Open AccessArticle

Method of Estimating Energy Consumption for Intermodal Terminal Loading System Design

Faculty of Transport, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland

Collegium of Business Administration, Warsaw School of Economics, Niepodległości 162, 02-554 Warsaw, Poland

Author to whom correspondence should be addressed.

Energies 2024, 17(24), 6409; https://doi.org/10.3390/en17246409

Submission received: 16 November 2024 / Revised: 10 December 2024 / Accepted: 13 December 2024 / Published: 19 December 2024

(This article belongs to the Section G1: Smart Cities and Urban Management)

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Figure 1
(a) ITUs/TEUs carried; (b) transport work and cargo volumes in intermodal transport in 2012–2023. Source: authors’ own study, inspired by the approach outlined in [<a href="#B2-energies-17-06409" class="html-bibr">2</a>,<a href="#B3-energies-17-06409" class="html-bibr">3</a>]. "> Figure 2
A layout of a satellite terminal (a) and a hub integrated with a satellite terminal (b) for lift-on/lift-off container transshipments [<a href="#B53-energies-17-06409" class="html-bibr">53</a>]. "> Figure 3
Container flow through the handling system of an intermodal terminal. "> Figure 4
Measurement system diagram [<a href="#B43-energies-17-06409" class="html-bibr">43</a>]. "> Figure 5
Energy consumption estimation model for handling equipment. "> Figure 6
Required designations for calculating gantry crane handling cycle durations. "> Figure 7
The container transition path through an intermodal terminal: (a) delivery service; (b) pick-up service. "> Figure 8
Layout of handling area. "> Figure 9
The number of cranes operating in each of the intermodal terminal’s scenarios. "> Figure 10
The level of performance utilization against the unit energy consumption of RMG cranes (a) and AGVs (b). The same was performed for the RTG cranes—see <a href="#energies-17-06409-f011" class="html-fig">Figure 11</a>. "> Figure 11
The level of performance utilization against unit the energy consumption of RTG cranes. "> Figure 12
The daily energy consumption of (a) gantry cranes (b) AGVs with a fixed workload during the working day. "> Figure 13
The daily consumption of machinery operating with a variable workload during the working day. "> Figure 14
Energy consumption over the course of a day. "> Figure 15
Sensitivity analysis for RTGs (a) and RMGs (b). ">

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Abstract

Numerous studies address the estimation of energy consumption at intermodal terminals, with a primary focus on existing facilities. However, a significant research gap lies in the lack of reliable methods and tools for the ex ante estimation of energy consumption in transshipment systems. Such tools are essential for assessing the energy demand and intensity of intermodal terminals during the design phase. This gap presents a challenge for intermodal terminal designers, power grid operators, and other stakeholders, particularly in an era of growing energy needs. The authors of this paper identified this issue in the context of a real business case while planning potential intermodal terminal locations along new railway lines. The need became apparent when power grid designers requested energy consumption forecasts for the proposed terminals, highlighting the necessity to formulate and mathematically solve this problem. To address this challenge, a three-stage model was developed based on a pre-designed intermodal terminal. Stage I focused on establishing the fundamental assumptions for intermodal terminal operations. Key parameters influencing energy intensity were identified, such as the size of the transshipment yard, the types of loading operations, the number of containers handled, and the selection of handling equipment. These parameters formed the foundation for further analysis and modeling. Stage II focused on determining the optimal number of machines required to handle a given throughput. This included determining the specific parameters of the equipment, such as speed, span, and efficiency coefficients, as well as ensuring compliance with installation constraints dictated by the terminal layout. Stage III focused on estimating the energy consumption of both individual handling cycles and the total consumption of all handling equipment installed at the terminal. This required obtaining detailed information about the operational parameters of the handling equipment, which directly influence energy consumption. Using these parameters and the equations outlined in Stage III, the energy consumption for a single loading cycle was calculated for each type of handling equipment. Based on the total number of loading operations and model constraints, the total energy consumption of the terminal was estimated for various workload scenarios. In this phase of the study, numerous test calculations were performed. The analysis of testing parameters and the specified terminal layout revealed that energy consumption per cycle varies by equipment type: rail-mounted gantry cranes consume between 5.23 and 8.62 kWh, rubber-tired gantry cranes consume between 3.86 and 7.5 kWh, and automated guided vehicles consume approximately 0.8 kWh per cycle. All handling equipment, based on the adopted assumptions, will consume between 2200 and 13,470 kWh per day. Based on the testing results, a methodology was developed to aid intermodal terminal designers in estimating energy consumption based on variations in input parameters. The results closely align with those reported in the global literature, demonstrating that the methodology proposed in this article provides an accurate approach for estimating energy consumption at intermodal terminals. This method is also suited for use in ex ante cost–benefit analysis. A sensitivity analysis revealed the key variables and parameters that have the greatest impact on unit energy consumption per handling cycle. These included the transshipment yard’s dimensions, the mass of the equipment and cargo, and the nominal specifications of machinery engines. This research is significant for present-day economies heavily reliant on electricity, particularly during the energy transition phase, where efficient management of energy resources and infrastructure is essential. In the case of Poland, where this analysis was conducted, the energy transition involves not only switching handling equipment from combustion to electric power but, more importantly, decarbonizing the energy system. This study is the first to provide a methodology fully based on the design parameters of a planned intermodal terminal, validated with empirical data, enabling the calculation of future energy consumption directly from terminal technical designs. It also fills a critical research gap by enabling ex ante comparisons of energy intensity across transport chains, an area previously constrained by the lack of reliable tools for estimating energy consumption within transshipment terminals.

Keywords:

intermodal terminals design; intermodal operations; energy intensity; energy demand calculation; intermodal terminals design

1. Introduction

The primary aim of this research is to develop a method that assists future designers and analysts in estimating energy demand during the design phase of intermodal terminals.

Intermodal transport involves the movement of cargo using the same transport unit (e.g., container, semi-trailer, swap body) or heavy-duty truck (HGV) across multiple modes of transport, where only the transport unit is transshipped, and the cargo itself remains secured within the unit throughout the entire route [1]. This mode of transport has grown increasingly important in recent years. In Poland, for instance, the number of intermodal transport units (ITUs) and twenty-foot equivalent units (TEUs) transported, along with transport work (measured in tonne-kilometres (tkm)) and cargo volumes, has doubled over the past decade—as illustrated in Figure 1.

Transshipment terminals are an integral part of intermodal transport. These facilities enable the transfer of goods between different modes of transport using either lift-on/lift-off (i.e., vertical transshipment) or roll-on/roll-off (i.e., horizontal transshipment) technology. Vertical transshipment uses equipment such as gantry cranes or reachstackers. On the other hand, horizontal systems are based on railcar technology linked to loading ramp technology or are fully integrated into the railcar. From the operational point of view, a distinction should be made between local satellite terminals and hubs (inland hubs and seaports) [4]. In inland networks, satellite terminals handle local traffic, whereas hubs focus primarily on consolidating and deconsolidating cargo flows from and to various directions. Seaports, by contrast, serve container ships and combine functions typical of both inland hubs and other intermodal terminals.

A substantial body of research has been dedicated to locating terminals within rail transport networks [5,6,7] and designing intermodal terminals [8,9,10,11,12,13,14]. However, there is a clear lack of literature addressing the determination of energy demand [15] at intermodal terminals during the design stage. This is a pressing issue, as the ongoing energy transition demands and will increasingly necessitate a reduction in the energy intensity of both the overall economy and individual processes [16,17]. In this context, a justified and critical question arises: is it feasible to develop a reliable calculation method that can be applied during the design phase of an intermodal terminal layout while simultaneously enabling the optimization of logistics processes and energy consumption? Furthermore, how does the total energy consumption of a logistics facility depend on factors such as input parameters, intermodal infrastructure specifications, types of loading equipment, and handling operations?

To address these questions, the authors of this article developed a procedure for estimating the energy consumption of handling equipment, applying it to a real-life case study encountered during the pre-design of intermodal terminals as part of the planning process for new railway lines on the Polish network by the CPK Company (Centralny Port Komunikacyjny, Warszawa, Poland).

In 2023–2024, the CPK Company, along with subcontractors, initiated a pre-design process for numerous inland rail–road intermodal terminals employing both lift-on/lift-off and roll-on/roll-off technology. In the case of lift-on/lift-off terminals, these include both small satellite terminals and large-scale facilities that combine consolidation functions with local traffic operations. The issue of energy consumption arose during the pre-design stage, raised by power grid designers, as well as during the cost–benefit analysis (CBA). The authors of this paper also face the challenge of developing a detailed technical specification for pre-designing intermodal terminals along new or modernized railway lines, intended as a guideline that could be widely recommended for future railway projects. To conduct such analyses, it was necessary to gather data on the energy consumption of handling equipment. One approach could involve using publicly available data from the literature, while another approach might involve generic calculations, as terminals designed by CPK are likely to exhibit unique energy consumption characteristics due to their dimensions, nature, and scale of operations. Consequently, data from the literature may not be directly applicable.

Since no studies were found addressing the relationship between electricity consumption at an intermodal terminal and the aforementioned factors, a unique model was developed. The model comprises the following stages:

Stage of defining operational assumptions for an intermodal terminal: This stage involved establishing the design and operational assumptions required for the intermodal terminal. The process began with identifying the type of intermodal terminal to be planned. Next, assumptions were defined regarding throughput (based on forecast demand), the number of train pairs per day, daily working hours, and the intensity of truck handling during pick-up and delivery operations at different times of the day. Additional considerations included train load factors, container type distribution, and other relevant parameters. Subsequently, the type of machinery needed for container handling was selected, and its maximum transshipment workload was determined. At the same time, the proportions of various container types were defined. Finally, the layout of the transshipment yard was drafted, and the maximum number of each machinery type that could fit within the terminal area was calculated, considering spatial and site constraints.
Stage of determining the number of machines to handle a given container throughput: At this stage, the performance of each piece of handling equipment was determined. This process began with estimating the handling cycle durations for the individual equipment. Next, the performance capabilities of each type of handling equipment were calculated. Following this, the required number of each type of equipment needed to handle the given container throughput was determined. An empirical formula, which accounted for the critical level of operations, was used for this calculation. Additionally, it was necessary to verify whether the specified number of handling equipment would exceed the maximum allowable number for installation at the intermodal terminal. If the calculated number exceeded the maximum capacity for the terminal’s layout, the container throughput would need to be reduced accordingly. Otherwise, the process could proceed to stage three of the tests.
Stage of estimating the electricity consumption of handling equipment: This stage focused on estimating the energy consumption of the various types of handling equipment. The unit energy consumption for each piece of equipment was determined using publicly available technical data, following their global energy consumption for different design scenarios. The total energy consumption was then calculated for all machines selected in Stage II. At this stage, the results obtained were also exemplified and discussed.

