Model-Based Energy Management Strategy for Hybrid Electric Vehicle. Haroune AOUZELLAG*, Hassina ABDELLAOUI, Koussaila IFFOUZAR, Kaci GHEDAMSI University of Bejaia, Algeria 06000, Faculty of Technology, Department of Electrical Engineering, Laboratory of Renewable Energy Mastery *Corresponding author. Tel.:+213 699 13 35 12. E-mail address:
[email protected] Abstract_In FC/UC HEV, an adequate power management approach is one essential objective of the researches in this area. In this paper, an advanced control strategy managing the power distribution among the two energy sources is elaborated using state-flow bloc of Matlab/Simulink. For the FC power demand, an algorithm with filtering power vibrations is developed. This algorithm, depending on the UC state of charge (SOC) and the vehicle speed to minimize the FC power demand transitions and enhance its life time. Keywords— energy management strategy; hybrid electric vehicle; fuel cell; ultra-capacitor.
I.
INTRODUCTION
The problem of the use of more than one energy source is the power management strategy. In the literature, different strategies have been appeared to solve this problem. For example in [11], the FC supplied power to UC source to maintain them charged but this strategy is not economic in terms of hydrogen consumption and there are not more benefit in braking energy recuperation. A power management strategy and structure of HEV enveloping operation modes using a battery as secondary source depending on the power demand and the SOC of the battery was developed in [14] but the use of the battery as a second source return to same problem such as the recharging in braking mode and it does not support abrupt power variations. Also, an others type of control strategies and HEV structures was regrouped by authors of [15][16] and [17] to reduce the hydrogen consumption. Others used a fuzzy logic control to supervise the power exchange between the FC and the UC in FC/UC HEV. This control was simply presented in [18], cascaded with wavelet strategy in [19] and combined with the flatness control technique in [20]. A several fuzzy supervisor developed by authors of [21] to an online controller in order to reduce power losses. The problem of management with fuzzy logic is the necessity of a great numerical memory for calculations of fuzzification and deffuzification of the data. In [22], the energy management strategy is based on neural network and wavelet transform here it pose the same problem cited before, all strategies with artificial intelligence need more and high electronic equipments which increase the cost of the HEV. This work proposes a strategy of management that, in addition of the SOC of UC, the speed of vehicle as second parameter in control strategy and a few of the strategies
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mentioned above took into consideration the vehicle speed. This control using State-flow do not need more time or memory for calculation and it give the control in few time. This paper is decomposed as follows. First, the FC, the UC and the HEV system models were presented. After, the control of the converters, speed regulation and the proposed energy management was explained. Before finishing, the simulation results were showed. Finally, discussions and conclusions were given. II. FC/UC HYBRID ELECTRIC VEHICLE MODEL The power system of the FC/UC vehicle is represented in figure 1. The two energy sources (FC and UC) exchange power with a DC bus. For the FC, a boost converter unidirectional in current is utilized to connect the FC to the DC bus; although, the UC requires DC/DC converter bidirectional in current to supply power and to recover the breaking energy. The two inductances added as filters and to respect sources alternation. The DC bus which is a capacitor supplies the both traction machines with employing a five phase inverter for each one to convert the DC power into AC power. This system gives the torque control of each wheel in dependently with a significantly high accuracy, which can enhance the stability of the HEV, reduce clutter caused by the mechanical part such as mechanical differential and transmission shafts and give more frees space in the vehicle for UC and hydrogen tank.
Figure 1. The FC/UC hybrid electric vehicle model.
A. PEMFC modeling The PEMFC is the main energy source for the vehicle. Its cell voltage and its total power are defined by the following equations [24]: (1)
V = E N ern st + U a ct − U ohm − U co nd
2.5 181.5 1 + 0.03( I FC ) + 0.6 T I FC (2) 303 S cell S cell I FC = I + S R FC cell c U ohm S cell λ − 0.0633 − 3 I FC exp[4.1(1 − 303 )] T S cell
U a ct = b1 + b 2 T F C + b 3 T F C ln ( I 5 .2 1 0 − 3 )
U cond = − BFC ln(1 −
I FC I FC ,max
(3) (4)
)
The expression of the Nernst equation according to JC Amphlett is given as:
E
Nernst
= 1.229 + 0.8510−3 (TFC − 298.15)4.308510−5 TFC 0.5ln( pH2 )n( pO2 ) (5)
B. UC system modeling The UC is chosen as a second energy source because of its considerably high power densities and its unlimited number of charge/discharge compared to the battery [26]. Moreover, it is robust and maintenance free. The model of a UC cell equivalent circuit illustrated in figure 2 is composed of a capacitance C cell, a series resistance rs corresponding to the charge and discharge resistance, a parallel resistance rp consisting of the self-discharge losses.
