Active Disturbance Rejection Control Applied to …Active Disturbance Rejection Control Applied to...

Active Disturbance Rejection Control Applied to Variable Speed Micro-Hydropower Plant

UMR CNRS 5269 - Grenoble-INP – Université Grenoble Alpes

Baoling GUO1, Seddik BACHA1, Mazen ALAMIR2

1 Université Grenoble Alpes, CNRS, Grenoble INP, G2Elab, 38000 Grenoble 2 Université Grenoble Alpes, CNRS, Grenoble INP, GIPSA lab, 38402 Saint Martin d'Hères

17/05/2018 18 Février 2016

Content

 1. Work context

 2. Control context

 3. ADRC based variable speed control

(Active Disturbance Rejection Control)

 4. Experimental validation

 5. Conclusions

 6. Future research discussion

•  2 17/05/2018

Fig.1: Diagram of a micro-hydro power plant (Source: https://www.tva.gov/Energy)

1

2 3

1. Work context

AC/DC/AC

•  3 17/05/2018 Journée GDR CSE

h wP g H Qρ= ⋅ ⋅ ⋅

mec wP g H Qη ρ= ⋅ ⋅ ⋅ ⋅

𝝆 (kg/m3) the volume density of water;

𝒈 (m/s2) the gravity acceleration; (m/s2) the gravity acceleration;

𝑸↓𝒘 (m3/s) the water flow rate;

𝑯(m) the net water head; (m) the net water head; A (m2) the area swept by rotor blades;

𝜼 the hydraulic turbine efficiency.

Hydraulic power:

Net mechanical power:

p Modelling of a Micro-hydro power plant

•  4 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR

1. Work context

1

1 90 50( , ) [( 0.78) exp( )] 3.332

[1 / ( 0.089) 0.035]

w w wi i

i

Q Q Qη λλ λ

λ λ −

⎧ = + + ⋅ − ⋅ ⋅⎪⎨⎪ = + −⎩

[1] Marquez, J. L., Molina, M. G., and Pacas, J. M. (2010). Dynamic modeling, simulation and control design of an advanced micro-hydro power plant for distributed generation applications. International journal of hydrogen energy, 35(11), 5772-5777.

Fig. 2: Hydraulic Efficiency curves

/ wR A Qλ ω= ⋅ ⋅

p Modelling of a Micro-hydro power plant


1. Work context

[2] L. Belhadji, S. Bacha, I. Munteanu, A. Rumeau, and D. Roye, “Adaptive MPPT Applied to Variable-Speed Micro-hydropower Plant,” IEEE Trans. Energy Convers., vol. 28, no. 1, pp. 34–43, 2013.

Fig. 3: Adaptive MPPT performances

𝐾=1 𝐾=5 𝐾↓𝑎𝑑𝑎𝑝𝑡𝑖𝑣𝑒 

p Adaptive MPPT technique


1. Work context

Note: Maximum Power Point Tracking (MPPT)

Begin

)(),( ttP ω

)1()( −−=Δ kk ωωω)1()( −−=Δ kPkPP

∫+−

−

=ek

k

Tt

t adap dttK1

1

)(* δω

)()1( kk ωω =−)()1( kPkP =−)()1( kk δδ =−

Return

Update variables

Input sample

Compute change

Update reference

Adaptive P&O MPPT diagram

PMSG

aibi

DC link

PWM PWM

ci saisbisci

Current sensor

N

Current sensorVoltage sensor

Generator current control

Grid current control

Generator side converter Grid side converterAC/DC DC/AC

Speed control DC bus control

MPPT Power management

*ω

*Gi

*Gu *

Su

*Si

*DCu

1st level

2nd level

3rd level

Fig. 4: Global architecture design of a micro-hydro power plant

1. Work context


Content

 1. Work context





 5. Conclusions


•  8 17/05/2018

n  Ziegler-Nichols PID tuning. n  Model-based control methods: Loop shaping, Pole placement … n  Model-based active disturbance injection control: Disturbance

Observer (DoB), Unknown Input Observer (UIO) … n  Partial-model-based control methods:

Ø Passive disturbance injection: Robust control, Adaptive control. Ø Active disturbance injection: ADRC.

p Classification of control methods

Fig. 5: PID controller diagram Fig. 6: Pole placement •  9 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR

2. Control context

p PMSG speed control with various disturbances

Fig. 7: PMSG variable speed control system with disturbance diagram

( )cG s eT*ω ω

n

LT

eKqi 1

Js B+

1

3

2

Note: Permanent Magnet Synchronous Generator (PMSG)

2. Control context


Content

 1. Work context





 5. Conclusions


•  11 17/05/2018

1 2

1

1 1 2 0 1 2

1

( , , , , ( ), ) ( , , , )n n

n n n

x x

x xx x x x x x xf w t t f buy x

−

=

=

⎧⎪⎪⎪⎨⎪ = + +⎪

=⎪⎩

&

&&

M

L L

𝑥↓1 , 𝑥↓2 ⋯ 𝑥↓𝑛  the state variables; 𝑦 the plant output; u the control input; 𝑤(𝑡) the uncertain external disturbance;

