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Electric Power Components and Systems
ISSN: 1532-5008 (Print) 1532-5016 (Online) Journal homepage: http://www.tandfonline.com/loi/uemp20
The Squirrel-Cage Induction Motor Model and ItsParameter Identification Via Steady and DynamicTests
Onofre A. Morfín, Carlos E. Castañeda, Riemann Ruiz-Cruz, Fredy A.Valenzuela, Miguel A. Murillo, Abel E. Quezada & Nahitt Padilla
To cite this article: Onofre A. Morfín, Carlos E. Castañeda, Riemann Ruiz-Cruz, Fredy A.Valenzuela, Miguel A. Murillo, Abel E. Quezada & Nahitt Padilla (2018) The Squirrel-Cage InductionMotor Model and Its Parameter Identification Via Steady and Dynamic Tests, Electric PowerComponents and Systems, 46:3, 302-315, DOI: 10.1080/15325008.2018.1445140
To link to this article: https://doi.org/10.1080/15325008.2018.1445140
Published online: 20 Apr 2018.
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Electric Power Components and Systems, 46(3):302–315, 2018Copyright C© Taylor & Francis Group, LLCISSN: 1532-5008 print / 1532-5016 onlineDOI: 10.1080/15325008.2018.1445140
The Squirrel-Cage Induction Motor Model and ItsParameter Identification Via Steady and DynamicTests
Onofre A. Morfín,1 Carlos E. Castañeda,2 Riemann Ruiz-Cruz,3 Fredy A. Valenzuela,4
Miguel A. Murillo,1 Abel E. Quezada,1 and Nahitt Padilla1
1Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, Chihuahu, México2Centro Universitario de los Lagos, Universidad de Guadalajara, Guadalajara, Jalisco, México3Instituto Tecnológico de Estudios Superiores de Occidente, Zapopan Jalisco, México4Universidad Juárez Autónoma de Tabasco, Villahermosa Tabasco, México
CONTENTS
1. Introduction
2. The Squirrel-Cage Induction Motor Model
3. Induction Motor Parameter Identification
4. Induction Motor Model, Observers, and Parameter
Identification Validation
5. Conclusions
Funding
References
Keywords: dynamic test, electrical and mechanical parameters, fixed statorcoordinate frame, load torque observer, parameter identification, real timeexperimental validation, rotor flux observer, simulation results, squirrel-cageinduction motor model, steady-state tests
Received 15 July 2016; accepted 11 February 2018
Address correspondence to Carlos E. Castañeda, Departamento de CienciasExactas y Tecnología, Centro Universitario de los Lagos, Universidad deGuadalajara, Av. Enrique Díaz de León 1144, Colonia, Paseos de laMontaña, Lagos de Moreno, Jalisco C.P. 47460, México. E-mail:[email protected]
Color versions of one or more of the figures in the article can be found onlineat www.tandfonline.com/uemp.
Abstract—One of the most important bases for designing robustclosed-loop controllers applied to induction motor with high perfor-mance is establishing its mathematical model and state observers, aswell as the parameter identification with high accuracy. In this paper,a step-by-step mathematical model of the squirrel-cage inductionmotor is described at αβ coordinate frame where the parameters aredefined in detailed form; the rotor flux linkages and load torque areestimated via an asymptotic observer; the induction motor parameteridentification is performed via a data acquisition board, applyingdynamic and steady-state tests. Inductances of the induction motormodel are calculated using the proposed relationships between themagnetically coupled circuit and equivalent circuit model. Themathematical model, state observers, and parameter identificationprocedure of squirrel-cage induction motor are validated via com-parison of simulation signals with their corresponding real-timesignals. This validation is made experimentally by a steady-statetest, where load conditions are changed via a dynamometer which isbelt coupled with the squirrel-cage induction motor.
1. INTRODUCTION
The induction machine is one of the most common electricalmotors used today. This motor has many applications, duethat, it is a rugged, highly reliable, low cost, and almostmaintenance-free electromechanical device. Despite of beinga common device, one drawback of this motor is that itsmathematical model is very complex, due to its non-linearityand time variant parameters. The procedure to develop aninduction motor model, and the procedure to identify itsparameters is difficult. Several authors have been addressedmodeling and parameter identification, which are very impor-tant aspects for designing control algorithms, but they donot present many details. A novel parameter identification
302
Morfín et al.: Modeling and parameter identification of the squirrel-cage induction motor 303
process where a single-phase AC test is applied to makethe induction motor stand-still is proposed in [1], [2], and[3], diverse AC signals are feeding in only two terminalsand no electromagnetic torque is generated. They propose amonophasic equivalent circuit at terminals a − b and applyan input–output test with the prediction error method toobtain indirectly the parameter vector with components: Rs,Ls, σ , and Tr. The work reported in [1] and [2] includessaturation magnetic in both total-leakage inductance andmagnetizing inductance. They discretize the standstill-testcircuit impedance to apply an input–output test and obtainthe parameter vector. In [3], the input and output signals,i.e., voltage and current stator, respectively, are analyzed bythe fast Fourier transform algorithm; the analog low-passfilters are used to cut off the harmonics around the switchingfrequency of these signals. The stator voltage, stator current,and their derivatives, necessary for the recursive least-squarealgorithm, are obtained using the vector constructing method.[1], [2], and [3] do not present the relationships between theinductances values obtained with the ones used in the dynamicmodel. The parameter identification process results a littlecomplex and the mechanical parameters are not obtained.
The off-line motor parameter identification method apply-ing the no-load and rated-running tests with measurements inthe sinusoidal steady-state mode is other technique; this pro-cess applies linear regression and estimates the equivalent cir-cuit parameters, [4], [5], and [6]. In [4], a recursive simpleleast-square algorithm is applied using the real and complexcomponents of the transfer function between voltages and cur-rents by simulations with different noise sources. They applyDC-test for estimating Rs; no-load test for estimating R f andXm, and rated-load test for estimating Xl and R. However, therelationships between the inductances from equivalent circuitproposed and the ones of the dynamic model are not clearwhich makes it difficult to interpret. Moreover, they do notreport the mechanical parameters. In [5], this paper deals withoff-line parameter identification from input–output data (sta-tor voltages–stator currents and velocity) supplying the motorwith steady-state sinusoidal voltages. The parameter identifi-cation is made by the standard recursive least-square (RLS)algorithm for minimizing the model prediction error, but theydo not consider the rotor leakage inductance and determineonly the equivalent circuit parameters. In [6], the authors pro-pose an off-line motor parameter identification method apply-ing model reference adaptive system (MRAS) scheme thatuses a global optimization algorithm based on sparse gridmethod named the hyperbolic cross point (HCP) algorithm.The measured and simulated stator currents are compared ina cost function to define in recursive form the following set ofparameters: Rs, R′
r, LLs, Ls, H , and LL. The authors commit a
mistake defining the mutual inductance for dynamical modelbecause they forget the coefficient term of 3/2.
