Operation of Transformer in On-Load Condition: Phasor Diagram, Load Effects

Operation of Transformer in On-Load Condition

To understand the operation of a transformer in load, let us first recall its on-load condition. In the on-load state, when an input voltage is applied across the primary winding, a small on-load current flows. This current establishes a magnetic flux in the transformer core.

What is a Transformer?

A transformer is an electrical device that transfers alternating current (AC) electrical energy from one circuit to another through electromagnetic induction. It consists mainly of:

• Primary winding: Connected to the input voltage source.
• Secondary winding: Connected to the load.
• Magnetic core: Provides a path for magnetic flux linking both windings.

Transformers operate on the principle of Faraday’s law of electromagnetic induction: a changing current in the primary coil creates a varying magnetic flux in the core, inducing an electromotive force (EMF) in the secondary coil.

Load Condition in a Transformer

Definition of On-Load Condition

The on-load condition of a transformer refers to the state when the secondary winding of the transformer is connected to an external load and current flows through the secondary circuit. This means the transformer is actively supplying electrical energy to a load.

Unlike the no-load condition where only a small exciting current flows, in on-load condition, both primary and secondary currents carry significant load current, and the transformer operates under full or partial load.

Transformer in On-Load Condition on the Secondary Side

Now, when a load is connected to the secondary winding, the situation changes:

1. Load Connection
   As soon as the secondary winding is connected to a load, the magnetic flux in the core induces an electromotive force (EMF) in the secondary winding. According to Faraday’s Law of Electromagnetic Induction, this EMF drives a current through the load.
   
2. Effect on Primary Winding
   The flow of current in the secondary winding produces its own magnetic field, which tends to oppose the original flux (as per Lenz’s Law). To maintain the original flux level, the primary winding draws an additional current from the supply.
   
3. Flux Direction Determination
   The direction of the magnetic flux at any instant can be determined using the Right-Hand Thumb Rule. In this rule, if you curl the fingers of your right hand around the conductor in the direction of current flow, your thumb will point in the direction of the magnetic flux.
   
4. Balance of Power
   The additional primary current ensures that the magnetizing flux remains constant, allowing the transformer to transfer electrical power from the primary to the secondary winding efficiently, with only small losses.
   
   

Behavior of Currents and Voltages During Load

Now, when the secondary side is closed by connecting a load, the mutually induced emf produces a current I₂ in the secondary winding. The direction of this current is governed by Lenz’s law, which states that I₂ must flow such that the flux produced by I₂ opposes the original flux. This situation is illustrated in Fig. 3.15(b).

Consequently, there are two fluxes in the core: the original flux φ and the opposing flux produced by the secondary current, which we denote φ₂. The net flux in the core becomes φ_net = φ − φ₂, which is less than the original flux φ.

Because the net flux has reduced, the magnitude of the self-induced emf in the primary also reduces. Note that the applied primary voltage V₁ remains the same, but the counter emf (which opposes V₁) has decreased. As a result, the primary draws more input current from the supply.

Let the additional current drawn by the primary due to loading be denoted I_a. If the no-load (magnetizing) current is I₀, then the resultant primary current under load is:

Ī = Ī₀ + Ī_a

Here the overbars indicate phasor (vector) quantities when dealing with alternating currents and voltages.

This increased primary current balances the ampere-turns produced by the secondary current so that the core flux remains approximately constant under steady-state loading, enabling efficient transfer of power from primary to secondary with minimal change in core magnetization.

Currents and Voltages During Load

The additional primary current (I′₂), which flows due to the presence of load, is called the load component of the primary current. This current flows in the same direction as the no-load current (I₀) and produces its own magnetic flux (φ′₂) in the same direction as the original flux (φ).

Now, in the core, there are three fluxes:

• φ: the original magnetizing flux.
• φ₂: the flux produced by the secondary current .
• φ′₂: the flux produced by the load component of the primary current (in the same direction as φ).

