Robust online scheduling for optimal short-term operation of cascaded hydropower systems under uncertainty

Abstract The uncertainties in system and model parameters arising from the volatility of market, weather and operating conditions pose a major challenge to the optimal short-term operation of cascaded hydropower systems. The dynamic operating environment resulting from the fluctuating parameters greatly impacts the scheduling of power generation and generating unit commitment in such systems. This article focuses on the development and implementation a novel rolling horizon robust online scheduling framework that utilizes stochastic optimization within a model-based feedback scheme to tackle the uncertainties in electricity prices, electric power demands, water inflows and plant model parameters. The efficacy of this approach is demonstrated through application to a variety of case studies for different types of uncertainty. Case studies demonstrate significant improvements in system performance with the proposed strategy, in terms of system economics and constraint satisfaction, over schedules generated without feedback or use of a nominal online scheduling scheme.

[1]  R. Weron Electricity price forecasting: A review of the state-of-the-art with a look into the future , 2014 .

[2]  Efstratios N. Pistikopoulos,et al.  Dynamic optimization and robust explicit model predictive control of hydrogen storage tank , 2010, Comput. Chem. Eng..

[3]  Jay H. Lee,et al.  Robust model predictive control of nonlinear systems using input-output models , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[4]  Mayuresh V. Kothare,et al.  An e!cient o"-line formulation of robust model predictive control using linear matrix inequalities (cid:1) , 2003 .

[5]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[6]  C. Floudas,et al.  Production Scheduling of a Large-Scale Industrial Batch Plant. II. Reactive Scheduling , 2006 .

[7]  Christopher L. E. Swartz,et al.  Uncertainty management via online scheduling for optimal short-term operation of cascaded hydropower systems , 2020, Comput. Chem. Eng..

[8]  Gabriela Hug,et al.  Real-Time Optimization of the Mid-Columbia Hydropower System , 2017, IEEE Transactions on Power Systems.

[9]  Darrell G. Fontane,et al.  Operation of large multireservoir systems using optimal-control theory , 1992 .

[10]  Manuel Chazarra,et al.  Stochastic optimization model for the weekly scheduling of a hydropower system in day-ahead and secondary regulation reserve markets , 2016 .

[11]  Christos T. Maravelias,et al.  Mixed-integer optimization methods for online scheduling in large-scale HVAC systems , 2020, Optim. Lett..

[12]  Carlos E. Garcia,et al.  QUADRATIC PROGRAMMING SOLUTION OF DYNAMIC MATRIX CONTROL (QDMC) , 1986 .

[13]  Jay H. Lee,et al.  From robust model predictive control to stochastic optimal control and approximate dynamic programming: A perspective gained from a personal journey , 2014, Comput. Chem. Eng..

[14]  John J. Martínez,et al.  Decentralized-coordinated model predictive control for a hydro-power valley , 2013, Math. Comput. Simul..

[15]  S. Macchietto,et al.  Minimizing the effects of batch process variability using online schedule modification , 1989 .

[16]  Secundino Soares,et al.  A predictive control approach for long term hydrothermal scheduling , 2009, 2009 IEEE/PES Power Systems Conference and Exposition.

[17]  Ove Wolfgang,et al.  Applying successive linear programming for stochastic short-term hydropower optimization , 2016 .

[18]  Daniel Sarabia,et al.  Improving scenario decomposition algorithms for robust nonlinear model predictive control , 2015, Comput. Chem. Eng..

[19]  David Q. Mayne,et al.  Robust output feedback model predictive control of constrained linear systems: Time varying case , 2009, Autom..

[20]  Marianthi G. Ierapetritou,et al.  Reactive scheduling using parametric programming , 2008 .

[21]  Christos T. Maravelias,et al.  A General State-Space Formulation for Online Scheduling , 2017 .

[22]  B. L. Cooley,et al.  Robust model predictive control of multivariable systems using input-output models with stochastic parameters , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[23]  Allen J. Wood,et al.  Power Generation, Operation, and Control , 1984 .

[24]  Christos T. Maravelias,et al.  A state-space model for chemical production scheduling , 2012, Comput. Chem. Eng..

