Sensorless Plug-and-Play Control of Industrial Drives

Sensorless Plug-and-Play Control of Industrial DrivesFocus on Induction Motor Drives

Marko Hinkkanen

IEEE SLED 2019, Torino, Italy10 September, 2019

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Introduction

V/Hz Control

Observers

Sensorless Identification at Standstill

Sensorless, More or Less

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Industry Applications

I Major industry applicationsI Pumps, fans, compressors (> 75%)I ConveyorsI Elevators and escalatorsI Cranes and hoistsI Machine tools, rolling mills, etc.

I Sensorless general-purpose drivesare typically used

I Induction motors dominate (> 90%),but the share of synchronous motorsis increasing

Figure: Google (Hamina data center).3 / 48

Induction motor1 Synchronous reluctance motor2

1Tesla, “Electro-magnetic motor,” U.S. Patent 382,279, 1888.2Kostko, “Polyphase reaction synchronous motors,” J. Amer. Inst. Elect. Eng., 1923.

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Market for Low-Voltage General-Purpose Drives in 2018

I Motors and drives: e21 billionI Drives: e10 billion (> 20 M units)I End-users require self-commissioning

and easy wiring (no external sensors)

Source: IHS Markit (partly). Figure: ABB.5 / 48

Plug-and-PlayVector Control

I High performance (if properlycommissioned)

I Current (torque) easy to limitI Torque reference as the speed

controller output signal allowssimple tuning

Tref

iss

M

Torquecontroller

udc

Speedcontroller

ωm,ref

ωm

1. Identify the motor model automatically

2. Configure the control system

3. Drive the motor in an optimal manner

Motor parameters, magnetic model

Controller and observer gains, lookup tables

0. Request user input

Motor type, nameplate data

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Introduction

V/Hz Control

Observers

Sensorless Identification at Standstill

Sensorless, More or Less

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V/Hz Control: Plug and Play?

I Feedforward control based on thesteady-state equations

I Minimal amount of parametersI User defines the V/Hz curve and

the acceleration rampsI Some versions use the measured

current for RI and slipcompensations3

I Open-loop V/Hz control isconsidered in the following

M

uss,ref

ωs,refPWM

udc

eϑsJ

1

s

us,ref

ϑs

3Munoz-Garcıa, Lipo, and Novotny, “A new induction motor V/f control method capable of high-performance regulation at low speeds,” IEEE Trans.Ind. Appl., 1998.

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Stable Operating Region Under Open-Loop V/Hz Control?

ωs0 = 1 p.u.ψs0 = 1 p.u.

T0

ωm0

ωs0 = 2 p.u.ψs0 = 0.5 p.u.

Breakdown

ωs0 = 0ψs0 = 1 p.u.

torque Tb

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Inverse-Γ Model

I State equations in synchronouscoordinates rotating at ωs

Lσdisdt

= us − (RσI + ωsLσJ)is

+ (αI− ωmJ)ψR

dψR

dt= RRis − [αI + (ωs − ωm)J]ψR

I Electromagnetic torque

T = iTs JψR

dψss

dtωmJψs

R

RRissRs

uss LM

dψsR

dt

Lσ

Equivalent circuit in stator coordinates

I Total resistance Rσ = Rs +RR

I Inverse rotor time constant α = RR/LM

I Electrical rotor speed ωm

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Model in the Steady State

I Steady state: d/dt = 0 insynchronous coordinates

I Steady-state operating pointmarked with the subscript 0

is0 ωs0LσJ

RR

ωr0/ωs0us0

Rs

ωs0LMJ ωs0JψR0ωs0Jψs0

Steady-state equivalent circuit

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Linearized Model of an Induction Machine4,5

I Electrical subsystem

d

dt

[isψR

]=

[−RσLσ

I− ωs0J1Lσ

(αI− ωm0J)

RRI −αI− ωr0J

]︸ ︷︷ ︸

A

[isψR

]+

[ 1Lσ

I

0

]us +

[− 1Lσ

JψR0

JψR0

]︸ ︷︷ ︸

b

ωm

T =[−ψT

R0J iTs0J]︸ ︷︷ ︸

c

[isψR

]

I Transfer function from speed to torque

G(s) =T (s)

ωm(s)= c(sI−A)−1b

ωm

is

Electricalus

Tsubsystem1

sJm

TL

4Fallside and Wortley, “Steady-state oscillation and stabilisation of variable-frequency invertor-fed induction-motor drives,” Proc. IEE, 1969.5Nelson, Lipo, and Krause, “Stability analysis of a symmetrical induction machine,” IEEE Trans. Power App. Syst., 1969.

