power consumption of seawater pumps compared with conventional methods. Simulation tests were conducted using approximately 11 days of operational data to verify the effectiveness of the proposed control strategy in achieving energy savings. The proposed controller combination saves approximately 277.4 kWh of power over 11 days compared to conventional control methods.

1. Introduction

Energy efficiency in ship operations has become an increasingly important factor owing to rising fuel costs and stricter environmental regulations [1,2]. According to various reports, the share of energy consumption costs in maritime transport can amount to 30–50%, and even 40%, and 63%, respectively [3,4,5]. The central cooling system of a ship is essential for maintaining the optimal temperature conditions of key machinery and is one of the more significant energy-consuming auxiliary systems [6]. However, conventional cooling systems typically use fixed-speed seawater pumps [7], which lead to high energy consumption and inefficient temperature control.

To address these inefficiencies, as shown in Figure 1, variable-speed pump control strategies are being applied to enhance energy efficiency, reduce operational costs, and minimize environmental impact. Several advanced control methods have been proposed to improve the performance of these variable-speed pumps, including PI/PID control, Model Predictive Control (MPC), Fuzzy Logic Control, Adaptive Control, Reinforcement Learning (RL)-based control, and feedforward control. Each of these approaches has its advantages and limitations [8].

PI/PID control remains one of the most commonly used strategies due to its simplicity and stability in operation [9,10]. However, its adaptability to rapidly changing conditions is limited, necessitating improvements in response speed and adaptability. MPC is known for its predictive capabilities and effectiveness in handling multivariable systems [11,12], but its high computational demand makes real-time implementation challenging for shipboard applications. Fuzzy Logic Control offers advantages in handling nonlinear systems [13,14], yet it requires expert-defined rules, which can be difficult to generalize for diverse maritime conditions. Adaptive control allows automatic parameter adjustment based on system variations, making it suitable for dynamically changing environments [15], but its complex tuning process raises concerns about stability. RL-based AI control has shown potential for optimizing complex scenarios [16,17], yet it requires extensive data and long training times, making it computationally expensive for real-time ship operations. Feedforward control [18], by contrast, improves response time by anticipating disturbances before they occur, making it particularly effective for handling seawater temperature fluctuations.

While MPC, adaptive control, and AI-driven RL approaches have shown promise in optimizing energy efficiency across various industries, their implementation on ships is challenging due to computational complexity and practical constraints. Traditional PI/PID controllers continue to be widely used due to their simplicity and reliability, but their limitations in handling rapid fluctuations in seawater temperature and engine loads must be addressed.

To overcome these challenges, this study proposes an Internal Model Control (IMC)-based PI-PID control strategy combined with a feedforward PI controller for optimizing variable-speed seawater pump operations. The IMC-based PI-PID control method improves conventional PID tuning by incorporating an internal system model, ensuring greater stability, faster response, and improved control precision. Additionally, integrating feedforward PI control allows the system to anticipate disturbances such as seawater temperature fluctuations and proactively adjust pump speed, resulting in reduced energy consumption and more stable temperature regulation.

IMC-based PI-PID control is the optimal approach for this application due to its ability to handle the complex dynamic characteristics of the ship’s cooling system while maintaining robust performance under varying operating conditions. Unlike traditional PID controllers that rely solely on real-time feedback, IMC enhances system reliability by incorporating a model of the process into the control structure. This ensures that control actions are not only responsive but also predictive, leading to a more stable and efficient cooling system. Furthermore, the inclusion of a feedforward PI controller enhances the system’s ability to preemptively compensate for external disturbances, reducing the likelihood of inefficiencies caused by lagging feedback corrections.

Compared to alternative methods such as MPC or adaptive control, the IMC-based PI-PID approach offers a balance between computational feasibility and precise control. While MPC excels in predictive modeling, it requires significant computational power, which may not be readily available on ships. Adaptive control, on the other hand, can introduce complexity in parameter tuning and stability assurance. The IMC-based approach circumvents these issues by utilizing a structured tuning methodology that ensures optimal control performance without excessive computational demand, making it highly practical for real-world maritime applications.

