Circuit Analysis IV Assignment.pdf Ch

7/28/2019 Circuit Analysis IV Assignment.pdf Ch

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PRACTICAL SIMULATION REPORT

SEMESTER 1-2013

FACULTY OF

ENGINEERING, SCIENCE AND BUILT ENVIRONMENT

DEPARTMENT OF

ELECTRICAL POWER ENGINEERING

CIRCUIT ANALYSIS IV

TITTLE:

TRANSIENT DAMPING ANALYSIS

4/25/2013 Lecturer:Student number: 21141631 Mr. John WimbushVunda CF


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Contents

Abstract.................................................................................................................................................. 2

1-Introduction........................................................................................................................................ 2

2- The theory......................................................................................................................................... 3

2.1-Under damped circuit (1) ........................................................................................................ 6

3- Effect of the damping ratio on the response of a circuit. ........................................................... 8

3.1- Under damped circuit............................................................................................................... 8

3.2- Critically damped circuit .......................................................................................................... 8

3.3- Over damped circuit ................................................................................................................. 8

4- Effects of transients......................................................................................................................... 84.1- Electronic equipment: .............................................................................................................. 8

4.2- Motors: ....................................................................................................................................... 8

4.3- Lighting: ..................................................................................................................................... 9

5- Avoiding problems caused transients........................................................................................... 9

6- Conclusion ........................................................................................................................................ 9

7- Reference ......................................................................................................................................... 9

List of tablesTable 1: Under damped .............................................................................................. 3Table 2: Critically damped .......................................................................................... 5Table 3: Over damped ................................................................................................ 7

List of figures

Figure 1: Under damped Circuit Diagram ................................................................... 3Figure 2: Under damped current and voltage wave form ........................................... 4Figure 3: Critically damped circuit diagram ..................................................................... 5

Figure 4: Critical damped current and voltage wave form .......................................... 6Figure 5: Over damped circuit diagram ........................................................................... 6Figure 6: Over damped current and voltage wave forms ............................................ 8


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Abstract

Transient in electrical circuits results from the sudden release of previously storedenergy. Some transients may be voluntary and created in the circuit due to inductiveswitching, commutation voltage spikes, etc. and may be easily suppressed since

their energy content is known and predictable. Other transients may be createdoutside the circuit and then couple into it. These can be caused by lightning,substation problems, or other such phenomena. These transients, unlike switchingtransients, are beyond the control of the circuit designers and are more difficultidentify, measure and suppress.

In this paper, section 2 studies the behaviour of an under damped circuit, section 3describes the behaviour of a critically damped circuit and section 4 studies thebehaviour of an over damped circuit.

1-Introduction

In this experiment, we will study the behaviour of an RLC circuit whose responsevaries according to the different damping ratio applied, also checking the current andvoltage waveforms across the resistance.The circuit is under damped if the damped ratio () is less than 1, critically damped ifthe damping ratio is equal to 1, and over damped if the damping ratio is greater than1.

The circuit is made of a resistance, inductance, and a capacitor (49,9F), the circuitbeing closed for a long time and suddenly at instant t=0 its opened.


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2- The theory

Figure 1: Under damped Circuit Diagram

2.1-Under damped circuit (


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i(t) = B + C ------- (5), then at t=0,and i(0)= 376,18A substituting in (5) we get: B= 376.18A

Now differentiate equation (5) with respect to t we get:

=-7854,143B -30421,4B -7854,143C + 30421,4C ----- (6)Then from (1):

= = = -11,82x --(7)

Hence, substitute (7) and at t=0 into (6) we get:

-11,82x = -7854,143B + 30421,4C, so C= -291.42, then equation (5) becomes:

i (t) = 376,18

- 291,42

(A)

Figure 2: Under damped current and voltage wave form


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2.2-Critically damped circuit (=1)

Figure 3: Critically damped circuit diagram

Before we simulate the circuit for under damped condition, we need to determinecertain parameters: The resistance (R), and the inductance (L). The table-2 and thefollowing steps below show how the current expression can be determined.

Table 2: Critically damped

Givens: Formulae Calculations

C= 49.9Ffn =5Kz = 1

vs= 120V

fn= , so L=

R=

; n =

; i(0)=

L= 20.3xHR= 1.275n = 31419.68rads

i(0)= 94.12A

When the switch is opened and t=0, the circuit will have following equation:

Ri+ +Vc=0 ------ (1), and to solve for i(t) we use the following equation:

x +

+i =0 ------ (2), putting the data the equation is going to be:

1.09x + 63.65x + i =0 ---- (3), this is a second order differentialequation, since the damping ratio (=1) so this is critically damped circuit. Which as

the following solution:

i(t) = ------ (4) , then the equation becomes:i(t) = ------- (5), then at t=0, and i(0)= 94.12A substituting in (5)We get: B= 94,12A


=- 31419,68 C ----- (6)


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Then from (1): = = = -11,82x -- (7)

Hence, substitute (7) at t=0 into (6) we get:

-11,82x = -31419,68B + C, so C= -8.86 x =, then equation (5) becomes:i (t) = (A)

Figure 4: Critical damped current and voltage wave form

2.3-Over damped circuit (>1)

Figure 5: Over damped circuit diagram

Before we simulate the circuit for under damped condition, we need to determinecertain parameters: The resistance (R), and the inductance (L). The table-2 and thefollowing steps below show how the current expression can be determined.


