CN107220752A - Consider the lithium battery energy storage battery frequency modulation Cost accounting method of life-span impairment effect - Google Patents
Consider the lithium battery energy storage battery frequency modulation Cost accounting method of life-span impairment effect Download PDFInfo
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Abstract
The present invention is a kind of lithium battery energy storage battery frequency modulation Cost accounting method for considering life-span impairment effect, its feature, including the Influencing Mechanism that operating condition is detracted to the lithium battery energy storage battery life-span is analyzed, lithium battery energy storage battery system participates in the control strategy design of power system frequency modulation and considers the contents such as the energy storage frequency modulation the cost accounting model structure of life-span detraction.The problem of this method is difficult to adjust for the frequency modulation cost that lithium battery energy storage battery performance degradation in operating condition is brought, consider lithium battery quiescent dissipation under operating condition, dynamic loss, initial outlay, operation expense and energy storage and participate in many factors such as the control strategy of frequency modulation, accurate Cost accounting method is provided to adjust energy-storage system participation power grid frequency modulation, the development for participating in power system assisted hatching to promotion energy storage is significant, with scientific and reasonable, strong applicability, the advantages of effect is good.
Description
Technical field
The present invention relates to technical field of new energy power generation, be a kind of lithium battery energy storage battery frequency modulation for considering life-span impairment effect into
This accounting method.
Background technology
As large-scale wind power concentrates access power network, because the strong fluctuation and Wind turbines near-zero of wind power are used to
Property, high wind-powered electricity generation infiltration power system frequency modulation faces the frequency modulation burden of sternness, and wind power fluctuation causes traditional frequency modulation machine
Group frequent movement, makes mechanical devices wear and tear, detracts the service life of frequency modulation unit, so high wind-powered electricity generation infiltration power network is badly in need of newly
Frequency modulation means.
Energy-storage system has flexible, quick power adjusting response characteristic, and participating in power system using extensive energy storage adjusts
Frequency is received significant attention, but because current energy storage is relatively expensive, and China not yet sets up effective energy storage frequency modulation compensation
Mechanism, the enthusiasm that energy storage participates in power system frequency modulation is not yet excited, and it is to formulate energy storage frequency modulation to mend to adjust energy storage frequency modulation cost
The important evidence of strategy is repaid, there is important value to promoting energy storage to participate in the development of power system assisted hatching；Energy storage frequency modulation
Cost was both relevant with the Technical Economy of energy-storage system itself, also with the factor such as energy storage chirping strategies, system frequency wave characteristic
Relevant, the nominal service life that energy-storage system manufacturer provides is the energy-storage system cycle charge-discharge under specific charge and discharge mode
Number of times is weighed, but energy storage is when participating in power grid frequency modulation, and its charge and discharge mode can not possibly be complete with life test charge and discharge mode
Consistent and then cause energy storage life-span and producer nominal life under hopping pattern to differ greatly, conventional cost accounting is based on nominally
Cost is shared equally in the life-span time limit, and this is very big with actual cost difference, therefore, is needed structure badly and is considered energy-storage battery life-span impairment effect
Energy storage frequency modulation Cost accounting method want to solve and unsolved technical barrier so far always to solve this area.
The content of the invention
The technical problems to be solved by the invention are the influence machines that actual condition is detracted to the lithium battery energy storage battery life-span of analyzing
Reason, builds frequency modulation control strategy, sets up the lithium battery energy storage battery frequency modulation the cost accounting model for considering life-span detraction, analyzes different frequency modulation
Energy-storage system frequency modulation estimates service life and average annual cost, a kind of lithium battery storage for considering life-span impairment effect of proposition under dead band
Can frequency modulation Cost accounting method.
