1. Introduction
The use of railway systems in the transport sector presents advantages relative to other systems regarding energy efficiency, environmental impact, reliability, security and economic feasibility [
1,
2]. Railways present some common characteristics. The friction coefficient is very low resulting in low friction. As a result, the track gradient has to be very gentile due to the low friction coefficient. High peak power is demanded during braking and uphill climbing [
3], creating big differences between average power and peak power in freight trains considering storage and diesel demand, respectively.
New infrastructure comprising electrification, improved operation through the optimization of timetables for maximizing the use of the regenerated energy [
4], as well as storage devices [
5] are ways of increasing the transport efficiency of a railway system. Regenerative braking is an interesting technology to increase efficiency [
6,
7], consisting of inverting the propulsion machine functioning mode from motor to generator. It is feasible for locomotives with electric traction motors, both electric and diesel-electric.
With the purpose of maximizing the regenerated energy, the Bellman–Ford algorithm has been used in [
8] to optimize the braking and speed of a train. The train speed optimization is also proposed in [
9] under the point of view of the energy recovered in the braking in different scenarios. Another optimization approach, based on the dual speed curve method, is presented in [
1], to determine the effective speed curve for maximizing the energy economy. In [
10] the authors present a comparison between different storage configurations in regenerative braking systems of locomotives, in railways electrified by a micro DC network connected to the electrical network by a unidirectional substation. The referred work proposes a braking system with a control algorithm that considers the mass variation and the resistances that participate in the breaking, pointing out the off-board system as the more interesting in the considered condition.
Research on advantages and drawbacks of different technologies applied to regenerative braking of locomotives can also be found in the literature. Recent applications of systems with batteries, flywheels, capacitors, and hybrid devices are described in [
11]. Information on specific capacity of permanent and temporary batteries for saving energy is given in [
12]. Data on energy density, lifetime and operating temperature of batteries, in turn, are presented in [
13]. A review of technologies for the management of regenerative braking energy is made in [
2], which comprises reversible substations and tariff scenarios. Ultracapacitors are considered in [
14], for a hierarchical control strategy that consists of energy management and converter control layers in urban railway, as well as in [
15], through practical examples of eco-friendly solutions implementation in urban municipal transport.
The methodology proposed in [
13] seeks to determine the sizing of a hybrid energy storage system for regenerative braking involving batteries and ultracapacitors. The advantage of the hybrid system is to combine the energy capacity of the batteries with the power density of ultracapacitors. Electrochemical double-layer capacitors and Li-ion batteries are evaluated as storage options. In [
16], a methodology is proposed for optimal operation of railway electric energy systems considering renewable energy sources (solar panels and wind turbines), regenerative braking capabilities and hybrid electric energy storage devices (ultracapacitors and batteries). The authors of [
17] presented an optimized sizing and scheduling of hybrid energy storage systems for high-speed railway traction substations integrated with removable energy, with the intention of minimizing the total cost throughout the project service period. The battery degradation and replacement cost were taken into account.
On the other hand, the onboard storage is indicated as the most worthwhile option in [
18] for diesel-electric locomotives in non-electrified railways. A small size fuel cell based on a proton exchange membrane (PEM) is evaluated in [
19] for energy management of a train with a focus on the maximum propulsion system efficiency, considering losses in auxiliary components. The efficiency is assessed both for individual components and the integrated propulsion system during steady-state and dynamic conditions, under different control strategies. The analysis performed in [
20] evaluates the potential energy recovery from regenerative braking of diesel-electric locomotives in freight service, by using and comparing locomotive event recorder data with results obtained from computer simulations. The purpose is the sizing of the storage capacity by carrying out economic and environmental analyses that consider, among the candidate technologies, batteries, supercapacitors, and flywheels. The context is near the Brazilian railway scenario. However, the economic feasibility analysis should be updated regarding technologies and scale gains.
The analysis of energy recovering and storage in locomotives consists of an open and promising topic for research, particularly concerning the more suitable alternatives for a given type of system and its interactions [
21]. Moreover, most of the studies are devoted to systems for electric locomotives, whereas the number of contributions for diesel-electric locomotives in non-electrified railways is still relatively low. Such systems can operate in an independent way, where each train can be considered as a microgrid with onboard generation and consumption.
