Impact of the controller model complexity on MPC performance - - PowerPoint PPT Presentation

▶
impact of the controller model complexity on mpc
SMART_READER_LITE
LIVE PREVIEW

Impact of the controller model complexity on MPC performance - - PowerPoint PPT Presentation

Feb 09, 2023 142 likes •524 views

Impact of the controller model complexity on MPC performance evaluation for building climate control Damien Picard a , Jn Drgoa b , Lieve Helsen a , c , and Michal Kvasnica b a KU Leuven, Department of Mechanical Engineering, Leuven, Belgium b

slide-1
SLIDE 1

Impact of the controller model complexity on MPC performance evaluation for building climate control

Damien Picarda, Ján Drgoňab, Lieve Helsena,c, and Michal Kvasnicab

aKU Leuven, Department of Mechanical Engineering, Leuven, Belgium bSlovak University of Technology in Bratislava, Slovakia cEnergyVille, Thor Park, Waterschei, Belgium

September 14, 2016

Acknowledgment: The Authors gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV 0551-11.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 1 / 21

slide-2
SLIDE 2

Building Control Motivation

Problem: EU spends 400 billion EUR/year on energy.

40% goes into thermal comfort in buildings.*

Goal: Reduce the energy consumption Solution: MPC-based control

* International Energy Agency, ‘Energy efficiency requirements in building codes, energy efficiency policies for new buildings’ 2013 OECD/IEA.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 2 / 21

slide-3
SLIDE 3

Building Control Motivation

Problem: EU spends 400 billion EUR/year on energy.

40% goes into thermal comfort in buildings.*

Goal: Reduce the energy consumption Solution: MPC-based control

* International Energy Agency, ‘Energy efficiency requirements in building codes, energy efficiency policies for new buildings’ 2013 OECD/IEA.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 2 / 21

slide-4
SLIDE 4

Building Control Motivation

Problem: EU spends 400 billion EUR/year on energy.

40% goes into thermal comfort in buildings.*

Goal: Reduce the energy consumption Solution: MPC-based control

* International Energy Agency, ‘Energy efficiency requirements in building codes, energy efficiency policies for new buildings’ 2013 OECD/IEA.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 2 / 21

slide-5
SLIDE 5

Building Control Motivation

Problem: EU spends 400 billion EUR/year on energy.

40% goes into thermal comfort in buildings.*

Goal: Reduce the energy consumption Solution: Thermal comfort control

* International Energy Agency, ‘Energy efficiency requirements in building codes, energy efficiency policies for new buildings’ 2013 OECD/IEA.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 2 / 21

slide-6
SLIDE 6

Model Predictive Control

Pros: Satisfy thermal comfort constraints Minimize energy consumption Obey technological restrictions Cons: Implementation in early stages Need for a good controller model

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 3 / 21

slide-7
SLIDE 7

Model Predictive Control

Pros: Satisfy thermal comfort constraints Minimize energy consumption Obey technological restrictions Cons: Implementation in early stages Need for a good controller model

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 3 / 21

slide-8
SLIDE 8

Model Predictive Control

Pros: Satisfy thermal comfort constraints Minimize energy consumption Obey technological restrictions Cons: Implementation in early stages Need for a good controller model

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 3 / 21

slide-9
SLIDE 9

Model Predictive Control

Pros: Satisfy thermal comfort constraints Minimize energy consumption Obey technological restrictions Cons: Implementation in early stages Need for a good controller model

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 3 / 21

slide-10
SLIDE 10

Model Predictive Control

Pros: Satisfy thermal comfort constraints Minimize energy consumption Obey technological restrictions Cons: Implementation in early stages Need for a good controller model

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 3 / 21

slide-11
SLIDE 11

What is the Best Model?

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 4 / 21

slide-12
SLIDE 12

What is the Best Model?

