circuits 2 laboratory

FAMU-FSU College of Engineering Department of Electrical & Computer Engineering

EEL3112L Laboratory Number 9

AC Power

EEL3112L Advanced Circuits with Computers Lab

Lab #9 9-1

Laboratory Number 9 AC Power

Outline 9.1 Theoretical background 9.2 Preliminary lab assignments

aReading (b) Pre-lab exercises

9.3 Experiment (a) Parts and equipment (b) Procedure and post-lab exercises

9.4 Lab reports

Objective In this experiment, the key concepts of AC power are examined. The essential techniques are utilized to study an AC power system of simple configuration. The objective is to facilitate the students learn the following basic ideas:

Instantaneous power versus average power Power triangle: complex power is the sum of real power and reactive power Power factor Maximization of real power supplied by the source Maximization of real power absorbed by the load

The dual process of running simulations in the NI Multisim and making measurements of simple AC power systems on the NI ELVIS II benchtop workstation is adopted. The following exercises are conducted in this lab to achieve the objective:

1. Pre-lab exercisesMultisim simulations results are used to: Measure transmission line impedance with known load Maximize real power supplied by the source via power factor correction Maximize real power absorbed by the load via power factor correction

2. In-lab exercisesThe techniques implemented in the pre-lab exercises are applied to basic power transmissionsystems modeled on the NI ELVIS prototyping board.

3. Post-lab exercises Examine the agreement or disagreement between experimental and theoretical results. Identify the possible causes of disagreement between experiment and theory.


Lab #9 9-2

9.1 Theoretical Background AC power is omnipresent in virtually every aspect of the modern-day life. Engineers of all disciplines are exposed to AC power systems throughout their careers. In this experiment, the basic elements as well as concepts essential for the analysis of AC power systems are examined. Simple models of power transmission systems are used to illustrate these elements and concepts.

(a) Basic Power Transmission System A very basic circuit model of a power transmission system is depicted in Figure 9-1. It consists of three sections: Transmission line

The transmission line is the physical waveguide structure that supports the propagation ofelectromagnetic energy from the source to the load. In the most basic circuit form, atransmission line is modeled as a two-terminal circuit with impedance LineZ . The source

injects an AC signal into the input terminal at the sending end of the line, whereas the loadconnected to the output terminal at the receiving end of the line absorbs the signal power.

Source: Thevenin equivalent circuitThe source generates an AC signal to be sent to the load through the transmission line. It istypically modeled by a Thevenin equivalent circuit containing an AC source )( jTV with

internal impedance TZ at frequency .

LoadThe load at the receiving end absorbs the signal power delivered through the transmissionline by the source at the sending end. The load is typically modeled as a passive circuit withterminal voltage )( jLV , current )( jLI , and impedance LZ at frequency .

Figure 9-1: Circuit representing a basic power transmission system


Lab #9 9-3

In practice, the electrical characteristics of the transmission line are known. One may then further simplify the Thevenin equivalent circuit at the sending end to a single effective source )( jsV

as shown in Figure 9-2. Clearly, the effective voltage source )( jsV depends on the parameters

of the Thevenin equivalent circuit and the electrical properties of the transmission line. This simplified power transmission system will be the focus of AC power analysis for both pre-lab exercises as well as in-lab experiments.

Figure 9-2: Simplified power transmission system

(b) Measures of AC Power Without any loss of generality, it is sufficient to consider various measures of power absorbed by the load at the receiving end of the transmission line of a simple AC power system shown in Figure 9-1.

Let )(and)( titv LL be the instantaneous terminal voltage and terminal current of the load, respectively. The corresponding phasor load voltage and phasor load current are denoted by

)(and)( jj LL IV . These voltages and currents can be expressed as follows:

)()()(

)()(where

)(])([)()(

)(])([)()(

jjXjRj

jj,

ω

θt,

ω

θt

eIjttcosItcosIti

eVjttcosVtcosVtv

LLL

LL

ii

vv

jLLiLiLL

jLLvLvLL

i

v

I

VZ

I

V

(9-1)

In equation (9-1), the parameters iv and denote the phase shifts of the load voltage and load

current, respectively. The corresponding time delays are denoted by the parameters iv tt and .

