A Life Cycle Cost Analysis of Different Shore Power Incentive Policies on Both Shore and Ship Sides based on System Dynamics and a Chinese Port Case

9 Shore power (SP) is widely recognized as an efficient strategy for reducing air 10 pollution in port areas. Unfortunately, the adoption of SP has been relatively low, 11 resulting in limited emission reductions and financial losses. To address these 12 challenges, this paper focuses on enhancing the utilization rate of SP. We propose a 13 system dynamics model that assesses the impact of various incentive policies on the 14 economic and environmental benefits of SP. The model considers the life cycle cost and 15 comprises four subsystems. By conducting a case study on Nansha Port, we find that 16 price subsidies are more effective than construction subsidies in overcoming economic 17 barriers. Furthermore, we observe that the overall economic benefits only increase 18 when the electricity price decreases. This is because lowering the electricity price 19 enhances the profitability of ships without negatively affecting port revenue. 20 Additionally, it is the proportion of the electricity price and service price that determines 21 the overall economic benefits, rather than the SP price itself. Hence, it is recommended 22 to provide preferential subsidies for the electricity price.


Graphical abstract 1. Introduction
The frequency of economic and trade interactions between countries is increasing due to the promotion of global integration.In this context, shipping plays a crucial role, accounting for over 90% of the global trade flow (UNCTAD, 2018).While striving to promote economic prosperity, the emissions of air pollutants resulting from shipping activities have reached alarming levels, posing a significant threat to both the environment and human health (Innes and Monios, 2018;Sadek and Elgohary, 2020;Tawfik et al., 2023).Approximately 70% of shipping emissions occur in the port area, with emissions from berthed vessels being significantly higher than emissions from other port activities.In fact, berthed vessels account for 60-90% of total port emissions (Ballini and Bozzo, 2015;Qi et al., 2020).Berthed vessels use auxiliary engines to power themselves in a traditional way, which releases CO2, SOX, NOX, and PM particles.
Without implementing relevant emission reduction measures, it is anticipated that shipping emissions will increase by 50-250% by the year 2050 (International Maritime Organization, 2018).Therefore, the control and reduction of air pollutant emissions from vessels in port areas have become significant research areas that are gaining more attention, particularly in the current context of low carbon and emission reduction efforts (Chen et al., 2019;Hsu et al., 2023;Lozano et al., 2019;Peng et al., 2021).
As a significant method of preventing and controlling air pollution, shore power (SP) has a positive impact on emissions reduction and has been widely adopted by many countries.SP enables berthed vessels to shut down their shipborne auxiliary engines and utilize shore-side electricity to power their operations and meet the power demand of all onboard facilities (Bjerkan and Seter, 2021;Martínez-López et al., 2021).In 2017, the U.S. Environmental Protection Agency found that the use of SP by ports in America, Europe, and Asia resulted in a significant reduction of air pollutant emissions from vessels by 60-80% (Wu and Wang, 2020).However, many complex factors exist that hinder the implementation of SP in many countries, including high construction investment costs (Daniel et al., 2022;Peng et al., 2019), the "chicken and egg" dilemma (Winkel et al., 2016;Wu and Wang, 2020), and the principal-agent problem among stakeholders (Qi et al., 2020).Unattractive economic advantages are key barriers (Yu et al., 2019).Promotion of SP faces challenges due to the lack of favorable economic benefits for both ports and shipping companies (Dai et al., 2019).In general, the primary factors that vessels consider when deciding whether to utilize SP are the costs of shore power and fuel oil (Yin et al., 2020;Zis, 2019).Furthermore, without incentives for the usage of SP, vessels tend to opt for fuel burning instead of utilizing SP when the price of SP is higher than the constantly fluctuating price of fuel oil.
In fact, the construction of shore-side power equipment has been mostly completed in most ports.According to the relevant report, the installation rate of shore-side power in China's inland river ports has basically reached 100%, and the average installation rate in 13 coastal ports reached 73% in 2021 (Clean Air Asia, 2022a).Nevertheless, the installation rate of shipborne power-receiving facilities is low, resulting in a low utilization rate of SP in coastal ports.In 2021, only 7.9% of container ships and 1.8% of bulk carriers among the international ships sailing to and from China's coastal ports were equipped with SP receiving facilities (Clean Air Asia, 2022b).Furthermore, Tan et al. (2023) reported that the utilization of SP is less than 20%.The low installation rate and utilization rate of shipborne SP facilities not only leads to inadequate emission reduction effects but also prevents the realization of economic benefits, resulting in significant losses for the port.Therefore, it is crucial to incentivize shipping companies to install SP facilities and enhance their utilization rate.To address this issue, governments have introduced subsidies for ports and vessels in order to promote the installation and utilization of SP (Wang et al., 2021b).Financial assistance has a significant influence on SP implementation because huge investment is a major obstacle for the users in the initial stages of SP construction (Chen et al., 2021;Tseng and Pilcher, 2015).
In order to tackle these practical problems outlined above, we are undertaking this research endeavor.The remainder of this article is organized as follows.Section 2 provides a summary of the related literature.Section 3 presents a cost-benefit analysis model and a system dynamic model, which includes the economic sub-model of ports, the economic sub-model of shipping companies, the environmental benefits sub-model of SP, and the government subsidy sub-model.Additionally, a case study of the Port of Nansha is presented in order to evaluate the economic benefits of SP from the perspectives of ports and shipping companies.Section 4 conducts sensitivity analysis and discussions to identify effective ways to enhance the benefits of SP.Finally, Section 5 offers conclusions and policy suggestions.

