## Abstract

Large commercial buildings may display demand flexibility, which reduces electric energy expenses for the building owner and carbon emissions from grid operations, provides distributed energy resources, and increases the penetration of renewable energy sources. Demand-controlled ventilation (DCV) and building thermal mass control can individually and jointly provide such flexibility. The performance and financial payback of these technology options can be dramatically improved if based on hourly electric prices and carbon emissions rates. In this study, a modeled but actual large office building, simulated using New York City hourly electric prices, hourly CO_{2e} emissions rates, and weather data for the summer 2019 cooling season is based on these dynamic driving parameters. A joint optimization of a building’s thermal mass and indoor CO_{2} content is presented. Superior energy savings and carbon emissions reductions are found for the joint optimization scenario when compared to both the baseline operation and individual optimization of building thermal mass and indoor CO_{2} content. These findings motivate the development of a real-time joint control system that utilizes closed-loop model predictive control (MPC) to optimally harness both sources of demand flexibility, a system that would require the future development of forecasting algorithms for external and control-oriented system models.

## 1 Introduction

Commercial buildings were estimated in 2020 to have consumed 13.6 quads of electricity (35% of electricity consumed in the United States) [1] and generated 826 million metric tons of carbon emissions (16% of all US carbon emissions) [2]. The opportunity for commercial buildings to play a role in reducing global carbon emissions is immense. Emission reductions can result not only from higher efficiency buildings but also in the form of increased load flexibility. That is, when a building consumes electricity is as important as how much a building consumes. More flexible buildings cannot only reduce operational costs but also increase the self-consumption of renewable energy resources, specifically photovoltaics (PV) and wind [3,4]. This transition to flexible load that can follow supply will become increasingly important as the grid increases its renewable generation.

Large commercial buildings represent good candidates for such flexibility due to their immense thermal mass. Central plants and interzone airflow, both common features of large commercial buildings that couple zones together, are likely to increase load-shifting performance [5]. Basic control strategies are not capable of producing such flexibility; advanced controls will be needed to address this problem. However, the integration of sufficient sensors and controls is not observed throughout the majority of the current commercial building stock. Demand flexibility requires optimal thermal control and ventilation strategies such as demand control ventilation (DCV) with grid-interactive aspects. This article presents a methodology to achieve just that: an optimization of DCV and thermal mass is showcased using a framework that considers forecast weather, hourly electricity prices, and hourly carbon emission rates.

### 1.1 Advanced HVAC Control and Demand Flexible Buildings.

Advanced heating, ventilation, and air conditioning (HVAC) controls give buildings the opportunity to provide acceptable indoor air quality (IAQ) while simultaneously achieving aggressive goals like peak power reduction, load shifting, demand response, carbon emission reductions, and others. Extensive research has been done evaluating advanced building control [6,–18]. Much of this work consists of optimal activation of thermal mass, the use of model predictive control (MPC), application of forecast hourly electric prices and emission rates, and the optimal control of portfolios of buildings in pursuit of energy savings, peak load reduction, and providing grid services.

MPC holds the promise to work well when applied to HVAC systems because it allows the current control to be optimized while keeping future disturbances and system performance in mind. This enables the controller to anticipate future events like weather, building utilization changes, electricity prices, $CO2$ emission rates, and it can take control actions to prepare for these, all while abiding by HVAC system and control constraints. The ability to take into account future disturbances presents the opportunity for buildings to achieve a multitude of electric grid goals. The solutions presented in this article are a product of an optimal control problem. The implementation of MPC was left for future work.

In 2012, QCoefficient showcased optimal activation of thermal mass while controlling 13 of the 108 floors in Chicago’s Willis Tower. Through precooling strategies, they were able to replace 1530 MWh of peak-time demand with 630 MWh of off-peak demand, saving approximately $250,000 and 900 tons of $CO2$ emissions in the process [19]. Seven years later, a similar demonstration was done in a large sophisticated LEED Gold office building in Manhattan. Here, HVAC energy was reduced by 20% and HVAC peak demand by 30% for the 2019 cooling season [20].

