Team Members
- Wendy Barrot, Program Director R&D, GLWA
- Christopher Nastally, Manager, GLWA
- Branko Kerkez, Assistant Professor, University of Michigan
- Sara Troutman, Ph.D. Student, University of Michigan
- Abhiram Mullapudi, Ph.D. Student, University of Michigan
- Gregory Ewing, Research Scientist, University of Michigan
In a collaboration between the GLWA (Great Lakes Water Authority) and Real-Time Water Systems Lab at the University of Michigan, we investigate the application of dynamic control to existing infrastructure in real-time to:
- Maximize current storage utilization
- Reduce combined sewer overflows
- Equalize flow to the water resources recovery facility
We aim to deliver a web-based decision support dashboard to be used by operators of the sewer network during wet-weather events (see below). The tool is informed by control algorithms developed through the LIFT Challenge.
Within this repository are functions that execute the control algorithms used to inform the decision support tool. While we do not share the underlying GLWA system model, those interested will be able to apply the control functions to their own system. The underlying model is an EPA SWMM input file; system states and control actions for system assets (e.g., gate positions, pump target settings) are accessed via PySWMM, a Python language SWMM wrapper.
The control algorithm employed here is Market-Based Control in which decisions are made in a virtual marketplace where a commodity is bought and sold by system agents. In this case, the commodity is volumetric capacity within the sewer system, the buyers of this commodity are upstream storage agents (e.g., pump stations, storage basins, inflatable storage dams), and the sellers are downstream points within the sewer network, more specifically the water resources recovery facility. The downstream point has an operator-defined setpoint to achieve; the downstream capacity is determined as the current volume above or below this setpoint. Price of the commodity fluctuates through time and is based on the current state of the system: how much capacity is available and how greatly it is demanded by upstream agents. Water is moved throughout the system via ''purchases'' of capacity by upstream agents, which dictate how much stored water each upstream agent can release to the downstream agents. Because the system considered here is so large and spatially distributed, we divide the system into sub-markets, each with its own price of capacity, one seller/downstream agent, and potentially several buyers/upstream agents.
Each buyer/upstream agent has a particular wealth with which to ''purchase''
capacity which is based on its current volume normalized to its maximum volume
capacity; thus, if a storage agent is close to using all of its available
volume, it poses more wealth to ''purchase'' more capacity from downstream,
that is release more water to avoid flooding locally. The wealth for upstream
agent
is computed via
where
is a weighting parameter describing priority toward mitigating
local upstream flooding,
is the normalized volume of upstream agent
.
The sum of wealth within each sub-market is computed via
where
is a binary matrix denoting the sub-market that each upstream
agent belongs to.
Each seller/downstream agent determines the cost it places on
the commodity based on its current volume about the desired setpoint. The cost
of downstream agent
is computed as
where
is the normalized volume of downstream agent
,
is the operator-defined normalized volumetric setpoint of agent
, and
is a weighting parameter describing priority toward achieving the setpoint.
The price of volumetric capacity within sub-market
is computed via
where
is the number of buyers/upstream agents in sub-market
. It is crucial to note that this results in a pareto optimal distribution of
capacity for each sub-market, meaning that any benefit to one agent would result
in a detriment of other agents.
The purchasing power of each upstream agent
in sub-market
is computed via
The available volumetric capacity in sub-market
is computed as
where
is the maximum possible volume at downstream agent
.
Thus, the available flow capacity in sub-market
is
where
is the timestep of the simulation.
Finally, the flow to be released from buyer/upstream agent
is computed as