One may recall that )( jRL is the AC resistance and )( jX L is the reactance of the load at frequency .


Lab #9 9-4

Instantaneous Power The instantaneous power )(tpL absorbed by the load is defined as the voltage-current product in the time domain:

vi

ivLLLL

ivLLLLL

θθ

θθtcosIV

cosIV

θtcostcosIVtitvtp

where

(W) watts)(22

)(2

)()()()()(

(9-2)

One may recognize from equation (9-2) that )(tpL consists of a DC (constant) component and an AC (sinusoidal) component. Further, the phase angle is the difference in the phase shifts

between )(and)( titv LL . It signifies a time delay /t between the successive peaks of the

load voltage )(tvL and the load current )(tiL .

Average Power The average power avP absorbed by the load is obtained by computing the average value of the

instantaneous power )(L tp over a given time period (0, T) as follows:

(W) watts)()(22

)(2

])(2)([2

)(1

(rms)(rms)

00

cosIVcosIV

cosIV

dtθθtcoscosT

IVdttp

TP

LLLLLL

T

ivLL

T

Lav

(9-3)

The terms (rms)LV and (rms)LI denote the root-mean-square values of the load voltage and load

current, respectively.

Power Factor The term )(cos is referred to as the power factor, which assumes only non-negative values in the range 1)(0 cos . It indicates the degree of time synchronization between the load voltage and load current. When the load voltage and current are perfectly synchronized in time, their phase difference is 0 . Hence, the power factor is 1. Conversely, if the load voltage and

current are out of phase with phase difference 09 , then the power factor is 0.


Lab #9 9-5

Complex Power The notion of complex power S is introduced to provide a measure of AC power absorbed by the load in the frequency domain. It is defined in terms of the phasor load voltage )(L jV and load

phasor current )(L jI as follows:

)()()()(2

1(rms)(rms) jjjj LLLL

IVIVS (9-4)

Since the phasor load voltage and current are related by )()( jj LLL IZV , one may readily deduce the following:

)(2

1)()(

2

1

2

1)()(

2

1

2

222

LLLLLL

LL

LLL

L

LL

jXRIjj

XR

jXRV

jj

IIZ

Z

VVS

(9-5)

Furthermore, one may also observe that

jQP

sinIjVcosIVsinIV

jcosIV

eIV

eIV

eIeV

LLLLLLLL

jLLθθjLLjθL

jθL

viiv

(rms)(rms)(rms)(rms)

)(

22

222

1S

(9-6)

Real Power P The real part of the complex power is called the real power. It is evident from equation (9-5) the real power is actually the average power absorbed by the load, namely

LL

LL

LL

avLLLL

RI

XR

RV

PcosIVcosIV

P

22

(W) watts2

}{

2

22

2

(rms)(rms)

SRe

(9-7)

Reactive Power Q The imaginary part of the complex power is called the reactive power, namely

LL

LL

LL

LLLL

XI

XR

XV

sinIVsinIV

mQ

22

(VAR) 2

}{

2

22

2

(rms)(rms)

SI

(9-8)


Lab #9 9-6

The units of the reactive power Q are volt-amperes reactive (VAR). The reactive power performs no real work but simply provides a measure of the energy stored in the load capacitors and load inductors. Its time-average value is identically zero because of the periodic excahnge of stored energy between the load and the source.

Power Triangle The complex power jQP S can be represented geometrically by the power triangle depicted in Figure 9-3 below. The relationships among S, P, and Q are characterized by the power factor

cos .