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Feedback Interconnection of Passive Systems Is Passive

I Stable transfer function G(s) is passive (positive real) if and only if

Re{G(jω)} ≥ 0 for all ω ∈ [−∞,∞]

I Corresponds to |∠G(jω)| ≤ 90◦ for all frequenciesI Mechanical subsystem and PI controller (with positive gains) are passiveI G(s) = T (s)/ωm(s) is not passive in some operating regions

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Eigenvalues of the Electrical Dynamics

I Parameters of a 2.2-kW motorI Stator frequency ωs0 is variedI Mechanical dynamics omitted

(constant speed or Jm =∞)

T0 = 0 ωs0 = −1 . . . 1 p.u.

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Effect of the Mechanical Dynamics

I Total inertia Jm = 2.2Jrotor

I Jm →∞: blue and grey locioverlap

I Poor damping about ωs0 = 0.6 p.u.I RI compensation is ideally

parametrized in the followingsimulation examples

Electrical dynamics

Mechanicaldynamicsincluded

T0 = 0 ψs0 = 1 p.u. ωs0 = −1 . . . 1 p.u.

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Simulation: TL = 0.5TN after t = 1 s

T0 = 0.5TN ψs0 = 1 p.u. ωs0 = −1 . . . 1 p.u.

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Simulation: TL = TN after t = 1 s

T0 = TN ψs0 = 1 p.u. ωs0 = −1 . . . 1 p.u.

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Simulation: TL = 1.5TN after t = 1 s

T0 = 1.5TN ψs0 = 1 p.u. ωs0 = −1 . . . 1 p.u.

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Simulation: quadratic load torque

I Comments on the previous casesI Dynamics in the motoring and

regenerating modes are differentI Stable operating region depends on

the mechanical parametersI Magnetic saturation was omitted in

the simulations for simplicityI Works well in simple applicationsI V/Hz curve and ramps could be preset

based on the identified motor model

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Introduction

V/Hz Control

Observers

Sensorless Identification at Standstill

Sensorless, More or Less

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Sensorless Vector Control of Induction Motors

is,ref

ωm

isse−ϑsJ

eϑsJ

M

us,refCurrentcontroller

ψR

is

Observer

uss,ref

PWM

udc

Referencecalculation

Tref

inverternonlinearitycompensation

loss minimization, and flux brakingIncludes field weakening,

ϑs

Includes

I Essentially the same observer can be used in rotor-flux-oriented control,stator-flux-oriented control, direct torque control, model-predictive control, . . .

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Speed-Adaptive State Observer6

I State observer: state equations corrected with feedback

Lσdisdt

= us − (RσI + ωsLσJ)is + (αI− ωmJ)ψR +K1(is − is)

dψR

dt= RRis − [αI + (ωs − ωm)J]ψR +K2(is − is)

I Error signal for speed estimation

ε =ψ

T

RJ(is − is)‖ψR‖2

=iq − iqψR

I System resembles the open-loop motor model

kp +kis

ωm

is

us

ε

ψR

observerState is

6Kubota, Matsuse, and Nakano, “DSP-based speed adaptive flux observer of induction motor,” IEEE Trans. Ind. Appl., 1993.22 / 48

