J Syst Sci Complex (2018) 31: 325–342
Variable Universe Fuzzy Control for Battery Equalization∗ ZHENG Jian · CHEN Jian · OUYANG Quan
DOI: 10.1007/s11424-018-7366-7 Received: 4 November 2017 / Revised: 15 December 2017 c The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2018 Abstract In order to avoid the overcharge and overdischarge damages, and to improve the lifetime of the lithium-ion batteries, it is essential to keep the cell voltages in a battery pack at the same level, ´ i.e., battery equalization. Based on the bi-directional modified Cuk converter, variable universe fuzzy controllers are proposed to adaptively maintain equalizing currents between cells of a serially connected battery pack in varying conditions. The inputs to the fuzzy controller are the voltage differences and the average voltages of adjacent cell pairs. A large voltage difference requires large equalizing current while adjacent cells both with low/high voltages can only stand small discharge/charge currents. Compared with the conventional fuzzy control method, the proposed method differs in that the universe can shrink or expand as the effects of the input changes. This is important as the input may change in a small range. Simulation results demonstrate that the proposed variable universe fuzzy control method has fast equalization speed and good adaptiveness for varying conditions. Keywords
1
Cell equalization, lithium-ion battery, variable universe fuzzy control.
Introduction
Due to the development and popularity of hybrid vehicles, rechargeable lithium-ion batteries, as an alternative type of vehicle power source, has drawn significant attention from both industry and academia[1–3] . Due to the electrochemical characteristics of the lithium-ion battery materials, the voltage of a single cell is generally lower than the demanding working voltage. Therefore, a number of cells are usually serially connected as a battery pack. However, the existing battery design and production technologies cannot guarantee the consistence of the parameters in different cells, such as the internal resistance, the aging speed, the degradation rate and the temperature distribution etc. The differences of these cell parameters could finally result in cell imbalance of cells in the same battery pack[4] . Moreover, to avoid the overcharge and overdischarge damages, the process of charging and discharging must be terminated when ZHENG Jian · CHEN Jian (Corresponding author) · OUYANG Quan The State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China. Email:
[email protected]. ∗ This research was supported by the National Natural Science Foundation of China under Grant Nos. 61433013 and 61621002. This paper was recommended for publication by Guest Editor XIN Bin.
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one of the cells is with the state of charge (SOC) of 100% and /0, respectively[5] . The strongest cell determines the charge capacity and the weakest one limits the discharge capacity, which behaves like the cask effect reference. Therefore, in order to make the battery pack’s operation time longer, it is very essential to equalize the cells in a battery pack. The literature on battery equalization can be divided mainly into passive cell balancing methods[6] and active cell balancing methods[7] . By the passive cell balancing methods, cells with high voltages transform the excess energy to heat through the shunt resistor to make the cells’ voltages close to accordance[8] . Generally, the equalizing current is limited to a very small value[6] . With the active cell balancing methods, cells with high voltages transfer charge to those weak cells through capacitors, inductors or transformers[9–13] . Compared with the passive equalizing methods, the active balancing strategies have many advantages such as faster equalization speed and less dissipative energy. ´ The bi-directional modified Cuk converter[14] is one of the active balancing circuits, and is easy to be integrated and extended[15] . Compared with other kinds of bi-directional equal´ izing circuits, the bi-directional modified Cuk converter has a relatively low price and power [6] ´ converter, an intelligent battery equalization algoriconsumption . Utilizing the modified Cuk thm[16] is proposed to regulate the frequency of the pulse width modulation (PWM) signal to equalize the voltage of the battery cells. An SOC estimation-based quasi-sliding mode controller is proposed in [17] to avoid the cell’s current exceeding its limitation during the equalization pro´ model, a fuzzy controller is presented in [18] to balance the cells’ cess. With analysis of the Cuk voltage with the converters operated in discontinuous inductor conduction mode (DICM)[19] . Zero-current switching of MOSFETs is achieved, and switching loss is reduced. A fuzzy controller for balancing the cell’s voltages is proposed in [20]. By designing appropriate rules and analyzing the influence of the relationships between input and output signals, it is demonstrated how the fuzzy control