Other parameter identification process is applied fromthe starting-test results to refer some output variables withrespect to slip changes, [7] and [8]. In [7], based on steady-state circuit equivalent, the parameter identification is realizedusing electric torque and motor current measures, which aretaken at different slip values. The parameter estimation isperformed off-line using a multi-objective genetic algorithmto minimize the error between the measured data and the dataobtained from equivalent circuit. The genetic algorithm repre-sents a high computational load, which makes a complicatedimplementation. In addition, that research does not presentthe relationships between the inductances values obtainedwith the ones used in the dynamic model, and the mechanicalparameters are not obtained. In [8] from starting no-loadtest at low voltage, the resistance and reactance curves aredepicted in function of the slip rate, then the recursive least-square (RLS) algorithm combined with a particle swarmoptimization method is applied to optimize the equivalent cir-cuit parameters. However, the friction coefficient and inertialmoment are calculated via the equation movement from theelectromagnetic torque using the rotor resistance whose valueis sensitive to temperature changes.
On-line parameter estimation consists of identifying theevolution of the machine parameters without removing themachine from service, [9]–[10]. In [9], a two-step approach toidentify the parameters of an induction machine from the mea-sures of the stator currents at starting test is presented. Thisproposal uses both simulation and estimation processes; in thefirst stage, an input–output response of the forward inductionmotor model with low-quality initial guesses is used to gen-erate a set of predictions of the stator currents is; then, in thesecond stage, the input is the mismatch between the estimatedand measured stator current vector having as output a param-eter vector; this process is made in recursive form applyingthe Levenberg–Marquardt algorithm until the mismatch ofcurrents is minimized. In [10], a multi-rate real time model-based parameter estimation algorithms for induction motorare applied. The proposed multi-rate EFK method combinesmulti-rate control and EFK to estimate motor load torque,introducing both input and output algorithms. The method isimplemented in real time on a PC cluster node that acts asa controller to an induction motor experimental set-up. Thispaper only estimates the rotor time constant and the methodrepresents a high computational load, which makes a compli-cated implementation.
After having reviewed some research about parametricestimation and modeling of the induction motor, we have iden-tified the importance of establishing, in a detailed and clear
304 Electric Power Components and Systems, Vol. 46 (2018), No. 3
way, the procedure for obtaining the model of the inductionmotor and the identification of all parameters, both electricaland mechanical. Thus, from this base knowledge, moreaccurate innovative identification techniques can be applied.Therefore, the main contributions of this research are: (1) adetailed procedure to obtain the mathematical model for thesquirrel-cage induction motor where the rotor inductance,stator inductance, and mutual inductance are defined formallywhen setting the model at αβ coordinate frame; this method-ology can be applied to obtain the mathematical model of anyother type of AC machine, such as the doubly fed inductiongenerator, synchronous machine, and permanent-magnetmachine; (2) the electrical parameter identification is madevia a data acquisition board including the electrical variablesof all phases and computing the consumed power in eachone test with accuracy; in addition, the synchronous test wasmade to quantify the core loss; (3) for comparison purposes,a complete equivalent circuit including core-loss is proposedwith goal of validating the common approaches performedin standstill test and no-load test which define the equivalentcircuit model.
This paper is organized as follows. In Section 2, the induc-tion motor mathematical model at αβ frame, rotor flux link-ages observer, and load torque observer, are developed indetail. The identification procedure for estimating the elec-trical and mechanical parameters of the induction motor ispresented in Section 3, where each experiment is explainedin detail. In order to validate the mathematical model andits parameter identification, a comparison between simulatedand real-time experimental results is discussed in Section 4.Finally, the conclusions are given in Section 5.
2. THE SQUIRREL-CAGE INDUCTION MOTORMODEL
The voltage vector equations in machine variables for the sta-tor winding and rotor winding, respectively, are:
vABC = RsiABC + d
dtλABC, (1)
v′abc = Rri
′abc + d
dtλ′
abc, (2)
with
Rs =⎡⎣ Rs 0 0
0 Rs 00 0 Rs
⎤⎦ , Rr =
⎡⎣ R′
r 0 00 R′
r 00 0 R′
r
⎤⎦ .
In the above equations, capital letter suffixes are used to iden-tify the stator variables and lowercase letters to rotor variables.Rs is the stator resistance per phase, and R′
r is the rotor resis-tance per phase referred to stator winding. When considering
linearity in the flux linkages–current relation (λ − i), the sta-tor and rotor flux linkages vector equations may be expressedin abc system as
λABC = LsiABC + Lsriabc , (3)
λ′abc = Lriabc + L�
sriABC , (4)
with
Ls =
⎡⎢⎣
Lss Lsm Lsm
Lsm Lss Lsm
Lsm Lsm Lss
⎤⎥⎦ ,
Lsr = Lsrm
⎡⎢⎣
cos θr cos(θr + 2π
3
)cos
(θr − 2π
3
)cos
(θr − 2π
3
)cos θr cos
(θr + 2π
3
)cos
(θr + 2π
3
)cos
(θr − 2π
3
)cos θr
⎤⎥⎦ ,
Lr =
⎡⎢⎣
L′rr L′
rm L′rm
L′rm L′
rr L′rm
L′rm L′
rm L′rr
⎤⎥⎦ ,
where Lss and Lsm are the stator self-inductance per phase andstator mutual-inductance between two phases, respectively;and Lsrm is the amplitude of the mutual inductances betweenstator and rotor windings; L′
rr and L′rm are the rotor self-
inductance per phase and rotor mutual-inductance betweentwo phases, respectively; both are referred to the stator side.It is important to remark that the mutual-inductances betweentwo windings vary periodically due to the relative movementbetween the stator winding and rotor winding.
