WO2010029355A2

WO2010029355A2 - State of charge estimation

Info

Publication number: WO2010029355A2
Application number: PCT/GB2009/051151
Authority: WO
Inventors: Peter Miller
Original assignee: Ricardo Uk Limited
Priority date: 2008-09-09
Filing date: 2009-09-09
Publication date: 2010-03-18
Also published as: GB0816459D0; WO2010029355A3; GB2463297A

Abstract

A method of calculating the state of charge of a power source, the method comprising the steps of; providing a plurality of equivalent circuit models; selecting an equivalent circuit from the provided equivalent circuits; calculating the input power to the equivalent circuit; calculating the losses from the equivalent circuit; determining an initial state of charge for the power source from the calculated input power and losses of the equivalent circuit; subsequently recalculating the value of one or more of the component parts of the equivalent circuit based on the temperature behaviour of the cell; and determining a state of charge using one or more of the recalculated component parts.

Description

State of charge estimation

Technical field

The following invention relates to, method of and apparatus for estimating state of charge particularly, but not exclusively, of a battery or ultracapacitor such as in a vehicle

Background to the invention

In most battery driven applications it is important to know how much energy there is remaining in the battery, or ultracapacitors used to power applications. A knowledge of the amount of energy remaining allows for an estimate of the approximate time a battery or cell may power a specific device. This is particularly useful in devices where the battery is the main, or sole, source energy.

Furthermore, when charging a battery or ultracapacitor it is important to know how much energy is stored in the battery. This is relevant in determining if the battery is undercharged, or overcharged which may cause the cell to fail, leak or is some circumstances explode.

It is also important to know the amount of charge of each cell so that the charges across all the cells can be balanced to increase the life time and usefulness of the battery.

The measure of the amount of energy available in a battery is called the "state of charge" (SOC). The SOC is particularly important in hybrid, electric and fuel cell vehicles where the SOC is a measure of the "fuel" and consequently is often referred to as the "fuel gauge" of a battery. In electric or hybrid vehicles the SOC allows for an estimate of the potential distance that may be travelled by the vehicle. The SOC is normally measured as a percent of the cell capacity with a fully charged battery being 100% and fully discharged 0%. The definition of fully charged/ discharged is dependent on the chemistry and application of the battery. The reference of the SOC is rated capacity of the cell, so if a cell has a SOC of 100% it is at full rated capacity of the cell. The rated capacity of the cell is known to deteriorate over time, with the maximum capacity that a battery may reach decreasing overtime as the chemistry and internal properties of the battery deteriorate.

There are several known methods for estimating the SOC of a battery:

The current based SOC estimate. This method involves Coulomb counting or integration as the battery discharges. The charge available in a cell/ battery/ ultracapacitor is equal to the current from the battery multiplied by the time for which the current flowed. However, the current that flows from a discharging battery is not constant and therefore to accurately measure the charge one must either accurately model the variations of the current over time or allow the battery to fully discharge and integrate the total current. Both methods can be impractical, as the flow characteristics will also change with the time and state of the battery, whilst it is clearly undesirable to fully discharge the battery to ascertain its charge.

An instantaneous voltage based SOC estimate. The open circuit voltage of a battery is measured and from a voltage vs. time graph (which plots the discharge of the battery) an estimate of the remaining capacity of the battery may be made. This works well for lead acid cells where the voltage is directly proportional to the capacity of the cell. However, for certain chemistries of cells, especially Lithium-Iron Phosphate cells the voltage remains approximately constant for the majority of the batteries lifetime and therefore it is impossible to accurately determine the SOC from the voltage alone. Figure 1 shows a discharge graph for a Li-Ion cell. As can be seen the voltage remains approximately constant for the majority of the discharge time and therefore a measurement of the voltage will not give an accurate reading of the state of charge of the cell.

A further method is a measure of the rest open circuit voltage or a rest SOC estimation. As with the instantaneous voltage based method the method relies on the fact that the open circuit voltage is proportional to the capacity of the battery. This method is known to fail for certain battery chemistries. Yet another method is the specific gravity measurement. In wet batteries the specific gravity of the solution is directly proportional to the SOC of the battery. This technique only works for very specific battery chemistries.

It is known in the prior art to use empirical evidence of previous batteries and make an estimate of the SOC using this information, often in the form of look-up tables. These tables require extrapolation between published values and are unable to predict future behaviour of the source.

