Optimal Control Strategy of Onboard Supercapacitor Storage System for Light Railway Vehicles

Diego Iannuzzi, Pietro Tricoli Department of Electrical Engineering - University of Naples Federico II

iandiego@unina.it, ptricoli@unina.it

Abstract-The paper deals with the use of onboard supercapacitors for Light Rail Vehicles. The practical utilization of supercapacitors requires suitable control strategy of bidirectional dc/dc power converters for the regulation of power flows between the contact line and the electrical drives of the power-train. The control strategy is based on the simplified mathematical model of both the electrical drive and the electrical railway network. A one-side dc supplied streetcar contact line has been considered. The target of the control is to minimize the mean square voltage deviation at the vehicle pantograph and the power losses along the line. This allows to limit the peak currents of the contact line and to recover partially the kinetic energy of the vehicle during the braking periods. Optimization theory has been used for the determination and implementation of the real time control strategy. Experimental tests made on a laboratory scale prototype have proved that the suggested control strategy is very effective and applicable to a real streetcar. Index Terms-Supercapacitors, light vehicles, optimization control, control strategy.

I. NOMENCLATURE

r0 resistance of the full length line xν position occupied by the ν-th streetcar I(x,t) current flowing in the point x of the line at time t Is current supplied by the electrical substation Isc,ν current of onboard supercapacitor of ν-th streetcar JT,ν current required for traction by the ν-th streetcar Jν total current of the ν-th streetcar L total length of the line S(x) cross-sectional area of the line in the point x V1 voltage at streetcar pantograph δ(x) Dirac Delta function σ(x,t) current density in the point x of the line at time t ρ resistivity of the wires of the contact line Δv(x,t) voltage drop in the point x at time t

II. INTRODUCTION

Light transportation systems as tramways, urban and subway metro-systems and trolleybuses are complex electrical systems characterized by continuous load changing. These systems, because of their attractive characteristics in terms of costs, environmental pollution and energy efficiency, will be exploited more and more in the next future. Their foreseen expansion of the tracks and the increasing of both the power requested and frequency of running trains have

determined a significant increase of line power losses and voltage drops. In this context, energy storage devices, which may be on board or located wayside in both the substations or stops, are very interesting means for enhancing energy saving, energy efficiency, pantograph voltage stabilization and power peak reduction.

Among different storage technologies, the most suitable ones for light transportation systems appear to be Supercapacitors (SC), Flywheels (FW) and Superconducting Magnetic Energy Storage (SMES). Some interesting papers have investigated the possibility of employing these equipments for real time energy optimization and voltage regulation [1-3]. For example, consistent reductions of power peaks required by feeding substations during the acceleration and braking phase have been presented in [4-7]. Moreover, the use of a storage device, interfaced with the light transportation system by a properly controlled power converters, allows also to improve the dynamic response of the overall system.

At present, the technical solutions suggested in literature are mainly oriented to the management of regenerative braking of trains directly into substations, using front-end active inverters and wayside storage devices [8-16]. Both solutions present the problem concerning the management of power flows between substations and trains. In fact, the recovery of kinetic energy during braking is subject to unpredictable traffic conditions. Actually the estimated recovered energy is not greater than 10% of that drawn during the acceleration. A promising solution is the use of onboard storage devices [17]. Regenerative energy is stored during the braking of the train and reused in the next acceleration. This permits the limitation of contact line voltage drop during accelerations since the peak power is supplied by the storage devices. Respect to the solution with wayside storage devices, the onboard storage simplifies significantly the power control in the substations.

Actually, studies made and results published so far in the technical literature do not seem to be supported by an appropriate control strategy experimentally validated. Moreover the suggested controls do not take into account directly the electrical requirements of the line, i.e. compensation of line drop voltage, train voltage stabilization and line power losses compensation [18]. Stenier, Klohr and Pagiela made different experimental tests on a prototype light rail vehicle of the Bombardier Transportation, equipped by onboard supercapacitors (1 kWh with a mass of 450 kg), in order to evaluate the energy saving capability of the train, equal approximately to 30% [19, 20].

