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Basamaklı gerilim dalgalarının sincap kafesli motor momentine yaptığı etkilerin incelenmesi

Basamaklı gerilim dalgalarının sincap kafesli motor momentine yaptığı etkilerin incelenmesi

##### Dosyalar

##### Tarih

1993

##### Yazarlar

Mohaddes, Majid

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

Institute of Science and Technology

Institute of Science and Technology

##### Özet

Bu çalışmada, basamaklı gerilim dalgalarının asenkron makinasında meydana getirdikleri harmonik momentleri ve harmonik akımlarının, toplam moment ve toplam akım üze rindeki etkileri incelenmiştir. Harmonik momentleri, basamakların başlangıçlarını be lirleyen &k acılarından etkilenmektedir. Amaç toplam harmonik momentlerinin en etkin olduğu 6 acılarını bul mak ve toplam moment üzerinde meydana getirdiği değişim aralıklarını belirlemektir. Bu çalışmanın i' inci bölümünde eviricilerden kısıca söz edilmişitr. Çalışmanın 2* inci bölümünde ise basa maklı çıkışın en genel halde ve bazı özel durumları için fourier analizi yapılarak harmonik ifadeleri bulunmuştur. Tezin üçüncü bölümünde elde edilen zaman harmoniklerinin eşdeğer devreleri ve 2, 3 ve 4 basamaklı gerilim dalga ları motor terminallerine uygulanarak meydana getirdik leri harmonik moment ve akımları bulunmuştur. Bölüm 2 de ayrıca farklı firmalar tarafından üretilen ve aynı güçte olan iki asenkron motor gözönüne alınmıştır. Seçilen asenkron motorlar aynı güç, gerilim, frekans ve kutup sayısına sahip olmalarına ragmen, aynı kayma değerlerin de farklı momentler üretmektedirler. Bu iki makinanm çalışma şartlarının (moment ve kayma) eşitliği için har monik momentlerinin etkileri kullanılmıştır. Fakat harmonik momentlerinin en etkin olduğu &k tetikleme açılarında bile bu eşitlik sağlanamamıştır. Tezin en son bölümünde iki makinanm çıkış momentlerinin birbi rine eşitlenmesi için, çıkış momenti daha yüksek olan makinanm eşdeğer devrsindeki elemanlarının kayma ile değişimi ve bu değişim sırasında makinanm verimi ve güç katsayıları bulunmuştur.

