A METHOD FOR PREDICTING STATE-OF-POWER OF A MULTI-BATTERY ELECTRIC ENERGY STORAGE SYSTEM

Abstract

A method for predicting a state-of-power, SoP, of an electric energy storage system, ESS, comprising at least two battery units electrically connected in parallel. The method includes obtaining operational data from the at least two battery units of the ESS during operation of the ESS; computing the state-of-power of the ESS based on the obtained operational data and by using an algorithm based on a system-level model of the ESS, wherein the system-level model of the ESS takes into account on one hand each one of the at least two battery units of the ESS, and on the other hand at least one electrical connection between the at least two battery units, and wherein the system-level model of the ESS further takes into account a dynamic parallel load distribution between the at least two battery units.

Claims

1. A method for predicting a state-of-power, SoP, of an electric energy storage system, ESS, comprising at least two battery units electrically connected in parallel, the method comprising: obtaining operational data from the at least two battery units of the ESS during operation of the ESS; computing the state-of-power of the ESS based on the obtained operational data and by using an algorithm based on a system-level model of the ESS, wherein the system-level model of the ESS takes into account on one hand each one of the at least two battery units of the ESS, and on the other hand at least one electrical connection between the at least two battery units, and wherein the system-level model of the ESS further takes into account a dynamic parallel load distribution between the at least two battery units, wherein operating limits of at least one constrained variable of each one of the at least two battery units are used as input to the system-level model, wherein the at least one constrained variable includes at least one of battery unit current, battery unit terminal voltage, battery unit temperature, battery unit state-of-charge, and battery unit open circuit voltage, wherein the step of computing the state-of-power of the ESS comprises solving a constrained optimization problem, in which a possible load current magnitude and/or a possible load power magnitude for the ESS is/are maximised subject to the operating limits of the at least one constrained variable, wherein the state-of-power is predicted for a predefinable prediction time horizon ([t0, t0+Δt]), and wherein the estimation comprises predicting an evolution of the at least one constrained variable during the prediction time horizon ([t0, t0+Δt]), wherein a maximum possible load current magnitude and/or a maximum possible load power magnitude for the ESS is/are set to be constant over the prediction time horizon ([t0, t0+Δt]), and wherein for each individual battery unit, a battery unit load power or load current is allowed to vary over time during the prediction time horizon ([t0, t0+Δt]).

2. The method according to claim 1, wherein the system-level model of the ESS takes into account a plurality of variables of each one of the at least two battery units.

3. The method according to claim 1, wherein the system-level model of the ESS is a dynamic mathematical model based on an equivalent circuit model in which the at least one electrical connection between the at least two battery units is modelled as at least one resistance.

4-8. (canceled)

9. The method according to claim 1, wherein the prediction of the state-of-power comprises: predicting the maximum possible load current magnitude and/or the maximum possible load power magnitude for the ESS over the prediction time horizon ([t.sub.0, t.sub.0+Δt]), which maximum possible load current magnitude and/or maximum possible load power magnitude is the load current and/or load power of maximum magnitude that may be used without violating the operating limits of the at least one constrained variable, and setting the state-of-power of the ESS to the predicted maximum possible load current magnitude and/or the maximum possible load power magnitude.

10. The method according to claim 9, wherein predicting the maximum possible load current magnitude and/or the maximum possible load power magnitude comprises: predicting end values of the possible load current magnitude and/or the possible load power magnitude of the ESS at a beginning and an end of the prediction time horizon, based on the predicted end values, setting a preliminary estimate of the maximum possible load current magnitude and/or the maximum possible load power magnitude, determining whether the preliminary estimate is feasible, wherein, if the preliminary estimate is determined to be feasible, the preliminary estimate is set as the predicted maximum possible load current magnitude and/or the predicted maximum possible load power magnitude.

11. The method according to claim 10, wherein, if the preliminary estimate is not determined to be feasible, the method further comprises: solving an optimization problem to determine the maximum possible load current magnitude and/or the maximum possible power magnitude of the ESS during the prediction time horizon.

12. The method according to claim 1, wherein an updating frequency of the estimation of the state-of-power of the ESS is at least 1 Hz, or 5 Hz, or Hz, and wherein the prediction time horizon is set to at least 1 s, or 2 s, or 5 s, or 10 s, or 30 s.

