boss_notes/T-06a_OC_Test.md

7.3 KB · commit d2f3b6e

← T-05: Voltage Regulation | 🏠 Index | T-06b: SC Test →

T-06a: Open-Circuit (OC) Test

Section: A | Priority: 🔴 MUST | Exam Frequency: 7/7 years Sources: Theraja Ch-32 (Art. 32.23–32.25), VK Mehta Ch-7 (Art. 7.18–7.19), Slides L-10 S17

Why This Topic Matters

The OC/SC test is the single most certain question in the entire exam. It appeared in ALL 7 papers (2017–2024). The format is always the same: given OC and SC test data, find the equivalent circuit parameters, then calculate efficiency and/or voltage regulation. This is your guaranteed 5–10 marks if you know the procedure. The OC test finds the shunt branch parameters ( $R_{c}$ , $X_{m}$ ) and the iron loss.

📝 Key Definitions

Open-Circuit (OC) Test (No-Load Test): "The purpose of this test is to determine (i) the iron losses and (ii) no-load current $I_{0}$ which is helpful in finding the parameters of the equivalent circuit — $R_{c}$ and $X_{m}$ . In this test, one winding of the transformer (usually the low-voltage winding) is connected to the supply at rated voltage. The other winding is left open. The input voltage, no-load current and input power are measured." — VK Mehta, Art. 7.18

Iron (core) loss ( $P_{F e}$ ): "The iron loss consists of hysteresis loss and eddy current loss. Both depend on flux density in the core. Since $B \propto V / f$ , and the supply voltage is nearly constant, iron loss is essentially constant at all loads." — From explanation notes

Test Setup and Procedure

Open-Circuit (OC) Test Circuit Diagram

Connections (VK Mehta, Art. 7.18):

Connect the LV winding to the rated supply voltage through a variac.
Leave the HV winding open-circuited (no load connected).
Connect measuring instruments on the LV side:
- Voltmeter ( $V_{0}$ ) across the winding
- Ammeter ( $I_{0}$ ) in series
- Low power factor (LPF) wattmeter ( $W_{0}$ )

Why LV side? Two reasons:

Rated voltage on the LV side is lower (safer, easier to supply).
Current measuring instruments can handle the no-load current more easily.

Readings taken: $V_{0}$ , $I_{0}$ , $W_{0}$ when voltage reaches rated value.

Parameter Extraction

Since the secondary is open, the only current flowing is the no-load current $I_{0}$ . This is small (2–10% of rated). The copper loss $I_{0}^{2} R_{1}$ is negligible.

All power input = iron loss:

$P_{F e} = W_{0}$

This iron loss is constant at all loads. It does not change whether the transformer is at no-load, half-load, or full-load.

No-load power factor:

$cos ϕ_{0} = \frac{W _{0}}{V _{0} I _{0}}$

Current components:

$I_{w} = I_{0} cos ϕ_{0} (core-loss component)$

$I_{μ} = I_{0} sin ϕ_{0} (magnetizing component)$

Shunt branch parameters (referred to the side where OC test is done):

$R_{c} = \frac{V _{0}}{I _{w}} = \frac{V _{0}^{2}}{W _{0}}$

$X_{m} = \frac{V _{0}}{I _{μ}}$

🏆 Golden Questions (Past Exam Archive)

🎯 Q1: Explain the procedure of the OC test and what parameters it determines.

Appeared: 2021 Q2(b) — 4 marks

Full Answer:

Setup: Connect the LV winding to rated supply voltage through a variac. Leave HV winding open-circuited. Place ammeter ( $I_{0}$ ), voltmeter ( $V_{0}$ ), and LPF wattmeter ( $W_{0}$ ) on the LV side.

Procedure: Gradually increase the supply voltage from zero to rated value using the variac. Record $V_{0}$ , $I_{0}$ , and $W_{0}$ at rated voltage.

