**4. Induction motor under sudden change load**

The dynamics of sudden change load on the motor shaft is considered. Induction motors are connected directly to the grid, as in previous case, and at chosen moment the first induction motor is starting up, loaded of *T*lIM1 =0.05 p.u. When the first motor has run-up successfully, the second induction motor (IM2) is connected and it starts with *T*lIM2 =0.05 p.u. load on its shaft. Before the second induction motor is connected to the grid the aggregate was led to the steady operation conditions. During start-up of the second induction motor, sudden load change at the first induction motor shaft appeared.

Two cases are considered. In the first case, the impact load of additional 0.1 p.u. on the first induction motor IM1, is applied. While in the second case, the motor is suddenly unloaded, 0.05 p.u. is disconnected from its shaft. Thus, after disconnecting the load the first induction motor run at idle. Transients of air-gap torque and speed transient of induction motors for both cases are presented in Figure 11 and 12.

Direct on line starting of induction motors induces high strain on the power system. This strain arises when the second motor is connected, and additionally is growing up at the instant of impact 0.1 p.u. load on the first motor shaft. When the second induction motor is connected to the grid, it begins to accelerate and the torque of the first induction motor is changed. The electromagnetic torque of the first induction motor becomes negative and motor speed slows down, achieving about 0.95 p.u. Later on, the speed of the first induction motor starts recovery. At the instant of impact additional load on the motor shaft the speed 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 and Fig. 12a).

84 Induction Motors – Modelling and Control

loaded

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

The dynamics of sudden change load on the motor shaft is considered. Induction motors are connected directly to the grid, as in previous case, and at chosen moment the first induction motor is starting up, loaded of *T*lIM1 =0.05 p.u. When the first motor has run-up successfully, the second induction motor (IM2) is connected and it starts with *T*lIM2 =0.05 p.u. load on its shaft. Before the second induction motor is connected to the grid the aggregate was led to the steady operation conditions. During start-up of the second induction motor, sudden

Two cases are considered. In the first case, the impact load of additional 0.1 p.u. on the first induction motor IM1, is applied. While in the second case, the motor is suddenly unloaded, 0.05 p.u. is disconnected from its shaft. Thus, after disconnecting the load the first induction motor run at idle. Transients of air-gap torque and speed transient of induction motors for

Direct on line starting of induction motors induces high strain on the power system. This strain arises when the second motor is connected, and additionally is growing up at the instant of impact 0.1 p.u. load on the first motor shaft. When the second induction motor is connected to the grid, it begins to accelerate and the torque of the first induction motor is changed. The electromagnetic torque of the first induction motor becomes negative and motor speed slows down, achieving about 0.95 p.u. Later on, the speed of the first induction motor starts recovery. At the instant of impact additional load on the motor shaft the speed

**4. Induction motor under sudden change load** 

load change at the first induction motor shaft appeared.

both cases are presented in Figure 11 and 12.

**Figure 11.** Transients of: air-gap torque (*T*eIM1, *T*eIM2) and speed transient of induction motors (IM1, 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 (IM1, IM2); during sudden change load: a) impact load b) load disconnected, detail of Fig. 11.

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, momentarily increases to 0.31 p.u. and then, with damped oscillation tend to decrease. At the moment of impact additional load the current of the first induction motor is growing up (Fig. 13a). Air-gap torque of the first induction motor, after short term negative value of 0.27 p.u., oscillate about the positive average and tend to decrease.