### 1.2 Indoor Air Quality and Ventilation.

In the world of indoor air quality $CO2$ concentration is often used as a proxy variable for IAQ. Although carbon dioxide is not generally considered to be a health concern at concentration levels found indoors, it is commonly used as a tracer gas when evaluating ventilation rates in procedures such as the indoor air quality procedure (IAQP) [21,22]. In this way, the total indoor $CO2$ content can be viewed as an IAQ storage medium similar to the total energy stored in the building’s thermal mass.

In contrast to thermal mass optimization, ventilation optimization has seen less attention. Important to this article, ventilation optimization is not yet informed by hourly electric prices and carbon emission rates, as necessary to achieve electric grid goals. The pandemic made clear that acceptable IAQ and associated operations expense would be an important consideration in a grid-interactive, renewable world. The relationship between adverse health effects and a lack of ventilation has been well documented [23–30]. It is also well known that high ventilation rates contribute heavily to a building HVAC load, which can account for a large portion (40–50%) of a building’s energy consumption [31,32]. The need for optimal control of ventilation is evident.

The work of Rackes and Waring [33] presented ventilation optimized over a time horizon with a multiobjective framework that can balance IAQ and energy use. They designed a ventilation strategy of coupled outdoor air (OA) flowrates and zone temperature setpoints. By using this approach, they found that in January, HVAC site savings of 20–40% could be obtained. This work focused solely on reducing overall site energy consumption (while improving IAQ) without consideration of operational cost. By contrast, the findings presented in this work take into consideration day-ahead electricity prices and carbon emission rates to meet operational cost and carbon objectives.

Rackes and Waring joined now by Ben-David et al. continued work with ventilation optimization [34]. This study attempts to optimize constant ventilation rates (L/s/occupant) over an annual time horizon. They develop Pareto fronts based on the trade-off between energy and IAQ; however, this time the IAQ axis is based on the metric of IAQ$profit$ including both lost productive worktime due to lost work performance and lost productive worktime due to excess absence rates. The metric is in units of work hours lost per occupant per year. This IAQ profit metric was based on a relationship established in other studies [35–37]. While this study looked to optimize on an annual basis with constant ventilation rates, the work presented here focuses on a daily timescale and provides hourly resolution for OA flowrates. This resolution is necessary to leverage DCV for grid services.

The simultaneous optimization of temperature setpoints and OA intake has been shown to produce up to 30.4% [38]. Mossolly et al. used a genetic algorithm (GA) to optimize the fresh air rate and the supply air temperature of a multizone variable air volume air conditioning system. They represented the IAQ within the cost function with a hyperbolic tangent function allowing $CO2$ concentration to fall between 350 ppm and 1350 ppm. Both advanced control strategies successfully adhere to ASHRAE standard 62 requirements. This along with the work of House and Smith [39] shows that simultaneously optimizing multiple control variables will result in a significant reduction in the overall energy consumption compared. While this work seeks to minimize energy consumption, the work presented here seeks to minimize hourly informed energy costs and carbon emissions realized on the grid scale.

### 1.3 Building Energy Models and Optimization Environments.

To evaluate control sequences and zone conditions while performing optimizations like those described in Sec. 1.1, building energy models (BEMs) are required. BEMs can be described in three categories: physics-based (white box) models, purely empirical (black box) models, and models with some of both attributes (gray box models). White box models are time-consuming and difficult to develop but offer high accuracy, especially when trying to capture short timescale dynamics of large commercial buildings. For this reason, the physics-based software tool energyplus was used throughout this work. Specifically, a matlab–energyplus optimal control environment testbed was used during this research. The environment used is the product of a multiyear, multidisciplinary collaboration between QCoefficient, Inc. and the University of Colorado Boulder [15–20,40–42]. The environment was previously used by May-Ostendorp et al. [17] to reduce cooling- and ventilation-related building energy consumption through optimal control of a mixed-mode building. The framework for this environment is shown in Fig. 1.

