Chapter 4. Synchronous Generators. Basic Topology

Transcription

1 Basic Topology Chapter 4 ynchronous Generators In stator, a three-phase winding similar to the one described in chapter 4. ince the main voltage is induced in this winding, it is also called armature winding. In rotor, the magnetic field is generated either by a permanent magnet or by applying dc current to rotor winding. ince rotor is producing the main field, it is also called field winding. Two rotor designs are common: 1 2 o alient-pole rotor with protruding poles The peed of Rotation of a ynchronous Generator lip rings Where n P m f = e 120 (a) f e = electrical frequency, in Hz o Round or Cylindrical rotor with a uniform air gap n m = mechanical speed of magnetic field, in rpm = rotor speed, in rpm B R P = number of poles End View ide View 3 4 1

2 The Internal Generated Voltage of a ynchronous Generator It was shown previously, the magnitude of the voltage induced in a given stator phase was found to be = 2 = The induced voltage is proportional to the rotor flux for a given rotor angular frequency in electrical Radians per second. ince the rotor flux depends on the field current I F, the induced voltage E A is related to the field current as shown below. This is generator magnetization curve or the open-circuit characteristics of the machine. (a) Plot of flux versus field current for a synchronous generator. (b) The magnetization curve for the synchronous generator. 5 6 The Equivalent Circuit of a ynchronous Generator 3 Reasons why 1. Armature Reaction distortion of the air gap flux produced by the stator created magnetic field. 2. elf Inductance of the armature coils (X). 3. Resistance of the armature coils (R). jx AR jx l R A The Equivalent Circuit of a ynchronous Generator Armature Reaction: If a load is connected to the stator windings a current will flow resulting in a magnetic field Bs. This varying field produces a voltage in the stator windings Es so that = + The net magnetic field in the air gaps is = + E A + E AR - + E net - I A + V ϕ - We can represent the armature reaction by a reactance X of the form = 7 8 2

3 The Equivalent Circuit of a ynchronous Generator The two reactances (self + armature) may be combined into a single reactance called the synchronous reactance of the machine: X X X = + AR l The Equivalent Circuit of a 3Φ ynchronous Generator The per phase equivalent circuit of a synchronous generator. 9 The Phasor Diagram of a ynchronous Generator The Kirchhoff s voltage law equation for the armature circuit is E = V + I (R + jx ) A ϕ A A The phasor diagrams for unity, lagging, and leading power factors load are shown here: Power and Torque in ynchronous Generators Unity Lagging Leading The angle between is known as the torque angle δ < = < < 11 Figure 4-15: The power-flow diagram of a synchronous generator. 12 3

4 The input mechanical power is given by The power converted from mechanical to electrical power is given by P P = τ ω in app m = τ ω = E I Cos( γ ) conv ind m A A If the armature resistance is ignored (ince R A << X ), E in( δ ) A I Cos( θ ) = A X P COV P OUT 3 VφE in( δ ) A = X = The real and reactive electrical output power is given by P Q OUT OUT = 3 V I Cos( θ ) φ A = 3 V I in( θ ) φ A 13 ote: 1.Pout = Pconv for Ra = Pout (max) occurs for δ = Induced torque of the generator is given by τ ind 3 VφE in( δ ) A = ω X m ote that this equation offers an alternative form for the induced torque presented before by τ = KB B in( δ ) ind net R The Effect of Load Changes on a ynchronous The behavior of a synch. Gen under load depends on the power factor of the load and whether the generator is acting alone or in parallel with other synchronous generators. An increase in load is an increase in the real and/or reactive power supplied by the generator. uch a load increase results in an increase in. With constant field resistance the field current and field flux will remain constant. If also the prime mover maintains constant speed ω, then the internal voltage = is also constant

5 The Effect of Load Changes on a ynchronous At constant field current and rotor speed a. Lagging p.f. with load at same p.f.... The Effect of Load Changes on a ynchronous At constant field current and rotor speed The Effect of Load Changes on a ynchronous At constant field current and rotor speed The Effect of Load Changes on a ynchronous At constant field current and rotor speed

6 The Effect of Load Changes on a ynchronous ynchronous Generator Example ynchronous Generator Example 1 ynchronous Generator Example

7 ynchronous Generator Example 1 ynchronous Generator Example ynchronous Generator Example 2 Ex 2 ynchronous Generator Example 2 Ex

8 ynchronous Generator Example 2 Ex 2 ynchronous Generator Example 2 Ex