Electrical Transformers with Theory of Transformers

Definition of Electrical Transformer

The transformer is a static device that transforms electrical energy from one circuit to another without changing its frequency.

The transformer works on the principle of mutual induction.

Types of Electrical Transformer

Depending upon the applications we can subdivide transformers into three different categories.

Power Transformers

Generally, we refer to the transformers used in power generation and transmission systems as Power Transformers.

Generator Power Transformers: Electrical Transformers associated with generating stations are Generator Power Transformers. These transformers are Step Up Transformers. The electrical power generating stations produce power at low voltage levels. Because it is technically justified and economical. But a high voltage transmission is more efficient and economical than a low voltage transmission. Therefore for transmission purpose stepping up of generated low voltage power becomes essential. This is the reason all Generator Power Transformers are Step Up Transformers. The capacity of these transformers is significantly high. Normally it is more than 60 MVA.

Primary Transmission Power Transformers: These transformers step down the transmitted power at primary transmission substations for secondary transmission purposes. These are obviously step down transformers. The typical range of capacity for Primary Transmission Power Transformers is 50 MVA and above.

Secondary Transmission Power Transformers: These transformers are also step down transformers. The purpose of these transformers is to step down the voltage level of the power from the primary transmission levels to the secondary transmission levels. The capacities of these transformers are generally from 10 MVA to 50 MVA.

Bulk Supply Power Transformers: These transformers are also step down transformers. The Bulk Supply Transformers supply power to large consumers from secondary transmission ends. The typical range of capacities of these transformers is from 0.5 MVA to 20 MVA.

Distribution Transformers: The location of Distribution Transformers is at the junction of transmission and distribution networks. These transformers step down the voltage level of power from secondary transmission levels to distribution levels. These transformers are generally of 5 MVA and 6.3 MVA ratings.

Instrument Transformers

There are some special purpose transformers used in power systems. These transformers facilitate measurings and protections of the system. In the power system network, we generally refer to these transformers as Instrument Transformers. These are of two types.

Current Transformers: Instead of voltage these transformers step down the line current to a practical measurable current for measurement and protection purposes.

Potential Transformers: The Potential Transformers step down the line voltage to a practical measurable voltage level for measurement and protection purposes. The CVT or Capacitive Voltage Transformer also comes under the category of Potential Transformer.

We can also categorize Electrical Transformers as per their primary construction.

Core Type Transformers

In the core-type transformer, the windings are cylindrical. The limbs of the core hold the low voltage and high voltage winding one upon another.

Shell Type Transformers

The construction of the core in a shell type transformer is a little bit different from that of the core type transformer. In a single-phase shell type transformer, there are two windows in the core. The entire LV and HV windings are divided into a number of subsections. Each of the subsections is wounded in a disc-like shape. The central limb holds the subsections one-by-one alternatively.

Working Principle of Electrical Transformer

An Electrical Transformer works depending upon the principle of mutual induction between two windings.

Basic Principle of Mutual Induction: When an alternating current flows through a coil or winding an alternatingly changing flux appears surrounding the winding. Then the changing flux links with the other windings placed nearby the first winding. The changing flux linkage induces EMF in the windings.

The external circuits connected to the windings can take power due to the induced EMF across the windings. The flux linkage will be maximum if there is any magnetic medium for the efficient linkage of flux between the windings. In other words, if the windings are commonly wound on the same magnetic core there will be maximum flux linkage between the windings.

electrical transformer

Two windings and a closed magnetic core form the most basic structure of a transformer. The winding takes power from the source is the primary winding. The winding delivers power to the external circuit is the secondary winding.

EMF Equation of Transformer

As we told already whenever an alternating current flows through the winding, the alternatingly changing flux passes through the magnetic core. Let us consider the expression of that alternating flux is as follows.

The quantity of alternating current through the winding connected to the supply is the current required for magnetizing the core only. We refer to this current as the magnetizing current of the transformer. Now the EMF induced per turn is the rate of change of flux linkage with respect to time with the turn of the winding. Therefore the expression EMF induced per a turn is as follows.

Therefore the EMF induced across the secondary winding of T2 turns is

The RMS value of the secondary induced emf is

Similarly, the EMF induced across the primary winding of T1 turns is

The RMS value of the primary induced emf is

Turns Ratio and Voltage Ratio of Transformer

The ratio of induced EMF across the primary and secondary windings is

Since this ratio is the same as the ratio of numbers of turns of the windings, we refer to this ratio as the turns ratio of the transformer.

Current Ratio of Transformer

Whenever we connect a load across the terminals of the secondary winding, the secondary current starts flowing through it. As a result, the secondary winding produces an additional flux in the core. To neutralize this additional flux the primary winding has to produce equivalent opposite flux in the core. Therefore the primary winding needs to extract current from the source. After neglecting the magnetizing current in the primary, we can say the MMF produced by the secondary current is exactly equal to the MMF produced by the primary current of the transformer. Therefore we can write the following relations.

Phasor Diagram of a Transformer

transformer phasor diagram

Magnetizing Current: Here we first keep open the secondary circuit of the transformer. For drawing the phasor diagram of a transformer we first need to draw the pure magnetizing current in the primary winding as the reference vector. Since the magnetizing current (Im) produces the magnetic flux (φm) in the core both of these are cophasal.

Primary Induced EMF: Obviously the self-induced EMF (E1) in the primary winding will be in quadrature with the magnetizing current. Due to the inductive effect of the winding, the EMF lags the current by 90° (electrical).

Core Loss Component of Primary Current: Actually, the magnetization of core does not consume the entire current drawn by the primary winding. The core losses occurred in the magnetizing core consumes a small portion of the current (Ic). We refer to this component of current as core loss component. Since the core loss is wattage loss, the associated current will be in the same phase with the induced voltage.

