Name: modeling transformer losses with equivalent circuits
Uploaded: 2024-11-21T14:54:19.000Z
Duration: 1 min 28 s
Channel: JoVE

Equivalent circuits of practical single-phase two-winding transformers differ from their ideal counterparts due to winding resistance and finite core permeability.
Unconfined magnetic flux results in real and reactive power losses. Resistance and leakage reactance, in series with each winding, account for resistive losses, leakage flux-induced voltage drop, and reactive power loss, respectively.
Finite core permeability implies non-zero magnetomotive force in Ohm&#39;s law for magnetic circuits.
Rearranging and substituting the induced voltage across the left winding results in a magnetizing current, which lags the induced voltage by 90 degrees, represented by a shunt inductor.
Additionally, a shunt branch, represented by a resistor, carries the core loss current in phase with the induced voltage. When the right winding current is zero, two components in the left winding current - core loss and magnetizing currents - account for real power and reactive power losses.
These losses can be minimized using high-grade alloy steel. Three alternative equivalent circuits can be drawn, including when resistance and leakage reactance are referred to left winding, exciting current is neglected, and winding resistances are ignored.

equivalent circuits for practical transformers

The practical equivalent circuits of single-phase two-winding transformers exhibit significant deviations from their idealized versions due to the inherent properties of winding resistance and finite core permeability. These properties result in real and reactive power losses, affecting the transformer&#39;s performance. Understanding these deviations is crucial for designing more efficient transformers.
In a practical transformer, each winding exhibits resistance and leakage reactance. The winding resistance contributes to resistive losses, manifesting as heat, while the leakage reactance, associated with the leakage flux, causes a voltage drop and results in reactive power loss. These elements are modeled in series, with each winding in the transformer&#39;s equivalent circuit, providing a more accurate representation of the transformer&#39;s behavior under load conditions.
The finite permeability of the transformer&#39;s core implies that a non-zero magnetomotive force (MMF) is required, as described by Ohm&#39;s law for magnetic circuits. This requirement results in a magnetizing current, which is essential for establishing the magnetic flux in the core. When the induced voltage across the primary winding is considered, the magnetizing current lags the induced voltage by 90 degrees. This relationship is represented by a shunt inductor in the equivalent circuit, accurately modeling the reactive power component due to core magnetization.
Core losses, primarily due to hysteresis and eddy currents within the core material, are represented by a shunt resistor in the equivalent circuit. This resistor models the core loss current, which is in phase with the induced voltage. When the secondary winding current is zero, the primary current comprises two components: the magnetizing current and the core loss current. These components are responsible for the reactive and real power losses, respectively.
To reduce these losses, high-grade alloy steel is often used for the core material. This material has superior magnetic properties, reducing hysteresis and eddy current losses, thereby improving transformer efficiency.
Three primary alternative equivalent circuits can be constructed for a practical transformer:
<ol>
	<li>When the resistance and leakage reactance are referred to the primary winding.</li>
	<li>When the exciting current (the sum of the magnetizing and core loss currents) is neglected for simplicity.</li>
	<li>When the winding resistances are ignored, focusing solely on the reactive components.</li>
</ol>
Each of these equivalent circuits provides insights into different aspects of transformer performance and simplifies analysis for specific applications. By understanding and modeling these non-ideal characteristics, engineers can design transformers that better meet the demands of various electrical systems.

Equivalent Circuits for Practical Transformers

Equivalent circuits of practical single-phase two-winding transformers differ from their ideal counterparts due to winding resistance and finite core ...

equivalent-circuits-for-practical-transformers

Education

JoVE Core

Electrical Engineering

Unit 1

Power Transformers

KEY TERMS AND CONCEPTS

modeling transformer losses with equivalent circuits

Practical transformer equivalent circuits show how winding resistance, leakage reactance, and finite core permeability change transformer behavior. These non-ideal features create real and reactive power losses, so they matter when a transformer is under load.

Each winding has resistance and leakage reactance. Winding resistance causes resistive loss, which appears as heat. Leakage reactance comes from leakage flux, and it creates a voltage drop and reactive power loss. In the equivalent circuit, these elements are placed in series with each winding so the model matches real operation more closely.

The transformer core also needs a non-zero magnetomotive force, or MMF, because its permeability is finite. That need creates a magnetizing current, which establishes the magnetic flux in the core. When the induced voltage across the primary winding is considered, this magnetizing current lags the induced voltage by 90 degrees. It is shown as a shunt inductor in the circuit because it represents the reactive part of the core magnetization current.

Core losses are caused mainly by hysteresis and eddy currents in the core material. These losses are modeled with a shunt resistor. The core loss current through that resistor is in phase with the induced voltage, so it represents real power loss. When the secondary current is zero, the primary current contains both the magnetizing current and the core loss current. Together, these currents account for the reactive and real power losses in the transformer.

High-grade alloy steel is often used for the core to reduce these losses. Its better magnetic properties help lower hysteresis and eddy current loss, which improves efficiency. Engineers can also build three useful alternative equivalent circuits for a practical transformer. In one, the resistance and leakage reactance are referred to the primary winding. In another, the exciting current, which is the sum of magnetizing and core loss currents, is neglected for simplicity. In a third, winding resistances are ignored so the focus stays on the reactive components. Each form helps with a different kind of analysis and gives insight into transformer performance.

Modeling Transformer Losses with Equivalent Circuits

modeling-transformer-losses-with-equivalent-circuits

the ideal transformer

Transformer Core Flux and Turn Ratio

Single-phase two-winding transformers use two windings around a magnetic core. The core has a cross-sectional area A and magnetic permeability μ. A phasor current i1 enters the left winding, and i2 exits the right winding. These parts work together to move energy by electromagnetic means. Ampere’s law explains the magnetic field inside the transformer. It says that the closed-path integral of the magnetic field intensity’s tangential component equals the net current enclosed. For a...

Practical transformer equivalent circuits show how winding resistance, leakage reactance, and finite core permeability change transformer behavior. These non-ideal features create real and reactive power losses, so they matter when a transformer is under load. Each winding has resistance and leakage reactance. Winding resistance causes resistive loss, which appears as heat. Leakage reactance comes from leakage flux, and it creates a voltage drop and reactive power loss. In the equivalent...

three-winding transformers

Three-Winding Transformer Models

Three-winding transformer models show how three identical single-phase transformers can be combined into a three-phase transformer connection. The high-voltage windings are labeled A, B, and C. The low-voltage windings are labeled a, b, and c. This notation separates the high-voltage side from the low-voltage side and matches each phase to its own winding. For a grounded Y-Y three-phase transformer, the per-unit equivalent circuit uses common base quantities to simplify analysis. The base...

transformers with off-nominal turns ratios

transformers-with-off-nominal-turns-ratios

Modeling Parallel Transformers with Base Mismatch

Parallel transformers can be modeled with per-unit values even when the chosen voltage bases do not match the transformer ratings. This case creates an off-nominal turns ratio, which means the base voltages are not proportional to the rated voltages. To handle that mismatch, the transformer voltage relation is adjusted by using the ratio of the selected bases. One way to represent the transformer is as two series transformers. The first is the standard per-unit model, which includes the...

key terms and concepts

Learn how practical transformer equivalent circuits model winding resistance, leakage reactance, magnetizing current, and core losses for grades 9–12.

Modeling Transformer Losses with Equivalent Circuits | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

Modeling Transformer Losses with Equivalent Circuits

Description

Transcript

Tags