State of Charge (SOC) Determination

State of Charge (SOC) Determination

 

The State of Charge of a battery is its available capacity expressed as a percentage of its rated capacity. Knowing the amount of energy left in a battery compared with the energy it had when it was new gives the user an indication of how much longer a battery will continue to perform before it needs recharging. Using the analogy of a fuel tank in a car, SOC estimation is often called the "Gas Gauge" or "Fuel Gauge" function.

 

Note that the SOC reference is normally the rated capacity of a cell, that is a new cell. It is not the fully charged capacity of the cell when it was last charged (i.e. the current charge-discharge cycle). This is because the cell capacity gradually reduces as the cell ages and it is also affected by temperature and discharge rate. For example, towards the end of the cell's life its actual capacity will be approaching only 80% of its rated capacity and in this case, even if the cell were fully charged, its SOC would only be 80%. This difference is important if the user is depending on the SOC estimation as he would in a real gas gauge application in a car.

These ageing and environmental factors must therefore be taken into account if an accurate estimate is required.

 

If the SOC reference was defined as the current fully charged capacity of the cell, then the adjustment factors would have to be applied to the rated capacity to determine the new reference capacity. In this case a fully charged cell would have an SOC of 100% but it would only have a capacity of 80% of a new cell. For cell balancing applications, it is only necessary to know the SOC of any cell relative to the other cells in the battery chain. Since all the cells will have been subject to the same influences during their lifetime, the ageing and environmental adjustments, which apply equally to all cells, can be ignored for this purpose.

 

Methods of Determining the State of Charge

 

Several methods of estimating the state of charge of a battery have been used. Some are specific to particular cell chemistries. Most depend on measuring some convenient parameter which varies with the state of charge.

 

Direct Measurement

This would be easy if the battery could be discharged at a constant rate. The charge in a battery is equal to the current multiplied by the time for which it flowed. Unfortunately there are two problems with this. In all practical batteries, the discharge current is not constant but diminishes as the battery becomes discharged, usually in a non-linear way. Any measurement device must therefore be able to integrate current over time. Secondly, this method depends on discharging the battery to know how much charge it contained. In most applications except perhaps in qualification testing, the user (or the system) needs to know how much charge is in the cell without discharging it.

 

It is not possible either to measure directly the effective charge in a battery by monitoring the actual charge put into it during charging. This is because of the coulombic efficiency of the battery. Losses in the battery during the charge - discharge cycle mean that the battery will deliver less charge during discharge than was put into it during charging.

The coulombic efficiency or charge acceptance is a measure of how much usable energy is available during discharging compared with the energy used to charge the cell. Charge efficiency is also affected by temperature and SOC.

 

SOC from Specific Gravity (SG) Measurements

This is the customary way of determining the charge condition of lead acid batteries. It depends on measuring changes in the weight of the active chemicals. As the battery discharges the active electrolyte, sulphuric acid, is consumed and the concentration of the sulphuric acid in water is reduced. This in turn reduces the specific gravity of the solution in direct proportion to the state of charge. The actual SG of the electrolyte can therefore be used as an indication of the state of charge of the battery. SG measurements have traditionally been made using a suction type hydrometer which is slow and inconvenient.

Nowadays electronic sensors which provide a digital measurement of the SG of the electrolyte can be incorporated directly into the cells to give a continuous reading of the battery condition. This technique of determining the SOC is not normally suitable for other cell chemistries.

 

Voltage Based SOC Estimation

This uses the voltage of the battery cell as the basis for calculating SOC or the remaining capacity. Results can vary widely depending on actual voltage level, temperature, discharge rate and the age of the cell and compensation for these factors must be provided to achieve a reasonable accuracy. The following graph shows the relationship between the Open Circuit Voltage and the Remaining Capacity at constant temperature and discharge rate for a high capacity Lead Acid cell. Note that the cell voltage diminishes in direct proportion to the remaining capacity.

 

Lead Acid Battery

 

Problems can occur with some cell chemistries however, particularly Lithium which exhibits only a very small change in voltage over most of the charge/discharge cycle. The following graph shows the discharge curve for a high capacity Lithium-ion cell. This is ideal for the battery application in that the cell voltage does not fall appreciably as the cell is discharged, but for the same reason, the actual cell voltage is not a good measure of the SOC of the cell.

