Reservoir balance

The reservoir balance constraint balances the volume of water stored in the reservoir with the flow of water in and out of the reservoir. The change in volume of the reservoir from the previous time step to the current one must equal the difference between inflow and outflow of water.

The balance consist of different parts:

• The reservoir volume variables. This could be a single variable for the volume, or a sum of segments in the case of a minimum and maximum segment.

• Waterways leading in and out of the reservoir. This includes:

  • Discharge paths

  • Bypass paths

  • Spillage paths

  • Tunnels

  • Pumps

• Inflow from the surrounding area

The balance constraints are normally indexed by the set of reservoirs (i) and the number of time steps (k). Using the optional feature of reservoir balance relaxation [REF], some of the constraints are replaced by a version with a single step. Broadly, the balance is expressed like this:

\[\begin{split} \\{i \in reservoirs,\ k = 0 \\}\end{split}\]

\[ RESBAL(i,k): Volume(i,k) - VolumeStart(i) = Inflow(i,k) - Outflow(i,k)\]

For the rest of the time steps the variable from the previous time steps is used.

\[\begin{split} \\{i \in reservoirs,\ k = [1,timesteps\rangle\\}\end{split}\]

\[ RESBAL(i,k): Volume(i,k) - Volume(i,k-1) = Inflow(i,k) - Outflow(i,k)\]

An example of a balance and its constituents:

\[ RESBAL(i,k): res(i,k) - res(i,k-1) = Inflow(i,k) - (dis(i,k) + byp(i,k) + spi(i,k))\]