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 4 / 21

slide-13
SLIDE 13

Methodology

Controller model order Plant model order RBC PID MPC

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 5 / 21

slide-14
SLIDE 14

Building Description

Floor area [m2] 48.3 Conditioned volume [m3] 130.6 Total exterior surface area [m2] 195 Windows [-] 5 Walls [-] 22 Roof and floor surfaces [-] 12 Thermal zones [-] 6

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 6 / 21

slide-15
SLIDE 15

Linearisation1

Controller model order Plant model order RBC PID MPC

1Picard, D., Jorissen, F., and Helsen, L. 2015. Methodology for Obtaining Linear State Space Building Energy Simulation

  • Models. In 11th International Modelica Conference, pages 51–58, Paris
  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 7 / 21

slide-16
SLIDE 16

Linearisation Error

Z

  • n

e 1 Z

  • n

e 2 Z

  • n

e 3 Z

  • n

e 4 Z

  • n

e 5 Z

  • n

e 6 −1.0 −0.5 0.0 0.5 1.0 [K]

Original

Z

  • n

e 1 Z

  • n

e 2 Z

  • n

e 3 Z

  • n

e 4 Z

  • n

e 5 Z

  • n

e 6 −1.0 −0.5 0.0 0.5 1.0

Renovated

Z

  • n

e 1 Z

  • n

e 2 Z

  • n

e 3 Z

  • n

e 4 Z

  • n

e 5 Z

  • n

e 6 −1.0 −0.5 0.0 0.5 1.0

Light weight

Full year open-loop simulation linearization error below 1 K.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 7 / 21

slide-17
SLIDE 17

Model Order Reduction2

Controller model order Plant model order RBC PID MPC

Square root balanced truncation algorithm, based on Hankel singular values.

2 Antoulas, A. C. and Sorensen, D. C. 2001. Approximation of large-scale dynamical systems: An overview. Applied Mathematics and Computer Science.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 8 / 21

slide-18
SLIDE 18

Reduced Order Models – Error Bounds

State [-] 50 100 150 200 250 Error bound [-] 10 -10 10 -5 10 0 Error bounds

Original Renovated Light weight

State [-] 5 10 15 20 25 30 Error bound [-] 10 -2 10 -1 10 0 10 1 Error bounds

Original Renovated Light weight

Guarantees of an error bounds and preserves most of the system characteristics in terms of stability, frequency, and time responses.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 9 / 21

slide-19
SLIDE 19

Reduced Order Models – Open Loop Simulation

T [° C]

15 20 25

TZone 1 TZone 2 TZone 3

1 2 3 4 5 6 7

T [° C]

15 20 25

TZone 4 Time [Day]

1 2 3 4 5 6 7

TZone 5

4 7 10 15 20 30 40 100 SSM 1 2 3 4 5 6 7

TZone 6

Orders of ROM:

Single week open loop simulation with realistic control inputs and disturbances.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 9 / 21

slide-20
SLIDE 20

Reduced Order Models – Prediction Errors

  • 3
  • 2
  • 1

1 2

1-step ahead

ROM 4 ROM 7 ROM 10 ROM 15 ROM 20 ROM 30 ROM 40 ROM 100

  • 3
  • 2
  • 1

1 2

10-step ahead

ROM 4 ROM 7 ROM 10 ROM 15 ROM 20 ROM 30 ROM 40 ROM 100

  • 3
  • 2
  • 1

1 2

40-step ahead

ROM 4 ROM 7 ROM 10 ROM 15 ROM 20 ROM 30 ROM 40 ROM 100

[K]

The central line is the median, the box gives the 1st and 3rd quartiles, the wiskers contain 99.5% of the data, the crosses are the outliers.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 9 / 21

