Methodology to Determine Electrical Power Required for Connecting Ships to Onshore Power Grids in Ports

Abstract

The global shipping fleet uses vast quantities of fossil fuels and releases significant levels of pollution. Supplying ships moored at quays in ports with onshore power allows them to shut down onboard engines, cutting fossil fuel use and reducing emissions. This is particularly significant when ports utilize green electricity. Equipping ports to connect serviced ships to onshore power grids involves substantial investments, which must be carefully optimized. The aim of this article is to develop a methodology, grounded in probability theory, for determining the electrical power required to connect ships to onshore power grids in ports. The proposed methodology was developed and validated through a case study of container terminal operations. By applying this methodology and considering the conditions of ship service in ports, it is possible to estimate both the number of ships and their berthing durations at quays, as well as the electrical power required from onshore networks to connect the vessels. The results of this research may be of interest to port managers, terminal operators, shipowners, and other stakeholders involved in the development of onshore power grids for ship connections in ports.

1. Introduction

Ships spend a substantial amount of time moored at port quays, during which electricity is needed both for onboard operations and for various services related to the vessel and its cargo, such as powering equipment used for cargo handling, refrigerated containers, and other operational needs [1]. At present, this electricity is typically supplied by the ship’s auxiliary diesel generators, which consume significant amounts of fossil fuel (diesel) and consequently produce considerable emissions [2]. An alternative approach increasingly employed in ports is the connection of ships to onshore power grids, which can significantly reduce these emissions [3]. Different types of ships serviced in ports have varying electricity demands and can, therefore, be classified into groups based on their expected power requirements or energy consumption [1,3].

The imperative to substantially reduce emissions from ships, particularly while they are in port, is highlighted in international regulations adopted by the International Maritime Organization (IMO), as well as in guidelines established by regional bodies and national legislation [4]. Emissions from ships in port can be mitigated by connecting them to shore-side electricity networks, which enable ships to switch off their auxiliary engines while moored and thereby avoid or minimize the use of fossil fuels for electricity generation [5].

Ship auxiliary engines are typically high-powered, fuel-intensive, and emit pollution [6]. Many ports implement measures to reduce ship emissions in accordance with IMO regulations, as well as regional and national guidelines for greenhouse gas reduction [7,8,9]. Concurrently, ports aim to attract a large number of vessels, including larger ships, to maximize operational throughput. In some cases, terminal operators may overestimate the required electricity supply capacity for ships scheduled to moor at the quays, either due to a lack of knowledge or excessive precaution [1,6,9]. Therefore, it has been observed that planned investments in connecting ships to onshore electricity networks are increasing significantly. Nevertheless, ports sometimes delay the initiation and implementation of these investments.

Taking into account the rapid development of ports and individual port terminals and the use of new passenger services and cargo handling technologies, the time of ships’ service in ports has significantly shortened [10]. Furthermore, each port operates under unique conditions. In certain cases, planning the electricity demand requires accounting for the stochastic arrival of tramp (irregular) ships, which in some ports represent a significant proportion of incoming vessels. Additionally, ship masters and agents aim to minimize the duration of a vessel’s stay in port, which further influences the estimation of the required electrical energy [11].

The IMO has introduced specific regulations aimed at reducing the environmental impact of ships while in port and facilitating the use of shore-side electricity to meet their operational energy needs [7]. In accordance with IMO requirements, by 2030, ports are expected to be equipped to connect ships to onshore electricity networks, and vessels must be fitted with the necessary equipment to enable such connections [12,13,14]. Some ports have already implemented these capabilities for certain ship types; for example, ro-ro terminals in Rotterdam, Southampton, and other locations are equipped to provide shore-side electricity to cruise ships [15,16].

While ships are in port, connecting them to the shore power grid can present numerous challenges that must be addressed. A primary issue concerns the preparation of ships for connection to onshore power systems. This challenge is especially pertinent for older vessels, the majority of which were constructed without the equipment necessary for such connections [2,3,6,14]. Installing such equipment requires substantial investments from both ships and ports. For instance, the cost of equipping a Ro-Pax vessel for connection to the onshore power grid on a single side of the ship is approximately one million euros [17,18]. For a cruise ship, these costs may range from EUR 1.5 to 2.0 million [19]. Consequently, a large proportion of cruise ships are equipped to connect to the onshore power grid from only one side, which restricts operational flexibility during service. Another challenge arises with connecting large vessels to the shore power grid. In cases where it becomes necessary to switch the ship’s power supply back to its onboard generation systems, even when these systems are in “standby” mode, the transition typically requires 10–15 min—an interval that may be excessively long in emergencies or similar critical situations, potentially leading to serious consequences [3,6,10,17,19].

