Open and Short Circuit Test of Transformer: Procedure, Formulas, Errors & Applications

Introduction

A transformer is considered the backbone of the power system. It helps transfer electricity safely and efficiently from one voltage level to another. But before any transformer is commissioned in a real power network, certain standard tests are carried out to check its safety and efficiency.

The most important of these tests are –

• Open Circuit Test (OC Test)
• Short Circuit Test (SC Test)

These tests are special because:

• They help determine core losses, copper losses, efficiency, voltage regulation, and equivalent circuit parameters.
• The transformer does not need to be fully loaded to perform these tests, making them safe, economical, and easy.

📘 In this guide, you will learn:

• The definition of the Open Circuit Test and Short Circuit Test.
• Test setup and step-by-step procedure.
• Necessary formulas and calculations.
• Practical importance and safety considerations of these tests.
• Common mistakes and limitations.
• Standards and advanced information.
• Frequently Asked Questions (FAQs).

What is an Open Circuit Test?

The Open Circuit Test (OC Test), also called the No-Load Test, is performed to determine a transformer’s core (iron) losses and no-load current.

In this test, the secondary side of the transformer (usually the HV side) is kept open, while the primary side (usually the LV side) is supplied with rated voltage.

At no-load, the input power drawn represents the core loss, as the copper loss is negligible.

Working Principle of Open-Circuit Test

In the Open Circuit Test, the secondary winding is kept open. As a result, no current flows in the secondary:

I₂ = 0

Therefore, the output power is zero.

Still, the wattmeter on the primary side records some input power (Wₒ). This is because the transformer requires energy for two main purposes:

1️⃣ Magnetizing the Core

• To produce alternating magnetic flux in the transformer.
• Represented by the magnetizing current (Iµ).

2️⃣ Overcoming Core Losses

• To compensate for hysteresis loss and eddy current loss in the transformer core.
• Represented by the active current (Iw).

Thus, during the open-circuit test, the total input power is used only to cover the iron/core losses.

⚡ Key Point:

• No-load copper loss is negligible because I₀ is only 1–5% of full-load current.
• Therefore, the wattmeter reading (Wₒ) can be considered equal to the transformer’s iron loss (Pᵢ) at rated voltage.

🎯 Purpose

• To measure the core (iron) losses of the transformer.
• To determine the no-load parameters (R₀, X₀) of the transformer’s equivalent circuit.
• To calculate no-load current and power factor.

⚙️ Test Setup (Open Circuit Test Setup)

• Apply rated voltage on the LV side.
• Keep the HV side completely open.
• Connect wattmeter, ammeter, and voltmeter on the LV side.

🔹 Measurements

• V₁ = Applied voltage
• I₀ = No-load current
• W₀ = Input power (core loss)

🧮 Formulas (OC Test)

No-load power factor (cos φ₀):
cos φ₀ = W₀ / (V₁ × I₀)

Components of no-load current:
Iw = I₀ × cos φ₀ (Active component – core loss)
Im = I₀ × sin φ₀ (Reactive component – magnetizing current)

Equivalent Circuit Parameters:
R₀ = V₁ / Iw, X₀ = V₁ / Im

Xo = Vo / Iµ → No-load reactance of transformer, linked to magnetizing branch.
Pi = Wo → Input power at no-load equals iron (core) losses only.
Ro = Vo / Iw → Equivalent resistance representing core losses.
Iµ = √(Io² – Iw²) → Derived magnetizing current using Pythagoras’ relation.

🔹 Why Test on LV Side?

• LV side has a lower rated voltage, making it safer and easier to apply.
• Testing on the HV side requires instruments and insulation to withstand high voltage.

⚠️ Precautions and Common Mistakes

• Keep the secondary completely open.
• Apply only rated voltage – do not exceed or reduce.
• Loose connections may cause sparking.
• For low power factor, ensure the wattmeter is properly calibrated.

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What is a Short Circuit Test?

The Short Circuit Test (SC Test / Impedance Test) is primarily performed to determine a transformer’s:

• Copper losses (I²R losses)
• Equivalent Resistance (Rₑq)
• Equivalent Reactance (Xₑq)

In this test, the secondary side of the transformer (usually the LV side) is short-circuited, and a low voltage is applied to the primary side (usually the HV side) so that full-load current can flow.

Since the applied voltage is very low, the core loss is negligible.

