CN111260185A - Method for evaluating operation reliability of power generation and transmission system with retired electric vehicle battery as large-scale energy storage - Google Patents
Method for evaluating operation reliability of power generation and transmission system with retired electric vehicle battery as large-scale energy storage Download PDFInfo
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Abstract
The invention discloses a method for evaluating the running reliability of a power generation and transmission system with retired electric automobile batteries as large-scale energy storage, which mainly comprises the following steps: 1) establishing a capacity degradation model of the retired battery; 2) obtaining a plurality of retired batteries, and evaluating the health states of the retired batteries by using a retired battery capacity degradation model; 3) and establishing a battery module capacity probability model and a battery module operation reliability model. 4) Designing a battery module based on a battery module capacity probability model and a battery module operation reliability model, and connecting the retired battery to a power generation and transmission system; 5) establishing a power generation and transmission system operation reliability evaluation model containing retired batteries; 6) and establishing a return/cost analysis model of the power generation and transmission system containing the retired battery, and determining a secondary retirement time table of the retired battery. The invention verifies the feasibility and effectiveness of using the retired battery in the power generation and transmission system and determines the retired schedule of the secondary retired battery.
Description
Technical Field
The invention relates to the technical field of system operation reliability analysis, in particular to a method for evaluating the operation reliability of a power generation and transmission system with retired electric automobile batteries as large-scale energy storage.
Background
Electric vehicle technology is continuously developing, and the recycling and application of batteries eliminated from electric vehicles face new challenges. An electric vehicle battery is typically considered retired once it has fallen to 80% state of health (SOH).
The capacity degradation rate of the retired battery is large, and the influence of the capacity degradation rate is not negligible in power system analysis. The failure probability of a retired battery is higher and less predictable than a brand new battery. Modeling capacity degradation rate and failure probability of retired battery and incorporating same into operation of power generation and transmission system
Reliability assessment becomes a new challenge.
The existing research on the capacity attenuation of the lithium battery is basically based on the obtained data of an accelerated aging experiment and can be divided into two types according to a model: empirical models and electrochemical mechanistic models. While empirical models involve little to no intrinsic processes that lead to capacity fade during cycling, models built using electrochemical mechanisms are typically developed using data collected under tightly controlled experimental conditions, and are not present in practical applications and are therefore prone to error. Another way to quantify the degradation process is to use available manufacturer data, however, these data cannot be used to determine the capacity loss of an individual cell in other types of charge-discharge cycles or applications.
Generally, the end of life (EoL) of a battery is defined as a state where the capacity is reduced to 80% of its initial capacity, below which the battery life is considered to be drastically shortened. Despite the life analysis of secondary batteries in three fixed applications (energy arbitrage, autonomous use and islanding installation), this method is only a direct extrapolation of the existing model and is therefore not practically suitable for secondary use of retired batteries. The battery manufacturer does not disclose data after the end of battery life, and there is currently no study on state of health degradation models with capacities below 80%. That is, to date, there has been no study on a retired battery capacity degradation model.
It is well known that energy storage in power systems facilitates eliminating fluctuations from renewable energy integration and improves supply continuity. The Battery Energy Storage System (BESS) can be built quickly and the capacity can be gradually increased, which is suitable for planning and extension of the power system.
There are several studies on the evaluation of operational reliability of power systems with energy storage. However, the storage system model under current research is a general storage system model that is not directed to retired batteries. Furthermore, all studies only considered the power generation load system, but neglected the effects of the installation location of the battery energy storage system and the power transmission system, which may have a significant impact on the evaluation results.
Disclosure of Invention
The present invention is directed to solving the problems of the prior art.
The technical scheme adopted for achieving the purpose of the invention is that the method for evaluating the running reliability of the retired electric automobile battery as a large-scale energy storage power generation and transmission system mainly comprises the following steps:
1) and establishing a capacity degradation model of the retired battery.
Further, the main steps for establishing the retired battery capacity degradation model are as follows:
1.1) calculating the state of health SOH of the battery, namely:
in the formula, QiniIs the initial capacity of the unused battery. Q is the maximum discharge capacity of the currently retired battery.
1.2) calculating a calendar degradation factor α for battery capacitycapAnd a cyclic degradation factor βcapNamely:
αcap＝(7.543×V-23.75)×106×e-6976/T(2)
wherein V is a voltage. T is the temperature.
Is the second order average voltage. DoD is the depth of discharge. DoD ∈ [0,1 ]]。
1.3) calendar degradation factor α using battery capacitycapAnd a cyclic degradation factor βcapUpdating the state of health SOH of the battery, namely:
wherein t is time, QtIs the charge throughput.
2) Obtaining a plurality of retired batteries, and evaluating the health states of the retired batteries by using a retired battery capacity degradation model.
Further, the main steps of evaluating the health state of the retired battery by using a retired battery capacity degradation model are as follows:
2.1) judging that the maximum discharge capacity Q of the current retired battery is more than or equal to 80 percent QiniAnd if so, inputting the maximum discharge capacity Q of the current retired battery into a retired battery capacity degradation model, and calculating to obtain the SOH of the retired battery. If not, go to step 2.2).
2.2) acquiring retired battery capacity attenuation process data by using a retired battery capacity degradation model, and fitting the retired battery capacity attenuation process data to obtain a retired battery capacity attenuation function.
The retired battery capacity decay function is as follows:
in the formula, ai、biAnd ciThe fitting parameters are indicated. i is 1,2, 3. And x is the equivalent charge-discharge cycle number or the equivalent service time.
