**3. Induction motor starting**

At the beginning, two induction motors are connected directly to an isolated electrical grid. The first induction motor (IM1) is connected to the terminals of the aggregate and later, when the first motor has run-up successfully, the second induction motor (IM2) is connected to the grid.

The synchronous generator is initially in a steady state unloaded condition. However, in this condition stator current is zero, rated voltage is on its terminals, while rotation speed of the diesel engine (DM) is equal to the speed of the generator (SG) and is equal to 1 p.u.

The first observed dynamics is for the case of the starting of unloaded induction motors and in the second case dynamics of loaded induction motors are considered. Transients of: airgap torque and speed transient of induction motors, terminal voltage, speed transient of synchronous generator and diesel engine, for both cases are presented in Figure 4.

Initially, the first induction motor is starting from rest, the rated voltage is applied on its terminals and there is no mechanical load on the motor shaft. When the induction motor is connected, the load on the aggregate is instantaneously increased, defined in the initial (subtransient) phase of the transitional phenomenon by locked-rotor torque of the induction motor. As the motor accelerates, its torque grows and the generator load rises. When maximum torque is achieved, the load of the synchronous generator reaches its maximum and then decreases rapidly.

78 Induction Motors – Modelling and Control

**Figure 3.** Induction motor model

to the grid.

diesel engine (

**3. Induction motor starting** 

At the beginning, two induction motors are connected directly to an isolated electrical grid. The first induction motor (IM1) is connected to the terminals of the aggregate and later, when the first motor has run-up successfully, the second induction motor (IM2) is connected

The synchronous generator is initially in a steady state unloaded condition. However, in this condition stator current is zero, rated voltage is on its terminals, while rotation speed of the

The first observed dynamics is for the case of the starting of unloaded induction motors and in the second case dynamics of loaded induction motors are considered. Transients of: airgap torque and speed transient of induction motors, terminal voltage, speed transient of

Initially, the first induction motor is starting from rest, the rated voltage is applied on its terminals and there is no mechanical load on the motor shaft. When the induction motor is connected, the load on the aggregate is instantaneously increased, defined in the initial (subtransient) phase of the transitional phenomenon by locked-rotor torque of the induction motor. As the motor accelerates, its torque grows and the generator load rises. When

synchronous generator and diesel engine, for both cases are presented in Figure 4.

SG) and is equal to 1 p.u.

DM) is equal to the speed of the generator (

At the instant of starting, as one can see in Fig. 4a, the air-gap torque is momentarily increased; reaches maximum value of 0.86 p.u. and change in it can be noticed during the whole start-up period of the first induction motor. The instantaneous torque oscillates about positive average value.

**Figure 4.** Transients of: air-gap torque of induction motors (*T*eIM1, *T*eIM2) and speed transient of induction motors (IM1, IM2); terminal voltage (*u)*, speed transient of synchronous generator (SG) and diesel engine (DM), during direct-on-line starting of: a) unloaded b) loaded induction motors

The oscillations in the air-gap torque are caused by the interactions between the stator and rotor flux linkage. The negative oscillations in the electromagnetic torque of the induction motor are presented at the beginning of the start-up period. These are periods of momentary deceleration that occur during regeneration when the electromagnetic torque becomes negative. The rotor speed only increases when the torque is positive. The oscillations that are present in transient of air-gap torque of the first induction motor are damped at the end of start up period and finally the steady state condition is attained without oscillations.

The response of the air-gap torque is in accordance with the response of the motor currents. Transients of stator currents of induction motors and their components, for both cases, are presented in Figure 5.

Under this condition the starting current is large. The starting current of an induction motor is several times larger than the rated current since the back emf induced by Faraday's law grows smaller as the rotor speed increases. However, a large starting current tend to cause the supply voltage to dip during start-up and can cause problems for the other equipment that is connected to the same grid.

