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On Board Energy System Based on Batteries and Supercapacitors

2007, IFAC Proceedings Volumes

The on-board energy system permits the storage/delivery energy in electrical vehicles. It can use different energy devices working together, like batteries and supercapacitors. The energetic performances of batteries make them efficient, but for supplying pulsating loads, supercapacitors must be added. In this paper, the design of the system is presented and the dynamic model is described using the Port-Hamiltonian formalism. The Passivity-Based Control strategy is proposed according to achieve the best energy management of the system. Simulation results of the system processes are presented in order to prove that the model and the control strategy applied can ensure the global system stability.

IFAC Workshop ICPS'07 2007, July 09-11 Cluj-Napoca, Romania            ON BOARD ENERGY SYSTEM BASED ON BATTERIES AND SUPERCAPACITORS   C. Lungoci1, M.Becherif2, A. Miraoui3, E. Helerea1   1 Electrical Engineering Department, UNITBV, Brasov, ROMANIA 2 SeT, UTBM, Belfort (cedex) 90010, FRANCE 3 L2ES, UTBM, Belfort (cedex) 90010, FRANCE     Abstract: The on-board energy system permits the storage/delivery energy in electrical vehicles. It can use different energy devices working together, like batteries and supercapacitors. The energetic performances of batteries make them efficient, but for supplying pulsating loads, supercapacitors must be added. In this paper, the design of the system is presented and the dynamic model is described using the Port-Hamiltonian formalism. The Passivity-Based Control strategy is proposed according to achieve the best energy management of the system. Simulation results of the system processes are presented in order to prove that the model and the control strategy applied can ensure the global system stability. Copyright © 2007IFAC.  Keywords: Electrical vehicle, Supercapacitors, Batteries, Passivity-Based Control.      1. INTRODUCTION The Passivity Based Control strategy is focused on applied for the control of the DC bus voltage and supercapacitors current. This control strategy analyzes the characteristics of the system from the point of view of energy and combines the highest energy flow management to system stability (Yang, et al, 2004). Finally, simulation results are presented, while conclusions and indications about the future work are discussed.  In the automotive fields, a great importance is accorded to the optimization of the on-board energy system, with the aim to increase the efficiency of the motor drive. Most recent researches proved that it is suitable to use a hybrid solution for the on-board systems architecture, by combining many energy storage/delivery devices (Becherif, et al., 2007; Becherif, et al., 2006; Becherif, 2006). In papers developed by Lungoci, et al. (2006), and Lungoci, and Helerea (2006) it was studied a model of an energy supply-system, including energy devices, converters and a DC motor. The proposed energy devices were batteries - which deliver a constant energy and the supercapacitors - which ensure the picks of power during the transient. This paper comes to advance the researches by using another simplified equivalent circuit model for the supercapacitors. Also, according to obtain a high energy management of the system and to reduce the energy losses, bidirectional converters are proposed. The new design of the system is presented and the dynamical model is given. The Port-Hamiltonian theory is used to exhibit important physical properties.   2. DESIGN AND MODEL OF THE SYSTEM In (Lungoci, et al. 2006) the general architecture of the on-board energy system is explained. It consists of batteries, the boost and bidirectional converters, supercapacitors and the motor as load. In the new proposed design, the boost is replaced by a bidirectional converter. In this way, during braking phases of the motor, the energy can be stored in both storage devices: batteries and supercapacitors, which leads to benefits in terms of energy management of the system (Camara, et al, 2006). The used model for the pack of supercapacitors is based on the first order model, containing an internal resistance in series with a varying capacity. -197- di sc dt di Lm m dt V 0  R sc i sc  (1  U sc )V dc L sc The structure of the system is presented in the Fig.1:  (3)  R m i m  V dc  k e p : The control variables U cb , U sc are reported to the converters and each arm of them is controlled by complementarities law, as follows:  Fig. 1. On board energy system structure.  