Solving the scheme of its technical problem use is, a kind of lithium battery energy storage battery frequency modulation cost core for considering life-span impairment effect
Calculation method, it is characterized in that, it comprises the following steps：
1) service life of lithium battery impairment model
Described service life of lithium battery refers to that stored energy capacitance conservation rate is not less than rule under given environment temperature and charge and discharge mode
The persistent loop discharge and recharge number of times allowed during constant volume,
Service life of lithium battery loss is the life-span caused by the deterioration of lithium battery material functional characteristic and the change of lithium battery working condition
Loss, it is closely related with lithium battery use time, charging and discharging state and temperature factor, represented with the percent reduction in life-span,
Service life of lithium battery loss is divided into quiescent dissipation and dynamic loss, is (1) formula：
X=XS+XD (1)
Quiescent dissipation XSTo be lost caused by the deterioration of lithium battery material functional characteristic, this partition losses and operating condition without
Close, only with battery standing duration linear correlation, year quiescent dissipation XSIt is calculated as (2) formula：
In formula：T is battery shelf-life/year,
Dynamic loss XDCorrespondence lithium battery operational state change caused by be lost, mode of operation include depth of discharge and
Speed, the discharge and recharge dynamic process of correspondence lithium battery, because actual condition is acyclic charge and discharge process, so caused
Life consumption is also nonlinear, it is necessary to calculate its dynamic loss, dynamic loss X with reference to actual conditionDIt is calculated as (3) formula：
In formula：Ck(ij)For k-th of discharge and recharge interval state-of-charge SOC, cycle charge-discharge is actual to lithium battery between i to j
Capacity is maintained at the maximum cycle that 60%~100% nominal capacity is allowed, and i is that discharge and recharge starts SOC value, j discharge and recharges
Terminate SOC value, n is charge or discharge periodicity in sample time；
Dynamic loss 1/Ck(ij)For (4) formula：
In formula：Ci60% is maintained at for cycle charge-discharge between SOC=i to SOC=100% to lithium battery actual capacity~
The maximum cycle that 100% nominal capacity is allowed, the dynamic loss 1/C of (4) formulak(ij)SOC is interpreted as between i to j
Dynamic loss subtracts dynamic loss of the SOC from j to 100% equal to dynamic loss of the SOC from i to 100%；
Life-span in year impairment model is (5) formula to lithium battery in the process of running：
It is (5) formula according to life-span in year impairment model, need to only analyzes cycle-index and state-of-charge SOC or the electric discharge of lithium battery
Relation between depth DOD, just can refine calculating lithium battery in actual condition, the life-span of the interval lithium battery of any discharge and recharge
It is lost, and then calculates lithium battery and estimates service life in actual condition；
2) influence of the depth of discharge to lithium battery service life
The cycle life test condition of international regulations lithium battery and requirement, the main test event of UN lithium ion battery standards and
Index, with constant current constant voltage mode 1C charging system discharge and recharge under 20 ± 5 degree of room temperature conditions, with depth of discharge DOD=80%
For each discharge and recharge index, the cycle life of lithium battery is maintained at circulation time more than 60% nominal capacity for actual capacity
Number,
The measured data provided according to producer, under standard condition, using different depth of discharge as each charge and discharge criteria,
Cycle-index when lithium battery actual capacity conservation rate drops to rated capacity below 60%, is in given depth of discharge situation
The functional relation of the cycle life number of times of lower lithium battery, depth of discharge DOD and cycle life is approximately e index relation, and to following
Ring life-span and DOD measured data carry out e index fitting, and fitting formula is (6) formula：
In formula：CiIt is DOD for depth of discharge DODiIn the case of cycle life number of times,
By DODi=1-SOCi, represent with DODiFor depth of discharge index, lithium battery charge state SOC is in 100% and SOCi
Between cycle charge-discharge, the functional relation for obtaining cycle life and state-of-charge SOC is (7) formula：
To sum up, it is considered to which the lithium battery year life-span impairment model of depth of discharge influence is (8) formula：
3) lithium battery energy storage battery system participates in the control strategy of power grid frequency modulation
Energy storage power output is constrained to (9) formula：
Pmin(t)≤P(t)≤Pmax(t) (9)
In formula：P is the charge-discharge electric power of lithium battery energy storage battery system, P (t)>0, lithium battery energy storage battery system is operated in charging shape
State, P (t)<0, lithium battery energy storage battery system is operated in discharge condition；
Energy storage charge state is constrained to (10) formula-(11) formula：
SOCmin≤SOC(t+Δt)≤SOCmax (11)
In formula：EESSFor the rated capacity of lithium battery energy storage battery system, wfrFor the frequency modulation electricity of energy storage, η is lithium battery energy storage battery system
The efficiency of system, SOCminFor the minimum value of lithium battery charge state, SOCmaxFor the maximum of lithium battery charge state, lithium battery storage
Energy system will meet capacity and state-of-charge constraint in the process of running；
Lithium battery energy storage battery system enters line frequency regulation, is the two-way flow using the energy content of battery, to prevent system frequency
Deviate the regulative mode of critical field；When power network is powered more than workload demand, system frequency is increased beyond upper threshold frequency fref1
When lithium battery energy storage battery system with frequency departure and unit power regulation KESSProduct be charge power value, from power network absorb electric energy,
