Real Time Health Estimation of DESD

Yuhua Du, Rishabh Jain, Srdjan LukicObjective:

Technical Approach:

Accomplishments:

• Adapt the Lifetime Prediction Model[1] based on NCA chemistry to Lithium-titanate chemistry.

• Develop an on-board real time battery health estimationtool for cost-benefit sensitive operation of the unit in aFREEDM System.

• Implementation of battery life predictive model.• Arbin unit setup for the latest model of Toshiba SCiBTM battery ongoing at

Advanced Transportation Energy Center (ATEC).

• Analysis of the cycling data recorded by Arbin for adaptation of the degradation model for SCiB battery;

• Validation of the Life Predictive Model against the experimental degradation data;

• Implement the real time version of DESD State of health estimation;

• Real time battery health and potential degradation assessment for cost-benefit analysis;

• Use the above information for residential DESD economic operation.

Rainflow Algorithm & Miner’s Rule:• Rainflow cycle counting breaks up

complex duty cycle into individualmacro-& micro-cycles, ΔDODi. It alsotracks whether each cycle was a full orsingle-ended cycle, Ni.

• Miner’s rule is used to combine thedegradation effects of various magnitudecycles Ni to cumulative .

Experimental Analysis:

(Resistance Growth)

(Capacity Loss)

where:The Life Predictive Model[1]

can be written as:• Arbin BT2000 is a programmable

battery cycler used for comprehensive reproduction of degradation caused by the duty cycles of storage unit.

• The experimental results will be usedto validate the life predictive model[1]

and develop a real time battery healthestimation unit operating on the DSP.

𝑅𝑅 = 𝑎𝑎0 + 𝑎𝑎1𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙1/2 + 𝑎𝑎2𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

𝑄𝑄𝑠𝑠𝑙𝑙𝑠𝑠𝑙𝑙𝑠𝑠 = 𝑐𝑐0 − 𝑐𝑐2𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

𝑄𝑄𝐿𝐿𝑙𝑙 = 𝑏𝑏0 − 𝑏𝑏1𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙1/2

𝑄𝑄 = min(𝑄𝑄𝐿𝐿𝑙𝑙 ,𝑄𝑄𝑠𝑠𝑙𝑙𝑠𝑠𝑙𝑙𝑠𝑠)