Other factors which are known to affect the SOC are the age of the battery, temperature, self-discharging of the battery, manufacturing tolerances etc. To accurately measure the SOC of a battery these effects must be taken into account.

The prior art also does not provide a sufficiently accurate method for determining the SOC for ultracapacitors, asymmetric ultracapacitors and batteries, which also takes into account the various factors that affect the SOC of a power source. Many of the methods described above also do not provide results in real time, limiting their use in applications such as hybrid vehicles where an instantaneous measure of the available power is desirable. Additionally the SOC provided may not be useful as a raw number in some instances, for example as a useful guide to a driver. Since the length of time/miles of journey that the charge will last will depend on how the temperatures and other parameters are likely to vary the present SOC value alone may not be useful.

A further output that can be determined for batteries is the state of health (SOH). The SOH is taken to be a measure of the condition or health of the battery. Overtime a battery will undergo repeated charge/discharge cycles which will reduce the amount of charge that may be stored. There is no universally accepted measure of the SOH of a battery, but any parameter that is known to vary with the age of a battery may be used as a measure of the SOH.

In practice, most of these parameters can be weighted according to experience which requires a certain amount of experimental data and or knowledge of the cell especially when used in a particular application. Summary of the invention

To mitigate the above, and other problems in the prior art, there is provided a method of measuring the SOC and SOH for batteries, ultracapacitors and asymmetric ultracapacitors, which is able to adapt to cell manufacturing tolerances and aging of the cells.

According to an aspect of the invention there is provided a method of calculating the state of charge of a power source, the method comprising the steps of; providing a plurality of equivalent circuit models; selecting an equivalent circuit from the provided equivalent circuits; calculating the input power to the equivalent circuit; calculating the losses from the equivalent circuit; determining an initial state of charge for the power source from the calculated input power and losses of the equivalent circuit; subsequently recalculating the value of one or more of the component parts of the equivalent circuit based on the temperature behaviour of the cell; and determining a state of charge using one or more of the recalculated component parts.

According to an aspect of the invention there is provided a method of calculating the state of charge of a battery modelled as an equivalent circuit of resistors and capacitors, the method comprising the steps of: calculating an input power for the equivalent circuit; calculating the losses of the equivalent circuit; determining a SOC by integrating the input power minus loses and scaling the integrated power by a factor of the battery capacity. According to an aspect of the invention there is provided a method of calculating the state of charge of symmetric and asymmetric ultracapacitors, wherein the ultracapacitors is modelled as an equivalent circuit of resistors and capacitor, the method comprising the steps of; determining the ratio of the square of the voltage on the capacitor of the equivalent circuit to the square of the of the maximum allowed voltage of the one or capacitors.

According to an aspect of the invention there is provided a method of recalculating the state of charge of an equivalent circuit for a power source, the method comprising; determining an initial state of charge for the equivalent circuit; subsequently recalculating a value of a component of the equivalent circuit; determining a factor to describe the temperature dependence between the initial value and recalculated value; subsequently utilising said factor to determine the value of the component.

According to an aspect of the invention there is provided a method of determining the state of health of a power source, the method comprising; determining an equivalent circuit to describe the power source; subsequently recalculating a value of a component of the equivalent circuit; calculating a factor to model the changes between the initial component value and subsequently recalculated value; comparing the change of the factor over time to determine a state of health.

According to an aspect of the invention there is provided apparatus for estimating the state of charge of a power source the apparatus comprising: a power source; an ammeter; a voltmeter a memory with a predetermined equivalent circuits to model the their behaviour of the power source; a processor programmed to compare the behaviour the power source and the models stored in the memory; the processor further enabled to refine the parameters of the selected equivalent circuit based on the temperature behaviour of the cell; and calculating a state of charge based on the refined parameters.

According to an aspect of the invention there is provided apparatus for determining the state of charge of a power source the apparatus comprising: a power source; an ammeter; a voltmeter, a memory with a predetermined store of a plurality of equivalent circuits and models of their behaviour; a processor enabled to calculate the input power to the equivalent circuit; calculate the losses from the equivalent circuit; determine an initial state of charge for the power source from the calculated input power and losses of the equivalent circuit; subsequently recalculate the value of one or more of the component parts of the equivalent circuit based on the temperature behaviour of the cell; and determine a state of charge using one or more of the recalculated component parts. Preferably wherein the selection of the model is based on matching the charge discharge cycle of the circuit with model charge discharge cycles.