Until system frequency drops to upper threshold frequency fref1Untill interior；Power network is powered less than workload demand, and system frequency is decrease beyond
Limit inferior frequency fref2When, battery lithium battery energy storage system is with frequency departure and unit power regulation KESSProduct for electric discharge work(
Rate value, discharges electric energy, until system frequency rises to limit inferior frequency f to power networkref2Untill interior；Lithium battery energy storage battery system unit
Adjust power KESSValue is directly connected to the effect of control strategy；The charge power of lithium battery energy storage battery system is (12) formula
By (12) formula it can be seen that the upper threshold frequency f of Regulation dead-band, i.e. Regulation dead-bandref1, limit inferior frequency fref2Really
Surely the charge-discharge electric power P of lithium battery energy storage battery system is directly influenced, the frequency modulation electricity of lithium battery energy storage battery system is also just directly affected
And life consumption, finally influence energy storage estimates service life TLC；
4) the energy storage frequency modulation the cost accounting model of life-span impairment effect is considered
The cost accounting model of lithium battery energy storage battery system by the initial outlay total cost of energy storage, lithium battery energy storage battery system it is pre-
Estimate service life and operation and maintenance cost is together decided on, its frequency modulation cost model is (13) formula：
CA=CINV/TLC+CO&M (13)
In formula：CAFor the average annual cost of lithium battery energy storage battery system, CINVFor lithium battery energy storage battery system initial outlay totle drilling cost,
TLCTo consider that service life (year), C are estimated in the energy storage of life-span impairment effectO&MFor the year operation maintenance expense of lithium battery energy storage battery system
With；
CINV=λPPESS+λEEESS (14)
In formula：PESSFor the rated power of lithium battery energy storage battery system, λPFor lithium battery energy storage battery system power unit price, EESS
For the rated capacity of lithium battery energy storage battery system, λEFor lithium battery energy storage battery power system capacity unit price；
Energy storage participates in power grid frequency modulation and is mainly benefited from frequency modulation electricity wfr, for any frequency modulation interval t=i to t=j's
Frequency modulation electricity wfrBe calculated as (15) formula：
In formula：PtFor frequency modulation period t=i to t=j lithium battery energy storage battery system charge-discharge electric power,
For energy storage frequency modulation period t=i to t=j, the state-of-charge variable quantity of lithium battery energy storage battery system is：
In formula：wfr(ij)For the lithium battery energy storage battery system frequency modulation electricity of the frequency modulation period, EESSFor lithium battery energy storage battery system
Rated capacity；
According to SOC (tj) and SOC (ti) combine the dynamic that (4) formula and (7) formula just can be derived that t=i to the t=j frequency modulation periods
X is lostD, because quiescent dissipation is linearly to lose, the quiescent dissipation X of t=i to t=j frequency modulation periods is calculated according to (2) formulaS, it is comprehensive
Dynamic loss XD(3) formula of calculating, the life consumption of t=i to t=j frequency modulation periods is calculated as (17) formula,
Similarly, according to given frequency curve and Regulation dead-band, lithium battery energy storage battery system each frequency modulation period in 1 year is calculated
△ SOC changes, with reference to the life-span impairment model of lithium battery in the process of running in (8) formula, try to achieve a year energy storage year operation longevity
Life loss Xy；
Assuming that annual frequency modulation demand is close with First Year, energy storage actual capacity after 1 year is regard as Second Year lithium battery energy storage battery
The rated capacity of system, the corresponding storage energy operation life consumption for calculating Second Year, by that analogy, when storage energy operation life consumption enters
Journey reaches 100%, just show that the lithium battery energy storage battery system under corresponding Regulation dead-band estimates service life TLC,
Service life T is estimated according to lithium battery energy storage battery system under different Regulation dead-bandsLC, just can with reference to (13) formula and (14) formula
Enough calculate the average annual cost C under corresponding Regulation dead-bandA。
A kind of lithium battery energy storage battery frequency modulation Cost accounting method of consideration life-span impairment effect of the present invention, has taken into full account reality
The influence that the energy storage life-span detracts under the operating mode of border, and be introduced among energy-storage system participation power grid frequency modulation the cost accounting model,
The accuracy that energy-storage system participates in power grid frequency modulation cost accounting is improved, gives full play to that energy-storage system is flexible, quick power is adjusted
Response characteristic is saved, the development for participating in power system assisted hatching to promotion energy storage is significant, with scientific and reasonable, be applicable
Property strong, the advantages of effect is good.
Brief description of the drawings
Energy-storage battery capability retention view under Fig. 1 difference depth of discharges；
The fit correlation figure of Fig. 2 depth of discharges and cycle life；
Fig. 3 energy-storage system control structure schematic diagrames；
Fig. 4 energy-storage systems estimate service life and annual cost calculation FB(flow block).
Embodiment
Below with drawings and examples to the present invention a kind of consideration life-span impairment effect lithium battery energy storage battery frequency modulation into
This accounting method is described further.