The Dynamics of Induction Motor Fed Directly from the Isolated Electrical Grid 87

induction motor continues recovering the whole start-up period of the second induction motor (Fig. 11b). At the moment of sudden unload, the current of the first motor continues decreasing and with damped oscillation reaches steady state (Fig. 13b). Air-gap torque of the first induction motor continues decreasing reaches steady state faster than in the first

The inrush current that is appeared at the beginning of the start-up period of the second induction tends to reducing, and after the first induction motor is suddenly unloaded continues decreasing (Fig. 13b). Oscillations in transients of air-gap torque are shorter present and are damped at the end of start up period of the second induction motor, as one can see in figure (Fig. 12b). Corresponding transients of stator flux linkage, in both cases, are presented in Fig. 14. As the grid is unloaded the voltage is recovered, and start-up period of

**Figure 14.** Transients of stator flux linkages of induction motors (*Ψ*IM1, *Ψ*IM2) and their components in d

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

The transients of the first induction motor current in *abc* coordinate system (*i*abcIM1), in both cases, are presented in Fig. 15, while the current of synchronous generator (*i*abcSG) is

Frequency variation during sudden change load is presented in Figure 17 and, as one can see, that impact load on the motor shaft results in short-term frequency decreasing. When load is switched off, short-term increase of frequency is appeared. Sudden change load affects on speed of aggregate and torque in the coupling, for both cases, is presented in

case, in case of sudden impact load (Fig. 12b).

the second induction motor is now shorter, it takes about 260 ms.

(*Ψ*dIM1, *Ψ*dIM2) and *q* (*Ψ*qIM1, *Ψ*qIM2) axis during sudden change load:

a) impact load b) load disconnected

presented in Fig. 16.

Figure 18.

**Figure 13.** Transients of stator currents of induction motors (*i*IM1, *i*IM2) and their components in *d* (*i*dIM1, *i*dIM2) and *q* (*i*qIM1, *i*qIM2) axis during sudden change load: a) impact load b) load disconnected

Thereafter, the air-gap torque is increased, oscillates about the higher positive average then before impact additional load. The electromagnetic torque, as one can see in Fig. 12a, with damped oscillation reaches maximal value of 0.2 p.u. at the end of the start up period of the second induction motor.

The inrush current that is appeared at the beginning of the start-up period of the second induction motor reaches the magnitude of the first oscillation of 1.73 p.u. This current causes the voltage drop at the motor terminals that are connected on the same grid as the second one. The voltage drop results that the motor speed slows down. Because the motor rotor slows down the higher current is appeared on the grid and voltage are reduced even more.

As the additional load is connected the voltage is slowly recovered and start-up period of the second induction motor takes 300 ms.

In the second case, the motor is suddenly unloaded, 0.05 p.u. is disconnected from its shaft at the beginning of the start-up period of the second induction motor. After starting, the second motor begins to accelerate and the torque of the first one is changed, as mentioned before it becomes negative and motor speed slows down. Thereafter, the speed of the first induction motor continues recovering the whole start-up period of the second induction motor (Fig. 11b). At the moment of sudden unload, the current of the first motor continues decreasing and with damped oscillation reaches steady state (Fig. 13b). Air-gap torque of the first induction motor continues decreasing reaches steady state faster than in the first case, in case of sudden impact load (Fig. 12b).

86 Induction Motors – Modelling and Control

second induction motor.

the second induction motor takes 300 ms.

more.

momentarily increases to 0.31 p.u. and then, with damped oscillation tend to decrease. At the moment of impact additional load the current of the first induction motor is growing up (Fig. 13a). Air-gap torque of the first induction motor, after short term negative value of 0.27

**Figure 13.** Transients of stator currents of induction motors (*i*IM1, *i*IM2) and their components in *d* (*i*dIM1,

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

Thereafter, the air-gap torque is increased, oscillates about the higher positive average then before impact additional load. The electromagnetic torque, as one can see in Fig. 12a, with damped oscillation reaches maximal value of 0.2 p.u. at the end of the start up period of the

The inrush current that is appeared at the beginning of the start-up period of the second induction motor reaches the magnitude of the first oscillation of 1.73 p.u. This current causes the voltage drop at the motor terminals that are connected on the same grid as the second one. The voltage drop results that the motor speed slows down. Because the motor rotor slows down the higher current is appeared on the grid and voltage are reduced even

As the additional load is connected the voltage is slowly recovered and start-up period of

In the second case, the motor is suddenly unloaded, 0.05 p.u. is disconnected from its shaft at the beginning of the start-up period of the second induction motor. After starting, the second motor begins to accelerate and the torque of the first one is changed, as mentioned before it becomes negative and motor speed slows down. Thereafter, the speed of the first

*i*dIM2) and *q* (*i*qIM1, *i*qIM2) axis during sudden change load: a) impact load b) load disconnected

p.u., oscillate about the positive average and tend to decrease.