2.3) calculating to obtain the capacity Q of the retired battery after attenuation by using a capacity attenuation function of the retired battery, inputting the capacity Q of the retired battery after attenuation into a capacity degradation model of the retired battery, and calculating to obtain the SOH of the retired battery.
3) And establishing a battery module capacity probability model and a battery module operation reliability model.
4) And designing a battery module based on a battery module capacity probability model and a battery module operation reliability model, and connecting the retired battery to a power generation and transmission system.
Further, the main steps of establishing the probability model of the battery module capacity are as follows:
4.1) the state of health of the battery is divided into N levels, namely:
g＝{g1,g2,...,gN} (6)
wherein g represents the health status grade.
Calculating the probability q that the capacity of the current retired battery belongs to the health state level llNamely:
ql＝F(gl_high)-F(gl_low)(7)
wherein F (x) is a cumulative distribution function of a normal distribution, gl_highAnd gl_lowRespectively the highest and lowest health status of class i.
4.2) adjusting the domain to obtain the domain-adjusted cumulative distribution function F1(x) Namely:
4.3) updating the probability Q 'of belonging to the health state grade l when the capacity of the retired battery is Q'lNamely:
4.4) generating a decommissioned battery state of health function, namely:
4.5) determining the battery health state function when the retired batteries are connected in series and the battery health state function when the retired batteries are connected in parallel based on the formula 10.
The battery state of health function when retired batteries are connected in series is as follows:
the battery state of health function when the retired batteries are connected in parallel is as follows:
4.6) updating the health state function of the retired battery by using a formula (11) to obtain the health state function of any series circuit in the battery module, namely:
in the formula, ksIs the synthetic health status grade after the defined tandem composition operation. f. ofsIndicating the probability corresponding to each level.
4.7) calculating to obtain the health state functions of the battery modules with a plurality of parallel circuits based on the formula (13), namely:
in the formula, hsIs the resultant health level after parallel operation. p is a radical ofsIs the corresponding probability.
4.8) based on the formula (14), calculating the health state probability distribution of the battery module, namely:
wherein f (x) and F (x) are the probability density function and the cumulative distribution function of the healthy state of the battery module.
Further, the battery module operation reliability model is as follows:
wherein Q is the maximum discharge capacity of the battery module. Si,jIs the state parameter of the retired battery. P is the probability of failure of each cell. QrealThe available capacity of the battery module is taken into account.
Wherein, the state parameter S of the retired batteryi,jAs follows:
during operation of the battery Si,jWhen the battery is not operating, S is 1i,j0, may be determined using a monte carlo sampling method.
In the formula, the random number U is generated from a uniform distribution U (0, 1). Si,jOut-of-service battery operation is denoted by 1. Si,j0 indicates that the retired battery is not operating.
5) And establishing a power generation and transmission system operation reliability evaluation model containing the retired battery.
Further, the main steps of establishing the operation reliability evaluation model of the power generation and transmission system containing the retired battery are as follows:
5.1) establishing an objective function of an operation reliability evaluation model of the power generation and transmission system with the retired battery, namely:
in the formula, ωiIs an important factor of the load of the node i, CiIs the load reduction amount of the node i.
And 5.2) establishing constraint conditions of the operation reliability evaluation model, wherein the constraint conditions comprise a line power flow constraint, a line rated capacity constraint, a power balance constraint of a power generation and transmission system, a generator power upper limit and lower limit constraint, a wind turbine generator output power constraint, a node load reduction constraint, a battery power limit condition, an energy limit condition of a battery in charging and discharging cycles and a starting and stopping state of charge condition of the battery within 24 hours.
The current constraints for each line are as follows:
T(S)＝A(S)(PG+PW-W-PD+C+PB) (20)
the line rated capacity constraints are as follows:
the power balance constraints of a power generation and transmission system are as follows:
the constraints of the generator power upper and lower limits of the power generation and transmission system are as follows:
the output power constraint of the wind turbine generator is as follows:
the node load shedding constraints are as follows:
0≤Ci,t≤PDi,t(i∈ND,t＝1,2,...,24) (25)
the battery power limit conditions are as follows:
the energy limit conditions of the battery during the charge and discharge cycles are as follows:
SoC(t)＝SoC(t-1)-PB/SoCmax(t＝1,2,...,24) (27)
10％≤SoC(t)≤95％(t＝1,2,...,24) (28)
the start-stop state-of-charge conditions for the cell over 24 hours are as follows:
in the formula, NBM is a node set connected with an energy storage system, ND is a load node set, NW is a node set connected with a wind farm, and NG is a generator node set. T (S) is the active vector of the interrupt state S, A (S) is the incidence matrix of the active power and power injection of the interrupt state S, PG is the active power injection vector, PW is the wind energy output vector, W is the wind curtailment vector, PD is the active load vector, C is the load curtailment vector, PB is the battery charging or discharging vector, T (S) is the active power vector of the interrupt state S, A (S) is the incidence matrix of the active power and power injection of the interrupt state SkIs the flow of power on the line k,
is the limit of the power flow on the line k,
is the lower active power limit of generator node i,
is the upper active power limit of the generator node i,
is the output power limit of the wind turbine node i,
is the maximum power limit during discharge of the battery,
is the maximum power limit, SoC, during battery chargingmaxIs the battery capacity, soc (t) is the state of charge of the battery at time t. L is the total number of lines.