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Table 3: Over damped

Givens: Formulae Calculations

C= 49.9F

fn =5Kz = 2vs= 120V

fn= , so L=

;

R=

; n=

;

1= ;

2 = i(0)=

L= 20.3xHR= 2.55

n = 31419.68rads1=8423,752=117192i(0)= 47,1A

When the switch is opened and t=0, the circuit will have following equation:

Ri+ +Vc=0 ------ (1), and to solve for i(t) we use the following equation:

x + +i =0 ------ (2), putting the data in the equation is going to be:

1.09x + 1.273 x +i=0 ---- (3), this is a second order differentialequation, since the damping ratio (>1) so this is an overdamped circuit. Which asthe following solution:

i(t) = B+ C ------ (4) , then the equation becomes:i(t) = B+ C ------- (5), then at t=0, and i(0)= 47,1A substituting in(5) we get: B + C= 47,1 ------- (6)


=- 8423,75B - 117192C ----- (7)

Then from (1): = = = -11,82x -- (8)

Hence, substitute (8) and at t=0 into (7) we get:

-11,82x = -8423,75B - 117192C, ---- (9) so, solving equation (6) & (9)simultaneously we get the following: B= -57,92 and C =105,02, therefore equation(5) becomes:

i (t) = -57,92 +105,02 (A)


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Figure 6: Over damped current and voltage wave forms

3- Effect of the damping ratio on the response of a circuit.

3.1- Under damped circuitThe under damped response the decay of the transient current is with oscillation(sinusoid).

3.2- Critically damped circuit

The critically damped response represents the circuit response that decays in thefastest possible time without going into oscillation.

3.3- Over damped circuit

The over damped response the decay of the transient current is without oscillation

4- Effects of transients

4.1- Electronic equipment:

Electronic devices may operate erratically. Equipment could lock up or producedgarbled results. These types of disruptions may be difficult to diagnose becauseimproper specification and installation of transient voltage surge suppressionequipment can actually INCREASE the incidents of failure as described above.

4.2- Motors:Motors will run at higher temperatures when transient voltages are present.Transients can interrupt the normal timing of the motor and result in "micro-jogging".

This type of disruption produces motor vibration, noise, and excessive heat. Motorwinding insulation is degraded and eventually fails


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4.3- Lighting:

Transient activity causes early failure of all types of lights. Fluorescent systemssuffer early failure of ballasts, reduced operating efficiencies, and early bulb failures.One of the most common indicators of transient activity is the premature appearance

of black "rings" at the ends of the tubes.

5- Avoiding problems caused transients

To avoid problem caused by transients, several techniques are being used such as:Gas discharge tube, thyristor surge protecting device, transient voltage suppressor,metal oxide varistor (MOV), etc.

6- Conclusion

The damping ratio plays a vital role in an RLC circuit, because it is the one whichdetermines the nature of the circuit. If the circuit is under damped, critically dampedor over damped. It is also directly proportional to the resistance of the circuit. Thegreater the damping ratio the bigger the resistance and the smaller the current.

7- Reference

Books

1. BOYLESTAD, R. L. 2003. Introductory circuit analysis, Upper Saddle River,N.J, Prentice Hall.

2. MERSEREAU, R. M. & JACKSON, J. R. 2006. Circuit analysis: a systemsapproach, Upper Saddle River, N.J, Pearson Prentice Hall.

3. ZORNESKY, J. & MAYBAR, S. H. 2000. Circuit analysis: an integratedapproach, Upper Saddle River, N.J, Prentice Hall.

Internet links

http://www.onsemi.com/pub_link/Collateral/TND335-D.PDFhttp://www.ti.com/lit/an/slva233a/slva233a.pdfhttp://www.pge.com/includes/docs/pdfs/about/news/outagestatus/powerquality/avoid_pwr_disturb.pdf

http://www.irf.com/technical-info/designtp/dt97-3.pdf
http://www.onsemi.com/pub_link/Collateral/TND335-D.PDFhttp://www.ti.com/lit/an/slva233a/slva233a.pdfhttp://www.pge.com/includes/docs/pdfs/about/news/outagestatus/powerquality/avoid_pwr_disturb.pdfhttp://www.pge.com/includes/docs/pdfs/about/news/outagestatus/powerquality/avoid_pwr_disturb.pdfhttp://www.irf.com/technical-info/designtp/dt97-3.pdfhttp://www.irf.com/technical-info/designtp/dt97-3.pdfhttp://www.pge.com/includes/docs/pdfs/about/news/outagestatus/powerquality/avoid_pwr_disturb.pdfhttp://www.pge.com/includes/docs/pdfs/about/news/outagestatus/powerquality/avoid_pwr_disturb.pdfhttp://www.ti.com/lit/an/slva233a/slva233a.pdfhttp://www.onsemi.com/pub_link/Collateral/TND335-D.PDF

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Circuit Analysis IV Assignment.pdf Ch