𝑓↓1  ( 𝑥↓1  , 𝑥↓2  ⋯ 𝑥↓𝑛  , 𝑤(𝑡),𝑡) the unknown disturbances; 𝑓↓0 (𝑥↓1 , 𝑥↓2 ⋯ 𝑥↓𝑛 ) the known disturbances. [3] J. Han, "From PID to Active Disturbance Rejection Control," in IEEE Transactions on Industrial Electronics, vol. 56, no. 3, pp. 900-906, March 2009.

p Canonical form


3. ADRC based variable speed control

0 1 0ˆ ˆ( , ) ( , ) ( , )x f x w bu f x w f x w b u

y x

= + = + +

=

⎧⎨⎩

&

1.5mecn f

qT BP

iJ J J

ω ωψ

= − −&

q Canonical form

q Dynamic mechanical model

𝒙 is the state variable; 𝒘 is uncertain external disturbances; 𝒖 is the control input of the plant; 𝒚 is the output of the plant.

Known disturbances

Unknown disturbances

𝑷↓𝒏  is the number of pole pairs; 𝐓↓𝐦𝐞𝐜  is the mechanical torque; 𝚿↓𝒇   is the magnet flux vector; 𝝎 is the rotation speed; 𝒊↓𝒒  is the stator current vector of q axis; 𝑱 is the total inertia; 𝑩 is the friction factor.



Step 3: Disturbance definition

0

1.5 n fPb

Jψ

=

0( , , , ) mecmec

T Bf T J BJ J

ωω − −=)

)))

qi u yω→ →Step 1:

Step 2: Order of ADRC →1

1*

0 0( )( , , , )mec qff T J B b iyω ω

ω

⋅⎧ = + +⎪⎨

=⎪⎩

))&0 1 0( , ) ( ) ( )x f x w bu f f b u

y x

= + = ⋅ + ⋅ +

=

⎧⎨⎩

& 1.5mecn f

qT BP

iJ J J

ω ωψ

= − −&


[4] Guo, S. Bacha, M. Alamir and H. Iman-Eini, "An anti-disturbance ADRC based MPPT for variable speed micro-hydropower plant," IECON 2017 , pp. 1783-1789.


ESO

Kp+

−

+

−Internal

Disturbance

MHPGS

ExternalDisturbance

0b 0/1 b

+ +

+

+

1z2z

e

ADRC

*qi*ω ω

0u

Compensation in the closed loop

disturbances estimated

),,ˆ,ˆ(0 JBTf mecω

Fig. 8: Diagram of ADRC based speed control design


Kp


q Linear extended state observer

𝑧↓1  is the estimation of speed; 𝑧↓2  is the total disturbances; 𝑏↓0  is the estimation of 𝑏; 𝜔↓0  the bandwidth of LESO.


1 1

1 2 0 1

2 1

0 020

2 ˆˆ( , )mec

z

z z b

z

u f T

ε ω

ω ε

ω ε

ω

= −

= − +

= −

⎧⎪

+⎨⎪⎩

&

&s1

02ω

20ω

+

s1

+

+

−

ω 1z 2z

+

u

Linear ESO design

Fig. 9: Linear ESO design diagram

ü  Practical parameter tuning. ü  Frequency response analysis. ü  Nearly the same performance.


[5] Gao, Zhiqiang. "Scaling and bandwidth-parameterization based controller tuning." Proceedings of the American control conference. Vol. 6. 2006.

* 2 01

0

ˆˆ( , )( ) mecp

z f Tu k zbω

ω+

= − −

q Feedback control law

Feedback control

Disturbance compensation

𝑧↓1  is the estimation of speed; 𝑧↓2  is the total disturbances estimated; 𝜔  is the rotation speed estimated; 𝑇 ↓𝑚𝑒𝑐  is the hydraulic mechanical torque estimated.

m̂ecT



•  Loop-‐up tables from GE Hydro

•  Prony brake torque sensors •  Mathema;cal on-‐line iden;fica;on

Torque = force × distance http://www.flight-mechanic.com/reciprocating-engine-power-and-efficiencies-part-three/

q Load torque estimation



Load torque estimation

[6] LIU, Z. G., & LI, S. H. (2008). Active disturbance rejection controller based on permanent magnetic synchronous motor model identification and compensation [J]. Proceedings of the CSEE, 24, 022.

