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Summary

Battery Degradation models the decline in usable energy capacity and round-trip efficiency over time. PlantPredict implements two degradation mechanisms: cycle degradation (based on cumulative discharge energy) and calendar degradation (based on system age). Both mechanisms affect usable capacity and DC round-trip efficiency independently.

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Inputs

NameSymbolUnitsDescription
Usable Energy Capacity Year 1Emax,1E_{max,1}WhInitial usable energy capacity
Round-Trip DC Efficiency Year 1ηRTE,1\eta_{RTE,1}—Initial DC round-trip efficiency
Usable Capacity Cycle Degradation RatedE,cycled_{E,cycle}—/cycleCapacity loss per normalized cycle
Usable Capacity Calendar Degradation RatedE,cald_{E,cal}—/yearCapacity loss per year
RTE Cycle Degradation Ratedη,cycled_{\eta,cycle}—/cycleEfficiency loss per normalized cycle
RTE Calendar Degradation Ratedη,cald_{\eta,cal}—/yearEfficiency loss per year
Previous AC DischargePAC,discharge,prevP_{AC,discharge,prev}WAC discharge power from previous timestep
Previous Maximum CapacityEmax,prevE_{max,prev}WhMaximum capacity from previous timestep
Time Countertt—Timestep index
Time IntervalΔt\Delta tminutesWeather data time interval

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Outputs

NameSymbolUnitsDescription
Current Maximum CapacityEmaxE_{max}WhDegraded usable energy capacity
Current Round-Trip EfficiencyηRTE\eta_{RTE}—Degraded DC round-trip efficiency
Cumulative Cycle Capacity DegradationDE,cycleD_{E,cycle}—Total capacity loss from cycling
Cumulative Calendar Capacity DegradationDE,calD_{E,cal}—Total capacity loss from aging
Cumulative Cycle RTE DegradationDη,cycleD_{\eta,cycle}—Total efficiency loss from cycling
Cumulative Calendar RTE DegradationDη,calD_{\eta,cal}—Total efficiency loss from aging

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Detailed Description

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System Age

System age is calculated from the timestep counter: SystemAge=t8760×60/Δt\text{SystemAge} = \frac{t}{8760 \times 60 / \Delta t} where 8760 is the number of hours per year.

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Cycle Degradation

Cycle degradation accumulates based on discharge energy normalized by maximum capacity. Cumulative Capacity Cycle Degradation: DE,cycle=PAC,discharge,prev/ηinvEmax,prev×dE,cycle+DE,cycle,prevD_{E,cycle} = \frac{P_{AC,discharge,prev} / \eta_{inv}}{E_{max,prev}} \times d_{E,cycle} + D_{E,cycle,prev} Cumulative RTE Cycle Degradation: Dη,cycle=PAC,discharge,prev/ηinvEmax,prev×dη,cycle+Dη,cycle,prevD_{\eta,cycle} = \frac{P_{AC,discharge,prev} / \eta_{inv}}{E_{max,prev}} \times d_{\eta,cycle} + D_{\eta,cycle,prev}

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Calendar Degradation

Calendar degradation is proportional to system age. Cumulative Capacity Calendar Degradation: DE,cal=dE,cal×SystemAgeD_{E,cal} = d_{E,cal} \times \text{SystemAge} Cumulative RTE Calendar Degradation: Dη,cal=dη,cal×SystemAgeD_{\eta,cal} = d_{\eta,cal} \times \text{SystemAge}

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Degraded Parameters

Current Maximum Capacity: Emax=Emax,1×(1−(DE,cycle+DE,cal))E_{max} = E_{max,1} \times \left(1 - (D_{E,cycle} + D_{E,cal})\right) Current Round-Trip Efficiency: ηRTE=ηRTE,1×(1−(Dη,cycle+Dη,cal))\eta_{RTE} = \eta_{RTE,1} \times \left(1 - (D_{\eta,cycle} + D_{\eta,cal})\right)

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Degradation Model Characteristics

  • Cycle and calendar degradation effects are additive
  • Degradation is applied before SOC calculation each timestep
  • Capacity degradation reduces the maximum energy the battery can store
  • RTE degradation increases losses during charging