What it determines:

(1) Iron (core) loss: $P_{F e} = W_{0}$ . The wattmeter reading directly gives the iron loss because: (a) secondary is open so $I_{2} = 0$ (no copper loss in secondary), and (b) the no-load current $I_{0}$ is so small (2–5% of rated) that primary copper loss $I_{0}^{2} R_{1}$ is negligible.

(2) Shunt branch parameters: $R_{c} = V_{0}^{2} / W_{0}$ (resistance representing core loss) and $X_{m} = V_{0} / I_{μ}$ (magnetizing reactance).

(3) No-load current and power factor: $cos ϕ_{0} = W_{0} / (V_{0} I_{0})$ . This is typically very low (0.1–0.3).

(4) Turns ratio verification: By measuring both primary and open-circuit secondary voltages: $a = V_{1} / V_{2}$ .

Why LV side? Lower voltage is safer. Current instruments can handle the small no-load current more easily.

🎯 Q2: Draw circuit diagrams for OC and SC tests.

Appeared: 2020 Q2(c) — 2 marks

Full Answer:

OC Test Circuit: LV winding connected to rated AC supply through variac. Ammeter in series, voltmeter across, wattmeter measuring input. HV winding open-circuited.

OC Test Circuit

SC Test Circuit: HV winding connected to variable AC supply through variac. Ammeter in series, voltmeter across, wattmeter measuring input. LV winding solidly short-circuited with a thick copper conductor.

SC Test Circuit

🎯 Q3: Why are OC and SC tests preferred over direct load test?

Appeared: 2024 Q3(a) — 4 marks

Full Answer:

Testing a 500 kVA transformer by direct load test would require:

A load bank of 500 kVA (resistors, inductors, capacitors): expensive, large, and dangerous.
Continuous power dissipation of ~15 kW in losses per hour.
Only one load condition at a time. Different loads require reconfiguration.

What OC and SC tests do instead:

OC test: Apply rated voltage to LV winding (HV open). Only the no-load current flows (2–5% of rated). Power consumed = iron losses only (about 0.3–0.5% of rated kVA). For a 500 kVA transformer: test power is only 1.5–2.5 kW. Tiny.

SC test: Apply 5–10% of rated voltage to HV winding (LV short-circuited). Full-load current flows but at very low voltage. Power consumed = copper losses only (about 0.8–1.5% of rated kVA). Again tiny.

From two simple, low-power tests, you get everything:

Core loss $P_{F e}$ (from OC test)
Full-load copper loss $P_{C u, F L}$ (from SC test)
All four equivalent circuit parameters ( $R_{c}$ , $X_{m}$ , $R_{01}$ , $X_{01}$ )
Efficiency at any load and any power factor (by formula)
Voltage regulation at any load and any power factor (by formula)

Key insight: Efficiency and VR are calculated analytically using the measured parameters. You never need to actually apply real loads. This is why OC/SC tests are universally preferred.

⚡ Exam Tips & Common Mistakes

OC test gives iron loss, not copper loss. $W_{0} = P_{F e}$ because $I_{0}$ is too small for significant copper loss.
OC test is done on LV side. Not HV. The reason is safety and convenience.
$R_{c}$ and $X_{m}$ are referred to the side where the test is done. To refer to the other side, multiply by $a^{2}$ (or divide, depending on direction).
Iron loss is CONSTANT. It does not change with load.

T-06b: SC Test — The companion test for series parameters
T-06c: Efficiency — Uses $P_{F e}$ from OC test
T-04: Equivalent Circuit — The circuit whose parameters we're finding
T-03a: No-Load Operation — The physics of what happens during OC test

← T-05: Voltage Regulation | 🏠 Index | T-06b: SC Test →

boss_notes/T-06a_OC_Test.md

7.3 KB · commit d2f3b6e

← T-05: Voltage Regulation | 🏠 Index | T-06b: SC Test →

T-06a: Open-Circuit (OC) Test

Section: A | Priority: 🔴 MUST | Exam Frequency: 7/7 years Sources: Theraja Ch-32 (Art. 32.23–32.25), VK Mehta Ch-7 (Art. 7.18–7.19), Slides L-10 S17

