2016 International Symposium on Power Electronics, Electrical Drives, Automation and Motion
Sliding Mode Control for Frequency-Based Energy Management Strategy of Hybrid Storage System in Vehicular Application J. Snoussi 1 , S. Ben Elghali 2 , R. Outbib 2 , and M.F Mimouni1 1
2
Engineering School of Monastir (ENIM), University of Monsatir, Tunisa Laboratory of Information Science and Systems (LSIS), Aix-Marseille University, Marseille, France 1 Email:
[email protected]
Abstract—All hybrid electric systems require an energy management strategy to share out the energy flow between its several sources or storage devices. This paper proposes a sliding mode control of battery ultracapacitor hybrid system associated to a frequency-based energy management strategy. The adopted energy management ensures the distribution of the load power requirement between the two sources taking into account its dynamic and energetic constraints. Simulation results, obtained R R / Simulink , are given in order to highlight by using Matlab the relevance of the proposed approach. Index Terms—Battery, ultracapacitor, buck/boost converter, frequency energy management, sliding mode control.
I. I NTRODUCTION To increase the energy security and resolve the problem of pollution caused by engine emission, the researches in automotive sector are moved to the technologies of Hybrid Electric Vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs) and all Electric Vehicles (EVs) [1]. In general, these devices use more than one electric source to improve the efficiency and the autonomy of the power supply during operation [2]. An attractive combination is well applied in such applications it consists of a battery associated to a pack of ultracapacitors [1], [3], [4]. In fact, the development of these Energy Storage Systems (ESS) has been underway since the early 1990s. It has presented the subject of several studies for many years[5], [6], [7] and has significantly affected the applications of electric propulsion [8], [9], power generation and distribution [10], renewable energy systems [11], aircraft [12], [13] and communications [14]. Indeed, the battery which is characterized by a high energy density, a low dynamic response and a short life cycle is considered as the main source in the studied system, it supplies the average of the load demand. However the ultracapacitors known by its high power density, fast dynamic operation, a long life cycle and a poor specific energy supply pulse power requirement. Therefore, to optimize the system operation and extend the durability of the sources all of these characteristics must be respected during vehicle operation [15]. A various management strategies are explored in the literature such as the Fuzzy Logic Control (FLC) studied in [16], the Artificial Neural Network technique
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(ANN) illustrated in [17], the Optimal Control (OC) developed in [18] and the Dynamic Programming DP treated in [19]. In the cases of FLC and ANN, the optimality and the effectiveness of the solution depend essentially on humans expertise and mission duration. Moreover, the OC and DP present an off line methods, it can optimize system operations but the entire load profile needs to be known in advance which is impossible in our case. In this paper, a strategy of energy management (SEM) based on a frequency approach is proposed. This method offers the ability to perform a real-time optimization and it has been applied in the previous researches [13], [20] in which the main goal of the filtering approach was the sizing of the electric system to reduce the weight of the hybrid generator without taking into account the fluctuation in the output voltage under fast load variation. In addition, in the topology proposed in [20] the battery is directly connected to the DC bus so in absence of a boost converter it must supply the entire bus voltage which leads to an oversized battery. The contribution of this work is to develop an energy management strategy associated with a nonlinear controller to optimize the distribution of the energy between a battery and a pack of ultracapacitors maintaining at the same time the output voltage constant around the standardized Power Net voltage 42V [4]. The main idea is to filter the load current using a low pass filter and to generate the current required to each source. The references are assigned to the battery and the ultracapacitor using a Sliding Mode Control (SMC). This method can be implemented without specific or detailed information of the load. The paper is organized as follows: Section 2 provides the topology of the hybrid system and the models of the sources. Section 3 explains the energy management based on the frequency approach. Section 4 illustrates the SMC strategy used to generate the duty cycles of the converters and section 5 provides and discusses the results of simulations obtained R R using Matlab /Simulink .
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Fig. 3. Electric circuit of the ultracapacitors pack
Where Cbat is the battery nominal capacity and socbat (0) is its initial state of charge. C. The RC circuit model of the ultracapacitors pack The ultracapacitors pack is composed of 10 series elements of a BOOSTCAP3000 device. The equivalent ultracapacitor RC circuit is described in figure 3 [21], [24], [25]. The ultracapacitor voltage vuc is expressed by (3): vuc = vc − ruc .iuc
(3)
where vc is the voltage of the equivalent capacitor Cuc . and ruc is the equivalent internal resistance of the pack. The ultracapacitor state of charge of the socuc is illustrated in (4): vuc (4) socuc (t) = max vuc
Fig. 1. Topology of the considered hybrid energy system
max where vuc is the maximal voltage of the ultracapacitors.
