CN104657520B - A kind of fuel cell modelling method based on Large Copacity energy storage lithium ion battery - Google Patents

Abstract

The present invention proposes a kind of fuel cell modelling method based on Large Copacity energy storage lithium ion battery, and method includes establishing the equivalent-circuit model based on high capacity lithium ion battery, the model parameter under identification different conditions on the basis of model, model parameter and the method for proposing model parameter smooth change when state switches according to corresponding to different running status selections.The model that the present invention establishes has the charge and discharge characteristic for being capable of accurate description battery, the accuracy advantage of the precision of models fitting, the validity of model analysis and model emulation is improved, being capable of the effectively design of boosting battery management system and the exploitation of Premium Features algorithm.

Description

A kind of fuel cell modelling method based on Large Copacity energy storage lithium ion battery

Technical field

The present invention relates to intelligent grid and technical field of lithium ion, is related specifically to one kind and is based on Large Copacity energy storage lithium The fuel cell modelling method of ion battery.

Background technology

Recently as the fast development of lithium ion battery technology, application of the high capacity lithium ion battery in power network energy storage Technology is gradually ripe.Under intelligent grid construction and the promotion of new energy power generation grid-connection, power network battery energy storage technology receives extensively General concern.At the same time, power network energy storage, work of the people to lithium ion battery economically are carried out using battery for greater safety Conducted in-depth research as characteristic.

Battery model is the important tool for reflecting battery working characteristic, and fuel cell modelling mainly has three in energy-storage system research The effect of aspect：System emulation analysis, state estimation algorithm research and battery management system（BMS）Circuit design.Need to be directed to The type of battery model used by the content studied determines.For example, if the dynamic response of research battery system is, it is necessary to build Battery model with dynamic characteristic, if the polarization characteristic of research battery system is, it is necessary to build the electricity for including polarity effect element Pond module.In state-of-charge（SOC）, health status（SOH）With in internal resistance algorithm for estimating, it is necessary to determine algorithm according to battery model Parameter, while pass through model emulation result and experimental record data comparison verification algorithm.Set carrying out battery management system circuit Before meter, often circuit simulation is first carried out according to the characteristic of battery, determine circuit parameter.Due to energy-storage system Simulation results Authenticity and reference value depend on the precision of model, Accurate Model is advantageous to carry out the previous work of circuit design, split Hair battery management system acts the effect got twice the result with half the effort.

Frequently with equivalent-circuit model in battery applications technology, including Rint models, wear Vernam model, PNGV models, GNL models and with this derivative various new model.In electric automobile, because using proprietary charger to carry out constant current constant voltage during charging Charge and often ignore charge characteristic, therefore battery model also only focuses on the flash-over characteristic of reflection battery.In energy-accumulating power station, electricity Pond group connection energy conversion system（PCS）Charge and discharge, charging and discharging currents or voltage are not constant, charge and discharges Operation can switch at any time.And battery is during charge and discharge, the chemical reaction of inside battery simultaneously differs, what outside was presented Electrical characteristics are also different.Therefore, in order to accurately reflect the charge and discharge characteristic of battery, foundation is based on charge-discharge characteristic solution The battery model of coupling is particularly important.

The content of the invention

Present invention seek to address that technical problem existing for existing battery model, particularly solves model and is difficult to accurate description The shortcomings that two various process characteristics of battery charge and discharge, and the validity of model analysis and the standard of model emulation can be improved True property.