The performance of induction motor when subjected to a nonsinuBoidal voltage waveform has been analysed by many authors. It has been found that the destruc tive effects of the time harmonics reduces the efficiency of the drive system due to increased additional losses. Many authors have worked on the construction of waveforms and inverter electronics to eliminate the low order harmonics which cannot be filtered by the machine impedance. These works have become successful and found practical applications. Since the semiconductors work as a switch, the output of an inverter circuit is nonsinusoidal and generates harmonics. There &re basicaly two methods to eliminate harmonics: 1. Pulse width modulation 2. Pulse amplitude modulation The first has been studied by many authors and found widely practical applications. Some of these studies sire as follows. Analytical and experimental investigation on steady state and transient behaviour of an induction motor fed from nonsinusoidal power supplies is presented in Cİ3- The analaytical investigations &re based on a direct three phase model developed for this purpose. Simula tion procedure for computing the exact nature obtained from a pulse with modulated (PWM) inverter is described Transient studies exhibiting the effects of specific PWM pattern changing on the induction motors are outlined. In reference E23, traditional PWM ac motor drives perform well over a large speed range and have many positive features demonstrated with their simplicity. However, the waveforms used a.re significantly less than ideal at high modulation depths and low switching rates, especially with regard to harmonically induced motor losses. An improved strategy for digitally pro ducing PWM based on conventional triangulation methods are presented. A new technique for reducing the (viii) harmonic losses resulting from sinusoidal PWM waveform analysed in depth and realised on a 40 KVA inverter. Tests with this inverter on 7.5 KW and İ5 KW motors confirm that the inverters performance is significantly enhanced for certain operating conditions, without any sacrifice. In reference £33» PWM voltage waveforms sre analysed for a motor drive application. The switching patterns are developed in three - phase bridge inverter. The approach is based upon the minimising the harmonic con tent of the current flowing into the motor. PWM waveforms were analysed to obtain loss- optimal PWM waveforms for variable speed induction motor drives. PWM waveforms were induced differently and novel waveforms were demonstrated. Effects of supply voltage waveforms on iron losses were examined in an induction motor in referance £43 and £53. In reference £63 the harmonic torques in an induction motor which is fed from PWM inverter are computed for an unsaturated operation. Their effects on the fun damental harmonic are used to obtain preselected drive conditions given for a different motor. The equivalent circuit of an induction motor is considered for time harmonics and subjected to 2, 4 and 8 PWM voltage waves of equal pulse duration. The induction motors selected having same rating but manufactured by different comp anies, are supplied by PWM waves» have produced differ ent torques and slips. It is shown that the equality of drive parameters { torque and slip ) can be obtained by properly selecting the PWM voltage waveform even if the motors are not identical. As a result of this analysis the functions of the equivalent circuit par - ameters in terms of pulse- width are obtained for given torque and slip. The analysis is proved that an in verter driven induction motor replaced by a spare motor will certainly necessetate to alter the drive condition. The curve of the torque- slip of two different motor are approached one another and in order to avoid such changes to maintain the previous torque and slip values as they were, either the supply waveform or the equi valent circuit parameters must necessarily have new values. In referance £73, the second type of modulation is taken into consideration. The optimisation of harmonic distortion in the output waveform of stepped- wave inverter circuits is investigated. However, it is im- posible to obtain a sinusoidal waveform without any output filter, because the silicon devices act as switching elements. It is shown that the harmonic dis tortion of step waves, which can be performed by square pulses, remain in lower ranges as compared to output waves of other forms. It is observed that the (ix) theoretically achieved step waveform contains very low harmonic distortion in comparison with other waveforms which are proposed for inverter output- For example the total harmonic distortion of a six step wave is approximatelly B7. and the lowest existing harmonic is the thirteenth. However, the total harmonic distortion of a pulse width modulated waveform with six pulses pro half cycle is in the range of 25% - In £83, A new method of synthesizing stepped current waveform with (12n+i)th harmonic components is proposed. Suitable cascaded inverter configuration and commuta tion scheme are developed. Such a system requires a Y- Y transformer of Ö- 3 times the motor power (kVA) rating. A new scheme of cascaded current source inver - ters of conventional and PWM type has been developed to eliminate lower order line current harmonics in an induction machine drive system. A suitable commutation scheme has been_ chosen and analaysed. The propose 1 scheme has (12n+i)th harmonics and reduced size trans former. In reference C93, A number of voltage-control schemes in 3- phase bridge inverters are investigated. These control schemes are applied to dual 3- phase cascaded bridge inverters with fifth- and seventh- harmonic neutralization to realize pulse- width and amplitude controlled waveforms. fcVA ratings of filter component are calculated to realize a total harmonic distortion of 5% in the output waveform. The control scheme with two pulses per half cycle spaced 60" apart in individ ual inverters gives the lowest total harmonic distortion and requires the lowest filter kVA rating. The theor etical results are experimental ly verified and are in close agreement. Four control schemes have been pre sented for stepped- wave inverters with dual 3- phase bridge inverters connected in cascade using harmonic neutralization for fifth and seventh harmonics. A multistage pulse-width modulation system for generating three-phase controlled stepped voltage wave form is taken into consideration in referrance E±?