This study sets itself apart from previous research by utilizing real operational data collected from an 11-day ship voyage, providing more reliable and practical insights into controller performance. The proposed strategy is evaluated through MATLAB/Simulink simulations, comparing three different control configurations: (1) Conventional PI-PI control, (2) PI-PID without feedforward control, and (3) PI-PID with feedforward control (the proposed method).

The effectiveness of the proposed approach is assessed based on power consumption, system stability, and response time, with results demonstrating a 277.4 kWh energy reduction over an 11-day period, translating into significant cost savings and environmental benefits.

The remainder of this paper is organized as follows: Section 2 presents the conditions of the simulation test and the proposed control method. Section 3 describes the tuning of the controllers and provides detailed procedures and parameter selection criteria for the IMC PI and PID controllers. Section 4 presents simulation test results. Section 5 discusses the findings, and Section 6 provides the conclusions.

2. Materials and Methods

The central cooling system comprises a central heat exchanger, seawater supply pump, freshwater supply pump, and three-way valve. To verify the energy-saving performance of the proposed method, a comparison was performed using a central cooling system with IMC-based PI control tuning applied to a conventional system. In addition, to confirm the energy savings, actual operational data from a real ship (M/V Hanjin Europe, IMO Number: 9502908) were applied to a model [9] simulating the central cooling system through MATLAB Simulink R2024a, and the energy consumption of the seawater pump motor was compared.

2.1. Conditions of Simulation Test

This study verifies the energy savings through simulation tests using approximately 11 days of actual ship-operation data. The specific route of the ship’s global positioning system data is shown in Figure 2.

The operational data of the ship from the waters off Vietnam, calling at Hong Kong, and finally arriving at the Hangzhou port, were used. The data included seawater and freshwater temperature inputs to the central heat exchanger. The seawater inlet temperature and freshwater input temperature obtained from the vessel’s operating route in Figure 2 show that the seawater temperature changes from high to low as the vessel moves from lower to higher latitudes. Additionally, the freshwater inlet temperature varies owing to fluctuations in the main engine load caused by the departure and arrival of the vessel. The operational data spanned approximately 11 days, equivalent to 957,700 s.

2.2. Proposed Control Method

In this study, we propose a combination and tuning of controllers that achieves both energy savings and enhanced control performance. Figure 3 illustrates the configuration of the central cooling system along with the proposed controller combination.

Generally, the opening degree of the three-way valve and the rotational speed control of the seawater pump equipped with V.F.D. in the central cooling system use the TT_v value, which measures the mixed temperature of the bypassed freshwater from the three-way valve and the freshwater coming out of the heat exchanger, as the feedback signal. However, the proposed seawater pump speed controller uses the TT_s value, which measures the temperature of the freshwater exiting the heat exchanger, instead of using the measured temperature of TT_v as the feedback signal. The TT_s are indicated by blue dashed circles in Figure 3. Even if the rotational speed of the seawater pump increases and the seawater supply flow rate increases, the response of the system to rapid changes in the freshwater input temperature or seawater temperature owing to heat exchange in the heat exchanger is slow because of the considerable time constant of the heat exchanger. Therefore, to compensate for the rapid changes in the mixed freshwater temperature owing to the operation of the three-way valve, a feedforward controller, PI_ff, is added. This is indicated by red dashed circles in Figure 3.

Figure 4a presents a schematic of the controller section illustrated in Figure 1 and Figure 3. The reference temperature value is set to 36 °C, matching the set temperature of the actual operating data obtained from the ship. The proposed controller combination shown in Figure 4c is hereafter referred to as the feedforward controller combination. This setup builds upon the configuration in Figure 4c by adding feedforward control to enhance the performance, as shown in Figure 4b.

Additionally, the combination of the seawater supply pump speed controller, PI_sw, and the three-way valve opening degree controller, PI_3v, in Figure 4a is hereafter referred to as the conventional controller combination.

