ESO 210 Introduction to Electrical Engineering

Transcription

1 ESO 210 Introduction to Electrical Engineering Lecture-19 Magnetic Circuits and Introduction to Transformers

2 2 SERIES CONNECTION OF MUTUALLY COUPLED COILS A mutual term will alter the total inductance of the series combination When referring to the voltage induced across the inductance L1 (or L2) due to the change in flux linkages of the inductance L2 (or L1, respectively), the mutual inductance is represented by M12. This type of subscript notation is particularly important when there are two or more mutual terms.

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5 5 Finally, The subscript (+) was included to indicate that the mutual terms have a positive sign and are added to the self-inductance values to determine the total inductance. If the coils were wound such as shown in Fig. below, where ø 1 and ø 2 are in opposition, the induced voltages due to the mutual terms would oppose that due to the self-inductance, and the total inductance would be determined by

6 6 The mutual Inductance M 12 can be determined by Above equation is very effective in determining the mutual inductance between two coils. It states that the mutual inductance is equal to one-quarter the difference between the total inductance with a positive and negative mutual effect. It should be clear that the mutual inductance will directly affect the magnitude of the voltage induced across a coil since it will determine the net inductance of the coil. On a network schematic where it is inconvenient to indicate the windings and the flux path, a system of dots is employed that will determine whether the mutual terms are to be positive or negative. The dot convention is shown in Fig. on the next slide for the series coils

7 The dot convention is shown in Fig. below for the series coils 7

8 8? If the current through each of the mutually coupled coils is going away from the dot as it passes through the coil, the mutual term will be positive, as shown for the case in Fig. above. If the arrow indicating current direction through the coil is leaving the dot for one coil and entering the dot for the other, the mutual term is negative. The dot convention also reveals the polarity of the induced voltage across the mutually coupled coil. If the reference direction for the current in a coil leaves the dot, the polarity at the dot for the induced voltage of the mutually coupled coil is positive.

9 EXAMPLE: Find the total inductance of the series coils of Fig. below. 9

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11 EXAMPLE: Write the mesh equations for the transformer network in Fig. shown below. 11

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13 What is this? 13

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17 17 Transformers are an integral part in any modern power system

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19 19 Transformers: The most important components of any power system. Basically change the level of voltages from one value to the other at constant frequency. Being a static machine the efficiency of a transformer could be as high as 99%. (Typically more than 95%) Big generating stations are located at hundreds or more km away from the load center (where the power will be actually consumed). Since long transmission lines carry the power to the load centre from the generating stations. Generator is a rotating machines and the level of voltage at which it generates power is limited to several kilo volts only a typical value is 11 kv.

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21 21 To transmit large amount of power (several thousands of mega watts) at this voltage level means large amount of current has to flow through the transmission lines. The cross sectional area of the conductor of the lines accordingly should be large. Hence cost involved in transmitting a given amount of power rises many folds. Not only that, the transmission lines has their own resistances. This huge amount of current will cause tremendous amount of power loss or I 2 r loss in the lines. This loss will simply heat the lines and becomes a wasteful energy. In other words, efficiency of transmission becomes poor and cost involved is high without Transformers. The poor efficiency problems may be addressed if we could transmit power at a very high voltage say, at 200 kv or 400 kv or even higher at 800 kv.

22 22 Since, a generator is incapable of generating voltage at these level due to its own practical limitation. The solution to this problem is to use an appropriate step-up transformer at the generating station to bring the transmission voltage level at the desired value. Obviously when power reaches the load centre, one has to step down the voltage to suitable and safe values by using transformers. Thus transformers are an integral part in any modern power system. Transformers are located in places called substations. In cities or towns you must have noticed transformers are installed on poles these are called pole mounted distribution transformers. These type of transformers change voltage level typically from 3-phase, 6 kv to 3-phase 440 V line to line.

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24 Transformer 24

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