5.3) optimizing the objective function based on the constraint conditions of the operation reliability evaluation model, namely:
6) and establishing a return/cost analysis model of the power generation and transmission system containing the retired battery, and determining a secondary retirement time table of the retired battery.
The method mainly comprises the following steps of establishing a return/cost analysis model of a power generation and transmission system with retired batteries:
6.1) establishing an objective function of a return/cost analysis model of a power generation and transmission system with retired batteries, namely:
min T＝I+O+R (33)
where I, O and R are the total available cost, operating cost, and risk cost, respectively.
6.2) calculating the annual cost of the power generation and transmission system with the retired battery, namely:
where a is the equivalent annual cost of the power plant. V is the equipment purchase cost. i is the discount rate. n is the economic life of the device.
6.3) calculating return/cost T' of the power generation and transmission system with the retired battery, namely:
T′＝Ow+Rw-(Oo+Ro)-I＞0 (35)
in the formula, OwAnd RwIs the operational and risk cost of a system containing retired batteries. O isoAnd RoIs the operating and risk cost of a battery-less system. I is the total cost available.
6.4) determining a secondary retirement time table of the retired battery so as to satisfy the formula (36):
the technical effect of the present invention is undoubted. In order to solve the problems in the prior work and verify the feasibility and effectiveness of using the retired battery in the power generation and transmission system, the invention analyzes the economical efficiency and the operational reliability of the power generation and transmission system using the retired electric vehicle battery as large storage, and firstly provides an operational reliability evaluation method of the power generation and transmission system (not only the power generation system) with a battery energy storage system. The invention fits a Gaussian function based on data obtained by using an integral aging model, and the aging method can simulate the capacity reduction process of the retired battery under different operating conditions. The invention provides a new battery capacity degradation model, which takes into account different working conditions and rapid degradation rates of retired batteries. The invention models the probability capacity distribution of a battery module consisting of hundreds of retired batteries by means of a generic generation function (UGF). The invention verifies the feasibility and effectiveness of using the retired battery in the power generation and transmission system and determines the retired schedule of the secondary retired battery. The present invention can save a large amount of battery cost, and compared with a power system without any battery energy storage, the operation reliability is improved.
Drawings
Fig. 1 is a flow chart of a method for evaluating the operation reliability of a retired electric vehicle battery as a power generation and transmission system with large-scale energy storage.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
referring to fig. 1, the method for evaluating the operation reliability of the retired electric vehicle battery as a power generation and transmission system with large-scale energy storage mainly comprises the following steps:
1) and establishing a capacity degradation model of the retired battery.
Further, the main steps for establishing the retired battery capacity degradation model are as follows:
1.1) calculating the state of health SOH of the battery, namely:
in the formula, QiniIs the initial capacity of the unused battery. Q is the maximum discharge capacity of the currently retired battery.
1.2) calculating a calendar degradation factor α for battery capacitycapAnd a cyclic degradation factor βcapNamely:
αcap＝(7.543×V-23.75)×106×e-6976/T(2)
wherein V is a voltage. T is the temperature.
Is the second order average voltage. DoD is the depth of discharge. DoD ∈ [0,1 ]]。
1.3) calendar degradation factor α using battery capacitycapAnd a cyclic degradation factor βcapUpdating the state of health SOH of the battery, namely:
wherein t is time, QtIs the charge throughput.
2) Obtaining a plurality of retired batteries, and evaluating the health states of the retired batteries by using a retired battery capacity degradation model.
Further, the main steps of evaluating the health state of the retired battery by using a retired battery capacity degradation model are as follows:
2.1) judging that the maximum discharge capacity Q of the current retired battery is more than or equal to 80 percent QiniAnd if so, inputting the maximum discharge capacity Q of the current retired battery into a retired battery capacity degradation model, and calculating to obtain the SOH of the retired battery. If not, go to step 2.2).
2.2) acquiring retired battery capacity attenuation process data by using a retired battery capacity degradation model, and fitting the retired battery capacity attenuation process data to obtain a retired battery capacity attenuation function.
The retired battery capacity decay function is as follows:
in the formula, ai、biAnd ci(i ═ 1,2,3) denotes fitting parameters. And x is the equivalent charge-discharge cycle number or the equivalent service time.
2.3) calculating to obtain the capacity Q of the retired battery after attenuation by using a capacity attenuation function of the retired battery, inputting the capacity Q of the retired battery after attenuation into a capacity degradation model of the retired battery, and calculating to obtain the SOH of the retired battery.
3) And establishing a battery module capacity probability model and a battery module operation reliability model.
4) And designing a battery module based on a battery module capacity probability model and a battery module operation reliability model, and connecting the retired battery to a power generation and transmission system.
Further, the main steps of establishing the probability model of the battery module capacity are as follows:
4.1) the state of health of the battery is divided into N levels, namely:
g＝{g1,g2,...,gN} (6)
wherein g represents the health status grade. Subscripts 1, …, N represent the rank numbers.
Calculating the probability q that the capacity of the current retired battery belongs to the health state level llNamely:
ql＝F(gl_high)-F(gl_low) (7)
wherein F (x) is a cumulative distribution function of a normal distribution, gl_highAnd gl_lowRespectively the highest and lowest health status of class i. 1, …, N.
4.2) adjusting the domain to obtain the domain-adjusted cumulative distribution function F1(x) Namely:
in the formula, F (1) and F (0) represent cumulative distribution function values when the variable x is 1 or 0.