To achieve these goals, the present invention proposes a kind of fuel cell modelling side based on Large Copacity energy storage lithium ion battery Method, comprise the following steps：

（1）The modified second order thevenin equivalent circuit model of Large Copacity energy storage lithium ion battery is established, row write equivalent electric The mathematic(al) representation of road model is as follows：

u_c(k)=E(u_soc(k))+u_s(k)+u_l(k)+R_i·i_c(k) （II）

Formula（I）It is the state equation of model, formula（II）It is the output equation of model；Wherein, u_soc(k)、u_sAnd u (k)_l(k) For three quantity of states of kth moment model, the capacitance voltage of reflection battery charge state is represented respectively, reflects the fast mistake of polarity effect The capacitance voltage of journey, the capacitance voltage for reflecting polarity effect slow process, E (u_soc(k) it is) electromotive force of kth moment battery, i_c (k) it is the input quantity of kth moment model, represents the electric current by battery, u_c(k) it is the output quantity of kth moment model, represents electricity The voltage at pond both ends；△ t are the time interval at kth moment and the moment of kth+1, C_socFor reflection battery can charge/discharge capacity electricity Hold, R_sAnd C_sTo reflect the RC network parameter of polarity effect fast process, R_lAnd C_lTo reflect the RC network of polarity effect slow process ginseng Number, R_iFor the ohmic internal resistance of battery；

（2）Parameter in equivalent-circuit model is recognized by charge-discharge test, including：C_soc、E(u_soc)、R_s、C_s、R_l、C_l And R_i；

（3）Definition Model state space X (ω), including three charged state, discharge condition and static condition values, respectively It is designated as ω_c、ω_dAnd ω_s, the state of any moment battery is one in this three states；ω_cRepresent that battery charges, should Model parameter under state is designated as ψ_c；ω_dRepresent that battery discharges, the model parameter under the state is designated as ψ_d；ω_sRepresent electricity Pond is in static condition, and battery is under static condition, it is necessary to determine whether the previous state of static condition, works as static condition Previous state when being charged state, then model parameter is designated as ψ_s|c, when the previous state of static condition is discharge condition, then Model parameter is designated as ψ_s|d；

（4）Time series T={ t of Definition Model fitting₀,t₁,t₂,...,t_n, T is equally spaced, interval time T_s, In t₀The model parameter that the fitting of moment battery uses is ψ_t0=(ψ_s|c+ψ_s|d)/2, hereafter any instant t_kModel parameter ψ_tkBy preceding One moment t_k-1Model parameter ψ_tk-1Determine that relational expression is with the battery status at current time：

ψ_tk=η·ψ_tk-1+(1-η)·ψ_α（V）

Formula（V）In, ψ_αFor the battery status at current time, ψ_α∈{ψ_c,ψ_d,ψ_s|c,ψ_s|d, η is weight coefficient, η ∈ (0, 1)。

Further, the step（2）Method comprise the following steps：

（2-1）The maximum charging voltage for defining battery is V_max, minimum discharge voltage is V_min.Battery is with constant current charge Reach V to voltage_maxFull charge state is defined as, battery is discharged to voltage with constant current and reaches V_minIt is defined as putting state entirely.Electricity Pond releases the numerical value of electricity as C from full charge state to the state of putting entirely_socNumerical value；

（2-2）Since battery reach V putting state entirely with low current charge to voltage_max, then with low discharging current to electricity Stream reaches V_min, record the cell voltage u changed over time in whole process_cWith the capacitance voltage of reflection battery charge state u_soc, obtain two u based on charging and based on electric discharge_c(u_soc) relation curve, the median of two curves is taken as E (u_soc) close It is curve；

（2-3）Battery is from put state carries out " charging-standing-charging " circulation experiment up to filling shape entirely with constant current entirely State, then " electric discharge-standing-electric discharge " circulation experiment is carried out until putting state entirely with constant current, charging is stood and discharged respectively The voltage data changed over time during standing extracts, and using the time as independent variable x, using voltage as dependent variable y, row write pass It is that formula is as follows：

Formula（III）In,For the charge or discharge electric current before standing,Reflect the electricity of battery charge state during to stand Hold voltage, parameter fitting is carried out using least square method, the R of charging and discharging process is calculated_s、C_s、R_l、C_l, will charge quiet Put parameter corresponding to process and be denoted as R_s,c、C_s,c、R_l,c、C_l,c, parameter corresponding to electric discharge standing process is denoted as R_s,d、C_s,d、R_l,d、 C_l,d；

