GMR in Power System: Calculate Inductive Reactance Quiz and Flashcards

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Questions and Answers

What is the relationship between coincident factor and average contribution factor?

They are inversely proportional

They are directly proportional

They are not related

They are equal (correct)

How is load factor defined?

Ratio of peak load to average load

Ratio of average load to peak load (correct)

Ratio of energy served to peak load

Ratio of peak load to energy served

Why is the load factor less if the time period (T) is large?

Because the average load decreases (correct)

Because the average load increases

Because the energy consumption decreases

Because the peak load decreases

What does annual load factor represent?

Total energy served over one year Signup and view all the answers

How is loss factor defined?

Ratio of peak-load power loss to average power loss Signup and view all the answers

What is the relationship between coincidence factor and contribution factor in Case-2?

They are equal Signup and view all the answers

What is the relationship between load factor and loss factor in Case-1 when off-peak load is zero?

Equal to a constant t/T Signup and view all the answers

In Case-3 where the load is steady, what is the relationship between the loss factor and the load factor?

LLF = LF Signup and view all the answers

According to Equation (1.36), what is the approximate formula to relate the loss factor (LLF) to the load factor (LF)?

LLF = 0.3LF + 0.7(LF)2 Signup and view all the answers

What happens to the loss factor when there is a very short-lasting peak according to Equation (1.33)?

Loss factor approaches 1.0 Signup and view all the answers

How is the load at the end of the m-th year calculated according to Equation (1.37)?

$P_m = P_0(1 + g)^m$ Signup and view all the answers

What can be concluded about the relationship between loss factor and load factor based on Equation (1.35)?

$(LF)^2 < LLF < LF$ Signup and view all the answers

In a bundled conductor line with four conductors per bundle, if the diameter of each sub-conductor is 3.146 cm and they are placed at the corners of a square with a side length of 25 cm, what is the GMR of this configuration?

15.73 cm Signup and view all the answers

For a single-phase 35 km long transmission line with two solid round conductors, each having a radius of 4.5 mm and a conductor spacing of 2.5 m, what is the equivalent radius of a hollow, thin-walled conductor with the same equivalent inductance as the original line?

5.7 mm Signup and view all the answers

What is the value of the inductance per conductor in the single-phase 35 km long transmission line with two solid round conductors and a conductor spacing of 2.5 m?

38 mH Signup and view all the answers

Calculate the inductive reactance per km at 50 Hz for the three-phase line configuration shown in Figure 2.33.

0.213 ohm/km Signup and view all the answers

What is the radius of the equivalent single conductor line that would have the same inductive reactance as the given three-phase line in Figure 2.33?

26.72 cm Signup and view all the answers

In a three-phase, 60 Hz transposed transmission line with a line reactance of 0.486 ohm/km and a conductor GMR of 2.0 cm, what is the value of D as shown in Figure 2.34?

10 m Signup and view all the answers

What is the line-to-line capacitance between the conductors according to the given text?

0.0121 mF/km Signup and view all the answers

If the line charging current for a transmission line is 4 A/km, what is the capacitance C12 and voltage V12?

C12 = 1 mF/km, V12 = 4 kV Signup and view all the answers

In a balanced three phase system, what should be the sum of qa, qb, and qc?

0 Signup and view all the answers

What is the capacitance between each conductor and a neutral for a transmission line?

0.0242 mF/km Signup and view all the answers

If r1 = r2 = r, what is the value of C12 in terms of r according to the text?

$pÎo D \ln r$ Signup and view all the answers

In equation (3.9), what does 'log (D r)' represent?

Line-to-line capacitance between conductors Signup and view all the answers

What is the effect of the ground and shield wires considered to be in the given scenario?

Negligible Signup and view all the answers

What is the per phase equivalent capacitance to neutral in the scenario provided?

0.0242 R| D.d.d.d log S |T r.d.d Signup and view all the answers

How is the effect of earth on capacitance accounted for?

By the method of image charges introduced by Kelvin Signup and view all the answers

What remains constant for section-II and section-III of the transposition cycle?

