Transformer

A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit. Transformers play a crucial role in the generation, transmission, and distribution of electrical power across the world. These essential devices enable the efficient transfer of electrical energy between circuits with different voltage levels, ensuring the reliability and stability of modern power systems. In this article, we will explore the principles behind transformers, their various types, and their widespread applications in our daily lives.

The Principle of Electromagnetic Induction

Transformers operate based on the principle of electromagnetic induction, which was first discovered by Michael Faraday in 1831. Faraday’s Law states that a change in magnetic flux within a closed loop of wire induces an electromotive force (EMF) in the loop. This induced EMF creates an electric current in the wire, allowing energy to be transferred between circuits without direct electrical contact.

Transformers utilize this principle by employing two or more coils of wire, known as windings, wrapped around a shared magnetic core. The primary winding is connected to the input voltage, while the secondary winding is connected to the output circuit. When an alternating current (AC) flows through the primary winding, it generates a varying magnetic field, which induces an EMF in the secondary winding.

Calculation of Transformer – Turns Ratio & Turns per Volt

Calculating a transformer involves determining its specifications based on the required input and output voltages, current, and power. The most critical parameters include the turns ratio, the number of turns in primary and secondary windings, and the wire size.

Turns ratio and turns per volt are two important concepts in transformer design and analysis.

1. Turns ratio: The turns ratio is the ratio of the number of turns in the primary winding (Np) to the number of turns in the secondary winding (Ns). It determines the relationship between the input (primary) and output (secondary) voltages of a transformer. The turns ratio can be expressed as:

Turns ratio (N) = Np / Ns

According to the transformer’s basic voltage equation, the ratio of the primary voltage (Vp) to the secondary voltage (Vs) is equal to the turns ratio:

Vp / Vs = Np / Ns

For step-up transformers, the turns ratio is greater than 1, as the number of turns in the primary winding is less than the secondary winding, resulting in a higher output voltage. Conversely, for step-down transformers, the turns ratio is less than 1, as the number of turns in the primary winding is greater than the secondary winding, yielding a lower output voltage.

2. Turns per volt (Tpv): Turns per volt is a parameter used in transformer design that represents the number of turns needed in the winding for each volt of output. It is dependent on the core material, core size, and operating frequency. The turns per volt value helps determine the number of turns required for both primary and secondary windings to achieve the desired voltage transformation.

The turns per volt can be calculated using the following formula:

Tpv = (4.44 * 10^4 * Ae * Bm * f) / Vp

Where:

• Ae is the effective cross-sectional area of the core (cm² or m²)
• Bm is the maximum flux density of the core material (T, Tesla)
• f is the operating frequency (Hz)
• Vp is the primary voltage (V)

Once the turns per volt value is calculated, the number of turns for the primary and secondary windings can be determined:

Primary winding turns (Np) = Vp * Tpv Secondary winding turns (Ns) = Vs * Tpv

In summary, the turns ratio is essential for understanding the voltage transformation between the primary and secondary sides of a transformer, while turns per volt is a critical parameter in transformer design, helping to determine the appropriate number of turns in the windings.

Example

Here’s a step-by-step example of how to calculate a transformer:

Suppose we want to design a single-phase step-down transformer that converts 240V AC input voltage to 12V AC output voltage with a power rating of 120W.

Step 1: Determine the turns ratio. The turns ratio (N) is the ratio of the primary voltage (Vp) to the secondary voltage (Vs). N = Vp / Vs

In this example, N = 240V / 12V = 20

Step 2: Calculate the primary and secondary currents. To determine the currents, we’ll use the power rating (P) and the input/output voltages.

For the primary side (Ip): Ip = P / Vp Ip = 120W / 240V = 0.5A

For the secondary side (Is): Is = P / Vs Is = 120W / 12V = 10A

Step 3: Select the core size and calculate the number of turns. The core size depends on the power rating and the operating frequency. In this example, we’ll use a core with a cross-sectional area (Ae) of 1.5 cm² for a 50 Hz frequency. The number of turns per volt (Tpv) can be calculated using the following formula:

Tpv = (4.44 * 10^4 * Ae * Bm * f) / Vp

Where Bm is the maximum flux density (T) and f is the frequency (Hz). Assuming a Bm of 1.1 T for the core material:

Tpv = (4.44 * 10^4 * 1.5 * 1.1 * 50) / 240V = 1.375 turns/volt

Now, we can calculate the number of turns in the primary and secondary windings.