4.3) updating the probability Q 'of belonging to the health state grade l when the capacity of the retired battery is Q'lNamely:
4.4) generating the decommissioned Battery health State function USOH(z), namely:
wherein z is a state of health level related variable of the retired battery.
4.5) determining the battery health state function when the retired batteries are connected in series and the battery health state function when the retired batteries are connected in parallel based on the formula 10.
Battery state of health function omega (U) when retired batteries are connected in seriesSOH,i(z),USOH,j(z)) is as follows:
where the indices i and j represent different retired batteries.
Battery state of health function omega (U) when retired batteries are connected in parallelSOH,i(z),USOH,j(z)) is as follows:
4.6) updating the health state function of the retired battery by using the formula (11) to obtain the health state function U of any series circuit in the battery modulestring(z), namely:
in the formula, ksIs the synthetic health status grade after the defined tandem composition operation. f. ofsIndicating the probability corresponding to each level. Omega (U)SOH,1(z),...,USOH,Ns(z)) represents the state of health function of the NS retired batteries in series.
4.7) calculating to obtain a health state function U of the battery modules with a plurality of parallel circuits based on the formula (13)module(z), namely:
in the formula, hsIs the resultant health level after parallel operation. p is a radical ofsIs the corresponding probability. Omega (U)chain,1(z),...,Uchain,Np(z)) represents the state of health function of NP retired batteries in parallel.
4.8) based on the formula (14), calculating the health state probability distribution of the battery module, namely:
wherein f (x) and F (x) are the probability density function and the cumulative distribution function of the healthy state of the battery module.
Further, the battery module operation reliability model is as follows:
in the formula, Q is the maximum discharge capacity of the battery module, that is, the actual maximum capacity without considering the failure condition. Si,jIs the state parameter of the retired battery. P is the probability of failure of each cell. QrealThe available capacity of the battery module is taken into account.
Wherein, the state parameter S of the retired batteryi,jAs follows:
during operation of the battery Si,jWhen the battery is not operating, S is 1i,j0, may be determined using a monte carlo sampling method.
In the formula, the random number U is generated from a uniform distribution U (0, 1). Si,jOut-of-service battery operation is denoted by 1. Si,j0 indicates that the retired battery is not operating.
5) And establishing a power generation and transmission system operation reliability evaluation model containing the retired battery.
Further, the main steps of establishing the operation reliability evaluation model of the power generation and transmission system containing the retired battery are as follows:
5.1) establishing an objective function of an operation reliability evaluation model of the power generation and transmission system with the retired battery, namely:
in the formula, ωiIs an important factor of the load of the node i, CiIs the load reduction amount of the node i.
And 5.2) establishing constraint conditions of the operation reliability evaluation model, wherein the constraint conditions comprise a line power flow constraint, a line rated capacity constraint, a power balance constraint of a power generation and transmission system, a generator power upper limit and lower limit constraint, a wind turbine generator output power constraint, a node load reduction constraint, a battery power limit condition, an energy limit condition of a battery in charging and discharging cycles and a starting and stopping state of charge condition of the battery within 24 hours.
The current constraints for each line are as follows:
T(S)＝A(S)(PG+PW-W-PD+C+PB) (20)
the line rated capacity constraints are as follows:
the power balance constraints of a power generation and transmission system are as follows:
the constraints of the generator power upper and lower limits of the power generation and transmission system are as follows:
the output power constraint of the wind turbine generator is as follows: (24)
the node load shedding constraints are as follows:
0≤Ci,t≤PDi,t(i∈ND,t＝1,2,...,24) (25)
the battery power limit conditions are as follows:
the energy limit conditions of the battery during the charge and discharge cycles are as follows:
SoC(t)＝SoC(t-1)-PB/SoCmax(t＝1,2,...,24) (27)
10％≤SoC(t)≤95％(t＝1,2,...,24) (28)
the start-stop state-of-charge conditions for the cell over 24 hours are as follows:
in the formula, NBM is a node set connected with an energy storage system, ND is a load node set, NW is a node set connected with a wind farm, and NG is a generator node set. T (S) is the active vector of the interrupt state S, A (S) is the incidence matrix of the active power and power injection of the interrupt state S, PG is the active power injection vector, PW is the wind energy output vector, W is the wind curtailment vector, PD is the active load vector, C is the load curtailment vector, PB is the battery charging or discharging vector, T (S) is the active power vector of the interrupt state S, A (S) is the incidence matrix of the active power and power injection of the interrupt state SkIs the flow of power on the line k,
is the limit of the power flow on the line k,
is the lower active power limit of generator node i,
is the upper active power limit of the generator node i,
is the output power limit of the wind turbine node i,
is the maximum power limit during discharge of the battery,
is the maximum power limit, SoC, during battery chargingmaxIs the battery capacity, SoC (t) is the state of charge of the battery at time t. L is the total number of lines.
5.3) optimizing the objective function based on the constraint conditions of the operation reliability evaluation model, namely:
the optimization objective includes three aspects: firstly, load reduction is reduced to the maximum extent so as to ensure the operation reliability of the system; secondly, the running cost of the unit is reduced to the maximum extent, and the economical efficiency of the system is ensured. And thirdly, the abandoned wind is reduced to the greatest extent, so that the operation is more environment-friendly.
6) And establishing a return/cost analysis model of the power generation and transmission system containing the retired battery, and determining a secondary retirement time table of the retired battery.
