Name: modeling parallel transformers with base mismatch
Uploaded: 2024-11-21T14:54:19.000Z
Duration: 1 min 25 s
Channel: JoVE

与实际量值模型相比，标幺值模型简化了变压器的分析。理想情况下，当电压基准比值与绕组的电压额定值相匹配时，变压器绕组的影响将被消除。
然而，对于具有不同额定值的并联变压器，选择电压基准具有挑战性。
对于此类情况，需建立具有非额定变比的标幺值模型，其中所选定的基准电压与变压器的额定电压不成比例。
考虑一个变压器，其额定电压由参数 a 关联。
若所选电压基准满足与项 b 的关系，则项 c 为其比值，并代入额定电压关系式中。
该系统可通过两个串联的变压器进行建模：其中一个表示包含损耗的标准标幺值模型，另一个为理想变压器。在此模型中，为简化起见，忽略了并联励磁支路。
该模型可能不适用于无法容纳理想变压器绕组的计算机程序。
另一种方法是采用节点方程，通过导纳参数来表示计算机程序中非标称变比的变压器。
对于实际的 c，可以建立一个π型电路网络模型。

非标称匝数比变压器

Transformers with Off-Nominal Turns Ratios

在涉及具有不同额定值的并联变压器的情况下，开发标幺模型需要考虑非标称匝数比。当所选基准电压与变压器的额定电压不成比例时，就会出现这种情况。考虑一个变压器，其额定电压与项 a 相关。如果所选电压基准满足涉及项 b 的关系，则项 c 定义为这些基准的比率。然后将此比率代入额定电压关系中。

为了解决非标称匝数比问题，可用两个串联变压器来表示关系:
<ol>
 <li>标准标幺模型:该模型包括所有相关损耗，代表变压器的实际方面。</li>
 <li>理想变压器:该模型简化了电压比表示，不考虑损耗。</li>
</ol>

在这个组合模型中，通常会忽略并联励磁支路以简化分析。然而，虽然这种方法在理论上是有效的，但它可能不适合不支持理想变压器绕组表示的计算机程序。

另一种建模方法是使用节点方程来提供导纳参数。这种方法有利于在计算机程序中表示具有非标称匝数比的变压器。节点方程提供了一种直接的方法来整合导纳参数，使模型与大多数模拟软件兼容。

对于项 c 为实数的情况，可以使用 pi 电路网络对变压器进行建模。pi 网络可以准确、实用地表示变压器的行为，尤其是在处理非标称匝数比时。该模型可以有效反映阻抗特性，并且与大多数计算工具兼容。

总之，虽然传统的标幺模型可以有效简化变压器分析，但在处理非标称匝数比和变化的电压基准时，它们会面临局限性。通过采用节点方程和 π 电路网络，工程师可以开发更通用、更准确的模型，这些模型适用于基于计算机的分析。这些方法确保在复杂的电气系统中准确地表示和分析具有不同额定值和非标准电压基准的变压器。

标幺值模型相较于实际值模型可简化变压器分析。理想情况下，当电压基准…时，变压器绕组可被消除。

transformers-with-off-nominal-turns-ratios

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Power Transformers

电力变压器

KEY TERMS AND CONCEPTS

关键术语与概念

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 associated losses and keeps the practical transformer behavior. The second is an ideal transformer, which shows only the voltage ratio and ignores losses. In this combined model, the shunt-exciting branches are usually left out to keep the analysis simpler.

This two-transformer approach is useful in theory, but it may not work well in computer programs that cannot represent ideal transformer windings. For that reason, another method uses nodal equations to build admittance parameters. These equations make it easier to include transformers with off-nominal turns ratios in simulation software.

When the ratio is a real number, the transformer can also be modeled with a pi circuit network. A pi network is a practical circuit model that captures impedance behavior. It is especially useful for off-nominal turns ratios and fits well with many computational tools. Together, these methods extend per-unit analysis so transformers with different ratings and non-standard voltage bases can be modeled more accurately.

Modeling Parallel Transformers with Base Mismatch

modeling-parallel-transformers-with-base-mismatch

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...

equivalent circuits for practical transformers

equivalent-circuits-for-practical-transformers

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...

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

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 per-unit models handle parallel transformers when voltage bases do not match ratings, using ideal transformers, nodal equations, and pi networks.

Modeling Parallel Transformers with Base Mismatch | 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 Parallel Transformers with Base Mismatch

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