EABOT - تجزیه و تحلیل پر انرژی به عنوان پایه ای برای بهینه سازی قوی سیستم تولید سه گانه با برنامه ریزی خطی

The optimization of synthesis, design and operation in trigeneration systems for building applications is a quite complex task, due to the high number of decision variables, the presence of irregular heat, cooling and electric load profiles and the variable electricity price. Consequently, computer-aided techniques are usually adopted to achieve the optimal solution, based either on iterative techniques, linear or non-linear programming or evolutionary search. Large efforts have been made in improving algorithm efficiency, which have resulted in an increasingly rapid convergence to the optimal solution and in reduced calculation time; robust algorithm have also been formulated, assuming stochastic behaviour for energy loads and prices. This paper is based on the assumption that margins for improvements in the optimization of trigeneration systems still exist, which require an in-depth understanding of plant’s energetic behaviour. Robustness in the optimization of trigeneration systems has more to do with a “correct and comprehensive” than with an “efficient” modelling, being larger efforts required to energy specialists rather than to experts in efficient algorithms. With reference to a mixed integer linear programming model implemented in MatLab for a trigeneration system including a pressurized (medium temperature) heat storage, the relevant contribute of thermoeconomics and energo-environmental analysis in the phase of mathematical modelling and code testing are shown.