 

The rapid fall in cell voltage at the end of the cycle could be used as an indication of imminent, complete discharge of the battery, but for many applications an earlier warning is required. Fully discharging Lithium cells will dramatically shorten the cycle life and most applications will impose a limit on the DOD to which the cell is submitted in order to prolong the cycle life. While the cell voltage can be used to determine the desired cut off point, a more accurate measure is preferred for critical applications.

 

Current Based SOC Estimation

This measures the current entering and leaving the cells as a basis for remaining capacity calculation. The charge transferred in or out of the cell is obtained by accumulating the current drain over time. This method, known as Coulomb counting, provides higher accuracy but it still needs compensation for the operating conditions as with the voltage based method. The simplest method of determining the current is by measuring the voltage drop across a low ohmic value, high precision, series, sense resistor. This method of measuring current causes a slight power loss in the current path and also heats up the battery. Hall effect and magneto-resistive transducers avoid this problem but they are more expensive. The former is inaccurate for low currents and the latter can not tolerate high currents and is susceptible to noise.

 

Other State of Charge Measures

With a constant load and constant ambient conditions, Lithium cells have a linear SOC discharge characteristic over time which could possibly allow the SOC to be determined from running time, or in the case of a pure electric vehicle, distance travelled. This method depends on maintaining a constant driving pattern and major inaccuracies will be introduced if the driving pattern changes. It can also not be applied when intermittent charging is involved as with HEVs.

While the measure may not be suitable as a basis for BMS in automotive use, it could be used for simple applications such as bicycle range indicators and it could also provide a verification check of the BMS model predictions for safety purposes.

 

During the cell charge - discharge cycles the composition of the active chemicals in the cell changes as the chemicals are converted between the charged and discharged states, and this will be reflected in changes to the cell impedance. Thus measurements of cell internal impedance can also be used to determine SOC however these are not widely used due to difficulties in measuring the impedance while the cell is active as well as difficulties in interpreting the data since the impedance is also temperature dependent. Fuzzy Logic models have been used to overcome these problems and ASICs have been developed for this purpose.

 

Other Factors Influencing the State of Charge

 

Unfortunately neither voltage measurement nor coulomb counting alone is sufficient for high accuracy fuel gauging because the remaining usable capacity depends on both the short term and long term operating conditions of the cell.

 

Charge - Discharge Rates

The effective capacity of a cell depends on the rate at which it is charged and discharged as illustrated in the graph on Discharge Rates. This is because the electrochemical actions in the cell take a finite time to complete and they can not follow instantaneously the electrical stimulus or load placed on the cell. This is explained in the section on Charging Times. If a cell is subject to short term charging and discharging pulses, as in EV and HEV applications, the chemical effect of a charging pulse may not be fully completed before the subsequent discharge pulse starts to reverse the process. Even with coulomb counting this can lead to errors in determining the SOC of the cell unless the rates of the chemical actions are taken into account.

 

Temperature and Discharge Rate

The following graph shows how the capacity of a lithium cell varies with temperature and discharge rate. It shows that at normal working temperatures the coulombic efficiency of the cell is very high, but at low temperatures there is a major drop in efficiency particularly at high discharge rates which can give rise to serious errors in the estimation of the SOC. This phenomenon is not peculiar to lithium cells as other cell chemistries also demonstrate a deterioration in performance at low temperatures.

 

 

The graph shows a lithium cell working between its specified upper and lower voltage cut -off limits of 4.2.Volts and 2.5 Volts respectively. These are considered the fully charged and the empty conditions of the cell. The "Full" line is the point at which the cell reaches full charge using the constant current - constant voltage charging method at the corresponding temperature. Two "Empty" lines are shown corresponding to two different discharge rates 0.2C and 1.0C.

The capacity of the cell at a given rate and temperature is the difference from the "Full" line and the corresponding "Empty" line.