The method mainly comprises the following steps of establishing a return/cost analysis model of a power generation and transmission system with retired batteries:
6.1) establishing an objective function of a return/cost analysis model of a power generation and transmission system with retired batteries, namely:
min T＝I+O+R (33)
where I, O and R are the total available cost, operating cost, and risk cost, respectively.
6.2) calculating the annual cost of the power generation and transmission system with the retired battery, namely:
where a is the equivalent annual cost of the power plant. V is the equipment purchase cost. i is the discount rate. n is the economic life of the device.
6.3) calculating return/cost T' of the power generation and transmission system with the retired battery, namely:
T′＝Ow+Rw-(Oo+Ro)-I＞0 (35)
in the formula, OwAnd RwIs the operational and risk cost of a system containing retired batteries. O isoAnd RoIs the operating and risk cost of a battery-less system. I is the total cost available.
6.4) determining a secondary retirement time table of the retired battery so as to satisfy the formula (36):
example 2:
the experiment for verifying the operation reliability evaluation method of the retired electric automobile battery as the large-scale energy storage power generation and transmission system mainly comprises the following steps:
1) establishing a capacity degradation model of the retired battery:
the degradation of the battery capacity can be quantified by a change in the state of health (SOH) of the battery, which is defined as the ratio of the current maximum discharge capacity to its initial capacity:
wherein QiniIs the initial capacity of the new battery and Q is the maximum discharge capacity of the current battery, all in watt-hours.
Battery life is affected by other factors besides manufacturing quality, such as temperature, depth of discharge (DoD), discharge current, average state of charge (SOC), and number of cycles, all of which will affect the useful battery life. Obtaining an accurate capacity fade prediction is difficult and therefore it is not possible to account for all influencing factors. However, when stored as a large-scale battery in an electric power system, excessive charge and discharge and some other factors can be avoided by appropriate control. In this case, the number of charge and discharge cycles, the depth of discharge, and the temperature are considered as main factors that affect the capacity fade.
The capacity fade model of the battery is a function of time and charge throughput, i.e., a calendar degradation model and a cycle degradation modelcapIs a calendar degradation factor, and for the cycle degradation model, is a cycle degradation factor βcapThe depth of discharge DoD and the average state of charge SOC are accounted for, as shown in (3).
αcap＝(7.543×V-23.75)×106×e-6976/T(2)
Where V is the voltage, T is the temperature,
is the second order average voltage and DoD is the depth of discharge (in the range 0-1).
Thus, the overall degradation function is a superposition of the calendar and the cycle degradation functions, as shown in (4).
Where t is time, QtIs the charge throughput.
However, this global degradation model is only applicable to new batteries, i.e. from capacity down to 80% of their initial capacity. If such an overall degradation model is applied directly to a retired battery, the estimation of capacity fade may be too optimistic because capacity may drop dramatically during secondary use. Determining the life of a battery system in use is very difficult, expensive, and often can damage the system itself. This patent therefore uses experimental data from the battery research group of the advanced life cycle engineering center (CALCE) university of maryland, usa.
Four lithium batteries (numbered CS2-35, CS2-36, CS2-37 and CS2-38, respectively) underwent the same charging process according to a standard constant current/constant voltage process, respectively, with numerous successive full charge and discharge cycles until the state of health drops to about 15%.
Based on these continuous capacity fade data, functions were selected for curve fitting, using RMSE and R2Two statistical measures are used to compare goodness of fit.
The results are shown in Table 1. The number (i) after the statistic data is the degree of a gaussian function and an exponential function or a polynomial function and a power function.
TABLE 1 goodness of fit of CALCE experimental data
Of all candidate functions, the sum of the three gaussian functions (as shown in (5)) works best to fit all four battery capacity fade data.
Wherein, ai、biAnd ci(i ═ 1,2,3) denotes fitting parameters.
Therefore, it is assumed that the sum of the three gaussian functions can represent the capacity degradation process of the lithium battery. Based on this assumption, a new battery capacity degradation model is proposed. First, when the battery capacity is greater than 80% of its initial capacity, the overall degradation model is used to obtain capacity fade process data, and then a new gaussian function is fitted to these data for extrapolation to obtain a battery degradation model when the state of health drops below 80%. In this way, the capacity fade of the battery can be accounted for at different life cycles and under different operating conditions.
2) Establishing a probability model and an operational reliability model of the capacity of the battery module:
a large-sized battery module used in a power system is composed of a plurality of batteries connected in series or parallel, or a combination thereof. For the operation reliability evaluation technology of the power system containing the battery energy storage system, energy storage capacity in watt-hour is mainly considered, and capacity distribution of the retired battery is described by adopting normal distribution.
For the performance of a battery module consisting of hundreds of batteries, a general generation function is used to estimate the capacity distribution of the battery module, and the function is widely used for the performance analysis of a multi-state system.
It is assumed that the state of health of the battery may be divided into N levels, each level being defined by a range of states of health, e.g., 99.9% -100%, 99.8% -99.9%, etc. g represents a health status level, set to:
g＝{g1,g2,...,gN} (6)
calculate the probability for each capacity class:
ql＝F(gl_high)-F(gl_low) (7)
wherein q islIs the cell probability of state of health class l, F (x) is the cumulative distribution function of the normal distribution, gl_highAnd gl_lowRespectively the highest and lowest health status of class i.
All qlThe sum of (a) and (b) is equal to 1. The normal distribution has a domain of total real numbers, and the healthy state has a domain of [0,1 ]]. Therefore, some adjustments should be made to ensure qlThe sum of (a) and (b).