Therefore, there is a clear rationale for examining the supply of electrical energy to ships from onshore power grids using a probabilistic approach. To minimize emissions and mitigate potential adverse consequences while ships are moored at port quays, it is essential to consider various possible scenarios for connecting vessels to shore-side power networks.

The aim of this article is to develop a methodology, grounded in probability theory, for determining the electrical power required to connect ships to onshore power grids in ports. This methodology allows for the calculation of both the number of ships and their berthing durations at quays, as well as the electrical power demand from shore-side supply systems necessary for ship connection. Importantly, the application of this methodology enables the analysis of various ship service scenarios and the corresponding capacity requirements of port onshore electrical networks, without compromising the safety of ships or port operations.

The article includes Section 2, where the available literature related to connecting ships to onshore power grids is analyzed. The methodology used to conduct the research and the mathematical model are shown in Section 3. Section 4 contains the results of the research conducted. Discussion and conclusions are presented in Section 5.

2. Literature Review

Nowadays, ports are increasingly focusing on the implementation of environmentally friendly energy solutions, including the construction of wind farms, the development of solar energy production, and the integration of renewable energy sources. This trend is supported by evidence presented in recent studies. For example, Kosek et al. [20] examined the impact of offshore wind farm supply chains on regional economic development, focusing on the strategic role of ports in facilitating these operations. Key cause–effect relationships that shape the readiness of selected local ports for offshore wind energy development were investigated [21]. Wilson et al. [22] analyzed the scenario of an electrical charging infrastructure application at the Port of Los Angeles, supported fully by wind and solar energy sources, to recharge future battery-powered ships. D’Agostino et al. [23] proposed an optimal sizing methodology for a green smart port with the presence of renewable energy resources, considering two energy carriers: electricity and hydrogen. The shore-to-ship power demand was simulated based on data obtained from a real port. The green transformation of ports is an important development direction, and ports are working to minimize their impact on the environment [24,25].

One of the initiatives currently undertaken by ports is the development of systems for connecting ships to onshore power grids. However, port electrical networks must also be adapted to supply power to a variety of equipment [26,27], highlighting the need to carefully assess overall energy demand within ports.

Ports service ships of various types and sizes, making the provision of their connections to onshore power grids a complex task. In many ports, particularly large ones, terminals handle both passenger traffic and specific types of cargo transported by different vessels [28]. By considering the specialization of port terminals, it is possible to predict the electrical energy demand within the power grids to which particular ship types can be connected. This approach also allows for a more targeted design of power networks, thereby partially optimizing the process of connecting ships to onshore power grids.

Ships are significant sources of emissions while in port [27], and servicing them requires substantial electrical power capacity, particularly for cruise ships, container vessels, and ships carrying temperature-controlled cargo [29]. Currently, many ships rely on their own diesel generators to produce the required electricity, consuming fossil fuels in the process [30]. Consequently, reducing fossil fuel consumption by substituting onboard generation with electricity supplied from onshore power grids represents a key priority for port operations [24,25,28,30].

Considering the required electrical power, ships of different types and sizes, calling at specific port terminals, can be conditionally divided as follows [29]:

• LNG storage and regasification units (vessels), floating storage regasification units (FSRU): average electrical power—about 12–14 MW;
• cruise ships: about 4–12 MW;
• container ships: about 1–3 MW;
• tankers: about 1–2 MW;
• general cargo ships: about 0.5–1.0 MW;
• bulk carriers: about 0.3–1.0 MW;
• other ships (mostly small ships): about 0.1–2.0 MW.

Given that most ports are increasingly pursuing green transformations—such as generating their own renewable electricity through solar power plants, developing wind farms, and integrating other renewable energy sources—the provision of green electricity to ships has been extensively examined in the literature [23,31]. Considering that ships are capable of generating their own electricity, the use of green electricity supplied by ports can substantially reduce the consumption of fossil fuels by vessels while in port [32].

Furthermore, port terminals are increasingly implementing more efficient and innovative handling equipment, which reduces the time ships spend in port. For instance, modern container block loading systems are being implemented, enabling the simultaneous loading of two 40-foot containers or four 20-foot containers in a single operation—while the simultaneous loading of two 20-foot containers with one crane movement has already become standard in many container terminals [33]. The adoption of such advanced handling technologies allows port terminals to significantly decrease both electricity and fossil fuel consumption during cargo operations.

Let us consider the example. Two container terminals serving ocean-going and feeder vessels can simultaneously accommodate three container ships at the first terminal and up to six ships of various types at the second terminal. Observations over a five-year period revealed that when the terminals operated at full quay capacity, less than 5% of the time did any moored ships refrain from loading—such instances typically occurred due to awaiting favorable weather conditions for departure or conducting technical maintenance. The monthly distribution of ships moored at the quays of the analyzed terminals during a representative sample month is presented in Figure 1.