Working Principle

• Since the secondary is shorted, the terminal voltage is zero and output power = 0.
• Still, the wattmeter records some input power (Wsc).
• The applied voltage (Vsc) is much lower than the rated voltage → hence, iron/core losses are negligible.
• Therefore, the entire wattmeter reading (Wsc) represents the full-load copper loss (Pcu(FL)).

🎯 Purpose

• To measure the copper losses of the transformer.
• To determine the Equivalent Resistance (Rₑq), equivalent leakage reactance (Xsc), and Equivalent Reactance (Xₑq).
• To evaluate the Voltage Regulation of the transformer.

⚙️ Test Setup (Short Circuit Test Setup)

• The secondary winding is short-circuited.
• A low voltage (Vsc) is applied to the primary winding, just enough to allow rated full-load current (Isc) to flow in both windings.
• Measuring instruments like an ammeter, a voltmeter, and a wattmeter are connected on the primary (HV) side..

🔹 Measurements Taken

• Vsc = Applied voltage
• Isc = Short-circuit current (rated value)
• Wsc = Input power (copper loss)

🧮 Formulas (SC Test)

Copper Loss (Full Load):
Pc = Wsc

Equivalent Resistance:
Rₑq = Wsc / Isc²

Equivalent Impedance:
Zₑq = Vsc / Isc

Equivalent Reactance:
Xₑq = √(Zₑq² – Rₑq²)

%Z = (Vsc / Vrated) × 100 → Percentage impedance, important for fault level and voltage regulation calculations.

🔹 Why Test on HV Side?

• Full-load current on the HV side is smaller, making it easier to conduct the test at low voltage.
• Can be easily measured with available lab equipment.

⚠️ Precautions and Common Mistakes

• Short-circuit the LV side with a firm, low-resistance conductor.
• Gradually increase the applied voltage until full-load current flows.
• Ensure instruments are rated for low voltage and high current measurements.

difference between OC and SC test

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Purpose of OC Test and SC Tests

The main purpose of the Open Circuit Test (OC Test) and Short Circuit Test (SC Test) is to determine important losses and parameters without operating the transformer under actual load.

1️⃣ Open Circuit Test (OC Test) → Iron/Core Loss

• In this test, the secondary winding of the transformer is kept open.
• The test determines the iron loss (core loss), which occurs in the core due to hysteresis and eddy current losses.
• It also provides the transformer’s no-load parameters, such as:
  • Magnetizing Current
  • Shunt branch values of the equivalent circuit

2️⃣ Short Circuit Test (SC Test) → Copper Loss

• In this test, the secondary winding of the transformer is short-circuited.
• The test determines the copper loss (I²R loss), which occurs due to the resistance of windings when current flows.
• It also helps determine the series resistance and leakage reactance of the transformer’s equivalent circuit.

Test Setup & Diagrams: open and short circuit test of transformer

Calculations & Solved Examples

Below are two clean, step-by-step solved problems—one for the Open-Circuit (OC) Test and one for the Short-Circuit (SC) Test—with all formulas written in bold.

Example 1: Open-Circuit (OC) Test

Given (measured):

• Applied voltage, Vo = 230 V
• No-load current, Io = 2.0 A
• Wattmeter reading, Wo = 120 W

Find: No-load power factor (cosφ₀), current components (Iw, Iµ), and shunt parameters (Ro, Xo).

Step 1: No-load Power Factor

cosφ₀ = Wo / (Vo × Io) = 120 / (230 × 2.0) = 120 / 460 = 0.261

Step 2: Current Components

Active (loss) component:
Iw = Io × cosφ₀ = 2.0 × 0.261 = 0.522 A

Magnetizing component (by geometry):
Iµ = √(Io² – Iw²) = √(2.0² – 0.522²) = √(4.000 – 0.272) = 1.93 A

(You may also use Iµ = Io × sinφ₀ .)

Step 3: Shunt Branch Parameters

No-load resistance:
Ro = Vo / Iw = 230 / 0.522 = 440 Ω

Magnetizing reactance:
Xo = Vo / Iµ = 230 / 1.93 = 119 Ω

Results (OC Test):
cosφ₀ ≈ 0.261, Iw ≈ 0.522 A, Iµ ≈ 1.93 A, Ro ≈ 440 Ω, Xo ≈ 119 Ω.
(Iron loss at rated voltage: Pi = Wo = 120 W.)