Following the previously described research line and the relative lack of works for diesel-electric locomotives in non-electrified railways, the present work seeks to evaluate the application of onboard regenerative braking for energy recovery in freight trains, considering a realistic scenario for a Brazilian railway system and real technical aspects of the storage devices. The objective is to present an approach to determine the recoverable energy potential from the application of an energy storage system (ESS) and to maximize net present value (NPV).
The paper is outlined as follows.
Section 2 introduces the general energy recovery and storage devices in railway systems.
Section 3 details the proposed methodology to estimate the recoverable energy from regenerative brake systems and also the investment analysis tools used to evaluate the ESS. In
Section 4, the case study comprising a Brazilian railway is presented as a case study together with the results for this system. Finally, conclusions are drawn in
Section 5.
3. Methodology
This section presents the energy balance related to the movements of trains. Thus, a method to estimate the potential energy recovery from regenerative braking is presented. Additionally, this section shows the choice and sizing of the storage device, as well as the economic analysis used to choose the best option.
3.1. Energy Balance—Train Movement
There are a number of forces involved in the train’s drive cycle. The forces are grouped in the thrust, as the positive thrust of brake force (
), the friction forces (
) representing power losses, and the railway profile, descending or ascending, representing the weight component parallel to the ground that contributes to the gain or loss of potential energy (
). The force balance is presented in Equation (1) gives the exceeding force that contributes to the train’s acceleration.
Each term of Equation (1) will be detailed.
3.1.1. Power Term Related to Friction Losses
The friction losses can be estimated with the classical experimental model that considers the resistance forces proportional to the speed in a second-order equation, also known as the Davis’ equation, seen in Equation (2), which gives the friction coefficient.
The terms
A,
B, and
C are obtained through experimental results. The calculation of these coefficients for locomotives and wagons are described in
Table 1.
From the friction coefficient, the force resulting from the resistance to the movement can be found as presented by Equation (3).
From the previous friction force, the friction power losses can be calculated as shown in Equation (4).
Therefore, given the main features of the vehicles, such as mass, the number of axes, and frontal area, it is possible to estimate the friction as a function of velocity, by combining Equations (2)–(4), together with the coefficients from
Table 1.
3.1.2. Power Term Related to Gravity
Gravity can have a positive or negative impact on the energy balance of the train’s movement. Railway profiles do not present high inclinations because of the low friction coefficient between wheel and rail. Those inclinations are represented as a percentage value. For example, a ramp has 1% inclination if it presents a vertical variation of 1 m for 100 m of horizontal movement. That is, the tangent of the inclination angle is 0.01.
The necessary power for the train to climb a ramp can be described as presented in Equation (5).
3.1.3. Power Term Related to the Motor or Brakes
The power provided by the locomotive is given by the throttle position, since the fuel consumption depends on the throttle position or notch, as presented in
Table 2 for the studied locomotive.
The throttle presents 10 positions: eight acceleration points, neutral notch, and dynamic brake. The dynamic brake is controlled by a second lever that can vary continuously from the minimum to the maximum point. These values are registered in the black box in a percentage range, from 0% to 100%, representing the increasing level of energy dissipation in the resistor banks of the dynamic brake.
It is possible to extract the number of times the acceleration lever has been used in each position during the trip, and therefore the fuel consumption and energy demand at each point. Additionally, the number of times and percentage usage of the dynamic brakes can be extracted. Thus, the first step to the proposed approach is to evaluate a complete trip.
Considering that the energy density of the diesel oil is 11.1 kWh/L, the consumption can be rewritten in terms of power, as presented in Equation (6).
The power dissipation in the resistors’ banks is related to the use of the dynamic brake. To define this relation, the data from the black box of different locomotives in different parts of the railway are depicted in
Figure 2. A strong linear correlation between these two variables can be seen.
A linear approximation of the data displayed in
Figure 2 is presented in Equation (7) and gives the power dissipated as a function of the dynamic brake use, as a percentage.
The measured point at high dynamic brake usage with low power dissipation corresponds to moments when the locomotive is moving slow, so little energy can be converted before the train stops. The breaking power behavior is linear other than the moments at very high or low speed. From the previous information of power demand, obtained by the acceleration or braking points from the black boxes, a demand profile can be estimated for the complete trip. Those steps will be developed afterwards and are the basis of the storage system dimensioning and preliminary financial analysis.
3.1.4. Power Term Related to the Resulting Forces
The energy balance considers the mechanical energy conservation and energy losses due to the friction and dissipation in the brakes. There is a resulting force that acts accelerating or deaccelerating the train when the friction and the gravity in the direction of the movement are other than zero, as ruled by Newton’s second law.