The Dynamics of Induction Motor Fed Directly from the Isolated Electrical Grid 81

The starting of loaded induction motor is more difficult transition regime for the aggregate,

Thus, in the second case, the dynamics of the starting of loaded induction motors is analyzed, however, the load on the first one is *T*lIM1=0.15 p.u. while *T*lIM2=0.2 p.u. is applied on the second one. In this case the acceleration time is longer than in the previous case when motors are started unloaded (Fig. 4a), the voltage of synchronous generator is recovering slower, and will be lower then 80%*U*n during greater part of start up period, as presented in

The initial part of the transients of electromagnetic torque is equal in both cases (load and non-load condition). At the time of the starting of the first induction motor the torque *T*eIM1

At the instant of connection to power supply the instantaneous torque is independent of the balanced source voltages because the machine is symmetrical, even air-gap torque depends upon the values of source voltages though the stator currents. In addition, the air-gap torque oscillates with higher magnitude, about lower average then in case of unloaded motor. These oscillations are damped at the end of the start-up period of the induction motor as

The component of air-gap torque, which appears because of mutual acting of free currents in stator as well as in rotor windings acts as counter torque on motors shaft and disappears before the end of the run-up. As one can see in Fig 4 the duration of the start-up of both induction motors is longer than in the previous case, in which the motors run-up unloaded. Thus, this acceleration period of second induction motor is 500 ms, while in the previous case lasted 230 ms. In Fig. 5b stator currents, in *dq* axis, and their components, during start up of loaded induction motor, are presented. As the induction motor is directly connected to the terminals of unloaded synchronous generator that means that stator current of induction

At the beginning of the transient phenomena inrush current which appears during the first half period is dominating but disappears quickly. After initial damping, oscillations of free currents will continue with slightly greater magnitude than at the beginning of transients. These currents, which also can be seen during the start up period of unloaded induction motor, disappear at the end of start up. Corresponding stator flux linkage, during direct-on-

The transients of the first induction motor current in *abc* coordinate system (*i*abcIM1), in both cases, are presented in Fig. 7. The current of synchronous generator (*i*abcSG), in both cases, is

The phenomena of voltage and frequency deviation are typical for isolated electrical grid which in turn affects the quality of electric power systems. The short-term frequency deviation, during direct-on-line starting unloaded and loaded induction motors are presented in Figure 9. There is relatively strong electrical coupling between synchronous

presented in Fig. 8. This is the total current that motors draw from the electrical grid.

motor is at the same time the armature current of synchronous generator.

line starting of unloaded and loaded induction motor are presented in Fig. 6.

therefore, the transients of aggregate are slower.

Fig. 4b.

reaches a value of 0.86 (p.u.).

presented in Figure 4b.

**Figure 5.** Transients of stator currents of induction motors (*i*IM1, *i*IM2) and their components in *d* (*id*IM1, *id*IM2) and *q* (*iq*IM1, *iq*IM2) axis during direct-on-line starting of: a) unloaded b) loaded induction motors

At the instant of starting, when the supply has just been switched on the induction motor, the first magnitude of starting current momentarily reaches maximum value of 1.61 p.u. as it is presented in Fig. 5a. The damped oscillations, that are present in stator current transients, disappear at the end of the starting period of the induction motors. When the first motor has run-up successfully, the second induction motor (IM2) is connected to the loaded synchronous generator. Involvement of the second induction motor to the isolated electrical grid the network load instantaneously increased and voltage drop occurs.

The terminal voltage is momentary decreased (Fig. 4a) and after few damped oscillations reached minimal value. However, the high starting currents are appeared. High inrush current, in the first moments, as one can see in Figure 5, reaches the magnitude of the first oscillation of 1.73 p.u. The air-gap torque of the second induction motor *T*eIM2 momentarily achieves 0.94 p.u.

At the moment of switching on to the grid, the second induction motor begins to accelerate and oscillations are present in its transients of air-gap torque during the acceleration period. At the time of the starting of second induction motor (IM2), the reverse torque impulse of 0.31 p.u. in air-gap torque of the first one (IM1) is appeared but decayed rapidly. As the torque of the first induction motor becomes negative motor speed slows down. Thereafter, damped oscillations that are present in the response of electromagnetic torque of the first motor as well as oscillations in electromagnetic torque of the second one are stifled at the end of the run-up period of the second induction motor.

At the beginning of the start-up period of the second motor, the speed of the first one decreases and afterwards recovers. Overshoot in the speed transient occurs at the end of start-up period of the second induction motor.