Estimation-Error Dynamics

I 5th-order systemI Risk of unstable regions both

at low and high speeds7

I Closed-form passivity-basedstabilizing observer gain available8

I Explicit pole placement not possible

7Hinkkanen, “Analysis and design of full-order flux observers for sensorless induction motors,” IEEE Trans. Ind. Electron., 2004.8Sangwongwanich, Suwankawin, Po-ngam, et al., “A unified speed estimation design framework for sensorless AC motor drives based on

positive-real property,” in Proc. PCC-Nagoya, 2007.23 / 48

Reduced-Order Flux Observer9

I Back-EMF induced by the rotor flux

e = us −Rsis − Lσdisdt− ωsLσJis

e = RRis − (αI− ωmJ) ψR

I Reduced-order observer

dψR

dt+ ωsJψR = e+K(e− e)

I K = 0 yields the voltage model, K = I yields the current modelI Flux observer is independent of speed estimation (inherently sensorless) if

KJψR = 0

9Verghese and Sanders, “Observers for flux estimation in induction machines,” IEEE Trans. Ind. Electron., 1988.24 / 48

Speed Estimation10

I Error signal for speed estimation

ε =ψ

T

RJ(e− e)

‖ψR‖2=eq − eqψR

I Gain αo is directly the speed-estimation bandwidthI Equals the slip-relation-based estimation in the case of

inherently sensorless observers

dωm

dt= αo

(ωs −

RRiq

ψR

− ωm

) αo

s

ωm

is

us

ε

ψR

observerFlux

10Harnefors and Hinkkanen, “Complete stability of reduced-order and full-order observers for sensorless IM drives,” IEEE Trans. Ind. Electron., 2008.25 / 48

Estimation-Error Dynamics11

I Standard linearization procedure gives

dψR

dt= − [ωs0J +K0 (αI− ωm0J)] ψR +K0JψR0ωm

ε =ψT

R0J (αI− ωm0J)

‖ψR0‖2ψR + ωm

I Inherently sensorless case simplifies since

K0JψR0 = 0

11Hinkkanen, Harnefors, and Luomi, “Reduced-order flux observers with stator-resistance adaptation for speed-sensorless induction motor drives,”IEEE Trans. Power Electron., 2010.

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Voltage Model: K = 0

I Unstable at ωs0 = 0 due to thedouble pole at the origin

I Problems in starting the motorand in speed reversals

I Marginally stable at ωs0 6= 0

I Very sensitive to the Rs estimateat low speeds

I These drawbacks are difficult toremove without introducingunstable regions

T0 = TN ωs0 = −1 . . . 1 p.u.

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Inherently Sensorless Current Model12

Improves motoring at low speeds

K =ψRψ

T

R

‖ψR‖2

T0 = TN ωs0 = 0 . . . 0.15 p.u.

Makes regenerating unstable

T0 = TN ωs0 = −0.15 . . . 0 p.u.

12Ambrozic, Nedeljkovic, and Nastran, “Sensorless control of induction machine with parameter adaptation,” in Proc. IEEE ISIE, 1999.28 / 48

General Stabilizing Gain

I Analytical stability conditions can be derived from the linearized modelI General stabilizing gain for inherently sensorless observers13

K =

[bI +

(c

ωs− ωs

)J

]αI + ωmJ

α2 + ω2m

ψRψT

R

‖ψR‖2

where b > 0 and c > 0 are the design parametersI Poles can be easily placed, since the design parameters correspond to the

characteristic polynomial s2 + bs+ c of the linearized systemI To reduce sensitivity to parameter errors, the closed-loop flux-observer poles

should be placed close to the open-loop poles14

13Hinkkanen, Harnefors, and Luomi, “Reduced-order flux observers with stator-resistance adaptation for speed-sensorless induction motor drives,”IEEE Trans. Power Electron., 2010.

14Hinkkanen, Saarakkala, Awan, et al., “Observers for sensorless synchronous motor drives: Framework for design and analysis,” IEEE Trans. Ind.Appl., 2018.