system (FCS) adapt the equalization current to the changing input[21] . However, if the inputs change in a very small range while the universe is large, which would happen if the inputs are associated with cell imbalance, the number of the designed rules should be big enough to adapt to the small change of inputs[22] , which is very complex and difficult to achieve in practice. In order to improve the equalization speed and better tune the equalizing current for various conditions, a variable universe fuzzy controller[23] is proposed. Variable universe means that the universes of the discourse of the input and output variables can change along with the change of the input variables. Variable universe fuzzy controller is much more effective than the conventional fuzzy controllers. Variable universe fuzzy controller is one of the efficient tools for dealing with nonlinear systems[23] . With better adaptivity and efficiency than conventional fuzzy control method for dealing with nonlinear systems, variable universe fuzzy control method can be a good choice for battery equalization as the cell model has strong nonlinear properties. On the one hand, large equalization current is required to accelerate the equalizing speed when the difference between neighbouring cells’ voltage is large. On the other hand, to prevent the excessive balancing, a small difference means that the cells in a pack are in a slight imbanlance which cannot be equalized by a large current. Futhermore, adjacent cells with either too low or too high voltage cannot sustain big current
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during the balancing process. ´ In this paper, bi-directional modified Cuk converters are utilized as the equalizing circuits and are designed to operate in DICM to reduce the switching loss of MOSFETs. Specifically, for an n-cell serially connected battery pack, (n − 1) online voltage estimation based variable universe fuzzy controllers are proposed to tune the duty cycles of PWM signals during the equalizing process. The proposed variable universe fuzzy controllers can deal with the equalization problem well without designing too many rules for the fuzzy set. Simulation results of both the proposed variable universe fuzzy control method and the conventional fuzzy control method are provided. It is demonstrated that the proposed variable universe fuzzy controller has faster equalization speed and better adaptability. The rest of the paper is organized as follows. In Section 2, the cell equalization system is introduced and analyzed, including the battery model and the equalizing circuit model. In Section 3, appropriate inputs are selected and fundamentals of the variable universe fuzzy control is presented. Then, variable universe fuzzy controllers are proposed to tune the equalizing current based on designed rules. In Section 4, simulation results are provided to compare the performance of the proposed variable universe fuzzy controller and the conventional fuzzy controller. Conclusions are given in Section 5.
2
Model of the Cell Equalization System
´ Generally, an n-cell battery requires (n − 1) modified Cuk converters as the cell equalizers. To the best of our knowledge, the converters are then controlled separately to transfer energy only between two adjacent connected cells. In this section, the dynamic models of the cells and the converters are given separately. 2.1
Battery Cell Model
For the serially connected cells in a battery pack, every single cell should be modeled separately. The electrical battery model in [24] is utilized here to estimate the SOC and V-I (the relationship between voltage and current) performance of battery cells. The structure of the cell model is illustrated in Figure 1. Capacitor Cb denotes the full-charge capacitor, which can be considered as cell’s nominal capacity. Rsd denotes the self-discharge resistor, which can be simplified as a large constant resistor. R0 and two RC networks (Rf , Cf ) and (Rs , Cs ), represent the V-I response of the battery cell. A voltage-controlled voltage source is utilized to indicate the nonlinear mapping from the cell’s SOC to the open circuit voltage VOC as VOC = f (SOC), where f (·) is a nonlinear function.
(1)
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0
(SOC)
SOC
Figure 1
Equivalent circuit model of the battery cell
According to the circuit, the dynamics of the voltages across the capacitors SOC(t), Vf (t) and Vs (t) can be expressed as follows 1 1 SOC − IB , Rsd Cb Cb 1 1 V˙ s = − Vs + IB , Rs (SOC)Cs (SOC) Cs (SOC) 1 1 V˙ f = − Vf + IB , Rf (SOC)Cf (SOC) Cf (SOC)
˙ =− SOC
(2)
where IB is the current of the battery cell, and is positive/negative when the cell is in the discharging/charging mode, respectively. The capacitance values Cs and Cf are nonlinear functions of the SOC, and the resistance values Rs , Rf and R0 are functions of the SOC and battery’s current direction (charing or discharging). The terminal voltage of the battery cell VB (t) can be obtained as VB = VOC − R0 (SOC)IB − Vf − Vs .
