Replication StudiesEnsemble Calibration of lumped parameter retrofit building models using Particle Swarm Optimization
Introduction
Current European policy targets a reduction of greenhouse gas (GHG) emissions by at least 80% below 1990 levels by 2050, including a 95% abatement of GHG emissions in the building sector [1]. Buildings represent 40% of global energy consumption and account for nearly 30% of energy related global GHG emissions [2]. In the Irish context, the residential sector represents 25% of the primary energy supply [3] and a quarter of energy related CO2 emissions in 2015 [4]. One approach to decarbonise the Irish residential sector using current technologies is the implementation of effective Energy Conservation Measures (ECMs), including upgrades of heating systems [5]. Ahern et al. [6] determined that building retrofit measures have the potential to reduce by 65% the heating costs and CO2 emissions for detached rural houses built prior to 1979 (approximately 20% of the Irish domestic dwelling stock). Ahern et al. conclude that government incentives (such as the Better Energy Homes scheme [7]) are required to incentivise retrofit, given the significant upfront cost for end users. Without monetary or economic incentives, home owners are unlikely to carry out energy efficiency measures [8].
The Irish Government estimates an investment of 35 billion EUR (20,000 EUR per dwelling) is required to bring the domestic stock (as of 2015) to an efficient level of energy performance (BER rating B) [9]. There is a need for the study of techno-economic mechanisms by which the environmental and economic benefits of government investment in Energy Conservation Measures are maximized. One such mechanism corresponds to the electrification of domestic space heating and domestic hot water supply. Under this mechanism, efficient electrified heating technologies such as heat pumps and storage heating [10] displace the CO2 emissions arising from fossil fuel consumption for heating. The displaced CO2 emissions are abated by the usage of low-carbon electricity generation assets. In 2015, fossil fuels accounted for 61% of energy-related CO2 emissions in the residential sector [4]. During the same period, electricity accounted for only 25% of residential final energy use [3]. Furthermore, wind generation represents 23% of electricity generation and it is likely to increase in order to meet the Irish Government target of 40% generation using Renewable Energy sources [11]. Storage heating becomes a technology of interest as it has the potential to provide power system operators with demand management alternatives while increasing the usage of electricity generation assets [12].
The interconnection between building retrofits, electrified heating technologies and low-carbon electricity generation is evident. If energy efficiency measures and electrified heating systems are combined, the carbon emissions associated with domestic space heating and domestic hot water can potentially be displaced by low-carbon power generation. At an aggregated level, building and grid model integration has the potential to reduce peak electricity consumption and defer future investments in electricity generation capacity. Furthermore, heating storage can further minimize generation cost by shifting demand from excess wind production to domestic heat storage units. The integrated assessment of building retrofit measures, electrified heating technologies and variable energy generation requires the development of an integrated building-to-grid retrofit modelling framework by which the overall environmental and economic benefits can be maximized.
Techno-economic building retrofit optimization often relies on the coupling of heuristic optimization techniques (e.g., Genetic Algorithms) and Building Energy Model Simulation (BEMS) tools [13], [14], [15], [16]. In such a framework, the heuristic optimization solver uses BEMS models in an iterative manner for cost function evaluation purposes. However, power systems investment planning problems are often defined using classical optimization models such as Mixed-Integer Linear Problems (MILP) (e.g., [17], [18]). Prior work that has addressed building-to-grid analysis focussed on methodologies that use BEMS and power systems optimization in a sequential manner. This typically involves the use of BEMS to generate synthetic building performance data as an input to power systems optimization tools. Ault et al. [19] adopted this approach by pre-calculation of heating demand profiles using the ESP-r simulation environment [20]. These heating profiles were used as input to a power systems optimization study.
A disadvantage associated with this approach is that BEMS are unable to adapt to dynamic events occurring in the power systems model (e.g., availability of variable generation or demand response events) unless a potentially sub-optimal iterative and computationally-expensive strategy is considered. For integrated energy scenario analysis, where building and grid models need to be combined, a linear representation of building energy performance is required. Integrated models of this nature will facilitate comprehensive building thermal performance assessment, such as building retrofit analysis or the effect of increased penetration of electrified space and water heating systems, in the context of wider integration of renewable energy generation into the electricity grid.
The current paper introduces three automated calibration methodologies, each capable of transforming any residential BEMS archetype model into a lumped parameter archetype building model, representative of an ECM configuration. In the current paper, an ECM configuration is defined as a combination of ECM measures (e.g., 100 mm of external wall insulation combined with 200 mm of ceiling insulation). For any BEMS archetype, several ECM configurations can exist. The first methodology, denoted Sequential Calibration, exploits a semi-physical interpretation of the lumped parameter modelling framework, to define a selected building model parameter (e.g., external wall resistance), as a function of monotonic increments in an individual building fabric ECM (e.g., increments in external wall insulation thickness). These functions are defined as retrofit functions. To date, there has been no attempt to formulate lumped parameter building models automatically as functions of ECMs. Sequential Calibration is constrained to the identification of a suitable baseline (i.e., pre-retrofit) lumped parameter building model. The second calibration methodology introduced in the current paper addresses this limitation by simultaneously identifying the baseline model and the retrofit function associated with each ECM. This methodology, denoted as Simultaneous Calibration, is shown to potentially result in a calibration bias (e.g., retrofitted models with low levels of insulation may be calibrated with less accuracy than the retrofitted models with higher levels of insulation).