A kind of lithium battery energy storage battery frequency modulation Cost accounting method of consideration life-span impairment effect of the present invention, it is characterized in that, it
Comprise the following steps：
1) service life of lithium battery impairment model
Described service life of lithium battery refers to that stored energy capacitance conservation rate is not less than rule under given environment temperature and charge and discharge mode
The persistent loop discharge and recharge number of times allowed during constant volume,
Service life of lithium battery loss is the life-span caused by the deterioration of lithium battery material functional characteristic and the change of lithium battery working condition
Loss, it is closely related with lithium battery use time, charging and discharging state and temperature factor, represented with the percent reduction in life-span,
Service life of lithium battery loss is divided into quiescent dissipation and dynamic loss, is (1) formula：
X=XS+XD (1)
Quiescent dissipation XSTo be lost caused by the deterioration of lithium battery material functional characteristic, this partition losses and operating condition without
Close, only with battery standing duration linear correlation, year quiescent dissipation XSIt is calculated as (2) formula：
In formula：T is battery shelf-life/year,
Dynamic loss XDCorrespondence lithium battery operational state change caused by be lost, mode of operation include depth of discharge and
Speed, the discharge and recharge dynamic process of correspondence lithium battery, because actual condition is acyclic charge and discharge process, so caused
Life consumption is also nonlinear, it is necessary to calculate its dynamic loss, dynamic loss X with reference to actual conditionDIt is calculated as (3) formula：
In formula：Ck(ij)For k-th of discharge and recharge interval state-of-charge SOC, cycle charge-discharge is actual to lithium battery between i to j
Capacity is maintained at the maximum cycle that 60%~100% nominal capacity is allowed, and i is that discharge and recharge starts SOC value, j discharge and recharges
Terminate SOC value, n is charge or discharge periodicity in sample time；
Dynamic loss 1/Ck(ij)For (4) formula：
In formula：Ci60% is maintained at for cycle charge-discharge between SOC=i to SOC=100% to lithium battery actual capacity~
The maximum cycle that 100% nominal capacity is allowed, the dynamic loss 1/C of (4) formulak(ij)SOC is interpreted as between i to j
Dynamic loss subtracts dynamic loss of the SOC from j to 100% equal to dynamic loss of the SOC from i to 100%；
Life-span in year impairment model is (5) formula to lithium battery in the process of running：
It is (5) formula according to life-span in year impairment model, need to only analyzes cycle-index and state-of-charge SOC or the electric discharge of lithium battery
Relation between depth DOD, just can refine calculating lithium battery in actual condition, the life-span of the interval lithium battery of any discharge and recharge
It is lost, and then calculates lithium battery and estimates service life in actual condition；
2) influence of the depth of discharge to lithium battery service life
The cycle life test condition of international regulations lithium battery and requirement, the main test event of UN lithium ion battery standards and
Index, with constant current constant voltage mode 1C charging system discharge and recharge under 20 ± 5 degree of room temperature conditions, with depth of discharge DOD=80%
For each discharge and recharge index, the cycle life of lithium battery is maintained at circulation time more than 60% nominal capacity for actual capacity
Number,
Fig. 1 is the energy-storage battery capability retention view under the different depth of discharges that producer provides, in standard work
Under condition, using different depth of discharge as each charge and discharge criteria, when lithium battery actual capacity conservation rate drops to rated capacity 60%
Cycle-index when following, is the cycle life number of times of the lithium battery in the case of given depth of discharge, depth of discharge DOD and is followed
The functional relation in ring life-span is approximately e index relation, and carries out e index fitting, Fig. 2 to cycle life and DOD measured data
It is depth of discharge and the fit correlation figure of cycle life, fitting formula is (6) formula：
In formula：CiIt is DOD for depth of discharge DODiIn the case of cycle life number of times,
By DODi=1-SOCi, represent with DODiFor depth of discharge index, lithium battery charge state SOC is in 100% and SOCi
Between cycle charge-discharge, the functional relation for obtaining cycle life and state-of-charge SOC is (7) formula：
To sum up, it is considered to which the lithium battery year life-span impairment model of depth of discharge influence is (8) formula：
3) lithium battery energy storage battery system participates in the control strategy of power grid frequency modulation
Energy storage power output is constrained to (9) formula：
Pmin(t)≤P(t)≤Pmax(t) (9)
In formula：P is the charge-discharge electric power of lithium battery energy storage battery system, P (t)>0, lithium battery energy storage battery system is operated in charging shape
State, P (t)<0, lithium battery energy storage battery system is operated in discharge condition；
Energy storage charge state is constrained to (10) formula-(11) formula：
SOCmin≤SOC(t+Δt)≤SOCmax (11)
In formula：EESSFor the rated capacity of lithium battery energy storage battery system, wfrFor the frequency modulation electricity of energy storage, η is lithium battery energy storage battery system
The efficiency of system, SOCminFor the minimum value of lithium battery charge state, SOCmaxFor the maximum of lithium battery charge state, lithium battery storage
Energy system will meet capacity and state-of-charge constraint in the process of running；
Lithium battery energy storage battery system enters line frequency regulation, is the two-way flow using the energy content of battery, to prevent system frequency
Deviate the regulative mode of critical field；When power network is powered more than workload demand, system frequency is increased beyond upper threshold frequency fref1
When lithium battery energy storage battery system with frequency departure and unit power regulation KESSProduct be charge power value, from power network absorb electric energy,
Until system frequency drops to upper threshold frequency fref1Untill interior；Power network is powered less than workload demand, and system frequency is decrease beyond
Limit inferior frequency fref2When, battery lithium battery energy storage system is with frequency departure and unit power regulation KESSProduct for electric discharge work(
Rate value, discharges electric energy, until system frequency rises to limit inferior frequency f to power networkref2Untill interior；Lithium battery energy storage battery system unit
Adjust power KESSValue is directly connected to the effect of control strategy；The charge power of lithium battery energy storage battery system is (12) formula
By (12) formula it can be seen that the upper threshold frequency f of Regulation dead-band, i.e. Regulation dead-bandref1, limit inferior frequency fref2Really
Surely the charge-discharge electric power P of lithium battery energy storage battery system is directly influenced, the frequency modulation electricity of lithium battery energy storage battery system is also just directly affected
And life consumption, finally influence energy storage estimates service life TLC；Fig. 3 is that the energy-storage system designed according to control strategy controls to tie
Structure schematic diagram.
