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Abstract
This thesis concerns methods and algorithms for power production planning in contemporary and future power systems. Power production planning is a task that involves decisions across different time scales and planning horizons. Hoursahead to daysahead planning is handled by solving a mixedinteger linear program for unit commitment and economic dispatch of the system power generators. We focus on a minutesahead planning horizon, where unit commitment decisions are fixed. Economic model predictive control (EMPC) is employed to determine an optimal dispatch for a portfolio of power generators in realtime. A generator can represent a producer of electricity, a consumer of electricity, or possibly both. Examples of generators are heat pumps, electric vehicles, wind turbines, virtual power plants, solar cells, and conventional fuelfired thermal power plants. Although this thesis is mainly concerned with EMPC for minutesahead production planning, we show that the proposed EMPC scheme can be extended to daysahead planning (including unit commitment) as well.
The power generation from renewable energy sources such as wind and solar power is inherently uncertain and variable. A portfolio with a high penetration of renewable energy is therefore a stochastic system. To accommodate the need for EMPC of stochastic systems, we generalize certaintyequivalent EMPC (CEEMPC) to meanvariance EMPC (MVEMPC). In MVEMPC, the objective function is a tradeoff between the expected cost and the cost variance. Simulations show that MVEMPC reduces cost and risk compared to CEEMPC. The simulations also show that the economic performance of CEEMPC can be much improved using a constraint backoff heuristic.
Efficient solution of the optimal control problems (OCPs) that arise in EMPC is important, as the OCPs are solved online. We present specialpurpose algorithms for EMPC of linear systems that exploit the high degree of structure in the OCPs. A Riccatibased homogeneous and selfdual interiorpoint method is developed for the special case, where the OCP objective function is a linear function. We design an algorithm based on the alternating direction method of multipliers (ADMM) to solve inputconstrained OCPs with convex objective functions. The OCPs that occur in EMPC of dynamically decoupled subsystems, e.g. power generators, have a blockangular structure. Subsystem decomposition algorithms based on ADMM and DantzigWolfe decomposition are proposed to solve these OCPs. Subproblems that arise in the decomposition algorithms are solved using structureexploiting algorithms. To reduce computation time of the EMPC algorithms further, warmstart and earlytermination strategies are employed. Benchmarks show that the specialpurpose algorithms are significantly faster than current stateoftheart solvers.
As a potential application area of EMPC, we study power production planning in small isolated power systems. A critical part of power production planning in small isolated power systems is operational reserve planning. The operational reserves are activated to balance production and consumption in realtime. An EMPC scheme is presented for activation of operational reserves. Simulations based on a Faroe Islands case study show that signi_cant cost savings can be achieved using this strategy. For efficient planning of the operational reserves, we present an optimal reserve planning problem (ORPP). The ORPP is a contingencyconstrained unit commitment problem that addresses low inertia challenges in small isolated power systems.
In summary, the main contributions of this thesis are:
 A meanvariance optimization strategy for EMPC of linear stochastic systems.
 Tailored algorithms for solution of the OCPs that arise in EMPC of linear stochastic systems.
 Methods for power production planning in small isolated power; the ORPP for unit commitment and economic dispatch, and an EMPC scheme for activation of operational reserves.
The power generation from renewable energy sources such as wind and solar power is inherently uncertain and variable. A portfolio with a high penetration of renewable energy is therefore a stochastic system. To accommodate the need for EMPC of stochastic systems, we generalize certaintyequivalent EMPC (CEEMPC) to meanvariance EMPC (MVEMPC). In MVEMPC, the objective function is a tradeoff between the expected cost and the cost variance. Simulations show that MVEMPC reduces cost and risk compared to CEEMPC. The simulations also show that the economic performance of CEEMPC can be much improved using a constraint backoff heuristic.
Efficient solution of the optimal control problems (OCPs) that arise in EMPC is important, as the OCPs are solved online. We present specialpurpose algorithms for EMPC of linear systems that exploit the high degree of structure in the OCPs. A Riccatibased homogeneous and selfdual interiorpoint method is developed for the special case, where the OCP objective function is a linear function. We design an algorithm based on the alternating direction method of multipliers (ADMM) to solve inputconstrained OCPs with convex objective functions. The OCPs that occur in EMPC of dynamically decoupled subsystems, e.g. power generators, have a blockangular structure. Subsystem decomposition algorithms based on ADMM and DantzigWolfe decomposition are proposed to solve these OCPs. Subproblems that arise in the decomposition algorithms are solved using structureexploiting algorithms. To reduce computation time of the EMPC algorithms further, warmstart and earlytermination strategies are employed. Benchmarks show that the specialpurpose algorithms are significantly faster than current stateoftheart solvers.
As a potential application area of EMPC, we study power production planning in small isolated power systems. A critical part of power production planning in small isolated power systems is operational reserve planning. The operational reserves are activated to balance production and consumption in realtime. An EMPC scheme is presented for activation of operational reserves. Simulations based on a Faroe Islands case study show that signi_cant cost savings can be achieved using this strategy. For efficient planning of the operational reserves, we present an optimal reserve planning problem (ORPP). The ORPP is a contingencyconstrained unit commitment problem that addresses low inertia challenges in small isolated power systems.
In summary, the main contributions of this thesis are:
 A meanvariance optimization strategy for EMPC of linear stochastic systems.
 Tailored algorithms for solution of the OCPs that arise in EMPC of linear stochastic systems.
 Methods for power production planning in small isolated power; the ORPP for unit commitment and economic dispatch, and an EMPC scheme for activation of operational reserves.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  249 
Publication status  Published  2016 
Series  DTU Compute PHD2015 

Number  377 
ISSN  09093192 
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 1 Finished

Stochastic Model Predictive Control with Applications in Smart Energy Systems
Sokoler, L. E. (PhD Student), Jørgensen, J. B. (Main Supervisor), Madsen, H. (Supervisor), Zavala, V. (Examiner), Bemporad, A. (Examiner), Poulsen, N. K. (Supervisor) & Knudsen, J. K. H. (Examiner)
01/07/2012 → 31/03/2016
Project: PhD