The inrush current that is appeared at the beginning of the start-up period of the second induction tends to reducing, and after the first induction motor is suddenly unloaded continues decreasing (Fig. 13b). Oscillations in transients of air-gap torque are shorter present and are damped at the end of start up period of the second induction motor, as one can see in figure (Fig. 12b). Corresponding transients of stator flux linkage, in both cases, are presented in Fig. 14. As the grid is unloaded the voltage is recovered, and start-up period of the second induction motor is now shorter, it takes about 260 ms.

**Figure 14.** Transients of stator flux linkages of induction motors (*Ψ*IM1, *Ψ*IM2) and their components in d (*Ψ*dIM1, *Ψ*dIM2) and *q* (*Ψ*qIM1, *Ψ*qIM2) axis during sudden change load: a) impact load b) load disconnected

The transients of the first induction motor current in *abc* coordinate system (*i*abcIM1), in both cases, are presented in Fig. 15, while the current of synchronous generator (*i*abcSG) is presented in Fig. 16.

Frequency variation during sudden change load is presented in Figure 17 and, as one can see, that impact load on the motor shaft results in short-term frequency decreasing. When load is switched off, short-term increase of frequency is appeared. Sudden change load affects on speed of aggregate and torque in the coupling, for both cases, is presented in Figure 18.

The Dynamics of Induction Motor Fed Directly from the Isolated Electrical Grid 89

**Figure 18.** Torsional torque during sudden change load: *T*ta-impact load, *T*tb-load disconnected

With the aim to get a better insight into the dynamics of induction motor fed directly from the isolated electrical grid the short-term interruptions in the motor power supply are

**5. Induction motor under short term voltage interruption** 

considered.

*fa*–impact load*,* 

*fb-*load disconnected

**Figure 17.** Frequency variations during sudden change load:

**Figure 15.** Stator current (*i*abcIM1) of first induction motor, during sudden change load: a) impact load b) load disconnected

**Figure 16.** Stator current (*i*abcSG) of the grid (synchronous generator), during sudden change load: a) impact load b) load disconnected

b) load disconnected

a) impact load b) load disconnected

**Figure 15.** Stator current (*i*abcIM1) of first induction motor, during sudden change load: a) impact load

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

**Figure 16.** Stator current (*i*abcSG) of the grid (synchronous generator), during sudden change load:

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

**Figure 17.** Frequency variations during sudden change load: *fa*–impact load*, fb-*load disconnected

**Figure 18.** Torsional torque during sudden change load: *T*ta-impact load, *T*tb-load disconnected

### **5. Induction motor under short term voltage interruption**

With the aim to get a better insight into the dynamics of induction motor fed directly from the isolated electrical grid the short-term interruptions in the motor power supply are considered.

Direct starting of induction motors on an isolated electrical grid produce disturbance for supply network and local consumers. This disturbance, such as voltage dips and reduction of aggregate speed, will cause decrease of network power quality. The significant voltage dips appear due to faults in power supply, and also, due to certain faults on loads connected to the isolated electrical grid. These voltage dips cause changes in transients of induction motors, as well as in transients of diesel generator unit. Besides the voltage dips, voltage interruption can also appear, which further effects the operation of the induction motor.

