Monitoring techniques for 12-V lead–acid batteries in automobiles

14 Monitoring techniques for 12-V leadeacid batteries in automobiles E. Schoch, M. Ko¨nigsmann, J. Kizler, C. Schmucker, B. Kronenberg, M. Bremmer, J. Scho¨ttle, M. Ruch Robert Bosch GmbH, Leonberg, Germany

14.1 Historic overview towards battery sensors The requirements for performance, reliability and robustness of electric power-supply systems have increased over the last years and will be further increasing. Reasons are additional comfort demand and more stringent limits for CO2 emissions. The fulfilment of these topics has led to additional electrical loads (see Table 14.1) increasing the electrical power demand, but as well leading to new driving and control strategies, such as idleestop (startestop), intelligent alternator control and coasting, which reduce the time for power generation. We will also see the introduction of a new voltage level of 48 V to support so-called boost recuperation systems as an entry into hybridization. The introduction of autonomous driving (AD) will cause additional safety requirements since it will require a highly reliable electric power-supply system. Fig. 14.1 shows a standard power-supply system and an example of how a future power-supply system could look. All the previously mentioned requirements lead to additional stress on the battery, like higher cycling, and will result in a higher risk for a vehicle breakdown due to discharged or defective battery. A countermeasure against this is the introduction of a complex electrical energy management (EEM) based on the calculated battery performance [1], which was introduced first in 2001 at Audi and Daimler using an electrical

LeadeAcid Batteries for Future Automobiles. http://dx.doi.org/10.1016/B978-0-444-63700-0.00014-3 Copyright © 2017 Elsevier B.V. All rights reserved.

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Table 14.1 Additional electrical loads Electrical load Electric water pump Electrical power-steering Electric cabin heaters Electric cooling fan Heated windscreen Electric charger Roll stabilization Active suspension

Figure 14.1 Standard and future electric power-supply system.

battery management control unit from Bosch. In 2004, the first dedicated battery sensor was introduced into the market [2] and is now a standard in most vehicles with idleestop operation. Fig. 14.2 shows the different generations of the battery management electronic control units. The effectiveness of the EEM has been proven in the breakdown statistics of the German ADAC (allgemeiner deutscher automobil-club), but the number of breakdowns due to battery topics can be reduced further by improving the accuracy of the battery state detection (BSD) algorithms.

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Figure 14.2 History of battery management electronic control units (ECUs).

14.2 Requirements of battery sensors 14.2.1 System requirements Battery sensors measure basic battery data, such as current, voltage and temperature, with high accuracy. Based on these data, the actual battery state and even future behaviour is calculated by diagnostic algorithms on the sensor. The energy management of the overall vehicle is usually calculated in the master control unit of the sensor, based on the transmitted battery state. Requirements regarding measurement ranges, operation conditions, current consumption and communication interface include:








current measurement accuracy and range: 1 mAe1500 A supply voltage range (normal operation): 6e18 V temperature measurement range: 40eþ115 C operation temperature range: 40eþ85 C (ambient temperature) quiescent current consumption <100 mA IP Class: IPX5K5 communication with master control unit: local interconnect network (LIN) interface

The battery sensor is typically located on the negative battery pole and integrated into the battery clamp of the cable to vehicle ground. Versions integrated at the ground end of the same cable or into the positive terminal clamp have been proposed, but did not succeed in the mass market. The sensor shall provide flexible mounting scenarios and different directions for ground cable and connector interface. The resistance the battery sensor

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Figure 14.3 Cabling of electronic battery sensor (EBS).

contributes to the vehicle’s starter circuit has to be minimized and should be <250 mOhm. The mechanical assembly of the sensor should be designed to withstand battery current profiles of permanent 200 A, 1500 A for 0.5 sec and 300,000 startestop cycles over lifetime. An exclusive sense line for voltage measurement with high accuracy is recommended (see Fig. 14.3, Picture A). The voltage drop on the supply line is below 1 mV if the ohmic resistance of this line is smaller than 50 mU. In some vehicle electric power-supply systems, the sense line is routed through a fuse box (see Fig. 14.3, Picture B). In such a setup, acceptable accuracies are still feasible if the ohmic resistance of the overall sense line is low and no highload consumers use the same line.

14.2.2 Hardware requirements Battery state evaluation requires that the battery sensor measures the analogue signals with high accuracies within a temperature range of 40 C to þ105 C and an analogue to digital conversion rate of 103 s1. The accurate measurement of the current is the most challenging task (see Table 14.2). The current during engine crank exceeds 1000 A, while the current during the quiescent phase is in the range of several mA. The voltage measurement accuracies have to be independent from the current load, and the sampling must be aligned with the current measurement sampling to avoid failures in the Ri calculation (see Table 14.3). The temperature measurement accuracy requirements are strongly dependent on the used BSD algorithm. Between 40 C and þ115 C, accuracies of about 3 K are achievable with state-of-the-art microcontrollers. More accurate temperature measurement can be achieved with external temperature sensors.

