Improved Stator Flux Estimator for Speed Sensorless Induction Motor Drives

0885-8993 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Seehttp://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TPEL.2014.2328617, IEEE Transactions on Power Electronics

Abstract—In this paper an improved induction motor (IM)

stator flux estimation method is proposed, based on a novel integrator scheme with a closed loop dc offset compensation algorithm. When compared to the existing stator flux estimators, the proposed solution represents an improved programmable low pass filter. Namely, by introducing a novel closed loop dc offset compensation structure, two major drawbacks of existing stator flux estimators are overcome; their stability and accuracy at low frequencies, and the estimator response time over the whole frequency range, introducing an estimation algorithm much simpler than existing solutions. The performance of the novel stator flux estimator is tested by means of simulation runs and experimental tests, with the proposed algorithm used for the estimation of the stator flux, rotor flux, and rotor speed in a DFOC IM control algorithm. The simulations and experimental results show that the proposed estimator enables accurate and stable operation in all operating conditions, including the critical low stator frequency range.

Index Terms— Stator flux estimation, induction motor, sensorless drive, low pass filter, variable cutoff frequency

I. INTRODUCTION In an induction motor (IM) speed sensorless drives that

are field oriented and direct torque controlled (DTC), stator flux estimation is one of the fundamental tasks that determines the stability and accuracy of the drive’s operation. The voltage model pure integrator based stator flux estimator is the simplest solution, but it is prone to several problems [1]: (i) sensitivity in relation to the dc drift present in the pure integrator input, which causes integrator saturation, and (ii) pure integrator initial conditions that cause an undesirable dc offset in the stator flux estimate signal.

In order to address these shortcomings, several different approaches have been adopted by various authors. In [1], three different closed loop modified integration algorithms are proposed, designed for different modes of IM drive operation. The first, based on saturable feedback, successfully compensates the integrator dc offset, especially at high speeds, while its accuracy is determined by the saturation limit level. The second is based on a modified integrator with limited amplitude, aimed at drives that operate with constant flux amplitude. Consequently, the adaptive compensation integrator is proposed, which, in combination with the previous two solutions, determines a stable and accurate solution, constrained by its complexity and dc offset compensation response time.

The authors are with the University of Belgrade, Electrical Institute

“Nikola Tesla”, Faculty of Electrical Engineering, Belgrade, Serbia (e-mail: [email protected], [email protected], [email protected], [email protected]).

In [2]–[4] and [19] observer based closed loop stator flux estimation schemes are proposed, based on the full-order IM model. Unlike pure integrator stator flux estimators that are based on a voltage IM model, the full-order observers [2] and [3] are based on a current IM model. Although they do not suffer from the dc offset, the current model estimators are based on the full set of the IM model parameters and on the rotor speed estimation. In [2], the estimator stability is improved by introducing a non-linear IM observer. In this way adaptive speed observer gains are introduced that enable the estimator’s operation in wide operating condition ranges, as opposed to linearized observers that may suffer from a stability decrease for varying drive speeds and loads. In [3], a current model MRAS speed and rotor flux estimation scheme is proposed, based on a novel stator current observer scheme. In this way, the robustness of the speed and flux estimator is improved, when compared to existing MRAS techniques. In [5], two stator flux estimation techniques are proposed, the first based on a sliding-mode non-linear flux observer, and the second based on an integrator modified by a proportionally-integral (PI) based offset compensator. In the first case, the observer dynamics is improved by the sliding-mode based observer action. In the second case, a closed loop offset cancellation procedure is proposed, which has a fast transient time. However, both solutions rely on known stator current and stator flux reference values, used for the calculation of the stator flux estimates, which may cause a stationary state error, especially in DTC drives. Furthermore, in [6] a closed loop flux and rotor speed observer is proposed, based on extended Kalman filters.

Apart from closed loop based stator flux estimators, there are several open loop solutions designed to eliminate the shortcomings of the pure integrator used for stator flux estimation. They generally belong to the group of solutions based on LPF instead of a pure integrator for the stator flux estimation, and they may be divided into several typical subgroups. Namely, LPF flux estimators represent the simplest form of an open loop substitute for a pure integrator based stator flux estimator. However, they introduce significant flux amplitude and phase errors, especially for sensorless IM drives operating in the low frequency range. Consequently, several different subgroups of LPF stator flux estimator solutions have been developed, which differ in the approaches used to compensate the estimation error: (i) first order LPF estimators with a fixed pole value that include an estimation error compensation algorithm; (ii) several cascaded first order LPF filters, with a programmable pole value calculated in order to achieve a zero flux phase error, which also include an amplitude error compensation algorithm; and (iii) programmable LPF filters

Improved Stator Flux Estimator for Speed Sensorless Induction Motor Drives

Djordje Stojic, Milan Milinkovic, Slavko Veinovic, Ilija Klasnic



with poles equal to the stator frequency value or its multiples, which include a flux vector rotation and amplification algorithm used to compensate the estimated flux phase and amplitude error.