978-1-4244-6392-3/10/$26.00 ©2010 IEEE 280

For this reason, authors suggest a multi-objective control strategy based on the optimization theory. The target of the control is to minimize the mean square voltage deviation at vehicle pantograph and the power losses along the line. Experimental results are also reported, with reference to a simple reduced scale model, in order to validate the proposed control strategy.

III. SYSTEM CONFIGURATIONS OF STREETCAR LINES AND SIMPLIFIED MATHEMATICAL MODEL

Two standard configurations of contact lines have been considered and their mathematical models have been derived referring to the generalized function theory. The mathematical models are then used to carry out design algorithms that enable the selection of the more proper set of supercapacitor stations. The two standard configurations of contact lines are listed below. 1) Two side dc supplied contact lines (see Fig. 1).

Both contact lines for going and going back ways are supplied by terminal dc substations. The ends of each line are considered to have always the same voltage value. The maximum voltage drop is reached when the vehicle is in the mean position. 2) One side dc supplied contact lines (see Fig. 2).

Both contact lines for going on and going back ways are supplied by a single dc substation located at one end of each line. The voltage drop follows the car displacement and its maximum is reached at the final terminal (not directly supplied terminal).

The intensity of the electrical current required by the streetcar depends on the time and on its location along the way. Currents are supplied by feeding station(s) and flow from the source to the user. It is easily recognised that in every contact line two different currents can be defined as time and location functions: a transverse current, J [x(t),t], taken out by streetcars and a longitudinal current, I [x(t),t], flowing along the line. The former one is a function connected with the locations of streetcar and with the power required by each of them. The last one is a function of the time and of the curvilinear abscissa of the line.

Transverse current functions represent the input data of the

mathematical model. Longitudinal current functions represent the unknown quantities of the problem. It is possible to define also the current density along the contact line cross-section, σ(x,t). In the following, reference is made to a line supplying n different streetcars, each one characterised by the progressive subscript 1 ≤ ν ≤ n. Each streetcar carries a current Jν[x(t),t] in the point xν(t). Therefore, it is possible to write that:

( ) ( ) ( )∫∫ −=⇒=⋅x

dxtxctItxIdSI0Σ

,,0,0n ,

where:

( ) ( ) ( )[ ]∑−

=

−=1

0ννν δ,,

n

txxtxJtxc

It is, therefore:

( ) ( )( ) ( ) ( ) ( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡−== ∫

x

dxtxctIxSxS

txItx0

,,01,,σ .

The quantity σ(x,t) leads immediately to the definition of line voltage drop, i.e.:

( ) ( )∫=x

dxtxtxv0

,σρ,Δ ,

In the case of one side dc supplied contact line, the current in the last branch is always zero and therefore the current of the feeder is the sum of the load currents:

( ) ( ) ( )∑=

==n

s tJtItI1ν

ν,0 . (1)

If xν(t)< x < xν+1(t), the voltage drop in the generic point of the line is given by:

( ) ( ) ( ) ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡+= ∑∑

=+=

ν

1ρρρ

1νρρ

ρ,Δ tJtxtJxS

txvn

(2)

if for simplicity the cross-sectional area, S, is constant. If supercapacitors are located onboard of each streetcar, the load current, Jρ, is given by the difference between the train current and supercapacitor’s current: ( ) ( ) ( )tItJtJ scT ρ,ρ,ρ −= . (3) In the next sections, the control strategy makes reference to a single streetcar (n = 1).

IV. CONTROL STRATEGY BASED ON OTIMIZATION THEORY

A. Basic formulation of optimization theory The optimization techniques are intrinsically candidate

tools for improving as far as possible the performances of electrified transit systems. Their potentialities can be used in order to obtain a multi-objectives control strategy. Furthermore, a constrained optimization problem can result a powerful mean for identifying in the planning stage and during operating conditions the optimal references for the energy management of the trains.

