Method and device for determining the remaining run time of a battery

The invention relates to a method for determining the remaining run time (Δti) of a battery (4) that is supplying power to an appliance (2). The method comprises the steps of: —during operation of the appliance (2) measuring the voltage (Ui) supplied by the battery (4) at different points in time (ti) in order to obtain time-voltage-pairs (t,U,), and—calculating the remaining run time (Δti) of the battery (4), wherein the calculation is based on the measured time-voltage-pairs (ti, Ui) and on a relationship between the measured voltage (Ui), the corresponding point in time (ti) and the total run time (T1) of the battery (4) which can be derived from a time dependent formulation of the Nernst equation for this relationship.

The invention relates to a method and a device for determining the remaining run time of a battery that is supplying power to an appliance. In particular the method and the device are adapted to determine the remaining run time of the battery while the appliance is running.

The prediction of the end of the run time or the remaining run time of a battery is of particular relevance for devices powered by a battery that need to run without interruption. These devices include medical devices, such as infusion pumps infusing medication or nutrients for a (par)enteral nutrition into a patient.

Such methods and corresponding devices are known from the prior art. One known method to determine the state of charge of a battery, relies on a measurement of the current delivered by the battery. Integrating the current over time corresponds to the consumption of charge. If the initial state of charge is known, the present state of charge can thus be deduced.

Another method is based on a battery model relating to the measurement of the battery parameters, such as voltage, current and temperature. The state of charge of the battery is deduced from these measurements by neural networks or Kalman filter techniques using an appropriate model. This method however requires a calibration of the model parameters and high performance calculation resources.

It is an object of the present invention to provide a method for determining the remaining run time of a battery that provides precise results without the need for high performance calculation resources. In particular the precision should be such that the results determined by the method can be used to trigger an alarm, wherein standards relating to the time delay between the alarm signal and the end of the run time of the battery are respected.

According to claim1the method comprises measuring the voltage supplied by the battery at different points in time during operation of the appliance in order to obtain time-voltage-pairs and performing a calculation to determine the remaining run time of the battery. The calculation is based on the measured time-voltage-pairs on the one hand and on a relationship between the measured voltage, the corresponding points in time and the total run time of the battery on the other hand. This relationship is derived from a time dependent formulation of the Nernst equation.

According to an embodiment, the calculation of the remaining run time of the battery is carried out (only) if the measured voltage drops below (or reaches) a predetermined voltage threshold value. Before reaching the predetermined voltage threshold value, the voltage can be measured alone without measurement of the corresponding point in time. Once the measured voltage has dropped below (or reaches) the predetermined voltage threshold value, the voltage is measured in combination with the corresponding point in time. Alternatively, the time-voltage-pairs can be measured throughout the entire method, before and after the predetermined voltage threshold value has been reached. In any case, once the measured voltage has dropped below (or reaches) the predetermined voltage threshold value, the voltage is measured in combination with the corresponding point in time. As the calculation is not performed during the entire operation of the appliance, but only in case that the measured voltage is found to be below a predetermined voltage threshold value, the computing capacity necessary to carry out the method can be reduced. The remaining run time can be determined by substracting the actual point in time from the calculated total run time.

The relevant time dependent formulation of the Nernst equation can be expressed by

with—Uibeing the measured voltage supplied by the battery at the point in time ti,C1being a constant relating to the standard cell potential ΔE0of the battery,C2being a constant that depends on the type of battery,T being the temperature,T1being the total run time of the battery, andT2being a parameter depending on the initial state of the battery.

More specifically, the time dependent Nernst equation reads

with—Uibeing the measured voltage at the point in time ti,ΔE0being the standard cell potential of the battery in Volts,R being the the universal gas constant (R=8.314 JK−1mol−1),T being the temperature in Kelvin,z being the number of exchanged electrons,F being the Faraday constant (F=96485.34 JV−1mol−1),T1being the total run time of the battery, andT2being a parameter depending on the initial state of the battery.

As will be shown below, the time dependent Nernst equation may be reformulated to read

According to a further aspect of the invention, the total run time of the battery can be determined by linear regression of the time-voltage-pairs using a relationship between the measured voltage, the corresponding points in time and the total run time of the battery which can be expressed by a linear equation that is derived from a time dependent formulation of the Nernst equation. A calculation based on a linear equation requires less computing capacity than a calculation based on the logarithmic Nernst equation. In particular, the computing capacity required by a method using a linear equation derived from the Nernst equation requires less computing capacity than neural networks or Kalman filter techniques known from the prior art.