Primary winding turns (Np): Np = Vp * Tpv Np = 240V * 1.375 turns/volt ≈ 330 turns

Secondary winding turns (Ns): Ns = Vs * Tpv Ns = 12V * 1.375 turns/volt ≈ 16 turns

Construction of Transformers

Transformers are essential electrical devices that transfer energy between circuits with different voltage levels through electromagnetic induction. Their construction can vary depending on their application, power rating, and type. However, there are some fundamental components common to most transformers:

1. Magnetic Core: The magnetic core is the central part of a transformer and serves as a path for the magnetic flux. It is typically made of iron or other ferromagnetic materials such as silicon steel, which have high magnetic permeability and low hysteresis loss. The core is often laminated to reduce eddy current losses and improve efficiency.
2. Windings: Windings are coils of insulated copper or aluminum wire wound around the magnetic core. There are two main windings in a transformer: the primary winding, which is connected to the input voltage source, and the secondary winding, which is connected to the output circuit. The number of turns in each winding determines the voltage ratio between the primary and secondary sides.
3. Insulation: Insulating materials are used to separate the windings from the core and each other, ensuring electrical isolation between the circuits. Insulation also prevents short-circuits and protects the transformer from damage due to overheating or voltage surges. Common insulating materials include paper, varnish, and specialized insulating films.
4. Cooling system: As transformers operate, they generate heat due to resistive and magnetic losses. To maintain optimal performance and prevent damage, a cooling system is employed. Small transformers may rely on natural air convection, while larger transformers often use oil or a combination of oil and forced-air or water cooling systems. The cooling medium absorbs heat from the windings and core and dissipates it to the surrounding environment.
5. Enclosure: The enclosure, or housing, protects the transformer from external factors, such as dust, moisture, and physical damage. The enclosure also provides support for the internal components and may include features for mounting the transformer in its intended location. Transformer enclosures can be made of various materials, such as metal, plastic, or a combination of both, depending on the application and environmental requirements.
6. Bushings: Bushings are insulating devices that provide a safe passage for the high-voltage conductors from the transformer windings to the external electrical connections. They are designed to withstand the electrical stress and prevent flashovers, ensuring the safe and reliable operation of the transformer.
7. Tap changer: Some transformers are equipped with tap changers, which allow for the adjustment of the turns ratio between the primary and secondary windings. Tap changers can be either on-load (OLTC) or off-load (DETC) types. On-load tap changers can adjust the turns ratio while the transformer is energized, while off-load tap changers require the transformer to be de-energized for adjustments. Tap changers enable voltage regulation and maintain the desired voltage levels in power systems.
8. Conservator tank (for oil-filled transformers): In oil-filled transformers, a conservator tank is used to store the insulating oil and accommodate its expansion and contraction due to temperature variations. The conservator tank is connected to the main transformer tank and includes a breather to maintain the oil’s moisture and air content within acceptable limits.
9. Protection devices: Transformers are often equipped with various protection devices to ensure their safe and reliable operation. These may include temperature sensors, pressure relief devices, and gas detectors for oil-filled transformers. Additionally, protection relays and circuit breakers can be used to monitor and disconnect the transformer from the power system in case of faults or abnormal conditions.

Types of Transformers

Transformers can be broadly classified into two main categories: step-up and step-down transformers.

1. Step-up transformers: These transformers increase the voltage from the primary to the secondary winding, while decreasing the current proportionally. Step-up transformers are commonly used in power plants to raise the voltage of the generated electricity, reducing power losses during long-distance transmission.
2. Step-down transformers: In contrast, step-down transformers decrease the voltage from the primary to the secondary winding, while increasing the current proportionally. These transformers are used to reduce the high transmission voltages to lower, safer levels suitable for residential and industrial consumers.

In addition to these primary categories, transformers can be further classified based on their construction, cooling method, and application, such as power transformers, distribution transformers, and instrument transformers.