The optimal control of the energy storage device has contemporaneously to guarantee the line power losses and the

Fig. 1. Two side dc supplied contact line

Fig. 2. One side dc supplied contact line

281

drop voltage profile minimization at the vehicle pantograph. The following objective functional φ can be chosen:

( ) ( )[ ]dtIwVVwdttxfT

sref

T

∫∫ +−==ϕ0

22

211

0

, (4)

where w1 and w2 are suitable weight coefficients which are able to handle the two previously mentioned objectives, V1 is the voltage at streetcar pantograph and Vref is the rated line voltage.

The optimisation has to be effected by taking into account also the network and technical constraints. In mathematical terms, the constrained optimisation problem can be summarized in a compact way as:

( )

( )( ) 0,

,0,,min

≤ψ=θ

ϕ

mxmx

mx (5)

where x is the state vector, m is the vector of the control variables of the static optimization, θ(x,m) = 0 refer to the dc electrical load-flow relationships, i.e. the electrical equations between supercapacitors and the contact line. If the cyclic nature of the load traction has to be retained in the modeling, a further constraint needs for imposing the equality between initial value of supercapacitor voltage and the final one; ψ(x,m) ≤ 0 takes into account in a compact way all the technical constraints with respect to substations, trains, line and storage device.

B. Control Strategy In the examined case, the problem described by (5) has

been solved analytically by mean of the determination of supercapacitor current, Isc,1, that minimizes the power losses of the line and mean square voltage deviation at vehicle pantograph. This current represents the reference current of dc/dc power converter.

The optimization problem, described by (5), can be approached making reference to the following augmented functional:

,θλ2

1∑

=

+=h

hha ff

where θh represents the constraints of streetcar line mathematical model, as shown by (1) and (2):

,θ

,θ

1,1,2

011

scTs

s

IJI

ILxrEV

+−=

+−=

and λh are Lagrange multipliers. A further constraint needs for imposing the isoperimetric condition of supercapacitors, that is:

∫ =T

sc dtIV0

1,1 0 , (6)

In this case the augmented functional, fa, becomes:

,1,1

2

1sc

hhha IVff γ+θλ+= ∑

=

where γ is real constant. The optimal control law, Isc,1, is obtained by solving the following set of equations:

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

=

=∂∂

==∂∂

∫ .0

,0

2,1,0λ

0

1,1

1,

T

sc

sc

a

h

a

dtIV

If

hf

(7)

The set (7) is represented by four equations in the following unknown quantities: V1, Isc,1, Is and γ. Solving the 1st, 2nd and 3rd of (7) for Isc,1, the control law is:

Lxr

Lxrww

LxrwV

LxrwE

Lxr

LxrwwJ

IrefT

sc

0

2

012

01010

2

0121,

1,

γ

2γ

2γ

+⎟⎠⎞

⎜⎝⎛+

+⎟⎠⎞

⎜⎝⎛ +−

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟

⎠⎞

⎜⎝⎛+

= . (8)

The value of γ is finally obtained substituting (8) in (6) and solving the integral.

Fig. 3 shows the block diagram of the control technique proposed. The desired train voltage at the pantograph, Vref, and weight coefficients w1 and w2 are the inputs of optimization control block, whereas the variable line contact resistance and train current are, respectively, the identified and measured quantities. The output of control block is the supercapacitor current, Isc,1, given by (8). Then, the line reference current is obtained by the difference between the actual value of train current and the supercapacitor reference current. The new reference value is compared with the actual value of line current as depicted in the Fig. 3. The output of PI control is processed in the duty-cycle block on the basis of actual value of supercapacitor voltage. The output value is, then, compared with triangular waveform with a switching frequency of 2 kHz. The outputs of PWM block are TTL signals which impulse the gates of the switches.

The identification of line contact resistance is obtained by means of measured line current and line voltage. All measured quantities are digitally filtered in order to reduce the noise.