Next, the results obtained from these calculations for the model terminals used in this research were compared with publicly available data on energy consumption from existing intermodal terminals. It was found that the results align closely with those reported in the global literature. It was determined that rail-mounted gantry (RMG) cranes consume between 5.23 and 8.62 kWh per cycle, rubber-tired gantry (RTG) cranes consume between 3.86 and 7.5 kWh, and automated guided vehicles (AGVs) consume approximately 0.8 kWh per cycle.

The calculations demonstrated that it is possible to estimate the energy consumption of an intermodal terminal during its design phase, enabling the assessment of the terminal’s projected energy intensity.

The analysis revealed a strong correlation between design parameters and overall energy consumption. Factors such as the type of intermodal terminal, the specifications of the handling equipment, and the dimensions and layout of the handling yard were found to significantly impact energy consumption, as confirmed by the sensitivity analysis. This study contributes to the international literature by addressing a notable gap, as research examining the relationship between these factors and energy consumption at intermodal facilities remains scarce.

Our research is among the first scientific publications to comprehensively address both the planning of logistics processes at intermodal terminals and the estimation of energy consumption based on these processes. The model offers a relatively accurate representation of unit energy consumption per handling cycle, accounting for factors such as equipment mass, span, and travel distances.

The key parameter influencing total energy consumption in this study was container throughput. Variations in container throughput, whether increasing or decreasing, directly impacted the number of handling operations. This, in turn, affected the required quantity of handling equipment, which subsequently influenced the amount of energy needed to power the handling machinery. For the CPK terminal, it was calculated that all handling equipment, based on the adopted assumptions, will require between 2200 and 13,470 kWh per day.

This paper is structured as follows: Section 2 reviews the literature on energy consumption in intermodal transportation, the design of transshipment systems at intermodal terminals, and methods for estimating the energy consumption of handling equipment. Section 3 outlines a model for estimating the energy consumption of handling equipment, Section 4 presents a calculation example based on the research model, Section 5 interprets the results, and Section 6 provides generalized conclusions.

2. Literature Review

The following provides an overview of the research addressing the dimensioning of logistics processes in intermodal terminals and their impact on energy consumption estimation.

2.1. Energy Consumption Aspects in Intermodal Transportation

Intermodal transportation and intermodal terminals have received significant attention in the world literature. Many bibliographic sources address topics such as intermodal route optimization [18,19,20,21,22], yard and quay crane scheduling [23,24,25,26,27], operation optimization [26,28,29], storage activities in the yard [30,31], the distribution of containers in the storage yard and loading intermodal trains [20,32,33,34,35], environmental issues [36,37], etc. Recently, increased focus has been placed on the energy efficiency of logistics processes at such facilities. For example, experts [38] developed a genetic algorithm to determine the optimal container loading sequence at an intermodal terminal. They examined factors affecting energy efficiency in container loading operations and created an optimization model to minimize total handling time and container reshuffling. The authors of [20] explored the problem of energy efficiency at intermodal terminals in smart cities, focusing on crane operations during train loading processes. Interestingly, their model employed the quantitative analysis of crane energy consumption, considering factors such as container location in the storage yard, rehandling operations, crane movement strategies, and the analysis of hoist, trolley, and gantry movements. A similar topic was addressed in bibliography reference [39]. Its authors studied the behavior of the RTG system, focusing on the interaction between the motor hoist, trolley, and gantry. They aimed to optimize power allocation to enhance energy efficiency in crane operations. In some reports [40], the energy performance of handling equipment was also examined in the context of greenhouse gas emissions and cost-effectiveness. It was found that optimization solutions can reduce both environmental impact and operational costs.

In general, it is clear that most of the available literature on energy consumption in intermodal transportation primarily focuses on strategies for energy consumption optimization [41]. In these types of research works, experts usually concentrate on handling operations performed by loading machines, i.e., RMGs [20,42], RTGs [43,44], reachstackers [45], AGVs [46,47], or ship-to-store cranes (STS) [48]. They also develop new algorithms to enhance overall terminal performance, taking into account various types of handling equipment [49].

Undoubtedly, there is a noticeable gap in the global literature regarding articles that directly link terminal design with energy consumption. One notable attempt to address this issue was made in [50]. In their study, the authors estimated energy consumption and CO₂ emissions based on variations in container terminal layouts. Energy consumption in their case study was calculated using utility data, along with fuel and electricity usage for each type of container-handling equipment. Similar relationships were also analyzed in [51,52].

What is notable is that literature supporting the estimation of energy consumption in intermodal terminals at the design stage is rather scarce. Several reasons may explain this. Assumptions for designing new terminals are often not publicly available due to company confidentiality, meaning the input data remain unknown. When conducting CBAs for intermodal terminals, experts typically estimate total energy consumption using values from bibliographic sources or other projects, often on a lump-sum basis rather than through self-calculated energy consumption models. Simultaneously dimensioning logistics processes and energy consumption at logistics facilities is time-consuming, as it requires identifying various parameters often beyond the expertise of the designers—unless full access to terminal design data is available. Designing new intermodal terminals is a rare process, particularly for complex hubs. It is worth noting that most inland intermodal terminals, due to their satellite nature, are far less complex than the terminal that served as the basis for the research problem addressed in this paper.

Given their experience in designing intermodal terminals and access to all necessary data on terminal dimensions and logistics processes, the authors of this article decided to develop a model focused on estimating energy consumption and evaluating energy efficiency at intermodal terminals during the design stage. This model aims to assist future designers in terminal planning and energy consumption estimation, using real-case inputs provided by technical and logistics process designers.

2.2. Designing of Intermodal Terminals

It is reasonable to assume that the type of intermodal terminal, the nature of its handling operations, and the layout of the handling yard significantly affect its energy consumption. For example, when most terminal operations involve direct transit—such as transshipment from one means of transport to another (e.g., railcar to railcar or railcar to truck)—there is typically only one handling operation per container. In contrast, for the same container throughput, if the majority of operations include storage, there are two or more handling operations per container (e.g., transshipment from one means of transport to the yard and from the yard to another means of transport). The number of handling operations directly impacts the workload of the machines, which in turn impacts energy consumption.

The design of an intermodal terminal’s layout, including the handling yard, is crucial in determining its energy consumption. The dimensions of the handling yard directly influence the distances that loading machines must travel during each handling cycle. These travel distances, combined with the type and number of machines employed, have a direct impact on the duration of loading cycles [1].

Example layouts of container terminals are presented below: a satellite terminal and a small hub integrated with a satellite terminal (Figure 2). A satellite terminal handles only local cargo transported to or from the terminal by HGVs. In addition to transshipments from wagons to HGVs, the satellite terminal should also offer container storage services, including both temporary storage auxiliary to handling operations and long-term storage outside the transshipment yard. A small hub terminal integrates the functionalities of both a hub and a satellite terminal. This terminal is designed to facilitate not only the handling of local cargo but also the transfer of containers from one container train to another. A small hub terminal is designed to handle fewer transit destinations than a large terminal. As a result, it does not require a large transit storage yard between the tracks [53,54].

Knowing the layout of the handling area, it is possible to determine the duration of handling cycles for individual machines. Gantry cranes, including RMGs, RTGs, and reachstackers, are typically installed at rail–road inland intermodal terminals. AGVs are expected to replace terminal tractors, in particular, in newly designed terminals. For this research, specific indices were assigned to each type of handling equipment:

r = 1

—denotes an RMG;

r = 2

—denotes an RTG;

r = 3

—denotes an AGV or terminal tractor;

r = 4

—denotes a reachstacker.

The handling time of the

r - t h

piece of handling equipment (the time during which the handling equipment performs all the movements necessary to handle one container)

(T_{r})

can be calculated using the following Formula (1) [55]:

T_{r} = t_{1}^{r} + t_{2}^{r} + t_{3}^{r} + t_{4}^{r} + t_{5}^{r} [m i n]

(1)

where

t_{1}^{r}

—time for the

r - t h

machine to drive to the loading point;

t_{2}^{r}

—time for the

r - t h

machine to lift the load;

t_{3}^{r}

—time for the

r - t h

machine to drive to the unloading point;

t_{4}^{r}

—time for the

r - t h

machine to lower the load;

t_{5}^{r}

—time for the

r - t h

machine to return to the starting point.

An expanded version of the above formula is available in the literature [56].

The handling time for gantry cranes

(r = 1,2)

is determined using the following formula:

f o r r = 1,2; T_{r} = \sum_{z = 1}^{2} \frac{d_{z, r}^{E}}{v_{z, r}^{E}} + \sum_{z = 1}^{2} \frac{d_{z, r}^{F}}{v_{z, r}^{F}} + 2 \cdot (\frac{d_{3, r}^{E}}{v_{3, r}^{E}} + \frac{d_{3, r}^{F}}{v_{3, r}^{F}}) [m i n]

(2)

where

d_{z, r}^{E}, d_{z, r}^{F} —

the drive distance of the

z - t h

component of the

r - t h

crane when empty and full;

v_{z, r}^{E}, v_{z, r}^{F} —

the drive speed of the

z - t h

component the of

r - t h

crane when empty and full,

where

z = 1 -

gantry;

z = 2 -

trolley;

z = 3 -

hoist.

In the case of AGVs or terminal tractors

(r = 3)

, the formula for handling cycle

(T_{r})

time is expressed by the following equation [42]:

f o r r = 3; T_{r} = t_{W}^{r} + t_{E}^{r} + t_{F}^{r} [m i n]

(3)

where

t_{W}^{r} — r - t h

machine standstill for loading/unloading;

t_{E}^{r} — r - t h

machine drive time when empty;

t_{F}^{r} — r - t h

machine drive time when full.

The subsequent components of the above formula are expanded as follows:

t_{E}^{r} = \frac{d_{r}^{E}}{v_{r}^{E}} [\min], t_{F}^{r} = \frac{d_{r}^{F}}{v_{r}^{F}} [m i n]

(4)

where

d_{r}^{E}, v_{r}^{E} —

the length of the distance travelled and the drive speed when the

r - t h

machine is empty;

d_{F}^{r}, v_{F}^{r} —

the length of the distance travelled and the drive speed when the

r - t h

machine is full.

The handling cycle duration

(T_{r})

for reachstackers

(r = 4)

is determined using the following formula [42,57]:

f o r r = 4; T_{r} = 2 \cdot t_{s a}^{r} + t_{t t}^{r} + t_{f z}^{r} [m i n]

(5)

where

t_{f z}^{r} —

the average time required for the

r - t h

machine to dock/undock one container to/from the spreader;

t_{s a}^{r} —

the time required for the

r - t h

machine to handle containers (lifting and horizontal movements) during storage and retrieval from the stacking yard;

t_{t t}^{r} —

the time required for the

r - t h

machine to transport the container from the stacking (storage) yard to the loading place.

