active disturbance rejection control applied to variable ... · e Δp Δ p ω ω* mppt pi ω jbtˆ...
TRANSCRIPT
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
• 5 17/05/2018 Journée GDR CSE
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
• 6 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR
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
• 7 17/05/2018 Journée GDR CSE
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
• 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
• 10 17/05/2018 Journée GDR CSE
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
• 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
• 12 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR
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.
3. ADRC based variable speed control
• 13 17/05/2018 Journée GDR CSE
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
= − −&
3. ADRC based variable speed control
[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.
• 14 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR
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
3. ADRC based variable speed control
Kp
• 15 17/05/2018 Journée GDR CSE
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.
3. ADRC based variable speed control
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.
• 16 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR
[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
3. ADRC based variable speed control
• 17 17/05/2018 Journée GDR CSE
• 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
3. ADRC based variable speed control
• 18 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR
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
3. ADRC based variable speed control
Fig. 10: Mathematical on-line torque estimation diagram
• 19 17/05/2018 Journée GDR CSE
Fig. 11: Generator side control diagram of a micro-hydropower plant PMSG
3. ADRC based variable speed control
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
• 20 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR
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
• 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
• 22 17/05/2018 Journée GDR CSE
4. Experimental validation
• 23 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR
0 0
𝑇↓obs (5𝑁.𝑚/𝑑𝑖𝑣)
𝑇(5𝑁.𝑚/𝑑𝑖𝑣)
𝑡(0.2𝑠/𝑑𝑖𝑣)
𝑡(0.2𝑠/𝑑𝑖𝑣)
Fig. 13: Torque observer performance
0 0
𝑇↓obs (5𝑁.𝑚/𝑑𝑖𝑣)
𝑇(5𝑁.𝑚/𝑑𝑖𝑣)
𝑡(0.2𝑠/𝑑𝑖𝑣)
𝑡(0.2𝑠/𝑑𝑖𝑣)
𝑇↓obs (5𝑁.𝑚/𝑑𝑖𝑣)
𝑇(5𝑁.𝑚/𝑑𝑖𝑣)
Fig. 14: Variable speed operation of ADRC with and without torque compensation (a) Without torque compensation (b) With torque compensation
4. Experimental validation
• 24 17/05/2018 Journée GDR CSE
Step torque disturbance
Cycle torque disturbance
Step torque disturbance
Cycle torque disturbance
Fig. 15: Comparison between PI and ADRC under torque disturbance
4. Experimental validation
• 25 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR
4. Experimental validation
PI
ADRC
𝜔
Fig. 15: Comparison between PI and ADRC under torque disturbance
• 26 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR
Fig. 16: Robustness test of ADRC based control under different inertia variations
4. Experimental validation
• 27 17/05/2018 Journée GDR CSE
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
• 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
• 29 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR
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?
• 30 17/05/2018 Journée GDR CSE
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
2. ADRC based variable speed control
• 33 17/05/2018 Journée GDR CSE
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
• 34 17/05/2018 Baoling GUO, Seddik BACHA, Mazen ALAMIR
Fig. 18: MPPT performance under sinusoidal torque fluctuations
Fig. 17: MPPT performance under random torque fluctuations
3. Simulation study
• 35 17/05/2018 Journée GDR CSE