The Dynamics of Induction Motor Fed Directly from the Isolated Electrical Grid 91

IM1, IM2)

**Figure 19.** 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

**Figure 20.** Transients of stator currents of induction motors (*i*IM1, *i*IM2) and their components in *d* (*i*dIM1, *i*dIM2) and *q* (*i*qIM1, *i*qIM2) axis during the short-term interruptions: a) motors are in steady state condition

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

In the second case, interruption in the first induction motor power supply appeared at the

At the time of connecting the second induction motor, the current is momentarily increased to 1.7 p.u. and has a decreasing tendency. By the time of short term power interruption on

during the short-term interruptions that is appeared on the first induction

b) at the beginning of the start up period of the second one

beginning of the start up period of the second induction motor.

Two cases are considered. In the first case, a short term interruption appeared after both motors have run-up successfully. In that moment motors are in steady state condition. In the second case, interruption of power supply on the first induction motor appeared at the beginning of the start up period of the second one.

Motors are started loaded and load on the first induction motor shaft is 0.1 p.u., while the load of 0.05 p.u. is applied on the second induction motor shaft. At the beginning, the first induction motor (IM1) starts and after it has run-up successfully, the second one (IM2) is connected to the grid. At the chosen moment, as motors are in steady state condition, the first induction motor is shortly disconnected from the network, and then, after 100 ms reconnected to the power supply (Fig. 19 and 20).

At the time of voltage interruption, a large negative impulse of the torque of the first induction motor occurs. This reverse torque impulse rapidly decays and the air-gap torque (*T*eIM1) becomes equal to zero. Changes in the electromagnetic torque of the second induction motor (*T*eIM2) occurs at the time of disconnection of the first one.

Transients of air-gap torque and speed transient of induction motors; during the short-term interruptions that is appeared on the first induction motor, in case of steady state condition is presented in Figure 19a. However, in Figure 19b, the transients obtain in case of interruption in the first induction motor power supply that appeared at the beginning of the start up period of the second induction motor is presented. Transients of stator currents of induction motors and their components in *d* and *q* axis during the short-term interruptions, for both cases are presented in figure 20.

As one can see in Fig. 20a, at the time of voltage interruption, current of the first induction motor momentarily reaches approximately 2 p.u., while current of the second one reaches approximately 0.6 p.u. Thus, by restoring the supply, at the beginning of the transients the current of the first induction motor momentarily reaches 2 p.u., at the same time as the current of the second induction motor reaches maximal value of 0.35 p.u. A negative impulse of the torques *T*eIM1 and *T*eIM2 instantaneously appears. Thus, the speed of the first induction motor at the beginning of the transients additionally is shortly decreased, and afterwards continues recovering.

At the instant of the supply recovery air-gap torque of second induction motor suddenly reaches negative value and, as one can see in Fig. 21a, the speed of second induction motor is decreased and than rapidly recovers.

beginning of the start up period of the second one.

reconnected to the power supply (Fig. 19 and 20).

for both cases are presented in figure 20.

afterwards continues recovering.

is decreased and than rapidly recovers.

motor (*T*eIM2) occurs at the time of disconnection of the first one.

motor.

Direct starting of induction motors on an isolated electrical grid produce disturbance for supply network and local consumers. This disturbance, such as voltage dips and reduction of aggregate speed, will cause decrease of network power quality. The significant voltage dips appear due to faults in power supply, and also, due to certain faults on loads connected to the isolated electrical grid. These voltage dips cause changes in transients of induction motors, as well as in transients of diesel generator unit. Besides the voltage dips, voltage interruption can also appear, which further effects the operation of the induction

Two cases are considered. In the first case, a short term interruption appeared after both motors have run-up successfully. In that moment motors are in steady state condition. In the second case, interruption of power supply on the first induction motor appeared at the

Motors are started loaded and load on the first induction motor shaft is 0.1 p.u., while the load of 0.05 p.u. is applied on the second induction motor shaft. At the beginning, the first induction motor (IM1) starts and after it has run-up successfully, the second one (IM2) is connected to the grid. At the chosen moment, as motors are in steady state condition, the first induction motor is shortly disconnected from the network, and then, after 100 ms

