A Monte Carlo Based Method for Assessing Energy-Related Operational Risks in Railway Undertakings

Abstract

The main task of a railway undertaking is to transport passengers and/or freight safely and cost-effectively. This task is enabled by the use of energy carriers. Since most of the rolling stock operated by major railway undertakings is electric, an additional area of activity involves managing electricity consumption and supply processes. Every business activity entails risk, including energy-related operations. The aim of this paper is to develop a method for assessing the risks associated with a railway undertaking from an electrical perspective and, based on this method, to perform such an assessment. As part of the research, a universal risk assessment approach based on the M_o_R^® (Management of Risk) methodology was developed. Risk identification was performed using the risk description principle, followed by risk estimation. The study proposes national-level variables and a procedure for determining them using publicly available data. Risk assessment and process evaluation were carried out using Monte Carlo simulation as a probabilistic tool for uncertainty propagation. As a result, the potential losses and gains that a railway undertaking may experience from an electrical perspective were estimated for scenarios in which the identified risks materialize.

1. Introduction

The main task of a railway undertaking (railway company, transport operator) is to transport passengers and/or freight. The effective implementation of transport tasks requires the acquisition and conversion of energy, primarily for traction purposes. In 2024, the share of electric rolling stock in the total fleet of traction vehicles in Poland reached approximately 78.4% [1]. This indicates that the vast majority of traction vehicles operating on the Polish railway market are powered by electricity. Consequently, the activities of railway undertakings also include the management of electricity consumption and supply processes. In addition to high electricity prices, these activities are driven by the European Union’s climate policy (climate neutrality) and regulatory requirements.

As already mentioned, a railway undertaking not only transports passengers and/or freight (operating in the transport market) but also functions as an electricity consumer within the energy market. From an electrical perspective, three fundamental aspects of railway undertaking operations can be distinguished:

• Technical capabilities for transport operations—electricity enables efficient and reliable railway operations; deficits in availability (e.g., power outages), inadequate quality (e.g., significant voltage drops at the ends of sections supplied from different traction substations), or reduced technical parameters (e.g., during adverse weather conditions) may negatively affect railway operations; these impacts may manifest as reduced rolling stock reliability, lower punctuality of train services, and potential safety degradation, directly leading to financial losses for railway undertakings; such effects may be mitigated through advanced technologies in railway traffic organization (timetabling) and railway traffic control;
• Economic efficiency of the company—energy costs account for approximately 21.8% of the total operating costs of a railway undertaking [1], making them a significant cost component; railway operators therefore seek to reduce these costs through effective energy management measures, including monitoring actual energy consumption [2] (e.g., installation of on-board energy meters), the use of energy-saving systems [3], and regenerative braking; operators may also influence energy-related costs through the selection of energy suppliers and contractual arrangements for electricity procurement;
• Environmental and social profile of the company—the use of electricity as a traction energy carrier contributes to the implementation of the European Union’s climate policy; as a result, railway undertakings participate in the decarbonization of the transport sector [4] and operate in accordance with the principles of sustainable development.

As profit-oriented enterprises, railway undertakings must conduct their activities with full awareness of opportunities and threats arising in both the transport and energy markets. For this reason, research addressing the role of energy-related aspects in railway operations is justified. One effective tool for such analyses is risk assessment. It should be noted that, in this study, energy security is not assessed at the system level, but is reflected indirectly through its operational and cost-related consequences for railway undertakings.

The aim of this article is to develop a method for assessing the risk of railway undertaking operations from an electrical perspective and to apply this method in practice. To achieve this objective, the following structure is adopted. Section 2 provides a review of the relevant literature. Section 3 develops a method for assessing energy-related operational risks of railway undertakings based on the Management of Risk (M_o_R^®) methodology [5]. The methodological framework and assumptions for risk identification and assessment are presented. Section 4 reports the results of the risk identification, estimation, and evaluation. Section 5 presents a holistic assessment of risk exposure, while Section 6 summarizes the main findings and conclusions.

2. Railway Undertaking Operations from an Electrical Perspective: A Literature Review

This article addresses two main areas of research. The first area of research concerns the activities of railway undertakings from an electrical perspective. First, EU legislation must be considered. The energy subsystem [6] is one of the structural subsystems of the European Union’s railway system. Therefore, Technical Specifications for Interoperability (TSI) [7] have been developed for it. This document contains all the technical information necessary to implement railway interoperability in the EU with regard to energy. Railway operators should take into account the provisions of the TSI, in particular regarding the interoperability of the energy subsystem, in their activities. It should be noted that it is important to distinguish between system elements that are directly controllable by the railway undertaking and those that depend on the infrastructure manager (IM). The railway undertaking is responsible for managing its energy consumption, contracts, and on-board metering, while the infrastructure manager is responsible for power supply continuity, quality, and system design. It should be noted that these are not the only relevant normative documents. Other requirements relating to rolling stock are contained in a number of European standards (concerning, among other issues of electromagnetic compatibility and traction system parameters).

There are many publications in the literature dealing generally with the electric railway transport system. The principles of operation of electric railway transport systems were presented by Brenna et al. [8]. On the other hand, the basics of railway system operation from the point of view of management and engineering, including from an electrical perspective, were presented by Profillidis [9].

Feng et al. [10] presented general considerations regarding traction energy savings in rail transport. They identified the factors affecting energy costs, discussed ways to control costs, and indicated what can be done to reduce costs in the areas of track construction, train traffic, and railway system operation. Similar considerations were presented by Kawasaki et al. [11] and Mierzejewski et al. [12]. The analysis covered many points of view, which are sometimes contradictory. Douglas et al. [13] presented possible measures that could be taken to reduce traction energy consumption in railway networks and critically evaluated them.

Ren et al. [14] conducted an analysis of factors that influence electricity consumption. The study was based on real operational data for electric traction units. They developed mathematical relationships that allow the amount of energy consumed to be estimated. Similar research was conducted by Wang et al. [15]. Feng et al. [16] presented a method for assessing traction power supply capacity and voltage quality, which allows for the assessment of the situation in terms of the absence of power interruptions.

One of the most effective methods of saving energy is its recuperation. This process involves returning the electrical energy obtained during braking to the traction network or to energy storage devices installed on the vehicle. This makes it possible to reuse the recovered energy for propulsion purposes. Research in this area has been conducted by Lingaitis et al. [17] and Urbaniak et al. [18], as well as Bartłomiejczyk et al. [19].

Gołębiowski et al. [20] analyzed the process of organizing freight rail transport. When selecting the most advantageous transport service option, they took into account energy and environmental aspects—they examined the amount of energy consumed to perform the transport and the amount of harmful emissions during transport. Dolinayová et al. [21] conducted an analysis of the economic efficiency of changing from electric to diesel traction vehicles and vice versa when entering from electrified to non-electrified infrastructure. They noted that, in freight transport, operators sometimes use two locomotives (electric and diesel) within the same consist. In the case of passenger transport, however, the locomotive is usually changed. Currently, a gradual hybridization process is taking place, and two vehicles with different drives are being replaced by a single dual-drive vehicle.

It should be noted that railway undertakings may build and manage a service facility whose function may be related to fuel (energy) issues. According to the law, it must be accessible to all interested parties on the basis of equal access. Stolorz [22] describes the activities of a railway operator related to the operation of a service infrastructure facility dedicated to electrical issues. During the construction or modernization of railway lines, the problem of choosing the right power supply system may arise. Szeląg et al. [23] proposed a multi-criteria method to support decision-making in this matter.

An important element in the activities of a railway undertaking from an electrical perspective is the issue of energy efficiency [24] and sustainable transport development. Scientific research on energy efficiency in rail transport is also being conducted as part of Europe’s Rail project [25]. A report prepared by UIC and UNIFE contains an assessment of energy consumption in rail transport, ways to improve efficiency, and energy-saving strategies. UIC publishes statistics on energy efficiency and carbon dioxide emissions in rail transport [26].

