Two-stage MINLP algorithm for the optimal synthesis and design of networks of CHP units

Abstract

This paper proposes a Mixed Integer Non Linear Programming (MINLP) model and two-stage optimi-zation algorithm for determining the most profitable synthesis and design of Combined Heat and Power units within a district heating network with heat storage while taking into account the optimal scheduling of the units over the year. A two-stage algorithm for tackling the challenging MINLP problem is devised: at the upper level the selection and sizing of the units is optimized by means of specifically selected evolutionary algorithms, while at the lower level the operational scheduling problem is line-arized and optimized with a commercial Mixed Integer Linear Programing solver. Three different approaches, based on two different evolutionary algorithms and discrete variable relaxation, are devised and compared to tackle the upper level problem. Moreover a bounding technique is proposed to limit the computational time required to solve the lower-level problem. The overall algorithm is tested on an industrial scale problem to find the two system designs leading to the minimum energy consumption and the minimum total annual cost. Computational results indicate that the continuous relaxation of the plant sizes significantly helps to improve the convergence rate of the tested evolutionary algorithm and to find improved solutions. For the considered test case, the design optimized for the minimum energy consumption allows to save 64% of primary energy compared to the minimum total annual cost solution, but with a 28% higher total annual cost.

Time series aggregation for energy system design: Modeling seasonal storage

“…In order to validate the new model formulation for many different systems with acceptable computational resources, an easily comprehensible simple Mixed-Integer Linear Program has been selected as the system model. More precise models that consider more detailed the size effects of units and investment costs can be found in Bahl et al [13], Elsido et al [23], Gabrielli et al [24] and Schütz et al [61].…”

Simultaneous design and operation optimization of renewable combined cooling heating and power systems

“…MINLP formulation can capture component nonlinear behavior; however, its combinatorial and nonconvex nature makes solution computationally expensive and thus is only applicable to small-scale problems. [17][18][19][20] Hence, for tackling large-scale problems without compromising solution accuracy, there is a need to address this issue and at the same time include performance degradation for renewable CCHP design and operation. The main contributions of this work are summarized as follows:…”

A Comprehensive Methodology for the Integrated Optimal Sizing and Operation of Cogeneration Systems with Thermal Energy Storage

“…For example, Kuang et al [11] applied a dynamic programming technique to define the most economical operation schedule of trigeneration systems. Elsido et al [12] proposed a MINLP formulation for a district heating network, combining evolutionary algorithms with mathematical programming. The optimal design and operation for both economic and environmental objectives of a CHP system with a thermal storage tank was investigated by Fuentes-Cortés et al [13], by exploiting commercial MINLP solvers.…”

“…The general problem of the integrated optimal sizing and operation of cogeneration systems usually results in a non-linear problem. Among the available optimization techniques, the state-of-the-art approach to solve this problem consists in linearizing the original problem to obtain a mixed integer linear programming (MILP) problem [12]. This is mainly due to the guarantee of the global optimality of the solution and to the effectiveness of the available commercial MILP solvers.…”