Easy How To Draw The Equivalent Circuit Diagram Of 3 Phase Induction Motor Now

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Brasil - Estimation of Three-Phase Induction Motor Equivalent Circuit

Three-phase induction motors (TIM) full of life sedated steady-state regime are commonly modeled using a per phase equivalent circuit, which enables the calculation‚  The single phase equivalent circuit is largely used to model the three-phase induction motors in steady-state operation and under sinusoidal balanced voltages. Depending vis-а-vis the desired application, the circuit may or may not represent core losses, a double cage or even the variation of parameters due to skin effect and saturation. However, the drive get-up-and-go of the circuit parameters through welcome methods, such as those described in IEEE usual conventional 112, may not be doable in many situations given the lack of the necessary resources. This paper presents initially a survey vis-а-vis the dream of circuit parameters from swap methods, i.e., non-standard tests. Special focus is given to methods which employ solitary data usually provided by manufacturers on catalogs and nameplates. Six analytical methodologies used in the context of efficiency estimation at steady-state operation are assessed, compared and after that gather together in order to count results. The assessment is based nearly the closeness of the resulting parameter values to reference values and on the inexistence of absurd results, such as negative electrical resistances. The incorporation of methods has augmented the correctness exactness of calculations for the studied motors.



Three-phase induction motors (TIM) in action operational out cold asleep steady-state regime are commonly modeled using a per phase equivalent circuit, which enables the adding up of quantities such as line current, capability factor, input and output facility and efficiency helpfully as a function of supply voltage, frequency and slip. The circuit parameter values are traditionally determined through tests described vis-а-vis IEEE up to standard 112 [1[1] IEEE suitable 112, IEEE pleasing procedure for polyphase induction motors and generators, IEEE Nov. 2004, pp. 1 - 87.], such as no load and locked rotor tests. Although such proceedings provide well-behaved results, their requisites may be impractical in some places or situations. First, the necessary instrumentation is not often straightforward where the motor is operating, so demanding the transference of the machine to a psychoanalysis site or laboratory. Second, the necessary deferment in the operation of the motor is undesired in essential industrial processes. Finally, the knowledge of the circuit parameter values may be desired prior to acquisition for energy of even didactic purposes.

These situations have provoked forced the develop of substitute methods for parameter values determination, ranging from analytical calculations based something like nameplate data to frequency admission analysis. The estimated model is destined to various applications, e.g., efficiency assessment and starting simulation, which as well as define the details. A particular organization society of methods, based all but guidance provided by manufacturers concerning catalogs or nameplates, stands out in steady-state applications for its simplicity and its nonintrusive characteristic.

This paper presents a review re parameter values estimation of the equivalent circuit of three phase induction motors based almost data provided by manufacturers going on for catalogs, taking into account bearing in mind special immersion going on for those dedicated to efficiency estimation. Section II consists all but an overview of methods for parameter identification in several contexts. Section III summarizes the main methods for equivalent circuit drive get-up-and-go from catalog data by analytical and numerical means. all but Section IV, the analytical methods described all but the previous section are applied to a bureau of motors and their conduct yourself is assessed and compared.

According to [2[2] D. Lindenmeyer, H.W. Dommel, A. Moshref, P. Kundur, An induction motor parameter estimation method, in International Journal of Electrical aptitude & moving picture Systems, Vol. 23, no. 4, pp 251-262, May 2001.], methods for identification of TIM parameter values can be classified as:

Calculation from construction data: requires the detailed knowledge of the machine's geometry and of the properties of the employed materials, besides software for electromagnetic calculation. It is considered to be the most precise procedure, although costly, and it is employed basically by manufacturers, designers and researchers.

Estimation based roughly speaking steady-state motor models: the parameter values are obtained through the supreme of equations derived from state-models employing data from tests, measurements or provided by manufacturers. This class includes the standard scrutiny methods.

Frequency-domain parameter estimation: the parameter values are estimated from the transfer deed observed during tests. It is not a common industry practice.

Time-domain parameter estimation: the parameter values are adjusted so as the reaction calculated when a system of differential equations fits the observed time response.

Real-time parameter estimation: commonly applied to controllers for continuous tuning of parameters of simplified models, compensating parameter variation due to temperature change, saturation and other effects in the machine.

This take action focuses approximately methods belonging to the second group, especially almost those employing data provided by manufacturers roughly speaking nameplates or obscure catalogs. These data contain counsel of rated output power, torque, current, efficiency, capability factor (for sinusoidal waveforms, or displacement factor more precisely), speed, among others. Academic literature all but this subject aims at three main applications: efficiency calculation; calculation of torque and current curves; vivaciousness of transient regime and control analysis.

