Nonlinear Model Predictive Control Energy Management Strategy for Hybrid Power Ships Based on Working Condition Identification

Abstract

Hybrid power technology for ships is an effective way to promote the green and low-carbon development of the maritime industry. The development of pattern recognition technology provides new research ideas for the rational allocation and utilization of energy in hybrid power ships. To reduce fuel consumption, a nonlinear model predictive control energy management strategy based on working condition identification is proposed for optimal energy management to solve the problem of real-time optimal adjustment of generators and batteries. The core of the strategy is to identify the ship’s working conditions and the nonlinear model predictive control algorithm. Firstly, to achieve the working condition identification task, a ship working condition dataset based on a hybrid supply power ship data is constructed. The labeled dataset is trained using deep learning techniques. Secondly, based on the identification results, a nonlinear model predictive control algorithm is designed to adjust the generator speed and the battery current to achieve energy optimization control under constraints. Finally, the effectiveness of the proposed strategy in optimizing energy control and reducing fuel consumption is verified through simulation. The proposed strategy can reduce the generator fuel consumption by 5.5% under no noise disturbance when compared with conventional predictive control. Under 10% noise disturbance, it is still able to reduce the fuel consumption by 2.6%.

1. Introduction

In 2018, the International Maritime Organization (IMO) adopted a greenhouse gas reduction strategy, marking the shipping industry’s entry into carbon reduction efforts. By 2023, IMO passed a series of amendments aimed at reducing air pollution and improving ship energy efficiency [1], highlighting the industry’s increasing demand for energy-saving and emission-reduction technologies. Clearly, further development and improvement of energy control technologies to meet the requirement of reducing ship fuel consumption remains a key direction for the industry. Hybrid power technology is driving the shipping industry toward greener development [2,3,4]. The integration of operating condition identification technology and energy management strategies (EMS) for hybrid ships has provided new opportunities for reducing fuel consumption [5].

In the field of hybrid vehicles, many studies suggest that identifying vehicle working conditions provides valuable decision-making information for energy management strategies, enabling the reduction of fuel consumption. Experimental validations show that accurate identification of working conditions positively impacts the reduction of vehicle operating costs [6,7,8,9]. However, for hybrid ships, distinguishing working conditions is more challenging due to the complexity of the water environment and ship operations. This presents difficulties and challenges in applying operating condition identification technology to optimize fuel consumption in hybrid ships. On one hand, the lack of comprehensive operating condition datasets hinders the analysis of ship operation patterns and anomaly detection. On the other hand, the low accuracy of operating condition identification impairs the performance of energy management strategies, leading to poor optimization and increased fuel consumption, which in turn exacerbates carbon and nitrogen oxide emissions, resulting in significant environmental pollution.

Numerous scholars have conducted research on EMS and operating condition identification technologies, aiming to effectively coordinate multiple power sources in hybrid systems to reduce fuel consumption and lower emissions. EMS can be categorized into rule-based, global optimization-based, and instantaneous optimization strategies [5]. Rule-based EMS often relies on fuzzy logic rules, but such strategies lack flexibility and may not adapt well to complex environments and changing energy demands [10,11,12]. EMS based on global optimization is difficult to implement and is not conducive to practical engineering applications [13,14]. Instantaneous optimization strategies, such as model predictive control (MPC), equivalent fuel consumption minimization, and swarm intelligence algorithms, require real-time performance and high computational speed [15,16]. Operating condition identification methods can be divided into physics-based and data-driven approaches. Physics-based methods require a deep understanding of the equipment and system, involving significant prior knowledge and computation. For example, in [16], nonlinear model predictive control (NMPC) was used to reduce fuel consumption and optimize CO₂ emissions by considering the impact of random waves on the propeller load of hybrid ships. In contrast, data-driven methods rely on large datasets for training and validation and do not require an accurate pre-established system model. These methods can be further categorized into supervised and unsupervised learning. Both types rely on data as a foundation [17]. However, unsupervised learning methods are highly dependent on data quality and features, and the resulting models may be difficult to interpret or apply to all datasets [18,19]. Supervised learning has the advantage of allowing for model correction and optimization, but it requires manual data labeling [20]. For instance, in [20], Least Squares Support Vector Machine (LSSVM) was used to distinguish between fast-varying and slow-varying conditions, and RBF neural networks and Markov Chain models were applied to predict load demands, but without addressing energy management optimization. In [21], a hierarchical distributed control method for hybrid systems was proposed to reduce battery current fluctuations and stabilize bus voltage. Yuan et al. [22] applied Support Vector Machine (SVM) models for operating condition identification and used multi-step Markov Chain models to predict power demands under various conditions, though with relatively low accuracy.

