# Equivalent Circuit Cell Model Simulation Coursera Quiz Answers

### All Weeks Equivalent Circuit Cell Model Simulation Coursera Quiz Answers

This course can also be taken for academic credit as ECEA 5731, part of CU Boulder’s Master of Science in Electrical Engineering degree.

In this course, you will learn the purpose of each component in an equivalent circuit model of a lithium-ion battery cell, how to determine their parameter values from lab-test data, and how to use them to simulate cell behaviors under different load profiles.

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### Equivalent Circuit Cell Model Simulation Coursera Quiz Answers

#### Quiz 1: Equivalent Circuit Cell Model Simulation

Q1. Which of the following statements regarding coulombic efficiency are true? (Select all that apply.)

• We model coulombic efficiency η[k]≤1 whenever current is flowing into the cell.
• Coulombic efficiency and energy efficiency are two different names for the same basic quantity.
• We model coulombic efficiency η[k]=1 whenever current is being drawn from a cell.
• One reason for imperfect coulombic efficiency has to do with unwanted side reactions occurring in the cell.

Q2. Consider the following experiment: A lithium-ion cell having total capacity of 10Ah is first fully charged. Then, 2Ah of charge is removed. What is the state of charge of the cell at the conclusion of this experiment (express your answer as a decimal number between 0 and 1).

Answers:

Q3. Which of the following is true about a cell’s open-circuit voltage (OCV)?

• OCV as a function of state-of-charge is the same for every type of lithium-ion battery cell.
• OCV generally increases as the cell’s depth-of-discharge increases.
• OCV is a cell’s terminal voltage when it has been disconnected from its load and has been allowed to rest until the voltage stabilizes to a constant value.
• OCV is a cell’s terminal voltage at every point in time that the input current to the cell is zero (i(t) = 0i(t)=0).

#### Quiz 2: Equivalent Circuit Cell Model Simulation

Q1. Which of the following phenomena (which are actually observed behaviors of lithium-ion cells) does the Rint model describe? (Select all that apply.)

• The fact that a cell’s terminal voltage relaxes over time toward open-circuit voltage whenever the cell is allowed to rest (i.e., whenever i(t) = 0i(t)=0).
• The fact that a cell’s terminal voltage is greater than open-circuit voltage while charging the cell.
• The fact that a cell’s terminal voltage is less than open-circuit voltage while discharging the cell.
• The fact that open-circuit voltage changes over time as the cell is charged and/or discharged.

Q2. Which of the following are true regarding diffusion voltages? (Select all that apply.)

• When a cell has recently been charging, and is subsequently allowed to rest (by setting i(t)=0, the cell’s terminal voltage decreases toward a steady-state value as charge re-distributes inside the cell due primarily to diffusion processes.
• When a cell has recently been discharging, and is subsequently allowed to rest (by setting i(t)=0), the cell’s terminal voltage increases toward a steady-state value as charge re-distributes inside the cell due primarily to diffusion processes.

Q3. What is the difference between the Thévenin equivalent-circuit model versus the Rint equivalent-circuit model?

• The Rint model is the same as the Thévenin model, except that the Rint model adds parallel resistor-capacitor sub-circuit(s) to model diffusion voltage.
• The Thévenin model is the same as the Rint model, except that the Thévenin model adds series resistor-capacitor sub-circuit(s) to model diffusion voltage.
• The Thévenin model is the same as the Rint model, except that the Thévenin model adds parallel resistor-capacitor sub-circuit(s) to model diffusion voltage.
• The Rint model is the same as the Thévenin model, except that the Rint model adds series resistor-capacitor sub-circuit(s) to model diffusion voltage.

#### Quiz 3: Equivalent Circuit Cell Model Simulation

Q1. What is the difference between the Randles equivalent-circuit model and the equivalent-circuit models (e.g., the Thévenin model) we studied earlier this week?

• The Randles model is derived based on a physical understanding of the electrochemical processes occurring in the cell whereas the earlier models were derived based on modeling observed phenomena.
• The Randles model includes resistors and capacitors to model time constants in cell dynamics whereas earlier models did not.
• The Randles model describes the effect of a double-layer capacitance on cell voltage whereas earlier models did not.
• The Randles model describes the effect of electrolyte resistance on cell voltage whereas earlier models did not.

Q2. How many parallel resistor-capacitor sub-circuits must be placed in series to model a Warburg impedance exactly?

• Four.
• Three.
• An infinite number.
• One.

Q3. What challenges are introduced by a Warburg impedance when trying to simulate battery dynamics accurately? (Select all that apply.)

• The Warburg impedance cannot be described as a standard ordinary differential equation, so standard calculus tools cannot be used.
• It is necessary to have studied electrochemistry in order to simulate a Warburg impedance.
• The Warburg impedance is a “constant phase” element having magnitude response that slopes at -10 dB/decade and constant phase response of -45^\circ∘.
• It is no more difficult to simulate a Warburg impedance than other linear-circuit elements like sources, resistors, capacitors, or inductors.