In actual practice, the cell may be charged at one temperature and discharged at a different temperature and this must be taken into account when calculating the effective capacity of the cell. Note that the cell is very inefficient at giving up its charge at high discharge rates and low temperatures. In other words, its coulombic efficiency deteriorates dramatically at low temperatures. Note also that the cell above could be fully discharged at the high current rate yet could be further discharged at the low current rate by the number of milliamp-hours between the two "Empty" points that correspond to the present cell temperature.

 

Cell Ageing

The graph below shows how ageing affects the cell capacity. To account for this, the formulas for calculating remaining capacity must be capable of dynamically changing over time to remain accurate.

 

The cycle life of a cell is usually considered complete when the cell capacity has fallen to 80% of its value when the cell was new.

 

Self Dischrge

In addition to the charge being put into and taken out of the battery during the normal charge - discharge process, the continuing long term effect of self discharge consuming the available energy in the cell must also be taken into account. This becomes more significant the longer the periods between charging.

 

Other Factors

Other factors such as charge/discharge efficiency also affect the cell capacity.

 

Calculating the SOC

As noted above, voltage or current measurements can provide a rough indication of the SOC of a battery, but for more precision, other factors must be taken into account. This is normally accomplished building a model which replicates the battery characteristics in software and developing algorithms which apply adjustment factors to the measured values to derive a more accurate estimate of the SOC. The battery model thus characterises in a software algorithm, the behaviour of the battery in response to various external and internal conditions. This method of course needs sensors to provide the measurement data, memory to store the model and a microprocessor to calculate the results.

 

Batteries are non-linear. Voltage characteristics are a function of discharge rate, temperature and age. The individual cell model can be constructed from a set of "Look Up Tables" which provide stepwise approximations of the performance response curves which represent the cell discharge performance as a function of temperature, discharge rate or other parameters. The necessary Look Up Tables are developed from laboratory measurements under controlled conditions and will be different for each cell chemistry and cell construction.

 

For an accurate representation of the charge / discharge characteristics of the cell, similar Look Up Tables must be developed for all the known factors which significantly affect the cell capacity (Ah) and impedance, such as cell temperature, ambient temperature, charge and discharge rates, heat dissipation rates, the cell self discharge rate charge or coulombic efficiency and the capacity degradation over the lifetime of the cell.

 

A mathematical model or algorithm representing the cell behaviour in response to all relevant parameters is then constructed from the relevant set of Look Up Tables and incorporated into the memory of a microprocessor module which uses this algorithm to predict the battery performance.

 

Sensors in the battery provide analogue inputs representing temperatures, cell voltages and currents to the model and precision A/D converters translate these inputs into digital form. Further information such ambient temperatures and the status of various alarms if necessary can also be provided to the model. These inputs are constantly monitored and updated at the request of the microprocessor which controls the model.

 

The model can then use these inputs to estimate the status of the battery at any instant in time.

 

The SOC is determined essentially by integrating the current flow over time, modified to take account of the factors noted above which affect the performance of the cells, then subtracting the result from the known capacity of the fully charged battery.

 

In dynamic applications such as automotive batteries, inputs must be monitored at least once per second to ensure that no significant charge flows or critical events are missed and the SOC prediction for every individual cell in the battery must be completed during the sampling interval. Because of the complexity of the algorithm and the number of inputs involved the system must perform over a million or more floating point calculations per second. This requires a very powerful microprocessor. An example of the need for continual updating of SOC estimations in a working system is given in the section on Battery Management Systems.

 

The accuracy of the SOC determination will depend on the accuracy of the data used to construct the Look Up Tables, the tolerances on the components, the data quantifying errors and the precision of the clock. An overall error of over 5% is typical and this error may diverge even more as the cells grow older. HEV systems have the added complication that they are subject to cumulative errors since under normal operating conditions the battery never reaches its fully charged condition when the system can be reset to a known level of charge.

 

Several different techniques such as Fuzzy Logic, Kalman Filtering, Neural Networks and recursive, self-learning methods have been employed to improve the accuracy of the SOC estimation as well as the estimation of SOH.