𝑇 ↓𝑚𝑒𝑐 (𝑠) = [ 𝑘↓𝑚 𝑖↓𝑞 (𝑠)−𝐵𝜔(𝑠)− 𝐽𝑠𝜔(𝑠)] 1/𝑇↓0 𝑆+1 

𝐽𝑑𝜔/𝑑𝑡 = 𝑘↓𝑚 𝑖↓𝑞 − 𝑇↓𝑚𝑒𝑐 −𝐵𝜔

Laplace transformation


Fig. 10: Mathematical on-line torque estimation diagram


Fig. 11: Generator side control diagram of a micro-hydropower plant PMSG


SVPWM

abc

diqi

ai

bi

aS

bS

cSLADRC PI

+

−

+

−

* 0di =

*qi

dcVdcV

eθ*dv

*qv

αβ

dq

*vα

*vβ

Phase Sensor

dq

eθ

PΔωΔ

P

ω *ωMPPT

PI

ω

mecT̂J B

Torque obsever dt

dθ

ω

qipn


Content

 1. Work context





 5. Conclusions


•  21 17/05/2018

Fig. 12: Hardware-in-the-loop testing benchmark

Grid

DCM

DS1005

PMSG

DS1005

TMS320F240

Direct current motorPermanent magnet synchronous generator

AC/DC DC/ACDC/DC

DS1005

Variable speed generation system Hydraulic turbine torque simulator

mecTeT

4. Experimental validation




0 0

𝑇↓obs (5𝑁.𝑚/𝑑𝑖𝑣)

𝑇(5𝑁.𝑚/𝑑𝑖𝑣)

𝑡(0.2𝑠/𝑑𝑖𝑣)


Fig. 13: Torque observer performance

0 0







Fig. 14: Variable speed operation of ADRC with and without torque compensation (a) Without torque compensation (b) With torque compensation



Step torque disturbance

Cycle torque disturbance

Step torque disturbance

Cycle torque disturbance

Fig. 15: Comparison between PI and ADRC under torque disturbance




PI

ADRC

𝜔

Fig. 15: Comparison between PI and ADRC under torque disturbance


Fig. 16: Robustness test of ADRC based control under different inertia variations



Content

 1. Work context





 5. Conclusions


•  28 17/05/2018

  A variable speed micro-hydro power plant is a typical nonlinear system disturbed by large uncertainties.

  ADRC is a kind of partial-model-based control method.

  ADRC can actively estimate both the internal dynamics and the external disturbances in real time.

  The speed control could be smoothed by incorporating the load torque identification.

  ADRC achieves higher robustness compared with the classical PI controller.

5. Conclusions


6. Future research discussion

Ø How to tune and apply the nonlinear ADRC more efficiently?

Ø ADRC based control applied to grid side control: DC bus

regulation and grid current control.

Ø How to estimate the high frequency disturbance?

Ø PI ↔ PR, ESO ↔ R-ESO?


Thank you for your attention!

3. Adaptive P&O MPPT technique

Ref: L. Belhadji, S. Bacha, I. Munteanu, A. Rumeau, and D. Roye, “Adaptive MPPT Applied to Variable-Speed Microhydropower Plant,” IEEE Trans. Energy Convers., vol. 28, no. 1, pp. 34–43, 2013.

Begin

)(),( ttP ω

)1()( −−=Δ kk ωωω)1()( −−=Δ kPkPP

∫+−

−

=ek

k

Tt

t adap dttK1

1

)(* δω

)()1( kk ωω =−)()1( kPkP =−)()1( kk δδ =−

Return

Update variables

Input sample

Compute change

Update reference

Adaptive P&O MPPT diagram

𝑃: gird input power

𝜔: rotation speed

𝛿(𝑡)=𝑠𝑔𝑛(∆𝑃)𝑠𝑔𝑛(∆𝜔)

𝐾↓𝑎𝑑𝑎𝑝𝑡 : perturbed coefficient

𝛥𝐷=|∆𝑃⁄∆𝜔 | 𝐾↓𝑎𝑑𝑎𝑝𝑡𝑖𝑣𝑒 

•  32 30/10/2017

1 1

1 2 1 1 1

2 2 1 2

0 0( , , )

( , , )

ˆˆ( , )mec

z

z z fal b

z fal

u f T

ε ω

β ε α δ

β ε α δ

ω

= −

= − +

= −

⎧⎪

+⎨⎪⎩

&&

q Nonlinear Extended State Observer 𝑧↓1  is the estimation of speed; 𝑧↓2  is the total disturbances; 𝛽↓1 , 𝛽↓2  are the observer gains; 𝑏↓0  is the estimation of 𝑏.

Fig. 13: ‘large error, small gain; small error, large gain’

(a) (b)

𝜀↓1  𝜀↓1  0 0

𝛼↓1 =0.25

𝛼↓2 =0.5

𝛼↓3 =1.0

𝛿↓1 =0.5

𝛿↓2 =1.0 𝛿↓3 =2.0

𝛿=0.5 𝛼=0.5



Q(m3/s)

Fig. 16: MPPT speed tracking performance with different types of water flow rates

Case3:

Case1:

Case2:

3. Simulation study

Case1: base water flow rates

Case2: flow rates with fluctua;ons

Case3: ramping flow rates


Fig. 18: MPPT performance under sinusoidal torque fluctuations

Fig. 17: MPPT performance under random torque fluctuations

3. Simulation study


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