Overall, previous research has rarely focused on utilizing operating condition identification technology to provide decision-making information for the Energy Management System (EMS) of hybrid ships. On one hand, much of the existing research on ship working conditions has concentrated on prediction and analysis. On the other hand, the integration of operating condition identification with EMS has not been sufficiently explored, and the low accuracy of identification hinders effective energy optimization under varying operating conditions. The model accuracy rates of Gao et al. [20] and Yuan et al. [22] are 41.5% and 90.88%, respectively. The accuracy of the models still needs to be further improved. Therefore, the focus of this study is on improving the accuracy of operating condition identification using deep learning techniques and integrating it with NMPC to optimize the energy control of hybrid ships, to reduce fuel consumption. The research begins by analyzing ship operational data and creating an operating condition dataset. To enhance identification accuracy, a deep learning approach utilizing Convolutional Neural Networks (CNN) is employed to train an operating condition recognition model, incorporating Efficient Channel Attention (ECA) [23,24,25,26,27]. In terms of energy management, NMPC is used as the core strategy to address real-time performance requirements and nonlinear system constraints.

The proposed method integrates operating condition identification with EMS, enabling the identification of operating conditions to provide valuable decision-making information for EMS. Furthermore, this approach has significant implications for reducing fuel consumption in hybrid ships and is expected to contribute to advancing future research on ship working conditions.

The main contributions of this paper are as follows:

• A working condition dataset was constructed based on the historical data of a hybrid supply vessel. The dataset was classified using clustering methods, and the ship’s status corresponding to each category was analyzed.
• An offline working condition identification model was trained based on CNN, with an identification accuracy of up to 99.8%.
• Taking a hybrid supply vessel as the research object, this study emphasizes practical engineering applications. The speed of the diesel generator and the output current of the energy storage battery are set as control objectives, aiming to optimize fuel consumption. The NMPC-based EMS achieves optimal control under different working conditions, reducing fuel consumption by 2.6–5.5%.

This study is structured as follows: Section 2 introduces the research object and scheme. Section 3 elaborates in detail on the case ship power system model. Section 4 presents the EMS based on the working condition identification, and Section 5 shows the simulation results and analysis. Section 6 presents the conclusions and offers future perspectives.

2. Research Object and Scheme

2.1. Research Object

In this study, a hybrid supply power ship is used as the research object, named “CNOOC 257”. The ship mainly navigates between docks and offshore oil platforms. It is tasked with supplying and transporting workers to and from the platforms. Its propulsion system features dual propellers and engines in a parallel arrangement, composed of propellers and bow thrusters. The main diesel engines provide the propulsion power, while the thrusters, via an AC bus, offer lateral movement capabilities. The key parameters of the ship such as length, breadth, and draft are listed in

Table 1. Ship parameters.

Description	Value
Ship length	79 m
Ship breadth	16 m
Draft	8 m
Mass	15,000~20,000 ton

.

The topological structure of the power system is shown in Figure 1; shaft generators, auxiliary generators, and the energy storage battery are the power supply equipment in the grid. The shaft generators are SG1 and SG2. The auxiliary generators are DG1, DG2, and DG3. There is a 1021 kWh energy storage battery equipped with this power management system, which can handle a maximum input and output power of 400 kW through a bidirectional DC/AC converter.

BUS A, BUS B, BUS C1, and BUS C2 serve as the ship’s AC buses. Power for the energy storage battery is typically supplied from shore or a shaft generator SG1 or SG2. It can be provided flexibly and independently to shipboard electrical equipment via any AC bus. The power system structure includes two main thrust propellers and three thruster units with two bow thrusters. Thruster units BT1 and BT2 and one stern thruster, ST, are shown in Figure 1.

In Figure 1, the operations of the hybrid power ship are more complicated and are summarized as follows: (1) The propellers that provide forward power are driven by the diesel main engines. (2) The shaft generator, auxiliary generator, and energy storage battery can provide electricity to the thruster units. However, the shaft generators only work in power take-off operating mode and only run when the ship is being propelled, thereby increasing fuel consumption as power is supplied to electrical devices through the AC buses. (3) The power topology is complex, and the power difference between the shaft generator and the auxiliary generator is huge and does not allow parallel operation for a long time. These working conditions pose challenges in reducing fuel consumption and maintaining ship stability, necessitating an effective EMS.

2.2. Scheme

Simplified operation: Setting up the shaft generator does not participate in the power supply of the side-thrust device but only charges the energy storage battery.

The proposed scheme in this paper is shown in Figure 2. Reducing diesel fuel consumption is the research goal and motivation of this paper. It achieves this by identifying the working conditions to maintain the stable operation of the hybrid power ship. The methodology involves modeling the electrical system, utilizing operating condition identification methods, and implementing an NMPC energy management strategy for optimal control. Finally, the contribution is demonstrated by validating the effectiveness of the proposed strategy through energy consumption analysis and real-time performance indicators.

Working condition identification is achieved through deep learning technologies. To begin with, a ship working condition dataset will be established, and then a CNN-based model will be trained for the identification task. Then, the proposed strategy can adjust in real time based on the identification results to complete the task of energy allocation under different conditions. At the same time, the optimal control of the ship is also realized. Finally, the effectiveness of the working condition identification on the EMS will be verified by Simulink simulations. Fuel consumption, battery state of charge (SOC), and real-time performance metrics will be analyzed to evaluate the strategy.

