Three-Sided Electrical Transformer

Introduction

Electrical power is generated in the form of three-phase voltages with values up to 13 kV and sometimes up to 35 kV, and energy is transmitted on high-voltage lines and cables with values up to 220, 500 and sometimes up to 750 kV, thus the need for three-phase transformers appears to raise the value of the generation voltage to the transmission voltage and also to reduce the transmission voltage to the distribution voltage values that reach 66 and then to 11 kV. 

In the case of electrical systems with 380 V tri-directional voltage values, the three-phase transformer has emerged as an alternative to the use of three single-sided transformers, which were commonly used in the past due to operators' lack of experience with tri-directional transformers.  One of the advantages of using three-sided transformers is that they require less space, less weight, and a 15% lower cost compared to three single-sided transformers.

 

2- Installation of three-sided transformers

Three-sided transformers are similar in terms of installation quality to the two types of single-sided transformers with a core  or  shell type. Figure (1) shows the basic structure of a trihedral transformer, where the initial coil connected in the shape of a star is shown by a trifacial source. The core of each face is 120 degrees apart from the other, and the legs are in contact with  each other. It is noted that this middle leg carries a magnetic field proportional to the sum of the facet currents IR+IY+IB. Since the sum of these currents of balanced systems is equal to zero, there is no need for this intermediate man.

In this case, either of the two hearts acts as a complement to the third heart magnetic field path, and this is similar to the distribution of currents in the three-point systems.

Figure (2) shows the development of the three-sided transformer and the three coils in the form of rectangles, and it is observed that the magnetic field , shown at a given moment in time, is distributed between the three cores according to the three-phase system. Figure (3) shows the coils in a cylindrical shape around the iron core.

 

Figure (1)

 

 

Figure (3)

Figure (2)

 

Trifacial coil envelope transformers are similar to unifacial ones of the same type. The three three-sided uniconverters can be combined to form a three-sided transformer, but the ferrous material can be provided with the design shown in Figure (4).  

The saving of the ferrous material is represented by the combined use of magnetic flux pathways. The three faces are a little more independent than the heart transformer, because each face has an independent magnetic circuit.

 

Figure (4)

There is a disadvantage in the tri-sided converter that if one of the faces is lost, the converter needs to be turned off, and the tri-encapsulated converter can be excluded when connecting files in a delta image but technically it is not convenient. It is noted that in the case of the three single transformers, the damaged transformer can be excluded without affecting the overall function.   

Example (1): 

A 3-phase, 50-Ht transformer has a delta-connected primary and star-connected secondary, the line voltages being 22,000 V and 400 V respectively.  The secondary has a star-connected balanced load at 0·8-power factor lagging. The line current on the primary side is 5 A.   Determine the current in each coil of the primary side is 5 A in each secondary line.  What is the output of the transformer in k W?

Solution.  It should be noted that in three-phase transformers, the phase transformation ratio is equal to the turn ratio but the terminal or line voltages depend upon the method of connection employed. The ∆ / Y connection is shown in Fig. (1).

Fig. (1)

Phase voltage on primary side = 22.000 V

Phase voltage on primary side = 400 / √3

K = 400/22,000 x √3      = l/55√ 3

Primary phase current    = 5/√3A

Secondary phase current           = 275 A

Secondary line current   = 275 A

Output                              = √3 V_L I_L cos f

= √3 x 400 x 275 x 0.8 = 152.42 kW           

Example (2):

A 3-phase, 3,300/400-V transformer high-voltage winding connected in delta and the low-voltage connected in star. If a load consisting of three-impedance 6+j8 ohm is joined in delta across the low voltage side, calculate (a) the kW delivered to the kW delivered to the load (b) currents in the low and high-voltage windings and the current drawn by the transformer from line. Neglect losses and no-load current of the transformer.

Solution.  The transformer connection diagram is shown in Fig. (2).

Fig. (2)

Power delivered to the load = √3 V_L I_L cos f

Now, consider the D -connected load

V_ph=V_L=2400 V     Z_ph = √( 6² + 8²)= 10 W

I_ph = 400/10= 40 A    I_L = √3 x 40 = 69 · 3 A

cos f = 6/10 =0·6

P= √ 3 x 400 x 69· 3 x 0· 6 = 28,807 W

(b) Primary phase voltage                     = 3.300 V

Secondary phase voltage           = 400 / √ 3

Current in low-voltage winding i.e. secondary is I₂ = 40 x √3 = 69.3A

Current in low-voltage winding i.e. secondary is I₁=KI₂= 4.85 A

Line current on the primary side = √3 x 4.85 = 8.4 A