In order to remove the time dependency of the mutual-inductances between the stator and rotor windings, the Clarkesimilitude transformation is applied to change the electricalvariables from abc system to αβ0 coordinate frame, whoseaxes are fixed on the stator winding and the α-axis is alignedwith the phase-a axis [11], see Figure 1. The Clarke transfor-mation matrix and its inverse matrix applied to stator variablesare defined as
Ts = 2
3
⎡⎢⎢⎣
1 − 12 − 1
2
0√
32 −
√3
2√2
2
√2
2
√2
2
⎤⎥⎥⎦ , (5)
T−1s =
⎡⎢⎢⎣
1 0√
22
− 12
√3
2
√2
2
− 12 −
√3
2
√2
2
⎤⎥⎥⎦ . (6)
Conducive to transform the rotor variables into a new coor-dinate system, the displacement angle θr must be considered,as it is depicted in Figure 1. Then, the similitude transforma-tion and its inverse representation applied to rotor variables
Morfín et al.: Modeling and parameter identification of the squirrel-cage induction motor 305
FIGURE 1. Clarke transformation applied to stator and rotorvariables.
are defined as
Tr = 2
3
⎡⎢⎣
cos θr cos(θr + 2π
3
)cos
(θr − 2π
3
)sin θr sin
(θr + 2π
3
)sin
(θr − 2π
3
)√
22
√2
2
√2
2
⎤⎥⎦ , (7)
T−1r =
⎡⎢⎢⎣
cos θr sin θr
√2
2
cos(θr + 2π
3
)sin
(θr + 2π
3
) √2
2
cos(θr − 2π
3
)sin
(θr − 2π
3
) √2
2
⎤⎥⎥⎦ . (8)
By applying the Clarke transformation (5)–(6) to statorvoltage equation (1) gives the next result:
vαβ0s = Rsiαβ0s + d
dtλαβ0s, (9)
with
Rs =⎡⎣ Rs 0 0
0 Rs 00 0 Rs
⎤⎦ .
Meanwhile, the stator flux linkages vector in αβ0 takes thefollowing form, when the similitude transformations (5)–(6)and (7)–(8) are applied into (3):
λαβ0s = Lsiαβ0s + Lsriαβ0r , (10)
with
Ls =⎡⎣ Ls 0 0
0 Ls 00 0 Lss + 2Lsm
⎤⎦ , Lsr =
⎡⎣ Lm 0 0
0 Lm 00 0 0
⎤⎦
where the stator-inductance and mutual-inductance aredefined, respectively, as
Ls = Lss − Lsm , (11)
and
Lm = 3
2Lsrm. (12)
By applying the similitude transformation (7)–(8) into (2),the rotor voltage vector in αβ0 frame becomes:
vαβ0r = Rriαβ0r + �rλαβ0r + d
dtλαβ0r, (13)
where
Rr =⎡⎣ R′
r 0 00 R′
r 00 0 R′
r
⎤⎦ , �r =
⎡⎣ 0 ωr 0
−ωr 0 00 0 0
⎤⎦
with ωr = P
2ωm be the rotor frequency, P is the number of
poles, and ωm is the rotor angular velocity.Using the similitude transformations (5)–(6) and (7)–(8)
into the rotor flux linkages vector (4), results:
λαβ0r = Lriαβ0r + Lsriαβ0s , (14)
with
Lr =⎡⎣ Lr 0 0
0 Lr 00 0 Lrr + 2Lrm
⎤⎦ , Lsr =
⎡⎣ Lm 0 0
0 Lm 00 0 0
⎤⎦ ,
where the rotor-inductance is defined as
Lr = Lrr − Lrm. (15)
The simplest representation of the induction motor modeluses the stator current vector is is and rotor flux linkages vec-tor λr as state variables, and its order is reduced using onlycomponents in α and β axes, since the variables at 0 axis arenot present due to the neutral connection at stator winding isnot grounded. By solving for ir into rotor flux linkages vector(14), we obtain:
ir = L−1r (λr − Lsris). (16)
Substituting Eq. (16) in the rotor voltage equation (13),defining vr = 0 due to the conducting bars are shorted at both
ends via rings in the rotor’s squirrel-cage, and solvingd
dtλr
in Eq. (13), we obtain the state equation of rotor flux linkagesvector in αβ frame as follows:
d
dt
[λαr
λβr
]=
[− 1
Tr−P
2 ωmP2 ωm − 1
Tr
] [λαr
λβr
]
+[
Lm
Tr0
0 Lm
Tr
] [iαs
iβs
]. (17)
306 Electric Power Components and Systems, Vol. 46 (2018), No. 3
Now, substituting the stator flux linkage equation (10) into thestator voltage equation (9), results in
vs = Rsis + Lsd
dtis + Lsr
d
dtir. (18)
Substituting the differentiation of the rotor current vector
(16) into Eq. (18), and solving for the termd
dtis, we obtain
the state equations of stator current vector in αβ frame asfollows:
d
dt
[iαs
iβs
]=
[δTr
P2 δωm
−P2 δωm
δTr
][λαr
λβr
]
+[−γ 0
0 −γ
] [iαs
iβs
]+
[1
σLs0
0 1σLs
] [vαs
vβs
]. (19)
On the other hand, the electromagnetic torque developed byinduction motor, as a torsional force, is defined by the vari-ation of stored magnetic field energy with respect to electricangular position as
Te =(
P
2
)dWf
dθr, (20)
where P is the poles number of machine, and the stored fieldenergy is defined by [11], [12]:
Wf = 1
2(iABC )� LssiABC + (iABC )� Lsriabcr
+ 1
2(iabc)� Lrriabc. (21)
Because Lss and Lrr are not functions of θr, substituting thestored field energy (21) into (20) yields the electromagnetictorque in abc system:
Te =(
P
2
)∂
∂θr[(iABC )�Lsriabc] . (22)
Applying the similitude transformations (5)–(6) and (7)–(8) tostator current and rotor currents, respectively, in (22); and sub-stituting the mutual-inductance Lm defined in (12), the elec-tromagnetic torque in terms of αβ coordinate frame takes theform:
Te =(
3
2
) (P
2
)Lmi�s
[0 1
−1 0
]ir. (23)
Now, substituting the rotor current equation (16) into (23), theelectromagnetic torque, expressed with the rotor flux linkagesand stator current vectors as state variables, is defined as
Te = 3P
4
Lm
Lr(iβsλαr − iαsλβr) . (24)
Once defined the electromagnetic torque, the angular move-ment equation of the induction motor is defined by
Jmd
dtωm = 3P
4
Lm
Lr(iβsλαr − iαsλβr) − Bmωm − TL, (25)
where the term of the left side is defined as the accelera-tion torque, the second term of the right side is the frictionaltorque, and the last term is the torque established for themechanical load driven by the motor. After the whole pro-cess, the induction motor model is defined combining the stateequations of the rotor flux linkages vector (17), stator currentvector (19), and rotor angular velocity (25). Then, the math-ematical model of squirrel-cage induction motor on the αβ
coordinated frame is
d
dtωm = KT (iβsλαr − iαsλβr) − Bm
Jmωm − 1
JmTL
d
dt
[λαr
λβr
]=
[− 1
Tr−P
2 ωmP2 ωm − 1
Tr
] [λαr
λβr
]
+[
Lm
Tr0
0 Lm
Tr
] [iαs
iβs
](26)
d
dt
[iαs
iβs
]=
[δTr
P2 δωm
−P2 δωm
δTr
] [λαr
λβr
]
+[−γ 0
0 −γ
] [iαs
iβs
]+
[1
σLs0
0 1σLs
] [vαs
vβs
]
with the following parameter constants defined as: KT =3P
4
Lm
JmLr, Tr = Lr
Rr, δ = 1 − σ
σLm, γ = 1
σTs+ 1 − σ
σTr, σ = 1 −
L2m
LsLr, and Ts = Ls
Rs. The machine parameters are defined as:
Rs is the stator resistance per phase, R′r is the rotor resistance
per phase referred to stator winding, Ls is the stator induc-tance, which is defined in (11), Lm is the mutual-inductancedefined in (12), and Lr is the rotor inductance defined in (15).P is the number of poles, Bm is the friction coefficient of theshaft, and Jm is the inertial moment. TL is the load torque asmechanical input, vαs and vβs are the input voltages that feedthe stator winding.