3. Model Establishment

The ship power system model will be established from the point of view that the hybrid ship power system conforms to the conservation of energy. The hybrid power system topology for CNOOC 257 is shown in Figure 1. At the same time, the model of the energy storage battery and auxiliary generator will be constructed by the data fitting method.

3.1. Hybrid Power Ship Power System Model

The ship’s thruster is powered by the auxiliary generator, an energy storage battery. Based on the law of conservation of energy, and ignoring mechanical losses and some electrical losses, the model description of its power can be expressed by

$$\left\{\begin{array}{l}{P}_{load}=P_{dg}+P_{bat},P_{bat}\ge 0\\ \left|P_{bat}\right|=P_{sg},P_{bat}<0\end{array}\right.$$

(1)

wherein $P_{load}$ is the power demanded by the ship’s thrusters and on-board electrical equipment. $P_{dg}$ is the power provided by the auxiliary generator. The ship’s energy storage device is a lithium iron phosphate power battery. $P_{bat}$ is the power provided by the battery. When $P_{bat}$ is greater than zero, the battery is discharged and outputs power. Otherwise, the battery is charged and inputs power. $P_{sg}$ is the power provided by the shaft generator. This is used here to illustrate the energy source of the energy storage battery.

3.2. Energy Storage Battery

The internal resistance equivalent model is adopted as shown in Figure 3. Its current is calculated as follows [13]:

$$I_{bat}={\displaystyle \frac{V_{oc}-\sqrt{V_{oc}^2-4P_{bat}{R}_0}}{2R_0}}$$

(2)

wherein $V_{oc}$ is the open circuit voltage of the internal resistance model. $P_{bat}$ is the output power of the storage battery. $R_0$ is the internal resistance of the storage battery.

The SOC of the battery is calculated as follows:

$$SOC=SO{C}_0-{\displaystyle \frac{{\displaystyle {\int }_{t_0}^t{I}_{bat}dt}}{3600Q}}$$

(3)

wherein $SO{C}_0$ is the initial state of charge. $Q$ is the battery capacity. $I_{bat}$ is the energy storage battery current.

The powers of the battery are constrained as follows:

$$P_{bat,min}\le P_{bat}\le P_{bat,max}$$

(4)

wherein $P_{bat,\mathit{min}}$ is the minimum charging power. $P_{bat,\mathit{max}}$ are the maximum charging power.

The limits for battery SOC and current are constrained as follows:

$$\begin{array}{l}SO{C}_{min}\le SOC\le SO{C}_{max}\\ I_{bat,min}\le I_{bat}\le I_{bat,max}\end{array}$$

(5)

The ship’s energy storage battery has four operating modes, as shown in Figure 4: (a) Mode 1 denotes the operating mode where the shaft generator charges the energy storage battery through BUS A; (b) Mode 2 denotes the operating mode where the shaft generator charges the energy storage battery through BUS B; (c) Mode 3 denotes the operating mode where the energy storage battery provides power through BUS C1; and (d) Mode 4 denotes the operating mode where the energy storage battery provides power through BUS C2 to provide power.

3.3. Auxiliary Generator Model

The auxiliary generator primarily consists of a diesel main engine and generator. The output power of the diesel generator is related to the engine speed and exhibits a nonlinear relationship. The rotational speed and output power of the auxiliary generator are fitted by the scheme of modeling the auxiliary generator in reference [13]. The formula for calculating the output power of the auxiliary generator is denoted as follows:

$$P_{dg}={\displaystyle \sum _{i=0}^3{a}_i}{\omega }_{dg}^i$$

(6)

where ${\omega }_{dg}$ is times the rotational speed of the generator, and $a_i$ and $i$ are the coefficients and exponents of the approximate polynomial, respectively.

The specific fuel oil consumption (SFOC) of the diesel engine and the auxiliary generator output power are calculated by the following formula [13]:

$$m_f={\displaystyle \sum _{j=0}^3{b}_j{P}_{dg}^j}$$

(7)

where $P_{dg}^j$ is the output power of the auxiliary generator, and $b_j$ and $j$ are the coefficients and exponents of the approximate polynomial, respectively.

The constraints of the diesel generator are shown by:

$$P_{dg,min}\le P_{dg}\le P_{dg,max}$$

(8)

wherein $P_{dg,min}$ is the minimum output power. $P_{dg,max}$ is the maximum output power.

4. EMS Based on Working Condition Identification

The EMS is regarded as the core of energy distribution schemes for hybrid power ships. Working condition identification can obtain the current condition of the ship and provide decision-making information for the EMS, but it has rarely been considered in previous literature. To address this challenge, this paper combs and classifies the data of the supplying ship to train the identification model. To cope with the energy optimization problem under different conditions, this paper targets the relevant parameters from diesel generators and batteries and uses NMPC for rolling optimization.

4.1. Working Condition Identification

Due to the complexity of ship operation conditions, the IMO has not established a unified standard of working conditions for ships, which is very unfavorable for the research on the working conditions of ships. However, identifying the ship’s condition only from the status of the shipboard equipment is not able to incorporate the subjective initiative of human beings. Therefore, the study from the perspective of data is an effective method.