Over the analyzed period of more than five years, the maximum number of ships moored at Terminal 1 reached 66% of the total available berths, whereas Terminal 2 experienced full berth occupancy (100%) on several days during the same period. The average monthly berth occupancy was approximately 30% for Terminal 1 and 49% for Terminal 2.

In cases where a system for connecting ships to onshore power grids was not originally planned or installed, the existing onshore power grid capacity may be insufficient to meet the electricity demands for ship connections. Under such circumstances, it is crucial to adopt appropriate methods for assessing energy demand. One available approach is to estimate the required electrical power using principles of probability theory [34]. Based on the example illustrated in Figure 1, the maximum electricity capacity required over time can be determined as follows:

• In Terminal 1, the probability that three ships will berth at the terminal quays during loading operations is about 0%, the probability that two ships will berth at the quays is about 17%, and the probability that one ship will berth at the quays is about 33% of the time;
• In Terminal 2, the probability of six ships mooring at the terminal quays during loading operations is about 0%, the probability of five ships mooring at the quays is about 10%, and the probability of four ships mooring at the quays is about 40% of the total time.

When calculating the required onshore power capacity, terminal operators—while the port administration is responsible for the port infrastructure, including power grids—typically assume the provision of the maximum possible power. As a result, ports frequently encounter situations where the planned power cannot be supplied due to limitations in electricity generation or insufficient grid capacity, potentially delaying the implementation of projects for connecting ships to onshore power grids. The power grid capacity estimated using this approach is often suboptimal, and the associated projects can become difficult to execute due to unjustified cost increases.

Given that both ship masters and terminal operators aim to minimize the time vessels remain in port [31], the actual electricity demand from ships may be correspondingly lower.

In analyzing ship berthing times and the feasibility of connecting vessels to onshore power grids, several critical factors must be considered: the number of ships present simultaneously at a given terminal, the probability of peak ship congestion at the terminal, and the magnitude and probability of electricity demand from ships moored concurrently at the terminal quays.

By assessing the probability distribution of required electrical power at a specific terminal, it becomes possible to design the port’s electrical network while accounting for potential developments in handling technologies. The most predictable scenarios for evaluating ship connection times to onshore power networks were found at cruise ship terminals, where vessels generally berth for a consistent duration regardless of passenger numbers, reflecting the standardized nature of cruise ship operations in ports. In contrast, other types of ships remain at the quays for periods dictated by the time needed to complete loading operations and formalities.

The existing literature has explored multiple aspects of ship connection to onshore power grids, including the preparedness of ports to support such connections and the environmental implications of utilizing shore-side electricity for vessels [35,36].

Tan et al. [37] stated that the over-investment of the power capacity may cause lower utilization and capital waste; however, the under-investment may affect the service congestion. A multi-objective optimization model for the coordinated allocation of shore power and berth scheduling, integrating economic benefits, environmental benefits, and operational efficiency, was developed by Zhang et al. [38].

Power grid capacities used in ports were also examined in the available studies [39]. A universal shore-to-ship charging concept for multi-vessel onshore power supply and charging of onboard batteries was examined by Karimi et al. [40]. A capacity expansion plan of the shore power system and the necessary measures for capacity expansion of the shore power system were considered by Jin et al. [41].

Modeling of the container handling and logistics process at both quay and yard sides, while jointly optimizing the energy management strategy of the energy system, was carried out by Lv et al. [42]. This modeling took into consideration multiple uncertainties arising from ship arrival times, cargo demand, and renewable energy generation.

Technical challenges of interconnection between the shore-side grid and the vessels were investigated by Papalexopoulos et al. [43]. An energy market design framework has been introduced, enabling ports to participate as energy hubs in wholesale and retail energy markets. Okoth et al. [44] analyzed the reduction in emissions by the container vessels supplied from onshore power in ports. In turn, Jia et al. [45] analyzed the economic effects of applying vessel charging stations participating in multiple grid interactive services in ports.

However, in the scientific literature, possible probabilistic scenarios, when the connection of ships, especially large ones, to the onshore power grid does not reduce the level of ship safety in ports, were analyzed to a small extent. In available studies, mainly economic and environmental aspects of connecting ships to the onshore power grids were considered, without investigation of related safety aspects [17,46].

An optimization strategy for the integrated “ship-shore-grid” collaborative energy supply network architecture based on an improved Mayfly algorithm was proposed by Jingwei et al. [47]. In turn, Binot et al. [48] proposed a methodology for optimizing the size and energy management of seaport microgrids, including cold ironing, to minimize costs and CO₂ emissions. Sun et al. [49] presented an abstract model that incorporates information such as port distribution, pure electric ship parameters, and charging pile configuration to predict the load of each port in multiple scenarios and stages. In this model the probability and statistical analysis of electric ship navigation energy consumption and charging demand were considered. Lin et al. [50] focused their attention on the stability and economic operation challenges faced by the port power grid after integrating distributed renewable energy and shore power systems. An optimization model for reactive power allocation in port area grids was proposed. An integrated multi-port shore-to-ship charging system designed for heterogeneous electric vessels, enabling flexible vessel–grid interconnection and power flow dispatching, was proposed by Wu et al. [51].

