Optimal Siting and Sizing of Stationary Supercapacitors in a Metro Network using PSO Vito Calderaro, Vincenzo Galdi, Giuseppe Graber, Antonio Piccolo Department of Industrial Engineering University of Salerno Fisciano (SA), Italy
[email protected],
[email protected],
[email protected],
[email protected]
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Two main ESS configurations are usually implemented for railway systems: mobile ESSs, installed on-board vehicle, and stationary ones, installed at the substation level or along the track [6]. Compared to on-board ESSs, stationary ones have the advantage to not be subject to weight and size constraints imposed by vehicle and to be able to balance the voltage at weak points of the network [7]. Regarding ESSs implementation, several solutions are proposed in literature: new battery technologies, supercapacitors (SCs), and flywheels [7-9]. Among them, SCs based ones seems to be the most attractive due to the high-speed characteristics of SCs response, their “power source” working mode and the expected development of this technology.
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Abstract—In this paper, we investigate the design of stationary ESSs based on supercapacitors (SCs) for metro network (MN). We implement a simulation tool in order to estimate the power flow among the metro vehicles and the ESSs through the MN. A new formulation of the ESSs siting and sizing optimisation problem is proposed and solved using particle swarm algorithm. The optimisation process minimises the energy supplied by the electrical substations and the whole ESSs capacity taking into the electrical line constraints in the metro network simulator. Several simulations are performed in order to design the number, the position along the track and the required capacity of the SCs. Using commercially available modules, a realistic design solution is compared with the theoretical one obtained by solving the optimisation algorithm. Finally, we estimate the energy delivered from the electric substations and the energy saved using the real ESSs configuration.
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Keywords—metro network, regenerative braking, energy storage, siting, sizing, supercapacitors, PSO algorithm, optimisation.
I.
INTRODUCTION
Several papers are written on stationary ESSs implementation based on SC, focusing mainly on the sizing and siting problems, that are treated usually severally: the SCs sizing is usually designed equating the maximum kinetic energy of the metro vehicles with the energy that can be stored by SCs [10], or using an optimisation approach without considering the related SCs siting [11]. In [12], Clemente et al. address the SCs sizing problem using a stochastic approach by calculating the probability density function of the interest variables. On the other hand, the only SCs siting problem, is usually solved placing the SCs in arbitrary position along the track or using heuristic method to find the best position [13]. Only a few paper consider jointly siting and sizing design issues, for instance, formulating and solving the optimisation problem by using the Lagrange multiplier [14].
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The heavy impact in terms of pollution and meaningful contribution to the whole energy consumption [1] is leading to a radical change in transportation systems, encouraging penetration of electric energy compared to fossil fuels. This has led not only to the appearance of the first electric cars (commercially and technically competitive) but above all to a significant deployment in urban and metropolitan areas of mass transportation such as subways, trams and light rail with increasing energetic performances in terms of efficiency [2]. To reduce energy consumption in metro systems, research mainly focuses on development of more efficient drive train technologies and designs [3]. Another way, immediately possible, to increase efficiency in railway systems is to implement metro vehicles speed profiles minimizing the energy consumption (Eco-drive) [4]. On the other hand, one of the most effective methods to reduce the energy consumption in metro networks is to recover the vehicles braking energy [2].
In a conventional metro network equipped with irreversible DC substations, braking energy is only usable if other vehicles are simultaneously demanding energy, otherwise, it is wasted as heat on the vehicles braking resistors. In order to avoid this energy wasting, energy storage systems (ESSs) represent a very interesting option to store the metro vehicles braking energy making it available for the next traction operation with consequent lower use of energy from the feeding network [5].
