Transmission and Distribution System Experiments

Introduction

Electrical power systems transport energy from generating stations to consumers through transmission networks, substations, feeders, distributors, service mains, transformers, and protective equipment. Laboratory experiments provide a controlled way to connect theoretical models with measurable quantities such as voltage, current, power, power factor, losses, regulation, and efficiency.

A typical laboratory arrangement uses a low-voltage equivalent of a transmission or distribution line. Although the voltage and power ratings are reduced, the relationships among resistance, inductance, capacitance, load power factor, voltage drop, reactive power, and losses remain significant. Safe laboratory work therefore requires both electrical theory and disciplined measurement practice.

Learning Objectives

After completing this chapter, a student should be able to:

1. Determine approximate line resistance, inductance, capacitance, and impedance from experimental data.
2. Measure and interpret voltage regulation and the Ferranti effect.
3. Examine real-power transfer, power factor, and reactive-power compensation.
4. Compare radial, ring-main, and interconnected distribution systems.
5. Analyze transformer operation, feeder voltage drop, grounding, technical losses, and efficiency.
6. Select suitable instruments, calculate uncertainty, and report results professionally.
7. Evaluate practical improvements while recognizing safety, regulatory, and environmental constraints.

1. Experimental Model of a Power Line

A transmission line is commonly represented by distributed parameters: series resistance R, series inductance L, and shunt capacitance C. For short laboratory lines, a lumped model is usually sufficient. A nominal-π model places half the total shunt admittance at each end and the total series impedance between them.

For a balanced sinusoidal three-phase system, the per-phase series impedance is

where R is resistance in Ω per phase, X_L is inductive reactance in Ω, L is inductance in H, j = √−1, and ω = 2πf is angular frequency in rad/s. The shunt capacitive reactance is represented through susceptance

where C is capacitance per phase in F. The assumptions are sinusoidal steady state, balanced phases, constant frequency, and linear components.

The approximate receiving-end voltage drop for a three-phase line is

for a lagging load, where I is line current, φ is the load power-factor angle, and ∆V_L is line-to-line voltage drop. For a leading load, the reactive term changes sign. This expression is an approximation and is most reliable when the voltage drop is small relative to the system voltage.

The line losses are predominantly copper losses:

The factor 3 applies to a balanced three-phase line and R is the resistance of one phase. Core, dielectric, corona, and auxiliary losses may need to be added in a complete system model.

Measuring line parameters

A resistance test is performed with the circuit de-energized. A known direct current is applied and the resistance is obtained from

The measured value may require correction for conductor temperature because copper resistance varies approximately as

where R_0 is resistance at reference temperature T_0, R_T is resistance at temperature T, and α is the temperature coefficient in °C⁻¹. The relation is an approximation over a moderate temperature range.

Inductance can be estimated from a no-load or low-current AC test. If the measured impedance magnitude is |Z| and R is known,

Capacitance can be estimated from charging current under an applied sinusoidal voltage:

For a single-phase test, C = I_C/(ωV). Instrument loading and leakage resistance must be considered.

2. Voltage Regulation and the Ferranti Effect

Voltage regulation indicates how much the receiving voltage changes between no-load and a specified load while the sending voltage is maintained constant. A common receiving-end definition is

where V_R0 is receiving-end voltage at no load and V_RL is receiving-end voltage at the specified load. Some laboratory manuals use V_R0 as the denominator; the chosen definition must be stated explicitly.

For a short three-phase line with sending-end voltage approximately constant, a useful approximate regulation expression is

with lagging power factor. Leading power factor can produce lower or negative regulation because capacitive reactive power offsets inductive voltage drop.

Ferranti effect

The Ferranti effect is the rise of receiving-end voltage above sending-end voltage when a sufficiently long AC line is lightly loaded or open-circuited. It results from the line’s shunt capacitance and charging current. The effect is more pronounced for long, high-voltage lines and underground cables, whose capacitance is higher than that of overhead lines.

In a simplified lossless long-line model,

where V_S and V_R are sending- and receiving-end phase voltages, I_R is receiving-end current, β is phase constant in rad/km, l is line length, and Z_C is characteristic impedance. For an open circuit I_R = 0, so V_S = V_R cos(βl), giving V_R = V_S/cos(βl), which is greater than V_S for small positive βl. This ideal relation neglects resistance and conductor losses.

Experiment: regulation and Ferranti effect

Connect the line simulator, verify the rated voltage and protective earth, and record sending and receiving voltages at no load. Apply balanced resistive, inductive, and capacitive loads in steps. At each step record line voltage, current, real power, reactive power, and power factor. Plot receiving voltage against load current and compare lagging and leading cases. Never switch a capacitor bank into a circuit unless discharge and inrush provisions are provided.

