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University of Colorado System

Battery State-of-Health (SOH) Estimation

University of Colorado System and University of Colorado Boulder via Coursera


This course can also be taken for academic credit as ECEA 5733, part of CU Boulder’s Master of Science in Electrical Engineering degree.

In this course, you will learn how to implement different state-of-health estimation methods and to evaluate their relative merits. By the end of the course, you will be able to:
- Identify the primary degradation mechanisms that occur in lithium-ion cells and understand how they work
- Execute provided Octave/MATLAB script to estimate total capacity using WLS, WTLS, and AWTLS methods and lab-test data, and to evaluate results
- Compute confidence intervals on total-capacity estimates
- Compute estimates of a cell’s equivalent-series resistance using lab-test data
- Specify the tradeoffs between joint and dual estimation of state and parameters, and steps that must be taken to ensure robust estimates (honors)


  • How does lithium-ion cell health degrade?
    • As battery cells age, their total capacities generally decrease and their resistances generally increase. This week, you will learn WHY this happens. You will learn about the specific physical and chemical mechanisms that cause degradation to lithium-ion battery cells. You will also learn why it is relatively simple to estimate and track changes to resistance, but why it is difficult to track changes to total capacity accurately.
  • Total-least-squares battery-cell capacity estimation
    • Total capacity is often estimated using ordinary-least-squares (OLS) methods. This week, you will learn that this is a fundamentally incorrect approach, and will learn that a total-least-squares (TLS) method should be used instead. You will learn how to derive a weighted OLS solution, to use as a benchmark, and how to derive a weighted TLS solution also.
  • Simplified total-least-squares battery-cell capacity estimates
    • Unfortunately, the weighted TLS solution you learned in week 2 is not well suited for efficient computation on an embedded system like a BMS. As an intermediate step toward finding an efficient weighted TLS method, you will first learn a proportionally weighted TLS method this week. You will then learn how to generalize this to an "approximate weighted TLS" (AWTLS) method, which gives good estimates, and is feasible to implement on a BMS.
  • How to write code for the different total-capacity estimators
    • So far this course, you have learned a number of methods for estimating total capacity. This week, you will learn how to implement those methods in Octave code. You will also explore different simulation scenarios to benchmark how well each method works, in comparison with the others. The scenarios are representative of hybrid-electric-vehicle (HEV) and battery-electric-vehicle (BEV) applications, but the principles learned can be extrapolated to other similar application domains.
  • A Kalman-filter approach to total capacity estimation
    • In the third course of the specialization, you learned how to use extended Kalman filters (EKFs) and sigma-point Kalman filters (SPKFs) to estimate the state of a battery cell. In this honors week, you will learn how to extend those concepts to apply EKF and SPKF to estimating the parameters of a battery-cell model if the state is known, and also how to simultaneously estimate both the state and parameters of a cell model.
  • Capstone project
    • You have learned several different total-capacity estimation methods. Some of these methods work better than others in general, but any method is only as good as the data you give it. In this project, you will explore a different way to determine the "x" and "y" data you use as input to the total-capacity estimation methods.

Taught by

Gregory Plett


4.7 rating at Coursera based on 151 ratings

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