slide-21
SLIDE 21

Control Setup

Controller model order Plant model order RBC PID MPC

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 10 / 21

slide-22
SLIDE 22

Control Scheme

MPC Building Estimator d y u r ˆ x, ˆ p

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 11 / 21

slide-23
SLIDE 23

Estimator and Augmented Model

ˆ xk|k = ˆ xk|k−1 + L

  • ym,k − ˆ

yk|k−1

  • ˆ

xk+1|k = Aˆ xk|k + Buk|k + Edk|k ˆ yk|k = Cˆ xk|k + Duk|k

  • ˆ

xk+1 ˆ pk+1

  • ˜

xk+1

=

  • A

I

  • ˜

A

  • ˆ

xk ˆ pk

  • ˜

xk

+

  • B
  • ˜

B

uk +

  • E
  • ˜

E

dk ˆ yk =

  • C

F

  • ˜

C

  • ˆ

xk ˆ pk

  • +
  • D
  • ˜

D

uk

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 12 / 21

slide-24
SLIDE 24

Estimator and Augmented Model

ˆ xk|k = ˆ xk|k−1 + L

  • ym,k − ˆ

yk|k−1

  • ˆ

xk+1|k = Aˆ xk|k + Buk|k + Edk|k ˆ yk|k = Cˆ xk|k + Duk|k

  • ˆ

xk+1 ˆ pk+1

  • ˜

xk+1

=

  • A

I

  • ˜

A

  • ˆ

xk ˆ pk

  • ˜

xk

+

  • B
  • ˜

B

uk +

  • E
  • ˜

E

dk ˆ yk =

  • C

F

  • ˜

C

  • ˆ

xk ˆ pk

  • +
  • D
  • ˜

D

uk

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 12 / 21

slide-25
SLIDE 25

MPC Formulation

min

u0,...,uN−1 N−1

  • k=0
  • ||sk||2

Qs + ||uk||2 Qu

  • s.t. xk+1 = Axk + Buk + Edk

yk = Cxk + Duk lbk − sk ≤ yk ≤ ubk + sk u ≤ uk ≤ u x0 = ˆ x(t) ∀k ∈ {0, . . . , N − 1}

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 13 / 21

slide-26
SLIDE 26

State Condensing

x1 = Ax0 + Bu0 + Ed0 x2 = A (Ax0 + Bu0 + Ed0) + Bu1 + Ed1 . . . xk+1 = Ak+1x0 + . . .

  • AkB . . . AB B

uT

0 . . . uT k

T + . . .

  • AkE . . . AE E

dT

0 . . . dT k

T

yk = CAkx0 + . . . C

  • Ak−1B . . . AB B

uT

0 . . . uT k−1

T + . . .

C

  • Ak−1E . . . AE E

dT

0 . . . dT k−1

T + Duk + Fp0

Significantly reduces the number of the optimization variables.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 14 / 21

slide-27
SLIDE 27

Simulation Setup

One year performances of RBC, PID, MPC. Three types of 6-zone buildings, with 300 states.

2 6 10 14 18 22 26 30 34 38 42 46 [%] 96 98 100

Total comfort level Original Renovated Light weight

prediction horizon [] 2 6 10 14 18 22 26 30 34 38 42 46 [MWh / year] 5 10 15

Total heating cost

2 6 10 14 18 22 26 30 34 38 42 46 [1e3 s] 1 2 3 4

CPU time

1 1 1 1 1 1 1 e + 6 1 e + 7 1 e + 8 1 e + 9 1 e + 1 [%] 50 100

Total comfort level

weighting factor [] 1 1 1 1 1 1 1 e + 6 1 e + 7 1 e + 8 1 e + 9 1 e + 1 [MWh / year] 5 10 15

Total heating cost

1 1 1 1 1 1 1 e + 6 1 e + 7 1 e + 8 1 e + 9 1 e + 1 [1e3 s] 0.9 1 1.1 1.2 1.3

CPU time

Ts = 900, N = 40 steps (i.e., 10 hours), Qs

Qu = 108.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 15 / 21

slide-28
SLIDE 28

Simulation Setup

One year performances of RBC, PID, MPC. Three types of 6-zone buildings, with 300 states.

2 6 10 14 18 22 26 30 34 38 42 46 [%] 96 98 100

Total comfort level Original Renovated Light weight

prediction horizon [] 2 6 10 14 18 22 26 30 34 38 42 46 [MWh / year] 5 10 15

Total heating cost

2 6 10 14 18 22 26 30 34 38 42 46 [1e3 s] 1 2 3 4

CPU time

1 1 1 1 1 1 1 e + 6 1 e + 7 1 e + 8 1 e + 9 1 e + 1 [%] 50 100

Total comfort level

weighting factor [] 1 1 1 1 1 1 1 e + 6 1 e + 7 1 e + 8 1 e + 9 1 e + 1 [MWh / year] 5 10 15

Total heating cost

1 1 1 1 1 1 1 e + 6 1 e + 7 1 e + 8 1 e + 9 1 e + 1 [1e3 s] 0.9 1 1.1 1.2 1.3

CPU time

Ts = 900, N = 40 steps (i.e., 10 hours), Qs

Qu = 108.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 15 / 21

slide-29
SLIDE 29

Disturbance Profiles

time [days]