Economic incentive of shore power
Researchers have reached a consensus that economic challenges pose significant obstacles to the widespread adoption of SP.These challenges include various factors such as the high initial investment required, long payback periods, and the high cost of using SP (Chen et al., 2019;Dai et al., 2019;Tseng and Pilcher, 2015;Wang et al., 2021b;Winkel et al., 2016;Zis et al., 2016).Ports and shipping companies have a tendency to prioritize their own economic interests and profitability.In terms of ports, the implementation of sustainable practices primarily yields profitability through service fees.As for vessels, the main financial benefits come from cost savings compared to using auxiliary engines (Ölçer and Ballini, 2015).It is important to conduct an in-depth analysis of the economic benefits for both ports and shipping companies.
Several studies have utilized some so-called Cost Benefit Analysis models to assess the economic advantages of SP's utilization for ports and vessels.They have employed indicators like net present value (NPV) and payback period to evaluate the financial benefits (Dai et al., 2019;Yin et al., 2020;Zis et al., 2016;Zis, 2019).Dai et al. (2019) selected the Port of Shanghai as a case study and conducted a techno-economic analysis of SP, considering shore-side SP installation rate in its analysis.
To incentivize the utilization rate of SP, many governments have implemented various measures such as offering construction subsidies or price subsidies.For instance, the European Union (EU) has provided financial support to ship owners who have installed shipborne power-receiving facilities for purchasing electricity and to certain EU ports for the construction of shore-side power (International Transport Forum, 2019).Government subsidies have a positive effect on the economic benefits of SP's utilization (Song et al., 2017;Yin et al., 2020).A number of studies have examined subsidies for SP construction, while only a few studies have explored subsidies for SP prices.Wang et al. (2021b) proposed that the government should first provide subsidies for port facility construction and then continue to subsidize the SP price in the following years.Government subsidies alone do not guarantee the full utilization of SP.Actually, the rate of installation of shipborne power-receiving facilities is low due to a lack of government authority to enforce the use of SP on ships.Therefore, it is crucial to optimize the efficiency of government subsidy portfolio and scheme.
Several government subsidy plans aiming to maximize emissions reduction at ports were independently developed by Wu and Wang (2020), Wang et al. (2021b) and Wang et al. (2022) .These plans were optimized to ensure the optimal utilization of government subsidies.
Although China is making efforts to promote the use of SP, there still exists a gap between the actual utilization of SP and the expectations (Wan et al., 2021).In fact, most ports in China are capable of providing SP, but a large number of vessels lack the equipment to receive SP. Considering the significant difference in coverage between shore-side SP facilities and ship-side SP facilities, if the ship-side SP coverage rate is not improved promptly, a large number of shore-side SP facilities will remain idle (Zhen et al., 2022).Therefore, it is imperative for the government to seek strategies to enhance the installation or retrofitting of shore power facilities on ships.In addition to the economic subsidies, ships are also concerned about the implementation of priority berthing policies in port zones (Yin et al., 2020).Zhen et al. (2022) compared the impact of a government-subsidy-based incentive policy with a berthing-priority-based incentive policy on the deployment of shipborne power-receiving facilities.Qi et al. (2020) discovered that captains typically choose not to use shipborne power-receiving facilities at the operational level due to the complexity of the connection process and the lack of significant economic benefits.Therefore, offering incentives to captains, such as providing certain compensation or rewards for every successful utilization of SP, would be an effective way to stimulate the utilization of SP.Until now, there has been limited academic research conducted in this area, which deserves more attention.