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Table 14.2 Requirements for current measurement Range 1: ±1 A

Range 2: D200 A

Range 3: ±1500 A

Max

Max

Max

Unit

Resolution

1

1

5

mA

Data rate

1

1

1

kHz

65

55

120

mA

10 (1)

100

500

mA

1

1

%

Current range

Output noise ( sigma) Offset error

35 (2) 1

Relative error

Table 14.3 Requirements for voltage measurement

Voltage range Resolution

Min

Max

Unit

6

18

V

0.1

mV

Data rate

Hz

Output noise (3 sigma) Offset error Relative error

1

mV

10

mV

0.26

%

Since the battery sensor is a permanently supplied electronic unit, the quiescent consumption has a direct influence on the discharge of the battery and therefore on the vehicle standby time. The BSD algorithm requires measurement of quiescent current and quiescent voltage. The battery sensor therefore wakes up periodically to measure these parameters. The wakeup interval depends on the implementation of the BSD algorithm. This could lead to a higher quiescent consumption. In active mode, the current consumption should not exceed 20 mA; in quiescent mode, a maximum current of 100 mA is required. Last but not least, the measurement results should be stable against external influences such as temperature variability, magnetic field and humidity. This must be considered in the electrical and mechanical design.

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Figure 14.4 Inductive current sensor.

14.2.3 Comparison of shunt with inductive current sensor Basic energy management functionalities like idleestop decisions can be realized without battery sensors, but with basic current sensors (see Fig. 14.4). The main drawback is the limited accuracy of quiescent current measurement, which especially reduces state-of-charge (SoC) accuracy significantly due to low accuracy of quiescent voltage determination required for SoC recalibration. SoC algorithms with current sensors are mainly based on a full charge detection (which is never literally reached in automotive leadeacid battery applications), triggering recalibration to SoC ¼ 100%. After the full charge event, SoC is tracked by current integration. From time to time, the full charge would have to be repeated in order to keep an adequate accuracy. In addition, calculation of internal resistance is difficult due to nonsynchronous current and voltage measurements (voltage is measured in the master control unit in this case). By contrast, a resistive current measurement by a 100-mOhm shunt with analogue to digital conversion in two or three measurement ranges enables the full variety of energy management functions, including intelligent alternator control and coasting. Among the advantages is a significantly improved availability of the idleestop function and therefore improved fuel economy because the full charge events are not needed. In addition, advanced functions like ageing algorithms can be provided by a battery sensor. Because of the obvious benefits, there has been a clear trend to exchange current sensors against integrated battery sensors with shunts that have been established as a low-cost commodity at very high volumes. Since its introduction in 2004, the vast majority of vehicles with energy management use battery sensors.

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Figure 14.5 Interface between battery state detection (BSD) and electrical energy management (EEM).

14.3 Leadeacid battery monitoring functions 14.3.1 Interface to electrical energy management (EEM) Fig. 14.5 shows the interface between the battery sensor and the vehicle’s master control unit, which is responsible for the vehicle’s EEM, based on the battery state signals provided by the leadeacid battery monitoring software of the battery sensor. Parts of the EEM functionalities closely related to the battery as the battery management may also be implemented on the battery sensor. Communication between battery sensor and the master control unit is typically realized by an LIN interface. Monitoring algorithms for leadeacid batteries calculate the battery state given as signals for SoC, state-of-function (SoF) and state-of-health (SoH) from the battery current, voltage and temperature measured by the battery sensor hardware, while the vehicle’s EEM ensures voltage stability of the electric power-supply system, engine crankability or realizes fuel-saving functionalities as idleestop, recuperative braking or coasting based on the battery state signals provided by the battery sensor.

14.3.2 Battery state detection signals and electrical energy management functionalities 14.3.2.1 State-of-charge The most important information about the leadeacid battery required by the EEM is its actual SoC, which provides the information of how much charge Q

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Figure 14.6 State-of-charge (SoC) definitions.

related to its full charge capacity can be drawn from the battery until voltage breaks down below 10.5 V under nominal conditions at a temperature of 25 C, and the nominal discharge current I20 ¼ Cnom/20 h. As shown in Fig. 14.6, standard SoC definitions would normalize the deliverable charge Q to the nominal capacity Cnom of the new battery given on the nameplate. If actual capacity C20 of the battery is determined by the BSD algorithm, an alternative SoC definition is useful, exchanging nominal capacity Cnom by actual capacity C20. Thus, even in the case of aged batteries, which suffered capacity loss Qloss, SoC ¼ 100% is reached at full charge. For a full picture, the actual C20 capacity of the battery has to be provided additionally. SoC is used in EEM, for example, for intelligent alternator control, load management, enable/disable of idleestop and to improve battery service life by preventing too-high cycling and deep discharge.