>3- A four stage system is discussed. Voltage control is achieved by pulse- width modulation. Harmonics are eliminated by suitable transformer connection. In the four - stage system the eleventh and thirteenth harmonics predominate in its three-phase output voltage waveform. Both voltage and harmonic controls are incorporated within the inverter. In reference [113, A DC/AC whose voltage is con structed from discrete low DC sources to form a stepped sine wave-like output is introduced, the criterion of optimal approximation of the stepped waveform to a sine- wave was the minimum mean square error. The internal resistance of the generated source voltage is time :es in 90 ' electrical angle. Assuming this symmetry for the general step waveform, the Fourier series coefficients are derived as function of "m" variables when "m" is equal to the number of steps in the quarter - cycle. These "m" variables are the commutation angles Ök which define the level changes (>;i) in one quarter- cycle of the step wave. For this reason only one quarter-cycle of the wave is considered in the investigation. It is shown that harmonics of the wave can be changed by changing commutation angles In this study the harmonic equivalent circuit and magnitude of harmonic voltage have been formulated by using the methods of harmonic analysis. The inverter and the induction motor are considered as a system. It is well known that the machine parameters for the same frame size and revolution are different as depending upon the manufacturers. Therefore, the copper losses and iron losses occured in the machine will have different values for the same frame size. The analyses of system is based on two important variables, current and torque which depend on step duration. The former is vital component because of incresing losses and it is effected strongly by Ök. The currents and torques caused by harmonics are calculated individually. The torque and current calcu lations are made for dominant harmonics, known as i, 5 and 7 and higher order harmonics are neglected due to low voltage magnitudes and high frequencies which increase the reactances by their harmonic order. The variation of harmonic content of the stepped- wave is achived by introduction of B which show the first step starting angle. In this study two induction motor are considered of same ratings but manufactured by different companies. It is unavoidable that the equivalent circuit parameters would not be equal to each other, but would have almost approximate values to keep up requirements of power, revolution and torque. One of two machines is used for emergency purpose in case of any failure occurs in the main driver fed by a stepped-wave modulating inverter. In case of a failure the first motoris to be replaced by the second to continue the process. After the replacement, if the output waveform of the inverter is not changed to a new waveform, the second motor will not be able to satisfy the same running conditions provided by the first motor. The slip, torque and efficiency would have different values. Some applica tions which are not sensitive to rpm change would not be influenced by the replacement of the motors. But some applications may require unchanged slip and torque values even if the motor is replaced by its spare. Under these circumstences the readjustement of output waveform of the some inverter types like the PWM inverter would help to matter £63. The aim is to play with harmonic magnitudes by resetting the positions of steps or switching to a new waveform of different step number. The higher the harmonic magnitude, the larger the harmonic torque is obtained, or opposit. (xii) The fundemental voltage magnitude and total harmonic torque must be unchanged to obtain same running condi tions. It is known that the harmonic torques 1, 7 and 13 support each other while 5 and il cause breaking effects on total. Hence it is understood that, if the torque of the spare motor is larger than that of the main motor at a given slip, the braking effect producing torques are to be supported to reduce the total harmonic torque. If the case is in opposition to that given above, the counter process is used to increase total harmonic torque. In this paper the motors are supplied by 2, 3 and 4 stepped waveforms at a pre selected slip. The alteration of step positions causes harmonic change in voltage and torques. In reference E&3 » 2, 4 and 8 PWM voltage waveforms are applied to motors and almost 19% change is achived in total torque when in this study the change in total torque is about 3.1% for spare motor. Thus, it shows that the PWM voltage waveform is more proper than the stepped- wave voltages to provide same running condi tions when the motor is replaced with spare one. Heanwhile, it is shown that the total current is strongly effected by steps of starting angles 6k and at some angles the change in total current is about 14Q% for motor A and 707. for motor B. The magnitude of harmonic currents and harmonic torques Sire not only dependent on step angles but also on the equivalent circuit parameters.