Different models are adopted for each application, as shown in Fig. 1 and Fig. 2. approximately the single-cage model, R1 and X1 are the resistance and leakage reactance of the stator, respectively, Rc represents the core losses, Xm is the magnetizing reactance, R2 and X2 are the resistance and leakage reactance of the rotor referred to the stator, respectively, s is the per unit slip and V1 is the phase voltage. a propos the double-cage model, R21 and X21 decide match to the inner cage resistance and leakage resistance referred to the stator, while R22 and X22 permit to the outer cage. The single-cage model without core losses, depicted roughly speaking Fig. 1 excluding Rc, usually provides satisfactory truthfulness for torque and current calculations [3[3] K. Lee, S. Frank, P. K. Sen, L. G. Polese, M. Alahmad and C. Waters, Estimation of induction motor equivalent circuit parameters from nameplate data, North American talent Symposium (NAPS), 2012, Champaign, IL, 2012, pp. 1-6.]. For efficiency determination, it is necessary to judge the core losses, added to the circuit as Rc, as well as friction, winding and stray-load losses, which are considered a posteriori. Both models following constant parameters are pleasing for the operation range together with synchronous enthusiasm and maximum torque [4[4] J. Pedra and F. Corcoles, Estimation of induction motor double-cage model parameters from manufacturer data, in IEEE Transactions around cartoon Conversion, vol. 19, no. 2, pp. 310-317, June 2004.], [5[5] M. H. Haque, desire of NEMA Design Induction Motor Parameters From Manufacturer Data, in IEEE Transactions on the order of dynamism Conversion, vol. 23, no. 4, pp. 997-1004, Dec. 2008.]. In order to properly represent the starting and acceleration conditions, a double-cage model can be used [4[4] J. Pedra and F. Corcoles, Estimation of induction motor double-cage model parameters from manufacturer data, in IEEE Transactions as regards moving picture Conversion, vol. 19, no. 2, pp. 310-317, June 2004.], or the parameters of the single-cage model can be dependent as regards the slip [5[5] M. H. Haque, aspiration of NEMA Design Induction Motor Parameters From Manufacturer Data, in IEEE Transactions a propos animatronics Conversion, vol. 23, no. 4, pp. 997-1004, Dec. 2008.].

In [6[6] A. Bellini, A. De Carli, M. La Cava, Parameter identification for induction motor simulation, in Automatica, vol. 12, no. 4, pp. 383-386, July 1976.], the parameter values of the single-cage model without core losses (SCM) are identified through iterative least-squares curve fitting from torque and current measurements at several points from startup to synchronous speed. Natarajan and Misra [7[7] R. Natarajan, V.K. Misra, Parameter estimation of induction motors using a spreadsheet program just about a personal computer, in Electric capacity Systems Research, vol. 16, no. 2, pp 157-164, 1989.] pioneered the identification of parameter values from manufacturer data, using analytical relationships to calculate the single-cage model similar to core losses (SCM-CL) in order to build curves of efficiency and skill factor. For transient life purposes, [8[8] S. Ansuj, F. Shokooh and R. Schinzinger, Parameter estimation for induction machines based more or less sensitivity analysis, in IEEE Transactions on the subject of with reference to Industry Applications, vol. 25, no. 6, pp. 1035-1040, Nov/Dec 1989.] employed sensivity analysis to determine the SCM-CL based in the region of catalog data, however including locked rotor capacity factor and slip at maximum torque, which are rarely informed by manufacturers. Rotor parameters R2 and X2 are not considered constant, but functions of slip. Haque [9[9] M. H. Haque, Estimation of three-phase induction motor parameters, in Electric capability Systems Research, vol. 26, no.3, pp 187-193, 1993.] suggests an iterative procedure for the totaling of all SCM-CL and mechanical losses from catalog data, presenting through the resulting efficiency and skill factor curves its unfriendliness more than Natarajan and Misra's method.

To avoid indecent convergence, [10[10] R. R. Bishop and G. G. Richards, Identifying induction machine parameters using a genetic optimization algorithm, Southeastcon '90. Proceedings., IEEE, additional Orleans, LA, 1990, pp. 476-479 vol.2.] employed genetic algorithms (GA) to decide the values of four parameters of SCM-CL using few experimental data. GA are taking into consideration more employed in [11[11] R. Nolan, P. Pillay and T. Haque, Application of genetic algorithms to motor parameter determination, Industry Applications group charity Annual Meeting, 1994., Conference cassette of the 1994 IEEE, Denver, CO, 1994, pp. 47-54 vol.1.] to determine the SCM and produce develop current and torque curves from catalog data. Four configurations of GA are compared in the course of themselves and to Newton's method, showing that a small malformation in relation to the initial definite can make the latter to diverge while GA are obedient in this context.

Aiming at showground efficiency hope at swing intrusion levels, the Oak Ridge National Laboratory recommended the Nameplate Equivalent Circuit (NEQ) method [12[12] Kueck, J. D., et al. Assessment of methods for estimating motor efficiency and load frozen field conditions. ORNL (1996).], where the SCM-CL is derived from the nameplate data by an iterative procedure. A typical irregularity of 3.6 % in efficiency was observed, despite the use of a typical value of rated capacity factor, given its absence in NEMA suitable nameplates. considering a same thesame objective, [13[13] P. Pillay, V. Levin, P. Otaduy and J. Kueck, In-situ induction motor efficiency purpose using the genetic algorithm, in IEEE Transactions vis-а-vis Energy Conversion, vol. 13, no. 4, pp. 326-333, Dec 1998.] uses GA to determine four parameter values of SCM-CL based almost measurements of current and input capability at four load conditions. Values of stray-load losses and ratio of leakage reactances are assumed according to IEEE Std. 112 [1[1] IEEE suitable 112, IEEE welcome procedure for polyphase induction motors and generators, IEEE Nov. 2004, pp. 1 - 87.], while R1 is measured directly.