14.3.2.2 State-of-function SoF is defined as an application-dependent variable, which provides the information about the power and/or energy reserve that is available in the battery to supply special consumers like electrical starter, steering or braking devices. There is no defined formula for calculation of SoF as for SoC. In many cases, the predicted voltage drop while applying the specified consumer load is used as a measure for SoF, as shown in Fig. 14.7A. A more sophisticated SoF measure is the predicted deliverable charge at actual battery state and discharge current until battery power falls below a minimum value required for successful operation of the regarded vehicle function. As shown in Fig. 14.7B, the BSD algorithm predicts the charge reserve ‘Ah left’ based on the actual discharge current until a specific EEM functionality can just be performed specified by the load current amplitude x, duration y and the minimum battery voltage z required by the EEM functionality.

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Figure 14.7A State-of-function defined as predicted voltage drop.

Figure 14.7B State-of-function defined as predicted charge reserve.

Within EEM, SoF is mainly used to ensure battery power and charge reserve, for example, for idleestop, coasting, electric steering, etc.

14.3.2.3 State-of-health Since leadeacid batteries suffer from different ageing mechanisms like loss of active-mass, sulfation and positive plate corrosion, which affect discharging and charging power and energy of the battery, there is no common definition for SoH of a leadeacid battery. One feasible approach is to define different SoH values for the different ageing effects, as shown in Fig. 14.8. Since loss of active-mass mainly affects deliverable charge, nominal capacity reduced by the corresponding capacity loss is a suitable measure for this ageing effect. Compared with ageing by loss of active-mass, sulfation reduces chargeable capacity of the battery in the upper SoC range. Hence, the maximum reached SoC at nominal charging conditions is a measure for the amount of sulfation. Corrosion mainly affects deliverable battery power due to increasing internal resistance.

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Qloss(SUL) sulfation

SoH(LAM) [%] = (1-Qloss(LAM)/Cnom)*100% SoH(SUL) [%] = (1-Qloss(SUL)/Cnom)*100%

Q, available charge

C20, actual capacity

Cnom, nominal capacity

SoH(CORR) [%] = Rinom,new/Rinom,aged*100%

Qloss(LAM) loss of active mass

Figure 14.8 State-of-health signals related to ageing effects.

Thus, a feasible measure for this ageing effect is the ratio between actual ohmic resistance and that of the new battery normalized to defined temperature (e.g., 25 C) and SoC (e.g., 100%). In general, for each SoF value, a corresponding SoH value can be derived by relating it to a defined battery temperature (e.g., 25 C) and SoC (e.g., 100%). Within EEM, this kind of SoH value can then be used to permanently deactivate special functionalities like idleestop if the aged battery is not able to support it anymore or even to indicate that the battery should be replaced.

14.3.3 Battery defects detection Due to growing reliability demands for applications like coasting or AD, battery defect detection as part of battery monitoring attracts growing interest. This includes, for example, detection of internal soft shorts and increased gassing/water loss of the leadeacid battery.

14.3.3.1 Internal soft short Internal soft short-circuits in a cell can be induced by growth of dendrites between the plates, especially at low acid densities, and leads to slow discharge of the cell, ending up in battery voltage reduced by about 2 V. On the other hand, growth of positive grids due to corrosion or mechanical stress within the plates caused by volume change during cycling and breaking away of active-material can also induce cell short-circuits.

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14.3.3.2 Increased gassing/water loss Increased gassing and water loss of leadeacid batteries may result from dissolving of alloy parts of the electrode grids in the acid over time, which reduces gassing potential. Another reason may be that the battery is exposed to high temperatures, for example, if it is installed in the engine compartment of a vehicle that is driven in high-temperature climate zones. Water loss leads to capacity and power loss of the battery and therefore has to be detected in time to prevent overcharging and further increased gassing of the battery by reduction of the charging voltage.

14.4 Algorithms for battery state detection of leadeacid batteries 14.4.1 General requirements The main requirement to BSD algorithms from EEM point of view is to continuously provide information about the power and energy storage capability of the leadeacid battery comprising signals as SoC, SoF and SoH. These signals have to be reliable and accurate within the battery’s operating condition range regarding temperature (40 to þ60 C), current (1500e200 A), voltage (0e18 V) and SoC (0e100%). Since battery temperature cannot be sensed within the battery, it has to be derived from the temperature measured on the battery sensor, for example, by a mathematical temperature model within the BSD algorithm regarding thermal connections between sensor, environment and battery as well as self-heating of sensor and battery due to power dissipation. Since the battery state signals have to be robust and accurate over the lifetime of the battery, the BSD algorithm has to adapt to the different ageing effects, such as sulfation, loss of active-mass or corrosion that reduces power and/or capacity of the battery. Furthermore, the BSD algorithms must deal with all kinds of vehicle usage in different climate zones regarding drive cycles from taxi to commuter as well as consumer usage resulting in varying battery cycling at different SoC levels. BSD algorithms shall cope with all types and sizes of leadeacid batteries, whether flooded, enhanced flooded or absorptive glass-mat (AGM), that are intended to be used in the regarded vehicle, even if the original equipped battery was exchanged by the end customer by an aftermarket type exhibiting higher tolerances. BSD not only has to estimate state variables like SoC, but also battery parameters as internal ohmic resistance (Ri), since it directly correlates with the power capability of the battery. BSD signals derived from battery state and parameters must be available to the EEM within a short time after mounting