（2-4）According to（2-3）In cycle charge-discharge experiment, will charge to respectively standings, standing it is quiet to charging, being discharged to Put and stand to electric discharge four in the case of voltage variety and current change quantity extract, voltage variety is denoted as △ u, electricity Stream variable quantity is denoted as △ i, and the R in the case of four kinds is obtained according to relationship below_i, R is denoted as respectively_i,cs、R_i,sc、R_i,dsAnd R_i,sd：

R_i=△u/△i。

Further, the model parameter ψ under the charged state, discharge condition_c、ψ_dRespectively：

ψ_c=[C_soc E(u_soc) R_s,c C_s,c R_l,c C_l,c R_i,cs],

ψ_d=[C_soc E(u_soc) R_s,d C_s,d R_l,d C_l,d R_i,ds],

The battery is in static condition, and the previous state of static condition is charged state, then：

ψ_s|c=[C_soc E(u_soc) R_s,c C_s,c R_l,c C_l,c R_i,sc],

The battery is in static condition, and the previous state of inactive state is discharge condition, then：

ψ_s|d=[C_soc E(u_soc) R_s,d C_s,d R_l,d C_l,d R_i,sd]。

The beneficial effects of the present invention are：

The present invention recognizes the model parameter under different conditions on the basis of improved battery equivalent circuit model, according to not Model parameter corresponding to same running status selection, it is proposed that the method for model parameter smooth change when state switches, there is energy The charge and discharge characteristic of enough accurate description batteries, improves the precision of models fitting, the validity of model analysis and model and imitates Genuine accuracy advantage, can the effectively design of boosting battery management system and the exploitation of Premium Features algorithm, improve Build the economic benefit of energy-accumulating power station.

Brief description of the drawings

Fig. 1 is the modified thevenin equivalent circuit figure of embodiment of the present invention；

Fig. 2 is the E (u of LiFePO4 in equivalent circuit shown in Fig. 1_soc) curve；

The pulse charge-discharge test that identification model parameter is carried out in Fig. 3 equivalent circuits shown in Fig. 1；

Fig. 4 is ω_cWith ω_dE (u under state_soc) curve；

Fig. 5 is identification of Model Parameters and process for using.

Embodiment

The invention will now be described in further detail with reference to the accompanying drawings.

Fig. 1 schematically shows the equivalent-circuit model according to one embodiment of the present invention.Circuit is divided into two Point, the right and left connects a stream control current source and a voltage controlled voltage source respectively, incite somebody to action both by control electric current and control voltage It is linked together, preferably to describe the electromotive force of battery with SOC.The right and the source-series circuit of voltage include an internal resistance and Two RC shunt circuits, impedance operator and polarity effect are represented respectively.

Wherein, u in the circuit of the left side_socWith electric capacity C_socBoth end voltage characterizes the SOC states of battery.As capacity is 100Ah Cell, C_soc=100×3600F。u_socExcursion be 0~1V, corresponding SOC excursion is 0~100%.E (u_soc) representing cell emf, i.e. battery standing reaches the open-circuit voltage after stabilization.Battery cell is under the different SOC stages Electromotive force it is different, as the electromotive force of ferric phosphate lithium cell changes between 2.5~3.6V, SOC is bigger, and electromotive force is higher, such as Shown in Fig. 2.R_iThe ohmic internal resistance of battery is represented, is reflected when the electric current for flowing through battery changes, the violent journey of voltage change Degree, i.e. R_i=△V/△I.The polarity effect of battery is reflected with two RC shunt circuits, is R respectively_sAnd C_s、R_lAnd C_l.They when Between constant differ, be designated as τ_sAnd τ_l, Fast Process and slow procedure are represented respectively.

