Water demand forecasting for the optimal operation of large-scale drinking water networks the Barcelona case study

A.K. Sampathirao*, J.M. Grosso**, P. Sopasakis*, C. Ocampo-Martinez**, A. Bemporad* and V. Puig**

* IMT Institute for Advanced Studies Lucca, Lucca, Italy, ** Automatic Control Dept., Technical University of Catalonia (UPC), Barcelona, Spain.

DWN Control: Goals ¡  Reduce energy consumption for pumping,

¡ Meet the demand requirements,

¡ Deliver smooth control actions,

¡  Keep the storage above safety limits,

¡  Respect the technical limitations: pressure limits, overflow limits & pumping capabilities,

¡  Have foresight: predict how the water demand and energy cost will move and act accordingly.

Outline ¡ Description of the overall control system,

¡  Hydraulic model of the DWN,

¡ Modelling of the uncertain water demand time series,

¡  Economic MPC: the control algorithm,

¡  Simulation results.

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2

4

6

8

10

12

x 10−3 Prediction Error

Past Data

Observed

Forecast

The Control Module

Energy Price

Water Demand

Drinking Water Network

Online Measurements

Flow Pressure Quality

Forecasting Module

History Data

Data Validation Module

Validated Measurements

Commands Model Predictive Controller

(Uncertain) estimates

EFFINET Deliverable report D2.1, “Control-oriented modelling for operational management of urban water networks.”

Hydraulic model

xk+1 = Adxk +Bduk +Gddk,

0 = Euk + Eddk

¡  Based on mass balance equations,

¡  Linear time-invariant discrete time system,

¡ with input-disturbance couplings

State: Storage in tanks

Input: Pumping

Disturbance: Water demand

Constraints mandated by mass balance equations.

C. Ocampo-Martinez, V. Puig, G. Cembrano, R. Creus, and M. Minoves. Improving water management efficiency by using optimization-based control strategies: the barcelona case study. Water Sci. & Tech.: Water supply, 9(5):565–575, 2009.

Water demand forecasting ¡  Three approaches bore fruit: SARIMA, BATS and

RBF-SVM,

¡  The predictive ability of the models was evaluated using the average PMSE-24, that is:

PMSEHp =1

THp

k0+TX

k=k0

HpX

i=1

(d̂k+i|k � dk+i)2

Water demand forecasting

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12

x 10−3 Prediction Error

Past Data

Observed

Forecast

SARIMA model

¡  PMSE24 = 0.0158,

¡  25 parameters (quite simple) determined up to a high statistical significance.

Water demand forecasting

RBF-SVM model

¡  PMSE24 = 0.0065,

¡  229 parameters (complex),

¡  10-fold cross-validation gave q2 = 0.9952,

¡  Explanatory variables: 200 past demands plus a set of binary calendar variables,

¡  Stringent confidence intervals.

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10x 10

−3

Time [hr]

Dem

and [m

3 h

r−1]

RBF−SVM Prediction

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0.01

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0.03

0.04

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0.07

Time [h]

Wa

ter

De

ma

nd

Flo

w [

m3/h

]

Forecasting of Water Demand

Future Past

Water demand forecasting

BATS model

¡  Box-Cox transformation, ARMA errors, Trends and Seasonality,

¡  PMSE24 = 0.0043,

¡ with just 26 parameters,

¡ Very stringent confidence intervals.

Prefer to pump when the price is low!

Stay above the safety storage volume

PAST FUTURE

Volume in tank (m3)

Time (h)

Do not overflow!

Time (h)

Pumping (m3/h)

Avoid pumping when the price is high!

Account for pumping capabilities

Why MPC:

¡  Optimal: Computes the control actions by optimizing a performance criterion,

¡  Realistic: Accounts for the operational constraints,

¡  Predictive: Has foresight; acts early before the price or the demand changes.

How MPC works

J. B. Rawlings and D. Q. Mayne. Model predictive control: theory and design. Madison: Nob Hill Publishing, 2009.

Economic MPC for DWN

From the forecasting module: dk+j|k = d̂k+j|k + ✏k+j|k

Estimation error, essentially bounded in:

Ek+j|k = {✏ : ✏min

k+j|k ✏ ✏max

k+j|k}

xk+j|k = x̂k+j|k +jX

l=1

A

l�1Gd✏k+l|kThe state sequence will satisfy:

Nominal state sequence satisfying the dynamics:

x̂k+j+1|k = Adx̂k+j|k +Bduk+j|k +Gdd̂k+j|k

Economic MPC for DWN

Economic MPC for DWN

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1.8 x 104

Time [hr]

Volu

me

[m3 ]

Safety Volume

Minimum Volume

Maximum Volume

MPC Upper Bound

MPC Lower Bound

Predicted Trajectory

Closed−loop trajectory

x̂k+j|k 2 X iM

j=1

A

j�1GdEk+j|k

Bounds on the predicted state sequence calculated by:

The sparsity of Gd enables this computation!

Economic MPC for DWN

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1.6

1.8 x 104

Time [hr]

Volu

me

[m3 ]

Safety Volume

Minimum Volume

Maximum Volume

MPC Upper Bound

MPC Lower Bound

Predicted Trajectory

Closed−loop trajectory

x̂k+j+1|k = Adx̂k+j|k +Bduk+j|k+

+Gdd̂k+j|k

Predicted state sequence according to:

MPC: Performance

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MPC Control Action (1~20)

Contr

ol A

ctio

n

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0.6

0.8

MPC Control Action (21~46)

Contr

ol A

ctio

n

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0.1

0.2

Time [hr]

Wate

r C

ost

[e.u

.]

MPC in action •  88 demand nodes •  63 tanks •  114 pumping stations •  17 flow nodes

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Economic Cost (E.U.)

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1

1.5

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Smooth Operation Cost

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2

4

6Safety Storage Cost (× 107)

Low price à Pumping

The system operator has information about the current and the predicted operation cost.

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Closed−loop MPC Simulation

Time [hr]

Reple

tion [

%]

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0.5

1

1.5

Time [hr]

Dema

nd [m

3 /s]

MPC: Performance

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0.8

MPC Control Action (1~20)

Contr

ol A

ctio

n

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0.6

0.8

MPC Control Action (21~46)

Contr

ol A

ctio

n

10 20 30 40 50 60 70 80 900

0.1

0.2

Time [hr]

Wate

r C

ost

[e.u

.]

Foresight: Tanks starts loading up before a DMA asks for water.

Work in progress ¡  Formulation of the control problem as a

stochastic economic MPC problem,

¡ Algorithms for the solution of large-scale optimisation problems,

¡ GPGPU implementations for the efficient solution of such optimisation algorithms.

Thank you for your attention.

This work was financially supported by the EU FP7 research project EFFINET “Efficient Integrated Real-time monitoring and Control of Drinking Water Networks,” grant agreement no. 318556.