Alfieri et al. [27] proposed a concept of energy efficiency for the rail transport sector. This concept is mainly applicable when modernizing railway lines or constructing new ones. It assumes the appropriate placement of electrical equipment along the railway line so that the power of the substation is sufficient for the needs of railway traffic. This issue is related to the rational arrangement of the train timetable. By implementing optimization measures, it is possible to achieve a situation where when one train brakes (and electricity is fed back into the grid during the recuperation process), another train will start up. Research in this area has been conducted by Urbaniak et al. [18,28] and Kierzkowski et al. [29]. Rational energy consumption can also be achieved through the application of appropriate railway traffic control principles (see Song et al. [30]). Energy efficiency can also be achieved by train drivers applying eco-driving principles. The key principle is to reduce energy consumption by using the appropriate driving technique. Ćwil et al. [31] conducted research that allowed them to conclude that the application of eco-driving principles will enable the implementation of the principles of sustainable development of the transport system.

Sitarz [32] presented a method for auditing the purchase of new rolling stock from the point of view of its operational efficiency and electricity consumption. This publication contains a number of guidelines for the purchase of new rolling stock, allowing for the provision of energy-efficient traction vehicles. The energy efficiency of a railway undertaking’s operations can be ensured by the use of on-board energy consumption measurement systems (EMS) in their traction vehicles, which are designed to transmit data to collective energy accounting systems. These solutions are promoted by the EU in various EU documents [7,33]. The European solutions used in this area are described by Van der Spiegel et al. [34].

Energy management is an important aspect of a railway carrier’s operations. The key document on this issue is ISO 50001 [3]. This standard regulates the implementation and improvement of energy management systems by companies. Its aim is to improve the energy efficiency of companies and reduce the costs associated with energy procurement and processing. One of its elements is to consider the risks associated with the energy activities of companies. This standard also emphasizes the integration of energy management with risk-based thinking, which aligns with the approach adopted in this study.

Davoodi et al. [35] reviewed the literature with a view to developing an energy management system for small railway networks. As part of their work, they reviewed optimization mathematical models that would allow for intelligent management of the railway network from the point of view of electricity consumption. Kuzior et al. [36] conducted a study on energy management by railway operators. They reviewed methods and their limitations in this area. Detailed research was conducted on the example of one of the Polish freight operators.

The second area of research is risk assessment in railway transport. In this context, risk assessment methods are essential not only for safety management but also for operational and economic decision-making in energy-dependent railway systems. The key document relating to risk in rail transport is Directive 2016/798 on railway safety [37], which contains uniform methods for monitoring, conformity assessment, supervision, and risk assessment and evaluation. This directive establishes common safety methods (CSMs), one of which concerns risk assessment and evaluation methods [38]. A detailed description of these methods is provided by Gołębiowski in [39]. The same source also provides a comparison of the methods proposed in the regulation [38] with the M_o_R^® methodology [5]. In addition, The Office of Rail Transport (Polish National Safety Authority) has published a guide [40], referring to regulation [38], containing recommendations for the use of various methods of risk assessment and evaluation at a specific stage. Due to the fact that the subject of the article concerns an electrical perspective, further considerations will be conducted with regard to this topic.

Licciardello et al. [41] conducted a general review of risk analysis. They noted that, at the time of writing (2014), it was mainly used in air transport. They therefore reviewed the methods that could be used in rail transport. They identified the limitations and opportunities associated with this. Andrić et al. [42] and Macura et al. [43] focused their considerations on identifying risks occurring in railway projects.

An important trend in the literature is the issue of risk assessment in relation to rail transport organizations (e.g., An et al. [44]). Work in this area has been carried out by, among others, Dinmohammadi et al. [45] in the field of rolling stock failures and Gołębiowski et al. [46] in the field of rolling stock work planning. Szaciłło et al. [47] conducted considerations with regard to the organization of freight transport. Nedeliakova et al. [48] noted that sustainable development in rail transport services can be achieved by applying the Lean philosophy to risk management.

Lin et al. [49] assessed the risk of the traction power supply system. This assessment was carried out for high-speed rail lines, where the power supply system is subjected to high loads. The research was conducted for a 24 h period of the timetable. The article resulted in a risk assessment concerning the impact on the implementation of the train timetable. Feng et al. [50] conducted a risk assessment for the electric traction system in rail transport. They took into account geographical and meteorological factors.

The literature contains publications referring to risk assessment in relation to the railway traffic control system. Ciszewski et al. [51] assessed the risk of damage to the power supply system from the point of view of railway traffic control devices. Feng et al. [52] assessed the risk of electromagnetic compatibility for high-speed railways from the perspective of the on-board signaling system.

An important group of studies concerns risk assessment from the point of view of safety [53]. Matsika et al. [54] conducted analyses of the risk of a terrorist attack on a train. Kyriakidis et al. [55] analyzed the risk of an accident in the subway.

In addition to technical and operational aspects, the energy-related risk profile of a railway undertaking is significantly influenced by market and contractual factors (Alston [56]). The volatility of wholesale electricity prices, the differences between long-term contract tariffs and short-term spot market rates, and the growing share of imbalance settlements in energy billing expose operators to financial and procurement risks (Eriksson et al. [57], Leśniak et al. [58]). Furthermore, changes in network tariffs and capacity charges affect the predictability of operating costs. Contractual clauses defining energy supply conditions (e.g., indexation formulas or minimum consumption thresholds) may also create risk exposure that cannot be fully mitigated through operational measures (Ait Ali et al. [59]).

It should be emphasized that the approach adopted in this study is consistent with the general principles of ISO 31000 [60] and IEC 31010 [61], which recommend the use of probabilistic methods such as Monte Carlo simulation for quantifying uncertainty.

The review of the existing literature reveals that while numerous studies address the efficiency of railway traction energy use, eco-driving techniques, or energy recovery, very few examine energy-related risks from the perspective of railway undertakings. Most publications focus either on the technical performance of the traction power supply system or on the application of general risk assessment frameworks, such as the Common Safety Method (CSM RA), to infrastructure management. In particular, no study to date has combined the Management of Risk (M_o_R^®) framework with probabilistic modeling using Monte Carlo simulation to quantify such risks under real-world national conditions from an electrical perspective. Therefore, this paper addresses a clear research gap by developing and applying a comprehensive and quantitative method for assessing energy-related risks in railway undertakings from an electrical perspective, integrating managerial and probabilistic approaches. The novelty of this study does not lie in the Monte Carlo method itself, which is a well-established analytical tool, but in its integration with a management-oriented risk identification framework (M_o_R^®) and in its application to the quantitative assessment of energy-related operational risks of railway undertakings using nationally reported aggregated data.

3. Method for Assessing the Risk of Railway Undertaking Operations from an Electrical Perspective

3.1. General Characteristics of the Method

This article focuses on the assessment of energy-related operational risks of railway undertakings from an electrical perspective. The electrical perspective refers to issues related to the acquisition and conversion of electrical energy for transport purposes, taking into account both rolling stock–related aspects and infrastructure-related aspects of rail transport. In order to do this, an assessment method must first be developed. As mentioned in the introduction to the article, the principles of the M_o_R^® (Management of Risk) methodology dedicated to risk management will be used for this purpose. According to this methodology, risk is an uncertain future event or set of events, which, if it occurs, will affect the achievement of objectives [5]. This impact can be both negative (in which case the event is a threat) and positive (in which case the event is an opportunity). According to the M_o_R^® methodology [5], the risk management process consists of four main steps:

• Identify: context (background of the problem) and risk (specific risks);
• Assess: estimate (estimating the probability, impact, and proximity of a given risk) and evaluate (evaluating the level of exposure to the risk of a given problem);
• Plan (develop a reaction to the materialization of risks);
• Implement (implement a reaction to risks and monitor the situation).

For the purposes of this article, it is assumed that risk assessment is included in the first two steps of the risk management method, i.e., identify and assess. Further considerations will only concern these steps.

For the purposes of assessing the risk of railway operators’ activities from an electrical perspective, a method was developed, the scheme of which is presented in Figure 1.

The first step of the method is to identify the process for which the risk assessment will be performed. The process analyzed in the article is the activity of a railway undertaking from an electrical perspective. In order to effectively assess the risk for the indicated process, it is proposed to decompose it into smaller components. For the purposes of this article, the decomposition consists of dividing the process into six areas and identifying and assessing the risk for each of them. The evaluation of the process will be conducted holistically. For the purposes of the assessment, the following risk groups (areas for which the risk was assessed) were identified:

• Risks related to rolling stock;
• Risks related to energy infrastructure;
• Risks related to technical facilities;
• Risks related to transport organization and operation;
• Risks related to energy purchases;
• Risks related to external factors.

A description of each group is provided in Section 3.2 of the article.

