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DOE OSTI2021

A review of machine learning in building load prediction

The surge of machine learning in recent years has been empowering engineer modeling in various fields. The decreasing hardware cost, increasing data accessibility, and advances of building automation system (BAS) allow the collection and storage of a significant amount of building operation data. The two facts provide great opportunities of applying machine learning to building energy systems modeling and analysis. There are a great number of research papers on this topic but there lacks a comprehensive and general review to summarize the current development, limitations, gaps and future trend. In this review paper series, machine learning techniques in building energy system modeling and analysis are reviewed under the organization and logic of the machine learning definition by Tom M. Mitchell: a computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E. This paper is the first part of the review paper series, which focuses on building load prediction. First, the applications of building load prediction model (task T) are reviewed. Then, the modeling algorithms improving machine learning performance and accuracy (performance P) are reviewed. At the same time, the literature on the data perspective for modeling (experience E), including data engineering from sensors level to data level, pre-processing, feature extraction and selection, is reviewed. Finally, what is well-studied and what is lacking but with great potential are concluded; the gaps between present and future utilization of machine learning techniques are identified; the future trend and development are also predicted. The target readers of this paper are not only researchers from the building side who can get exposed to cutting edge machine learning tools, but also those from machine learning side who can understand the potential and challenge to apply machine learning in buildings.

Liang, Zhang↗
DOE OSTI2024

Design Heating and Cooling Load Calculation Versus Building Load Simulation for Cold Climate Heat Pumps: Understanding the "Gap"

This report explores the differences between Manual J-equivalent block load calculations and building HVAC energy simulation results using EnergyPlus™ calculations when designing cold climate heat pump systems for residential use. This study will help HVAC researchers and advanced designers understand the impacts of oversizing heat pumps on home energy use.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Coupled management of electric vehicle workplace charging and office building loads

Significant building energy savings are realized through heating, ventilation, and air conditioning (HVAC) setpoint adjustment and daylighting control. Workplace charging (WPC) enables colocation of electric vehicles (EVs) with office building loads. We proposed managing energy use of workplace EV charging and the office building and determined the number of EVs that building energy savings can facilitate charging. We simulated building energy savings in typical medium offices in Chicago IL, Baltimore MD, and Houston TX, spanning three US climate regions. Considering the EV hosting capacity of the saved building energy and travel patterns of roundtrip commuting, we minimized EV charging costs under time-of-use electricity pricing. Managed WPC can reduce charging electricity bills compared to first-come, first-served charging. The ratio of EVs to chargers, the coincident period of commuters’ dwell time and lower electricity prices, and the number of EVs in the office impacted the economic benefits achieved through charging management.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Comparison of time-frequency-analysis techniques applied in building energy data noise cancellation for building load forecasting: A real-building case study

Time-frequency analysis that disaggregates a signal in both time and frequency domain is an important supporting technique for building energy analysis such as noise cancellation in data-driven building load forecasting. There is a gap in the literature related to comparing various time–frequency-analysis techniques, especially discrete wavelet transform (DWT) and empirical mode decomposition (EMD), to guide the selection and tuning of time–frequency-analysis techniques in data-driven building load forecasting. This article provides a framework to conduct a comprehensive comparison among thirteen DWT/EMD techniques with various parameters in a load forecasting modeling task. A real campus building is used as a case study for illustration. The DWT and EMD techniques are also compared under various data-driven modeling algorithms for building load forecasting. The results in the case study show that the load forecasting models trained with noise-cancelled energy data have increased their accuracy to 9.6% on average tested under unseen data. This study also shows that the effectiveness of DWT/EMD techniques depends on the data-driven algorithms used for load forecasting modeling and the training data. Hence, DWT/EMD-based noise cancellation needs customized selection and tuning to optimize their performance for data-driven building load forecasting modeling.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Application of Intelligent Load Control to Manage Building Loads to Support Rapid Growth of Distributed Renewable Generation

