BEE3133 ELECTRICAL POWER SYSTEMS

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BEE3133 ELECTRICAL POWER SYSTEMS

• Chapter 3
• The Per-Unit System
• Nor Laili Ismail

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Learning Outcomes

• Students should be able to
• Identify the symbols and draw the one-line
  diagram
• Construct the impedance diagram and find the per
  unit values.
• Solve the per unit problems of a single-phase and
  three-phase circuit.
• Identify the advantages of per unit system.

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One Line Diagram

• Represent the interconnection of the power system
  components.
• Also referred as Single-line Diagram
• Advantage Simplicity
• One phase represents all three phases of the
  balanced system.
• Equivalent circuit of the components are replaced
  by their standard symbols
• The completion of the circuit through the neutral
  is omitted.

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One Line Diagram
Symbols used in one line diagram
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Impedance Diagram
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Per-Unit System

• In power systems there are so many different
  elements such as Motors, Generators and
  Transformers with very different sizes and
  nominal values.
• To be able to compare the performances of a big
  and a small element, per unit system is used.

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Per Unit System

• Power system quantities such as voltage, current
  and impedance are often expressed in per unit or
  percent of specified values.
• Per unit quantities are calculated as

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Per Unit System
Per Unit Values
Conversion of Per Unit Values
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Per Unit System

• Usually, the nominal apparent power (S) and
  nominal voltage (V) are taken as the base values
  for power (Sbase) and voltage (Vbase).
• The base values for the current (Ibase) and
  impedance (Zbase) can be calculated based on the
  first two base values.

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Per Unit System
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Per Unit System

• The percent impedance
• e.g. in a synchronous generator with 13.8 kV as
  its nominal voltage, instead of saying the
  voltage is 12.42 kV, we say the voltage is 0.9
  p.u.

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Transformer Voltage Base
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Per Unit in 3? Circuit

• Simplified
• Concerns about using phase or line voltages are
  removed in the per-unit system
• Actual values of R, XC and XL for lines, cables,
  and other electrical equipment typically phase
  values.
• It is convenient to work in terms of base VA
  (base volt-amperes)

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Per Unit in 3? Circuit

• Usually, the 3-phase SB or MVAB and
  line-to-line VB or kVB
• are selected
• IB and ZB dependent on SB and VB

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Change of Base

• The impedance of individual generators
  transformer, are generally in terms of
  percent/per unit based on their own ratings.
• Impedance of transmission line in ohmic value
• When pieces of equipment with various different
  ratings are connected to a system, it is
  necessary to convert their impedances to a per
  unit value expressed on the same base.

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Change of Base
1
2
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Change of Base
From (1) and (2), the relationship between the
old and the new per unit value
If the voltage base are the same,
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Advantages

• Transformer equivalent circuit can be simplified
  by properly specifying base quantities.
• Give a clear idea of relative magnitudes of
  various quantities such as voltage, current,
  power and impedance.
• Avoid possibility of making serious calculation
  error when referring quantities from one side of
  transformer to the other.

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Advantages

• Per-unit impedances of electrical equipment of
  similar type usually lie within a narrow
  numerical range when the equipment ratings are
  used as base values.
• Manufacturers usually specify the impedances of
  machines and transformers in per-unit or percent
  in nameplate rating.

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Advantages

• The circuit laws are valid in per unit systems,
  and the power and voltage equation are simplified
  since the factor v3 and 3 are eliminates in the
  per-unit systems.
• Ideal for the computerized analysis and
  simulation of complex power system problems.

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Review

• Study the examples.
• Try to solve the problems in your tutorials.