Preferably wherein a root mean square of the difference between the model and the measured plots for the circuit is calculated for the plurality of stored equivalent circuits and the model circuit with the lowest root mean square is selected.

Preferably rematching the voltage versus time graph whenever there is change such as a step increase in input current.

Preferably wherein the component values in the equivalent circuit are adjusted based on measurement of temperature and stored trends of component varying with temperature.

Brief description of the drawings

An embodiment of the invention is presented, by way of non-limiting example, wherein:

Figure 1 is a discharge graph of a typical Li-Ion battery;

Figure 2 shows a flow chart of the method to calculate the SOC according to an aspect of the invention;

Figure 3 a voltage against time plot for a LI-ion cell;

Figure 4 shows an example of a 1^st order equivalent circuit;

Figure 5 shows an example of a second order equivalent circuit;

Figure 6 is a schematic of the apparatus of an embodiment of the invention;

Figure 7 is a voltage against time plot for a LI-ion cell; Figure 8 is a zeroth order circuit;

Figure 9 is an output plot from the zeroth order circuit of Figure 8

Figure 10 is an output plot from a first order circuit ; and

Figure 11 shows example test results of an embodiment of the invention;

Figure 12 shows an example of a thermal equivalent circuit.

Detailed description of an embodiment of the invention

During the course of the specification the term power source will be taken to include batteries, ultracapacitors and asymmetric ultracapacitors. A power source, be it a battery or ultracapacitor may consist of a cell or a pack of interconnected cells. The terms cell and pack are taken to be interchangeable.

Figure 2 is a flow chart describing the overall process used to estimate the SOC, 100, of a power source. There is shown the step of selecting a model equivalent circuit at step S 102; making an initial estimate of the SOC at step S 104; calculating the extent of the input changes S 106; recalculating the parameters used to define the equivalent circuit step S 108; calculating a SOC based on the newly calculated parameters at step SI lO and predicting the future behaviour of the source at step Sl 12.

When determining the SOC of a cell it is often easiest to model the cell as an equivalent circuit of resistors and capacitors. The equivalent circuit creates a simple model of the cell that may easily be modified to take into account the different characteristics of different power sources.

In the preferred embodiment three basic models of equivalent circuits are used. Figures 4 and 5 show examples of a basic 1^st and 2^nd order model of an equivalent circuit. Figure 4 shows a typical 1^st order circuit 130, with resistors Rl 132 and R2 134 a capacitor 136 and a voltage source 138. A typical first order circuit has R2 134 and the voltage source 138 in series, and the capacitor 136 in parallel with them both.

Figure 5 shows a 2^nd order model of Figure 4. There is shown the 2^nd order model 140 and resistors Rl 132 and R2 134 a capacitor 136 and a voltage source 138. There is also shown the 2^nd order features of a further resistor R3 142 and a second capacitor 144.

The values of R3 142 and the second capacitor 144 are typical much smaller than Rl 132 or R2 134 and of the first capacitor 136 as they model the high frequencies effects. Where the values of R3 142 and the second capacitor 144 are much larger than the other components they may be ignored (in this case a 1^st order model such as that shown in figure 4 is preferable to use).

Rl 132, may be taken to represent the internal structure of the cell and the resistances associated with the metals and the electrolyte of the cell. Rl 132, increases with age as the cell suffers from degradation. R2 134, represents the time constant of the chemical speed of the reactions of the cell. R2 134, changes slightly with age as the volume of reactive chemical material decreases in a cell as side reactions occur.

A key aspect of the invention is the selection of the appropriate equivalent circuit model. As the cell will always be modelled as an resistor-capacitor equivalent circuit, of varying orders of complexity, a voltage versus time plot of the circuit will be characteristic of the elements used in the equivalent circuit.

Figure 3 shows an example of a voltage versus time plot 120 for a typical cell. There is shown the voltage axis 122, time axis 124, charge cycle 126, discharge cycle 128, the cell behaviour 130 and the model 132. A portion of this plot is shown in more detail in figure 7, which also defines a number of voltage measurements P,A,M. with P the peak maximum voltage, A the finals steady state voltage and M is the minimum voltage.

The shape and size of the voltage versus time plot in figure 7 are characterised by the component parts of the circuit.

