The supply of economy and society with energy from sustainable renewable or regenerative energy sources (renewable energies).
Through the energy transition, the proportion of fossil fuels such as oil, natural gas, coal and the nuclear fraction in the German energy mix should be reduced to the benefit of renewable energies.

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The Dunkelflaute describes the simultaneous occurrence of darkness and wind calm. This weather typically occurs in winter and leads to low yields from solar and wind energy in times of seasonally high electricity demand. A Dunkelflaute can last several days, and is then called cold Dunkelflaute.

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CO2 avoidance costs describe the costs of reducing a given amount of CO2 compared to a reference technology (or a reference time). The investment and operating costs as well as the consumption-related costs are stated here. Proceeds from electricity and heat sales are not included in the calculation. Avoidance costs are usually stated specifically in € per kgCO2.

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Life Cycle Assessment (LCA) is an analysis of all the environmental impacts of a product throughout its life cycle ("from cradle to grave"). This can be in the form of a single analysis or a comparison of several products / services / processes.

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An *electricity market* is a market for electrical energy. The amount of energy that can be generated in power plants is sold in advance to companies that either use them themselves or sell them to their customers. Different technical conditions in power supplies lead to differences between the various energy markets. For example, storages for electrical energy are available only to a very limited extent (unlike for the natural gas market), so that the generation must largely follow the temporal fluctuations of the power consumption.

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The energy industry describes the order in which power-generating power plants are used to ensure the economically optimal power supply as *Merit Order*. The merit order is based on the lowest marginal costs, ie the costs incurred by a power plant for the last megawatt-hour produced. The merit order is therefore independent of the fixed costs of a power generation technology. The power plants, which continuously produce electricity at very low prices, are the first to be connected to the feed system according to the merit order. After that, power plants with higher marginal costs will be added until demand is covered.

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Security of supply is a central goal of any energy policy. It must be ensured that the required energy demand can be satisfied at all times.

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Cost savings that occur for a given production function (production technology) as a result of constant fixed costs if output quantity grows. (If company size increases the average total costs decrease to the so-called minimum optimal technical operating or enterprise size. Cost per unit produced becomes smaller). Economies of scale are therefore a cause of company concentration.

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The circular economy is a model of production and consumption that shares, leases, reuses, repairs, recycles and existing materials and products as long as possible. This prolongs the life cycle of the products. In practice, this means that waste is reduced to a minimum. After a product reaches the end of its life, resources and materials remain as long as possible in the economy. They can be used productively again in order to continue to generate added value.
The circular economy is in contrast to the *traditional*, linear economic model ("disposable economy"). This model relies on large quantities of cheap, easily accessible materials and energy. The "planned obsolescence" against which the European Parliament calls for action is also part of this model.

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In the event of a power outage ("blackout"), only certain power plants or power plant units are able to restore the power supply completely autonomously. Because only they can produce electricity,which is used by other supply-relevant power plants to restart. Because these power plants or power plant units do not need any external energy for this purpose, this phenomenon is called a "black start" and the corresponding plants are capable of black start.

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The rate of change of performance (eg, in units of megawatts per minute) describes the change of electrical capacity by a power plant, such as in load following operation. Depending on the type and exact design of a power plant, the rate of change of performance is technically limited.

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Minimal downtime refers to the minimum amount of time that a power plant should be out of service. This does not represent a hard physical constraint but an economic limit as )
operators are interested in minimizing the number of start-ups and shut-downs to reduce the high thermal loads on the power plant components.

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Efficiency is generally the ratio of delivered desired power to supplied power. Since this ratio is not the same for all operating points of a technical plant, the efficiency at partial load (at a different operating point than that at rated load) is referred to as "partial load efficiency". This designates not a single value, but any efficiency that the system has outside the operating point at rated load.

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Reliability must-run (RMR) units are power plants that are required during certain operating conditions to ensure safety of the energy system in a competitive environment.

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The marginal cost is the cost increase of the total cost of producing another unit of goods for a given production quantity. As long as the marginal cost of producing each additional unit of goods is less than the marginal revenue, the increase in production will bring a profit to the company. The production or sales volume that gives the company the greatest possible profit is achieved when the marginal costs correspond to marginal revenues.