This paper proposes an heuristic method for the joint siting and sizing design of stationary SCs, taking into account the i) track topology - slopes and curves – ii) the electrical features of the feeding line, iii) the mechanical characteristics of the vehicle and its time-table. We solve the siting and sizing problem using a particle swarm optimisation (PSO) based algorithm and the obtained results are compared and discussed. The metro network model is implemented in a simulation routine based on the ‘quasi static’ backwards looking method, described in [15], [16]. The proposed design solution allow to maximize energy efficiency, to minimize the number and capacity of SCs and then, consequently, to reduce the costs. The paper is organised as follow: Section II describes kinematic of the vehicle and, the models of the metro network, ESSs and vehicles used for the implementation of the simulation routine. In Section III is formulated the ESSs siting and sizing
optimisation problem and the PSO based solution algorithm is presented, whereas case study and results of several simulations are presented and discussed in Section IV. Finally, conclusions are listed in Section V. MODELLING OF THE METRO SYSTEM
A. Metro vehicle Usually, in the literature the metro system is modelled by using the mass-point model of metro train [4], [6], [14]. The longitudinal dynamic of vehicles evolves according to the force balance equation described by the model expressed by
m v
dv F RBASE v RLINE x dt dx dt
where m is the mass of the vehicle, ρ is a correction factor taking into account the rotating mass, v and x are the metro train speed and position respectively, F is the traction or braking force, which is lower and upper bounded, [17]. RBASE(v) is the basic resistance including roll resistance and air resistance, and RLINE(x) is the line resistance caused by track slopes and curves, and they are expressed by RBASE m(1 2 v 2 ) RLINE mg sin x mg
a r x b
efficiency and the inverter efficiency. Fr is total resistive forces, computed as sum of two terms: the basic resistance RBASE, and the line resistance RLINE, defined in (2). To bring into account that the voltage along the track is not constant, the metro train is modelled as an ideal current generator IVEHICLE, whose value is calculated as the ratio between vehicle power and line voltage VLINE, (3). B. Stationary ESS model The stationary ESS model includes the SC modules, the DC/DC converter and the power flow controller (Fig. 1). During the charging period, SCs receive the regenerative power from the vehicles and during the discharging period, they deliver power to the metro trains: therefore, the ESSs are modelled as ideal current sources. A power flow controller commands the DC/DC converter to charge or discharge the SCs, using an energy management strategy, according to the line voltage and the SCs State of Charge (SoC). The secondorder equivalent circuit of SC consists of four elements and is depicted in Fig. 1, [16]. The equivalent series resistance Rs represents the power loss during the charging and discharging operations; the self-charge resistance Rp models the losses due to the leakage current; the inductance L results primarily from the SC physical construction and its value is usually very small. Finally, the capacitor C, that models SC’s capacity, changes linearly with the SC electrodes voltage Vsc according to the following:
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Fig. 1. ESS model and supercapacitor electric model.
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The proposed model is obtained by the integration of three different sub-models: one related to the metro vehicle and its kinematics, the second one related to the stationary ESSs, and the last one related to the metro network supply system.
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II.
Ac
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In (2) 1 and 2 depend on the train characteristics and the train speed, and can be calculated by the train data or obtained by literature; g is the gravitational acceleration and γ(x) is the slope grade. Second term of RLINE is the curve resistance given by empirical formulas, as the Von Röckl’s formula, where r(x) is curvature radius, and a, b are coefficients which depend on the track gauge, tabled in [18]. Metro trains are modelled as current sources absorbing power at the accelerating time or generating power at the regenerative breaking time. The power at the wheels, required to overcome the vehicle inertia, slopes and curves, aerodynamic friction, and rolling friction, is calculated starting from a given speed cycle. Going upstream the vehicle components and their related efficiencies, the power requested from the electrical substations is determined by the following equation:
PVEHICLE
dv m Fr v dt P AUX _ SERVICES
IVEHICLE
g m i
PVEHICLE VLINE .