4.1.1. Working Condition Dataset for Hybrid Power Ship

The operational data of the vessel “CNOOC 257” was collected and analyzed through hifleet.com (accessed on 27 April 2023). On average, the vessel spends 2.24 h per day in port, 13.6 h offshore, and 8.16 h sailing. A ship operating condition dataset was created by collecting the vessel’s operational data over a week. The sampling frequency was set to 1 Hz, and key feature parameters included ship speed, load power, load voltage, load current, propulsion power, propulsion voltage, propulsion current, and propulsion torque. This dataset comprises 98,143 data entries.

The K-means clustering algorithm and clustering evaluation methods were applied to determine data categories. The elbow method was used as the clustering evaluation algorithm. This method evaluates clustering performance by calculating the sum of squared errors (SSE), which measures the squared distance between each data point and its respective cluster center, across different numbers of clusters. The “elbow” is identified as the point where the SSE curve shows a significant reduction, indicating the optimal number of clusters.

Figure 5 illustrates the clustering results using the elbow method. As shown in this figure, a distinct elbow point occurs when the number of clusters is four. Thus, four clusters were chosen as the basis for classification.

As shown in Figure 6, the ship speed and load power data for the four categories are presented. Ship speed and load power are two critical factors for determining the operational state of the vessel. Statistical analyses were performed for the four categories of data. The power range for Type 1 is approximately 0–300 kW, and the ship speed is around 0–7 Kn. The power range for Type 2 is between 280–800 kW, and the ship speed is 0–7 Kn. For Type 3, the power range is approximately 0–300 kW, and the ship speed is around 6–14 Kn. Type 4 has a power range of approximately 150–450 kW, and the ship speed is around 7–14 Kn.

Figure 7 illustrates the median, mean, and proportion of ship speed and demand power within the dataset for the four operating conditions. These metrics provide a comprehensive overview of the characteristics of each operational category. As shown in Figure 7, the proportions of operating conditions of Type 1 and Type 4 are relatively large, while those of Type 2 and Type 3 are relatively small. By comparing the mean and median values, the differences for operating conditions of Type 1 and Type 3 are relatively small, while the differences for Type 2 and Type 4 are more significant. This indicates that the power and ship speed data of operating conditions of Type 2 and Type 4 show a skewed distribution. Additionally, the average demand power for operating conditions of Type 2 and Type 4 is around 400 kW, while the average power demand for operating conditions of Type 1 and Type 3 is 100 kW or less.

Through cluster analysis and detailed examination of each data category, the ship’s status was linked to each data type based on two critical indicators: ship speed and load power. The results are presented in

Table 2. Working condition information and number.

Conditions	Description	Ship Status
Type 1	The shipload power is low, and the speed is low.	Mooring operations or low-speed navigation
Type 2	The shipload power is high, and the speed is low.	Accelerating navigation and the operating equipment running
Type 3	The shipload power is low, and the speed is high.	Ship’s high-speed navigation status
Type 4	The shipload power is high, and the speed is high.	High-speed navigation operational equipment running

.

4.1.2. Working Condition Identification Model

The core of the operating condition identification model is a CNN model enhanced with an ECA attention mechanism. CNN, as a representative algorithm in deep learning, is known for its feature learning capabilities. It can perform translation-invariant classification of input data based on its hierarchical structure, making it suitable for learning from the dataset established in this study. Moreover, numerous studies have demonstrated that attention mechanisms can help models focus on important features and improve generalization performance. Therefore, this study employs ECA-net, whose principle is based on a dimensionality-preserving local cross-channel interaction strategy and an adaptive method for selecting the size of one-dimensional convolution kernels, thereby enhancing model performance [24,25,26].

The following steps describe the training and prediction process of the proposed operating condition identification model using the ship operating condition dataset:

• Split the dataset into a training set and a validation set with an 8:2 ratio.
• Normalize the data, and train the classification model.
• Normalize the test dataset, and use the trained model to make predictions, evaluate the model, and obtain the results.
• Normalize the collected ship operating condition data or test dataset, use the trained classification model to make predictions, and evaluate the model.

The CNN model used in this study is based on the models proposed by Wang et al. [26], Yang et al. [27], and Zhang et al. [28]. Through multiple experiments, the structure of the CNN is determined. The criteria for the structure are twofold: firstly, the training time should be as short as possible, and secondly, the identification should be accurate. Therefore, the identification model consists of one input layer, three convolutional layers, two ECA-net modules, three pooling layers, and two fully connected layers. The details of dataset preprocessing, the structure of the CNN model, and its parameter settings during training are shown in Figure 8.