Why This Topic Matters

📝 Key Definitions

Open-Circuit (OC) Test (No-Load Test): "The purpose of this test is to determine (i) the iron losses and (ii) no-load current $I_{0}$ which is helpful in finding the parameters of the equivalent circuit — $R_{c}$ and $X_{m}$ . In this test, one winding of the transformer (usually the low-voltage winding) is connected to the supply at rated voltage. The other winding is left open. The input voltage, no-load current and input power are measured." — VK Mehta, Art. 7.18

Iron (core) loss ( $P_{F e}$ ): "The iron loss consists of hysteresis loss and eddy current loss. Both depend on flux density in the core. Since $B \propto V / f$ , and the supply voltage is nearly constant, iron loss is essentially constant at all loads." — From explanation notes

Test Setup and Procedure

Open-Circuit (OC) Test Circuit Diagram

Connections (VK Mehta, Art. 7.18):

Connect the LV winding to the rated supply voltage through a variac.
Leave the HV winding open-circuited (no load connected).
Connect measuring instruments on the LV side:
- Voltmeter ( $V_{0}$ ) across the winding
- Ammeter ( $I_{0}$ ) in series
- Low power factor (LPF) wattmeter ( $W_{0}$ )

Why LV side? Two reasons:

Rated voltage on the LV side is lower (safer, easier to supply).
Current measuring instruments can handle the no-load current more easily.

Readings taken: $V_{0}$ , $I_{0}$ , $W_{0}$ when voltage reaches rated value.

Parameter Extraction

Since the secondary is open, the only current flowing is the no-load current $I_{0}$ . This is small (2–10% of rated). The copper loss $I_{0}^{2} R_{1}$ is negligible.

All power input = iron loss:

$P_{F e} = W_{0}$

This iron loss is constant at all loads. It does not change whether the transformer is at no-load, half-load, or full-load.

No-load power factor:

$cos ϕ_{0} = \frac{W _{0}}{V _{0} I _{0}}$

Current components:

$I_{w} = I_{0} cos ϕ_{0} (core-loss component)$

$I_{μ} = I_{0} sin ϕ_{0} (magnetizing component)$

Shunt branch parameters (referred to the side where OC test is done):

$R_{c} = \frac{V _{0}}{I _{w}} = \frac{V _{0}^{2}}{W _{0}}$

$X_{m} = \frac{V _{0}}{I _{μ}}$

🏆 Golden Questions (Past Exam Archive)

🎯 Q1: Explain the procedure of the OC test and what parameters it determines.

Appeared: 2021 Q2(b) — 4 marks

Full Answer:

Procedure: Gradually increase the supply voltage from zero to rated value using the variac. Record $V_{0}$ , $I_{0}$ , and $W_{0}$ at rated voltage.

What it determines:

(2) Shunt branch parameters: $R_{c} = V_{0}^{2} / W_{0}$ (resistance representing core loss) and $X_{m} = V_{0} / I_{μ}$ (magnetizing reactance).

(3) No-load current and power factor: $cos ϕ_{0} = W_{0} / (V_{0} I_{0})$ . This is typically very low (0.1–0.3).

(4) Turns ratio verification: By measuring both primary and open-circuit secondary voltages: $a = V_{1} / V_{2}$ .

Why LV side? Lower voltage is safer. Current instruments can handle the small no-load current more easily.

🎯 Q2: Draw circuit diagrams for OC and SC tests.

Appeared: 2020 Q2(c) — 2 marks

Full Answer:

OC Test Circuit: LV winding connected to rated AC supply through variac. Ammeter in series, voltmeter across, wattmeter measuring input. HV winding open-circuited.

OC Test Circuit

SC Test Circuit

🎯 Q3: Why are OC and SC tests preferred over direct load test?