At the time of voltage interruption, a large negative impulse of the torque of the first induction motor occurs. This reverse torque impulse rapidly decays and the air-gap torque (*T*eIM1) becomes equal to zero. Changes in the electromagnetic torque of the second induction

Transients of air-gap torque and speed transient of induction motors; during the short-term interruptions that is appeared on the first induction motor, in case of steady state condition is presented in Figure 19a. However, in Figure 19b, the transients obtain in case of interruption in the first induction motor power supply that appeared at the beginning of the start up period of the second induction motor is presented. Transients of stator currents of induction motors and their components in *d* and *q* axis during the short-term interruptions,

As one can see in Fig. 20a, at the time of voltage interruption, current of the first induction motor momentarily reaches approximately 2 p.u., while current of the second one reaches approximately 0.6 p.u. Thus, by restoring the supply, at the beginning of the transients the current of the first induction motor momentarily reaches 2 p.u., at the same time as the current of the second induction motor reaches maximal value of 0.35 p.u. A negative impulse of the torques *T*eIM1 and *T*eIM2 instantaneously appears. Thus, the speed of the first induction motor at the beginning of the transients additionally is shortly decreased, and

At the instant of the supply recovery air-gap torque of second induction motor suddenly reaches negative value and, as one can see in Fig. 21a, the speed of second induction motor

**Figure 19.** Transients of: air-gap torque (*T*eIM1, *T*eIM2) and speed transient of induction motors (IM1, IM2) during the short-term interruptions that is appeared on the first induction

**Figure 20.** Transients of stator currents of induction motors (*i*IM1, *i*IM2) and their components in *d* (*i*dIM1, *i*dIM2) and *q* (*i*qIM1, *i*qIM2) axis during the short-term interruptions: a) motors are in steady state condition b) at the beginning of the start up period of the second one

In the second case, interruption in the first induction motor power supply appeared at the beginning of the start up period of the second induction motor.

At the time of connecting the second induction motor, the current is momentarily increased to 1.7 p.u. and has a decreasing tendency. By the time of short term power interruption on the first induction motor, the current of the second one suddenly increases to 2.2 p.u. Further, the current oscillates around a higher average value than before and the damped oscillations are rapidly decreasing (Fig. 20b).

The Dynamics of Induction Motor Fed Directly from the Isolated Electrical Grid 93

**Figure 22.** Voltage (*u*abcIM1), during the short-term interruptions: a) motors are in steady state condition

(a) (b) *u*aIM 1 *u*bIM 1 *uc* IM1

**Figure 23.** Stator current (*i*abcIM1) of first induction motor, during the short-term interruptions: a) motors

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

Sudden impact load on the isolated electrical grid induces a large strain on the diesel generator unit shaft. After the first induction motor is started, the diesel engine accepts the load and later reaches the steady speed. As a result of the starting of the loaded IM2, the speed of the diesel engine decreased and reached a minimum value of 0.97 p.u., while the

are in steady state condition b) at the beginning of the start up period of the second one

speed of the synchronous generator reached a value of about 0.96 p.u. (Fig. 24a).

b) at the beginning of the start up period of the second one

The transient of air-gap torque of induction motors are presented in Fig. 21. However, the air-gap torque of the first induction motor, at the time of voltage interruption occurred, momentarily reaches negative impulse of approximately 0.6 p.u. (Fig. 21b). The speed of the first induction motor (IM1) decreases at the beginning of the start up period of the second induction motor and tend to increase when fault occurs. As voltage interruption occurred the speed continuous reducing. In the speed transient of the second induction motor (IM2) one can see that is short term decreased appeared at the beginning of interruption and after that the motor continuous accelerates.

**Figure 21.** Transient of electromagnetic torque (*T*eIM1, *T*eIM2) and speed transient of induction motors (IM1, IM2); during the short-term interruptions: a) motors are in steady state condition b) at the beginning of the start up period of the second one detail of Fig. 20.

Terminal voltage (*u*abcIM1) of the first induction motor, during the short-term interruptions, for the both cases is presented in Figure 22, while corresponding stator currents (*i*abcIM1) of first induction motor are shown in Figure 23.

