A Practical Exercise 20 Ohm Electrical Voltage E X

Power Factor Correction – Simulator Applet Updated 20 JUN 2019

A Practical Exercise Name:________________ Section: ____________

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T

T

Electrical

Power

Company

TT

IS

T

R1 =

560 Ohm

Induction motors with 20

ohms of internal resistance

T

Power line resistance

Heaters

Steel Mill

RL =

20 Ohm

XL =

188.5

OhmsR2 = 10 Ohm

Line

Voltage

ELine = 5V

I. Purpose.

1. Review the determination if the real, reactive and apparent power to a load.

2. Introduce the determination power factor.

3. Introduce a method for correcting a circuit’s power factor.

II. Equipment.

Circuit Simulator Applet

An introduction to the Circuit Simulator Applet

III. Pre-Lab Calculations

Step One: Introduction

• A very small steel company has been notified by the electrical power company that their steel

mill is drawing too much current from the electrical power grid. The grid can handle 20 mA.

• The electrical power company can upgrade the electrical power grid, but the small steel

company would have to pay for it. The small steel company determined that it would be too

costly to upgrade the electrical power grid, and has decided to re-configure their steel mill, so

the steel mill would draw less current from the electrical power grid.

Step Two: Impedance, Current, and Power Calculations.

□ Compute the impedance of the steel mill (the shaded portion of the circuit of Figure 1).

Figure 1

Zmill = ______________

13 Ohm

13

http://www.falstad.com/circuit/circuitjs.html

http://bait-consulting.com/publications/circuit_simulator_manual.pdf

Power Factor Correction – Simulator Applet

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cos

sin

T S S

T T

T T

S I E

P S

Q S

=

= =

= =

=

□ Use Ohm’s law and the predicted impedance (Zmill) to calculate the source current assuming

that the electrical power company is supplying a line voltage of 5 VRMS at 30 kHz with zero

phase angle.

IS = _____________

□ Calculate the steel mill’s power factor (FP), and indicate whether it is leading or lagging.

FP = cos (θZ ) =

FP = ______________

LEADING LAGGING

□ Calculate the total reactive power, total active power, and total apparent power, using the

value of IS above and the 5V line voltage.

|ST| = ______________

PT = ______________

QT = ______________

| | | || |

| |

| |


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2 2

1 1

2 2

C L

C C

C C

C

C

Q Q

V VQ X

X Q

X CfC fX

= −

= → = =

= → = =

Step Three: Power Factor Correction

□ Draw on Figure 1 where a capacitor would be connected to correct the power factor.

□ Calculate the capacitor’s value (F) required to correct the steel mill’s power factor to unity.

Capacitor’s value = ______________

□ Calculate the new impedance of the mill with this capacitor installed.

Zmill-corrected = ______________

□ Use Ohm’s law and this corrected impedance (Zmill-corrected) to calculate the new source

current.

IS-corrected = _____________

How was the source current affected by the correction to the power factor?

Stayed the same__________ Increased__________ Decreased___________

□ Calculate the new total apparent power of the mill, using the value of IS above and the 5V

line voltage.

|Scorrected| = ______________

Step Four: Instructor or lab assistant verification that pre-lab calculations are complete.

______________________________


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IV. Lab Procedure. Time Required: 40 minutes. Check-off each step as you complete it.

Step One: Construct an AC series/parallel circuit

□ In the Circuit Simulator Applet, construct the ac series/parallel circuit in Figure 1.

The inductor is 1mH.

NOTE: It is important to draw the components as discussed in the Intro to Scope Function Lab.

If this is not done correctly, your phase angles may be 180o different from the Pre-Labs.

□ Set the Voltage Source to output a sine wave at 30 kHz, with a VP = 7.07 V.

□ Change the “Time step size(s)” to nanoseconds (n).

Refer to Step 1 of the Series AC Circuit Lab for a refresher on how to perform this task.

□ Insert a Scope Probe to measure the line voltage downstream of the power line resistor.

Adjust the voltage source amplitude until the Scope displays 5.00 VRMS (+/- 0.1 V).

Note: Sliders can be added to the side bar on the right side of the screen by right clicking the

component (in this case the voltage source) and selecting “Sliders…”, then select “Max Voltage”

and insert the range for the slider, 5 to 10 volts.


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ELine = ____________

□ Using the “View in Scope”, measure the phase difference between The power company voltage,

Es, and the voltage across the power line resistor, VR2.

Refer to Step 3 of the Intro to Scope Function Lab for a refresher on how to perform this task.

NOTE: For this circuit, because VR2 is so small, it may be easier to calculate Δt by stacking the

scopes and using the “Max Scale” feature.

□ Calculate Δt

Δt = _____________

□ Calculate the phase shift (θ) between the waveforms.

∆θ = (Δt /T) X 360◦

∆ θ = _________

0°

Adjust Slider until VScope Probe = 5 VRMS;

make small adjustments; it will take some

time for the scope to update the RMS

value


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□ Using the “View in Scope”, determine the RMS voltage across R2, the power line resistor, and

then write VR2 in phasor form. The phase angle of VR2 is the phase angle measured above

(negative if lagging, positive if leading).


Vpower line resistor = ____________

□ Determine the actual IS based upon the measured Vpower line resistor and the resistance of the 10

ohm power line resistor.

IS = ____________

□ Determine the apparent power being consumed by the steel mill, using IS and the 5V line

voltage.

|ST| = ______________

□ How do these values of VR2, IS, and ST compare to the values calculated in step two of the pre-

lab section?

