Practical state of health estimation of power batteries based on Delphi method and grey relational grade analysis

Bingxiang Sun, Jiuchun Jiang, Fangdan Zheng, Wei Zhao, Bor Yann Liaw, Haijun Ruan, Zhiqiang Han, Weige Zhang

Research output: Contribution to journalArticlepeer-review

64 Citations (Scopus)


The state of health (SOH) estimation is very critical to battery management system to ensure the safety and reliability of EV battery operation. Here, we used a unique hybrid approach to enable complex SOH estimations. The approach hybridizes the Delphi method known for its simplicity and effectiveness in applying weighting factors for complicated decision-making and the grey relational grade analysis (GRGA) for multi-factor optimization. Six critical factors were used in the consideration for SOH estimation: peak power at 30% state-of-charge (SOC), capacity, the voltage drop at 30% SOC with a C/3 pulse, the temperature rises at the end of discharge and charge at 1C; respectively, and the open circuit voltage at the end of charge after 1-h rest. The weighting of these factors for SOH estimation was scored by the 'experts' in the Delphi method, indicating the influencing power of each factor on SOH. The parameters for these factors expressing the battery state variations are optimized by GRGA. Eight battery cells were used to illustrate the principle and methodology to estimate the SOH by this hybrid approach, and the results were compared with those based on capacity and power capability. The contrast among different SOH estimations is discussed.

Original languageEnglish
Pages (from-to)146-157
Number of pages12
JournalJournal of Power Sources
Early online date2 Feb 2015
Publication statusPublished - 15 May 2015
Externally publishedYes


This work is supported by the National High Technology Research and Development Program of China (Grant No. 2012AA050211).


  • State-of-health (SOH)
  • Power batteries
  • Delphi method
  • Grey relational grade analysis
  • Battery management systems
  • Power capability

ASJC Scopus subject areas

  • Renewable Energy, Sustainability and the Environment
  • Energy Engineering and Power Technology
  • Physical and Theoretical Chemistry
  • Electrical and Electronic Engineering


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