Equivalent-circuit-and-SG-operating-alone.ppt
- 1. Synchronous Machines Mrs.P.Vijayapriya Asst.Prof (SG) SELECT Room No. TT 130B UNIT – I Synchronous Generator Constructional details – Types of rotors – mmf of distributed AC winding – emf equation – synchronous reactance – Armature reaction – Voltage regulation – e.m.f , m.m.f, z.p.f and A.S.A methods – synchronizing and parallel operation – Synchronizing torque – Change of excitation and mechanical input – Two reaction theory – Determination of direct and quadrature axis synchronous reactance using slip test – Operating characteristics – capability curves
- 2. Three-phase equivalent circuit of a cylindrical-rotor synchronous machine The voltages and currents of the three phases are 120o apart in angle, but otherwise the three phases are identical. + Ia1 Ef1 jXs Ra + I a 2 E f 2 j X s R a + I a 3 E f 3 j X s R a + VL-L VL-L =3Vt Vt
- 3. Short-circuit Ratio Another parameter used to describe synchronous generators is the short-circuit ratio (SCR). The SCR of a generator defined as the ratio of the field current required for the rated voltage at open circuit to the field current required for the rated armature current at short circuit. SCR is just the reciprocal of the per unit value of the saturated synchronous reactance calculated by . u . p in X I I SCR sat _ s Iscrated _ f Vrated _ f 1 Ef or Vt (V) Air-gap line OCC Isc (A) SCC If (A) Vrated Isc,rated If_V rated If_Isc rated
- 4. Equivalent Circuit – single phase equivalent • Since – for balanced loads – the three phases of a synchronous generator are identical except for phase angles, per-phase equivalent circuits are often used.
- 5. Power and torque in synchronous generators A synchronous generator needs to be connected to a prime mover whose speed is reasonably constant (to ensure constant frequency of the generated voltage) for various loads. The applied mechanical power is partially converted to electricity Where is the angle between EO and IL. The power-flow diagram of a synchronous generator. m app m P cos 3 int L O m conv I E P
- 6. The real output power of the synchronous generator is The reactive output power of the synchronous generator is In real synchronous machines of any size, the armature resistance RA << XS and, therefore, the armature resistance can be ignored. Thus, a simplified phasor diagram indicates that cos 3 cos 3 L L P P out I V I V P sin 3 sin 3 L L P P out I V I V Q Xs Eo IL sin cos Power and torque in synchronous generators
- 7. Then the real output power of the synchronous generator can be approximated as Here is the torque angle of the machine – the angle between V and EA. The maximum power can be supplied by the generator when = 900 : The maximum power specified is called the static stability limit of the generator. Normally, real generators do not approach this limit: full-load torque angles are usually between 150 and 200 . Power and torque in synchronous generators Xs EoV P P out 3 ) ( sin sin 3 perphase Xs EV P or Xs EoV P P out
- 8. The Synchronous generator operating alone A synchronous generator operating at a lagging power factor has a fairly large positive voltage regulation. A synchronous generator operating at a unity power factor has a small positive voltage regulation. A synchronous generator operating at a leading power factor often has a negative voltage regulation. Normally, a constant terminal voltage supplied by a generator is desired. Since the armature reactance cannot be controlled, an obvious approach to adjust the terminal voltage is by controlling the internal generated voltage Eo = K. This may be done by changing flux in the machine while varying the value of the field resistance RF, which is summarized: 1. Decreasing the field resistance increases the field current in the generator. 2. An increase in the field current increases the flux in the machine. 3. An increased flux leads to the increase in the internal generated voltage. 4. An increase in the internal generated voltage increases the terminal voltage of the generator.
- 9. Terminal characteristics of synchronous generators All generators are driven by a prime mover, such as a steam, gas, water, wind turbines, diesel engines, etc. Regardless the power source, most of prime movers tend to slow down with increasing the load. This decrease in speed is usually nonlinear but governor mechanisms of some type may be included to linearize this dependence. A typical speed vs. power plot A typical frequency vs. power plot A similar relationship can be derived for the reactive power Q and terminal voltage VT. When adding a lagging load to a synchronous generator, its terminal voltage decreases. When adding a leading load to a synchronous generator, its terminal voltage increases.
- 10. Summarize • When a generator is operating alone supplying the load: 1.The real and reactive powers are the amounts demanded by the load. 2.The governor of the prime mover controls the operating frequency of the system. 3.The field current controls the terminal voltage of the power system.