In Figure 8 is shown a zeroth order equivalent circuit which can be used to represent a cell. Figure 9 shows the voltage time plot generated by such a model

It can be calculated from ohms law that:

Charge resistance = (P-A)/35 (From Ohms law - as 35 Amps charge current)

= 9.71 milliOhms for cell Discharge resistance= (A-M)/47 (from Ohms law as 47 Amps discharge current)

= 9.79 milliOhms for cell Cell voltage (V) = A

= 3.3 V for cell We now define R as the average of the charge and discharge resistances.

If we move to a 1^st order model (as shown in figure 4), we can use the same definitions of P,A,M and a voltage time plot predicted by the 1^st order model shown in figure 10. As shown the plot in Figure 10 is considerably closer to the actual plot in Figure 7 as it captures the "slopes" on the top and bottom of the waveforms. However we also need to have additional measurements J,K,C as shown in Figure 10. Now we can calculate Rl=(J-K)/35

R2=R-R1 (R calculated as in the 0^th order model ) Cl selected to match slopes C.

From the Figures it is clear that the cell 130 is well modelled by the model 132 and accordingly the parameters of the model would be suitable for use as the equivalent circuit.

The present invention utilises a store of different equivalent circuits with varying parameters and orders of the circuit. A range of equivalent circuits are stored and , an "expert system" is used to provide initial estimates for the component values (in a similar manner to as done "by hand" above for the simple 0^th and 1^st order examples), A range of values around these initial estimates can be tried (by simulating the equivalent circuit with the measured currents and comparing the simulated and measured voltages) to find the best match. Therefore, by matching a measured voltage versus time plot against the calculated voltage versus time plots for equivalent circuits with known capacitance and resistance, the most likely equivalent circuit for a cell is found.

In the preferred embodiment, the matching is done by a standard optimisation process. The root mean squared (r.m.s.) of the difference between the model and the actual measured voltage versus time for the circuit is calculated for all the stored model circuits and a range of component values and the circuit with the lowest r.m.s. error is used as the equivalent circuit. Other matching processes such as sum of errors, weighted fitting functions etc., may also be used to determine a match.

It is possible to construct higher order models in order to better match the model to the data, thereby reducing the r.m.s. error. However, in practice a lower order equivalent circuit is preferable as it requires less complex calculations, and if a lower order equivalent circuit (such as the one shown in Figure 4) is found to produce an acceptable match within a pre-determined limit of the r.m.s. error it is preferentially chosen above the higher order circuit (e.g. the circuit shown Figure 5). Therefore, the invention will select the lowest order/ simplest circuit that matches the actual cell charge/discharge cycle to within a pre-defined tolerance.

As the parameters of the equivalent circuit (size of capacitor, resistance, order of the circuit etc.), vary with temperature, SOC, direction of current, etc. the resistance and capacitance of the equivalent circuit will change. The actual temperature of the cell is measured and the temperature of the model is known from the test data. It is necessary to take into account these changes to satisfactorily model the SOC of a cell. The present invention allows for two methods of modelling these changes. The first method of modelling the changes is to rematch the voltage versus time graph to the stored data either a the start of each use of the battery or whenever a condition is met that requires the re-evaluation of the components of the equivalent circuit e.g. a step increase in the input current. This method does not take into account the cause of the changes of parameters, rather the effects of the change, Beneficially this requires very little processing power assuming especially if just the component values are changed (it has been found that the order of the model does not need to be changed and is defined by the chemistry).

The second method is to assume that the basic form of the equivalent circuit does not vary over time, so that the same basic model chosen is constant and the parameters of the resistance and capacitance are used as starting values. In this embodiment the equivalent circuit for the cell is defined post production, preferably by the r.m.s method. Once the equivalent circuit is defined, test data for that equivalent circuit is generated. The test data empirically models the cell's behaviour when the parameters have been changed, and the data is used to refine the parameters. For instance, it is known that a change in the temperature of the cell will lead to change in Rl 132. By empirically modelling the relationship between the change in temperature and resistance for a particular equivalent circuit, the data can be used to refine the parameters of the model selected by the r.m.s method. For example, the model selected may assume a cell temperature of 303 Kelvin and a corresponding resistance of 7mΩ for Rl 132. However, the actual measured cell temperature may be 300 Kelvin and from the modelling data it is known that a drop of 3 Kelvin increases the resistance by 0.1 mΩ for a particular cell type and chemistry. Therefore, the value of Rl 132 used for to model the cell would be 7.1 mΩ. Those skilled in the art will appreciate that this refinement may be used to model the changes across the full gamut ofparameters.

