A Y-Δthree-phase transformer is connected to a 60 -kVA load...

A $Y-\Delta$ three-phase transformer is connected to a 60 -kVA load with 0.85 power factor (leading) through a feeder whose impedance is $0.05+j 0.1 \Omega$ per phase, as shown in Fig. 13.122 below. Find the magnitude of: (a) the line current at the load, (b) the line voltage at the secondary side of the transformer, (c) the line current at the primary side of the transformer.

A $Y-\Delta$ three-phase transformer is connected to a 60 -kVA load with 0.85 power factor (leading) through a feeder whose impedance is $0.05+j 0.1 \Omega$ per phase, as shown in Fig. 13.122 below. Find the magnitude of:
(a) the line current at the load,
(b) the line voltage at the secondary side of the transformer,
(c) the line current at the primary side of the transformer.

Key Concepts

Phasor Analysis and Power Factor

Phasor analysis is a method of representing sinusoidal quantities (like voltage and current) as complex numbers, which allows for the easy handling of magnitude and phase angle information. The power factor, defined as the cosine of the phase angle difference between voltage and current, indicates how effectively power is being used. A non-unity power factor (leading or lagging) requires careful phasor calculations to accurately determine current magnitudes, voltage drops, and overall system performance in AC power analysis.

Impedance and Voltage Drop in AC Circuits

In AC circuits, impedance—a combination of resistance and reactance—affects the voltage drop along a conductor. When a feeder or any connecting conductor has a given complex impedance, the voltage drop experienced due to the flowing current must be calculated using phasor (complex) arithmetic. This is particularly important in power systems, where voltage regulation and efficiency depend on understanding and mitigating these drops.

Three-Phase Transformer Connections

This concept involves the different ways of connecting transformer windings (such as Y or wye, and ? or delta) in three-phase power systems. In a Y–? transformer, one side of the transformer (usually the primary or secondary) is connected in a wye configuration, while the other side is connected in a delta configuration. Each configuration affects the relationship between line and phase voltages and currents, and influences phase shifts and load balancing in the network.

Three-Phase Power Calculations

This concept encompasses the relationships between line voltages, phase voltages, line currents, and the overall apparent power in three-phase systems. Calculations typically use formulas like S = ?3 V_L I_L for balanced loads, with adjustments for power factor to determine the real and reactive components. Understanding these relationships is essential for analyzing and designing three-phase electrical networks, where accurate determination of currents and voltages is critical.

Transcript

0:00 Hello everyone.

00:01 Let us do the following question.

00:03 In the question we have given a wide delta three -phase transformer is connected to 60 kilowalt ampere load with the 0 .85 power factor and whose impedance is each face is connected with the impedance of 0 .05 plus j plus 0 .1 -hom.

00:20 Find the magnitude of line current at the load.

00:23 The line voltage at the secondary side of the transformer.

00:26 The line current at the primary side of the transformer.

00:30 Firstly, we will say that we will find this value at the load.

00:35 We will follow this equation at the load.

00:37 At the load, this can be written as bl.

00:40 Value of this can be written as 240 volt.

00:43 Voltage of this is written as a, b.

00:46 If we have to write voltage of a with respect to n, this value can be written as bl under the root 3.

00:54 If we will find this value, we will get this value as 138 .56.

01:00 Value of this is 138 .56 volts.

01:02 Next, if we find complex power, then value of this is under the root 3 vl into il and then we will get the value of for il as 60 ,000 as given in the question divided by 240 under the root 3.

01:21 Value of this can be written as 144 .34 ampere.

01:26 This is the value.

01:28 Now in the second question, in the second question, in the second part we have to find v primary voltage along scatry circuit.

01:36 So we will say that let value of bn is can be written as v an into zero degree.

01:44 This can be written.

01:45 If we write this value, this can be written as 138 .56 into zero degree.

01:51 If we have to find value of course theta, this is equals to power factor or power factor is given in the question 0 .85.

02:00 From this, we will write value of theta as 31 .79 degree...