In [7]–[9], solutions that belong to the first group of LPF solutions are proposed, represented by a first order LPF with fixed cutoff frequency, which include phase and amplitude error compensation based on the fact that the back EMF is orthogonal to the stator flux vectors. However, although a zero stator flux estimation error is achieved, these algorithms suffer at low stator frequencies ωe since the amplitude error compensation algorithm includes the division by ωe.

In [10] and [11], algorithms belonging to the second group of LPF solutions are proposed, based on cascaded programmable LPF filters. Namely, in these solutions, a high order cascade of first order LPF filters is used for the stator flux estimation, with the LPF cutoff frequency calculated so as to obtain zero phase error when compared to the pure integrator. However, in order to achieve the zero amplitude error, a compensation is required that includes division by the stator frequency value ωe,. This is the major drawback when a sensorless drive operates at low frequencies, since the dc drift present at the estimator inputs is in that case multiplied by the very large gains, causing a high estimation error and instability in the drive operation.

The third group of LPF based stator flux estimators is of the most interest from the point of view of this paper, since the novel algorithm belongs to this group. Namely, it consists of the programmable LPF stator flux estimators, with the LPF pole values equal to or multiples of the current stator frequency value ωe, [12]–[16]. In this way, programmable LPF solutions are obtained that enable zero phase and amplitude error in the stator flux estimates, with less computational effort required when compared to programmable filters [10]–[11].

In [12]–[13] variable cutoff frequency first order LPF flux estimators are proposed with the LPF pole proportional to the stator excitation frequency ωe. When compared to [7]–[11], the major drawback, division by ωe, is avoided, but the proposed solutions suffer from the fact that a complicated stator flux vector rotation and amplification is required in order to obtain accurate flux estimates. In [14], a similar solution is proposed, by means of a second order

VCF LPF. This solution has the problem that it introduces a static gain proportional to ωe, causing the estimator to behave as a zero gain at zero stator frequency.

In [15] and [16] improved versions of VCF LFP are proposed that reduce the estimator sensitivity to any input dc drift at low frequencies. This is achieved by means of the differential action included in the LFP. Also, the estimated stator flux amplitude and phase errors are compensated by the appropriate flux vector amplification and rotation. However, these solutions suffer from various drawbacks listed in Table I.

In this paper, an improved stator flux estimator is proposed, based on a closed loop dc offset compensation of the integrator used for the estimation. In this way, a solution that behaves equivalently to the class of programmable LPF solutions is achieved, improved by introducing a much simpler estimator structure. Namely, the dc offset compensation is carried out by means of a closed loop action proportional to the stator excitation frequency, implemented in a novel estimator topology. In this way, as shown in the later part of the paper, the following improvements in the stator flux estimation are enabled: (i) the division by ωe used for the dc offset compensation, present in [7]–[11], is avoided; (ii) the complicated stator flux vector multiplication, rotation, and frequency reversal, typical of [12]–[13], is avoided by means of a simplified estimator structure; (iii) multiplication by ωe, which leads to the estimator’s behaving as a zero gain at zero stator frequency, typical of [14]–[16] is avoided; (iv) the proposed estimator at low (and zero) stator frequencies behaves as a pure integrator, as opposed to [15]–[16], which behave as multiple order integrators, (v) the problem related to the stator flux estimator response time is resolved by increasing the estimator cutoff frequency by means of a single feedback gain, similar to [12]–[13]. The use of the proposed estimator improves the dynamic performance of sensorless IM drives, especially in the low frequency range, which is critical for the accuracy and stability of the stator flux estimation [17]. In Table I, the systematization of the features for the different groups of stator flux estimators given in the literature is outlined, enabling more intuitive insight in their individual advantages and shortcomings.

Closed loop

estimators ([1]-[6])

First order LPF with static error compensation

([7]-[9])

Cascaded LPF with fixed cutoff

frequency ([10]-[11])

Programmable LPF with cutoff

frequency ωe ([14]-[16])

Programmable LPF with cutoff frequency Kωe

([12]-[13]) Required speed estimate majority no no no no

Division by ωe / yes yes no no Multiplication by ωe / no no yes no

Equivalent low frequency behavior

/

first order LPF

cascade of multiple LPFs

multiple integrator cascade

single integrator

Flux vector rotation and frequency reversal

/

no

yes

yes

yes

Table I: Overview of the comparison of estimators Consequently, a stator flux estimation scheme that

belongs to the group "Programmable LPF with cutoff frequency Kωe" in Table I, which both statically and dynamically behaves similarly to [12]–[13], is proposed in

this paper, with the novelty consisting of a much simpler estimator algorithm, which does not require the complicated flux vector rotation, multiplication, and frequency reversal algorithms present in [12]–[13].