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the battery sensor on the battery, even with lowered accuracy. Hence, the BSD algorithm must be able to adapt battery state variables and parameters within seconds. To be able to adapt battery parameters like ohmic resistance, the BSD algorithm typically requires appropriate excitations, for example, current amplitudes >0.5 A in frequency range f > 350 Hz. These can be induced either by the electric power-supply system during consumer switching, engine cranking, alternator charging or by the battery sensor itself with the help of an active excitation unit, which, for example, switches a small battery load at high frequency. Some battery parameters, such as battery type (flooded, AGM), nominal capacity (C20) or cold cranking current are normally coded within the monitoring software at end of line, since it is not possible to self-adapt all parameters accurately within a short time after battery change. If lower accuracy of the BSD signals is accepted by the customer, end-of-line battery coding can be avoided by hard coding one or more average battery parameter sets related to different battery size clusters within the BSD software. A size detection algorithm will then choose the appropriate one by itself after battery change. The BSD algorithm not only has to detect the actual battery’s state and parameters, but even has to predict the future capability of the battery to deliver power and/or energy. This, for example, means for idleestop application that the algorithm has to predict the power of the battery that will be available for engine cranking at the end of a stop phase in order to decide whether the engine may be switched off or not at the next vehicle stop. To summarize, main common requirements for BSD algorithms are to accurately adapt actual battery state and parameters independent of size, type, operating condition and ageing state of the battery over its lifetime and to predict available battery power and energy required by the EEM functionalities implemented in the vehicle. Fig. 14.9 shows a schematic of a BSD algorithm that comprises these common requirements. It is divided into an estimator block, which adapts the actual state variables x and parameters p of the battery from the actual measured battery current I, voltage U and temperature T, starting with the parameters as coded at end of line, and a predictor block, which calculates the predicted deliverable charge (SoC) and power (SoF) that are available for a requested EEM functionality based on the estimated battery state x and parameters p as well as SoH signals dedicated to the different ageing effects. The predictor can be flexibly configured to predict the available power or energy related to a specific EEM functionality by the given load current profile Iload(t) of the

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Figure 14.9 Schematic of battery state detection with estimator and predictor.

consumer that is controlled by the said EEM functionality, for example, the starter motor.

14.4.2 Monitoring algorithms for leadeacid batteries 14.4.2.1 Empirical monitoring algorithms Empirical leadeacid battery monitoring techniques do not use deep knowledge of the specific electrochemistry to detect battery state and parameters, but are looking at the relationship between measured voltage and current. Such algorithms may, for example, indicate full charge of the battery if charge current falls below a certain limit at constant voltage charging (>SoC), or they may signal low battery power if voltage drop is high when a defined power load (e.g., the starter motor) is switched on (>SoF). A measure for ageing in sense of loss of active-mass can be derived from the SoC level at which battery voltage starts to fall nonlinearly at constant current discharge related to the amplitude of the discharge current (>SoH). Different approaches for SoH detection based on empirical methods are given in [3e6]. Since empirical algorithms do not use battery knowledge, they have problems to extrapolate and predict the battery state when operating conditions to detect them by voltage and current behaviour are not given. A common method used, for example, for SoC extrapolation, is current integration (coulomb counter), although this leads to increasing error over time due to current offset error, charging losses and self-discharge, thus requiring recalibration from time to time. Empirical monitoring algorithms are very robust since they directly derive battery state information from the measured battery voltage, current and

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temperature, and have no feedback loops enabling continuous estimation of battery state and parameters. On the other hand, their accuracy is limited. Due to the simple estimation methods based on actual voltage and current measurements, empirical algorithms impose low requirements on calculation resources.

14.4.2.2 Model-based monitoring algorithms Model-based monitoring algorithms take into account electrochemical properties and processes of the leadeacid battery, such as electrode reactions and acid diffusion. Their estimated state variables, like quiescent voltage, and parameters, like internal ohmic resistance, are comparable to the physical variables of the real battery, which, for example, is helpful for validation of both battery model and BSD algorithms. Another advantage of model-based approaches is that internal battery state variables and parameters can be adjusted online by adequate state observers and parameter estimators to that of the real battery by feedback of the error between model outputs (such as battery voltage) and the corresponding measured value. Since accurate determination of battery state variables as quiescent voltage and parameters as ohmic resistance typically require defined operating conditions e.g., quiescent phases or excitation from the electrical powersupply system e.g., engine cranks these values cannot be estimated continuously but have to be extrapolated by the battery model in case the mentioned battery conditions are not present. The leadeacid battery model or a simplified version can also be used to predict the available battery charge or power reserve to support a specific EEM functionality.