The starting of loaded induction motor is more difficult transition regime for the aggregate, therefore, the transients of aggregate are slower.

80 Induction Motors – Modelling and Control

achieves 0.94 p.u.

**Figure 5.** Transients of stator currents of induction motors (*i*IM1, *i*IM2) and their components in *d* (*id*IM1, *id*IM2) and *q* (*iq*IM1, *iq*IM2) axis during direct-on-line starting of: a) unloaded b) loaded induction motors

grid the network load instantaneously increased and voltage drop occurs.

end of the run-up period of the second induction motor.

start-up period of the second induction motor.

At the instant of starting, when the supply has just been switched on the induction motor, the first magnitude of starting current momentarily reaches maximum value of 1.61 p.u. as it is presented in Fig. 5a. The damped oscillations, that are present in stator current transients, disappear at the end of the starting period of the induction motors. When the first motor has run-up successfully, the second induction motor (IM2) is connected to the loaded synchronous generator. Involvement of the second induction motor to the isolated electrical

(a) (b) IM1 *i* qIM1 *i* dIM1 *i* IM <sup>2</sup> *i* qIM<sup>2</sup> *i* dIM<sup>2</sup> *i*

The terminal voltage is momentary decreased (Fig. 4a) and after few damped oscillations reached minimal value. However, the high starting currents are appeared. High inrush current, in the first moments, as one can see in Figure 5, reaches the magnitude of the first oscillation of 1.73 p.u. The air-gap torque of the second induction motor *T*eIM2 momentarily

At the moment of switching on to the grid, the second induction motor begins to accelerate and oscillations are present in its transients of air-gap torque during the acceleration period. At the time of the starting of second induction motor (IM2), the reverse torque impulse of 0.31 p.u. in air-gap torque of the first one (IM1) is appeared but decayed rapidly. As the torque of the first induction motor becomes negative motor speed slows down. Thereafter, damped oscillations that are present in the response of electromagnetic torque of the first motor as well as oscillations in electromagnetic torque of the second one are stifled at the

At the beginning of the start-up period of the second motor, the speed of the first one decreases and afterwards recovers. Overshoot in the speed transient occurs at the end of Thus, in the second case, the dynamics of the starting of loaded induction motors is analyzed, however, the load on the first one is *T*lIM1=0.15 p.u. while *T*lIM2=0.2 p.u. is applied on the second one. In this case the acceleration time is longer than in the previous case when motors are started unloaded (Fig. 4a), the voltage of synchronous generator is recovering slower, and will be lower then 80%*U*n during greater part of start up period, as presented in Fig. 4b.

The initial part of the transients of electromagnetic torque is equal in both cases (load and non-load condition). At the time of the starting of the first induction motor the torque *T*eIM1 reaches a value of 0.86 (p.u.).

At the instant of connection to power supply the instantaneous torque is independent of the balanced source voltages because the machine is symmetrical, even air-gap torque depends upon the values of source voltages though the stator currents. In addition, the air-gap torque oscillates with higher magnitude, about lower average then in case of unloaded motor. These oscillations are damped at the end of the start-up period of the induction motor as presented in Figure 4b.

The component of air-gap torque, which appears because of mutual acting of free currents in stator as well as in rotor windings acts as counter torque on motors shaft and disappears before the end of the run-up. As one can see in Fig 4 the duration of the start-up of both induction motors is longer than in the previous case, in which the motors run-up unloaded. Thus, this acceleration period of second induction motor is 500 ms, while in the previous case lasted 230 ms. In Fig. 5b stator currents, in *dq* axis, and their components, during start up of loaded induction motor, are presented. As the induction motor is directly connected to the terminals of unloaded synchronous generator that means that stator current of induction motor is at the same time the armature current of synchronous generator.

At the beginning of the transient phenomena inrush current which appears during the first half period is dominating but disappears quickly. After initial damping, oscillations of free currents will continue with slightly greater magnitude than at the beginning of transients. These currents, which also can be seen during the start up period of unloaded induction motor, disappear at the end of start up. Corresponding stator flux linkage, during direct-online starting of unloaded and loaded induction motor are presented in Fig. 6.