III. STRATEGY OF THE ENERGY MANAGEMENT
Fig. 2. The battery electric circuit
II. HYBRID ENERGY STORAGE SYSTEM A. Hybrid system topology The electrical system studied in this work is shown in figure 1. The system consists of a battery and a pack of ultracapacitors connected to a DC bus via two buck/boost converters. This topology offers the advantage to charge and discharge separately the two power supplies and to reduce their sizes [21], [22], [23]. Lbat , Luc are the inductors that limit the battery and ultracapacitors current harmonics. C1 , C2 are the output capacitances (Cdc = C1 + C2 ) used to filter the bus voltage. B. Model of the lead-acid battery A 12V/50Ah lead-acid battery is used in this application. The electric model is shown in figure 2 [13]. The battery voltage vbat is given by equation (1): vbat = ebat − rbat .ibat
(1)
Where ebat is the battery open circuit voltage, ibat is the battery current and rbat is the battery internal resistance. The battery state of charge socbat is given in (2): 1 ibat (τ )d(τ ) (2) socbat (t) = socbat (0) − Cbat
Storage system performance characteristics for any power applications can be described in terms of two parameters, i.e., specific power and specific energy. Figure 4 shows different types of energy storage systems in the energy-power plane called Ragone Charts and includes information about the suitable application time period for each element [26],[27]. As it can be noticed, batteries are more suitable for applications with long term variations on the scale of minutes to several hours, while superconducting magnetic energy storage systems and ultra-capacitors are more adapted for applications on the time scale of several seconds. In order to create a relation between the power flow dynamics and the different storage system technologies, the notion of specific frequency [28] is introduced and defined as the ratio between the power density ρP ower and the energy density ρEnergy : fc [Hz] =
ρP ower [W/kg] ρEnergy [J/kg]
(5)
Therefore, the different elements of the Ragone chart can be reported on frequency plane using equation (5) as shown in Figure 5. The strategy developed in this work is based on the frequency decomposition of the load profile [29]. The idea is to decompose the total required current into a high and a low frequency components using a low pass filter (figure 6). The transfer function of the low pass filter is expressed in (6):
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H(s) =
2πfc 2πfc + s
(6)
Fig. 7. Frequency decomposition of the load profile
IV. SLINDING MODE CONTROL
Fig. 4. Ragon diagram
A. Principle of operation
Fig. 5. Power Ragone chart in frequency plane
Where fc is the filter cut off frequency selected according to the load demand and the specific energy and power of the sources [20]. It represents the adjustable parameter of the proposed approach. The SEM allows to generate the current references that will be assigned to the battery and the ultracapacitor pack. Indeed, the filtered current representing the low frequency harmonics forms the setpoint of the battery control while the fast dynamic component, is sent to the ultracapacitors. This reference is obtained by subtracting the battery current reference from the total load demand. The frequency-based energy management approach is described by figure 7.
The Sliding Mode Control approach is recognized as one of the efficient tools to design robust controllers for complex and non linear dynamic system which can operate under uncertainty conditions [30]. This nonlinear control is low sensitive to the variation of the plant parameters and disturbances. In general, an efficient sliding mode controller must satisfy three principle conditions [31]. • Attraction condition • Existence condition • Stability condition 1) The attraction condition: To force the controller to converge to the sliding surface the control signal u switches between two values u+ and u− according to the sign of S [32]. For a DC-DC converter u presents its duty cycle (αbat or αuc ) so the attraction condition will be: 1, if S(x, t) > 0. (7) u= 0, if S(x, t) < 0. 2) The Existence condition: The existence condition of the SMC is resumed in (8): ⎧ ⎨ lim+ S˙ < 0 x→0 (8) ⎩ lim S˙ > 0 − x→0
Otherwise S S˙ < 0 where S˙ is the sliding surface slope. The fulfillment of this inequality ensures the sliding mode existence around the sliding surface S. 3) The Stability condition: The stability condition of the SMC is given in (9) ⎧ ⎨ lim+ S˙ < 0 x→0 ∀t > th (9) ⎩ lim S˙ > 0 − x→0
Fig. 6. Principle of the frequency management strategy
Where th is the time spent by the system to reach the sliding surface.
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B. Current control of the battery converter The sliding surface Sbat defined to control the battery current is illustrated in (10) [31]. Sbat = K1 (ibat − iref bat )
(10)
where K1 is a positive constant and iref bat is the battery current setpoint. The stability of the controller is verified for any positive value of K1 . The control signal of the battery converter ensuring the convergence of the current to its reference is given by (11)[32]. 1 (11) (1 − sign(Sbat )) 2 C. Current and voltage control of the ultracapacitor converter ubat =
response of the ultracapacitors verify the effectiveness and the performance of the proposed management strategy. Hence, the mode of operation of the system leads to relieve the strain on the battery limiting its corresponding number of charge/discharge cycles due to the ultracapacitors pack witch covers the transients as shown in figure 13 and in figures 15 to 18. Furthermore, the simulation results given in figures 14, 19 and 20 validate the sliding mode technique applied to control the system converters. As we can note here, the system output voltage is regulated to the desired voltage trajectory (vdc = 42V ) despite the high and fast variations detected in the load demand. Moreover, we demonstrate in figures 11, 12 and 13 that currents track perfectly their references maintaining the sliding surfaces of the SMC equal to zero.