Model approach Fig. 14.10 shows a leadeacid battery model as an electrical equivalent circuit typically used in model-based monitoring algorithms. The electrochemical processes that govern the performance of a leadeacid battery, such as the kinetics of the electrode reactions and acid diffusion between electrolyte and the electrodes, are represented as simple RjjC couples with different time constants ranging from a few ms for the electrode reactions up to several minutes for acid diffusion. The ohmic resistance Ri sums up the ohmic resistances of the lead and acid parts of the battery ranging from about 2 to 20 mOhm, while the capacitor C0 represents the acid capacity of the battery ranging from about 100,000 to 350,000 F related to the amount of acid. The voltage drop at C0, named UC0, is the quiescent voltage of the battery, which is the most important internal battery state variable, since it almost

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IBatt ohmic resistance acid capacity

URi

State variables:

Ri

UC0

Quiescent voltage UC0 Acid diffusion polarisation Uk

C0

Electrode polarisations Udl.p, Udl.n acid diffusion

Uk

Ck

Rk

UBatt

Main parameters: Ohmic resistance Ri

kinetics of positive electrode

Udl.p

kinetics of negative electrode

Udl.n

Cdl.p

Rct.p UPol

Acid capacity C0 Acid diffusion resistance Rk

Cdl.n

Rct.n

Charge transfer resistances Rct.p, Rct.n

Figure 14.10 Electric-equivalent circuit of leadeacid battery.

linearly depends on the SoC of the battery ranging from about 11.5 V up to 13 V. The remaining state variables are the voltage Uk at the acid diffusion capacity CK and the voltages Udl,p, Udl,n at the double-layer capacities Cdl,p, Cdl,n of the electrodes, also called polarizations, which result from electrode reactions and acid diffusion processes. In equilibrium state, for example, if the battery is left unloaded for several hours, they settle to zero, and battery voltage finally equals quiescent voltage UC0. In this situation, measured battery voltage UBatt is a direct measure for SoC, for example, useful for recalibration of coulomb counting SoC estimation methods. Fig. 14.11 shows the quiescent voltage UC0 versus SoC characteristic of a leadeacid battery, which is almost linear within the SoC range of 30e100%.

Figure 14.11 Quiescent voltage versus state-of-charge (SoC) characteristic curve.

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It has to be stated that almost all model components are temperature and SoC-dependent, as the electrochemical reactions and processes are. Moreover, the charge transfer resistors Rct,p and Rct,n of the electrodes nonlinearly depend on the corresponding electrode polarizations Udl,p, Udl,n due to the nonlinear relationship between charge transfer current and electrode potential of electrochemical reactions described by the so-called Butler-Volmer equation. Some of the battery model parameters, mainly Ri, Rct,p and Rct,n, are significantly affected by ageing effects and therefore have to be adjusted over battery lifetime by adequate parameter estimation methods.

Estimation of internal battery state variables and parameters For state estimation, so-called state observers are commonly used in control theory. These methods are based on a dynamic state space model of the battery and designed to minimize the mean error or the error variance between estimated and real battery state variables by recursive least square methods. The internal state variables of the battery model are adjusted to the real values by feedback of the error between the measured variables like battery voltage and the corresponding model outputs, as shown in Fig. 14.12. One frequently used least-squares method for state estimation is the socalled Kalman filter [7] that explicitly takes into account the statistics of the noises assumed as Gaussian related to the measured variables and the inaccuracies of the underlying battery model. It is an optimal filter in the sense that it minimizes the error variance of the estimated state variables. The Kalman filter not only estimates the internal state variables, but also their error variances. Thus, it additionally provides a measure for the accuracy of

I U T

Unit of feedback

+ -

>

Estimator for parameters and states

U Model of the battery

X – (state variables)

Adaption of parameters

p – (model parameters)

Figure 14.12 Online estimation of battery state variables and parameters.

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the estimated state variables, which can be used to indicate their validity to the EEM. Since the Kalman filter is restricted to linear systems, but leadeacid battery models are highly nonlinear, model equations must be linearized around the operating point before this method can be used for BSD. Such a Kalman filter for nonlinear systems is called Extended Kalman filter (EKF) [8]. Due to the necessity of online linearization of the model equations at every sample step, the EKF requires high calculation effort, which might be reduced, for example, by model simplification or decoupling of model parts [9]. Table 14.4 shows a summary of the discrete EKF equations that have to be calculated at every sample step. The battery model is given as a nonlinear dynamic state space model for the state variables xk. Measurement noise and model noise are regarded by the Gaussian distributed zero mean inputs vk

Table 14.4 Extended Kalman filter equations Discrete extended Kalman filter equations
Nonlinear dynamic model: xk ¼ f(xkl) þ wk1

wk w N(0, Qk) (model noise)

yk ¼ h(xk) þ vk

vk w N(0, Rk) (measurement noise)


