### All Weeks Battery State-of-Charge (SOC) Estimation Quiz Answers

This course can also be taken for academic credit as ECEA 5732, part of CU Boulder’s Master of Science in Electrical Engineering degree.

### Battery State-of-Charge (SOC) Estimation Week 01 Quiz Answers

#### Quiz 1: Battery State-of-Charge (SOC) Estimation

Q1. Which of the following would be considered “states” of a lithium-ion cell (as opposed to “parameters”)? Select all that apply.

**Cell diffusion resistor current.****Cell state-of-charge.**- Cell total capacity Q.
**Cell equivalent-series resistance***R*0.**Cell hysteresis voltage.**

Q2. What do you think might be some advantages of a “simple” state-of-charge estimator, as compared to a “complicated” state-of-charge estimator? Select all that apply.

**A simple estimator is easier to implement in code on a BMS.**- A simpler estimator will work better than a complicated estimator as the cells in the battery pack get older.
- A simple estimator will usually produce better estimates than a complicated estimator.
**The code implementing a simple estimator is easier to validate under all operating conditions.****A simple estimator can be implemented on a less expensive microcontroller, reducing the cost of a BMS.**

Q3. What could be some advantages of implementing an estimator that produces very high-fidelity estimates of state of charge? Select all that apply.

**Consistently good estimates of SOC will unlock greater pack performance.****Consistently good estimates of SOC enable smaller battery packs for the same design requirements.****Consistently good estimates of SOC will help increase pack longevity.****Consistently good estimates of SOC enhance power-system reliability.****Consistently good estimates of SOC produced by the BMS can reduce the cost of the battery pack needed to meet specific design requirements.**

#### Quiz 2: Battery State-of-Charge (SOC) Estimation

Q1. Consider an electrode material for which *cs*,max=31368molm−3. If \theta_{0\%}=0.04*θ*0%=0.04 and \theta_{100\%}=0.74*θ*100%=0.74

what is the average concentration of lithium in the electrode for a cell state-of-charge of 50%? Enter your answer in

{mol}{m}^{-3}3,, rounded to the nearest integer.

Enter answer here

Q2. Suppose that 4.5 Ah of charge is removed from a fully charged lithium-ion battery cell when it is discharged at a 2C rate until its terminal voltage reaches the minimum cutoff voltage of v_l(T)v

What type of cell capacity is equal to 4.5 Ah?

- Residual capacity.
- Nominal capacity.
**Discharge capacity.**- Total capacity.

Q3. Consider a cell having total capacity of 10 Ah and residual capacity of 2 Ah. What is the state of charge of the cell? Enter your answer as a fraction between 0 and 1, with two digits to the right of the decimal point.

Enter answer here

#### Quiz 3: Battery State-of-Charge (SOC) Estimation

Q1. Before attempting this quiz, please execute the Jupyter notebook for this lesson. The quiz will require that you enter results that can be computed based on the code in that notebook.

The simplest voltage-based SOC estimation method simply looks up the cell voltage under load in a table of SOC versus OCV. Using this method, for the dataset supplied, what is the root-mean-squared (rms) SOC estimation error for this dataset? Please enter your answer in percent, rounded to the nearest integer percent.

Note that rms error can be computed in Octave as sqrt(mean((true_value – estimated_value).^2)).

Enter answer here

Q2. A slightly more complex voltage-based SOC estimation method first removes the ohmic voltage-drop term from measured voltage, and then looks up the modified voltage in a table of SOC versus OCV. Using this method, for the dataset supplied, what is the root-mean-squared (rms) SOC estimation error for this dataset? Please enter your answer in percent, rounded to the nearest integer percent.

Enter answer here

Q3. Suppose that we implement a coulomb-counting method to compute cell SOC, but that our initial SOC estimate has 5% error. If everything else is ideal (i.e., no measurement error, no error in parameter values), what is the SOC estimation error after the SOC estimator runs for a period of one hour? Enter your answer in percent, rounded to the nearest integer percent.

