The various types of costs for ship charging and swapping station mainly include construction costs, operation and maintenance costs, and equipment replacement costs, namely, Equation 1: C Ship = C Inv + C OM + C Rep (1)

Among the various types of costs for ship charging and swapping station, the construction cost C Inv mainly includes the procurement costs of charging, discharging, and other equipment. The specific calculation expression is as follows Equation 2: C Inv = f ShipC ⋅ P ShipC , ⁡ max + f ShipG ⋅ P ShipG , ⁡ max + f ShipST ⋅ V ST ⋅ 1 365 ⋅ R (2)

Generally, P ShipC , ⁡ max is composed solely of energy storage, while P ShipG , ⁡ max includes not only energy storage but also transformers in the ship charging and swapping station. Therefore, P ShipG , ⁡ max > P ShipC , ⁡ max ; R is the annualization factor, and its calculation expression is as follows Equation 3: R = r 1 + r T   pro 1 + r T   pro − 1 (3)

Notably, the costs of other equipment (the f ShipST ⋅ V ST term) also include the modernization of port infrastructure. This includes investments in the power grid system, charging docks, communication networks, and safety systems necessary for the efficient operation of electric ships. Modernizing port infrastructure to accommodate ship charging requires substantial capital expenditure, especially for upgrading electrical systems to handle higher capacities, establishing fast-charging facilities, and improving safety protocols. As the port infrastructure becomes increasingly adapted to electric ships, the associated costs are expected to decrease over time. With improved standardization, larger-scale adoption of electric ships, and continued technological advancements, the overall financial burden on ports will be reduced, ultimately contributing to the lowering of long-term operating costs.

The operation and maintenance costs of ship charging and swapping station are divided into annual fixed maintenance costs and variable maintenance costs. The former is mainly determined by the scale of the ship charging and swapping station, while the latter is related to the energy throughput of the station Equation 4. C OM = 1 365 ⋅ f OM , fix ⋅ P ShipC , max + P ShipG , max + f OM , var ⋅ ∑ t = 1 T P ShipC , t + P Ship G , t (4)

The expression for the replacement cost of the ship charging and swapping station is as follows Equation 5: C Rep = C Inv ⋅ ∑ j = 1 k 1 1 + r j T cyc ⋅ R (5) where k is the total number of replacements for the ship charging and swapping station during the project period, rounded up to the nearest whole number if it is not an integer.

The operational model of ship charging and swapping station describes the constraints that need to be met during operation, mainly including output constraints, single condition operation constraints, and backup constraints.

The output constraints of ship charging and swapping station require that the power absorbed (or released) during the charging (or discharging) process stays within the upper and lower limits, namely, Equation 6: P ShipC , min ⋅ u ShipC , t ≤ P ShipC , t ≤ P ShipC , max ⋅ u ShipC , t P ShipG , min   ⋅ u ShipG , t ≤ P ShipG , t ≤ P ShipG , ⁡ max ⋅ u ShipG , t (6) where u CAESC , t is the binary variable representing the charging working state at time period t, where 1 indicates charging state and 0 indicates idle state; u ShipG , t is the binary variable representing the discharging working state at time period t, where 1 indicates discharging state and 0 indicates idle state.

The single condition operation constraint requires that the ship charging and swapping station can only operate in one condition or be completely idle, namely, Equation 7: u ShipC , t + u ShipG , t ≤ 1 (7)

The ship charging and swapping station has the ability to provide both positive and negative reserves under different operating conditions. However, due to the potential issue of reserve discontinuity when providing reserves across different conditions, this paper does not consider providing reserves across different conditions. The specific constraint expressions are as follows Equation 8: R Ship , t up = R ShipC , t up + R ShipG , t up R Ship , t down = R ShipC , t down + R ShipG , t down (8)

The provision of positive and negative reserve power by the ship charging and swapping station comes at the expense of reducing the range of charging and discharging power. The relationship between them is as follows Equations 9, 10: P ShipC , t − R ShipC , t up ≥ P ShipC , ⁡ min P ShipG , t + R ShipG , t up ≤ P ShipG , ⁡ max (9) P ShipC , t + R ShipC , t down ≤ P ShipC , ⁡ max P ShipG , t − R ShipG , t down ≥ P ShipG , ⁡ min (10)