4.2. NMPC-Based EMS Based on Working Condition Identification

In this study, NMPC is selected as the optimization algorithm for energy management strategies, which is the main representative algorithm for transient optimization strategies. The core of NMPC is its rolling optimization capability, and its cost function can be given by a non-quadratic programming form, unlike the MPC. However, the design of the NMPC cost function affects the optimization results. At each moment, NMPC solves the optimal control sequence of the optimization problem takes the first set of values in the solved control sequence as control inputs and then repeats the process at the next moment. Therefore, in this paper, the SOC of the battery and the instantaneous fuel consumption of the auxiliary generator are taken as the main optimization objectives, and the diesel generator and the battery are used as the control objects, the state variables $x(k)={[SOC,m_f]}^T$, control variables $u(k)={[I_{bat},{\omega }_{dg}]}^T$, output variables $y(k)={[SOC,m_f]}^T$. The nonlinear model is given by the following:

$$x(k+1)=f(x(k),u(k))=\left[\begin{array}{c}{x}_1(k)-{\displaystyle \frac{{\displaystyle \int u_1(k)dt}}{3600Q}}\\ {\displaystyle \sum _{j=1}^3{b}_j{\left({\displaystyle \sum _{i=1}^3{a}_i}{\left(u_2(k)\right)}^i\right)}^j}\end{array}\right]$$

(9)

The cost function is designed in the following form:

$$\begin{array}{c}\min J={\beta }_{1,w}{\displaystyle \sum _{N-1}^{i=1}}{(SO{C}_i-SO{C}_{ref})}^2+{\beta }_{2,w}{\displaystyle \sum _{N-1}^{i=1}}{m}_{f,i}^2+{\mu }_{1,w}{\displaystyle \sum _{N-1}^{i=1}}{P}_{bat,i}^2\\ +{\mu }_{2,w}{\displaystyle \sum _{N-1}^{i=1}}{P}_{dg,i}^2+{\phi }_{1,w}{\left(SO{C}_N-SO{C}_{ref,N}\right)}^2+{\phi }_{2,w}{m}_{f,N}^2\\ s.t.\left\{\begin{array}{c}{u}_{m,min}⩽u_m⩽u_{m,max}\\ \stackrel{.}{u_{m,min}}⩽\stackrel{.}{u_m}⩽\stackrel{.}{u_{m,max}}\\ SO{C}_{min}⩽SOC⩽SO{C}_{max}\\ P_{load}=P_{bat,i}+P_{dg,i}\end{array}\right.\end{array}$$

(10)

wherein ${\left(SO{C}_i-SO{C}_{ref}\right)}^2$ is a penalty for battery SOC deviation, which ensures avoiding excessive battery discharge variations in energy demand throughout the entire operating cycle. $SO{C}_{ref}$ is the reference input for the battery SOC. $m_{fc,i}^2$ is the penalty term for minimizing the fuel consumption. $P_{bat,i}^2$ and $P_{dg,i}^2$ are minimizing system inputs. ${\left(SO{C}_N-SO{C}_{ref,N}\right)}^2$ and $m_{f,N}^2$ are terminal constraints. ${\beta }_{1,w},{\beta }_{2,w},{\mu }_{1,w},{\mu }_{2,w},{\phi }_{1,w},{\phi }_{2,w}$ are the penalty coefficients. Their values are determined by the working condition type $w$. $u_m$ is the control variable, which should satisfy the constraints of (4) and (8). Meanwhile, to keep the control variables from changing too drastically and to keep the rate of change within a certain range, the energy storage battery SOC is constrained by (5). Finally, the energy conservation of the ship is incorporated into the control strategy in the form of equation constraints.

Based on the results of operating condition identification, the adjustment of the penalty coefficient is determined by the different motion states of the vessel under various operating conditions. These differences affect the proportion of power output from the diesel generator and the battery. The selection of penalty coefficients is performed manually. Through the Monte Carlo experimental method, 1000 sets of penalty coefficients are randomly generated. For each set of penalty coefficients, the objective function values are calculated based on the mean load power under different operating conditions and the fuel economy range of the auxiliary generator. Statistical analysis is then performed on these objective function values. Ultimately, a set of penalty coefficients is determined for each type of operating condition. In the Type 1 operating condition, for example, the battery output should be increased, while the diesel generator’s power output should be reduced accordingly.

The identification must match the computational speed of the EMS, and the time series of the proposed strategy is shown in Figure 9, with the time units in seconds. The time required for one calculation of the experimental platform is as follows:

$$\begin{array}{l}\Delta t=\Delta t_1+\Delta t_2\\ s.t.\Delta t\le 1\end{array}$$

(11)

wherein $\Delta t_1$ represents the working condition identification time, and $\Delta t_2$ represents the solution time for the NMPC controller.

Figure 9. Time series of the proposed strategy.

Figure 9. Time series of the proposed strategy.

The block diagram of the proposed EMS based on working condition identification is shown in Figure 10. It is mainly divided into the working condition identification module, the NMPC controller, and the controlled system consisting of the diesel generator and the energy storage battery.