Vs = Rs is +
d Λs dt
(8)
where:
Λ s = Λ ss + Λ m = Lss is + Λ m
(9)
Rs, is and Ʌs are the stator resistance, currents and flux linkage matrices, respectively. Lss is the stator inductance matrix, which includes the self and mutual inductances of the stator phases and varies with rotor position due to the salient form of the rotor. Λm is the flux linking the stator due to the permanent magnet and, considering sinusoidal circulation, is expressed as: sin(θ r ) sin( − 2π ) θr 5 4π sin(θ r − ) = 5 Λm λ m 4π sin(θ r + ) 5 2π sin(θ r + 5 )
(10)
The following equations in the (q–d–z1–z2–z3) reference frame are written as follows: The stator flux linkages are given by :
λds = Ld ids + λm λ = L i q qs qs L λ = z1 s ls i z 1 s λ = L i ls z 2 s z2s L = λ z 3 s ls i z 3 s
(11)
The stator voltage equations in the d-q frame:
Figure 2 – Equivalent circuit of UC bank. The modeling of the UC units is detailed by the following equations:
V
c ell
=
r i s
c e ll
+
1 C c ell
∫ (i
ce ll
−
V C ce ll rp
)
VUC = nUCVcell
(6) (7)
C. Five Phase Permanent Magnet Machine Model The electrical equations of five phases permanent magnet synchronous machine (PMSM) in abc frame can be expressed as follows [1]:
d λ qs v qs = rs iqs + ωλ ds + dt v = r i − ωλ + d λ ds s ds qs ds dt
(12)
where: L q = L d =
L L
ls ls
+
L + L
mq
(13)
md
The electromagnetic torque can be expressed as:
T =
5 P (φ m iqs + ( L d − L q ) iqs ids ) 2 2
(14)
where P the PMSM poles number. The torque and rotor speed are given as follow: T = J
dΩ + Tl + b Ω dt
(15)
Ω=
2 ω P
(16)
where J, Ω, ω, Tl and b total inertia brought back to the rotor, rotor mechanical speed, electrical speed, load torque and friction coefficient of PMSM respectively.
Therefore, from equation (22) and the expression of the tractive power of the vehicle as a function of the speed the acceleration dv is:
and
dt
Pm = v( M v
D. Modeling Of The Vehicle
dv 1 + ρ aer v 2 SCx + M v g sin α + M v gCr cos α ) (24) dt 2
III. CONTROL SYSTEMS AND REGULATION
The forces acting on the vehicle is shown in figure 3.
The power management of the two energy sources and the traction system are detailed in this section. The control of the UC converter allows the regulation of the DC bus voltage. The vehicle speed is adjusted by the inverters controls. For the FC converter, the improved algorithm is implemented to control the reference power. A. Speed regulation by sliding mode
Figure 3. Forces acting on a vehicle The equations that preside the vehicle dynamics are given as follows:
Mv
dv = ∑ Fext dt
(17)
(18)
(19) is given by the
Fr = − Pv Cr cos α x
(20)
From figure 2 it can be seen that the component of the pulling force on the x axis.
