Modelling and Optimal Control of a Sewer Network

C.1 Hydraulic application (6.9.2012)

Georges Schutz, David Fiorelli, Stefanie Seiffert, Mario Regneri, Kai Klepiszewski

09/06/12 Modelling and Optimal Control of a Sewer Network 2

Overview

Case study• The system that is analyzed and controlled

Modelling and calibration• Use of different model types• What are the models• Model calibration & comparison

Model predictive control• MPC Principals• Objectives of MPC underlying optimization• Results based on simulation

Implementation issuesConclusions

09/06/12 Modelling and Optimal Control of a Sewer Network 3

The studied sewer system

Artificial Lake, mainly used for drinking waterCombined sewer network to drain to central WWTP24 controllable CSOTs

• 8 are in operation nowMix of pressured and free flow pipes

Haute-Sûresto

rage l

ake

River Sûre

Sc hli rbach

2000 m

RingelTadlermühle

Tadler

Kuborn

HeiderscheidEschdorf

Hiereck

Bavigne

Flébour

Baschleiden

Boulaide

Buurgfried

Insenborn

Nothum

Mecher

Liefrange

Goesdorf

WWTP

Dahl

Büderscheid

HeischtergronnEsch/Sauer

Kaundorf

Nocher

Lultzhausen

Bockholtzmühle

Nocher-Route

concrete dam

Pumping stationCombined sewage overflow tankSewerSewer system in operation 2010Subcatchment / VillageCatchment border

River Sûre

Summer 2010

Population equivalents

3869

Impervious surface 80 ha

CSOT 8

Total CSOT volume 1600 m 3

PS 4

Total transport sewer length

19.7 km

Pressure conduits 4.1 km

09/06/12 Modelling and Optimal Control of a Sewer Network 4

Modelling and calibrationUse of different model types

Hydrodynamic model• Planing, case studies, network analysis• In the context of the research project and the

project planning• Creates data for the calibration of the other

models (offline virtual reality)Simple time-delayed model

• Used inside to the model predictive control• Implemented in Matlab for offline simulations

and Python for the MPC pilot implementationHydrological model

• Used for long time simulations and as virtual reality for testing the MPC approach

• Integrated Control Sewer & WWTP (PhD)

Pro

ject

pl

anin

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ealiz

atio

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Phas

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Pha

se 2P

hase

1

Acco

mpa

nyin

gre

sear

ch p

roje

ct

Net

wor

k op

erat

ion

MP

C p

ilot

MP

C a

pplic

atio

n

Hyd

rody

nam

ic m

odel

Hyd

rolo

gica

l mod

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mpl

e tim

e de

laye

d m

odel

Tim

e-lin

e

09/06/12 Modelling and Optimal Control of a Sewer Network 5

Modelling and calibrationFlow time and profile test

Test design and properties• dry weather situation• Impounding of the dry weather flow

in CSOTs• Release of the throttled volumes in a

given temporal sequence for each CSOT

Test goal• Allocation of the QinWWTP pattern to

QoutCSOT,i

• identification of individual flow times from each CSOT to the WWTP

• Validation of the hydrodynamic model• Evaluation of the other models

Qout_K

Qout_G

Qout_N

Δh Q in_w

Qou

t_W h

TemporalMeasurement

t

Q K

t

Q G

t

Q N

t

Q

K GN

WWTP

09/06/12 Modelling and Optimal Control of a Sewer Network 6

Modelling and calibrationResult and discussion

• Hydrodynamic model fits quite good to the monitored flows• NL hydrological model much less detailed compared to the HD-

Model but is able to reproduced most of the dynamics.• Translation Model gets the timing of of the waves good enough for

the use in the MPC context.