13. A method for controlling loading of an ESS comprising at least two battery units electrically connected in parallel, the method comprising: predicting a state-of-power of the ESS according to claim 1, based on the predicted state-of-power of the ESS, determining a planned load current and/or load power to be used for loading of the ESS; controlling loading of the ESS based on the determined planned load current and/or load power.

14. A control unit of an electric energy storage system comprising at least two battery units electrically connected in parallel, wherein the control unit is configured to execute the steps of the method according to claim 1.

15. A computer program comprising instructions to cause a control unit to execute the steps of the method of claim 1.

16. A computer readable medium having stored thereon the computer program according to claim 15.

17. An electric energy storage system comprising at least two battery units electrically connected in parallel and a control unit according to claim 14.

18. The electric energy storage system according to claim 17, wherein the at least two battery units comprise at least two battery modules electrically connected in parallel, each battery module comprising a plurality of battery cells.

19. A vehicle comprising an electric energy storage system according to claim 17.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0078] With reference to the appended drawings, below follows a more detailed description of embodiments of the invention cited as examples.

[0079] In the drawings:

[0080] FIG. 1 shows a vehicle in which a method according to the invention may be implemented,

[0081] FIG. 2 is an example embodiment of an electric energy storage system according to the invention;

[0082] FIG. 3 is a flow-chart illustrating a method according to an embodiment of the invention,

[0083] FIG. 4 is an example of a system-level equivalent circuit model of an ESS that may be used in a method according to the invention,

[0084] FIG. 5 is another flow-chart illustrating steps of a method according to an embodiment of the invention.

[0085] The drawings are schematic and not necessarily drawn to scale.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS OF THE INVENTION

[0086] In the present detailed description, embodiments of the method according to the present invention are mainly described with reference to an all-electric bus, comprising a propulsion system in the form of battery powered electric motors. However, it should be noted that various embodiments of the described invention are equally applicable for a wide range of hybrid and electric vehicles.

[0087] FIG. 1 shows a simplified perspective view of an all-electric vehicle in the form of a bus 100, which according to an embodiment is equipped with an electric propulsion unit 4 for propulsion of the bus. Of course, other loads may be provided in addition to or instead of the electric propulsion unit 4, for example auxiliary systems requiring electric power, and/or an on-board charger, and/or a power take-off.

[0088] The bus 100 carries an electric energy storage system (ESS) 1 comprising a plurality of parallel-connected battery units in the form of battery modules 2, each battery module 2 comprising a plurality of battery cells (not shown). The battery cells are connected in series to provide an output DC voltage having a desired voltage level. Suitably, the battery cells are of lithium-ion type, but other types may also be used. The number of battery cells per battery module 2 may be in the range of 50 to 500 cells, or even more, such as up to 10,000 cells. It is to be noted that the ESS may also include a plurality of battery packs, each comprising one or more battery modules 2. The battery packs may be connected in parallel.

[0089] Sensor units (not shown) may be arranged for collecting measurement data relating to operating conditions of the ESS, i.e. measuring temperature, voltage and current level of the battery cells. Measurement data from each sensor unit is transmitted to an associated ESS control unit 3, which is configured for managing the ESS 1 during operation of the bus 100. The ESS control unit 3 can also be configured for determining parameters indicating and controlling the condition or capacity of the ESS 1, such as the state-of-charge (SoC), the state-of-health (SoH), the state-of-power (SoP), the state-of-capacity (SoQ), the state-of-resistance (SoR) and the state-of-energy (SoE) of the battery pack 1. A single control unit 3 is shown, which may be e.g. a so-called Domain Control Unit, DCU, configured to implement complete control functionality on all levels of the ESS. However, it is to be understood that the ESS may instead be provided with multiple control units. For example, the ESS may be provided with battery management units, BMUs (not shown), for managing individual battery units, such as battery packs and/or battery modules, of the ESS 1. The BMU of each battery unit then receives and processes measurement data corresponding to its associated battery unit and also estimates state-of-capacity SoQ(i), SoR(i), SoH(i), and SoC(i). Each BMU then sends this data to the ESS control unit. It is possible to have either a dedicated ESS Master Control Unit or to select one of the BMUs and let it function as an ESS master control unit in addition to its battery unit level functionality.