Based on the handling time and the performance of the

r - t h

machine, the machine’s performance

{(W}_{r})

can be calculated using the following Formula (6) [1,23]:

f o r r \in R; W_{r} = \frac{T L}{T_{r}} \cdot σ_{r}^{P R} \cdot σ_{r}^{T E C} [\frac{o p e r a t i o n s}{d a y}]

(6)

where

T L —

the terminal working hours;

σ_{r}^{P R} —

the practical performance coefficient of the

r - t h

machine;

σ_{r}^{T E C} —

the technical performance coefficient of the

r - t h

machine.

Knowing the number of operations (which can be multiple for one container) that must be carried out in the

p - t h

transition through the terminal, it is possible to determine the number of

r - t h

machines

(M_{r})

required to handle a given container throughput:

f o r r \in R; M_{r} = \frac{\sum_{p} K_{p}^{r} \cdot m_{r, p}}{T L \cdot W_{r}} [p c s .]

(7)

where

K_{p}^{r} —

the number of containers subject to the

p - t h

transition and transhipped through the

r - t h

machine;

m_{r, p} —

the number of operations carried out by the

r - t h

machine in the

p - t h

transition through the terminal.

The design of handling operations (whether direct or indirect) is also crucial for estimating energy consumption, with the identification of appropriate rules for container flow through the facility playing a significant role. The authors of [1,9,58] distinguished the following types of container terminal transitions:

p = 1,2 —

direct and indirect rail transit (with storage);

p = 3,4 —

direct and indirect road transit (with storage);

p = 5,6 —

direct rail-to-road and road-to-rail transshipment;

p = 7,8 —

indirect rail–road transshipment with one- and two-yard operations;

p = 9,10 —

indirect road–rail transshipment with one- and two-yard operations.

A graphical representation of terminal operations is provided in Figure 3.

The machine’s handling time enables the estimation of energy consumption per single handling operation. Subsequently, the product of the operations carried out and the unit energy consumption can be used to calculate the total energy consumption of all

r - t h

machines.

It is worth noting that the formulae presented in this chapter are only part of the set of formulae for designing the handling system of intermodal terminals. Others have been omitted due to their lack of relevance to the calculations presented in this paper.

2.3. Estimating Energy Consumption of Handling Equipment

Growing global electricity consumption, coupled with rising energy costs, has brought the issue of energy usage to the forefront of international literature [16,17,59,60]. This topic frequently arises in the context of intermodal terminal operations [38]. In [20,43], experts analyzed the energy consumption of handling equipment at a seaport on a per-container basis. This research examined the diesel consumption of RTG cranes and the electricity consumption of STS cranes. The study also classified the terminal’s equipment based on the type of power supply available (Table 1).

The most reliable method of testing electricity consumption is through empirical measurements. Such tests were carried out by experts [43] observing the operation of an RTG crane. In their experiment, they used a data logger to collect information from a Programmable Logic Controller (PLC) on electricity consumption during handling operations. A diagram of the measurement system is shown in Figure 4.

Researchers have found that the energy produced or consumed by all the motors of a gantry crane is proportional to the product of the energy output of each motor required to perform the work and the duration of the work [43]:

P = \frac{d E}{d t} \to \int_{t_{0}}^{t_{f b}} P d t \to E ≅ t \cdot \sum_{i = 1}^{N - 1} P_{i, r} [k W h]

(8)

where

P —

the power generated by the engine,

E —

consumed energy;

t —

sampling time;

t_{0} —

operation start time;

t_{f b} —

operation end time;

P_{i, r} —

the power of the

i - t h

motor required to overcome the given motion resistance for the

r - t h

machine (in the given example,

P_{i, r} = \sum_{z} P_{i, z, r}

—see formula below). The approximation assumes constant power for discrete sampling times t. This simplification is reasonable for practical applications.

For the

i - t h

engine of the

z - t h

component of the

r - t h

gantry crane, the generated engine power for

{(P}_{i, z, r})

can be calculated using the following equation [61]:

f o r r = 1,2; i = 1,2, 3,5; P_{I, z, r} = \frac{F_{I, z, r} \cdot v_{z, r}^{E / F}}{η_{z, r}} [k W]

(9)

where

F_{i, z, r} —

the force required to overcome resistance to motion on the

z - t h

component of the

r - t h

machine calculated for the

i - t h

motor;

v_{z, r}^{E / F} —

the speed of the motion of the

z - t h

component of the

r - t h

machine working empty or full;

η_{z, r} —

the efficiency of the

z - t h

component of the

r - t h

machine.

An exception is made for calculating the power required to overcome resistance due to the acceleration of rotating masses:

f o r r = 1,2; i = 4; P_{i, z, r} = \frac{{M K}_{i, z, r} \cdot {n k}_{z, r}^{E / F}}{9550} [k W]

(10)

where

{n k}_{z, r}^{E / F} —

the engine rotating speed of the

z - t h

component of the

r - t h

machine working empty or full;

{M K}_{i, z, r} -

the engine torque on the

r - t h

crane’s

z - t h

component, required to calculate the

i - t h

engine power.

The calculation of drag forces for individual crane components is provided below:

Nominal Force

For the running gear and trolley, proceed as follows:

f o r r = 1,2; i = 1; z = 1,2; F_{i, z, r} = {(W}_{z, r} + m c) \cdot f [k N]

(11)

For the lifting mechanism, proceed as follows:

f o r r = 1,2; i = 1; z = 3; F_{i, z, r} = {(W}_{z, r} + m c) \cdot g [k N]

(12)

where

m c —

the mass of the lifted container;

f —

the rolling resistance of the crane wheels;

W_{z, r} —

the mass of the

z - t h

component of the

r - t h

machine.

Resistance Due to Current Supply or Festoon System:

F o r r = 1,2; i = 2; z = 2

F_{i, z, r} = 1.5 kN

for a rope driven trolley;

F_{i, z, r} = 3 - 4 kN

= 3–4 kN for a motor trolley.

Resistance Due to Wind:

f o r r = 1,2; i = 3; F_{i, z, r} = \sum_{z = 1}^{Z} A_{z, r} \cdot c_{z, r} \cdot q_{z, r} [k N]

(13)

where

A_{z, r} —

the effective frontal area of the component under consideration for the

r - t h

machine and its

z - t h

component;

c_{z, r} —

the shape coefficient in the direction of the wind for the component under consideration for the

r - t h

machine and its

z - t h

component;

q_{z, r} —

the wind pressure corresponding to the appropriate design condition for the

r - t h

machine and its

z - t h

component.

This resistance will be excluded from the calculations due to its irrelevance, as in [61].

Resistance Due to Accelerating the Rotating Masses:

f o r r = 1,2; i = 4; z \in Z; {M K}_{i, z, r} = \frac{{J O}_{z, r} \cdot {ω_{z, r}}^{2}}{{t α}_{z, r}} [k N]

(14)

where

{t α}_{z, r} —

the acceleration time for the

r - t h

machine and its

z - t h

component;

{J O}_{z, r} —

the moment of inertia of the rotating masses (including engines, brake sheaves, couplings, and gearbox, reduced) for the

r - t h

machine and its

z - t h

component;

ω_{z, r} —

the angular speed for the

r - t h

machine and its

z - t h

component, with

ω_{z, r} = \frac{2 \cdot π \cdot {n k}_{z, r}^{E / F}}{60} [\frac{r a d}{s}]

(15)

Resistance Due to Accelerating the Linear Masses:

f o r r = 1,2; i = 5; z \in Z; F_{i, z, r} = \frac{(W_{z, r} + m c) \cdot v_{z, r}^{E / F}}{{t α}_{z, r}} [k N]

(16)

where

m c = 0 —

for movement when empty.

The energy consumption for each handling machine can be calculated using the above formulae with appropriate conversions. For instance, in the case of AGVs and terminal tractors

(r = 3)

, the energy consumption

(E^{r})

during a single handling cycle is estimated as follows [42]:

f o r r = 3; E^{r} = P_{W}^{r} \cdot t_{W}^{r} + P_{E}^{r} \cdot t_{E}^{r} + P_{F}^{r} \cdot t_{F}^{r} [k W h]

(17)

where

P_{W}^{r}, P_{E}^{r}, P_{F}^{r} —

the engine power of the

r - t h

machine generated when waiting, traveling empty, and traveling full;

t_{W}^{r}, t_{E}^{r}, t_{F}^{r} —

the total time of the

r - t h

machine spent waiting, traveling empty, and traveling with the container.

For reachstackers

(r = 4)

, the energy consumption is calculated using the following equation [58,61]:

f o r r = 4; E^{r} = \frac{P_{I C}^{r} \cdot t_{I C}^{r}}{η_{I C}^{r}} + \frac{P_{E L}^{r} \cdot t_{E L}^{r}}{η_{E L}^{r}} - E_{R E C}^{r} [k W h]

(18)

where

P_{I C}^{r} —

the power output of the internal combustion engine of the

r - t h

machine;

t_{I C}^{r} —

the operational time using the internal combustion engine of the

r - t h

machine;

η_{I C}^{r} —

the efficiency of the internal combustion engine;

P_{E L}^{r} —

the power output of the electric system of the

r - t h

machine;

t_{E L}^{r} —

the operational time using the electric system of the

r - t h

machine;

η_{E L}^{r} —

the efficiency of the electric system of the

r - t h

machine;

E_{R E C}^{r} —

the energy recovered from the regenerative systems (e.g., braking or load lowering) of the

r - t h

machine.

Since electric reachstackers are still rarely used, simplified methods for converting diesel consumption to electricity consumption are currently applied, assuming similar energy intensity. However, in practice, energy demand can vary significantly between diesel and electric-powered engines due to design factors and the performance of modern batteries, which are influenced by external conditions such as weather. For instance, colder temperatures can reduce battery efficiency and capacity, resulting in shorter operational periods and more frequent charging. Similarly, high-intensity operations or improper charging cycles can shorten battery lifespan, further affecting overall energy efficiency. Moreover, the infrastructure required for charging electric reachstackers, including high-capacity charging stations and potential grid upgrades, may influence their practicality and total energy demand compared to diesel-powered machines.

3. Energy Consumption Estimation Model for Handling Equipment

Drawing on the expertise of professionals involved in designing intermodal terminals and estimating energy consumption, a model has been developed to determine the energy consumption of all handling equipment operating within an intermodal terminal. The terminal’s energy consumption is closely tied to the parameters defined during the initial phase of the research. A key limitation of this model is the restriction on the maximum number of handling equipment that can be installed at an intermodal terminal. This limit is determined by factors such as the terminal type and the dimensions and configuration of the transshipment yard. Incorporating a parameter for the maximum number of handling equipment ensures that the calculated energy demand aligns with the realistic operational requirements of a given terminal.

