**5. Summary**

The results of the analysis presented in this chapter are summarised in the following.

*A) Effect of voltage magnitude on motor power losses and motor reactive loads* 

The results of the research show dependencies of the input power and reactive load on voltage magnitude, as given in Fig. 2.

	- a. reactive loads decreasing
		- from 1% to 2%, at loads from 100% to 75%, respectively, for motors above100 kW,

Effects of Voltage Quality on Induction Motors' Efficient Energy Usage 153

*C) The most important conclusions regarding motor operation with the non-sinusoidal voltage* 



does not change for higher harmonic frequencies.

shown in Fig. 13, is used (Kostic, 2010):

**Figure 13.** Equivalent Г-circuit of induction machine

*em N em N*

Equation (9) is completely derived in this Appendix.

*s*

**Appendix** 

following:

respectively, and therefore:

*em N em N*

8. The given results show that, at the maximum permitted content of harmonics in supply voltage, *Uh,i* = 5%, *i* = 1 to 37), the percentage of harmonic losses is relatively small:

9. When the induction motors are supplied by rectangular shaped voltage with high levels of harmonic voltages, an increase in harmonic losses in stator and rotor windings are:

The increase in harmonic power losses for lower power motors is much higher than it was noted in the literature (5-10%) because it is (wrongly) believed that the resistance of the rotor

For deriving equations for electromagnetic torque and power, the equivalent Г-circuit,

1. Electromagnetic power (Pem,N) **at rated load**, i.e. at slip s=sN, can be expressed as

2 2 2 2

*I R U Rs P T*

*2Rr/sN = (20÷100)·*

, ,1 2 2 2 2

For motors with power within the range of 1÷200kW, values for sN are 0.05÷0.01,

*sRs* and

 

, ,1 22 2 2

*L sr sr N*

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

*L sr sr N*

2 2 2 2 2

/

(52)

1

 

*N ss s r ss s r N*

*s R R X Rs*

*sXs + s*

*N sr N sr N*

*s R s R s*

( )( /)

1 1

(1.15 1.05) ( / ) (1.15 1.05)( / )

 

/

*2Xr) ≈0.20·*

*s 2Rr/sm.* 

> 

(51)

	- from (-0.1%) to 0.1%%, respectively at loads from 100% to 50%, for motors above100 kW
	- from 0% to 0.6%, respectively at loads from 100% to 25%, for motors about 10 kW,
	- from 0% to 1.6%, respectively, at loads from 100% to 25%, for motors below 1 kW.

## *B) The most important conclusions regarding motor operation with the unbalanced voltage*

	- about 2.109% *PCu,N*, for motors of lower power (< 5 kW), and
	- about 4.256%*PCu,N*, for motors of greater power (> 100 kW).
	- around 30-35% *PCu,N*, for high power motors (> 100 kW), and
	- around 15-20% *PCu,N*, for lower power motors (3–10 kW).

The increase in harmonic power losses for lower power motors is much higher than it was noted in the literature (5-10%) because it is (wrongly) believed that the resistance of the rotor does not change for higher harmonic frequencies.