In identification model the step of each parameter and method is：

A, battery is with 0.5C/3.5V constant current constant voltages（CCCV）Charge to cut-off current 0.05C and be referred to as full charge state, with 0.5C Constant current（CC）It is discharged to blanking voltage 2.7V and referred to as puts state entirely, the electricity that battery is released by full charge state to the state of putting entirely claims For battery can charge/discharge capacity, i.e. C_soc。

B, battery since it is complete put state with 0.5C/3.5V constant current constant voltages（CCCV）Charge 6min, stands 30min, then fill Electric 6min simultaneously stands 30min, is circulated with this up to reaching charge cutoff electric current 0.05C, i.e. full charge state, records each standing stage The voltage and SOC of end point, as ω_cE (the u of state_soc) curve, similarly according to above-mentioned steps constant-current discharge, by full charge state To state is put entirely, make ω according to the record value for standing end point_dE (the u of state_soc) curve, and with ω_cAnd ω_dThe E of state (u_soc) curve identical SOC points average value as ω_iE (the u of state_soc) curve.Experimental record is as shown in figure 3, E (u_soc) Curve is as shown in Figure 4.

C, according to the experimental procedure described in B, the ohmic internal resistance of battery is calculated when electric current changes, obtain charging and The internal resistance value in different SOC stages in discharge process.

D, according to the experimental procedure described in B, the data identification RC network in a stage of constant current hold is utilized Parameter, using least square fitting.Pay attention to, when electric current is not zero, with the progress of charge or discharge, the SOC of battery is sent out It is raw to change, therefore cell emf also changes, and needs to exclude the voltage change caused by electromotive force changes in fit procedure Influence.Finally give the RC network parameter under four kinds of different conditions.

0~100% is obtained by pulse charge-discharge test at equal intervals（5%）Share 21 SOC points, i.e., above all of parameter It is corresponding SOC 21*n rank matrixes, E (u_soc) it is 21*3 rank matrixes, R_iFor 21*2 rank matrixes, P (P ∈ { R_s,C_s,R_l,C_l) be 21*4 rank matrixes.

Battery uses different model parameters under different running statuses.In ω_iUnder state, model parameter takes E (ω_i, SOC), because battery is without discharge and recharge under original state, the open-circuit voltage of battery is equal to electromotive force, and remaining parameter exports to model Do not influence, can appoint and take；In ω_cUnder state, model parameter takes E (ω_c,SOC)、R_i(ω_c, SOC) and P (ω_c,s, SOC), wherein P ∈{R_s,C_s,R_l,C_l, battery carries out discharge and recharge in this case, if electric current does not change, SOC becomes according to constant speed Change, and be slow change procedure, model output voltage does not change in a short time, changes in long-time with SOC, if electric Stream size changes but direction does not change, ω_cState is constant, still using same group model parameter；Similarly, in ω_dUnder state, Model parameter takes E (ω_d,SOC)、R_i(ω_d, SOC) and P (ω_d,s, SOC), wherein P ∈ { R_s,C_s,R_l,C_l, as long as state is not sent out Raw to change, the group of model parameter is constant；In ω_sUnder state, it is necessary to according to being that charged state or discharge condition are selected before standing Model parameter is selected, if charged state, takes E (ω_c,SOC)、R_i(ω_c, SOC) and P (ω_s,c, SOC), if discharge condition, its Middle P ∈ { R_s,C_s,R_l,C_l, under static condition, there is no electric current to flow through on battery, the SOC of battery keeps constant, each model ginseng Number is constant, i.e., only 6 fixed SOC model parameter.

