Abstract
Non-convex scheduling of energy production allows for more complex models that better describe the physical nature of the energy production system. Solutions to non-convex optimization problems can only be guaranteed to be local optima. For this reason, there is a need for methodologies that consistently provide low-cost solutions to the non-convex optimal scheduling problem. In this study, a novel Monte Carlo Tree Search initialization method for branch and bound solvers is proposed for the production planning of a combined heat and power unit with thermal heat storage in a district heating system. The optimization problem is formulated as a non-convex mixed-integer program, which is incorporated in a sliding time window framework. Here, the proposed initialization method offers lower-cost production planning compared to random initialization for larger time windows. For the test case, the proposed method lowers the yearly operational cost by more than 2,000,000 DKK per year. The method is one step in the direction of more reliable non-convex optimization that allows for more complex models of energy systems.
Highlights
IntroductionThere are four formulations of the optimal scheduling problem, linear programming (LP) (Lozano et al 2009; Rong and Lahdelma 2005), mixed-integer linear programming (MILP) (Söderman and Pettersson 2006; Arcuri et al 2007), non-linear programming (NLP) (Bindlish 2016) and mixed-integer nonlinear programming (MINLP) (Deng et al 2017; Lésko et al 2018)
Scheduling of district heating production is a well-studied problem in literature (Deng et al 2017; Lésko et al 2018; Gopalakrishnan and Kosanovic 2015; Rong and Lahdelma2007)
This paper proposes a new warm start initialization procedure based on a stochastic discrete tree search, called Monte Carlo Tree Search (MCTS), which constructs initial feasible solutions for a multi-period steady-state scheduling problem in a District Heating (DH) system with a combined heat and power unit and thermal storage
Summary
There are four formulations of the optimal scheduling problem, linear programming (LP) (Lozano et al 2009; Rong and Lahdelma 2005), mixed-integer linear programming (MILP) (Söderman and Pettersson 2006; Arcuri et al 2007), non-linear programming (NLP) (Bindlish 2016) and mixed-integer nonlinear programming (MINLP) (Deng et al 2017; Lésko et al 2018). The advantage of MILPs and LPs is that they can be solved with commercially available solvers for a global optimum Despite this feature, using linear models to describe physical systems that typically are highly non-linear introduces error into the model, as a linear model of a non-linear system can at best only be a good approximation. A common technique for dealing with mixed-integer non-linear models is to approximate the models as mixed-integer linear programs via linearization in order to guarantee that the solution is globally optimal (Lésko et al 2018; Elsido et al 2017b). Each segment introduces additional variables to the model which makes the model bigger and more complex
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