Exact__________ Very close__________ Very Different_________

Step Four: Power Factor Correction

□ Connect the variable capacitor in parallel with the steel mill. Similar to the Voltage Source, add

a slider to the capacitor with a range of 1 nF to 40 nF.

□ Initially setting a value of 1 nF.

|ST| = |ET||IT|


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□ Select “View in Scope” for the voltage source, Es.

Note: For this step, you will only view the scope for the source, but you will compare the voltage, Es,

and current, IS, from the source. Remember that the purpose for adding of the capacitor is to counter the

reactance of the inductor such that the circuit looks purely resistive to the source. For a purely resistive

circuit, the voltage and current will be in phase. Therefore, the capacitance of the capacitor will need to

be adjusted until the source voltage and current are in phase.

□ Starting at 1nF, slowly slide the bar on the variable capacitor until you observe Es and IS are in

phase. It will take some take for the graph in the scope to update, so be patient.

□ Record the value of the variable capacitor.

Capacitor value = ________________

How does this experimentally determined value compare to the predicted capacitor value from

step three of the pre-lab calculations?

Exact__________ Very close__________ Very Different______

ES IS


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□ Determine the actual IS and write it as a phasor using the values you just obtained in the previous

step.

IS-corrected= ____________



□ Determine the apparent power being consumed by the steel mill, using the new value of IS and

the 5 V line voltage.

|Scorrected| = ______________

How do these corrected values of IS and ST compare to the predicted values from step three of

the pre-lab calculations?


Step Five: Circuit Submission

□ Save the circuit to your computer and submit the circuit text file to your instructor for lab credit.

0°


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T

T

Electrical

Power

Company

TT

IS

T

R1 =

560 Ohm

Induction motors with 20

ohms of internal resistance

T

Power line resistance

Heaters

Steel Mill

RL =

20 Ohm

XL =

188.5

OhmsR2 = 10 Ohm

Line

Voltage

ELine = 5V

Practical Exercise Submission Form Name:________________ Section: _____

III. Pre-lab calculations. Show all work.

Step Two: Impedance, Current, and Power Calculations.

□ Compute the impedance of the steel mill (the shaded portion of the circuit of Figure 1).

Figure 1

Zmill = ______________

□ Use Ohm’s law and the predicted impedance (Zmill) to calculate the source current assuming

that the electrical power company is supplying a line voltage of 5 VRMS at 30 kHz with zero

phase angle.

IS = _____________

□ Calculate the steel mill’s power factor (FP), and indicate whether it is leading or lagging.

FP = cos (θZ ) =

FP = ______________

LEADING LAGGING

13 Ohm

13


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2 2

1 1

2 2

C L

C C

C C

C

C

Q Q

V VQ X

X Q

X CfC fX

= −

= → = =

= → = =

cos

sin

T S S

T T

T T

S I E

P S

Q S

=

= =

= =

=

□ Calculate the total reactive power, total active power, and total apparent power, using the

value of IS above and the 5V line voltage.

|ST| = ______________

PT = ______________

QT = ______________

Step Three: Power Factor Correction

□ Draw on Figure 1 where a capacitor would be connected to correct the power factor.

□ Calculate the capacitor’s value (F) required to correct the steel mill’s power factor to unity.

Capacitor’s value = ______________

□ Calculate the new impedance of the mill with this capacitor installed.

Zmill-corrected = ______________

| | | || |

| |

| |


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□ Use Ohm’s law and this corrected impedance (Zmill-corrected) to calculate the new source

current.

IS-corrected = _____________



□ Calculate the new total apparent power of the mill, using the value of IS above and the 5V

line voltage.

|Scorrected| = ______________

Step Four: Instructor or lab assistant verification that pre-lab calculations are complete.

______________________________

IV. Lab Procedure.

Step One: Construct an AC series/parallel circuit

□ Insert a Scope Probe to measure the line voltage downstream of the power line resistor.

Adjust the voltage source amplitude until the Scope displays 5.00 VRMS.

ELine = ____________

□ Measure the phase difference between the power company voltage, Es, and the voltage across

the power line resistor, VR2.

□ Calculate Δt

Δt = _____________

□ Calculate the phase shift (θ) between the waveforms.

∆θ = (Δt /T) X 360◦

∆ θ = _________

0°


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□ Determine the RMS voltage across R2, the power line resistor, and then write VR2 in phasor form.

The phase angle of VR2 is the phase angle measured above (negative if lagging, positive if

leading).


Vpower line resistor = ____________

□ Determine the actual IS based upon the measured Vpower line resistor and the resistance of the 10

ohm power line resistor.

IS = ____________

□ Determine the apparent power being consumed by the steel mill, using IS and the 5V line

voltage.

|ST| = ______________

□ How do these values of VR2, IS, and ST compare to the values calculated in step two of the pre-

lab section?

Exact__________ Very close__________ Very Different_________

Step Four: Power Factor Correction

□ Record the value of the variable capacitor.

Capacitor value = ________________

How does this experimentally determined value compare to the predicted capacitor value from

step three of the pre-lab calculations?


□ Determine the actual IS and write it as a phasor using the values you just obtained in the previous

step.

IS-corrected= ____________



|ST| = |ET||IT|

0°


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□ Determine the apparent power being consumed by the steel mill, using the new value of IS and

the 5 V line voltage.

|Scorrected| = ______________

How do these corrected values of IS and ST compare to the predicted values from step three of

the pre-lab calculations?


Step Five: Circuit Submission

□ Save the circuit to your computer and submit the circuit text file to your instructor for lab credit.

A Practical Exercise 20 Ohm Electrical Voltage E X

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