1. The self-inductance of windings (Laa, Lbb, Lcc) have fluctuation. Ls (which is a constant) is the average self-inductance of each of the stator windings. Please refer to the equation Laa, Lbb, and Lcc on the documentation page for a better understanding of Lm..
2. Lm is the stator inductance fluctuation. The fluctuation of self-inductances (Laa, Lbb, Lcc) of stator windings and the fluctuation of mutual inductances (Lab, Lbc, Lca) between each two stator windings are always the same value (i.e., Lm). Please refer to the equation Laa, Lbb, Lcc, Lab, Lbc, and Lca on the documentation page.
3. Ms comes from the measurement of mutual inductances (Lab, Lbc, Lca) between each two stator windings. There is no strict magnitude relationship like Ms = 1/10*Ls.
4. L0 is the leakage inductance of the stator windings. L0 is always less than Ld and Lq.
5. The derivation of the machine inductances are derived in Chapter 1 (Section 1.5) of the following book.
Krause, P.C., O. Wasynczuk, and S.D. Sudhoff. Analysis of Electric Machinery and Drive Systems. IEEE Press, 2002.
Equations (1.5-25), (1.5-26), (1.5-27), (1.5-29), (1.5-30),(1.5-31) on Page 52 are equivalent to the inductance equations (Laa, Lbb, Lcc, Lab, Lbc, and Lca) shown in the documentation page.