(3)
Based on (2) and (3), the cell model can be obtained as x˙ = Ax + bu, (4) y = g(x) = f (x1 ) − R0 (x1 )u − x2 − x3 , where ⎡ ⎢ ⎢ x˙ = ⎢ ⎣
dSOC dt dVs dt dVf dt
⎤ ⎥ ⎥ ⎥, ⎦
⎡ − 1 ⎢ Rsd Cb ⎢ A=⎢ 0 ⎣ 0
0
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− Rs (VSOC1)Cs (SOC)
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− Rf (VSOC1)Cf (SOC)
⎤ ⎥ ⎥ ⎥, ⎦
⎡
− C1b
⎤
⎢ ⎥ ⎢ ⎥ 1 b = ⎢ C (SOC) ⎥, ⎣ s ⎦ 1 Cf (SOC)
u = IB , y = VB . 2.2
Cell Balancing Circuit Model ´ The bi-directional modified Cuk converters in [25] are utilized as the cell balancing circuits. The dynamical response of the i-th converter (1 ≤ i ≤ n − 1) in DICM operation can be divided
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into three states in one switching period as illustrated in Figure 2. Battery cells i and i + 1 are connected with the i-th converter. The converter includes two uncoupled inductors Li1 and Li2 , two MOSFETs Qi1 and Qi2 with body diodes di1 and di2 , and an energy transferring capacitor Ci . The circuit of the converter is driven by PWM signals which control the MOSFETs’ switching on and off to achieve the cell equalizing. The duty cycles of the PWM signals Di1 and Di2 are chosen as the control variables for cell equalizing. The converters are designed to operate in DICM to reduce the switching loss of MOSFETs[26] .
i
Figure 2
i
The periodic dynamics of the converter in DICM
As the structure of the bi-directional converter is symmetrical, without loss of generality, it can be assumed that the charge transfers from the i-th cell to the (i + 1)-th cell. For the DICM operation, the dynamic response of the converter can be divided into three states in one time period Ts as follows[18] . State 1 There is no current through the converter described above, which means iei1 = iei2 = 0. State 2 MOSFET Qi1 is on. Then cell i discharges to Li1 , and Li1 stores the energy. The capacitor Ci discharges to cell i + 1 and Li2 , and Li2 stores energy. State 3 MOSFET Qi1 is off and di2 is forced to turn on. Then cell i discharges to Li1 and capacitor Ci , and both Li1 and C store energy. Moreover, Li2 discharges to cell i + 1.
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When the current reduces to 0, the converter reaches the initial state. A battery equalization loop contains the three states described above. Based on [19], the average equalization currents of the i-th and (i+1)-th cell can be deduced as follows 1 Di1 Ts VBi (Di1 + Di2 ) , Iei1 = fi1 (Di1 ) = 2 Li1 (5) 1 Di1 Ts (VCi − VBi+1 )(Di1 + Di2 ) Iei2 = fi2 (Di1 ) = , 2 Li2 where the average cells’ equalization currents Iei1 , Iei2 and average capacitor voltage VCi are constants. ´ For the i-th bi-directional Cuk converter, MOSFET Qi1 and Qi2 cannot be turned on simultaneously, and can be formulated that Di1 (k)Di2 (k) = 0,
(6)
´ which ensures that the modified Cuk converter transports energy from cells to their adjacent ones in particular directions at particular time periods. For a typical Di1 , the relationship between Iei1 and Iei2 is determined.
3
Variable Universe Fuzzy Equalizing Controller
Due to the lack of quantitative analysis and modeling of the relationship between cells’ imbanlance and equazation speed, it is hard to design a controller based on traditional methods. On the contrast, cells’ imbanlance and equazation speed can be easily qualitatively classified into some levels and expressed as linguistical variables such as large, small and so on. A general fuzzy controller consists of the membership functions of inputs and outputs, rules database, and inference methods[27] . In this section, we first introduce the fundamentals of the variable universe fuzzy control, and present the selected inputs to the fuzzy control design. Then, variable universe fuzzy controllers are proposed to tune the equalizing current based on designed rules. 3.1
Selection of Inputs
Based on the the equalizing circuit model, equalizing process can be driven by the duty cycles of the PWM signals to MOSFETs. Besides the speed of equalizing process, the performance of an equalizer is also evaluated by the protection of cells. Therefore, a fixed duty cycle is insufficient to achieve satisfactory overall performance. Therefore, it is important to tune the duty cycles and equally tune the equalizing currents in designing the equalizing system. Generally, the inputs of a fuzzy controller should reflect the concerned factors, so that the controller can determine a proper value of the control variables. The concerned factors affecting the equalizing performance in this study are the equalizing speed and cell protection. Therefore, two corresponding cell states are utilized as the inputs: 1) The voltage difference of adjacent cells (ΔVBi = |VBi +1 − VBi |): Battery equalization aims at maintaining voltages among all cells at the same level. Thus, the larger the input ΔVBi