This paper has four sections. In Section II, the scheme of the novel stator flux estimator is outlined, based on the complex variables calculated in a stationary reference frame by means of the Clarke transformation. In that section, the dynamics of the proposed estimator is analysed, together with the closed loop dc offset compensation gain tuning procedure. In Section III, simulation tests are presented that illustrate the estimator’s behavior in several typical modes of operation. In Section IV, the results of experimental tests are presented, with the proposed algorithm used for the rotor speed estimation.

II. THE NOVEL STATOR FLUX ESTIMATOR In this paper, an IM stator flux estimation is proposed

that is based on the voltage IM model. Namely, voltage model based stator flux estimation is carried out by means of IM stator variables and measurements that do not require either measurement or estimation of the IM rotor speed. However, this type of stator flux estimation relies on the precise knowledge of the stator resistance, which may be a significant obstacle, especially at low IM stator excitation frequencies [17]. Nevertheless, in this paper, the problem of estimating the value of the stator resistance variable is not addressed, since it is examined in several papers [17].

Consequently, the voltage IM model is derived from the set of equations (1) that describe the IM behavior in the complex domain, by means of complex IM variables defined in the stationary reference αβ frame (in the form x = xα + j xβ ).

smrrr

rmsss

rrrrr

ssss

ILIL

ILIL

jdtdIR

dtdIRV

+=

+=

−+=

+=

ψ

ψ

ψωψ

ψ

0 (1)

Here, Vs=Vαs+jVβs represents the stator voltage, Is=Iαs+jIβs the stator current, Ir=Iαr+jIβr the rotor current, ψs=ψαs+jψβs the stator flux, ψr=ψαr+jψβr the rotor flux, Rs the stator resistance, Rr the rotor resistance, Ls the stator inductance, Lr the rotor inductance, Lm the mutual inductance, and ωr the rotor speed.

Consequently, a stator flux estimator based on the voltage IM model is derived from the first equation in (1), which describes the IM stator behavior. Namely, from this equation, there can be derived the basic stator flux estimation equation

( )s

IRVdtIRVdte ssssssss

−=−== ∫∫ ψ̂ . (2)

However, as mentioned in the Introduction, pure integrator based stator flux estimation (2) is prone to dc offset caused by the initial condition error that occurs during fast variations in either the stator voltage amplitude or the stator voltage frequency. Consequently, in order to compensate the integrator dc offset, it is necessary to define an algorithm for dc offset detection and a closed loop based elimination.

The dc offset detection is based on the steady state integrator transfer function

es

s

je ωψ 1

= , (3)

where ωe is the stator excitation frequency and es is the induced stator back EMF. Consequently, a signal Ds proportional to the integrator dc offset may be derived from (3):

jIRV

sIRV

jeD ssssss

es

ses−

−−

=−= ωψω (4)

After detecting the signal Ds, the integrator dc offset is compensated by means of the negative feedback signal that includes the compensation feedback gain Kd, which is fed into the integrator input. Consequently, the novel stator flux estimation scheme with the compensated integration dc offset is given by the following equation, based on Ds from (4).

( )s

DKIRV sdssss

−−=ψ̂ (5)

Since the estimator needs to operate for both positive and negative values of the stator excitation frequency ωe, the estimator scheme needs to be expanded by the factors sgn(ωe) and |ωe| necessary for the frequency reversal operation, as illustrated in Fig. 1.

Fig. 1. The novel stator flux estimator The basic idea of the integrator dc offset compensation

scheme given in Fig. 1 is to use the negative feedback action Kd to eliminate the erroneous integrator initial condition that manifests itself as the dc component in the estimator output. However, the dc offset compensation transient time is determined by the poles of the novel estimator transfer function given in Equation (6), based on the diagram given in Fig. 1.

( ) ( )ed

ed

s

se Ks

Kjje

sGωωψ

++

==sgn1ˆ (6)

In order to examine whether a stator flux estimation stationary state exists for the proposed algorithm (6), the amplitude and phase responses of Ge(s) are calculated for s = jωe. Consequently, the following estimator (6) frequency response is obtained

( )e

jse jsG

e ωω

1 ==

, (7)

which is equal to the frequency response of an integrator, proving that the proposed estimation scheme behaves as an integrator in the stationary state, and, consequently, does not introduce error in either the estimated stator flux amplitude or phase.