Appeared: 2024 Q3(a) — 4 marks

Full Answer:

Testing a 500 kVA transformer by direct load test would require:

A load bank of 500 kVA (resistors, inductors, capacitors): expensive, large, and dangerous.
Continuous power dissipation of ~15 kW in losses per hour.
Only one load condition at a time. Different loads require reconfiguration.

What OC and SC tests do instead:

From two simple, low-power tests, you get everything:

Core loss $P_{F e}$ (from OC test)
Full-load copper loss $P_{C u, F L}$ (from SC test)
All four equivalent circuit parameters ( $R_{c}$ , $X_{m}$ , $R_{01}$ , $X_{01}$ )
Efficiency at any load and any power factor (by formula)
Voltage regulation at any load and any power factor (by formula)

Key insight: Efficiency and VR are calculated analytically using the measured parameters. You never need to actually apply real loads. This is why OC/SC tests are universally preferred.

⚡ Exam Tips & Common Mistakes

OC test gives iron loss, not copper loss. $W_{0} = P_{F e}$ because $I_{0}$ is too small for significant copper loss.
OC test is done on LV side. Not HV. The reason is safety and convenience.
$R_{c}$ and $X_{m}$ are referred to the side where the test is done. To refer to the other side, multiply by $a^{2}$ (or divide, depending on direction).
Iron loss is CONSTANT. It does not change with load.

T-06b: SC Test — The companion test for series parameters
T-06c: Efficiency — Uses $P_{F e}$ from OC test
T-04: Equivalent Circuit — The circuit whose parameters we're finding
T-03a: No-Load Operation — The physics of what happens during OC test

← T-05: Voltage Regulation | 🏠 Index | T-06b: SC Test →

azazarfin60/Electrical_Machine_I_Semester_Final

boss_notes/T-06a_OC_Test.md

T-06a: Open-Circuit (OC) Test

Why This Topic Matters

📝 Key Definitions

Test Setup and Procedure

Parameter Extraction

🏆 Golden Questions (Past Exam Archive)

🎯 Q1: Explain the procedure of the OC test and what parameters it determines.

🎯 Q2: Draw circuit diagrams for OC and SC tests.

🎯 Q3: Why are OC and SC tests preferred over direct load test?

⚡ Exam Tips & Common Mistakes

Report a problem

azazarfin60/Electrical_Machine_I_Semester_Final

boss_notes/T-06a_OC_Test.md

T-06a: Open-Circuit (OC) Test

Why This Topic Matters

📝 Key Definitions

Test Setup and Procedure

Parameter Extraction

🏆 Golden Questions (Past Exam Archive)

🎯 Q1: Explain the procedure of the OC test and what parameters it determines.

🎯 Q2: Draw circuit diagrams for OC and SC tests.

🎯 Q3: Why are OC and SC tests preferred over direct load test?

⚡ Exam Tips & Common Mistakes

Report a problem

T-06a: Open-Circuit (OC) Test

Why This Topic Matters

📝 Key Definitions

Test Setup and Procedure

Parameter Extraction

🏆 Golden Questions (Past Exam Archive)

🎯 Q1: Explain the procedure of the OC test and what parameters it determines.

🎯 Q2: Draw circuit diagrams for OC and SC tests.

🎯 Q3: Why are OC and SC tests preferred over direct load test?

⚡ Exam Tips & Common Mistakes

🔗 Related Topics

T-06a: Open-Circuit (OC) Test

Why This Topic Matters

📝 Key Definitions

Test Setup and Procedure

Parameter Extraction

🏆 Golden Questions (Past Exam Archive)

🎯 Q1: Explain the procedure of the OC test and what parameters it determines.

🎯 Q2: Draw circuit diagrams for OC and SC tests.

🎯 Q3: Why are OC and SC tests preferred over direct load test?

⚡ Exam Tips & Common Mistakes

🔗 Related Topics