The sliding surface Suc used to control the bus voltage and the UC current is provided by (12) ref Suc = K2 (iuc − iref uc ) + K3 (vdc − vdc )
(12)
is the Where K2 , K3 are two positive constants, iref uc ref is the bus voltage ultracapacitor current setpoint and vdc setpoint. The control signal ensuring the convergence of the current and the voltage to its references is given by (13). 1 (13) (1 − sign(Suc )) 2 To satisfy the stability of the controller, the inequality (14) must be verified [15]. uuc =
K2 Luc iout uc > K3 C2 vuc
Fig. 8. ECE-15 driving cycle
(14)
Where iout uc is the output current of the ultracapacitor converter. V. SIMULATION RESULTS To validate the proposed strategy, the overall system was simulated using SimPowerSystem library of Matlab. In order to test the behavior of the sources and converters during operation, an urban driving cycles ECE-15 is applied to the EV as shown in figure 8. The load power Pout requested for a vehicle speed v is given by (15). dv v (15) Pout = 0.5ρvSCx + M gCr + M dt Where v, ρ, Cx , S, M, Cr , and g represent the vehicle speed, the air density, the aerodynamic drag coefcient, the vehicle frontal surface, the vehicle mass, the rolling resistance coefcient, the gravitational acceleration constant respectively. For the small system adopted in this application, simulations are carried out under a small scale load profiles as viewed in figures 9 and 10. The parameters of the storage system and vehicle are given in table I and II. During operation, the load current iout is filtered giving the references of the battery and ultracapacitors currents illustrated in figures 11 and 12. Figure 13 shows the characteristics of the currents stored or supplied by the battery and the ultracapacitors, the smooth behavior viewed in the battery current and the fast dynamic
Fig. 9. The load power of the system
Fig. 10. The load current of the system
VI. C ONCLUSION A sliding mode control associated to a frequency-based energy management strategy for a battery/ultracapacitor system
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Fig. 11. The setpoint of the battery current
Fig. 15. The battery voltage
Fig. 12. The setpoint of the ultracapacitor current
Fig. 16. The ultracapacitor voltage
Fig. 13. The currents of the battery and ultracapacitors
Fig. 17. The state of charge of the battery
Fig. 14. The DC bus voltage
Fig. 18. The state of charge of the ultracapacitors
TABLE I PARAMETERS OF SOURCES AND CONVERTER MODELS Cbat ebat rbat
50 Ah 13.06 V 2.4 mΩ
Lbat Cuc ruc
52.5 μH 300 F 2.9 mΩ
Luc Cdc Vdc
TABLE II PARAMETERS OF THE ELECTRIC VEHICLE
52.5 μH 20 mF 42 V
ρ M
1.223 Kg/m3 1000 kg
Cx Cr
0.35 0.01
S g
2 m2 9.81 N/Kg
is designed and investigated in this paper. Using this advanced
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Fig. 19. The Sliding surface of the battery control
Fig. 20. The sliding surface of the ultracapacitor control
technique, we have achieved a good tradeoff between the stabilization of the output voltage and the minimization of the battery current changes to take account dynamic and energetic constraints of the hybrid system. The well defined system model and simulation results obtained under peak load reR R quirement via the Matlab /Simulink environment validates the performance and the effectiveness of the proposed control design. For future work, we will move to the experimental verification of the studied control technique. R EFERENCES [1] K.Jorgensen. Technologies for electric, hybrid and hydrogen vehicles: electricity from renewable energy sources in transport. Utilities Policy,2008. [2] P.Thounthong, V.Chunkag, P.Sethakul, B.Davat, M. Hinaje. Comparative Study of Fuel-Cell Vehicle Hybridization with Battery or Supercapacitor Storage Device. IEEE Transactions on vehicular technology, vol. 58, no. 8, October 2009. [3] N.Janiaud. Modelisation du systeme de puissance du vehicule electrique en regime transitoire en vue de l’optimisation de l’autonomie, des performances et des couts associes. PhD thesis, University of Paris-Sud XI, 2011. [4] J.N. Marie-Francoise,H. Gualous, R. Outbib, A. Berthon. 42V Power Net with supercapacitor and battery for automotive applications. Journal of Power Sources 143, 2005. [5] X.Luo, J.Wang, M.Dooner, J.Clarke. Overview of current development in electrical energy storage technologies and the application potential in power system operation. Applied Energy 137, 2015. [6] S.V.Rajani. V.J.Pandya, V.A.Shah. Experimental validation of the ultracapacitor parameters using the method of averaging for photovoltaic applications. Journal of Energy Storage 5, 2016. [7] I.S. Ike, I.Sigalas, S.Iyuke, K.I.Ozoemena. An overview of mathematical modeling of electrochemical supercapacitors/ultracapacitors. Journal of Power Sources 273, 2015. [8] M. Rajabzadeh, S.Mohammad, T.Bathaee, M.A.Golkar. Dynamic modeling and nonlinear control of fuel cell vehicles with different hybrid power sources . International Journal of Hydrogen Energy 41, 2016.
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