Polyphase systems
A single-phase AC power system consists of a power source connected through a pair of wires to a load. There are circuits and systems where the AC power source operates at the same frequency and magnitude of voltage but in different phases known as polyphase systems. The most common polyphase systems are 3-phase systems where 3 power sources have the same frequency and amplitude but a phase difference of 120°. Why particularly 120° because the armature coils in the generator are placed 120° apart.
The three-phase systems can be wired in two ways:
Star connection
In a Star Connection, the three-phase wires converge at a central point known as the star or common point, from which the Neutral connection is derived. This configuration is alternatively termed Y or Wye connection due to its resemblance to these shapes. When solely the three-phase wires are employed, it’s referred to as a 3 Phase 3 Wire system. However, if the Neutral point is also utilized, which is commonly the case, it becomes a 3 Phase 4 Wire system.
Delta connection
In a Delta Connection, a three-phase electrical setup comprises three elements arranged in a triangular configuration. This connection is alternatively termed a mesh connection. Delta configuration specifically incorporates solely three phase wires without the utilization of a neutral wire.
Line voltage-currents and Phase voltage-currents
- The line current IL represents the current that moves from the generator to the load through each transmission line within a three-phase system.
- The line voltage VL refers to the voltage across each line pair (line to line), not including the neutral line if it is present.
- The phase current IP represents the current that passes through each phase within a three-phase load.
- The phase voltage VP denotes the voltage specific to each phase.
VP1, VP2, VP3 are the phase voltages. VL1, VL2, VL3 are the line voltages. IP1, IP2, IP3 are the phase currents. IL1, IL2, IL3 are the line currents.
Comparison between star and delta connection
A table of comparison is mentioned below:
| Difference | Star Connection | Delta Connection |
|---|---|---|
| Connection | In a STAR Connection, three coils have their corresponding ends (similar ends) connected to create a neutral point resembling the letter “Y”. From this neutral point, a shared wire is extracted, referred to as the Neutral Wire. | In a DELTA Connection, the opposite ends of three coils are linked, shaping the configuration akin to the Greek alphabet "Δ". Put differently, the end of each coil is linked to the starting point of another coil, forming the connections for the three-phase wires. |
| Neutral point | A point known as the Neutral or Star Point exists. | Delta Connection does not include a Neutral Point. |
| Number of conductors | The star connection comprises four conductors, consisting of line wires along with one neutral wire. | The delta connection consists of only three conductors (line wires) |
| Line and phase current for balanced circuit | Line current = Phase current | Line current = √3 X Phase current |
| Line and phase voltage | Line voltage = √3 X Phase voltage | Line voltage = Phase voltage |
| Speed of a motor | Assuming phase load is same in both star or delta connection. For same line voltage, the phase voltage is √3 times lesser. So, motor speed is less. | Assuming phase load is same in both star or delta connection. For same line voltage, the phase voltage is equal to line voltage. So, motor speed is higher. |
| Usage | Generator | Motor |
| Preference | The star connection is frequently employed in appliances requiring a lower starting current because phase current is lower than delta connection, typically for small-load applications. | The delta connection finds common use in high starting torque applications because phase current is higher than star connection, such as powering large electric motors utilized in various industrial settings. |
Applications of Star and Delta connections
- The star connection is used in the generator side for long distance transmission of electric power. where resistive losses (I2R) should be minimal. This is due to the fact that the star connection gives a line voltage that is √3 greater than the delta connection. Hence for the same power, line current is √3 times smaller.
- Delta connection are not desirable in long distance transmission because of possibility of circulating current.
- Three phase power is used in industrial wiring where large power is required.
Star-delta transformation
Star-to-delta transformation or Delta-to-star transformation is a technique that is particularly useful when analyzing or simplifying complex circuits. While it simplifies the circuit for analysis purposes, it does not alter the overall resistance value of the network.
Star to Delta conversion calculator
Star-to-delta conversion, also known as the “Y-to-Δ” transformation, is a technique to convert a resistive circuit from a star (Y) configuration to a delta (Δ) configuration, or vice versa.
$$R_{CA}=\cfrac{R_{AN}R_{CN}+R_{AN}R_{BN}+R_{BN}R_{CN}}{R_{BN}}$$
$$R_{AB}=\cfrac{R_{AN}R_{CN}+R_{AN}R_{BN}+R_{BN}R_{CN}}{R_{CN}}$$
$$R_{BC}=\cfrac{R_{AN}R_{CN}+R_{AN}R_{BN}+R_{BN}R_{CN}}{R_{AN}}$$
| Star | |||
|---|---|---|---|
| Delta | RCA= | RAB= | RBC= |
Delta to Star conversion calculator
$$R_{AN}=\cfrac{R_{AB}R_{CA}}{R_{AB}+R_{CA}+R_{AB}}$$
$$R_{BN}=\cfrac{R_{BC}R_{AB}}{R_{AB}+R_{CA}+R_{AB}}$$
$$R_{CN}=\cfrac{R_{BC}R_{CA}}{R_{AB}+R_{CA}+R_{AB}}$$
| Delta | |||
|---|---|---|---|
| Star | RAN= | RBN= | RCN= |