The second step of the method involves identifying risks for the decomposed process, i.e., the activities of a railway undertaking from an electrical perspective, divided into six areas (risk groups). The risk description principle recommended by the M_o_R^® methodology will be applied for this purpose [5]. It consists of indicating the following for each identified risk:

• Cause, i.e., an event that may cause a given risk to occur;
• Risk, i.e., an event which, if it occurs, may affect the achievement of the process objectives;
• Effect, i.e., the manner in which the process objectives are modified as a result of the materialization of a given risk.

The identification of risks for the analyzed process was carried out in Section 4.1.

The third step of the method is to estimate the risks for the decomposed process. Risk estimation is otherwise referred to as assessing the impact of individual risks on the process objective. According to the M_o_R^® methodology [5], it involves determining the probability of a given event (risk) occurring, its impact (the effect that a given risk may cause), and its proximity (the moment when the risk may occur) in order to determine the priority of a given risk. For the purposes of the research conducted in this article, the proximity assessment will be omitted. The authors of this article want the method developed to be as universal as possible and usable with publicly available data. For this reason, the impact assessment will be carried out by defining national variables, i.e., variables specific to a given country, which can be found in the mandatory reporting collected and published by various state authorities [1]—e.g., the national railway safety authority (in Poland, this is the Office of Rail Transport). Since the assessment covers profit-oriented companies, it would be best to use cost values. It is proposed to use five national variables, which method of determination is set out in Section 3.3 of this article. These variables are as follows:

• Total costs of the railway undertaking’s operations expressed in PLN/year;
• Costs related to delays generated by trains of individual undertakings expressed in PLN/year;
• Costs related to the deterioration of travel comfort expressed in PLN/year;
• Costs related to electricity consumption by trains expressed in PLN/year;
• Profits related to the use of recuperation in the railway system expressed in PLN/year.

These variables were selected because they reflect measurable and reportable indicators of a railway undertaking’s energy-related performance and financial exposure. The use of publicly available national data enhances transparency and comparability between operators. It should be noted that the obtained results represent aggregated sector-level risk exposure. For practical application, these values may be proportionally allocated to individual railway undertakings based on their share in national operational work, allowing operator-level interpretation without altering the methodological structure.

The probability assessment of the distribution will be presented in the form of a probability distribution of a given national variable. For each variable, characteristic values from the distribution are presented. Based on the research conducted so far, it is recommended to use a triangular probability distribution for all national variables [39,46]. This distribution was adopted due to the limited availability of continuous empirical data and the dominant share of estimated and expert data. For a triangular distribution, the characteristic parameters are as follows: minimum value, most likely value, and maximum value, which define bounded uncertainty intervals derived from national statistical reporting and expert assessment, rather than frequency-based probabilities. Risk estimation is presented in Section 4.2 of the article.

The fourth step of the method is to evaluate the risks, i.e., determine the level of exposure [5] of a given process area (from the perspective of the risks collected in the relevant group). This can be done using Equation (1):

$$\forall g\in \mathit{G}\hspace{1em}\forall r\in \mathit{R}\left(g\right)\hspace{1em}E\left(g,r\right)=P\left(g,r\right)\cdot I\left(g,r\right)$$

(1)

where

• G—set of risk group numbers,
• g—risk group number, g ∈ G, g ∈ ℕ,
• R(g)—set of risk numbers in group number g, g ∈ G,
• r—risk number, r ∈ ℕ,
• E(g,r)—expected value of risk number r belonging to group number g,
• P(g,r)—probability of occurrence of risk number r belonging to group number g,
• I(g,r)—impact of occurrence of risk number r belonging to group number g.

Probabilistic risk models, specifically the Monte Carlo method, will be used in the research conducted in this article. In this method, random values of national variables are generated for each element based on probability distribution and constraints. The generation is performed a specified number of times (a specified number of trials). On this basis, a risk assessment can be made. It is presented in Section 4.3 of this article. It should be noted that probability distributions are used to represent uncertainty in the magnitude of impacts, conditional on risk occurrence, rather than the probability of occurrence itself. The proposed approach does not replace classical probability—impact risk assessment, but complements it in contexts where occurrence frequencies cannot be reliably quantified.

The final step of the method is to evaluate the entire process from the point of view of risk exposure. In this case, considerations are made with regard to the entire process. This article discusses the activities of a railway operator from an electrical perspective, without dividing them into specific areas. It was assumed that a railway undertaking cannot incur multiple losses or make multiple profits valued using the same national variables. Therefore, from an energy perspective, it would be best to assess the activity as the sum of the values of national variables (losses were treated as positive values and profits as negative values for the purpose of aggregation) and then simulate them using the Monte Carlo method. This was performed in Section 5 of the article.

3.2. Assumptions for Risk Identification

As already mentioned in Section 3.1 of the article, in order to effectively assess the risks to the railway undertaking’s operations from an electrical perspective, these risks have been broken down into six areas, i.e., six risk groups. These are as follows:

• Risks related to rolling stock—this group of risks includes the consequences of electrical failures of traction vehicles that were assigned to operate a train and are no longer capable of continuing to operate, the consequences of the age of rolling stock (especially its electrical equipment), the consequences of damage to one or more traction vehicle components, which did not render them unfit for service, and failure to comply with eco-driving rules when driving traction vehicles;
• Risks related to energy infrastructure—this group of risks includes the consequences of damage to the catenary system at the operating control post or on the open line, the consequences of power supply interruptions in the catenary system, the consequences of power supply system overload, the consequences of the lack of energy recovery infrastructure, and the consequences of delays in the electrification of railway lines (consequences of not completing construction on time);
• Risks related to technical facilities—this group of risks includes the consequences of electrical failures in the technical facilities of railway undertakings, the consequences of using energy-intensive equipment in technical facilities, and the consequences of poor management of inventories of parts necessary for the repair of electric traction vehicles;
• Risks related to transport organization and operation—this group of risks includes the consequences of not having an electric traction vehicle with the appropriate parameters to operate a given train, the consequences of improper timetable scheduling from the point of view of energy recovery, excessive power consumption by electric traction vehicles, consequences of an electric traction vehicle breakdown at an operating control post or on the open line, and consequences of not installing eco-driving support devices in electric traction vehicles;
• Risks related to energy purchases—this group of risks includes the consequences of the economic situation in a given country and worldwide, especially on the energy market, and the consequences of delays in the electrification of railway lines (energy has been contracted but the infrastructure has not been built on time);
• Risks related to external factors—this group of risks includes the consequences of the economic situation in a given country and worldwide, especially on the energy market, the consequences of adverse weather conditions, the consequences of delays in the electrification of railway lines on the part of the contractor, and the consequences of a cyberattack on the power supply system.

This classification ensures that both internal (technical, organizational) and external (market, environmental) sources of risk are covered, allowing for a comprehensive evaluation of the railway undertaking’s exposure.

3.3. Assumptions for Risk Estimation

To determine the values of national variables, publicly available data published annually by the national railway transport safety authority, the Office of Rail Transport, was used. This body publishes a report on the functioning of the railway transport market in a given year [1], which contains a wealth of statistical data. The values of the adopted variables can be determined as follows.

• Total costs of the railway undertaking’s operations expressed in PLN/year

• The costs generated per passenger in 2024 amounted to 29.43 PLN/passenger [1].
• The number of passengers carried in 2024 amounted to approximately 407,533,000 passengers/year [1].
• Therefore, the total costs of passenger transport operations in 2024 amounted to approximately 12 billion PLN/year (11,993,696,190 PLN/year).
• The number of passenger trains operated in 2024 was 2,050,000 trains/year [1].
• As a result, the cost of operating a passenger train in 2024 was 5850.58 PLN/train.
• The operational work performed by passenger rail operators in 2024 amounted to 205,600,000 train-kilometers/year [1].
• Consequently, the distance traveled by passenger trains in 2024 amounted to 205,560,000 km/year.
• The average mileage of a passenger train is 100.29 km/train.
• The cost of operating one passenger train per kilometer in 2024 was 58.34 PLN/train-kilometer.
• Fuel accounts for 21.8% of the cost of operating a passenger train [1]—12.72 PLN/train-kilometer.
• Taking into account the average price of 1 MWh of energy needed for traction purposes (1400.9 PLN/MWh [1]) and the average price of m³ of fuel used for traction purposes (4874.2 PLN/m3 [1]), it can be estimated that the fuel component in the unit cost of operation can take a minimum value of 6.36 PLN/train-kilometer and a maximum value of 19.08 PLN/train-kilometer. This may result in the total costs of a passenger operator’s activities in 2024 ranging from 10,685,008,800 PLN/year to 13,299,732,000 PLN/year.