The inputs to the condition identification module are the eight data parameters mentioned in Section 4, i.e., ship speed $\widehat{S}(k)$, load power ${\widehat{P}}_{load}(k)$, load voltage ${\widehat{V}}_{load}(k)$, load current ${\widehat{I}}_{load}(k)$, propulsion power ${\widehat{P}}_{propulsion}(k)$, propulsion voltage ${\widehat{V}}_{propulsion}(k)$, propulsion current ${\widehat{I}}_{propulsion}(k)$, and propulsion torque ${\widehat{T}}_{propulsion}(k)$, which are fed back from the controlled system. Its output is the result of the four types of conditions described, called $w$. The results of the identification are used to adjust the constraints and the penalty coefficients of the cost function.

The NMPC controller is used for rolling optimal control of the energy control of the auxiliary generator, ${\widehat{P}}_{dg}(k)$ and storage battery, ${\widehat{P}}_{bat}(k)$. The controlled system feeds back the measured output power of the auxiliary generator and the measured output power of the storage battery to the NMPC controller to complete the closed-loop control.

5. Experimentation and Analysis

The experimental platform is equipped with a GPU, NVIDIA GeForce RTX 4060, and a CPU, Intel Core i7-13700H. The construction and training of the identification model are both carried out in MATLAB software (R2022b).

5.1. Accuracy of the Working Condition Identification Model

The performance of the model based on deep learning technology on the ship condition dataset can be evaluated through indicators such as the confusion matrix, accuracy, and loss. The confusion matrix is an important indicator for evaluating the classification model. As shown in Figure 11, it includes the number of true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN). Therefore, when analyzing and evaluating the working condition identification model using the confusion matrix metrics, certain conclusions can be drawn from the proportion of the diagonal elements TP and TN in Figure 11.

The definition and calculation formula for the model’s accuracy are as follows:

$$Accuracy={\displaystyle \frac{TP+TN}{TP+TN+FP+FN}}$$

(12)

wherein $TP$, $TN$, $FP$, and $FN$ are consistent with the definitions in Figure 11, respectively.

One of the important indicators for measuring the training process of deep learning is the loss, calculated as follows:

$$Loss=-{\displaystyle \sum _i^n{y}_i\log (p_i)}$$

(13)

wherein $y_i$ is the data sample label. When the data sample belongs to the class $i$, $y_i$ is 1; otherwise, it is 0. $p_i$ is the probability that the data sample belongs to the class $i$. As the name suggests, the smaller the loss of the model, the better the model performance on the dataset, and the better the model fits the data.

The loss and accuracy during the training of the proposed identification model are shown in Figure 12. As the number of training increases, the accuracy of the model increases, and the loss degree decreases. The loss of the model can decrease to 0.035; the accuracy can increase to 98.6%.

The comparison of the training set and test set prediction results is shown in Figure 13. The training set contains a total of 78,514 data entries, and the test set includes a total of 19,629 data entries. The proposed identification model achieves an accuracy of 99.8268% for both datasets, predicting a result different from the actual situation for only a small number of data entries.

For further analysis, the confusion matrices of the training set data and the test set data are plotted in Figure 14. In Figure 14a, the training set contains 25,036 data entries for condition Type 1, of which 24,996 are correctly identified, 10 are incorrectly identified as Type 2, and 30 are incorrectly identified as Type 3. There are 4808 data entries, of which 4799 are correctly identified and 9 are incorrectly identified as Type 1; for condition Type 3. There are 16,329 data entries, of which 16,095 are correctly identified and 234 are incorrectly identified as Type 1. For condition Type 4, there are 32,341 data entries, all of which are correctly identified.

Figure 14b indicates that in the test set, there are 6352 data entries for condition Type 1, of which 6341 are correctly identified, one is incorrectly identified as Type 2, and 10 are incorrectly identified as Type 3. For condition Type 2, there are 1186 data entries, with 1180 correctly identified and 6 incorrectly identified as Type 1. For condition Type 3, there are 4083 data entries, with 4028 correctly identified and 55 incorrectly identified as Type 1. For condition Type 4, there are 8080 data entries, all of which are correctly identified.

In summary, the identification accuracy of working conditions Type 1, Type 2, and Type 4 is higher than 99%; Type 3 has 98% identification results. Type 1 has 1% of the data classified as Type 3. Type 3 has 1.4% of the data classified as Type 1. Due to the low number of incorrectly identified data, it can be recognized as a small probability event. From the analysis, the proposed identification model can accomplish the working condition identification task.

5.2. Computational Time of Working Condition Identification

The proposed identification model must match the computational speed of the EMS. For this reason, the identification speed of the working condition identification model is evaluated through comparative experiments. They are divided into two parts: (1) testing the time required to train the model and (2) the time required to use the model to complete the working condition identification task. This study designs two sets of controlled experiments on the same experimental platform, comparing the models based on the SVM identification model and the proposed model used in this paper.

• Experiment 1: This sets the parameters of the identification model proposed as shown in Figure 8. The identification model is based on SVM, and the RBF function is chosen as the kernel function. Both models are trained 100 times. The training time of each time is counted as a comparison term.
• Experiment 2: Among the two identification models trained in Experiment 1, the two models with relatively good accuracy are selected. Select 1000 pieces of data from the ship’s working condition dataset to form the test data of Experiment 2, with condition types 1, 2, 3, and 4 each accounting for 25% of the test data. Record the time required for each identification model to complete the identification task.