No Load Current: Therefore the total current (Io) drawn the primary winding is the resultant of the pure magnetizing current (Im)and the core loss component (Ic). Since we have already kept the secondary of the transformer open, we refer to the total current (Io) drawn by the primary at that condition as the no-load current of the transformer.

Secondary Voltages

Secondary Induced EMF: Now, the magnetizing flux (φm) also induces EMF (E2) across the secondary winding. Hence, the secondary induced EMF (E2) also lags the pure magnetizing current (Im) by 90° (electrical). Therefore both the primary and secondary induced EMFs are cophasal.

Secondary Resistive Voltage Drop: Now we connect the load with the secondary winding. Therefore due to the induced EMF (E2) across secondary winding, the load current (I2) starts flowing. As a result, there will be a resistive drop (I2R2) in the secondary circuit of the transformer. Obviously this resistive voltage drop (I2R2) will be in phase with the secondary current (I2).

Secondary Reactive Voltage Drop: As we have already told that the secondary current (I2) produces additional flux in the magnetic core. The maximum part of this flux will link with the primary winding. But still, a small portion of secondary flux will bypass the core and passes outside the core. Consequently, this leakage or bypassed flux will not take part in mutual induction. But this leakage flux causes a self-induced EMF (jI2X2) across the secondary winding. Since the secondary current (I2) produces this leakage flux, this flux will be in phase with the secondary current of the transformer. Therefore the self-induced EMF (jI2X2) for this flux will be in quadrature with the secondary current (I2). Obviously the self-induced EMF (jI2X2) opposes its cause that is the mutually induced secondary EMF (E2).

Secondary Load Voltage: Therefore the load receives the voltage (V2) after losing resistive and inductive voltages in the secondary circuit. In other words, the vector sum of load voltage (V2), resistive drop (I2R2), and inductive drop (jI2X2) equals the induced EMF (E2) across the secondary winding.

Primary Current

Primary Load Current: The secondary current (I2) produces additional flux that is an additional MMF in the magnetic circuit. Therefore to neutralize this additional secondary MMF the transformer needs an equal and opposite MMF. Therefore, the primary winding needs to draw extra current (I1) from the supply. The value of this extra primary current (I1) will be such that the ampere-turn of both primary and secondary will be equal and opposite to each other (I1 T1 – I2 T2 = 0). Therefore the phase of this primary current (I1) will be just opposite to that of the secondary current.

Total Primary Current: The total primary current (I’1) drawn from the supply is the vector sum of the no-load current (Io) and the additional drawn primary current (I1) for the load.

Primary Voltage

There is always a difference between the primary supply voltage (V1) and the induced voltage (E1) across the primary winding. This is because there will be a resistive and an inductive voltage drop in the primary circuit of the transformer. Obviously the resistive drop (I’1R1) will be along the direction of the primary load current. But for a similar reason as in the secondary winding, the reactive voltage drop (jI’1X1) in the primary circuit lags 90° the primary load current (I’1).

Primary Supply Voltage: Obviously the primary supply voltage (V1) is the vector sum of negative primary induced voltage (- E1), primary resistive voltage drop (I’1R1), and primary inductive voltage drop (jI’1X1).

Equivalent Circuit of a Transformer

In a very basic form of a transformer, a magnetic core links two circuits. One circuit is primary and another is the secondary circuit.

Primary Circuit

As per the phasor diagram, there are three currents drawn by the primary circuit of the transformer. These currents are the pure magnetizing current (Im), core loss component of the current (Ic), and the primary load current (I1). To represent these three currents we need to have three parallel paths in the primary circuit of a transformer. The core loss component of the current flows through a pure resistance (ro) representing the core loss of the transformer. The pure magnetizing current flows through an inductor (xo) representing the magnetization of the core. The primary load current (I1) flows through the inductor representing the primary winding of the machine.

There will be resistive and reactive drops in the primary circuit. To represent these voltage drops, we have to draw one resistance (r1) and one reactance (x1) in series with the circuit. We need to draw them before the circuit gets divided into three parallel paths. This is because the voltage drops occur due to the flow of the entire current in the primary circuit.

Secondary Circuit

The secondary circuit of the transformer only has one component that is secondary current. Because the secondary circuit only delivers current to the load and does not take part in the magnetizing and core loss events of the core. But after the phasor diagram of a transformer, there will be a secondary voltage drop due to secondary resistance and reactance of the circuit. We can represent these voltage drops by simply drawing a resistor and an inductor in series in the circuit.

equivalent circuit of transformer

Equivalent Circuit of the Transformer Referred to Primary

Sometimes for sake of the calculation of different parameters of the transformer we need to refer the entire circuit to primary as well as secondary.

Now suppose the turns ratio of the transformer is unity. That indicates that the induced voltage across primary and secondary windings are equal to each other. Therefore we can easily erase the windings from our equivalent circuit. But in the case of step-up or step-down transformers, the turns ratio is not unity. In that case, we have to imagine that the number of turns of the secondary winding is exactly equal to the number of turns of the primary winding. For balancing the MMF that is ampere-turns, the secondary and primary currents will also become equal. Now I can omit the primary and secondary windings of the equivalent circuit.

There is always copper loss occurring in the secondary circuit. To keep the characteristics of the circuit unaltered that secondary copper loss remains the same even for the equivalent primary current flowing to the secondary. So to do that we need to change the resistive value of the secondary circuit accordingly.

The percentage of leakage reactance drop in respect of the secondary induced voltage also remains unaltered.

Lastly, we can calculate the actual secondary voltage of the transformer by multiplying turns ratio with the equivalent voltage appearing across the output terminals.

In the same way, we can draw the equivalent circuit of a transformer referred to the secondary side.


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