#### Quiz 4: Equivalent Circuit Cell Model Simulation

Q1. Consider the continuous-time state-space system modeled as

x˙(t)=−2x(t)+3u(t)

\qquad y(t) = 0.5 x(t) + 0.8 u(t).y(t)=0.5x(t)+0.8u(t).

We wish to convert this to a discrete-time state-space model of the form

\qquad x[k+1] = a_d x[k] + b_d u[k]x[k+1]=adx[k]+bdu[k]

\qquad y[k] = c_d x[k] + d_d u[k].y[k]=cdx[k]+ddu[k].

Assume that the sample period \Delta t = 1Δt=1s.

What is the value of a_dad​? Round your answer to two digits to the right of the decimal point

Enter answer here

Q2. For the same continuous-time system as defined in Question 1, and for the same sampling period, what is the value of b_db
d

? Round your answer to two digits to the right of the decimal point.

Enter answer here

Q3. For the same continuous-time system as defined in Question 1, and for the same sampling period, what is the value of d_dd
d

? Round your answer to two digits to the right of the decimal point.

Enter answer here

#### Quiz 5: Equivalent Circuit Cell Model Simulation

Q1. Consider the voltage response of a lithium-ion cell to a discharge-pulse test:

Answers:

For the test, | \Delta i | = 10∣Δi∣=10A, | \Delta v_0 | = 50∣Δv0​∣=50mV, and | \Delta v_\infty | = 130∣Δv∞​∣=130mV.

What is the approximate value of R_0R0​ in a Thévenin equivalent-circuit cell model? Enter your answer in m\OmegaΩ.

Q2. Consider again the experiment described in Question 1. What is the value of R_1R1​ in a Thévenin equivalent-circuit model? Enter your answer in m\OmegaΩ.

Answers :

Q3. Consider again the experiment described in Question 1. What is the value of C_1C1​ in a Thévenin equivalent-circuit model? Enter your answer in kilo-farads (kF).

Answers:

#### Quiz 6: Equivalent Circuit Cell Model Simulation

Q1. Which of the following statement(s) regarding hysteresis are true? (Select all that apply.)

• Hysteresis voltage and diffusion voltage are basically the same thing, and cannot be distinguished by experiment.
• During a long interval where a cell is being charged, its hysteresis voltage becomes more and more negative.
• During a long interval where a cell is being charged, its hysteresis voltage becomes more and more positive.
• If a cell is allowed to rest (i(t)=0i(t)=0) for a long time, the hysteresis voltage will decay toward zero.

Q2. In the simple hysteresis model presented in this lesson, what is the function of the gamma (\gammaγ) parameter?

• It describes the maximum value of dynamic hysteresis voltage at the present state-of-charge.
• It describes the sign of the most recent non-negligible value of cell electrical current.
• It describes the rate at which the dynamic hysteresis state moves from one side of the major hysteresis branch to the other as state-of-charge changes.
• It describes the magnitude of instantaneous hysteresis voltage at the present state-of-charge.

Q3. What is the difference between dynamic hysteresis and instantaneous hysteresis?

• Instantaneous hysteresis changes the moment that the sign of cell input current changes, while dynamic hysteresis changes more slowly as state-of-charge changes.
• Dynamic hysteresis changes the instant that the sign of cell input current changes, while instantaneous hysteresis changes more slowly as state-of-charge changes.
• Dynamic hysteresis is a random phenomenon that varies in unpredictable ways, while instantaneous hysteresis is completely predictable.
• Instantaneous hysteresis depends on the entire history of cell input current versus time, whereas dynamic hysteresis depends only on the most recent history.

#### Quiz 7: Equivalent Circuit Cell Model Simulation

Q1. Which of the following variables are members of the ESC model “state equation”? (Select all that apply.)

• The cell’s resistor-capacitor voltage(s).
• The cell’s dynamic hysteresis level.
• The cell’s open-circuit voltage.
• The cell’s state of charge.

Q2. Which of the following variables are members of the ESC model “output equation”? (Select all that apply.)

• The cell’s instantaneous hysteresis voltage.
• The cell’s state of charge.
• The cell’s resistor-capacitor voltage(s).
• The cell’s open-circuit voltage.

Q3. Which of the following statement(s) is/are true regarding the ESC cell model? (Select all that apply.)

• It describes state-of-charge-dependent open-circuit voltage, ohmic and diffusion voltages, and hysteresis.
• With appropriate parameter values, it can describe the Rint model and the Thévenin model that we studied earlier this week.
• It comprises two coupled equations in a (nonlinear) “state-space” form.
• With appropriate parameter values, it can describe the input/output (current/voltage) dynamics of a lithium-ion cell with arbitrarily small error.

#### Quiz 8: Equivalent Circuit Cell Model Simulation

Q1. Consider the following experiment: A lithium-ion cell having total capacity of 5Ah is first fully charged. Then, 2Ah of charge is removed. What is the state of charge of the cell at the conclusion of this experiment (express your answer as a decimal number between 0 and 1).

Enter answer here

Q2. What is the difference between the Thévenin equivalent-circuit model versus the Rint equivalent-circuit model?

