Conference Paper

Robust optimal identification and scheduling of modernization measures for typical buildings

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Abstract

Optimization approaches for the modernization of buildings mostly consider one-time investments for the design decision. Also the uncertainty of boundary conditions is rarely taken into account. In this work, we propose a robust extension of a mixed-integer linear program that determines modernization schedules considering multiple points in time for the design decision. An initially conducted sensitivity analysis of the original model reveals high influences of user behavior, emission factors and economic parameters on the objectives and design decisions. By applying the method to a typical building, it is shown that robust differ from nominal solutions. The shown investigation of different degrees of robustness should facilitate the decision for a modernization path in the future.

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... With this MILP, modernization roadmaps of single buildings can be determined for observation periods of up to 30 years. Since most of the yearly parameters in this model underlie uncertainty by observing these long observation periods, a robust extension of this MILP was proposed in [16] to handle this uncertainty. In [17], the MILP was extended by the possibility of setting emission goals at specific points in time during a modernization roadmap. ...
... (2) Quantify resources in economic optimal unlimited roadmap. Basically, there are two options to limit resources res in the model: Either, the sum of a resource over the whole roadmap may be limited by Equation (16) where red res is the reduction parameter of a resource that can be set between 0 and 1. Thereby, roadmaps with different levels of a limited resource can be determined. ...
... It is possible to quantify the influences of these uncertainties with sensitivity analyses as proposed in [61]. Furthermore, stochastic (e.g., [12]) or robust (e.g., [16]) optimization approaches can handle the uncertainties inside the optimization. ...
Article
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Great potential for saving carbon emissions lies in modernizing European buildings. Multi-year modernization roadmaps can plan modernization measures in terms of time and are able to consider temporal interactions. Therefore, we have developed a mixed-integer program that determines modernization roadmaps. These roadmaps include changing the energy supply system, improving the envelope, and considering annually varying boundary conditions. High craftwork capacities are required to implement the necessary modernizations to meet climate goals. Unfortunately, studies showed that the current shortage of craftworkers will intensify in the next years. Other important limitations correspond to energy resources. Recent crises show that many energy systems need to handle these limitations. Therefore, we extended the mixed-integer program by a method to handle these limitations inside the roadmaps. By the use of data from 90 interviews with craftwork specialists about the time needed to realize modernization measures, the method is applied. The main purpose is to analyze how modernization strategies change under limited resources, especially in terms of craftwork capacities. Hence, the method is exemplified by a representative single-family dwelling. Within this use case, modernization roadmaps with different craftwork capacity levels were calculated. The results show that modernization roadmaps change comprehensively over these levels. Key findings are that costs and emissions rise with decreasing craftwork capacities. Furthermore, smaller storages and pv systems are implemented at low craftwork capacities. The electrification of the heat supply supported by medium insulation standards should also be implemented with limited craftwork capacities.
... In addition, in their case study, the myopic approach leads to higher overall costs of the energy system. On building level, multi-period approaches have been successfully applied to optimize building retrofit schedules [39,40] and investment pathways for building energy systems [41,42,30,43]. On district level, Wei et al. [44] optimized a microgrid (modeled as single node) and consider long-term trends of declining investments for batteries. ...
... However, especially for long-term design problems with long planning horizons, these parameters are subject to substantial uncertainties. Therefore, robust optimization approaches could be added to the model formulation, as presented in [24,41]. However, robust optimization models substantially increase the computational complexity and make results more difficult to communicate to decision makers in real-world design problems (compared to straight-forward scenario analyses). ...
... With this MILP, modernization roadmaps of single buildings can be determined for time horizons of about 30 years. Since most of the yearly parameters in this model underlie uncertainty by observing these long time horizons, a robust extension of this work was proposed in [12] to handle this uncertainty. In contrast to stochastic optimization which is often used to consider uncertainty, robust optimization does not have the need of probability distributions for parameters. ...
... The robust extension of the described MILP is described in detail in [12]. An uncertainty characterization of all parameters as well as a sensitivity analysis was done. ...
