A Genetic Algorithm Approach for Sensorless Speed Estimation by using Rotor Slot Harmonics

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1 A Genetic Algorithm Aroach for Sensorless Seed Estimation by using Rotor Slot Harmonics Hayri Arabaci Abstract In this aer a sensorless seed estimation method with genetic algorithm for squirrel cage induction motors is resented. Sensorless seed estimation methods generally are based on motor current. Frequency sectrum of the current has comonents reresenting rotor slot harmonics. These frequency comonents are used to estimate the seed of the motor given the number of rotor slots. In the literature, individual algorithms have been used to calculate the seed from the rotor slot harmonics. Unlike the literature, genetic algorithm is used to extract the motor seed from rotor slot harmonics comonents in the roosed method. The exerimental study was carried out to rove this method under steady state conditions. The exerimental results show that the roosed method is suitable for sensorless seed estimation and its average error is the 0.29 rm at 50 Hz. Index Terms Genetic algorithm, induction motor, rotor slot harmonics, sensorless seed estimation T I. INTRODUCTION HE induction motors are widely used in industry because of inexensive cost and their robustness. The motors drive various vital comonents and loads in industrial rocesses. Condition monitoring for both inductions motor and combined systems has become necessary to avoid unexected failure. Fault detection algorithms deendent on the current sectrum analysis and the detection of some harmonic comonents which occur according to motor seed [1-3]. In such algorithms, accuracy of seed knowledge is critical for the effective condition monitoring and fault diagnosis. Moreover, motor seed and rotor osition require a feedback for various alications, but most of these systems do not have any seed sensor in industrial setus. Seed sensors such as encoders, tacho-generator and Hall effects sensors are connected to the system to obtain the seed value. These sensors need cabling to connect to motor. It makes the cost of the motor system increased. In addition to this, faulting robability of the seed sensors is higher then induction motor. Robustness of whole system decreases. The Manuscrit received Aug 06, 2015; revised Aug 08, This work suorted by Scientific Research Project Coordinating of Selçuk University (SUBAP). H. Arabacı is with the Deartment of Electrical and Electronics Engineering, Technolagy Faculty, Selcuk University, 42075, Konya, Turkey. (corresonding author s hone: ; fax: ; hayriarabaci@selcuk.edu.tr). sensorless seed estimation is a viable alternative to avoid the roblems which associates with the system including seed sensor. Many aroaches have been done to obtain the seed from electrical quantities of motor during recent years. Various motor seed estimation methods have been resented. They can be summarized in two main sections as follows [4]: Methods are based on motor mathematical models to deduce observers and adative schemes, Methods are based on sectral comonent estimation of the voltage or current. The methods using motor mathematical models have advantage of short rocessing time. But, they have disadvantages deending on many time variations and requiring a lot of knowledge of motor arameters. Otherwise, current and voltage sensing are required for these methods [5]. The second mentioned methods need only voltage or only current measurement. There are also indeendent of electromagnetic motor arameters. But, these methods cause longer rocessing times according to first mentioned methods. Current and voltage measurement equiments are generally resent to rotect from over voltage and over current in most industrial systems including motor. The voltage and current data could be obtained by adding some hardware. Using of voltage measurements has some roblems such as distorted waveform (esecially system with induction motor which is sulied by inverter). So, the algorithms, which is based on voltage sectral analysis, have not been encouraged this roblem. Motor current have been referred due to the filtering behavior of the motor stator winding. Because the seed observers of a squirrel cage induction motor are available in the stator currents, the seed could be obtained by analysis of frequency sectrum of the current [6]. Harmonic comonents in the sectrum are related to the number of rotor slots and named Rotor Slot Harmonics (RSH). Resolution of the frequency sectrum effects directly seed estimation accuracy. The high resolution imroves accuracy of calculations, but it increases the number of comutation. Different sectral analysis methods are comared in detail in [7] and [8] (such as Chir-Z Transform (CZT), Fast Fourier Transform (FFT), Hilbert Transform, and Interolated FFT). The CZT gives good sectral resolution, but it increases the number of oerations. Adequate accuracy level is obtained by using FFT. Moreover, the number of oerations is lesser than