2 4 6

[K]

265 270 275 280 285

Temperature disturbances

time [days]

2 4 6

[W]

50 100 150 200

Power disturbances

time [days]

2 4 6

[W/m 2]

50 100 150 200 250 300 350 400 450

Power per surface disturbances

52 disturbances

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 16 / 21

slide-30
SLIDE 30

Control Profiles – RBC

time [days] 1 2 3 4 5 6 7 y 2 [ °C] 20 25 30

Indoor temperature

time [days] 1 2 3 4 5 6 7 u2 [W] 200 400 600

Heating

Comfort satisfaction, spanning from 93.9% to 95.2%. Energy savings around xx.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 17 / 21

slide-31
SLIDE 31

Control Profiles – PID

time [days] 1 2 3 4 5 6 7 y 2 [ °C] 20 25 30

Indoor temperature

time [days] 1 2 3 4 5 6 7 u2 [W] 200 400 600

Heating

Comfort satisfaction, spanning from 95.6% to 99.6%. Energy savings around 6%.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 18 / 21

slide-32
SLIDE 32

Control Profiles – MPC

time [days] 1 2 3 4 5 6 7 y 2 [ °C] 20 25 30

Indoor temperature

time [days] 1 2 3 4 5 6 7 u2 [W] 200 400 600

Heating

Comfort satisfaction, close to 100.0%. Energy savings around 13%.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 19 / 21

slide-33
SLIDE 33

Performance Evaluation

(a) PID RBC ROM 4 ROM 7 ROM 10 ROM 15 ROM 20 ROM 30 ROM 40 ROM 100 SSM [%] 50 100 Total comfort rate (b) PID RBC ROM 4 ROM 7 ROM 10 ROM 15 ROM 20 ROM 30 ROM 40 ROM 100 SSM [ MWh / year ] 5 10 15 20 Total heating cost (c) PID RBC ROM 4 ROM 7 ROM 10 ROM 15 ROM 20 ROM 30 ROM 40 ROM 100 SSM [1e4 Kh / year ] 5 10 15 20 Total one-step ahead prediction error

Original Renovated Light weight Original (OSF) Renovated (OSF) Light weight (OSF)

(d) PID RBC ROM 4 ROM 7 ROM 10 ROM 15 ROM 20 ROM 30 ROM 40 ROM 100 SSM [1e3 s] 2 4 6 8 CPU time

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 20 / 21

slide-34
SLIDE 34

Conclusions

1

Influence of controller model accuracy on controller performance.

2

Minimum of 30 states was necessary for 6-rooms house.

3

When a dense formulation is used a CPU time becomes independent

  • f the number of states of the controller model.

4

Use a controller model which emulates the real building as accurately as possible!

Acknowledgment: The Authors gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV 0551-11.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 21 / 21

slide-35
SLIDE 35

Conclusions

1

Influence of controller model accuracy on controller performance.

2

Minimum of 30 states was necessary for 6-rooms house.

3

When a dense formulation is used a CPU time becomes independent

  • f the number of states of the controller model.

4

Use a controller model which emulates the real building as accurately as possible!

Acknowledgment: The Authors gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV 0551-11.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 21 / 21

slide-36
SLIDE 36

Conclusions

1

Influence of controller model accuracy on controller performance.

2

Minimum of 30 states was necessary for 6-rooms house.

3

When a dense formulation is used a CPU time becomes independent

  • f the number of states of the controller model.

4

Use a controller model which emulates the real building as accurately as possible!

Acknowledgment: The Authors gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV 0551-11.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 21 / 21

slide-37
SLIDE 37

Conclusions

1

Influence of controller model accuracy on controller performance.

2

Minimum of 30 states was necessary for 6-rooms house.

3

When a dense formulation is used a CPU time becomes independent

  • f the number of states of the controller model.

4

Use a controller model which emulates the real building as accurately as possible!

Acknowledgment: The Authors gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV 0551-11.

  • J. Drgoňa (STU Bratislava)

EUCCO, Leuven, Belgium September 14, 2016 21 / 21