 

Fuzzy Logic

Fuzzy Logic is simple way to draw definite conclusions from vague, ambiguous or imprecise information. It resembles human decision making with its ability to work from approximate data to find precise solutions.

Unlike classical logic which requires a deep understanding of a system, exact equations, and precise numeric values, Fuzzy logic allows complex systems to be modelled using a higher level of abstraction originating from our knowledge and experience. It allows expressing this knowledge with subjective concepts such as big, small, very hot, bright red, a long time, fast or slow. This qualitative, linguistic representation of the expert knowledge presents a natural rather than a numerical description of a system and allows relatively easy algorithm development compared to numerical systems. The outputs can then be mapped into exact numeric ranges to provide a characterisation of the system. Fuzzy logic is used extensively in automatic control systems.

Using this technique we can use all the information available to us about the performance of a battery to derive a more accurate estimation of its state of charge or the state of health. Software packages are available which simplify this process.

 

Kalman Filter

Kalman filtering addresses an age-old question: How do you get accurate information out of inaccurate data? More pressingly, How do you update a "best" estimate for the state of a system as new, but still inaccurate, data pour in? An HEV automotive application is an example of this situation. The battery SOC is affected by many simultaneous factors and is continually changing due to the user driving pattern. The Kalman filter is designed to strip unwanted noise out of a stream of data. It operates by predicting the new state and its uncertainty, then correcting this with a new measurement. It is suitable for systems subject to multiple inputs and is used extensively in predictive control loops in navigation and targeting systems. With the Kalman Filter the accuracy of the battery SOC prediction model can be improved and accuracies of better than 1% are claimed for such systems.

As with Fuzzy Logic, standard software packages are available to facilitate its implementation.

 

Neural Networks

A Neural Network is a computer architecture modelled upon the human brain's interconnected system of neurons which mimics its information processing, memory and learning processes. It imitates the brain's ability to sort out patterns and learn from trial and error, discerning and extracting the relationships that underlie the data with which it is presented.

 

Each neuron in the network has one or more inputs and produces an output; each input has a weighting factor, which modifies the value entering the neuron. The neuron mathematically manipulates the inputs, and outputs the result. The neural network is simply neurons joined together, with the output from one neuron becoming input to others until the final output is reached. The network learns when examples (with known results) are presented to it; the weighting factors are adjusted on the basis of data - either through human intervention or by a programmed algorithm-to bring the final output closer to the known result. In other words, neural networks "learn" from examples (as children learn to recognise dogs from examples of dogs) and exhibit some capability for generalisation beyond the training data.

 

Neural networks thus resemble the human brain in the following two ways:

1. A neural network acquires knowledge through learning.
2. A neural network's knowledge is stored within inter-neuron connection strengths known as synaptic weights.

The true power and advantage of neural networks lies in their ability to represent both linear and non-linear relationships and in their ability to learn these relationships directly from the data being modelled. Among the many applications are predictive modelling and control systems.

 

Neural Network techniques are useful in estimating battery performance which depends on quantifying the effect of numerous parameters most of which can not be defined with mathematical precision. Algorithms are refined with the aid of experience gained from the performance of similar batteries.

 

Consumer Battery Condition Indicators

Small primary cells are now available with a on-cell analogue SOC indicators known as battery testers or fuel gauges. On the side of the cell they incorporate a printed strip resembling a thermometer which provides a rough indication of the remaining capacity in the battery.

Based on thermochromic and conductive inks, a thin layer of conductive ink is applied in a wedge shape. The narrowest point indicates the lowest charge level and the widest area indicates a full charge. When the circuit is completed and current flows through the conductive ink and the resistance of the ink causes it to heat up. A small amount of current can generate enough heat to affect the smallest area of the wedge but as the area widens more current is needed to raise its temperature. The thermochromic ink printed on top of the conductive ink changes colour depending on the temperature and the extent of the colour change along the wedge indicates the magnitude of the current and hence the battery voltage.

The design is completed with a masking layer of normal ink which provides the illusion of a thermometer or analogue fuel gauge.

The measurement accuracy is dependent on the ambient temperature.

 

SOC of Capacitors

The state of charge of a capacitor is represented by the voltage across its terminals.