The linear equation may be expressed by

xi=10((Ui-Δ⁢⁢E0)⁢zF2.3⁢⁢RT).
The linear equation is an approximation of the equation

xi=T1-tiT2+ti
and is a particularly good representation of the Nernst equation for those measured time-voltage-pairs with values for tiapproaching T1. The underlying expression

xi=T1-tiT2+ti
is nothing else than a reformulation of the above Nernst equation as will be shown in the following:

The total run time of the battery can be determined by making a least square fit of the time-voltage-pairs for values of tiapproaching T1and using the linear equation

In order to reduce noise that might adversely affect the quality of the calculation, the measured values can be smoothed. Preferably, smoothing is applied only to the values measured after the predetermined voltage threshold value has been reached. In the case that the time-voltage-pairs are measured throughout the entire method, smoothing can alternatively be applied also to the values measured before the predetermined voltage threshold value has been reached or to the entire set of measured values. Smoothing can be performed by applying a gliding window to the measured time-voltage-pairs, the time-voltage-pair with the maximum voltage value being selected from each window to perform the calculation.

If the calculated remaining run time is found to be below a predetermined threshold value, an output signal can be generated warning a user of the (imminent) end of the run time of the battery.

According to yet another aspect of the invention the above-mentioned problem is solved by a device for determining the remaining run time of a battery according to claim11and by a machine-readable storage medium according to claim14.

FIG. 1shows an appliance2powered by a battery4and comprising a device6for determining the remaining run time Δtiof the battery4that is supplying power to the appliance2. The appliance2can be a medical device, such as a syringe pump. The battery4may be an electrochemical cell, for example a Nickel-metal hydride battery.

The device6comprises a measuring device8and a computing device10. In the embodiment shown inFIG. 1the device6further comprises output means12.

The measuring device8is adapted to measure the voltage Uisupplied by the battery4. Additionally, the measuring device8is adapted to measure the corresponding point in time ti. Preferably, the measuring device8measures the voltage Uithroughout the entire discharge of the battery4. After having reached a predetermined voltage threshold value Utr, the voltage measurement may be performed periodically, e.g. every second. Before reaching this predetermined voltage threshold value Utr, the frequency of the voltage measurement may be reduced. According to an alternative, the voltage measurement is performed only on request by a user of the device6. The measurement of the corresponding point in time tiis preferably performed only after the predetermined voltage threshold value Utrhas been reached. Alternatively, the measurement of the corresponding point in time tican be performed throughout the entire discharge of the battery4together with the voltage measurement. When the voltage measurement is performed together with the measurement of the corresponding points in time ti, time-voltage-pairs ti, Uiare generated. Each measured voltage Uican be attributed to a specific point in time ti.

The computing device10comprises a comparator14, a memory16and a central processing unit (CPU)18.

The comparator14is adapted to compare the measured voltage Uiwith the predetermined voltage threshold value Utr. The voltage threshold value Utrmay depend on the nature of the appliance2and/or on the type of battery4. During discharge of the battery4, its voltage level behaves roughly constant over a significant time interval. The voltage threshold value Utrmay in particular be chosen such as to be slightly below this constant voltage level.

The memory16is a machine-readable storage medium and adapted to save the measured time-voltage-pairs ti, Uias well as the predetermined voltage threshold value Utrand a machine readable program code adapted to calculate the remaining run time Δtiof the battery4. Alternatively the measured time-voltage-pairs ti, Uiand the predetermined voltage threshold value Utrcan be stored in a separate memory (not shown).

The CPU18is linked to the comparator14and to the memory16. The CPU18is adapted to analyse the output of the comparator14. In case that the measured voltage Uiis below the voltage threshold value Utr, the CPU18initiates and performs a calculation to determine the remaining run time Δtiof the battery4on the basis of the program code saved in memory16. In case that the measured voltage Uiis found to be above the voltage threshold value Utr, the CPU18does not initiate said calculation.

The result of the calculation is used to trigger an alarm signal. More specifically, the determined remaining run time Δtiis compared to a predetermined time threshold value Δttrand if the determined remaining run time Δtiis equal to or smaller than the predetermined time threshold value Δttr, the alarm signal is triggered. The alarm signal may be provided by the output means12. The ouput means12can be visual (e.g. a display) and/or audible (e.g. loud speakers) means.