Here, φ₂ and φ′₂ are in opposite directions, as shown in Fig. Since the magnetomotive force (mmf) of the primary side equals the mmf of the secondary side:

N₁ I′₂ = N₂ I₂

Therefore, the magnitudes of φ′₂ and φ₂ are equal:

|φ′₂| = |φ₂|

These opposing fluxes cancel each other, leaving only the original flux (φ) in the core. As a result, the net flux in the core remains essentially constant from no-load to full-load conditions. In practice, this variation is very small, typically between 1% and 3%. Because of this property, a transformer is often called a Constant Flux Machine.

The magnitude of the load component of the primary current is given by:

|I′₂| = (N₂ / N₁) |I₂| = K |I₂|

where K is the transformation ratio.

Introduction to Load Current and Reflected Load Current

• The load current I2​ in the secondary side depends on the load impedance Zload​:
  = I2 =V2/Zload​​
  
• This current induces a reflected load current I2′ in the primary side, which opposes the magnetizing current but adds to the overall primary current demand.
• The primary winding draws current from the supply sufficient to balance the magnetizing current and load demand, maintaining the flux in the core nearly constant.

5. Voltage Drops in Transformer Windings (Resistive and Reactive)

• Resistance R: Copper losses occur due to resistance in the primary and secondary windings. These cause voltage drops proportional and in phase with the current:
  Vr=IR
  
• Leakage Reactance X: Caused by leakage flux that does not link both windings, producing inductive reactance. Voltage drops due to reactance lead the current by 90°:
  Vx=jIX
  
• Total voltage drop in each winding is the vector sum of resistive and reactive voltage drops.
• The primary terminal voltage V1​ is related to induced EMF, E1 and voltage drops: V1=E1+I1(R1+jX1)
• Similarly, the secondary terminal voltage V2​ is related to induced EMF, E2 and voltage drops:
  V2=E2+I2(R2+jX2)

These voltage drops cause the terminal voltage to differ from the ideal induced EMF.

6. Phasor Diagram for On-Load Condition

When a transformer is connected to a load, new currents I₂ and I₁ appear, significantly modifying the phasor diagram from its no-load version. Under load conditions, the interplay between primary and secondary circuits becomes more complex, and voltage drops across winding resistances and leakage reactances must be considered.

Steps to Draw Phasor Diagram on Load

1. Reference Flux ∅:
   Draw the core magnetic flux ∅ as the reference axis.
   
2. Induced EMFs E1and E2:
   Draw E1 and E2​ lagging flux ∅ by 90°. (Since EMF is proportional to rate of change of flux.)
   
3. Simplification for Primary Phasors:
   Reverse the E1​ phasor on the upper side and consider its magnitude only. This places all primary winding phasors above the flux axis and secondary phasors below it.
   
4. Magnetizing Current Iμ:
   • Draw Iμ in phase with flux ∅
   • Draw the core loss component Ic leading Iμ​ by 90°.
   • Add Iμ​ and Ic using the parallelogram method to get resultant no-load current I0​.
     
5. Secondary Voltage V2
   • Draw V2 lagging E2 by a small load angle δ
   • Depending on the load type, draw the secondary current I2 accordingly (in phase, lagging, or leading V2).
     
6. Primary Load Current Component:
   • Draw I2, the load component of the primary current, 180° out of phase with I2​ (according to reflected load current).
   • Add I2′​ and I0​ using the parallelogram method to get the total primary current I1
     
7. Primary Voltage V1:
   • From the tip of ∣−E1, draw the resistive voltage drop I1R1​ in phase with I1​.
   • Draw the inductive voltage drop I1X1 leading I1 by 90° from the tip of I1R1.
   • Add these voltage drops and ∣−E1 vectorially (polygon method) to get input voltage V1.
     
8. Secondary Voltage V2:
   • Similarly, draw voltage drops I2R2​ and I2X2​ on the secondary side to get resultant E2.

Load Conditions:

• Purely Resistive Load: Current is in-phase with voltage.
• Inductive Load: Current lags voltage.
• Capacitive Load: Current leads voltage.

Effects of Different Types of Load on Transformer Operation

Transformers are designed to efficiently transfer electrical energy from primary to secondary windings, but their performance can significantly vary depending on the types of load connected. The load affects current flow, voltage regulation, losses, heating, and overall system stability. Understanding these effects is crucial for proper transformer design, operation, and maintenance.