According to simulations in temporal domain of the systems based on supercapacitors, the variable capacity represented is the load capacity part which depends on the load voltage of supercapacitors V0 . The charge of supercapacitors follows the relation: C sc C 0  kV0 ! 0 ­Tb 1 ½ Ucb 1: ® ¾,Tb ¯Tb 0¿ ­Tb 0½ Ucb 0 : ® ¾,Tb ¯Tb 1 ¿ ­°Tsc 1 ½° Usc 1: ® ¾, Tsc °̄Tsc 0°¿ ­Tsc 0½ Usc 0 : ® ¾,Tsc ¯Tsc 1 ¿ Eb  Rb ib (1) (4) closed, Tsc open open, Tsc closed x 1 1 > x 4  (1  U cb ) x 2 @ Cs x 2 1 >E b  R b x 2  (1  U cb ) x 1 @ Lb x 3 1 >x 4  x 7  (1  U sc ) x 6 @ C dc x 4 1 >x 1  x 3 @ L dc x 5  x 6 1 >x 5  R sc x 6  (1  U sc ) x 3 @ L sc x 7 1 > R m x 7  x 3  k e p : @ Lm (2) The equivalent circuit of motor is composed by a resistance in series with an internal inductance and an electromotive force. The dynamics of the system are described by the following: dVs idc  (1  U cb )ib dt di Lb b Vb  (1  U cb )Vs dt dV C dc dc idc  im  (1  U sc )i sc dt di Ldc dc Vs  Vdc dt dV (C 0  kV0 ) 0 i sc dt open, Tb closed To obtain the state space model of the system, equations system (3) can be rewritten into the state equations: where k is the coefficient representing the dependence on voltage (Rafik, et al, 2007). The battery is represented by its electromotive force e.m.f. in serial with its internal resistance. The mathematical model is: Vb closed, Tb open Cs (5) 1 x6 C 0  kx 5 where the state variables vector is: (3) x >x1 >Vs x2 x3 ib Vdc x4 idc x5 V0 x6 i sc and control variables vector is: u x7 @ T im @ T >U cb U sc @ . T The principal goal is to maintain a desired value of the DC bus voltage, which imposes to have a constant energy delivered by the battery, without big fluctuations. Moreover, for minimizing energy losses -198- in the system, it is necessary to feed back the energy during the braking phases of the motor, especially into the supercapacitors. In order to accomplish these tasks, the output variables vector is proposed to be: y >y1 y2 @ >x3 T x6 @ >Vdc T where: H system, isc @ T and the desired equilibrium point is defined by: ­ib ct1 ;Vdc ® ¯V0 ct 3 ; i sc Vd ; idc ct 2 ; 0; im ct 4 ; : 1 T x Qx is the scalar energy function of the 2 Q diag ^C s , Lb , C dc , Ldc , C sc , Lsc , Lm `, J R is the interconnection matrix, J T T R ! 0 is the damping matrix and G is matrix of proper dimensions. The energy H of the (passive) uncontrolled system decreases until a minimal value which usually doesn’t correspond to the desired equilibrium point. The PBC technique aims to develop a state feedback u that shapes the total energy function of the system to obtain closed-loop energy with a minimum in the desired equilibrium point x . All the computations are made after the following x x  x , in order to have a variable change ~ steady state regulation error equal to zero. The desired energy function of the system is: ½ ¾ :d ¿ where Vd is the desired DC bus voltage and : d is the desired motor speed. Generally the internal resistance rb is very low, so the Joules losses on it are negligible compared to the power delivered by the battery. In these conditions, after calculations, the desired equilibrium state space vector is: x >x1 x2 x3 x4 x5 x6 x7@ Hd T 1 ~T ~ x Qx 2 (7) T ª Vd (Vd ke p:d) V k p: º V k p: Vd d e d V0 0 d e d » «Vd Rm ¼ Rm Rm ¬ Eb The new error dynamics model of the system is: ~ x1 1 ~ > x4  x4  (1Ucb )(~x2  x2 )@ Cs ~ x2 1 >Eb  Rb~x2  Rb x2 (1Ucb)(~x1  x1)@ Lb 1 ~ ~ >x 4  x 7  (1  U sc ) ~x 6 @ C dc 1 ~ ~ >x1  x3 @ Ldc 1 ~  x6 C0  k (~ x5  x5 ) 1 ~ >x5  x5 Rsc~x6  (1Usc )(~x3  x3 )@ Lsc 1 > Rm (~x7  x7 )  ~x3  x3  ke p:@ Lm  k (~ x5  x5 ) C sc >0 and the equilibrium control vector is: u >U U sc @ T cb ª Eb V º R  b (Vd  ke p:d ) 1  0 » «1  Vd ¼ ¬ Vd Eb Rm T ~ x 3 ~ x 4 Using the PCH: Port Controlled Hamiltonian representation, the PBC: Passivity Based Control technique will be implemented for the system control. ~ x 5 ~ x6 3. PASSIVITY BASED CONTROL STRATEGY ~ x7 From the system theory perspective, the concept of energy is lost; hence it is necessary to adopt another viewpoint on dynamical systems. In the PCH theory, systems are considered as energy-transformation devices which we interconnect to achieve the desired behaviour (Ortega, et al, 2000). The classical state variables become energy variables and the effect of the input and output signals are to modify the system total energy. In this way, the energy system properties are explicitly shown in their mathematical description (Machelli, 2003). The PCH representation of the system is the following: x ( J  R) y wH G wx wH  Gu wx C0 (8) The gradient of the desired energy variable is: wHd wx and: (6) T -199- >Cs~x1 T Lb~ x2 Cdc~ x3 Ldc~ x4 Csc~ x5 Lsc~ x6 Lm~ x7 @ 1Ucb 1 ª 0 0 « 0 CsLb CsLdc « «(1Ucb) Rb 0 0 0 2 « CsLb Lb « 1 « 0 0 0 0 « CdcLdc « 1 1 0 0 0 J R « CdcLdc « CsLdc « 0 0 0 0 « 0 « (1Usc) 1 « 0 0 « 0 CdcLsc CscLsc « 1 « 0 0 0 0 « CdcLm ¬ º 0 » » 0 0 » » » 1Usc 1 » CdcLsc CdcLm» » 0 0 » » » 1 0 » CscLsc » Rsc » 0 » 2 Lsc » Rm » 0 2 Lm »¼ T dH d dH d dt dx T dH  d Rd dx 0 (12) dH d d0 dx and the damping matrix: Rm º 2» Lm »¼ ª Rb R  rV 0 0 0 sc 2 d diag«0 2 Lsc «¬ Lb Rd t0 (13) In this way, the controlled system behaves as a dissipative element, the energy system decreases and the system reach the configuration corresponding to minimum energy in the desired equilibrium point x . The system configuration becomes: ~ x T dH d dH ( J d Rd ) d dx dx ~ x º ª 1 « C ( x4  (1  U cb ) x2 ) » s » « « 1 ( E  R x  (1  U ) x ) » 1 b 2 cb » « Lb b » 0 wH d « » ( J  R) « wx « 0 » » « 0 » « 1 « ( x5  (1  U sc ) x3 ) » » « Lsc »¼ «¬ 0 4. SIMULATIONS The results obtained with the proposed controller are reported in the figure below. In order to limit the current requirements during the motor start, the DC bus reference voltage profile is created using many staircases. It is considered the initial voltage of the supercapacitors having V (t 0) 12V (full charge). The controller coefficient r has been chosen in supply/recover the maximum of energy. The control law u is developed such that the resulting closed-loop PCH dynamics will be given by: order to 24.5 ( J d  Rd ) wH d wx 24 (9) V b (V) ~ x 23.5 23 Rd T t 0 the new 22.5 interconnection and damping matrices. In this order, one of the possible choices for the feedback laws is: 40 with J d T  J d and Rd 0 1 2 3 4 5 time(s) 6 7 8 9 10 0 1 2 3 4 5 time(s) 6 7 8 9 10 U cb U cb U sc U sc  r~ x6 , r ! 0 i b (A) 20 0 10) -20 where r is a design parameter. The global stabilization around desired equilibrium point x is achieved if: the desired energy function is a negative semi-definite function: dH d d0 dt Fig. 2. Voltage Vb and current ib on battery. Fig.2 presents the variation of the battery voltage Vb and the current ib . According to the changes on (11) the DC bus reference voltage, the terminal voltage of the battery indicates small variations, which are smoothed by the presence of supercapacitors. The current moves in opposition of voltage fluctuations. It can be observed that: -200- . 100 V d , V dc (V) 80 60 40 20 0 2 4 6 8 10 6 8 10 time(s) 10 i m (A) 8 6 4 2 0 0 2 4 time(s) Fig. 5. Control signals U cb and U sc . Fig. 3. DC bus voltage Vdc , reference voltage Vd Fig.5 presents the control signals of the bidirectional U cb is related to the bidirectional converters. and motor current i m . battery current i m . The two characteristics show that the bidirectional converter control at the output of the supercapacitors. The control values are in the set [0, 1]. In the fig.6 the power of the batteries Pb , DC bus voltage and the motor current have the same allure. One can see that the DC Bus voltage is tracking its reference with no steady state error and very small overshoot. converter and U sc Fig.3 shows the DC voltage Vdc and the motor represent the