Battle of the Water Futures 🚰

Pumping stations

Pumping stations are the infrastructure connecting water sources to municipalities and are responsible for distributing the water produced by each source into the network. Each pumping station contains one or more identical pumps operating in parallel.

Whenever a new source is opened, participants must define which pump option (selected exclusively from a pre-defined list of available pumps) and how many units are installed at that source’s pumping station. Similarly, participants can decide to replace pumps at existing locations or add new ones of the same type as installed.

Whether replacing old pumps or being added in new pumping stations, the capital investment associated with the installation of pumps in water utility \(w\) at year \(y\) is:

\[ \text{CAPEX}^\text{pumps}_w(y) = \sum_{n \in \mathcal{N}_w} \sum_{p \in \mathcal{P}_{n}} \mathbf{1}_{\{\tau_p = y\}}\cdot c^\text{pump}(\gamma_p, y) \qquad{(1)}\]

where \(n\) is the pumping station index within the set of the water utility’s pumping stations (\(\mathcal{N}_w\)), \(p\) is the p-th pump in that pumping station set (\(\mathcal{P}_n\)), \(\tau_p\) is the pump installation time, \(\mathbf{1}_{\{\tau_p = y\}}\) is an indicator function equal to 1 if the installation happened in year \(y\) (0 otherwise), and \(c^\text{pump}(\gamma_p, y)\) the unit cost for the selected pump option \(\gamma_p\).

While a water source’s daily outflow is constrained by its nominal capacity, the pumping station’s configuration limits the source’s peak outflow rate (\(m^3/hour\)).

The only operational cost component of a pumping station is its energy expenditure, calculated during the network hydraulic simulation based on the energy consumption and tariffs. Peak demand charges are not included, as we assume utilities have agreements in place with electrical grid providers (see more details in sec. ¿sec:energy-model?). Maintenance costs and other fixed yearly operational costs are included in the initial construction cost of each pump.

Thus, the operational expenditure associated with pumping in water utility \(w\) at year \(y\) is:

\[ \mathrm{OPEX}^{\text{pumps}}_w(y) = \sum_{n \in \mathcal{N}_w} c^{\text{el}}(y) \cdot E^{\text{grid}}_n(y) \qquad{(2)}\]

where \(n\) is the pumping station index within the set of the water utility’s pumping stations (\(\mathcal{N}_w\)), \(c^\text{el}(y)\) is the dynamic electricity price, and \(E^{\text{grid}}_n(y)\) is the electricity consumption from the grid for the n-th pumping station in year \(y\). This quantity is computed as:

\[ E^{\text{grid}}_n(y) = \sum_{t \in \mathcal{Y}} \max\bigl( \sum_{p \in \mathcal{P}_{n}} E_p(t) - E^{\text{PV}}_n(t), 0\bigr) \qquad{(3)}\]

where \(t\) is the simulation timestep, \(\mathcal{Y}\) is the set of timesteps in year \(y\), \(E_p(t)\) the p-th pump energy consumption at time \(t\), \(\mathcal{P}_n\) the set of pumps in pumping station \(n\), and \(E^\text{PV}_n(t)\) is electricity generated by the photovoltaic panels associated with pumping station \(n\) at time \(t\).

Pumps performances remain constant over time (no degradation in efficiency or similar wear effects). However, pumps do age normally and have an expected lifetime. The actual lifetime is randomized, and when a pump reaches its end of life, it must be replaced. Participants do not need to communicate this decision, as replacements will be automatically implemented, but they must account for this “unexpected” cost in their planning.

Note that the provided pump curves only describe the working range of the pumps and must not be extrapolated beyond the values presented in the tables.