EXP 04
Short Description
EE...
Description
Table 4.1
Delta to Wye Transformation
Del ta
R1
R2
R3
RL
I1
I2
Va
Vb
Vc
Measured
23
3
10
2011
- 5.46A
- 2.25mA
- 10.47V
15V
4.23V
Wye
Ra
Rb
Rc
RL
I1'
I2'
Va'
V b'
Vc'
Measured
1.1967
0.8333
6.3889
2011
- 5.46A
- 2.25mA
- 10 10.47V
15V
4.23V
Calculated
1.1967
0.8333
6.3889
2011
-
-
-
-
-
I1
I2
Va
Vb
Vc
13.28V
15V
1.27V
Va'
V b'
Vc'
13.28V
15V
1.27V
-
-
-
Table 4.2
Wye to Delta Transformation
Del ta
R1
R2
R3
RL
Measured
23
3
10
2011
Wye
Ra
Rb
Rc
RL
Measured
109.6667
32.9
14.3043
2011
Calculated
109.6667
32.9
14 14.3043
2011
-5 - 577.02mA - 855.27uA
I1'
I2'
- 57 577.02mA - 85 855.27uA -
-
For Table 4.1
Delta to Wye Transformation
Wye (Calculated)
For Table 4.2
Wye to Delta Transformation
Delta (Calculated)
Delta to Wye Transformation 25
20
15
10
5
0
R1
R2
R3
Delta
23
3
10
Wye
1.9167
0.8333
6.3889
This graph shows the relationship of the resistances between Delta resistor connection to the wye resistor connection. The three points used in this graph were from the data obtained from the experiment. The values of the resistors in delta are greater than the resistor values in wye. This is always true if the wye and delta connection are equivalent.
The fourth experiment is concerned with wye to delta and delta to wye transformation. In order to assist us in the analysis of the facts provided by the experiment, certain predefinitions are enlisted. One of which is the threephase electric power systems. In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating current voltages that are offset in time by one-third of the period. A three-phase system may be arranged in delta ( Δ) or wye (Y) (also denoted as star in some areas). Since three-phase is used so often for power distributions systems, it makes sense that three-phase transformers are needed to be able to step the voltages up or down. A three-phase transformer is made of three sets of primary and secondary windings, each set wound around one leg of an iron core assembly. Those sets of primary and secondary windings will be connected in either Δ or Y configurations to form a complete unit. Y connections provide the opportunity for multiple voltages, while Δ connections enjoy a higher level of reliability. A delta-wye transformer is a type of three-phase electric power transformer design that employs delta-connected windings on its primary and wye/star connected windings on its secondary. A neutral wire can be provided on wye output side. It can be a single three-phase transformer, or built from three independent single-phase units. An equivalent term is delta-star transformer. Delta-wye transformers are common in commercial, industrial, and high-density residential locations, to supply three-phase distribution systems. It is not to be confused with wye-delta transform. In wye-delta transform, the transformation is used to establish equivalence for networks with three terminals. Where three elements terminate at a common node and none are sources, the node is eliminated by transforming the impedances. For equivalence, the impedance between any pair of terminals must be the same for both networks.
Wye (Y) connection is a method of connecting the ends of the windings of a poly-phase transformer; each of the three windings is joined at a common point; the other ends of the windings provide the line-to-line voltages. A delta connection, meanwhile, is a combination of three components connected in series to form a triangle like the Greek letter delta. Delta connection is also known as mesh connection.
Three terminal network, delta and wye, is said to be equivalent to each other if the corresponding resistances measured between the pair of terminals are equal. To convert delta connection to wye connection, we use the formula given below:
To convert wye connection to delta connection, we use the formula given below:
The transformation formula is based in the concept that if the two connections are equivalent then the resistances seen across the pair of terminals are also equivalent.