Rs Is

Vs +

-

j

sgn(ωe)

Kd

- +

Ds

-

+

s

1

1 |ωe |

ψs es



It is also necessary to examine the stator flux estimator response time, by analyzing its transfer function (6). Based on (6), it can be concluded that the estimator time constant τe is determined by the pole of the given transfer function pe= - Kd |ωe|, and is equal to τe =1 / pe = 1 / (Kd |ωe|). Consequently, the estimator response speed is proportional to the stator excitation frequency ωe multiplied by the factor Kd. Furthermore, this means that a decrease in ωe may lead to a decrease in the estimator response speed, which, however, can be increased by introducing the appropriate Kd feedback gain value. However, the increase of Kd may also influence the amplification of the harmonics and other high frequency components present in the stator voltage. This is examined by the means of the estimator (6) Bode plots calculated for ωe = 10 rad/s and for three different values Kd = [1, 10, 100], compared with the Bode plot of a common integrator used for the stator flux estimation.

Fig. 2. The influence of the Kd on the stator voltage

harmonic amplification

By analyzing the Bode plots given in Fig. 2 it can be concluded that the excessive increase of the estimator cutoff frequency, i.e. Kd value, could lead to the undesired amplification of harmonics and other high frequency components present in stator voltage. In order to avoid a possible degradation of IM drive performance, the following algorithm for the Kd calculation is adopted

( ) ( )

⎪⎪⎩

⎪⎪⎨

⎧

≥

<=

++

== ,

, ,

sgn1ˆ

C

CC

KKs

Kjje

sGc

ee

c

ce

ded

ed

s

se ω

ωωω

ωω

ωωψ (8)

In this way, a combination of variable and fixed cutoff frequency filter is adopted, operating with variable cutoff frequency at low and with fixed cutoff frequency at high ωe frequency range. Consequently, the error free stator flux compensation is achieved in both low and high ωe frequency range, without the need for the division by ωe in the low frequency range [7]-[11], while operating with the limited, yet sufficient, maximum cutoff frequency. This is done in order to avoid harmonics and other high frequency component amplification. The choice of C and ωc values is discussed in the Experimental Tests section of the paper.

Consequently, the equivalent scheme of the proposed estimator, in α and β stationary frame coordinates, is shown in Fig.3(a), together with the equivalent scheme of [12]-[13] in Fig.3(b), in order to illustrate the simplification introduced in this paper.

Fig. 3. Equivalent schemes of (a) the novel stator flux estimator, and (b) estimators given in [12]-[13]

In the following section, the novel stator flux estimator is tested through a set of simulation runs, which include stator voltage frequency and amplitude variations.

III. SIMULATION TESTS In the first part of this section, the simulation runs based

on Matlab/Simulink of the proposed stator flux estimator are presented, followed by the simulation of the rotor speed estimator based on this stator flux estimator.

The simulation of the behavior of the proposed estimator is carried out for two different induction motor excitation cases: open loop control with the fixed excitation frequency and variable stator voltage amplitude and closed loop control based on a sensorless DFOC drive. In both cases, an ac voltage source is connected to the IM simulation model; it has the same parameter values as the IM later used in the experimental test runs. The IM stator currents and stator

voltages are fed into the proposed stator flux estimator (8), together with the estimators [14] and [15] given in Fig. 4 that belong to the same group of solutions - LPF with programmable cutoff frequency. Consequently, the three estimator outputs are compared with the stator flux responses obtained by means of the IM model. The simulation responses of the proposed estimator are not compared with [12]-[13], since they behave similarly.

Fig. 4. Stator flux estimators (a) [14], and (b) [15], compared with the proposed method (8) by the means of

simulation

Vs – Is Rs 2ωe

(a)

( )2es ω+

ψs Vs – Is Rs j8sωe4

( )6es ω+

ψs

(b)

Vαs – Iαs Rs +

Vβs – Iβs Rs

+

Kd sgn(ωe)

Kd sgn(ωe)

+

-

s+Kd |ωe |

(a)

s+Kd |ωe |

1

ψαs

ψβs

1 s+Kd |ωe |

21 dK+ ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛− −

de K

1tansgn2

cos 1ωπVαs – Iαs Rs

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛− −

de K

1tansgn2

sin 1ωπ

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛− −

de K

1tansgn2

sin 1ωπ

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛− −

de K

1tansgn2

cos 1ωπ

s+Kd |ωe |

21 dK+Vβs – Iβs Rs

ψαs

ψβs

+

+

+

-

(b)



Based on the scheme given in Fig. 1, in order to implement the estimator it is necessary to determine the values of two parameters: the stator resistance Rs and the feedback gain Kd. Consequently, the estimator feedback gain C in (8) (i.e, Kd for ωe < ωc /C) is set at 10, while ωc in (8) is set at 100 rad/s.