4) the energy storage frequency modulation the cost accounting model of life-span impairment effect is considered
The cost accounting model of lithium battery energy storage battery system by the initial outlay total cost of energy storage, lithium battery energy storage battery system it is pre-
Estimate service life and operation and maintenance cost is together decided on, its frequency modulation cost model is (13) formula：
CA=CINV/TLC+CO&M (13)
In formula：CAFor the average annual cost of lithium battery energy storage battery system, CINVFor lithium battery energy storage battery system initial outlay totle drilling cost,
TLCTo consider that service life (year), C are estimated in the energy storage of life-span impairment effectO&MFor the year operation maintenance expense of lithium battery energy storage battery system
With；
CINV=λPPESS+λEEESS (14)
In formula：PESSFor the rated power of lithium battery energy storage battery system, λPFor lithium battery energy storage battery system power unit price, EESS
For the rated capacity of lithium battery energy storage battery system, λEFor lithium battery energy storage battery power system capacity unit price；
Energy storage participates in power grid frequency modulation and is mainly benefited from frequency modulation electricity wfr, for any frequency modulation interval t=i to t=j's
Frequency modulation electricity wfrBe calculated as (15) formula：
In formula：PtFor frequency modulation period t=i to t=j lithium battery energy storage battery system charge-discharge electric power,
For energy storage frequency modulation period t=i to t=j, the state-of-charge variable quantity of lithium battery energy storage battery system is：
In formula：wfr(ij)For the lithium battery energy storage battery system frequency modulation electricity of the frequency modulation period, EESSFor lithium battery energy storage battery system
Rated capacity；
According to SOC (tj) and SOC (ti) combine the dynamic that (4) formula and (7) formula just can be derived that t=i to the t=j frequency modulation periods
X is lostD, because quiescent dissipation is linearly to lose, the quiescent dissipation X of t=i to t=j frequency modulation periods is calculated according to (2) formulaS, it is comprehensive
Dynamic loss XD(3) formula of calculating, the life consumption of t=i to t=j frequency modulation periods is calculated as (17) formula,
Similarly, according to given frequency curve and Regulation dead-band, lithium battery energy storage battery system each frequency modulation period in 1 year is calculated
△ SOC changes, with reference to the life-span impairment model of lithium battery in the process of running in (8) formula, try to achieve a year energy storage year operation longevity
Life loss Xy；
Assuming that annual frequency modulation demand is close with First Year, energy storage actual capacity after 1 year is regard as Second Year lithium battery energy storage battery
The rated capacity of system, the corresponding storage energy operation life consumption for calculating Second Year, by that analogy, when storage energy operation life consumption enters
Journey reaches 100%, just show that the lithium battery energy storage battery system under corresponding Regulation dead-band estimates service life TLC,
Service life T is estimated according to lithium battery energy storage battery system under different Regulation dead-bandsLC, just can with reference to (13) formula and (14) formula
Enough calculate the average annual cost C under corresponding Regulation dead-bandA；Fig. 4 is that energy-storage system estimates service life and annual cost calculation stream
Journey block diagram.
Instantiation：Analyzed using northeast wind power plant measured data, it is double that the wind power plant assembles 64 G58-850kW
Present induction wind driven generator group, wind power plant rated power PNWF=54.4MW, corresponding configuration energy-storage system rated power is Δ PESS
=4.352MW, is rounded as 5MW；To reach synchronous generator primary frequency modulation effect, energy-storage system difference coefficient and synchronous hair are adjusted
Motor is consistent, draws energy-accumulating power station with unit power regulation KESS=0.4 × PNWF=21.76MW/Hz；According to power system frequency modulation
Demand (including first and second frequency modulation) is about 30min, stored energy capacitance EESS=5MW × 0.5h=2.5MWh；Energy-storage battery is selected
The best ferric phosphate lithium cell of current application prospect；Energy-storage system power capacity price is as shown in table 1；Wind power plant practical frequency number
It it is 1 minute according to the sampling period, data volume is 525600；
The system of table 1 installation situation and energy-storage system power/capacity parameter
Under above-mentioned example environment, service life and its average annual cost are estimated to energy-storage system such as using the inventive method
Under：
When the action reference value of frequency modulation is participated in using different Regulation dead-bands as energy-storage system, calculate and stored up under different Regulation dead-bands
Can system estimate service life and annual cost such as table 2,
Service life and average annual cost are estimated in energy storage under the different Regulation dead-bands of table 2
As shown in Table 2, if sharing within 15 years calculating equally according to producer's nominal life, the average annual cost of energy storage is only 76.7 ten thousand
Member, and under actual condition, only setting Regulation dead-band could be close to this data, when Regulation dead-band is as ± more than 0.06Hz
During ± 0.033Hz, energy storage to estimate service life minimum, only 5.95, its average annual 1750000 yuan of cost is also remote super to share cost equally
76.7 ten thousand yuan, it is found that with given Regulation dead-band set it is smaller, the action of lithium battery energy storage battery system is more frequent, lithium electricity
The service life of pond energy storage is also shorter, and corresponding average annual cost is also bigger, if the complete feelings of following assistant service mechanism
Under condition, the year frequency modulation benefit under corresponding Regulation dead-band can be more than the average annual cost of energy storage, just illustrate that energy-storage system can be realized
True profit.