3. Tuning of the Controllers

3.1. Tuning of Seawater Supply Pump Speed Controller

The seawater supply pump motor was an induction motor, and its rotational speed could be controlled by varying the frequency of the power supply through an inverter. The process of tuning the rotational speed controller PI_sw for the seawater supply pump motor was guided by the Internal Model Control principles. This involves adjusting the controller based on the system model, which considers the voltage frequency of the electric power supply of the seawater pump motor as the input variable, and the freshwater outlet temperature from the heat exchanger as the output variable. This model, known as $\widetilde{G_{sw}}\left(s\right)$, operates under the assumption of a constant three-way valve-opening degree [9]. It can be simplified as a first-order system because, as the rotational speed increases, the output temperature decreases, considering external variables such as pipe roughness, length, and other factors, as per Equation (1).

$$\widetilde{G_{sw}}\left(s\right)={\displaystyle \frac{k_{sw}}{{\tau }_{sw}s+1}}$$

(1)

The model $\widetilde{G_{sw}}\left(s\right)$ is expressed as a first-order lag system. The IMC-based controller $K\left(s\right)$ for the feedback control system is represented in the form of a proportional–integral (PI) controller, as shown in Equation (2).

$$K_{sw}\left(s\right)={\displaystyle \frac{{\tau }_{sw}}{k_{sw}{\lambda }_{sw}}}+{\displaystyle \frac{1}{k_{sw}{\lambda }_{sw}}}{\displaystyle \frac{1}{s}}=K_p+{\displaystyle \frac{K_p}{T_i}}{\displaystyle \frac{1}{s}}=K_p+K_i{\displaystyle \frac{1}{s}}$$

(2)

where $k_{sw}$ is the gain of $\widetilde{G_{sw}}\left(s\right)$, ${\lambda }_{sw}$ is the IMC filter value, and $K_p$ and $K_i$ are the proportional and integral gains of the PI controller, respectively [19,20,21,22].

3.2. Tuning of Three-Way Valve Opening Controller

Tuning of the PI_3v and PID_3v controllers for the three-way valve opening was also based on IMC principles. The system model $\widetilde{G_{3v}}\left(s\right)$, which uses the three-way valve opening as the input and the freshwater outlet temperature from the three-way valve as the output, was employed. This model assumes a constant speed for the seawater pump and is represented as a second-order system, as shown in Equation (3) [9].

$$\widetilde{G_{3v}}\left(s\right)={\displaystyle \frac{k_{3v}(\beta s+1)}{({\tau }_{s}s+1)({\tau }_{b}s+1)}}$$

(3)

Here, $k_{3v}$, ${\tau }_b, {\tau }_s$, and β are the gain and system constants of $\widetilde{G_{3v}}\left(s\right)$.

To develop an IMC-based PID controller for a second-order system, we start by defining the lead–lag compensatory function, denoted as $f_{3v}\left(s\right)$, as shown in Equation (4). This approach follows the same methodology as that used to derive the seawater pump speed controller discussed in Section 3.1.

$$f_{3v}\left(s\right)={\displaystyle \frac{\gamma s+1}{{\lambda }_{3v}s+1}}$$

(4)

Here, γ and ${\lambda }_{3v}$ represent the IMC filter values.

Then, using the models $\widetilde{G_{3v}}\left(s\right)$ and $f_{3v}\left(s\right)$, we derive the IMC-based controller $K_{3v}\left(s\right)$ for the feedback control system, as shown in Equation (5).

$$K_{3v}\left(s\right)={\displaystyle \frac{\widetilde{G_{3v}}{\left(s\right)}^{-1}{f}_{3v}\left(s\right)}{1-\widetilde{G_{3v}}\left(s\right)\widetilde{G_{3v}}{\left(s\right)}^{-1}{f}_{3v}\left(s\right)}}$$

$$={\displaystyle \frac{\frac{\left({\tau }_{s}s+1\right)\left({\tau }_{b}s+1\right)}{k_{3v}\left(\beta s+1\right)}\frac{\left(\gamma s+1\right)}{({\lambda }_{3v}s+1)}}{1-\frac{\left(\gamma s+1\right)}{({\lambda }_{3\mathrm{v}}s+1)}}}$$

$$={\displaystyle \frac{\left({\tau }_b+\gamma \right)}{k_{3v}\left({\lambda }_{3v}-\gamma \right)}}\left(1+{\displaystyle \frac{1}{{\tau }_b+\gamma }}{\displaystyle \frac{1}{s}}+{\displaystyle \frac{{\tau }_b\gamma }{{\tau }_b+\gamma }}s\right){\displaystyle \frac{\left({\tau }_{s}s+1\right)}{\left(\beta s+1\right)}}$$