In the last decade, a growing interest has been observed for combined heat and power (CHP) or combined heat, cooling and power (CHCP) applications in buildings. This is obviously due to the high conversion efficiency of polygeneration systems and the consequent energy and pollutant-emissions savings, but also due to favourable external conditions, like the new opportunities existing in the liberalised energy market and the growth of a “small scale CHP” market, which has gradually reduced the purchase and installation cost of CHP units (typically, in the order of 600–800 €/kWe). These promising perspectives have stimulated the efforts of scientists towards the definition of criteria for the optimization of CHCP design and operation for applications in the civil sector. Several analyses have been oriented to assess the potential benefits in terms of energy and pollutant-emissions savings [1] and [2] and, in some cases, some peculiar aspects were examined adopting thermoeconomic cost-accounting methods [3] or pinch analysis [4]. In order to understand the complexity of the optimization problem, the following aspects can be remarked: – Safety of supply and flexibility are usually ensured by redundancy, i.e. the system is designed as a “facility of systems of a same product”, where different components may alternatively contribute to cover the demand of a specific energy vector. – The problem is time-dependent: the variability in energy loads and prices requires the adoption of flexible plant operation strategies; in the civil sector, discretization on hourly basis is usually pursued, resulting in a high number of decision variables as concerns plant operation. Discussions have arisen on the possibility to adopt a reduced set of “standard days” (typically defined on seasonal and “working–non-working” bases) without loss of reliability, but this is a controversial argument which needs ad hoc considerations for each case. – The decision variables have a non-homogeneous nature, both as concerns the way they affect the objective function and the values they can assume. Either in case of profit, energy or pollutant-emission saving-oriented optimizations, the objective function depends on annual results, calculated as sum of single values obtained for each time-step. The optimization problem can be divided into three different sub-problems: (a) Synthesis: in order to optimize the plant configuration, i.e. to select what components should be installed, a starting redundant “superconfiguration” is usually adopted, that is a general CHCP scheme where several components are included and a high level of interconnections among them is assumed. The decision variables at synthesis level are 0–1 variables, each indicating the decision to include/not include a certain component. (b) Design: CHCP systems for buildings applications are usually made up by highly standardised components (gas turbines, reciprocate engines, water–lithium bromide absorption chillers, etc.), which can be regarded as black boxes and modelled by defining their part load behaviour. The absence of variables involving the thermodynamic state of working fluids (the optimization of heat exchangers represents a 2nd refinement level, not considered in this paper) makes the design optimization easier than usual. Only a relatively small number of design variables representing the size of plant components is included. (c) Operation: the optimization of plant operation is more complex than usual; in fact, CHCP systems offer several possibilities of loading the different components to cover energy requests, the optimal solution depending on efficiency figures, energy loads and prices. This optimization level involves both 0–1 variables (the on/off state for each component) and continue variables (the load level of each component). Also, the optimization routine must be applied on hourly basis, because both energy load and prices are time-dependent. The variables of the different sub-problems are not of a “same rank”; for instance, operational variables could be optimized only once fixed values for the decision variables at synthesis and design level have been assumed. This aspect heavily influences the choice of the most appropriate resolution technique. Evolutionary search, for instance, which has been extensively used in the optimization of energy systems by genetic algorithms (GA), is not suitable for our problem because of the deficiency in handling highly constrained problems; also, GA could be preferably adopted to optimize plant operation as internal routine of an iterative synthesis-design optimization [5] and this approach is not suitable for the examined problem due to the huge number of different operating conditions. Several heuristic approaches have been proposed, oriented to determine near-optimal solutions basing on “aggregate thermal load” duration curves [6] or thermoeconomics [7]; most of them, however, do not include an “integrated” optimization process, but assume a priori a sub-optimal management strategy (either “heat tracking” or “electricity tracking” operation modes). More recently, linear programming (LP) techniques have been extensively used [8] and [9], due to the possibility to solve large scale problems with thousands variables approaching the “multi-level” optimization problem by an “horizontal algorithm”, where synthesis, design and operational variables are threaten similarly. More refined approaches have been proposed in [10], where a robust optimization included a sensitivity analysis in LP to consider stochastic energy loads, and in [11], where an efficient algorithm was proposed, which resulted much faster than an efficient sparse simplex code. The fact that the production of the three energy vectors follows a joints characteristic makes often convenient to include thermal energy storages (TESs, i.e. hot water and/or chilled water tanks); usually, the TES is used to maximise power production during peak hours (where high value electricity is produced), storing eventual surplus heat/cooling energy to reuse it during off-peak hours. The inclusion of a TES significantly varies the structure of the optimization problem, introducing dynamic constraints; a clear overview of the techniques proposed in the literature to deal with storage constraints was provided in [12]. Let us here briefly resume the two main currencies: – Decoupling the time-dependent storage constraint, a set of small-size single-period sub-problems may be solved. In [12] and [13] Lagrangian relaxation (LR) methods were used, which decompose the original problem into multiple underlying Lagrangian sub-problems. In [13], the unit commitment (where the on/off state of each component is determined) and the economic dispatch (the optimal production rates) are solved by isolating the economic dispatch problem (a unit commitment is assumed known, which is in its turn optimized by LR) and relaxing the time-coupling constraint obtaining a dual problem which does not require dynamic programming. – Treating the multi-period large-size problem as unique and solving it by Simplex or interior point methods require larger computational efforts, but a less complicate problem formulation. The first of the two above currencies has been attracting more interest among researchers and the optimization of trigeneration systems has gradually become a research field for experts in operational research. Innovative methods frequently converge to optimal solutions whose energetic consistence might be said controversial, as evident when considering that a same lay-out, optimized by different algorithms and adopting a same set “objective function + constraints + boundary conditions”, frequently converges to quite different solutions [14]. In particular, the solutions achieved are often too sensitive to slight variations in the boundary conditions, which reflects a non-comprehensive representation of energetic conversion processes. Analytical CHCP modelling should be more closely interrelated to energetics, as may be observed in [15] where reliability of results is ensured by an energo-environmental analysis of plant performance. In this paper we put into evidence that only an in-depth energetic analysis may properly reflect the “formation” of the values of the objective function, which ultimately drive any optimization algorithm towards a final solution. Hence, no enhanced efficiency algorithms are proposed; on the contrary, a common Linear-Programming Interior Point method (a variant of Mehrotra’s predictor–corrector method) was used, which is the default option for large scale optimization in MatLab. All the analyses that will be presented have been used to code a MatLab tool, EABOT (Energy Analysis-Based Optimization of Trigeneration plants), which represent a module of a larger-scale software for the optimization of CHCP-based μ-grids [16] not completed yet. Ahead in the paper four main concepts are critically examined: 1. Is the definition of a few “reference days” (as concerns load profiles) necessary? At what extent selecting a small number of reference days affects the reliability of results and reduces the consumption of computational resources? 2. Once all operational constraints have been properly defined, is it possible to determine additional conditions based on advanced energetic analyses in order to make the optimization algorithm converge faster? 3. Can multi-objective optimization offer a more relevant contribute in CHCP decision making? A pure profit-oriented optimization would not properly reflect all the implications related to polygeneration: the support mechanisms in force, like tax exemption or dispatching priority, and the recent legislation for CHP eligibility give a particular focus on the energo-environmental effects, which will become more and more profit-conditioning. 4. Does the testing phase of CHCP optimization tools require energo-environmental analysis?

Starting from the assumption that large progresses have been made in the use of efficient algorithms for the optimization of synthesis, design and operation of a CHCP system including thermal energy storages, a new approach was proposed in this paper, focusing the attention on the energetic analysis of the plant. Considering that MILP optimization of trigeneration systems represents a quite approximate approach due to the linearization of components’ behaviour and cost figures, some simplifications were introduced, like the exclusion of binary variables for the hour by hour unit commitment problem which significantly reduces the consumption of computational resources. An in-depth analysis of trade-off profit conditions was proposed, partially based on thermoeconomics, allowing us to formulate an artificial (i.e. non-physical) constraint which essentially superimposes a pre-fixed operation strategy. Implementing the proposed approaches into a tool allowed us to perform multi-objective optimizations for two large buildings in the civil sector and to derive a few conclusions about the optimal number of days to be used for the optimization (which resulted from a compromise between the objectives of results’ reliability and fastness of the optimization) and the consistence of the hypotheses introduced. This paper was only intended to offer a new perspective on the problem of the improvement of MILP techniques for CHCP optimization; such analysis must be evidently coupled with those most typically proposed by operational research specialists.