It is important to mention that the procedure to obtain themathematical model of the induction motor is not new, butthe proposed methodology for establishing the mathematicalmodel of the squirrel-cage induction motor is highly detailed,where the rotor inductance, stator inductance, and mutualinductance are defined formally when setting the model atαβ coordinate frame. The proposed methodology can be eas-ily applied for obtaining the mathematical model of any othertype of AC machine, such as the doubly fed induction genera-tor, synchronous machine, and permanent-magnet machine.
Morfín et al.: Modeling and parameter identification of the squirrel-cage induction motor 307
2.1. Rotor Flux Linkages Observer
From induction motor model (26) and considering the angularvelocity ωm as a known input, electrical model becomes linearand it is represented by
d
dt
[λr
is
]=
[A11 A12
A21 A22
] [λr
is
]+
[0
B
]vs
y = [0 1
] [λr
is
], (27)
where the output variable is defined by the stator current vec-tor is, which is the measurement variable. The system (27) canbe transformed to new system of reducer order as
d
dtλr = A11λr + A12is
d
dtis − A22is − Bvs = A21λr , (28)
where the known inputs define the system output. Thereduced-order observer model for rotor flux linkages, frommodel defined in (28), is
˙λr = A11λr + A12is + L
(d
dtis − A22is − Bvs − A21λr
),
(29)where the last term in (29) is a mismatch between the knownand observed outputs, and it corrects the system continuouslywith this error signal.
If the rotor flux observation error variable is defined as
ελ = λr − λr, (30)
then the observation error dynamics is given by subtracting(29) from (28) to obtain:
˙ελ = (A11 + LA21)ε, (31)
where its characteristic equation is defined by
det [sI − (A11 + LA21)] = 0, (32)
the matrix L defines the reasonably fast eigenvalues of (31) sothat observation error variable decays asymptotically to zeroin finite time. These eigenvalues must be at least four or fivetimes faster than the natural eigenvalues of system (28) [13].
By ordering terms in (29), the observer model of the rotorlinkages flux takes the form:
˙λr = (A11 − LA21)λr + (A12 − LA22)is − LBvs + L
d
dtis.
(33)If we define
λ∗r = λr − Lis , (34)
FIGURE 2. Scheme of the rotor flux linkages observer.
then the rotor flux linkage observer is defined by
˙λ∗
r = (A11 − LA21)λr + (A12 − LA22)is − LBvs, (35)
andd
dtis no longer appears directly. A block diagram of the
reduced-order rotor flux observer is pictured in Figure 2.
2.2. Load Torque Observer
Based to induction motor model (26) and by taking the statorcurrent and rotor flux as known inputs, the mechanical modelresults in
ωm = KT λ�r Mis − Bm
Jmωm − 1
JmTL
TL = 0. (36)
A load torque observer can be set as
˙ωm = KT λ�r Mis − Bm
Jmωm − 1
JmTL + l1(ωm − ωm)
˙TL = l2 (ωm − ωm) . (37)
If we define the observation error variable to be
ε =[
ωm − ωm
TL − TL
]. (38)
Then the dynamic of this observation error variable is givenby subtracting (37) from (36) to get
[ ˙εω
˙εT
]=
[−
(Bm
Jm+ l1
)− 1
Jm
−l2 0
] [εω
εT
], (39)
where the values of l1 and l2 define the reasonably fast eigen-values of (39), so that the observation error variable is asymp-totically steered toward zero in finite time. These eigenvaluesmust be at least four or five times faster than the natural eigen-values of system (36) [13].
308 Electric Power Components and Systems, Vol. 46 (2018), No. 3
3. INDUCTION MOTOR PARAMETERIDENTIFICATION
For the purposes of this research, parameter identification ofthe squirrel-cage induction motor model is made with off-line dynamics and steady-state tests via an acquisition boardto determine both electrical and mechanical parameters. Themeasurement of the DC resistance of the stator winding, no-load test, and blocked-rotor test is applied to induction motorto identify the equivalent circuit model. In addition, we havemade the synchronous velocity test to obtain a good approx-imation of the core loss and calculate the friction loss fromthe rotational loss. In each one of the tests mentioned, voltageand current measurements of all phases are taken for includ-ing any electric unbalance in the stator winding; while, theaverage power is calculated with very good accuracy by fil-tering the instantaneous three-phase power. A dynamic test ismade when the motor is turned-off and a vector of the velocityfall is captured to obtain an approximate value of the inertialmoment Jm using the friction coefficient Bm which is obtainedfrom the consumed power before de-energizing the motor.
3.1. Stator Resistance
In this test, ordered pairs consisting of voltage–current mea-surements are obtained by tuning a DC-voltage source fromsmall to rated current values [12]. The stator winding resis-tance is calculated applying Ohm’s law and assuming star con-nection of the winding, i.e., we must calculate the resistanceas two windings connected in series at a − b terminals, laterdivide this value by two. The average resistance is obtainedfrom the next set of replications between terminals: b − c andc − a, being the result Rs = 12 .