Amaral et al. [52] proposed a methodology for assessing power needs for onshore power supply in ports. They estimated the payback period for the implementation of this technology in the Port of Lisbon based on real data. However, this methodology did not take into account the probability of changes in the values under consideration.

In some regions of the world, very sudden hydro-meteorological changes can occur within a very short period of time, i.e., within a few minutes [53]. Therefore, it is important to predict such changes (which can be done based on the principles of probability theory [34,54,55]), in order to be able to assess the situation and react appropriately. Considering the probability that connecting ships to onshore power networks in ports reduces ship safety, it is necessary to develop a legal framework to ensure that ship masters, in the event of an increased probability of risk to the ship due to the connection of ships to an onshore electricity network, can disconnect the ship from this network without consequences for the ship and the captain.

The literature review and empirical analysis of individual ports [15,16,27,29] indicate that ports are increasingly striving to enable ships moored at quays to connect to shore-based power grids. However, a considerable number of ports lack sufficient shore-based power grid capacity and are often financially constrained from installing the necessary infrastructure to facilitate ship connections [1,12,14,26,40]. Furthermore, it was estimated that, once the required infrastructure is implemented, the cost of supplying electricity to ships may become less competitive compared to electricity generated onboard [23,36,38,45]. It was revealed that one key challenge in connecting ships to shore power grids remains and deals with the suboptimal planning and justification of the shore power infrastructure. Accordingly, the research presented in this article is focused on the optimization of shore power grids’ capacities needed for ship connections.

Based on the literature review and empirical observations of ship connections to port electrical networks, it can be stated that there is a clear need to develop a methodology for assessing the electrical power demand required to connect ships to onshore power grids. Such a methodology should be grounded in probability theory and account for the connection of different ship types while ensuring the safety of serviced vessels.

3. Methodology

3.1. Research Framework

The steps used to conduct the research are presented in Figure 2. Following a comprehensive literature review and observations of ship connections to onshore power grids in various ports, a mathematical model grounded in probability theory was developed. In the proposed approach, a multi-criteria forecasting method was also used.

The developed mathematical model allows for calculating the number of ships moored simultaneously at the quays in port, and assessing the electrical power needed to connect ships moored at quays to onshore power networks.

The case study of ships moored at the container terminal was considered, and calculations based on real data were carried out.

In order to sum up the research, the conclusions were drawn, and directions for future research were determined.

3.2. Mathematical Model

Let us assume that the probability distribution of a ship’s berthing time at a quay depends on the organization of ship servicing and port operations, the type of cargo, and the technological characteristics of passenger services and cargo-handling processes. Loading and unloading rates vary across terminals, resulting in different service durations for ships. Based on empirical observations, notable changes in ship servicing practices in ports can be identified. In many ports, vessels are now serviced at terminals for relatively short periods, while quays remain unoccupied for comparatively longer intervals. As the duration of ship connections to onshore power grids decreases, the required capacity of such power systems may consequently be reduced. Therefore, it is very important to correctly plan and install a power grid in the port to optimize the investments.

The probability ($P_q$) of the quay being occupied by moored vessels can be calculated using Equation (1) [34,54]:

$$P_q=(1-{\displaystyle \frac{\sum T-T_q}{\sum T}}),$$

(1)

where $T_q$ is the time when the quay is occupied by moored ships for cargo handling or other operations; $\sum T$ is the total time of quay usage, which can be estimated on the basis of annual port or terminal statistics, represents the number of hours per year during which ships are moored at a given quay.

The time may be measured in hours, days, weeks, months, years, or other periods.

If more than one ship can be serviced simultaneously at a quay within a terminal, as is often the case at container terminals, it is necessary to determine the relative occupancy of the quay. This includes assessing the proportion of the quay occupied by moored vessels and the probability of quay occupancy at a given time, for example, over a day, week, month, or year. The probability of quay occupancy by moored ships can be calculated as follows (Equation (2)) [34,54,55]:

$$P_{qS\left(t\right)}=(1-{\displaystyle \frac{n_{q0}-n_{qS\left(t\right)}}{n_{q0}}}),$$

(2)

where $n_{q0}$ is the number of ship mooring places at the quay; $n_{qS\left(t\right)}$ is the number of ships moored at the analyzed quay during a specific time period $t$ (hour, day, week, month, year), that could be calculated as follows (Equation (3)):

$$n_{qS\left(t\right)}={\displaystyle \frac{Q_{T\left(t\right)}}{Q_S{k}_s}},$$

(3)

where $Q_{T\left(t\right)}$ is the terminal capacity (turnover) over time $t$ (day, week, month, year); $Q_S$ is the average vessel carrying capacity, for example, container capacity; $k_s$ is the vessel carrying capacity utilization factor (taken from statistical vessel utilization data, for example, for general cargo vessels it is about 0.85–0.95, for bulk carriers about 0.95–0.98, and so on, obtained from the results of authors’ research conducted in the relevant terminals [27,29], as well as from literature sources [3,10,11,19,38,44].