The use of the reference current (8) implies the presumptive knowledge of load train duty cycle. In fact the coefficient γ is known only by solving the isoperimetric condition given by the (6). If during the load cycle the actual train current is different from the expected value, the isoperimetric condition is no more satisfied. In this case, it is possible to solve the set (7) without the isoperimetric condition (γ = 0). The correspondent reference supercapacitor current is:

( )

2

012

0

1,1,

⎟⎠⎞

⎜⎝⎛+

−−=

Lxrww

EVLxr

JIref

Tsc . (9)

282

Fig. 3. Control scheme of the suggested control technique

In Fig. 4 the line reference current is plotted as a function of train position. The function presents a maximum in correspondence of a value of line contact resistance equal to:

( ) .2

1,1

2

2max,

1

2max,1 EV

ww

wI

wwr ref

refs −== (10)

In order to optimize the stored energy of supercapacitors during the braking and steady-state operations of the train, the value r1,max must be lower than the line contact resistance r1 at the end of line (equal to r0), and the maximum current value Iref

s,max must be lower than the maximum value of train current J1,max. This implies that the weight coefficients must be chosen appropriately on the basis of the above mentioned conditions.

V. EXPERIMENTAL VALIDATION ON LABORATORY SCALED PROTOTYPE

In order to verify experimentally the effectiveness of the suggested control strategy, a single light metro-train line has been simulated in the laboratory. Because of the impossibility to reproduce the moving mass and the power of light vehicles on real DC track line, an electromechanical simulator has been set-up and scaled opportunely [18]. The scale model is located in the Electrical Machines Laboratory of the Department of Electrical Engineering of the University of Naples Federico II. The main characteristics of the real system and simulator are reported in [21].

A. Electromechanical Simulator The electrical drive of the simulator consists of a voltage

source inverter and an induction motor of rated powers 20 kVA and 5.5 kW respectively, simulating the power train of the light metro transit system. The storage system is realized by supercapacitors interfaced with DC traction line by means of a bidirectional 20 kVA interleaved dc/dc converter. The maximum allowable current at the supercapacitors side is 150 A. The rated DC bus voltage is

430 V. The remote control of the inverter allows to emulate different load conditions, by suitably selection of the motor speed and its acceleration. An opportune variable resistor is placed in order to simulate the variation of the track line resistance according to the vehicle movement. The block diagram of the test bench with the data acquisition system is shown in Fig. 5. The dynamic load is simulated by means of a mechanical scale model, reproducing an Italian typical train in terms of friction forces and inertia. The simulator is mainly composed of a mechanical transmission unit (motor, gearbox, wheel-set), located on a mobile frame, and four wheels set on a rigid axle.

Fig. 4. Line current reference as function of train position

 

μp

IM3

TA

TV

TA

TV

NIDAQ

id iLoad

vsc

vdDC/AC Inverter

isc

ωr

Supercaps Device

Cdc

400V DC

50 Hz 380V

lf

rd

Scale model of railway vehicle

PC Remote Station

ld

Texas Intruments TMS320VC33

rb

c

Fig. 5. Block diagram of the test-bench with data acquisition system

283

The transmission and the mobile frame lean on a couple of wheels by means of a wheel-set, which represents a pair of driving wheels of the locomotive. In order to obtain different friction forces between the pairs of contacting wheels, it has been added a mass fixed on the mobile frame. The flywheels represent the inertia of translating masses, which is directly related to the mass of the real train. The storage device has been realized by two series supercapacitors modules, each of one with a rated voltage equal to 75 V and rated capacitance equal to 3.3 F. The variable contact line resistance has been simulated with a variable rheostat of maximum value 2.2 Ω.

The unit control is based on two independent Digital Signal Processor boards. The first one is used for the implementation of the vector control of induction motor, whereas the second one is devoted to the power management of supercapacitors storage device. This last one is based on the Texas Instruments TMS320VC33 platform The sampling time is T = 400 µs. The data acquisition system consists of two voltage and current transducers, one encoder of 2000 pulses/rotation and a National Instrument data acquisition board with eight inputs channel available.