Design conditions, legend, table in the embodiment of the present invention etc. are only used for that the present invention is further illustrated, not thoroughly
Lift, do not constitute the restriction to claims, the enlightenment that those skilled in the art obtain according to embodiments of the present invention,
Other substantially equivalent replacements are would occur to without creative work, are all fallen in the scope of protection of the present invention.
Claims (1)
1. a kind of lithium battery energy storage battery frequency modulation Cost accounting method for considering life-span impairment effect, it is characterized in that, it includes following step
Suddenly：
1) service life of lithium battery impairment model
Described service life of lithium battery refers to that stored energy capacitance conservation rate is not less than regulation appearance under given environment temperature and charge and discharge mode
The persistent loop discharge and recharge number of times allowed during amount,
Service life of lithium battery loss is life consumption caused by the deterioration of lithium battery material functional characteristic and the change of lithium battery working condition,
It is closely related with lithium battery use time, charging and discharging state and temperature factor, represented with the percent reduction in life-span, by lithium electricity
Pond life consumption is divided into quiescent dissipation and dynamic loss, is (1) formula：
X=XS+XD (1)
Quiescent dissipation XSIt is to be lost caused by the deterioration of lithium battery material functional characteristic, this partition losses is unrelated with operating condition, only
With battery standing duration linear correlation, year quiescent dissipation XSIt is calculated as (2) formula：
<mrow>
<msub>
<mi>X</mi>
<mi>S</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>100</mn>
<mi>%</mi>
</mrow>
<mi>T</mi>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：T is battery shelf-life/year,
Dynamic loss XDIt is lost caused by the operational state change of correspondence lithium battery, mode of operation includes depth of discharge and speed,
The discharge and recharge dynamic process of correspondence lithium battery, because actual condition is acyclic charge and discharge process, so the caused life-span
Loss is also nonlinear, it is necessary to calculate its dynamic loss, dynamic loss X with reference to actual conditionDIt is calculated as (3) formula：
<mrow>
<msub>
<mi>X</mi>
<mi>D</mi>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mn>1</mn>
<mo>/</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>k</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mi>j</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：Ck(ij)For k-th of discharge and recharge interval state-of-charge SOC between i to j cycle charge-discharge to lithium battery actual capacity
The maximum cycle that 60%~100% nominal capacity is allowed is maintained at, i is that discharge and recharge starts SOC value, and j discharge and recharges terminate
SOC value, n is charge or discharge periodicity in sample time；
Dynamic loss 1/Ck(ij)For (4) formula：
<mrow>
<mfrac>
<mn>1</mn>
<msub>
<mi>C</mi>
<mrow>
<mi>k</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mi>j</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>2</mn>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>2</mn>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：CiFor cycle charge-discharge between SOC=i to SOC=100% 60%~100% is maintained to lithium battery actual capacity
The maximum cycle that nominal capacity is allowed, the dynamic loss 1/C of (4) formulak(ij)It is interpreted as dynamic damages of the SOC between i to j
Consumption subtracts dynamic loss of the SOC from j to 100% equal to dynamic loss of the SOC from i to 100%；
Life-span in year impairment model is (5) formula to lithium battery in the process of running：
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<mi>X</mi>
<mo>=</mo>
<msub>
<mi>X</mi>
<mi>S</mi>
</msub>
<mo>+</mo>
<msub>
<mi>X</mi>
<mi>D</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>100</mn>
<mi>%</mi>
</mrow>
<mi>T</mi>
</mfrac>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mo>|</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>2</mn>
<msub>
<mi>C</mi>
<mrow>
<mi>k</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>2</mn>
<msub>
<mi>C</mi>
<mrow>
<mi>k</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>|</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
It is (5) formula according to life-span in year impairment model, need to only analyzes the cycle-index and state-of-charge SOC or depth of discharge of lithium battery
Relation between DOD, just can refine calculating lithium battery in actual condition, and the life-span of the interval lithium battery of any discharge and recharge damages
Consume, and then calculate lithium battery and estimate service life in actual condition；
2) influence of the depth of discharge to lithium battery service life
The cycle life test condition of international regulations lithium battery and requirement, the main test event of UN lithium ion battery standards and refer to
Mark, with constant current constant voltage mode 1C charging system discharge and recharge under 20 ± 5 degree of room temperature conditions, using depth of discharge DOD=80% as
Each discharge and recharge index, the cycle life of lithium battery is the cycle-index that actual capacity is maintained at more than 60% nominal capacity,
The measured data provided according to producer, under standard condition, using different depth of discharge as each charge and discharge criteria, works as lithium
Cycle-index when battery actual capacity conservation rate drops to rated capacity below 60%, is the lithium in the case of given depth of discharge
The functional relation of the cycle life number of times of battery, depth of discharge DOD and cycle life is approximately e index relation, and to the circulation longevity
Life and DOD measured data carry out e index fitting, and fitting formula is (6) formula：
<mrow>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>28270</mn>
<msup>
<mi>e</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mn>2.401</mn>
