Explanation of Voltage Regulation of Transformer

Say an electrical power transformer is open circuited, means load is not connected with secondary terminals. In this situation, the secondary terminal voltage of the transformer will be its secondary induced emf E₂. Whenever full load is connected to the secondary terminals of the transformer, rated current I₂ flows through the secondary circuit and voltage drop comes into picture. At this situation, primary winding will also draw equivalent full load current from source. The voltage drop in the secondary is I₂Z₂ where Z₂ is the secondary impedance of transformer. Now if at this loading condition, any one measures the voltage between secondary terminals, he or she will get voltage V₂ across load terminals which is obviously less than no load secondary voltage E₂ and this is because of I₂Z₂ voltage drop in the transformer.

Expression of Voltage Regulation of Transformer

Expression of Voltage Regulation of Transformer, represented in percentage, is

What is Eddy Current Loss ?

In transformer, we supply alternating current in the primary, this alternating current produces alternating magnetizing flux in the core and as this flux links with secondary winding, there will be induced voltage in secondary, resulting current to flow through the load connected with it. Some of the alternating fluxes of transformer; may also link with other conducting parts like steel core or iron body of transformer etc. As alternating flux links with these parts of transformer, there would be a locally induced emf. Due to these emfs, there would be currents which will circulate locally at that parts of the transformer. These circulating current will not contribute in output of the transformer and dissipated as heat. This type of energy loss is called eddy current loss of transformer. This was a broad and simple explanation of eddy current loss.

Hysteresis Loss in Transformer

Hysteresis loss in transformer can be explained in different ways. We will discuss two of them, one is physical explanation and the other is mathematical explanation.

Physical Explanation of Hysteresis Loss

The magnetic core of transformer is made of ′Cold Rolled Grain Oriented Silicon Steel′. Steel is very good ferromagnetic material. This kind of materials are very sensitive to be magnetized. That means, whenever magnetic flux would pass through, it will behave like magnet. Ferromagnetic substances have numbers of domains in their structure. Domains are very small regions in the material structure, where all the dipoles are paralleled to same direction. In other words, the domains are like small permanent magnets situated randomly in the structure of substance. These domains are arranged inside the material structure in such a random manner, that net resultant magnetic field of the said material is zero. Whenever external magnetic field or mmf is applied to that substance, these randomly directed domains get arranged themselves in parallel to the axis of applied mmf. After removing this external mmf, maximum numbers of domains again come to random positions, but some of them still remain in their changed position. Because of these unchanged domains, the substance becomes slightly magnetized permanently. This magnetism is called " Spontaneous Magnetism". To neutralize this magnetism, some opposite mmf is required to be applied. The magneto motive force or mmf applied in the transformer core is alternating. For every cycle due to this domain reversal, there will be extra work done. For this reason, there will be a consumption of electrical energy which is known as Hysteresis loss of transformer.

Mathematical Explanation of Hysteresis Loss in Transformer

Determination of Hysteresis Loss

Consider a ring of ferromagnetic specimen of circumference L meter, cross - sectional area a m² and N turns of insulated wire as shown in the picture beside,

Let us consider, the current flowing through the coil is I amp,

Magnetizing force,

Let, the flux density at this instant is B,
Therefore, total flux through the ring, Φ = BXa   Wb

As the current flowing through the solenoid is alternating, the flux produced in the iron ring is also alternating in nature, so the emf (e′) induced will be expressed as,

According to Lenz,s law this induced emf will oppose the flow of current, therefore, in order to maintain the current I in the coil, the source must supply an equal and opposite emf. Hence applied emf ,

Energy consumed in short time dt, during which the flux density has changed,

Thus, total work done or energy consumed during one complete cycle of magnetism,

Now aL is the volume of the ring and H.dB is the area of elementary strip of B - H curve shown in the figure above,

Therefore, Energy consumed per cycle = volume of the ring X area of hysteresis loop.
In the case of transformer, this ring can be considered as magnetic core of transformer. Hence, the work done is nothing but the electrical energy loss in transformer core and this is known as hysteresis loss in transformer.

Emf Equation of Transformer

EMF Equation of transformer can be established in a very easy way. Actually in electrical power transformer, one alternating electrical source is applied to the primary winding and due to this, magnetizing current flowing through the primary winding which produces alternating flux in the core of transformer. This flux links with both primary and secondary windings. As this flux is alternating in nature, there must be a rate of change of flux. According to Faraday's law of electromagnetic induction if any coil or conductor links with any changing flux, there must be an induced emf in it.

