Method of determining the state of charge of a battery used in an electric vehicle

A method of determining the state of charge (SOC) of a battery. The method may employ a transformation technique that linearizes a nonlinear model by converging close to a measured value and thereby estimating the state of charge accurately without affecting the computation time and load on the system. The transformation technique employs an adaptive unscented Kalman filter (UKF).

BACKGROUND

The present disclosure relates to a method for determining the state of charge of a battery.

Batteries are used as the source of energy for many electrical systems, especially in hybrid electric vehicles (HEVs) and electric vehicles (EVs). In these vehicles, the battery interacts with other components by means of a Battery Management System (BMS) to provide power to the vehicle and meet the vehicle's energy demand while maintaining the safety of the electrical system. The battery is typically a high voltage (HV) battery. Plug-in Hybrid Electric Vehicles (PHEV, HEV) and full electric vehicles depend on the battery as a secondary and primary source of energy, respectively, to propel the vehicle. Therefore, it is imperative to track the available energy from the battery to prevent the battery from overcharging or under discharging. To ensure a safe and maximum utilization of the available energy from the battery, such vehicles employ a BMS that controls the functioning of the battery and determines its performance.

The reliability of these electrical systems is highly dependent of the health and safety of the battery, and therefore on the ability of the BMS to provide operation data that allows for peak performance without jeopardizing the health and safety of the battery. Controlling and monitoring a battery installed in an HEV or EV is much more challenging without a fast and accurate model of the battery to be used by the BMS. Models are used for estimating metrics of the battery, including state-of-charge (SOC), state-of-health (SOH), state-of-energy (SOE) and state-of-power (SOP). Also, the models are employed to help BMSs with the functions of battery control, real-time observation, parameter estimation, and optimization of the battery.

The State of Charge (SOC) gives a measure of the remaining usable capacity of the battery in real time as the battery is charged through external charging or regen mechanism and discharged during driving. The SOC determines the capability of the battery to provide the required energy and accurate estimation of the SOC prevents the degradation of the battery as a result of excess charge and discharge. Typically, the SOC is the ratio of the current battery capacity to the maximum batter capacity.

It is important that the BMS accurately determine the battery state of charge in real time. By doing so, the BMS can ensure maximum performance output from the battery while minimizing effects that shorten of life of the battery.

The BMS should be able to estimate the state of charge of the battery in any given condition. If the SOC determined by the BMS is inaccurate, for example, if the SOC is underestimated, this may result in overcharge of the battery. The overcharging of the battery could create dangerous events such as thermal runaway of the battery. On the other hand, if the SOC is overestimated, the overall capability of the battery will be limited thereby affecting the performance and allowing for less energy to be drawn from the battery.

The typical method of determining the SOC is based on the integral of the current over a period, times the inverse of the remaining capacity of the battery. Other methods of determining the SOC use the estimation technique such as Kalman filters, extended Kalman filter (EKF) suffer from limitations due to estimating the non-linear behavior of the battery (KF) and/or inaccuracies due to the linearization methodology employed (EKF). Furthermore, advanced methods such as learning algorithms (e.g., machine learning, neural networks) have high computational complexity that cannot be applied in real time for estimation of the SOC.

It would be desirable to find a method of determining the SOC that including using a non-linear data modeling and providing updates in real time.

DETAILED DESCRIPTION

As used herein, vector notations are defined as follows:

Reference throughout this document to “one embodiment,” “certain embodiments,” “an embodiment,” or similar term means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of such phrases in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner on one or more embodiments without limitation.

FIG. 1shows an exemplary electric vehicle1with a drivetrain100. The exemplary vehicle includes an internal combustion engine10, a generator11, and one or more electric motors for driving rotation of the wheels of the vehicle. The internal combustion engine10drives the generator11to produce electrical power for a battery12and the motors14/14′. A generator inverter16for the generator11may also be provided. A gearbox13is provided to provide the required drive ratio for the vehicle. Power to the motor is communicated via inverters15/15′, which transforms DC power provided to the AC power required by the motors14/14′. The inverters15/15′ may include multiple phases corresponding to each phase of the motors14/14′. The system and method described below may be used in conjunction with a battery such as the battery12shown inFIG. 1.