### 1.4 Research Contribution and Novelty.

The specific question this article attempts to answer is can the joint optimization of zone temperatures and outdoor air intake show potential for improving building flexibility and DCV performance by taking into consideration hourly electric prices and hourly carbon emission rates. That is, can the secondary storage medium of indoor $CO2$ be better optimized for electric grid expense and carbon emission reductions? Analogous to changing zone temperature setpoints strategically throughout the day, a building’s OA intake can be modulated to shift and shed sensible and latent ventilation loads while staying within the bounds of acceptable IAQ. This article also aims to analyze the degree to which optimizing ventilation in tandem with zone temperature setpoints for thermal mass control can provide synergistic effects to better achieve both electric expense and carbon emission objectives.

The points of departure of this article are that it:

provides a methodology for optimizing an hourly ventilation flow fraction schedule in energyplus models;

presents a framework for optimizing DCV control, minimizing both carbon and expense objectives, while maintaining acceptable IAQ; and showcases a ventilation strategy with lower electric expense and carbon emissions than conventional DCV;

presents a framework for a joint optimization of both temperature setpoints and OA flow fractions and showcases the synergy of a simultaneous optimization of thermal mass and IAQ storage mediums;

demonstrates building HVAC operational flexibility and its importance to a post-COVID, renewable energy future.

## 2 Methodology

The methodology presented in this article starts by outlining the building being simulated along with all external influences affecting its operation (i.e., weather, electric, and carbon emission rates). Following that is a description of the optimization environment and its parameters. Two baseline cases (DEF referring to default operation and DCV referring to demand-controlled ventilation) are then described. Finally, five optimization case studies are outlined. Three case studies feature unique decision spaces:

First is an outdoor air fraction optimization showcasing control of the building’s ventilation, constrained in the same manner as DCV (this case will be referred to as OA).

Second is a temperature setpoint optimization demonstrating the already significant and proven performance of optimal thermal mass control (this case will be referred to as TEMP).

Third is the joint optimization of temperature and ventilation at the same time showcasing the synergy between thermal mass and IAQ storage mediums (this case will be referred to as DUAL).

To evaluate the synergy of the DUAL case, two additional cases were developed featuring two sequential optimizations. Sequential optimizations take the results of a single optimization, hard code those setpoints into the model then perform an additional optimization on new decision variables:

First is a temperature followed by an outdoor air optimization (this case will be referred to as $SeqTO$).

Second is an outdoor air followed by a temperature optimization (this case will be referred to as $SeqOT$).

All optimizations consider forecast hourly electric prices and carbon emission rates. All simulation cases are summarized in Table 1.

Case | Decision variable(s) | Optimization type |
---|---|---|

DEF | NA | NA |

DCV | NA | NA |

OA | OA fraction | Single |

TEMP | Zone temp. setpoint | Single |

DUAL | OA fraction & zone temp. setpoint | Single |

$SeqTO$ | Zone temp. setpoint then OA fraction | Sequential |

$SeqOT$ | OA fraction then zone temp. setpoint | Sequential |

Case | Decision variable(s) | Optimization type |
---|---|---|

DEF | NA | NA |

DCV | NA | NA |

OA | OA fraction | Single |

TEMP | Zone temp. setpoint | Single |

DUAL | OA fraction & zone temp. setpoint | Single |

$SeqTO$ | Zone temp. setpoint then OA fraction | Sequential |

$SeqOT$ | OA fraction then zone temp. setpoint | Sequential |

### 2.1 Building and Model Description.

The building used throughout this analysis is a LEED Gold 74,322 m$2$ (800,000 sq. ft.), 40-story office building physically located in Chicago. However, for this study, hourly weather, price, and carbon emission rates were used to simulate its operation in New York City (NYC). The building has two 1250-ton centrifugal water-cooled chillers. Chiller 1 is an efficient mag-bearing chiller with a coefficient of performance (COP) of 6.382, and chiller 2 is an older, less efficient, constant speed chiller with a 4.4. The building features nine air handling units (AHU) and variable air volume (VAV) terminal units serving each of the zones with an associated design airflow. Table 2 summarizes additional building features.