As the current source to primary is sinusoidal, the flux induced by it will be also sinusoidal. Hence, the function of flux may be considered as a sine function. Mathematically, derivative of that function will give a function for rate of change of flux linkage with respect to time. This later function will be a cosine function since d(sinθ)/dt = cosθ. So, if we derive the expression for rms value of this cosine wave and multiply it with number of turns of the winding, we will easily get the expression for rms value of induced emf of that winding. In this way, we can easily derive the emf equation of transformer. Let's say, T is number of turns in a winding, Φ_m is the maximum flux in the core in Wb.

As per Faraday's law of electromagnetic induction,

Where φ is the instantaneous alternating flux and represented as, As the maximum value of cos2πft is 1, the maximum value of induced emf e is, To obtain the rms value of induced counter emf, divide this maximum value of e by √2. This is EMF equation of transformer. If E₁ & E₂ are primary and secondary emfs and T₁ & T₂ are primary and secondary turns then, voltage ratio or turns ratio of transformer is,

Types of Transformer

Transformers can be categorized in different ways, depending upon their purpose, use, construction etc. The types of transformer are as follows,

1. Step Up Transformer & Step Down Transformer - Generally used for stepping up and down the voltage level of power in transmission and distribution power network.
2. Three Phase Transformer & Single Phase Transformer - Former is generally used in three phase power system as it is cost effective than later but when size matters, it is preferable to use bank of three single phase transformer as it is easier to transport three single phase unit separately than one single three phase unit.

3. Electrical Power Transformer, Distribution Transformer & Instrument Transformer - Transformer is generally used in transmission network which is normally known as power transformer, distribution transformer is used in distribution network and this is lower rating transformer and current transformer & potential transformer, we use for relay and protection purpose in electrical power system and in different instruments in industries are called instrument transformer.
4. Two Winding Transformer & Auto Transformer - Former is generally used where ratio between high voltage and low voltage is greater than 2. It is cost effective to use later where the ratio between high voltage and low voltage is less than 2.
5. Outdoor Transformer & Indoor Transformer - Transformers that are designed for installing at outdoor are outdoor transformers and transformers designed for installing at indoor are indoor transformers.

Use of Power Transformer

Generation of electrical power in low voltage level is very much cost effective. Hence electrical power is generated in low voltage level. Theoretically, this low voltage level power can be transmitted to the receiving end. But if the voltage level of a power is increased, the current of the power is reduced which causes reduction in ohmic or I²R losses in the system, reduction in cross sectional area of the conductor i.e. reduction in capital cost of the system and it also improves the voltage regulation of the system. Because of these, low level power must be stepped up for efficient electrical power transmission. This is done by step up transformer at the sending side of the power system network. As this high voltage power may not be distributed to the consumers directly, this must be stepped down to the desired level at the receiving end with the help of step down transformer. These are the uses of electrical power transformer in the electrical power system. Two winding transformers are generally used where ratio between high voltage and low voltage is greater than 2. It is cost effective to use auto transformer where the ratio between high voltage and low voltage is less than 2. Again three phase single unit transformer is more cost effective than a bank of three single phase transformer unit in a three phase system. But still it is preferable to use than the later where power dealing is very large since such large size of three phase single unit power transformer may not be easily transported from manufacturer's place to work site.

Equivalent circuit

Winding joule losses and leakage reactances are represented by the following series loop impedances of the model:

• Primary winding: R_P, X_P
• Secondary winding: R_S, X_S.

In normal course of circuit equivalence transformation, R_S and X_S are in practice usually referred to the primary side by multiplying these impedances by the turns ratio squared, (N_P/N_S) ² = a².

Real transformer equivalent circuit

Core loss and reactance is represented by the following shunt leg impedances of the model:

• Core or iron losses: R_C
• Magnetizing reactance: X_M.

R_C and X_M are collectively termed the magnetizing branch of the model.
Core losses are caused mostly by hysteresis and eddy current effects in the core and are proportional to the square of the core flux for operation at a given frequency.^[31] The finite permeability core requires a magnetizing current I_M to maintain mutual flux in the core. Magnetizing current is in phase  with the flux, the relationship between the two being non-linear due to saturation effects. However, all impedances of the equivalent circuit shown are by definition linear and such non-linearity effects are not typically reflected in transformer equivalent circuits.^[31] With sinusoidal supply, core flux lags the induced EMF by 90°. With open-circuited secondary winding, magnetizing branch current I₀ equals transformer no-load current.^[30]
The resulting model, though sometimes termed 'exact' equivalent circuit based on linearity assumptions, retains a number of approximations.^[30] Analysis may be simplified by assuming that magnetizing branch impedance is relatively high and relocating the branch to the left of the primary impedances. This introduces error but allows combination of primary and referred secondary resistances and reactances by simple summation as two series impedances.
Transformer equivalent circuit impedance and transformer ratio parameters can be derived from the following tests: open-circuit test,^[m] short-circuit test, winding resistance test, and transformer ratio test.