Enter answer here

#### Quiz 4: **Battery State-of-Charge (SOC) Estimation**

Q1. The mean or expected value of a scalar random variable is a special case of the expression for the mean of a vector random variable. If a scalar random variable has pdf

*f**X*(*x*), then its mean is computed as \mathbb{E}[X]=\int_{-\infty}^{\infty} x f_X(x)\,\mathrm{d}xE[*X*]=∫−∞∞*x**f**X*(*x*)d*x*

For this problem, consider a scalar random variable XX having the following pdf:

fX(x)={10 1<x<2 otherwise..

What is \mathbb{E}[X]E[X]? Enter your answer with one digit to the right of the decimal point.

Enter answer here

Q2. The variance of a scalar random variable is a special case of the expression for the covariance of a vector random variable. If a scalar random variable has pdf f_X

For this problem, consider a scalar random variable X*X* having the following pdf:

*fX*(*x*)={10 1<x<2 otherwise.

For this problem, consider a scalar random variable XX having the following pdf:

fX(x)={1/120 -6<x<6 otherwise..

What is the variance of random variable XX? Enter your answer with one digit to the right of the decimal point. (Hint: \mathbb{E}[X]=0E[X]=0 for this particular random variable.)

Enter answer here

Q3. Consider a vector random variable XX having multivariable Gaussian pdf with mean

Enter answer here

#### Quiz 5: Battery State-of-Charge (SOC) Estimation

Q1. If two jointly distributed random variables are independent, are they uncorrelated also?

**Yes: they are always uncorrelated also.**- Sometimes: they may be correlated or they may be uncorrelated.
- No: they are never uncorrelated also.

Q2. If two jointly distributed random variables are uncorrelated, are they independent also?

- Yes: they are always independent also.
**Sometimes: they may be independent or they may not be independent.**- No: they are never independent also.

Q3. If f_{X|Y}(x|y) = f_{X}(x)fX∣Y(x∣y)=f X

(x), what can we say about random variables XX and YY? (Select all that must apply.)

**XX and YY are independent.****XX and YY are uncorrelated.**- XX and YY have a joint Gaussian distribution.
**The conditional pdf f Y∣X (y∣x)=f Y**

#### Quiz 6: Battery State-of-Charge (SOC) Estimation

Q1. Consider two random processes X_k and Y_k where we compute the value Y_k = 0.8 X_k + 0.2 X_{k-1}Y=0.8X k +0.2X k−1. If X_k is a white-noise process, what can we say about Y_k?

- Y_k is also a white-noise process.
**Y_k cannot be a white-noise process.**- Y_k may or may not be a white noise process.

Q2. Consider two random processes X_k and Y_k where we compute the value Y_k = X_k + 1.Y k is a white-noise process, what can we say about Y_k?

- Y_k is also a white-noise process.
**Y_k cannot be a white-noise process.**- Y_k may or may not be a white-noise process.

Q3. Which of the following statements are always true about Gaussian random processes. Select all that apply.

**The pdf of the random process at any point in time can be completely specified by the mean and covariance of the process at that point in time.****They can be reasonable models of noises that are themselves caused by the summation of many independent random causes.**- Gaussian random processes are always stationary.
- Gaussian random processes are always white.

#### Quiz 7: Battery State-of-Charge (SOC) Estimation

Q1. Which of the following would be considered “states” of a lithium-ion cell (as opposed to “parameters”)? Select all that apply.

- Cell total capacity Q.
- Cell diffusion resistor current.
- Cell hysteresis voltage.
- Cell equivalent-series resistance R0

Cell state-of-charge.

Q2. What could be some advantages of implementing an estimator that produces very high-fidelity estimates of state of charge? Select all that apply.

