Behavior of Synchronous Machines Subjected to Voltage Sags of type A, B and E

Voltage sags and voltage interruptions are huge power quality problems for many industries. Voltage sags cause apart from eventual tripping, large torque peaks, which may cause damage to the shaft or equipment connected to the shaft. This paper illustrates how the stator flux in a synchronous machine changes during voltage sags. These changes result in torque peaks. An analytical time dependent expression of the stator flux during voltage sags explains the behaviour of synchronous machines and why there are high torque and current peaks during voltage sags. Simulations verify the expressions, and illustrate the dependence of torque and current peaks on voltage sag duration and magnitude. Fig. 1: Voltage sag types Table 1: Rated data of synchronous machine Quantity Symbol Value Unit Speed n 1500 r/min Voltage line-line Ull 10.5 kV Apparent power S 4150 kVA Current I 228 A Power factor cos φ 0.9 capacitive Pole pairs p 2 Inertia J 960 kgm2 Stator resistance Rs 213 mΩ Inductance d Ld 151 mH Transient inductance d L’d 25 mH Subtransient inductance d L”d 17 mH Inductance q Lq 75 mH Subtransient inductance q L”q 26 mH Mutual inductance LdD, LfD 134 mH Mutual inductance Ldf 186 mH Mutual inductance Lmq 58 mH Time constant armature Ta 0.1 s Time constant field winding Td0 4.33 s Fredrik Carlsson, Chandur Sadarangani This model does not include saturation effects. The damper windings (subscript D and Q) reduce the rotor oscillations during transient mode, since speed changes in the rotor will induce currents in the short-circuited damper windings that will generate a magnetic field, which will try to maintain the speed of the rotor. The voltages ud and uq are derived from the applied voltage by using Park’s dq-transformation [9]. The constant voltage of the field winding is uf = 38 V and the field winding resistance is Rf = 92 mΩ. The damper windings in the dand q-direction are short circuited, which is why the associated voltages are set to uD = uQ = 0. The stator resistance Rs = 213 mΩ is the same in both the dand q-direction. The mutual inductances in dand q-direction are LdD, Ldf, LfD and Lmq.