(5)

If ${\lambda }_{3w}$ > $\gamma$, ${\tau }_b$ > $\gamma$, and ${\tau }_b$ > ${\tau }_s$, the parameters of the PID_3v controller are as shown in Equation (6).

$$K_p={\displaystyle \frac{\left({\tau }_b+\gamma \right)}{k_{3w}\left({\lambda }_{3w}-\gamma \right)}},\hspace{1em}{K}_i={\displaystyle \frac{K_p}{{\tau }_b+\gamma }},\hspace{1em}{K}_d=K_p{\displaystyle \frac{{\tau }_b\gamma }{{\tau }_b+\gamma }}$$

(6)

3.3. Tuning of the Feedforward Controller

The tuning of the feedforward PI_ff controller was also based on the IMC approach, similar to the tuning of the PI_sw controller of the seawater supply pump’s PI_sw controller. However, to reduce the error between the freshwater output temperature and setpoint more rapidly, the PI_ff controller tuning sets the IMC filter parameter ${\lambda }_{sw}$ to a smaller value than that of the seawater pump speed controller, allowing for a faster response of the seawater pump speed.

The PI_ff controller improves the slow response of the seawater pump speed that occurs when the PI_sw controller adjusts the freshwater temperature using the heat exchanger, particularly during variations in the freshwater inlet temperature or seawater inlet flow rate.

By configuring the controllers in this manner, when the freshwater inlet temperature increases, the three-way valve first regulates the freshwater outlet temperature to the setpoint, and the PI_ff controller preemptively increases the speed of the seawater supply pump. Conversely, when the freshwater inlet temperature drops, the three-way valve increases the bypass flow around the heat exchanger, and the PI_ff controller preemptively decreases the speed of the seawater supply pump.

Thus, while the PI_ff controller is tuned in the same manner as the PI_sw controller, its IMC filter parameter $\lambda$ is set to a smaller value to ensure a faster response. Another difference is that the feedback signal for the PI_ff controller used the freshwater outlet temperature at the three-way valve.

Referring to the system transfer functions [9] as per Equation (7),

Table 1. The tuned parameters of IMC-based PI and PID controllers.

Parameter	IMC Filter	${\mathit{K}}_{\mathit{p}}$	${\mathit{K}}_{\mathit{i}}$	${\mathit{K}}_{\mathit{d}}$
$\mathrm{PI} \mathrm{controller} \mathrm{for} G_{sw}\left(s\right)$	${\lambda }_{sw}$ = 1.0	−584.80	−6.15	-
Feedforward PI controller	${\lambda }_{sw}$ = 0.92	−635.65	−6.68	-
$\mathrm{PID} \mathrm{controller} \mathrm{for} G_{3v}\left(s\right)$	${\lambda }_{3v}=1.5, \gamma =$ 0.45	−13.81	−0.11	−6.19

summarizes the parameter values for each controller tuned based on the IMC approach.

$$\widetilde{G_{sw}}\left(s\right)={\displaystyle \frac{-0.1627}{95.147s+1}}, \widetilde{G_{3v}}\left(s\right)={\displaystyle \frac{-28.6s-0.1456}{{\mathrm{s}}^2+2.112s+0.0165}}$$

(7)

$\mathrm{PI} \mathrm{controller} \mathrm{for} G_{sw}\left(s\right)$${\lambda }_{sw}$${\lambda }_{sw}$$\mathrm{PID} \mathrm{controller} \mathrm{for} G_{3v}\left(s\right)$${\lambda }_{3v}$$=1.5, \gamma =$

3.4. Step Response Analysis of PI and PI/PID Controller Combinations

The ship used in the simulation had a total tonnage of 9196 tons, with a main engine output of 8997 ps at Maximum Continuous Rating (MCR) and 7647 ps at Normal Continuous Rating (NCR). The model is shown in Figure 4, and the specifications of the equipment are based on the details provided in

Table 2. Factory acceptance test record of the heat exchanger.