In one embodiment tests are performed at a range of temperatures, and at each temperature an equivalent circuit model is calculated (of the same order), then the changes of the individual parameters are plotted and will normally fit a smooth curve An example of such results are shown in Figure 11 in a graph of Rl against temperature . An example of results are shown in Figure 11. If there is such a smooth curve (as in Figure 11) then this smooth curve can be used to estimate the values of this parameter at all temperatures. If the curve is not smooth (as in Voltage in the table in fig 11) then extra testing is required before a suitable relationship can be found. In the test that generated the results of Figure 11 because V depends upon SOC each test was done at slightly different SOCs, so V is actually a function of both temperature and SOC).

This selection of equivalent circuit and subsequent modelling of the cell's behaviour is optimally performed for each variety of cell chemistry and preferably manufacturer. Once a particular cell type has been modelled e.g. same manufacturer, and specification, this model may be applied to all appropriate cells e.g. those of the same make and model. In a battery management system (BMS) in for example a hybrid vehicle it is preferable to have such information before installation of the battery.

Once a model of the cell has been selected and the parameters optimised for the conditions of the cell an initial estimate of the SOC of the cell is performed at step S104.

The method used to determine the SOC is dependent on the nature of the cell. Different methods are used according to whether the cell is battery or a ultracapacitor (asymmetric or symmetric).

For batteries the invention implements a power based SOC estimate and measurement. The invention integrates the input power minus the losses to calculate an input power. It is found that the input power is optimally updated every 0.1 seconds using the average current and voltage over that time period.

The power and losses are calculated from the equivalent circuit. At any time the power is simply the current in times by the voltage in. The losses are calculated for the components of the equivalent circuit. The losses for the resistors Rl 132 and R2 134 are given as I²R, where R is the value of the resistance for the particular component.

It is found that the majority of the losses are well modelled using the power loss from Rl 132. As R2 134 represents the chemical time constant, its effects are visible in Figure 2 as the curvature of the beginning and end of the charge discharge slopes. This is not a loss mechanism, however the equivalent circuit model is only an approximation, so a better match with actual SOC may be obtained by considering a fraction of R2 as providing a loss. The extent of the loss can be determined empirically from test data, and as with the temperature resistance relationship used to calculate the size of the R2 134 loss.

As the SOC is expressed as percentage referenced to the cell capacity it is necessary to convert the calculated integrated power into a percentage. The invention divides the integrated power by the cells capacity expressed in Watt-hours. The cell capacity is the capacity at the time of the manufacture of the cell. The resulting figure is then multiplied by 36 so that it may be expressed as a percentage.

For ultracapacitors the value of R2 134 is much greater than Rl 132. This allows R2 134 to be ignored when calculating the SOC. The SOC in ultracapacitors may be expressed as the ratio of the energy stored on the capacitor to the maximum allowed energy for the capacitor. As the energy stored on a capacitor is ¹A CV² the SOC of the ultracapacitor is therefore:

SOCultracap = 100 (V_ci²/ V_pack_ma_X ²); Equation 1.

where V_cl is the voltage across the capacitor 136 and V_pack _max the maximum allowed voltage from the pack. As the voltage across the capacitor V_cl is dependent on the circuit, a knowledge of Rl 132 and R2 134 allows for a determination of V_cl. This formulation for the SOC of an ultracapacitor, will therefore automatically include the losses of the cell.

The above method will give the results for a typical cell (based on the measurements used for step 102). In practice cells will all be different due to manufacturing tolerances, and their parameters will change with age. It is thus important that the relevant parameters in the model are varied to track those in the real cells.

The SOC is updated at discrete intervals, again preferably approximately every 0.1 seconds. It is possible to continually check for changes of the parameter and make minor adjustments to the Rl 132 according to the changes in temperature using the empirical data, as described above. It has been found that changes with temperature are generally very simple (typically linear or a low order polynomial) so can be done every update. Actually varying component values to track e.g. aging requires certain conditions (e.g. a step change in current) and so is only be done when this occurs - but again the computation required becomes simple. The changes of the input parameters (voltage and current) are measured at step S 106. This is performed by comparing the input current and voltage to the previous values. If there is a significant change in either the input current or voltage the invention re-evaluation the equivalent parameters at step S 108.