1. Resistive Load

Characteristics:

• A purely resistive load (e.g., heating elements, incandescent bulbs) draws current that is in phase with the voltage.
• Power factor is unity (1.0), meaning all power drawn is active power (real power), with no reactive component.

Load Effects on Transformer Operation:

• Voltage and Current in Phase:
  Since current and voltage are synchronized, voltage drops due to winding resistance dominate, while drops due to leakage reactance are minimal because reactance voltage drops depend on current phase.
• Voltage Regulation:
  Voltage regulation is generally moderate—the terminal voltage decreases slightly under load due to copper losses in windings, but this is predictable and stable.
• Losses and Heating:
  Copper losses (I²R losses) in windings increase proportional to the square of load current, causing transformer heating. Since there’s no reactive power, core losses remain relatively constant.
• System Stability:
  Resistive loads do not contribute to reactive power or phase angle shifts, leading to stable and efficient transformer operation.

2. Inductive Load

Characteristics:

• Inductive loads (e.g., motors, transformers, fluorescent lighting ballasts) cause the load current to lag the voltage by an angle ϕ (power factor less than 1, lagging).
• The current has both active and reactive power components.

Load Effects on Transformer Operation:

• Current Lagging Voltage:
  The lagging current causes larger voltage drops in the transformer’s leakage reactance X because reactance voltage drop is proportional to the current magnitude and leads it by 90°. This leads to a substantial voltage drop across the leakage reactance.
• Voltage Regulation:
  Voltage regulation is higher than resistive loads. Under heavy inductive load, terminal voltage drops more significantly compared to no-load voltage.
• Reactive Power Flow:
  The transformer supplies reactive power to the inductive load, increasing the overall current in the system without delivering useful work, which reduces the power factor.
• Heating and Efficiency:
  Increased current flow leads to higher copper losses and heating. Also, reactive current increases losses without contributing to active power output, reducing overall transformer efficiency.
• System Stability:
  Inductive loads cause phase shifts and reactive power flow, which can stress power systems by increasing losses, voltage drops, and requiring reactive power compensation devices for stable operation.

3. Capacitive Load

Characteristics:

• Capacitive loads (e.g., capacitor banks for power factor correction) cause the load current to lead the voltage by an angle ϕ.
• Power factor is less than 1 but leading instead of lagging.

Load Effects on Transformer Operation:

• Current Leading Voltage:
  The leading current reduces the net reactive current demand from the power source because capacitors supply reactive power back to the system.
• Improved Voltage Regulation:
  Capacitive loads can improve voltage regulation by partially canceling out the inductive reactance voltage drops inside the transformer windings. This may result in the secondary terminal voltage being higher than the induced EMF at certain load levels.
• Reduced Reactive Power Demand:
  By supplying reactive power, capacitive loads reduce the burden on the transformer and the upstream supply, potentially reducing losses and improving overall system efficiency.
• Losses and Heating:
  Although capacitive loads supply reactive power, they still draw active power, so copper losses occur. However, reduced reactive current flow can lead to lower overall heating and losses compared to inductive loads of the same apparent power.
• System Stability:
  While capacitive loads can improve power factor and voltage levels, excessive capacitive loading can cause overvoltages and resonance conditions, potentially leading to system instability and equipment damage if not managed properly.

Summary of Load Effects on Transformer

Practical Implications

• Transformer Sizing:
  Transformers must be rated to handle the maximum expected load current and type. Inductive loads often require transformers with higher thermal rating due to higher losses and heating.
• Power Factor Correction:
  Capacitive loads are often intentionally added to improve lagging power factors caused by inductive loads, thereby reducing losses and improving voltage profiles.
• Load Management:
  Utilities and industries monitor load types to optimize transformer operation, minimize losses, and maintain grid stability.
• Protection Settings:
  Overcurrent and thermal protection schemes consider load types to avoid nuisance tripping or failure.

Summary

A transformer’s behavior changes significantly between no-load and load conditions. At no-load, only a small current flows, maintaining the magnetic flux and causing core losses without power transfer. Under load, the transformer delivers power, increasing current and losses, with voltage drops across internal impedances.

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