2.

Costs related to delays generated by trains of individual undertakings expressed in PLN/year

• The number of passenger trains operated in 2024 was 2,050,000 trains/year [1].
• The punctuality rate for passenger trains in 2024 was 91.64% [1].
• The number of passenger trains running late in 2024 was therefore 171,380 trains.
• The average delay time for passenger trains in 2024 was 8.7 min/train [1].
• Compensation for each minute of delay, which the party causing the delay must pay to the party affected by the delay, in accordance with the Network Statement of the largest railway infrastructure manager in Poland—PKP Polskie Linie Kolejowe S.A., amounted to 5.85 PLN/min [62].
• The maximum compensation amount in 2024 was therefore 8,722,382.1 PLN/year.
• In an ideal situation, trains would run on schedule, so the total compensation amount could be 0 PLN/year, and the average amount would be 4,361,191.05 PLN/year.

3.

Costs related to the deterioration of travel comfort expressed in PLN/year

• Operational work that should have been performed by passenger trains in 2024, but was performed by replacement bus services, amounted to 3,800,000 train-kilometer [1].
• The cost of operating one passenger train per kilometer in 2024 was 58.34 PLN/train-kilometer.
• The cost of operating trains to carry out the above-mentioned operational work in 2024 would amount to approximately 221,673,373.16 PLN.
• The cost per vehicle-kilometer for bus transport in Poland is approximately 15 PLN/vehicle-km. As a result, the cost of the above-mentioned transport service would amount to approximately 57,000,000 PLN.
• The cost of reducing travel comfort can therefore be expressed as the difference between the cost of transport by train and by bus, i.e., approximately 164,692,000 PLN/year.
• Taking into account fluctuations in the cost per vehicle-kilometer in bus transport, it can be assumed that the minimum cost of reducing comfort would be 145,692,000 PLN/year, and the maximum 183,692,000 PLN/year.

4.

Costs related to electricity consumption by trains expressed in PLN/year

• The total costs of passenger transport operations in 2024 amounted to approximately 12 billion PLN/year (11,993,696,190 PLN/year).
• Fuel accounts for 21.8% of passenger transport operators’ operating costs in 2024 [1], that is 2,614,625,769.42 PLN/year.
• In 2024, there were 1590 electric traction vehicles in operation, accounting for 78.4% of the market share [1]. Considering that the price of 1 m³ of diesel fuel is 3.48 times the price of 1 MWh of electricity, it can be assumed that the average electricity consumption costs are 2,049,866,603.23 PLN/year.
• It was assumed that costs may vary by +/−5%. Consequently, the minimum cost is approximately 1,947,373,273.07 PLN/year, and the maximum cost is approximately 2,152,359,933.39 PLN/year.

5.

Profits related to the use of recuperation in the railway system expressed in PLN/year

• The average electricity consumption costs are 2,049,866,603.23 PLN/year.
• It was assumed that the profit from recuperation could be as follows: minimum 0% of costs (recuperation is not used), average 2.5%—51,246,665.08 PLN/year, and maximum 5%—102,493,330.16 PLN/year.

The estimates for each variable were verified against publicly available annual reports of the Office of Rail Transport and sensitivity-tested within a ±5% range to reflect data uncertainty. The sensitivity analysis confirmed that the relative ranking of risk groups and the overall scale of estimated losses remain stable under reasonable variations of the input parameters. These verified values were subsequently used as input parameters for the Monte Carlo simulation described in Section 4.

4. Risks of Railway Undertaking Operations from the Electrical Perspective—Results

4.1. Risk Identification

The first stage of assessing the risks of a railway undertaking’s operations from an electrical perspective is to identify the risks (step 2 in Figure 1).

Table 1. Identification of risks related to rolling stock (group 1) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	Cause (Due to the Fact That …)	Risk (There is a Risk That …)	Effect (Which Will Cause …)
1.1	… there may be a failure of the electric traction vehicle designated to operate a given train, making it impossible for it to continue operating,	… a given train may be operated by a diesel traction vehicle (with the same or lower parameters),	… the costs of operating a given train may be higher, travel comfort may be lower, and delays may occur.
1.2	… there may be a failure of the electric traction vehicle designated to operate a given train, making it impossible for it to continue operating,	… a given train may be replaced by a replacement bus service,	… travel comfort may be lower, and delays may occur.
1.3	… there may be a failure of the electric traction unit designated to operate a given train, making it impossible for it to continue operating,	… a given train may be replaced by a replacement train in the form of a traction vehicle (with the same or lower parameters) and carriages,	… the costs of operating a given train may be higher, travel comfort may be lower, and delays may occur.
1.4	… there may be a failure of the electric traction vehicle designated to operate a given train, making it impossible for it to continue operating,	… a given train may be canceled,	… claims for compensation may arise for failure to provide transport services at the appropriate level.
1.5	… the rolling stock may be outdated,	… energy consumption by electric traction vehicles may be higher than for modern rolling stock,	… electricity consumption costs may be higher.
1.6	… there may be a failure of components of the electric traction vehicle designated to operate a given train,	… the comfort of travel on a train composed of a given electric traction unit or driven by an electric traction vehicle in the carriages hauled by it may experience reduced comfort,	… claims for compensation may arise for failure to provide transport services at the appropriate level.
1.7	… traction vehicles are operated in an uneconomical manner,	… the energy consumption of electric traction vehicles may be higher than when eco-driving principles are applied,	… electricity consumption costs may be higher.

,

Table 2. Identification of risks related to energy infrastructure (group 2) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	Cause (Due to the Fact That …)	Risk (There is a Risk That …)	Effect (Which Will Cause …)
2.1	… failure of the catenary system at an operating control post or on the open line may occur,	… the train will have to wait for the restoration of traffic, which will cause a long delay or may result in damage to the traction vehicle, making it impossible to continue the journey,	… the railway operator may incur losses and claims for compensation may arise for failure to provide the transport service at the appropriate level.
2.2	… a power supply failure may occur at an operating control post or on the open line,	… the train will have to wait for the restoration of traffic, which will cause a long delay or may result in damage to the traction vehicle, making it impossible to continue the journey,	… the railway operator may incur losses and claims for compensation may arise for failure to provide the transport service at the appropriate level.
2.3	… there may be a power outage in the catenary system at an operating control post or on the open line,	… the train will have to wait for the restoration of traffic, which will cause a long delay or may result in damage to the traction vehicle, making it impossible to continue the journey,	… the railway operator may incur losses and claims for compensation may arise for failure to provide the transport service at the appropriate level.
2.4	… there may be an overload of the power supply system at an operating control post or on the open line,	… the train will have to wait for the restoration of traffic, which will cause a long delay or may result in damage to the traction vehicle, making it impossible to continue the journey,	… the railway operator may incur losses and claims for compensation may arise for failure to provide the transport service at the appropriate level.
2.5	… traction vehicles may not be equipped with on-board energy recovery devices,	… the ability to recover energy during braking and starting may be limited,	… the profits from the recuperation process (reduction in energy consumption) may not be that high.
2.6	… the infrastructure manager may have delays in the implementation of the railway electrification process,	… it will be necessary to continue using diesel traction vehicles instead of electric traction vehicles,	… the costs of operating a given train may be higher, and the purchased electric vehicles may not be used efficiently.

