Battle of the Water Futures 🚰

Water Sources

Water sources represent the entire process of water abstraction and treatment consolidated at a single location. Each source has a nominal production capacity which represents a hard limit on the amount of water that can be delivered throughout any consecutive 24-hour window.

In the BWF, three macro-types of water sources are modelled: groundwater, surface water, and desalination. The main trade-off is that groundwater sources are generally smaller (< 25 \(Mm^3/year\)) and cheaper to operate, as the water has higher quality and requires less treatment. Surface water treatment plants and desalination plants are generally much larger (30-45 \(Mm^3/year\)) but are considerably more expensive and energy-intensive to run. Moreover, surface water sources differ as they are affected by climate conditions; specifically, low inflows within rivers could temporarily shut down treatment plants downstream (effectively reducing their capacity to zero for those days). Instead, groundwater sources have an extraction permit (expressed in \(m^3\) per year). This is not a hard physical constraint such as the nominal production capacity, but rather a “soft” legislative constraint checked by the government at the end of each year. This penalty effectively represents compensation for the hydrological displacement affecting farmers and natural areas due to the overextraction. The fine amount is set by law and can therefore change at any time based on political decisions.

The cost of water production at every source \(s\) is a combination of four components:

\[ \mathrm{OPEX}_s(y) = F_s + c^{\text{el}}(y) \cdot E^{\text{grid}}_s(y) +c^\text{vol}_s(y) \cdot Q_s(y) + c^\text{extra}_s(y) \cdot \max\bigl(Q_s(y)-\phi_s \cdot Q^*_s, 0 \bigr) \qquad{(1)}\]

where:

• \(F_s\) represents fixed costs, including personnel, taxes, and planned maintenance.
• \(c^\text{el}(y)\cdot E^{\text{grid}}_s(y)\) represents volumetric costs for energy.
• \(c^\text{vol}_s(y) \cdot Q_s(y)\) represents the volumetric costs for non-energy related expenditures, such as chemicals and filters.
• \(c^\text{extra}_s(y) \cdot \max\bigl(Q_s(y)-\phi_s \cdot Q^*_s, 0 \bigr)\) represent the extra volumetric costs incurred when production exceeds the planned threshold.

In eq. 1, \(Q_s(y)\) is the total volume produced by the source in year \(y\), \(Q^*_s\) is the source nominal capacity, and \(\phi_s\) is the capacity target factor (source-type dependent), which defines the ideal operating point above which additional costs are applied.

Additionally, the variable \(E^{\text{grid}}_s(y)\) represents the electrical grid energy consumed for water production by the source \(s\) in year \(y\) and it is calculated as: \[ E^{\text{grid}}_s(y) = \sum_{t \in \mathcal{Y}} \max\bigl(E_s(t) - E^{\text{PV}}_s(t), 0\bigr) \qquad{(2)}\]

where \(t\) is the simulation timestep, \(\mathcal{Y}\) is the set of timesteps in year \(y\), \(E_s(t)\) represents the energy consumed by the sources \(s\) at time \(t\), and the \(E^{\text{PV}}_s(t)\) is electricity generated by the photovoltaic panels associated with the source \(s\) at time \(t\).

The source energy consumption \(E_s(t)\) is:

\[ E_s(t) = \epsilon_s \cdot Q_s(t) \qquad{(3)}\]

where \(\epsilon_s\) is the source specific energy and \(Q_s(t)\) is the volume produced by the source at timestep \(t\).

To complete the accounting, the total operational expenditure associated with all the sources in water utility \(w\) at year \(y\) is:

\[ \mathrm{OPEX}^{\text{sources}}_w(y) = \sum_{s \in \mathcal{S}_w} \mathrm{OPEX}_s(y) \qquad{(4)}\]

where \(\mathcal{S}_w\) represents the collection of water sources managed by utility \(w\), and \(\mathrm{OPEX}_s(y)\) is the individual source cost defined in eq. 1.

Similarly to municipalities, sources can also open and close over time. Participants can decide to close production locations and open new ones within the constraints of the problem (available locations and sizes) to make the supply system more efficient. However, a closed source cannot be reopened and no direct cost is associated with this action. When activating a new source, participants must decide the nominal capacity, but the possible size is limited by different rules depending on the source type:

• Desalination and surface water sources have an upper limit defined in the competition data (see Appendix A)
• Groundwater sources cannot exceed the permit by more than 30%

New water sources have an uncertain construction time, so participants must communicate the construction start date, and the activation date will be randomized.

The capital investment associated with the construction of new sources in water utility \(w\) at year \(y\) is:

\[ \text{CAPEX}^\text{sources}_w(y) = \sum_{s \in \mathcal{S}_w} \mathbf{1}_{\{\tau_s = y\}} \cdot c^\text{source} (\text{class}(s),y) \cdot Q^*_s \qquad{(5)}\]

where for a source \(s\) in the set of the water utility’s sources (\(\mathcal{S}_w\)), \(\tau_s\) is its starting construction time, \(\mathbf{1}_{\{\tau_s = y\}}\) is an indicator function equal to 1 if the construction begins in year \(y\) (0 otherwise), \(Q^*_s\) is the requested source nominal capacity, and \(c^\text{source} (\text{class}(s),y)\) the unit cost, which depends on the year of construction and the source class (see tbl. 1).

One limitation of the BWF is that we do not model water quality differences between sources, which would typically prevent mixing in practice. This simplification keeps the problem tractable given its existing complexity.

The key parameters and decision variables governing the Water Sources Module are detailed in tbl. 2. The actual values for these variables can be inspected within the data files, which are mapped in Appendix A.