Conference Paper
Design decisions concerning future energy systems of existing buildings must be made to realize necessary building modernizations. Previous research has mainly used single-year investment approaches for these design decisions. This approach cannot consider parameter changes over time, such as energy price changes. The uncertainty of these parameters is also rarely respected. The main goal of this work is to consider time-varying effects of parameters and their uncertainty. Thus, in addition to deciding about optimal technologies, we propose a multi-year approach to optimize the time for the implementation of these technologies in a building. A robust extension of this approach allows finding optimal solutions under many possible parameter scenarios. We develop a robust mixed-integer linear program to determine modernization investment roadmaps that include yearly decisions concerning the energy supply system and envelope insulation of a building. Parameters and constraints of the model are also set separately for each year. By conducting a multi-objective optimization , total costs and emissions of a considered time horizon are minimized. In a second optimization, we set emission goals for specific years while minimizing costs. Furthermore, different levels of robustness are calculated. These levels indicate how much uncertainty of the parameters is considered. Based on developed characteristic values for the roadmaps, solutions are compared for typical buildings and over multiple levels of robustness. The results show that setting emission goals leaves large savings potentials unused compared to minimizing cumulative emissions of the time horizon considered. Another key finding is that higher degrees of robustness tend to lead to more investments in the energy supply system and less in the insulation of the envelope.
... A good overview is given by Ben-Tal et al. (2009) or more recently by Bertsimas and Hertog (2022), where both books also cover adjustable robustness. Robust optimization for energy supply design was for example done by Moret et al. (2020) and for building renovation by Richarz et al. (2021). ...
Preprint
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Optimizing a building's energy supply design is a task with multiple competing criteria, where not only monetary but also, for example, an environmental objective shall be taken into account. Moreover, when deciding which storages and heating and cooling units to purchase (here-and-now-decisions), there is uncertainty about future developments of prices for energy, e.g. electricity and gas. This can be accounted for later by operating the units accordingly (wait-and-see-decisions), once the uncertainty revealed itself. Therefore, the problem can be modeled as an adjustable robust optimization problem. We combine adjustable robustness and multicriteria optimization for the case of building energy supply design and solve the resulting problem using a column and constraint generation algorithm in combination with an ε\varepsilon-constraint approach. In the multicriteria adjustable robust problem, we simultaneously minimize worst-case cost regret and carbon emissions. We take into account future price uncertainties and consider the results in the light of information gap decision theory to find a trade-off between security against price fluctuations and over-conservatism. We present the model, a solution strategy and discuss different application scenarios for a case study building.
Thesis
The energetic modernization of buildings has a high carbon emission savings potential. This potential can be leveraged through the strategic planning of modernization measures. In addition to the identification of measures, this planning should include the chronological sequence of measures and incorporate boundary conditions that change over time. Therefore, the core of this work is the development of an optimization model that determines both measures for the energy supply system and the building envelope, as well as their implementation times. For this purpose, physical effects of the building envelope as well as the operation of a building's energy supply system are modelled on an hourly level. Modernization measures for the entire building energy system are planned over decades on the basis of economic interrelationships to determine optimal modernization roadmaps. Changes in economic and ecological boundary conditions are incorporated into the model and a robust extension of the model integrates the uncertainties of these conditions into the optimization. Another optimization model uses pareto-optimal modernization roadmaps of single buildings as input to determine modernization roadmaps for building portfolios. The methods determine economically optimal modernization strategies for single buildings and building portfolios to save cumulative carbon emissions. Furthermore, the influence of emission target paths, uncertain boundary conditions, and the availability of craftwork capacities on these strategies are investigated. The methods are applied to typical German residential and non-residential buildings as well as to a building portfolio created from these. The results show that modernization measures should be coordinated in time. The electrification of the heat supply combined with building envelope measures of medium level depending on the age of the building form the basis of most of the strategies identified. Considering emission saving paths leads to economically inefficient strategies in single buildings, but can contribute to an accelerated decarbonization at the portfolio level. Compared to nominal strategies, robust strategies incur higher costs while decreasing emissions and increasing the share of renewable energy sources. Limited availability of craftwork capacities leads to higher costs and higher emissions. In individual buildings, this effect can be counteracted by larger thermal and electrical storage units, which increase the self-consumption of solar power and require low capacities for installation. Since autonomously calculated individual building roadmaps represent the input for the portfolio model, modernization measures in portfolio roadmaps often occur at the same time and the possibility of distributing craftwork capacities over time is severely restricted.