Genetic algorithms are along with used in [14[14] P. Nangsue, P. Pillay and S. E. Conry, Evolutionary algorithms for induction motor parameter determination, in IEEE Transactions on the subject of with reference to animatronics Conversion, vol. 14, no. 3, pp. 447-453, Sep 1999.], to determine the parameter values of the double cage model without core losses (DCM) from catalog data in order to plot torque and current curves, and in [15[15] B. Abdelhadi, A. Benoudjit and N. Nait-Said, Application of genetic algorithm in imitation of a novel adaptive scheme for the identification of induction machine parameters, in IEEE Transactions all but vigor Conversion, vol. 20, no. 2, pp. 284291, June 2005. doi: 10.1109/TEC.2004.841508https://doi.org/10.1109/TEC.2004.841508 ], to identify the parameter values of the SCM from current curves for control applications, while adapting the search ventilate to accelerate convergence.

The identification of SCM parameter values is proposed in [16[16] K. S. Huang, W. Kent, Q. H. Wu and D. R. Turner, Parameter identification of an induction machine using genetic algorithms, Computer Aided Control System Design, 1999. feat of the 1999 IEEE International Symposium on, Kohala Coast, HI, 1999, pp. 510-515. doi: 10.1109/CACSD.1999.808700https://doi.org/10.1109/CACSD.1999.80870 ] by measuring the current waveform during motor starting and fitting the simulated waveform. In [2[2] D. Lindenmeyer, H.W. Dommel, A. Moshref, P. Kundur, An induction motor parameter estimation method, in International Journal of Electrical capability & spirit Systems, Vol. 23, no. 4, pp 251-262, May 2001.], all parameter values of both SCM and DCM are identified from nameplate data through restricted nonlinear optimization taking into consideration the effects of saturation.

In [17[17] F. Corcoles, J. Pedra, M. Salichs and L. Sainz, Analysis of the induction machine parameter identification, in IEEE Transactions not far off from dynamism Conversion, vol. 17, no. 2, pp. 183-190, Jun 2002. doi: 10.1109/TEC.2002.1009466https://doi.org/10.1109/TEC.2002.1009466 ], the identification of parameter values of the equivalent circuit is analyzed theoretically, evidencing the existence of a maximum number of parameters that can be univocally distinct from voltage, current and keenness measurements. Starting from the equation of per-phase equivalent impedance as a discharge duty of circuit parameters, supply frequency and slip, the concept of model invariants is introduced as the minimum number of constants that can be achieved by rearranging the equation. If the number of circuit parameters is greater than the number of model invariants, the parameter values cannot be determined univocally and additional equations are needed. However, if the number of parameters is equal to the number of invariants, all parameter values can be distinct as a unique solution. Table I summarizes the numbers of circuit parameters and model invariants for each of the four models presented previously, evidencing that the equality occurs unaided in the SCM- CL. The values of the model invariants can be positive clear by solving the equations of the legitimate and imaginary parts of the equivalent impedance at a number of measurement points equal to half the number of invariants, although supplementary secondary points are useful to filter deviations.

An extensive review not far off from parameter estimation for control applications, based in the region of 207 references, is carried out not far off from [18[18] H. A. Toliyat, E. Levi and M. Raina, A review of RFO induction motor parameter estimation techniques, in IEEE Transactions going on for activity Conversion, vol. 18, no. 2, pp. 271-283, June 2003. doi: 10.1109/TEC.2003.811719https://doi.org/10.1109/TEC.2003.811719 ]. Many of the methods described employ the purpose determination systems to deed tests or impose special excitations during the system startup.

The fsolve perform of Matlab is used in [4[4] J. Pedra and F. Corcoles, Estimation of induction motor double-cage model parameters from manufacturer data, in IEEE Transactions in the region of enthusiasm Conversion, vol. 19, no. 2, pp. 310-317, June 2004.] to identify parameter values of the SCM and the DCM based approximately few catalog data to manufacture torque curves. The same appear in is used in [5[5] M. H. Haque, drive get-up-and-go of NEMA Design Induction Motor Parameters From Manufacturer Data, in IEEE Transactions going on for enthusiasm Conversion, vol. 23, no. 4, pp. 997-1004, Dec. 2008.], which aims at efficiency and torque calculations later than the SCM-CL.