F (x) is the cumulative distribution function of the normal distribution, F1(x) Is the domain-adjusted cumulative distribution function:
the probability for each health state level is modified as follows:
the general generating function for battery state of health is as follows:
the "Σ" in the generic generation function does not represent an algebraic addition, representing a sequence.
It is assumed that the battery module is operated at a constant voltage. The current flowing through all cells in the series circuit is equal, and the generic generator function series operator is defined as:
for parallel circuits, the capacity is the sum of each series circuit. In calculating the health state, it should be the average health state of each circuit. The general generate function parallel operator is defined as:
according to the above general generating function series operators, the general generating function of one circuit in the battery module can be defined as:
wherein k issIs the synthetic health status grade after the defined tandem composition operation; f. ofsIndicating the probability corresponding to each level.
The general generation function for a battery module using the defined parallel operator is:
wherein h issIs the synthetic health status level after parallel operation; p is a radical ofsIs the corresponding probability.
The health state probability distribution of the battery module:
equations (15) and (16) are a probability density function and a cumulative distribution function of the state of health of the battery module, respectively. The "Σ" in equations (14) and (15) represents algebraic addition, unlike the general generating function operator.
The failure rate of the retired battery is high and cannot be ignored. If the failure probability of each battery is P, the available capacity to account for the failure probability is as follows:
wherein Q is the maximum discharge capacity of the battery module; si,jIs the state of the battery, when the battery is in operation Si,jWhen the battery is not operating, S is 1i,j0, may be determined using a monte carlo sampling method.
Wherein the random number U is generated according to a uniform distribution U (0, 1).
Under the condition that the number of batteries is the same, the battery module with the smaller number of batteries in each series circuit in the topological structure has better operation reliability. However, too many parallel circuits result in too high currents, resulting in high performance requirements for the associated power electronics components, while requiring more equipment investment. Thus, operational reliability and economy of using retired batteries as storage should be traded off.
3) Establishing an operation reliability evaluation model of a power generation and transmission system containing retired batteries:
through the proposed battery degradation model and battery module probability model, the feasibility and effectiveness of using retired batteries as power system storage can be verified by evaluating operational reliability and system operating costs.
3.1) evaluation of operational reliability
Operational reliability refers to the ability of electrical equipment and power systems to provide uninterrupted power to customers during operation. The expected energy starvation (EENS) and the loss load frequency (LOLF) are used as operational reliability indicators. For power systems containing energy storage batteries, operational reliability can be evaluated by the following optimization problem.
An objective function:
in the formula, ωiIs an important factor of the load of the node i, CiIs the load reduction amount of the node i.
Constraint conditions are as follows:
T(S)＝A(S)(PG+PW-W-PD+C+PB)(20)
0≤Ci,t≤PDi,t(i∈ND,t＝1,2,...,24) (25)
SoC(t)＝SoC(t-1)-PB/SoCmax(t＝1,2,...,24) (27)
10％≤SoC(t)≤95％(t＝1,2,...,24) (28)
where NBM is the set of nodes with the energy storage system connected, ND is the set of load nodes, NW is the set of nodes with wind farm connections, and NG is the set of generator nodes. T (S) is the active vector of the interrupt state S, A (S) is the incidence matrix of the active power and power injection of the interrupt state S, PG is the active power injection vector, PW is the wind energy output vector, W is the wind curtailment vector, PD is the active load vector, C is the load curtailment vector, PB is the battery charging or discharging vector, T (S) is the active power vector of the interrupt state S, A (S) is the incidence matrix of the active power and power injection of the interrupt state SkIs the current on line k, TmaxkIs the current limit on line k, PGminiIs the active power lower limit, PG, of generator node iminiIs the upper limit of active power, PW, of node i of the generatorminiIs the output power limit of the wind turbine node i,
is the maximum power limit during discharge of the battery,
is the maximum power limit, SoC, during battery chargingmaxIs the battery capacity, soc (t) is the state of charge of the battery at time t.
Equation (20) calculates the power flow for each line. The constraints (21) define the rated capacity of the line. Equation (22) ensures power balance of the network. Constraints (23) are the upper and lower limits of the conventional generator power. The constraint (24) is a limit on the output power of the wind turbine. Constraint (25) is a load shedding limit for each node, constraint (26) defines the power limit of the battery, PB is the time when the battery is chargingi<0; at the time of discharge, PBi>0. Constraints (27) - (30) are energy limits of the battery during charge and discharge cycles to avoidAvoiding overcharge and overdischarge. Equation (31) assumes that the state of charge at the start-stop time of the battery is equal within 24 hours.
3.2) System running cost assessment
The optimization objective includes three aspects: firstly, load reduction is reduced to the maximum extent so as to ensure the operation reliability of the system; secondly, the running cost of the unit is reduced to the maximum extent, and the economical efficiency of the system is ensured. And thirdly, the abandoned wind is reduced to the greatest extent, so that the operation is more environment-friendly. For details, see (32), the constraints are already indicated in (20) - (31).
3.3) benefit/cost analysis
The objective of the overall economic analysis is to maximize the benefit, i.e., minimize the total cost.
min T＝I+O+R (33)
Where I, O and R are the investment, operation, and risk costs, respectively.
Estimating annual investment of new power equipment using the coefficient of capital recovery:
where A is the equivalent annual investment in electrical equipment, V is the actual investment in purchasing the equipment, i is the discount rate, and n is the economic life of the equipment.
For the optimization objective shown in (32), the first part is the risk cost R in (33), and the second and third parts are the operating cost O in (33).