Item	Unit	Hot Water Side	Cold Water Side
Fluid Name		Freshwater (F.W.)	Seawater (S.W.)
Flow Rate	m3/h	4.44 × 10−2	200.0
Inlet Temperature	°C	54.7	32.0
Outlet Temperature	°C	36.0	47.5
Density	kg/m3	1000	1025
Specific Heat	J/kg·K	4184	3931.6
Thermal Conductivity	W/m·K	2.26	2.26
Viscosity, Inlet	Pa·s	5.6 × 10−4	8.2 × 10−4
Viscosity, Outlet	Pa·s	7.1 × 10−4	6.4 × 10−4
Pressure Drop	Pa	68,697	98,066
Heat Exchanged, Duty	W	3.49 × 106
Log Mean Temperature Difference (L.M.T.D)	°C	5.43
O.H.T.C Clean	W/m·K	7167
O.H.T.C Service	W/m·K	6092
Fouling Margin	%	15.0
Heat Transfer Area	m2	90.4
Total Number of Plates	-	115
Plate Material/Thickness	-	Titanium/0.5 mm
Connection Diameter	-	200A	200A
Fluid Volume	m3	1.355 × 10−1	1.355 × 10−1

,

Table 3. Three-way valve model parameters.

Parameter	Unit	Value
Fluid Type	-	Freshwater
Flow Rate	m3/s	2.22 × 10−1
Inlet Pressure	Pa	39.23 × 104
Pressure Drop	Pa	1.275 × 104
Temperature	°C	36
Calculated Cv	-	1697
Rate and Size (connection)	-	JIS 5K/200A
Characteristic	-	Linear
Rated Cv/Port	-	2590/Full
Leakage (of Rated Cv)	%	1.8
Max. Flow Rate	m3/s	3.37 × 10−1

and

Table 4. S.W. supply and F.W. circulation pump factory acceptance test record.

Measuring Points	Unit	1	2	3	4	5	6
Flow	Capacity m3/min	0	4.816	6.225	7.165	7.949	8.761
Discharge	Indication kgf/cm2	3.25	2.80	2.50	2.30	2.10	1.90
	Head m	32.5	28.0	25.0	23.0	21.0	19.0
Suction	Indication mmHg	50.0	75.0	85.0	95.0	100.0	105.0
	Head m	0.680	1.019	1.155	1.291	1.359	1.427

.

The rated power of the motor driving the seawater pump was 45 kW, and the power supply used was a 440 V 3-phase, 60 Hz. Additionally, the frequency of the power supply ranged from a minimum of 30 Hz to a maximum of 60 Hz.

Table 5. Factory acceptance test record of S.W. supply pump motor.

Measuring Points	1	2	3	4	5	6
Voltage V	440	440	440	440	440	440
Amperes A	61.3	63.9	66.6	69.6	69.8	70.5
Power Input kW	38.8	40.8	43.1	45.3	45.5	45.7
Motor Efficiency %	91.7	91.7	91.7	91.7	91.7	91.7
Brake Horsepower kW	35.58	37.414	39.523	41.54	41.754	41.907
Pump Efficiency %	0	63.687	71.956	74.793	75.328	75.625

presents the measurement results of the motor used during the seawater supply pump test, as outlined in Table 4.

The tuned controllers were combined into three configurations and applied to the central cooling water model, as shown in Figure 5. The response to the step input of freshwater and seawater temperatures, which corresponds to disturbances, was then observed and compared for each model. The three control configurations are as follows: first, a conventional configuration using PI controllers for both the seawater supply pump speed control and the three-way valve opening control; second, the proposed control configuration consisting of the PI_sw, PID_3v, and PI_ff controllers; and third, a combination excluding the feedforward controller PI_ff from the proposed configuration, thus using only the PI_sw and PID_3v controllers.

Figure 6 illustrates the modeling of the seawater supply pump motor driver and freshwater circulation pump motor driver [23]. As shown in Figure 6b, the freshwater circulation pump operates at a fixed speed; therefore, it is set to a fixed-rate RPM considering slip. Although the power supply for the seawater supply pump motor is provided as AC power, which passes through a rectifier and inverter before being supplied to the motor, it is simply modeled as DC power being directly supplied to the inverter, as shown in Figure 6a.