2 using CZT. So, FFT is generally used to obtain the frequency sectrum of the current. In the literature, authors have mainly focused on the otimization of search algorithms of the rotor slot sectral comonents [8-11]. Various studies are available such as fast orthogonal search algorithm, which s result data have lower resolution current sectrum, could be used to identify RSH [12]. The algorithm allows estimation of the seed for real-time erformance by an embedded digital signal rocessor. A scheme, which combines Hilbert transform and interolated FFT, is used to imrove the estimation accuracy of the seed [13]. Hence, the algorithm realizes direct motor torque control and soft-starting rocess control without any tachometer. Eventually, most of studies have been focused on methods which are used to transform time domain to frequency domain. Determination of RSH comonents and estimation of seed according to RSH are made by individual aroaches in their studies. Some studies using Artificial Neural Network (ANN) [14-16] and genetic algorithm (GA) [17-19] are available in the literature. But these studies use methods which are based on motor mathematical model. An ANN aroach is resented for sensorless seed estimation using RSH in [21]. To calculate the motor seed, each related RSH comonent is extracted from the sectrum by using ANN. 1.5 rm average calculation error is reached. In this aer, the motor current sectrum is obtained by using FFT due to a smaller number of oerations and adequate accuracy level. RSH in the sectrum are used to estimate motor seed by using GA. II. MATERIAL AND METHOD Various sensorless seed estimation techniques have been received with increasing attention for squirrel cage induction motor. These techniques can be divided two main arts. One of them is model based aroaches. But, most of these aroaches are sensitive to motor arameters and load tye. Accuracy of these arameters directly affects erformance of these methods. So, the accuracy of seed estimation is limited for the model-based aroaches. In the second art is based on the sectrum analysis of stator current. The stator current harmonics are included RSH which are roortional to motor seed [5]. RSH could be used to estimate the motor seed deending on the number of rotor slots [1]. Moreover, an accurate model of the motor arameters and the load tye information are not required in these methods. In this aer, the seed estimation is made by using RSH in frequency sectrum of motor current. Only this method is mentioned in this section because the roosed algorithm bases on RSH analysis of the current. A. The seed estimation by using rotor slot harmonics The stator current data of squirrel cage induction motor has seed observers. The motor seed can be estimated by mean of sectrum analysis of the current. The seed estimation method does not deend on any motor arameters. The method requires only the knowledge of the number of rotor slots and the number of motor ole airs. The rotor slots roduce changes on air-ga flux with a satial distribution deendent on the number of rotor slots. These changes are rotor slot mmf harmonics and these effect the stator current in continuous variations. Frequency of RSH comonents is calculated by using Eq. (1) [1]. 1 s f sh f k R n 1 d v where: n d = 0, ±1, ±2, k = 0, 1, 2, v = 0, ±1, ±3, f 1 is fundamental frequency comonent of stator current. is the number of ole airs of motor. R is the number of rotor slots (bars). s is er unit motor sli. v is the order of stator time harmonics resenting in the stator current. n d is known as eccentricity order and it s value is zero for healthy motor. When n d = 0 and k = 1 values are relaced in Eq. (1), rincial slot harmonic is obtained as in Eq. (2). 1 s f sh f R 1 v The rincial slot harmonic comonents corresonding to v values are calculated by using s and Eq. (2). Then motor seed is obtained in rm by Eq. (3). 60 f 1 s n (1 ) The values of can be calculated from namelate information of motor. The fundamental frequency comonent f 1 is easily determined from the frequency sectrum. It is need that R value is informed from manufacturer of the motor. But R is always integer and motor seed is aroximately known under no-load condition. So, this R values could be obtained by no-load motor test [6]. The main roblem is to determine that the concerned RSH comonent in Ed. (2) occurs due to which v value. Furthermore, RSH comonent for whole values of v is not available in the sectrum. In addition to this, amlitude of certain RSH comonent may be very small. To estimate the motor seed from RSH is difficult because of above mentioned reasons. In the literature individual algorithms have been used for seed estimation [4,6,8,13]. In this aer, the roosed method uses GA to extract the v value and sli knowledge by using one of the RSH comonents in scanning region of current sectrum. B. The roosed sensorless seed estimation method The roosed method uses frequency sectrum of stator current. The frequency sectrum is obtained by using FFT. Many frequency comonents are available in the sectrum.