It must be observed that the freight trains work in a more constant velocity when compared to passenger trains. Thus, the locomotive runs in many parts of the railway at a constant velocity, so there is no resulting force. This consideration simplifies the present analysis.
3.2. Recoverable Power Potential
The main focus of the present paper is the estimation of recoverable power from regenerative brakes. Therefore, the most important term of the force balance, Equation (1), is related to the brake system. Black boxes in the locomotives register information such as time, velocity, direction, distance run, throttle notch, brake usage that can be pneumatic (automatic or independent brake) or electrical (dynamic brake). Such information is stored on a second basis and is available in a data bank. The energy consumption by motors and the energy dissipation by brakes can be estimated by using these data.
Thus, the implemented program or MatLab
® script reads the data bank from black boxes recorded in real railway trips and converts the data in an estimate demand profile, calculating the energy excess. In order to illustrate, the black box data bank is similar to the data presented in
Table 3.
One can estimate the power requirement from the Davis equation to calculate the losses and the track profile to calculate the force balance (Equation (1)). The excess energy from braking can be obtained from the power formulated by Equation (7) together with the data from the black box presented in
Table 3, second by second. Thus, it is possible to find the total amount of recoverable energy from the system. Based on this information, the optimal size of a storage system can be determined, based on storage systems characteristics.
3.3. Determining the Size of the Energy Storage
The energy balance previously presented with the data from the dynamic brake recorded at the black box is performed second by second. The flowchart in
Figure 3 presents the algorithm to estimate the recovery capacity. This analysis is repeated for different energy storage sizes. The energy recovered and the energy curtailment when the battery is full is accounted to be used in the economic analysis.
The amount of power in or power out from the battery, as well as the amount of diesel are defined based on the recoverable potential ), the energy level , the battery charge and discharge efficiencies, diesel engine efficiency , and the power demand at each time interval.
During dynamic braking, the battery bank stores energy. When the brake dynamics have been turned off, the battery bank contributes to the power demand. The power balance, second by second, referenced from to the power electric demand, is presented in Equation (8) during dynamic braking and in Equation (9) for the train’s motor traction operation mode.
The and have upper bounds defined by the rated power of charge and discharge , respectively. The is bounded by the depth of discharge (DOD) and maximum state of charge . If , , whereas implies .
With the power injection or extraction from the ESS, the demand profile is determined in order to estimate the size of the ESS. By comparing the demand of diesel when considering the ESS and the regenerative brake with the situation without ESS, one can estimate the financial economy, as the diesel is the only sort of fuel used in this kind of freight train. Thus, the economy is determined from comparison involving the integral of the variable in each previous situation.
The maximum values for the power injection (), extraction , and energy storage must be defined according to the type of ESS under evaluation. A direct way to achieve the optimal size of ESS, whatever kind of technology considered, can be by simulating different system sizes.
Notice either the battery or diesel engine is working at traction stage, i.e., the battery can be considered as the primary power supplier compared with diesel engine at this stage, through a system known as auto engine start stop (AESS).
3.4. Economic Analysis
In order to properly evaluate the proposed solution, it is necessary to consider economic parameters to guarantee a proper return on the investment for the railway company. Thus, the net present value (NPV) can be considered at first. Additionally, the intern return rate (IRR) and the payback period can be of interest to companies even considering the drawbacks of the use of both methods [
40].
The NPV is a significant parameter for the economic analysis of projects. It seeks to evaluate the viability of a given project and is based on the calculation of the present value of a series of future payments, subtracted by the capital expenditures. The NPV equation is represented in Equation (10).
where
is the cash flow of each period
t and
i is the discount rate considered that depends on the risk of the investment, the company’s opportunity cost, and liquidity. This discount rate is usually called minimum attractive rate of return (MARR) and varies from company to company.
The internal rate of return (IRR) is another important parameter when evaluating a project and is defined as the rate of return that turns the NPV equal to zero. Thus, IRR represents the rate of return of a given project and can be compared with the MARR. Given an IRR greater than the MARR, the investment is economically attractive [
41].
Another general financial index is the payback period, which is the time required to recover the capital invested. In order to better consider the time value of money, the discounted payback period is used in the present work [
42].
Given the technical parameters of the storage device for the energy recovery from the regenerative brake, it is possible to conduct a preliminary economic analysis of the investment. Therefore, the investment analysis indexes are calculated for each proposed size of storage device.