Figure 9-3: Power traingle associated with complex power S

The magnitude of complex power S is called the apparent power with units in volt-amperes (VA), namely

(VA)22 QP S (9-9)

The real (average) power P is the projection of the complex power S onto the real axis and is related to the power factor as follows:

(W)22 cosQPcosP S (9-10)

The reactive power Q is the projection of the complex power S onto the imaginary axis and is given by

(VAR)22 sinQPsinQ S (9-11)


Lab #9 9-7

For an inductive load, the current lags the voltage resulting in 0 . Hence, the reactive power

is positive, namely 0 sinQL S . Conversely, for a capacitive load, the current leads the

voltage resulting in 0 . Thus, the reactive power sinQC S is negative.

(c) Power Factor Correction A given load manifests its ability to absorb real power at a given frequency in the power factor. It is therefore imperative to understand how the load can be adjusted so as to improve the power factor. The central purpose of power factor correction is to introduce a compensating reactance to the load so as to make the power factor closest to 1, thereby maximizing the amount of real power delivered to the load.

To understand how the power factor can be affected by adjusting the load, the AC power tranmission system shown on Figure 9-2 is considered. It should be noticed that the load voltage and current at frequency can be expressed as follows:

linelinelinelineline

lineline

)()(where

)(1

)(,)()(

jjLLLL

jss

jLL

sL

LsL

LL

ejXR,ejXR

eVj,eVj

jjjj

L

sL

ZZZZ

VV

VZZ

IVZZ

ZV

(9-12)

Line Impedance A point of interest should be noted upon examining equation (9-12). One may recognize that

ω

θθttt

tjexpV

Vθθjexp

V

V

j

j

LssL

L

L

s

LsL

s

L

s

L

where

)(])([)(

)(

line ZZ

Z

V

V

(9-13)

It is follows directly from equation (9-13) that

1)()()( linelineline tjexp

V

VjjXRj

L

sL ZZ (9-14)

If the load impedance )( jLZ is known, the transmission line impedance lineZ at frequency

can be determined by measuring the time delay of the load voltage with respect to the source voltage, namely

ω

θθttt LssL

(9-15)


Lab #9 9-8

Compensating Reactance The complex power delivered to the load is given by

LL

s

L

LLLLL

LL

jjL

L

sLL

V,

R

Xtan,XR

jjQjPsinjcos

eeV

jjj LL

ZZZ

SZ

SS

SZZZ

IVS

2line

2122

2line

2

2where

)()(

2)()(

2

1)(

(9-16)

The following observations can be made upon examining equation (9-16): The phase angle L of the load impedance LZ determines the power factor Lcos .

To make the power factor 1, namely 0L , the load should be compensated such that its

effective reactance is zero: 0LX

Resistive Load: 0with LLL XRZ When the load is purely resistive, the load voltage and load current are always in phase. Hence, the power factor at the load is identically 1. In this situation, one elects to correct the power factor at the source so as to maximize the real power supplied by the source. This can be achieved by adding a compensating reactance )( jX C to the load via series connection as

depicted in Figure 9-4. Specifically, the compensating reactance )( jX C should be chosen to

annihilate the reactance due to the transmission line, namely

)()( line jXjX C (9-17)

For an inductive line 0)(line jX , a capacitor should be used for correction. For a capacitive

line 0)(line jX , an inductor should be used for correction. The power transmission system as

a whole effectively becomes a resonant circuit after the load is compensated.

Figure 9-4: When the load is purely resistive ( LR ), the power factor at the source can be

maximized by adding a compensating reactance ( CX ) to the load via series connection.


Lab #9 9-9

Arbitrary Load: LLL jXR Z When the load is arbitrary, its reactance can be either positive or negative. In this case, one elects to maximize the power factor at the load. This can be achieved by introducing a compensating reactance )( jX C to the load via parallel connection as depicted in Figure 9-5. Specifically, the

compensating reactance )( jX C should be chosen to cancel out the reactance due to the load in

the manner analyzed below:

L

LLC

CLLCL X

XRX

Xj

jXRjX

220

1111

ImIm

Z (9-18)

For an inductive load 0)( jX L , a capacitor should be used for correction. In the case of a

capacitive load with 0)( jX L , an inductor should then be used for correction.