In this study, thermal generation is utilized as the main supply due to its foundational role in many power systems. Thermal power plants are reliable and provide consistent baseload power, making them essential for maintaining grid stability, especially in scenarios with fluctuating renewable energy sources. Thermal generation plays a crucial role in frequency regulation and balancing power supply and demand in the grid, and is often used as a key backup source to ensure stable and predictable electricity supply, which is critical in the operational model for ship charging and swapping stations within smart grid applications. Additionally, wind power has become a key renewable energy source due to its scalability, cost-effectiveness, and low environmental impact once deployed. In this study, incorporating wind power generation allows the model to reflect the growing importance of renewable energy in modern grids, where reducing dependency on fossil fuels is a priority. In summary, this paper considers both thermal and wind power generation in the economic analysis method for ship charging and swapping stations in smart grid applications.

To minimize the total investment and operating costs, a typical daily optimal scheduling model for ship charging and swapping station in smart grid application scenarios is constructed. The total investment and operating costs mainly include the total operating costs of thermal power units, the total costs of ship charging and swapping station, and the cost of wind power curtailment. The expression is Equation 11 obj = min C G + C Ship + C W _ cut (11)

In the process of deep peak shaving of thermal power units, the operating cost needs to consider both the basic operating costs of the units, such as fuel cost, start-up cost, and reserve cost, and the additional costs, such as deep peak shaving loss cost, deep peak shaving fuel cost, and deep peak shaving subsidy income. The specific expression is as follows Equation 12: C G = C G , run + C G , DP + C G , DPRO + C G , start + C G , reserve − E G (12)

The expressions for the above six cost items are as follows Equation 13: C G , run = ∑ t = 1 T ∑ i = 1 N G a G i ⋅ P G i , t + b G i ⋅ u G i , t C G , start = ∑ t = 1 T ∑ i = 1 N G S G i ⋅ 1 − u G i , t − 1 ⋅ u G i , t C G , reserve = ∑ t = 1 T ∑ i = 1 N G c G i ⋅ R G i , t up + d G i ⋅ R G i , t down C G , DP = ∑ t = 1 T ∑ i = 1 N G S Buy , G i 2 N F , G i , t ⋅ β 1 ⋅ k G i , t DPR + β 2 ⋅ k G i , t DPRO C G , DPRO = ∑ t = 1 T ∑ i = 1 N G Q oil , i , t ⋅ S oil E G = ∑ t = 1 T ∑ i = 1 N G P G i , ⁡ min RPR − P G i , t ⋅ f 1 ⋅ k G i , t DPR + P G i , ⁡ min DPR − P G i , t ⋅ f 2 ⋅ k G i , t DPRO + P G i , ⁡ min RPR − P G i , ⁡ min DPR ⋅ f 1 ⋅ k G i , t DPRO ⋅ Δ t (13)

The expression for wind power curtailment penalty cost is as follows Equation 14: C W _ cut = ∑ t = 1 T f Wc ⋅ P fW , t − P sW , t (14)

The operational constraints of the model mainly include power balance constraints, reserve constraints, renewable energy output constraints, thermal power unit operation constraints, and constraints on ship charging and swapping station, which are explained sequentially below.

The power balance constraint is primarily used to ensure the real-time balance between the system’s electricity supply and demand Equation 15. ∑ i = 1 N G P G i , t + P ShipG , t + P sW , t = P Load , t + P ShipC , t (15)

The reserve constraints require the system to maintain a certain amount of positive and negative spinning reserve capacity to mitigate the impacts of uncertainties in wind power and load forecasting, ensuring the safe and stable operation of the system, namely, Equation 16 ∑ i = 1 N G R G i , t up + R Ship , t up ≥ ε L ⋅ P Load , t + ε W ⋅ P fW , t ∑ i = 1 N G R G i , t down + R Ship , t down ≥ ε L ⋅ P Load , t + ε W ⋅ P fW , t (16)

The renewable energy output constraint requires that the actual wind power dispatch output cannot exceed the wind power forecast output, namely, Equation 17 0 ≤ P sW , t ≤ P fW , t (17)

The operational constraints for thermal power units include output constraints, start-up and shutdown constraints, ramping constraints, and reserve constraints. The specific calculation expressions for these constraints are as follows.

