• No results found

Unbalanced and Fluctuated Voltages in the Literature

Perfect balanced voltages can never be maintained, because the loads are continually changing, causing the phase-voltage unbalance to vary continually [44]. Unbalanced voltages can cause serious problems that can bring any induction motor to a premature failure. The severe effect of voltage unbalance on the performance of the induction motors was the area of interest of many researchers since 1930’s of the last century [45] when Reed and Koopman tried to analyze the performance of three-phase induction motors operating under unbalanced voltages by using the equivalent circuit and symmetrical components. In the 1950’s, few researchers presented other useful approaches to the same issue [46] [47] [48] [49].

In [50], Gafford et al. concluded that the temperature rise above balanced operating temperature is due to increased copper loss. It was demonstrated that the negative sequence

13

current has a significant effect in terms of heating the motor, rather than an equal value of positive sequence, and that is due to the high negative sequence rotor resistance. It was also proven that core losses and friction and windage losses remain essentially independent of unbalance of negative sequence voltage that is less than 15%. It was also observed that negative sequence components cause vibration that may be injurious to bearings, to insulation, and to interconnecting mechanical parts of the machine.

The study in [51] by Berndt and Schmitz examined three 5 hp, 220 volts, 1800 rpm, NEMA design type B motors, from different manufacturers which were tested for temperature rise. To derate the machines, they were run under fixed unbalance and different loads. Two different methods were used to measure the winding temperature: (a) Change in winding resistance; and (b) thermocouples. The exact temperature at shut-off was extrapolated by having many resistance measurements for different elapsed time readings. 14 thermocouples were used to determine the hot spots. The negative sequence voltage was the main parameter that was used to derate the three motors. This study concluded that there is a need for a severe reduction in the rating of induction motors when operated with unbalanced line voltages.

In [34], Woll presented an important curve which shows the relationship between the percentage of voltage unbalance and the percentage of increase of motor losses and motor heating as shown in Figure 1-5. The motor heating curve in Figure 1-5 was drawn according to (1.4).

%∆T~(%∆VU)2 DisplayText cannot span more than one line!

where %∆T is the percentage increase of temperature, and %∆VU is the percentage increase in voltage unbalance.

14

Kersting and Phillips in [52] conducted a practical study which showed that “It is not sufficient to merely know the percent voltage unbalance, but it is equally important to know how they are unbalanced”. In this study, a detailed mathematical technique to analyze the performance of an induction motor under unbalanced voltages. The proposed technique shortened the conventional mathematical equations needed to achieve the same performance analysis on the machine. The study concluded that, beside what mentioned above of the importance of knowing the manner of the unbalanced voltages and its marked effect on the increase in losses, the rotor losses increase at a faster rate than the stator losses as the voltages become more unbalanced. The analysis included only the magnitude of the positive and negative sequence voltages without considering the effect of the angle on the performance of the machines.

The National Electrical Manufacturers Association has set a derating curve in ANSI/NEMA MG 1-2011 (shown in Figure 1-6 ) for medium polyphase induction motors working under unbalanced voltage up to 5% is established.

According to the amount of unbalance, the motor’s rated output power should be multiplied by the derating factor, obtained from the curve, to have a new reduced full-load value that makes the motor running safely without the risk of overheating that is caused by the effect of unbalanced voltage if the motor kept running with its rated output power.

15

Lee claimed in [43] that the derating factor given by NEMA in Figure 1-6 is set in accordance only with voltage unbalance factor (VUF), without considering the many voltage unbalance cases which have the same VUF. The study conducted in [43] investigated 8 voltage unbalanced cases, which are as follows:

(a) Single phase undervoltage unbalance. (b) Two-phase undervoltage unbalance. (c) Three-phase undervoltage unbalance. (d) Single phase overvoltage unbalance. (e) Two-phase overvoltage unbalance. (f) Three-phase overvoltage unbalance. (g) Unequal single phase angle displacement. (h) Unequal two-phase angle displacement.

The study is conducted on 2 different classes of induction motors (2 hp and 3 hp)(1). The study showed that the worst case of temperature rise due to 4% and 6% VUF was with three- phase undervoltage unbalance.

An important study on the derating of induction motors operating with a combination of unbalanced voltages and over or undervoltages was conducted by Pillay and Hofmann in 2002 [33]. In this study, it was found that for a given percentage of voltage unbalance, based on the NEMA definition, there was a range of percentage unbalance, based on the true definition of

(1) The author did not mention the classes of the two machines.

16

unbalance which is the ratio of negative sequence voltage to positive sequence voltage. The derating factor was determined according to (1.5).

Derating Factor=Pout, calculated

Prated (1.5)

The study outcome was a practical extended NEMA derating curve as shown in Figure 1-7. The three curves were obtained from the following three cases:

(a) Case 1: a motor was supplied with unbalanced voltages at rated average voltage.

(b) Case 2: a motor was supplied with 10% overvoltage in combination with unbalanced voltages up to 5%.

(c) Case 3: a motor was supplied with 10% undervoltage in combination with unbalanced voltages up to 5%.