In this experiment, several objectives are set in order to facilitate better understanding of the lesson. First is to identify the delta connection of resistance and wye connection in complicated network circuits. Second is to demonstrate and verify the corresponding responses between delta connected resistors and its equivalent wye connected resistors. Finally, the experiment aims to learn and demonstrate the transformation principles involved in converting the delta connection of resistors top the wye connection or vice versa. The experiment is performed individually with the help of a computer software called Tina Pro. The class individually simulated values based from their student number and came up with values for the current and voltage of delta to wye connections and wye to delta connections. On the first part of the experiment (delta to wye transformation), I observed that circuits in delta configuration can be converted into wye configuration. With 15V as the voltage, the total resistance across the circuit in delta should be the same as the wye for the two configurations to be equivalent. The resistors in delta ( Δ) can be replaced by resistors connected in wye (Y), with the total resistance for both cases constant, in order to do the transformation. The resulting current for both the delta and wye connection are the same which proves that the experiment is correct. On the second part of the experiment (wye to delta transformation), I observed that wye configured resistors can be converted into delta configured connection. The total resistance for both cases is also constant. The current measured in the wye configured connection is the same as the delta configured connection. There were some who encountered errors in the experiment which is mainly due to incorrect values when converting the resistors for the delta to wye or the wye to delta transformation. It is therefore recommended to check the computations thoroughly before entering the values in Tina Pro.
1. When is the delta connection of resistors equivalent to the wye connection resistors? The delta connected resistors can be replaced by the equivalent wye connected resistor circuit through mathematical transformation. The two circuits are said to be equivalent because when they are connected to an external source, or sources, they exhibit identical behavior. In order for the two circuits to be equivalent, they must exhibit resistances between a, b, and c terminals. Each resistor in the wye network is the product of the resistors in the two adjacent delta branches, divided by the sum of the three delta resistors. 2.
What are the practical applications of the technique delta-wye transformation? Discuss briefly the different practical applications. Delta-wye is a common type of 3-phase transformer configuration. It offers a good voltage gain and the delta transformer is useful in unstable systems for removing the third harmonics. Transformers need not be connected in the same pattern on the primary and the secondary. Depending on the desired voltage level and level of step-up (increase) or step-down (decrease), the patterns may change. To get the greatest step-up, the transformation ratio is best if the primary is connected delta and the secondary is connected wye. Likewise, to get the largest decrease in voltage, the ratio of transformation is the greatest if the primary is connected wye and the secondary is connected delta. The transformation is necessary for analyzing the circuit.
3.
Determine the total resistance across the terminals from the figure below.
a.
Transform the delta (upper loop) to wye
b.
Find the total resistance
( ) 4.
Determine the total resistance across the terminals from the figure below.
a. Transform Loop A and B (which are in delta) to wye.
b. Find total resistance.
{[ ] } 5.
Determine the total resistance across the terminals from the figure below.
a.
Combine R75Ω and R25Ω : Ra Ra = 75Ω+25Ω = 100Ω
b.
Combine R15Ω and R35Ω : Rb Rb = 15Ω+35Ω = 50Ω
c.
d.
Transform
∆ to
Y (upper: R100Ω, R20Ω, R30Ω; and lower R30Ω, R20Ω, R50Ω)
Combine the resistors in parallel
Let: Sum of resistors on the right in series be R c
Rc = 40Ω + 10 + 10 = 60
Ω
Let: Sum of resistors on the right in series be R d
Rd = 26Ω + 8 + 6 = 40
Ω
Rd||Rc: Re
e.
Find RT
RT = 24
Ω+1 Ω+10 Ω+15 Ω
=
Ω
6.
Determine io from the given circuit below.
Transform the upper loop into wye.
a.
Find total resistance
b.
Find total current
c.
Find I1 and I2
By Current Divider Principle
) ( ) ( d.
Find io
Using Kirchhoff’s Voltage Law (Lower Triangular Loop] from the original Figure) – clockwise
–(50 )(i )-(9 )(14A) = 0
(46 )(
o
http://www.engineersblogsite.com/delta-to-wye-and-wye-to-delta-conversion.html http://en.wikipedia.org/wiki/Y-%CE%94_transform http://www.electronics-tutorials.ws/dccircuits/dcp_10.html http://www.allaboutcircuits.com/vol_1/chpt_10/13.html http://www.allaboutcircuits.com/vol_2/chpt_10/6.html http://www.answers.com/Q/Application_of_Y-delta_transformations http://en.wikipedia.org/wiki/Three-phase#Conversion_to_other_phase_systems
View more...
Comments