The statistical results of the experiments are shown in Figure 15. The training time of the proposed model in this paper ranges from 30 to 90 s in Figure 15a, with an average training time of 58.76 s. The training time of the SVM-based model for the identification ranges from 1 to 7 s, with an average training time of 2.48 s. In Figure 15b, the time required for the model used to identify the test data of Experiment 2 ranges from 0.01 to 0.4 s, with an average identification time of 0.08 s. The identification time of the SVM-based model ranges from 0.05 to 3.5 s, with an average identification time of 1.31 s.

Scheme 1 and 2 are shown in

Table 3. Results of the identification experiments.

Model	Real-Time Performance
SVM	0.05–3.5 (1000 times/s)
The proposed method	0.01–0.4 (1000 times/s)

. Considering that working condition identification only needs to be performed offline, the training time is used as a reference for evaluating the models. The accuracy and real-time performance are the focus of the comparison experiments. In summary, it can be seen that the experimental results of the model used in this paper are all better than those of the SVM-based identification model. Therefore, the proposed identification model in this paper can improve the accuracy and real-time performance of working condition identification and better complete the task of identification.

5.3. Experimentation and Analysis of EMS Based on Working Condition Identification

To validate the optimization effect and fuel economy of the proposed strategy, simulation experiments were conducted using MATLAB software. The simulation model parameters and control parameters are shown in

Table 4. Simulation model parameters.

Description	Parameter	Symbol	Value
Battery	Capacity	$Q$	1100 kWh
	Internal resistance	$R_0$	0.0065 Ω
	Maximum voltage	$V_{oc}$	750 V
Diesel generators	Speed range	${\omega }_{dg}$	0–1800 RPM
	Efficiency	${\eta }_{dg}$	0.98
	Fitted coefficient	$a_i,i=0,1,2,3$ $b_j,j=0,1,2,3$	$[-409.3,1.599\times {10}^{-1},6.458\times {10}^{-4},-2.608\times {10}^{-7}]$ $[302.3,4.78\times {10}^{-1},1.36\times {10}^{-3},-1.213\times {10}^{-6}]$

and

Table 5. Results of the experiments.

Description	Symbol	Value
Battery initial SOC	$SO{C}_0$	0.9
Battery maximum SOC	$SO{C}_{max}$	0.99
Battery minimum SOC	$SO{C}_{min}$	0.20
Battery maximum current	$I_{bat,max}$	600 A
Battery minimum current	$I_{bat,min}$	−600 A
Coulombic efficiency	${\eta }_{bat}$	0.98
DG maximum output power	$P_{dg,max}$	450 kW
DG minimum output power	$P_{dg,min}$	0 kW
DG maximum speed	${\omega }_{dg,max}$	1800 RPM
DG minimum speed	${\omega }_{dg,min}$	0 RPM

.

The load demand of the simulated ship is shown in Figure 16, with a sampling frequency of 1 Hz. The load power covers the four types of working conditions, with each type accounting for approximately 25%. This setup was used to test the effectiveness and real-time performance of the working condition identification NMPC-based EMS. In the simulation experiment, at each sampling point, the eight feature data including load power were either test set data or data generated by interpolation from the test set data. The source of the ship speed data is based on the analysis of ship speed shown in Figure 6 and Figure 7.

To test the robustness of the proposed strategy, the method from reference [21] is used to add 80 dB of Gaussian noise to the load demand, which accounts for 10% of the maximum demand power. Simulations are performed under this condition using the conventional NMPC strategy and the proposed strategy. The power tracking of the ship demand power is performed using the NMPC-based EMS and the strategy proposed, with the simulation results shown in Figure 17.

As in Figure 17a,b, it shows the diesel generator output power and battery output power of the proposed strategy versus the conventional NMPC strategy when tracking the demand power. It is seen that the diesel generator and battery can meet the demand power at all times, with relatively stable output power. Figure 17c,d depict the SFOC and battery SOC changes; compared to each other, the proposed strategy can reduce SFOC, with the end SOC differing by about 10%. In Figure 17e,f, the output current of the battery and the speed of the diesel generator are shown. In Figure 17g, the computation time required for each sampling point is shown. It is seen that the average computation time of the proposed strategy in this paper is less.

Comparing the NMPC EMS and the strategy proposed in this study for power tracking the demand power of the ship with 10% noise, the simulation results are presented in Figure 18.

In Figure 18a,b, the diesel generator output power and the battery output power using the NMPC strategy and the strategy proposed in this paper are shown. It is seen that the diesel generator and battery can meet the demand for power with 10% noise. In Figure 18c,d, the instantaneous fuel consumption and battery SOC variations are demonstrated. It is shown that the SOC values at the end of the simulation do not differ much, but the proposed strategy significantly reduces fuel consumption. In Figure 18e,f, the battery output current and diesel generator speed cases are displayed. The proposed strategy has a sudden decrease in generator speed and battery current at the 2000th and 5000th sampling points. But the sudden increase and decrease in this case is not significant. In Figure 18g, the computation time required at each sampling point is shown.