3.2. No-Load Test
The no-load test gives information about the magnetizingbranch impedance and rotational loss: friction, windage, andcore losses, as it is explained in [12]. This test is performed byapplying balanced three-phase nominal voltage to the statorwinding at the rated frequency. The rotor is kept uncoupledfrom any shaft of driven equipment. The equivalent circuitmodel of the no-load test is depicted in Figure 3(a), wherethe branch of the rotor circuit is not considered due to therotor current is significantly smaller than magnetizing current,due to that in no-load condition the slip is very small and therotor resistance value is high. The non-load test was carriedout at angular velocity of 1798 r.p.m. with a consumed powerof 29.04 W. This value was obtained computing and filter-ing the instant three-phase power to define the average powerwith very good accuracy. Voltage and current measurements
FIGURE 3. Equivalent circuit of standard tests: (a) no-load,(b) blocked rotor, and (c) synchronous velocity.
are made in each of the phases to involve any electric imbal-ance of the stator winding. These measurements are reportedin Table 1.
The rotational losses Prot are calculated from the no-loadpower Pnl as follows [12]:
Prot = Pnl − Rs
(I2a + I2
b + I2c
). (40)
By substituting the no-load test measurements in(40), the rotational losses are Prot = 13.5 W.
From the no-load test measurements, an equivalent reac-tance is calculated which is composed of two reactances con-nected in series: the stator leakage reactance Xls, and magne-tizing reactance Xmag, see Figure 3(a). For both no-load andblocked rotor tests, the following relationships (41)–(43) areused:
|Ztest| = 1
3
(Va
Ia+ Vb
Ib+ Vc
Ic
), (41)
Rtest = Ptest(I2a + I2
b + I2c
) , (42)
Xtest =√
|Z2test| − R2
test . (43)
Substituting the measurements of no-load test in (41)–(43),results in Znl = 182.6 , Rnl = 22.4 , and Xnl = 181.2 .
Stator phase Voltage (V) Current (A)
A 119.8 0.67B 119.8 0.65C 119.8 0.65
TABLE 1. Measurements of no-load test.
Morfín et al.: Modeling and parameter identification of the squirrel-cage induction motor 309
Stator phase Voltage (V) Current (A)
a 43.6 1.5b 43.8 1.5c 44.7 1.55
TABLE 2. Measurements of block-rotor test.
3.3. Blocked-Rotor Test
The blocked-rotor test gives information about the leakageimpedances and rotor resistance referred to stator side, as itis explained in [12]. In this test, the rotor is blocked by awooden bar so that the motor cannot rotate, and a low volt-age is adjusted with a variable supply voltage via a three-phaseautotransformer, so that the rated-current flows in stator wind-ing. The power consumption during the test was calculated as132.4 W. The voltage and current measurements in all phasesof this test are reported in Table 2.
As this test is made at low voltage and the slip s = 1 due tothe rotor is standstill, then the rotor resistance is small and thecurrent that flows by the magnetizing branch can be neglected.From the equivalent circuit of this test, see Figure 3(b), thestator leakage reactance Xls and rotor leakage reactance X ′
lr
are estimated. Additionally, a first approximation of the rotorresistance R∗
r referred to stator side is obtained.By substituting the blocked-rotor measurements in (41)–
(43), we obtain Zbl = 29.0 , Rbl = 19.2 , Xbl = 21.7 . Ifone applies the following common approximation to definethe stator and rotor leakage reactances, then Xls = X ′
lr = Xbl2 =
10.8 , where X ′lr is referred to stator side by assuming that the
turns ratio is a = 1. Once we know the stator leakage reac-tance, the magnetizing reactance is calculated from no-loadtest as Xmag = 170.4 .
From Figure 3(b), a first approximated value of the rotorresistance referred to stator side can be calculated by
R∗′r = Rbl − Rs = 19.2 − 12 = 7.2 .
The rotor resistance value is very important in the induc-tion motor performance because it models largely the powerconverted from electrical to mechanical energy. Therefore,this value is now improved involving the magnetizing branchin the equivalent circuit [12]. The new value for rotor resis-tance is calculated considering the real part of the Theveninimpedance that is pointed by the arrows in Figure 4(a), whichis
R∗′r = X 2
mag
R′2r + (X ′
2 + Xmag)2R′
r . (44)
Because (X ′lr + Xmag)2 � R
′2r in (44), the enhanced value
of the rotor resistance is
R′r =
(X ′
lr + Xmag
Xmag
)2
R∗′r , (45)
and substituting the values of rotor and magnetizing reactancein (45) yields R′
r = 8.1 .
3.4. Synchronous Velocity Test
The synchronous velocity test gives information about thecore loss and magnetizing branch impedance with better accu-racy than the no-load test. In this test, a DC-motor drivesthe induction machine at synchronous velocity and then theinduction machine is feeding at rate voltage. The DC-motorfeeds the friction and windage loss for both machines; while,the power supply feeds the Joule loss and core loss in theinduction machine because there are no induced currents
FIGURE 4. (a) Equivalent circuit model and (b) completeequivalent circuit model.
310 Electric Power Components and Systems, Vol. 46 (2018), No. 3
Stator phase Voltage (V) Current (A)
A 119.9 0.67B 120.0 0.65C 120.6 0.66
TABLE 3. Measurements of synchronous test.
in rotor winding. The equivalent circuit model of the syn-chronous velocity test is depicted in Figure 3(c). The con-sumed power in this test was calculated as 18.1 W. The voltageand current measurements in each of the phases are reportedin Table 3.
The core loss Pc is calculated by similar form as rotationalloss Prot (40) in no-load test, by
Pc = 18.1 − 12(0.672 + 0.652 + 0.662) = 2.4 W.
3.5. Mechanical Parameters
The inertial moment Jm and frictional coefficient Bm are themechanical parameters which model the shaft masses andfriction in the support points, respectively; these parame-ters are involved in the movement equation (25). Due to thesquirrel-cage induction motor is mechanically coupled with adynamometer with which it is possible to vary the load condi-tions, then the masses and support points of both machinesshould be considered in the definition of the mechanicalparameters. In order to determine the frictional coefficient Bm,the squirrel-cage induction motor is fed at rated voltage with-out applying load torque. In this test, the consumed power was87.3 W at 1778 r.p.m. The voltage and rotor measurements inall phases of this test are reported in Table 4.
