**1. Introduction**

#### *1.1. Overview of the Present Work*

Energy supply is one of the most important problems for modern industrial facilities. Usually, when a plant is built, it is connected to the grid allowing it to purchase electricity for its operation. The same holds for heating, water, or other requirements where public services are available. However, environmental regulations play an increasing role, and small to medium scale power plants are becoming popular. Such power sources have the ability to supply the needs of individual residential homes or firms. These can have significant investment costs, but operation in the long-term may make them cost-efficient solutions. There is no absolute winner technology in terms of costs.

The power supply decision can be a complex problem. Several different energy sources have to be taken into account. Renewable energy sources like biomass can have a limited availability and are usually neither economical nor environmentally friendly if they need to be transported over long distances. Different technologies and energy supply methods may coexist, but each having different investment and operational costs, for which capacity is also limited. Energy demands can also vary, not only from one year to the other, but even from month to month, according to the seasons. This is especially true for heating requirements.

The P-Graph framework is a modeling tool with which one can define Process Network Synthesis (PNS) problems. In a PNS, a system of complex possible flow of materials is given, and a cost-optimal selection of possible operating units must be found. The P-Graph framework consists of the mathematical model of P-Graphs, the corresponding theorems and algorithms, and also software in which we can solve PNS problems.

This work presents a case study made for a manufacturing plant, for which decision makers needed to consider alternative energy sources like solar power and local biomass availabilities, instead of purchasing all the electricity and heating need required. Naturally, the method of modeling we present here can be adopted for any plant if the available technology options, energy sources and demands are specified.

The optimization problem for finding the minimal operating cost of the firm during the course of the investments' considered horizon is modeled as a PNS problem, and then solved utilizing the P-Graph framework. The model uses the multi-periodic modeling technique to address fluctuating demands in two di fferent seasons. The pelletizer and biogas plant equipment units are modeled with a new technique allowing mass-based capacities and flexible inputs simultaneously. Several di fferent investment horizons are investigated, and the best solutions for each scenario are presented. In the end, we can conclude that all energy options can be an economical replacement of direct energy purchase, but a long horizon must be assumed to be so.

#### *1.2. Importance of Sustainability*

Sustainability is at its core about finding practically possible ways to maintain conditions on Earth suitable for civilized human life. This is considered to be quite a challenge for several reasons:


Note that manufacturing consumes an enormous amount of energy, for example, 2.2 EJ in 2010 [4]. Energy generation at present still heavily relies on fossil fuels [5], and this has a wide range of environmental impacts. The most widely known is the emission of carbon dioxide which contributes significantly to climate change. Therefore, a possibly e ffective way in decreasing the human footprint is to target manufacturing. This can be done by the provision of alternative energy supply options for operating plants, especially when shifting to more e fficient energy use and to the use of renewable and low environmental impact forms of energy generation. The importance of this is established by the fact that increasing population and consumption will likely result in the increase in manufacturing needs, hence energy consumption. It is a common idea that instead of purely relying on a highly centralized network for electricity or heating, each firm resolves its own energy demands locally. Of course, this implies additional investment costs compared to the ordinary scheme. Particular examples for locally feasible energy supplies are the usage of biomass or solar cells. Nevertheless, decreasing demands by alternative production technologies or more e fficient energy usage can also be promising options.

Synthesis of supply chains of renewable energy sources, for example solar, wind, hydropower, and biomass utilization, possibly simultaneously to other sources, until the potential demands of energy or water, is a challenging task in general, and has drawn much attention [6,7]. The complexity of the systems to be designed optimally yields for adequate modeling and optimization tools, regardless of the scope being a single plant or a whole region. Novel, general methods are published [8], using mathematical programming solutions which are a conventional way of modeling. But due to

their limitation in solving larger or too special problems, specific case studies may require other model developing techniques.