In (3), PAUX_SERVICES is the necessary power for lighting and cooling (or heating) services, m is the total mass of the metro train - including the passengers -, v is the vehicle speed, ηg, ηm, and ηi represent, respectively, the gear box efficiency, the motor
C C0 1 Vsc
where C 0 is the SC’s capacity constant value and λ [V-1] represents the SC’s capacity voltage coefficient. C. DC feeding system Substations are represented by ideal DC voltage sources, series resistance and series diode only if the substations are not reversible, [10]. The contact wire is modelled as a set of electric resistances that change their value according to the vehicle position [6], [15]. If x(kΔt) is the metro train position at the time kΔt, the value of the resistance upstream Ra and downstream Rb to the metro vehicle towards a generic node of the railway feeding system (electric substation, ESS or another train) are calculated by:
Ra r xkt Rb r d xkt
where, R a and Rb are expressed in [Ω], r [Ω/km] represents resistive coefficient, d [km] is the distance between the two nodes, upstream and downstream the metro train, and x(kΔt)
[km] is the distance between the train and the upstream node at the each time step kΔt. Finally, the electric model of the overall network with the substations, the SC storage units, and the metro vehicle is shown in Fig. 2. Furthermore, it is necessary to improve the model with some small capacitances in parallel to the vehicles in order to describe the receptivity of the network under regenerative braking conditions [15]. They models the voltage rise along the contact wire during the first phase of the regenerative breaking that is used by the ESS control to detect the availability of breaking energy along the track.
t T , n 1,..., N t T , n 1,..., N t T , n 1,..., N
SoCn (t )
2 VSCn (t ) VSC2 m ax
The isoperimetric constraint of SoC - the last in (8) - used in the optimisation problem guarantees that the energy stored by each SC is the same at the beginning and at the end of the trip cycle. B. PSO solution algorithm PSO is a quite recent heuristic method inspired by the choreography of a bird flock [19]. In the real number space, each individual possible solution is modelled as a particle that moves through the problem hyperspace. At each iteration, the velocities of the individual particles are stochastically adjusted according to the historical best position for the particle itself and the neighbourhood best position. Both the best particle and the neighbourhood best are derived according to a user defined fitness function.
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A. Problem formulation The problem we aim to solve consists in finding the optimal number, positioning and sizing of ESSs on the track, taking into account its topological characteristics and the vehicle timetable. The positioning of the ESSs and their related capacity are the input variables of the optimisation problem. We consider as objective function the sum of energy supplied by the substation during the trip and the energy stored by all the ESSs, thus the minimization problem can be written as
t T
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The optimization of the SC siting and sizing can be formulated as a Mixed-Integer Non-Linear Problem. The great difficulty and the too computationally demand in solving these problems, has suggested to find heuristic algorithms to explore more quickly the solution space. So the optimisation problem is addressed using a PSO based algorithm as solving method.
t T
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PROBLEM FORMULATION AND METHOD OF SOLUTION
t T
where T is the total simulation time, VSCn is the voltage at the n-th SC terminals, ISSE and PSSE are the substation current and power, respectively; PTrain is the vehicle absorbed (or generated) power, PBRAKE is the maximum vehicle generated power during the braking phase, PTRACTION is the metro vehicle absorbed power during the traction phase. Finally, SoCn(t) represent the value of the n-th SC state of charge and it is defined in (9).
Fig. 2. Metro network overall electric model.
III.
VLINE min VLINE VLINE max 0 I SSE PSSE max VLINE min P BRAKE max PTrain PTRACTION max V V V SC min SCn SC max SoCmin SoCn Socmax SoCn (t T ) SoCn (t 0)
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J min CP J E ( P, C ) E (C ) SS SC N
ce
N
Ac
where α and β are the fitting weight coefficients, P is the SCs position vector, C is SCs capacity vector and N is the number of ESSs on the track. ESS is the energy supplied by substation and ESC is the total energy that can be stored by all the ESSs. In particular,
The flow chart of the proposed PSO siting and sizing algorithm is shown in Fig. 3. The metro network model was implemented in a simulation routine based on the ‘quasi static’ backwards looking method, due to its short simulation times for estimating energy consumption of vehicles following an imposed speed cycle [15], [16]. The speed cycle is divided in time steps during which all the variables are supposed to be in the steady state. The power needed to satisfy the speed cycle is determined at the wheel level. Then, the power provided by the feeding line is estimated calculating the consumption of the upstream vehicle components. The calculation direction is the opposite of the real power flow direction. Finally, the objective function in (6), is evaluated using a railway simulation tool implementing the models just presented and able to calculate the energy supplied by the substations for a particular siting and sizing configuration.