Property | Value | Units |
---|---|---|

Floors | 40 | NA |

Floor area | 74,322.43 | m$2$ |

WWR^{a} | 0.5 | NA |

Occupant density | 29.77 | m$2person\u22121$ |

Lighting power density | 9.8 | $Wm\u22122$ |

Equipment power density | 4.63 | $Wm\u22122$ |

Infiltration | 0.55 | ACH |

Property | Value | Units |
---|---|---|

Floors | 40 | NA |

Floor area | 74,322.43 | m$2$ |

WWR^{a} | 0.5 | NA |

Occupant density | 29.77 | m$2person\u22121$ |

Lighting power density | 9.8 | $Wm\u22122$ |

Equipment power density | 4.63 | $Wm\u22122$ |

Infiltration | 0.55 | ACH |

WWR, window-to-wall ratio.

All densities represent the peak value, and schedules of multiplier values adjust the levels throughout the day. Thermal mass was modeled in EnergyPlus using “Internal Mass” objects. Within each thermal zone were three objects, interior furnishing, interior wall, and structural elements, each defined with a specific area exposed to zone air. Interior furnishing was defined as “Wood 6in,” interior walls were two layers of “Gypsum 5/8in” separated by an air space, and structural elements was defined as a layer of “Concrete HW Solid 8in” followed by a “Gypsum 1/2in” layer.

### 2.2 Simulation Parameters

#### 2.2.1 Location.

New York City is the location of this study due to the abundance of large office buildings, NYC carbon emission reduction legislation, and New York (NY) renewable energy legislation. The City Council passed Local Law 97 in 2019 requiring buildings over 2,322 m^{2} to meet new energy efficiency and greenhouse gas emission limits by 2024, with stricter limits set to take effect in 2030 [43]. NY State also signed into law the Climate Leadership and Community Protection Act [44], calling for the addition of several thousand megawatts of renewable energy—both distributed PV and wind—over a comparable time horizon. This puts a premium on building demand flexibility and makes NYC an outstanding test bed for energy efficiency and carbon reduction strategies.

#### 2.2.2 Time Frame.

A single-day optimization was selected for this study. This decision was motivated by the large impact previous days of operation have on the thermal and indoor $CO2$ concentration state of the building. A single day highlights the differences in control decisions among the TEMP, OA, DUAL, $SeqTO$, and $SeqOT$ cases. All models have the same thermal history and $CO2$ concentration profile leading into the optimization period due to a warmup period. This creates a level playing field for each optimization technique to show its savings from the baseline.

All case studies occur on Tuesday, Jul. 30, 2019. This day was selected for having high temperatures for that season and significant intra-day variation in hourly day-ahead electricity prices and carbon emission rates, creating key hours to reduce energy consumption. The external conditions affecting the building on Tuesday are summarized in Fig. 2.

#### 2.2.3 Weather and Electricity Rates.

The weather files used in this case study were based on forecasted weather data from the National Weather Service and National Oceanic and Atmospheric Administration (NOAA) [45].

All energy prices used throughout this study are day-ahead rates sourced from the New York Independent System Operator (NYISO) [46]. Day-ahead prices pair well with the real-world implementation of optimal control in buildings because strategies for the upcoming day can be evaluated the day before. Day-ahead prices have been used in many of the studies showcasing the optimal control of thermal mass [15,16,18].

#### 2.2.4 Carbon Emission Rates.

Marginal hourly CO$2e$ emission rates that reflect Security Constrained Unit Commitment (SCUC) for NYC are used throughout this study. This contrasts with the average emission rates promulgated by the Environmental Protection Agency (EPA) and more commonly adopted in the energy industry.

In Independent System Operators (ISOs) day-ahead energy markets, efficiency measures affect how many and which baseload generating plants are available for operation the next day—through a process called SCUC. In ISO real-time energy markets, efficiency measures can only then affect the optimal dispatch of such already committed baseload generating plants. The efficiency measures evaluated in this study are intended to affect SCUC in the day-ahead energy market and therefore require marginal CO$2e$ emission rates that reflect SCUC as shown in Fig. 3.

