01 equivalent circuits

7/31/2019 01 Equivalent Circuits

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Equivalent Circuit of Power System ComponentsGenerator

Equivalent Circuit of an AC Generator

Eg generated emf at no load due to the field excitation

Xar: reactance due to the armature reaction known as

fictitious reactance.Xl: reactance due to the leakage flux known as leakage

reactance orpotier reactance.

Xs: summation of Xar and Xl known as synchronous

reactance.

Ra: resistance die to armature winding known as armature

resistance.

Er: voltage behind the armature reaction effect.

Vt: terminal voltage.

If the resistance Ra is very small as compared to Xs, the equivalent circuit of an ac generator can be

simplified as shown in the following figure (a). Similarly, the simplified equivalent circuit of an ac

motor can be given as shown in figure (b).

Transformer (XF)The transformer is a device for transferring electrical energy from one circuit to another circuit without

a change in frequency.

Features of a Transformer

1. Transfer electrical energy from one circuit to another circuit by changing voltage and current2. Frequency cannot be changed3. Energy transformation is accomplished by electromagnetic induction4. Electrical circuits are magnetically coupled no direct electric connection5. Efficiency is high and mantainence is simpler since there has no rotating parts

Main Components of a Transformer

1. The magnetic core2. Primary and secondary windings3. Insulation of windings4. Lead and tapping for coils with their supports, terminals and terminal insulator5. Tank, oil, cooling arrangement etc.

Application of Transformer

1. Stepping-up of voltage


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2. Stepping-down of voltage3. Electrical Isolation4. Impedance matching5. Link between AC and DC systems6. Instrument extension

Classification of Transformer

Transformer can be classified according to the following ways:1. Based on number of phases

(a)Single-phase transformer(b)Three phase transformer

2. Based on relative position (construction) of winding and core(a)Core type transformer(b)Shell type transformer

3. Based on number of winding per phase(a)One winding per phase(b)Two winding per phase(c)Three winding per phase

4. Based on volt-ampere and voltage ratings(a)Low voltage transformer [VHV < 1.1 kV](b)Medium voltage transformer [1.1 kV VHV < 11 kV](c)High voltage transformer [VHV 11 kV]

5. Based on service conditions(a)Power transformer(b)Distribution transformer(c) Instrument Transformer

i. Current transformerii. Potential transformer

6. Based on method of cooling(a)Air Natural(b)Air Blast(c)Oil Natural(d)Oil Blast(e)Forced Oil Cooling(f) Oil and Water Cooled(g)Forced Oil and Water Cooled

Current (or Series) Transformer (CT)Used with low-range ammeters to measure current in high-current ac circuit

Step up the voltage

Step down the current

Has a primary coil with one or more turns of thick wire connected in series with the line whose current

is to be measuredHas a secondary coil with a large number of turns of fine wire and connected across the ammeter

terminals


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If the current transformer has primary to secondary current ratio (I1/I2) of 100:5, then it steps up the

voltage 20 times whereas it steps down the current to (1/20) th of its actual value.

One of the most commonly used current transformer is the one knownclamp-type orclip-on type.

Since the ammeter resistance is very low, the current transformer normally works short circuited.

The secondary of a current transformershould never be left open under any circumstances. If this not

done, then due top the absence of counter amp-turns of the secondary, the unopposed primary mmf

will set up an abnormally high flux in the core which will produce excessive core loss with subsequent

heating and a high voltage across the secondary terminals.

Potential Transformer (PT)Used with low-range voltmeter to measure high

voltage in high-voltage ac circuit

Step down the voltage

Step up the current

For safety, the secondary should be completely

insulated from the high-voltage primary andshould be, in addition, grounded for affording

protection to the operator.

Equivalent Circuit of a Practical Transformer

R1, X1, I1, V1, E1: primary side resistance, leakage reactance, current, voltage, and counter (or self

induced) emf, respectively.


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R2, X2, I2, V2, E2: secondary side resistance, leakage reactance, current, voltage, and counter (or self

induced) emf, respectively.

R0 (orRc orRm),X0 (orXm): core loss resistance, mutual inductance, respectively.

I0,I (orIc) Iw: no-load current, magnetizing current, and working or core loss current, respectively.

If all secondary parameters are referred to the primary side then the equivalent circuit becomes:

R2= R2/K

2;X2

= X2/K

2;E2

=E2/K=E1; V2

=V1/K.


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Parameters of Transmission (TM) LineThe basic transmission-line parameters are:

1. Series resistance: Series resistance accounts for copper (or ohmic or I2R) losses.The resistance of a conductor at a specified temperature is

A

l=

dcR

Resistance of a conductor depends of the following factors:

(a)Spiraling(b)Temperature(c)Frequency (due o skin effect)(d)Current magnitude magnetic conductor

2. Series inductance (or inductive reactance): Series inductive reactance gives rise to series voltagedrops along the line.

The inductance of a magnetic circuit that has a constant permeability can be obtained by

determining the following:

(a)Magnetic field intensityHfrom Amperes Law(b)Magnetic flux densityB (B=H)

(c)Flux linkage (d)Inductance from flux linkage per ampere (L=/I)

3. Shunt capacitance (or capacitive reactance): Shunt capacitive reactance gives rise to line-charging current.

The capacitance between conductors in a medium with constant permittivity canobtained by

determining the following:

(a)Electric field strengthE, from Gausss Law(b)Voltage between conductors(c)Capacitance from charge per unit volt (C=q/V)

4. Shunt conductance (or admittance): Shunt conductance accounts for real power (V2G) linelosses due to leakage currents between conductors or between conductors and ground. Shunt

conductance of overhead line is usually neglected since this loss is very small compared to copper

loss..

This power loss is due to leakage currents at insulators and to corona.