The device6may further comprise input means (not shown) allowing a user of the device6to enter data and/or information to be used by the computing device10.

In the embodiment shown inFIG. 1, the device6is integrated into the appliance4that is powered by the battery4and the remaining run time Δtiof which is to be determined by the device6. Alternatively, the device6may be provided as a module separate from the appliance2. The separate module can be connected to the battery4supplying power to the appliance2or to the electric circuit of the appliance2. According to a further alternative, the memory16can be provided as separate storage medium that is machine-readable and that stores a machine readable program code adapted to calculate the remaining run time Δtiof the battery4.

The device6for determining the remaining run time Δtiof a battery4is adapted to carry out the following method for determining the remaining run time Δtiof said battery4:

In a first step, the voltage Uisupplied by the battery4during operation of the appliance2is measured periodically. The measured voltage values are compared with a predetermined voltage threshold value Utr. For a Nickel-metal hydride battery supplying a maximum voltage of 5.6V, the voltage threshold value Utrcan be chosen to amount to 4.8V. The comparison is performed by the comparator14. Once the measured voltage value has dropped below (or reached) the predetermined voltage threshold value Utr, the corresponding points in time tiare also measured by the measuring device8. Alternatively, the measurement of the corresponding points in time tiis independent from the predetermined voltage threshold value Utr. The resulting time-voltage-pairs ti, Uiare stored in the memory16. An example of a typical voltage signal of a battery4is shown inFIG. 2. Here, the abscissa shows the time in seconds and the ordinate shows the measured voltage in Volts.

The measurement of the time-voltage-pairs ti, Uishown inFIG. 2does not start from the beginning of the total run time of the battery4, but from a point in time ti=0 that corresponds to approximately 90% of the total run time T1. The overall voltage signal decreases as time passes. In particular, a slight decay of the measured voltage Uiis followed by an abrupt voltage drop.

On a smaller time scale, voltage drops can be perceived that appear to be (nearly) periodical. These voltage drops result from the appliance2consuming power supplied by the battery4.

In general, the voltage signal fluctuates from one measuring point to the following one. This shot-to-shot fluctuation exists in principle throughout the entire measurement. However, due to the resolution chosen inFIG. 2, it becomes visible in particular towards the end of the measurement.

In order to suppress the voltage signal fluctuations due to power consumption and the shot-to-shot fluctuations, the signal of the measured time-voltage-pairs ti, Uiis smoothed in a second step of the method. To this end a gliding window is applied to the measured signal and the maximum voltage value max(Ui) is selected for each window for further processing. The resultant smoothed signal is shown inFIG. 3. Alternatively other conventional smoothing methods may be applied.

The comparison of the measured voltage values with the predetermined voltage threshold value Utrin particular serves to trigger the calculation of the remaining run time Δti. If the measured voltage Uiis greater than the predetermined voltage threshold value Utr, no calculation is performed. By contrast, if the measured voltage Uiis smaller than the predetermined voltage threshold value Utr, the calculation of the remaining run time Δti, is initiated in a third step.

The calculation is performed by the CPU18of the computing device10which executes a program code that is stored in memory16. The calculation basically relies on a relationship between the measured voltage Ui, the corresponding point in time ti, and the total run time T1of the battery4. Said relationship can be derived from a time dependent formulation of the so-called Nernst equation.

The Nernst equation generally describes an electrochemical cell (like the battery4) in its equilibrium state, i.e., without any current flowing. As in the second step of the method only the maximum voltage value max(Ui) is selected for each window (that is the value Uicorresponding to minimum current flow), the Nernst equation is a reasonable approximation for the description of the battery4that is supplying power to the appliance2.

A battery is typically composed of two half cells. In a Nickel-metal hydride battery for example, one half cell consists of a Nickel oxyhydroxide (NiOOH) electrode in an alkaline electrolyte bath and the other half cell consists of a metal hydride (MH) electrode in an alkaline electrolyte bath, wherein the alkaline electrolyte baths comprise hydroxide (OH−) ions. The Nernst equation for a battery correlates the potential difference (or voltage) Uibetween two half cells of the battery and the electrolyte concentration in each half cell of the battery.