The rotational loss in both machines applying equation(40) is Prot = 69.5 W, while the friction loss is the rotationalloss (69.5 W) minus core loss (2.4 W), calculated in the syn-chronous test; then, the friction loss is Pfric = 67.1 W. Conse-quently, from the mechanical power consumed in this test, thefriction coefficient Bm can be approximated as
Bm ≈ Pfric
ω2m
= 67.1
186.22= 0.00194 N m s. (46)
From this same test, the inertial moment Jm can be obtainedwhen the induction motor is turned off and a falling velocityvector (see Figure 5) is captured with an acquisition board.
Stator phase Voltage (V) Current (A)
a 119.8 0.70b 119.9 0.69c 120.6 0.72
TABLE 4. Measurements of coupling no-load test.
FIGURE 5. Supply disconnection of the induction motor.
Once the motor is de-energized and it does not drive anymechanical load, the movement equation (25) takes the fol-lowing form:
Jmd
dtωm = −Bmωm. (47)
Based on Figure 5, it can be seen that the non-filtered andfiltered signals of the angular velocity fall when the motoris turned off and the motor shaft stops in 5 sec, approxi-mately. In this figure, note that two points (2.78 sec, 110.7rad/sec) and (3.12 sec, 90.33 rad/sec) can be used for lin-earizing the motor’s deceleration around the base velocityωm0 = 100 rad/sec; by approximating the derivative at thispoint, and solving for Jm into (47), the inertial moment canbe approximated by
Jm ≈ �t
�ωmBmωm0 ≈ (3.12 − 2.78)
(110.7 − 90.33)(0.00194)(100)
= 0.00324 N m s2. (48)
It is important to remark, that the electrical and mechanicalparameter identification is made via a data acquisition board,and the voltages and currents are measured in all phases, incontrast to the traditional method where the voltage and cur-rent measurements are made in only one phase. Moreover, theconsumed power in each one test is computed with accuracyby filtering the instantaneous power, in contrast with tradi-tional method where a wattmeter is used to measure the con-sumed power in only one phase. In addition, the synchronoustest was made to quantify the core loss which is subtractedfrom the rotational loss, obtained in no-load test, for estimat-ing the friction coefficient with acceptable accuracy. From theno-load test, the motor is turn-off and a falling velocity vectoris captured with an acquisition board for approximating thevelocity derivative for estimating the inertial moment value.The proposed procedure to obtain the mechanical parameters
Morfín et al.: Modeling and parameter identification of the squirrel-cage induction motor 311
contrasts with the work reported in [8], where the two param-eters are calculated via the equation movement from the elec-tromagnetic torque which is estimated through rotor resistancewhose value is sensitive to temperature changes.
3.6. Relationships Between Magnetically CoupledCircuit and Equivalent Circuit
It is important to note that the inductance parameters usedin the induction motor model (26) correspond to the mag-netically coupled circuit model with the stator-inductanceLs, mutual-inductance Lm, and rotor-inductance Lr whichare defined in (11), (12), and (15), respectively; while theinductance parameters obtained from the standard tests whichdefine the equivalent circuit model are the stator leakageinductance Xls, magnetizing inductance Xmag, and rotor leak-age inductance X ′
lr. Therefore, it is necessary to define theequivalence relationships between the magnetically coupledcircuit and equivalent circuit. At the first step, the voltageequations for two magnetically coupled circuits are definedas
v1 = L11d
dti1 + L12
d
dti2
v2 = L12d
dti1 + L22
d
dti2 , (49)
where L11 and L22 are the self-inductances of the pri-mary and secondary windings, respectively; and L12 is themutual-inductance between primary and secondary windings.Thereafter, including the turns ratio a = N1/N2 in diverseterms of system (49), keeping the original system, yields
v1 = L11d
dti1 + aL12
d
dt
i2a
av2 = aL12d
dtis + a2L22
d
dt
i2a
. (50)
Later, adding and subtracting a different term in each equa-tion of (50) yields
v1 = L11d
dti1 + aL12
d
dt
i2a
+(
aL12d
dti1 − aL12
d
dti1
)
av2 = aL12d
dtis + a2L22
d
dt
i2a
+(
aL12d
dt
i2a
− aL12d
dt
i2a
).
(51)
Finally, rearranging terms in (51), we obtain a model thatcorrespond to the equivalent circuit model, which is shown inFigure 6, and this model takes the form:
v1 = (L11 − aL12)d
dti1 + aL12
(d
dti1 + d
dt
i2a
)
av2 = aL12
(d
dti1 + d
dt
i2a
)+ (
a2L22 − aL12) d
dt
i2a
.(52)
FIGURE 6. Equivalence between magnetically coupled andequivalent circuits.
Now, comparing Figures 4(a) and 6, without consideringthe resistances, we can set the relationships that define theinductance equivalence between the magnetically coupled cir-cuit and the equivalent circuit of the following form:
Lls = L11 − aL12, (53)
Lmag = aL12, (54)
L′lr = a2L22 − aL12 . (55)
It is common practice to consider the turns ratio a = 1 forthe squirrel-cage induction motor. From (12) and (54), therelationship between the mutual-inductance Lm, which is usedin the induction motor model (26), and magnetizing induc-tance Lmag results in
Lm = 3
2Lmag . (56)
From (53) and (11), and considering that the mutual-
inductance between two stator phases is Lsm = −1
2Lmag [11],
we obtain the stator inductance which is used in the model(26) as
Ls = Lls + 3
2Lmag . (57)
With a same procedure, the rotor inductance used in model(26) is defined as
Lr = L′lr + 3
2Lmag . (58)
By applying (56), (57), and (58), the equivalence betweenmagnetically coupled model and equivalent circuit model isdefined. In Table 5, values obtained from parameter identifi-cation process for induction motor model (26) have been sum-marized. In Table 6, squirrel-cage induction motor nameplatedata (rated values) are reported.
312 Electric Power Components and Systems, Vol. 46 (2018), No. 3
Parameter Value
Rs 12
Rr 8.1
Ls 0.7066 HLr 0.7066 HLm 0.678 HBm 0.00194 N m sJm 0.00324 N m s2
TABLE 5. Induction motor model parameters.