Ft following y is zero, equations are taken only
dv 1 Mv x = ( − ρ aer v 2 SC x − M v g sin α − M v gC r cos α + Ft ) x (21) dt 2
Expression of the mechanical tensile force Ft is: Ft = M v
dv 1 + ρ aer v 2 SC x + M v g sin α + M v gC r cos α (22) dt 2
Mechanical power (Pm) necessary to the advancement of the vehicle is equal to the product of the force of traction and speed. Pm = v Ft
(25)
where Ωref reference mechanical speed The derivative of this surface is given by the expression:
Faer on the
1 Faer = − ρ aer v 2 ACx x 2 The resistance of the wheels on the floor following formula:
The principle of this control is to keep the error between the desired reference and the measurement to control in a sliding surface. If the measurement to control is the angular speed Ω, the sliding surface is noted S(Ω) and it is expressed as follow: S ( Ω ) = Ω ref − Ω
dv Mv = Faer + Pv + Fr + Ft + Rr dt The force equivalent to the air resistance vehicle is given by the equation:
Sliding mode control for speed regulation is employed to generate the total reference torque or force for the both fivephase PMSM. The reference current iqs,ref is calculated using the sum of the two equations (27) and (28).
(23)
T ɺ b 5 P( Ld − Lq ) Sɺ (Ω) = Ω + l + Ω ids + φm ids (26) ref − 2 2J J J
i
eq qs , ref
T b ɺ Ω+ l +Ω ref J J = 5 P ( L d − Lq ) ids + φ m 2 2J
iqsn , ref = K Ω sign( S (Ω))
(27)
(28)
where KΩ positive gain, given as follow:
K Ω < m ax 2
(Tl − b Ω ) Pφ m
(29)
This method of control is the same for the both inverters of each five-phase PMSM. Figure 4 shows the global structure of the proposed control.
PUC ,ch arg e = S1 0.6 PFC , no min al + Pv ,braking
(30)
The FC power reference is limited to its maximum value as in equation (31) and then divided by the FC voltage to obtain the FC reference current and a PI corrector adjusts the FC current to the desired value. The current should be limited in a slope so as to respect constraints related with FC dynamics. m a x ( PF C , r ef ) = 0 .6 PF C , n o m in a l + m a x ( Pv )
Figure 4. Structure of the SMC speed regulator
(31)
Figure 7. FC converter control.
Figure 5. Speed regulation and inverter control. The figure 5 show the vector control of the machine and it is not detailed for this work. B. DC bus voltage regulation and UC converter control The regulation of the DC bus voltage is showed in figure 6. The UC power is controlled indirectly by the regulation of the DC bus voltage. If there is power demand by the vehicle, the DC bus voltage decrease, an error voltage with its reference will be generated and give the rapport cyclic α1 to control the IGBTs of the converter. The UC gives the necessary power to keep up the DC bus voltage. If the DC bus voltage is increased such as in braking mode, the UC absorbs the excess power and the voltage decrease to its reference. This method allows to control also the UC current and make it a limitation to IUC,max and IUC,min.
The filter is added to eliminate all power vibration caused as in rapid acceleration. The high frequency part is provided by the UC bank and the low frequency part is from the FC bank. The FC stress can be release because some part of the required power is transfer to UC bank. Also peak power is remarkably decrease if the power from the FC is low frequency part. So it is positive to extend the life cycle. Faults perturbations in traction machine or in any others reasons can be transmitted to UC bank and protect the FC system. The filter adapted for this application is the low pass filter and the parameters can be tuned during tests. IV. ENERGY MANAGEMENT STRATEGY The FC power reference depends not only on the SOC, but also on the speed of the vehicle. The SOC is brought to remain in a fixed range [0.47, 0.75] by increasing or decreasing the generated FC power. In this range, the UC system has the capability to charge or discharge [26]. The FC delivers only the required power by the vehicle PFC,ref = PFC,req even if the SOC is above the top value. In the two other modes, the FC power will be at the minimum level or the maximum one. The control take account SOC and vehicle speed to build the following algorithm: • If 47 ≤ SOC ≤ 75 and 10< vv
< 60 , the UC fulfils the
power lack or receives the extra power from braking while the SOC oscillates in this fixed range. Figure 6. DC bus voltage regulation and the UC converter control. C. FC converter control The method of control power for the FC system is presented in figure 7. The rapport cyclic α2 is generated by the error between the IFC,ref and IFC. If the SOC of the UC system is low, the control allows charging the UC with the high efficiency for the FC and the UC system as follow:
• If 47 ≤ SOC ≤ 75 and
vv > 60 the vehicle speed is
in low level and the power demand is delivered by le UC system. • If SO C >75 : there is no need to charge the UC because the SOC is in high level of charge. •
If SOC 60 SO C >75 SOC 60
SOC