To accurately estimate the energy consumption of handling equipment, a three-step model has been proposed. This model aids in understanding the problem, formulating it mathematically, and deriving a solution—see Figure 5.

The model components are described below:

Stage I—Defining Operational Assumptions for an Intermodal Terminal

Step 1: Identify the type of rail–road inland container intermodal terminal to be designed.

Terminals are classified as follows:

s = 1 —

satellite terminal;

s = 2 —

hub terminal;

s = 3 —

transit terminal (a pure hub, with no local traffic, like a cross-border transshipment terminal).

Step 2: Define the input parameters to be considered, combining technical design and logistics planning.

From the perspective of rail service, a key parameter is the number of train pairs the terminal can accommodate, determined by its size (based on demand forecasts) and the limitations of the railway network. Other key parameters include the terminal’s working hours per day and the distribution of truck operations throughout those hours. The latter often depends more on local customer preferences and logistical requirements than on the assumptions of the terminal operator. These and other parameters are summarized in Table 2.

In the table above,

T L = (t l : t l = \bar{1, T L})

, with

t l —

working hours,

J = (j : j = \bar{1, J})

, and

j —

terminal workload scenario.

Step 3A: Select the type of handling equipment.

The length and width of the transport aisles depend on the type of machine, which directly influences the transport cycle time.

Step 4A: Due to space constraints, determine the maximum number of

r - t h

machines that can operate at the

s - t h

terminal

({B H}_{r, s}^{m a x})

This is calculated using the following formula:

{B H}_{r, s}^{m a x} = \frac{{D F}_{r, s}}{{K R}_{r, s}^{m i n}} [p c s .]

(19)

where

{D F}_{r, s} —

the handling yard length dedicated to the

r - t h

machine’s operation at the

s - t h

terminal;

{K R}_{r, s}^{m i n} —

the minimum working aisle length required for the

r - t h

machine’s operation at the

s - t h

terminal.

Step 3B: Reconstruct the container transition path through the terminal.

This step identifies the types of container transitions (see Figure 3 and their share in the throughput. The number of containers involved in the

p - t h

transition through the

s - t h

terminal in the

j - t h

scenario with average daily throughput

(K_{p, s}^{j})

can be calculated as follows:

j \in J K_{p, s}^{j} = 2 \cdot λ^{j} \cdot L K \cdot ϕ \cdot {F D}_{p, s} [I T U]

(20)

where

{F D}_{p, s} —

the share of containers involved in the

p - t h

transition through the

s - t h

terminal;

α —

the peak coefficient.

The number of containers involved in the

p - t h

transition through the

s - t h

terminal in the

j - t h

scenario with an average peak throughput

{(K H}_{p, s}^{j})

can be modeled as follows:

j \in J {K H}_{p, s}^{j} = 2 \cdot λ^{j} \cdot L K \cdot ϕ \cdot {F D}_{p, s} \cdot α [I T U]

(21)

At a satellite terminal

(s = 1)

p = < 3,10 >

operations, and at a hub terminal

(s = 2)

or a transit terminal

(s = 3)

p = < 1,10 >

operations are carried out.

Step 4B: Design the layout of the intermodal terminal, incorporating the configuration of its handling yards.

This layout establishes a critical framework for determining handling cycle durations in subsequent stages of analysis.

Stage II—Determining the Number of Machines to Handle a Given Container Throughput

Step 1A: Determine the handling cycle durations for individual pieces of handling equipment.

An example of the designations needed to calculate the handling cycles for gantry cranes is shown in Figure 6.

The parameter designations required for determining the handling cycle durations of AGVs and terminal tractors have not been exemplified. Their loading cycle is similar to the loading time of other handling equipment, such as forklifts. To determine the loading cycle time for these machines, only the travel distance and speed of the machine, both full and empty (

d_{r}^{E}, d_{r}^{F}, v_{r}^{E}, v_{r}^{F}

), are required.

Step 1B: Use Formulaes (24) and (25) to determine the handling cycle duration of a particular machine.

Step 2: Calculate the performance of the individual machine types using the components of Formula (27).

At this stage, the terminal’s working hours must be established, typically spanning either 24 or 16 h per day. Additionally, the technical

(σ_{r}^{T E C})

and practical

(σ_{r}^{P R})

performance of the handling equipment must be determined. According to the literature, these values generally range from 0.75 to 0.9 [1,62].

Step 3: Designate the number of

r - t h

machines required to handle the given container throughput

({M C}_{s, j}^{r})

The critical equipment threshold relative to the maximum capacity must be considered to ensure safe and stable operation. For handling equipment of the

r - t h

machine operating under the

j - t h

terminal workload, the required number of machines to maintain a constant workload with an average daily throughput can be calculated using the following formula:

{M C}_{s, j}^{r} = ⌈\frac{\sum_{p} K_{p, s}^{j} \cdot m_{r, p} \cdot γ}{T L \cdot W_{r}}⌉ \leq {B H}_{s, r}^{m a x} [p c s .]

(22)

Machines operating at a variable workload are calculated differently. The distribution of pickup/delivery HGV traffic across different hours is considered. For each hour, we assume the percentage

{(u}^{t l})

of vehicles arriving at the terminal. The number of

r - t h

machines required during the

t l - t h

hour, in the

j - t h

terminal workload scenario, with an average daily throughput

(M Z_{s, j}^{r, t l})

, is determined as follows:

M Z_{s, j}^{r, t l} = ⌈\frac{\max_{tl \in TL} \{u^{t l}\} \cdot \sum_{p} K_{p, s}^{j} \cdot m_{r, p} \cdot γ}{W_{r}}⌉ \leq {B H}_{s, r}^{m a x} [p c s .]

(23)

In both cases, it must be ensured that the number of machines installed does not exceed the limit imposed by the handling yards. If the calculated number exceeds

({B H}_{s, r}^{m a x})

, the process returns to Step 2 to test the scenario with a lower container throughput.

Stage III—Estimating the Electricity Consumption of Handling Equipment

Step 1: Estimate the energy consumption per single handling cycle of the

r - t h

machine

(E^{r})

By modifying Formulaes (24) (cranes) and (25) (AGVs/terminal tractors), energy consumption can be determined as follows:

f o r r = 1,2; E^{r} = \sum_{i = 1}^{I} \sum_{z = 1}^{Z} P_{i, z, r}^{E} \cdot (\frac{d_{z, r}^{E}}{v_{z, r}^{E}}) + \sum_{i = 1}^{I} \sum_{z = 1}^{Z} P_{i, z, r}^{F} \cdot (\frac{d_{z, r}^{F}}{v_{z, r}^{F}}) [\frac{k W h}{c y c l e}]

(24)

f o r r = 3; E^{r} = P_{W}^{r} \cdot t_{W}^{r} + P_{E}^{r} \cdot (\frac{d_{r}^{E}}{v_{r}^{E}}) + P_{F}^{r} \cdot (\frac{d_{r}^{F}}{v_{r}^{F}}) [\frac{k W h}{c y c l e}]

(25)

where

P_{i, z, r}^{E} —

the power used by the

i - t h

engine power of the

z - t h

component of the

r - t h

crane when operating empty;

P_{i, z, r}^{F} —

the power used by the

i - t h

engine power of the

z - t h

component of the

r - t h

crane when operating full;

P_{W}^{r} —

the power used by an AGV

(r - t h

) machine during a standstill;

P_{E}^{r} —

the power used when the

r - t h

machine is driving empty;

P_{F}^{r} —

the power used when the

r - t h

machine is driving full.

Note: It is assumed that AGVs do not travel empty at the terminal; thus,

d_{r}^{E} = 0 .

Under this assumption, the waiting time

{(t}_{W}^{r})

for the

(r - t h

) AGV during a single handling cycle for container issuance under RTG and RMG cranes can be calculated using Formula (26):

f o r r = 3; t_{W}^{r} = \{\begin{matrix} (\frac{d_{2,1}^{E}}{v_{2,1}^{E}} + \frac{d_{3,1}^{E}}{v_{3,1}^{E}} + 2 \cdot \frac{d_{3,1}^{F}}{v_{3,1}^{F}} + \frac{d_{2,1}^{F}}{v_{2,1}^{F}}) + \frac{d_{2,2}^{E}}{v_{2,3}^{E}} + \frac{d_{2,2}^{F}}{v_{3,3}^{F}} [m i n], w h e n l o a d i n g w i t h R M G a n d u n l o a d i n g w i t h R T G \\ (\frac{d_{2,2}^{E}}{v_{2,2}^{E}} + \frac{d_{3,2}^{E}}{v_{3,2}^{E}} + 2 \cdot \frac{d_{3,2}^{F}}{v_{3,2}^{F}} + \frac{d_{2,2}^{F}}{v_{2,2}^{F}}) + \frac{d_{2,1}^{E}}{v_{2,1}^{E}} + \frac{d_{3,1}^{F}}{v_{3,1}^{F}} [m i n], w h e n l o a d i n g w i t h R T G a n d u n l o a d i n g w i t h R M G \end{matrix}

(26)

Step 2: Determine the energy consumed per working day by all

r - t h

machines installed at the intermodal terminal, broken down into the following:

Machines of the

r - t h

type operating at a constant workload in the

j - t h

scenario

(E_{C C}^{r, j})

E_{C C}^{r, j} = \sum_{p} K_{p, s}^{j} \cdot m_{r, p} \cdot E^{r} [k W h]

(27)

Subject to a constraint:

\sum_{p} K_{p, s}^{j} \cdot m_{r, p} \cdot \frac{1}{T L} \leq {M C}_{s, j}^{r} \cdot W_{r} \cdot γ

(28)

Machines of the

r - t h

type operating at a variable workload in the

j - t h

scenario

(E_{S T}^{r, j})

E_{S T}^{r, j} = \sum_{t l = 1}^{T L} {\sum_{p} K_{p, s}^{j} \cdot m_{r, p} \cdot E^{r} \cdot u}^{t l} [k W h]

(29)

Subject to a constraint:

\sum_{p} K_{p, s}^{j} \cdot m_{r, p} \cdot u^{t l} \leq M Z_{s, j}^{r, t l} \cdot W_{r} \cdot γ

(30)

It must be ensured that the number of operations carried out in a given hour does not exceed the maximum capacity for the designated machines from Step 2.

4. Case Study and Results

This case study, based on the pre-designs of intermodal terminals along new railway lines carried out by the CPK Company, demonstrates the practical application of calculations to determine ex ante the energy consumption of handling equipment at an inland rail–road container intermodal terminal. As noted, the energy consumption of handling equipment depends on various variables and parameters, such as container throughput, handling yard dimensions and configuration, and working technology. To begin assessing the energy demand, it is essential to first prepare a comprehensive set of input parameters and establish the terminal’s layout. This foundation is critical for calculating the duration of handling cycles, determining the required number of handling equipment, and ultimately estimating the energy demand.

