3. THEORY
Generation of Three-phase Voltage:
R-R’, Y-Y’, and B-B’ are three coils separated 120° apart in a circular stator. When the rotor (magnetic poles) is rotated at a constant speed by some means, EMFs will be induced in all three coils. The magnitudes of the EMFs induced in all three coils are equal, but they will have a phase difference of 120° with each other.
Mathematically, these voltages are represented by:
\(V_{R} = V_{m} \sin(\omega t)\)
\(V_{Y} = V_{m} \sin(\omega t – 120^{\circ})\)
\(V_{B} = V_{m} \sin(\omega t + 120^{\circ})\)
Star Connection:
In this connection, the finishing ends of the coils are connected to a common point ‘N’, known as the Neutral point. In a balanced condition, the phasor sum of currents through the neutral line is zero. The voltage across a phase winding is Phase Voltage, and the voltage between two lines is Line Voltage.
The relationship between Line Voltage (\(V_{L}\)) and Phase Voltage (\(V_{P}\)) is:
\(V_{L} = \sqrt{3} V_{P}\) or \(V_{P} = \frac{V_{L}}{\sqrt{3}}\)
In a star connection, Line Current (\(I_{L}\)) equals Phase Current (\(I_{P}\)): \(I_{L} = I_{P}\)
Delta Connection:
In this connection, the starting end of one coil is connected to the finishing end of the other coil.
For a delta connection, Line Voltage (\(V_{L}\)) equals Phase Voltage (\(V_{P}\)): \(V_{L} = V_{P}\)
The relationship between Line Current (\(I_{L}\)) and Phase Current (\(I_{P}\)) is:
\(I_{L} = \sqrt{3} I_{P}\) or \(I_{P} = \frac{I_{L}}{\sqrt{3}}\)
Wattmeter:
A wattmeter is an electrical instrument used to measure electric power in watts. It’s essential for determining power consumption in various applications.
4. OBSERVATION TABLES
For Star Connection
| S.N. |
R (Ω) |
\(I_{L} = I_{P}\) (A) |
\(V_{L}\) (V) |
\(V_{P}\) (V) |
Power (W) |
| 1. |
400 |
0.15 |
400 |
231 |
51.96 |
| 2. |
1200 |
0.42 |
400 |
231 |
145.49 |
Calculation: Active Power = \(\sqrt{3} V_{L} I_{L} \cos\phi\)
For Delta Connection
| S.N. |
R (Ω) |
\(I_{L}\) (A) |
\(I_{P}\) (A) |
\(V_{L} = V_{P}\) (V) |
P (W) |
| 1. |
400 |
1.08 |
0.67 |
400 |
374.12 |
| 2. |
1200 |
0.36 |
0.21 |
400 |
124.7 |
Calculation: % Error = \(\frac{| \text{Measured } I_P – \text{Calculated } I_P |}{\text{Calculated } I_P} \times 100 = \frac{|0.67 – 1.08/\sqrt{3}|}{1.08/\sqrt{3}} \times 100 = 7.45\%\)
Power Measurement
| S.N. |
R (Ω) |
W₁ (W) |
W₂ (W) |
\(W_T = W₁ + W₂\) (W) |
V (V) |
I (A) |
P.F (cosφ) |
| 1. |
300 |
262 |
240 |
502 |
400 |
0.55 |
0.375 |
| 2. |
400 |
196 |
180 |
376 |
400 |
0.42 |
0.385 |
| 3. |
600 |
124 |
116 |
240 |
400 |
0.28 |
0.404 |
| 4. |
1200 |
44 |
40 |
84 |
400 |
0.15 |
0.615 |
Calculation: Power Factor (cosφ) = \(\frac{\text{Active Power}}{\text{Apparent Power}} = \frac{W_T}{\sqrt{3} \times V \times I}\)
5. RESULT
The phase difference and magnitude of current and voltage from line to neutral wires in a three-phase AC circuit were studied. Also, the various parameters of a three-phase AC circuit, including phase voltage, line voltage, phase current, and line current, were studied with the help of star and delta connections of resistors powered by a 3-phase AC supply.
6. DISCUSSIONS
The experiment was performed to understand the phase and magnitude relationship between line and phase quantities in a three-phase balanced system. The calculated phase voltage was found to be 231V. At 400Ω resistance in star connection, the current was 0.15A, and at 1200Ω, the current was 0.42A. Similarly, in the Delta connection, the current was found to be 1.08A at 400Ω and 0.36A at 1200Ω resistance. We observed the relationship between phase voltage & phase current and line voltage & line current.
In the star connection, the \(I_{L} = I_{P}\) & \(V_{L} = \sqrt{3}V_{P}\) relationship was proved by the observed data. In the delta connection, the \(V_{L} = V_{P}\) and \(I_{L} = \sqrt{3}I_{P}\) relationship was also proved, although we got just a small error. The error obtained may be due to the insensitivity of electrical equipment to slight changes or variations in current and voltage. The error can be reduced by using more sensitive appliances. The instruments we used are not perfectly ideal, so there is some amount of power loss in their internal resistance.
7. CONCLUSION
Hence, line voltage, phase voltage, line current, and phase current were measured in Star and Delta connections, and power was also measured in a three-phase balanced load.
