1. Introduction
All-electric ships (AESs) combine propulsion and service load through an energy management system [
1]. The flexibility, safety, and energy utilization efficiency are improved compared with conventional mechanical propulsion ships [
2]. Furthermore, for China to achieve the ambitious target of carbon peaking by 2030 and carbon neutrality by 2060, the research and promotion of AES are crucial.
In [
3,
4,
5,
6], the unit combination, generation scheduling, sizing of the energy storage system, and energy management of the ship power system have been intensively studied. As the above study, the influence of the voyage information on the optimization objective is ignored. Being a mobile microgrid, the propulsion load of the AES accounts for more than 70% of the total load demand [
7]. Therefore, the optimization of ship speed by scheduling propulsion load and the generation scheduling by variable load demand need to be considered simultaneously to constitute joint generation and voyage scheduling [
8,
9].
To solve this problem, many improved optimization models have been proposed to jointly optimize AES generation and load dispatch in recent years [
7,
8,
9,
10,
11,
12,
13]. The authors of [
10] integrated the voyage scheduling and power system dispatching of AESs to develop the carbon price, and the method can better incentivize AESs to achieve emission control. In [
7], a two-layer robust optimization model is used to minimize the fuel consumption and energy efficiency operational indicator by considering the ship speed loss due to wave and wind uncertainties for joint power generation and voyage schedules. In [
11], a stochastic programming model is adopted to avoid the operational risk caused by renewable energy generation and load-side uncertainty. They introduced the conditional value-at-risk indicator in the objective function. Joint optimization of the voyage and multi-objective energy management is achieved by coordinating the AES with the hybrid energy storage system [
12]. The study in [
13] tries to extend the GHG emissions as an objective function to the AES joint scheduling model, which is solved using the non-dominated sorting genetic algorithm II algorithm. However, the studies mentioned above for AES voyage optimization only focus on economic and GHG emission targets. The dynamic reliability level of ship operation optimization has not been focused on.
The voyage conditions of tugboats are significantly different from those of conventional ships, where the power demand is high during towing, with a total load factor of more than 90% [
14,
15]. In contrast, the load level is lower during berthing or cruising. Therefore, it challenges the optimal economic dispatch of power under guaranteed reliability conditions when the operating conditions are variable. The studies show that resistance generated by wind and waves causes loss of ship speed [
16,
17]. The above study considered the effect of ship speed loss in AES operation optimization due to wind and wave variation. However, the propulsion power variation required to maintain the predefined voyage is not considered, which is significant for the reserve power in the ship’s power system at each moment. Additional power reserves are required to maintain the preset speed, considering the added resistance caused by waves. It is necessary to avoid power shortages under heavy load conditions. Therefore, the chance-constrained model [
18,
19,
20] is used in this study. Stochastic outages of equipment components such as generators and batteries under load uncertainty are considered to avoid overly optimistic scheduling decisions.
Solving the voyage and power generation scheduling model with wind and wave uncertainty and random component outages has several issues to be addressed. First, the typical equation of ship speed and propulsion power used in the literature [
11,
13,
21] does not apply to tugboats. When a tug is in dragging condition, its speed will change due to the additional resistance of the towed vessel. Therefore, it is necessary to model the propulsion system under the influence of the meteorological environment according to different working conditions of the tugboat [
17]. Secondly, the piecewise linearization methods mentioned in the above studies convert nonlinear functions into MILP by equally spaced segmentation. However, introducing too many integers increases the burden of the solution. In addition, probabilistic constraints in the model need to be approximately transformed while considering balancing accuracy and computational efficiency [
22,
23]. The study in [
14,
19] used battery balancing for power fluctuations in the system, but the effect of cyclic and irregular charging/discharging strategies on the battery life was not considered. Consequently, the battery loss model needs to be established so that the control strategy can be optimized [
24,
25,
26].
The following are the main contributions of this paper. This paper proposes a joint optimal scheduling model for navigation and power generation considering tugboat operation’s reliability to solve the above-proposed problem. The main contributions are as follows.
(1) System operational reliability has not been a concern in previous AES operational optimization problems. In this study, a combined navigation and power generation scheduling model is constructed for different operating conditions of tugboats. A probabilistic constraint on operational reliability is adopted instead of the traditional deterministic constraint to avoid over-optimistic optimization schemes.
(2) The typical ship speed and propulsion power formula do not apply to tugboats. Nonlinear expressions for the tugboat’s speed in calm water and the propulsion power for the variable operating conditions of the tugboat departure, docking, dragging, cruising, and berthing are developed. Due to the increased resistance caused by wind speed and waves, the preset speed of the ship is effectively maintained by dispatching the corresponding reserve power. This way, ships’ operational reliability and arrival rate can be enhanced.
(3) For nonlinear and chance constraints in the model, the optimal adaptive piecewise linearization and the probability distribution discretization method are employed to transform them into linear deterministic constraints. Previous studies have not been concerned with the piecewise linearization method’s effect on the calculation’s accuracy. The improved model used in this study significantly reduces the number of decision variables and decreases the computational burden.
(4) The energy storage system consisting of battery units combined with generator units can improve energy utilization and flatten power fluctuations. Conventional battery charging and discharging strategies do not consider the economic loss due to degradation. In this study, the loss of energy storage lifetime is quantified and translated into an economic loss. It effectively mitigates the loss of battery life.
The rest of this article is organized as follows:
Section 2 presents the mathematical model of the problem.
Section 3 illustrates the optimization problem formulations. The solution method for the optimal operation of tugboats is introduced in
Section 4. Then,
Section 5 provides case studies and a discussion of the results.
Section 6 concludes the work.
6. Conclusions
This paper combines the operating conditions of electric tugboats and proposes a new joint optimal scheduling model of navigation and power generation, considering the reliability of tugboat operation. The relationship between propulsion load and voyage as influenced by navigation speed and waves is first established. The risk scenarios (equipment outages and load fluctuations) that occur in the system are transformed into readily solvable mixed integer problems solved by probability distribution discretization and an improved piecewise linearization method. Finally, it is calculated by the CPLEX solver. The effect of various influencing factors on the scheduling results is verified and compared through four simulation experiments so that operators can adjust the navigation speed and generation scheme according to different demands.
This paper innovatively incorporates operational reliability opportunity constraints into the joint optimization to balance economy and reliability by adequately scheduling system reserve power. The simulation results show that the system can satisfy the power increment demand caused by wind and waves by enhancing the reserve power after adding the operational risk constraint and guaranteeing the operational safety of the ship throughout the voyage. Furthermore, the effect of segmentation points on precision is not studied in the traditional piecewise linearization method. In this paper, the improved linearization method with optimized segment points reduces the decision variables by 6.07% while ensuring the accuracy of the operation and improving the computational efficiency. Meanwhile, the economic indicator of battery degradation added to the optimization objective effectively avoids frequent charging and discharging, and the results show that the battery life loss is decreased.
The proposed scheduling model can be improved to consider other practical factors. The configuration and sizing of the energy storage system, combined with the tugboat’s working conditions, is essential. These will be further investigated.