 # Module G1 Electric Power Generation and Machine Controls

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Module G1 Electric Power Generation and Machine Controls
James D. McCalley

Overview Energy transformation into electrical form
Generation operation Revolving magnetic field Phasor diagram Equivalent Circuit Power relationships Generator pull-out power Excitation control Turbine speed control

Energy Transformation
Transformation processes: Chemical photovoltaic electromechanical Electromechanical: conversion of energy from coal, petroleum, natural gas, uranium, water flow, geothermal, and wind into electrical energy Turbine-synchronous AC generator conversion process most common in industry today

Click on the below for some pictures of power plants
and synchronous generators ISU Power Plant ISU Power Plant synchronous generator Ames Power Plant Ames Power Plant synchronous generator

Feedback Control Systems for Synchronous Generators
Turbine-generator basic form Governor and excitation systems are known as feedback control systems; they control the speed and voltage respectively

Synchronous Machine Structure
Phase A STATOR (armature winding) ROTOR (field winding) + N Phase B + DC Voltage S The negative terminal for each phase is 180 degrees from the corresponding positive terminal. + Phase C A Two Pole Machine (p=2) Salient Pole Structure

Salient Pole Construction Smooth rotor Construction

Synchronous Machine Structure
A Four Pole Machine (p=4) (Salient Pole Structure)

Generation Operation The generator is classified as a synchronous machine because it is only at synchronous speed that it can develop electromagnetic torque = frequency in rad/sec = machine speed in RPM p = number of poles on the rotor of the machine

For 60 Hz operation (f=60)

For 60 Hz operation (f=60) No. of Poles (p) Synchronous speed (Ns)

Fact: hydro turbines are slow speed,
steam turbines are high speed. Do hydro-turbine generators have few poles or many? Do steam-turbine generators have few poles or many? Fact: salient pole incurs significant mechanical stress at high speed. Do steam-turbine generators have salient poles or smooth? Fact: Salient pole rotors are cheaper to build than smooth. Do hydro-turbine generators have salient poles or smooth?

Generation Operation A magnetic field is provided by the DC-current carrying field winding which induces the desired AC voltage in the armature winding Field winding is always located on the rotor where it is connected to an external DC source via slip rings and brushes or to a revolving DC source via a special brushless configuration Armature winding is located on the stator where there is no rotation The armature consists of three windings all of which are wound on the stator, physically displaced from each other by 120 degrees

Synchronous Machine Structure
Phase A voltage induced in phase wdgs by flux from field wdg current in phase wdgs produces flux that also induces voltage in phase wdgs. + N Phase B + DC Voltage S + Phase C

Generation Operation: The revolving magnetic field
= flux associated with the revolving magnetic field which links the armature windings. It will have a flux density of B. At any given time t, the B-field will be constant along the coil. By Faraday’s Law of Induction, the rotating magnetic field will induce voltages phase displaced in time by 120 degrees (for a two pole machine) in the three armature windings Let’s consider just the A-phase.

Generation Operation: The revolving magnetic field (cont’d)
If each of the three armature windings are connected across equal impedances, balanced three phase currents will flow in them producing their own magnetic fields = = = resultant field with associated flux obtained as the sum of the three component fluxes is the field of armature reaction The two fields represented by and are stationary with respect to each other The armature field has “locked in” with the rotor field and the two fields are said to be rotating in synchronism The total resultant field =

Generation Operation: The phasor diagram
From Faraday’s Law of Induction, a voltage is induced in each of the three armature windings: where N = number of winding turns All voltages, ,lag their corresponding fluxes, ,by 90 degrees The current winding a, denoted by , is in phase with the flux it produces

Generation Operation: The phasor diagram (cont’d)
Note:

Generation Operation: The equivalent circuit model
Develop equivalent model for winding a only; same applies to winding b and c with appropriate 120 degree phase shifts in currents and voltages given a balanced load

Generation Operation: The equivalent circuit model (cont’d)

Generation Operation: The equivalent circuit model (cont’d)

Generation Operation: The equivalent circuit model (cont’d)
You can perform per-phase equivalent analysis or you can perform per-unit analysis. In per-phase, Ef and Vt are both line to neutral voltages, Ia is the line current, and Z is the impedance of the equivalent Y-connected load. In per-unit, Ef and Vt are per-unit voltages, Ia is the per unit current, and Z is the per unit load impedance.

Let From the equivalent circuit, So here we see that

Assign Vt as the reference: Then, So here we see that This gives an easy way to remember the relation between load, sign of current angle, leading/lagging, and sign of power angle.

Phasor Diagram for Equivalent Circuit
jXs Ef Zload Vt From KVL:

Phasor Diagram for Equivalent Circuit
This equation gives directions for constructing the phasor diagram. 1. Draw Vt phasor 2. Draw Ia phasor 3. Scale Ia phasor magnitude by Xs and rotate it by 90 degrees. 4. Add scaled and rotated vector to Vt Ef jXsIa jXsIa Vt Ia Try it for lagging case. XsIa

Phasor Diagram for Equivalent Circuit
This equation gives directions for constructing the phasor diagram. 1. Draw Vt phasor 2. Draw Ia phasor 3. Scale Ia phasor magnitude by Xs and rotate it by 90 degrees. 4. Add scaled and rotated vector to Vt You do it for leading case.

Phasor Diagram for Equivalent Circuit
Let’s define the angle that Ef makes with Vt as For generator operation (power supplied by machine), this angle is always positive. For motor operation, this angle is negative.