,

Table 3. Identification of risks related to technical facilities (group 3) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	Cause (Due to the Fact That …)	Risk (There is a Risk That …)	Effect (Which Will Cause …)
3.1	… there will be an electrical failure in the technical facilities (damage to the catenary system, power supply failure, etc.),	… trains departing from their originating stations will be delayed (known as “start-up delay”),	… the railway operator may incur losses (including the need to pay compensation for the delay caused) and claims for compensation may arise for failure to provide the transport service at the appropriate level.
3.2	… there will be an electrical failure in the technical facilities (damage to the catenary system, power supply failure, etc.),	… vehicles may not be properly prepared for departure (i.e., unable to complete the required technological process),	… the railway operator may incur losses (including the need to pay compensation for the delay caused) and claims for compensation may arise for failure to provide the transport service at the appropriate level.
3.3	… the technical facilities use equipment that is highly energy-intensive,	… energy consumption may be higher than that of modern devices,	… electricity consumption costs may be higher.
3.4	… in the technical facilities, devices are used in a manner characterized by high energy consumption,	… energy consumption may be higher than that of modern devices,	… electricity consumption costs may be higher.
3.5	… the technical facilities will run out of components for repairing traction vehicles,	… in the case of a breakdown of a traction vehicle that was planned to operate a train, it may not be possible to repair it,	… the costs of operating a given train may be higher, travel comfort may be lower, and delays may occur.
3.6	… there will be an electrical failure in the technical facilities (damage to the catenary system, power supply failure, etc.),	… there may not be enough space on the sidings for the next train/trains,	… the railway operator may incur losses (including the need to pay compensation for the delay caused) and claims for compensation may arise for failure to provide the transport service at the appropriate level.

,

Table 4. Identification of risks related to transport organization and operation (group 4) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	Cause (Due to the Fact That …)	Risk (There is a Risk That …)	Effect (Which Will Cause …)
4.1	… there may be a lack of traction vehicles with the appropriate parameters (adequate to the parameters declared in the timetable) to operate a given train,	… a traction vehicle may be assigned to operate a given train whose parameters are not appropriate in relation to the parameters specified in the timetable,	… the railway operator may incur losses (including the need to pay compensation for the delay caused) and claims for compensation may arise for failure to provide the transport service at the appropriate level.
4.2	… the train timetable may be arranged in an unreasonable manner from the point of view of energy recovery,	… the ability to recover energy during braking and starting may be limited,	… the benefits of the recuperation process (reduction in energy consumption) may not be as high as expected.
4.3	… the train timetable may be arranged in an unreasonable manner, and the train driver will have to use reduced travel times in order to maintain the train’s punctuality,	… energy consumption by electric traction vehicles may be higher than when normal driving times are used (where eco-driving principles can be applied),	… electricity consumption costs may be higher.
4.4	… an electric traction vehicle may suffer a breakdown at an operating control post or on the open line, which may prevent it from continuing its journey,	… other trains may be suspended or restricted, and delays will occur,	… the railway operator may incur losses (including the need to pay compensation for the delay caused) and claims for compensation may arise for failure to provide the transport service at the appropriate level.
4.5	… there may be a breakdown on the train’s main route, which may result in it being diverted to an alternative route,	… finding a reasonable detour route may be difficult due to the limitations of electric traction vehicles,	… the railway operator may incur losses and claims for compensation may arise for failure to provide the transport service at the appropriate level.
4.6	… electric traction vehicles may not be equipped with systems supporting rational driving (eco-driving support systems).	… energy consumption by electric traction vehicles may be higher than when eco-driving principles are applied,	… electricity consumption costs may be higher.

,

Table 5. Identification of risks related to energy purchases (group 5) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	Cause (Due to the Fact That …)	Risk (There is a Risk That …)	Effect (Which Will Cause …)
5.1	… the economic situation in a given country and worldwide is uncertain,	… there may be an increase in the price of energy used for traction purposes,	… electricity consumption costs may be higher.
5.2	… the economic situation in a given country and worldwide is uncertain,	… there may be an increase in the price of energy used for non-traction purposes,	… electricity consumption costs may be higher.
5.3	… the economic situation in a given country and worldwide is uncertain,	… during the signing of the contract for electricity supply, the cost per kilowatt-hour or the duration of the fixed-rate contract may be overestimated,	… electricity consumption costs may be higher.
5.4	… there may be delays in the implementation of investments related to electrification,	… at the time of concluding the contract, the energy supplier’s offer may not be as attractive as it would be at the time of the planned implementation of the investment,	… electricity consumption costs may be higher.

and

Table 6. Identification of risks related to external factors (group 6) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	Cause (Due to the Fact That …)	Risk (There is a Risk That …)	Effect (Which Will Cause …)
6.1	… the economic situation in a given country and worldwide is uncertain,	… an energy crisis may occur,	… electricity consumption costs may be higher, or there may be a shortage of electricity for traction and non-traction purposes.
6.2	… difficult weather conditions may occur,	… there may be disruptions in the supply of electricity for traction and non-traction purposes,	… the railway operator may incur losses and claims for compensation may arise for failure to provide the transport service at the appropriate level.
6.3	… there may be delays in the implementation of investments related to electrification,	… electric traction vehicles that were purchased for investment purposes at the right time may not be operated effectively,	… the railway operator may incur losses.
6.4	… a cyberattack on the power supply system may occur,	… there may be disruptions in the supply of electricity for traction and non-traction purposes,	… the railway operator may incur losses and claims for compensation may arise for failure to provide the transport service at the appropriate level.

present the identification of risks for the respective risk groups. The identification of risks related to rolling stock (group 1) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 1.

The identification of risks related to energy infrastructure (group 2) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 2.

The identification of risks related to technical facilities (group 3) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 3.

The identification of risks related to transport organization and operation (group 4) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 4.

The identification of risks related to energy purchases (group 5) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 5.

The identification of risks related to external factors (group 6) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 6.

4.2. Risk Estimation

The second stage of assessing the risks of a railway undertaking’s operations from an electrical perspective is risk estimation, corresponding to step 3 in Figure 1.

Table 7. Identification of national variables describing the impact of risks related to rolling stock (group 1) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	National Variables Describing the Impact	Proposed Probability Distribution for the National Variable
1.1	1. Total costs of the railway undertaking’s operations 2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	1. Triangular distribution (min. 10.685 billion PLN/year, mid. 11.994 billion PLN/year, max. 13.3 billion PLN/year) 2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
1.2	2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
1.3	1. Total costs of the railway undertaking’s operations 2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	1. Triangular distribution (min. 10.685 billion PLN/year, mid. 11.994 billion PLN/year, max. 13.3 billion PLN/year) 2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
1.4	3. Costs related to the deterioration of travel comfort	3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
1.5	4. Costs related to electricity consumption by trains	4. Triangular distribution (min. 1.947 billion PLN/year, mid. 2.05 billion PLN/year, max. 2.152 billion PLN/year)
1.6	3. Costs related to the deterioration of travel comfort	3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
1.7	4. Costs related to electricity consumption by trains	4. Triangular distribution (min. 1.947 billion PLN/year, mid. 2.05 billion PLN/year, max. 2.152 billion PLN/year)

,

Table 8. Identification of national variables describing the impact of risks related to energy infrastructure (group 2) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	National Variables Describing the Impact	Proposed Probability Distribution for the National Variable
2.1	2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
2.2	2. Costs related to delays generated by trains of individual undertakings, 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
2.3	2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
2.4	2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
2.5	5. Profits related to the use of recuperation in the railway system	5. Triangular distribution (min. 0 PLN/year, mid. 51.247 million PLN/year, max. 102.493 million PLN/year)
2.6	1. Total costs of the railway undertaking’s operations	1. Triangular distribution (min. 10.685 billion PLN/year, mid. 11.994 billion PLN/year, max. 13.3 billion PLN/year)

,

Table 9. Identification of national variables describing the impact of risks related to technical facilities (group 3) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	National Variables Describing the Impact	Proposed Probability Distribution for the National Variable
3.1	2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
3.2	2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
3.3	4. Costs related to electricity consumption by trains	4. Triangular distribution (min. 1.947 billion PLN/year, mid. 2.05 billion PLN/year, max. 2.152 billion PLN/year)
3.4	4. Costs related to electricity consumption by trains	4. Triangular distribution (min. 1.947 billion PLN/year, mid. 2.05 billion PLN/year, max. 2.152 billion PLN/year)
3.5	1. Total costs of the railway undertaking’s operations 2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	1. Triangular distribution (min. 10.685 billion PLN/year, mid. 11.994 billion PLN/year, max. 13.3 billion PLN/year) 2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
3.6	2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)

