Transformers: Principles, Connections, and Applications
Transformers
Schedule Index
The process for determining the rate schedule is as follows:
- For single-phase transformers, represent the primary winding so that terminal A is at the top of the diagram (coinciding with the number 12 of an imaginary clock placed overlapping the vector diagram).
- Represent the secondary winding, noting that primary and secondary windings located in the same column produce in-phase FEMs (homologous terminals).
- Overlap both diagrams. The schedule is the angle formed by two vectors: one passing through the PTO and the center of the diagram, and the other passing through terminal A and the same center.
Harmonics
If a sinusoidal voltage is applied to a single-phase transformer and the core undergoes magnetization, the exciting current takes on a bell-shaped waveform with odd harmonic content. Apart from the fundamental harmonic, the most significant is the third harmonic. The load current of the transformer can be represented as:
i0 = i0.1 + i0.3 = √2I0.1cos(wt + ö1) + √2I0.3cos(3wt + ö3)
Considering a bank of three single-phase transformers in a three-phase system:
- Third harmonic currents produce voltage drops in phase with each other, leading to distortion and imbalance in the resulting line voltage. This is why neutral feedback is often unavailable in high-voltage lines.
- The absence of the third harmonic in the exciting current indicates a sinusoidal current, forcing the magnetic flux to lose its sinusoidal characteristic.
Three-Phase Transformers with Magnetic Core
In a three-phase Yy core transformer, there is no neutral in the primary power line. Consequently, there is no current path for third-harmonic excitation currents, and the issues mentioned earlier with currents and flux arise. The third-harmonic flux tends to close through the fourth column, which is the air return path. This path has high reluctance, resulting in significant third-harmonic flux penalties. To eliminate third-harmonic flows and prevent them from flowing through the air, the secondary winding is connected in a delta configuration.
Connections
a) Yy Connection
For a given line voltage (VL), the voltage across each phase of a star-connected transformer is VL/√3. In contrast, for a delta-connected transformer, the voltage across each coil is VL. The current in each coil of a star-connected transformer is equal to the line current (IL), while in a delta-connected transformer, it is IL/√3.
Therefore, under the same conditions, a star-connected transformer winding requires fewer turns and a larger cross-section than an equivalent delta-connected transformer, making its construction less expensive. The Yy connection is advantageous when connecting two systems with relatively high voltages and no phase shift between primary and secondary voltages is required.
However, the Yy connection has two drawbacks:
- Unbalanced loads result in alternating currents in the phases.
- Third-harmonic voltages are present.
These problems can be mitigated by solidly grounding the transformer neutrals, particularly on the primary side, or by adding a third winding connected in delta.
b) Yd Connection
This connection handles unbalanced loads effectively, as the delta winding redistributes imbalances. However, the delta connection introduces a 30° phase shift in the secondary voltages compared to the primary voltages. This can cause issues when paralleling the secondaries of two transformer groups, as it requires identical hourly rates for the groups. The Yd connection is suitable for transformers in high-voltage systems at the reducing end of the line.
c) Dy Connection
This connection shares the advantages and the 30° phase shift of the Yd connection. It is commonly used in distribution transformers, with the star connection on the low-voltage side to enable both three-phase and single-phase loads. The delta-connected primary helps mitigate imbalances caused by single-phase loads.
d) Dd Connection
This connection is suitable for low-voltage transformers as it requires more turns per phase for a given cross-section. It performs well under unbalanced loads.
e) Yz Connection
The zigzag connection is used only on the low-voltage side, typically in distribution networks. It effectively handles load imbalances.
Parallel Coupling of Transformers
Parallel coupling of transformers enhances electrical installations by allowing for increased capacity during peak consumption periods. This improves efficiency and provides redundancy in case of transformer failure.
Two transformers are considered to be in parallel when their homologous terminals are connected on both the primary and secondary sides, with negligible resistance and reactance in the connections. Parallel coupling is suitable when there are no internal circulating currents between the transformers when operating under no load, or when there is an unequal power distribution when feeding a common load.
The requirements for ideal parallel coupling are:
- Identical hourly rates for both transformers.
- Identical transformation ratios.
- Identical relative short-circuit voltages.
Autotransformers
An autotransformer is a special type of transformer with a single continuous winding acting as both primary and secondary. This means the output voltages are not isolated from each other. Unlike a two-winding transformer, an autotransformer transfers energy between circuits through magnetic coupling and direct electrical connection.
A conventional transformer requires N1 turns on the primary and N2 turns on the secondary. In contrast, an autotransformer uses only N1 turns, with a portion of these turns (N1-N2) carrying current I1, while the remaining N2 turns carry current I2-I1.
The weight of copper in each case is proportional to the number of turns and the current flowing through them. The relationship between the weight of copper in an autotransformer (Ga) and a conventional transformer (Gt) is:
Ga/Gt = (N2/N1)(1 – N2/N1)
This demonstrates material savings with an autotransformer compared to a conventional transformer. The reduced turn count allows for smaller core windows, resulting in less iron and overall weight. Consequently, autotransformers exhibit lower copper and iron losses, improving efficiency and voltage regulation.
However, autotransformers have two main disadvantages:
- Lower resistance and reactance lead to a lower short-circuit impedance, resulting in high short-circuit currents.
- High transformation ratios can pose a safety risk due to the common terminal shared by the high-voltage and low-voltage windings.
Due to these drawbacks, autotransformers are typically used when the voltage difference between V1 and V2 is small. It is crucial to ground the common terminal of both windings for safety.
Voltage Transformers
run almost empty and so the internal voltage drop is very small. Additionally, a terminal of its secondary should be grounded to prevent the danger of accidental contact between primary and secondary. The voltage transformer must provide a secondary voltage proportional to primary voltage. On the other hand, must be taken that the voltage drops are as minimal as possible as these processors should file a small reactor and a reduced load current, which forces to design the system with little leakage flux and a magnetic circuit required a small current vacuum.
However, these processors also have error: error in connection or voltage and phase error or angle.
Current transformers
Their mission is to reduce the mains current to the most appropriate values for the scales of the instruments. In the secondary are connected in series ammeter ammeters and coils of the measuring apparatus. Due to the low impedance of these devices, current transformers work virtually shorted, so low inductions used in the core.
In low voltage networks are also used, for convenience, a current transformer type called tongs or tweezers to measure the flow of a line without interrupting their operation.
As for the dangers to be avoided strictly left open circuit a current transformer. If you want to change a load you can interrupt the service line to proceed with the necessary changes or the operation can be performed without disconnecting the network if previously shorted transformer secondary.
Moreover, this processor also has errors such as intensity or ratio error and phase error.