3. Power Transfer and Reactive Compensation

In a simplified lossless two-bus system, real power transfer is approximated by

where P is transmitted real power in W, V_S and V_R are voltage magnitudes on a consistent per-phase or equivalent basis, X is transfer reactance in Ω, and δ is the power-angle difference. The equation assumes negligible resistance, constant voltage magnitudes, and sinusoidal steady-state operation. It shows that power transfer is increased by raising voltage or reducing reactance, but thermal, stability, insulation, and fault-level limits remain.

For a balanced three-phase load,

and

where V_L and I_L are line voltage and line current, P is real power in W, and Q is reactive power in var. Apparent power is

Power-factor correction reduces current for a specified real power. If a load changes from power factor cos φ₁ to cos φ₂, the required capacitor rating is

where Q_C is capacitive reactive power in var. The formula assumes the capacitor operates at the same fundamental frequency and that harmonic effects are neglected.

Worked example

A balanced three-phase load consumes 30 kW at 400 V line voltage and 0.75 lagging power factor. Find the line current and capacitor rating needed to improve the power factor to 0.95.

Initial angle: φ₁ = cos⁻¹(0.75), so tan φ₁ ≈ 0.882. Final angle: φ₂ = cos⁻¹(0.95), so tan φ₂ ≈ 0.329.

Thus, an approximately 16.6 kVAr capacitor bank is required under the stated assumptions. The improved current is approximately 45.6 A. In practice, a standard stepped bank, detuning reactors, switching transients, harmonics, and overvoltage conditions must be assessed.

4. Feeders and Distribution Configurations

A feeder carries power from a substation to distribution areas and is normally designed primarily for current-carrying capacity and voltage drop. A distributor has multiple consumer tappings, so its voltage profile depends on the magnitude and location of loads. A service main connects a distributor to an individual consumer.

Radial system

A radial system has one normal supply path from substation to load. It is simple, inexpensive, and easy to protect, but a fault or maintenance interruption can disconnect all downstream consumers.

Ring-main system

A ring main forms a loop, often operated with one normally open point. Loads can be supplied from either direction after switching. Reliability and voltage profile improve, although protection coordination and switching procedures become more complex.

Interconnected system

An interconnected network has several sources and parallel paths. It offers high reliability, improved load sharing, and operational flexibility. However, fault currents, relay coordination, power-flow control, and system stability become more demanding.

For a radial feeder section, approximate voltage drop is found by summing the current-dependent drops of each section. The position of each load matters: a load near the substation contributes less upstream drop than the same load at the remote end.

A laboratory comparison should use identical total load and voltage. Measure remote-end voltage, feeder current, power, and losses for radial, ring, and interconnected arrangements. Record the switching state and ensure that parallel sources are synchronized before connection.

5. Transformer Experiments

Transformers transfer AC power between voltage levels by electromagnetic induction. For an ideal transformer,

and

where V, I, and N denote voltage, current, and turns, and a is the turns ratio. The apparent powers are equal in the ideal case. Real transformers have winding resistance, leakage reactance, core loss, magnetizing current, and finite efficiency.

Efficiency is

Transformer voltage regulation may be approximated by

where R_eq and X_eq are equivalent secondary-referred resistance and reactance, I₂ is secondary current, and the plus sign applies approximately to lagging power factor while the minus sign applies to leading power factor.

Open-circuit tests estimate core loss and the shunt branch; short-circuit tests estimate equivalent series impedance and copper loss. These tests must be conducted at appropriate rated or reduced quantities and with protective devices in place.

6. Grounding and Safety

Grounding provides a deliberate reference and a low-impedance path for fault current. Protective grounding connects exposed conductive parts to earth so that a fault can operate a fuse, circuit breaker, or residual-current device. System grounding describes how the source neutral is connected to earth. These functions must not be confused with ordinary return conductors.

Earth resistance can be measured using an approved earth tester and an appropriate electrode method. Results depend on soil resistivity, electrode spacing, moisture, temperature, parallel metallic paths, and frequency. A low measured resistance alone does not guarantee effective protection; bonding continuity, protective-device operation, touch voltage, step voltage, and local electrical regulations must also be checked.

Laboratory rules include isolation before rewiring, lockout/tagout where applicable, discharge of capacitors, use of current transformers correctly, correct meter category ratings, single-point authorization for energization, and verification of absence of voltage. Students must never defeat interlocks or protective earth connections.

7. Technical Losses and Efficiency Improvement

Technical losses include conductor I²R losses, transformer copper and core losses, contact losses, dielectric losses, and losses in power-electronic equipment. Non-technical losses, such as unmetered energy or incorrect billing, are not physical network losses and require different controls.