This chapter concludes with an analysis of energy consumption across various terminal throughput scenarios. The results are validated by examining the values of selected input parameters.

4.1. Algorithm Implementation, Calculations, and Results

4.1.1. Stage I

Stage I model testing began with the selection of the type of intermodal terminal for energy consumption analysis. An

s = 2

intermodal hub was selected. Two authors of this paper are actively involved in the pre-design of intermodal terminals, addressing both technical and economic aspects. For the largest of these terminals, evaluating future energy consumption was identified as a key priority. The analyses conducted for this terminal formed the foundation for the calculations presented in this article. These analyses were based on pre-design layouts and data, encompassing railway, storage, and road infrastructure, as well as the necessary handling equipment, demand forecasts (including throughput), and operational assumptions. The selected site, identified as the optimal location among several alternatives, also presented specific constraints. As is often the case in economically developed regions, identifying a flawless location proved challenging, highlighting the inherent trade-offs involved in such decisions.

Next, in Step 2, the basic parameters to be used in subsequent calculations were prepared (see Table A1 in Appendix A).

It was assumed that the terminal operates continuously, 24/7, to ensure the highest possible level of service. The length of the transshipment yard was determined based on the AGCT/TEN-T agreements [63,64]. The number of containers was calculated under the assumption that a 750 m long train can accommodate up to 110 TEUs. For this analysis, it was further assumed that trains carry forty 40-foot containers and thirty 20-foot containers, resulting in a total of seventy containers per train. The average train load factor and critical equipment thresholds were derived from empirical values.

Step 3A of Stage I involved determining the type of handling equipment. Based on the container throughput and terminal type, it was assumed that RMGs (

r = 1

), RTGs (

r = 2

), and AGVs/terminal tractors (

r = 3

) would operate at the facility. This equipment is distinguished by its high performance compared to other options available for intermodal terminal operations.

Step 3B of Stage I outlined the container transition path through the terminal. In this process, HGVs delivering containers to the terminal or arriving to collect them proceed to a storage yard managed by RTGs. At the storage yard, the RTG crane removes the container from the HGV and places it onto a waiting AGV, which then transports it to the transshipment yard and positions itself within reach of an RMG crane to facilitate the loading of the container onto a train. Occasionally, containers may be stored temporarily in the storage yard for extended periods before being moved to the transshipment yard.

In outbound operations, containers unloaded from a train by the RMG crane are initially placed on an AGV, transported to the storage yard, and either stored for medium- or long-term periods or directly transferred onto an HGV platform by the RTG crane. Once the container is loaded or unloaded, the HGV leaves the terminal, heading to its designated destination, whether it is a customer site or a transport hub (Figure 7).

It was assumed that the handling equipment performs the following types of operations:

p = 1,2 —

direct and indirect rail transit (with storage);

p = 4

—direct and indirect road transit (with storage);

p = 7,8

—indirect rail–road transshipment with one- and two-yard operations;

p = 9,10

—indirect road–rail transshipment with one- and two-yard operations.

Truck-to-truck transit operations were excluded from further calculations due to their sporadic nature. The distribution of containers by the type of operation is presented in Table 3.

Since RMG cranes do not handle road traffic, they were assumed to operate with a constant workload. RTG cranes, however, handle road traffic and are subject to fluctuations in vehicle activity throughout the day. Therefore, RTG cranes were assumed to operate with a variable workload.

In Step 4B, the necessary input data were prepared based on the preliminary design of the handling yard layout for the terminal selected for analysis (Figure 8). Considering the terminal size, handling equipment parameters, transshipment yard length (to accommodate 750 m trains), transport aisle width, and intertrack spacing, the transshipment yard length for the

r - t h

machines was calculated.

Based on figure posted above, the following assumptions were made in Step 4A: the yard length under the RMGs is

{D F}_{1,2} = 750 m

, and the yard length under the RMGs is

{D F}_{2,2} = 2 \cdot 750 = 1500 m

The minimum working aisle length for

r - t h

machines, based on empirical observations, is

{K R}_{1,2}^{m i n} / {K R}_{2,2}^{m i n} = 187.5 m .

The maximum number of RMG cranes will therefore amount to

{B H}_{1,2}^{m a x} = 4

, while for RTG cranes, it is

{B H}_{2,2}^{m a x} = 8

4.1.2. Stage II

In Step 1 of Stage II, determining the handling cycle duration for the machinery operating at the intermodal terminal was a key task. This step involved establishing the values of the parameters used in Equations (2) and (3) (see Table A2 in Appendix A).

It turned out that the average handling cycle duration for an RMG crane is

T_{1} = 5.20 m i n / c y c l e

when

d_{1,1}^{E}, d_{1,1}^{F} = 375 m, T_{1} = 3.95 m i n / c y c l e

when

d_{1,1}^{E}, d_{1,1}^{F} = 187.5 m, T_{1} = 3.0 m i n / c y c l e

when

d_{1,1}^{E}, d_{1,1}^{F} = 125 m

, and

T_{1} = 2.5 m i n / c y c l e

when

d_{1,1}^{E}, d_{1,1}^{F} = 93.5 m

. For RTG cranes, the handling cycle duration is

T_{2} = 8.59 m i n / c y c l e

when

d_{1,2}^{E}, d_{1,2}^{F} = 375 m,

T_{2} = 5.11 m i n / c y c l e

when

d_{1,2}^{E}, d_{1,2}^{F} = 187.5 m,

T_{2} = 3.96 m i n / c y c l e

when

d_{1,2}^{E}, d_{1,2}^{F} = 125 m, a n d T_{2} = 3.4 m i n / c y c l e

when

d_{1,2}^{E}, d_{1,2}^{F} = 93.75 m

. For AGVs, the average handling cycle duration is

T_{3} = 3.68 m i n / c y c l e

The performance of RMG machines Is

E_{1} = 9.3 c y c l e / h

E_{1} = 12.3 c y c l e / h

E_{1} = 16.3 c y c l e / h

, and

E_{1} = 19.1 c y c l e / h

, respectively. For RMG cranes, the performance is

E_{2} = 5.6 c y c l e / h

E_{2} = 9.5 c y c l e / h

E_{2} = 12.3 c y c l e / h

, and

E_{2} = 14.4 c y c l e / h

. In the case of AGVs, it is, on average,

E_{3} = 13.2 c y c l e / h

By substituting the data into Formulaes (22) and (23), the required number of RMG cranes (

r = 1

), RTG cranes (

r = 2

), and AGVs (

r = 3

) for each scenario (

j

) was determined, as shown in Table A3 in Appendix A.

It should be noted that the number of RTGs was calculated for an hour

(t l = 6)

, for which

u^{t l} = 5.5 %

Using the data from the table above, a graph was created to illustrate the number of cranes operating under each of the terminal’s loading workload scenarios in comparison to the maximum number of machines that the terminal can accommodate (Figure 9).

Figure posted above illustrates that four RMG cranes are required to handle 8–11 pairs of intermodal trains per day (scenario

j = 1, 2, 3, 4

). Three RMG cranes are sufficient for the scenario

j = 5, 6, 7, 8

, two for the scenario

j = 9, 10

, and one for the scenario

j = 1

. In contrast, eight RTG cranes will be required to handle the volume for 8–11 pairs of trains per day (scenario

j = 1, 2, 3, 4

). Six RTG cranes are sufficient for the scenario

j = 5, 6, 7

, four for the scenario

j = 8, 9, 10

, and one for the scenario

j = 11

. In the case of AGVs, four units will be required to handle the volume of containers in the scenario

j = 1, 2, 3

, three in the scenario

j = 4, 5, 6,

two units in the scenario

j = 7, 8, 9

, and two units in the scenario

j = 10, 11

4.1.3. Stage III

In Step 1 of Stage III, the task was to calculate energy consumption per handling cycle for each machine at the intermodal terminal, using parameters from Formulae (24) and (25) (see Table A4 in Appendix A).

The energy consumption per cycle was determined as follows:

An RMG uses

8.62 k W h / c y c l e

(

d_{1,1}^{E}, d_{1,1}^{F} = 375 m

6.96 k W h / c y c l e

(

d_{1,1}^{E}, d_{1,1}^{F} = 187.5 m

5.80 k W h / c y c l e

(

d_{1,1}^{E}, d_{1,1}^{F} = 125 m

), and

5.23 k W h / c y c l e

(

d_{1,1}^{E}, d_{1,1}^{F} = 93.5 m

). An RTG uses

7.5 k W h / c y c l e

(

d_{1,2}^{E}, d_{1,2}^{F} = 375 m

5.08 k W h / c y c l e

(

d_{1,2}^{E}, d_{1,2}^{F} = 187.5 m

4.27 k W h / c y c l e

(

d_{1,2}^{E}, d_{1,2}^{F} = 125 m

), and

3.86 k W h / c y c l e

(

d_{1,2}^{E}, d_{1,2}^{F} = 93.5 m

). An AGV uses

0.8 k W h / c y c l e

Figure 10 presents the level of performance utilization relative to the unit energy consumption for each scenario for RMG cranes and AGVs.

Figure 10. The level of performance utilization against the unit energy consumption of RMG cranes (a) and AGVs (b). The same was performed for the RTG cranes—see Figure 11.

Figure 11. The level of performance utilization against unit the energy consumption of RTG cranes.

Figures posted above illustrate that the specific energy consumption per cycle decreases as the number of handling equipment installed at the terminal increases. In scenarios where

j = 1, 2, 3, 4

, the unit energy consumption decreases by 39% for RMG cranes and by 49% for RTG cranes compared to scenario where

j = 11

. For AGVs, the energy consumption remains constant across all scenarios. Optimal energy consumption for both RMG and RTG cranes is achieved in the scenario where

j = 6

. In later scenarios, the unit energy consumption rises disproportionately to the number of operations performed. Conversely, in earlier scenarios, the unused performance reserve increases disproportionately relative to the energy consumed.

In Step 2 of Stage II, the total energy consumed by the

r - t h

machine in each scenario was calculated. Figure 12 below illustrate the daily energy consumption of machines operating under a constant workload throughout the working day, based on the assumed throughput scenario and the number of handling equipment installed.

Figure 13 illustrates the daily energy consumption of machines operating under a variable workload throughout the working day.

Figures posted above illustrate the energy consumption of handling equipment under various scenarios.

The daily energy consumption of handling equipment varies depending on the number of installed units and the scenario.

For RMG cranes, in scenarios where j = 1, 2, 3, 4, with four units installed, daily energy consumption ranges from 5268 to 7244 kWh. In scenarios where j = 5, 6, 7, 8, with three units, consumption decreases to 2925–5119 kWh per day. In scenarios where j = 9, 10, with two units, daily consumption is between 1755 and 2632 kWh. For the scenario where j = 1 1, with one unit, daily consumption is 1087 kWh.

