Q19Basic Electrical Engineering

In a three-phase power system, three identical AC voltage sources (phases), displaced from each other by exactly $120^{\circ }$ electrically, supply power to loads. These loads or generators can be interconnected in two primary configurations: Star (Wye/Y) and Delta (Mesh/$\Delta$).

1. Star (Y) Connection: In a Star connection, the similar ends (either starting or finishing ends) of all three phase windings are joined together at a common central point. This common point is called the Neutral Point (N). The remaining three ends are brought out as the three line terminals (R, Y, B). - Voltage Relationship: Because a voltmeter placed between any two lines spans two phase windings, the Line Voltage ($V_L$) is heavily dependent on the vector difference of the phase voltages. Mathematically, $V_L=\sqrt{3}\times V_{ph}$. The Line voltage leads the phase voltage by $30^{\circ }$. - Current Relationship: Since the line conductor is in direct series with the phase winding, the current flowing in the line is identical to the current in the phase. $I_L=I_{ph}$. - Usage: Star is universally used in distribution transformers (secondary side) because it provides a neutral wire, allowing for mixed single-phase (lighting) and three-phase (motor) loads.

2. Delta ($\Delta$) Connection: In a Delta connection, the starting end of one phase winding is connected to the finishing end of the adjacent phase winding, forming a closed triangular loop. There is no neutral point. - Voltage Relationship: The line terminals are directly connected across the ends of the phase windings. Therefore, the Line Voltage is exactly equal to the Phase Voltage. $V_L=V_{ph}$. - Current Relationship: At every node (corner of the delta), the line current splits into two phase currents. By applying Kirchhoff's Current Law and vector addition, the Line Current is $\sqrt{3}$ times the Phase Current. $I_L=\sqrt{3}\times I_{ph}$. The line current lags the phase current by $30^{\circ }$. - Usage: Delta is preferred for high-power industrial motors and transmission line transformers where high reliability is needed (if one phase fails, it can still operate in an open-delta configuration).

Total Power: Regardless of whether the balanced system is Star or Delta connected, the total active power ($P$) consumed is always given by the same universal formula based on line values: $P=\sqrt{3}\cdot V_L\cdot I_L\cdot \cos (\varphi )$.