In the context of efficiency estimation when SCM-CL, [19[19] S. C. Sabharwal, Methodology for Estimating pretend Characteristics of Three Phase Induction Motor functional Direct-on-Line or subsequent to Six Pulse Inverter, capability Electronics, Drives and excitement Systems, 2006. PEDES '06. International Conference on, extra Delhi, 2006, pp. 1-4. doi: 10.1109/PEDES.2006.344343https://doi.org/10.1109/PEDES.2006.34434 ] identifies all parameter values from catalog data gone analytical expressions. The performances of Newton's method, Particle Swarm Optimization (PSO) and Simulated Annealing (SA) are compared in [20[20] B. Lu, W. Qiao, T. G. Habetler and R. G. Harley, 'Solving Induction Motor Equivalent Circuit using Numerical Methods for an In-Service and Nonintrusive Motor Efficiency Estimation Method, facility Electronics and pastime Control Conference, 2006. IPEMC 2006. CES/IEEE 5th International, Shanghai, 2006, pp. 1-6.] by determining four parameters from low-intrusion arena measurements. An iterative linear least-squares method is employed in [21[21] G. Wang and S. W. Park, 'Improved Estimation of Induction Motor Circuit Parameters similar to Published Motor play a part Data, 2014 Sixth Annual IEEE Green Technologies Conference, Corpus Christi, TX, 2014, pp. 25-28.] to search all parameters based something like efficiency and gift factor values at four load levels. A hybrid search method is proposed in [22[22] K. Sundareswaran, H. N. Shyam, S. Palani and J. James, 'Induction motor Parameter Estimation using Hybrid Genetic Algorithm, 2008 IEEE Region 10 and the Third international Conference roughly speaking Industrial and opinion guidance Systems, Kharagpur, 2008, pp. 1-6.] to determine four parameter values from current, capacity factor and eagerness measurements. The conclusive model is calculated in [3[3] K. Lee, S. Frank, P. K. Sen, L. G. Polese, M. Alahmad and C. Waters, Estimation of induction motor equivalent circuit parameters from nameplate data, North American capacity Symposium (NAPS), 2012, Champaign, IL, 2012, pp. 1-6.] through an iterative procedure, assuming a typical distribution of losses at rated condition, and through an analytical and attend to method in [23[23] J. M. C. Guimares, J. V. Bernardes, A. E. Hermeto and E. C. Bortoni, 'Determination of three-phase induction motors model parameters from catalog information, 2014 IEEE PES General Meeting | Conference & Exposition, National Harbor, MD, 2014, pp. 1-5.] to obtain torque, current and efficiency curves, which is applied to an extensive number of motors.

The following data are usually provided by TIM manufacturers on catalogs: rated power Pr; line voltage Vl; full-load current Ifl; starting current Ist/Ifl; starting torque Tst/Tfl; psychoanalysis torque Tm/Tfl; efficiency at three load levels (100%), (75%), (50%); gift factor at three load levels cos(100%), cos(75%), cos(50%); rated frequency f; full-load keenness N; gratifying and category. around the nameplate attached to the machine, unaccompanied rated power, voltage, frequency, full-load and starting current, full-load efficiency, power factor and enthusiasm are informed.

Some of methods cited in the previous section succeed to the desire of equivalent circuit parameter values from catalog data. Others, although originally conceived for auditorium application, can be converted for this application by employing catalog data as a temporary stand-in for measured data. The main methods are described as follows.

In [7[7] R. Natarajan, V.K. Misra, Parameter estimation of induction motors using a spreadsheet program around a personal computer, in Electric capability Systems Research, vol. 16, no. 2, pp 157-164, 1989.], efficiency and capability factor are calculated in the same way as the SCM-CL, which parameter values are distinct from catalog data. An approximate freshening for losses is given by (1), where Po is the mechanical output power, I1 is the line current and Pconst is the constant loss given by the sum of friction and windage losses Pfw and core losses Pc. Applying this equation to two load operation points which data is understandable in this area catalog, the system can be algebraically solved for Pconst and (R1+R2). The core losses are assumed to be equal to one half of the constant losses and the voltage E beyond the magnetizing branch is assumed to be in the region of equal to V1, for that reason enabling the adding together of Rc.

The magnetizing current Im flowing through Xm (see Fig. 1) is calculated in a same thesame artifice by solving the linear system obtained by applying (2) to two load operation points for Im and (I2sin2), which is the imaginary ration of rotor current referred to the stator I2, while 2 is the rotor impedance angle. Assuming E approximately equal to V1, Xm can be calculated as E separated by Im.

The authenticated ration of the rotor current at full-load is calculated in the same way as (3), and its absolute value I2 is sure from the authentic true and imaginary parts. Through (4), R2 is Definite and subtracted from (R1+R2) to result in R1. Using the starting and breakdown torques in (5), X2 is calculated and multiplied to a constant to result in X1.

In [9[9] M. H. Haque, Estimation of three-phase induction motor parameters, in Electric capability Systems Research, vol. 26, no.3, pp 187-193, 1993.], an iterative method is proposed to identify the parameter values of the SCM-CL for efficiency and capability factor calculation, consisting on the order of the following steps:

Line current at 50% of rated load is calculated from efficiency and aptitude factor data, while initial values are assumed for E, Pfw and I2.

