Increased utilization of batteries in electrical power and transportation systems puts an emphasis on charging efficiency and battery life, and related battery ...
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Battery Current and Voltage Control System Design with Charging Application Danijel Pavković, Mihael Lobrović, Mario Hrgetić, Ante Komljenović and Viktor Smetko University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture IEEE MSC 2014, Antibes, France, October 2014. 1
Introduction Increased utilization of batteries in electrical power and transportation systems puts an emphasis on charging efficiency and battery life, and related battery current control system performance. Typically the so-called constant-current constant-voltage (CCCV) charging technique is used when recharging high-power batteries from partially or fully discharged state. However, batteries are also characterized by notable electromotive force and internal resistance variations with state-of-charge, which may affect the battery control system behavior. Hence, this presentation outlines the design of an adaptive voltage/ current cascade control system for CCCV charging application suitable for a wide variety of battery types. The effectiveness of the proposed charging control system is verified experimentally for the case of valve-regulated lead-acid (VRLA) battery, and a lithium-iron-phosphate (LiFePO4) cell. 2
Experimental setup The setup comprises a PLC-controlled IGBT-based two-quadrant DC chopper (a buck/ boost converter) operating at 1 kHz, thus facilitating bidirectional current control for battery testing and charging purposes. The setup features measurements of battery voltage and current, as well as battery temperature and DC link voltage for diagnostics purposes. The high-level supervision and signal processing are implemented in LabView with CompactRIO system used for data acquisition.
Principal schematic of battery test setup.
Test setup photograph. 3
Constant-current/constant-voltage battery charging strategy The constant-current/constant-voltage (CCCV) charging strategy needs to facilitate the following requirements: 1. The battery is initially charged by a maximum allowed battery current which is maintained until the battery terminal voltage approaches the target fully-charged voltage value due to battery EMF steady increase (constant-current mode). 2. Once the target voltage is reached, the charging current is gradually decreased, while maintaining constant terminal voltage, and charging is performed in the constant-voltage regime until the current drops below a predefined threshold.
Constant current
Battery current
Constant voltage Time
Battery electromotive force Eb [V]
Battery voltage
Time
Illustration of constant-current/constant voltage charging profile.
Illustration of battery electromotive force (EMF) vs. SoC dependence.
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Battery charging control system design The cascade control system, with superimposed voltage controller and inner current controller, has been chosen for the charging task because it naturally facilitates the constant-current/constant voltage mode transition. Moreover, the fully-charged voltage and current limit are specific for each battery type, and represent principal charging controller parameters. Target (fully-charged) Battery charging battery voltage current limit
Block diagram representation of battery voltage/current cascade control system structure.
Slowlyvarying EMF “disturbance”
Other advantages of cascade control system: (i) disturbance suppression at local level, and (ii) control system modularity (step-by-step design). 5
Current and voltage controller tuning The controller tuning is based on Damping Optimum Criterion, which is a pole-placement-like method of designing linear continuous-time control systems with a full or reduced-order controller. Control loop design is based on the following closed-loop characteristic polynomial formulation: Characteristic ratios, optimal D = 0.5 (for 6% overshoot) i
Ac ( s) =
D2n −1 D3n − 2
L Dn Ten s n
+ L + D2Te2 s 2
Current control loop: Gci ( s) =
Tei,min =
K ci =
Voltage control loop:
1 TΣ 0TLTci s (TΣ 0 + TL )Tci s 2 (1 + K ci K L )Tci s + + +1 K ci K L K ci K L K ci K L 3
TΣ 0 1 D2i D3i 1 + TΣ 0 TL
1 KL
TΣ 0 + TL 1 − D T 2i ei
Equivalent time constant, + Te s + 1 closed-loop rise time ≈ 2Te
Gcu ( s) =
1 TΣuTeiTcu 3 (TΣu + Tei )Tcu 2 (1+ K cu Rb )Tcu s + s + s +1 K cu Rb K cu Rb K cu Rb
Equivalent time constant depends on both process and design parameters D T Tci = Tei 1 − 2i ei TΣ 0 + TL
Analytical expressions
D T Tcu = Teu 1 − 2u eu TΣu + Tei
Teu,min =
TΣu 1 D2u D3u 1 + TΣu Tei
K cu =
1 Rb
TΣu + Tei 1 − D T 2u eu
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Current control system robustness analysis Battery electromotive force is characterized by slow operating point changes, which are easily suppressed by current controller. Battery internal resistance variations, even though rather slow, may be quite emphasized, and they directly affect the overall resistance and dominant process lag. To this end, the current control loop robustness is analyzed by means of root-locus plots. A decrease in battery internal resistance from nominal value may result in weaker damping of dominant closed-loop modes.