<msub>
<mi>DOD</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msup>
<mo>+</mo>
<mn>2.214</mn>
<msup>
<mi>e</mi>
<mrow>
<mo>(</mo>
<mn>5.901</mn>
<msub>
<mi>DOD</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：CiIt is DOD for depth of discharge DODiIn the case of cycle life number of times,
By DODi=1-SOCi, represent with DODiFor depth of discharge index, lithium battery charge state SOC is in 100% and SOCiBetween
Cycle charge-discharge, the functional relation for obtaining cycle life and state-of-charge SOC is (7) formula：
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<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>28270</mn>
<msup>
<mi>e</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mn>2.401</mn>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>SOC</mi>
<mi>i</mi>
</msub>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</msup>
<mo>+</mo>
<mn>2.214</mn>
<msup>
<mi>e</mi>
<mrow>
<mo>(</mo>
<mn>5.901</mn>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>SOC</mi>
<mi>i</mi>
</msub>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
To sum up, it is considered to which the lithium battery year life-span impairment model of depth of discharge influence is (8) formula：
<mrow>
<mi>X</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>100</mn>
<mi>%</mi>
</mrow>
<mi>T</mi>
</mfrac>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mo>|</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>2</mn>
<mo>&times;</mo>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<mn>28270</mn>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mn>2.401</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>SOC</mi>
<mi>i</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</msup>
<mo>+</mo>
<mn>2.214</mn>
<msup>
<mi>e</mi>
<mrow>
<mn>5.901</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>SOC</mi>
<mi>i</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>2</mn>
<mo>&times;</mo>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<mn>28270</mn>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mn>2.401</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>SOC</mi>
<mi>j</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</msup>
<mo>+</mo>
<mn>2.214</mn>
<msup>
<mi>e</mi>
<mrow>
<mn>5.901</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>SOC</mi>
<mi>j</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mfrac>
<mo>|</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
3) lithium battery energy storage battery system participates in the control strategy of power grid frequency modulation
Energy storage power output is constrained to (9) formula：
Pmin(t)≤P(t)≤Pmax(t) (9)
In formula：P is the charge-discharge electric power of lithium battery energy storage battery system, P (t)>0, lithium battery energy storage battery system is operated in charged state, P
(t)<0, lithium battery energy storage battery system is operated in discharge condition；
Energy storage charge state is constrained to (10) formula-(11) formula：
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<mi>S</mi>
<mi>O</mi>
<mi>C</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>+</mo>
<mi>&Delta;</mi>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>S</mi>
<mi>O</mi>
<mi>C</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>w</mi>
<mrow>
<mi>f</mi>
<mi>r</mi>
</mrow>
</msub>
<mi>&eta;</mi>
</mrow>
<msub>
<mi>E</mi>
<mrow>
<mi>E</mi>
<mi>S</mi>
<mi>S</mi>
</mrow>
</msub>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
SOCmin≤SOC(t+Δt)≤SOCmax (11)
In formula：EESSFor the rated capacity of lithium battery energy storage battery system, wfrFor the frequency modulation electricity of energy storage, η is lithium battery energy storage battery system
Efficiency, SOCminFor the minimum value of lithium battery charge state, SOCmaxFor the maximum of lithium battery charge state, lithium battery energy storage battery system
System will meet capacity and state-of-charge constraint in the process of running；
Lithium battery energy storage battery system enters line frequency regulation, is the two-way flow using the energy content of battery, to prevent system frequency from deviateing
The regulative mode of critical field；When power network is powered more than workload demand, system frequency is increased beyond upper threshold frequency fref1Shi Li
Battery energy storage system is with frequency departure and unit power regulation KESSProduct be charge power value, from power network absorb electric energy, until
System frequency drops to upper threshold frequency fref1Untill interior；Power network is powered less than workload demand, and system frequency decrease beyond lower pole
Limit frequency fref2When, battery lithium battery energy storage system is with frequency departure and unit power regulation KESSProduct be discharge power value,
Electric energy is discharged to power network, until system frequency rises to limit inferior frequency fref2Untill interior；Lithium battery energy storage battery system unit is adjusted
Power KESSValue is directly connected to the effect of control strategy；The charge power of lithium battery energy storage battery system is (12) formula
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<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>p</mi>
<mo>=</mo>
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</msub>
<mo>&times;</mo>
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<mi>r</mi>
<mi>e</mi>
<mi>f</mi>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>p</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
<mtd>
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<mi>f</mi>
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<mi>r</mi>
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<mi>f</mi>
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<mo>(</mo>
<mi>f</mi>
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<mi>r</mi>
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</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
By (12) formula it can be seen that the upper threshold frequency f of Regulation dead-band, i.e. Regulation dead-bandref1, limit inferior frequency fref2Determination it is straight
