2.1 Transmission line modeling and parameters

Transmission lines are the backbone of power systems, carrying electricity over vast distances. They consist of conductors, insulators, and supporting structures, each playing a crucial role in efficient power delivery. Understanding their components and parameters is key to optimizing power transmission.

Modeling transmission lines is essential for analyzing their performance. From short to long line models, engineers use various techniques to represent line behavior. These models help predict voltage regulation, power transfer capability, and efficiency, enabling better planning and operation of power systems.

Transmission Line Structure

Components and Materials

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• Transmission lines transmit electrical power over long distances from generating stations to load centers
• Conductors carry high currents with minimal power losses and are typically made of aluminum, copper, or aluminum conductor steel reinforced (ACSR)
• Insulators provide electrical isolation between the conductors and the supporting structures, preventing current leakage and flashovers
  • Insulators are commonly made of ceramic or polymer materials
• Supporting structures, including towers and poles, provide mechanical support for the conductors and maintain proper clearances between conductors and the ground

Classification and Voltage Levels

• Transmission lines are classified based on their voltage levels
  • High-voltage (HV) lines
  • Extra-high-voltage (EHV) lines
  • Ultra-high-voltage (UHV) lines
• Higher voltage levels allow for more efficient power transmission over longer distances
• The choice of voltage level depends on factors such as the amount of power to be transmitted, the distance, and the cost of the transmission infrastructure

Transmission Line Parameters

Resistance, Inductance, and Capacitance

• Resistance (R) represents the opposition to the flow of electric current in the conductors, causing power losses in the form of heat
  • Resistance depends on the conductor material, cross-sectional area, and length
  • Larger cross-sectional area and shorter length result in lower resistance
• Inductance (L) arises from the magnetic field generated by the current flowing through the conductors
  • Inductance is influenced by the geometric configuration of the conductors, such as spacing and transposition
  • Transposition involves periodically exchanging the positions of the conductors to balance the inductance
• Capacitance (C) exists between the conductors and between the conductors and the ground
  • Capacitance is determined by the spacing between conductors, conductor size, and the presence of grounded conductors or earth wires
  • Larger spacing and smaller conductor size result in lower capacitance

Series Impedance and Shunt Admittance

• The series impedance of a transmission line consists of the resistance and inductance
  • Series impedance determines the voltage drop and power losses along the line
• The shunt admittance is primarily due to the capacitance
  • Shunt admittance affects the charging current and the voltage profile along the line
• The electrical parameters are distributed along the length of the transmission line and are expressed per unit length (e.g., ohms/km or siemens/km)
  • Distributed parameters account for the continuous nature of the transmission line
  • Lumped parameter models approximate the distributed parameters using discrete components

Equivalent Circuits for Transmission Lines

Lumped Parameter Models

• Lumped parameter models represent the transmission line using discrete electrical components, such as resistors, inductors, and capacitors
• The choice of model depends on the length of the transmission line and the required accuracy
• Three common lumped parameter models are:
  • Short transmission line model
  • Medium transmission line model (nominal pi model)
  • Long transmission line model (equivalent pi model)

Short, Medium, and Long Transmission Line Models

• The short transmission line model ignores the shunt admittance and represents the line using a series resistance and inductance
  • Suitable for lines shorter than 80 km (50 miles)
  • Simplifies calculations but may not capture the effects of shunt capacitance
• The medium transmission line model, also known as the nominal pi model, includes the series impedance and shunt admittance
  • The shunt admittance is divided into two equal parts and placed at the sending and receiving ends of the line
  • Provides a more accurate representation compared to the short line model
• The long transmission line model, or the equivalent pi model, also includes the series impedance and shunt admittance but distributes the shunt admittance uniformly along the line
  • Suitable for lines longer than 250 km (150 miles)
  • Captures the distributed nature of the line parameters more accurately

ABCD Parameters

• The ABCD parameters, or the transmission line constants, relate the sending-end voltage and current to the receiving-end voltage and current
• The ABCD parameters are expressed as a 2x2 matrix:
  • A: Voltage ratio with receiving end open-circuited
  • B: Transfer impedance with receiving end short-circuited
  • C: Transfer admittance with sending end short-circuited
  • D: Current ratio with sending end open-circuited
• ABCD parameters are used to analyze the performance of the transmission line, such as voltage regulation and power transfer capability
• They can be cascaded to represent multiple line sections or combined with other network elements

Transmission Line Performance under Load

Voltage Regulation and Power Transfer Capability

• Voltage regulation is the difference between the sending-end and receiving-end voltages, expressed as a percentage of the receiving-end voltage
  • Indicates the ability of the line to maintain a constant voltage at the load end
  • Lower voltage regulation implies better voltage stability and power quality
• The power transfer capability of a transmission line depends on its surge impedance loading (SIL)
  • SIL is the characteristic impedance of the line and determines the maximum power that can be transmitted without causing instability or excessive voltage drop
  • Operating the line at or near its SIL maximizes power transfer and minimizes voltage variations

Efficiency and Losses

• Transmission line efficiency is the ratio of the power delivered at the receiving end to the power input at the sending end
• Efficiency is affected by line losses, which include:
  • Conductor losses (I^2R): Caused by the resistance of the conductors
  • Corona losses: Caused by the ionization of the air surrounding the conductors at high voltages
• Minimizing line losses improves the overall efficiency of power transmission
• Techniques to reduce losses include using larger conductor sizes, bundled conductors, and optimizing conductor spacing

Loading Conditions and Compensation

• The performance of a transmission line is influenced by the loading conditions, such as the magnitude and power factor of the load
• Inductive loads (e.g., motors) cause the receiving-end voltage to be lower than the sending-end voltage, while capacitive loads have the opposite effect
• Shunt compensation devices, such as capacitors or reactors, can be used to improve voltage regulation and power factor
  • Capacitors provide reactive power support and boost the voltage
  • Reactors absorb excess reactive power and control overvoltages
• Series compensation, using series capacitors, can be employed to reduce the effective series impedance of the line and enhance power transfer capability

Ferranti Effect

• Ferranti effect occurs in lightly loaded or open-ended transmission lines
• Due to the line's capacitance, the receiving-end voltage becomes higher than the sending-end voltage
• This voltage rise can lead to overvoltages and may require reactive power absorption or voltage control measures
• Ferranti effect is more pronounced in long transmission lines with high capacitance and low loading
• Understanding and mitigating the Ferranti effect is important for ensuring voltage stability and preventing equipment damage