The electricity demand for a ship moored at a specific quay is dependent on the ship’s type. Therefore, considering the total number of ships moored at the quay, the required electricity demand for the moored ships ($N_E$) over the expected period can be determined as follows (Equation (4)):

$$N_E={n_{qS\left(t\right)}P}_{qS\left(t\right)}{N}_{Sa},$$

(4)

where $N_{Sa}$ is the average electrical power required by a moored ship.

It is proposed to apply the multi-criteria forecasting method to calculate the required electrical power for connecting ships to the onshore power grid in the port and to estimate the number of ships at the quay [56,57]. Maximum distribution or dispersion methods may be used to assess the accuracy of the forecast and possible deviations from the obtained predicted values [58,59]. The maximum distribution method [58], based on available statistical data and forecasts, enables the estimation of expected peak electrical power demand and the determination of possible deviation limits. The dispersion method [59] allows for the assessment of forecast accuracy by defining the probability band associated with the estimated electrical power requirements.

While applying the multi-criteria forecasting method for estimating the number of ships at quays [56,57], the following main factors ($F_{Ei}$) should be taken into account:

• Ships moored at specific quays;
• Changes in the world and regional economies;
• Changes in the parameters of ships designed for the transportation of specific cargoes;
• Changes and forecasts of the ships’ electrical power for the planned period;
• Other possible factors.

A multi-criteria forecast of the required electrical power ($N_{ET}$) can be calculated using the following formula (Equation (5)):

$$N_{ET}=(N_{En}+BT)M_{Nc},$$

(5)

where $N_{En}$ is the electrical power for ships moored at a specific quay at the last statistical point; $B$ is the forecasting coefficient, calculated based on available statistical data [56,57]; $T$ is the forecasting period; and $M_{Ec}$ is the multi-criteria forecasting coefficient, which can be calculated using Equation (6):

$$M_{Ec}={\displaystyle \frac{1}{{\eta }_k}}{\sum }_1^i{F}_{Ei}{k}_{Ei},$$

(6)

where ${\eta }_k$ is the correlation coefficient, applied if there is similarity between factors; ${\sum }_1^i{F}_{Ei}$ is the sum of the factor’s values; and $k_{Ei}$ is each factor’s weight coefficient. In all cases, the sum of the weight coefficients must be equal to one.

The principal factors considered in assessing the electrical power demand of ships moored at a port quay include the following:

• The available electrical power capacity at the investigated quay;
• The types of ships and their corresponding electrical power requirements while berthed;
• The average duration of ship berthing at the quay;
• The implementation of advanced cargo-handling technologies that may reduce the time ships spend moored at the quay;
• Other relevant influencing factors.

The calculated electricity forecast accuracy (${\sigma }^2$) can be calculated applying the variance method (Equation (7)) [59]:

$${\sigma }^2={\displaystyle \frac{1}{n-1}}{\sum (N_{\mathrm{E}\mathrm{i}}-M_E)}^2,$$

(7)

where $n$ is the number of statistical data available for the analyzed period; $N_{\mathrm{E}\mathrm{i}}$ is the demand for electricity used for each period, for example, hour, day, week, month, year; $M_E$ is the average (mathematical expectation) demand for electricity for the analyzed period; ${\sum (N_{\mathrm{E}\mathrm{i}}-M_E)}^2$ represents the sum of a particular factor minus the average value of each factor.

The average demand for electricity at the considered quay ($M_E$) can be assessed based on data from the available statistical database for at least the last five years and can be calculated as follows (Equation (8)):

$$M_E={\displaystyle \frac{1}{n}}\sum N_{Ei}.$$

(8)

where $\sum N_{Ei}$ represents the sum of a particular factor.

The size of the error bar ($\sigma$) can be determined using Equation (9):

$$\sigma =\pm \sqrt{{\sigma }^2}.$$

(9)

In this manner, the deviation bar of the requested electricity power ($\delta$) on the quay can be determined as follows (Equation (10)):

$$\delta =M_E\pm \sigma .$$

(10)

Then the relative demand for electricity ($∆M_{Ei}$) can be calculated using Equation (11):

$$∆M_{Ei}={\displaystyle \frac{{N_{ET}}_i}{M_E}},$$

(11)

where $N_{ETi}$ is the forecasted electricity capacity for a specific period.