Based on their construction, purpose, and application, transformers can be classified into several types:

1. Power transformers: Power transformers are used in power generation and transmission systems to step up or step down voltage levels. They are typically larger, have higher power ratings, and are designed for high efficiency and low losses. These transformers operate at or near full load capacity and are located in power plants, substations, and grid interconnections.
2. Distribution transformers: These transformers are used to step down the voltage from transmission lines to levels suitable for residential, commercial, and industrial consumers. Distribution transformers are smaller than power transformers and are designed for continuous operation at lower loads. They are commonly found on utility poles, in underground distribution systems, and in commercial or residential buildings.
3. Instrument transformers: Instrument transformers are designed to provide accurate voltage and current measurements for metering, protection, and control purposes in power systems. There are two main types of instrument transformers:a. Current transformers (CT): These transformers are used to step down high currents in primary circuits to lower, safer levels for measurement and protection devices.b. Voltage transformers (VT) or potential transformers (PT): These transformers step down high voltages in primary circuits to lower, standardized levels for measurement and protection devices.
4. Autotransformers: Autotransformers have a single winding with a shared magnetic core, where both the primary and secondary voltages are derived from the same winding. They are more compact and efficient than conventional two-winding transformers but do not provide electrical isolation between the input and output circuits. Autotransformers are commonly used in power systems, audio equipment, and voltage regulators.
5. Pulse transformers: Pulse transformers are designed for the efficient transfer of short-duration, high-voltage pulses between circuits. They are used in communication systems, radar equipment, and power electronics applications, such as switching power supplies and gate drive transformers in high-power semiconductor devices.
6. Toroidal transformers: Toroidal transformers have a doughnut-shaped magnetic core made of a continuous strip of high-permeability magnetic material. The primary and secondary windings are wound around the core, resulting in a compact, low-profile design with low electromagnetic interference (EMI) and high efficiency. They are used in audio equipment, power supplies, and lighting applications.

Energy Losses in Transformers

Energy losses in transformers can be broadly classified into two categories: core losses and copper (or winding) losses. These losses result in reduced efficiency and increased operating temperature, which can impact the transformer’s performance and lifespan.

1. Core losses:

Core losses, also known as iron losses or magnetic losses, occur in the transformer’s magnetic core due to alternating magnetic fields. They consist of two main components:

a. Hysteresis loss: Hysteresis loss is caused by the constant reversal of the magnetic field in the core material as the alternating current flows through the primary winding. The energy dissipated as heat during the magnetization and demagnetization cycles of the core material results in hysteresis loss. The hysteresis loss is proportional to the frequency of the AC supply and can be reduced by using core materials with low hysteresis coefficients, such as silicon steel.

b. Eddy current loss: Eddy current loss is caused by the circulation of induced currents within the core material itself. These currents generate heat and result in energy loss. Eddy current losses are proportional to the square of the supply frequency and the square of the core’s thickness. To minimize eddy current losses, the transformer cores are laminated with thin, insulated layers of core material, reducing the effective thickness and thus the eddy currents.

2. Copper losses (winding losses):

Copper losses, also known as winding losses or ohmic losses, occur due to the resistance of the transformer’s windings (primary and secondary). When current flows through the windings, the resistance generates heat, leading to energy loss. Copper losses are proportional to the square of the current and can be expressed as:

a. Primary winding loss: Pp = I_p^2 * R_p

b. Secondary winding loss: Ps = I_s^2 * R_s

Where Pp and Ps represent the power losses in the primary and secondary windings, respectively; I_p and I_s are the currents in the primary and secondary windings, respectively; and R_p and R_s are the resistances of the primary and secondary windings, respectively.

Copper losses can be minimized by using larger diameter conductors, which have lower resistance, or by using materials with better conductivity, such as high-purity copper or aluminum.

In addition to core and copper losses, there are other minor losses, such as stray load losses and dielectric losses, which can also contribute to the overall energy losses in transformers. However, these losses are typically smaller and less significant compared to core and copper losses.

Applications of Transformers

Transformers play a vital role in a wide range of applications, including:

1. Power generation and transmission: Transformers are used to step up the voltage generated by power plants before transmission over long distances, minimizing power losses. At substations, step-down transformers reduce the voltage to appropriate levels for distribution to consumers.
2. Industrial applications: Transformers are employed in various industrial processes, such as induction heating, welding, and electrochemical processes, where precise voltage control is required.
3. Electronics: Small transformers are commonly found in electronic devices, such as power supplies, chargers, and adapters, to convert the mains voltage to the specific voltage levels required by the device.
4. Lighting: Transformers are used in lighting systems, such as halogen lamps and LED drivers, to provide the appropriate voltage for the light source.
5. Medical equipment: In medical facilities, transformers are utilized in devices like X-ray machines and MRI scanners, where precise voltage control is essential for accurate imaging and patient safety.

Conclusion

Transformers are indispensable components of modern power systems, enabling the efficient generation, transmission, and distribution of electrical energy. By understanding the principles behind transformers and their various applications, we can appreciate their critical role in powering our daily lives and advancing technological progress.