R2 results from (6), R1 and Pfw are the pure of the linear system formed by applying (7) to two load operation points. Rc is calculated from E and Pc equal to half of Pconst, X1 and X2 are calculated next (8) and truth ratio X1/X2. Xm is inferred from the reactive aptitude balance.

The unconditional object target in [11[11] R. Nolan, P. Pillay and T. Haque, Application of genetic algorithms to motor parameter determination, Industry Applications work Annual Meeting, 1994., Conference photo album of the 1994 IEEE, Denver, CO, 1994, pp. 47-54 vol.1.] is the accumulation of torque and current curves from motor starting to synchronous speed. The authors use GA to search all parameter values of the SCM from starting torque, breakdown torque, full-load torque, full-load skill factor and full-load speed.

From the model, it is practicable to freshen the torque at the three aforementioned conditions as functions of R1, R2 and improve leakage reactance, given by the sum of X1 and X2, assuming that the parameter values are constant in the desired range and that the magnetizing current is negligible at starting. An object target piece of legislation given by the quantity total of the squares of the deviations amid the calculated torques and the reference values is minimized by the GA. The enhance reactance is subsequently next not speaking according to solution ratios surrounded by with the reactances, and Xm is finally sure through the reactive aptitude balance.

A bill from the Oak Ridge National Laboratory (ORNL), presented in [12[12] Kueck, J. D., et al. Assessment of methods for estimating motor efficiency and load sedated dome conditions. ORNL (1996).], assesses methods for dome efficiency estimation and divides them in three groups according to the intrusion level. The NEQ method, based nearly the SCM-CL, is rangy as the most precise from the low intrusion outfit subsequently a typical idiosyncrasy of 3.6 %.

The stator resistance is measured directly or, for NEMA design B motors, estimated from (9), where p is the number of poles and the units of Pr and Vl are horse talent and volts, respectively.

The stray-load losses are estimated from the percentages suggested almost IEEE Std. 112 and are subsequently next included in the circuit as a resistance in the rotor branch. Friction and windage losses are assumed as a supreme unmodified percentage of full-load input power, equal to 1.2 % for four pole design B motors. Based as regards fullload slip, technical equivalent phase impedance, X1/X2 ratio and starting current, the permanent parameters are iteratively calculated, although the details of the employed algorithm are not provided. The full-load slip calculated from nameplate data is raw-boned as the major cause of deviation, since it has a tolerance of 20 % according to NEMA standards.

The analytical methodology presented in [19[19] S. C. Sabharwal, Methodology for Estimating accomplish Characteristics of Three Phase Induction Motor vigorous Direct-on-Line or as soon as Six Pulse Inverter, talent Electronics, Drives and liveliness vibrancy Systems, 2006. PEDES '06. International Conference on, extra Delhi, 2006, pp. 1-4. doi: 10.1109/PEDES.2006.344343https://doi.org/10.1109/PEDES.2006.34434 ] yields values of the six parameters of the SCM-CL from catalog data for torque, efficiency and aptitude factor calculation. Friction, windage and stray-load losses are neglected, while the remaining losses are considered either constant or proportional to the square of output power, as given in (10). The linear system formed by applying it to two load operation points is solved for a and Pconst, the latter subconscious fully endorsed to Rc, further calculated by assuming E equal to V1.

Neglecting the magnetizing component of the starting current, R2 is approximated by (11), which is derived from the ventilation of air-gap power. Using the starting torque, X2 results from (12), and X1 from the X1/X2 ratio.

The magnitude and phase of the rotor current at full-load are given by (13) and (14), respectively. The balance of reactive current yields Xm, and finally R1 is certain through the balance of augment losses.

A method for dome efficiency assessment employing the SCM-CL is suggested in [20[20] B. Lu, W. Qiao, T. G. Habetler and R. G. Harley, 'Solving Induction Motor Equivalent Circuit using Numerical Methods for an In-Service and Nonintrusive Motor Efficiency Estimation Method, talent Electronics and Motion Control Conference, 2006. IPEMC 2006. CES/IEEE 5th International, Shanghai, 2006, pp. 1-6.], gone few measurements and no craving of load decoupling. The stator resistance is measured directly. The strayload losses are estimated according to the percentages of rated capacity indicated in IEEE Std. 112, while friction and windage losses are assumed as a answer percentage of rated power, e.g., 1.2 % for NEMA design B four pole motors below 200 hp. The ratio along with X1 and X2 is furthermore definite according to the motor design.

The unshakable circuit parameters are Definite by a numeric optimization algorithm which minimizes the quantity total of squares of deviations amongst calculated and measured data. The valid and imaginary parts of the equivalent impedance are calculated from measured voltage and current phasors at two load levels, yielding four equations. The solution of the resulting nonlinear system is performed by three methods: Newton's method, PSO and SA.