A comparison between graphical and mathematical methods of analyzing the performance of induction motors operated with unbalanced voltages was presented by Huang et al. in [32].

The complex voltage unbalance factor (CVUF) was used by Wang in [53]. This study showed the importance of the angle of the CVUF in analyzing the effect of unbalance on the performance of the induction motors. A method was proposed for determining the value of the

17

angle for the worst cases that could cause a motor to be overheated.

An interesting study conducted by Faiz et al. in [54] suggested that the available definitions of unbalanced voltages are not comprehensive and complete. For example, in an unbalanced voltage case, the phase voltages can have any phase angel, however, in NEMA and IEEE definitions, only the voltage amplitudes have been included. The study also mentioned that in many studies, only general qualitative results were presented and no precise numerical values and characteristics have been provided, and it also claimed that the definition of unbalanced voltage and the resulting motor characteristics have not received attention and that what the study was about to prove. The study showed that an infinite number of line voltages can give the same voltage unbalance as illustrated in Figure 1-8. This figure shows that a 6% voltage unbalance, based on NEMA definition or True definition, will not lead to a unique terminal voltage of the motor. Each of those infinite number of line voltages that belongs to the same value of %VUF has different influence on the performance of the motor.

Two methods were suggested in [54] to reduce the range of input voltage variation for a given VUF. The first method was by specifying the positive sequence voltage component (V1), and the second method was by using the complex voltage unbalance factor (CVUF) which has similar definition of VUF and it is calculated by using (1.6).

18

%CVUF=100×V2

V1 (1.6)

where V1 and V2 are the positive and negative vector components of the voltage, respectively. By using the two methods, the infinite numbers shown in Figure 1-8 were reduced to the

highlighted areas in Figure 1-10. A comparison between the results using NEMA and True definitions and the proposed method was carried out and showed that the variation in pull-out torque, starting torque, full-load torque, and efficiency of a motor under test were very large comparing to the results obtained by using the proposed first method of specifying a value for the positive sequence voltage.

The same author presented a practical example in [36] of induction machine’s derating showing that the value of derating factor was 90% at 2.42% unbalance by using the CUVF, while its value for the same degree of unbalance was 94% using the NEMA derating curve.

A loss of life estimation technique due to operating induction motors on unbalanced voltages with a combination of over or undervoltage were proposed by Pillay and Marubini in [55]. The motor life is predicted by estimating the stator winding insulation life by using Arrhenius’ equations. Five cases were tested and they were as follows:

(a) Case 1: a motor was run at full-load with unbalanced voltages. (b) Case 2: the motor was derated to 95%.

(c) Case 3: the motor was derated to 85%.

(d) Case 4: a motor was run at full-load with 10% overvoltage in combination with 0% to 5% unbalanced voltages.

19

(e) Case 5: the motor run at full-load with 10% undervoltage in combination with 0% to 5% unbalanced voltages.

The loss of life curve produced by the study is illustrated in Figure 1-9. It can be clearly seen that Case 5 is the worst condition that can shorten the life of an induction motor.

In [56] and [42], a research for Gnacinski was published in 2008 and 2009 respectively,

Figure 1-10. Terminal voltage variation of motor for VUF=6%. (a) with V1=230 V, (b) with θ=120o. [54].

20

which investigated the effect of simultaneous voltage unbalance and over or undervoltage on winding temperature and thermal loss of life of induction machines. The influence of angle of the CVUF was considered. The two studies showed that machines’ saturated circuit property has a significant influence on the derating factor in the conditions of unbalanced voltage combined with over or undervoltage.

The latest research in regards to the induction machines derating issue was conducted by Anwari and Hiendro and published in 2010 [57]. In this research, a detailed symmetrical component mathematical procedure has been presented to estimate the efficiency of induction motor operating under unbalanced voltages with their associated phase angles. The only issue within the calculations was that the author didn’t include the core and mechanical losses to estimate the output power of the machine under test.

The author used the complex voltage unbalance factor CVUF instead of VUF. The CVUF was presented as in (1.7).

kv=Vs2

Vs1=kv∠θv (1.7)

where kv is the magnitude of the CVUF and θv is the angle.

It was again shown that for a certain value of kv, there are infinite combinations of terminal voltages. It was proposed to reduce the large range of terminal voltage variations by considering the phase angle and a new proposed factor which is called by the author “coefficient of unbalance” which was given the letter “f” and it is shown in (1.8).

Vs1=f(Vab+a.Vbc+a2.Vca

3 ) ∠θs1 (1.8)

where a is the Fortescue operator, a=-1

2+j √3 2, and a 2=-1 2-j √3 2

The study demonstrated an important comparison between the peak losses with balanced voltages when f=1, with under-unbalanced voltages when f<1, and with over-unbalanced voltages when f>1. For the example presented, the increase in the stator losses was 254% and 217%, and the increase in the rotor losses was 293% and 210%, for f=0.8 and f=1.2 respectively. This can indicate clearly that a motor operates in undervoltage unbalance condition can be under

21

high risk of overheating.

Related documents