In one embodiment, the estimation method of determining the SOC uses the battery parameters based on a 2nd-order RC equivalent circuit model of the battery (e.g., as shown inFIG. 2) and estimates the voltage based on the circuit model.FIG. 2is a circuit diagram depicting an exemplary embodiment of a RC model200for use in the SOC estimation method300. In one embodiment, all RC parameters (including but not limited to R0, C1, R1, C2, R2, and Open Circuit Voltage (OCV)) may be generated by fitting the parameter with data obtained from tests performed on the battery cell215. In one embodiment, R0is determined as a function of the state of charge (SOC) of the battery cell215, the battery cell215temperature Tcell, and the state of health (SOH) of the battery cell215. In one embodiment, OCV is determined as a function of the state of charge (SOC) of the battery cell215, the battery cell215temperature Tcell, and the state of health (SOH) of the battery cell200. In one embodiment, C1, R1, C2, and R2are determined as a function of the state of charge (SOC) of the battery cell215, the equivalent circuit current I, the battery cell215temperature Tcell, and the state of health (SOH) of the battery cell200.

FIG. 3is a block diagram of a plurality of modules that may be employed in the BMS300for carrying out the method of determining or estimating the SOC for a vehicle battery. The system includes a controller that includes a SOC estimation module330. The system also includes look up tables for various battery parameters that may be created and stored in a Lookup Table module310. The system may further include a module320for estimating or determining the remaining capacity of the battery based on the SOH of the battery. Further, the system includes a module340for performing a Noise Covariance Update of the SOC estimation. Where the term covariance refers to the joint variability of two or more random variables.

The aforementioned modules may be integrated into a single controller or microprocessor. Alternatively, one or more of the modules may be packaged separately in one or more microprocessor or controller.

The system is configured to make a probabilistic determination or estimation of the state of charge (SOC) based on the innovation sequence (the difference between the observed value of a variable and the optimal forecast of that value based on prior information) given by the voltage estimation error and corrects the SOC calculated by the model equation. The method of determining the SOC involves two “update” steps for estimating the battery voltage and determining the SOC. The first update step is a measurement update, where the model predicts the state of charge and battery voltage based on the variance of the estimated value from the true value. The second update step is a time update of the prediction based on the innovation error computed from the voltage estimation error to correct the predicted state of charge.

The method of determining the SOC may employ a transformation technique that linearizes the nonlinear model used in this method by converging close to the measured value and thereby estimating the state of charge accurately without affecting the computation time and load on the system. The transformation technique employs an adaptive unscented Kalman filter (UKF) based on a technique called the unscented transform for linearizing the nonlinear model equation, wherein an initial point determines the probability of the convergence of the estimation.

Additionally, the method for determining the SOC may employ a methodology known as a normalized innovation sequence (NIS) to update the noise covariance matrix that measures the deviation of the estimate due to additive noise that may not be Gaussian in nature (whereas UKF assumes that the noise present in the system is Gaussian). The use of the NIS enables the model of the battery capacity to adapt to the changing noise covariance and update the state vector.

The estimation method of determining the SOC additionally updates the noise covariance of the estimated states by adapting to the estimation error (known as “innovation sequence”) based on the moving average error method. The update ensures that the method is robust and estimates the state (i.e., the SOC) accurately.

FIG. 4shows a flow chart of a method of estimation the SOC performed by the BMS300system show in simplified form inFIG. 3. As a first step of the method the system establishes an initial value of the SOC and of a covariance error Q in step410.