[0090] The ESS control unit 3 may include a microprocessor, a microcontroller, a programmable digital signal processor or another programmable device. Thus, the ESS control unit 3 comprises electronic circuits and connections (not shown) as well as processing circuitry (not shown) such that the ESS control unit 3 can communicate with different parts of the bus 100 or with different control units of the bus 100. The ESS control unit 3 may comprise modules in either hardware or software, or partially in hardware or software, and communicate using known transmission buses such a CAN-bus and/or wireless communication capabilities. The processing circuitry may be a general purpose processor or a specific processor. The ESS control unit 3 comprises a non-transitory memory for storing computer program code and data. Thus, the skilled person realizes that the ESS control unit 3 may be embodied by many different constructions. This is also applicable to other control units of the ESS 1.

[0091] FIG. 2 shows an ESS 1 including three battery units 2, 2′, 2″ in the form of battery packs. The battery units 2, 2′, 2″ are electrically connected in parallel with a load 4 in the form of an electric propulsion unit, e.g. an electric motor/generator, a charger, or an auxiliary load. A control unit 3 as described above is connected to control, directly or indirectly, the load 4, as well as to control each battery unit 2, 2′, 2″. Load current or load power that the load 4 uses for loading of the ESS 1 may thereby be controlled. A measurement unit 5 is provided for collecting measurement data relating to operating conditions of each one of the battery units 2, 2′, 2″. For simplicity, the measurement unit 5 is shown as a single unit but it may of course be provided as a plurality of separate measurement units, e.g. one per battery unit 2, 2′, 2″, and it may comprise, or be configured to communicate with, a plurality of sensors.

[0092] A method for predicting a state-of-power, SoP, of an ESS 1 such as the one illustrated in FIG. 2 according to an embodiment of the invention is schematically illustrated in FIG. 3. The steps are carried out repeatedly, such as at a certain time interval, but may not necessarily be carried out in the order shown in FIG. 2. The method steps may in this embodiment be carried out in the ESS control unit 3.

[0093] In a first step S1-1, operational data are obtained from the battery units 2, 2′, 2″ of the ESS 1 are obtained during operation of the ESS 1. This operational data may comprise terminal current, terminal voltage, state-of-charge, temperature, state-of-capacity, and state-of-resistance, of each battery unit 2, 2′, 2″, at the present time instant. The operational data may be measurement data, and/or operational data derived from measurement data.

[0094] In a second step S1-2, the state-of-power, SoP, of the ESS 1 is computed based on the obtained operational data and by using an algorithm based on a system-level model of the ESS 1, wherein the system-level model is a dynamic mathematical model of the ESS 1 which is herein based on an equivalent electrical circuit model 10 as shown in FIG. 4. The system-level model of the ESS 1 takes into account on one hand each one of the battery units 2, 2′, 2″ of the ESS 1, and on the other hand at least one electrical connection between the at least two battery units. It further takes into account a dynamic parallel current distribution between the battery units 2, 2′, 2″, i.e., it is capable of making dynamic predictions of current distribution between the battery units 2, 2′, 2″. For instance, the model is adapted to predict different load distribution among the battery units 2, 2′, 2″ at several future time instants. The SoP of the ESS 1 is determined without intermediate estimation of the SoP of the individual battery units 2, 2′, 2″. The system-level model enables prediction of how load power distribution, during transient as well as at steady-state conditions, will take place in this ESS 1 when loaded by the load 4 as shown in FIG. 2.

[0095] In some embodiments, the invention relates to a method for controlling loading of the ESS 1 based on the predicted SoP. In this case, the method may further comprise the steps of:

[0096] S2: Based on the predicted SoP of the ESS 1, determining a planned load current or load power to be used for loading, either for charging or discharging, of the ESS 1; and

[0097] S3: Controlling loading, i.e. charging or discharging, of the ESS 1 based on the determined planned load current or load power.

[0098] An exemplary embodiment of a system-level model that may be used to determine the SoP of an ESS 1 comprising a single battery pack including a plurality of battery modules connected in parallel will now be described in greater detail with reference to FIG. 4, which shows an equivalent circuit model (ECM) diagram 10 of such a battery pack comprising M parallel strings, battery strings, with N battery cells in series per string. The parallel-connected battery strings thus constitute parallel-connected battery units. To analyse, evaluate, and control the battery pack operation, the system needs to be appropriately modelled, including both individual battery cells and their connection topology. The battery ECM is deployed here to model each battery cell, and all wires connecting battery cells are characterized by resistors. In the following, the term “battery pack” may be understood as an ESS, and terms such as “pack current” and “pack voltage” may thus be understood as ESS current and ESS voltage, respectively.