Prediction equations: x^() ¼ f(x^(þ) k k1) y^k ¼ h(x^() k ) a priori covariance matrix: ðÞ

Pk

ðþÞ

ðÞ

¼ Fk1 Pk1 FTk1 þ Qk1 , Fk1 ¼ vfðxÞ=vxjx ¼ x ^k1 (transition matrix)


Update of the predicted estimates by the measurement: x^(þ) ¼ x^() þ Kk(yk  y^k) k k Kalman filter gain: . h i1 ðÞ ðÞ ðÞ , Hk ¼ vhðxÞ vxj x ¼ x^k (output matrix) Kk ¼ Pk HTk Hk Pk HTk þ Rk a posteriori covariance matrix: ðþÞ

Pk

ðÞ

¼ ½1  Kk Hk Pk

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and wk. At every sample step, first predicted state variables x^() and model K outputs y^K are calculated by the nonlinear state space model. Besides the a is calculated from the linearized model priori error, covariance matrix P() K equations at the actual operation point. At the following update step, predicted state variables and the a priori error covariance matrix are corrected by the error ykey^K between measured variables and model outputs weighted by the Kalman filter gain matrix Kk. This matrix results from solving the optimization problem with the quality criterion to minimize the error variance of the estimated state variables. The Kalman filter is designed as a state observer, but by declaring parameters as state variables, it can also be used for parameter estimation. For that, the state space equations of the model have to be extended by the first order derivatives dp/dt ¼ 0 for each parameter p that shall be estimated. Thus, the original Kalman filter equations can be applied to the augmented state vector [x p]. The stability of the EKF cannot be proven as is the case for the Kalman filter for linear systems, but there are different variants of Kalman filters for nonlinear systems (such as the adaptive robust EKF or the unscented Kalman filter) that explicitly take into account robustness aspects in their design [10]. Compared with empirical monitoring algorithms, model-based algorithms including self-adaptation of state variables and parameters allow much better accuracy and robustness against measurement noise and varying battery parameters.

Parameter identification in frequency domain As an alternative to parameter estimation in time domain, for example, by EKF, parameters of the equivalent circuit shown in Fig. 14.10 can also be identified in frequency domain by electrochemical impedance spectroscopy. For that, the complex impedance of the battery at different frequencies is analyzed, which is typically shown by a Nyquist plot, as given in Fig. 14.13. Different parts of the Nyquist curve can be assigned to the components of the electrical equivalent circuit and parameter values derived from it. For example, ohmic resistance Ri can be derived from the complex impedance Z(ju) of the battery, which is calculated by the measured voltage response U(ju) divided by the measured current excitation I(ju) if it is evaluated at the frequency u0 for which U(ju) and I(ju) are in phase: Ri ¼ Zðju ¼ ju0 Þ ¼ Uðju0 Þ=Iðju0 Þ; :Uðju0 Þ ¼ :Iðju0 Þ This evaluation is only valid if there is enough current excitation amplitude from the electric power-supply system around the frequency range of u0 z 350e1000 Hz. Generally, this applies to vehicles for cranking, alternator charging or (pulse width modulation) PWM-controlled consumers.

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Figure 14.13 Nyquist plots of leadeacid batteries.

Besides, it has to be stated that due to the strongly nonlinear dependency of the battery parameters on temperature, SoC and current Nyquist plots must be taken over the full range of operating points of the leadeacid battery if a complete parameterization of the model is required. Different approaches for identification of battery ageing based on impedance methods are shown in [11e14].

14.4.2.3 Artificial neural networks approach Artificial neural networks are kind of models inspired by biological neural networks, such as the human brain. They are built up from different interconnected neuron layers, as shown in Fig. 14.14, including input, hidden and output layers. The interconnections between the neurons have numerical weights that can be adjusted by feeding the inputs with measured data of a real system and comparing the network’s outputs with the measured response data. Thus, the neural network can be trained by special learning algorithms to adapt the dynamic behaviour of the real system without having knowledge of this system, resulting in a black box model. Such a self-adaptive model approach can be used for BSD without knowledge of the electrochemical processes and ageing effects behind the leadeacid battery. However, to be accurate and robust, this method requires a large number of measurement data covering the whole range of battery types, operating conditions and ageing states relevant for the regarded application

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Figure 14.14 Artificial neural network.

for initial training of the neural network. Considering the relationships between measured variables (voltage, current, temperature), internal battery state variables and parameters and output battery state signals (SoC, SoF, SoH), a complex neural network is required, which demands high computational power and memory resources. Ref. [15] shows the performance of Neural Networks in comparison to the Kalman filter in SoC estimation, while [16] provides an example for SoH detection using artificial intelligence methods.