During discharge of the Nickel-metal hydride battery the following reactions take place:
First half cell: MH+OH−M→H2O+e−
Second half cell: NiOOH+H2O+e−→Ni(OH)2+OH−

Assuming that the concentration of hydroxide ions in the first half cell, i.e., the hydroxide ions to be consumed during discharge of the battery, is the limiting factor for the discharge reaction in a (Nickel-metal hydride) battery, the Nernst equation for the first half cell reads:

with—E1being the electrode potential of the first half cell,E10being the standard electrode potential of the first half cell,R being the the universal gas constant (R=8.314 JK−1mol−1),T being the temperature in Kelvin,z being the number of exchanged electrons,F being the Faraday constant (F=96485.34 JV−1mol−1),[OH−], being the concentration of hydroxide ions in the first half cell.

Correspondingly, the Nernst equation for the second half cell reads:

with—E2being the electrode potential of the second half cell,E20being the standard electrode potential of the second half cell,R being the the universal gas constant (R=8.314JK−1mol−1),T being the temperature in Kelvin,z being the number of exchanged electrons,F being the Faraday constant (F=96485.34 JV−1mol−1),[OH−]2being the concentration of hydroxide ions in the second half cell.

The potential difference ΔE=E2−E1between both half cells describes the voltage U supplied by the battery (4) which is measured in the first step of the method. The Nernst equation for the entire battery thus reads:

with—U being the voltage supplied by the battery, andΔE0=E20−E10being the standard cell potential of the battery in Volts.

Independent of the type of half cells, the Nernst equation of a battery can generally be expressed as:

with—U being the voltage supplied by the battery,ΔE0being the standard cell potential of the battery in Volts,R being the the universal gas constant (R=8.314 JK−1mol−1),T being the temperature in Kelvin,z being the number of exchanged electrons,F being the Faraday constant (F=96485.34 JV−1mol−1),c1being the electrolyte concentration in the first half cell, andc2being the electrolyte concentration in the second half cell.

During operation of the battery4, the concentrations c1and c2change, in particular c1decreases while c2increases. The voltage Uiprovided by the battery4at different points in time tithus depends on the concentration changes. This dependency can be expressed in the Nernst equation as follows:

with—Uibeing the voltage supplied by the battery at the point in time ti,c10being the electrolyte concentration in the first half cell at the beginning of discharge (ti=0),c20being the electrolyte concentration in the second half cell at the beginning of discharge (ti=0), andk being the reaction rate constant of the electrochemical reaction.

Normalization of the logarithmic term of equation (V) by k yields:

where T1=c10/k and T2=c20/k. As c10is the concentration of the electrolyte to be consumed in the first half cell in a reaction with the reaction rate constant k, T1represents the time period between t1=0 and the point in time when this electrolyte is consumed. That is, T1represents the total run time of the battery. T2is a parameter that depends on the initial electrolyte concentration in the second half cell.

In order to determine the total run time T1, a linear regression of the time-voltage-pairs ti, Uiis performed. The linear regression is performed using time-voltage-pairs ti, Ui, where the measured voltage U1is smaller than the predetermined voltage threshold value Utr, i.e., where the time values tiapproach the end of the total run time T1. The linear regression is based on a linear equation that is derived from the Nernst equation (VI).

Firstly, the Nernst equation (VI) is rewritten as

As T2is much larger than ti, equation (VII) can be approximated by

Equation (VIII) is a linear equation with parameters T1and T2and variables xiand ti. The variable xidepends on the measured voltage Uiand on (constant) parameters so that xican be calculated directly from the measured voltage value Ui. Assuming that

A=-1T2⁢⁢and⁢⁢B=T1T2
equation (VIII) can be written as
xi=Δti+B.(IX)

The linear regression is performed by searching the least square fit for n time-voltage pairs ti, Uiusing equation (IX). For example, the linear regression is performed with n=200 time-voltage pairs ti, Ui. Accordingly, the parameters A and B have to be chosen to minimize the function

The resulting values for A and B, also referred to as best fit parameters, are

The CPU18finally determines the remaining run time Δtiat the point in time tiof the battery4according to
Δti=T1−ti.  (XI)

In a fourth step of the method, an output signal is generated by the output means12warning a user that the appliance2will soon shut down for lack of power, if the remaining run time Δtiis below the predetermined time threshold value Δttr. The time threshold value Δtimay depend on the type of the appliance2and is chosen such as to comply with (inter)national standards and requirements. According to one embodiment, the time threshold value Δtiis between 15 and 90 minutes, preferably between 30 and 60 minutes.