The performance of induction motor when subjected to a nonsinuBoidal voltage waveform has been analysed by many authors. It has been found that the destruc tive effects of the time harmonics reduces the efficiency of the drive system due to increased additional losses. Many authors have worked on the construction of waveforms and inverter electronics to eliminate the low order harmonics which cannot be filtered by the machine impedance. These works have become successful and found practical applications. Since the semiconductors work as a switch, the output of an inverter circuit is nonsinusoidal and generates harmonics. There &re basicaly two methods to eliminate harmonics: 1. Pulse width modulation 2. Pulse amplitude modulation The first has been studied by many authors and found widely practical applications. Some of these studies sire as follows. Analytical and experimental investigation on steady state and transient behaviour of an induction motor fed from nonsinusoidal power supplies is presented in Cİ3- The analaytical investigations &re based on a direct three phase model developed for this purpose. Simula tion procedure for computing the exact nature obtained from a pulse with modulated (PWM) inverter is described Transient studies exhibiting the effects of specific PWM pattern changing on the induction motors are outlined. In reference E23, traditional PWM ac motor drives perform well over a large speed range and have many positive features demonstrated with their simplicity. However, the waveforms used a.re significantly less than ideal at high modulation depths and low switching rates, especially with regard to harmonically induced motor losses. An improved strategy for digitally pro ducing PWM based on conventional triangulation methods are presented. A new technique for reducing the (viii) harmonic losses resulting from sinusoidal PWM waveform analysed in depth and realised on a 40 KVA inverter. Tests with this inverter on 7.5 KW and İ5 KW motors confirm that the inverters performance is significantly enhanced for certain operating conditions, without any sacrifice. In reference £33» PWM voltage waveforms sre analysed for a motor drive application. The switching patterns are developed in three - phase bridge inverter. The approach is based upon the minimising the harmonic con tent of the current flowing into the motor. PWM waveforms were analysed to obtain loss- optimal PWM waveforms for variable speed induction motor drives. PWM waveforms were induced differently and novel waveforms were demonstrated. Effects of supply voltage waveforms on iron losses were examined in an induction motor in referance £43 and £53. In reference £63 the harmonic torques in an induction motor which is fed from PWM inverter are computed for an unsaturated operation. Their effects on the fun damental harmonic are used to obtain preselected drive conditions given for a different motor. The equivalent circuit of an induction motor is considered for time harmonics and subjected to 2, 4 and 8 PWM voltage waves of equal pulse duration. The induction motors selected having same rating but manufactured by different comp anies, are supplied by PWM waves» have produced differ ent torques and slips. It is shown that the equality of drive parameters { torque and slip ) can be obtained by properly selecting the PWM voltage waveform even if the motors are not identical. As a result of this analysis the functions of the equivalent circuit par - ameters in terms of pulse- width are obtained for given torque and slip. The analysis is proved that an in verter driven induction motor replaced by a spare motor will certainly necessetate to alter the drive condition. The curve of the torque- slip of two different motor are approached one another and in order to avoid such changes to maintain the previous torque and slip values as they were, either the supply waveform or the equi valent circuit parameters must necessarily have new values. In referance £73, the second type of modulation is taken into consideration. The optimisation of harmonic distortion in the output waveform of stepped- wave inverter circuits is investigated. However, it is im- posible to obtain a sinusoidal waveform without any output filter, because the silicon devices act as switching elements. It is shown that the harmonic dis tortion of step waves, which can be performed by square pulses, remain in lower ranges as compared to output waves of other forms. It is observed that the (ix) theoretically achieved step waveform contains very low harmonic distortion in comparison with other waveforms which are proposed for inverter output- For example the total harmonic distortion of a six step wave is approximatelly B7. and the lowest existing harmonic is the thirteenth. However, the total harmonic distortion of a pulse width modulated waveform with six pulses pro half cycle is in the range of 25% - In £83, A new method of synthesizing stepped current waveform with (12n+i)th harmonic components is proposed. Suitable cascaded inverter configuration and commuta tion scheme are developed. Such a system requires a Y- Y transformer of Ö- 3 times the motor power (kVA) rating. A new scheme of cascaded current source inver - ters of conventional and PWM type has been developed to eliminate lower order line current harmonics in an induction machine drive system. A suitable commutation scheme has been_ chosen and analaysed. The propose 1 scheme has (12n+i)th harmonics and reduced size trans former. In reference C93, A number of voltage-control schemes in 3- phase bridge inverters are investigated. These control schemes are applied to dual 3- phase cascaded bridge inverters with fifth- and seventh- harmonic neutralization to realize pulse- width and amplitude controlled waveforms. fcVA ratings of filter component are calculated to realize a total harmonic distortion of 5% in the output waveform. The control scheme with two pulses per half cycle spaced 60" apart in individ ual inverters gives the lowest total harmonic distortion and requires the lowest filter kVA rating. The theor etical results are experimental ly verified and are in close agreement. Four control schemes have been pre sented for stepped- wave inverters with dual 3- phase bridge inverters connected in cascade using harmonic neutralization for fifth and seventh harmonics. A multistage pulse-width modulation system for generating three-phase controlled stepped voltage wave form is taken into consideration in referrance E±?