B. Experimental results The performed tests aim to evaluate the capability of the

storage device of supporting the electrical substation during train accelerations and of energy recovering during the braking. Therefore source and load currents, train and supercapacitor voltages have been collected by a data acquisition board. The speed cycle considered for the tests is shown in Fig. 6. The simulated vehicle starts from standstill, accelerates up to 18.5 km/h (equivalent to a motor speed equal to 500 rpm), has a coasting phase of about eight seconds and brakes in seven seconds until it stops. During the starting phase (Δt ≅ 10 s), the reference speed has been set to 500 rpm and, since the DSP controlling the motor sets a maximum torque equal to 1.2 times the rated torque, the vehicle accelerates with approximately constant acceleration. After the coasting, the trains brakes with the same torque of the acceleration, i.e. 1.2 times the rated torque.

Fig. 7 shows the comparison between the actual and the reference source current, given by the optimization procedure explained in the previous section. It can be noted that the two currents exhibit the same behaviour, except during coasting.

Fig. 6. Angular speed of the train motor for the sample case considered

Fig. 7. Comparison between actual source current and reference current

This can be justified making reference to Fig. 8, which shows the load current drawn by the train during the cycle. It is evident from the figure that, during coasting, the current is not constant as expected but there are high oscillations, due to mechanical torque vibrations, that are not taken into account in the model. The presence of these unexpected oscillations implies that the actual current follows the reference only with its average behaviour.

The dynamic behaviour of supercapacitors is shown in Figs. 9 and 10. Fig. 9 depicts the voltage at supercapacitor terminals and it is possible to observe their discharge and charge respectively during the accelerating, coasting and braking operations of the train. Moreover in Fig. 10, the compensation of line drop voltage can be observed: in fact the maximum train drop voltage is equal to 418 V. If the control of supercapacitors was not active, the train voltage would reach the minimum value of 408 V in correspondence of the load current peak (12 A).

VI. CONCLUSIONS

In this paper, a new control strategy has been presented for light railway vehicles based on the optimization theory. The main goal of the control is the compensation of train voltage drop and the reduction of line current peaks. The optimization procedure followed allow the determination of supercapacitor optimal reference current in order to minimize a given objective function.

Fig. 8. Load current drawn by the train for the cycle of Fig. 6

284

Fig. 9. Supercapacitor voltage during the cycle

Fig. 10. Diagram of the voltage at the train pantograph

The effectiveness of the proposed control technique has been experimentally verified by an opportune scale model arranged in the laboratory. Experimental results show that the actual source current tracks the reference with a good agreement, allowing a consistent reduction of voltage drop at train pantograph. Moreover, the controller is capable of managing the power flows of supercapacitors in order to reduce line current peaks and to recover the energy available during the train braking. Experimental tests have also put in evidence that mechanical vibrations of the scale model are not negligible and imply high oscillation of actual line current. Further studies will be devoted to simply take into account those vibrations and to modify accordingly the control technique. Moreover, the robustness of the control technique against the uncertainty of model parameters will be carefully analyzed in order to find the optimal values of weight coefficient w1 and w2.

REFERENCES

[1] R. Rizzo, and P. Tricoli, “Power flow control strategy for electric vehicles with renewable energy sources,” Proc. of 1st International Power and Energy Conference PECon 2006, Putrajaya, Malaysia, pp. 34-39. 2006

[2] D. Iannuzzi and P. Tricoli, “Integrated storage devices for ropeway plants: useful tools for peak shaving,” Proc. of 33rd Annual Conference of the IEEE Industrial Electronics Society IECON’07, Taipei, Taiwan, pp. 396-401, 2007.

[3] D. Iannuzzi, L. Piegari, and P. Tricoli, “Use of Supercapacitors for Energy Saving in Overhead Travelling Crane Drives,” Proc. of 2nd

International Conference on Clean Electrical Power, Capri, Italy, pp. 562-568, 2009.

[4] A. B. Turner, “A study of wayside energy storage systems for railway electrification,” IEEE Trans. Ind. Appl., Vol. 1A-20, pp. 484-494, May 1984.

[5] A. Rufer, D. Hotellier and P. Barrade, “A Supercapacitor-based energy storage substation for voltage compensation in weak transportation networks,” IEEE Trans. Power Del., Vol. 19, (2), pp. 629-636, Apr. 2004.