,

Table 10. Identification of national variables describing the impact of risks related to transport organization and operation (group 4) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	National Variables Describing the Impact	Proposed Probability Distribution for the National Variable
4.1	2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
4.2	5. Profits related to the use of recuperation in the railway system	5. Triangular distribution (min. 0 PLN/year, mid. 51.247 million PLN/year, max. 102.493 million PLN/year)
4.3	4. Costs related to electricity consumption by trains	4. Triangular distribution (min. 1.947 billion PLN/year, mid. 2.05 billion PLN/year, max. 2.152 billion PLN/year)
4.4	2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
4.5	2. Costs related to delays generated by trains of individual undertakings, 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
4.6	4. Costs related to electricity consumption by trains	4. Triangular distribution (min. 1.947 billion PLN/year, mid. 2.05 billion PLN/year, max. 2.152 billion PLN/year)

,

Table 11. Identification of national variables describing the impact of risks related to energy purchases (group 5) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	National Variables Describing the Impact	Proposed Probability Distribution for the National Variable
5.1	4. Costs related to electricity consumption by trains	4. Triangular distribution (min. 1.947 billion PLN/year, mid. 2.05 billion PLN/year, max. 2.152 billion PLN/year)
5.2	4. Costs related to electricity consumption by trains	4. Triangular distribution (min. 1.947 billion PLN/year, mid. 2.05 billion PLN/year, max. 2.152 billion PLN/year)
5.3	4. Costs related to electricity consumption by trains	4. Triangular distribution (min. 1.947 billion PLN/year, mid. 2.05 billion PLN/year, max. 2.152 billion PLN/year)
5.4	4. Costs related to electricity consumption by trains	4. Triangular distribution (min. 1.947 billion PLN/year, mid. 2.05 billion PLN/year, max. 2.152 billion PLN/year)

and

Table 12. Identification of national variables describing the impact of risks related to external factors (group 6) in the context of a railway undertaking’s operations from an electrical perspective (source: own study).

No.	National Variables Describing the Impact	Proposed Probability Distribution for the National Variable
6.1	2. Costs related to delays generated by trains of individual undertakings 4. Costs related to electricity consumption by trains	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 4. Triangular distribution (min. 1.947 billion PLN/year, mid. 2.05 billion PLN/year, max. 2.152 billion PLN/year)
6.2	2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)
6.3	2. Costs related to delays generated by trains of individual undertakings	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year)
6.4	2. Costs related to delays generated by trains of individual undertakings 3. Costs related to the deterioration of travel comfort	2. Triangular distribution (min. 0 PLN/year, mid. 4.361 million PLN/year, max. 8.722 million PLN/year) 3. Triangular distribution (min. 145.962 million PLN/year, mid. 164.692 million PLN/year, max. 183.692 million PLN/year)

present the estimation of risks for the respective risk groups. The third column shows the characteristic values for the proposed distribution: min.—minimum value; mid.—most likely value; max.—maximum value. The identification of national variables describing the impact of risks related to rolling stock (group 1) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 7.

The identification of national variables describing the impact of risks related to energy infrastructure (group 2) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 8.

The identification of national variables describing the impact of risks related to technical facilities (group 3) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 9.

The identification of national variables describing the impact of risks related to transport organization and operation (group 4) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 10.

The identification of national variables describing the impact of risks related to energy purchases (group 5) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 11.

The identification of national variables describing the impact of risks related to external factors (group 6) in the context of a railway undertaking’s operations from an electrical perspective is presented in Table 12.

4.3. Risk Evaluation

A Monte Carlo simulation was performed for individual risks related to the activities of a railway undertaking from an electrical perspective, broken down into individual groups and national variables.

Table 13. Results of Monte Carlo simulations for risks related to rolling stock (group 1) in the context of a railway undertaking’s operations from an electrical perspective (source: own study using RiskAMP software version 5.12.1, developed by Structured Data, LLC, New York, NY, USA).

Risk Group Number . Risk Number . National Variable Number	Minimum Value (min.) [PLN/Year]	Most Likely Value (mid.) [PLN/Year]	Maximum Value (max.) [PLN/Year]	Average Value from Simulations [PLN/Year]
1.1.1.	10,685,008,800.00	11,993,696,190.00	13,299,732,000.00	12,754,027,565.11
1.1.2.	0.00	4,361,191.05	8,722,382.10	5,294,083.96
1.1.3.	145,692,000.00	164,692,000.00	183,962,000.00	156,910,100.89
1.2.2.	0.00	4,361,191.05	8,722,382.10	4,384,216.34
1.2.3.	145,692,000.00	164,692,000.00	183,962,000.00	158,435,008.03
1.3.1.	10,685,008,800.00	11,993,696,190.00	13,299,732,000.00	11,271,672,501.52
1.3.2.	0.00	4,361,191.05	8,722,382.10	6,711,083.36
1.3.3.	145,692,000.00	164,692,000.00	183,962,000.00	177,371,883.35
1.4.3.	145,692,000.00	164,692,000.00	183,962,000.00	168,033,663.16
1.5.4.	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,095,937,737.06
1.6.3.	145,692,000.00	164,692,000.00	183,962,000.00	155,027,041.79
1.7.4.	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,044,904,390.70
Risk group—1	12,778,074,073.07	14,212,615,984.28	15,644,776,315.49	15,051,444,322.78

,

Table 14. Results of Monte Carlo simulations for risks related to energy infrastructure (group 2) in the context of a railway undertaking’s operations from an electrical perspective (source: own study using RiskAMP software version 5.12.1, developed by Structured Data, LLC).

Risk Group Number . Risk Number . National Variable Number	Minimum Value (min.) [PLN/Year]	Most Likely Value (mid.) [PLN/Year]	Maximum Value (max.) [PLN/Year]	Average Value from Simulations [PLN/Year]
2.1.2.	0.00	4,361,191.05	8,722,382.10	4,863,742.29
2.1.3.	145,692,000.00	164,692,000.00	183,962,000.00	165,675,056.00
2.2.2.	0.00	4,361,191.05	8,722,382.10	3,401,450.80
2.2.3.	145,692,000.00	164,692,000.00	183,962,000.00	176,607,390.83
2.3.2.	0.00	4,361,191.05	8,722,382.10	4,212,490.01
2.3.3.	145,692,000.00	164,692,000.00	183,962,000.00	162,730,853.82
2.4.2.	0.00	4,361,191.05	8,722,382.10	2,410,415.05
2.4.3.	145,692,000.00	164,692,000.00	183,962,000.00	169,990,302.44
2.5.5.	0.00	51,246,665.08	102,493,330.16	67,093,905.00
2.6.1.	10,685,008,800.00	11,993,696,190.00	13,299,732,000.00	11,783,719,602.12
Risk group—2	10,830,700,800.00	12,111,502,715.97	13,389,923,051.94	11,087,241,757.12

,

Table 15. Results of Monte Carlo simulations for risks related to technical facilities (group 3) in the context of a railway undertaking’s operations from an electrical perspective (source: own study using RiskAMP software version 5.12.1, developed by Structured Data, LLC).

Risk Group Number . Risk Number . National Variable Number	Minimum Value (min.) [PLN/Year]	Most Likely Value (mid.) [PLN/Year]	Maximum Value (max.) [PLN/Year]	Average Value from Simulations [PLN/Year]
3.1.2.	0.00	4,361,191.05	8,722,382.10	3,220,052.16
3.1.3.	145,692,000.00	164,692,000.00	183,962,000.00	161,998,956.70
3.2.2.	0.00	4,361,191.05	8,722,382.10	6,060,499.47
3.2.3.	145,692,000.00	164,692,000.00	183,962,000.00	173,684,769.80
3.3.4.	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	1,988,694,965.09
3.4.4.	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,092,210,189.52
3.5.1.	10,685,008,800.00	11,993,696,190.00	13,299,732,000.00	11,937,436,259.70
3.5.2.	0.00	4,361,191.05	8,722,382.10	6,526,673.67
3.5.3.	145,692,000.00	164,692,000.00	183,962,000.00	155,845,021.41
3.6.2.	0.00	4,361,191.05	8,722,382.10	6,256,345.24
3.6.3.	145,692,000.00	164,692,000.00	183,962,000.00	159,664,422.96
Risk group–3	12,778,074,073.07	14,212,615,984.28	15,644,776,315.49	14,305,275,475.01

,

Table 16. Results of Monte Carlo simulations for risks related to transport organization and operation (group 4) in the context of a railway undertaking’s operations from an electrical perspective (source: own study using RiskAMP software version 5.12.1, developed by Structured Data, LLC).