3 Squirrel cage induction motors under steady state oeration run in the sli region that is between the sli corresonding to maximum torque and synchronous seed. The sli corresonding to maximum torque deends on the structure of the motor. It is generally below the 10%. Therefore, search region of the frequency sectrum is determined by using Eq.(2) for s values between 0 and 10% and. The determined search region is shown in Fig. 1. RSH comonents are searched in this region. But, there are many comonents which are amlitude are at small level. These comonents are eliminated by determining a threshold value. It reduces the number of oerations at searching rocess of robable RSH. Any oeration is not done for fundamental harmonic comonents in this region because of easy determination. RSH comonents, fundamental harmonic comonents and threshold value are shown in Fig. 2. Because motor seed is known from Fig. 1. The determined region to scan the RSH. Fig. 3. The block diagram of the roosed method. Fig. 2. The frequency comonents of scanned region for rm at 50 Hz.. exerimental study, v values are directly shown in the sectrum for every RSH comonents in Fig. 2. However, in the ractice motor seed is unknown and wants to find out. So, it is not certain that RSH comonent corresonds to which v value. For overcoming of this roblem GA is used in this aer. Frequency value of any RSH comonent in the region is used in GA rocess. End of the GA rocess, s and v values are found out. So, motor seed is calculated by using the obtained s value and Eq. (3). The block diagram of the roosed method is given in Fig. 3. C. GA aroach in sensorless seed estimation The methods, which are based on RSH for sensorless seed estimation, generally use similar rocess stages. Initially, motor current is samled from one stator coil. Then frequency sectrum of the current is obtained by using time-frequency transformation. RSH comonents are determined from the frequency sectrum. Motor seed is calculated via the RSH, v value, Eq. (2) and Eq. (3). But it needs to certainly know that the selected RSH frequency is for which the v value. This is main roblem of the method. To date, individual algorithms have been used to calculate the motor seed from RSH comonents by Eq. (2). In this aer, GA is used to determine v and s values corresonding to related RSH comonent. Processing stes of the used GA algorithm are given as follows: 1- Adat the structure of chromosome according to constraints and limits of arameters 2- Form the objective function 3- Generate the initial oulation 4- Aly crossover, mutation, selection 5- Calculate the fitness and enalty values 6- Convergence and reeat of the test from ste 4 until achieving the otimum solution. In this study, aim is to find the value of v, and thus to x 1 x Fig. 4.. The structure of chromosome.