The parameter that identification of Model Parameters obtains is the matrix based on different SOC discrete points, is inserted when parameter selects using linear The method of value is different SOC state match parameters.Such as the SOC under charged state is 17%, and there was only 5% times in parameter matrix Number SOC respective value, the parameter used according to linear interpolation is P (ω_c,0.17)=0.6P(ω_c,0.15)+0.4P(ω_c, 0.20), wherein P ∈ { E, R_i,R_s,C_s,R_l,C_l}。

Time series T={ t of Definition Model fitting₁,t₂,...,t_n, T can be equally spaced or unequal interval.This Embodiment is using sequence at equal intervals, the interval time at intervals of Sampling interrupt at two neighboring time point, as sample frequency is 48kHz, AD conversion result are 16, the size 1024Bytes of sampled data buffering area, and interrupt type is in buffer full It is disconnected, i.e., interruption is produced when sampled data fills up buffering area, then time interval is △ t₁=t_n+1-t_n=1024÷2÷(48×1000) ×1000ms=10.67ms.Battery pack working condition is a random process based on TEach determine Time point corresponding state X (ω) ∈ { ω_i,ω_c,ω_d,ω_s}.Each state is a stochastic variable, and with a upper shape State is unrelated.Except original state ω_iIn addition, other three states can be changed mutually, ω_iCan only be to ω_cAnd ω_dIt is unidirectional to turn Change, as shown in figure 5, totally 8 kinds of switching types.Model parameter is not undergone mutation when switching for guarantee state, after state switching A period of time △ t_m=t_n+m-t_nIt is interior, using the weighted value of the model parameter of two states before and after switching.In this embodiment, such as ω_cIn t_nMoment switches to ω_s, model parameter is ω_cState parameter and ω_sThe combination of state parameter, P (ω, SOC)=η P (ω_c, SOC)+(1-η)P(ω_s, SOC), wherein, P ∈ { E, R_i,R_s,C_s,R_l,C_l, weight factor η=((t_n+m-t_k)/△t_m)²。

Finally it should be noted that：The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, knot Close above-described embodiment the present invention is described in detail, those of ordinary skills in the art should understand that to：This area skill Still the embodiment of the present invention can be modified by art personnel or equivalent substitution, but these modifications or change exist Apply among pending claims.

Claims (3)

1. a kind of fuel cell modelling method based on Large Copacity energy storage lithium ion battery, comprises the following steps：

(1) the modified second order thevenin equivalent circuit model of Large Copacity energy storage lithium ion battery is established, row write equivalent circuit mould The mathematic(al) representation of type is as follows：

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u_c(k)=E (u_soc(k))+u_s(k)+u_l(k)+R_i·i_c(k) (II)

Formula (I) is the state equation of model, and formula (II) is the output equation of model；Wherein, u_soc(k)、u_sAnd u (k)_l(k) it is kth Three quantity of states of moment model, the capacitance voltage of reflection battery charge state is represented respectively, reflects polarity effect fast process Capacitance voltage, the capacitance voltage for reflecting polarity effect slow process, E (u_soc(k) it is) electromotive force of kth moment battery, i_c(k) it is The input quantity of kth moment model, represent the electric current by battery, u_c(k) it is the output quantity of kth moment model, represents battery two The voltage at end；Δ t is the time interval at kth moment and the moment of kth+1, C_socFor reflection battery can charge/discharge capacity electric capacity, R_s And C_sTo reflect the RC network parameter of polarity effect fast process, R_lAnd C_lTo reflect the RC network parameter of polarity effect slow process, R_i For the ohmic internal resistance of battery；

(2) parameter in equivalent-circuit model is recognized by charge-discharge test, including：C_soc、E(u_soc)、R_s、C_s、R_l、C_lAnd R_i；

(3) Definition Model state space X (ω), including three charged state, discharge condition and static condition values, are designated as respectively ω_c、ω_dAnd ω_s, the state of any moment battery is one in this three states；ω_cRepresent that battery charges, the state Under model parameter be designated as ψ_c；ω_dRepresent that battery discharges, the model parameter under the state is designated as ψ_d；ω_sRepresent at battery In static condition, battery is under static condition, it is necessary to the previous state of static condition be determined whether, before static condition When one state is charged state, then model parameter is designated as ψ_s|c, when the previous state of static condition is discharge condition, then model Parameter is designated as ψ_s|d；