Environment performance of shore power
Rapid growth in international trade has contributed to significant port developments in the last couple of decades.However, port development has also brought environmental challenges.Particularly in recent years, increasing environmental awareness has created new challenges for the development and management of ports (Sun and Zhao, 2023;Tang et al., 2023).Referred to as the "International Maritime Organization 2020" regulation, this policy restricts the amount of sulphur in ship fuel oil utilized in areas outside of designated emission control zones to 0.50% m/m, which marks a substantial decrease from the previous limit of 3.5%.Prior to this, stricter limits of 0.10% were already enforced within specific designated emission control zones (Jiang et al., 2020;Qi et al., 2021).The primary source of emissions at the port arises from vessels when they are docked, with between 60% and 90% of these emissions coming from auxiliary engines used during the berthing procedure (Tan et al., 2021).
By replacing auxiliary engines, SP can assist in reducing pollution and meeting the power needs of vessels while they are docked (Colarossi and Principi, 2020;Spengler and Tovar, 2021;Ye et al., 2022).Undoubtedly, utilizing a SP system is an optimal choice for vessels that remain in port for extended periods of time or dock at ports with strict emission regulations (Seddiek et al., 2014;Zis, 2019).For instance, since 2014, the California Air Resources Board has enforced a regulation requiring that half of the ships arriving at major ports in California either adopt SP or reduce their utilization of auxiliary power generation on board by a minimum of 50% compared to a benchmark derived from a historical baseline (Vaishnav et al., 2016) .Many scholars have discovered that the widespread utilization of shore power facilities at ports can lead to a substantial reduction in emissions of carbon dioxide, sulfur dioxide, nitrogen oxides, and black carbon in the port area (Seddiek et al., 2014;Wan et al., 2021;Zis et al., 2014).
Top-down and bottom-up evaluations are common methods used to calculate emissions from vessels.The top-down method relies on macroscopic data, such as reported quantities of marine bunker fuel, to calculate emissions.On the other hand, the bottom-up method uses microscopic data, such as different movements and operations, to gather the emissions (Fan et al., 2022;Miola and Ciuffo, 2011).Some researchers employed the top-down approach (Endresen et al., 2007;Hulskotte and Denier van der Gon, 2010), while others utilized the bottom-up approach (Adamo et al., 2014;Budiyanto et al., 2022;Hall, 2010); meanwhile, a fraction of scholars opted to combine these two methods (Topic et al., 2021;Winkel et al., 2016).All of these studies demonstrate the remarkable environmental performance and benefits of SP's utilization.
Therefore, the government should spare no effort in developing and promoting the utilization of shore power.