The power of electricity required for a ship moored at a quay depends on the type of ship and its service process; therefore, it is very important to accurately predict the time the ship will be moored at the quay ($T_{Sb}$). This time is impacted by the type of ship, its carrying capacity, and the terminal’s handling efficiency, and can be estimated using Equation (12):

$$T_{Sb}={\displaystyle \frac{Q_{SiF}}{q_{TL}}}+T_{ao},$$

(12)

where $Q_{SiF}$ is the predicted handling capacity of ships loaded at a specific quay for each stopover; $q_{TL}$ is the terminal loading intensity; $T_{ao}$ is the time of additional operations needed for the ship service, such as preparing the ship for loading, completing formalities, and others.

The relative loading intensity at the analyzed quay ($∆q_{ini}$) depends on the available loading equipment and technologies applied for the ship’s service. This intensity can be calculated as follows (Equation (13)):

$$∆q_{ini}={\displaystyle \frac{q_{iniF}}{q_{in0}}},$$

(13)

where $q_{iniF}$ is the loading intensity at the quay of each planned ship arrival; $q_{in0}$ is the average loading intensity during a statistical fixed period (recommended period: over the last 5 years).

The relative berthing time of ships at the quay, during which the ship can be connected to the onshore power grid ($∆T_T$), is influenced by several factors, including the ship type and its handling capacity, as well as the loading equipment and technologies employed at the port quay. This time can be determined using Equation (14):

$$∆T_T={\displaystyle \frac{T_{SiF}}{T_{S0}}},$$

(14)

where $T_{SiF}$ is the average planned time of ship mooring at the quay during the forecasted period each year; $T_{S0}$ is the average time of a ship moored at the quay during a statistical fixed period (recommended period: over the last 5 years).

The implementation of new loading technologies at the quay is usually included in the terminal’s strategic plans. In most cases, its usage is caused by the need to shorten ship handling operations. If the possibility of increasing handling time is not constrained by the structural characteristics of the ships themselves—for example, when the loading rate of PANAMAX-type tankers cannot exceed 6000 t/h—the average planned berthing time of a ship at the quay ($T_{SiF}$) can be calculated as follows (Equation (15)):

$$T_{SiF}=Q_{SiF}/\left(q_{iniFi}{n}_{TLL}{k}_{TL}\right)+T_{SF}+T_{AD},$$

(15)

where $q_{iniFi}$ is the terminal single-line handling intensity; $n_{TLL}$ is the number of loading lines used for the ship’s handling; and $k_{TL}$ is the terminal single-line utilization coefficient, whose maximum value can be up to 0.90—0.95. This value is obtained from the results of authors’ research carried out in the relevant terminals [27,29], as well as from literature sources [3,10,11,19,38,44], assuming the terminal operates in three shifts. $T_{SF}$ is the time for processing the arrival and departure of the ship, if these procedures are performed after the ship is moored at the quay. $T_{AD}$ is the additional time spent by the ship at the quay, for example, obtaining a sanitary certificate, provisioning with food supplies, and similar activities.

Given the expected number of ships arriving at the terminal within a specified time period and the duration of their stay at the quay, it is possible to estimate the number of ships that may be simultaneously present at the quay (or terminal). The probability that the number of ships at the quay (or terminal), ($n_{qS\left(0\right)}$), during the designated time period, exceeds the average can be determined using Equation (16):

$$n_{qS\left(0\right)}={\displaystyle \frac{T_{SiF}{n}_{qS\left(t\right)}}{T_i{P}_{qS\left(t\right)}}},$$

(16)

where $T_i$ is the planned time period, for example, a year.

Based on the planned electrical power demand at a given quay and the terminal’s loading capacity, it is possible to calculate the electrical power required to connect ships to the quay’s (or terminal’s) onshore power network, as well as to estimate the probabilities associated with ships’ berthing times at specific quays within the terminal.

To forecast the required electrical power, a multi-criteria forecasting approach can be employed, which considers key factors such as the following:

• Expected cargo flows;
• Expected ship parameters;
• Periodicity of ship arrivals to the port;
• Probability of hydro-meteorological impact, statistical data on hydro-meteorological factors taken from the port or the nearest hydro-meteorological stations for at least the last five years;
• Ship parameters and their electricity demand;
• Probability of non-standard situations, taken from port statistical data as a recurring Process for at least the last five years;
• The ability of port terminals to accommodate the maximum number of ships;
• Other factors.

Finally, the electrical power demand of a specific quay or terminal electrical network ($N_{TS}$) required for connecting the moored ships can be calculated as follows (Equation (17)):

$$N_{TS}={\displaystyle \frac{1}{ɳ}}\left(N_{ET}{n}_{qS\left(0\right)}\right),$$

(17)

where $ɳ$ is the correlation coefficient, which estimates the unevenness of the electrical power used by ships, is in most cases around 0.90–0.98, obtained from the results of authors’ research conducted in the relevant terminals [27,29], as well as from literature sources [3,10,11,19,38,44].