Deq and Ds Signup and view all the answers

In equation (3.35), what does 'Can' represent?

Capacitance of Transmission Lines Signup and view all the answers

How are phase conductors treated within their groups?

Transposed Signup and view all the answers

Study Notes

Capacitance of Transmission Lines

The capacitance between two conductors can be calculated using the formula: C12 = ε₀ / (D ln(r1/r2)) where C12 is the capacitance, ε₀ is the permittivity of free space, D is the distance between the conductors, and r1 and r2 are the radii of the conductors.
The line-to-line capacitance between two conductors can be calculated using the formula: C12 = q1 / V12 where q1 is the charge on one conductor and V12 is the potential difference between the two conductors.
The line-to-neutral capacitance can be calculated using the formula: C1n = 2C12 where C1n is the line-to-neutral capacitance and C12 is the line-to-line capacitance.

Three-Phase Transmission Lines

The capacitance between each conductor and a neutral can be calculated using the formula: C1n = C2n = 2C12 where C1n and C2n are the capacitances between each conductor and a neutral, and C12 is the line-to-line capacitance.
The line charging current can be calculated using the formula: IC = jωC12V12 where IC is the line charging current, ω is the angular frequency, C12 is the line-to-line capacitance, and V12 is the potential difference between the two conductors.

Load Factor and Loss Factor

Load factor is the ratio of the average load over a designated period of time to the peak load occurring on that period.
Load factor is defined as: LF = Average load / Peak load
Annual load factor is defined as: LF = Total annual energy / (Annual peak load × 8760)
Loss factor is the ratio of the average power loss to the peak-load power loss during a specified period of time.
Loss factor can be related to load factor for three different cases: Case-1: Off-peak load is zero, Case-2: Very short lasting peak, and Case-3: Load is steady.
The formula to relate the loss factor to the load factor is: LLF = 0.3LF + 0.7(LF)²

Load Growth

Load growth is the most important factor influencing the expansion of distribution systems.
Forecasting of load increases is essential to the planning process.
If the load growth rate is known, the load at the end of the m-th year can be calculated using the formula: Pm = P0(1 + g)ᵐ where Pm is the load at the end of the m-th year, P0 is the initial load, and g is the load growth rate.

GMR of a Bundle Consisting of n Similar Subconductors

The GMR of a bundle consisting of n similar subconductors can be calculated using the formula: GMR = √(nR^n) where R is the radius of each subconductor.
The inductive reactance per km at 50 Hz can be calculated using the formula: X = 0.291 ohm/km.
The radius of the equivalent single conductor line that would have the same inductive reactance as the given line can be calculated using the formula: r = 26.72 cm.

Configuration of a Three-Phase Transmission Line

The configuration of a three-phase transmission line can be represented as shown in Fig. 2.33.
The inductive reactance per km at 50 Hz can be calculated using the formula: X = 0.291 ohm/km.
The radius of the equivalent single conductor line that would have the same inductive reactance as the given line can be calculated using the formula: r = 26.72 cm.

Calculation of GMR

The GMR of a bundle consisting of n similar subconductors can be calculated using the formula: GMR = √(nR^n) where R is the radius of each subconductor.
The GMR of a bundle consisting of four subconductors placed at the corners of a square can be calculated using the formula: GMR = 12.826 cm.

Capacitance of a Three-Phase Transmission Line

The capacitance of a three-phase transmission line can be calculated using the formula: C = 0.0242 mF/km.
The capacitance of a three-phase transmission line can also be calculated using the formula: C = ε₀ / (D ln(r1/r2)) where C is the capacitance, ε₀ is the permittivity of free space, D is the distance between the conductors, and r1 and r2 are the radii of the conductors.
The effect of the presence of earth on the capacitance can be accounted for by the method of image charges introduced by Kelvin.

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Description

Test your knowledge on calculating the Geometric Mean Radius (GMR) and inductive reactance in electrical power systems. Includes calculating the inductive reactance per kilometer at 50 Hz and finding the equivalent single conductor radius. Diagrams and step-by-step calculations are provided.

Determine GMR and Inductive Reactance in Electrical Power Systems

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