Research methodology
Life cycle cost refers to the total costs incurred by a product throughout its useful life, which includes development, production, usage, and disposal (Yan, 2015).The LCC concept was originally proposed by the US Department of Defense for the procurement of military equipment (Ilyas et al., 2021).Gradually, this approach was extended to encompass equipment selection, renewal, and renovation, as well as maintenance cost control within asset-intensive industries such as power grids (Li et al., 2019), railroads (Shi et al., 2021), bridges (Han et al., 2021;Karabulut et al., 2021), ports (Berawi et al., 2018) and vessels (Wang et al., 2021a).With this approach, it is possible to evaluate the overall long-term economic efficiency and make the optimal strategic choice from a financial perspective (Bui et al., 2022;Kumari et al., 2022;Leiva-Maldonado et al., 2023).Specifically, for projects characterized by long product life cycles and substantial maintenance expenses, such as SP, LCC proves to be a suitable method (Colarossi and Principi, 2023;Huo et al., 2017;Liu et al., 2023).
However, existing literature fails to consider the LCC when analyzing the economic benefits of SP (Dai et al., 2019;Wang et al., 2021b;Ye et al., 2022).Utilizing LCC to quantify the cost of SP offers the advantage of accurately representing the economic benefits for stakeholders.
System dynamics (SD) theory has been increasingly utilized in transportationrelated domains since the 1990s (Liu et al., 2021).However, its utilization in the shipping sector has been relatively limited (Kong et al., 2022).SD can be used to examine system behavior and model the connections between a system's structure and function.The issue with continuous and dynamic quantities interrelated in feedback loops and circular causality can be effectively addressed through the use of SD (Sterman, 2018).Jing et al. (2021) designed a SD model to assess the long-term carbon dioxide emissions generated by Arctic shipping.The study also constructed twelve scenarios incorporating different fuel consumption scenarios.Kong et al. (2022) designed a maritime supply chain SD model to evaluate the effects and financial gains of ports and shipping companies under various carbon reduction strategies.Their findings indicate that shore power holds promise as an effective measure for reducing emissions.Nonetheless, a comprehensive analysis of the profitability involved in the implementation of shore power was not conducted.Other researchers have paid attention to SP from different perspectives.Some have used the SD model alone, while others have combined it with game theory (Chen et al., 2021;Xu et al., 2021).Some have investigated subsidy and penalty policies together (Jin and Zhao, 2021;Zhao et al., 2021), while others have studied subsidy (Li et al., 2020) and penalty (Li et al., 2022) separately.Little et al. (2016) have suggested that the SD model can provide an effective simulation environment for addressing the complexity of long-term policies.
Through the review of the relevant literature mentioned above, we believe that the system dynamics model can be applied to our research.
To summarize, the current body of literature on shore power has made considerable strides in conducting thorough analyses of the environmental implications of reducing pollutant emissions.While certain studies have also examined the economic factors associated with shore power and suggested strategies for its widespread adoption, there remains an opportunity for additional research in this field.A research gap exists in utilizing the SD model for assessing the economic and environmental advantages of shore power.This study aims to bridge this gap by employing a cost-benefit analysis, rooted in the LCC theory and SD model, to analyze the economic and environmental benefits of shore power.

Model development
The economic factor is a significant determinant for ports and shipping companies when considering the adoption of SP.In order to assess the economic viability of investing in SP and to identify the factors that influence SP utilization, it is crucial to ascertain the incomes and costs associated with SP for ports and shipping companies.
Therefore, conducting a cost-benefit analysis of SP is essential for these entities.This section presents a case study of the Port of Nansha, analyzing and evaluating the economic and environmental benefits of SP from the perspective of ports and shipping companies.