Electricity utilities are faced with the mounting challenge of providing a stable supply of power to meet the growing demand while also integrating rapid growth in distributed variable renewable generation. Traditional means of balancing short- and long-term supply and demand imbalance will be expensive. Alternative approaches of using flexible loads in buildings are needed to mitigate the imbalance at a lower cost. This paper shows how the intelligent load control (ILC) process can be used to manage loads in buildings by dynamically prioritizing loads for curtailment using both quantitative and qualitative criteria. The ILC process can be deployed on low-cost computing platforms without the need for any additional sensing. ILC was first validated in a simulation environment to provide two grid service use cases: (1) managing monthly peak electricity demand and (2) managing buildings’ electricity consumption during a capacity bidding event. After being successfully tested in a simulation environment, ILC was deployed on real buildings to manage electricity consumption to provide two different use cases under different outdoor operating conditions. Both the simulation tests and the real building experiments were deployed using VOLTTRON™, a distributed sensing and control platform. The results from the tests and experiments showed that ILC was able to manage the controllable loads (heat pumps) in the building to maintain the electricity consumption at the desired level without a significant impact on occupant comfort. Overall, the results demonstrate that the ILC allows coordination of the controllable loads and provides a more intelligent means of load management than the traditional duty-cycling approach.

Kim, Woohyun↗
DOE OSTI2020

Modeling occupancy-driven building loads for large and diversified building stocks through the use of parametric schedules

Building energy modeling provides a fundamental tool to assess the potential for energy efficiency to contribute to reducing world energy consumption and global emissions. Occupancy-related operations are a key source of uncertainty for building energy analysis, particularly for aggregated building stocks. At a district or city level, it is critical to estimate aggregated power load profiles for sizing power grid infrastructure, power plant capacity allocation, and energy efficiency measures. The stochastic nature of behavior-related operations complicates the creation of models that accurately capture building load profiles for entire building stocks. This research introduces a new methodology called parametric schedules to model occupancy-driven schedules for large and diverse building stocks. In contrast to computationally expensive methodologies proposed in the literature, our work does not use a recursive time-consuming step. Occupancy is estimated by the extrapolation of operation times directly from metered electric consumption data; occupancy-related schedules are stochastically assigned to each building model, guaranteeing diversity of operation times in the stock. Our procedure has been tested on a large, diversified data-set of 25,000 commercial buildings in Los Angeles, California. It proved to be able to adequately represent the stochastic schedules diversity of the stock and to refine the stock calibration process by 1%. This innovative approach represents a useful asset for utility companies, grid operators, urban planners, and balancing authorities, seeking to improve building stock modeling and better estimate the impact of energy conservation measures. – This work is part of a larger stock modeling tool called ComStock, which is under development by NREL.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Simulating dispatchable grid services provided by flexible building loads: State of the art and needed building energy modeling improvements

End-use electrical loads in residential and commercial buildings are evolving into flexible and cost-effective resources to improve electric grid reliability, reduce costs, and support increased hosting of distributed renewable generation. This article reviews the simulation of utility services delivered by buildings for the purpose of electric grid operational modeling. We consider services delivered to (1) the high-voltage bulk power system through the coordinated action of many, distributed building loads working together, and (2) targeted support provided to the operation of low-voltage electric distribution grids. Although an exhaustive exploration is not possible, we emphasize the ancillary services and voltage management buildings can provide and summarize the gaps in our ability to simulate them with traditional building energy modeling (BEM) tools, suggesting pathways for future research and development.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

A Two-Level Model Predictive Control-Based Approach for Building Energy Management including Photovoltaics, Energy Storage, Solar Forecasting and Building Loads

This paper uses a two-level model predictive control-based approach for the coordinated control and energy management of an integrated system that includes photovoltaic (PV) generation, energy storage, and building loads. Novel features of the proposed local controller include (1) the ability to simultaneously manage building loads and energy storage to achieve different operational objectives such as energy efficiency, economic cost efficiency, demand response and grid optimization through the design of specific power trajectory tracking performance functionals, (2) an energy trim function that minimizes the impact of solar forecasting errors on system performance, and (3) the design of a state of charge controller that uses day-ahead forecast of solar power and building loads to intialize energy storage at the start of each day. The local controller is tested in simulation using an exemplary system with PV generation, energy storage and dispatchable building loads. Two sample days with different PV forecasts and multiple case scenarios are considered, and the performance of the algorithm in managing the real and reactive net building load trajectories and the ramp rate of PV injections into the utility network are evaluated. The simulations are based on actual forecasted and measured PV data, and the results show that the local controller meets the tracking requirements for real and reactive power within the operating constraints of the building.