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is, the faster equalizing speed is required. When the difference of adjacent cells reaches a certain criterion, the equalization process stops. 2) The average voltage of adjacent cells VBi = 12 (VBi + VBi +1 ) : Because the overcharge and overdischarge damages should be prevented, the cell with low voltage cannot support large discharge current. Meanwhile, a cell with high voltage cannot stand large charge current. When a pair of adjacent cells are both with low/high voltages, even if the ΔVBi is pretty big, large equalizing speeds are avoided. Therefore, to prevent cell from overcharge and overdischarge damages, the protection input VBi is essential to the system. Essentially, fuzzy reasoning is equal to a interpolation. On the one hand, the response function of the interpolation should be as close to the real response function as possible. This requires the distance of peak points in fuzzy control to be small enough, which means that the number of fuzzy rules could be large. On the other hand, it could be hard to realize for the fuzzy controller with a large number of fuzzy rules based on expert knowledge[23] . Based on the inputs proposed above, a controller should map the input vector to the equal ization current, i.e., establish a function F : Iei = F ΔVBi , VBi . The initial universe of ΔVBi is [−Ei , Ei ], where Ei is real. As the running of the control process, ΔVBi decreases to zero. If the fuzzy logic rules, i.e., the membership functions of input ΔVBi are fixed, the universe [−Ei , Ei ] could be too large for the scaled-down input ΔVBi , and the control performance could be degraded. Thus, the variable universe fuzzy control method is provided. Based on the premise that the shape of rules is fixed, the universe shrinks/expands as the input ΔVBi decreases/increases. For better understanding, the situation of a variable universe changing is shown in Figure 3. It is easy to find that though only seven rules are given, any number of rules can be generated by compressing the universe. 1 NL
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−α(x')E α(x')E 0 (Contracting universe)
Figure 3
The diagram of variable universe changing
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The initial universe [−Ei , Ei ] is transformed into [−α(ΔVBi )Ei , α(ΔVBi )Ei ] through a contraction-expansion factor α(ΔVBi ), where α(ΔVBi ) is the continous function of input variable ΔVBi α : [−Ei , Ei ] → [0, 1] , ΔVBi → α (ΔVBi ) . (7) The universe is changing correspondingly while the input changes, and finally reaches the point that the effect of controlling is invariant. Therefore, the variable universe is suitable for high precision control. For method of variable universe, expert knowledge is not necessary in the designing of fuzzy controller. The fuzzy rules can be obtained as follows: If ΔVBi is Aij and VBi is Bik , then Iei is Cl ,
(8)
where j = 1, 2, · · · , m1 , k = 1, 2, · · · , m2 , l = 1, 2, · · · , m1 , Iei is the output variable and its universe is [−U, U ]. Ai = Aij (1 ≤ j ≤ m1 ) defines a fuzzy partition on ΔVBi (i = 1, 2, · · · , n) and C = Cl (1 ≤ l ≤ m1 ) represents a fuzzy partion on Iei . Suppose that ΔVBij is the peak point of Aij , VBij is the peak point of Bij and IBij is peak point of Cj . The fuzzy logic system (FLS) can be represented as m1
m2
Aij (ΔVBi ) Bik VBi Iej , Iei ΔVBi , VBi = F ΔVBi , VBi
(9)
j=1 k=1
where Iei ΔVBi , VBi is an n-ary piecewise interpolation function. The universe of ΔVBi changes while the variable changes, denoted by Ei (ΔVBi ) = [−αi (ΔVBi ) Ei , αi (ΔVBi ) Ei ] ,
(10)
where α (ΔVBi ) (i = 1, 2, · · · , n) and β (Iei ) are contraction-expansion factors of the universe ΔVBi and Iei , respectively. The contraction-expansion factor used in this paper is given as τ |ΔVBi | α (ΔVBi ) = + ε, τ > 0. (11) Ei The distance of interpolation nodes will be sufficiently small, and the precision of interpolation will satisfy a given ε > 0 naturally. 3.2
Implementation of Variable Universe Fuzzy Controller
The inference methods are the same as the default settings of fuzzy logic toolbox given by Matlab. As shown in Figure 4, the membership functions of inputs and outputs are determined based on the experiences and basic knowledge of cell equalization, where VS = very small, S = small, M = middle, L = large and VL = very large. The rule database is provided in Table 1 and the decision surface is show in Figure 5. The range of the voltage difference is set as [0V, 0.6V] since the voltage difference of adjacent cells is generally smaller than 0.6V. The proposed fuzzy control law can adapt the output equalizing current to the voltage difference. Specifically, when the voltage difference is large,
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Degree of membership
fast equalizing speed is chosen to accelerate the equalization speed. When the voltage difference decreases to zero, the equalizing current is reduced to keep up with the voltage difference. Thus, the battery equalization can be achieved. 1 VS
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Figure 4
The membership function of input and output variables in the proposed controller
Table 1 Rules Datebase in the Proposed Fuzzy Controller Output
ΔVBi
VBi
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0.6
i
Ie [A]
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4
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0.1 0
V B [V] i
Figure 5
The decision surface in the proposed fuzzy controller
The systematic design procedures and results for the proposed FLC-BEC are summarized as follows. Step 1 Obtain the true value for the i-th input membership function for x and the j-th input membership function for y using ωij = min{uAi (x), uBj (y)}, for i = 1, 2, · · · , 5; j = 1, 2, 3.
