Têkşîna Nîrvana Vanên Transformeran

Tranzistordan Daran

Çünki tranzistor elektrikî bir cihaz ve statîk bir durumda hafifde, tranzistorda mekanîk daran nisbeydên çêkerin. Biz genelde sadece tranzistorda elektrikî daranê hesab edin.

Her cihazda daran, girdiya guhurtina ve derketina guhurtê di mesel de difirrê hatine taybet kirin. Heke guhurtiyeke ser piramîna tranzistora verin, bêhêve pêca wê guhurtê ji bo şeriyê core loss (core loss) û eddy current loss (eddy current loss) û bêhêve pêca wê guhurtê ji bo I2R loss û bi serînîn derserî werin.

Yekemê li gorî core loss an iron loss (core loss an iron loss) û yek din li gorî ohmic loss an copper loss (ohmic loss an copper loss) hatine nisandirin. Yek daranê din da Stray Loss hatine, ku ji Stray fluxes û serbestîya mekanîk û serbestîya wirîyan reyînûn gotin.

Copper Loss in Transformer

Copper loss I²I2R loss e, me I12R1 li ser piramîna ve û I22R2 li ser rastina. Ji heevre, I1 û I2 piramîna û rastina currents ne, û R1 û R2 resistance of the windings ne. Çünki wan currents bi loada dependin, copper loss in a transformer bi loada vary dike.

Core Losses in Transformer

Hysteresis loss û eddy current loss her du li gorî magnetic properties of the materials used to construct the core of transformer û designa we hatine. Nisbeyd li gorî load current û load current dependin. Core losses in transformer alternatively known as iron loss in transformer can be considered as constant for all range of load.

Hysteresis loss in transformer is denoted as,

Eddy current loss in transformer is denoted as,

Kh = Hysteresis constant.

Ke = Eddy current constant.

Kf = form constant.

Copper loss can simply be denoted as,

IL2R2′ + Stray loss

Where, IL = I2 = load of transformer, and R2′ is the resistance of transformer referred to secondary.

Now we will discuss Hysteresis loss and Eddy current loss in little bit more details for better understanding the topic of losses in transformers.

Hysteresis Loss in Transformer

Hysteresis loss in transformers can be explained in two ways: physically and mathematically.

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 is 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 the same direction. In other words, the domains are like small permanent magnets situated randomly in the structure of the 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. When an external magnetic field (mmf) is applied, the randomly directed domains align parallel to the field.

After the field is removed, most domains return to random positions, but some remain aligned. 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 magnetomotive 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 a 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 is,

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

Therefore, Energy consumed per cycle = volume of the ring × 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.

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. The detail explanation of this loss is not in the scope of discussion in that chapter.