1. Introduction
Electric rail transit systems are continuously developing, in order to provide fast and reliable services to their ever-increasing customers. A critical challenge for electric rail transit systems is the recuperation of regenerative braking energy. Regenerative braking energy is the energy produced by trains during deceleration. In other words, it is the energy mechanically stored in the rotor inertia, which can be converted back into electricity and injected into the rail during deceleration [
1]. One possible solution of recuperating regenerative braking energy is through the installation of energy storage systems (ESS) next to the third rail (the power rail next to the running rail). ESS would capture this energy and later release it, when needed. Typical applications of recuperated energy include energy saving, peak demand reduction, and voltage regulation [
2]. Different ESS technologies have been proposed and implemented in rail transit systems worldwide. For instance, a flywheel was installed in the Los Angeles Metro for energy saving, and a supercapacitor was installed in several European countries for energy saving and voltage regulation [
3]. A sodium-sulfur (NA-s) battery was used in the Long Island railroad, and a Li-ion battery was used in the Philadelphia transit system [
4]. Among these technologies, flywheel and supercapacitors show superior characteristics and performances, compared to other available technologies, in terms of power capacity and charge/discharge time.
In this paper, we investigated these two technologies and their applications in electric rail transit systems. A portion of a DC electric rail transit system was modeled in MATLAB/Simulink. The energy storage system was installed in a specific substation, and the performance of these two technologies in providing services, including peak demand reduction and voltage regulation, was tested and compared.
The rest of this paper is organized as follows:
Section 2 describes flywheel energy storage (FESS) and supercapacitor energy storage (SESS), and compares their general characteristics.
Section 3 presents a description of an electric rail transit system that was used as a case study in this paper.
Section 4 presents case study and simulation results.
Section 4.3 presents a cost analysis. Finally,
Section 5 presents the conclusion.
3. System under Study
To investigate the performance of FESS and SESS in the electric rail transit system, a portion of an electric rail transit system, including four passenger stations and three substations, was selected and simulated in the MATLAB/Simulink environment. A schematic of the system under study is presented in
Figure 4.
In this system, substations consisted of two parallel sets of transformers and unidirectional converters, which were responsible for converting the AC voltage (13 kV) from the utility grid to the DC voltage (650 V) desired by the transit system. Power and traction rails were modeled by variable resistors to represent train movement; their values changed based on the train position. A train was assumed to be moving from passenger station 1 to passenger station 4. Trains were modeled using a backward modeling approach. In this approach, the speed of the wheel was used as an input to the model using vehicle dynamic equations (Equations (6)–(11)), and the required torque and the angular speed from the gearbox was calculated. Using gearbox equations (Equations (12)–(14)), the required torque and speed from the motor drive was calculated. The schematic of the electric drive and its controller is presented in
Figure 5 and
Figure 6, respectively. Using an electric drive motor, the power consumed by the train for each specific speed profile can be calculated as:
where
FR,
FW, and
Fg are the friction force, the force due to the wind, and the gravity force, respectively; which could be overcome by the tractive effort (
FT) produced by the electric drives in each car.
Tw and
ωw are the required torque and angular speed of the wheel.
Mmetro is the weight of the train;
fR is the friction factor;
g is the acceleration gravity; and
Cw,
A, and
γ are drag coefficient, the front area of the train, and air density, respectively. The velocity dependent part of the running resistance was considered in the rolling resistance coefficient. The number of cars and the radius of the wheels are presented by
n and
r, respectively.
TG and
ωG are the torque and the speed of the gearbox.
ηG is the gearbox efficiency,
γG is the gearbox ratio, and
B represents the vehicle losses.
A train consisted of several connected cars, and each car had one or two electric drives that controlled the torque and the speed of the wheels, as presented in
Figure 5. The model used in this paper was validated using real data from the New York City subway system. More information on system simulation can be found in the literature [
14,
15].
FESS and SESS were placed in the middle substation (substation B) to provide voltage regulation and peak demand reduction during the transit rush hours. The flywheel was modeled by additional inertia added to the permanent magnet synchronous machine, as presented in
Figure 7 [
15].
The supercapacitor was modeled by a controlled voltage source, as presented in
Figure 8. The internal voltage of the supercapacitor is described as follows:
where
Ns and
Np are the number of series and parallel capacitors,
Ne is the number of electrode layers, and
ε and
ε0 are permittivity of material and air, respectively.
R and
T are ideal gas constant and operating temperature, respectively, and
Ai is the interfacial area between electrodes and electrolyte. To connect SESS to the third rail, a bidirectional DC/DC converter was used. The schematic and the control circuit of this converter are presented in
Figure 9 [
16].
S1 only gets a turn on signal for charging, and S2 is turned on during discharging. More information about this type of bidirectional DC/DC converter can be found in the literature [
28]. The ESS energy management unit was responsible for the command signal (I_command) and worked based on some general rules, as follows:
If the voltage of the line at the point of connection (VPCC) of the ESS was greater than the voltage set for triggering the charging process, it would charge until the state of charge ESS reached an upper limit. Similarly, if the VPCC was smaller than a specific limit set for discharging, the ESS would discharge until the state of charge reached a lower limit. For safe operation, the upper and lower limits were considered in this paper to be 90% and 40%, respectively. Other than these two conditions, the ESS remained idle.