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ωs0 = −1 . . . 1 p.u. Zoomed in

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Equations in Estimated Rotor-Flux Coordinates

I Back-EMFs

ed = ud −Rsid − Lσdiddt

+ ωsLσiq

eq = uq −Rsiq − Lσdiqdt− ωsLσid

ed = RR

(id −

ψR

LM

)

I Observer

dψR

dt= ed + kd(ed − ed)

dϑsdt

=eq + kq(ed − ed)

ψR

= ωs

I Gains

kd =bα− (c/ωs − ωs)ωm

α2 + ω2m

kq =bωm + (c/ωs − ωs)α

α2 + ω2m

I Speed estimation

dωm

dt= αo

(ωs −

RRiq

ψR

− ωm

)I Resistance adaptation at low speeds

dRs

dt= k(ed − ed)

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Experimental Results: 45-kW Induction Motor

Speed reference stepsand load steps

Torque stepsat zero speed

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Slow torque reversalat zero speed

Slow speed reversalunder rated load

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Introduction

V/Hz Control

Observers

Sensorless Identification at Standstill

Sensorless, More or Less

34 / 48

Equivalent Circuit ModelsMathematically Equivalent in the Magnetically Linear Case

T model: Cannot be uniquely identified from terminals (overparametrized)Inverse-Γ model: Yields the simplest control equations

Γ model: Saturation characteristics can be included in a simple manner15

dψss

dtωmJψs

r

RrissRs

uss

dψsr

dt

L`

Ls

dψss

dtωmJψs

R

RRissRs

uss LM

dψsR

dt

Lσ

Γ modelInverse-Γ model

15Slemon, “Modelling of induction machines for electric drives,” IEEE Trans. Ind. Appl., 1989.35 / 48

Nonlinear Γ Model: Simple Physically Feasible ModelI Flux densities in the stator core depend on the stator flux linkage ψs = ‖ψs‖I Sinusoidally distributed winding, uniform airgap, no cross-saturation

ψs = ψs(im) or im = im(ψs) or Ls = Ls(im) or Ls = Ls(ψs)

dψss

dtωmJψs

r

RrissRs

uss

dψsr

dt

L`

Ls

ism

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I Magnetizing curve ψs = ψs(im) can be univocally determined by means of theno-load test (or the flux-integration test at standstill)

I Incremental inductance Lsi is comparable to L` at larger values of im

Magnetizing curve Corresponding inductances

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Corresponding Inverse-Γ Model Is Complicated

dψss

dtωmJψs

r

RrissRs

uss

dψsr

dt

L`

Ls

dψss

dtωmJψs

R

RRissRs

uss LM

dψsR

dt

Lσ

Saturated Γ model Corresponding inverse-Γ model

I Stator-core saturation affects almost everything in the inverse-Γ model

Lσ =LsL`Ls + L`

LM = Ls − Lσ RR =

(Ls

Ls + L`

)2

Rr

The equivalence holds in the steady state only, since some incremental inductance terms were omitted the transformation.38 / 48

Transient Impedance Under Single-Axis Excitation

I Standstill tests apply single-axis excitationI Nonlinear Γ model yields the impedance

Zs(s) = Rs + sLσi0 +sRRi0

s+ αi0

≈ Rs +RRi0 + sLσi0

I Impedance depends on the DC-bias currentis0 = ψs0/Ls0

Lσi0 =Lsi0L`Lsi0 + L`

RRi0 =

(Lsi0

Lsi0 + L`

)2

Rr

dψs

dtRr

is Rs

us

L`

Ls

Single-axis model at ωm = 0

Approximation holds for s � αi0, where αi0 = RRi0/LMi0 is the incremental inverse rotor time constant and LMi0 = Lsi0 − Lσi0.39 / 48

I Results of the standstill transient test can be misleadingI Common misinterpretation: Lσ saturates strongly as a function of is

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Stanstill Identification Procedure for the Nonlinear Γ Model

1. DC test: Identify Rs and inverter nonlinearities16

2. Flux-integration test: Identify magnetizing curve, i.e., Ls = Ls(ψs)17

3. Transient test: Identify Lσi0 and RRi018

4. Rotor parameters: Map Lσi0 and RRi0 to the constant parameters19

L` =Lsi0Lσi0Lsi0 − Lσi0

Rr =

(1 +

L`Lsi0

)2

RRi0

and compensate for the deep-bar effects

16Pellegrino, Bojoi, Guglielmi, et al., “Accurate inverter error compensation and related self-commissioning scheme in sensorless induction motordrives,” IEEE Trans. Ind. Appl., 2010.