For AGVs, in scenarios where j = 1, 2, 3, with four operating units, daily energy consumption ranges from 629 to 769 kWh. In scenarios where j = 4, 5, 6, with three units, consumption drops to 419–559 kWh per day. In scenarios where j = 7, 8, 9, with two units, daily consumption is 210–349 kWh. In scenarios where j = 10, 11, with one unit, daily consumption is 70–140 kWh.

For RTG cranes, in scenarios where j = 1, 2, 3, 4, with four units installed, daily energy consumption ranges from 4674 to 6427 kWh. In scenarios where j = 5, 6, 7, 8, with three units, consumption decreases to 3226–4517 kWh per day. In scenarios where j = 9, 10, with two units, daily consumption is between 1535 and 3069 kWh. For the scenario where j = 11, with one unit, daily consumption is 1134 kWh.

A graph illustrating energy consumption throughout the day is shown below (Figure 14).

Figure posted above demonstrates that energy consumption varies depending on the type of equipment, the scenario, and the time of day. RMG cranes consume an average of 728–4829 kWh of energy during the daytime tariff (06:00–22:00) and 358–2414 kWh during the night-time tariff (22:00–06:00). RTG cranes consume 804–4562 kWh during the day and 328–1863 kWh at night. AGVs consume 46–512 kWh during the day and 23–256 kWh at night. In total, the handling equipment consumes 1579–9904 kWh during the day and 710–4534 kWh at night. When considering energy consumption per hour of operation, RMG cranes consume an average of 45–301 kWh, while RTG cranes consume 50–285 kWh during the day and 41–232 kWh at night. AGVs consume 2–32 kWh per hour, regardless of the time of day. For the given type of operations and container flow, all handling equipment at the terminal can consume a total of 2200–13,470 kWh of energy over the combined day and night periods.

4.2. Sensitivity Analysis

To verify the accuracy of the obtained results, a sensitivity analysis was conducted to assess the impact of changes to specific parameters on the final results (see Table A5 in Appendix A).

For the sensitivity analysis, three sub-variants were created to evaluate the impact of changes in selected parameter values on the unit energy consumption for RTGs and RMGs compared to the baseline (Variant 0).

In Variant 1, the weight of the containers being handled and the components of the cranes were reduced by 20%. In Variant 2, the dimensions of the transshipment yard (e.g., length and width) were decreased by 20%, and it was assumed that containers were lifted to an average height of 9.6 m instead of 12 m. In Variant 3, the engine rotating speed parameters were increased by 20%. The results of the sensitivity analysis are presented in Figure 15.

The analysis revealed the following impacts on unit energy consumption for RMGs and RTGs:

In Variant 1, reducing the weight of crane components and containers by 20% resulted in an 18–19% decrease in unit energy consumption per container operation compared to Variant 0. In Variant 2, reducing the transshipment yard dimensions by 20% led to an 8–30% reduction in unit energy consumption for RTGs and a 20% reduction for RMGs. In Variant 3, increasing engine rotational parameters by 20% caused a 2–4.5% increase in unit energy consumption for RTGs and a 4.7–7.6% increase for RMGs.

The sensitivity analysis can be extended to include other parameters, such as the movement speed of specific crane components, the percentage share of different container operations at the terminal, train load factors, and more.

5. Discussion

The best validation of the obtained results is to compare the handling equipment’s energy consumption with values obtained in the international literature. For RMG cranes, experts [65] determined the unit energy consumption at 7.25 kWh per container operation. Other studies found values of 4.4 kWh per TEU [66,67], 5–7.25 kWh per operation [68], 3.1–4.2 kWh per operation [69], and 6 kWh per operation [70]. In [71], the RTG crane’s energy consumption was estimated at 3 kWh per container. In contrast, Qianjing Li [72] established the energy consumption of an electric RTG crane at 3.1–3.5 kWh per cycle, the Konecrane company [73] specifies 3.0–3.8 kWh per container, and Kusakaka [74] reports approximately ~3.47 kWh/cycle. The AGV’s energy consumption was estimated to be about 0.25 kW/min (about 15 kWh) [75].

In this study, the energy consumption of RMG cranes ranges from 5.23 to 8.62 kWh per cycle, RTG cranes consume 3.86 to 7.5 kWh per cycle, and AGVs consume approximately 10.46 kWh per operational hour. The non-standard size of the terminal (hub terminal), design parameters, and handling equipment significantly impacted the results.

For instance, the sensitivity analysis showed that reducing the weight of handling equipment by 20% decreased RMG energy consumption to 4.29–7.01 kWh per cycle and RTG energy consumption to 3.14–6.05 kWh per cycle. Reducing the length of the transshipment yard by 20% resulted in consumption levels of 4.18–6.89 kWh per cycle for RMG cranes and 2.7–6.86 kWh per cycle for RTG cranes.

In Variant 3, increasing the rotational parameters of handling equipment motors by 20% raised unit energy consumption to 5.62 kWh per cycle for RMG cranes and 4.02–7.67 kWh per cycle for RTG cranes. In Variant 1, energy reductions were primarily driven by lighter machines, which placed less strain on their motors. In Variant 2, shorter loading cycles reduced energy consumption by minimizing the required operating time. In Variant 3, energy consumption increased due to motors operating 20% more intensively.

Based on these findings, the results align closely with values reported in the international literature. The small discrepancies between this study and global data may arise from insufficient detail in terminal parameters within international reports. For example, this study assumes a transshipment yard length of 750 m, while many global terminals operate with yards of 600 m or less. Additionally, critical handling equipment parameters such as weight, span, engine speed, range, and efficiency are often omitted in the literature, making precise comparisons challenging. This lack of data, often due to proprietary restrictions, creates significant barriers to accurate modeling.

This study also demonstrates that total terminal energy consumption decreases as more machines are installed, primarily due to shorter handling cycle durations as travel distances are reduced. However, as the number of operations grows, so does the number of handling machines, leading to an overall increase in total energy consumption. For the planned CPK terminal, energy consumption is estimated to range from 2200 to 13,470 kWh per day, similar to values reported for comparable terminals [50]. Interestingly, energy consumption is not directly proportional to increases in handling operations, as variations in unit energy consumption depend on the number of machines installed.

The most significant contribution of this study is its comprehensive methodology for estimating the energy consumption of handling equipment before a facility becomes operational. Only a few publications combine the design of intermodal terminals with energy demand estimation [50,51]. Moreover, unlike most studies in the international literature—which typically analyze energy consumption based on existing facilities or selected elements of a terminal or its machinery [20,42,74,76,77,78]—this approach establishes a strong correlation between energy consumption and design parameters. These parameters can be optimized during the conceptual phase to minimize energy waste. It is worth noting that there is little scientific research globally on intermodal terminals offering such comprehensive energy parameterization.

While the proposed model is highly accurate, it has limitations. First, due to its scope, it focuses only on critical terminal components, specifically handling equipment. Second, the model does not account for energy recuperation, an increasingly relevant factor. Third, it does not differentiate between electric, hybrid, and diesel-powered machines. Incorporating these aspects would significantly increase complexity but could be addressed in future model iterations. Fourth, only certain elements of our model are applicable to container port design and energy estimation in such logistics facilities, as the logistics processes there differ from those at inland terminals.

Undoubtedly, this model can estimate energy consumption for newly designed intermodal terminals and calculate the terminal’s carbon footprint and operational costs, making it a valuable tool for cost–benefit analysis. The obtained results will play a key role in the evaluation of intermodal terminals designed by the CPK Company.

6. Conclusions

The research we conducted offers new insights into estimating energy consumption for handling equipment at intermodal terminals. The results we obtained align closely with the international literature, as evidenced by the case study findings and sensitivity analysis.

However, due to the algorithm’s complexity, certain factors influencing the energy consumption of handling equipment were omitted. For instance, this study did not account for temporary handover zones (sometimes referred to as “handshake areas”) between gantry cranes. These zones facilitate the transfer of containers between two cranes while minimizing interference and collision risk, which can slightly impact equipment performance and energy consumption. Incorporating this factor in future analyses may provide even more precise results.

In the future, it will be necessary to examine additional factors, such as acceleration times for handling equipment motors, operating speeds, motor efficiency, peaks in container deliveries, and the changing distribution of operations at intermodal terminals. Even at this stage, sensitivity analysis has revealed discrepancies in the results, underscoring the need for further investigation.

The current model allows for similar analyses to be conducted for both satellite terminals and hubs of various sizes and service profiles. Ultimately, the algorithm could form the basis of a computer application. This application would enable users to select parameters from a database through an intuitive interface, facilitating calculations of unit and total energy consumption, energy costs, CO₂ emissions, and levels of energy recuperation (to be incorporated into future formulae).

Such a model and application could lead to innovative tools for dimensioning and optimizing logistics processes and their energy intensity in internal transport. These advancements would represent a significant contribution to the literature on logistics and internal transport management.

In addition to further refining energy consumption analyses for handling equipment, a comprehensive methodology for estimating energy demands at intermodal terminals must address other operational aspects. These include energy requirements for less energy-intensive processes such as vehicle weighing, office operations, and control system functionalities. Only then can the methodology for calculating total terminal energy demand be considered complete.

Addressing these challenges will require a detailed understanding of the energy requirements of electric HGVs, based on field tests documented in the literature. These tests emphasize the discrepancies between manufacturer-provided specifications and real-world performance under operational conditions. Additionally, it will be necessary to develop charging cycle models tailored to electric HGVs serving the terminal. Such models should account for the terminal’s catchment area, typical vehicle movement patterns, and charging schedules for drayage operations. Operational parameters, including peak periods and load balancing, must also be integrated to optimize the placement and capacity of charging stations.

Developing a model to estimate energy consumption at an intermodal terminal was highly time-intensive due to the complexity of energy consumption formulae, the cycle times of individual machines, and the power required to overcome motion resistance. Additionally, acquiring certain machine data—such as engine rotational speed, acceleration, and moment of inertia—proved challenging, as these parameters are often proprietary to manufacturers. The model’s complexity is further amplified by the diversity of machinery, the extensive calculations that are required, and the numerous parameters affecting the outcomes. By incorporating these elements into the current model, it will be possible to refine energy consumption estimations while also providing valuable insights for optimizing terminal design in terms of both operational and energy efficiency. This approach has the potential to establish a comprehensive framework for planning energy infrastructure at intermodal terminals.

