**Author details**

Miloje Kostic

154 Induction Motors – Modelling and Control

(*Pem,Pm*) on the resistance

*sRs*. Consequently, it is:

*em Pm em Pm*

load branch impedance is *Z2,m=√*2*(*

(*sX*σ*s +s*

(5÷20) 

3. If *s*

2. **Regime with maximum input power,** i.e. at *s=sPm*, accrues when resistance

*sXσs+s*

depth of penetration *δr*(*smf1*) ≥ *Hb* -the bar (conductor rotor) height), so it is

and the electromagnetic power (*Pem,m*), in the regime with maximum input power, is:

 

*I RU X X <sup>U</sup> P T*

*sRs+s*

2 2 1 , ,1 2 2

Since for motors with power within the range of 1÷200kW, values for corresponding slip are *sPm* = 0.25÷0.05, respectively, the skin effect in the bars of the squirrel-cage is minor (the

22 2 (0.8 0.95) ( / ) (0.8 0.95) ( ) *s r Pm R s s s s r Pm R Rs ss s r*

, ,1 2 2 2

*sXσs+s*

/ (1.15 1.05) *ss sr N em N*

2 1

Reactive power in the load branch of Г-circuit, under rated condition, *Q2N≈ QLN* (*QLN* – load component of reactive power), can be expressed in terms of the electromagnetic power, *Pem,N*

2 , 2 2 /

*R Rs P P*

, 2

*em N N*

*X X Q P <sup>Q</sup>*

Since the relation between the electromagnetic power (*Pem,N*) and the rating power (*PN*) is:

2 2

 

 

2 2 1

2 *ss s r*

*<sup>U</sup> X X*

 

<sup>2</sup> ,

*<sup>U</sup> R Rs T*

*L sr ss s r*

22 2 2 2

 

, 1

*T*

2

1 1

*s X X XX* 

2

, 1 (0.8 0.95)

(58)

(59)

(60)

*em Pn*

(0.8 0.95) (1.15 1.05) / <sup>2</sup>

2

/ 1

*ss s r N em N LN ss sr N*

 

*R Rs*

( /) 1 *ss sr N*

*sr N N*

*R s s*

 

*Pm ss s r ss s r*

   

*R U Rs PT I s*

2 2

*Pm s r*

2( ) *r s r Pm*

 *X X* 

  /

 

*2Rr /sm*) are equal, i.e., and when the

*X X* 

 

*2Xσr*) is expressed from (A-5), then it is:

(56)

(57)

(0.8 0.95)( ) (0.8 0.95) 2 ( ) 2( )

   

 

(53)

*s*

*2Rr /sm* =

(54)

(55)

 

*2Xσ*r). Corresponding electromagnetic power

*2X*σ*r*) and reactance in load branch (

*2Rr /sm* is:

*em Pm em Pm L s*

*2Rr /sN* is expressed from (A-4), and (

On the base of (A-6) and (A-7), it is obtained:

 

 

 

 

2 2 ,

*X X T R Rs T*

*ss s r em N ss sr N em Pm*

 

*s*

*Electrical Engineering Institute "Nikola Tesla", Belgrade University, Belgrade, Serbia* 

### **6. References**


IEC 60034-30 (2008). *Efficiency classes of single speed three-phase cage induction motors*.


Kostic, M. & Nikolic, A. (August 2010). Negative Consequence of Motor Voltage Asymmetry and Its Influence on the Inefficient Energy Usage, *Wseas Transaction On Circuits And Systems*, Issue 8, Volume 9, August 2010, pp. 547-556.

**Chapter 6** 

© 2012 Krishnan and McCalley, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Krishnan and McCalley, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Role of Induction Motors in Voltage Instability** 

As the power system is being operated in an economic and environment friendly fashion, there is more emphasis on effective resource utilization to supply the ever increasing demand. Consequently system experiences heavy power transaction, and one of the very important stability phenomena, namely voltage stability, is capturing the attention of many power system engineers, operators, researchers, and planners. Concerns for voltage instability and collapse are prompting utilities to better understand the phenomenon so as

Past studies have investigated the intricate relationship that exist between insufficient reactive power support and unreliable system operation including voltage collapses [1, 2, 3, 4], as was observed in 2003 blackout of USA [5]. It is not just the amount of reactive support, but also the quality and placement of reactive support that matters. For instance, it is found that due to the presence of electric loads that are predominantly induction motors the voltage recovery of the system following a severe disturbance is delayed due to lack of fast responding reactive support, thereby threatening to have secondary effects such as undesirable operation of protective relays, electric load disruption, and motor stalling [6, 7]. While a number of techniques have been developed in the past to address the problems of voltage instability [8], there has been little work towards a long term reactive power (VAR) planning (RPP) tool that addresses both steady state as well as dynamic stability issues.

The available reactive power devices can be classified into static and dynamic devices [9]. The static devices include mechanically switched shunt capacitors (MSCs) and series capacitors that exert discrete open-loop control action and require more time delay for correct operation. The dynamic devices are more expensive power electronics based fastacting devices such as static VAR compensators (SVC), Static Synchronous Compensator (STATCOM), Unified Power Flow Controller (UPFCs) that exert continuous feedback

to devise effective, efficient and economic solutions to the problem.

**and Coordinated Reactive Power Planning** 

Venkat Krishnan and James D. McCalley

http://dx.doi.org/10.5772/52480

**1. Introduction** 

Additional information is available at the end of the chapter