>3- A four stage system is discussed. Voltage control is achieved by pulse- width modulation. Harmonics are eliminated by suitable transformer connection. In the four - stage system the eleventh and thirteenth harmonics predominate in its three-phase output voltage waveform. Both voltage and harmonic controls are incorporated within the inverter. In reference [113, A DC/AC whose voltage is con structed from discrete low DC sources to form a stepped sine wave-like output is introduced, the criterion of optimal approximation of the stepped waveform to a sine- wave was the minimum mean square error. The internal resistance of the generated source voltage is time :es in 90 ' electrical angle. Assuming this symmetry for the general step waveform, the Fourier series coefficients are derived as function of "m" variables when "m" is equal to the number of steps in the quarter - cycle. These "m" variables are the commutation angles Ök which define the level changes (>;i) in one quarter- cycle of the step wave. For this reason only one quarter-cycle of the wave is considered in the investigation. It is shown that harmonics of the wave can be changed by changing commutation angles In this study the harmonic equivalent circuit and magnitude of harmonic voltage have been formulated by using the methods of harmonic analysis. The inverter and the induction motor are considered as a system. It is well known that the machine parameters for the same frame size and revolution are different as depending upon the manufacturers. Therefore, the copper losses and iron losses occured in the machine will have different values for the same frame size. The analyses of system is based on two important variables, current and torque which depend on step duration. The former is vital component because of incresing losses and it is effected strongly by Ök. The currents and torques caused by harmonics are calculated individually. The torque and current calcu lations are made for dominant harmonics, known as i, 5 and 7 and higher order harmonics are neglected due to low voltage magnitudes and high frequencies which increase the reactances by their harmonic order. The variation of harmonic content of the stepped- wave is achived by introduction of B which show the first step starting angle. In this study two induction motor are considered of same ratings but manufactured by different companies. It is unavoidable that the equivalent circuit parameters would not be equal to each other, but would have almost approximate values to keep up requirements of power, revolution and torque. One of two machines is used for emergency purpose in case of any failure occurs in the main driver fed by a stepped-wave modulating inverter. In case of a failure the first motoris to be replaced by the second to continue the process. After the replacement, if the output waveform of the inverter is not changed to a new waveform, the second motor will not be able to satisfy the same running conditions provided by the first motor. The slip, torque and efficiency would have different values. Some applica tions which are not sensitive to rpm change would not be influenced by the replacement of the motors. But some applications may require unchanged slip and torque values even if the motor is replaced by its spare. Under these circumstences the readjustement of output waveform of the some inverter types like the PWM inverter would help to matter £63. The aim is to play with harmonic magnitudes by resetting the positions of steps or switching to a new waveform of different step number. The higher the harmonic magnitude, the larger the harmonic torque is obtained, or opposit. (xii) The fundemental voltage magnitude and total harmonic torque must be unchanged to obtain same running condi tions. It is known that the harmonic torques 1, 7 and 13 support each other while 5 and il cause breaking effects on total. Hence it is understood that, if the torque of the spare motor is larger than that of the main motor at a given slip, the braking effect producing torques are to be supported to reduce the total harmonic torque. If the case is in opposition to that given above, the counter process is used to increase total harmonic torque. In this paper the motors are supplied by 2, 3 and 4 stepped waveforms at a pre selected slip. The alteration of step positions causes harmonic change in voltage and torques. In reference E&3 » 2, 4 and 8 PWM voltage waveforms are applied to motors and almost 19% change is achived in total torque when in this study the change in total torque is about 3.1% for spare motor. Thus, it shows that the PWM voltage waveform is more proper than the stepped- wave voltages to provide same running condi tions when the motor is replaced with spare one. Heanwhile, it is shown that the total current is strongly effected by steps of starting angles 6k and at some angles the change in total current is about 14Q% for motor A and 707. for motor B. The magnitude of harmonic currents and harmonic torques Sire not only dependent on step angles but also on the equivalent circuit parameters.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1993

Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 1993

Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 1993

##### Anahtar kelimeler

Asenkron motorlar,
Eviriciler,
Harmonikler,
Induction motors,
Inverters,
Harmonics