Author Contributions

Conceptualization, M.B. (Mariusz Brzeziński); methodology, M.B. (Mariusz Brzeziński); formal analyses, M.B. (Mariusz Brzeziński); data curation, M.B. (Michał Budzik); original draft preparation, M.B. (Mariusz Brzeziński) and J.A.; visualization, M.B. (Michał Budzik); project administration, D.P.; supervision, D.P. and J.A.; writing—review and editing, D.P. and J.A.; funding acquisition, D.P. and J.A. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded from 82/2024 Open Science Program as part of the implementation at the Warsaw University of Technology of the project “Initiative of Excellence—research university” as well as the College of Business Administration, Warsaw School of Economics. Funding institution: Ministry of Education and Science.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analysis, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Glossary

CPK Company (Centralny Port Komunikacyjny)	company in Poland responsible for railway infrastructure design
HGV	heavy-duty truck
handling cycle duration	the time during which the handling equipment performs all the movements necessary to handle one container
RMG	rail-mounted gantry crane
RTG	rubber-tired gantry
AGV	automated guided vehicle
ITU	intermodal transport unit
TEU	twenty-foot equivalent unit
$T_{r}$	the handling time of the $r - t h$ piece of handling equipment
$t_{1}^{r}$	time for the $r - t h$ machine to drive to the loading point
$t_{2}^{r}$	time for the $r - t h$ machine to lift the load $t_{3}^{r} —$ time for the $r - t h$ machine to drive to the unloading point
$t_{4}^{r}$	time for the $r - t h$ machine to lower the load
$t_{5}^{r}$	time for the $r - t h$ machine to return to the starting point
$d_{z, r}^{E}$	drive distance of the $z - t h$ component of the $r - t h$ crane when empty
$d_{z, r}^{F}$	drive distance of the $z - t h$ component of the $r - t h$ crane when full
$v_{z, r}^{E}$	drive speed of the $z - t h$ component of the $r - t h$ crane when empty
$v_{z, r}^{F}$	drive speed of the $z - t h$ component of the $r - t h$ crane when full
$t_{W}^{r}$	$r - t h$ machine standstill for loading/unloading
$t_{E}^{r}$	$r - t h$ machine drive time when empty
$t_{F}^{r}$	$r - t h$ machine drive time when full
$d_{E}^{r}$	length of distance travelled when the $r - t h$ machine is empty
$v_{E}^{r}$	drive speed when the $r - t h$ machine is empty
$d_{F}^{r}$	length of distance travelled when the $r - t h$ machine is full
$v_{F}^{r}$	drive speed when the $r - t h$ machine is full
$t_{f z}^{r}$	average time required for the $r - t h$ machine to dock/undock one container to/from the spreader
$t_{s a}^{r}$	time required for the $r - t h$ machine to handle containers (lifting and horizontal movements) during storage and retrieval from the stacking yard
$t_{t t}^{r}$	time required for the $r - t h$ machine to transport the container from the stacking (storage) yard to the loading place
$T L$	terminal working hours
$σ_{r}^{P R}$	practical performance coefficient of the $r - t h$ machine
$σ_{r}^{T E C}$	technical performance coefficient of the $r - t h$ machine
$M_{r}$	the number of $r - t h$ machines required to handle a given container throughput
$K_{p}^{r}$	number of containers subject to the $p - t h$ transition and transhipped through the $r - t h$ machine
$m_{r, p}$	number of operations carried out by the $r - t h$ machine in the $p - t h$ transition through the terminal
$P_{i, r}$	power of the $i - t h$ motor required to overcome the given motion resistance for the $r - t h$ machine (in the given example, $P_{i, r} = \sum_{z} P_{i, z, r})$
$P_{i, z, r}$	power generated for the $i - t h$ engine power of the $z - t h$ component of the $r - t h$ gantry crane
$F_{i, z, r}$	force required to overcome resistance to motion on the $z - t h$ component of the $r - t h$ machine, calculated for the $i - t h$ motor
$v_{z, r}^{E / F}$	speed of motion of the $z - t h$ component of the $r - t h$ machine, working empty or full
$η_{z, r}$	efficiency of the $z - t h$ component of the $r - t h$ machine
${n k}_{z, r}^{E / F}$	engine rotating speed of the $z - t h$ component of the $r - t h$ machine, working empty or full
${M K}_{i, z, r}$	engine torque on the $r - t h$ crane’s $z - t h$ component, required to calculate the $i - t h$ engine power
$m c$	mass of the lifted container
$f$	rolling resistance of the crane wheels
$W_{z, r}$	mass of the $z - t h$ component of the $r - t h$ machine
$A_{z, r}$	effective frontal area of the component under consideration for the $r - t h$ machine and its $z - t h$ component
$c_{z, r}$	shape coefficient in the direction of the wind for the component under consideration for the $r - t h$ machine and its $z - t h$ component
$q_{z, r}$	wind pressure corresponding to the appropriate design condition for the $r - t h$ machine and its $z - t h$ component
${t α}_{z, r}$	acceleration time for the $r - t h$ machine and its $z - t h$ component
${J O}_{z, r}$	moment of inertia of the rotating masses (including engines, brake sheaves, couplings, and gearbox, reduced) for the $r - t h$ machine and its $z - t h$ component
$ω_{z, r}$	angular speed for the $r - t h$ machine and its $z - t h$ component
$P_{W}^{r}$	engine power of the $r - t h$ machine generated when waiting
$P_{E}^{r}$	engine power of the $r - t h$ machine generated when traveling empty
$P_{F}^{r}$	engine power of the $r - t h$ machine generated when traveling full
$t_{W}^{r}$	total time of the $r - t h$ machine spent waiting
$t_{E}^{r}$	total time of the $r - t h$ machine spent traveling empty
$t_{F}^{r}$	total time of the $r - t h$ machine spent traveling with the container
$P_{I C}^{r}$	power output of the internal combustion engine of the $r - t h$ machine
$t_{I C}^{r}$	operational time using the internal combustion engine of the $r - t h$ machine
$η_{I C}^{r}$	efficiency of the internal combustion engine
$P_{E L}^{r}$	power output of the electric system of the $r - t h$ machine
$t_{E L}^{r}$	operational time using the electric system of the $r - t h$ machine
$η_{E L}^{r}$	efficiency of the electric system of the $r - t h$ machine
$E_{R E C}^{r}$	Energy recovered from the regenerative systems (e.g., braking or load lowering) of the $r - t h$ machine
$λ^{j}$	average number of train pairs per day in the $j - t h$ scenario
$u^{t l}$	share of global pick-up/delivery traffic in a given hour $t l - t h$
$L K$	average number of containers per train
$ϕ$	average train load factor
$γ$	critical equipment threshold to maximum capacity
${B H}_{r, s}^{m a x}$	maximum number of $r - t h$ machines that can operate at the $s - t h$ terminal
${D F}_{r, s}$	handling yard length dedicated to the $r - t h$ machine’s operation at the $s - t h$ terminal
${K R}_{r, s}^{m i n}$	minimum working aisle length required for the $r - t h$ machine’s operation at the $s - t h$ terminal
$K_{p, s}^{j}$	number of containers involved in the $p - t h$ transition through the $s - t h$ terminal in the $j - t h$ scenario with average daily throughput
${K H}_{p, s}^{j}$	number of containers involved in the $p - t h$ transition through the $s - t h$ terminal in the $j - t h$ scenario with average peak throughput
${F D}_{p, s}^{r}$	share of containers involved in the $p - t h$ transition through the $s - t h$ terminal for $r - t h$ machine
$α$	peak coefficient
${M C}_{s, j}^{r}$	number of $r - t h$ machines required to handle the given container throughput
$M Z_{s, j}^{r, t l}$	number of $r - t h$ machines required during the $t l - t h$ hour, in the $j - t h$ terminal workload scenario, with average daily throughput
$P_{i, z, r}^{E}$	power used by the $i - t h$ engine power of the $z - t h$ component of the $r - t h$ crane when operating empty
$P_{i, z, r}^{F}$	power used by the $i - t h$ engine power of the $z - t h$ component of the $r - t h$ crane when operating full
$P_{W}^{r}$	power used by an AGV $(r - t h$ ) machine during standstill
$P_{E}^{r}$	power used when the $r - t h$ machine is driving empty
$P_{F}^{r}$	power used when the $r - t h$ machine is driving full
$E_{C C}^{r, j}$	energy consumed per working day by all $r - t h$ machines installed at the intermodal terminal operating at a constant workload in the $j - t h$ scenario
$E_{S T}^{r, j}$	energy consumed per working day by all $r - t h$ machines installed at the intermodal terminal operating at a variable workload in the $j - t h$ scenario

Appendix A

Table A1. Overview of specific parameters for selected terminal.

Parameter	Unit	Value
Average number of train pairs per day in the $j - t h$ scenario $(λ^{j})$	train pairs/day	variable
Terminal working hours $(T L)$	h/day	24
Share of global pick up/delivery traffic in a given hour $t l - t h$ $(u^{t l})$	%	$u^{t l} = \{\begin{matrix} {t l = < 6,15 >; u}^{t l} = 5.5 % \\ {t l = {5}; u}^{t l} = 5 % \\ {t l = \{16\}; u}^{t l} = 4.5 % \\ {t l = \{4,17,18\}; u}^{t l} = 4 % \\ {t l = \{19\}; u}^{t l} = 3.5 % \\ {t l = \{3,20,21,22\}; u}^{t l} = 3 % \\ {t l = \{1,2, 23,24\}; u}^{t l} = 2 % \end{matrix}$
Average number of containers per train $(L K)$	containers/train	70
Average train load factor $(ϕ)$	%	90
Critical equipment threshold to maximum capacity $(γ)$	%	90
The number of operations carried out by the $r - t h$ machine during the p $- t h$ transition $(m_{r, p})$	-	$m_{r, p} = \{\begin{matrix} r = 1, p = \{\{1\} \cup < 7,10 >\}; m_{r, p} = 1 \\ r = 1, p = 2; m_{r, p} = 1 \\ r = 2, p = \{7,9\}; m_{r, p} = 1 \\ r = 2, p = \{8,10\}; m_{r, p} = 2 \end{matrix}$

Table A2. Parameters used for calculating cycle duration of handling equipment.

Parameter	RMG	RTG	AGV
Drive distance (gantry) $(d_{1, r}^{E}, d_{1, r}^{F} [m])$	375 (for 1xRMG) 187.5 (for 2xRMG) 125 (for 3xRMG) 93.75 (for 4xRMG)	375 (for 2xRTG) 187.5 (for 4xRTG) 125 (for 6xRTG) 93.75 (for 8xRTG)	-
Drive distance (trolley) $(d_{2, r}^{E}, d_{2, r}^{F} [m])$	22.5	17.5	-
Lifting height (hoist) $(d_{3, r}^{E}, d_{3, r}^{F} [m])$	12	12	-
Drive speed (gantry) $(v_{1, r}^{E}, v_{1, r}^{F} [m / s])$	2.5/2	2.25/1.5	-
Drive speed (trolley) $(v_{2, r}^{E}, v_{2, r}^{F} [m / s])$	2.5/2	1.27/1.17	-
Lifting speed (hoist) $(v_{3, r}^{E}, v_{3, r}^{F} [m / s])$	1.5/0.75	1.03/0.52	-
Drive distance along the loading front ${(d}_{r}^{E}, d_{r}^{F})$	-	-	0/432.5
Drive distance along the loading front ${(v}_{r}^{E}, v_{r}^{F})$	-	-	5.83/3.5
Technical $(σ_{r}^{T E C})$ and practical ${(σ}_{r}^{P R})$ efficiency coefficient	0.9/0.9	0.9/0.9	0.9/0.9

Source: authors’ own study, inspired by the approach outlined in [1,17].