Figure 9-5: For an arbitrary load with impedance LLL jXR Z , the power factor can be

maximized by adding a compensating reactance ( CX ) to the load via parallel connection.

Important Many common loads in practice consist of motors; and they are predominantly inductive. Hence, power factor correction is always achieved by connecting a capacitor in parallel with the load. The required capacitance at a given frequency must satisfy the last equality in equation (9-18).


Lab #9 9-10

9.2 Preliminary Lab Assignments (a) Reading

EEL3112L lab user guide: Bing W. Kwan, NI Multisim and ELVIS II – An IntroductoryGuide

TextbookIrwin & Nelms, Basic Engineering Circuit Analysis, 9th Edition or 10th Edition

ReferenceGiorgio Rizzoni, Principles and Applications of Electrical Engineering, 5th Edition

(b) Pre-lab Exercises Exercise 9-1: Measurement of transmission line impedance Consider the circuit model of an AC power transmission system shown in Figure 9-6. The load has a resistance 100LR . The line impedance is comprised of a 10 resistor in series with a 2.2mH inductor.

Figure 9-6: Measurement of transmission line impedance

E1.1 Capture circuit model of the AC power transmission system in Multisim, including the placement of an AC voltage source and the oscilloscope. Include a captured image of the schematic in the lab report.

E1.2 Set the AC voltage source )(tvs at 1.5 kHz with 10 V peak amplitude, and 0 phase angle.

E1.3 Run the simulation. Adjust the settings of the oscilloscope so that the voltage waveforms are clearly shown. Use the cursors to measure the source voltage peak amplitude mV , the

load voltage peak amplitude LV , and the time delay t of the load voltage with respect to the source voltage. Record the measured results in Table 9-1. Capture an image of the oscilloscope display to be included in the lab report.


Lab #9 9-11

E1.4 Calculate the transmission line impedance )(line jZ . Show the calculation steps and enter

the result in Table 9-1. E1.5 Repeat Part E1.2 through Part E1.4 at frequency 4.5 kHz.

Table 9-1: Measurement of transmission line impedance

Frequency (Hz) mV (V) LV (V)

Time Delay t (s)

Measured

lineZ () Calculated

lineZ ()

1500

4500


Lab #9 9-12

Exercise 9-2: Maximization of real power supplied by the source Consider the circuit model of an AC power transmission system shown in Figure 9-6 again with the load resistance changed to 8LR . E2.1 Capture the circuit model of the AC power transmission system in Multisim, including the

placement of an AC voltage source and the oscilloscope. Include a captured image of the schematic in the lab report.


E2.3 Make use of the line impedance )(line jZ measured in Exercise 9-1 to calculate the

apparent power, power factor, real power, and reactive power supplied by the voltage source. Show the calculation steps and enter the results in Table 9-2.

E2.4 Determine the capacitance C of the compensating capacitor. Enter the result in Table 9-3. E2.5 Place the compensating capacitor between the transmission line impedance and the load

resistor. E2.6 Start the simulation. Adjust the settings of the oscilloscope so that the voltage waveforms

are clearly shown. Use the cursors to measure the source voltage peak amplitude mV , the

load voltage peak amplitude LV , and the time delay t of the load voltage with respect to the source voltage. Record the measured results in Table 9-3. Obtain a captured image of the oscilloscope display to be included in the lab report.

E2.7 Determine the transmission line impedance )(line jZ , including the reactance of the

compensating capacitor. Show the calculation steps and enter the result in Table 9-3. E2.8 Calculate the power factor at the voltage source after the correction. Show the calculation

steps and enter the result in Table 9-3. E2.9 Repeat Part E2.2 through Part E2.8 at frequency 4.5 kHz.

