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 ,..., N S ( 1 ,..., 1 1 NV ),..., ( N S ,..., N SV ) N 1 A is a discrete set of actions: A A S T is a transition function where T : S A S 0 ,1 T , , ' P s t 1 ' | s t , a t R is a reward function where R : S A R , rt | s t , a t 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 A * R , T , , ' V ' ' S The optimal policy are the actions obtained from arg max R , A * T , , ' V ' S * ' V * : Water Distribution System modeled as an MDP Topology of a typical water distribution system: States (everything that is important to control): Time – range: discrete: T T min T T Tank level – range: min max ,T H H discrete: 7 ,T S T , H 1 ,..., H N H min min T ,..., T ,H H H min max max ,H min H ,..., H max Water Distribution System modeled as an MDP Actions (what you can manipulate): A U 1 ,..., U N U U 0 ,1 Triggered directly: Associated with a VFD – range: U 0 ,1 discrete: U 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): BC 8 0 , U ,..., 1 Consumption: Demand: C D CC OP Pw ( t ) T POP ma x Pw ( t ) PDM BC R CC C D FP Pw ( t ) T P FP 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 Set of actions: where T 0 , 24 and H 1, 33 . 25 A U 1 ,..., U 11 Transition function: H ( t 1) f H ( t ), d ( t ), A ( t ) Reward function: 21:00 R ( t ) 30 T Pw ( t ) $ on peak t 9:00 Pw ( t ) $ max Pw ( t ) $ demand off peak t 21:00 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 paulo.fracasso@usp.br Av. Prof. Luciano Gualberto, trav.3, n.158, sala C2-50 CEP: 05508-970 - São Paulo, SP - Brazil Phone: +55-11-3091-5397 20

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# Energy Cost Optimization in Water Distribution Systems using