To verify the feasibility and effectiveness of using retired batteries in power systems, benefit/cost analysis was performed to demonstrate that the use of retired batteries has some economic benefit compared to systems that do not use battery energy storage:
T′＝Ow+Rw-(Oo+Ro)-I＞0 (35)
wherein O iswAnd RwIs a system containing a retired batteryRunning and risk costs of OoAnd RoIs the operating and risk cost of a battery-less system, and I is the investment cost.
A significant amount of new battery investment may be saved by using retired batteries of electric vehicles, but there are other investments in equipment (such as power transformers) used to connect retired batteries to the power system. To determine the secondary retirement schedule for a retired battery, benefit/cost analysis is employed to find the maximum benefit.
4) Performing benefit/cost analysis, and determining a secondary retirement schedule of the retired battery:
a flow chart for verifying the feasibility and effectiveness of using retired batteries in a power generation and transmission system operational reliability analysis is shown in fig. 1. Fig. 1 illustrates the whole process of fully utilizing the retired battery to evaluate the benefits in the power system, which includes the following detailed steps:
4.1) collecting the retired batteries from the electric vehicles and testing the health status of the batteries to obtain the performance distribution.
4.2) the battery is connected as a battery module and is ready for connection to the power system.
4.3) evaluating the operation reliability and the operation cost of the power generation and transmission system with the retired battery. It is assumed that the battery capacity per month in this patent remains unchanged, so the actual capacity of the battery module is updated once per month.
4.4) performing benefit/cost analysis and determining the secondary retirement time of the retired batteries.
Table 2 load shedding per load node in modified RTS-79 system
Claims (8)
1. The method for evaluating the running reliability of the retired electric automobile battery as a power generation and transmission system with large-scale energy storage is characterized by mainly comprising the following steps of:
1) and establishing the capacity degradation model of the retired battery.
2) Obtaining a plurality of retired batteries, and evaluating the health states of the retired batteries by using a retired battery capacity degradation model;
3) and establishing a battery module capacity probability model and a battery module operation reliability model.
4) Designing a battery module based on a battery module capacity probability model and a battery module operation reliability model, and connecting the retired battery to a power generation and transmission system;
5) establishing a power generation and transmission system operation reliability evaluation model containing retired batteries;
6) and establishing a return/cost analysis model of the power generation and transmission system containing the retired battery, and determining a secondary retirement time table of the retired battery.
2. The method for evaluating the running reliability of the retired electric vehicle battery as a large-scale energy storage power generation and transmission system according to claim 1 or 2, wherein the method for establishing the retired battery capacity degradation model mainly comprises the following steps:
1) calculating the state of health SOH of the battery, namely:
in the formula, QiniIs the initial capacity of the unused battery; q is the maximum discharge capacity of the current decommissioned battery;
2) calculating calendar degradation factor α for battery capacitycapAnd a cyclic degradation factor βcapNamely:
αcap＝(7.543×V-23.75)×106×e-6976/T(2)
wherein V is a voltage; t is the temperature;
is the second order average voltage; DoD is depth of discharge; DoD ∈ [0,1 ]]；
3) Calendar degradation factor α using battery capacitycapAnd a cyclic degradation factor βcapUpdating the state of health SOH of the battery, namely:
wherein t is time, QtIs the charge throughput.
3. The method for evaluating the operational reliability of the retired electric vehicle battery as a large-scale energy storage power generation and transmission system according to claim 1 or 2, wherein the method for evaluating the health state of the retired battery by using a retired battery capacity degradation model comprises the following main steps:
1) judging that the maximum discharge capacity Q of the current retired battery is more than or equal to 80 percent QiniIf yes, inputting the maximum discharge capacity Q of the current retired battery into a retired battery capacity degradation model, and calculating to obtain the SOH of the retired battery; if not, entering the step 2);
2) acquiring retired battery capacity attenuation process data by using a retired battery capacity degradation model, and fitting the retired battery capacity attenuation process data to obtain a retired battery capacity attenuation function;
3) and calculating to obtain the capacity Q of the retired battery after attenuation by using a retired battery capacity attenuation function, inputting the capacity Q of the retired battery after attenuation into a retired battery capacity degradation model, and calculating to obtain the SOH of the retired battery.
4. The method for evaluating the operational reliability of retired electric vehicle batteries as a large-scale energy storage power generation and transmission system according to claim 3, wherein: the retired battery capacity decay function is as follows:
in the formula, ai、biAnd ciRepresenting the fitting parameters; i is 1,2, 3; and x is the equivalent charge-discharge cycle number or the equivalent service time.
5. The method for evaluating the reliability of the operation of the retired electric vehicle battery as a power generation and transmission system with large-scale energy storage according to claim 1, wherein the method for establishing the probability model of the capacity of the battery module comprises the following main steps:
1) the state of health of the battery is divided into N levels, namely:
g＝{g1,g2,...,gN} (6)
wherein g represents a health status grade;
calculating the probability q that the capacity of the current retired battery belongs to the health state level llNamely:
ql＝F(gl_high)-F(gl_low) (7)
wherein F (x) is a cumulative distribution function of a normal distribution, gl_highAnd gl_lowHighest and lowest health status for class i, respectively;
2) adjusting the domain to obtain the domain-adjusted cumulative distribution function F1(x) Namely:
3) probability Q of belonging to health state class l when capacity of retired battery is updated to be Ql', i.e.:
4) generating a decommissioned battery state of health function, namely:
5) determining a battery health state function when the retired batteries are connected in series and a battery health state function when the retired batteries are connected in parallel based on a formula 10;
the battery state of health function when retired batteries are connected in series is as follows:
the battery state of health function when the retired batteries are connected in parallel is as follows:
6) updating the health state function of the retired battery by using a formula (11) to obtain the health state function of any series circuit in the battery module, namely:
in the formula, ksIs the synthetic health status grade after the defined tandem composition operation; f. ofsIndicating the probability corresponding to each level.