The rule-based control strategy proposed by Khan et al. [10] is applied to the ship in the case study. The rules are set as follows: (1) When the battery’s SOC is above 50%, the diesel generator and the battery bear 40% and 60% of the load power, respectively. (2) When the SOC is lower than 50% but higher than 20%, the diesel generator and the battery bear 60% and 40% of the load power, respectively. (3) When the SOC is lower than 20%, the battery stops working, and the load power is borne by multiple diesel generators. The simulation results are summarized in

Table 6. Comparison results of different strategies.

Method	Noise	Fuel Consumption	Final SOC	Real-Time Performance
Rule-based	no noise	2056.809 kg	56.17%	$1.7\times {10}^{-5}$ s
	10% noise	2057.435 kg	56.18%	$1.9\times {10}^{-5}$ s
NMPC	no noise	1973.789 kg	40.30%	$2.6\times {10}^{-3}$ s
	10% noise	1923.495 kg	45.70%	$4.0\times {10}^{-3}$ s
The proposed	no noise	1865.518 kg	48.10%	$1.16\times {10}^{-3}$ s
	10% noise	1874.001 kg	47.15%	$6.0\times {10}^{-4}$ s

.

Based on the simulation results of Figure 17 and Figure 18, the cumulative fuel consumption data, battery SOC, and real-time performance for different scenarios are summarized in Table 6.

In scenarios where demand power is free from noise interference, the proposed EMS achieves a fuel consumption reduction of 209.366 kg compared to the rule-based strategy, corresponding to a decrease of 10.2%. In scenarios where demand power is affected by noise interference, the proposed EMS reduces fuel consumption by 183.434 kg compared to the rule-based strategy, resulting in a decrease of approximately 8.9%. However, regarding the final SOC value and real-time performance, the proposed method does not perform as well as the rule-based strategy. If the SOC difference between the rule-based control and the proposed method is higher, at 8.07% and 9.03%, respectively, after converting the energy and translating it into fuel consumption, the fuel consumption is still higher than that of the method proposed in this study. The proposed method inherently requires a certain amount of computation. Therefore, compared to the rule-based strategy, the proposed method can reduce fuel consumption, but it performs poorly in terms of final SOC and computation time.

In the scenario without noise interference in demand power, the proposed EMS reduces fuel consumption by 108.271 kg compared to the conventional NMPC strategy, a decrease of 5.5%. In the scenario with noise interference in demand power, the proposed EMS reduces fuel consumption by 49.494 kg compared to the conventional NMPC strategy, a decrease of approximately 2.6%. In terms of battery SOC changes, the final SOC value of the proposed strategy is higher than that of the conventional NMPC strategy. In terms of real-time performance, the working condition identification helps to reduce the solution time of the NMPC controller and meets the constraints. In the scenario without and with noise, the identification time accounts for 34.4% and 13.3% of the entire solution time, respectively. Overall, the proposed strategy outperforms the conventional NMPC strategy.

Experimental simulations were conducted in this study. The effectiveness of the hybrid power ship in real-time identification of working conditions that can provide decision-making information to the EMS is verified. In addition, the effectiveness of the proposed strategy is also demonstrated from the perspective of cumulative fuel consumption. The identification model proposed in this paper shows better accuracy, which may be due to two main reasons: Firstly, the self-constructed dataset used in this paper contains more data features. Secondly, the experimental platform used in this paper is superior, which makes the model performance and real-time computational capability better.

6. Conclusions

Aiming at the problem of energy optimization control of hybrid power ships, a nonlinear model predictive control EMS based on working condition identification is proposed. Data acquisition, processing, and analysis were carried out based on the ship operation process. Data labeling work was performed to construct a ship working condition dataset. A condition identification model based on CNN was established, and the model was trained and tested using the dataset for offline identification of ship conditions, providing decision-making information for the EMS. Finally, by constructing the NMPC-based EMS, the energy optimization control of shipboard generators and the battery under different working conditions was realized, effectively reducing fuel consumption. The main conclusions are as follows:

(1)

The study takes the CNOOC 257 supply ship as its object, collects data about the ship operation process, creates a working condition identification dataset, and uses the proposed identification model to complete the task of identifying the working conditions of the ship, with an accuracy rate of over 99%.

(2)

Simulation results show that the EMS based on working condition identification using NMPC can reduce fuel consumption by 5.5% compared to the conventional NMPC strategy. Under the condition of adding 10% noise to the demanded power, it can further reduce fuel consumption by 2.6%. Additionally, the proposed strategy is able to meet the real-time requirements.

This study compares fuel consumption, battery SOC variation, and real-time performance. There is also a possibility that the identification may be disturbed by the environment in real applications. In the future, more factors will be considered in our work. For example, resistance to environmental interference, simulation scenario realism, and multi-model fusion to improve the accuracy of working condition identification.