The output constraints for thermal power units consider the output limits during conventional peak shaving, non-oil deep peak shaving, and oil-fired deep peak shaving, namely, Equations 18, 19 k G i , t RPR ⋅ P G i , ⁡ min RPR ≤ P G i , t ≤ k G i , t RPR ⋅ P G i , ⁡ max RPR k G i , t DPR ⋅ P G i , ⁡ min DPR ≤ P G i , t ≤ k G i , t DPR ⋅ P G i , ⁡ max DPR k G i , t DPRO ⋅ P G i , ⁡ min DPRO ≤ P G i , t ≤ k G i , t DRPO ⋅ P G i , ⁡ max DRPO (18) k G i , t RPR + k G i , t DPR + k G i , t DPRO = u G i , t (19) where u G i , t the binary variable for the operational state of thermal power unit i at time period t, where 1 indicates the unit is working and 0 indicates the unit is idle; k G i , t RPR , k G i , t DPR , and k G i , t DPRO represent the binary variables for the peak shaving state of thermal power unit i at time period t, where k G i , t RPR corresponds to conventional peak shaving, k G i , t DPR corresponds to non-oil deep peak shaving, and k G i , t DPRO corresponds to oil-fired deep peak shaving, with a value of 1 indicating the unit is in that peak shaving stage; we have P G i , ⁡ min RPR = P G i , ⁡ max DPR and P G i , ⁡ min DPR = P G i , ⁡ max DPRO .

The ramping constraints and start-up/shutdown time constraints for thermal power units are as follows Equation 20. T G i , t on ≥ T G i , ⁡ min on T G i , t off ≥ T G i , ⁡ min off P G i , t + 1 − P G i , t ≤ v G i up ⋅ Δ t P G i , t − P G i , t + 1 ≤ v G i down ⋅ Δ t (20)

The reserve constraints for thermal power units are as follows Equations 21, 22. P G i , t + R G i , t up ≤ P G i , ⁡ max RPR ⋅ u G i , t 0 ≤ R G i , t up ≤ v Ramp , G i up ⋅ Δ t (21) P G i , t − R G i , t down ≥ P Gi , ⁡ min DPRO ⋅ u Gi , t 0 ≤ R G i , t down ≤ v Ramp , G i down ⋅ Δ t (22)

The operational constraints for ship charging and swapping station are detailed in Section 2.2 and will not be elaborated here.

The decision variables of the model mainly include: the output of thermal power units, wind power output, the charging and discharging power of ship charging and swapping station, the reserve output of thermal power units and ship charging and swapping station, and various state variables.

While the developed model is primarily designed for ship charging and swapping stations within smart grid application scenarios, its universality extends to other regions and countries with appropriate adjustments. Different geographic locations often feature unique infrastructures, regulations, and environmental conditions that may require modifications to the original model. Incorporating region-specific constraints into the model can enhance its applicability across diverse geographical settings. For example, countries with stricter environmental regulations may require additional emissions constraints or noise control measures at charging stations (Sun et al., 2021). Areas with limited grid stability or intermittent renewable energy supply may need to incorporate more robust power balancing or energy storage constraints (Suberu et al., 2014). Similarly, regions with high congestion in port areas might require additional safety constraints related to energy storage and discharge processes (Roy et al., 2020). These location-based constraints can be integrated into the model to improve its reliability and ensure it aligns with local operational requirements. Through the incorporation of various adjustable parameters, the model can be fine-tuned to reflect the specific needs of different locations, whether by modifying operational constraints, adjusting cost functions, or introducing additional factors such as seasonal variations in shipping demand or grid capacity. This flexibility makes the model suitable for a variety of geographical contexts, supporting its potential adoption in global smart grid applications.

The case studies are conducted based on the modified IEEE 9-bus and IEEE 30-bus systems. The IEEE 9-bus system is shown in Figure 1A. In this system, the wind farm is connected to node 23, and the ship charging and swapping station is connected to node 23. The schematic diagram of the IEEE 30-bus system structure is shown in Figure 1B, and the wind farm and ship charging and swapping station are connected at node 23 of the system.

The minimum output of thermal power units during normal operation, non-oil deep peak shaving, and oil-fired deep peak shaving is 60%, 45%, and 30% of the rated output, respectively. The operational impact coefficients for non-oil and oil-fired deep peak shaving stages are 1.2 and 1.5, respectively. The oil price is set at 6130 yuan/ton, and the oil consumption for oil-fired deep peak shaving is 4.8 tons/hour per unit time. The unit electricity compensation prices for non-oil and oil-fired deep peak shaving are 0.2 yuan/kWh and 0.4 yuan/kWh, respectively. The unit power cost of the thermal power unit is 636.81 $/kW.