14.5 Validation of battery state detection output signals 14.5.1 State-of-charge validation The accuracy of the BSD output signals SoC, SoF and SoH is typically validated on the test bench by artificial test cycles at reproducible conditions as well as in a vehicle at different drive cycles under real conditions with activated battery-related EEM functionalities, such as idleestop. In both cases, accurate reference values are required. One SoC reference can, for example, be achieved by conditioning the battery to a defined initial SoC value before test start by full charge followed by defined amount of discharge at nominal conditions and propagating the SoC during the test cycle by current integration, taking into account charging losses. However, this method is only valid for new batteries without capacity loss. An alternative SoC reference also valid for aged batteries can be derived

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Figure 14.15 State-of-charge accuracy validation.

from the measured residual charge under nominal conditions at test end, which is back-propagated by backward current integration of the regarding gassing losses during charging periods. Fig. 14.15 shows the SoC validation results for an artificial bench test cycle with forward and backward current-integrated SoC references, along with a SoC flag that provides the actual relative SoC accuracy. Since the investigated battery is aged, the references differ, due to the battery’s capacity loss. Realistic absolute SoC accuracy achieved by up-to-date BSD algorithms is in the range of 5% to 10%. To maintain this accuracy over long time, SoC must be recalibrated from time to time by the BSD algorithm, for example, by ‘measured’ quiescent voltage during parking periods of several hours, or at full-charge events.

14.5.2 State-of-function validation SoF signal accuracy can easily be validated by comparing the predicted voltage drop with the measured voltage drop if the battery load related to the specific EEM functionality, for example, the starter motor is switched on. As an example, Fig. 14.16 shows an idleestop cycle with the SoF_V signal predicting the voltage drop at engine cranking. SoF tolerances related to the predicted voltage drop at high current loads of several 100 A are in the range of 200 mV for actual BSD algorithms.

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Figure 14.16 State-of-function accuracy validation.

14.5.3 State-of-health validation Since there are different SoH signals related to the different ageing effects, reference values for each of them are required. Regarding capacity loss by sulfation and loss of active-mass, reference values can be derived from the measured quiescent voltage characteristic curve UC0 (depth-of-discharge) of the aged battery compared to that of the new battery, as shown in Fig. 14.17.

14.5.3.1 State-of-health related to sulfation SoH related to sulfation is equivalent to the maximum reachable SoC at full charge, which is calculated from the difference of maximum quiescent voltage of new and aged battery as follows:   QSUL ½Ah ¼ UC0max;new  UC0max;aged  C0 =3600 SoHSUL ½% ¼ ðCnom  QSUL Þ=Cnom  100%

Figure 14.17 UC0 (depth-of-discharge, DoD) characteristic curve.

LeadeAcid Batteries for Future Automobiles

Absolute tolerance of SoHSUL that is achieved by actual BSD algorithms is in the range of 5% to 10%. For continuous and accurate determination of SoHSUL, frequent charging periods at high SoC levels >70% are normally required by the BSD algorithms.

14.5.3.2 State-of-health related to loss of active-mass SoH related to loss of active-mass is calculated from the measured actual capacity C20 without the capacity loss by sulfation QSUL: SoHLAM ½% ¼ ðC20 þ QSUL Þ=Cnom  100% Absolute SoHLAM accuracy that is achieved by actual BSD algorithms is in the range of 10% to 15%. The main problem here is that loss of active-mass typically is detected at low to mid-SoC below 50%, which at low SoC condition, the EEM would normally attempt to avoid in order to ensure crankability and availability of other functionalities. Thus, the chance to continuously adapt SoHLAM by actual BSD algorithms during normal battery usage in the vehicle is low. However, it increases with increasing loss of active-mass during battery lifetime.

14.5.3.3 State-of-health related to corrosion Since corrosion mainly increases internal ohmic resistance, a measure for this kind of ageing can be derived from the ratio of the normalized ohmic resistance Ri_nom,new of the new battery to Ri_nom,aged of the aged battery at a defined temperature (e.g., 25 C) and SoC (e.g., 100%):  SoHCORR ½% ¼ Ri nom;new Ri nom;aged  100% where Ri_nom ¼ Ri(T ¼ 25 C, SoC ¼ 100%). Reference values for SoHCORR can be provided, for example, by a milliohm metre, which measures the battery’s internal AC resistance at a frequency of 1 kHz. Relative accuracy of internal ohmic resistance estimated by stateof-the-art BSD algorithms is in the range of 5% to 10%.

14.6 Field experience 14.6.1 Battery issues 14.6.1.1 Acid stratification Acid stratification, as shown in Fig. 14.18, is an issue that occurs in flooded batteries caused by heavy cycling; see Section 5.3.3 in Chapter 5. Accumulation of sulfates in the lower part of the (negative) plates may lead to early capacity loss. More significantly for BSD accuracy, due to the inhomogeneous acid density, the quiescent voltage measured at the pole clamps will be elevated comparison to a battery with homogeneous concentration. That

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Figure 14.18 Acid stratification.

means terminal voltage of a stratified battery can no longer be uniquely assigned to SoC. Therefore, BSD algorithms based on SoC(UC0) characteristic will significantly lose accuracy or even become useless in case of acid stratification.