(12)
Step 2 Calculate the fuzzy output uoij (z) value using ωij , and the k-th output membership function according to each rule uok (z) as uoij (z) = min{ωij , uok (z)}, for k = 1, 2, · · · , 5.
(13)
Step 3 Determine the fuzzy set for output z, uout (z), using uout (z) = max{uo11 (z), uo12 (z), · · · , uo52 (z), uo53 (z)}.
(14)
Step 4 Find the output battery equalization current Iei of the FLC-BEC using the inference results through the defuzzification process by the center of gravity approach that is expressed as
m uout (zl )zl Iei = l=1 . (15) m l=1 uout (zl ) Step 5 Transform the output battery equalizing current IB into the corresponding duty cycles of the PWM driving signal of the proposed battery equalization scheme using (5), and rewrite as ⎧ ⎪ 2Li1 (VCi − VBi )Iei ⎪ ⎨ , cell i charges cell i + 1 Ts VBi VCi (16) Di1 = ⎪ ⎪ ⎩ 0, cell i + 1 charges cell i,
VARIABLE UNIVERSE FUZZY CONTROL FOR BATTERY EQUALIZATION
Di2
⎧ ⎪ 0, cell i charges cell i + 1 ⎪ ⎨ = 2Li2 (VCi − VBi+1 )Iei ⎪ ⎪ − , cell i + 1 charges cell i, ⎩ Ts VBi+1 VCi
335
(17)
Taking the i-th converter into account, the output of the nonlinear system described in (3) can be redefined as y(t) = ΔVBi . The main aim is to use variable universe fuzzy controllers to make the output of the plant of the system decrease to zero, that is, limt→∞ y(t) = 0. Based on the variable universe fuzzy control method mentioned above, a controller is proposed to deal with the nonlinear system (3), as uc (t) β(t)ω(y(t)), m1
m2
ω(y(t)) = U Aij (ΔVBi ) Bik VBi Iej ,
(18) (19)
j=1 k=1
where U determines the control value range of the system. Since the input variable VBi aims to preventing large currents when adjacent cells are both with low/high voltages, the initial universe does not need to be adjusted. On the contrary, the universe of ΔVBi shrinks as the input variable decreases, which can be expressed as τ ΔVBi E , (20) [0, E] → 0, E where E is the max voltage difference between two cells, and τ is a positive constant.
4
Simulation Results
To demonstrate the effectiveness of the proposed equalizing system, simulations are conducted using a four-cell model. The control period of the fuzzy controller is set to 1 s. The parameters in (20) are set as E = 0.6 V, τ = 0.6. The number of cells in the battery pack is n = 4, thus three controllers are utilized. Based on the accumulated variations, the voltages can be updated every period. In the fuzzy controller, the inputs ΔVBi and VBi are also caculated every period. Consequently, the duty cycles applied on MOSFETs will be tuned to realize an adaptive control and reach a satisfactory overall equalizing performance. Considering the accuracy of the voltage estimation in practice, the equalizing process will terminate when voltage differences are all smaller than 0.001 V. As the curve shown in Figure 6, the battery system is a nonlinear system, and the relationship between the terminal voltage and SOC is given as[24] VOCi = bekSOCi + a0 + a1 SOCi + a2 SOC2i + a3 SOC3i ,
(21)
where b = −1.031, k = −35, a0 = 3.685, a1 = 0.2156, a2 = −0.1178 and a3 = 0.3201. ´ For the i-th modified Cuk converter, the circuit parameters are selected as Li1 = Li2 = 100 μH, Ci = 470 μF , Rds = 30 mΩ, where Rds is the drain-to-source resistor of the MOSFET. The connected cells’ SOC are set as SOCi = 70% and SOCi+1 = 50%. The frequent and duty cycle of the PWM signal applied to MOSFET Qi1 are set to 7 kHz and 0.45, respectively. The
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cell currents and capacitor voltage curve are illustrated in Figure 7. It illustrates that the curve matches the previous analysis of the circuit, and the cell’s equalization current iei1 is slightly larger than iei2 . 4.2
4
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VOC [V]
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Figure 6
The relationship between a cell’s voltage and SOC
C
Voltage [V]
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i
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Ts
Figure 7
0.4004
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0.40055
D 'i1T s
Di1T s
Time [S]
´ Capacitor voltage and cell currents of the Cuk converter
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Figure 8
337
Initial voltages of the battery cells
