No-Load Transformer and Its Phasor Diagram
When a transformer operates with no load connected to its secondary winding, it draws a small current from the supply that reveals important information about core losses and magnetizing requirements. Understanding the no-load condition is essential for transformer testing, equivalent circuit modeling, and efficiency calculations.
What is No-Load Condition?
A transformer is said to be on no-load when the secondary winding is left open-circuited, meaning no external load is connected and the secondary current is zero (I₂ = 0). In this condition, the primary winding still draws a small current from the AC supply.
This small current — called the no-load current (I₀) — is typically 3 to 5 percent of the rated full-load primary current. Despite being small, it performs two critical functions: magnetizing the core and supplying core losses.
No-Load Current and Its Components
The no-load current I₀ is not a single-purpose current. It has two distinct components that serve different functions:
Magnetizing component (Im) — This is the reactive or wattless component. It produces the alternating magnetic flux in the transformer core. Since it creates the flux, Im is in phase with ϕ and lags the applied voltage V₁ by 90°.
Active component (Iw) — This is the wattful component that supplies the iron losses (hysteresis loss + eddy current loss) in the core. It is in phase with the applied voltage V₁ because it represents real power consumption.
The no-load current I₀ is the phasor sum of these two components — not their arithmetic sum.
Phasor Diagram at No-Load
The phasor diagram of a practical transformer under no-load condition illustrates the phase relationships between voltage, current, flux, and EMF quantities.
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| No-Load Phasor Diagram of a Practical Transformer |
Steps to construct the phasor diagram:
- Take flux ϕ as the reference phasor (horizontal axis)
- Draw Im in phase with ϕ (along the reference)
- Draw E₁ and E₂ lagging ϕ by 90° (both induced by the same flux, so they are in phase with each other)
- Draw V₁ opposite to E₁ (by Lenz's law, V₁ ≈ −E₁ when primary winding drops are neglected)
- Draw Iw in phase with V₁
- The phasor sum of Im and Iw gives I₀
- The angle θ₀ between V₁ and I₀ is the no-load power factor angle
Since E₁ and E₂ are induced by the same mutual flux, they are always in phase. The relationship between them is governed by the turns ratio: E₁/E₂ = N₁/N₂.
Key Formulas
No-Load Power Input
The power drawn by the transformer at no-load is consumed entirely in the core as iron losses (since copper loss at no-load is negligible due to very small I₀).
This power represents:
- Hysteresis loss — due to repeated magnetization and demagnetization of the core
- Eddy current loss — due to circulating currents induced in the core laminations
The no-load power factor cos(θ₀) is very low (typically 0.1 to 0.2) because the magnetizing component Im is much larger than the active component Iw. This means the no-load current is highly lagging and predominantly reactive.
Practical Significance of No-Load Test
The open-circuit (no-load) test is one of the two standard tests performed on transformers. Its practical applications include:
- Determining core losses (iron losses) which remain constant at all loads
- Finding the no-load current and power factor
- Calculating parameters of the shunt branch of the equivalent circuit (R₀ and X₀)
- Verifying the turns ratio by measuring V₁ and V₂ at no-load
- Checking for inter-turn faults — abnormally high I₀ indicates shorted turns
The test is always performed on the low-voltage side for safety and convenience, with the high-voltage side left open.
No-Load vs Full-Load Comparison
Frequently Asked Questions
1. Why is the no-load current of a transformer so small?
The no-load current is only 3–5% of rated current because it only needs to magnetize the core and supply iron losses. There is no secondary load demanding power transfer, so the primary draws minimal current.
2. What are the two components of no-load current?
The two components are: (1) Magnetizing component Im which sets up the flux in the core and is in phase with flux ϕ, and (2) Active component Iw which supplies hysteresis and eddy current losses and is in phase with applied voltage V₁.
3. Why is the no-load power factor of a transformer very low?
The no-load power factor is very low (0.1 to 0.2) because the magnetizing component Im is much larger than the loss component Iw. The current is predominantly reactive since its main job is to establish magnetic flux, not deliver real power.
4. What losses occur in a transformer at no-load?
At no-load, only iron losses (core losses) occur — these include hysteresis loss and eddy current loss. Copper losses are negligible because the no-load current is very small. The wattmeter reading during the open-circuit test directly gives the iron losses.
5. Why does E₁ lag behind the flux by 90° in the phasor diagram?
By Faraday's law, the induced EMF is proportional to the rate of change of flux (e = −dϕ/dt). When flux is sinusoidal, its derivative (the EMF) leads the flux by 90°. However, since the EMF opposes the change (Lenz's law), E₁ lags the flux by 90° in the standard phasor convention.