Example 2: Short-Circuit (SC) Test

Given (measured):

• Applied short-circuit voltage, Vsc = 18 V
• Short-circuit current (rated), Isc = 10 A
• Wattmeter reading, Wsc = 120 W

Find: Equivalent impedance (Zsc), equivalent resistance (Rsc), equivalent reactance (Xsc). (Optional: %Z if rated voltage is known.)

Step 1: Equivalent Impedance

Zsc = Vsc / Isc = 18 / 10 = 1.80 Ω

Step 2: Equivalent Resistance (from power)

Rsc = Wsc / Isc² = 120 / (10)² = 120 / 100 = 1.20 Ω

Step 3: Equivalent Reactance

Xsc = √(Zsc² – Rsc²) = √(1.80² – 1.20²) = √(3.24 – 1.44) = √1.80 = 1.34 Ω

Results (SC Test):
Zsc ≈ 1.80 Ω, Rsc ≈ 1.20 Ω, Xsc ≈ 1.34 Ω.

Optional: % Impedance (if rated voltage Vrated is known)
For example, if Vrated = 400 V (referred side):
%Z = (Vsc / Vrated) × 100 = (18 / 400) × 100 = 4.5%

Derived Parameters of Transformer & Their Uses

The data obtained from Open Circuit (OC) Test and Short Circuit (SC) Test provides the Equivalent Circuit Parameters of a transformer. These parameters are not just theoretical—they form the basis for performance analysis, design verification, condition monitoring, and operational planning.

Engineers use these parameters to:

• Predict transformer behavior under different loading conditions
• Ensure reliability
• Improve efficiency and save energy

1️⃣ Transformer Equivalent Circuit

The Equivalent Circuit is an electrical model of the transformer, allowing engineers to perform calculations using an analytical circuit instead of the physical transformer.

🔹 Parameters from OC Test (typically on LV side)

• R₀ = V₀ / Iw → Core loss resistance (represents iron loss)
• X₀ = V₀ / Iµ → Magnetizing reactance (represents magnetizing current)

🔹 Parameters from SC Test (typically on HV side)

• Rsc = Wsc / Isc² → Equivalent resistance (total copper loss of both windings)
• Xsc = √(Zsc² – Rsc²) → Equivalent leakage reactance (represents leakage flux)

🔹 Equivalent Circuit Structure

• Shunt Branch: R₀, X₀ → Core loss and magnetizing components
• Series Branch: Rsc, Xsc → Winding resistance and leakage reactance

🔎 Importance:

The equivalent circuit is used for:

• Load flow studies
• Designing protective relays
• Transformer performance evaluation
• System stability simulation

2️⃣ Transformer Efficiency (η)

Efficiency (η) indicates how effectively the transformer converts input power to output power.

Formulas:
η = Output Power / Input Power
η = (V₂ I₂ cosφ) / (V₂ I₂ cosφ + Pᵢ + Pcu)

• Pᵢ = Iron/Core Loss (from OC Test, W₀) → Constant loss
• Pcu = Copper Loss (from SC Test, Wsc) → Variable loss depending on load current

At any load fraction x:
Pcu(x) = x² × Pcu(FL)
η(x) = (x × V₂ I₂ cosφ) / (x × V₂ I₂ cosφ + Pᵢ + x² Pcu(FL))

🔎 Importance:

Efficiency analysis helps in:

• Economic operation
• Transformer loading decisions
• Energy saving and optimization

3️⃣ Voltage Regulation

Voltage Regulation indicates the transformer’s ability to maintain secondary voltage stability under varying load.

%Regulation = [(E₂ – V₂) / V₂] × 100

• E₂ = No-load secondary voltage (theoretical EMF)
• V₂ = Full-load secondary voltage

Using equivalent parameters:
%Regulation ≈ [(I₂ Rsc cosφ ± I₂ Xsc sinφ) / V₂] × 100

• ‘+’ → Lagging power factor (Inductive Load)
• ‘–’ → Leading power factor (Capacitive Load)

🔎 Importance:

Voltage regulation ensures stability and quality of power supply. Poor regulation can cause:

• Reduced reliability of supply
• Voltage drops
• Impact on equipment

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Phasor Diagrams of Transformer Open and Short Circuit Tests

Phasor diagrams for OC (Open Circuit) Test and SC (Short Circuit) Test help visualize the phase relationships between voltage and current in a transformer.