Table 9-2: Complex power supplied by the source before correction

Frequency (Hz)

Measured

lineZ () Apparent

Power Power Factor

Real/Average Power

Reactive Power

1500

4500

Table 9-3: AC power supplied by the source after correction


Time Delayt (s)

Comp. Cap. C (F)

Measured

lineZ () PF after

Correction

1500

4500


Lab #9 9-13

Exercise 9-3: Maximization of real power absorbed by the load Consider the circuit model of an AC power transmission system shown in Figure 9-6 again. Now the load consists of a 3.3mH inductor connected in series with an 8 resistor.

E3.1 Capture circuit model of the AC power transmission system in Multisim, including the placement of an AC voltage source and the oscilloscope. Include a captured image of the schematic in the lab report.


E3.3 Make use of the line impedance )(line jZ measured in Exercise 9-1 to calculate the

apparent power, power factor, real power, and reactive power absorbed by the load. Show the calculation steps and enter the results in Table 9-4.

E3.4 Determine the capacitance C of the compensating capacitor. Enter the result in Table 9-5. E3.5 Place the compensating capacitor and connect it in parallel with the load. E3.6 Start the simulation. Adjust the settings of the oscilloscope so that the voltage waveforms

are clearly shown. Use the cursors to measure the source voltage peak amplitude mV , the

load voltage peak amplitude LV , and the time delay t of the load voltage with respect to the source voltage. Record the measured results in Table 9-5. Obtain a captured image of the oscilloscope display to be included in the lab report.

E3.7 Determine the effective impedance of the load in parallel with the compensating capacitor, namely CL // ZZ . Show the calculation steps and enter the result in Table 9-5.

E3.8 Calculate the power factor at the load after the correction. Show the calculation steps and enter the result in Table 9-5.

E3.9 Repeat Part E3.2 through Part E3.8 at frequency 4.5 kHz.

Table 9-4: Complex power absorbed by the load before correction

Frequency (Hz)

Measured

lineZ () Apparent

Power Power Factor

Real/Average Power

Reactive Power

1500

4500

Table 9-5: AC power absorbed by the load after correction


Time Delayt (s)

Comp. Cap. C (F)

CL Z//Z

() PF after

Correction

1500

4500


Lab #9 9-14

9.3 Experiment (a) Parts and Equipment

NI Elvis II benchtop workstation NI Elvis II digital multimeter (DMM) soft front panel (SFP) NI Elvis II oscilloscope (Scope) soft front panel (SFP) NI Elvis II function generator (FGEN) soft front panel (SFP) Resistors, inductors, and capacitors of various values

(b) Initialization of ELVIS II Complete the following steps to initialize the ELVIS II workstation before performing the experiments described afterwards.

1. Turn the power on by flipping the switch on the back side at the right-hand corner of the NIELVIS II workstation. The orange USB READY light should now be on.

2. Caution: The power to the prototyping board (PB) should remain off (no green POWERlight).

3. Launch the virtual instrument interface by applying the click-command sequence:

>> Start >> All Programs Files >> National Instruments >> NI ELVISmx >>NI ELVIS Instrument Launcher

Note: One needs to ensure that the manual mode is turned off on the workstation so that thefunctions on the SFP are not disabled.

Attention: After completing Lab #1 through Lab #3, it is assumed that the students have gained sufficient familiarity with the usage and proper operations of various elements of the NI ELVIS II workstation. The experiment procedure for the current and future labs will be streamlined by outlining the key steps instead of providing the detailed step-by-step instructions as in Lab #1 through Lab #3. The students are cautioned to practice safety measures as instructed. In particular, they should adhere to the following rules:

1. Always bring the NI and ELVIS II user guide to the lab session.2. Before a circuit component is inserted onto or removed from the prototyping board (PB),

ensure that the power supply to the PB has been switched off. Notice that the system powerof the ELVIS II workstation should be switched on. The switch is located at the back of theworkstation.


Lab #9 9-15

(c) Procedure and Post-lab Exercises The lab TA will provide you with 1 resistor and 2 inductors needed to conduct the experiments in this lab. R0 is given as 180 ohms. RL and Rline are the parasitic resistances associated with the inductors LL = 10mH and Lline = 100mH respectively.