14 SOLAR ENERGY↗
DOE OSTI2021

Dynamic Building Load Control to Facilitate High Penetration of Solar Photovoltaic Generation (Final Technical Report)

Solar photovoltaic (PV) resources are the most common form of distributed generation in residential and commercial customer premises within electric distribution networks. A higher penetration of PV generation in distribution circuits will impose challenges on maintaining service voltages within the range of industry standards, power quality, and power flow. Buildings consume 74% of the electricity produced in the United States, and a significant portion of the building load is dispatchable, making them responsive to electrical grid needs. Oak Ridge National Laboratory—in collaboration with Southern Company; the University of Tennessee, Knoxville; and the Georgia Institute of Technology—is examining the PV integration issues in distribution-level electrical grids and developing integrated demand-side control and communication systems to enable responsive loads. The proposed responsive loads mechanism performs renewable generation following to increase the penetration of solar PV within each feeder. The specific objectives of this project are to (1) examine distribution-level PV integration scenarios to understand requirements, (2) undertake an end-to-end simulation-based design of a distributed control strategy of loads geographically near the PV generation asset to minimize the effect on the distribution feeder, (3) deploy and demonstrate the control technology developed in partnership with utilities, and (4) perform a scalability analysis at the utility scale. This 3-year integrated project aims to develop, demonstrate, and validate demand-side control technology to enable increased the penetration of renewables while mitigating challenges that arise due to their intermittency. Activities in Budget Period (BP) 1 focused on a literature review and the formal design of a control system for integrating local distribution with generation and loads. The team used modeling and simulation to evaluate the impact of varying buildings loads, variable PV generation, and power flow dynamics on the distribution circuit. The dynamic models developed in BP 1 were used in BP 2 to develop a model-based control design and a test bed. The test bed has enabled the simulation-based testing and comparison of different control designs and formulations applied to different configurations of the distribution grid, PVs, and building loads. The control approaches developed in BP 2 were implemented in BP 3 in the form of hardware deployed at the Central Baptist Church (CBC) in Knoxville, Tennessee, for testing and evaluation. The outcome of this project was the development and demonstration of open-source, low-cost, low-touch sensing and control retrofits to distributed PV generation and building loads that, in a coordinated fashion, provide the load-shaping response needed to integrate high levels of renewable penetration. This research addresses the target metrics by dynamically controlling a load with solar generation variability to minimize the extent of two-way power flow, enhance reliability, facilitate high PV penetration (>100% of peak load in a line segment), and generate scalable software and hardware solutions adaptable to any penetration levels. The research and development activities are focused and designed to be impactful within the relevant 2020 targets time frame.An accurate open-source integration simulation framework for end-to-end control design was developed and deployed at the CBC facility for testing and evaluation. This final report provides a detailed review of the technical results achieved during this 3-year integrated project. A novel spectral analysis of PV data is demonstrated to derive the requirements of the control design. A detailed simulation-based analysis of PV integration at increasing penetration levels is presented using 1 year of PV data to demonstrate the impact on the distribution circuits. Two different control strategies were developed and demonstrated via simulation to track variable PV generation with adaptive load dispatch. The report concludes with a summary of accomplishments and recommendations for a path forward.

14 SOLAR ENERGY↗
DOE OSTI2023

BuildingsBench: A Benchmark for Universal Building Load Forecasting [SWR-23-51]

