Suggestions: There appears to be a lack of References in this thread. Therefore, I am adding some to support my postings and their compliance with some References.
References:
1. Slemon G. R. "Magnetoelectric Devices Transducers, Transformers and Machines," John Wiley and Sons, Inc., 1966
2. Stevenson Jr. W. D., "Elements of Power System Analysis," Third Edition, McGraw-Hill Book Co., 1975
3. Fitzgerald A.E., Kingsley Jr. C., Umans S. D., "Electric Machinery," Fifth Edition, McGraw-Hill, Inc., 1990
4. IEEE Std 100-1984 "IEEE Standard Dictionary of Electrical and Electronics Terms"
5. Say M. G., "Alternating Current Machines," A Halsted Press Book, John Wiley & Sons, New York, 1976
My posting content is based on Reference 1, Figure 5.44 "Circle Diagram Showing Power Ps and Reactive Power Qs into Synchronous Machine at Various Constant Values of Field Current. Terminal Voltage Es Constant," that is based on complex power entering machine
Us=Ps+jQs=Is x Es*. The left half plane (Ps<0) covers generator and right half plane (Ps>0) covers motor. The upper plane is capacitive Qs and lower plane is inductive Qs.
This is consistent with Reference 2 Figure 2.6 "Capacitor considered (a) as a passive circuit element drawing leading current and (b) as a generator supplying lagging current." Please, notice that the "lagging current does not necessarily imply the inductor when it comes to generator. If the current flows into the capacitor, then it leads voltage and it is related to the passive capacitor element. If the current flows from the capacitive generator, then the current lags voltage. However, the Reference 2 Paragraph 2.5 "Complex Power" defines it as S=P+Q= V x I* which is different from Reference 1. It states that "To obtain the proper sign for Q, it is necessary to calculate S as VxI*, rather than V* x I, which would reverse the sign for Q." The Reference 2 defines the complex power in agreement with ANSI standard. Reference 2 Table 2.1 shows:
Generator action assumed:
If P is +, emf supplies power
If P is -, emf absorbs power
If Q is +, emf supplied reactive power (I lags E)
If Q is -, emf absorbs reactive power (I leads E)
Motor action is assumed:
If P is +, emf absorbs power
If P is -, emf supplies power
If Q is +, emf absorbs reactive power (I lags E)
If Q is -, emf supplies reactive power (I leads E)
Reference 3 Fig 5-15 "Capability curves of an 0.85 power factor, 0.80 short-circuit ratio hydrogen-cooled turbine generator." Shows the Per-Unit Reactive Power (lagging) versus Per-unit Power with field heating limited curves and armature heating limited curves in the first quadrant with per-unit scale positive. This first quadrant generator capability curves correspond to the second quadrant of Reference 1 Fig. 5.44 that incidentally is marked as capacitive Q. This is in agreement with Reference 2 Figure 2.6 (b). Reference 2 shows a construction used for the derivation of a synchronous generator capability curve in Figure 5-16 (in the first quadrant) based on P-jQ=V x I, which is consistent with Reference 2 Table 2.1 "If Q is +, emf supplied reactive power (I lags E)."
Reference 4 defines the phasor power as S=P+jQ=E x I*. IEEE Std 100-2000 (seventh edition, current edition) does not include that definition.
Notice that the capability curve will have the field heating limit in upper plane for S=I x E*=P+jQ power definition (P<0, Q>0 and capacitive), Reference 1, and in the lower plane for S=E x I*=P+jQ power definition (P<0, Q>0 and capacitive), Reference 2.
Reference 5 states in Paragraph "Operating Characterisctics" on page 376 that "For underexcitation the input current may lag for all loads, and the maximum power will obviously be reduced.
Some clarification is needed to the Peterb posting on February 19, 2000 that I am attaching below marked:
peterb (Electrical)
Feb 19, 2001
To correct two inaccuracies in jbartos's post of Feb 19, the field current limit applies to the
overexcited (inductive kVAR?????) portion of the curve and the stability limit applies to the
underexcited (capacitive kVAR????) portion of the curve.