For a measured interval, feeder efficiency is

If input and output energy are measured over time,

Improvement measures include increasing conductor cross-sectional area, raising transmission voltage, balancing single-phase loads, correcting power factor, optimizing transformer loading, shortening heavily loaded routes, improving joints, using distributed generation carefully, and installing voltage-control equipment. Each measure has trade-offs: capacitors can cause overvoltage and resonance; higher voltage requires stronger insulation; reconductoring requires investment and outage planning; and distributed generation can reverse power flow.

Measurement uncertainty

A reported result should include instrument accuracy and repeatability. For independent measurements x and y in a calculated product q = xy, a first-order relative uncertainty estimate is

This approximation assumes small, independent uncertainties. Calibration status, resolution, burden, waveform distortion, and connection errors may dominate in practical laboratory work.

8. Integrated Laboratory Investigation

A robust investigation can be organized as follows:

1. Inspect the circuit diagram, ratings, grounding, emergency stop, and instrument ranges.
2. Measure unloaded line voltage and verify phase sequence.
3. Determine R, L, and C using the appropriate de-energized or low-energy tests.
4. Apply balanced loads and record V, I, P, Q, and power factor.
5. Determine regulation for lagging, unity, and leading power factors.
6. Operate the line lightly loaded or open-circuited and observe the Ferranti effect.
7. Add compensation in controlled steps and observe current, voltage, and losses.
8. Compare radial and alternative distribution configurations under equivalent loading.
9. Perform transformer open-circuit and short-circuit tests where authorized.
10. Calculate losses and efficiency, estimate uncertainty, and compare results with the model.

A professional report includes a circuit diagram, equipment ratings, procedure, raw data, sample calculations, graphs, uncertainty, safety observations, discussion of deviations, and conclusions. Graphs should have units, scales, legends, and clearly identified operating conditions.

9. Illustrative Case Study: Voltage Improvement on a Rural Feeder

Background

This illustrative case concerns a 400 V three-phase rural feeder supplying motors and lighting loads. The remote-end voltage falls during evening operation because the feeder is long and several motors operate at lagging power factor.

Problem

At peak load, the feeder supplies 60 kW at 0.78 lagging power factor and 400 V. The measured feeder resistance per phase is 0.12 Ω. Neglecting reactance for a first estimate, determine current and copper loss.

Analysis

The current is

The three-phase resistive loss is

The loss is approximately 7.4% of the delivered 60 kW, before other losses. A capacitor bank improving power factor to 0.95 would reduce current to

The estimated resistive loss becomes about 3.0 kW, a reduction of approximately 1.45 kW under unchanged real power and voltage.

Approach and outcome

The utility installs switched compensation near the load, verifies that the bank does not create resonance, balances single-phase consumers, and replaces a deteriorated joint. Measurements show reduced current and improved remote voltage. The capacitor bank is controlled so that it disconnects during light load, preventing excessive voltage rise.

Learning points

Power-factor correction reduces current and I²R loss but does not replace conductor reinforcement when thermal or voltage constraints remain. Compensation must be coordinated with transformer taps, protection, harmonics, switching transients, and applicable distribution standards.

10. Contemporary Practice and Professional Responsibility

Modern distribution laboratories increasingly use digital power analyzers, programmable sources, phasor measurement, SCADA interfaces, and digital twins. AI-based anomaly detection can identify unusual voltage profiles or loss patterns, but its outputs require validated measurements, explainable thresholds, cybersecurity controls, and human engineering judgment. Automated switching must include fail-safe states and authorization controls.

Engineers are responsible for public safety, accurate reporting, equipment protection, environmental stewardship, and compliance with national wiring rules, utility codes, occupational-safety requirements, and relevant IEC or IEEE standards. Standards vary by jurisdiction; therefore, a laboratory result must not be treated as a construction approval without a formal design review.

Chapter Summary

Transmission and distribution experiments connect line models with practical measurements. Resistance, inductance, and capacitance determine impedance, voltage drop, charging current, regulation, and the Ferranti effect. Real and reactive power must be distinguished because power factor strongly affects current, losses, voltage profile, and equipment utilization. Radial, ring-main, and interconnected configurations provide progressively greater flexibility but require more complex protection and control. Transformer tests reveal core and copper behavior, while grounding and safe isolation protect people and equipment. Technical losses can be reduced through higher voltage, balanced loading, sound conductors and joints, optimized transformers, and appropriate reactive compensation. Reliable conclusions require calibrated instruments, explicit assumptions, uncertainty analysis, and compliance with safety and engineering standards.

Key Terms

Line parameter: Electrical property such as resistance, inductance, or capacitance describing a line.

Impedance: Complex opposition to sinusoidal current, expressed in ohms.