The residential and commercial building stock in the United States is responsible for a significant percentage of energy consumption and greenhouse gas emissions. Electrification of end-uses, as well as decarbonizing the electrical grid through renewable energy sources such as solar and wind, constitutes the pathway to zero-emission buildings. Forecasting day-ahead building energy consumption is an integral part of this solution. Currently, specialized forecasting models are hand-made for each individual building, which is time-consuming, expensive, and leads to duplicated efforts. BuildingsBench is a Python software framework for training and comparing generalized machine learning models for universal building load forecasting. This challenge tasks a single foundational model to generalize its forecasts for a wide variety of buildings, across geographic regions, building types, weather patterns, and more. This software provide code for pre-training such models and subsequently evaluating their performance on a suite of hundreds of diverse real and synthetic buildings. BuildingsBench is a platform for: - Large-scale pretraining with the synthetic Buildings-900K dataset for short-term load forecasting (STLF). Buildings-900K is statistically representative of the entire U.S. building stock and is extracted from the NREL End-Use Load Profiles database. - Benchmarking on two tasks evaluating generalization: zero-shot STLF and transfer learning for STLF. We provide an index-based PyTorch Dataset for large-scale pretraining, easy data loading for multiple real building energy consumption datasets as PyTorch Tensors or Pandas DataFrames, simple (persistence) to advanced (transformer) baselines, metrics management, and more.

Emami, Patrick↗
DOE OSTI2022

Hierarchical Model-Free Transactive Control of Building Loads to Support Grid Services

Residential buildings consume 4.4 quads of electricity annually, approximately 37% of the total electricity consumption in the United States. This represents a vast resource that can be used for demand management and other ancillary services. This project aims to develop a robust, scalable hierarchical transactional control mechanism incorporating elements of model-free control (MFC) and game theory to harness buildings to provide ancillary services to the grid. This approach is being taken to address the challenges of incorporating traditional transactional control schemes into existing buildings. The challenges include small individual building sizes requiring aggregation of many buildings, unpredictable energy usage that makes model identification difficult, and satisfying the sensitive occupant comfort constraints. In the proposed approach, by separating the control mechanism into two layers above and below the load aggregator, MFC can be used below the aggregator to modulate flexible building loads in response to pricing signals with guaranteed performance. This allows the burden of identifying an accurate model of the system to be shifted to the above-aggregator layer, where fluctuations in individual building usage have less impact on predicted building system behavior. Game theory concepts can then be used to determine pricing curves and control signals among regional aggregators. Managing this control in a game-theoretic approach will allow us to build in financial incentives that increase customer engagement. Additionally, the usage of MFC necessitates less burdensome computational and communication requirements, thus, it is easily deployable on small, embedded devices. In a broader sense, developing a strategy capable of effectively incorporating residential and small commercial buildings will allow greater throughput of existing and emerging grid services in addition to future transactive energy grid management methods. Using MFC within a hierarchical control architecture will allow the shifting of existing forecasting challenges to an aggregate level, where dynamics are slower and more predictable. This will enable a smooth interface between the grid services requests of utilities and the reliable control required by participating buildings. MFC, which supports distributed control architecture, permits a scalable solution that can be deployed to neighborhood-size systems as well as individual buildings. This project focuses on three objectives: (1) developing the mathematical framework, algorithm toolkit, and software toolset of the two-layer transactive control testbed; (2) developing a scalable solution for application over many residential and small-size commercial buildings with sparse distributed communication; and (3) field testing and implementation on hardware of the control strategies developed in the previous two objectives. The research and development activities are focused and designed to be impactful within the relevant 2025 targets timeframe. An open-source control framework for exploiting variability and dispatchability of building loads will be delivered as the outcome of the project. This capability enables greater participation of loads in electricity markets and ancillary services that are both useful for the utility and financially beneficial for building owners.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Building Load Control Using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. In this paper, we decide HVAC control schedules under uncertain PV generation, using a distributionally robust chance-constrained (DRCC) building load control model under two typical ambiguity sets: the moment-based and Wasserstein ambiguity sets. We derive mixed integer linear programming (MILP) reformulations for DRCC problems under both sets. Especially, for the Wasserstein ambiguity set, we use the right-hand side (RHS) uncertainty to derive a more compact MILP reformulation than the commonly known MILP reformulations with big-M constants. All the results also apply to general individual chance constraints with RHS uncertainty. Furthermore, we propose an adjustable chance-constrained variant to achieve tradeoff between the operational risk and costs. We derive MILP reformulations under the Wasserstein ambiguity set and second-order conic programming (SOCP) reformulations under the moment-based set. Using real-world data, we conduct computational studies to demonstrate the efficiency of the solution approaches and the effectiveness of the solutions. Summary of Contribution: The problem studied in this paper is motivated by a building load control problem that uses the aggregation of heating, ventilation, and air conditioning (HVAC) loads as flexible reserves to absorb uncertain solar photovoltaic (PV) generation. The problem is formulated as distributionally robust chance-constrained (DRCC) programs with right-hand side (RHS) uncertainty. In addition, we propose a risk-adjustable variant of the DRCC programs, where the risk level, instead of being predetermined, is treated as a decision variable. The paper aims to provide tractable reformulations and solution algorithms for both the (general) DRCC and the (general) adjustable DRCC models with RHS uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Reducing Grid Costs while Abating Emissions: Opportunities for Flexible Building Loads