Table A3. Number of machines required for each scenario.

$Terminal Workload Scenario (j)$	$Train Pairs in the j - t h$ $Scenario (λ^{j})$	$RMGs ({M C}_{2, j}^{1})$	$RTGs (M Z_{2, j}^{2, 6})$	$AGVs ({M C}_{2, j}^{3})$
1	11	4	8	4
2	10	4	8	4
3	9	4	8	4
4	8	4	8	3
5	7	3	6	3
6	6	3	6	3
7	5	3	6	2
8	4	3	4	2
9	3	2	4	2
10	2	2	4	1
11	1	1	2	1

Table A4. Parameters of individual components of handling equipment.

Parameter	RMG	RTG	AGV
Efficiency of the r $- t h$ crane’s $z - t h$ component ${(η}_{z, r})$	$η_{1,1} = 0.87$ $η_{2,1} = 0.9$ $η_{3,1} = 0.9$	$η_{1,2} = 0.87$ $η_{2,2} = 0.9$ $η_{3,2} = 0.9$	-
Handled container mass $(m c [k g])$	15,000	15,000	15,000
Mass of the r $- t h$ crane’s $z - t h$ component ${(W}_{z, r} [k g])$	$W_{1,1} = 185,000$ $W_{2,1} = 25,000$ $W_{3,1} = 10,000$	$W_{1,2} = 117,500$ $W_{2,2} = 22,500$ $W_{3,2} = 8000$	-
Engine torque when empty $({n k}_{z, r}^{E} [r p m])$	${n k}_{1,1}^{E} = 225$ ${n k}_{2,1}^{E} = 140$ ${n k}_{3,1}^{E} = 360$	${n k}_{1,2}^{E} = 225$ ${n k}_{2,2}^{E} = 140$ ${n k}_{3,2}^{E} = 360$	-
Engine torque when full $({n k}_{z, r}^{F} [r p m])$	${n k}_{1,1}^{F} = 200$ ${n k}_{2,1}^{F} = 140$ ${n k}_{3,1}^{F} = 180$	${n k}_{1,2}^{F} = 200$ ${n k}_{2,2}^{F} = 140$ ${n k}_{3,2}^{F} = 180$
Moment of inertia $({J O}_{z, r} [k g \cdot m^{2} \cdot 10^{- 3}])$	${J O}_{1,1} = 0.16$ ${J O}_{2,1} = 0.06$ ${J O}_{3,1} = 2.3$	${J O}_{1,2} = 0.16$ ${J O}_{2,2} = 0.06$ ${J O}_{3,2} = 2.3$	-
Acceleration time $({t α}_{z, r} [m / s^{2}])$	${t α}_{1,1} = 10$ ${t α}_{2,1} = 3.89$ ${t α}_{3,1} = 1.25$	${t α}_{1,2} = 9$ ${t α}_{2,2} = 4$ ${t α}_{3,2} = 4.5$	-
AGVs’ engine power generated when waiting for loading $(P_{w}^{r} [k W])$	-	-	9
AGVs’ engine power generated when travelling empty and full $(P_{E}^{r} / P_{F}^{r} [k W])$	-	-	14/16

Source: authors’ own study, inspired by the approach outlined in [42].

Table A5. Parameters for sensitivity analysis.

Variant	Parameter Value	Parameter Value	Parameter Value
0	$m c = 15,000$ $W_{1,1} = 185,000, W_{1,2} = 117,500$ $W_{2,1} = 25,000, W_{2,2} = 22,500$ $W_{3,1} = 10,000, W_{3,2} = 8000$	$d_{1,1}^{E}, d_{1,1}^{F}, d_{1,2}^{E}, d_{1,2}^{F} = \{\begin{matrix} 375 (f o r 1 x R M G, 2 x R T G) \\ 187.5 (f o r 2 x R M G, 4 x R T G) \\ 125 (f o r 3 x R M G, 6 x R T G) \\ 93.75 (f o r 3 x R M G, 6 x R T G) \end{matrix}$ $d_{3,1}^{E}, d_{3,1}^{F}, d_{3,2}^{E}, d_{3,2}^{F} = 12$ $d_{2,1}^{E}, d_{2,1}^{F} = 22.5, d_{2,1}^{E}, d_{2,1}^{F} = 17.5$	${n k}_{1,1}^{E} = 225, {n k}_{1,2}^{E} = 225$ ${n k}_{2,1}^{E} = 140, {n k}_{2,2}^{E} = 140$ ${n k}_{3,1}^{E} = 360, {n k}_{3,2}^{E} = 360$ ${n k}_{1,1}^{F} = 200, {n k}_{1,2}^{F} = 200$ ${n k}_{2,1}^{F} = 140, {n k}_{2,2}^{F} = 140$ ${n k}_{3,1}^{F} = 180, {n k}_{3,2}^{F} = 180$
1	$m c = 12,000$ $W_{1,1} = 148,000, W_{1,2} = 94,000$ $W_{2,1} = 20,000, W_{2,2} = 18,000$ $W_{3,1} = 8000, W_{3,2} = 6400$	-	-
2	-	$d_{1,1}^{E}, d_{1,1}^{F}, d_{1,2}^{E}, d_{1,2}^{F} = \{\begin{matrix} 300 (f o r 1 x R M G, 2 x R T G) \\ 150 (f o r 2 x R M G, 4 x R T G) \\ 100 (f o r 3 x R M G, 6 x R T G) \\ 75 (f o r 3 x R M G, 6 x R T G) \end{matrix}$ $d_{3,1}^{E}, d_{3,1}^{F}, d_{3,2}^{E}, d_{3,2}^{F} = 9.6$ $d_{2,1}^{E}, d_{2,1}^{F} = 18, d_{2,2}^{E}, d_{2,2}^{F} = 14$	-
3	-	-	${n k}_{1,1}^{E} = 270, {n k}_{1,2}^{E} = 270$ ${n k}_{2,1}^{E} = 168, {n k}_{2,2}^{E} = 168$ ${n k}_{3,1}^{E} = 432, {n k}_{3,2}^{E} = 432$ ${n k}_{1,1}^{F} = 240, {n k}_{1,2}^{F} = 240$ ${n k}_{2,1}^{F} = 168, {n k}_{2,2}^{F} = 168$ ${n k}_{3,1}^{F} = 216, {n k}_{3,2}^{F} = 216$

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Figure 1. (a) ITUs/TEUs carried; (b) transport work and cargo volumes in intermodal transport in 2012–2023. Source: authors’ own study, inspired by the approach outlined in [2,3].

Figure 2. A layout of a satellite terminal (a) and a hub integrated with a satellite terminal (b) for lift-on/lift-off container transshipments [53].

Figure 3. Container flow through the handling system of an intermodal terminal.

Figure 4. Measurement system diagram [43].

Figure 5. Energy consumption estimation model for handling equipment.

Figure 6. Required designations for calculating gantry crane handling cycle durations.

Figure 7. The container transition path through an intermodal terminal: (a) delivery service; (b) pick-up service.

Figure 8. Layout of handling area.

Figure 9. The number of cranes operating in each of the intermodal terminal’s scenarios.

Figure 12. The daily energy consumption of (a) gantry cranes (b) AGVs with a fixed workload during the working day.

Figure 13. The daily consumption of machinery operating with a variable workload during the working day.

Figure 14. Energy consumption over the course of a day.

Figure 15. Sensitivity analysis for RTGs (a) and RMGs (b).

Table 1. Breakdown of handling equipment by type of available power supply.

	Energy Source
Energy Consumer	Diesel	Petrol	Gas	Electricity
Ship-to-shore gantry	$\lor$	-	-	$\lor$
Mobile crane	$\lor$	-	-	$\lor$
Rail-mounted gantry	$\lor$	-	-	$\lor$
Reachstacker	$\lor$	-	-	$\lor$

Source: [43].

Table 2. Overview of input parameters for terminal design.

Parameter	Unit
Average number of train pairs per day in the $j - t h$ scenario $(λ^{j})$	train pairs/day
Terminal working hours $(T L)$	h/day
Share of global pick-up/delivery traffic in a given hour $t l - t h (u^{t l})$	%
Average number of containers per train $(L K)$	containers/train
Average train load factor $(ϕ)$	%
Critical equipment threshold to maximum capacity $(γ)$	%

Table 3. Overview of specific transitions at the terminal.

$Type of Transition (p)$	$Share of Containers ({F D}_{p, s} [%])$	$Type of Transition (p)$	$Share of Containers ({F D}_{p, s} [%])$
$p = 1$	10	$p = 8$	25
$p = 2$	20	$p = 9$	10
$p = 7$	10	$p = 10$	25
Total	100%

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Brzeziński, M.; Pyza, D.; Archutowska, J.; Budzik, M. Method of Estimating Energy Consumption for Intermodal Terminal Loading System Design. Energies 2024, 17, 6409. https://doi.org/10.3390/en17246409

AMA Style

Brzeziński M, Pyza D, Archutowska J, Budzik M. Method of Estimating Energy Consumption for Intermodal Terminal Loading System Design. Energies. 2024; 17(24):6409. https://doi.org/10.3390/en17246409

Chicago/Turabian Style

Brzeziński, Mariusz, Dariusz Pyza, Joanna Archutowska, and Michał Budzik. 2024. "Method of Estimating Energy Consumption for Intermodal Terminal Loading System Design" Energies 17, no. 24: 6409. https://doi.org/10.3390/en17246409

APA Style

Brzeziński, M., Pyza, D., Archutowska, J., & Budzik, M. (2024). Method of Estimating Energy Consumption for Intermodal Terminal Loading System Design. Energies, 17(24), 6409. https://doi.org/10.3390/en17246409

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Method of Estimating Energy Consumption for Intermodal Terminal Loading System Design

Abstract

1. Introduction

2. Literature Review

2.1. Energy Consumption Aspects in Intermodal Transportation

2.2. Designing of Intermodal Terminals

2.3. Estimating Energy Consumption of Handling Equipment

3. Energy Consumption Estimation Model for Handling Equipment

4. Case Study and Results

4.1. Algorithm Implementation, Calculations, and Results

4.1.1. Stage I

4.1.2. Stage II

4.1.3. Stage III

4.2. Sensitivity Analysis

5. Discussion

6. Conclusions

Author Contributions

Funding

Data Availability Statement

Conflicts of Interest

Glossary

Appendix A

References

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