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>

Low Frequency Oscillations in a Hydroelectric Generating System to the Variability of Wind and Solar Power

The penetration of multiple integrated renewable energies to the power grid are relevant for decision making in energy policy, environment and business. Such an electricity penetration is affected by the intermittent and volatile characteristics of integrated energies, mostly significantly related to the safe and stable electricity production and supply in real world. Here, this paper focuses on the low frequency oscillation analysis of the hydropower generation response to the wind and solar variability. To enable this analysis, a hybrid model of hydropower system integrating with the wind and solar power system is presented. The Nyquist and root-locus stability methods are used to investigate the sensitivity performance of the hydropower governor to the fluctuation of the integrated renewable energies. Additionally, to quantify the risk of the hybrid system, the low frequency oscillation response of hydropower system to wind/solar/hydropower quota and transmission line distance ratio is extensively investigated in this study. The results show that under the case of the wind, solar and hydropower ratio is 40: 1: 150, the optimal values for maximally reducing hydropower low frequency oscillation are finally determined as kp = 0.8, ki = 0.25 and kd =0.5. Regarding a certain wind/solar/hydropower quota, it is a promising strategy to increase the solar-load transmission line in order to achieve the safe and stable operation of the hybrid system and a relatively excellent dynamic regulation capacity of the hydropower governor. The model, methods and results implemented in this study are exploited to markedly improve new knowledge applications, policy management, low carbon emissions and investment competitiveness of future energy systems.