The stator resistance value is taken over from the following set of IM parameters of the motor used in the experimental tests: three pole pairs, 2 kW, 380 V, 50 Hz induction motor with Rs = 1.9 Ω, Rr = 1.8 Ω, Lm = 0.183 H, Ls = 0.19 H, Lr = 0.19 H.

In Fig. 5, the simulated estimator response is given for the constant stator excitation frequency ωe = 1 rad/s and a stator voltage amplitude varied in steps [20 V, 40 V, 60 V, 80 V, 100 V]. The simulation runs are carried out for three different estimators - (8), [14], and [15] - for intentionally detuned initial conditions of the estimators, in order to examine their corresponding estimation speeds.

Fig. 5. Simulated and estimated stator flux values for

three different types of estimators, (8), [14], and [15], (a) α components, (b) β components

By comparing the estimator responses with the simulated

stator flux components for variable stator voltage operation, especially the initial part of the trace that represents the corresponding estimator responses in relation to the initial dc offset, it can be concluded that the algorithm proposed in this paper (8) enables much faster stator flux estimation when compared to [14] and [15]. Namely, the (8) response time (which corresponds to the estimator cuttof frequency Kdωe = 10⋅1 rad/s and is equal to tr=3 / Kdωe = 0.3 s, for ωe = 1 rad/s) is 10 times faster then the response time of [14], while at least 30 times faster then [15].

In Fig. 6, the simulation results for two different values of the estimation parameter C in (8) are given for stator excitation frequency ωe = 1 rad/s and stator voltage amplitude varied in steps [20 V, 40 V, 60 V, 80 V, 100 V]. By comparing the estimator responses it can be concluded that for C = 1 the estimation time of (8) is ten times faster when compared to the estimator operating with C = 0.1. This is caused by the fact that, for ωe = 1 rad/s, in the firs

case (8) operates with the cutoff frequency equal to 1 rad/s, while in the second case with the cutoff frequency 0.1 rad/s.

Fig. 6. Simulated and estimated stator flux values for two values of parameter C in (8), C = 1 and C = 0.1: (a) α

components, (b) β components In the following part of the section, the simulation of a

closed loop DFOC IM control algorithm [13] was used to examine the performance of the estimator (8). The corresponding simulation results of [14] and [15] used in the same DFOC algorithm could not be provided, since it was difficult to attain a stable operation for [14] and [15], simulated for the same DFOC structure as in the case of the estimator (8). The basic outline of the used DFOC algorithm is given in Fig. 7.

Fig. 7. The closed loop DFOC IM control used for

simulation tests The DFOC control structure is based on the stator and

rotor flux estimation, with the rotor flux estimates used for the rotor speed and rotor angle value estimation. Based on the rotor angle estimate the Park transformation of the stator currents in the dq reference frame synchronous with the rotor is carried out. Consequently, the stator current controllers are implemented in the dq reference frame, with the I*

d reference value set according to the rotor flux |ψ*r|

reference value, and I*q reference determined by the outer

rotor speed control loop. The speed control is based on the rotor speed estimate, calculated by the means of the stator current measurements and rotor flux estimates in the dq reference frame synchronous with rotor flux.



The rotor flux estimates used in the DFOC are calculated from the stator flux estimates (8) and stator current measurements by means of (9).

sm

mrss

m

rr

sm

mrss

m

rr

IL

LLLLL

IL

LLLLL

βββ

ααα

ψψ

ψψ

2

2

ˆˆ

ˆˆ

−−=

−−=

(9)

The rotor flux angle used for the Park transformation in Fig. 7 is calculated from

⎟⎟⎠

⎞⎜⎜⎝

⎛= −

r

rr

α

β

ψψ

θˆˆ

tan 1 . (10)

The rotor speed estimate, used in DFOC in Fig. 7, is based on the equation

Pse

rωωω))

) −= , (11)

where P represents the number of IM pole pairs. In (11), the estimated slip frequency ωs is obtained by means of the equation (12)

r

q

r

ms

ITL

ψω

ˆ=) , (12)

while the stator frequency ωe estimate used in (11) is obtained by the means of the following equation

( ) ( )2

s

sssssssse

IRVIRV

ψ

ψψω βαααββ

)

))) −−−

= . (13)

Apart from the rotor speed estimation (11), the estimated stator frequency value (13) is, also, used in the proposed stator flux estimator (8). Consequently, the I*

d reference value is set to I*

d = |ψ*r| / Lm, where |ψ*

r| represents the rotor flux reference value.

The following closed loop simulation test consists of the DFOC scheme in Fig. 7. simulated for the rotor speed reference varied for the following set of values ω*

r = [-10 rad/s, -5 rad/s, 0 rad/s, 5 rad/s, 10 rad/s]. The low speed values have been chosen since the low speed region represents a critical operating regime from the point of stability and accuracy of stator flux estimation and sensorless IM drive operation.