The charge-discharge electric power P for having influence on lithium battery energy storage battery system is met, frequency modulation electricity and the longevity of lithium battery energy storage battery system is also just directly affected
Life loss, finally influence energy storage estimates service life TLC；
4) the energy storage frequency modulation the cost accounting model of life-span impairment effect is considered
The cost accounting model of lithium battery energy storage battery system estimates fortune by the initial outlay total cost of energy storage, lithium battery energy storage battery system
Row life-span and operation and maintenance cost are together decided on, and its frequency modulation cost model is (13) formula：
CA=CINV/TLC+CO&M (13)
In formula：CAFor the average annual cost of lithium battery energy storage battery system, CINVFor lithium battery energy storage battery system initial outlay totle drilling cost, TLCFor
Consider that service life (year), C are estimated in the energy storage of life-span impairment effectO&MFor the year operation and maintenance cost of lithium battery energy storage battery system；
CINV=λPPESS+λEEESS (14)
In formula：PESSFor the rated power of lithium battery energy storage battery system, λPFor lithium battery energy storage battery system power unit price, EESSFor lithium
The rated capacity of battery energy storage system, λEFor lithium battery energy storage battery power system capacity unit price；
Energy storage participates in power grid frequency modulation and is mainly benefited from frequency modulation electricity wfr, for any frequency modulation interval t=i to t=j frequency modulation
Electricity wfrBe calculated as (15) formula：
<mrow>
<msub>
<mi>w</mi>
<mrow>
<mi>f</mi>
<mi>r</mi>
</mrow>
</msub>
<mo>=</mo>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mi>i</mi>
</mrow>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mi>j</mi>
</mrow>
</msubsup>
<msub>
<mi>p</mi>
<mi>t</mi>
</msub>
<mi>d</mi>
<mi>t</mi>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mi>i</mi>
</mrow>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mi>j</mi>
</mrow>
</munderover>
<msub>
<mi>p</mi>
<mi>t</mi>
</msub>
<mo>&times;</mo>
<mi>&Delta;</mi>
<mi>t</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：PtFor frequency modulation period t=i to t=j lithium battery energy storage battery system charge-discharge electric power,
For energy storage frequency modulation period t=i to t=j, the state-of-charge variable quantity of lithium battery energy storage battery system is：
<mrow>
<mi>S</mi>
<mi>O</mi>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>S</mi>
<mi>O</mi>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>w</mi>
<mrow>
<mi>f</mi>
<mi>r</mi>
</mrow>
</msub>
<mi>&eta;</mi>
</mrow>
<msub>
<mi>E</mi>
<mrow>
<mi>E</mi>
<mi>S</mi>
<mi>S</mi>
</mrow>
</msub>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>16</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：wfr(ij)For the lithium battery energy storage battery system frequency modulation electricity of the frequency modulation period, EESSFor the specified of lithium battery energy storage battery system
Capacity；
According to SOC (tj) and SOC (ti) combine the dynamic loss that (4) formula and (7) formula just can be derived that t=i to the t=j frequency modulation periods
XD, because quiescent dissipation is linearly to lose, the quiescent dissipation X of t=i to t=j frequency modulation periods is calculated according to (2) formulaS, comprehensive dynamic
X is lostD(3) formula of calculating, the life consumption of t=i to t=j frequency modulation periods is calculated as (17) formula,
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<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mo>(</mo>
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<mi>X</mi>
<mi>S</mi>
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<msub>
<mi>X</mi>
<mi>D</mi>
</msub>
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<mn>365</mn>
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<mn>24</mn>
<mo>&times;</mo>
<mn>60</mn>
</mrow>
</mfrac>
<mo>*</mo>
<mn>100</mn>
<mi>%</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
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<mo>|</mo>
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<mn>1</mn>
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<mn>28270</mn>
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<mo>+</mo>
<mn>2.214</mn>
<msup>
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<mrow>
<mn>5.901</mn>
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<mo>(</mo>
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<mo>-</mo>
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<mn>17</mn>
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Similarly, according to given frequency curve and Regulation dead-band, the △ of lithium battery energy storage battery system each frequency modulation period in 1 year is calculated
SOC changes, with reference to the life-span impairment model of lithium battery in the process of running in (8) formula, tries to achieve year energy storage year service life and damages
Consume Xy；
Assuming that annual frequency modulation demand is close with First Year, energy storage actual capacity after 1 year is regard as Second Year lithium battery energy storage battery system
Rated capacity, the corresponding storage energy operation life consumption for calculating Second Year, by that analogy, when storage energy operation life consumption process reaches
To 100%, just show that the lithium battery energy storage battery system under corresponding Regulation dead-band estimates service life TLC,
<mrow>
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<mo>=</mo>
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<mi>C</mi>
</mrow>
</msub>
</mrow>
</munderover>
<msub>
<mi>X</mi>
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<mn>18</mn>
<mo>)</mo>
</mrow>
</mrow>
Service life T is estimated according to lithium battery energy storage battery system under different Regulation dead-bandsLC, just can be counted with reference to (13) formula and (14) formula
Calculate the average annual cost C under corresponding Regulation dead-bandA。
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