[6] M. Chymera, A. C. Renfrew and M. Barnes, “Energy storage devices in railway systems,” Seminar on innovation in the railways: evolution or revolution, Austin Court, Birmingham, UK, Sep. 2006.

[7] L. Battistelli, F. Ciccarelli, D. Lauria, and D. Proto, “Optimal design of DC electrified railway Stationary Storage System,” Conf. Rec. of 2nd ICCEP Conf., Capri, Italy, June 9-11, 2009.

[8] B. Mellitt, Z. S. Mouneimne, and C. J. Goodman, “Simulation study of DC transit systems with inverting substations”, IEE Proc. Electric Power Application, vol. 131, issue 2, pp. 38-50, 1984.

[9] Chang-han Bae, Dong-uk Jang, Yong-gi Kim, Se-ky Chang, and Jai-kyun Mok, “Calculation of regenerative energy in DC 1500V electric railway substations,” ICPE’07 7th International Conference on Power Electronics, 22-26 Oct. 2007, pp. 801-805.

[10] P. Terwiesch, S. Menth, and S. Schmidt, “Analysis of transients in electrical railway networks using wavelets,” IEEE Trans. Industrial Electronics, vol. 45, no. 6, pp. 955-959, Dec 1998.

[11] Chan-Heung Park, Su-Jin Jang, Byoung-Kuk Lee, Chung-Yuen Won, and Han-Min Lee, “Design and control algorithm research of active regenerative bidirectional DC/DC converter used in electric railway,” ICPE’07 7th International Conference on Power Electronics, 22-26 Oct. 2007, pp. 790-794.

[12] G. Morita, T. Konisihi, S. Hase, Y. Nakamichi, H. Nara, and T. Uemura, “Verification tests of electric double layer capacitors for static energy storage system in DC electrified Railway,” Proc. of IEEE International Conf. of Power Electronics SPEEDAM 2008, Ischia June 2008.

[13] A. Adinolfi, R. Lamedica, C. Modesto, A. Prudenzi, and S. Vimercati, “Experimental assessment of energy saving due to trains regenerative braking in an electrified subway line,” IEEE Trans. Power Delivery, vol. 13, issue 4, pp. 1536-1542, 1998.

[14] Y. Taguchi, M. Ogasa, H. Hata, H. Iijima, S. Ohtsuyama, and T. Funaki, “Simulation results of novel energy storage equipment series-connected to the traction inverter,” European Conference on Power Electronics and Applications, 2-5 Sept. 2007, pages 1-9.

[15] R. Barrero, X. Tackoen, and J. Van Mierlo, “Improving Energy efficiency in Public Transport: Stationary supercapacitor based energy storage systems for a metro-network,” Proc. of Vehicle Power and propulsion Conference VPPC’08, pp.1-8, 2008.

[16] Yicheng Zhang, Lulu Wu, Xiaojun Hu, and Haiquan Liang, “Model and control for supercapacitor-based energy storage system for metro vehicles,” Proc. of International Conference on Electrical Machines and Systems ICEMS’08, 2008.

[17] D. Iannuzzi: “Improvement of the Energy Recovery of Traction Electrical Drives using Supercapacitors,” Proc. of 13th International Power Electronics and Motion Control Conference 2008 EPE-PEMC, September 1-3, 2008 Poznan, Poland.

[18] W. Lhomme, P. Delarue, P. Barrade, A. Bouscayrol, and A. Rufer, “Design and Control of a supercapacitor storage system for traction applications,” Conf. Rec. 2005 Industry Applications Conference, 2005.

[19] M. Steiner, M. Klohr, and S. Pagiela, “Energy Storage System with UltraCaps on Board of Railway Vehicles,” Proc. European Conference on Power Electronics and Applications, 2007.

[20] M. Steiner and J. Scholten, “Energy storage on board of railway vehicles,” Proc. of 2005 European Conference on Power Electronics and Applications, 2005.

[21] P. Grassia and D. Iannuzzi, “A scale model for experimental evaluation of bogie vibrations: Design, manufacture and measurement techniques,” Proc. of Int. Conf. on Railway Traction systems, Capri, Italy, May 15-17, 2001.

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