class: center, middle # EE-362 ELECTROMECHANICAL ENERGY CONVERSION-II # Equivalent Circuit of Synchronous Machines ## Ozan Keysan [ozan.keysan.me](http://ozan.keysan.me) Office: C-113
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Tel: 210 7586 --- # Review: Torque in Synchronous Machines -- # \\(T = K \Phi\_f \Phi\_R sin (\delta)\\) ### \\(K\\): Constant (we'll see what it is in the following weeks) ### \\(\Phi_f\\): Field generated flux (rotor-side) ### \\(\Phi\_R\\): Resultant (or Air-gap) flux (\\(\Phi\_R = \Phi\_f + \Phi\_{ar}\\)) ## \\(\delta\\): Load-angle (very important!) --- # Torque vs Load Angle ## \\(\delta > 0 \\): Generating Action ## \\(\delta < 0 \\): Motoring Action ## \\(\delta = \pm \dfrac{\pi}{2} \\): Maximum torque point ## \\(\delta = 0 \\): Zero Torque (Donkey eats the carrot) --- # Torque vs Load Angle
--- # Simple Equivalent Circuit
--- # Equivalent Circuit ## The armature windings has some resistance: \\(R_a\\)
### Ra is usually around <5% of jXs so can be ignored --- ## Motoring and Generating Convention ### Remember synchronous machines are mostly used as generators.
--- # Most important definitions - ## Load Angle (\\(\delta\\)): Angle between phase voltage and field voltage - ## Power Factor Angle (\\(\theta\\)): Angle between phase voltage and current. --- # Load Angle and Power Factor
### Neglect \\(R\_a\\) for now. ### [Voltage and Current Waveforms](https://docs.google.com/spreadsheets/d/1K7vG-rez29gQ3fhGt3pZCsy4OtRYml2UaPSoeRor9wI/edit?usp=sharing) --- # Full Equivalent Circuit with Field Circuit
-- ### \\(L\_f\\) can be neglected at steady state (DC) conditions ## Remember \\(I\_f\\) can be controlled to adjust \\(E\_f\\) --- # Operation Modes: Standalone Generating ### Assume you have a single diesel generator supplying a load --
--- # Standalone Generating # Challenge: -- - ## Keep the terminal voltage constant -- - ## Keep the frequency of the electricity constant --- # Standalone Generation -- ## Assume we have a resistive load (unity pf) -- ## Assume the field current and speed is kept constant and see what happens to terminal voltage as we increase the load. --- ## Standalone Generation with Unity Power Factor ### Speed is kept constant. ### \\(I_f\\) is kept constant and hence magnitude of \\(E_f\\) constant --
## As load increases, \\(V_t\\) slightly decreases. [Animation](http://people.ucalgary.ca/~aknigh/electrical_machines/synchronous/stand_alone/sa_phasors.html) --- ## Standalone Generation with Lagging Power Factor ### Magnitude of \\(E_f\\) constant --
### As load increases, \\(V_t\\) considereably decreases. [Animation](http://people.ucalgary.ca/~aknigh/electrical_machines/synchronous/stand_alone/sa_phasors.html) ### [Animation](http://people.ucalgary.ca/~aknigh/electrical_machines/synchronous/sg_standalone.html) --- # Leading Power Factor
### As load increases, \\(V_t\\) slightly increases. [Animation](http://people.ucalgary.ca/~aknigh/electrical_machines/synchronous/stand_alone/sa_phasors.html) --- # Voltage Regulation -- ## \\(V\_{reg}= \dfrac{V\_{no-load}-V\_{full-load}}{V\_{full-load}}\\) --- ## In a standalone power system, we want to keep the frequency and voltage constant. -- # Solution? -- ## Control Field Current to adjust \\(E_f\\) so that constant \\(V_t\\) magnitude can be achieved --- # AVR? -- : Automatic Voltage Regulator --  --- --- # What does this device do?  ---  -- ## Speed Governor: ## Centrifugal Flyball System works as a speed controller --- # Watt's Steam Engine
-- ### [We're still using the same technology](https://www.youtube.com/watch?v=1VqS74JJ17U) --- # Speed control ensures constant frequency --- ## Full Control Scheme of a Diesel Generator
--- ## You can download this presentation from: [keysan.me/ee362](http://keysan.me/ee362)