supercapacitors Psc and the motor required power Pm are lay out. 12 700 V sc (V ) 11.999 600 11.998 500 11.997 400 0 1 2 3 4 5 time(s) 6 7 8 9 P b , P sc , P m (W) 11.996 10 10 0 300 200 i sc (A) 100 0 -10 -100 -20 0 1 2 3 4 5 time(s) 6 7 8 9 10 -200 0 Fig. 4. Voltage Vsc and current i sc on 1 2 3 4 5 time(s) 6 7 8 9 10 Fig. 6. Batteries power Pb , Supercapacitors supercapacitors. power Psc and Motor power Pm . Fig.4 illustrates the voltage on supercapacitors Vsc and the current i sc . The initial condition is that Studying the picks of storage devices power it can be seen that at the t 2.034 s time, when appears this pick power demand, the power values are: Pm 320.6W , Pb 199.5W , Psc 110.7W , the pack of the supercapacitors is charged. At the motor start, the supercapacitors deliver energy and the voltage decreases. In steady state the current is null, then in the braking motor regime, supercapacitors recover energy and the voltage increases. so 34% percents of the motor power is ensured by the supercapacitors and the rest, by the batteries. The energy delivered by the supercapacitors is E sc  1076.4 J and the recovered energy is E sc  1360.8 J . It can be seen that the potential for brake energy recovery is highly exploited due to -201- the presence of supercapacitors and the system is able to take up the power. Becherif, M., M.Y. Ayad and A. Miraoui (2006). Modeling and Passivity-Based Control of Hybrid Sources. In: Proceedings of 41St IEEE/IAS Annual Meeting, pp.1134-1139, USA. Becherif, M. (2006), Passivity-based control of hybrid sources: Fuel cell and Battery. In: 11th IFAC Symposium on Control in Transportation Systems (CTS’06), Netherlands. Camara, M.B., H. Gualous, F. Gustin and A. Berthon (2006). Control strategy of hybrid sources for transport applications using supercapacitors and batteries. In: Power Electronics and Motion Control Conference, IPEMC ’06 CES/IEEE, Volume 1, pp.1-5. Lungoci, C., E. Helerea and A. Munteanu (2006). On an energy supply combined system used in electric vehicle. In: Bulletin of Transilvania University, Series A, pp.213-218, Brasov. Lungoci, C. and E. Helerea (2006). 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In: IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies, Hong Kong. 5. CONCLUSIONS This paper deals with a modern on-board energy system based on batteries and supercapacitors. The hybridisation of the supercapacitors with storage batteries allows an optimised system design according to mission requirements. The presence of the supercapacitors supports a higher lifetime of the batteries and allows having a right sizing batteries in terms of weight and volume. In this way, the entire system can be designed at the low values of power, the power sizing is independent from the energy sizing and that improves the efficiency, volume, weight and costs. A new design of the on-board energy system is proposed, and then the state space model and the Controlled Port Hamiltonian form of the system are presented in order to obtain its dynamical and physical properties. The Passivity Based Control is applied, using the energy considerations and following to obtain a system with favourable dynamic characteristics. The global stability of the system is proved and simulation results come to demonstrate the viability of this new model of the on-board energy system. Simulations show that the presented architecture is more viable and the output controllers used are satisfying. The Passivity Based Control provides a simple linear control laws with few measurements to achieve the desired aims even with an under actuated nonlinear system (only the measure of the supercapacitor current is needed to achieve the described goal). In a next work, a comparison between the Passivity Based Control strategy and a classical controller will be treated, in order to find the best control strategy for the system requirements. REFERENCES  Becherif, M., M.Y. Ayad, A. Djerdir and A. Miraoui (2007). Electrical train feeding by association of supercapacitors, photovoltaic and wind generators. In: Proceedings of IEEE-ICEE, pp.55-60, Capri-Italy. -202-