The voltage dips as well as voltage interruption, which further effects the operation of the induction motor, causes changes in transients of diesel generator unit. A short-term power interruption will result, as shown, in significant changes of electrical and mechanical variables and will also cause torsional strain in the shaft line. The mechanical coupling of a diesel engine and a synchronous generator is considered to be a rotating system with two concentrated masses that are connected by flexible coupling. The flexible coupling allows these masses to rotate at a different speed in transients. Thus, in Fig. 24 the speed transients of diesel engine and synchronous generator are presented, while torque at coupling zone is presented in Figure 26.

oscillations are rapidly decreasing (Fig. 20b).

that the motor continuous accelerates.

(IM1, 

the first induction motor, the current of the second one suddenly increases to 2.2 p.u. Further, the current oscillates around a higher average value than before and the damped

The transient of air-gap torque of induction motors are presented in Fig. 21. However, the air-gap torque of the first induction motor, at the time of voltage interruption occurred, momentarily reaches negative impulse of approximately 0.6 p.u. (Fig. 21b). The speed of the first induction motor (IM1) decreases at the beginning of the start up period of the second induction motor and tend to increase when fault occurs. As voltage interruption occurred the speed continuous reducing. In the speed transient of the second induction motor (IM2) one can see that is short term decreased appeared at the beginning of interruption and after

**Figure 21.** Transient of electromagnetic torque (*T*eIM1, *T*eIM2) and speed transient of induction motors

beginning of the start up period of the second one detail of Fig. 20.

first induction motor are shown in Figure 23.

presented in Figure 26.

IM2); during the short-term interruptions: a) motors are in steady state condition b) at the

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

Terminal voltage (*u*abcIM1) of the first induction motor, during the short-term interruptions, for the both cases is presented in Figure 22, while corresponding stator currents (*i*abcIM1) of

The voltage dips as well as voltage interruption, which further effects the operation of the induction motor, causes changes in transients of diesel generator unit. A short-term power interruption will result, as shown, in significant changes of electrical and mechanical variables and will also cause torsional strain in the shaft line. The mechanical coupling of a diesel engine and a synchronous generator is considered to be a rotating system with two concentrated masses that are connected by flexible coupling. The flexible coupling allows these masses to rotate at a different speed in transients. Thus, in Fig. 24 the speed transients of diesel engine and synchronous generator are presented, while torque at coupling zone is

**Figure 22.** Voltage (*u*abcIM1), during the short-term interruptions: a) motors are in steady state condition b) at the beginning of the start up period of the second one

**Figure 23.** Stator current (*i*abcIM1) of first induction motor, during the short-term interruptions: a) motors are in steady state condition b) at the beginning of the start up period of the second one

Sudden impact load on the isolated electrical grid induces a large strain on the diesel generator unit shaft. After the first induction motor is started, the diesel engine accepts the load and later reaches the steady speed. As a result of the starting of the loaded IM2, the speed of the diesel engine decreased and reached a minimum value of 0.97 p.u., while the speed of the synchronous generator reached a value of about 0.96 p.u. (Fig. 24a).

The Dynamics of Induction Motor Fed Directly from the Isolated Electrical Grid 95

**Figure 26.** Transient of torsional torque during short-term interruptions:

period of the second induction motor, as one can see in Figure 26.