[25]  Silvano Martello,et al.  Piecewise linear approximation of functions of two variables in MILP models , 2010, Oper. Res. Lett..

[26]  Moritz Diehl,et al.  Handling uncertainty in economic nonlinear model predictive control: A comparative case study , 2014 .

[27]  John M. Wassick,et al.  From rescheduling to online scheduling , 2016 .

[28]  Christos T. Maravelias,et al.  Economic MPC and real-time decision making with application to large-scale HVAC energy systems , 2017, Comput. Chem. Eng..

[29]  Secundino Soares,et al.  Comparison between closed-loop and partial open-loop feedback control policies in long term hydrothermal scheduling , 2002 .

[30]  Mayuresh V. Kothare,et al.  Robust output feedback model predictive control using off-line linear matrix inequalities , 2002 .

[31]  Dhruv Gupta,et al.  On deterministic online scheduling: Major considerations, paradoxes and remedies , 2016, Comput. Chem. Eng..

[32]  Basil Kouvaritakis,et al.  Efficient robust predictive control , 2000, IEEE Trans. Autom. Control..

[33]  Rainer Manuel Schaich,et al.  Robust model predictive control , 2017 .

[34]  Abdollah Ahmadi,et al.  Mixed-integer Programming of Stochastic Hydro Self-scheduling Problem in Joint Energy and Reserves Markets , 2016 .

[35]  Moritz Diehl,et al.  A comparison of distributed MPC schemes on a hydro‐power plant benchmark , 2015 .

[36]  David Q. Mayne,et al.  Robust output feedback model predictive control of constrained linear systems , 2006, Autom..

[37]  Hartmut Linke A model-predictive controller for optimal hydro-power utilization of river reservoirs , 2010, 2010 IEEE International Conference on Control Applications.

[38]  Christos T. Maravelias,et al.  A mixed-integer linear programming model for real-time cost optimization of building heating, ventilation, and air conditioning equipment , 2017 .

[39]  Efstratios N. Pistikopoulos,et al.  Design of robust model-based controllers via parametric programming , 2004, Autom..

[40]  Christopher L. E. Swartz,et al.  Robust decision making for hybrid process supply chain systems via model predictive control , 2014, Comput. Chem. Eng..

[41]  Secundino Soares,et al.  Long-term hydropower scheduling based on deterministic nonlinear optimization and annual inflow forecasting models , 2009, 2009 IEEE Bucharest PowerTech.

[42]  Stein-Erik Fleten,et al.  Short-term hydropower production planning by stochastic programming , 2008, Comput. Oper. Res..

[43]  Nikolaos V. Sahinidis,et al.  A polyhedral branch-and-cut approach to global optimization , 2005, Math. Program..

[44]  Michel Gendreau,et al.  Optimizing profits from hydroelectricity production , 2009, Comput. Oper. Res..

[45]  Manfred Morari,et al.  Medium term scheduling of a hydro-thermal system using stochastic model predictive control , 2008, Autom..

[46]  Efstratios N. Pistikopoulos,et al.  Reactive Scheduling by a Multiparametric Programming Rolling Horizon Framework: A Case of a Network of Combined Heat and Power Units , 2014 .

[47]  Jay H. Lee,et al.  Period-robust repetitive model predictive control , 2006 .

[48]  Manfred Morari,et al.  Application of Model Predictive Control to a Cascade of River Power Plants , 2008 .

[49]  Sebastian Engell,et al.  Multi-stage nonlinear model predictive control applied to a semi-batch polymerization reactor under uncertainty , 2013 .

[50]  Christodoulos A. Floudas,et al.  ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations , 2014, Journal of Global Optimization.

[51]  David Q. Mayne,et al.  Tube‐based robust nonlinear model predictive control , 2011 .

[52]  Efstratios N. Pistikopoulos,et al.  DESIGN OF ROBUST PARAMETRIC MPC FOR HYBRID SYSTEMS , 2005 .

[53]  Efstratios N. Pistikopoulos,et al.  An algorithm for robust explicit/multi-parametric model predictive control , 2013, Autom..