**2. Carbon Emission-Constrained Electricity Planning for Aluminum Products**

Aluminum is widely available and is the second most widely used metal worldwide. Aluminum is used in several sectors, including transportation, packaging, building and construction, furniture, equipment and machinery. However, the aluminum industry is highly energy-consuming, especially in the production of primary aluminum. Aluminum production consumes about 3.5% of electricity globally [41], while in China [42] and the US [43], that figure is around 5% and in Montenegro it is more than 25% [44]. According to data from the Slovenian Ministry of Infrastructure [45] and the data collected by the authors, aluminum production in Slovenia consumed about 8.9% of the total electricity produced in 2017. Primary production of aluminum starts with bauxite mining and further refining of alumina from bauxite. Alumina is further processed into aluminum via electrolysis, known also as the Hall-Héroult process. Subsequently, aluminum is processed into a range of products by casting, rolling, extrusion and other operations [46]. The highest energy consumption and CO2 emissions are due to electrolysis [47]. The production of secondary or recycled aluminum, on the other hand, requires less than 5% of the energy required to produce aluminum from ore [48].

The aim of this study is to minimize CO2 emissions in order to meet specified CO2 emission limits, which could be set at the national or regional level. The emission limit (target) for this study was set at 0.376 t CO2/MWh [5]. This value was set by the European Commission in delegated regulation (EU) 2019/331, where transitional rules for the free allocation of emission allowances were set for the period 2021–2030. This emission factor is used for the determination of indirect emissions, where a given factor (0.376 t CO2/MWh) is multiplied by the electricity consumption required to produce specific products.

In this study, two aluminum products are considered, aluminum slugs and evaporator panels. The production of aluminum slugs and evaporator panels is described in Figure 1. Both products are made from molten aluminum produced by the electrolysis process, while slugs are also made from recycled aluminum produced as process waste material from the further processing of slugs. This study performs CCEP of aluminum products for a Slovenian aluminum company. In the company, aluminum slugs are produced from around 0.67 t of electrolysis aluminum per t of slugs; the remaining material used for their production is secondary aluminum. Aluminum evaporator panels are produced only from electrolysis aluminum, where from 1 t of molten aluminum, about 1 t of evaporator panels are produced.

**Figure 1.** Production of aluminum slugs and evaporator panels (modified from [47]).

Aluminum slug production (see Figure 1) consists of casting, the production of the narrow strip, hot and cold rolling, stamping, annealing, surface treatment and packaging [47]. The production process of Roll-Bond evaporator panels also consists of several steps: casting of the wide strip, rolling it into the band for evaporator panels, roll-bonding, recrystallization annealing, inflation of imprinted channels, final dimension cut or stamping and packaging, and final assembly of the evaporator panels according to the needs of the customer. Both production processes follow the same value chain up to slug and evaporator panel production.

For the sake of simplification, the same amount of the primary aluminum used in the production of aluminum slugs and evaporator panels is assumed; 0.67 t of primary aluminum is required for the production of 1 t of aluminum slugs, and the same amount of primary aluminum is used for 0.67 t of aluminum evaporator panels. To produce 0.67 t of primary aluminum, 0.063 MWh of electricity are required for the anode production and 9.12 MWh for the electrolysis. This consumption is the same for both products, since they follow the same value chain up to the final steps. They have similar electricity consumption, although the production of evaporator panels requires slightly more electricity. For slug production, an additional 0.263 MWh of electricity is required for 1 t of the product, while for evaporator panels, an additional 1.016 MWh of electricity is required for 0.67 t of the product. Total electricity consumption for 1 t of slugs is 9.446 MWh, and for 0.67 t of evaporator panels is 10.199 MWh.

The electricity delivered to a company is generated from a mix of fossil, nuclear and renewable energy sources. Electricity sources of fossil origin are coal, lignite, natural gas and oil. Hydro, wind, photovoltaics, geothermal, biomass, biogas and biodiesel are considered types of renewable energy. For the sake of simplification, energy sources are grouped into three main categories. Fractions of energy sources in the electricity mix, and emission factors of the different sources are summarized in Table 1. Average values for prices and emission factors are used for each energy source. The prices for each energy source are regarded as confidential and thus they are not presented.



Three different energy planning approaches (graphical, algebraic and optimization-based approaches) will be demonstrated in the following sections. The first two approaches are presented and illustrated on one aluminum product (aluminum slugs) and are shown for zero- and low-carbon energy sources (in the current work, the low-carbon energy source is renewable energy). The third approach deals with two aluminum products (aluminum slugs and evaporator panels) and considers two cases: the case where electricity is pinched for each product, and the hypothetical case where only one Pinch exists for both products. In the case of optimization, the trade-off solution is obtained between emissions and the cost of energy sources to achieve a given benchmark.

Graphical and numerical approaches consist of several steps and follow similar algorithms whose detailed steps are described in related previous papers. First, energy supply and demand are defined; then, they are arranged into emission intervals (segments) by increasing the emission factors from the lowest to the highest. By the graphical approach, the energy source and demand curves are then plotted on the energy consumption–emissions diagram. The energy source curve is further shifted horizontally until it intersects with the energy demand curve (at the "Pinch Point") [12]. By the numerical approach, the energy surplus/deficit is cascaded through the intervals, and the cumulative net energy consumption should be non-negative. The deficit should then be added to the zero- or low-carbon energy source [13]. The optimization approach, on the other hand, involves formulating a working model whose solution is determined numerically via established solution techniques (i.e., Simplex algorithm) that is embedded in standard optimization software. The data and variables should be defined, and together with the constraints, they form a feasible region. The optimal solution is then defined based on the given objective, which is minimized or maximized. The procedure for each approach is described in more detail, together with the case studies, in the following section.