17Erturk and Akin, “A robust method for induction motor magnetizing curve identification at standstill,” IEEE Access, 2019.18Kerkman, Thunes, Rowan, et al., “A frequency-based determination of transient inductance and rotor resistance for field commissioning purposes,”

IEEE Trans. Ind. Appl., 1996.19Khamehchi, Molsa, and Hinkkanen, “Comparison of standstill parameter identification methods for induction motors,” in Proc. IEEE SLED, 2018.

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Conventional Flux-Integration Test20,21

I Current step is0 is appliedI Induced voltage is integrated

ψs0 =

∫ τ

0

(us,ref − Rsis

)dt

I Long enough integration time τ ≥ 5/α forreaching the steady state: im0 = is0, us0 = Rsis0

I Result: single point on the magnetizing curve

ψs0 = ψs0(im0)

dψs

dtRr

is Rs

us

L`

Ls

im

20Stankovic, Benedict, John, et al., “A novel method for measuring induction machine magnetizing inductance,” IEEE Trans. Ind. Appl., 2003.21Peretti and Zigliotto, “Automatic procedure for induction motor parameter estimation at standstill,” IET Electr. Power Appl., 2012.

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Robust Flux-Integration Test22

I Current step is0 is appliedI Induced voltage is integrated

ψs0 =

∫ τ

0(us,ref − Rsis)dt

−∫ 2τ

τ(us,ref − Rsis)dt

Simulation: τ = 1 s and Rs = 0.9Rs

Robustmethod

Conven-tionalmethod

22Erturk and Akin, “A robust method for induction motor magnetizing curve identification at standstill,” IEEE Access, 2019. 43 / 48

Simulation: τ = 1 s and Rs = 0Corresponding identified

magnetizing curve

I Method is completely insensitiveto δRs and δus

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Introduction

V/Hz Control

Observers

Sensorless Identification at Standstill

Sensorless, More or Less

45 / 48

Sensorless Vector Control With DC-Link Measurements Only

Ts

01

0

00 2Ts

1

1

t (s)Ts

01

0

00 2Ts

1

1

t (s)Ts

01

0

00 2Ts

1

1

t (s)

SVPWM DPWM1 (zero vector 000) DPWM2 (zero vector 111)idc = iaidc = 0 idc = −icidc = 0 idc = 0 idc = 0

−ia

100

110010

011

001 101

uα

uβ

−ia

−ib−ib

−ic

−ic

ia

100

110010

011

001 101

uα

uβ

ia

ibib

icic

100

110010

011

001 101

uα

uβ

46 / 48

is,ref

ωm

eϑsJus,refCurrent

controller

ψR

is

Observer

uss,ref

DPWM

udc

Referencecalculation

Tref

ϑs

Midc

mode

mode ∈ {DPWM1,DPWM2}

I Phase-current samples from the DC-link current at fixed sampling interval areused as feedback for the observer

I Method has been patented and commercialized23

I In PMSM drives, signal injection is also possible with this approach24

23Virolainen, Heikkila, and Hinkkanen, “Method for determining output currents of frequency converter,” US Patent 7190599 B2, 2007.24Piippo, Suomela, Hinkkanen, et al., “Sensorless PMSM drive with DC-link current measurement,” in Conf. Rec. IEEE-IAS Annu. Meeting, 2007.

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ConclusionsI V/Hz control is plug-and-play due to its simplicity

I Unstable regions due to interaction of the electrical and mechanical dynamicsI Works well in simple applications (pumps and fans)

I Plug-and-play sensorless vector control enables a wider range of applicationsI Requires advanced observer and self-commissioning algorithmsI Can stabilize the system completely (except at zero stator frequency under load)I Temperature-dependent Rs can be tracked on-line, if the magnetic model knownI Magnetic model can be identified at standstill

I PMSMs and SyRMs were not covered hereI Similar problems (and similar solutions)I In addition, signal injection can be used to stabilize the lowest speeds

I Role of IoT and machine learning in the future?

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