Study on the Optimal Operation of a Hydropower Plant Group Based on the Stochastic Dynamic Programming with Consideration for Runoff Uncertainty

Hydropower plant operation reorganizes the temporal and spatial distribution of water resources to promote the comprehensive utilization of water resources in the basin. However, a lot of uncertainties were brought to light concerning cascade hydropower plant operation with the introduction of the stochastic process of incoming runoff. Therefore, it is of guiding significance for the practice operation to investigate the stochastic operation of cascade hydropower plants while considering runoff uncertainty. The runoff simulation model was constructed by taking the cascade hydropower plants in the lower reaches of the Lancang River as the research object, and combining their data with the copula joint function and Gibbs method, and a Markov chain was adopted to construct the transfer matrix of runoff between adjacent months. With consideration for the uncertainty of inflow runoff, the stochastic optimal operation model of cascade hydropower plants was constructed and solved by the SDP algorithm. The results showed that 71.12% of the simulated monthly inflow of 5000 groups in the Nuozhadu hydropower plant drop into the reasonable range. Due to the insufficiency of measured runoff, there were too many 0 values in the derived transfer probability, but after the simulated runoff series were introduced, the results significantly improved. Taking the transfer probability matrix of simulated runoff as the input of the stochastic optimal operation model of the cascade hydropower plants, the operation diagram containing the future-period incoming water information was obtained, which could directly provide a reference for the optimal operation of the Nuozhadu hydropower plant. In addition, taking the incoming runoff process in a normal year as the standard, the annual mean power generation based on stochastic dynamic programming was similar to that based on dynamic programming (respectively 305.97 × 108kW⋅h and 306.91 × 108kW⋅h), which proved that the operation diagram constructed in this study was reasonable.

A Stochastic Dynamic Programming Model for Hydropower Scheduling with State-dependent Maximum Discharge Constraints

<div>We present a medium-term hydropower scheduling model that includes state-dependent environmental constraints on maximum discharge. A stochastic dynamic programming algorithm is used to enable modelling of nonconvex relationships in the problem formulation. The model is applied in a case study of a Norwegian hydropower system with multiple reservoirs. We find that the maximum discharge constraint significantly impacts the water values and simulated operation of the hydropower system. A main finding is that the nonconvex characteristics of the environmental constraint is reflected in the water values, implying a nonconvex objective function. Operation according to the computed water values is simulated for cases with and without the environmental constraint. Even though operation of the system changes considerably when the environmental constraint is included, the total electricity generation over the year is kept constant, and the total loss in expected profit limited to less than 0.8%.</div>

A Stochastic Dynamic Programming Model for Hydropower Scheduling with State-dependent Maximum Discharge Constraints

<div>We present a medium-term hydropower scheduling model that includes state-dependent environmental constraints on maximum discharge. A stochastic dynamic programming algorithm is used to enable modelling of nonconvex relationships in the problem formulation. The model is applied in a case study of a Norwegian hydropower system with multiple reservoirs. We find that the maximum discharge constraint significantly impacts the water values and simulated operation of the hydropower system. A main finding is that the nonconvex characteristics of the environmental constraint is reflected in the water values, implying a nonconvex objective function. Operation according to the computed water values is simulated for cases with and without the environmental constraint. Even though operation of the system changes considerably when the environmental constraint is included, the total electricity generation over the year is kept constant, and the total loss in expected profit limited to less than 0.8%.</div>