The economic sub-model of ports
The economic benefits of ports gained from using SP can be calculated as the difference between incomes and costs.The port's annual total income ( _ ) is made up of the annual revenue of the port from SP ( _ ), government subsidies for the price of SP ( _ ), and government subsidies to the port for the construction of SP (  ).
For the sake of brevity, construction subsidies to the port are considered to occur in the first year of the SP life cycle.
In particular, the revenue of port from SP utilization is related to the SP price, the SP use time of a berth, and the total power of SP ( ℎ ).The SP price is the sum of the electricity price ( ℎ ) and the SP service price (  ) minus the subsidies for unit SP price (  ) when considering government subsidies for the SP price.The SP use time of a berth (  ) is related to the berth utilization rate () and SP utilization rate ().
Furthermore, it takes some time to connect the SP equipment because the connection procedure is complicated.Approximately 10% of the ship's berthing time is used to conduct SP equipment connection (Yin et al., 2020).
=  ×  −   = 365 × 24 ×  ×  × 0.9 (3) The life cycle cost, which consists of the initial investment cost (  ), operating cost ( _ ), maintenance cost ( _ ), failure cost ( _ ), and disposal cost (  ), is used to estimate the total cost of the port ( _ ) in this paper.We assume that the initial investment cost is incurred in the first year and the disposal cost is incurred in the last year of SP service years.The initial investment cost of SP equipment at a 100,000-DWT berth is 6.823 million CNY (Lai et al., 2016).The annual maintenance cost is estimated to be around 200,000 CNY.The annual fault cost and the residual value are 100,000 CNY and 250,000 CNY, respectively (Huo et al., 2017).
_ =   +   ( 5) The economic benefits of investing in SP at a port could be analyzed according to the Net Present Value (NPV) and dynamic payback period.The NPV is the difference between the investment value and the amount recovered at the end of the investment cycle (Das Neves et al., 2023;Yin et al., 2020).The NPV could be modeled as follows: The payback period is the time required to make the accumulated economic benefits equal to the initial investment cost.It can be divided into two categories, static payback period and dynamic payback period.Compared with the static payback period, the dynamic payback period (  ) takes into account the time value, which could be modeled as follows: Fig. 1 shows the internal relationships of the economic subsystem of ports and its interactions with external subsystems.

The economic sub-model of shipping companies
The economic benefits of ships gained from using SP come mainly from the cost savings compared to using auxiliary engines (Ölçer and Ballini, 2015;Yu et al., 2019).
The power generation cost of auxiliary engines (  ) and government subsidy to a ship for SP construction (  ) can be considered as making up the total income of a ship ( _ ).Construction subsidies are assumed to occur in the first year of the SP life cycle.
_ =   +   (9) In addition to the expense of fuel (  ), ships that use auxiliary engines to generate power also have to pay for environmental costs (   ) and auxiliary engine maintenance (  ).
Emission ratios and tax rates for pollutant emissions are listed in Table 1.

Table 1
Emission ratios and tax rates for pollutant emissions.* According to Yin et al. (2020) We apply the life cycle cost to calculate the cost of using SP for ships ( _ ).
According to the related literature (Huo et al., 2017;Innes and Monios, 2018), the initial investment cost is 2 million CNY, the annual maintenance cost is 100,000 CNY, the annual fault cost is 50,000 CNY, and the residual value is 100,000 CNY.

𝑇𝐶 𝑆_ 𝑖 = 𝐶𝐼 𝑆 + 𝐶𝑂 𝑆_ 𝑖 + 𝐶𝑀 𝑆_ 𝑖 + 𝐶𝐹 𝑆_ 𝑖 + 𝐶𝐷 𝑆 (13)
When calculating the operating cost, the cost of using SP at a certain SP utilization rate and the cost of using auxiliary machines should both be considered.Besides, ships have to use auxiliary engines to generate electricity during the SP connection process, so the cost of this period should also be considered.Thus, the operating cost ( _ ) could be formulated as follows: _ =  ℎ ×  × ( ℎ +   −   ) ×   × 0.9 10000 ⁄ +   ×  × 0.1 Similar to the port section, two indicators, net present value and dynamic payback period, are used to evaluate the SP economic benefits of ships.companies and its interactions with external subsystems.

The environmental benefits sub-model of SP
Since not enough data were available about the auxiliary engine power consumption for each ship, a rough value could be estimated in the following way (Adamo et al., 2014;Tseng and Pilcher, 2015): where  is the average power during ship berthing (kW),  is the average power tonnage ratio (kW/ton),  is the load factor for auxiliary engines,  is the gross register tonnage of a ship (ton), and   is the specific emission reduction (ton).
Fig. 3 shows the internal relationships of the environmental benefits subsystem of SP and its interactions with external subsystems.

The government subsidy sub-model of SP
The government will provide subsidies for ports and ships in order to speed up the construction and application of SP.The subsidies can be divided into SP construction subsidies to ports, SP price subsidies to ports, and SP construction subsidies to ships.
The annual government subsidy to the port for the SP charge ( _ ) is expressed as follows: Fig. 4 shows the internal relationships of the government subsidy subsystem of SP and its interactions with external subsystems.

The integrated model
Fig. 5 illustrates the cause-and-effect relationships among the model parameters of the benefits of using SP.From the perspective of pollutant emissions, ships emit air pollution by consuming energy while berthed.The emission reduction effect of using SP is particularly pronounced in ports with high throughput.To encourage the adoption of SP, the government offers financial subsidies.Moreover, the environmental benefits resulting from the use of SP also contribute positively to its promotion.As the utilization rate of SP increases, the substitution of auxiliary diesel power generation with electricity significantly reduces pollutant emissions, thereby positively impacting the environment and the promotion of SP.From the perspective of port benefits, on one hand, a portion of the SP price -namely, the electricity price -can be regarded as the port's payment to the power grid company, thereby negatively impacting the port benefits.On the other hand, the SP price can be seen as the ship's payment to the port, thus exerting a positive effect on the port benefits.From the vantage point of ship benefits, the benefit of utilizing SP is determined by the cost difference between using auxiliary power generation and utilizing SP.The higher the cost of auxiliary power generation, the more profitable it becomes for ships to utilize SP.Increasing environmental costs and fuel prices will result in higher costs for auxiliary power generation, thereby positively impacting ship benefits.Instead of receiving direct cash subsidies, ships are eligible to use SP at a discounted price, reducing the overall cost of SP utilization and consequently enhancing ship benefits.2.

Model validation
In order to validate the reliability of the proposed model, the simulated data can be compared with the actual values.Table 3 below presents the validation results.The Port of Nansha installed shore-side power for the first time in 2017.The data is derived from the statistics of the Government of port hinterland.The discrepancy ratios are all below 5%, indicating that the model is consistent with the actual state.

Table 3
Model validation results.

Sensitive analysis and discussions
In this section, we conduct a sensitive analysis and discussion to identify effective strategies for improving the economic benefits and emission reduction effect of SP usage in the Port of Nansha.To illustrate our findings, we focus on a 100,000-DWT berth at the container terminal and a container ship with a capacity of 5,000 TEUs.From both economic and environmental viewpoints, we explore the impact of various factors such as SP utilization rate, berth utilization rate, environmental costs, fuel prices, captain incentives, government subsidies, and SP prices on the overall effectiveness of SP.We begin by examining the advantages of shore-side SP and ship-side SP in the absence of government subsidies.Next, we examine construction subsidies and price subsidies separately and compare their respective impacts on SP promotion in a quantitative analysis.Finally, we delve into a comprehensive study on the strategy of implementing price subsidies.When government subsidies are not considered and the SP utilization rate is 100%, SP demonstrates good economic benefits.The dynamic payback period is approximately four years, which accounts for 20% of the total project duration, as shown in Fig. 8.At the end of the equipment's life cycle, a net present value of 12.47 million CNY can be attained.The port benefits increase by 335,600 CNY for every 1% increase in SP utilization rate.However, if the SP utilization rate is below approximately 60%, the port will incur a loss.Furthermore, it can be inferred that for every 1% increase in berth utilization rate, the port benefits are enhanced by 559,300 CNY, and the annual emissions decrease by 226 tons.The impact of increasing berth utilization rate on the payback period is greater for ports with low berth utilization rate than for ports with higher berth utilization.In reality, SP utilization rates are often low.For instance, when the SP utilization rate of a port is only 20%, a mere 2,711 tons of emissions are reduced annually.In summary, idle equipment not only fails to achieve the desired effect of emission reduction but also leads to significant financial losses for the port.Even if the oil price is high and the SP utilization rate of the ship is 100%, the economic benefits of the ship are not satisfactory without considering government subsidies.Fig. 9 illustrates that the dynamic payback period is approximately 11 years, which accounts for about 55% of the total duration.A net present value of 0.65 million CNY can be realized at the end of the equipment's life cycle.In order to achieve a positive net present value, ships need to achieve a higher utilization rate of SP compared to ports.The use of SP is only profitable for the ship when the utilization rate is higher than 80%.In Fig. 10, it is found that the higher the environmental tax and the fuel price, the greater the benefit of a ship.This is due to the increased cost of using auxiliary engines, which brings a cost advantage to SP. Due to the complex connection process and the principal-agent problem between shipping companies and captains, captains will not usually choose to use SP.To address this, various incentives such as berthing priority and financial rewards have been suggested to motivate captains to use SP (Qi et al., 2020;Zhen et al., 2022).It has been found that such incentives can enhance the ship's profitability under average fuel prices.However, in the case of low fuel prices, the effectiveness of the incentives may be diminished and could even have a reverse effect.