[0099] As illustrated in FIG. 4, each battery cell ECM is composed of one voltage source representing its open circuit voltage (OCV), V.sub.OC.sup.(m,n), m∈{1, 2, . . . , M}, n∈{1, 2, . . . , N}, one resistor characterizing its internal ohmic resistance, R.sub.0.sup.(m,n), and at least one parallel-connected RC pair to capture the dynamics of internal voltage loss, polarization. In each RC pair, the resistance and capacitance are denoted by R.sub.j.sup.(m,n) and C.sub.j.sup.(m,n), respectively, and the corresponding RC pair's voltage is denoted by V.sub.j(m,n), j=1, 2, . . . , J, where J denotes the order of the battery cell ECM. Here, only first-order ECM is shown for clear illustration, i.e., J=1. Based on FIG. 4, each cell's terminal voltage is:

V.sub.T.sup.(m,n)=V.sub.OC.sup.(m,n)+I.sub.S.sup.mR.sub.0.sup.(m,n)+Σ.sub.j=1.sup.JV.sub.j.sup.(m,n),

m∈{1,2, . . . ,M},n∈{1,2, . . . ,N},

where I.sub.S.sup.m denotes the current of all cells on the m:th string, i.e. the so-called string current.

[0100] To model the wiring among battery cells and a charger/load 4, connection resistors are added in FIG. 4. Specifically, all cell connection resistances on each string are aggregated into a connection resistance denoted by R.sub.Sc.sup.(m), m∈{1, 2, . . . , M}. Besides, between adjacent parallel strings, the connection resistance on the positive and negative terminals are denoted by R.sub.pc.sup.m and R.sub.nc.sup.m, respectively. In addition, the charger/load 4 is connected to the battery pack through a wire with its total resistance denoted by R.sub.Pc.

[0101] Based on the ECM, a state-space representation of serial cells on all strings may be generalized. First, for each battery cell, the OCV and the RC pair voltage are chosen as state variables and the system state vector x is defined by

x=[V.sub.OC.sup.(1,1), V.sub.1.sup.(1,1), . . . , V.sub.J.sup.(1,1), V.sub.OC.sup.(1,2), V.sub.J.sup.(1,2), . . . , V.sub.OC.sup.(M,N), V.sub.1.sup.(M,N), . . . , V.sub.J.sup.(M,N)].sup.T, x∈ custom-character .sup.(J+1)MN.

[0102] The state-space representation of all battery cells can be generalized as

{dot over (x)}=A.sub.Sx+B.sub.SI.sub.S,

[0103] wherein A.sub.S and B.sub.S are matrices whose elements are defined in terms of aforementioned known ECM parameters and I.sub.S is the string current vector.

[0104] Due to the dynamic current distribution among parallel battery strings, all string currents are interdependent on each other and are difficult to assign. Usually, it is the pack current I.sub.P of the entire battery pack, including multiple parallel-connected battery units, that is possible to control, which requires analysis of the relation between the string currents and the pack current, e.g. by applying Kirchhoff's voltage law to each loop composed of two adjacent battery strings and their connection resistors. It may thereby be possible to represent the string currents Is by the pack current I.sub.P as

I.sub.S=C.sub.Sx+D.sub.SI.sub.P,

[0105] wherein C.sub.S and D.sub.S are matrices whose elements are defined in terms of aforementioned known ECM parameters. It can be seen that a constant pack current I.sub.P leads to time-varying string and cell currents I.sub.S since the system state vector x is involved.

[0106] The state-space representation of the battery pack including parallel-connected battery units, and thereby of the ESS, using the pack current I.sub.P as input instead of string current Is, may be formulated as

{dot over (x)}=Ax+BI.sub.P,

[0107] wherein A is a matrix dependent on the matrix A.sub.S and wherein B is a matrix dependent on the matrix B.sub.S. The values of both matrices A and B are state-dependent due to the battery cell OCV-SoC curve, so that the state-space representation of the battery pack is a non-linear system or a time-varying linear system.

