Presented @ the 36th IAHR World Congress 2015 - The Hague

1. A convex optimization approach for automated
water and energy end use disaggregation
Dario Piga, Andrea Cominola, Matteo Giuliani, Andrea Castelletti, Andrea Emilio Rizzoli

2. The project
2
high resolution water
consumption data
interaction with customers
for socio-psychographic
data gathering
management strategies:
dynamic pricing
rewards

3. The project
3
SMART METERS
USER
MODEL
WDMS
customized
feedbacks
dynamic pricing
Toilet
Shower
Dishwasher
Washing machine
Garden
Swimming pool
GAMIFICATION | ONLINE BILL GAMIFICATION | ONLINE BILL

4. Water consumption disaggregation into end uses
Toilet
Shower
Dishwasher
Washing machine
Garden
Swimming pool
ONE MEASURE MANY END USES
Need for fully automated
disaggregation algorithms
overlapping, simultaneous
water end uses
human-dependent
vs
automatic fixtures
Personalized hints for reducing water/energy consumption
Information on potential saving in deferring to peak-off hours
Leak detection
Customized WDMS
3

5. Sparse optimization approach
Assumptions (appliance level)
Piece-wise constant consumption profiles
Finite number of operating modes
Knowledge of water consumption at each operating mode
𝑦"(𝑘) = 𝐵(
(")
… 𝐵*"
(")
𝜃(
(")
(𝑘)
⋮
𝜃*"
(")
(𝑘)
= 𝐵(")-
𝜃(")
(𝑘)
𝜃(")
(𝑘): unknown, sparse (only one component equal to 1)
4

6. Sparse optimization approach
Minimizing fitting error (least-squares)
min
1 2 3
4 𝑦 𝑘 − 4
𝐵(")-
𝜃(")
(𝑘)
𝑦"(𝑘)
6
"7(
89
37(
Not unique solution (solution not reliable)
5

7. Sparse optimization approach
Adding regularization
min
1 2 3
4 𝑦 𝑘 − 4
𝐵(")-
𝜃(")
(𝑘)
𝑦"(𝑘)
6
"7(
8
+ 𝛾( 4 4 𝜃(")
(𝑘) <
6
"7(
9
37(
9
37(
Ø l0-norm enforces sparsity in the vector 𝜃(")(𝑘)
Ø balances the tradeoff between fitting and sparsity𝛾(
non-convex optimization problem
𝑠. 𝑡. 𝜃 "
𝑘 ≥ 0, 𝜃(
"
𝑘 + …+ 𝜃*"
"
𝑘 = 1
6

8. Sparse optimization approach
Adding regularization (l1-norm)
min
1 2 3
4 𝑦 𝑘 − 4
𝐵(")-
𝜃(")
(𝑘)
𝑦"(𝑘)
6
"7(
8
+ 𝛾( 4 4 𝜃(")
(𝑘) (
6
"7(
9
37(
9
37(
Ø replace l0-norm with l1-norm
Ø l1-norm still promotes sparsity
convex optimization problem
𝑠. 𝑡. 𝜃 "
𝑘 ≥ 0, 𝜃(
"
𝑘 + …+ 𝜃*"
"
𝑘 = 1
7

9. Sparse optimization approach
Adding regularization (l1-norm)
min
1 2 3
4 𝑦 𝑘 − 4
𝐵(")-
𝜃(")
(𝑘)
𝑦"(𝑘)
6
"7(
8
+ 𝛾( 4 4 𝜔 "
(𝑘) ⊙ 𝜃(")
(𝑘) (
6
"7(
9
37(
9
37(
Ø replace l0-norm with l1-norm
Ø l1-norm still promotes sparsity
convex optimization problem
Ø fixed weights take into time-of-the-day probability𝜔 " (𝑘)
𝑠. 𝑡. 𝜃 "
𝑘 ≥ 0, 𝜃(
"
𝑘 + …+ 𝜃*"
"
𝑘 = 1
8

10. Sparse optimization approach
Enforce piece-wise constant consumption profiles
min
1 2 3
4 𝑦 𝑘 − 4
𝐵(")-
𝜃(")
(𝑘)
𝑦"(𝑘)
6
"7(
8
+ 𝛾( 4 4 𝜔 "
(𝑘) ⊙ 𝜃(")
(𝑘) (
6
"7(
+ 𝛾8 4 4 𝑘"
𝜃(
(")
𝑘 − 𝜃(
(")
(𝑘 − 1)
⋮
𝜃*"
(")
𝑘 − 𝜃*"
(")
(𝑘 − 1)
F
6
"7(
9
378
9
37(
9
37(
Ø penalize time variation of the vector
Ø only the largest variation is penalized
convex optimization problem
𝜃(")(𝑘)
Ø fixed weights to more penalize rarely time varying appliances𝑘"
𝑠. 𝑡. 𝜃 "
𝑘 ≥ 0, 𝜃(
"
𝑘 + …+ 𝜃*"
"
𝑘 = 1
9

11. Tests on high-resolution electricity data
AMPds dataset: S. Makonin et al., AMPDs: a public dataset for load disaggregation and eco-feedback research, In Electrical Power and
Energy Conference, 2013.
10

12. Tests on water data
WEEP dataset: Heinrich, Water End Use and Efficiency Project, New Zealand, 2007
31%
37%
32%
SPARSE OPTIMIZATION
34%
36%
30%
ACTUAL
Toilet
Tap
Shower
11

13. Conclusions and follow up
Ø New convex optimization based algorithm for end-use characterization
Ø Main assumption: piecewise constant consumption profiles (requires high-
resolution consumption readings)
Conclusions
Ø Development of final-refinements to deal with low-resolution data
Ø Development of tailored numerical solvers
Future works
12

14. consortium cluster

15. thank you
http://www.smarth2o-fp7.eu/
@smartH2Oproject
#SmartH2O
Andrea Cominola
andrea.cominola@polimi.it
Politecnico di Milano
Department of Electronics,
Information and Bioengineering