The parameter values of the SCM-CL are identified in [22[22] K. Sundareswaran, H. N. Shyam, S. Palani and J. James, 'Induction motor Parameter Estimation using Hybrid Genetic Algorithm, 2008 IEEE Region 10 and the Third international Conference concerning Industrial and recommendation Systems, Kharagpur, 2008, pp. 1-6.] in a arena application in the manner of low intrusion, using a hybrid methodology that combines GA and local search. The algorithm consists of two stages. In the first one, a GA finds a quasi-optimal solution. Next, a local search method (Rosenbrock's rotating coordinates method) extra refines the previous solution.

The stator resistance is measured directly, while the ratio of leakage reactances is fixed. By employing measured values of current, facility factor and speed, the long-lasting parameters are Definite by the hybrid algorithm, which minimizes the sum of squares of deviations of current magnitude and angle.

The parameter values of the SCM-CL are identified in [5[5] M. H. Haque, desire of NEMA Design Induction Motor Parameters From Manufacturer Data, in IEEE Transactions a propos liveliness vibrancy Conversion, vol. 23, no. 4, pp. 997-1004, Dec. 2008.] behind the dependency of parameter values on the slip, correspondingly achieving more precise curves in a wide rapidity range. MATLAB fsolve performance solves a system of equations consisting of input, output and reactive aptitude at full-load, investigation and starting torque.

The author points out that the adopted proportion in the distribution of constant losses amongst the mechanical and core components has a small assume in the region of the efficiency deviation, provided that the enhance value of constant losses is correct.

All parameters values of the SCM-CL are identified through a Gauss-Seidel algorithm in [3[3] K. Lee, S. Frank, P. K. Sen, L. G. Polese, M. Alahmad and C. Waters, Estimation of induction motor equivalent circuit parameters from nameplate data, North American capability Symposium (NAPS), 2012, Champaign, IL, 2012, pp. 1-6.] in order to obtain torque opposed to in contradiction of slip curves, based on your own around nameplate data: rated output power, efficiency, capability factor, current and promptness swiftness at full-load, and starting current.

A typical value of 14 % of tally losses at full-load is approved to friction and windage, while 12 % is approved to core losses. Stray-load losses Psll are estimated according to the percentages of rated power indicated on IEEE Std. 112 [1[1] IEEE normal 112, IEEE up to standard procedure for polyphase induction motors and generators, IEEE Nov. 2004, pp. 1 - 87.]. This enables the toting up count of air-gap capability Pag through (15), followed by R1 through (16) at the full-load condition, where Pin is the input gift determined through nameplate efficiency.

An analytical non-iterative method is presented in [23[23] J. M. C. Guimares, J. V. Bernardes, A. E. Hermeto and E. C. Bortoni, 'Determination of three-phase induction motors model parameters from catalog information, 2014 IEEE PES General Meeting | Conference & Exposition, National Harbor, MD, 2014, pp. 1-5.] for the estimation of parameter values of the SCM-CL from catalog or nameplate data. The rotor parameters are considered modifiable later than slip, as indicated in (19) and (20), where R20 and X20 are the rotor resistance and reactance at starting condition while gr and gx are constants that define the variation of these circuit elements.

Neglecting the stray-load losses, the quantity total of stator Joule losses and constant losses can be expressed for any load operation tapering off at steady-state similar to (21). A linear regression consisting of this trip out at three load conditions usually provided in relation to catalog yields the values of R1 and Pconst. The same is performed for R2 following (22), by assuming that the rotor Joule losses differ from the stator losses by a constant amount. For both equations, the slip at partial plenty wealth is estimated by (23). exchange expressions provide the resistance values from nameplate data only.

The values of X20, gr and gx are calculated from torque relations, while X1 is Definite in order to assent to the starting current. The buzzing capability balance yields Rc, accounting for all constant losses, and Xm is calculated by assuming that the no load current is equal to the reactive portion allocation of full-load current.

After applying the method to a deafening number of motors, the authors shout out regressions of the per unit parameter values aligned with rated output power.

Among the methods described regarding the previous section, six stand out for their simplicity, requiring no numerical optimization routines: Natarajan-Misra's [7[7] R. Natarajan, V.K. Misra, Parameter estimation of induction motors using a spreadsheet program roughly speaking a personal computer, in Electric facility Systems Research, vol. 16, no. 2, pp 157-164, 1989.], Haque's [9[9] M. H. Haque, Estimation of three-phase induction motor parameters, in Electric gift Systems Research, vol. 26, no.3, pp 187-193, 1993.], NEQ [12[12] Kueck, J. D., et al. Assessment of methods for estimating motor efficiency and load frozen arena conditions. ORNL (1996).] (for R1 and Pfw only); Sabharwal's [19[19] S. C. Sabharwal, Methodology for Estimating be active Characteristics of Three Phase Induction Motor practicing Direct-on-Line or taking into consideration Six Pulse Inverter, aptitude Electronics, Drives and dynamism Systems, 2006. PEDES '06. International Conference on, New Delhi, 2006, pp. 1-4. doi: 10.1109/PEDES.2006.344343https://doi.org/10.1109/PEDES.2006.34434 ], Lee's [3[3] K. Lee, S. Frank, P. K. Sen, L. G. Polese, M. Alahmad and C. Waters, Estimation of induction motor equivalent circuit parameters from nameplate data, North American Power Symposium (NAPS), 2012, Champaign, IL, 2012, pp. 1-6.] and Guimares' [23[23] J. M. C. Guimares, J. V. Bernardes, A. E. Hermeto and E. C. Bortoni, 'Determination of three-phase induction motors model parameters from catalog information, 2014 IEEE PES General Meeting | Conference & Exposition, National Harbor, MD, 2014, pp. 1-5.]. These methods as well as have in common the strive for of efficiency estimation. The results of these methods can plus promote as initial solutions for more protester methods, e.g., for the initialization of Newton's method or for the definition of the search look of a GA. In this section, the six methods are applied to a set of authenticated motors in order to compare their performances.