By analyzing the responses given in Fig. 8 it can be concluded that the proposed stator flux estimator (8) successfully operates in the conditions typical for a variable frequency IM drive. The estimator response speed varies

with the stator frequency, but even for the low speed operation the flux and speed estimates enable the stable and accurate sensorless drive operation. Namely, the resulting rotor speed estimation error did not exceed the 1% error margin during the simulation test.

Fig. 8. The DFOC responses of the simulated and estimated

(a) α stator flux component, (b) β stator flux component, and (c) rotor speed

In the following section, the results of the experimental

tests are presented, for an induction motor driven by means of a three phase voltage source inverter.

IV. EXPERIMENTAL TESTS The experimental tests were carried out by using the

DFOC IM control structure given in Fig. 7, implemented by means of the experimental setup given in Fig. 9.

Fig. 9. Experimental setup



The experimental setup consists of the following parts, presented in Fig. 9: (a) PC running the realtime control software (DFOC, stator current control, Park transformation, stator and rotor flux estimation, rotor speed estimation, speed control) operating at 3 kHz sampling frequency; (b) FPGA based control card connected to the PC parallel port (consisting of the A/D converters, three phase VSI PWM signal generator, chopper PWM generator, encoder based speed measurement); (c) measurement and protection electronics; (d) current transducers; (e) IGBT drivers; (f) induction motor (with parameters given in Section III), (g) DC motor mechanically connected with the IM used as an electromechanical brake for IM drive mechanic loading; (h) three phase IGBT VSI operating at 3 kHz switching frequency used for IM control; (i) chopper used for the DC brake control; and (j) signals from the encoder mounted on the DC brake.

In Fig. 10 the experimental results of a test similar to the simulation test presented in Fig. 8. in Section III are given, consisting of the sensorless DFOC drive operating with a set of different rotor speed reference step values ω*

r = [-10 rad/s, -5 rad/s, 0 rad/s, 5 rad/s, 10 rad/s], for C = 10 and ωc = 100 rad/s in (8).

Fig. 10. Responses of the experimental DFOC drive test for ω*

r = [-10 rad/s, -5 rad/s, 0 rad/s, 5 rad/s, 10 rad/s]: (a) α and β stator flux components, and (b) measured and

estimated rotor speed

By analyzing the step responses of the DFOC IM drive in Fig. 10 it can be concluded that the flux and speed estimation operates stably even at low speeds, which represent the most critical regime from the point of the sensorless IM drive operation. Namely, in Fig. 10 the rotor speed traces have the similar response time and overshot when compared to simulation results presented in Fig. 8. Furthermore, for the rotor speed ±10 rad/s the estimation error did not exceed 2% margin. However, this error margin is exceeded for lower rotor speeds – for rotor speed ±5 rad/s the error was 9%, while for the zero speed the error margin did not exceed 1.5 rad/s. When comparing traces in Fig. 8(c) and Fig. 10(b) it can be concluded that the decrease in rotor speed, i.e. the decrease in stator frequency value ωe, causes the increase in relative rotor speed estimation error, which is typical for IM sensorless drives. However, both simulation and experimental results show that proposed

stator flux estimator enables stable sensorless drive operation even in the cases of very low stator frequency operation. The case of the zero speed operation is further examined in the following two experiments, represented by the corresponding experimental results given in Fig. 11 and Fig. 12.

Namely, in the following figures the DFOC IM drive operating with the zero speed reference is mechanically loaded with the 1 pu external torque load by using the coupled DC motor. Consequently the estimated flux and rotor speed responses are given for two different sets of the flux estimator parameters (8), C = 10 in Fig. 11 and C = 1 in Fig. 12 respectively, with ωc = 100 rad/s in both cases.

Fig. 11. Experimental results of the DFOC drive for zero

speed reference and 1 pu external torque load for C = 10 and ωc= 100 rad/s: (a) stator flux estimates and (b)

measured and estimated rotor speed

Fig. 12. Experimental results of the DFOC drive for zero speed reference and 1 pu external torque load for C = 1 and ωc=100 rad/s: (a) stator flux estimates and (b) measured and

estimated rotor speed By comparing the experimental results given in Fig. 11

and Fig. 12 two conclusions can be made: (i) that the increase in C value leads to the increase in the speed estimation error, since in Fig. 11 the maximum speed estimation error reaches 1.3 rad/s value, while in Fig. 12.



the average speed estimation error is smaller; (ii) the increase in C value leads tho the increase in the estimated stator flux distortions, which can be examined by comparing the estimated stator flux traces in Fig. 11(a) and Fig. 12.(a). These distortions are to a large extent caused by the voltage distortions introduced by VSI switching elements, especially at low speeds [18].