09/06/12 Modelling and Optimal Control of a Sewer Network 7

Model predictive controlused principals

System• Measurements• Historic data• Controllable aggregates

Optimizer• Input forecasting• Model based output prediction• Objective-function• Optimization over prediction horizon

Control loop• Apply control for u(k+1)• Run the optimization in real time (Δ )t• Update to current system state

past future

k k+Hp

k+Hccontrol horizon

prediction horizon

Predicted Output ym

Predicted control inputs u

Inside MPC

Objectif

Optimiser

System

CommandsObjectives

Qout_K

Qout_G Qout_N

WWTP

QA(t) = Qout_1(t-12) + Qout_2(t-8)

QB(t) = QA(t-7)

QC(t) = QB(t-9)

QC(t) = Qout_1(t-28) + Qout_2(t-24) Output

r (t ) u (t) y (t)

Measurements

09/06/12 Modelling and Optimal Control of a Sewer Network 8

Model predictive controlfor the proposed sewer systems

Multi-Objective function

• Homogenous distribution of the storage

• Constant inflow to the WWTP

• Minimum overflow

φ1(n)=∑i=1

N

[V i(n)− V imax

∑i=1

N

V imax∑i=1

N

V i(n)]2

φ2(n )=[yref (n)−∑i=1

N *

Out i(n−d i)]2

φ3(n)=∑i=1

N

[Ovi(n )−NL ]2

subject to ci(x )=0 i∈Eci(x )≥0 i∈I

minimize J=∑n= t

t+Hp

λ φ1(n )+βφ2(n )+αφ3(n )

09/06/12 Modelling and Optimal Control of a Sewer Network 9

Model predictive controlsome results

0 1 0 2 0 3 0 4 0 5 00

5

1 0

CS

OT

#2

T i m e ( h )

0 1 0 2 0 3 0 4 0 5 00

2 0

4 0

CS

OT

#3

T i m e ( h )0 1 0 2 0 3 0 4 0 5 0

0

5

1 0

1 5

CS

OT

#24

T i m e ( h )

0 1 0 2 0 3 0 4 0 5 0

02468

1 01 21 41 6R

ain

In

ten

sity

(m

m/h

)0 1 0 2 0 3 0 4 0 5 0

2 03 04 05 06 07 08 09 01 0 0

M a x

R e f

Flo

w (

m3 /1

0min

)

T i m e ( h )

R a i n i n t e n s i t y a n d s e w e r o u f l o w t o t h e W W T P

o u t f l o w ( m 3 / 1 0 m i n )

n o r m a l i z e d v o l u m e

n o r m a l i z e d o v e r f l o w

m a x i m u m o u t f l o w ( m 3 / 1 0 m i n )m a x i m u m n o r m a l i z e d v o l u m eh i g h e s t n o r m a l i z e d o v e r f l o w

09/06/12 10

Model predictive controlsome results

-24%

Ref

StaticTheoretic

GPC (forecasting sensitivity)GPC (weighting sensitivity)

GPC (Qwwtp_REF sensitivity)

28000

30000

32000

34000

36000

38000

40000

Ove

rflo

w [m

3 ]

Static GPCforecasting sensitivity

TheoreticalGPC

weighting sensitivity

GPCQwwtp_ref sensitivity

-5%

-12%

-5%

-9%

-5%

-19%

100%

0%

Reduction of overflow volume...

Compared to a static controlphysically possible

80%

20%

09/06/12 Modelling and Optimal Control of a Sewer Network 11

Implementation

PLS – SCADA• centralize all

network variables• Via real time bus• User and Admin

interface for the GPCOPC interface

• Industrial standard• Exists for most SCADA hardware• Software libraries available in FOSS

Global Predictive Control implementation• Matlab → Python• End-User system feedback / training / issues• Fall-back strategies

CRP PC

PLS

V1

In1

Px

PLC1

RT-Bus

OPC ServerRT-Bus ↔ OPC

P1

Out1

OPC

Global predictiveControl

Local Control

Vi

Ini

PiOut

i

PLCi

Local Controls

Weighted sub-goals

αMinimize overflow

βConstant WWTP-inflow

λHomogeneous

storage use

Convex Optimization

09/06/12 Modelling and Optimal Control of a Sewer Network 12

Conclusions

Different models used in different phases of the projectVirtual reality

• important to demonstrate the possible gains of the GPC approach• important to analyze different control approaches• validate the effective gains of the controlled system after

implementationSimple sewer model (time delayed / plug flow)

• linear, robust model• calibration towards the real network affordable• convex optimization

Further works• Integrate a global quality component in the simple model• Handling structural network modifications in the GPC approach