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Optimization models for long-term energy planning often feature many uncertain inputs, which can be handled using robust optimization. However, uncertainty is seldom accounted for in the energy planning practice, and robust optimization applications in this field normally consider only a few uncertain parameters. A reason for this gap between energy practice and stochastic modeling is that large-scale energy models often present features - such as multiplied uncertain parameters in the objective and many uncertainties in the constraints - which make it difficult to develop generalized and tractable robust formulations. In this paper, we address these limiting features to provide a complete robust optimization framework allowing the consideration of all uncertain parameters in energy models. We also introduce an original approach to make use of the obtained robust formulations for decision support and provide a case study of a national energy system for validation.
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Thesis
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Various countries and communities are defining or rethinking their energy strategy driven by concerns for climate change and security of energy supply. Energy models, often based on optimization, can support this decision-making process. In the current energy planning practice, most models are deterministic, i.e. they do not consider uncertainty and rely on long-term forecasts for important parameters. However, over the long time horizons of energy planning, forecasts often prove to be inaccurate, which can lead to overcapacity and underutilization of the installed technologies. Although this shows the need of considering uncertainty in energy planning, uncertainty is to date seldom integrated in energy models. The main barriers to a wider penetration of uncertainty are i) the complexity and computational expense of energy models; ii) the issue of quantifying input uncertainties and determining their nature; iii) the selection of appropriate methods for incorporating uncertainties in energy models. To overcome these limitations, this thesis answers the following research question "How does uncertainty impact strategic energy planning and how can we facilitate the integration of uncertainty in the energy modeling practice?" with four novel methodological contributions. First, a mixed-integer linear programming modeling framework for large-scale energy systems is presented. Given the energy demand, the efficiency and cost of energy conversion technologies, the availability and cost of resources, the model identifies the optimal investment and operation strategies to meet the demand and minimize the total annual cost or greenhouse gas emissions. The concise formulation and low computational time make it suitable for uncertainty applications. Second, a method is introduced to characterize input uncertainties in energy planning models. Third, the adoption of a two-stage global sensitivity analysis approach is proposed to deal with the large number of uncertain parameters in energy planning models. Fourth, a complete robust optimization framework is developed to incorporate uncertainty in optimization-based energy models, allowing to consider uncertainty both in the objective function and in the other constraints. To evaluate the impact of uncertainty, the presentation of the methods is systematically associated to their validation on the real case study of the Swiss energy system. In this context, a novelty is represented by the consideration of all uncertain parameters in the analysis. The main finding is that uncertainty dramatically impacts energy planning decisions. The results reveal that uncertainty levels vary significantly for different parameters, and that the way in which uncertainty is characterized has a strong impact on the results. In the case study, economic parameters, such as the discount rate and the price of imported resources, are the most impacting inputs; also, parameters which are commonly considered as fixed assumptions in energy models emerge as critical factors, which shows that it is crucial to avoid an a priori exclusion of parameters from the analysis. The energy strategy drastically changes if uncertainty is considered. In particular, it is demonstrated that robust solutions, characterized by a higher penetration of renewables and of efficient technologies, can offer more reliability and stability compared to investment plans made without accounting for uncertainty, at the price of a marginally higher cost.
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Models and Sensitivity AnalysisMethods and Settings for Sensitivity Analysis – an IntroductionNonindependent Input FactorsPossible Pitfalls for a Sensitivity AnalysisConcluding RemarksExercisesAnswersAdditional ExercisesSolutions to Additional Exercises
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