Furthermore, based on the simulation results given in Fig. 6 it can be concluded that the increase in estimator parameter C in (8) leads to the increase in the flux estimator response speed. However, based on figures 11 and 12 the increase of C causes the amplifications of distortions introduced by the VSI. Hence, the C (8) value is limited by the level of the VSI distortions, which can, however, be significantly compensated by the techniques proposed in [18].

Consequently, the estimator parameter value C in (8) should be increased up to the value which results in the maximum speed estimation error allowed for the designed sensorless IM drive. Also, the C and ωc value in (1) should be chosen in accordance with the flux estimation speed required by the designed IM drive. For example, in the case of a DTC drive the flux estimation speed influences the direct stator flux control, and, consequently needs to be set to the appropriately high value.

For the case of the IM experimental drive used in this paper, in which the “dead-time” VSI effect was compensated by means outlined in [18], the estimator parameters C = 10 and ωc = 100 rad/s enabled the successful DFOC IM drive operation in wide range of operating conditions, including the near zero speed range.

V. CONCLUSION In this paper, a novel programmable low pass filter

based stator flux estimator was proposed. It includes an estimator feedback action that enables more accurate and stable low frequency operation and faster estimator response speeds over the whole frequency range, achieved by means of its much simpler estimator structure, when compared with the existing solutions. This is achieved by eliminating the division or multiplication by the stator frequency value typical for many LPF estimator solutions. Also avoided are the complicated algorithms for estimated flux vector rotation and multiplication typical of the previous solutions similar to the one proposed in this paper. The estimator’s accuracy and stability of performance was estimated by means of simulation and experimental runs, which illustrate the achieved improvements. Also, by means of the experimental tests, the influence of the estimator feedback gain on the VSI voltage distortion amplification, typical of low stator frequency operation, was examined. It was shown that an increase in feedback gain, which increases the estimator response speed, causes an increase in the estimates’ distortions in low frequency operations. Consequently, it can be concluded that a tradeoff between the estimator response speed and the distortion level is required when setting the value of the estimator feedback gain. Also, it should be noted that the distortions could be further decreased by compensating the VSI voltage nonlinear distortion level by means of an algorithm proposed in the literature [18].

ACKNOWLEDGMENTS This work was supported by the Ministry of Science of

the Republic of Serbia under project TR33020.

REFERENCES [1] J. Hu and B. Wu, "New integration algorithms for estimating motor

flux over a wide speed range," Power Electronics, IEEE Transactions on, vol. 13, pp. 969-977, 1998.

[2] M. Hinkkanen, "Analysis and design of full-order flux observers for sensorless induction motors," Industrial Electronics, IEEE Transactions on, vol. 51, pp. 1033-1040, 2004.

[3] T. Orlowska-Kowalska and M. Dybkowski, "Stator-current-based MRAS estimator for a wide range speed-sensorless induction-motor drive," Industrial Electronics, IEEE Transactions on, vol. 57, pp. 1296-1308, 2010.

[4] J. Maes and J. A. Melkebeek, "Speed-sensorless direct torque control of induction motors using an adaptive flux observer," Industry Applications, IEEE Transactions on, vol. 36, pp. 778-785, 2000.

[5] C. Lascu and G. D. Andreescu, "Sliding-mode observer and improved integrator with DC-offset compensation for flux estimation in sensorless-controlled induction motors," Industrial Electronics, IEEE Transactions on, vol. 53, pp. 785-794, 2006.

[6] M. Barut, S. Bogosyan, and M. Gokasan, "Speed-sensorless estimation or induction motors using extended Kalman filters," Industrial Electronics, IEEE Transactions on, vol. 54, pp. 272-280, 2007.

[7] N. R. N. Idris and A. H. M. Yatim, "An improved stator flux estimation in steady-state operation for direct torque control of induction machines," Industry Applications, IEEE Transactions on, vol. 38, pp. 110-116, 2002.

[8] M. Hinkkanen and J. Luomi, "Modified integrator for voltage model flux estimation of induction motors," Industrial Electronics, IEEE Transactions on, vol. 50, pp. 818-820, 2003.

[9] A. Choudhury, P. Pillay, and S. S. Williamson, "Modified stator flux estimation based direct torque controlled PMSM drive for hybrid electric vehicle," in IECON 2012—38th Annual Conference of IEEE Industrial Electronics Society, 2012, pp. 2965-2970.

[10] B. K. Bose and N. R. Patel, "A programmable cascaded low-pass filter-based flux synthesis for a stator flux-oriented vector-controlled induction motor drive," Industrial Electronics, IEEE Transactions on, vol. 44, pp. 140-143, 1997.

