BEE 3133 ELECTRICAL POWER SYSTEMS

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BEE 3133 ELECTRICAL POWER SYSTEMS

• Chapter 4
• Line Model and Performance
• Rahmatul Hidayah Salimin

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Introduction

• Analyze the performance of single-phase and
  balanced three-phase transmission lines under
  normal steady-state operating conditions.
• Expression of voltage and current at any point
  along the line are developed, where the nature of
  the series impedance and shunt admittance is
  taken into account.
• The performance of transmission line is measured
  based on the voltage regulation and line
  loadability.

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Transmission Line Representation

• A line is treated as two-port network which the
  ABCD parameters and an equivalent p circuit are
  derived.

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Transmission Line Representation

• To facilitate the performance calculations
  relating to a transmission line, the line is
  approximated as a seriesparallel
  interconnection of the relevant parameters.
• Consider a transmission line to have
• A sending end and a receiving end
• A series resistance and inductance and
• A shunt capacitance and conductance

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Transmission Line Representation

• The relation between sendingend and
  receivingend quantities of the twoport
  network can be written as

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Transmission Line Representation

• Short Line Model
• lt 80 km in length
• Shunt effects are neglected.
• Medium Line Model
• Range from 80240 km in length
• Shunt capacitances are lumped at a few
  predetermined points along the line.
• Long Line Model
• gt240 km in length.
• Uniformly distributed parameters.
• Shunt branch consists of both capacitance and
  conductance.

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Short Line Model
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Short Line Model
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Short Line Model

• Thus, the ABCD parameters are easily obtained
  from KVL and KCL equations as below

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Complex Power

• Sending end power
• Receiving end power

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Transmission Line Efficiency

• Total FullLoad Line Losses
• Transmission Line Efficiency
• Note that only Real Power are taken into account!

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Voltage Regulation

• ABCD parameters can be used to describe the
  variation of line voltage with line loading.
• Voltage regulation is the change in voltage at
  the receiving end of the line when the load
  varies from noload to a specified fullload at a
  specified power factor, while the sending end is
  held constant.

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Voltage Regulation
Noload receivingend voltage
Fullload receivingend voltage
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Voltage Regulation

• The effect of load power factor on voltage
  regulation is illustrated in phasor diagram.
• The phasor diagrams are graphical representation
  of lagging, unity and leading power factor.

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Voltage Regulation

• The higher (worse) voltage regulation occurs for
  the lagging pf load where VR(NL) exceeds VR(FL)
  by the larger amount.
• A smaller or even negative voltage regulation
  occurs in leading pf load.

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Voltage Regulation

• In practice, transmission line voltages decrease
  when heavily loaded and increase when lightly
  loaded.
• EHV lines are maintained within 5 of rated
  voltage, corresponding to about 10 voltage
  regulation.
• 10 voltage regulation for lower voltage lines
  also considered good operating practice.

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Line Loadability

• Another important issue that affect transmission
  line performance.
• 3 major line loading limits are
• Thermal limit
• Short transmission lines lt80 km length
• Voltage drop limit
• Longer line length 80300 km length
• Steady-state stability limit
• Line length over 300 km

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Example 1 Short TL

• A 220-kV, 50 Hz, three-phase transmission line is
  40 km long. The resistance per phase is 0.15 O/km
  and the inductance per phase is 1.5915 mH/km. The
  shunt capacitance is negligible. Use the line
  model to find the voltage and power at the
  sending end and the voltage regulation and
  efficiency when the line is supplying a
  three-phase load of
• 381 MVA at 0.8 pf lagging at 220 kV
• 381 MVA at 0.8 pf leading at 220 kV

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Example 2 Short TL

• A 220-kV, 50 Hz, three-phase transmission line is
  40 km long. The resistance per phase is 0.15 O/km
  and the inductance per phase is 1.5915 mH/km. The
  shunt capacitance is negligible. Use the line
  model to find the voltage and power at the
  sending end and the voltage regulation and
  efficiency when the line is supplying a
  three-phase load of
• 381 MVA at 0.8 pf lagging at 220 kV
• 381 MVA at 0.8 pf leading at 220 kV

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Solution (a)

• Given
• R 0.15 O/km , L 1.5915 mH/km
• S 381 MVA with pf 0.8 lag
• VR(line)220 kV

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Voltage Regulation,
Effiency,?
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Medium Line Model Nominal p Circuit
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Medium Line Model

• Shunt capacitor is considered.
• ½ of shunt capacitor considered to be lumped at
  each end of the line p circuit
• Total shunt admittance, Y

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Medium Line Model

• Under normal condition,
• shunt conductance per unit length (the leakage
  current) over the insulators and due to corona is
  negligible
• Thus, g 0

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Medium Line Model

• To obtain ABCD parameters, the current in the
  series branch is denoted as IL.
• Using KCL and KVL, the sendingend voltage is

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Medium Line Model
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Medium Line Model
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Medium Line Model

• Using KCL to obtain equation for sendingend
  current

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Medium Line Model

• Thus, the ABCD parameters can be obtained from
  equation 3 and 5

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Medium Line Model

• ABCD constant are complex since p model is a
  symmetrical two-port network
• A D
• The determinant of the transmission matrix is
  unity(1)
• AD BC 1 (Prove this!)

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Medium Line Model

• The receiving and quantities can be expressed in
  terms of the sending end quantities
• If, ignore the shunt capacitance of the TL, the
  shunt admittance, Y0, it become the short
  transmission line constant.

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Example 2 Medium TL

• A 345-kV, 60 Hz, three-phase transmission line is
  130 km long. The resistance per phase is 0.036
  O/km and the inductance per phase is 0.8 mH/km.
  The shunt capacitance is 0.0112 µF/km. Use the
  medium line model to find the voltage and power
  at the sending end and the voltage regulation and
  efficiency when the line is supplying a
  three-phase load of
• 325 MVA at 0.8 pf lagging at 325 kV
• 381 MVA at 0.8 pf leading at 325 kV

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Medium Line Model Nominal T Circuit
Find the ABCD Parameters for this circuit using
KVL and KCL
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Long Line Model
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Long Line Model

• The shunt capacitance and series impedance must
  be treated as distributed quantities
• The V and I on the line must be found by
  solving the differential equation of the
  transmission line.

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Long Line Model
? propagation constant Zc characteristic
impedance
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Long Line Model

• If ?l ltlt0 ? sinh (?l )/( ?l ) tanh (?l /2)/ (?l
  /2) 1.0
• The ABCD parameters

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ABCD Parameters
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Surge Impedance Loading

• When the line is loaded by being terminated with
  an impedance equal to its characteristic
  impedance, the receiving end current is
• For a lossless line, Zc is purely resistive. The
  load corresponding to the surge impedance at
  rated voltage is known as the surge impedance
  loading (SIL).

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Surge Impedance Loading

• Since VR VLrated/v3, SIL in MVA becomes

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Surge Impedance Loading

• SIL is useful measure of transmission line
  capacity as it indicates a loading where the
  lines reactive requirement are small.
• For loads significantly above SIL, shunt
  capacitor may be needed to minimize voltage drop
  along the line.
• While for light loads significantly below SIL,
  shunt inductors may be needed.

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Power Transmission Capability

• Power handling ability of a line is limited by
• Thermal loading limit
• Stability limit
• Thermal loading limit