In step420, the method generates updated sigma points for the SOC (x0) and the covariance (P0). The updates are generated using the following equations.
{circumflex over (x)}0=E[x0]
P0=E[(x0−{circumflex over (x)}0)(x0−{circumflex over (x)}0)T]∀k∈{1, . . . ,∞}

In step430the system performs a time update of the sigma points using the following equation.
χk-1=[{circumflex over (x)}k-1({circumflex over (x)}k-1+γ√{square root over (Pk-1)})({circumflex over (x)}k-1−γ√{square root over (Pk-1)})]
where E[x0] is the expected value of x0; γ=√{square root over (n+λ)}; λ=α2(L+κ)−L; α, κ are the scaling parameters; L=2n+1 sigma points; and n is number of state variables (in the primary embodiment, n=3).
{dot over (χ)}k=f(χk-1,uk)  (1)
yk=Vocv,k(SOCk,Tk)+Vrc1,k+Vrc2,k+IkR0,k(2)
where equation (1) is the state space equation which consists of equations for each state variable and using χk-1as sigma points at the previous time step, ykis the predicted voltage, ukis the control vector representing data measurements taken at time k, Vocv,kis determined from a lookup table, R0,kis a function of SOC, temperature and current and where f determines the updated values for {dot over (χ)}kas follows:

It should be noted that, as shown in block415, that the system is configured to generate the sigma points based on the UKF parameters (e.g., alpha, beta, gamma, Weights (W_c, W_m)).

In step432, the system is configured to perform a measurement update and update the states based on the measurement error and Kalman gain using the following equation:
{tilde over (x)}k={circumflex over (x)}k+K(Vmeasured−yk)
where {tilde over (x)}kis the corrected state, K is the Kalman gain (a weight function ranging between 0 and 1 indicating how much weight to assign to a predicted value versus a measured value) and Vmeasuredis the cell voltage measured by a sensor.

In step440, the update of the covariance matrix is made based on the innovation sequence of the system which is otherwise known as the error e in the voltage prediction. As shown inFIG. 3, the module340performs a consistency check of a NIS sequence as described below. The consistency check utilizes the following equations:
e=Vmeasured−yk
Qprocess=KE[eeT]KT
where Qprocessis the covariance of the process noise.

The measurement error is squared and normalized to give a sequence which is used to check for the consistency of the determination of the SOC made by the controller. In step440, this sequence is known as normalized innovation squared (NIS) and is given by,
NISk=ekSk−1ekT
where k is the time step, e is the error and S is the measurement error variance. An exemplary time step would 1 second. The NIS plot follows chi-squared distribution with zero mean and variance a. In one embodiment, the consistency check is performed by checking whether the NIS sequence lies within a confidence bound which is computed as,

(n-1)⁢σ2χn,1-α2<NIS<(n-1)⁢σ2χn,α2,
where σ2is the standard deviation of the NIS sequence, n−1=d.o.f. (degrees of freedom) of the chi-squared distribution, and χ1-α2is the chosen chi value (unrelated to the χ sigma points) for the confidence % α.

In step450, the system is configured to check if NIS is within accepted confidence bounds (step450) and, if NIS is not within the confidence bounds, then the module340is configured to update Q for the next time step as shown in step455ofFIG. 4.

If the cycle is complete (see step460) then the system is configured to end the process.

While this disclosure has been particularly shown and described with references to exemplary embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the claimed embodiments.

The following list is a non-limiting summary of the variables mentioned above, wherein state refers to the SOC:

x0: initial state

P0: initial covariance matrix

k−1: current step

k: next step in time

Pk-1: current covariance matrix

λ: sigma point scaling parameter

α: sigma point scaling parameter, spread of sigma points around {circumflex over (x)}

κ: sigma point scaling parameter

L: number of sigma points

n: number of states

{tilde over (x)}k: mean of state

χk: sigma points

Vmeasured: cell voltage measured by sensor

e: error in voltage prediction

Qprocess: process noise covariance matrix

Sk: measurement error variance

Vocv,k: open circuit voltage of RC model

Ik: current of RC model

R0,k: resistance of RC model (elements outside the RC parallel circuit sections)

R1,k: resistance of RC model (1stRC parallel circuit section)

R2,k: resistance of RC model (2ndRC parallel circuit section)

C1,k: capacitance of RC model (1stRC parallel circuit section)

C2,k: capacitance of RC model (2ndRC parallel circuit section)

Vrc1,k: voltage of RC model (1stRC parallel circuit section)

Vrc2,k: voltage of RC model (2ndRC parallel circuit section)

σ2: variance of the sequence

χ1-α2: chi value for the confidence % α