4. Case Study
In this section, the performance of FESS and SESS for the application of peak demand reduction and voltage regulation is investigated and compared. The cost analysis is also presented for each technology in each application.
4.1. Peak Demand Reduction
A typical train speed, current, power, and energy profile of a train are presented in
Figure 10. As illustrated, during acceleration (0–33 s), a train accelerates with a maximum rate to reach its maximum speed. During this interval, a significant amount of current/power is requested from a nearby substation. During the transit system rush hours, the number of trains increases, and trains run with shorter headway (2–3 min). Therefore, a considerable number of train acceleration events happen near each substation during each 15 min interval. Consequently, substations will have high peak demand. An example of a 24 h power profile of substation B in a typical weekday is presented in
Figure 11. As can be observed, there is peak demand for 2238 kW at around 5:30 p.m.
In this case study, FESS and SESS were controlled to discharge during train acceleration and charge by regenerative braking energy, to provide a 10% peak demand reduction in substation B. They were sized in a way that provided a 705 A current for 12.3 seconds (353 kW, 1.2 kWh). A Maxwell supercapacitor (K2 series) [
29,
30,
31,
32] and VYCON flywheel [
8] were used as the ESS technologies. Based on the ESS technology characteristics (for example, maximum voltage and current of the cell or module), they need to be oversized to provide the required current and voltage. ESSs sizing information is presented in
Table 4. The ESSs were separately placed in substation B and tested. The results are presented in
Figure 12. As can be seen, both ESS technologies were capable of reducing the peak of substation B for the desired value of 10%.
4.2. Voltage Regulation
When a train accelerates, a significant amount of power/current is drawn from the third rail; therefore, the third rail voltage drops inversely, proportional to the current to provide the requested amount of current/power. For example, in a system which is working with a nominal voltage of 650 VDC, the third rail voltage can drop to 580–620 VDC during acceleration. In a weak system, the voltage may drop to an even lower value. Since train acceleration happens frequently, these frequent voltage drops may affect train performance, and may cause damage to other equipment connected to the third rail. By installing ESSs, when the voltage drops below a certain level, the ESS will discharge to the third rail and thus prohibit any further voltage drop. This behavior for both SESS and FESS (modeled here as a current source) is presented in
Figure 13.
In this case study, ESS was sized to provide 13% voltage enhancement in the third rail next to substation B. ESS was sized to provide 4500 A with the duration of 17 s (2.93 MW, 66 MW.s) during train acceleration. A Maxwell supercapacitor (K2 series) and VYCON flywheel were used as the ESS technologies. For SESS, 9 strings of 180 cells in series were required, while for FESS 24, modules were required. As mentioned before, the voltage and current of ESS cells or modules were limited, and ESSs needs to be oversized to provide the required output.
4.3. Cost Analysis
To obtain an accurate selection of suitable technologies for each application, cost analysis of running ESS for 10 years was performed. The cost metrics that were considered included: initial cost (the cost normalized based on the power and energy of ESS), energy conversion cost, balance of plant cost (the owner’s cost for project engineering and project management, land, and grid connection equipment), operation and maintenance cost (O&M), and replacement cost [
10,
25].
The initial cost of the ESS was calculated based on Equation (16):
where
C$/kW and
C$/kWh are the cost per kW and kWh, respectively. The costs for SESS range from 100–300
$/kW and 300–2000
$/kWh. However, for FESS, costs range from 250–350
$/kW and 1000–5000
$/kWh. In this study, we considered the average value for each cost and each technology [
33]. The cost of energy conversion and balance of plant were 153
$/kW and 100
$/kW, respectively. Operation and maintenance costs were classified into fixed cost and variable cost. Fixed cost was considered 2% of the initial cost and included the cost of annual tax and insurance. The variable cost for the supercapacitor was 6.7
$/kW per year and included the cost of periodical inspection of the cells and interconnection cable and fixing, if there was a problem confirming the DC voltage and current. The variable cost of FESS was 9.1
$/kW per year and included the service cost for changing the air tank filter, oil, and bearing [
10]. The replacement cost was associated with the life of the energy storage system. For the supercapacitor, the end of life is the moment when capacity goes down to 80% of its initial capacity, or when its ESR doubles. A supercapacitor is claimed by manufacturers to have a 10 year life span, while a recent study showed that after almost 5 years the cells need to be replaced [
34]. To the best of the authors’ knowledge, there is no credible information available for the flywheel from real-world implementation; it is claimed by the manufacturer to have a 15–20 year life span. In this study, we considered the life span of the supercapacitor and flywheel, respectively, as 5 and 15 years. The results of the cost analysis for the application of peak demand reduction are presented in
Table 5.
Based on the aforementioned assumptions, it was concluded that the flywheel has a lower cost than the supercapacitor, and can be considered a more cost-effective solution for peak demand reduction.
The results of the cost analysis for application of voltage regulation are presented in
Table 6. It was concluded that the flywheel has a lower cost than the supercapacitor and can be considered as a more cost-effective solution for voltage regulation.