Energy Cost Optimization in Water Distribution Systems using
Download
Report
Transcript Energy Cost Optimization in Water Distribution Systems using
University of Sao Paulo
Department of Electrical and Computer Engineering
Intelligent Techniques Laboratory
Energy Cost Optimization in Water Distribution
Systems Using Markov Decision Processes
Paulo T. Fracasso, Frank S. Barnes and Anna H. R. Costa
Agenda
• Anatomy of Water Distribution Systems
• Problem relevancy
• Markov Decision Process
• Modeling a Water Distribution System as an MDP
• Monroe Water Distribution System
• Experiment results
• Conclusions
1
Water distribution system
• It is a complex system composed by pipes, pumps and other
hydraulic components which provide water supply to consumers.
Focus of
my work
2
Problem relevancy
• About 3% of US energy consumption (56 billion kWh) are used
for drinking water (Goldstein and Smith, 2002).
$2 billion/year
3
Source: Electric Power Research Institute,1994.
Markov Decision Process - MDP
MDP is a model for sequential decision making in fully observable
environments when outcomes are uncertain.
Advantages of MDP compared to other techniques:
Real world – operates in uncertain and dynamic domains
Planning – generates control policies to sequential decisions
Optimal solution – guarantees to achieve a higher future payoff
Disadvantages of MDP:
Discrete domains (state and action)
Course of dimensionality
4
Markov Decision Process - MDP
MDP is defined as a tuple S, A, T , R where:
S is a discrete set of states (can be factored in Nv features):
S 1,..., NS (11,...,1NV ),...,(N1 S ,...,NNSV )
A is a discrete set of actions:
A A
S
T is a transition function where T : S A S 0,1
T , , ' Pst 1 '| st , at
R is a reward function where R : S A
R , rt | st , at
5
Markov Decision Process - MDP
Solving an MDP consists in finding a policy , which is defined
as a mapping from states to actions, s.t. : S A
Bellamn’s equation allows to break a dynamic optimization
problem into simpler sub-problems:
V R , T , , 'V '
'S
The optimal value of the utility is:
V * max R , T , , 'V * '
A
'S
The optimal policy are the actions obtained from V * :
* arg max R , T , , 'V * '
A
'S
Water Distribution System modeled as an MDP
Topology of a typical water distribution system:
States (everything that is important to control): S T , H1,...,H N
Time – range: T T min,T max
discrete: T T min, T min T ,...,T max
Tank level – range: H H min, H max
discrete: H H min, H min H ,...,H max
7
H
Water Distribution System modeled as an MDP
Actions (what you can manipulate): A U ,...,U
1
Triggered directly: U 0,1
Associated with a VFD – range: U 0,1
NU
discrete: U 0, U ,...,1
Transition function (how the system evolves):
H t 1 f H (t ), D(t ), A(t )
Calculated by EPANET
Reward function (how much an action cost): R CC CD
FP
OP
Consumption: CC Pw(t ) T POP Pw(t ) T PFP
Demand: CD ma xPw (t ) PDM
BC
BC
8
Demand
Water Distribution System modeled as an MDP
Electrical power
Final result:
Markov
Decision
Processes
Control policy
Energy price
schema
9
Constraints
Understand MDP results
Control policy:
States variables: everything
that is important to control
(tank level and time)
Tank level
Maps state variables into a set
of actions
Set of actions: what you can
manipulate (pumps)
Indicates controllability (avoid
black region)
Correlated to demand curve
10
Time
Understand MDP results
Controller:
Actions are based just on tank
level and time
Pump trigger
Easy to implement and fast
to run in PLC (lookup table)
Tank level
Uses control policy map to
produce actions
11
Time
Monroe Water Distribution System
Characteristics:
11 pumps
1 storage tank
4 pressure monitoring
40k people served
182 miles of pipes
Diameters varying
from 2 to 42 inches
12
Monroe Water Distribution System
Demand curve (during summer season):
Average: 6 700 GPM
Minimum: 4 188 GPM
Maximum: 8 389 GPM
13
Pressure restrictions (in PSI):
J-6: 65 ≤ P ≤ 70
▪ J-131: 45 ≤ P ≤ 55
J-36: 50 ≤ P ≤ 60
▪ J-388a: 40 ≤ P ≤ 90
Monroe Water Distribution System
Pumps (E2, E3, E4, E5, E6, E7, W8, W9, W10, W11 and W12):
Energy price schema:
14
On-peak (09:00 – 20:59): $0.04014/kWh
Off-peak (21:00 – 08:59): $0.03714/kWh
Demand (monthly): $13.75/kW
MDP apply to Monroe WDS
Mathematical model:
Set of states: S T , H where T 0,24 and H 1,33.25
Set of actions: A U1,...,U11
Transition function: H (t 1) f H (t ), d (t ), A(t )
Reward function:
9:00
21:00
R(t ) 30 T Pw(t ) $on peak Pw(t ) $off peak maxPw(t ) $demand
t 21:00
t 9:00
Data flux diagram:
.INP FILE
15
EPANET
DLL
MATLAB
h(t 1)
Pw(t )
MDP results in Monroe WDS
Expected electrical power :
E5 and E7 consume 144.3kW
16
W11, E2 and E6 consume 320.4kW
MDP results in Monroe WDS
Number of activated pumps (27 possibilities):
on={E2,E6}
17
on{E5,E7}
on={W12,E3,E4,E5}
on={E2,E3,E4,E5}
MDP results in Monroe WDS
SCADA records:
obtained from historical data (July 6th, 2010)
75% of WTP consumption is considered to be used in pump
One day is extrapolated to one billing cycle (30 days)
Both approaches started in the same level (19.3 ft)
Energy expenses
Off-peak energy [$/month]
On-peak energy [$/month]
Demand [$/month]
Total [$/month]
18
SCADA records
3 210.57
3 750.78
3 836.25
10 797.60
MDP
2 608.32
3 768.51
3 603.67
9 980.50
Difference
-23.1%
+0.5%
-6.5%
-8.2%
Conclusions
MDP avoids restrictions (level, pressure, and pumps) and reduces
expenses with energy
To reduce energy consumption is different to reduce expenses with
energy (demand is the biggest villain)
Summer season imposes small quantity of feasible actions
Verify if it is possible to reduce the number of pump combination
MDP policy is easy to implement in a non-intelligent device (PLC)
19
Contact
Thank you for your attention
PAULO THIAGO FRACASSO
[email protected]
Av. Prof. Luciano Gualberto, trav.3, n.158, sala C2-50
CEP: 05508-970 - São Paulo, SP - Brazil
Phone: +55-11-3091-5397
20