The synchronous machine as a component in the electric power system

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Theodora Willis
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1 1 The synchronous machine as a component in the electric power system dφ e = dt

2 2 lectricity generation The synchronous machine is used to convert the energy from a primary energy resource (such as water, steam, geothermal steam, gas, oil, coal) into electricity. They rotate in synchronism to the system frequency (Nominal value 50 or 60 Hz) The frequency oscillates around these nominal values when generation and load seek a balance and the speed of rotation changes slightly. For instance when load increases, more steam or water flows into the turbine and more power is generated

shaft The turbine/generator set turn 1 revolutions for a given whole multiple of the

3 The generator an turbine are mechanically 3 connected to each other The generator and the turbine in a hydroelectric station are connected permanently to each other with the shaft The turbine/generator set turn 1 revolutions for a given whole multiple of the period for each oscillation of the 50/60 Hz frequency (1/50 or 1/60 sec) Turbine generator shaft

4 The synchronous machine in 4 the power system Therefore the synchronous machine is used almost exclusively to generate AC voltage and current in the power system. Other possibilities are for instance induction machines in wind generators. The primary parts of the machine are: The Stator, or the stationary part of the machine. The stator is permanently connected to the poaer system (3 phases) The Rotor or the moving part of the machine is connected with a shaft to the turbine. The excitation is an electrical connection to a DC source to magnetize the rotor. Round rotor: rpm (2-4 poles) Salient pole rotor: rpm. (many poles)

5 The characteristics of Power ngineering the - gill Benedikt Hreinsson 5 synchronous machine We have field windings on the rotor and armature windings on the stator. Double magnetization (Stator and rotor) xcitation with a DC Fixed speed of rotation The magnetic field in the air gap rotates with the same speed as the rotor Generates or consumes reactive power Applications: In an electric power system as a generator In industry where a constant rotational speed is needed

6 The synchronous machine What does the 6 rotor look like? Round rotor Uniform air gap distributed windings The reluctance in the stator circuit is independent of rotor position High rotational speed Used as a generator with gas turbines or steam turbines Salient pole rotor Non-uniform air gap concentrated windings on the pole The reluctance in the stator circuit is dependent of rotor position Slow speed of rotation Used as a generator with hydroelectric turbines

7 7 Comparison of rotor types A round rotor machine. The stator winding reactance is independent of rotor position A salient pole machine with a salient pole rotor. Then the stator winding reactance is dependent of rotor position

8 The 3-phase circuit for a synchronous machine 8 The synchronous machine has a single DC circuit on the rotor and a 3-phase AC circuit on the stator These are 4 main windings. DC voltage source xcitation or magnetization windings a b c In addition we can have damper windings rotor stator

9 Synchronous machine in 9 the electric power system The most common sizes of synchronous machines are MVA We often use another name: alternator The windings: The stator windings are 3-phase and connected to an external power system The rotor windings, also called field windings because they create the machine magnetic field (These are closed loop windings connected to a separate DC source) Damper windings (closed loop and not connected to any external source)

10 10 A 3 phase, 2 pole generator Rotor windings (or field windings) for Direct current with direction into the figure The stator windings for phase a with direction into the figure Rotor windings (or field windings) for Direct current with direction out of the figure A salient pole rotor The rotor The stator Magnetic poles, N and S The stator windings for phase a with direction out of the figure

11 The 3-phase stator current Power ngineering created - gill Benedikt Hreinsson a 11 rotating magnetic field: 3 different instants on the 50 Hz oscillation will create a MMF in 3 different directions

12 The equivalent circuit model for the 12 synchronous generator We start by noting a certain flux by the rotor circuit that links each of the stator windings Let us now move the rotor with the speed ω. Assume that this flux has a sinusoidal shape. Then we get from Faraday s law: Φ = dφ res V = = = ω Nφmax sinωt dt = sinωt fa Nφmax cosωt max = max 2π fnφ max

13 The equivalent circuit model for the 13 synchronous generator (2) By defining the winding factor, K w the RMS value of the voltage on the stator terminals is : max rms = 2π fnφ 2π fnφ max max = = fnφ max rms = 4.44K fnφ w max This RMS value, rms is directly proportional to the speed of rotation, f

14 A phasor diagram for the Power ngineering open - gill Benedikt circuit Hreinsson 14 condition on the stator d-axis Round rotor Φ f 1 The flux that links phase a on the stator due to the rotating field formed by the rotor current I Φ ad, 90 Φ res Φ aq, δ 90 φ Φ a res I 2 = q-axis d Φ fa dt 3 The voltage, induced in the stator in phase a and lags the flux by 90 degrees

15 A phasor diagram for the Power open ngineering - gill circuit Benedikt Hreinsson 15 voltage on the stator windings A round rotor Φ f d-axis 5 6 Φ res = Φ f +Φa I Φ a = LaaIa 90 Φ ad, Φ a Φ res Φ aq, 90 δ φ res I q-axis We assume a current in the stator windings which forms any given angle β=φ+δ relative to the voltage 7 res = dφ dt 4 res

16 16 A phasor diagram with round rotor 8 The open circuit induced voltage on the stator windings. This is the MF for the ideal voltage source,. φ 9 The current in the stator with an unspecified angle β=φ+δ relative to the voltage, δ β I V jix The terminal voltage on the stator terminals with current in the windings: V = Internal voltage drop, -V res = 10 dφ dt res

17 One phase equivalent circuit models 17 for a generator The generator can be represented as a voltage source behind a reactance + R1 I jω L1 1 V + Or the generator can be represented as a (complex) power source I + = V + I( R + jω L ) 1 1 S =P + jq V - ω L R 1 1

18 xamples of inductances (reactances) and 18 resistances for a generator Constants of salient pole hydro-electric generator-60 Hz (All values expressed as per unit on rating) X d X q X X X 2 X 0 R a X and X are direct axis quantities for both direct and quadrature value. R a = stator AC resistance per phase Reference: Book-"lectric Power Systems", by B. M. Weedy, (Wiley Second dition, reprint, 1978),

19 Real power generation in the synchronous 19 machine The previous model for power transfer across a single reactance is valid for the synchronous machine P( δ ) = V X sinδ The maximum ( pull-out ) power is obtained when the angle between the rotors and the system is 90 o P max = V X

20 20 One line diagram for a single generator A rough sketch I, S=P+jQ A more accurate representation A transformer A disconnect switch A circuit breaker used for synchronization

21 21 Synchronization Connect to an energized network 1. Control prime mover to accelerate generator 2. Magnetize field (and armature) winding 3. Make V close to V system to limit currents 4. Connect!

22 22 Synchronization conditions V close to V system if the voltages have Same phase order (abc) Same frequency Same magnitude Same phase

23 The traditional DC machine excitation in Búrfell power house 23 Traditionally the excitation apparatus was a direct current (DC) machine on top of the AC synchronous generator. The modern equivalent is using DC from AC to DC rectifier equipment

SYNCHRONOUS MACHINES

SYNCHRONOUS MACHINES The geometry of a synchronous machine is quite similar to that of the induction machine. The stator core and windings of a three-phase synchronous machine are practically identical