This study evaluates the value of technology-agnostic, shiftable flexible building loads in modeled 2030 and 2040 U.S. grids for four types of customers under three potential aggregated distributed energy resources programs. The value examined includes monetary value from providing grid services (e.g., energy, capacity, flexibility reserve, regulation reserve, contingency reserve) and from reducing greenhouse gas emissions. By comparing more than 845,164,800 simulated shifting opportunities, the study finds that the timing of consumption is critical for profit-driven customers. A program that is activated for 30 critical hours of system operation can result in to $73 per year in revenue for 1 kWh of shiftable load. Emission reduction, on the other hand, is best accumulated through a year-round program: 1 kWh of shiftable load can lead to up to 487.9 kg CO2e carbon reduction per year. The report also provides detailed insights on the trade-off between revenue and emissions, regional variation, short- versus medium- term value, and impacts from various building flexibility parameters, such as shifting window and dissipation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Occupancy-Driven Stochastic Decision Framework for Ranking Commercial Building Loads

For effective integration of building operations into the evolving demand response programs of the power grid, real-time decisions concerning the use of building appliances for grid services must excel on multiple criteria, ranging from the added value to occupants' comfort to the quality of the grid services. In this paper, we present a data-driven stochastic decision-support framework to dynamically rank load control alternatives in a commercial building, addressing the needs of multiple decision criteria (e.g. occupant comfort, grid service quality) under uncertainties in occupancy patterns. We adopt a stochastic multi-criteria decision algorithm recently applied to prioritize residential on/off loads, and extend it to i) consider complex load control decisions (e.g. dimming of lights, changing zone temperature set-points) in a commercial building; and ii) systematically integrate zonal occupancy patterns to better identify short-term (and time-varying) opportunities for grid service participation. We evaluate the performance of the proposed framework for curtailment of air-conditioning, lighting, and plug-loads in a multi-zone commercial office building for a range of design choices. With the help of a prototype system that integrates an interactive \textit{Data Analytics and Visualization} frontend we demonstrate a way for the building operators to monitor and change in real-time the available flexibility in energy consumption and to develop trust in the decision recommendations by interpreting the rationale behind the ranking.

Jain, Milan↗
DOE OSTI2020

Frequency Analysis of Solar PV Power to Enable Optimal Building Load Control

In this paper, we present a flexibility estimation mechanism for buildings’ thermostatically controlled loads (TCLs) to enable the distribution level consumption of the majority of solar photovoltaic (PV) generation by local building TCLs. The local consumption of PV generation provides several advantages to the grid operation as well as the consumers, such as reducing the stress on the distribution network, minimizing voltage fluctuations and two-way power flows in the distribution network, and reducing the required battery storage capacity for PV integration. This would result in increasing the solar PV generation penetration levels. The aims of this study are twofold. First, spectral (frequency) analyses of solar PV power generation together with the power consumption of multiple building TCLs (such as heating, ventilation, and air conditioning (HVAC) systems, water heaters, and refrigerators) are performed. These analyses define the bandwidth over which these TCLs can operate and also describe the PV generation frequency bandwidth. Such spectral analyses, in frequency domain, can help identify the flexible components of PV generation that can be consumed by the various TCLs through optimal building load utilization. Second, a quadratic optimization problem based on model predictive control is formulated to allow consuming most of the low and medium frequency content of the PV power locally by building TCLs, while maintaining occupants’ comfort and TCLs’ physical constraints. The solution to the proposed optimization problem is achieved using optimal control strategies. Numerical results show that most of the low and medium frequency content of the PV generation can be consumed locally by building TCLs. The remaining high-frequency content of the PV generation can then be stored/offset using energy storage systems.