[11] T. J. Vyncke, R. K. Boel, and J. Melkebeek, "A comparison of stator flux linkage estimators for a direct torque controlled PMSM drive," in Industrial Electronics, 2009. IECON'09. 35th Annual Conference of IEEE, 2009, pp. 971-978.

[12] M.-H. Shin, D.-S. Hyun, S.-B. Cho, and S.-Y. Choe, "An improved stator flux estimation for speed sensorless stator flux orientation control of induction motors," Power Electronics, IEEE Transactions on, vol. 15, pp. 312-318, 2000.

[13] M. Comanescu and L. Xu, "An improved flux observer based on PLL frequency estimator for sensorless vector control of induction motors," Industrial Electronics, IEEE Transactions on, vol. 53, pp. 50-56, 2006.

[14] G. Tan, X. Wu, Z. Ye, Y. Han, and P. Guo, "Dual three-level double-fed induction motor control based on novel stator flux observer," in Electrical and Control Engineering (ICECE), 2010 International Conference on, 2010, pp. 3668-3671.

[15] Y. Wang and Z. Deng, "An integration algorithm for stator flux estimation of a direct-torque-controlled electrical excitation flux switching generator," Energy Conversion, IEEE Transactions on, vol. 27, pp. 411-420, 2012.

[16] Y. Wang and Z. Deng, "Improved stator flux estimation method for direct torque linear control of parallel hybrid excitation switched-flux generator," Energy Conversion, IEEE Transactions on, vol. 27, pp. 747-756, 2012.

[17] J. Holtz and J. Quan, "Drift- and parameter-compensated flux estimator for persistent zero-stator-frequency operation of sensorless-controlled induction motors," Industry Applications, IEEE Transactions on, vol. 39, pp. 1052-1060, 2003.

[18] J. Holtz and J. Quan, "Sensorless vector control of induction motors at very low speed using a nonlinear inverter model and parameter identification," Industry Applications, IEEE Transactions on, vol. 38, pp. 1087-1095, 2002.

[19]F. C. Dezza, G. Foglia, M. F. Iacchetti, and R. Perini, "An MRAS observer for sensorless DFIM drives with direct estimation of the torque and flux rotor current components," Power Electronics, IEEE Transactions on, vol. 27, pp. 2576-2584, 2012.



Djordje Stojić received B.S., M.S., and Ph.D degrees in electrical engineering from the Faculty of Electrical Engineering, University of Belgrade, Serbia, in 1994, 1996, and 2004, respectively. From 1994 he is employed at the Electrical Engineering institute “Nikola Tesla”, University of Belgrade, Serbia where he is currently holding the position of the Consultant at the Control Department. His field of professional, research and development focus is at AC motor drives,

parameter estimation and model identification, synchronous generator excitation systems, power system stabilizers, turbine governors, robust and adaptive control systems.

Milan Milinković was born in Belgrade, Serbia, in 1983. He received the M.S. degree in electrical engineering from University of Belgrade, Faculty of Electrical Engineering, Belgrade, Serbia in 2008. He is currently working towards PhD degree at the same faculty. Since 2008 he is at the Control Department at Institute of Electrical Engineering “Nikola Tesla”, University of Belgrade, Serbia. He is currently holding Research Associate position and is responsible for development, installation and maintenance

of the synchronous generator excitation system controllers, which are installed in major thermal and hydroelectric power stations in Serbia. He co-authored several scientific papers at domestic and international conferences. His research interests include synchronous generator excitation system control, induction motor control, robust control, parameter estimation, adaptive control, power electronics and motor drives.

Slavko Veinović was born in Sombor, Serbia, in 1983. He received the B.Sc. degree in electrical engineering from the University of Belgrade, Serbia, in 2008. He currently attends Ph.D. program at Faculty of Electrical Engineering, University of Belgrade, Serbia. In 2009, he joined the Control Department at Electrical Institute “Nikola Tesla”, University of Belgrade, Serbia. His current research interests include control and measurement theory, electrical machines

and drives. During past four years, he was working on developing automatic voltage controller of excitation system for synchronous generator. He also interested in embedded system and device design.

Ilija Klasnić was born in Belgrade, Serbia, in 1989. He received the Masters degree in power converters and drives from the Faculty of Electrical Engineering, University of Belgrade, Serbia, in 2013. He is currently at Faculty of electrical engineering, University of Belgrade, Serbia and is working toward the Ph.D. degree. He, also, currently holds the Associate position at the Engineering Institute Nikola Tesla, University of Belgrade, Serbia. His research concerns the design of power converters, excitation systems and synchronous machine control.

Improved Stator Flux Estimator for Speed Sensorless Induction Motor Drives

Documents

Transcript of Improved Stator Flux Estimator for Speed Sensorless Induction Motor Drives