At step S 108, there has been a significant change in the conditions of the equivalent circuit. The actual temperature of the cell is measured and the difference between the temperatures used is noted. As changes, such as increase in current, may occur instantaneously in a circuit which would result in a decrease in resistance it is not true with an equivalent circuit. A decrease in Rl 132 in an equivalent circuit would suggest that the metal in the cell structure has changed instantaneously which would be a false assumption. Therefore, any significant change in the input current needs to be modelled correctly, and a filtering factor, f, is applied to the circuit to model the non-instantaneous change.

In the equivalent circuit it is assumed that the change in the input current will not affect the voltage across the capacitor, which resists the change. The change in the value of Rl, called Rest, is estimated to be:

Rlest ~ ΔV/ΔI Equation 2.

Where ΔV is the change in the voltage in and ΔI is the change in the current in. However, because of the assumption that Rl 132 is not expected to change instantaneously and that new value of Rl, Rl_new, is a combination of Rl_est and the original value of Rl, called Rl_Oπ_g, the filtering factor f is applied to the result, where f is between 0 and 1, thus allowing the delay in the increase of the resistance to be factored. The filtering factor also helps remove the noise that is present in the measurements of the current and voltage. The value of Rl_newis therefore given as:

Rlnew= Rloπg + (Rlest - R long) * f Equation 3. So if the filtering factor is 1 the new value of Rl is the value of R_est- The lower the value of f the slower the changes in the resistance are introduced. It is found, that the precise value of f is not critical to the estimation of the SOC and typically a value of ~ 0.1 models the changes to the desired level of accuracy.

The filtering factor also has the additional benefit of reducing the noise in the reading. The value of Rl new is heavily dependant on the value of Rl_est, which in turn will be affected by the noise in the reading. The noise is typically inversely proportional to the counts in the reading and as the value of the Rl_est is based on the small changes of voltage and current, the counts are low and therefore the noise is high. The resulting value of Rl_new is fed back into the equivalent circuit. As R2 134 represents the time constant of the chemicals in a battery, and therefore changes in R2 134, represents the changes in the physical composition of the battery, and need not be considered at this stage.

As the value of Rl 132 is fully recalculated at discrete intervals, in the preferred embodiment when there is a significant change in the input current, the recalculated value of Rl will not be accurate at all times, especially as the temperature of the cell varies. So once the value of Rl_new is calculated the invention will also calculate a correction factor for minor changes in temperature.

To model the changes in the resistance with temperature, the invention assumes that the ratio of Rl_new to the value of Rl calculated at step S102, with the correction factor of the cell being at the same temperature at Rl_new is constant. Therefore, if value of

Rlnew was calculated when the cell temperature was 313K and the value of Rl 132 calculated at step S 102, Rl_Oπ_g, was calculated with a temperature of 303K the correction of 1OK to Rl_Oπ_g is applied to calculate the value of Rl_orig newcondmons i.e. The value that Rl_orig calculated at step S 102 would have if it the cell temperature was

313K, that is to say the temperature of the cell when calculating Rl_est-

This ratio Rl_new/ Rloπ_g newconditions is called Rr and is constant and depends on the cell chemistry at that moment.

If a re-evaluation of the parameters of the equivalent is not required, or the parameters have been re-evaluated step S 108, the invention calculates the new SOC at step SI lO by factoring in the minor changes due to the change in the cell temperature. This requires a measurement of the cell temperature using known means.

At step SI lO, there are two separate scenarios which may occur resulting in different methods of measuring the SOC. In the first scenario, the invention has not passed through step S 108, and the parameters that are used are the parameters originally determined at step S 102. In the second, more common scenario, the cell has undergone a significant change in input current and the parameters of the model have been re-evaluated at step S 106 and the correction factor Rr has been determined for the circuit.

In the first scenario where the initial equivalent circuit calculated at step S 102 is being used i.e. The invention has not passed through step S 108, the changes of the parameter of Rl 132 with the variation of temperature is calculated by using the second method outlined in step S 102. The changes in resistance of the initial equivalent circuit are well modelled using the empirical data and this model is applied to calculate the value of Rl new The SOC is then recalculated using this new temperature adjusted value of Rl as described using the equations in step S 104.

