BASIC POWER

BASIC POWER ENGINEERINGEPO244 CHAPTER 1 THREE PHASE CIRCUITS 1.0 Introduction  A 3- φ cct power system consists of 3-φ generators, transmission lines and loads.  AC power systems have a great advantage over DC system in that their voltage levels can be changed with transformers.  3-φ power systems have 2 major advantages over single phase AC power system:  It is possible to get more power per kilogram of metal from 3-φ machine.  The power delivered to a 3-φ load is constant at all times, instead of pulsing as it does in single-φ system. 1.1 Generation of 3-φ Voltages and Currents A 3- φ generator consists of 3 1- φ generators, with the voltages are equal in magnitude but differing in phase angle from the others by 120° as in Figure 1.1. Figure 1.1: 3- φ connected together with a common neutral Figure 1.2 : Phasor diagram showing the voltages in each phase NORLEE HUSNAFEZA AHMAD 1 3: The 3-phases of the generator connected to three identical loads Figure 1.4: The voltages in each phases of the generator NORLEE HUSNAFEZA AHMAD 2 .BASIC POWER ENGINEERING EPO244 Figure 1. the currents flowing in the 3. I N  I cos     cos    cos 120  sin   sin 120  cos    cos 240  sin   sin 240  jI sin     sin    cos 120  cos   sin 120  sin    cos 240  cos   sin 240   1 3 1 3 I N  I cos     cos     sin     cos     sin    2 2 2 2     1 3 1 3  jI sin     sin     cos     sin     cos    2 2 2 2   IN  0 As long as the three loads are equal. the return current in the neutral is zero. I N  I A  I B  IC  I    I    120  I    240  I cos     jI sin     I cos    120  jI sin    120  I cos    240  jI sin    240  I cos     cos    120  cos   240  jI sin     sin    120  sin    240 Recall the elementary trigonometric identities: cos      cos  cos   sin  sin  sin      sin  cos   cos  sin  Applying these trigonometric identities yields.phases are: Current flowing in the neutral wire.BASIC POWER ENGINEERING EPO244 Since the current flowing to each load can be found from the equation.φ system. A 3.φ power system which have equal in magnitude and 120° different in phase. NORLEE HUSNAFEZA AHMAD 3 . called as a balanced 3. Therefore. connection Thus. NORLEE HUSNAFEZA AHMAD 4 .2 (a) Y.BASIC POWER ENGINEERING 1.2 EPO244 Voltages and Currents in a 3.φ Circuit 1. BASIC POWER ENGINEERING EPO244 1. NORLEE HUSNAFEZA AHMAD 5 .2 ( b) Δ-connection Thus. The 3-φ Power Equations Involving Phase Quantities.3 EPO244 Power Relationships in 3-φ Circuits a. NORLEE HUSNAFEZA AHMAD 6 . The 3-φ Power Equations Involving Line Quantities. The real. reactive and apparent powers supplied to a balanced 3-φ load for Y and Δ connection are given by: b.BASIC POWER ENGINEERING 1. BASIC POWER ENGINEERING EPO244 IMPORTANT to realize that the cosθ and sinθ term are the cosine and sine of the angle between phase voltage and the phase current. Figure 1. NORLEE HUSNAFEZA AHMAD 7 . currents and powers at various points in the circuit with a per-phase equivalent circuit.4 Analysis of Balanced 3-φ Systems 1.5 : Y-Δ transformation. 2. 1. NOT the angle between the line-to-line voltage and the line current. A Y-connected impedance of Z/3 Ω is totally equivalent to a Δ-connected impedance of Z Ω to any circuit connected to the load terminal. Solve it as common circuit in circuit theory. 3. Draw the per-phase equivalent circuit. Determine the voltages. For the simple power system.012Ω per phase. It is consists • Ideal 208-V Y-connected 3-Φ generator • 3-Φ Transmission line has an impedance 0. The power factor of the load e. The real. answer all question same as example 1. reactive and apparent powers consumed by the load d. 3-Φ power system is shown in figure below. The magnitude of the load's line and phase voltages VLL and VφL c. NORLEE HUSNAFEZA AHMAD 8 . The magnitude of the line current IL b.06 + j. • Load has an impedance of 12 + j9 Ω per phase. The real.BASIC POWER ENGINEERING EPO244 Example 1: A 208-V. find a. reactive and apparent powers consumed by the transmission line f. The real. reactive and apparent powers supplied by the generator g. The power factor of generator Example 2: From the figure above. NORLEE HUSNAFEZA AHMAD 9 .BASIC POWER ENGINEERING EPO244 Example 3: Figure above shows a one-line diagram of a small 480V industrial distribution system. The impedance of the distribution line is negligible. Find the overall power factor of the distribution system b. Find the total line current supplied to the distribution system. a.