- Consistently good estimates of SOC will unlock greater pack performance.
- Consistently good estimates of SOC enable smaller battery packs for the same design requirements.
- Consistently good estimates of SOC will help increase pack longevity.
- Consistently good estimates of SOC produced by the BMS can reduce the cost of the battery pack needed to meet specific design requirements.
- Consistently good estimates of SOC enhance power-system reliability.

Q3. Consider an electrode material for which c_{s,\mathrm{max}}=31368\,\mathrm{mol}\,\mathrm{m}^{-3}c

s,max

=31368molm

−3

. If \theta_{0\%}=0.04θ

0%

=0.04 and \theta_{100\%}=0.74θ

100%

=0.74, what is the average concentration of lithium in the electrode for a cell state-of-charge of 25%? Enter your answer in \mathrm{mol}\,\mathrm{m}^{-3}molm

−3

, rounded to the nearest integer.

Enter answer here

Q4. Suppose that 4.5 Ah of charge is removed from a fully charged lithium-ion before it is fully discharged. What type of cell capacity is equal to 4.5 Ah?

- Discharge capacity.
- Residual capacity.
- Nominal capacity.
- Total capacity.

Q5. Consider a cell having total capacity of 10 Ah and residual capacity of 4 Ah. What is the state of charge of the cell? Enter your answer as a fraction between 0 and 1, with two digits to the right of the decimal point.

Enter answer here

Q6. The mean or expected value of a scalar random variable is a special case of the expression for the mean of a vector random variable. If a scalar random variable has pdf f_X(x)f

X

(x), then its mean is computed as \mathbb{E}[X] =\int_{-\infty}^{\infty} x f_X(x)\,\mathrm{d}xE[X]=∫

−∞

∞

xf

X

(x)dx.

For this problem, consider a scalar random variable XX having the following pdf:

fX(x)={0.50 0<x<2 otherwise.

What is \mathbb{E}[X]E[X]? Enter your answer with one digit to the right of the decimal point.

Enter answer here

Q7. The variance of a scalar random variable is a special case of the expression for the covariance of a vector random variable. If a scalar random variable has pdf f_X(x)f

For this problem, consider a scalar random variable XX having the following pdf:

fX(x)={1/60 -3<x<3 otherwise.

What is the variance of random variable X=X? Enter your answer with one digit to the right of the decimal point. (Hint: \mathbb E[X]=0 for this particular random variable.)

Enter answer here

Q8. Consider a vector random variable XX having multivariable Gaussian pdf with mean

*x*ˉ=[01] and covariance \Sigma_{\widetilde{X}} = \left[2004\right].Σ*X*=[2004].

Compute f_X(x)*f**X*(*x*) for x = \left[11\right].*x*=[11]. Enter your answer with 3 digits to the right of the decimal point

Enter answer here

Q9. If two jointly distributed random variables are independent, are they uncorrelated also?

- Yes: they are always uncorrelated also.
- Sometimes: they may be correlated or they may be uncorrelated.
- No: they are never uncorrelated also.

Q10. If two jointly distributed random variables are uncorrelated, are they independent also?

- Yes: they are always independent also.
- Sometimes: they may be independent or they may not be independent.
- No: they are never independent also.

Q11. Consider two random processes X_k*Xk* and Y_k*Yk* where we compute the value Y_k = 0.8 Y_{k-1} + 0.2 X_{k-1}*Yk*=0.8*Yk*−1+0.2*Xk*−1. If X_k*Xk* is a white-noise process, what can we say about Y_k*Yk*?

- Y k is also a white-noise process.
- Y k cannot be a white-noise process.
- Y k may or may not be a white noise process.

Q12. Which of the following statements are always true about Gaussian random processes. Select all that apply.

- The pdf of the random process at any point in time can be completely specified by the mean and covariance of the process at that point in time.
- They can be reasonable models of noises that are themselves caused by the summation of many independent random causes.
- Gaussian random processes are always white.
- Gaussian random processes are always stationary.

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