(4) the time series T={ t of Definition Model fitting₀,t₁,t₂,...,t_n, T is equally spaced, interval time T_s, in t₀ The model parameter that the fitting of moment battery uses is ψ_t0=(ψ_s|c+ψ_s|d)/2, hereafter any instant t_kModel parameter ψ_tkBy previous Moment t_k-1Model parameter ψ_tk-1Determine that relational expression is with the battery status at current time：

ψ_tk=η ψ_tk-1+(1-η)·ψ_α

In above formula, ψ_αFor the battery status at current time, ψ_α∈{ψ_c,ψ_d,ψ_s|c,ψ_s|d, η is weight coefficient, η ∈ (0,1).

2. the fuel cell modelling method according to claim 1 based on Large Copacity energy storage lithium ion battery, it is characterised in that institute The method for stating step (2) comprises the following steps：

The maximum charging voltage that (2-1) defines battery is V_max, minimum discharge voltage is V_min, battery is with constant current charge to electricity Pressure reaches V_maxFull charge state is defined as, battery is discharged to voltage with constant current and reaches V_minBe defined as putting state entirely, battery from Full charge state to the state of putting entirely releases the numerical value of electricity as C_socNumerical value；

Since (2-2) battery reach V putting state entirely with low current charge to voltage_max, then reached with low discharging current to electric current To V_min, record the cell voltage u changed over time in whole process_cWith the capacitance voltage u of reflection battery charge state_soc, obtain To two u based on charging and based on electric discharge_c(u_soc) relation curve, the median of two curves is taken as E (u_soc) relation curve；

(2-3) battery puts state and carries out " charging-standing-charging " circulation experiment up to full charge state with constant current from complete, then " electric discharge-standing-electric discharge " circulation experiment is carried out with constant current until putting state entirely, charging is stood respectively and electric discharge was stood The voltage data changed over time in journey extracts, and using the time as independent variable x, using voltage as dependent variable y, row write relational expression such as Under：

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In above formula,For the charge or discharge electric current before standing,Reflecting the capacitance voltage of battery charge state during to stand, adopting Parameter fitting is carried out with least square method, the R of charging and discharging process is calculated_s、C_s、R_l、C_l, by the standing process pair that charges The parameter answered is denoted as R_s,c、C_s,c、R_l,c、C_l,c, parameter corresponding to electric discharge standing process is denoted as R_s,d、C_s,d、R_l,d、C_l,d；

(2-4) according to the cycle charge-discharge experiment in (2-3), will charge to respectively standings, stand to charge, be discharged to stand and Voltage variety and current change quantity in the case of standing extremely electric discharge four extract, and voltage variety is denoted as Δ u, and electric current becomes Change amount is denoted as Δ i, draws the R in the case of above-mentioned four kinds successively according to relationship below_i, R is denoted as respectively_i,cs、R_i,sc、R_i,dsWith R_i,sd：

R_i=Δ u/ Δs i.

3. the fuel cell modelling method according to claim 1 based on Large Copacity energy storage lithium ion battery, it is characterised in that：

Model parameter ψ under the charged state, discharge condition_c、ψ_dRespectively：

ψ_c=[C_soc E(u_soc) R_s,c C_s,c R_l,c C_l,c R_i,cs],

ψ_d=[C_soc E(u_soc) R_s,d C_s,d R_l,d C_l,d R_i,ds],

The battery is in static condition, and the previous state of static condition is charged state, then：

ψ_s|c=[C_soc E(u_soc) R_s,c C_s,c R_l,c C_l,c R_i,sc],

The battery is in static condition, and the previous state of inactive state is discharge condition, then：

ψ_s|d=[C_soc E(u_soc) R_s,d C_s,d R_l,d C_l,d R_i,sd]。