Figure 7 illustrates the changes in the freshwater control output temperature, seawater pump rotational speed, and three-way valve opening in response to the step inputs of freshwater and seawater temperatures.

Figure 7a shows the changes in the input temperatures of both freshwater and seawater. At 500 s, both inputs experienced a step increase, and at 2000 s, a step decrease was applied.

Figure 7b illustrates the controlled output temperature of freshwater. The temperature control performances of the two controller combinations were generally similar. However, the combination of PI_sw and PID_3v without the feedforward controller showed a slight increase in the temperature of approximately 700 s. The reason for the temperature increase is that the three-way valve increased the flow rate to the heat exchanger side and reduced the bypass flow to control the outlet temperature. However, although the flow of high-temperature freshwater to the heat exchanger increased, as shown in Figure 7c, the supply of seawater, which served as the coolant, did not increase. Consequently, the temperature of the freshwater outlet increased again.

Figure 7c presents the changes in the rotational speed of the seawater supply pump, which are closely related to the energy savings. The changes in the rotational speed of the seawater supply pump for the conventional and feedforward controller combinations were similar. However, the slowest and fastest decreases in the seawater pump speed were observed in the sequence of controller combinations without the feedforward controller, feedforward controller combination, and conventional controller combination.

Figure 7d shows the changes in the opening of the three-way valve. When the value is 1, it is completely closed, thus maximizing the bypass of the heat exchanger. When the value is 0, it is fully open, sending all freshwater to the heat exchanger for cooling. All three controller combinations yielded similar results. The conventional controller combination did not fully open the three-way valve. The degree of opening of the three-way valve is greatest in the sequence of controller combinations without the feedforward controller, feedforward controller combination, and conventional controller combination.

Based on the review of Figure 7, the controller combination without the feedforward controller is excluded from the simulation using ship data, as it is not suitable for temperature control owing to the increase in the freshwater output temperature. This indicates that the feedforward controller compensates for the response time differences between the PID_3v and PI_sw controllers in the event of rapid changes in the freshwater or seawater temperatures.

4. Simulation Test Results

Figure 8 compares the simulation results using actual seawater and freshwater inlet temperature data from an 11-day operation period of a real vessel.

Figure 8a illustrates the variations in seawater and freshwater inlet temperatures entering the central cooling system. The data, recorded at one-minute intervals, were used as input data by utilizing the Signal Builder block in Simulink. During the period of 11 days, the freshwater inlet temperature was approximately 35 °C, which corresponds to the vessel’s calling at Hong Kong port, as referenced in Figure 2. As the latitude increases, seawater inlet temperatures generally decrease. Additionally, the dataset included variations in freshwater inlet temperature corresponding to changes in the main engine load. Specifically, this occurs when the engine load transitions from full navigation to lower loads during port entry and departure operations. These temperature fluctuations were used to analyze the performance of the central cooling system under varying operational conditions.

Figure 8b presents the controlled freshwater outlet temperature. The target temperature was 36 °C, but it was observed to rise by approximately 0.5 °C at 2.9 days and 3.8 days. At these times, the seawater supply pump rotation speed in Figure 8c and the full opening of the three-way valve in Figure 8d indicate that the system has a maximum operational capacity. This is due to the freshwater inlet temperature rising to approximately 43.7 °C and the seawater inlet temperature reaching approximately 28 °C, thereby exceeding the heat exchange capacity of the heat exchanger.

In Figure 8d, the variation in the three-way valve opening demonstrates that the controller combination with the proposed feedforward controller mostly maintains a fully open valve, directing all the incoming freshwater to the heat exchanger. Additionally, examining the operational period from 7.1 days to 9.5 days in Figure 2 and Figure 8a,c,d, it is evident that, as the vessel departs from Hong Kong harbor and moves northward, resulting in lower seawater supply temperatures, the controller combination with the feedforward controller reduces the seawater supply pump speed while keeping the three-way valve fully open. In contrast, the conventional controller combination simultaneously reduces both the seawater supply pump speed and opening of the three-way valve.

Figure 8c demonstrates that the proposed control scheme exhibits greater variability in the seawater pump rotation speed than the conventional control scheme. However, it is evident that the proposed control scheme operates predominantly within a lower rotational speed range.

