Modeling of thermal storage systems in MILP distributed energy resource models
Introduction
Distributed Energy Resources (DER) are commonly defined as a set of technologies and strategies with potential to make energy use more efficient, accessible, and environmentally sustainable. These solutions include power generation and combined heat and power (CHP) production using conventional fuel-fired technologies, but also renewable technologies and energy management strategies such as demand response, load shifting and peak-shaving, and storage [1].
Key benefits of DER usage include increased power reliability, higher renewable grid penetration, reduced carbon emissions and improved use of local energy resources [2], [3]; however, DER systems can also lead to higher complexity of system design, as well as additional issues, such as the need for power quality management and access control infrastructure when interconnected to the grid [4].
Storage systems, both electric and thermal, can play a key role in DER deployment, not only by creating a buffer to arbitrage market prices, but also by allowing variable small-scale technology integration and promoting more efficient use of resources [5]. In this context, thermal energy storage (TES) is commonly seen as an effective way to reduce operational costs and increase overall efficiency and capacity factors of micro-CHP units, solar thermal units and heat pumps (HPs) [6], [7], [8].
In fact, the combined use of TES and micro-CHP units may significantly reduce utility demand, particularly during peak hours. This has been addressed in previous studies, such as [9], where it is shown that the peak utility demand is reduced by 23% using CHP coupled with TES for chilled water, compared to only 13% utility demand reductions achieved with CHP without TES. Similarly, the work described in [10] suggests that TES combined with micro-CHP units in commercial buildings in Chicago can be beneficial from an energy/cost perspective for buildings with a heat demand higher than their electricity demand; however, the TES model used in this particular study is simplified and does not consider any storage losses.
Traditionally, sensible water storage solutions have been used for most heat storage applications [7], [8], although there has been an increased interest in latent heat storage using phase change materials (PCM) over the last decade [11]. Latent heat storage using PCM offers some advantages over sensible hot water tanks, such as higher energy density [12] and less corrosion [11]. Despite the ongoing research, the costs associated with low temperature latent PCM (i.e. 50–100 °C) are still higher than for sensible water storage [13], [14], although they can be economically competitive under appropriate conditions as demonstrated in [12].
TES has traditionally been modeled using only the first law of thermodynamics [15], meaning that changes in entropy are neglected [7], although analyses based on the second law of thermodynamics, which consider entropy, have become more common in recent decades. This improvement can have a significant impact on achieving optimal design and operation of TES [16], and also increase accuracy of economic results [7], because the model considers not only energy lost to the surrounding but also mixing of hot and cold water in storage. This will affect the performance of other DER connected to the TES, e.g. the efficiency of CHP unit, HP and heat exchanger.
Given the wide range of available DER options, the problem of meeting customer energy loads can be addressed by a multitude of solutions. This large search space creates a highly complex problem and identifying optimal DER equipment portfolio and operation options becomes a major challenge. DER can be very valuable, both when considering their economic and environmental benefits; however, choosing the actual energy supply solution is often based on empirical guidelines and rules-of-thumb, which typically lead to sub-optimal system configurations.
To address such DER problems, the Distributed Energy Resources Customer Adoption model (DER-CAM) has been developed at the Lawrence Berkeley National Laboratory [17]. The main output of DER-CAM is the economically and/or environmentally optimal combination of distributed energy conversion, storage and management options. Until now, TES has been modeled in DER-CAM as sensible heat storage, using water as the storage medium, and considering only energy flows through the tank. Storage losses have been estimated solely based on the energy stored, with size and ambient temperature not considered. Although this approach is commonly used in such tools, e.g. [18], [19], [20], and provides useful insights, its main drawback is that temperature changes in the tank are not tracked, which limits accurate economic assessment of TES [7]. Temperature changes also affect storage losses and how different heat-consuming and -providing technologies utilize the TES. For example, absorption cooling systems need relatively high input temperatures of at least 80–100 °C [21], and the existing model is unable to comply directly with these constrains, possibly leading to overestimation of TES economic performance.