Due to the distinct seasonal characteristics of wind power and load, this chapter considers setting four typical days for analysis: spring, summer, autumn, and winter. Referring to the relevant data of typical days for each season in a certain region of China, the forecast curves for load and wind power on typical days in each season are shown in Figures 2, 3, respectively.

The average daily operating cost for the system over a year is obtained by performing weighted calculations based on the proportion of typical days in each season within a year. This is used to illustrate the economic benefits brought by the participation of the ship charging and swapping station system in system operations. The proportions for spring, summer, autumn, and winter are set to 0.17, 0.33, 0.17, and 0.33, respectively. Assuming the maximum forecast errors for load and wind power output are 5% and 20%, respectively, the unit capacity wind curtailment penalty cost is set to 200 $/MW.

To compare the economic efficiency of various types of ship charging and swapping station in detail, four scenarios are set up: Scenario 1 involves no participation of any ship charging and swapping station, only considering conventional thermal power units with deep peak shaving capability and wind power. Scenarios 2 to 4 build on Scenario 1 by respectively adding ship charging and swapping station with dual-ring network wiring mode, “double-petal” wiring mode, and two-main-two-backup wiring mode. It should be noted that the three wiring modes are widely-used in current substation. The followings are the brief overviews of these three wiring modes.

Dual-ring network wiring mode: The schematic diagram of the dual-ring network wiring mode is shown in Figure 4. In this mode, the two power sources of the first-level switching station come from different bus bars of the same substation or from different substations. The two power sources of the second-level switching station come from different bus bars of the upper-level switching station, and there are two dedicated tie lines between the two second-level switching stations. Four switching stations form a dual-sided power chain wiring. This wiring mode can meet the “N-2” shutdown requirements during maintenance and is easy to maintain, provided that the line transmission capacity is sufficiently large. However, this mode also requires the construction of dedicated tie lines, necessitating additional investment.

“Double-petal” wiring mode: The schematic diagram of the “double-petal” wiring mode is shown in Figure 5. Each substation’s main transformer leads out two lines, which, together with the two lines led out by the main transformers of other substations, form a “double-petal” wiring configuration. This wiring mode has relatively easily controlled short-circuit currents, which is beneficial for system stability and safety. When the line transmission capacity is sufficiently large, this mode can meet the “N-2” shutdown requirements during maintenance, further improving power supply reliability. However, the load transfer process between rings in this mode is relatively complex and requires distribution automation to complete load transfer during faults.

Two-main-two-backup wiring mode: The schematic diagram of the two-main-two-backup wiring mode is shown in Figure 6. In this wiring mode, the two power sources of the switching station come from different bus bars of the same substation or from different substations, and dedicated tie lines are set up between switching stations. In the event of losing both upper-level power sources, the switching station can still transfer loads, achieving lateral backup. Each bus bar segment of the switching station reserves one slot for a tie line, forming a hand-in-hand structure with adjacent switching stations. Compared to the “double-petal” wiring mode, this wiring mode provides more balanced load transfer during the ring network formation process, effectively improving the load rate of the switching station after a fault.

Table 1 demonstrates the simulation results of system investment and operating costs for the IEEE 9-bus system under four scenarios, highlighting significant cost variations. Scenario 1 incurs the highest total cost ($357,916.30) due to the elevated operating costs of thermal power units ($277,442.41) and wind curtailment costs ($34,957.78). In contrast, Scenario 3 achieves the lowest total cost ($302,611.11), attributed to reduced reserve costs ($15,982.79) and wind curtailment costs ($6,622.31). Scenario 2 also shows notable cost reductions with the lowest deep peak shaving loss cost ($627.55) and deep peak shaving fuel cost ($431.00), indicating enhanced operational efficiency. While Scenario 4 slightly increases total costs ($321,121.58) due to the investment in ship charging and swapping stations, it reflects the system’s effort to integrate renewable energy and electrification infrastructure. These results suggest that Scenarios 2 and 3 effectively balance operational efficiency and cost savings, with Scenario 3 emerging as the most economically optimal.