Impact of government subsidies on the economic and environmen tal benefits of SP
The government provides subsidies to ports and shipping companies for SP promotion, which can be classified into subsidies for SP construction and SP price.
Construction subsidies are provided to ports and ships for the purpose of constructing SP equipment, which directly impact the economic benefits of ports and ships.On the other hand, price subsidies are government subsidies given to ports in order to reduce the SP price, with the intention of attracting ships to use SP.Therefore, price subsidies do not have a direct impact on ports but affect ships by changing SP prices.The details of government subsidies are presented in Table 4. From Fig. 11, it can be observed that government subsidies have no effect on the magnitude of peak emission reductions.However, they can impact the speed at which SP achieves these reductions.The maximum pollutant emission reductions amount to 15,819 tons per year.The port's profit demonstrates a decreasing trend initially, followed by an increase.With a higher level of government subsidies, the port's performance will improve and reach an inflection point sooner.On the other hand, the ship's profit decreases initially and then stabilizes gradually, as indicated by Scenario 1-4.Although both ship construction subsidies and price subsidies can enhance economic benefits, the ship's profit remains consistently negative, pointing to the ship's low willingness to adopt SP.The NPV at the end of the ship's SP life cycle can only be slightly greater than 0 when the price subsidy is 0.2 CNY/kWh.Unlike construction subsidies, which are provided to the ship during its construction phase, price subsidies can give SP a price advantage and reverse the decreasing trend of the ship's profit.In Scenario 3, the construction subsidies are a one-time investment at the beginning, which is equivalent to 117,000 CNY per year after discounting.In Scenario 5, the price subsidies depend on the unit subsidy amount and SP utilization rate, resulting in an annual investment of 99,000 CNY after discounting.Comparing Scenario 3 and Scenario 5, we found that price subsidies are more effective than construction subsidies in improving the economic benefits of a ship, indicating a higher subsidy efficiency.In general, construction subsidies can help alleviate the capital shortage problem in the early stages of SP (shipbuilding project) construction.Additionally, price subsidies can enhance ships' profitability by reducing the SP price.The government can effectively utilize the combination of these two types of subsidies.It is recommended that subsidies be provided to ships in the early stages of SP construction, followed by a focus on subsidizing the price to make SP more appealing to ships.