Internal resistance vs. SoC for VRLA battery and LiFePO4 cell. Inductor (dominant lag) nominal parameters. Parameter Inductor inductance Lc Inductor resistance Rc Inductor time constant Tc
Value 0.7 mH 50 mΩ 14 ms
Current control loop root locus plots. 7
Control system adaptation In order to obtain the fast closed-loop response, without affecting the closed-loop damping, the PI current controller needs to be adapted on-line. A gain-scheduling controller would not be suitable for a general-purpose charging controller (intended for a wide range of battery designs), because it requires detailed a-priori recorded internal resistance maps. Hence, a Kalman filter-based parameter estimator is used instead for controller self-tuning. Internal resistance estimation is based on a simplified model of battery terminal voltage/ current variations (∆Eb ≈ 0): ∆u b (k ) = ub (k ) − u b (k − 1)
∆ib (k ) = ib (k ) − ib (k − 1)
∆ub (k ) = ∆ib (k ) Rb 14442444 3 y (k ) = ϕ (k )θ (k ) + e(k )
θ (k ) = θ (k − 1) + ν (k − 1)
Block diagram representation of Kalman filterbased estimator of battery internal resistance.
Suitable for Kalman filter-based parameter estimator design! 8
Experimental results – current control system validation The current control system is verified for lead-acid battery charging. In the case of PI current controller tuned for robust behavior (D3i = 0.3), the control system is characterized by well-damped but relatively slow behavior (step response time of about 200 ms is achieved). By moderately speeding-up the controller (D3i = 0.5), the step response time is reduced to around 100 ms, with favorable damping preserved. As expected, further speeding-up of closed loop response (D3i = 0.8) may weaken the closed-loop damping, especially in the presence of battery internal resistance uncertainty (in controller design). Experimental responses of non-adaptive current control system. 9
Experimental results – adaptation The Kalman filter-based internal resistance estimator adapts the PI current controller to the correct value of the battery internal resistance, in order to achieve favorable performance (fast and well damped response). The adaptive controller has been tested for the case of pulsed battery current reference profile. The parameter estimator response can be made rather fast (rise time of about 10 s), while also achieving a low level of noise. The same approach can be used for battery terminal voltage controller adaptation.
Experimental responses of adaptive current control system.
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Experimental results – charging application Battery charging control system based on cascade control system arrangement facilitates constant current-constant voltage charging with seamless transition between the aforementioned charging modes. Indeed, under cascade control the constant-current regime is maintained until the battery terminal voltage target is reached. The voltage controller being no longer saturated, gradually decreases the current reference, and consequently, a constant battery voltage is maintained. The constant-voltage mode is maintained until the battery enoof-charging condition is reached. Results of experimental verification of CCCV charging control system: partially discharged VRLA battery (a) and fully-discharged LiFePO4 cell (b).
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Conclusion A cascade control system design for battery constant-current/constantvoltage (CCCV) charging application has been presented based on battery current and voltage PI controllers. The controller design has been based on the damping optimum criterion which has yielded simple analytical expressions for controller parameters. The closed-loop robustness analysis has indicated that battery internal resistance variations may affect the control system closed-loop damping, which mandated controller adaptation via on-line parameter estimation. The effectiveness of proposed battery charging control system has been verified experimentally on the target battery test setup for different battery types (i.e. VRLA battery and LiFePO4 cell). The results have shown that the proposed adaptive charging control system can facilitate well-damped control system behavior, and that the cascade control system structure effectively facilitates intended battery constant-current constant-voltage charging regime. 12
Thank you! Questions?