[0108] In addition, as important variables constrained in predicting the battery pack SoP, the vector of cell terminal voltages, denoted by V.sub.T=[V.sub.T.sup.(1,1), V.sub.T.sup.(1,2), . . . , V.sub.T.sup.(M,N)].sup.T, V.sup.T∈ custom-character .sup.MN, can be derived from the above and viewed as another possible output of the state-space representation of the battery pack:

V.sub.T=C.sub.Tx+D.sub.TI.sub.P,

[0109] wherein C.sub.T and D.sub.T are so-called output and feedthrough matrices, respectively, when using cell terminal voltages as outputs.

[0110] To maintain the safe operation of a multi-battery ESS, herein represented by the battery pack, each battery cell/battery unit within the battery pack needs to operate within certain constraints commonly imposed on constrained variables of each battery cell/unit, the constrained variables including battery unit current, battery unit terminal voltage, battery unit temperature, battery unit state-of-charge, and/or battery unit open circuit voltage. In other words, operating limits are imposed on those constrained variables of the battery units.

[0111] In the following, ESS/battery pack SoPs considering various constraints will be studied based on the state-space representation of ESS/battery pack operation formulated above. For multi-battery ESSs comprising cell/module connection structures other than the one shown in FIG. 4, the proposed pack SoP estimation procedure is also applicable since the formulation of state-space representation and the following analysis are both presented in generic forms.

[0112] Computing the SoP of the ESS typically comprises solving a constrained optimization problem, in which a possible load current magnitude and/or a possible load power magnitude for the ESS is/are maximised subject to the operating limits of the at least one constrained variable. In other words, the problem is solved by maximizing the possible load current magnitude and/or the possible load power magnitude for the ESS without violating the operating limits of the at least one constrained variable. This type of optimization problem may mathematically be expressed as:

max |I.sub.P(t)|∀t∈[t.sub.0,t.sub.0+Δt],∀i∈{1, . . . ,M}, and ∀j∈{1, . . . ,N}

subject to

{dot over (x)}(t)=Ax(t)+BI.sub.P(t),

y(t)=Cx(t)+DI.sub.P(t),

|I.sub.S.sup.i(t.sub.0:t.sub.0+Δt)|≤I.sub.S,max.sup.i,

SoC.sub.min.sup.(i,j)≤SoC.sup.(i,j)(t:t+t.sub.h)≤SoC.sub.max.sup.(i,j),

V.sub.T,min.sup.(i,j)≤V.sub.T.sup.(i,j)(t.sub.0:t.sub.0+Δt)≤V.sub.T,max.sup.(i,j), and

T.sub.min.sup.(i,j)≤T.sup.(i,j)(t.sub.0:t.sub.0+Δt)≤T.sub.max.sup.(i,j),

[0113] i.e. wherein constraints apply to each string current I.sub.S.sup.i, state-of-charge SoC.sup.(i,j), terminal voltage V.sub.T.sup.(i,j), and temperature T.sup.(i,j) of each cell at position (i,j) in the battery pack, respectively. A, B, C, D are matrices as explained above.

[0114] Denote the present time instant by to, and consider a prediction horizon [t.sub.0; t.sub.0+Δt] for the SoP prediction. Then, during this prediction horizon, as long as the battery pack current is bounded by the pack SoP, none of the operating constraints considered would be violated. Note that, the multi-battery ESS/battery pack SoP needs to be updated frequently to adapt to the time varying system states and parameter values, e.g., an updating frequency of 10 Hz is typically applied to the battery pack SoP estimation in EVs. Denote the update period of pack SoP estimation by Δt.sub.u, Δt.sub.u≤Δt. Then, each battery pack SoP estimated at to for the following prediction time horizon Δt is valid until t.sub.0+Δt.sub.u.

[0115] During a sufficiently short prediction time horizon Δt, the battery cell's OCV-SoC slope can be approximately viewed as constant. Alternatively, it is possible to use a so-called piecewise affine approximation of the battery cell's OCV-SoC slope to handle longer prediction time horizons.

[0116] Moreover, while the model parameters in FIG. 4 are influenced by factors such as the cell current, SoC, temperature, and hysteresis, these factors do not change substantially given a constant pack current during a short prediction time horizon. The multi-battery ESS/battery pack SoP is defined by a constant pack current, and, thus, within a short prediction time horizon these model parameter values are assumed constant. As a result, during a single short prediction time horizon, the system matrices A, B can be approximately regarded as constant, and the battery pack state-space representation becomes a linear time invariant (LTI) system. In the case when the system behaviour over multiple prediction time horizons is considered, the battery pack's state-space representation will instead be a time-varying linear system.

