Nonlinearities in Reservoir Operation for Hydropower Production

Silva, Ligia M.; Zambon, Renato C.

doi:10.1061/9780784412947.239

Cited by 4 publications

(2 citation statements)

References 8 publications

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“… Mass balance equation:

S_{m, t + 1}^{i} = S_{m, t}^{i} + (W_{m, t}^{i} - R_{m, t}^{i} - S P_{m, t}^{i} - E V_{m, t}^{i}) \cdot Δ t_{t},

where

S_{m, t + 1}^{i}

and

S_{m, t}^{i}

are the storage of reservoir

m

at the ending and beginning of time period

t

under scenario

i

, respectively (

m^{3}

);

W_{m, t}^{i}

R_{m, t}^{i}

, and

S P_{m, t}^{i}

are the inflow, power release, and nonpower release (spill), respectively, from reservoir

m

in time period

t

under scenario

i

(

m^{3} / s

);

E V_{m, t}^{i}

is the evaporation rate [ Silva and Zambon , ] of reservoir

m

in time period

t

under scenario

i

(

m^{3} / s

); and

Δ t_{t}

is the time interval in each time period (s). Hydraulic continuity:

\begin{matrix} W_{m, t}^{i} ... \end{matrix}

…”

Section: Methodsmentioning

confidence: 99%

Scenario tree reduction in stochastic programming with recourse for hydropower operations

Zhong

Zambon

et al. 2015

Water Resources Research

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A stochastic programming with recourse model requires the consequences of recourse actions be modeled for all possible realizations of the stochastic variables. Continuous stochastic variables are approximated by scenario trees. This paper evaluates the impact of scenario tree reduction on model performance for hydropower operations and suggests procedures to determine the optimal level of scenario tree reduction. We first establish a stochastic programming model for the optimal operation of a cascaded system of reservoirs for hydropower production. We then use the neural gas method to generate scenario trees and employ a Monte Carlo method to systematically reduce the scenario trees. We conduct in-sample and out-of-sample tests to evaluate the impact of scenario tree reduction on the objective function of the hydropower optimization model. We then apply a statistical hypothesis test to determine the significance of the impact due to scenario tree reduction. We develop a stochastic programming with recourse model and apply it to real-time operation for hydropower production to determine the loss in solution accuracy due to scenario tree reduction. We apply the proposed methodology to the Qingjiang cascade system of reservoirs in China. The results show: (1) the neural gas method preserves the mean value of the original streamflow series but introduces bias to variance, cross variance, and lag-one covariance due to information loss when the original tree is systematically reduced; (2) reducing the scenario number by as much as 40% results in insignificant change in the objective function and solution quality, but significantly reduces computational demand.

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“… Mass balance equation: