For procedures, see your electrical laboratory manual.

Title: Three Phase AC Circuits


Aim

1. To verify the relationships between phase & line voltages and current in three-phase balance systems.
2. To measure power in three-phase systems by
— One wattmeter method
— Two wattmeter method

Theory

The system which has three phases, i.e., the current will pass through the three wires, and there will be one neutral wire for passing the fault current to the earth is known as the three-phase system. In other words, the system which uses three wires for generation, transmission, and distribution is known as the three-phase system.

The three-phase system is also used as a single-phase system if one of their phase and the neutral wire is taken out from it. The sum of the line currents in the 3-phase system is equal to zero, and their phases are differentiated at an angle of 120º.

The three-phase system has four-wire, i.e., the three current-carrying conductors and the one neutral. The cross-section area of the neutral conductor is half of the live wire. The current in the neutral wire is equal to the sum of the line current of the three wires and consequently equal to √3 times the zero phase sequence components of current.

The three-phase system has several advantages like it requires fewer conductors as compared to the single-phase system. It also gives a continuous supply to the load. The three-phase system has higher efficiency and minimum losses.

The three-phase system induces in the generator which gives the three-phase voltage of equal magnitude and frequency. It provides an uninterruptible power, i.e., if one phase of the system is disturbed, then the remaining two phases of the system continue to supply the power. The magnitude of the current in one phase is equal to the sum of the current in the other two phases of the system.

The three-phase systems are connected in two ways, i.e., the star connection and the delta connection.

Answers to Questions:

1. Three-phase Phasor Diagram


The phase voltages are all equal in magnitude but only differ in their phase angle. The three windings of the coils are connected together at points, a1, b1, and c1 to produce a common neutral connection for the three individual phases. Then if the red phase is taken as the reference phase each individual phase voltage can be defined with respect to the common neutral as.

Three-phase Voltage Equations


If the red phase voltage, VRN is taken as the reference voltage as stated earlier then the phase sequence will be R – Y – B so the voltage in the yellow phase lags VRN by 120°, and the voltage in the blue phase lags VYN also by 120°. But we can also say the blue phase voltage, VBN leads the red phase voltage, VRN by 120°.

One final point about a three-phase system. As the three individual sinusoidal voltages have a fixed relationship between each other of 120° they are said to be “balanced” therefore, is a set of balanced three-phase voltages their phasor sum will always be zero as Va + Vb + Vc = 0

2.