The third methodology, which is the main contribution of the current paper, is denoted as Ensemble Calibration. The key difference is that Simultaneous Calibration defines a single retrofit function per ECM, whereas Ensemble Calibration defines a group of retrofit functions, each one based on a combination of the other ECMs. For example, in Simultaneous Calibration there is only one single retrofit function associated with external wall insulation. In Ensemble Calibration, a retrofit function associated with external wall insulation is defined for every possible combination of ceiling insulation and internal insulation. Ensemble Calibration results in the identification of linear, lumped parameter models with a Mean Average Error (MAE) less than 0.5 °C, compared to the synthetic data generated using the associated BEMS archetype. This metric has been suggested in the literature as an acceptable calibration accuracy [21], [22], [23]. More importantly, the Ensemble Calibration methodology results in a number of lumped parameter building models with shared parameters (i.e., the baseline model). Therefore, the corresponding discrete-time linear building models are linearly dependent with respect to the discrete-time baseline model. This linearity is a key requirement of a building-to-grid co-optimization model used to assess optimal, large-scale ECM building configurations.
Ensemble Calibration is the first step towards the seamless integration of dynamic building energy models with grid models in an ECM investment decision-making framework. To date, this broader agenda has not been addressed in the literature. The proposed methodology is not designed to support retrofit decision-making of an individual building retrofit project. Instead, the combinatorial archetype lumped parameter models developed using the proposed methodology have the potential to enable planners to simultaneously assess both ECM investment decisions and economic investment decisions when considering integrated building thermal and electricity grid flexibility analysis, which are usually considered at scale (e.g., at a national level). A case in point being that building retrofit policy-making (e.g., end-use incentives) can now be influenced by varying levels of RES penetration and/or electricity system investment options without the need to re-compute the building heating loads for each desired ECM configuration. Both the building thermal models and the power systems models could be simultaneously optimized, in theory, during the retrofit decision-making process.
The proposed framework does not explicitly deal with building model uncertainty at this stage of development. The explicit modelling of building uncertainty in linear archetype building models results in a non-linear model with varying parameters associated with uncertainty distributions for selected building parameters. This is not consistent with the desirable modelling framework for tractable building-to-grid co-optimization (i.e., linear building modelling). To conclude, the methodologies introduced in the current paper assume the development of residential archetypes representative of a national building stock [24]. Residential archetypes are increasingly being used in building energy research at the urban and national level (e.g., [25], [26], [27]). The proposed contribution adds the possibility of integrating power systems issues with urban and national energy modelling via BEMS archetypes, which to date has not been addressed.
The current paper is organized as follows: Section 2 provides an overview of lumped parameter building modelling and model calibration via heuristics optimization. Section 3 describes methodologies to identify parametric evolution of a single ECM (Sequential Calibration) and multiple ECMs (Simultaneous Calibration). A third methodology (Ensemble Calibration) is proposed to improve the accuracy of Simultaneous Calibration. Section 4 shows the application of these methods in the calibration of different lumped parameter models, representative of an archetype of a semi-detached house model, for all possible insulation retrofit combinations of external, internal and ceiling insulation. Section 5 provides a discussion of the results. Section 6 closes with the conclusions of the research work.
Section snippets
Lumped parameter models
Simplified dynamic building energy models can be obtained from synthetic data using computing tools such as neural networks [28], [29], support vector machines [30], [31] and machine-learning methods [32]. Synthetic data can also be used to identify linear building models using linear regression [33], [34] and system identification methods [35]. Alternatively, archetype construction information and synthetic data can be used for the calibration of lumped parameter building models [36], [37].
Overview
The methodology framework is shown in Fig. 1. The assumptions made for the generation of synthetic data and for lumped parameter building modelling are discussed in Section 3.2 Throughout the current paper, a single lumped parameter building model representative of an archetype model without any ECMs (i.e., a building before retrofit) will be referred to as the baseline model. Section 3.3 discusses the calibration of the baseline lumped parameter building model using synthetic data and Particle
Simultaneous Calibration
The Simultaneous Calibration methodology (Section 3.5) was applied to the semi-detached house archetype model (Section 3.2). Only four calibration steps (baseline model plus three insulation increments) were considered for each dimension. A higher resolution was deemed to be computationally too expensive. The baseline model was simultaneously calibrated with three exponential parametrizations, each representing an ECM, as outlined in Algorithm 3. Table 1 describes eight different ECM
Discussion
The three proposed calibration methodologies result in the identification of continuous-time Ensemble models. The Ensemble models consist of a baseline lumped parameter building model, which when combined with exponential functions, describe the variations in model parameters due to different ECM configurations. While it could be argued that extending a baseline model with theoretical approximations (e.g., Eq. (9)) or other simplified models should suffice, it is known that the theoretical
Conclusions
The current paper introduced three calibration methodologies which aim to represent lumped parameter building models as mathematical functions of single or multiple ECMs (e.g., external wall insulation). The first methodology, Sequential Calibration, showed that lumped model parameter growth can be identified as an exponential function of monotonically increasing levels of an individual ECM (e.g., increments in external insulation layer thickness). The second methodology, Simultaneous
Acknowledgements
This work was conducted in the Electricity Research Centre, University College Dublin, Ireland, which is supported by the Electricity Research Centre's Industry Affiliates Programme (http://erc.ucd.ie/industry/). This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 646116.
William Turner is supported by the Science Foundation Ireland Strategic Partnership Programme (SFI/15/SPP/E3125) and the UCD Energy21 program,
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