(591f) Uncertainty Mitigation Via Short-Term Rescheduling in Cascaded Hydropower Systems

The rapid increase in global competitiveness, highly dynamic nature of operational and market conditions and greater regulatory pressures from pertinent agencies in the renewable energy sector motivate the need for development of efficient short-term scheduling strategies for the optimal operation of cascaded hydroelectric power systems. The objective of scheduling in such systems is to determine the optimal power generation and generating unit commitment schedules so as to optimize an economic performance indicator subject to different system and external constraints. The highly unpredictable nature of market and weather conditions give rise to uncertainties in electricity prices and water inflows. The uncertainty in the forecasts for these system parameters has a significant impact on the schedules for these systems. This gives rise to a phenomenon of significant variation in these schedules in response to slight fluctuations in electricity pricing termed “nervousness”, which is highly undesirable from an operational standpoint. These factors motivate the need for development of a rescheduling scheme incorporating feedback of updated system information for handling these parametric uncertainties.

A variety of reactive scheduling approaches across a wide range of applications have been proposed to tackle various uncertain disturbances and events after their realization. Li and Ierapetritou (2008) propose a multiparametric programming based reactive scheduling method involving the integration of disruptive events as uncertain parameters. Subramanian et al. (2012) express a general MILP chemical production scheduling model in state-space form for efficient closed-loop MPC based solution of a reactive scheduling problem with unforeseen events modeled as disturbances and discuss the relevance of concepts such as set-points and trajectories, stability and terminal conditions in the context of scheduling. Kopanos and Pistikopoulos (2014) propose a multiparametric programming based rolling horizon reactive scheduling approach involving the use of a state-space representation of the problem solved once and offline for application to combined heat and power units. Gupta and Maravelias (2016) highlight the differences between open-loop and closed-loop (online) scheduling for the deterministic case and emphasized the importance of periodic rescheduling even in the absence of trigger events. Gupta et al. (2016) extend this work to demonstrate the advantages of feedback based periodic online scheduling over traditional event-triggered rescheduling in the presence of uncertainty. Gupta and Maravelias (2017) present a generalized state-space formulation for online scheduling capable of handling a variety of unforeseen events and routinely encountered disturbances through feedback and uncertain parameters using robust scheduling.

There are several MPC based reactive scheduling approaches applied to hydropower systems operation in the literature. Nolde et al. (2008) present a multi-stage stochastic programming formulation for medium-term monthly scheduling of a hydrothermal system considering stochasticity from variations in water inflows and demand of electrical energy. Zambelli et al. (2012) provide a framework based on receding horizon MPC and deterministic nonlinear optimization to solve the long-term hydropower scheduling problem for large-scale systems. Zambelli et al. (2013) investigate the advantages of this nonlinear optimization technique for long-term scheduling of large-scale cascaded hydrothermal systems with inflow uncertainties in terms of the lowering of operational costs and improved management of energy. Hamann and Hug (2014) present a real-time optimization scheme for a cascaded hydropower system involving the three-dimensional piecewise linearization of the nonlinear non-convex hydropower production as a function of hydraulic head and turbine discharge. This approximation was implemented in a receding MPC framework aimed at tracking the power production based on energy demands and maximizing cascade efficiency through minimizing turbine discharge. Hamann et al. (2017) extend this work to use a piecewise planar approximation of the power generation function to solve a quadratic programming problem aimed at maximizing the hydraulic potential through the effective allocation of water within an MPC framework based on system hydraulics. None of the above approaches consider the discrete generating unit commitment decisions in their optimization formulations.

The present work involves the development of a novel rolling horizon periodic rescheduling scheme integrating forecasting, optimization and simulation to handle the uncertainties in electricity prices, water inflows and model parameters in the short-term operation of cascaded hydropower systems. The decision variables include both continuous (discharge flows) and discrete (generating unit commitment) decisions. The proposed approach involves the forecasting of electricity prices using historical data from a seasonal autoregressive integrated moving average (SARIMA) model. These forecasts are updated at each reoptimization step using realized electricity prices. The forecasts for water inflows and model parameters are obtained from industrial data and are not updated using new information in this scheme. The initial schedule is generated using these forecasts from a mixed-integer nonlinear programming (MINLP) optimization model aimed at maximizing total revenue from the sale of electricity and a successive linear programming (SLP) solution procedure to improve computational efficiency. Real-time application is simulated by applying the discharge flow decisions from the current schedule and the realized water inflows to a dynamic hydropower system model which propagates the water volumes. The water levels are evaluated using the reservoir storage – water elevation relationship. The updated water levels and volumes are fed back to the optimization model and the horizon is rolled forward for the generation of the successive schedule. The nervousness phenomenon is analyzed using a novel metric based on the variation in generating unit commitment between successive schedules. The undesirable effects of nervousness are alleviated using four novel mitigation strategies based on penalizing the deviations in discharge flows and generating unit commitment profiles between consecutive schedules. The performance of these strategies is evaluated and compared in terms of nervousness reduction and economic performance. The impact of varying rescheduling frequency on the system performance is assessed and the thresholds for economic improvement are established for different uncertain scenarios.

References

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