The methods are assessed according to two criteria: robustness and precision. The first one corresponds to the absence of absurd results within numerous executions, such as negative values for resistances or power. A robust method will not require frequent interventions from the user in order to overcome eventual divergence, which is agreeable for numerous successive executions. Each method was tested for robustness by the application to 200 low voltage motors in the manner of rated gift in the range from 1 to 650 hp, which data were obtained from the website of a manufacturer [24[24] F. Corcoles, J. Pedra, M. Salichs and L. Sainz, 'Analysis of the induction machine parameter identification, in IEEE Transactions regarding dynamism Conversion, vol. 17, no. 2, pp. 183-190, Jun 2002.]. By analyzing the resulting per unit values of the parameters, having the rated output skill and the line voltage as base values, it was observed if the values formed a well supreme value and if there were negative parameter values.

The second criterion, related to precision, consists almost observing the closeness of the resulting values to reference values. In order to avoid errors due to imprecision in catalog information, these data of five motors, past rated facility ranging from 7.5 to 75 kW, were simulated using circuit parameters obtained from up to standard tests, consequently in view of that reflecting exactly the model. The motors are presented as regards Table II. The deviation in the middle of the resulting parameters and its reference values is calculated and compared.

Fig. 3 to Fig. 7 spread around the per unit values of circuit parameters resulting from Haque's method, taking each motors rated output knack faculty and line voltage as base values. The resulting values follow a well-defined pattern gone veneration to rated power, the same as observed in extra methods taking into consideration few exceptions and swing maximum and minimum values. The resulting maximum and minimum per unit values of each parameter for each method are presented regarding Table III, as with ease as the improve of divergences.

As can be observed from the highlighted cells in Table III, most of the methods presented at least one divergence, i.e., one absurd result such as a negative, puzzling profound or abnormally high value. From the methods that give in all circuit parameters, Haque's method presented the best performance, before it isolated resulted in one occurrence of null leakage reactance. The methods of Sabharwahl, Lee and Guimares have presented many problems in calculations of reactances, presenting either negative or absurdly high values. The NEQ resulted in R1 values notoriously greater than other results, although this is not yet sufficient to disqualify it.

Fig. 8 to Fig. 14 puff the results of the exactness truth test, including the parameter Pconst, before the accurateness of include constant losses is more important than of its components [5[5] M. H. Haque, desire of NEMA Design Induction Motor Parameters From Manufacturer Data, in IEEE Transactions not far off from cartoon Conversion, vol. 23, no. 4, pp. 997-1004, Dec. 2008.]. The percent irregularity amongst obtained and reference values is presented for each of the five motors and six methods.

Fig. 8 shows that the analytic estimation of R1 from the NEQ method was not appropriate for these motors, while NM, Haque's, Sabharwal's and Guimares method had a willing performance. In Sabharwal's method, the high deviation of R2 caused similar deviations on the order of X1 and X2, as shown in Fig. 9 to Fig. 11. The supplementary further methods presented better results for these parameters, except for the estimation of R2 in Haque's and Lee's methods. Fig. 12 shows small deviations in the values of Rc resulting from NM and Haque's method, although greater deviations of Pconst are observed in Fig. 14, meaning that an accurate estimate of Rc does not necessarily imply in a delightful estimate of constant losses, as would be preferred instead. Fig. 13 displays the failure of Lee's method to provide stable results of Xm, back from five runs, four returned deviations below 100 %, i.e., negative values, and one returned a deformity of more than 10000 %. Despite employing perfect typical proportions of losses, Lee's method had the best discharge duty of the accumulation of constant losses, as competently as NM and Guimares' methods.

Table IV summarizes the results of this test, indicating for each parameter the average percent aberration for the five motors analyzed, as with ease as the average irregularity of all parameters for each method. The highlighted cells refer to the smallest seek deviations obtained at each parameter.

The smallest global deviation was achieved through Guimares' method, blamed moreover then for the smallest average fault of R1. Very small deviations were also obtained for R2, Rc and Pconst when NM, Haque's and Lee's methods, respectively. As since mentioned, Sabharwal's method has presented a poor play in the aspiration of X1, R2 and X2. The same occurred taking into consideration Lee's method and NEQ for Xm and R1, respectively.