7) Based on formula (13), calculating to obtain a health state function of the battery modules with a plurality of parallel circuits, namely:
in the formula, hsIs the synthetic health status level after parallel operation; p is a radical ofsIs the corresponding probability;
8) based on equation (14), the state of health probability distribution of the battery module is calculated, namely:
wherein f (x) and F (x) are the probability density function and the cumulative distribution function of the healthy state of the battery module.
6. The method for evaluating the operational reliability of the retired electric vehicle battery as a power generation and transmission system with large-scale energy storage according to claim 1, wherein the operational reliability model of the battery module is as follows:
in the formula, Q is the maximum discharge capacity of the battery module; si,jState parameters of the retired battery; p is the probability of failure of each cell; qrealThe available capacity of the battery module is taken into account;
wherein, the state parameter S of the retired batteryi,jAs follows:
during operation of the battery Si,jWhen the battery is not operating, S is 1i,j0, may be determined using a monte carlo sampling method.
Wherein the random number U is generated according to a uniform distribution U (0, 1); si,j1 represents the operation of the retired battery; si,j0 indicates that the retired battery is not operating.
7. The method for evaluating the operational reliability of a retired electric vehicle battery as a power generation and transmission system with large-scale energy storage according to claim 1, wherein the method for establishing the operational reliability evaluation model of the power generation and transmission system with the retired battery mainly comprises the following steps:
1) establishing an objective function of an operation reliability evaluation model of a power generation and transmission system containing retired batteries, namely:
in the formula, ωiIs an important factor of the load of the node i, CiIs the load reduction amount of the node i.
2) Establishing constraint conditions of an operation reliability evaluation model, wherein the constraint conditions comprise a line power flow constraint, a line rated capacity constraint, a power balance constraint of a power generation and transmission system, a power upper limit and lower limit constraint of a generator, a wind turbine generator output power constraint, a node load reduction constraint, a battery power limit condition, an energy limit condition of a battery in charging and discharging cycles and a charge state condition of the battery at the starting and stopping time within 24 hours;
the current constraints for each line are as follows:
T(S)＝A(S)(PG+PW-W-PD+C+PB) (20)
the line rated capacity constraints are as follows:
the power balance constraints of a power generation and transmission system are as follows:
the constraints of the generator power upper and lower limits of the power generation and transmission system are as follows:
the output power constraint of the wind turbine generator is as follows:
the node load shedding constraints are as follows:
0≤Ci,t≤PDi,t(i∈ND,t＝1,2,...,24) (25)
the battery power limit conditions are as follows:
the energy limit conditions of the battery during the charge and discharge cycles are as follows:
SoC(t)＝SoC(t-1)-PB/SoCmax(t＝1,2,...,24) (27)
10％≤SoC(t)≤95％(t＝1,2,...,24) (28)
the start-stop state-of-charge conditions for the cell over 24 hours are as follows:
in the formula, NBM is a node set connected with an energy storage system, ND is a load node set, NW is a node set connected with a wind farm, and NG is a generator node set. T (S) is the active vector of the interrupt state S, A (S) is the incidence matrix of the active power and power injection of the interrupt state S, PG is the active power injection vector, PW is the wind energy output vector, W is the wind curtailment vector, PD is the active load vector, C is the load curtailment vector, PB is the battery charging or discharging vector, T (S) is the active power vector of the interrupt state S, A (S) is the incidence matrix of the active power and power injection of the interrupt state SkIs the flow of power on the line k,
is the limit of the power flow on the line k,
is the active power of node i of the generatorThe lower limit of the rate is,
is the upper active power limit of the generator node i,
is the output power limit of the wind turbine node i,
is the maximum power limit during discharge of the battery,
is the maximum power limit, SoC, during battery chargingmaxIs the battery capacity, soc (t) is the state of charge of the battery at time t; l is the total number of lines;
3) optimizing the objective function based on the constraint conditions of the operation reliability evaluation model, namely:
8. the method for evaluating the reliability of the operation of the retired electric vehicle battery as a large-scale energy storage power generation and transmission system according to claim 1, wherein the method for establishing the return/cost analysis model of the power generation and transmission system with the retired battery mainly comprises the following steps:
1) establishing an objective function of a return/cost analysis model of a power generation and transmission system with retired batteries, namely:
min T＝I+O+R (33)
where I, O and R are the total available cost, operating cost, and risk cost, respectively.
2) Calculating the annual cost of the power generation and transmission system with the retired battery, namely:
wherein A is the equivalent annual cost of the power equipment; v is the equipment purchase cost; i is the discount rate; n is the economic life of the device;
3) calculating the return/cost T' of the power generation and transmission system with the retired battery, namely:
T′＝Ow+Rw-(Oo+Ro)-I＞0 (35)
in the formula, OwAnd RwIs an operational and risk cost of a system containing retired batteries; o isoAnd RoIs an operating and risk cost for a battery-less system; i is the total cost available.
4) Determining a secondary retirement schedule for a retired battery to satisfy equation (36):
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