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` One-line Diagram

BY

R

3-phase system single-phase system

One-line diagram is a simplified single-phase circuitdiagram of a balanced three-phase electric power system.

It is indicated by a single line and standard apparatussymbols .



One-line DiagramT he information on a one-line diagram is vary according to theproblem at hand and the practice of the particular company preparingthe diagram.

Load/ Power Flow Study

T ransient Stability Study

Example :



A dvantages of One-line DiagramSimplicity.One phase represents all three phases of the

balanced system.The equivalent circuits of the components arereplaced by their standard symbols.The completion of the circuit through the neutralis omitted.



Impedance and Reactance DiagramsImpedance (Z = R + jX) diagram is converted from one-line diagram showing the equivalent circuit of eachcomponent of the system. It is needed in order tocalculate the performance of a system under load

conditions (Load flow studies) or upon the occurrence of a short circuit (fault analysis studies).Reactance (jX) diagram is further simplified fromimpedance diagram by omitting all static loads, allresistances, the magnetizing current of eachtransformer, and the capacitance of the transmissionline. It is apply to fault calculations only, and not to loadflow studies.Impedance and reactance diagrams sometimes calledthe Positive-sequence diagram.



Z diagram X diagram

Derived from single line diagram Derived from Z diagram.

Covers equivalent components of all circuit components All static loads, resistances, magnetizing current of eachtransformer, and the capacitance of the transmission line are

omittedConsists of R and X Consists only X

Used to calculate both load/power flow and fault analysis Used to calculate fault analysis only

A bit complex More simpler

Formulated as Z=R+jX Formulated as Z=jX

Impedance and Reactance Diagrams



Impedance and Reactance DiagramsExample : One-line diagram of an electric power system



E1 E2 E3

G en.3

LoadB

Transformer T 2

TransmissionLine

Transformer T 1

Load A

G enerators

1 and 2

Impedance diagram corresponding to the one-line diagram of Example 1.2Impedance and Reactance Diagrams



R eactance diagram corresponding to the one-line diagram of Example 1.2

E1 E2 E1

G enerators

1 and 2

Transmission

LineTransformer

T 2

G en.

3Transformer

T 1

Impedance and Reactance Diagrams



E quivalent circuit for each component?



Per-unit RepresentationIn power systems there are so many different elementssuch as Motors, G enerators and Transformers with very

different sizes and nominal values.To be able to compare the performances of a big and asmall element, per unit system is used.



Per-unit RepresentationPower system quantities such as voltage, current andimpedance are often expressed in per unit or percent of

specified values.Per unit quantities are calculated as:

quantityof value base

quantityactualunit- per inQuantity !



` The advantages of per-unit quantities:The apparatus of the same general type of p.u. volt dropsand losses are in the same order, regardless of size.The use of 3 in three-phase calculations is reduced.By the choice of appropriate voltage bases, the solutionof networks containing several transformers is facilitated.Per-unit quantities more readily to digital computation.



` The formulas relate the various quantities for single-phase system:



` The formulas relate the various quantities for three-phase system:



Per-unit RepresentationUsually, the nominal apparent power (S) and nominalvoltage (V) are taken as the base values for power (S

base) and voltage ( V

base).

The base values for the current ( I base ) and impedance(Z base ) can be calculated based on the first two basevalues.



Per-unit Representation

b ase

base

b ase

b aseb ase

b ase

b aseb ase

b aseb ase

S V I V Z

V S I

givenS givenV

2

)(

!!

!



E xample in the module:



E xamples in the module:



C hanging the Base of Per-unit QuantitiesThe impedance of individual generators and transformersare generally in terms of % or pu quantities based on their own ratings (By manufacturer).For power system analysis, all impedances must beexpressed in pu on a common system base . Thus, it isnecessary to convert the pu impedances from one base toanother (common base, for example: 100 MV A ).

Per-unit impedance of a circuit element

2

k V)voltage,( base

MVA )( base)impedance,(actual v;!



The equation shows that pu impedance is directlyproportional to base MV A and inversely proportional tothe square of the base voltage.Therefore, to change from old base pu impedance tonew base pu impedance, the following equation applies:

¹¹

º

¸©©

ª

¨¹¹

º

¸©©

ª

¨!

old

new

2

new

oldoldnew MVA base

MVA basek V base

k V baseunit Z- per unit Z-Per

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