In the second scenario, the parameters of the equivalent circuit have been re-evaluated at step S 108, the value of Rr is known for the equivalent circuit, and is used to calculate the new temperature dependent value of Rl_new.

To take into account the temperature of the cell the value of Rl_Oπ_g in Equation 3 is replaced by Rr*Rl_oπg, with Rr factoring in the temperature dependence, therefore making the value of Rl_new at a certain temperature:

Rlnew = (Rr*Rl_oπg)+ (Rlest - (Rr*Rl_oπg)) * f. Equation 4.

This method for calculating Rl_new is valid and used for all times until there is another significant change in the input current which requires the full recalculation of Rl, and subsequent recalculation of Rr, as determined at step S 106.

Once the value of Rl_new has been calculated the SOC of the cell is recalculated using the method outline in step S 102. Once the SOC has been calculated using the above methods it is desirable to be able to check if the values obtained are accurate. A voltage based estimate of the SOC can be made for certain cell chemistries and SOC ranges. Figure 1 shows that whilst a voltage based estimate for the SOC would not work for the majority of the discharge of the cell it would work for the beginning and end of the cycle. Therefore, if the voltage is in a range where accurate results may be obtained from the voltage, a check of the SOC is made from a measurement of the voltage. If a discrepancy is found the voltage based estimate is taken to be accurate and the SOC made in step SI lO is corrected to match the voltage based estimate. If the voltage is outside the desired parameters then this checking step is ignored.

The determination of the state of health (SOH) of the cell is also important, especially in applications where the battery is the main power source. Over time the battery will deteriorate and will accept a reduced amount of charge. This process is irreversible and may eventually result in the need to change the battery.

Rr can also be used as a measure of the cells aging by tracking its change with time. Whilst the ratio Rr is constant during a particular use of the cell, the value is expected to change over time as its value is dependent on the chemistry of the cell. Therefore by tracking the value of Rr an estimate of the SOH of the cell can be made.

The variation of the voltage V, can be done in a similar way, when the current is constant for a period of time so the voltage on Cl 136 has stabilised.

Other ways of adapting the model parameters may be used for example using an observer to estimate the parameters in the equivalent circuit.

Once the SOC has been calculated at step SI lO, the future behaviour of the cell, known as the "look ahead" is predicted at step Sl 12. The SOC can be used to determine how much longer the pack will supply a given power before its SOC falls below a specified value or its temperature rises above a specified limit. In applications such as electric vehicles this would give an indication of the distance a car may travel before requiring the battery to be recharged. This prediction is performed by comparing the SOC to the empirical charge discharge cycles allowing for an estimate of the approximate time remaining before the cell is fully discharged. This information would typically be fed into the vehicles control system to optimise the control of the system and allow a determination of which cells need to be charged.

Furthermore, the future behaviour of the SOH may also be predicted at this stage. If the SOH is shown to be decreasing and approaching a level which would indicate that a new battery may be required an estimate of the time to such a fail level, preferably in terms of charges, may be estimated from the value of Rr over time.

The above description has focused on the modelling of the electrical behaviour of the cell as an equivalent circuit it is also possible to model the thermal behaviour of the cell using an equivalent circuit. It is important to be able to predict how the cell will react thermally to changes in the input current and voltage and the possible affects such changes will have. For instance, it is known in hybrid vehicles to use the breaking energy of the car to charge the battery. However, a battery may not be able to withstand a very high current over a short period of time without increasing the cell by an undesirable amount. Accordingly, by modelling the thermal component of the cell predictions on the future behaviour of the cell may also be made.

The thermal component is modelled using an electrical equivalent circuit , an example of which is shown in figure 12 containing a resistor Rthermal and capacitor Cthermal.

The losses are calculated as for example I²Rl (see earlier)

Tease is measured case temperature.

Voltage across capacitor Cthermal is the estimated cell internal temperature. This estimated cell internal temperature is what is used to scale the components in the cells electrical model. This approach correctly accounts for both changes in external ambient temperature and changes caused by the cells self heating.

The losses and associated heating form the losses are modelled as the cell is in use and the predicted changes in temperature from changes in input current and voltage may be determined. At step Sl 12 if the look ahead would be able to predict the associated rises in temperature from the increase of input energy. If the breaking energy would generate an input of 50 amps to the cell but it is found that such an input would increase the cell temperature above a safe level it would be used to stop such an input from occurring.