The electrical power demand of ships, calculated for a specific port quay or terminal, can serve as a critical parameter in the design of electrical networks intended to supply moored vessels with electricity and in evaluating the capacity of existing networks to meet operational requirements. When accounting for the stochastic arrival of ships, particularly tramp vessels, there may be periods during which the onshore electrical network capacity is insufficient. In such cases, terminals should be equipped to utilize generators powered by non-polluting energy sources, such as hydrogen, or implement regulations allowing ships to temporarily rely on their own onboard power generation without incurring penalties.

3.3. Case Study Description

In order to verify the proposed methodology, a case study was considered. The operation of the container terminal, which handles about 550,000 TEU per year and services arrivals of one or more container ships almost every day, was analyzed in detail. The average electrical power demand per ship while berthed at the quay is approximately 2 MW, which covers both the ship’s daily operational needs and the power required to maintain the temperature of refrigerated containers on board. The terminal quays can accommodate up to three ships simultaneously, and the available handling equipment enables servicing of all three vessels at the same time. Data on the number of ships moored at the terminal quays and the corresponding electrical power demand were collected over a five-year period. During this time, both the number of berthed ships and the required electrical power exhibited minimal variation, as the container terminal primarily serves liner shipping lines with regular, scheduled port calls. As an illustrative example, the number of ships at the terminal and the corresponding electrical power demand for a randomly selected month within the analyzed period are presented in Figure 3.

Analysis of the available data on ships moored at the terminal quays indicated that, on average, there are approximately 7 days per month during which no vessels are berthed. Examination of data for a randomly selected month revealed that 32 ships were moored at the terminal quays, with 7 days in which the quays remained unoccupied. Consequently, the estimated average quay occupancy for the analyzed month was approximately 1.4 ships.

The probability ($P_q$) of the quay being occupied by at least one vessel during the analyzed period was approximately 0.76, while the probability of overall terminal quay occupancy ($P_{qS\left(t\right)}$) was approximately 0.35.

Given an annual terminal throughput of about 550,000 TEU, an average container ship capacity of around 2000 TEU, and a ship capacity utilization factor of 0.9, the number of ships arriving at the terminal and berthed at the quays over a one-year period was estimated to be 300 vessels (Figure 4).

The methodology for evaluating the optimal capacity of shore-based electrical networks for connecting ships moored at quays has been developed and presented in this study. This approach enables ports to assess the required infrastructure for implementation under real operational conditions.

4. Results

Using the multi-criteria forecasting approach and the data presented in Figure 3, while considering the factors outlined in Section 3, it was estimated that the average electrical power demand for the case study over the next five years will be approximately 6 MW, with a maximum demand of up to 8 MW. The assessment also accounted for a forecast squared variance of approximately 1.96 and a mean square error of ±1.4 MW (Figure 5).

When forecasting the electrical power requirements for ships serviced at a terminal, it is essential to ensure that the onshore power grid has sufficient capacity to supply all moored vessels. This is necessary to prevent both power shortages and unnecessary additional investments in the electrical infrastructure. In evaluating the required grid capacity for connecting moored ships, it is also necessary to predict the duration of ship berthing at the quays. Using the methodology described in Section 3, the occupancy time of the quays by moored ships was assessed (Figure 6).

The duration of a ship’s stay at the quay depends on the type and specifications of the equipment used for cargo handling. For instance, when employing ship-to-shore (STS) cranes, the average productivity of a single crane is approximately 30–40 moves per hour. Taking into account the volume of cargo loaded and unloaded, as well as the time required for additional operations—such as border control, sanitary inspections, and preparation of cargo documentation—the berthing time of a ship at the quay can be determined (Figure 7).

A high degree of stochasticity in ship arrivals is observed at the analyzed port, particularly for tramp vessels. Based on several years of research conducted across several European ports, the stochasticity coefficient for container ship arrivals at the studied port was found to range from 0.3 to 0.7. In contrast, for liner vessels, such as Ro-Ro and Ro-Pax ships, the stochasticity coefficient is higher, ranging from 0.85 to 0.98. These coefficients were obtained from the results of authors’ research conducted in the relevant terminals [27,29], as well as from literature sources [3,10,11,19,38,44].

When evaluating the stochastic arrival of ships at the port, it was observed that maximum quay occupancy can occasionally occur, particularly when the available cargo-handling equipment is limited. For the analyzed container terminal, the expected number of ships simultaneously serviced at the quays can be determined based on the average cargo volume delivered by ships, the type of handling equipment employed, and the probabilistic stochasticity coefficient, which ranges from 0.4 to 0.7. This coefficient was derived from the authors’ research at relevant terminals [27,29] and corroborated by literature sources [3,10,11,19,38,44]. The expected number of ships simultaneously serviced at the quays may be determined (Figure 8).