**6. Discussion** 

*T*ta-motors are in steady state condition, *T*tb- at the beginning of the start up period of the second one

Occurrence of short-term power loss, at the time that motors are in steady state condition, speed of both machines increased. After, reconnected to the power supply the speed of synchronous generator as well as induction motor is reduced. Damped oscillations are presented during transients. In the second case, when the short-term interruption occurs at the beginning of the start up period of the second induction motor, speed of both machines continue decrease. In this case, the speed of synchronous generator is reduced to less of 0.92 p.u., while the speed of the diesel engine is reduced to less of 0.94 p.u. The oscillations appear with greater magnitude then in previous case. Speed deviation affects on frequency of grid and frequency variations during short-term interruptions, for both cases are presented in Figure 25. Significant disturbances appear in transients of torsional torque especially in case when short-term interruptions is appear at the beginning of the start up

The dynamics of induction motors fed directly from the isolated electrical grid is considered in the cases of: direct-on-line starting of induction motors, sudden change load on the motor shaft and during short-term voltage interruptions. Direct on line starting of induction motors on the isolated power system is the most difficult transition regime for units due to electricity loads and also due to torsional loads on the shaft line. The autonomous operation of the synchronous generator is characterized by a change in steady state which causes a change in voltage and frequency, which in turn affects the quality of electric power systems. During starting induction motors draw high starting current, known as locked rotor current,

**Figure 24.** Speed transient of synchronous generator (SG) and diesel engine (DM) during the shortterm interruptions: a) motors are in steady state condition b) at the beginning of the start up period of the second one

**Figure 25.** Frequency variations during short-term interruptions: *fa-* motors are in steady state condition, *fb-* at the beginning of the start up period of the second one

**Figure 26.** Transient of torsional torque during short-term interruptions: *T*ta-motors are in steady state condition, *T*tb- at the beginning of the start up period of the second one

Occurrence of short-term power loss, at the time that motors are in steady state condition, speed of both machines increased. After, reconnected to the power supply the speed of synchronous generator as well as induction motor is reduced. Damped oscillations are presented during transients. In the second case, when the short-term interruption occurs at the beginning of the start up period of the second induction motor, speed of both machines continue decrease. In this case, the speed of synchronous generator is reduced to less of 0.92 p.u., while the speed of the diesel engine is reduced to less of 0.94 p.u. The oscillations appear with greater magnitude then in previous case. Speed deviation affects on frequency of grid and frequency variations during short-term interruptions, for both cases are presented in Figure 25. Significant disturbances appear in transients of torsional torque especially in case when short-term interruptions is appear at the beginning of the start up period of the second induction motor, as one can see in Figure 26.

### **6. Discussion**

94 Induction Motors – Modelling and Control

**Figure 24.** Speed transient of synchronous generator (

**Figure 25.** Frequency variations during short-term interruptions:

*fb-* at the beginning of the start up period of the second one

the second one

condition,

(a) (b) *<sup>w</sup>*SG *<sup>w</sup>*DM

term interruptions: a) motors are in steady state condition b) at the beginning of the start up period of

SG) and diesel engine (

*fa-* motors are in steady state

DM) during the short-

The dynamics of induction motors fed directly from the isolated electrical grid is considered in the cases of: direct-on-line starting of induction motors, sudden change load on the motor shaft and during short-term voltage interruptions. Direct on line starting of induction motors on the isolated power system is the most difficult transition regime for units due to electricity loads and also due to torsional loads on the shaft line. The autonomous operation of the synchronous generator is characterized by a change in steady state which causes a change in voltage and frequency, which in turn affects the quality of electric power systems. During starting induction motors draw high starting current, known as locked rotor current, which are several times the normal full load current of the motor. This current causes a significant voltage dip on the isolated electrical grid, the terminal voltage is momentary decreased and after few damped oscillations reached minimal value. During this short period the voltage regulator does not affect jet. The voltage drop increases in case of starting loaded induction motor, the current momentarily reaches higher value of first magnitude and oscillates about higher average value than in previous case.