Risk Group Number . Risk Number . National Variable Number	Minimum Value (min.) [PLN/Year]	Most Likely Value (mid.) [PLN/Year]	Maximum Value (max.) [PLN/Year]	Average Value from Simulations [PLN/Year]
4.1.2.	0.00	4,361,191.05	8,722,382.10	2,508,032.81
4.1.3.	145,692,000.00	164,692,000.00	183,962,000.00	177,926,109.55
4.2.5.	0.00	51,246,665.08	102,493,330.16	34,555,267.81
4.3.4.	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,030,178,953.20
4.4.2.	0.00	4,361,191.05	8,722,382.10	3,604,481.12
4.4.3.	145,692,000.00	164,692,000.00	183,962,000.00	167,936,958.13
4.5.2.	0.00	4,361,191.05	8,722,382.10	1,565,172.48
4.5.3.	145,692,000.00	164,692,000.00	183,962,000.00	165,310,903.05
4.6.4.	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,016,096,148.71
Risk group–4	2,093,065,273.07	2,167,673,129.20	2,242,550,985.33	2,132,448,983.80

,

Table 17. Results of Monte Carlo simulations for risks related to energy purchases (group 5) in the context of a railway undertaking’s operations from an electrical perspective (source: own study using RiskAMP software version 5.12.1, developed by Structured Data, LLC).

Risk Group Number . Risk Number . National Variable Number	Minimum Value (min.) [PLN/Year]	Most Likely Value (mid.) [PLN/Year]	Maximum Value (max.) [PLN/Year]	Average Value from Simulations [PLN/Year]
5.1.4.	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,090,071,481.34
5.2.4.	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,067,092,614.67
5.3.4.	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,026,191,998.88
5.4.4.	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,009,787,568.26
Risk group–5	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,021,485,777.50

and

Table 18. Results of Monte Carlo simulations for risks related to external factors (group 6) in the context of a railway undertaking’s operations from an electrical perspective (source: own study using RiskAMP software version 5.12.1, developed by Structured Data, LLC).

Risk Group Number . Risk Number . National Variable Number	Minimum Value (min.) [PLN/Year]	Most Likely Value (mid.) [PLN/Year]	Maximum Value (max.) [PLN/Year]	Average Value from Simulations [PLN/Year]
6.1.2.	0.00	4,361,191.05	8,722,382.10	2,940,432.09
6.1.4.	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,041,056,092.87
6.2.2.	0.00	4,361,191.05	8,722,382.10	4,491,885.65
6.2.3.	145,692,000.00	164,692,000.00	183,962,000.00	176,894,384.56
6.3.2.	0.00	4,361,191.05	8,722,382.10	3,044,180.17
6.4.2.	0.00	4,361,191.05	8,722,382.10	5,179,572.13
6.4.3.	145,692,000.00	164,692,000.00	183,962,000.00	158,200,943.84
Risk group–6	2,093,065,273.07	2,218,919,794.28	2,345,044,315.49	2,232,111,020.70

report the minimum, most likely, maximum, and average (simulation) values. The last row of each table shows the sum of the minimum, most probable, and maximum values for the national variables used to assess the risk in a given risk group. It was assumed that a transport operator cannot incur the same loss several times or make the same profit several times; therefore, these variables, even though they sometimes occur several times, were aggregated only once per group—e.g., for the first group, the values for variables 1, 2, 3, and 4 were summed. Variable number 5 is profit, so it was taken into account with a negative sign in relation to costs. The average value from the simulation in the last row was obtained by performing a separate simulation using the values from the row (this is not the average of the average values). The number of trials in the simulation was 1000. The convergence of the results was verified by comparing the mean and median values after 900 and 1000 iterations, which confirmed the model’s stability.

Table 13 presents the results of Monte Carlo simulations for risks related to rolling stock (group 1) in the context of a railway undertaking’s operations from an electrical perspective.

If any of the risks classified in the first group materialize, the railway undertaking may incur a minimum loss of 0.00 PLN/year and a maximum loss of 13,299,732,000.00 PLN/year. The most likely value ranges from 4,361,191.05 PLN/year to 11,993,696,190.00 PLN/year. The average value from the simulation ranges from 4,384,216.34 PLN/year to 12,754,027,565.11 PLN/year.

Table 14 presents the results of Monte Carlo simulations for risks related to energy infrastructure (group 2) in the context of a railway undertaking’s operations from an electrical perspective.

If any of the risks classified in the second group materialize, the railway undertaking may incur a minimum loss of 0.00 PLN/year and a maximum loss of 13,299,732,000.00 PLN/year. The most likely value ranges from 4,361,191.05 PLN/year to 11,993,696,190.00 PLN/year. The average value from the simulation ranges from 2,410,415.05 PLN/year to 11,783,719,602.12 PLN/year. It should be noted that, in the case of national variable no. 5, the discussion concerns profit rather than loss. The minimum profit is 0.00 PLN/year, and the maximum is 102,493,330.16 PLN/year. The most likely value is 51,246,665.08 PLN/year, and the average value from simulations is 67,093,905.00 PLN/year.

Table 15 presents the results of Monte Carlo simulations for risks related to technical facilities (group 3) in the context of a railway undertaking’s operations from an electrical perspective.

If any of the risks classified in the third group materialize, the railway undertaking may incur a minimum loss of 0.00 PLN/year and a maximum loss of 13,299,732,000.00 PLN/year. The most likely value ranges from 4,361,191.05 PLN/year to 11,993,696,190.00 PLN/year. The average value from the simulation ranges from 3,220,052.16 PLN/year to 11,937,436,259.70 PLN/year.

Table 16 presents the results of Monte Carlo simulations for risks related to transport organization and operation (group 4) in the context of a railway undertaking’s operations from an electrical perspective.

If any of the risks classified in the fourth group materialize, the railway undertaking may incur a minimum loss of 0.00 PLN/year and a maximum loss of 2,152,359,933.39 PLN/year. The most likely value ranges from 4,361,191.05 PLN/year to 2,049,866,603.23 PLN/year. The average value from the simulation ranges from 1,565,172.48 PLN/year to 2,030,178,953.20 PLN/year. It should be noted that, in the case of national variable no. 5, the discussion concerns profit rather than loss. The minimum profit is 0.00 PLN/year, and the maximum is 102,493,330.16 PLN/year. The most likely value is 51,246,665.08 PLN/year, and the average value from simulations is 34,555,267.81 PLN/year.

Table 17 presents the results of Monte Carlo simulations for risks related to energy purchases (group 5) in the context of a railway undertaking’s operations from an electrical perspective.

If any of the risks classified in the fifth group materialize, the railway undertaking may incur a minimum loss of 1,947,373,273.07 PLN/year and a maximum loss of 2,152,359,933.39 PLN/year. The most likely value is 2,049,866,603.23 PLN/year. The average value from the simulation ranges from 2,009,787,568.26 PLN/year to 2,090,071,481.34 PLN/year.

Table 18 presents the results of Monte Carlo simulations for risks related to external factors (group 6) in the context of a railway undertaking’s operations from an electrical perspective.

If any of the risks classified in the sixth group materialize, the railway undertaking may incur a minimum loss of 0.00 PLN/year and a maximum loss of 2,152,359,933.39 PLN/year. The most likely value ranges from 4,361,191.05 PLN/year to 2,049,866,603.23 PLN/year. The average value from the simulation ranges from 2,940,432.09 PLN/year to 2,041,056,092.87 PLN/year.

5. Discussion: Assessment of the Risks of Railway Undertaking Operations from an Electrical Perspective

Section 4 of this article presented the risk assessment of a railway undertaking’s operations from the perspective of individual risks, which, if materialized, would result in either losses or gains for the operator. The assessment was also carried out at the level of risk groups.

To assess the overall risk of a railway undertaking’s activities from an electrical perspective, it was assumed that this could be achieved using previously defined national variables. As mentioned in Section 4, one or more national variables can describe the impact of individual risks on the operator’s activities, and the same variable may appear in several risk groups. However, it was assumed that a given variable could materialize only once within each group. The same assumption was applied to the overall assessment—each national variable was considered only once. The variable values (costs as positive, profits as negative) were then summed, and a Monte Carlo simulation was performed.

Table 19. Assessment of the risks of railway undertaking operations from an electrical perspective (source: own study using RiskAMP software version 5.12.1, developed by Structured Data, LLC).