[0117] To allow for various operating constraints, the LTI system output is expressed in a generic form:

y(t)=Cx(t)+DI.sub.P.

[0118] For instance, if it is desired to output the string current I.sub.S, C may be set to Cs and D may be set to Ds based on the above in order to find the time-domain solutions x(t) and y(t) during the prediction time horizon.

[0119] If a battery pack current I.sub.P.sup.SoP corresponding to the battery pack SoP is fed to the linear state-space system model, i.e. to the LTI system, at least a q*-th output entry out of a total of Q entries, such as one of the string current output entries and/or one of the terminal voltage output entries, will reach an output limit y.sup.lim at some time instant t* during the prediction time horizon [t.sub.0; t.sub.0+Δt], such that y.sub.q*(t*)=y.sup.lim. To predict a feasible battery pack/ESS SoP, both the particular output entry/ies q* hitting the limit and the time instant t* at which it/they hit/s the limit need to be identified.

[0120] If the q-th output entry y.sub.q reaches its limit y.sup.lim at the time instant t∈[t.sub.0, t.sub.0+Δt], then y.sub.q(t)=y.sup.lim. The corresponding battery pack current during the prediction time horizon is

[00001] $I_{P}^{SoP} (q, t) = \frac{y^{\lim} - I_{q} {Ce}^{A (t - t_{0})} x (t_{0})}{I_{q} ({CK}_{A} (t - t_{0}) B + D)},$ $q \in {1, 2, .Math., Q}, t \in [t_{0}, t_{0} + Δ t],$

[0121] where I.sub.q is the q-th row of the identity matrix of size Q, and the matrices A, B, C, and D are either pre-calculated or updated at t=t.sub.0. Given the output limit y.sup.lim, the corresponding input battery pack current I.sub.P.sup.SoP depends not only on the index of the requested output entry, but also on the time instant at which the limit is reached.

[0122] Different ESS/battery pack currents can be obtained depending on the specified output entry and its time of hitting the limit. To ensure safe operation of the multi-battery ESS, i.e. the battery pack, none of the entries in the output vector is allowed to exceed the limits throughout the prediction horizon. Thus, among all estimated possible battery pack load currents estimated, the load current of minimum magnitude is selected as the battery pack's SoP for charging and/or discharging, respectively:

[00002] $.Math. I_{P}^{SoP} .Math. = .Math. I_{P}^{SoP} (q^{*}, t^{*}) .Math. = \underset{t \in [t_{0}, t_{0} + Δ t]}{\min_{q \in {1, 2, .Math., Q},}} .Math. I_{P}^{SoP} (q, t) .Math. .$

[0123] In real applications, the exact battery pack SoP may be impossible to obtain by exhaustive search due to computational constraints. Therefore, a battery pack-model-based estimation algorithm, i.e. an algorithm based on the system-level model, using a multi-step approach, has been designed.

[0124] In short, an estimation algorithm for predicting the ESS SoP according to some embodiments of the invention is illustrated in a flow chart in FIG. 5. The estimation algorithm may comprise:

[0125] A: Predicting a maximum possible load current magnitude and/or a maximum possible load power magnitude for the ESS over the prediction time horizon, which maximum possible load current magnitude and/or a maximum possible load power magnitude is the load current and/or load power of maximum magnitude that may be used without violating the operating limits of the at least one constrained variable; and

[0126] B: Setting the predicted SoP of the ESS to the predicted maximum possible load current magnitude and/or the predicted maximum possible load power magnitude.

[0127] The step A may be carried out by the following sub-steps:

[0128] A-1: Predicting end values of the possible load current or load power of the ESS at a beginning and an end of the prediction time horizon, using primarily the equation for determining I.sub.P.sup.SoP(q, t) as defined above. It is in this case assumed that the maximum or minimum of the constrained variables over the prediction time horizon occurs at the beginning or end of the prediction time horizon, so that the end value may serve as an initial guess of the battery pack SoP.

[0129] A-2: Based on the predicted end values, setting a preliminary estimate of the maximum possible charging or discharging current or power, using the equation for determining |I.sub.P.sup.SoP| as defined above. This preliminary estimate serves as an initial guess. Under the assumption made in step A-1, the SoP is calculated based on each constrained variable separately at both end points. Thereafter, the minimum of these calculated SoP values is taken to compute the preliminary SoP estimates, one for charging and the other for discharging. Only if the aforementioned assumption is not true i.e., if the operational limits are not hit at the boundaries, a further search for an estimate is performed. In other words, further search and optimization are only performed if the operational limits are hit in-between two boundaries of the prediction time horizon.