Figure 6 shows a schematic of the invention. There is shown the battery 140, a voltmeter 142, an ammeter 142, a battery temperature monitor 144, a processor 146, a memory 148 and a vehicle control system 150.

The battery 140 is measured by the voltmeter 141, ammeter 142 and temperature monitor 144 which relays the information to the processor 146. The memory 148 stores the historic data and may be stored with the processor 146 or may be an external memory store. The processor 146 communicates to the vehicle control system 150 indicating the SOC, SOH and any look ahead function that is calculated.

Claims

1. A method of calculating the state of charge of a battery modelled as an equivalent circuit of resistors and capacitors, the method comprising the steps of: calculating an input power for the equivalent circuit; calculating the losses of the equivalent circuit; determining a SOC by integrating the input power minus loses and scaling the integrated power by a factor of the battery capacity.

2. A method of calculating the state of charge of a power source, the method comprising the steps of; providing a plurality of equivalent circuit models; selecting an equivalent circuit from the provided equivalent circuits; calculating the input power to the equivalent circuit; calculating the losses from the equivalent circuit; determining an initial state of charge for the power source from the calculated input power and losses of the equivalent circuit; subsequently recalculating the value of one or more of the component parts of the equivalent circuit based on the temperature behaviour of the cell; and determining a state of charge using one or more of the recalculated component parts, wherein the selection of the model is based on matching the charge discharge cycle of the circuit with model charge discharge cycles.

3. A method of calculating the state of charge of symmetric and asymmetric ultracapacitors, wherein the ultracapacitors is modelled as an equivalent circuit of resistors and capacitor, the method comprising the steps of; determining the ratio of the square of the voltage on the capacitor of the equivalent circuit to the square of the of the maximum allowed voltage of the one or capacitors.

4. A method of recalculating the state of charge of an equivalent circuit for a power source, the method comprising; determining an initial state of charge for the equivalent circuit; subsequently recalculating a value of a component of the equivalent circuit; determining a factor to describe the temperature dependence between the initial value and recalculated value; subsequently utilising said factor to determine the value of the component.

5. A method of determining the state of health of a power source, the method comprising; determining an equivalent circuit to describe the power source; subsequently recalculating a value of a component of the equivalent circuit; calculating a factor to model the changes between the initial component value and subsequently recalculated value; comparing the change of the factor over time to determine a state of health.

6. A method according to claim 1,4 or 5 wherein the equivalent circuit is a first order circuit comprising two resistors in series with the voltage supply and a capacitor in parallel with the voltage source and one of the resistors.

7. A method according to claim 1, 4 or 5 wherein the equivalent circuit is a second order circuit comprising two resistors in series with the voltage supply and a capacitor in parallel with the voltage source and one of the resistors, and a third resistor and second capacitor both in parallel with the first capacitor.

8. A method according to claim 2 wherein the equivalent circuit is chosen by matching a measured voltage against time plot with the calculated voltage against time plots for the plurality of equivalent circuits.

9. A method according to claim 8 wherein a root mean square of the difference between the model and the actual plots for the circuit is calculated for the plurality of stored equivalent circuits and the model circuit with the lowest root mean square is selected.

10. A method according to claim 8 or 9 comprising the step of rematching the voltage versus time graph whenever there is change such as a step increase in input current.

11. A method according to any preceding claim wherein the component values in the equivalent circuit are adjusted based on measurement of temperature and stored trends of component varying with temperature.

12. Apparatus for determining the state of charge of a power source the apparatus comprising: a power source; an ammeter; a voltmeter a memory with a predetermined store of a plurality of equivalent circuits and models of their behaviour; a processor enabled to calculate the input power to the equivalent circuit; calculate the losses from the equivalent circuit; determine an initial state of charge for the power source from the calculated input power and losses of the equivalent circuit; subsequently recalculate the value of one or more of the component parts of the equivalent circuit based on the temperature behaviour of the cell; and determine a state of charge using one or more of the recalculated component parts.

13. Apparatus for estimating the state of charge of a power source the apparatus comprising: a power source; an ammeter; a voltmeter a memory with a predetermined equivalent circuits to model the their behaviour of the power source; a processor programmed to compare the behaviour the power source and the models stored in the memory; the processor further enabled to refine the parameters of the selected equivalent circuit based on the temperature behaviour of the cell; and calculating a state of charge based on the refined parameters.