Part A: Preliminary procedure 1. Click on the DMM button in the instruments toolbar to open its SFP.2. Adjust the DMM settings properly to measure the resistance and inductance of the components

provided and record their values into Table 9-6.

3. Use the impedance analyzer to measure the internal resistance of the the inductors provided

at the given fequecies. This is the real part of the impedance. Enter their value into Table9-6 .

Table 9-6: Measured values of circuit components

Circuit Component Measured Value

Resistor 0R

Inductor LL Inductance =

Internal resistance RLine @1.5 kHz = Inductor Lline Inductance =

Internal resistance RLine @4.5 kHz =

Caution: The power to the prototyping board (PB) should be turned off after making each measurement. In particular, it should be OFF before embarking on the following experiments.

Internal resistance RL @1.5 kHz =

Internal resistance RL @4.5 kHz =


Lab #9 9-16

Part B: Measurement of transmission line impedance 1. Use the resistor R0 , and inductor ( Lline ) provided to build the AC power

transmission model shown in Figure 9-7 on the prototyping board, including the wireconnections for the use of the function generator (FGEN) SFP and the oscilloscope (Scope)SFP. Note RLine is the parasitic internal resistance of the inductor LLine.

Figure 9-7: Measurement of transmission line impedance on prototyping board

2. Switch on the prototyping board.3. Open the FGEN SFP and set it to generate a 1.5 kHz sine wave with 10V amplitude and 0V

DC offset. Start running.4. Open the Scope SFP. Adjust its settings so that the source voltage )(tvs and load voltage

)(tvL waveforms are clearly shown. Use the cursors to measure the source voltage peak

amplitude mV , the load voltage peak amplitude LV , and the time delay t of the load voltage

with respect to the source voltage. Record the measured results in Table 9-7. Obtain a captured image of the oscilloscope display to be included in the lab report.

5. Determine the transmission line impedance )(line jZ . Show the calculation steps and enter

the result in Table 9-7.6. Repeat Step 3 through Step 5 at frequency 4.5 kHz.7. Switch off the prototyping board.


Lab #9 9-17

Table 9-7: Measurement of transmission line impedance on prototyping board


Time Delay t (s)

Measured

lineZ () Calculated

lineZ ()

1500

4500

Post-lab Exercises for Part B B1. Discuss the agreement or disagreement of the calculated values with the measured values of

lineZ at both 1.5 kHz and 4.5 kHz. Explain the possible sources of errors.


Lab #9 9-18

Part C: Maximization of real power supplied by the source 1. Retain the circuit already built on the prototyping board in Part B.

2. Make use of the line impedance )(line jZ measured in Part B to calculate the apparent

power, power factor, real power, and reactive power supplied by the voltage source. Showthe calculation steps and enter the results in Table 9-8.

3. Set the FGEN SFP to generate a 1.5 kHz sine wave with 10V amplitude and 0V DC offset.

4. Determine the capacitance C of the compensating capacitor. Enter the result in Table 9-9.

5. Place the compensating capacitor with capacitance closest to C between the transmission lineimpedance Zline ( j ω) and the resistor Ro .

6. Switch on the prototyping board.7. Start running the function generator. Adjust the Scope SFP settings so that the source voltage

)(tvs and load voltage )(tvL waveforms are clearly shown. Use the cursors to measure the

source voltage peak amplitude mV , the load voltage peak amplitude LV , and the time delay

t of the load voltage with respect to the source voltage. Record the measured results inTable 9-9. Obtain a captured image of the oscilloscope display to be included in the labreport.

8. Determine the effective transmission line impedance )(line jZ , including the reactance of

the compensating capacitor. Show the calculation steps and enter the result in Table 9-8.9. Calculate the power factor at the voltage source after the correction. Show the calculation

steps and enter the result in Table 9-9.10. Repeat Step 3 through Step 9 at frequency 4.5 kHz.11. Switch off the prototyping board.