Corona occurs when a high value of electric field strength at a conductor surface causes the air to

become electrically ionized and to conduct. The real power loss due to corona, calledcorona loss,

depends on meteorological conditions, particularly rain, and on conductor surface irregularities.

Series impedance is including the series resistance and series inductive reactance

Representation of Transmission LineLet,

R is series resistance per unit length (/m) and per phaseG is shunt conductance per unit length (S/m) and per phase

L is series inductance per unit length (H/m) and per phase

Cis shunt capacitance per unit length (F/m) and per phase

z =R +jL is series impedance per unit length (/m) and per phase

y = G +jCis shunt admittance per unit length (S/m) and per phase

l is line length (m) and per phase


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Z=zl is total impedance () and per phase

Y=yl is total impedance (S) and per phase

Short-Transmission Line (less than 80 km): For a short-transmission line, shunt capacitance is so

small that it can be omitted entirely with little loss of accuracy, and we need to consider only the series

resistance and the series inductance for the total length of the line.

Medium Transmission Line (from 80 to 250 km): A medium-length line can be represented

sufficiently well by series resistance, series inductance as lump parameters with half the capacitance to

neutral of the line lumped at each end of the equivalent circuit.


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Fig. 5.6 Nominal- circuit of a medium-length transmission line

Fig. Nominal-T circuit of a medium-length transmission line

VS, VR are sending end and receiving end voltages.

IS,IR are sending end and receiving end currents.

Long Transmission Line (more than 250 km): The exact solution of any transmission line and the

one required for a high degree of accuracy more than approximately 150 mile long must consider the

fact that the parameters are not lumped but are distributed uniformly through out the length of the line.

xeZIVxeZIVV cRRcRR +=22

; xeIZVxeIZVI RcRRcR +=2

/2

/

yzZc /= ischaracteristic impedance of the line

jzy +== ispropagation constant

isattenuation constant

isphase constant


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Fig. 5.8 Equivalent- circuit of a long transmission line

The One Line or Single Line Diagram [1, 6.11, p. 155]In power engineering, a one-line or single-line diagram is a simplified notation for representing athree-phase power system.

A simplified diagram of an electrical system is called one-line or single-line diagram. The purpose of

the one-line diagram is to supply in concise form the significant information about the power system.

The one-line diagram has its largest application in power flow studies. Electrical elements such as

circuit breakers, transformers, capacitors, bus bars, and conductors are shown by standardized

schematic symbols as shown in the following Table 1.

Instead of representing each of three phases with a separate line or terminal, only one conductor is

represented. It is a form of block diagram graphically depicting the paths for power flow between

entities of the system.

Elements on the diagram do not represent the physical size or location of the electrical equipment, but

it is a common convention to organize the diagram with the same left-to-right, top-to-bottom sequence

as the switchgear or other apparatus represented.

Why one line diagram?

1. Power systems are extremely complicated2. Geographically spread system3. Three phase (3) System

Need a simple way to express the network

Characteristic

1. Concise form of basic arrangement of PS2. Not show the exact electrical connection3. Expressed in block diagram4. Diagram varies for different purposes

Fig. 6.26 is the one-line diagram of a very simple power system. Two generators, one grounded

through a reactor and one through a resistor, are connected to a bus and through a step-up transformer

to a transmission line. Another generator, grounded through a reactor, is connected to a bus and

through a transformer to the opposite end of the transmission lie. A load is connected to each bus. On

the diagram information about the loads, the rating of the generator and transformers, and reactances

of the different components of the circuit is often given.


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Fig. 6.26 One-line diagram of an electrical system.

Impedance and Reactance Diagram [1, 6.12, p.157]A single-phase circuit diagram is drawn from the one-line diagram to calculate the performance of a

system under load conditions or upon the occurrence of a fault.

Fig. 6.27 combines the equivalent circuits of the various components shown in Fig. 6.26 to form the

impedance diagram of the system.

The shunt admittance in an equivalent circuit of a transformer is usually omitted, since the magnetizing

current is usually insignificant compared with the full-load current.

Shunt conductance of overhead line is usually neglected since this loss is very small compared tocopper loss.

In transmission line, transformer and synchronous machine the resistance is very small as compared to

the reactance, so resistance is often omitted from the circuit when making fault calculation.

Fig. 6.27.1 is the simplified impedance diagram of Fig. 6.27.

Fig. 6.27 Impedance diagram corresponding to the one-line diagram of 6.26.

If a fault is occurred in the transmission line then loads are disconnected. If the impedance diagram is

simplified by omitting all static loads, all resistances, the magnetizing current of each transformer, all

the capacitance of the transmission line, the impedance diagram reduces to the reactance diagram of

Fig. 6.28. These simplification apply to fault calculations only and not to load-flow studies.


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Fig. 6.27.1 Simplified impedance diagram of Fig. 6.27.

Fig. 6.28 Reactance impedance diagram of Fig. 6.27.

References

[1] Willaim D. Stevenson, Elements of Power System Analysis, Fouth Edition, McGraw-HillInternational Editions, Civil Engineering Series, McGraw-Hill Inc.

[2] John J. Grainger, William D. Steevnson, Jr., Power System Analysis, McGraw-Hill Series in

Electrical and Conputer Engineering, McGraw-Hill Inc.

[3] J. Duncan Glover, Mulukutla S. Sharma, Thomas J. Overbye, Power System Analysis and Design,

Fouth Edition (India Edition), Course Technology Cengage Learning

[4] V. K. Mehta, Rohit Mehta, Principles of Power System, Multicolor Illustrative Edition, S. Chand

and Company Limited


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Home Work 01Draw the (i) simplified impedance diagram, and (ii) reactance diagram for the following figures.

Fig. (a) For example

Fig. (b) For example

Fig. (c) For example

01 equivalent circuits

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