dp_multi: Dynamic Programming with multiple objectives (supply, flood...

In swd-turner/reservoir: Tools for Analysis, Design, and Operation of Water Supply Storages

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,
  c2g,
  plot = TRUE
)

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.
c2g	vector. Optional end-state cost-to-go.
plot	logical. If TRUE (the default) the storage behavior diagram and release time series are plotted.

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)

swd-turner/reservoir documentation built on June 9, 2021, 12:27 a.m.