This paper contributes to the state of the art by introducing an improved TES model into DER-CAM. Due to the current high cost associated with PCM based TES [13], [14], the model still considers only a sensible heat system using water as the storage medium. Although a model based on the second law of thermodynamics would increase the accuracy, it would result in an endogenous optimization problem formulation when used in investment and planning tools, due to the need of temperature tracking. Such problems cannot be solved in MILP models, such as DER-CAM. Furthermore, to capture all benefits of such model it would require increased details on the technologies connected to the TES, such as CHPs, HPs and absorption chillers, resulting in increased need for computational capacity. Hence, the second law of thermodynamics is not considered. Nevertheless, the TES model now introduced estimates storage losses with higher accuracy by considering the ambient temperature and static storage losses (due to a lower temperature threshold in the tank), which were previously not recognized. Furthermore, the new formulation of TES enables storage to be charged by low temperature heat sources, as the storage tank is now modeled with two separate temperature sections for high and low temperature storage.
The changes introduced to the TES model in DER-CAM are analyzed by a case study where results are obtained with both versions of the model. The results are compared for three different building types in two different locations.
The structure of this paper is as follows:
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Section 2 introduces DER-CAM.
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Section 3 describes the new model of the TES and the storage loss estimation.
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Section 4 presents the data for the case study.
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Section 5 presents the result from the DER-CAM simulations, and
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Section 6 discuss the results and concludes the paper.
Section snippets
DER-CAM
DER-CAM is a mixed-integer linear program (MILP) written in the General Algebraic Modeling System (GAMS) [22]. Its objective is to minimize the annual costs or CO2 emissions for providing energy services to the modeled site, including utility electricity and natural gas purchases, plus amortized capital and maintenance costs for any DER investments. The key inputs are customer loads, electricity and natural gas tariffs, and data of DER technologies, including capital and O&M costs, conversion
New thermal energy storage model in DER-CAM
The nature of different heat loads typically translates into different heat temperature requirements. For instance, to provide heat to absorption chillers the heat source temperature must be above an approximate 90 °C minimum [34], while other heat loads such as space heating and domestic hot water may be served by heat sources at temperature levels around and below 65 °C [35].
Similarly, different technologies will be able to provide heat at different temperatures, depending on their technical
Case study
This section presents the most relevant data used in the case study where both the previous and improved DER-CAM TES models are compared. The load data is based on the California Commercial End Use Survey (CEUS) [38]. Three different building types were analyzed – a large college building (LCOLL), a large health care facility (LHLTH), and a large hotel (LHOT), each assumed to be located in both San Francisco and San Diego, California. The warmer climate in San Diego compared to San Francisco
Results
This section compares the key results obtained with both TES models for the buildings described in Table 1. Under the assumptions used, TES adoption is not strongly economically attractive in cost minimization runs. The reason is due to the large number of technologies available, other technology combinations crowd out TES deployment in the cost minimization runs. Consequently, the results presented here focus on CO2 minimization runs, as they produce higher TES adoption rates, and therefore
Conclusions and further work
This paper presents an improved TES model implemented in DER-CAM version 4.0.0. The adopted formulation consists of modeling TES with two different temperature sections, one high temperature and one low, to enable the possibility of charging the TES with low temperature providing technologies, such as heat pumps in addition to high temperature providing technologies like CHP. Additionally, the accuracy of the estimated storage losses within TES has been improved to better match a real TES. This
Acknowledgements
DER-CAM has been funded partly by the Office of Electricity Delivery and Energy Reliability, Distributed Energy Program of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The Distributed Energy Resources Customer Adoption Model (DER-CAM) has been designed at Lawrence Berkeley National Laboratory (LBNL). Furthermore, Chalmers Energy Initiative is greatly acknowledged for funding D. Steen’s guest research visit to Lawrence Berkeley National Laboratory.
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