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I. Monographs, general courses, textbooks
Demirchyan K.S., Neyman L.R., Korovkin N.V., Theoretical Electrical Engineering . Moscow, St.Petersburg: Piter, 2009. Vol. 1, 2 (In Russian).
Kuepfmueller K., Kohn G., Theoretische Elektrotechnik und Elektronik. 15 Aufl. Berlin, N.Y.: Springer, 2000. (In German).
Mueller G., Ponick B., Elektrische Maschinen, N.Y.:, J. Wiley, 2009. (In German).
Schuisky W., Berechnung elektrischer Maschinen. Wien: Springer, 1960. (In German).
Richter R., Elektrische Maschinen. Berlin: Springer. Band I, 1924; Band II, 1930; Band III, 1932; Band IV, 1936; Band V, 1950. (In German).
Mueller G., Vogt K., Ponick B., Berechnung elektrischer Maschinen. Berlin: Springer, 2007. (In German).
Korn G., Korn T., Mathematical Handbook, N.Y.: McGraw-Hill, 1961.
II, III. Asynchronous and synchronous machines. Papers, inventor’s certificates, patents
Boguslawsky I.Z., Kuss G., Investigation of the structure m-phase stator winding with a fractional number q. Proceedings of the Russian Academy of Sciences. Energetika, #5, 1998.
Boguslawsky I.Z., Twelve – zone stator winding with fractional number of slots per pole and phase for large slow–speed machines. Elektrotechnika, #1, 1978. (In Russian).
Boguslawsky I.Z., Winding factors of the 12-phase winding with fractional q for the synchronous slow-moving machines. Elektrotechnika, #7, 1976. (In Russian).
Boguslawsky I.Z., Features six-phase armature winding machines with non-sinusoidal power supply. Proceedings of the Russian Academy of Sciences. Energetika. #5, 1997. (In Russian).
Boguslawsky I.Z., The harmonics of armature field and frequencies of rotor loops currents of multiphase synchronous motor under nonsinusoidal feeding. Research Institute of Electric Machine Industry of Russian Academy of Science (Elektromach). No. 2, 1998. (In Russian).
IV. State Standards (IEC, GOST and so on)
GOST (Russian State Standard) R-52776 (IEC 60034-1). Rotating Electrical Machines. (In Russian).
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Appendices
Appendix 3.1
See Table 3.7.
List of Symbols
- a:
-
Number of parallel branches in phase
- bP :
-
Width of pole shoe
- AS:
-
Stator current load
- D:
-
Stator boring diameter
- \( {\text{F}}_{1} , \ldots ,{\text{F}}_{\text{m}} \) :
-
Amplitudes of spatial harmonics of stator winding phase MMF
- \( {\text{F}}_{\text{ST}} ( {\text{m}}_{\text{EL}} ,{\text{Q)}} \), \( {\text{F}}_{{{\text{ST}},{\text{RES}}}} ( {\text{x}},{\text{m}}_{\text{EL}} ,{\text{Q)}} \) :
-
Respectively, complex amplitude (phasor) and amplitude (modulus) of spatial harmonic of order of mEL and time harmonic of order Q of all winding phases mPH
- IQ :
-
Harmonic amplitude of order Q for stator phase current
- KW(m):
-
Winding factor for m order field harmonic
- kQ :
-
Relation of stator current harmonic amplitude of order Q > 1 to harmonic amplitude of order Q = 1
- m, mEL :
-
Orders of MMF spatial harmonics of MMF and stator fields
- mPH :
-
Number of stator winding phases
- Q:
-
Order of time harmonics
- QDIR, mDIR :
-
Order of time and spatial harmonics of direct field
- QAD, mAD :
-
Order of time and spatial harmonics of additional field
- n, nEL :
-
Orders of spatial harmonics of MMF and rotor fields
- SN :
-
Number of effective conductors in slot
- T:
-
Time
- P:
-
Number of machine pole pairs
- Q:
-
Number of slots per pole and phase of stator winding
- T, TEL :
-
Expansion periods of MMF and mutual induction field to harmonic series
- \( {\text{U}}_{ 1} , \ldots ,{\text{U}}_{\text{Q}} \) :
-
Amplitudes of time harmonics
- WPH :
-
Number of turns in stator winding phase
- \( {\text{Z}}_{ 1} \) :
-
Number of stator slots
- \( \upbeta \) :
-
Pitch shortening of stator winding
- \( {\upvarphi}_{{ 1 , {\text{U}}}}, \ldots,{\upvarphi}_{{{\text{Q}},{\text{U}}}} \) :
-
Initial phase angles of voltage harmonics
- τ:
-
Pole pitch
- \( \upomega_{ 1} , \ldots ,\upomega_{\text{Q}} \) :
-
Stator current circular frequencies
- \( \upomega_{\text{REV}} \) :
-
Angular rotation speed of rotor
- \( \upomega_{\text{BOR}} \) :
-
Angular rotation speed of MMF and stator field in air gap
- \( \upomega_{\text{ROT}} \) :
-
Circular frequency of EMF and rotor current
Brief Conclusions
-
1.
A number of mutual induction fields different in their periods and rotation speeds occur in A.C. machine air gap at non-sinusoidal power supply. The fields inducing EMF of the same frequency in rotor loops can be determined in them. Loops generating these fields are magnetically coupled, for instance, loops of rotor and stator (in Table 3.4). Except them, there are mutual induction fields inducing EMF of identical frequency in stator loops, but differing in order of spatial harmonics; loops corresponding to them are also magnetically coupled, for instance loops of rotor and stator (in Table 3.5). The machine processes are determined taking into account the interaction of these loops in the general system of Eqs.
-
2.
Two fields determined by time harmonics of various orders Q containing in expansion (3.1) and spatial harmonics of order m in expansion (3.4) at certain combination of these orders induce in rotor loops EMF of identical frequency, for example, at mAD = 5: QDIR = 1 and QAD = 11, and also QDIR = 7 and QAD = 17.
-
3.
Unlike fields in air gap of three-phase machine, fields in air gap of six-phase machine, determined by time harmonics of orders Q = 3 and spatial of order \( {\text{m}}_{\text{EL}} = 3 \) form rotating (but not pulsating) fields; in that specific case, the angular rotation speed of this fields is equal to rotor synchronous rotation speed. Consequently, this field does not induce any EMF in synchronous machine rotor loops in continuous operation mode \( ({\upomega}_{\text{REV}} =\upomega_{1}/{\text{p)}} \).
-
4.
For non-sinusoidal power supply it is possible to avoid the influence of series higher time harmonics on rotor loops using the stator winding scheme with phase number \( {\text{m}}_{\text{PH}} > 3 \). However, there are some drawbacks in winding with increased phase numbers.
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Boguslawsky, I., Korovkin, N., Hayakawa, M. (2017). Stator MMF Harmonics at Non-sinusoidal Machine Power Supply (for M ≥ 1, Q ≥ 1). In: Large A.C. Machines. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56475-1_3
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DOI: https://doi.org/10.1007/978-4-431-56475-1_3
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