Artificial Intelligence for Renewable Energy Systems. Группа авторов

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increases to approximately 105 rad/sec at the time when Te equal to Tl. At this time, accelerating torque is zero and the rotor is running above synchronous speed; hence, load angle δ, and thus motor torque Te will keep on decreasing. Decrease in torque Te results in decrease in output power of the machine that causes the rotor to decelerate toward synchronous speed. Hence, due to rotor inertia, it will continue to decelerate below synchronous speed, and consequently, load angle δ begins to increase, with increase in generated torque Te. In this way, damped oscillation of machine continues and settles to a new-steady state value.

Graph depicts the dynamic response of motor following the change in load torque showing (a) motor torque Te, (b) rotor speed ωr, and (c) load angle, delta. Graph depicts the d-q component of stator winding currents (a) Iq1, (b) Id1, (c) Iq2, and (d) Id2.

      For small signal stability analysis, eigenvalue is calculated from system characteristic equation:

      (1.54)image

      where unknown root λ is calculated (i.e., eigenvalue) with A and I as system matrix and identity matrix, respectively. For a system to be stable, all the real and/or real component of eigenvalues must be negative [15, 18–20].

Nomenclature Eigenvalues
Stator eigenvalue I −107.8 ± j104.7
Stator eigenvalue II −19.2 ± j110.3
Rotor eigenvalue −5.1 ± j38.2
Real eigenvalue −9136.3, −703.5, −21.0
Nomenclature Eigenvalues
Stator eigenvalue −38.3 ± j103.2
Rotor eigenvalue −27.9 ± j50.4
Real eigenvalue −8719.7, −503.3, −10.7

      In Equation (1.53), derivative component (i.e., with its elements with subscript p) is indicated by coefficient matrix E, with remaining terms (i.e., subscript k) of linearized machine equations are shown by the coefficient matrix F. Matrices E and F elements are defined in the Appendix.

      1.5.1 Parametric Variation of Stator

      During the analysis, it was assumed that the two sets of stator winding, say, abc and xyz, are identical. Hence, value of resistance and winding leakage inductance will be same (i.e., images It may be noted that in figures of the following sections, dark and dash line indicate the real and imaginary component of eigenvalue, respectively.

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