Impact of SP price on the economic benefits of SP
The SP price is composed of the electricity price and the SP service price.The details of the SP price setting can be found in Table 5.In Fig. 12(a), the curves of Charges 1, 4, 5, and Charge 3, 6 overlap respectively, indicating that changes in electricity price will not affect the economic benefits of the port.To improve the economic benefits of the port, it is necessary to raise the service price.Unlike the economic benefits of the port, changes in electricity and SP service price both impact the economic benefits of a ship, as shown in Fig. 12(b).Additionally, the economic benefits can only be positive when the SP price is below 0.95 CNY/kWh.
In Fig. 12(c), the curves of Charges 1-3 and Charges 5-6 almost overlap respectively, suggesting that changes in SP price will not affect the overall economic benefits.The overall economic benefits decrease as the electricity price increases, regardless of the SP service price and SP price.This is due to several factors.Firstly, the SP service price is an internal variable within the entire system of ports and ships.Its contribution to the economic benefits of ports is offset by its hindering effect on the economic benefits of ships.Secondly, the electricity price is an external variable that the entire system pays to the power grid company.It hinders the economic benefits of ships without changing the economic benefits of ports.The overall economic benefits display different results at the same SP price due to the different composition ratios of electricity price and SP service price.Fig. 12(d) illustrates that the overall economic benefits are better when the percentage of SP electricity price is lower.In fact, reducing the electricity price can increase the ship's profit without affecting the port's profit.Consequently, rather than providing subsidies for the SP service price, the government should consider subsidizing the electricity price to enhance the overall economic benefits of SP.

Conclusion
With the support of relevant policies in recent years, many ports have essentially completed the construction of shore power (SP) infrastructure.However, the utilization rate of SP is currently very low, which hinders the exploitation of its environmental and economic benefits.When the utilization rate of SP in a port is below 60%, or the utilization rate of SP by ships is below 80%, the use of SP will result in losses.Ideally, every 1% increase in berth utilization rate will lead to an increase in economic benefits by 559,300 CNY and a decrease in emissions by 226 tons.Hence, it is crucial for the government to prioritize the construction of SP infrastructure for terminals with busy operations and ensure that the utilization hours are maintained at a high level.
The installation rate of ship-side SP is far lower compared to shore-side SP.The payback period for SP installation on ships, without any subsidies, can reach up to 11 years, which is considerably longer than that of ports.As a result, it is crucial for the government to focus more on ship-side SP retrofits.In particular, the implementation of a mechanism that links the price of SP to the fuel price, as well as increasing the environmental cost and providing incentives to captains, can effectively encourage ships to adopt SP technology.Moreover, it is important to note that providing incentives to captains is not appropriate when fuel prices are low.
Due to the high investment cost of SP, both ports and ships require government subsidies.Construction subsidies and price subsidies work in different ways.
Construction subsidies to ports or ships provide an initial increase in economic benefits, but they cannot change the trend of continued decline in subsequent revenues.On the other hand, price subsidies offer a price advantage and fundamentally change the revenues.Furthermore, price subsidies have higher subsidy efficiency than construction subsidies in improving the economic benefits of a ship.In order to make SP appealing to ships, we propose subsidizing ships during the initial stages of SP construction and then focusing on subsidizing the price.
Last but not least, the economic benefits of a port are not related to the electricity price but they do increase with the SP service price.From the perspective of the ship, the economic benefits rise as the SP price falls.Looking at the bigger picture, the overall economic benefits only increase when the electricity price falls.Furthermore, even at the same SP price, the overall economic benefits can vary significantly.It is the proportion of the electricity price and SP service price, rather than the SP price itself, that determines the overall economic benefits.In fact, the overall economic benefits are enhanced when the proportion of the electricity price is lower.Therefore, it is suggested that the electricity price be preferentially subsidized.

Fig
Fig.2shows the internal relationships of the economic subsystem of shipping

Fig. 5 .
Fig.5.Causal loop diagram of the benefits of using SP.

Fig. 6
Fig.6illustrates the connections between the main factors and the structure of the subsystems.Fig.7portrays the system dynamics model, which was established by incorporating the four subsystems and their variable relationships.The complete model comprises sub-models for port economic benefits, ship economic benefits, environmental benefits, and government subsidies.The values of certain parameters in this system dynamics model are sourced from the references listed in Table2.

4. 1
Fig. 8. Port benefits and emission reduction under different SP utilization rate and berth utilization rate.

Fig. 10 .
Fig. 10.Relationship among environmental tax, fuel price, incentive for captain and ship benefits.

Table 2
Summary of related parameter values.

Table 4
Government subsidies assumption.

Table 5
SP price setting.