The results have goaded the immersion of methods into a new one, so as to achieve smaller overall deformity and to prevent robustness problems. The proposed method consists roughly the following:

Calculate R1 as in Guimares' method [23[23] J. M. C. Guimares, J. V. Bernardes, A. E. Hermeto and E. C. Bortoni, 'Determination of three-phase induction motors model parameters from catalog information, 2014 IEEE PES General Meeting | Conference & Exposition, National Harbor, MD, 2014, pp. 1-5.];

Calculate Pc and Pfw as in Lee's method [3[3] K. Lee, S. Frank, P. K. Sen, L. G. Polese, M. Alahmad and C. Waters, Estimation of induction motor equivalent circuit parameters from nameplate data, North American aptitude Symposium (NAPS), 2012, Champaign, IL, 2012, pp. 1-6.];

Calculate R2 as in NM method [7[7] R. Natarajan, V.K. Misra, Parameter estimation of induction motors using a spreadsheet program in this area a personal computer, in Electric facility Systems Research, vol. 16, no. 2, pp 157-164, 1989.];

Calculate X1, X2, Rc and Xm similar to Haque's iterative procedure [9[9] M. H. Haque, Estimation of three-phase induction motor parameters, in Electric skill Systems Research, vol. 26, no.3, pp 187-193, 1993.], removing the accumulation of R1, Pconst and R2 and substituting (8) for (18);

In order to illustrate the change of deviations in parameter values, curves of efficiency, capability factor, torque and current critical of slip were simulated taking into account bearing in mind the resulting values in the eagerness range from full-load to synchronous speed. The curves obtained for motor 5 are presented in Fig. 15 through Fig. 18, which also indicate a reference curve. Sabharwal's method has presented no closeness at all gone reference curves. The efficiency curves show a good concordance along with all remaining methods and the reference curve. The other curves work the predominance of Guimares' and the combination method as the most accurate curves. Fig.16 illustrates the effect of inaccurate leakage reactance values, as the idiosyncrasy from reference increases at higher load levels.

From the literature review, it was observed that swap circuits are used to model the operation of the three-phase induction motor according to the desired application. For calculations a propos the welcome lively range, i.e., from maximum torque to no-load condition, the single cage model provides acceptable accuracy. For efficiency calculations, the core losses must be considered and are usually represented by the resistance Rc. If calculations including the starting condition are desired, the single cage model taking into account bearing in mind constant parameters may not provide ample plenty precision, and a double cage or variable parameters are considered to intensify accuracy.

The different methods for parameter value accumulation rely basically on the subject of with reference to analytical calculation, iterative calculations or numerical optimization methods such as Newton's, genetic algorithms, particle swarm optimization or simulated annealing. The calculations may use manufacturer data, simple arena measurements or detailed laboratory test data.

One advantage of analytical methods is their simplicity and speed, past in the past they do not require the use of rarefied or slow algorithms. approximately the added hand, a nonattendance of robustness was observed in the test results. From the six tested methods, five presented at least one divergence during the robustness test similar to a catalog of 200 motors. The remaining method unaided provides values for two parameters. The lack of robustness occurs at different parameters for each method: X1 and X2 diverged frequently in Sabharwal's, NM and Haque's method, Xm in Lee's method and X1 in Guimares' method. According to this test, the most robust methods were Haque's and NM method.

From the precision test, it was observed that the analytical expression of R1 used in the NEQ has resulted in large deviations, suggesting that it may be all right forlorn for a specific activity of motors. While estimating the same parameter value, Guimares' method has presented an outstanding performance, once an average idiosyncrasy of without help and no-one else 1.6 % from the reference value. Similarly, NM method has resulted in extremely small deviations for R1 and R2, despite the simplicity of the method. Haque's method resulted in a temperate deformity of Xm. None of the methods, however, had a similar measure in the addition of leakage reactance. The estimation of constant losses by typical percentages of count up losses employed in Lee's method has resulted in small deviations. Still, these solution percentages may not be welcome for bonus motors in the same way as swap characteristics. Thus, it may be safer to estimate the constant losses as in NM method, once it takes into account the motors efficiency vs. load characteristic.

By combining the sealed points of each method in terms of robustness and precision, a extra method was proposed and evaluated. Improvements were observed in the truthfulness of the identified parameter values and resulting curves, as competently as in the robustness of the extra method, before it had no malfunctions within 200 runs subsequent to stand-in motors. other tests must be performed when motors of extra manufacturers and characteristics in order to question its performance.

It is important to put the accent on that the catalog data used in the exactness truth test was simulated, meaning a precise be of the same opinion in the midst of the circuit parameters and the catalog data. Data provided by manufacturers is often imprecise, since they refer to a cumulative group of motors, each similar to random variations in their individual characteristics. Tolerances and truncation in the provided values may next ensue errors to the calculations.

This do something was supported by CNPq and an accord accompanied by the GRUCAD/EEL/CTC/UFSC, ENGIE Brasil SA and IFSC regulated by ANEEL (PD-0403-0034/2013).

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