1️⃣ Open Circuit Test Phasor Diagram (OC Test)

Test Condition:

• Secondary winding open
• Rated voltage V₁ applied on the primary

Current:

• Only no-load current (I₀) flows, which is very small

Components of I₀:

• Iw → In phase with applied voltage V₁ → Represents core/iron loss
• Iµ → Lags V₁ by 90° → Represents magnetizing current

Input Power:

• Entirely used for core loss
• Copper loss is negligible (I₀ is very small)

Phasor Relationships:

• V₁ = Reference
• Iw in phase with V₁
• Iµ lags V₁ by 90°
• I₀ = Iw + Iµ (Vector sum)
• Core flux (Φ) ≈ proportional to Iµ, lags V₁ by 90°

OC Test Phasor Diagram:

         Iµ
         ↑
         |
         |
Iw ----->|----> V1 (Reference)
         \
          \
           Io (Resultant)

2️⃣ Short Circuit Test Phasor Diagram (SC Test)

Test Condition:

• Secondary winding short-circuited
• Low voltage Vsc applied to primary to allow full-load current

Current:

• Rated short-circuit current (Isc) flows

Losses:

• Copper losses dominate
• Iron loss is negligible (Vsc very low)

Phasor Relationships:

• Reference = I₁ = Isc
• Voltage drop across equivalent resistance (Isc × Rsc) → In phase with current
• Voltage drop across leakage reactance (Isc × Xsc) → 90° lead with current

Resultant Voltage:
Vsc = Isc × (Rsc + jXsc)

SC Test Phasor Diagram:

      jIscXsc (90° lead)
          ↑
          |
          |
IscRsc --->|----> Vsc (Resultant)

🔹 Key Differences: OC Test vs SC Test (Phasor Perspective)

Comparison of Transformer Tests

Different transformer test methods have varying purposes, advantages, and disadvantages. Below is a comparison of Direct Loading Test, Open Circuit Test, Short Circuit Test, and Sumpner’s Test.

Transformer Open and Short Circuit Tests – Limitations & Common Errors

Although OC and SC tests are safe and easy, they have certain limitations and potential errors. Understanding these ensures more accurate and reliable results.

🔹 1. Instrumental Errors

• Using incorrect or inaccurate wattmeters/ammeters can lead to wrong measurement of losses.
• Always use instruments with proper range and calibration.

🔹 2. Temperature Effects

• Copper losses increase at higher temperatures, causing deviations in results.
• Pay special attention to temperature rise during the SC test.

🔹 3. Frequency Variation

• Core losses depend on the transformer’s rated frequency.
• If the supply frequency changes, the results of the OC test may be affected.

🔹 4. Practical Constraints

• Large power transformers require high-capacity test equipment for a full test setup.
• For large transformers, the Direct Loading Method is less practical.

Transformer Open and Short Circuit Tests – Safety & Precautions

Safety is paramount when performing OC and SC tests on transformers. Improper practices can cause equipment damage, injury, or fire.

✅ Do’s

• Ensure proper earthing/grounding of the transformer before starting any test.
• Use properly calibrated instruments (wattmeter, ammeter, voltmeter) rated for the test conditions.
• Apply rated voltage carefully in the OC test (on the LV side).
• In the SC test, apply only a small fraction of the rated voltage to circulate full-load current.
• Keep protective devices (fuses, circuit breakers) in the circuit during testing.
• Continuously monitor instruments during the test.
• Keep the SC test duration short to prevent overheating.
• Ensure the test is performed by trained personnel under supervision.

❌ Don’ts

• Do not touch transformer terminals or connections while energized.
• Do not apply full rated voltage in SC test (can damage windings).
• Do not exceed the rated current during testing.
• Do not allow excessive heating of windings in the SC test.
• Do not use damaged or uncalibrated instruments.
• Do not perform the test without proper isolation and safety barriers.
• Do not leave the transformer energized unattended during the test.
• Do not conduct tests in wet or unsafe environments.

Conclusion

The Open Circuit Test and Short Circuit Test are essential diagnostic tools for transformers. Together, they help engineers determine equivalent circuit, efficiency, voltage regulation, and losses with minimal power consumption.

By understanding their procedures, applications, limitations, and safety measures, students and professionals can better design, maintain, and operate transformers safely and economically.

👉 Want to learn more? Explore our detailed guides on transformer polarity test, insulation class, and power factor improvement.

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