[0130] A-3: Determining whether the preliminary estimate is feasible. The preliminary estimate might be infeasible since all intermediate output values of the constrained values, i.e. between the beginning and end of the prediction time horizon, are ignored. Thus, the feasibility of the preliminary estimate still needs to be checked by feeding it to the state-space representation of the multi-battery ESS/battery pack and sampling the output values of the constrained variables through the output equations to find e.g. the cell terminal voltages VT and/or the string currents Is. In this way, any violations of the operating limits of the constrained variables among the sampling points will be detected.

[0131] If the preliminary estimate is found to be feasible, i.e. if no output violates the operating limit(s) of the constrained variable(s), the algorithm proceeds to step B. In other words, the preliminary estimate is output as the predicted SoP of the ESS.

[0132] If instead outliers violating the operating limits are detected, the preliminary estimate is deemed not to be feasible, and the algorithm proceeds by solving an optimization problem. This may include the following sub-steps:

[0133] A-4: Using model-based simulation, identifying a set of constrained variables whose operating limits are violated. This may be one or more constrained variables.

[0134] A-5: Assuming that each constrained variable from the set achieves a peak, or valley, and hits its operating limit (so-called incidence point) at least once between the two end points of the prediction time horizon. By setting a short-term prediction time horizon, such as 1 s, it may be assumed that the cell current and the cell terminal voltage will not oscillate during the prediction time horizon, and that only one peak or valley per variable will be found.

[0135] A-6: Finding the points in time at which each constrained variable achieves its peak or valley (time of incidence) by using the above assumption in the system-level model, and then solving for time for each constrained variable in the set.

[0136] A-7: Determining the magnitude of the ESS current by plugging in the corresponding time of incidence in the system-level model for each constrained variable in the set.

[0137] A-8: Predicting the SoP of the ESS, i.e. the maximum possible load current magnitude or load power magnitude, by taking the minimum of all the ESS current magnitudes computed in step A-7. The algorithm thereafter proceeds to step B.

[0138] Upper and lower limits of the battery cell SoC, commonly imposed to avoid over-utilising any battery cell in the ESS, has to be treated slightly differently in the battery pack SoP estimation, since the evolution of the cell OCV-SoC curve's slope from present cell SoC to its specified limit needs to be involved. The proposed algorithm is derived for a short prediction time horizon during which the curve can be assumed constant. The battery cell-SoC limited battery pack SoP may preliminarily be estimated based on the SoP estimates for other operating limits, e.g., the cell current and terminal voltage operating limits, and then followed by a feasibility check. If any cell SoC exceeds the limit during the prediction time horizon, it already gets sufficiently close to the SoC limit at the beginning. Thus, the proposed method for removing the excess can still be applied. When checking the feasibility of the preliminary estimate and removing the excess if detected, relevant output matrices may be derived as follows.

[0139] To track the battery cell SoC evolution in a battery pack including parallel connections, as compared to Coloumb counting through the integral of a time-varying cell current, it is computationally more efficient to study the battery cell OCV alternatively since it can be directly extracted from the system state vector x. Denoting the battery cell OCV vector by

V.sub.OC[V.sub.OC.sup.(1,1),V.sub.OC.sup.(1,2), . . . ,V.sub.OC.sup.(M,N)].sup.T,V.sub.OC∈ custom-character .sup.MN,

it may be expressed as the system output

V.sub.OC=C.sub.OCx+D.sub.OCI.sub.P.

[0140] By applying a generic linear battery pack model and derived analytical expressions, the proposed method and algorithm become more computationally efficient than by directly constructing a non-linear time-varying system model to which solutions can only be numerically searched.

[0141] It is to be understood that the present invention is not limited to the embodiments described above and illustrated in the drawings; rather, the skilled person will recognize that many changes and modifications may be made within the scope of the appended claims.

A METHOD FOR PREDICTING STATE-OF-POWER OF A MULTI-BATTERY ELECTRIC ENERGY STORAGE SYSTEM

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H02J2310/48

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B60L2260/50

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H02J7/0063

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H02J7/0014

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GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS

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Abstract

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