Slide 1Battery Degradation and Price Uncertainty
Miguel A. Ortega-Vazquez
UNIVERSITY of WASHINGTON
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Introduction
• The transportation sector is to part ways with carbon-generating fossil fuels
• Electric Vehicles (EVs) will be parked most of the time (at home)
• It is expected that EVs with constitute a significant component of the household demand
• EVs are equipped with a battery – pliant loads
• Take advantage of differences in real time pricing
• The degradation comes at a cost!
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• The service life of batteries degrades when subjected to charging/discharging cycles – Stress factors during storage (e.g. temperature)
– Characteristics of the battery cycling (e.g. charge/discharge rate, SoC, etc.)
• Highly dependent on the battery class and chemistry (e.g. LFP LNCA) – LFP are sensitive to total number of cycles
– LNCA not only to the total number of cycles, but also to their DoD
• No single model can be used for all chemistries!
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[1] M. A. Ortega-Vazquez, “Optimal Scheduling of Electric Vehicle Charging and Vehicle-to-Grid Services at
Household Level Including Battery Degradation and Price Uncertainty,” IET Generation, Transmission and
Distribution, vol. 8, no. 6, 2014.
Cycle-life performance characteristic
• Some chemistries (LFP) are (“linearly”) sensitive to the total number of cycles:
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B
100
k
= 60% C = $ 1.3436
Cycle-life against DoD
• Some other chemistries (LNCA) have a non-linear degradation as a function of the DoD:
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Examples: B = 29 kWh CB = 500 $/kWh
= 60% Losses 1 cycle out of (1/104.3 – 1/103.19)-1 at $ 5.0251
[3] Smith, K., Markel, T., Pesaran, A.: ‘PHEV battery trade-off study and standby thermal control’. Proc. 26th Int. Battery
Seminar & Exhibit, Fort Lauderdale, FL, 2009
EV charging/discharging schedule
• In a smart grid environment the pricing of electricity is expected to be dynamic, to better reflect the cost of electricity at different times of the day, as well as the utilization of the T&D networks
• The household energy manager will receive these prices and schedule the charging and V2G discharging of the EVs, always striving to minimize the total cost
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D V2G
, , ,min t v t v t v v t t T v V v V
t c d C
[1] M. A. Ortega-Vazquez, “Optimal Scheduling of Electric Vehicle Charging and Vehicle-to-Grid Services at
Household Level Including Battery Degradation and Price Uncertainty,” IET Generation, Transmission and
Distribution, vol. 8, no. 6, 2014.
EVs operating constraints
• SoC bounds
• Energy requirements
• V2G costs
July 2014





v t v
m v V t T
m
, v t v t v t vS S S B
v V t T
t c d v V





k C
C
Price uncertainty
• In reality, prices may not be known in advance with precision
• The uncertainty that surround the prices needs to be modelled in the decision making process
• We will seek a solution that remains not only feasible, but close to optimal for any materialization of prices
• Minimize cost for maximum possible uncertainties – Robust optimization
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Robust modelling
• In [3] is demonstrated that the minmax approach is equivalent to:
• Subject to all the EVs constraints plus:
July 2014


min D V2G
, , , 0 0 0min t v t v t v v t t t T v V v V t T
t c d C z q
max min 0 0 0t t t tz q y t J
0 0tq t T
v V
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Test Results • Let us assume a hypothetical household with two EVs:
July 2014
Battery capacity* (kWh) 29.0 29.0
Energy consumption (kWh/km) 0.21 0.18
Range (km) 138.0 161
Daily consumption (kWh/day) 7.35 9.0
Charge/discharge max. rate*** (kW) 3.3 3.3
Charging/discharging efficiency (%) 92.195 92.125
Battery cost ($/kWh) 500 500
• The SoC is kept between 25% and 95% of the battery capacity
• The prices follow the shape shown earlier with an average of 11 c/kWh
• The availabilities and motion schedules are taken from real traffic data
• The simulation resolution is 15 min over a 24 hrs. horizon
• MILP problem solved in Xpress
Night
= 1, m = 0
EV 1 0000-0645 hrs. 0645-0715 hrs. 0715-1615 hrs. 1600-1645 hrs. 1700-0000 hrs.
EV 2 0000-0745 hrs. 0745-0815 hrs. 0815-1645 hrs. 1630-1715 hrs. 1715-0000 hrs.
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• If we ignore the degradation costs and price uncertainty:
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• Optimizing using the robust formulation
• And including the degradation costs
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Sensitivity to the battery cost
• The cost of the batteries is expected to decrease as the technologies mature
• Itemized costs: a) Degradation insensitive to the DoD
b) Degradation sensitive to the DoD
Conclusions
• Degradation costs cannot be ignored when scheduling EVs
• These costs have a great impact not only on the amount charged, but also on the charging pattern
• The battery’s class and chemistry plays a major role on the scheduling of V2G services (if any)
• If the degradation is sensitive to the DoD, maintaining a high SoC is economical because the degradation costs are in the highest part of the degradation characteristic
• Under current battery prices, V2G services are unattractive
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Acknowledgement
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