14.6.1.2 Sulfation If leadeacid batteries stay at partial SoC state (PSoC) over a long time in vehicles, for example, during airport parking or as a consequence of EEM functionalities like regenerative braking, growth of lead sulfate crystals may reduce active surface for the charging reaction (see Fig. 14.19). Since big crystals are hardly dissolved during charging, the amount of rechargeable active-mass, and hence, battery capacity is reduced. This effect is called sulfation. As a consequence, BSD algorithms based on SoC(UC0) characteristic will not reach SoC ¼ 100% anymore at full charge for sulfated batteries, as might be expected by the customer. To prevent or at least reduce sulfation in vehicle use, especially if EEM requires PSoC operation, the battery must be fully charged periodically, which is also called refresh charging, at a high charging voltage 15 V. Refresh charging is initiated by the alternator control of the EEM, for example, based on the SoH signal related to sulfation.

14.6.1.3 Premature capacity loss Some leadeacid batteries, especially ones from the aftermarket, show heavy capacity loss of more than 25% after only a few discharge cycles due to loss of active-mass. This can lead to early deactivation of, for example, idleestop by the EEM after only a few months of service life. Hence, the customer will be irritated. Therefore, it is important that only battery types able to support the implemented EEM functionalities over service life are admitted for the vehicle.

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Figure 14.19 Growing of lead sulfate crystals.

14.6.1.4 Battery replacement by end customer If the battery is replaced by another type, most BSD algorithms require coding of the new battery parameters to initialize the algorithm in order to preserve the specified accuracies of the BSD signals. Since coding requires a diagnostic tool, end users might not always perform it. Thus, BSD signal accuracy might be reduced or even robustness of the BSD algorithm gets an issue if coded parameters differ widely from the installed battery. This can even lead to permanent deactivation of EEM functionalities as idleestop.

14.6.2 Electrical energy management issues Brake energy recuperation has been introduced in most new cars as a CO2 reduction measure: the alternator voltage is increased during vehicle deceleration. This requires PSoC control to allow enough headroom for reasonable charge-acceptance. Keeping the battery in this SoC area can promote sulfation. If the SoC recalibration algorithm is based on full charge events, the actual SoC set point may be gradually decreased, as sulfation degrades charge-acceptance. This may, in turn, accelerate the sulfation process and eventually lead to premature battery failures.

14.6.3 Electric power-supply system issues Fundamental to all higher-level battery sensor functions are the accurate measurements of current and voltage at the battery. While for current, this is reliably achieved in the ground cable battery sensor; the situation is different for the voltage measurement. In many vehicle applications, the sensor’s shared sense and supply line is connected to a fuse box. Any resistance between the battery plus terminal and supply line connector will lead to inaccuracies in voltage measurement. This error forms as the product of additional wiring resistance and the current consumption of the sensor itself. As one example of how this can affect the performance of battery state estimation, even small voltage drops caused by this, will have a direct impact

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Figure 14.20 Cabling of electronic battery sensor (EBS) sense line.

on SoC recalibration during quiescent phases. As a rule of thumb for typical leadeacid batteries, 10e15 mV offset in voltage measurement will correspond to 1% SoC difference. If the wiring used to supply the battery sensor is at least partly shared with other components, the error can be worse. Fig. 14.20 illustrates that depending on which load is switched on, how much current is drawn by each load and also on the ohmic wiring resistance, the voltage measured by the battery sensor may greatly differ from the actual battery voltage. As those loads will typically be switched on and off while the car is operated, this will affect the measurement of the internal resistance of the battery more severely than the open-circuit voltage measurement during quiescent phases.

14.7 Outlook on future development Integrated battery sensors, as reviewed in this chapter, have become a very widespread commodity that is included in almost every modern vehicle, driven by both CO2 reduction and electric load requirements. The market shows the needs to integrate the sensor into the battery’s pole niche to avoid packaging interference with other construction elements nearby. Future applications will more and more focus on this packaging area with requirements to reduce the battery sensor size and cost further. As alternatives to the shunt measurement principle, other possibilities to measure the battery current, as shown in Fig. 14.21, will continue to be evaluated. An important constraint will be the shrinking packaging space. Currently, there are no alternative solutions available to the shunt based battery sensors, which could fulfil requirements to size, environmental conditions, accuracies and cost. For applications in high-voltage battery packs for hybrid and electrical vehicles, electrical isolated current measurement principles are useful, dependent on the load profiles and software evaluation algorithms. Most applicable are the field-based sensors such as Hall effect and fluxgate

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Figure 14.21 Current sensing principles. AMR, Anisotropic magneto resistive; GMR, giant magneto resistive; TMR, tunneling magneto resistive.

sensors. Measures to avoid aliasing effects in digital signal processing have to be well considered. Regarding BSD software, a trend towards plug-in solutions is coming up. That means that vehicle manufacturers want to get flexible in combining battery sensor hardware with BSD software of different suppliers or their own one, which, in consequence, will require standardization of BSD software interface and BSD signals.

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