𝑎𝑎1 =𝑎𝑎1,𝑟𝑟𝑙𝑙𝑙𝑙

Δ𝑡𝑡𝑐𝑐𝑐𝑐𝑐𝑐exp∫ 𝑒𝑒𝑒𝑒𝑒𝑒 −

𝐸𝐸𝑎𝑎𝑅𝑅𝑢𝑢𝑢𝑢

1𝑇𝑇 𝑡𝑡

−1𝑇𝑇𝑟𝑟𝑙𝑙𝑙𝑙

. exp𝛼𝛼𝑎𝑎1𝐹𝐹𝑅𝑅𝑢𝑢𝑢𝑢

𝑉𝑉𝑜𝑜𝑐𝑐(𝑡𝑡)𝑇𝑇 𝑡𝑡

−𝑉𝑉𝑟𝑟𝑙𝑙𝑙𝑙𝑇𝑇𝑟𝑟𝑙𝑙𝑙𝑙

. 1 +max Δ𝐷𝐷𝐷𝐷𝐷𝐷𝑙𝑙Δ𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝑙𝑙𝑙𝑙

𝛽𝛽𝑎𝑎𝑎.𝑑𝑑𝑡𝑡

𝑎𝑎2 =𝑎𝑎2,𝑟𝑟𝑙𝑙𝑙𝑙

Δ𝑡𝑡𝑐𝑐𝑐𝑐𝑐𝑐exp∫ 𝑒𝑒𝑒𝑒𝑒𝑒 −

𝐸𝐸𝑎𝑎𝑅𝑅𝑢𝑢𝑢𝑢

1𝑇𝑇 𝑡𝑡

−1𝑇𝑇𝑟𝑟𝑙𝑙𝑙𝑙

. exp𝛼𝛼𝑎𝑎1𝐹𝐹𝑅𝑅𝑢𝑢𝑢𝑢

𝑉𝑉𝑜𝑜𝑐𝑐(𝑡𝑡)𝑇𝑇 𝑡𝑡

−𝑉𝑉𝑟𝑟𝑙𝑙𝑙𝑙𝑇𝑇𝑟𝑟𝑙𝑙𝑙𝑙

. 1 +max Δ𝐷𝐷𝐷𝐷𝐷𝐷𝑙𝑙Δ𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝑙𝑙𝑙𝑙

𝛽𝛽𝑎𝑎𝑎.𝑑𝑑𝑡𝑡

𝑎𝑎1 =𝑎𝑎1,𝑟𝑟𝑙𝑙𝑙𝑙

Δ𝑡𝑡𝑐𝑐𝑐𝑐𝑐𝑐exp∫ 𝑒𝑒𝑒𝑒𝑒𝑒 −

𝐸𝐸𝑎𝑎𝑅𝑅𝑢𝑢𝑢𝑢

1𝑇𝑇 𝑡𝑡

−1𝑇𝑇𝑟𝑟𝑙𝑙𝑙𝑙

. exp𝛼𝛼𝑎𝑎1𝐹𝐹𝑅𝑅𝑢𝑢𝑢𝑢

𝑉𝑉𝑜𝑜𝑐𝑐(𝑡𝑡)𝑇𝑇 𝑡𝑡

−𝑉𝑉𝑟𝑟𝑙𝑙𝑙𝑙𝑇𝑇𝑟𝑟𝑙𝑙𝑙𝑙

. 1 +max Δ𝐷𝐷𝐷𝐷𝐷𝐷𝑙𝑙Δ𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝑙𝑙𝑙𝑙

𝛽𝛽𝑎𝑎𝑎.𝑑𝑑𝑡𝑡

𝑎𝑎1 =𝑎𝑎1,𝑟𝑟𝑙𝑙𝑙𝑙

Δ𝑡𝑡𝑐𝑐𝑐𝑐𝑐𝑐exp∫ 𝑒𝑒𝑒𝑒𝑒𝑒 −

𝐸𝐸𝑎𝑎𝑅𝑅𝑢𝑢𝑢𝑢

1𝑇𝑇 𝑡𝑡

−1𝑇𝑇𝑟𝑟𝑙𝑙𝑙𝑙

. exp𝛼𝛼𝑎𝑎1𝐹𝐹𝑅𝑅𝑢𝑢𝑢𝑢

𝑉𝑉𝑜𝑜𝑐𝑐(𝑡𝑡)𝑇𝑇 𝑡𝑡

−𝑉𝑉𝑟𝑟𝑙𝑙𝑙𝑙𝑇𝑇𝑟𝑟𝑙𝑙𝑙𝑙

. 1 +max Δ𝐷𝐷𝐷𝐷𝐷𝐷𝑙𝑙Δ𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝑙𝑙𝑙𝑙

𝛽𝛽𝑎𝑎𝑎.𝑑𝑑𝑡𝑡

Rainflow Plot

Potential Impact:

Next Steps:

[1]Santhanagopalan S, Smith K, Neubauer J, et al. Design and Analysis of Large Lithium-Ion Battery Systems[M]. Artech House, 2014.

References:

Life Prediction Model

Pre-RainflowPlot

Model Tuning and Application:

𝑒𝑒 = {𝑎𝑎0, 𝑏𝑏0, 𝑐𝑐0,𝑎𝑎1,𝑟𝑟𝑙𝑙𝑙𝑙, 𝑎𝑎2,𝑟𝑟𝑙𝑙𝑙𝑙,𝑏𝑏1,𝑟𝑟𝑙𝑙𝑙𝑙 , 𝑐𝑐2,𝑟𝑟𝑙𝑙𝑙𝑙 ,𝐸𝐸𝑎𝑎,𝑎𝑎1,𝐸𝐸𝑎𝑎,𝑎𝑎2, 𝐸𝐸𝑎𝑎,𝑏𝑏1,𝐸𝐸𝑎𝑎,𝑐𝑐2,𝛼𝛼𝑎𝑎,𝑎𝑎1,𝛼𝛼𝑎𝑎,𝑎𝑎2, 𝛼𝛼𝑎𝑎,𝑏𝑏1,𝛼𝛼𝑎𝑎,𝑐𝑐2,𝛽𝛽𝑎𝑎,𝑎𝑎1,𝛽𝛽𝑎𝑎,𝑎𝑎2, 𝛽𝛽𝑎𝑎,𝑏𝑏1, 𝛽𝛽𝑎𝑎,𝑐𝑐2}

• This model has 19 fitting parameters: • Different variables are needed for different battery chemistries. Followings are possible requirements:𝑞𝑞 = {𝑇𝑇𝑒𝑒𝑇𝑇𝑒𝑒𝑒𝑒𝑇𝑇𝑎𝑎𝑡𝑡𝑇𝑇𝑇𝑇𝑒𝑒 𝑡𝑡 , 𝑆𝑆𝑆𝑆𝑆𝑆 𝑡𝑡 ,𝑉𝑉𝑆𝑆𝑉𝑉𝑡𝑡𝑎𝑎𝑉𝑉𝑒𝑒 𝑡𝑡 ,𝑆𝑆𝑇𝑇𝑇𝑇𝑇𝑇𝑒𝑒𝐶𝐶𝑡𝑡(𝑡𝑡)}

Objective Duty Cycle &

Temperature at one state of life of

the battery

Degradation Rates Formulas

Degradation RatesExpecting Capacity Loss & Resistance

Growth

CalculateUpdate

ApplyExperimental/

Manufacture Duty Cycle

Degradation Rates Formulas

Experimental/Manufacture

Degradation DataFitting Parameters

RegressFit

Apply

Temperature data

SoC-Vocdata

Rainflow algorithm data

Rainflow Cycle Counting

A. SCiB Battery B. Arbin BT2000 Unit