4 Proceedings of the World Congress on Engineering and Comuter Science 2015 Vol I estimate the motor seed (or s). Therefore, each chromosome consists of v and s values. Chromosome is formed to be binary code. So, the binary-code GA is used in the roosed algorithm. Values of v are odd number. Its minimum value and maximum value are -7 and 7 resectively. s is real number. Its minimum value and maximum value are 0 and 0.1 resectively is enough for resolution of s. Hence, length of each chromosome is 13 bits (13 genes). First 3 bits ( x1 ) reresent v value. Other 10 bits ( x2 ) reresent s value. The structure of this chromosome is given in Fig. 4. a- Initial oulation The initial oulation is generated randomly without any limit, because of definition of limit is done at forming rocess of chromosome. b- Constraints Eq. (2) is used to form the object function. Values of R and arameter are known. But, f1 is calculated from frequency sectrum of current. So, the constraint function is obtained as shown in Eq. (4). g ( x ) 1 x2 f sh f 1 R x1 where fsh is value of RSH comonent which is selected from the scanning region of sectrum. x1 is first 3 bits of jth x chromosome of every generation and is calculated as to Eq. (5). x1 2 x(1 : 3) 10 vmin otimum [20]. So the diversity is increased in the oulation. A number between 0 and 1 is roduced randomly for mutation. This number is comared the mutation rate. If the number is under the mutation rate, mutation is alied one gene of the related chromosome. The gene is selected randomly. If the selected gene is 0, it is made 1, else 0. f- Convergence test New individuals are achieved every loo of the rocedure. This rocess continues until reaching a redetermined generation number or meeting an object. The most imortant oint is to determine the stoing criterion. In the study, the generation number is chosen as stoing criterion. III. EXPERIMENTAL STUDY AND RESULTS Squirrel cage induction motor with 28 bars was used to carry out the exeriments study. Its secifications were 2.2 kw, 3 hases, 2 ole airs, 380V and 50 Hz. The exeriments were made in the laboratory by using an exerimental system. The motor was loaded by generator. Loading of the motor is leveled by using resistors which are conducted to the generator. The block diagram of the used exerimental system is given in Fig. 5. The hotograh of exerimental system and its comonents are also given in Fig. 6. One hase current of the motor was samled in steady state oeration for various seed levels. Verification of estimated results with real seed values is made by using an encoder combining to motor-generator shaft in the exerimental system. where vmin is minimum value of the v and determined to be -7 for study. x2 reresents motor sli and it s values is calculated by last 10 bits of jth x chromosome. Value of the x2 is calculated by using Eq. (6). x 2 smax x( 4 : 13) 10 smin where smax is accetable maximum value of the motor sli under steady state condition and aroved to be 0.1 for this study. smin is also determined to be 0. Penalty values are calculated for each generation. The enalty values are used for selection. c- Selection The obtained enalty values by Eq. (4) are comared other individuals of related generation. The best chromosome is saved and carried next generation. d- Crossover Crossover is an oerator used in order to roduce better chromosomes and increase the diversity of the oulation. One-oint is used for crossover is alied on the oulation. The individual oulations are chosen and aired randomly. The selected air of genes is exchanged from one oint which is determined randomly. e- Mutation Mutation is alied on the oulation to avoid local Fig. 5. The block diagram of exeriment system. Fig. 6. The hotograh of exeriment system and comonents.

5 The motor current was samled from Hall-effect current sensor by using data acquisition card. The samling rate was 5 khz. FFT with Hanning window was used to obtain frequency sectrum of this current data. RSH comonents were determined from the scanning region. One of these determined RSH comonents was used in objection function of GA. Then GA iteration was started. End of the iteration, the calculated s value was used to estimate the motor seed via Eq. (3). The estimated motor seeds and real seeds are comared and given in Table 1. Maximum error rate in rm is 0.064% (0.96 rm for 50 Hz). Finally the average error is calculated as 0.29 rm. TABLE I COMPARISON OF EXPERIMENTAL RESULTS AND REAL SPEED VALUES FOR DIFFERENT LOAD LEVELS Load Levels Estimated Seed Values [rm] Real Seed Values [rm] Estimation Error [rm] Estimation Error [%] Load Load Load Load Load Load Load Load Load Load Load Load Load Load Load Load Load Load IV. CONCLUSION This aer resents a GA aroach for sensorless seed estimation using RSH. Frequency sectrum of motor current is obtained by FFT to reach the RSH. Each RSH comonents in this sectrum corresond to v values which are required to calculate the motor seed. One of the RSH comonents is used for GA in roosed method unlike the literature. The exerimental results are obtained by means of a 2.2 kw induction motor running at 50 Hz under steady state conditions. The maximum calculation error is 0.96 rm (0.06%). The average calculation error is 0.29 rm (0.02%). Therefore, the exerimental results show that the roosed method is feasible to estimate the seed in high accuracy. Furthermore, this roosed algorithm can enhance the erformance and reliability of monitoring of squirrel cage induction motor without any seed sensor as in submersible induction motor alications. ACKNOWLEDGMENT The study has been suorted by Scientific Research Project of Selcuk University. REFERENCES [1] P. 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