• The Rint model is the same as the Thévenin model, except that the Rint model adds series resistor-capacitor sub-circuit(s) to model diffusion voltage.
• The Rint model is the same as the Thévenin model, except that the Rint model adds parallel resistor-capacitor sub-circuit(s) to model diffusion voltage.
• The Thévenin model is the same as the Rint model, except that the Thévenin model adds series resistor-capacitor sub-circuit(s) to model diffusion voltage.
• The Thévenin model is the same as the Rint model, except that the Thévenin model adds parallel resistor-capacitor sub-circuit(s) to model diffusion voltage.

Q3. What is the difference between the Randles equivalent-circuit model and the Thévenin equivalent-circuit model?

• The Randles model describes the effect of electrolyte resistance on cell voltage whereas the Thévenin model does not.
• The Randles model includes resistors and capacitors to model time constants in cell dynamics whereas the Thévenin model does not.
• The Randles model is derived based on a physical understanding of the electrochemical processes occurring in the cell whereas the Thévenin model was derived based on modeling observed phenomena.
• The Randles model describes the effect of a double-layer capacitance on cell voltage whereas the Thévenin model does not.

Q4. Consider the continuous-time state-space system modeled as

\qquad \dot{x}(t) = -3 x(t) + 2 u(t)
x
˙
(t)=−3x(t)+2u(t)

\qquad y(t) = 0.8 x(t) + 0.5 u(t).y(t)=0.8x(t)+0.5u(t).

We wish to convert this to a discrete-time state-space model of the form

\qquad x[k+1] = a_d x[k] + b_d u[k]x[k+1]=a
d

x[k]+b
d

u[k]

\qquad y[k] = c_d x[k] + d_d u[k].y[k]=c
d

x[k]+d
d

u[k].

Assume that the sample period \Delta t = 1Δt=1s.

What is the value of b_db
d

? Round your answer to two digits to the right of the decimal point.

Enter answer here

Q5. Consider the continuous-time state-space system modeled as

\qquad \dot{x}(t) = -4 x(t) + 3 u(t)
x
˙
(t)=−4x(t)+3u(t)

\qquad y(t) = 2 x(t) + 1.5 u(t).y(t)=2x(t)+1.5u(t).

We wish to convert this to a discrete-time state-space model of the form

\qquad x[k+1] = a_d x[k] + b_d u[k]x[k+1]=a
d

x[k]+b
d

u[k]

\qquad y[k] = c_d x[k] + d_d u[k].y[k]=c
d

x[k]+d
d

u[k].

Assume that the sample period \Delta t = 1Δt=1s.

What is the value of c_dc
d

? Round your answer to two digits to the right of the decimal point.

Enter answer here

Q6. Consider the voltage response of a lithium-ion cell to a discharge-pulse test:

For the test, | \Delta i | = 20∣Δi∣=20A, | \Delta v_0 | = 40∣Δv
0

∣=40mV, and | \Delta v_\infty | = 100∣Δv

∣=100mV.

What is the approximate value of R_1R
1

in a Thévenin equivalent-circuit cell model? Enter your answer in m\OmegaΩ.

Enter answer here

Q7. Consider the voltage response of a lithium-ion cell to a discharge-pulse test:

For the test, | \Delta i | = 10∣Δi∣=10A, | \Delta v_0 | = 40∣Δv
0

∣=40mV, and | \Delta v_\infty | = 130∣Δv

∣=130mV.

What is the approximate value of C_1C
1

in a Thévenin equivalent-circuit cell model? Enter your answer in kilofarads (kF), with one digit to the right of the decimal point.

Q8. In the simple hysteresis model presented this week, what is the function of the gamma (\gammaγ) parameter?

• It describes the sign of the most recent non-negligible value of cell electrical current.
• It describes the rate at which the dynamic hysteresis state moves from one side of the major hysteresis branch to the other as state-of-charge changes.
• It describes the maximum value of dynamic hysteresis voltage at the present state-of-charge.
• It describes the magnitude of instantaneous hysteresis voltage at the present state-of-charge.

Q9. Which of the following statement(s) regarding hysteresis are true? (Select all that apply.)

• Hysteresis voltage and diffusion voltage are basically the same thing, and cannot be distinguished by experiment.
• During a long interval where a cell is being charged, its hysteresis voltage becomes more and more negative.
• During a long interval where a cell is being charged, its hysteresis voltage becomes more and more positive.
• If a cell is allowed to rest (i(t)=0i(t)=0) for a long time, the hysteresis voltage will decay toward zero.

Q10. Which of the following statement(s) is/are true regarding the ESC cell model? (Select all that apply.)

• It describes state-of-charge-dependent open-circuit voltage, ohmic and diffusion voltages, and hysteresis.
• It comprises two coupled equations in a (nonlinear) “state-space” form.
• With appropriate parameter values, it can describe the input/output (current/voltage) dynamics of a lithium-ion cell with arbitrarily small error.
• With appropriate parameter values, it can describe the Rint model and the Thévenin model and can closely approximate the Randel model.
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