14 SOLAR ENERGY↗
DOE OSTI2022

Hierarchical Model-Free Transactional Control of Building Loads to Support Grid Services

A transition from generation on demand to consumption on demand is one of the solutions to overcome the many limitations associated with the higher penetration of renewable energy sources. Such a transition, however, requires a considerable amount of load flexibility in the demand side. Demand response (DR) programs can reveal and utilize this demand flexibility by enabling the participation of a large number of grid-interactive efficient buildings (GEB). Existing approaches on DR require significant modelling or training efforts, are computationally expensive, and do not guarantee the satisfaction of end users. To address the aforementioned limitations, this software code considers a scalable hierarchical model-free transactional control approach that incorporates elements of virtual battery, game theory, and model-free control (MFC) mechanisms. The developed approach separates the control mechanism into upper and lower levels. The MFC modulates the flexible GEB in the lower level with guaranteed thermal comfort of end users in response to the optimal pricing and power signals determined in the upper layer using a Stackelberg game integrated with aggregate virtual battery constraints. Additionally, the usage of MFC necessitates less burdensome computational and communication requirements, thus, it is easily deployable even on small, embedded devices. This software code enables the use of residential and small-size commercial buildings to offer a potentially substantial source of ancillary grid services that are currently underutilized. A hierarchical, model-free transactive building control provides a smooth interface between the grid service requests of utilities and the reliable control required by participating buildings. Model-free control, which supports distributed control architecture, will be a more scalable solution that can be deployed in neighborhood-size systems as well as individual buildings. The proposed approach contributes to the body of knowledge on two main aspects. First, it couples the MFC with the game-theoretic control and proposes a scalable model-free transactive control approach. MFC does not require any modeling effort or model training for the various building loads. This is very beneficial since deriving an accurate model for every single unit participating in DR programs and obtaining all the parameters about the units (e.g., thermal coefficients, standby losses) are infeasible. Also, MFC is computationally efficient, easily deployable even on small, embedded devices, and can be implemented in real time. Second, it integrates the concept of virtual battery into DR via the Stackelberg game. The concept of virtual battery enables efficient coordination and aggregation of a large number of flexible GEB with guaranteed thermal comfort of end users.

Olama, Mohammed [Oak Ridge National Lab. (ORNL), O↗
DOE OSTI2025

Considerations for Distributed Edge Data Centers and Use of Building Loads to Support Large Interconnections

The rapid expansion of artificial intelligence (AI) and machine learning is driving unprecedented electricity demand from data centers. It is predicted that by 2030, 90% of AI workloads will be inference-based, requiring interconnection of multiple low-latency edge data centers (<20 MW) sited closer to end users - often on already constrained distribution feeders. Although individually small, these loads can aggregate to large loads per feeder, straining infrastructure, creating multi-year interconnection delays, and driving up customer costs. This paper proposes a data center-focused grid-integration framework that combines feeder hosting capacity analysis with building energy efficiency, building load flexibility, and waste heat reuse to expand effective feeder and substation headroom. Such approaches can reduce interconnection delays, lower costs for ratepayers, and accelerate AI-ready infrastructure deployment.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Scheduling and Control of Flexible Building Loads for Grid Services Based on a Virtual Battery Model

This paper presents a framework for modeling, scheduling, and controlling residential thermostatically controlled loads (TCLs) to provide multiple grid services, such as energy shifting, peak load reduction, and ancillary services. A modeling method is proposed to characterize the aggregate flexibility from heterogeneous TCLs using a battery-equivalent model. Based on the flexibility model, a multi-period optimal scheduling formulation is developed to best utilize the flexibility from building loads and maximize total benefits from stacked value streams. An algorithm is proposed to control individual TCLs to follow the desired power consumption in real-time. The proposed methods are illustrated and validated through simulations.

Wu, Di↗