Therefore, by accounting for the probability of ship arrival times and varying the number of STS cranes employed for cargo handling, the required electrical power of the shore-based network for connecting ships at the quay can be estimated. For container ship operations using four or five STS cranes, a capacity of 4 MW is generally sufficient. When only three STS cranes are used, the required onshore electrical power may increase to approximately 6 MW, although the probability of this demand occurring is relatively low, ranging from 0.06 to 0.10.

5. Discussion

The article presents the methodology for assessing the electrical power demand required to connect ships to onshore power grids in ports. To develop the proposed methodology, principles of probability theory were applied in combination with a multi-criteria forecasting approach. The adoption of this methodology enables the prediction of the number of ships simultaneously moored at port quays and the estimation of the electrical power required to connect these vessels to the onshore power grid.

The application of the developed methodology facilitates the exploration of strategies to optimize the capacity of onshore power networks. However, several challenges remain. These include assessing the feasibility of integrating the electrical networks of different terminals to ensure optimal ship connections, efficient energy redistribution, and compatibility among the power systems of all, or a substantial portion, of the port terminals.

Another critical issue concerns the need for the timely disconnection of ships from the onshore power network in response to sudden changes in mooring conditions, such as those induced by hydro-meteorological or hydrological variations, emergencies, or other atypical scenarios [60,61]. A detailed investigation is required to analyze electrical power demand under such event scenarios.

Additionally, numerous legal and organizational challenges remain unresolved regarding the connection of ships to onshore power grids, particularly when available electrical capacity is insufficient. These challenges include the allocation of responsibility and the determination of taxation related to emissions when a moored vessel cannot access the onshore power supply due to capacity limitations or structural constraints of the ship (e.g., vessels equipped with plugs on only one side). Addressing these issues and examining the associated technical, legal, and operational challenges will constitute key directions for the authors’ future research.

It should be noted that the research results are limited to the specific case study analysis. The operation of the selected container terminal was considered. Therefore, it will be reasonable to repeat the research, investigating the operation of other terminals in ports and calculating the electrical power demand required to connect various vessels. This will provide the ground for comparative analysis and further investigations.

Moreover, the research results may be impacted by the input data, including coefficients that were derived from the authors’ research at relevant terminals and from available literature sources. Collecting data from different ports located in various geographical zones will provide a possibility to verify the input data and estimate coefficients.

6. Conclusions

In conclusion, it should be stated that the research aim was achieved, and the methodology for determining the electrical power required to connect ships to onshore power grids in ports was developed. The application of the developed methodology in planning onshore power networks enables determining the required electrical power for various port operational scenarios and helps minimize the investments needed for the development of electrical infrastructure, thereby supporting the safe servicing of ships in ports.

Based on the literature review and experiments carried out, it can be stated that the problem of connecting ships moored at quays to shore power grids remains relevant, since a significant proportion of ports around the world are not prepared for such activities [15,17,27,39]. The existing power grids in individual ports are not yet sufficiently developed, and possibilities for connecting ships moored at quays to the onshore power supply are insufficient. Moreover, a significant proportion of ships are not prepared for these operations. Increasing the capacity of port electrical infrastructure by even a few megawatts, as needed to connect ships to shore power systems, involves not only significant financial investment but also extensive physical works, including the construction of new substations and the installation of electrical cable routes. These activities are particularly challenging to implement in operational port environments [14,16,45]. Consequently, a thorough assessment of the current condition and capacity of port electrical networks is essential for optimizing the development of shore-side power infrastructure and supporting the effective achievement of port operational objectives.

It was revealed that for the analyzed case study, a power grid capacity of 4 MW is sufficient, considering the usage of four or five STS cranes for cargo handling from the ship. However, when only three STS cranes are used, the required onshore electrical power may increase to approximately 6 MW. This result shows that it is very important to plan vessel service operations appropriately, which may impact the demand for power.

The analysis of the readiness of ships and ports for connecting ships moored at quays to the onshore electrical power grids showed that there are still many unsolved problems, and it is necessary to look for theoretical and practical solutions to ensure the opportunity to connect the majority of moored ships to the mentioned grids by 2030.

Connecting ships to shore power grids is a relevant problem from a theoretical and practical point of view, both in terms of port and ship preparation; therefore, continuing scientific research in this area is very important and promising. A more detailed assessment of electrical power grid capacities in ports, considering different designs of quays in ports and service of various ship types, will constitute the direction of the authors’ future research.

It should be mentioned that the developed methodology can be used by various ports or their individual terminals (or quays). For this purpose, this methodology should be adjusted to the specific case of port operation. The proposed approach may be of interest to port managers, terminal operators, shipowners, and other stakeholders involved in the development of onshore power grid systems for connecting ships in ports.