Table 2 highlights the comparative economic benefits of ship charging and swapping stations under different scenarios for the IEEE 9-bus system. Scenario 3 demonstrates the most favorable economic outcome, with the lowest investment and operation cost ($9,364.18) and the highest output-to-input ratio (195.28%), indicating superior cost efficiency. Scenario 2 also exhibits strong economic benefits, with an output-to-input ratio of 128.03% and moderate costs ($14,571.11). In contrast, Scenario 4 shows the highest cost ($19,244.97) and the lowest output-to-input ratio (88.49%), suggesting reduced cost-effectiveness. These results underscore the importance of optimizing investment strategies to achieve economic efficiency in deploying ship charging and swapping stations.

The simulation results of the IEEE 30 system investment and operating costs for scenarios 1 to 4 are shown in Table 3. Analyzing the data in Table 3 reveals that although the introduction of ship charging and swapping station brings additional investment and maintenance costs, the overall economic efficiency of the system is still effectively improved. Various operating costs of thermal power units have decreased to different extents, with the reserve costs and deep peak shaving related costs of thermal power units showing significant reductions, decreasing by at least approximately 27.7% and 31.2%, respectively. Further analysis shows that the total system cost decreases the most in Scenario 3, by approximately 11.1%, and decreases the least in Scenario 4, by approximately 10.4%. In addition, the introduction of ship charging and swapping station significantly reduces wind curtailment, with wind curtailment costs generally decreasing by more than 80%.

For ease of analysis, the sum of the investment cost and the operation and maintenance cost of the ship charging and swapping station is referred to as the “investment and O&M cost of ship charging and swapping station.” The reduction in the total system operating cost after the introduction of ship charging and swapping station is referred to as the “operating benefit of ship charging and swapping station.” At the same time, the concept of the output-to-input ratio of the ship charging and swapping station is introduced, which is the ratio of the operating benefit to the investment and O&M cost of the ship charging and swapping station. The comparison of the economic benefits of different types of ship charging and swapping station is shown in Table 4. As can be seen from the table, the ship charging and swapping station with the dual-ring network wiring mode has the highest overall economic benefits, followed by the station with the “double-petal” wiring mode, and finally the station with the two-main-two-backup wiring mode.

Taking a typical winter day as an example, the operational conditions of the system in different scenarios are analyzed to compare the impacts brought by the introduction of different ship charging and swapping station. The operational conditions of the system on a typical winter day for scenarios 1 to 4 are shown in Figures 7–10. From the figures, it can be seen that when there are no ship charging and swapping station in the system, the thermal power units undertake all the regulation tasks and reserve requirements. Deep peak shaving of the thermal power units occurs more frequently, often during load valleys and high wind power output. During these times, fewer thermal power units are in operation, and their output is lower, necessitating deep peak shaving to provide space for wind power integration. After the introduction of ship charging and swapping station, the system’s flexible regulation capability is significantly enhanced. The frequency of deep peak shaving for thermal power units is markedly reduced, with part of the system’s reserve tasks also being shared. Additionally, the “low charge, high discharge” operation mode of the ship charging and swapping station effectively promotes the large-scale integration of wind power, improving the economic efficiency of system operations.

To further analyze the impact of the capacity configuration of ship charging and swapping station on system operation, the installed capacity of the ship charging and swapping station is changed while keeping other conditions unchanged. The operational benefits of different types of ship charging and swapping station under different capacities are analyzed based on the parameters in this chapter. The simulation results are shown in Table 5, and the trends are illustrated in Figure 11.

Analyzing Figure 11, it can be observed that as the installed capacity of ship charging and swapping station increases, the operational benefits and the output-to-input ratio of various types of ship charging and swapping station initially increase and then decrease. This is mainly because: when the installed capacity of ship charging and swapping station is relatively low, their investment and maintenance costs are also relatively low. Meanwhile, their benefits in reducing the operating, reserve, and deep peak shaving costs of thermal power units and in promoting large-scale wind power integration are significant. Additionally, the operational benefits brought by the increase in the capacity of ship charging and swapping station exceed the growth in investment and maintenance costs. Therefore, at this stage, the output-to-input ratio of ship charging and swapping station continues to rise. Later, as the installed capacity of ship charging and swapping station further increases, the demand and benefits of the station within the system gradually reach saturation. However, the rise in installed capacity continues to increase the investment and maintenance costs of the ship charging and swapping station, leading to a decrease in operational benefits and a decline in the output-to-input ratio.