dp_multi {reservoir}

Dynamic Programming with multiple objectives (supply, flood control, amenity)

Description

Determines the optimal sequence of releases from the reservoir to minimise a penalty cost function based on water supply, spill, and water level. For water supply: Cost[t] = ((target - release[t]) / target) ^ loss_exp[1]). For flood control: Cost[t] = (Spill[t] / quantile(Q, spill_targ)) ^ loss_exp[2]. For amenity: Cost[t] = abs(((storage[t] - (vol_targ * capacity)) / (vol_targ * capacity))) ^ loss_exp[3].

Usage

dp_multi(Q, capacity, target, surface_area, max_depth, evap, R_max = 2 *
  target, spill_targ = 0.95, vol_targ = 0.75, weights = c(0.7, 0.2, 0.1),
  loss_exp = c(2, 2, 2), S_disc = 1000, R_disc = 10, S_initial = 1,
  plot = TRUE, rep_rrv = FALSE)

Arguments

Q

vector or time series object. Net inflow totals to the reservoir. Recommended units: Mm^3 (Million cubic meters).

capacity

numerical. The reservoir storage capacity (must be the same volumetric unit as Q and the target release).

target

numerical. The target release constant. Recommended units: Mm^3 (Million cubic meters).

surface_area

numerical. The reservoir water surface area at maximum capacity. Recommended units: km^2 (square kilometers).

max_depth

numerical. The maximum water depth of the reservoir at maximum capacity. If omitted, the depth-storage-area relationship will be estimated from surface area and capacity only. Recommended units: meters.

evap

vector or time series object of length Q, or a numerical constant. Evaporation from losses from reservoir surface. Varies with level if depth and surface_area parameters are specified. Recommended units: meters, or kg/m2 * 10 ^ -3.

R_max

numerical. The maximum controlled release, in the same units as target.

spill_targ

numerical. The quantile of the inflow time series used to standardise the "minimise spill" objective.

vol_targ

numerical. The target storage volume constant (as proportion of capacity).

weights

vector of length 3 indicating weighting to be applied to release, spill and water level objectives respectively.

loss_exp

vector of length 3 indicating the exponents on release, spill and water level deviations from target. Default exponents are c(2,2,2).

S_disc

integer. Storage discretization–the number of equally-sized storage states. Default = 1000.

R_disc

integer. Release discretization. Default = 10 divisions.

S_initial

numeric. The initial storage as a ratio of capacity (0 <= S_initial <= 1). The default value is 1.

plot

logical. If TRUE (the default) the storage behavior diagram and release time series are plotted.

rep_rrv

logical. If TRUE then reliability, resilience and vulnerability metrics are computed and returned.

Value

Returns reservoir simulation output (storage, release, spill), total penalty cost associated with the objective function, and, if requested, the reliability, resilience and vulnerability of the system.

See Also

sdp_multi for Stochastic Dynamic Programming

Examples

layout(1:3)
dp_multi(resX$Q_Mm3, cap = resX$cap_Mm3, target = 0.2 * mean(resX$Q_Mm3), S_disc = 100)