The rotation speed of the seawater supply pump is closely related to the power consumption. Therefore, Figure 9 compares the power consumption of two parallel-operated seawater supply pumps when applying the proposed feedforward controller and the conventional controller.

To accurately calculate the power and energy consumption, the voltage and current consumed by the inverter supplying power to the seawater supply pump motors were measured. Power was calculated by considering the power factor using Equation (8), and energy consumption was calculated by integrating power over time using Equation (9).

$$P\left(t\right)=\sqrt{3}·V_{rms}\left(t\right)·I_{rms}\left(t\right)·cos\varphi \left(t\right)$$

(8)

$$E=\int P\left(t\right)dt$$

(9)

Over the entire simulation period, the power consumed by the seawater supply pumps using the conventional controller combination (PI_sw and PI_3v controllers) was 10,641.1 kWh. In contrast, the pumps using the proposed controller combination (PI_sw, PID_3v, and feedforward PI_ff controllers) consume 10,363.7 kWh. The difference in power consumption over approximately 11 days of navigation and berthing operations is approximately 277.4 kWh, indicating that the proposed controller combination is more energy-efficient.

5. Discussion

The findings of this study demonstrate that the proposed feedforward controller-equipped control scheme outperforms the conventional control scheme in terms of enhancing the efficiency of the central cooling system. Notably, the reduction in the power consumption of the seawater supply pump directly translates to operational cost savings, presenting substantial economic advantages. These results corroborate previous research, indicating that precise adjustment of controllers can considerably improve the energy efficiency of marine systems.

As shown in Figure 8, adjustments in the rotation speed of the seawater supply pump and the three-way valve opening in response to variations in seawater and freshwater temperatures played a crucial role in maximizing the system’s heat exchange capacity. In particular, during specific periods such as the vessel’s call at the Hong Kong port, where the freshwater temperature rapidly fluctuates, and during northern voyages with lower seawater temperatures, the proposed controller swiftly responded to prevent overload of the heat exchanger and maintain a stable freshwater outlet temperature.

Furthermore, as illustrated in Figure 9, the contribution of the proposed control scheme in reducing the power consumption is highly encouraging. The saving of 277.4 kWh over approximately 11 days of navigation and berth operations suggests greater energy savings during extended voyages.

The results of this study underscore the importance of controller design and adjustment for improving the operational efficiency of marine systems. Future research should further validate the performance of the controller under various routes, climatic conditions, and explore the optimization of real-time control algorithms to achieve even greater system efficiency.

6. Conclusions

This study investigated the performance of a central cooling system using simulations with PI and PID controller combinations, focusing on energy efficiency and operational performance. The optimized controller configurations, particularly those involving feedforward combined with conventional PI controllers, demonstrated improvements in energy efficiency. By accurately calculating the power and energy consumption through real-time monitoring of the voltage and current, the results indicated that approximately 277.4 kWh savings could be achieved over an 11-day operation. This outcome underscores the potential for reducing fuel consumption in marine operations, contributing to both cost savings and environmental benefits.

Despite these promising findings, this study also revealed certain limitations that warrant further consideration. Specifically, the simulation did not account for operational scenarios under port conditions, where only a single seawater cooling pump is typically in operation. This limitation may result in deviations in temperature control and energy efficiency under such circumstances, highlighting the need for more comprehensive modeling that includes diverse operational conditions. Additionally, it should be noted that the operational data used for the simulation were recorded from the AMS of a vessel over an 11-day period in specific regions and times. As such, the data may contain disturbances and generalizing the findings to all vessels and routes may be challenging.

Addressing these gaps in future research is crucial for enhancing the robustness and practical applicability of the proposed control strategies. Also, it would be valuable to explore machine learning-based approaches for adaptive control, enabling the system to respond more effectively to varying operational conditions. Experimental validation through full-scale sea trials and the consideration of diverse vessel types, seasonal variations, and operational routes could further enhance the generalizability of the findings.

In conclusion, the proposed control system exhibits significant potential for improving energy efficiency and reducing operational costs in maritime applications. Nevertheless, incorporating adaptive control strategies and addressing the identified limitations will further strengthen the reliability and effectiveness of the system, thereby ensuring its applicability across a wider range of operational scenarios.