Voltage regulation: Change in receiving voltage between specified load and no-load conditions.

Ferranti effect: Receiving-end voltage rise on a lightly loaded or open-circuited AC line.

Feeder: Conductor system carrying power from a substation toward distribution loads.

Distributor: Conductor with multiple consumer tapping points.

Service main: Connection from a distributor to an individual consumer.

Reactive power: AC power exchanged by inductive or capacitive elements, measured in var.

Power factor: Ratio of real power to apparent power.

Compensation: Deliberate injection or absorption of reactive power to control voltage or power factor.

Radial system: Distribution arrangement with one normal supply path.

Ring main: Loop distribution arrangement permitting alternative supply paths.

Interconnected system: Network with multiple sources and parallel power-flow paths.

Transformer regulation: Change in secondary voltage caused by loading.

Technical loss: Physical electrical energy loss in conductors, transformers, and equipment.

Grounding: Intentional connection of a system or exposed conductive part to earth.

Touch voltage: Voltage that may appear between simultaneously accessible points.

Nominal-π model: Lumped line model with series impedance and two shunt admittances.

Uncertainty: Quantified doubt associated with a measured or calculated result.

Review Questions

Short Answer Questions

1. What physical factors determine the series impedance of a transmission line?
2. Define voltage regulation and state one commonly used expression for it.
3. Why does the Ferranti effect occur?
4. Distinguish a feeder from a distributor.
5. State two purposes of grounding in a laboratory power circuit.

Long Answer Questions

1. Explain an experiment for determining line resistance, inductance, and capacitance, including safety precautions and assumptions.
2. Derive or explain the approximate voltage-drop relation for a balanced three-phase short line and discuss lagging and leading loads.
3. Compare radial, ring-main, and interconnected distribution systems with respect to reliability, cost, protection, and operation.
4. Explain transformer open-circuit and short-circuit tests and identify the parameters obtained from each.
5. Discuss technical-loss reduction methods and the limitations of power-factor correction.

Analytical / Application Questions

1. A 400 V, three-phase load consumes 45 kW at 0.80 lagging power factor. Calculate its line current and the capacitor kVAr required to reach 0.95 power factor.
2. A balanced feeder has 0.08 Ω resistance per phase and carries 80 A. Calculate its three-phase copper loss and explain how the loss changes if current is reduced by power-factor correction.
3. A receiving-end voltage rises when a long line is disconnected from its load. Identify the phenomenon, explain its physical cause, and propose two safe operating or design measures.

Multiple Choice Questions with Answers

Question 1

Which quantity primarily represents the series opposition of a sinusoidal transmission line?

A. Impedance

B. Admittance only

C. Power factor

D. Energy

Correct Answer: A. Impedance

Question 2

The Ferranti effect is most likely observed when an AC line is:

A. Heavily loaded at unity power factor

B. Lightly loaded or open-circuited

C. Short-circuited at the receiving end

D. Supplied only by DC

Correct Answer: B. Lightly loaded or open-circuited

Question 3

For a balanced three-phase line, copper loss is calculated by:

A. I²R

B. 3I²R

C. √3IR

D. 3VI

Correct Answer: B. 3I²R

Question 4

A capacitor bank used for power-factor correction primarily supplies:

A. Active power

B. Capacitive reactive power

C. Mechanical power

D. Core loss

Correct Answer: B. Capacitive reactive power

Question 5

Which distribution arrangement normally has one supply path to downstream loads?

A. Interconnected

B. Ring-main

C. Radial

D. Meshed double-bus

Correct Answer: C. Radial

Question 6

A feeder supplies 30 kW at 400 V, three phase, and 0.75 power factor. Its approximate line current is:

A. 28.9 A

B. 57.7 A

C. 86.6 A

D. 100 A

Correct Answer: B. 57.7 A

Question 7

In an ideal transformer, the voltage ratio equals the ratio of:

A. Resistances

B. Capacitances

C. Turns

D. Frequencies

Correct Answer: C. Turns

Question 8

For a lagging load, approximate line voltage drop includes which combination?

A. R cos φ + X sin φ

B. R sin φ − X cos φ

C. R + X only

D. X cos φ − R sin φ

Correct Answer: A. R cos φ + X sin φ

Question 9

If feeder current is reduced while resistance remains constant, I²R loss:

A. Increases linearly

B. Remains unchanged

C. Decreases with the square of current

D. Becomes equal to voltage

Correct Answer: C. Decreases with the square of current

Question 10

Which practice is unsafe during laboratory rewiring?

A. Isolating the supply first

B. Discharging capacitors

C. Verifying absence of voltage

D. Defeating the protective earth connection

Correct Answer: D. Defeating the protective earth connection