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With respect to the energy system analysis the analysis of the power flow within the electricity system including reactive and active power is referred to as AC powerflow analysis. However, the non-linearity of the problem results in a heavy computational burden and solvability issues. Therefore, AC powerflow can be simplified to a linear problem by introducing the linear direct current power flow analysis.

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The net capacity factor is the unitary ratio of actual electrical energy output over a period of time to the maximum possible electrical energy output over that period.

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Linear Programming (LP) refers to optimization problems with only continuous variables and only linear functions in the objective function and the constraints.

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Quadratic Programming (QP) refers to optimization problems with a quadratic objective function and linear constraints.

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Mixed Integer Linear Programming (MILP) refers to optimization problems with continuous and discrete variables as well as only linear functions in the objective function and the constraints.

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Mixed Integer Nonlinear Programming (MINLP) refers to optimization problems with continuous and discrete variables as well as nonlinear functions in the objective function and/ or the constraints.

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Warm start describes starting a mathematical optimization with initial values close to the target values (the optimum of the objective function to be optimized).

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For each deterministic algorithm, the input value uniquely maps the result. From this it can be concluded that every deterministic algorithm must be determined, because the same processing is always performed on an input X. In contrast, however, not every deterministic algorithm has to be deterministic; an algorithm can also process different steps, and yet it always comes to the same result.

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The algorithm is called deterministic if there can be a subsequent situation for each program situation. The subsequent step is uniquely determined at each point in time.

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Stochastic simulation algorithms provide a convenient method for simulating reactions that are inherently stochastic. Thus, the solutions contain the element of probability as opposed to deterministic solutions.

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The Monte Carlo simulation or Monte Carlo method is a method in which very frequently carried out random experiments represent the basis. On the basis of the results it is attempted to solve analytically unsolvable problems numerically in the mathematical context with the help of probability theory. The law of large numbers is seen as justification. The random experiments can either be performed real or by the generation of random numbers. Today, computer-generated random processes can be simulated on almost any scale.

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Parallelization is the use of two or more processors (cores, computers) in combination to solve a single problem simultaneously.

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Multithreading is a software-based splitting of slow processes into parallel threads, which are processed in parallel by additional instructions from the central processing unit (CPU). A task can contain one or more threads that can only be executed on specific processors. If a task contains multiple threads, they will run on multiple processors. However, this requires that the task is multithreaded.

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Branch-and-Bound is a mathematical method from operations research that aims to find the best solution for a given integer optimization problem. Branch-and-bound is one of the decision tree procedures. The branch-and-bound algorithm consists of two parts: the branch and the bound. One tries to keep the solution space to be examined as small as possible by identifying branches in the spanned decision tree as suboptimal and dropping them out of further consideration.

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Branch-and-Cut is a technique for solving integer linear optimization problems. The method consists of the combination of cutting plane algorithms and branch-and-bound.

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A cutting plane algorithm is an algorithm for solving integer linear optimization problems in applied mathematics. The basic idea is instead of an integer linear program to consider its LP relaxation (ie, without integerity conditions) and to gradually increase it by adding more inequalities until (ideally) an integer solution is found.

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Endogenous Technological Change describes the making of investment decisions within a cost optimization under the premise of cost minimization or profit maximization. In this way, certain technologies may be favored at specific times and consequently the model endogenously provides the development of certain technologies.

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The term greenfield refers to undeveloped land that is not subject to any other use. In the context of energy system modeling, it is a modeling approach that does not assume existing infrastructure and subsequently makes different judgments on investment decisions than models that need to build on existing and possibly outdated infrastructure.

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The so-called copper plate assumption is a modeling approach that disregards infrastructures and restrictions of energy transport. It is a simplistic assumption that all components of the system are in one place.

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The term "node", in the context of energy system modeling, describes locations where energy networks converge. If these are spatially aggregated, they can also be understood as entire regions. A single-node model unites all the components in one place according to the copper plate assumption. A multi-node model takes into account the spatial distribution of components and the interconnections (the networks) when building technologies.