So far we have obtained the electric parameters of theequivalent circuit (Figure 4(a)). Now, we propose a com-plete equivalent circuit just in order to obtain a compara-tive analysis between both models. The complete equivalentcircuit involves the core loss represented with a resistor Rc
(Figure 4(b)) and the values of the magnetizing reactanceXmag, rotor leakage reactance X ′
lr, and rotor resistance R′r are
more accurate due to the fact that now the analysis is madefrom synchronous velocity test and blocked-rotor tests. Thisis achieved by considering the Thevenin impedance pointedin Figure 4(b). By applying Eqs. (41), (42), and (43) to dataobtained from synchronous test in Table 3, we obtain Rsyn =13.85 and Xsyn = 181.57 , and solving the following non-linear system set from Figure 3(c):
Rsyn = Rs + RcX 2mag
R2c + X 2
mag
Xsyn = Xls + RcX 2mag
R2c + X 2
mag
, (59)
where Rs = 12 , Xls = 10.8 and the parameters Rc andXmag are unknown. The results obtained from (59) are: thecore loss Rc = 15, 765 , and magnetizing reactance Xmag =170.8 . In a similar form, by considering the results fromblocked-rotor test Rbl = 19.2 and Xbl = 21.7 , defining
K1 = RcXmag
R2c + X 2
mag
, and solving the following non-linear system
from Figure 4(b) for unknown parameters R′r and X ′
lr:
Unit Value
Volts 127/220Amperes 1.5r.p.m. 1750Hz 60HP 0.25
TABLE 6. Induction motor nameplate data.
Parameter Equivalent circuit (�)
Complete equivalent
circuit (�)
Rc ∞ 15,765Xmag 170.4 170.8R′
r 8.1 8.2X ′
lr 10.8 11.3
TABLE 7. Magnetizing and rotor branches parameters.
Rbl = Rs + K1AB + CD
E
Xbl = Xls + K1CB − AD
E, (60)
where A = R′rXmag − RcX ′
lr, B = K1Xmag + R′r, C = RcR′
r +X ′
lrXmag, D = K1Rc + X ′lr, and E = (K1Xmag + R′
r)2 + (K1Rc +X ′
lr )2.The results obtained from (60) are: rotor resistance
R′r = 8.2 and rotor leakage reactance X ′
lr = 11.3 . It isimportant to remark that the electric parameters of the com-plete equivalent circuit model are very close to parametersobtained from the no-load and blocked-rotor tests; conse-quently, the approximations made in these tests are justified.In Table 7, the minimum differences between the parametervalues of the magnetizing and rotor branches can be seen.
4. INDUCTION MOTOR MODEL, OBSERVERS,AND PARAMETER IDENTIFICATIONVALIDATION
Experimental validation was made using the followingdevices:
� A squirrel-cage induction motor (Lab-Volt 8221-02)coupled via belt with a dynamometer (Lab-Volt 8960-12) with velocity sensor, see Figure 7.
FIGURE 7. Induction motor-dynamometer group.
Morfín et al.: Modeling and parameter identification of the squirrel-cage induction motor 313
� dSPACE DS1103 data acquisition board with real-timeinterface (RTI) to display signals.
� A measurement interface for currents in each phase andtwo line-to-line voltages in stator terminals.
In order to validate the mathematical model (26), rotorflux linkages observer (35), load torque observer (37), and theparameter identification, the squirrel-cage induction motor isoperated under variable load conditions, where the load torqueis applied by a dynamometer. An array with 10 sec lengthand 100 µsec sampling time was captured for electrical andmechanical signals. Then, the similitude transformation wasapplied in real time to stator voltages vab, vcb, and stator cur-rents ia, ib, and ic to refer them at α − β coordinated frame.The angular velocity ωm and stator currents iαs (phase-a) arecompared graphically between their measured values and cor-responding results obtained via simulation. It is important toremark that the mathematical model (26) and rotor flux link-ages observer (35) are validated by means of the compari-son between the measured load torque with the observed loadtorque (37). With this, the mechanical oscillation equation(25) is fulfilled where the electromagnetic torque (24), as non-linear term, stands out, which involves a sum of two electricalstate space variables products of system (26).
The induction motor as electromechanical device has twoinputs: the stator voltages and the load torque. In the firsttest, the motor is subjected to step response by applying thenominal voltage at stator winding and the motor is turned-on.In the second test, the load torque is changed from no-loadcondition to nominal operation condition in five successivesteps establishing different points of operation of the motor.In Figure 8, the induction motor starts on under no-load con-dition is shown, the rotor velocity simulated and measured arevery close when the velocity arises, without the use of a filter
1.5 2 2.5 3 3.5 4 4.5 5−500
0
500
1000
1500
2000
2500
Time (s)
Ang
ular
vel
ocity
(r.p
.m.)
nm
measured
nm
estimated
FIGURE 8. Starting of induction motor.
FIGURE 9. Mechanical variables. (a) Rotor angular velocity,and (b) Load torque.
to avoid a delay in velocity measurement. By turning a poten-tiometer in DC-machine module, five load torque levels wereset up, from no-load to rated condition, where the rated torqueis TL = 1 N m. In Figure 9(a), rotor angular velocity ωm mea-sured by encoder and rotor velocity obtained via simulationof proposed model (26) are displayed. Note that in this figure,there are two indicated values at 5.0 sec time, which are 1746and 1740 r.p.m., measured and simulated velocities, respec-tively; and the difference between both velocities is mini-mal of 6 r.p.m. with a relative error of 0.3%. In Figure 9(b),the variations of load torque measured and load torque esti-mated via an asymptotic observer are depicted, where thereis not difference. In Figure 10(a), the stator current at α-axis,which corresponds with the phase-a of three-phase system isshown. When the load torque is changed, then the stator cur-rents change, too. The stator current iαs does not present goodapproximation between the measured (1.25 A rms) and simu-lated signal (0.95 A rms), as shown in Figure 10(b). The dif-ference between the stator current simulated and measured isnotorious due to core loss is not involved in parameter identi-fication process.
It is an important remark that all state variables areinvolved into movement equation; therefore, as the observedload torque is very close to the measured load torque, thenthe mathematical model and its parameter identification isvalidated.
314 Electric Power Components and Systems, Vol. 46 (2018), No. 3
FIGURE 10. (a) Stator current iαs (phase-a), (b) detail ofstator current at α-axis.