The cell’s capacity is set to 1Ah, the internal resistance 20mΩ, the value of inductor L = 1 100 uH and the period of PWM signals T s = 7000 s. The initial condition of SOCs in shown in Figure 8 with the initial voltages VB1 = 3.710V, VB2 = 4.033V, VB3 = 3.888V and VB4 = 3.773V, thus ΔVB1 = 0.323V, ΔVB2 = 0.145V and ΔVB3 = 0.115V. Simulation data of voltages of the cells under the conventional fuzzy control method is shown in Figure 9, where the voltages of cells after the terminal time is given in the subplot. The simulation data of SOCs is shown in Figure 10, and the terminal time is 7711s. After the equalizing process, ΔVB1 , ΔVB2 and ΔVB3 are all smaller than 0.001V. Figures 9 and 10 show that SOCs of the cells converge to the same level when the voltage based battery equalization is achieved, SOC1 = 0.495, SOC2 = 0.498, SOC3 = 0.501 and SOC4 = 0.504.
Bat 1 Bat 2 Bat 3 Bat 4
4
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Figure 9
Voltages of the cells under the conventional fuzzy control method
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Figure 10 SOCs of the cells under the conventional fuzzy control method
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Figure 11 Duty cycles of the converters under the conventional fuzzy control method
Simulation data of the duty cycles of the cells under the conventional fuzzy control method and variable universe fuzzy control method are shown in Figures 11 and 12, respectively. Be-
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Duty Cycle
cause the equalizers are utilized in the DICM, the upper bound of the duty cycles is set to 0.5. As the voltage differences of adjacent cell pairs decrease, the duty cycles are getting smaller. By the conventional fuzzy control method, when the voltage difference of a pair of cells changes within a fixed range, the duty cycle is only affected by the rule of the average voltage. However, for the variable univese control method, the universe of voltage differences changes with the input variable, and the system has not been stuck in the same rules.
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Figure 12 Duty cycles of the converters under variable universe fuzzy control method
The conventional fuzzy control method is compared with the proposed variable universe fuzzy controller, and the comparison simulation results are shown in Figures 13 and 14. The initial conditions of the cells under variable universe fuzzy control method and the conventional fuzzy control method are the same. It shows that the proposed variable universe fuzzy controllers are more effective for dealing with the equalization problem for the nonlinear battery system. The terminal time is 4437 s, which is much faster than the conventional fuzzy control method. Moreover, duty cycles of the converter between cell 1 and cell 2 under the variable universe fuzzy control method can change obviously as voltage difference decreases to zero at the end of the equalization process. This cannot be realized by the conventional fuzzy control method. The variable universe fuzzy control method shows better adaptiveness than the conventional fuzzy control method. The equalization process under variable universe control method is also much smoother than the equalization process of the conventional control method. The duty cycles under the conventional fuzzy control method jump to zero frequently while the
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variable universe fuzzy control method performs much better. Thus, variable universe fuzzy control method is much more effective than the conventional fuzzy control method for dealing with the same nonlinear equalization system.
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Figure 13 Voltages of the cells under variable universe fuzzy control method
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Figure 14 SOCs of the cells under variable universe fuzzy control method
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Conclusions
Based on the analysis of the equalizing circuit implemented by the bi-directional modified ´ converter, we propose variable universe fuzzy controllers to adaptively tune the duty cycles Cuk and equally tune the equalizing currents. The overall performance of proposed equalizers are evaluated by the equalizing speed and cell protection, and these indices are indicated by the voltage differences and the average voltages of all adjacent cell pairs, respectively. Membership functions and rule database for the proposed variable universe fuzzy controllers are established based on experience and knowldge of experts as well as the characteristics of cells. Simulations are conducted to demonstrate the shorter equalizing time, better adaptiveness, and higher energy efficiency of the proposed variable universe fuzzy controllers than the conventional fuzzy controllers.
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