The Dynamics of Induction Motor Fed Directly from the Isolated Electrical Grid 97

Sudden changes of active power have impact on both voltage and frequency but a start-up of electric motor influences disproportionately the voltage value due to relatively low power

The dynamics of induction motors fed directly from the isolated electrical grid is analyzed. In isolated electrical grid, such as for example ship's electrical grid, the main source is a diesel generator and induction motors are the most common loads. Induction machine plays a very important role in that application and a significant number of induction motors are used at critical points of on board processes. The connection of large induction motors (large relative to the generator capacity) to that grid is difficult transient regime for units due to electrical loads and also due to torsional loads on the shaft line. Direct on line starting of induction motors induces high strain on the power system and this strain arises when the next induction motor is connected to the grid. Sudden impact load on the induction motors shaft is an additional strain on the network, especially when impact load on a motor shaft occurs during start up of another one. This in turn affects the quality of electric power system and thus, the dynamic behavior of induction motors. The significant voltage dips appear due to faults in power supply, and also, due to certain faults on loads connected to the isolated electrical grid. These voltage dips cause changes in transients of induction motors, as well as in transients of diesel generator unit. Besides the voltage dips, voltage interruption can also appear, which further effects the operation of the induction motor. Factory production tests demonstrate the capability of the unit to supply defined loads applied in a defined sequence. In order to make changes to the loading of an existing isolated electrical grid, it is necessary to analyze and document the effect of the additional loads on its normal and transient performance. An induction motor starting study may be of use in analyzing the performance of small power systems. Such systems are usually served by limited capacity sources that are subject to severe voltage drop problems on motor starting, especially when large motors are involved. In some cases, specific loads must be accelerated in specially controlled conditions, keeping torque values in defined limits. The results obtained by this analysis can be used as a guideline in choosing as well as setting

*University of Dubrovnik, Department of Electrical Engineering and Computing, Croatia* 

The presented results are carried out through the researches within scientific projects "New structures for hydro generating unit dynamic stability improvement" and "Revitalization and operating of hydro generator" supported by Ministry of Science, Education and Sports

factor during the process.

parameters of the protection devices.

**Author details** 

Marija Mirošević

**Acknowledgement** 

in the Republic of Croatia.

**7. Conclusion** 

Disturbances in the system are present when the second induction motor is connected to the grid and additionally is growing up at the instant of impact additional load on the previous induction motor shaft. As load on the motor shaft grows up, the current of the motor is higher; oscillations are more damped and longer present in comparison with lightly load or no-loaded induction motor.

This current causes the voltage drop at the motor terminals that are connected on the same grid. The mutually effect between source and loads exists. The voltage drop results that the motor speed slows down. Because the motor rotor slows down the higher current is appeared on the grid and voltage are reduced even more.

At the instant of starting of induction motors the locked rotor torque appeared and as the rotor starts to rotate the air-gap torque oscillates about positive average value. Oscillations in transient of electromagnetic torque are damped at the end of start up period and finally the steady state condition is attained without oscillations. The oscillations are longer presented in case of bigger load torque on the motor shaft. Sudden change load on the motor shaft causes changes in air-gap torque. Damped oscillations are longer present in a case of impact additional load than during load disconnected. Both cases influence on the electrical grid and changes in transients of both induction motors as well as in synchronous generator are present.

The start-up period of the induction motor is longer when the bigger load torque on the motor shaft is applied. Also, decreasing the terminal voltage causes longer duration of speed transient in dynamics.

Sudden change load on a motor shaft, which occurs during operation period, results in speed change of the other motors that fed from the same grid.

Direct starting of induction motors on isolated electrical grid, as well as sudden change load, caused voltage dips and also reduces speed of aggregate. The significant voltage dips appear due to faults in power supply, as well as certain faults on loads connected to isolated electrical network. Besides the voltage dips, voltage interruption can also appear. This causes significant disturbances on the grid and affects the operation of other induction motor. If interruption of the supply lasts longer than one voltage period, many AC contactors will switch off the motor. However, in some cases, faulty contactor may produce multiple on and off switching. These interruptions affect the dynamics of both electrical and mechanical variables, which will also cause torsional stresses in the shaft line. The consequences of voltage interruption on the induction motor behavior are current and airgap torque peaks that appear at instant of fault and recovery voltage.

Sudden changes of active power have impact on both voltage and frequency but a start-up of electric motor influences disproportionately the voltage value due to relatively low power factor during the process.