5. CONCLUSIONS
In this paper, a step-by-step procedure is presented to obtainthe mathematical model of the squirrel-cage induction motorat αβ coordinate frame. In order to carry out the electricparameter identification procedure, no-load test and blocked-rotor test were applied in steady state to obtain the equivalentcircuit model of the induction motor. In addition, the syn-chronous velocity test was made to approximate the core losswhich is included in the results obtained at no-load test wherethe induction motor is coupled to a dynamometer via a belt.From this test, the friction coefficient Bm is approximatedfrom the mechanical power developed at the shaft which iscalculated separating the core loss from rotational loss; later,the inertial moment Jm is estimated from movement equationwhen the motor is de-energized by capturing velocity as itfalls and approximating its derivative. In addition, we proposethe equivalence relationships for changing the inductanceparameters from equivalent circuit model to magneticallycoupled circuit model. The equivalent circuit model is usedto predict the steady-state performance of the inductionmotor, meanwhile the mathematical model in αβ frame hasparameters of the magnetically coupled circuit model. Finally,in order to validate the mathematical model and its parameteridentification a steady-state test was made where the loadconditions are varied by a dynamometer. We can clearly seein the obtained signal plots, a very close similarity betweensimulation and measured signals of the induction motor. Itis important to remark that the mathematical model of the
induction motor, the state observer models, and the parameteridentification constitutes an important aspect in the designingof robust closed-loop controllers with high performance.
FUNDING
This work was supported by Departamento de Eléctrica yComputación del Instituto de Ingeniería y Tecnología dela Universidad Autónoma de Ciudad Juárez (México), Pro-grama para el Desarrollo Profesional Docente under grantPROMEP/103.5/11/901 Folio UACJ/EXB/155, and ConsejoNacional de Ciencia y Tecnología (México) by the retentionprogram no. 120489.
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BIOGRAPHIES
Onofre A. Morfin received the B.S. in Electromechani-cal Engineering in 1990 from the Technological Institute ofToluca, Mexico; the M.Sc. degree in Electrical Engineer-ing in 1994 from Monterrey Institute of Technology andHigher Education, Monterrey campus, Mexico; and the Ph.D.in Electrical Engineering in 2010 from the Advanced Stud-ies and Research Center of the National Polytechnic Insti-tute (CINVESTAV-IPN), Guadalajara campus, Mexico. Heis working as Professor in the Electrical and ComputingDepartment at Technology and Engineering Institute of theAutonomous University of Ciudad Juarez, Chihuahua, Mex-ico, since 2003. His research interests are energy saving sys-tems and loop-closed control system designs applied to elec-trical machines and renewable energy.
Carlos E. Castañeda was born in Lagos de Moreno, JaliscoMexico, in 1973. He received the B.S. in Communications andElectronics in 1995 from the Guadalajara University, Mex-ico, the M.Sc. degree in Electronics and Computer Systems in2003 from the La Salle University of Bajio, Mexico, and thePh.D. in Electrical Engineering in 2009 from the AdvancedStudies and Research Center of the National Polytechnic Insti-tute (CINVESTAV-IPN) Guadalajara, Mexico. He is also amember of the Mexican National Research System (Rank 1).He is working as Professor at Guadalajara University, Univer-sity Center of los Lagos, Mexico. His research interests areautomatic control and renewable energy sources using mainlyartificial neural networks and sliding modes in continuous-time and in discrete-time.
Riemann Ruiz-Cruz was born in Oaxaca, Oaxaca, Mexico,in 1983. He earned the B.S. from Technological Institute ofOaxaca, Oaxaca, Mexico, in 2006; and the M.Sc. degree andPh.D. in Electrical Engineering from the Advanced Studiesand Research Center of the National Polytechnic Institute(CINVESTAV-IPN), Guadalajara campus, Mexico, in 2009and 2013, respectively. Since August 2013, he has been work-ing in Western Institute of Technology and Higher Educa-tion (ITESO), Guadalajara, Jalisco, Mexico. He is a memberof the research group on the Research Laboratory on Opti-mal Design, Devices and Advanced Materials (OPTIMA),of the Department of Mathematics and Physics, ITESO. Heis also a member of the IEEE and the Mexican NationalResearch System (Rank 1). His current research interests
include neural control, block control, inverse optimal con-trol, and discrete-time sliding modes, and their applicationsto electrical machines and power systems.
Fredy A. Valenzuela received the M. Sc. degree in electri-cal engineering from the Graduate Program and Researchin Electrical Engineering of the Technological Institute ofMorelia, Michoacan, Mexico, in 2006; and the Ph. D. inElectrical Engineering from Advanced Studies and ResearchCenter of the National Polytechnic Institute, Guadalajaracampus, Jalisco, México, in 2010. He is a member of TabascoState-CONACYT Research System, Mexico. He is Professorat the Juarez Autonomous University of Tabasco, Mexico.His fields of interest are the analysis and control appliedto electrical machines, alternative energy systems and theefficient use of energy.
Miguel A. Murillo received the B.S. in Physics Engineeringand the M.Sc. degree in Electrical Engineering from theAutonomous University of Ciudad Juarez, Chihuahua, Mex-ico in 2012 and 2018, respectively. Since 2012 he has beenwith Autonomous University of Ciudad Juarez, where he iscurrently a professor of Physics, Mathematics and Engineer-ing B.S. programs. His fields of interest are mathematicalmodeling, classical electrodynamics, classical mechanics andoptimal control.
Abel E. Quezada received the B.S. in Electrical Engi-neering from the Technology and Engineering Institute ofthe Autonomous University of Ciudad Juarez, Chihuahua,Mexico, in 2002; he received the M.Sc. degree from Tech-nological Institute of La Laguna, Torreon, Coahuila, Mexico,in 2006. He has been a Professor of Electrical Engineeringat Autonomous University of Ciudad Juarez, since 2007.Actually, he is the Coordinator of the Electrical EngineeringProgram in the same University. His fields of interest areelectric machinery and quality energy.
Nahitt Padilla received the B.S. in Computer Engineeringfrom Technological Institute of Chihuahua II in 1999. In 2002,he received the M.Sc. degree in Electronics Engineering fromTechnological Institute of Chihuahua, also in 2003 he receivedthe M.Sc. degree in Computer Engineering from The Uni-versity of Texas at El Paso. He also received another M. Sc.in Computer Science and a Ph. D. in Electrical Engineering,both from The New Mexico State University in 2010 and 2017respectively. He has been Professor of Computer Engineeringat Autonomous University of Ciudad Juarez since 2004. He isa member of the IEEE and the ACM. His fields of interest aredistributed control and artificial Intelligence.