N 1 1 2 N 2 ESC C cnVSC VSC max cn max 2 n 1 2 n 1
In (7) pn and cn are the SC position and capacity of the n-th ESS, respectively, and VSCmax is the maximum allowable voltage at the SC terminals. Furthermore, we consider the following constraints:
IV.
SIMULATION RESULTS
In order to establish the effectiveness of the proposed solution method, a case study based on existing railway is presented. We evaluate the substations energy saving when there are SCs along the track and without SCs, the line voltage and the current supplied/absorbed by ESSs ensuring that all electrical constraints are complied. Finally, we propose a design solution using commercially available modules. The railways
TABLE I.
VEHICLE PARAMETERS
PARAMETERS
VALUE
Net weight [kg]
59357
Loaded weight [kg] (6 passengers per m2)
88170
Rotating mass [%]
10.46
Max. traction power [kW]
630
Accessories power [kW]
90
Coefficient of auxiliary use
0.75
Gear box efficiency
0.98
Motor efficiency
0.85
Inverter efficiency
0.90
TABLE II.
NETWORK PARAMETERS VALUE
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PARAMETERS
Fig. 3. Flow-chart of the siting and sizing PSO algorithm.
Track’s length [m]
1637
Casazza-Mompiano length [m]
1045
Mompiano-Europa length [m]
592
infrastructure simulation tool and the PSO algorithm are coded in Matlab™.
Rail electric resistance [Ω/km]
0.0133
A. Case study
Substation internal resistance [Ω]
Pa
750
0.0125
Maximum line voltage [V]
900
Minimum line voltage [V]
500
B. Numerical results Several simulations are carried out for the case study described in the previous subsection, in which one metro train moves in the two opposite directions implementing the same driving cycle. We impose 50.000 iterations and 25 particles by running the proposed algorithm on a workstation with an Intel® Core™ i7 (3.20 GHz, 64 bit) processor, 16 GB of RAM and Matlab™ R2013a. The comparison between the case study without ESSs and with one ESS sized and sited using the proposed method, is summarized in Table III.
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The tests are performed on the line EUROPA– MOMPIANO–CASAZZA that represents only a portion of the line PREALPINO–S.EUFEMIA, one of the Brescia metro network. The metro DC line is fed by two electric substations and consists in two subway line sections and three stations, one is intermediate and two are located at the beginning and the end of the line, in correspondence of the substations. Driving cycles and track elevations are shown in Fig. 4: speed cycles consist in repeating two times a first phase of acceleration, followed by a stretch of line path at a constant speed and finally ending with the braking phase.
Substation DC voltage [V]
Ac
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The maximum speed that the metro train can reach is fixed on the entire track to 60 km/h. We consider only one metro vehicle moving along the track. Metro vehicle and feeding network are characterized by the parameters listed in Table I and Table II, respectively.
Fig. 4. Vehicle drive cycle and track elevation EUROPA-CASAZZA.
TABLE III.
ONE ESS SITING AND SIZING
SITING [m]
SIZING [F]
SUBSTATION ENERGY [kWh]
EUROPACASAZZA
100
140
6.491
-
-
7.636
CASAZZA -EUROPA
200
140
9.239
-
-
10.197
LINE
The energy supplied by the electrical substations when there is only one ESS on the track according to its capacity and position is shown in Fig. 5. To minimize the substations delivered energy is necessary having the only one ESS where the vehicle should perform the uphill acceleration. The reduction of the supplied energy is different according to the track direction, although the installed ESS capacity is equal. In particular, the ESSs should be positioned at a distance of 100 m
from the first substation and 1450 m from the second, respectively. On the line EUROPA-CASAZZA, there is a reduction of the absorbed energy by 15.1% while in the opposite direction there is a smaller reduction equal to 9.4%. The results of the PSO siting and sizing procedure, assuming N=5 ESSs on the track, are listed in Table IV. TABLE IV.
CASAZZA -EUROPA
TABLE V.