The transients of the first induction motor current in *abc* coordinate system (*i*abcIM1), in both cases, are presented in Fig. 7. The current of synchronous generator (*i*abcSG), in both cases, is presented in Fig. 8. This is the total current that motors draw from the electrical grid.

The phenomena of voltage and frequency deviation are typical for isolated electrical grid which in turn affects the quality of electric power systems. The short-term frequency deviation, during direct-on-line starting unloaded and loaded induction motors are presented in Figure 9. There is relatively strong electrical coupling between synchronous

generator and loads as well as torsional strains in the shaft line. However, the torque in the coupling for both cases is presented in Figure 10. Oscillations in transients of torsion torque are longer present during direct-on-line starting loaded induction motor and damped at the end of start-up period.

The Dynamics of Induction Motor Fed Directly from the Isolated Electrical Grid 83

**Figure 8.** Stator current (*i*abcSG) of the grid (synchronous generator), during direct-on-line starting of:

(a) (b) *<sup>i</sup>*aSG *<sup>i</sup>*bSG *<sup>i</sup>*cSG

*fa*-motors are unloaded,

*fb* -motors are

a) unloaded b) loaded induction motors

**Figure 9.** Frequency variations during direct-on-line starting:

loaded

**Figure 6.** Transients of stator flux linkages of induction motors (IM1, IM2) and their components in *d* (*d*IM1, *d*IM2) and *q* (*q*IM1, *<sup>q</sup>*IM2) axis during direct-on-line starting of: a) unloaded b) loaded induction motors

**Figure 7.** Stator current (*i*abcIM1) of first induction motor, during direct-on-line starting of: a) unloaded b) loaded induction motors

**Figure 6.** Transients of stator flux linkages of induction motors (

end of start-up period.

(*d*IM1, 

motors

*d*IM2) and *q* (

b) loaded induction motors

*q*IM1, 

generator and loads as well as torsional strains in the shaft line. However, the torque in the coupling for both cases is presented in Figure 10. Oscillations in transients of torsion torque are longer present during direct-on-line starting loaded induction motor and damped at the

> IM1,

(a) (b) *Ψ*IM1 *Ψ*dIM1 *Ψ*qIM1 *Ψ*IM<sup>2</sup> *Ψ*dIM<sup>2</sup> *Ψ*qIM<sup>2</sup>

*<sup>q</sup>*IM2) axis during direct-on-line starting of: a) unloaded b) loaded induction

**Figure 7.** Stator current (*i*abcIM1) of first induction motor, during direct-on-line starting of: a) unloaded

(a) (b) aIM<sup>1</sup> *<sup>i</sup>* bIM<sup>1</sup> *<sup>i</sup>* cIM<sup>1</sup> *<sup>i</sup>*

IM2) and their components in *d*

**Figure 8.** Stator current (*i*abcSG) of the grid (synchronous generator), during direct-on-line starting of: a) unloaded b) loaded induction motors

**Figure 9.** Frequency variations during direct-on-line starting: *fa*-motors are unloaded, *fb* -motors are loaded

The Dynamics of Induction Motor Fed Directly from the Isolated Electrical Grid 85

IM1, 

IM2); during sudden

IM1,

is decreasing again. The speed of the first induction motor is recovering with strongly damped oscillations at the end of start-up period of the second induction motor (Fig. 11a

**Figure 11.** Transients of: air-gap torque (*T*eIM1, *T*eIM2) and speed transient of induction motors (

(a) (b) eIM1 *w*IM1 *T T*eIM2 *w*IM2

IM2); during sudden change load: a) impact load b) load disconnected

**Figure 12.** Transients of: air-gap torque (*T*eIM1, *T*eIM2) and speed transient (

Transients of stator currents of induction motors and their components, for both cases, are presented in Figure 13. The current of the first motor, at the moment of connection IM2,

(a) (b) eIM1 *w*IM1 *T T*eIM2 *w*IM2

change load: a) impact load b) load disconnected, detail of Fig. 11.

and Fig. 12a).

**Figure 10.** Torsional torque during direct-on-line starting: Tta-motors are unloaded, *T*tb-motors are loaded
