Elsevier

Energy

Volume 36, Issue 8, August 2011, Pages 4599-4608
Energy

Model-size reduction techniques for large-scale biomass production and supply networks

https://doi.org/10.1016/j.energy.2011.03.036Get rights and content

Abstract

This paper is concerned with developing several model-size reduction techniques for the analysis of large-scale renewable production and supply networks. They are (i) Reducing the connectivity in a biomass supply chain network, (ii) Eliminating unnecessary variables and constraints, (iii) Merging the collection centres. The proposed model-size reduction techniques brought computational time improvements of several magnitudes compared, with the high performance linear system solution techniques and still with a little loss in accuracy. When the methods are combined the time reductions are more significant. A proposed procedure for combining the methods can be implemented for any supply chain model with a large number of components.

Highlights

► Model-size reduction techniques has been developed for the analysis of large-scale renewable production and supply networks. ► Technique A is reducing the connectivity in a biomass supply chain network. ► Technique B is eliminating unnecessary variables and constraints. ► Technique C is aggregating the network and the synthesis process by merging the collection centres. ► These techniques brought computational time improvements with a little loss in accuracy.

Introduction

Several studies have predicted that the share of biomass as renewable energy source will be increased significantly in the future as a response to the climate change and energy issues [1], [2]. Biomass is usually available locally and is of a relatively low energy density. Typical locations of biomass sources are farms, forest, etc. The distributed nature of the sources require extensive infrastructures and large transport capacities for implementing the biomass supply networks. For regional biomass supply chains the road transport is a usual mode for collection and transportation. This tends to increases the complexity of the biomass supply chain network [3].

A typical biomass supply chain is shown in Fig. 1. The supply chain can be extended with the integration of food production and waste management [4], [5], and supplied with an optimal mix of primary resources.

Energy systems and supply chains involving biomass processing are generally complex to be modelled. The system mostly deliver a large number of alternative routes, which are introducing severe combinatorial complexities in addition to the processing and transportation unit operations. The first step to solve such problems employs simulation and Mathematical Programming (MP) techniques. For larger size problems this approache becomes increasingly difficult for the following reasons:

  • i

    The size of the algebraic optimisation problem grows, where the solver needs to examine clearly non- infeasible combinations of integer variable values.

  • ii

    The huge number of operating unit options makes it rather difficult to build the necessary problem superstructures heuristically without rigorous combinatorial tools.

Biomass production and supply network analysis are rather challenging due to the large sizes of the networks. In a real life application a biomass supply network usually covers a large region. This can be e.g. a large region or even a medium size country, which could involve more than 1000 zones. This creates a complex supply chain model with a large amount of variables. Huge number of redundant and unnecessary variables reduces model efficiency (time to solve the model and interpretation of the results). This large model is very difficult and in most cases, even impossible to be solved even with the most advanced MP software tools.

In the previous work [7], a complex supply model has been developed to provide scientific input into management decisions concerning the regional biomass products demand. However, the previous solution has been usually very time-consuming. An usual attitude is to seek reduced (in complexity) model-size that reproduces the performance measures of the large model (the full model).

Several papers concerned with identifying/developing reduction techniques in different disciplines have been published. For example the model reduction and optimisation of reactive batch distillation by Khazraee et al. [8], with the application of the adaptive neuro-fuzzy inference system (ANFIS). Barrio et al. [9], presented their model-size reduction techniques for thermal control applications in buildings with Moore method which is also called internal symmetrisation method. Friedler et al. [10], and Holló et al. [11] have developed efficient reduction techniques for the Process Network Synthesis (PNS) problems, which were successfully applied by Varbanov and Friedler [12].

In this paper are proposed three model-size reduction techniques for the analysis of large-scale renewable production and supply networks:

  • (i)

    Reducing the connectivity in a biomass supply chain network by setting the maximum allowable distance between the supply zones and the collection centres,

  • (ii)

    Eliminating unnecessary variables and constraints by dropping out of the model variables with zero-flows,

  • (iii)

    Aggregating the network and the synthesis process by merging the collection centres, and,

  • (iv)

    A combination of (i)–(iii).

A target has been to achieve computational time improvements up to several magnitudes compared to the high performance linear system solution techniques with insignificant loss in accuracy. The most significant reductions in processing time are reached when the methods are combined. Following this observation a procedure for combining the methods has been proposed. It can be implemented for any supply chain model with a large number of components.

An important target has been to achieve an ability to solve large size networks besides producing a ‘faster’ solution. The shorter solution time means that the size of the ‘manageable’ case study can be considerably enlarged and most of the real life problem can be successfully solved.

Section snippets

Mixed Integral Linear Programming (MILP) model for biomass supply chain network

A MILP supply chain model has been developed previously [7]. A four-layer supply chain superstructure has been utilised, which includes the harvesting, preparation, core processing, and distribution of products (see Fig. 2). The boundaries involve a region, which is divided into zones for optimising conversion operations and transportation flows. This MILP model has been formulated with profit maximisation as the optimisation criterion.

The following model summarises relevant mass balance

Technique A: reducing connectivity in the network

In the original model [16], each starting point is connected to each possible destination in the following layer. For example, full mapping between each supply Zone i in Layer 1 with each collection point m in Layer 2 creates a cross-product multi-dimensional set IxM. Similarly the full mapping between the collection centres and process plant produces a cross-product set MxN, and between the process plant and the demand site a set NxJ at the higher layers. All combinations of connectivity

Case study: large-scale biomass production network

The base case study presented in previous paper was extended. The types of plantation and the zones number were increased. The number of zones increased from 10 to 50, until the GAMS solver could not provide the optimize solution in one working day shift (8 h).

The geographical characters and features of this large-scale network are illustrated in Fig. 8 and the important data (supply and demand) are presented in Table 1 and Table 2. Most of the data such as the operating investment cost,

Error analysis of the study method

The simplified assumptions made in this paper have neglected some fluctuation in the parameters due to the specific geographical and weather conditions. These external conditions not depending on an HDV (Heavy Duty Vehicle) can have a strong influence on the fuel consumption. This could affect the transportation cost and carbon footprint calculation. For example:

  • 1)

    The road congestion. The fuel consumption of HDVs can vary more than 7% compare mid-night and mid-day and also it can vary as much as

Results and Discussions

The computational and statistical analyses to assess the performance of the different techniques proposed in the previous subsection have been tested and the experience gained summarised.

The solution time (computational processing time) is used as the comparison criterion for techniques’ performances and efficiencies. The result for the large-scale biomass production network before any reduction technique is shown in Table 3.

All methods have been coded in the same programming tool (GAMS), ran

Conclusions

The proposed techniques were tested and provided very positive results. The 50-zone case study demonstrated that the solution time significantly improved. The results for Combined Technique A, B and C shown especially good potential for implementing within a much larger case study. The real life case studies usually comprise more than 500 zones for a normal size country.

Future work is going to be directed towards tackling even larger regions with a higher number of zones, collection centres,

Acknowledgement

This work has been carried out as part of a Collaborative PhD study at the University of Maribor and the University of Pannonia, supported by the Bilateral SI-HU Project TET SI-11/2008 “Process systems engineering and sustainable development”. Also the financial support from the EC FP7 project Development of Efficient and Robust Controllers for Advanced Energy Systems – DECADE (Project No. 230659) and from the Slovenian Research Agency (Program No. P2-0032, Project No. L2-0358 and PhD research

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