5-ESSS SITING AND SIZING SUBSTATION ENERGY [kWh]
THEORETICAL AND REAL ESSS SIZING SUBSTATION ENERGY [kWh]
SITING [m]
THEORETICAL SIZING [F]
REAL SIZING [F]
200-
10
0
154.5
SIZING [F]
150
20
300
150
300
130
800
20
1000
60
1200
160
169
1150
10
1500-
20
0
1500
10
200
170
600
20
800
10
1000
70
1500
10
Pa
SITING [m]
6.185
8.901
6.392
0
SUBSTATION ENERGY [kWh]
6.505
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EUROPACASAZZA
composed by the series of four SC units to obtain SC modules with rating voltage 500 V and nominal capacity 15.75 F: each SC unit has rating voltage 125 V and nominal capacity of 63 F, as well as commercially available [20].
The real sizing allows to obtain a slightly higher (1.7%) value of energy delivered by the substations compared to the theoretical sizing because it presents a lower overall ESSs capacity, in the same siting condition. In Fig. 6, we illustrate the SC modules current trends related to their SoC trends on the line EUROPA-CASAZZA. The current supplied/recovered by the ESSs on the DC line reaching a peak value equal to 578 A. The SC modules hold their SoC value within the minimum and
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LINE
Fig. 6. ESSs current and SoC trends on the line EUROPA-CASAZZA.
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Fig. 5. Siting and sizing of one ESS on the line EUROPA-CASAZZA.
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The coefficients α and β in the objective function are chosen both equal to 1. The position and the capacity of the ESSs are discretised. In particular, the ESSs siting varies by 50 metres steps along the track and the SC capacity size varies by steps of 10 F starting from zero up to 300 F. The ESSs on the line EUROPA-CASAZZA, lead to a reduction of the absorbed energy by 19%, while in the opposite direction there is a smaller reduction (12.7%). In Table V, we report the comparison, in the same siting conditions, between the theoretical ESSs sizing and a real design solution obtained using commercially available SCs modules. We implement the theoretical sizing using the proposed PSO algorithm, considering both the track directions, and testing the results evaluating the energy supplied by the substation on the line EUROPA-CASAZZA. The real sizing, instead, is obtained by implementing the theoretical sizing with commercial SC modules. We consider each ESS module
Fig. 7. Comparison on line voltage: no ESSs and real ESSs sizing (line EUROPA-CASAZZA).
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maximum value equal to 40% and 90%, respectively. In Fig. 7, we show the line voltage trend in case of ESSs sized and positioned using the proposed method and without ESSs on the track. Although the line voltage has voltage drop well below the lower limit, using ESSs allow to reach slightly better performances. The ESSs hold also the line voltage value much lower than the maximum limit because is not required switching on the braking chopper and wasting energy. In Fig. 8, we illustrate the comparison between the current trends supplied from the substation using ESSs on the track and without ESSs respectively, on the line EUROPA-CASAZZA. We find a significant reduction (15%) in the supplied peak current, resulting in savings on energy delivered, and, in addiction, on the sizing of the power components of the substations converters too.
[6]
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Fig. 8. Comparison on substation current: no ESSs and real ESSs sizing (line EUROPA-CASAZZA).
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CONCLUSIONS
[10]
[11]
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V.
[12]
ACKNOWLEDGEMENT
[17] [18]
Ac ce
In this paper, we investigated the design of stationary ESSs based on supercapacitors for metro network. We modelled metro supply network, metro vehicles and stationary ESSs and a simulation tool to quantify the energy savings related to a particular ESSs design solution was implemented. A new methodology for solving the ESSs siting and sizing problems based on particle swarm optimization was proposed. We tested the proposed method on a real Italian metro network in which circulates a light driverless vehicle for passengers transport. Results proved that the joint procedure for ESSs siting and sizing allows to achieve an increase in energy savings. We obtained, in addition, a decrease of the maximum current delivered by substations resulting in reduction of the power converter devices ratings.
The obtained results are part of the activity carried out in the research project: “SFERE Sistemi Ferroviari: Ecosostenibilità e Risparmio Energetico”, developed with the financial support of National Operative Program PON R&C. The authors would like to thank the project coordinator, Dr. Luigi Fratelli of AnsaldoBreda.
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