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Shadow prices are a concept of linear programming and describe the opportunity costs of the displaced factors.

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Opportunity costs are lost revenues or benefits compared to the best, unrealized alternative action. The avoidance of opportunity costs follows from the profitability principle.

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Perfect-foresight is a model approach of linear cost optimization, which strives at each time step that the expected interest factor corresponds to the real interest factor of the same time step. This assumption can only be fulfilled if the solution of the entire period of observation is known or determined for each time step.

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Myopic-foresight is a model of linear cost optimization that, for each time step, uses the expected interest factor of the previous time step. So a decision is made on the basis of past developments and not with regard to the whole, partly future, observation period.

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Hardcoupling describes one of the two categories of component communication. Hard coupling has a fixed relationship between the input and output of a communication channel among a defined number of communication participants. With respect to energy system models and their overall cost optimization, this term is often used in the context of perfect-foresight, as it takes into account the entire period of observation at all times, which means that future communication between future and past time steps is clearly defined and bidirectional. However, perfect-foresight and hardcoupling are by no means to be used synonymously, since one describes an economic-mathematical model approach and the other represents an information-theoretical concept.

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Softcoupling describes one of the two categories of component communication. Softcoupling does not have a fixed relationship between the input and output of a communication channel among an undefined number of communication participants. In terms of energy system models and their overall cost optimization, this term is often used in the context of myopic-foresight, because new decisions are made based on investment decisions that have already been made, without considering the final state. However, myopic-foresight and softcoupling are by no means to be used synonymously, since one describes an economic-mathematical model approach and the other represents an information-theoretical concept.

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A variable is a variable that can take on different values.

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Constant data is a numeric variable that has an infinite number of values between any two values. Constant variables can consist of numeric or date / time values.

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Discrete variables are numeric variables that have a countable number of values between any two values. A discrete variable is always numeric. A discrete variable is always numeric.

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Categorical variables include a finite number of categories or unique groups. Categorical data does not necessarily have to be in logical order. Categorical predictors include gender, material type, and payment method.

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Secondary constraints limit the number of states that a system can be in to the realizable states of the system that satisfy those conditions. The number of realizable states depends on the secondary conditions to which the system is subject.

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Simulation is the evaluation of a large number of alternatives from different realistic scenarios that were previously determined from a decision-making process. It is important to emphasize that simulation facilitates decision-making for predefined options, but does not generate the optimal strategy itself.

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Optimization is a scientific-technical approach for decision-making that seeks to find an optimal or, in absolute terms, most efficient way to achieve a goal while complying with all constraints that constrain that goal. Usually, the objective function is to minimize or maximize an analytic mathematical function, e.g. a total cost function.

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Linearization, the linear development of a function, an operator or a system around a development point. In physics, the linearization is motivated by the fact that one wants to investigate a complicated function, a complicated operator or a complicated system of differential equations in the proximity of a particularly interesting point, operator or system.

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The objective function is to be minimized or maximized. A minimum or maximum value of that function is to be determined. Instead of minimizing and maximizing, one also speaks of optimization or the determination of an extremum or optimum, if one considers the problem in general and does not differentiate between minimum and maximum.

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Data Aggregation describes the process of aggregating raw data, e.g. for statistical investigations. For example, raw data may be aggregated over a particular time period to indicate such quantities as average, minimum, maximum, and sum. There are two types of aggregation:

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Temporal aggregation describes the aggregation of a given attribute over a period of time.

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Spatial aggregation describes the aggregation of a group of attributes over space.

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Clustering can be considered as the most important problem of unsupervised learning. It deals with finding a structure in a set of disordered data. A definition of clustering could be "the process of object organization into groups whose members are similar in some respects". In terms of energy system modeling, the method is used to determine type-days, which are particularly representative of the energy system. It is used as an aggregation method.

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Approaches to solve general problems that do not have a clear solution strategy or that do not make sense because of the effort involved contain primarily "rules of thumb" based on subjective experience and traditional behavior. Heuristic is mainly applied in poorly structured and difficult to handle problem areas.

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