National Variable Number	Minimum Value (min.) [PLN/Year]	Most Likely Value (mid.) [PLN/Year]	Maximum Value (max.) [PLN/Year]	Average Value from Simulations [PLN/Year]
1	10,685,008,800.00	11,993,696,190.00	13,299,732,000.00	12,942,881,246.52
2	0.00	4,361,191.05	8,722,382.10	4,790,567.93
3	145,692,000.00	164,692,000.00	183,962,000.00	158,907,277.82
4	1,947,373,273.07	2,049,866,603.23	2,152,359,933.39	2,092,922,820.64
5	0.00	51,246,665.08	102,493,330.16	75,157,549.91
SUM	12,778,074,073.07	14,161,369,319.20	15,542,282,985.33	14,160,588,863.66

assesses the risk of a railway undertaking’s operations from an electrical perspective. In accordance with the assumption, the assessment was made on the basis of the “SUM” column.

The Monte Carlo simulation resulted in the following statistical parameter values:

• Mean value—14,160,588,863.66 PLN/year;
• Number of trials—1000;
• Standard error—17,840,712.04 PLN/year;
• Minimum value—12,824,545,257.32 PLN/year;
• Maximum value—15,489,979,662.42 PLN/year;
• Median—14,159,617,595.70 PLN/year;
• Range—2,665,434,405.10 PLN/year;
• Standard deviation—564,455,149.31 PLN/year;
• Variance—318,609,615,576,962,000.00 (PLN/year)²;
• Skewness—0.00;
• Kurtosis—2.40.

Based on these parameters, the following conclusions can be drawn. The average annual loss that a railway undertaking may incur from an electrical perspective is approximately 14.16 billion PLN/year. A total of 1000 trials provides sufficient stability to assume that the estimated mean and standard error are statistically reliable. The standard error accounts for about 0.13% of the mean, ensuring high precision. The range between the minimum and maximum losses is about 2.67 billion PLN/year, indicating moderate dispersion (±9% around the mean).

The closeness of the median to the mean confirms that the resulting distribution is symmetric. The standard deviation further indicates low variability (±4% around the mean). The variance supports this moderate dispersion. The skewness value (0.00) confirms perfect symmetry, while the kurtosis value (2.40) indicates a slightly platykurtic distribution—that is, the data are concentrated near the mean with fewer extreme values.

The percentile distribution of the average annual value of losses that a railway undertaking may suffer from an electrical perspective is presented in Figure 2.

Table 20. Risk evaluation of the railway undertaking operations from an electrical perspective (source: own study using RiskAMP software version 5.12.1, developed by Structured Data, LLC).

Percentile	Average Value from Simulations [PLN/Year]	Risk Evaluation
0%	12,824,545,257.32	0
5%	13,215,290,603.91	660,764,530.20
10%	13,396,394,651.63	1,339,639,465.16
15%	13,534,635,328.14	2,030,195,299.22
20%	13,652,148,928.74	2,730,429,785.75
25%	13,753,968,835.22	3,438,492,208.81
30%	13,848,281,414.13	4,154,484,424.24
35%	13,933,447,954.09	4,876,706,783.93
40%	14,014,719,732.62	5,605,887,893.05
45%	14,089,062,241.14	6,340,078,008.51
50%	14,159,617,595.70	7,079,808,797.85
55%	14,231,547,832.91	7,827,351,308.10
60%	14,306,509,951.27	8,583,905,970.76
65%	14,385,484,729.83	9,350,565,074.39
70%	14,471,278,992.10	10,129,895,294.47
75%	14,565,342,459.21	10,924,006,844.41
80%	14,666,486,971.05	11,733,189,576.84
85%	14,784,178,027.18	12,566,551,323.10
90%	14,921,596,434.06	13,429,436,790.65
95%	15,104,087,538.89	14,348,883,161.95
100%	15,489,979,662.42	15,489,979,662.42

presents the risk evaluation of the railway undertaking operations from an electrical perspective.

The histogram of the occurrence of individual values of the average annual value of losses that a railway undertaking may suffer from an electrical perspective is presented in Figure 3.

Due to the aggregated nature of the input data, classical validation against individual historical events was not feasible. Instead, the results were validated at the sectoral level by comparing simulated outcomes with publicly reported cost structures and delay statistics. The consistency of these values supports the plausibility of the proposed approach.

6. Conclusions

High electricity prices, European Union climate policy, and other regulatory requirements mean that railway operators, in addition to their core activity of transporting passengers and/or freight, must also act as informed participants in the energy market. In this article, being an energy market participant is understood in a functional and operational sense, referring to informed decision-making regarding electricity procurement, contract structures, price exposure, and energy-related operational risk management. Given that the vast majority of railway undertakings operate electric rolling stock, these issues primarily concern electricity as a traction energy source. Consequently, a railway operator’s activities related to electricity procurement and consumption are particularly relevant due to their direct quantitative linkage with operating costs and exposure to energy-related risks.

Every activity involves risk. The same applies to the activities of a railway undertaking from an electrical perspective. In order to be able to predict the consequences of undesirable events (risks), all processes must be systematically evaluated from a risk perspective. The aim of the article was to develop a method for assessing the risk of a railway undertaking’s operations from an electrical perspective and then to perform this assessment on the basis of this method. As a result of the research, a five-step method was developed:

• Identification of the process to be risk assessed and its decomposition into components;
• Identification of risks for the decomposed process;
• Estimation of risks for the decomposed process;
• Assessment of risks for the decomposed process;
• Evaluation of the process from the point of view of risk exposure.

The novelty of this study lies in combining M_o_R^®-based qualitative risk identification with probabilistic Monte Carlo simulation to quantify energy-related operational risks in railway undertakings. The proposed approach enables the translation of risk exposure into monetary terms, supporting practical decision-making in energy management and operations. While the empirical analysis uses nationally aggregated data, the method can be directly scaled to individual operators. This positions the methodology as a practical analytical tool rather than a purely theoretical framework.

Based on the considerations presented in this article, the following conclusions can be drawn:

• Some processes occurring at railway undertakings are complex; one such process is the operation of a railway undertaking from an electrical perspective; the results confirm that aggregated assessment obscures differences between risk categories, while process decomposition enables more differentiated and informative risk evaluation; this approach is therefore embedded in the method proposed in the article.
• The application of the risk description principle proposed by the M_o_R^® methodology improves the interpretability and applicability of the results; identifying a set of causes makes it possible to better prevent the materialization of individual risks; identifying the effect facilitates their assessment.
• It is recommended to use publicly available data for risk assessment; this makes the developed method universal; changing the values of specific parameters that allow the national variable to be determined for individual countries will make it easy to compare risk exposure levels between countries; in addition, if the parameters are presented cyclically, it is easy to obtain national variable values for other periods of time; it should be noted that the universality of the proposed method refers to its structural framework and data requirements, rather than to uniform risk levels across countries; national specificities are captured through country-specific values of the adopted national variables.
• The use of a probabilistic risk model makes calculations more realistic; assigning an appropriate probability distribution to the national variable allows for the randomness of the materialization of individual risks to be reflected, thus enabling calculations that are close to reality; the use of this probabilistic risk model also has negative consequences, which is a general feature of model-based research; future research will focus on applying alternative probability distributions and comparing their results with those obtained using the triangular distribution in order to assess the sensitivity of the proposed method to distributional assumptions.
• The evaluation of the entire process from the point of view of risk exposure should be carried out in such a way that individual national variables are not included repeatedly in the calculations; using them once fully reflects issues related to the materialization of risks, and, in particular, the chances of making a profit or the risks of incurring a loss.

The results obtained in this study are intended to support operational and managerial decision-making of railway undertakings from the energy-related risk perspective. In particular, the proposed framework may be applied to the following:

• Prioritize risk mitigation actions across different operational areas by comparing the simulated magnitude of potential losses and profits;
• Support cost-based decision-making by assessing how the materialization of specific energy-related risks may affect total operating costs;
• Identify critical sources of delay- and comfort-related losses, enabling targeted measures to reduce exposure to compensation claims and service quality degradation;
• Support strategic decisions on energy procurement and contracting, including risk-aware evaluation of electricity price volatility and market exposure;
• Assess the economic justification of investments in energy recovery systems and energy efficiency measures, based on the simulated profit potential;
• Although the empirical results are presented for the Polish railway market, the proposed framework is methodologically transferable and may be applied to other national contexts using country-specific input data.