Table 9-8: Complex power supplied by the source on prototyping board before correction

Frequency (Hz)

Measured

lineZ () Apparent

Power Power Factor

Real/Average Power

Reactive Power

1500

4500

Table 9-9: AC power supplied by the source on prototyping board after correction


Time Delayt (s)

Comp. Cap. C (F)

Measured

lineZ () PF after

Correction

1500

4500

Post-lab Exercises for Part C C1. Discuss the agreement or disagreement of the power factor before and after the correction at

both 1.5 kHz and 4.5 kHz. Explain the possible sources of errors.


Lab #9 9-19

Part D: Maximization of real power absorbed by the load 1. Retain the circuit already built on the prototyping board in Part C but add and connect the

inductor LL in series with the resistor Ro as shown in Figure 9-8.

Figure 9-8: Maximization of real power absorbed by the load on prototyping board

2. Make use of the line impedance )(line jZ measured in Part B to calculate the apparent

power, power factor, real power, and reactive power absorbed by the load. Show thecalculation steps and enter the results in Table 9-10.

3. Set the FGEN SFP to generate a 1.5 kHz sine wave with 10V amplitude and 0V DC offset.4. Determine the capacitance C of the compensating capacitor. Enter the result in Table 9-11.5. Place the compensating capacitor with capacitance closest to C and connect it in parallel

with the inductor and resistor RO.6. Switch on the prototyping board.7. Start running the function generator. Adjust the Scope SFP settings so that the source voltage

)(tvs and load voltage )(tvL waveforms are clearly shown. Use the cursors to measure the

source voltage peak amplitude mV , the load voltage peak amplitude LV , and the time delay

t of the load voltage with respect to the source voltage. Record the measured results inTable 9-11. Obtain a captured image of the oscilloscope display to be included in the labreport.


Lab #9 9-20

8. Determine the effective impedance of the load in parallel with the compensating capacitor,namely CL // ZZ . Show the calculation steps and enter the result in Table 9-11.

9. Calculate the power factor at the load after the correction. Show the calculation steps andenter the result in Table 9-11.

10. Repeat Step 3 through Step 9 at frequency 4.5 kHz.11. Switch off the prototyping board.

Table 9-10: Complex power absorbed by the load on prototyping board before correction

Frequency (Hz)

Measured

lineZ () Apparent

Power Power Factor

Real/Average Power

Reactive Power

1500

4500

Table 9-11: AC power absorbed by the load on prototyping board after correction


Time Delayt (s)

Comp. Cap. C (F)

CL Z//Z

() PF after

Correction

1500

4500

Post-lab Exercises for Part D D1. Discuss the agreement or disagreement of the power factor before and after the correction at

both 1.5 kHz and 4.5 kHz. Explain the possible sources of errors.


Lab #9 9-21

9.4 Lab Reports Part 1: Pre-lab Exercises For each exercise (namely Exercise 9.1 through Exercise 9.3), the key elements to be included in the report are: (i) the circuit schematics; (ii) the results derived from simulation data in the form of tables, plots, or captured images of relevant screen displays; (iii) answers to the questions (if applicable); (iv) brief conclusion.

Part 2: Experiment The report should provide a brief discussion of the following topics: 1. Overview

(a) Objective(b) Equipment(c) Summary of experiment procedure

2. Analysis(a) Instantaneous power versus average power(b) Complex power: sum of real power and reactive power(c) Power triangle: a geometrical representation of complex power(d) Power factor(e) Maximization of real power supplied by the source(f) Maximization of real power absorbed by the load

3. Experimental evidence(a) Relevant circuit schematics(b) Measurement data, including tables, plots, or captured images of relevant screen displays(c) Results derived from measurement data, including tables and plots(d) Document answers to all the post-lab exercises, including calculations with logical steps if

applicable 4. Conclusion

A brief statement on what you have learned from this lab

circuits 2 laboratory

Documents