EPAs “Using eGrid for Environmental Footprinting of Electricity Purchases” excellently documents a method for using average regional emission rates for footprinting [47]. For the year 2020 in NYC, EPA recommends the use of an average CO$2e$ emission rate of 0.32 tons/MWh for footprinting. For evaluating the effect of efficiency measures at the margin, this same method recommends the use of an average fossil fuel CO$2e$ emission rate of 0.49 tons/MWh. This rate is “marginal” in that it properly reflects that efficiency measures reduce fossil plant operation, that is, do not reduce nuclear or renewable plant operation. However, this rate implicitly reflects the real-time market and not the opportunity provided by SCUC in the day-ahead market. The EPA rate also does not reflect time-of-use.

By necessity, EPA emission rates are a simplification of a significantly more complex underlying electric system. The EPA does not have the local knowledge needed to capture time-of-use or SCUC in marginal emission rates.

Figure 3 shows, first, that when a building uses electricity is just as important as how much a building uses electricity; second, those day-ahead hourly marginal emission rates are very large compared to the average emission rates suggested by the EPA; and third, those day-ahead marginal emission rates reveal a significant opportunity to reduce carbon emissions. These rates are where the red band of “High Carbon Rates” in Fig. 2 originates from. The red region represents an emission rate of 3 tons/MWh.

We acknowledge that the strength of the carbon and price signal will materially affect the control decisions. Given the wide variation of both, we chose an illustrative daily profile that highlights conditions in which carbon intensity and price variation were strong. This does not indicate that annual average performance would be in line with the findings found for this day but instead shows that strong incentive signals represent an opportunity for real-time optimization. Thus, this is a showcase rather than an expected average performance.

### 2.3 Optimization Environment.

The environment used in this article is built off the framework discussed in Sec. 1.3. Years of commercial operation and research and development have gone into improving the efficiency and flexibility of the framework. Two developments of this environment—the use of a genetic algorithm and multiple objectives—will be discussed in this section.

#### 2.3.1 Genetic Algorithms.

The optimization method used in this study was a common genetic algorithm. Typical of GA optimizations, the algorithm starts with an initial population of solutions (randomly generated within bounds and from seeded solutions), then repeatably modifies the population through subsequent generations. At the end of each step or generation, some solutions, or parents, are selected to create the children for the next generation.

There are numerous stopping criteria that can be used to determine when to stop the algorithm. Since optimization run-time was not of concern during this study, the stopping criteria were relaxed to allow sufficient exploration. The use of GAs can be applied to a variety of optimization problems. It is well suited for handling discontinuous, nondifferentiable, stochastic, or highly nonlinear objective functions.

#### 2.3.2 Multiple Objectives.

Multiobjective optimizations differ from this by computing $C1$, $C2$, to $Ck$ individually and maintaining those objectives to evaluate trade-offs between them. The result of this is a set of solutions where no individual objectives can be made better without making at least one other objective worse off. This set of solutions is said to be Pareto efficient and forms a Pareto front. To come to a singular solution, a decision rule needs to be implemented. This can be done with ranking algorithms based on objective weights or through simple engineering judgment. This study seeks to minimize two objectives, electric expense in dollars and local NYC carbon emissions in tons.

#### 2.3.3 Mathematical Formulation.

The optimization formulation for TEMP, OA, and DUAL all vary subtly due to their differing decision vector. The DUAL optimization, however, incorporates all components of the individual optimizations and so will be used to formulate the general problem. Each optimization features cost and carbon objective functions and several constraints.

**Objectives**:- Cost:(2)$Fcost(x)=min{xsch,t}t=1N\u2211t=1NretEt$
- Carbon:(3)$(x)=min{xsch,t}t=1N\u2211t=1NctEt$

**Problem Formulation**:where(4)$minF(x)=(Fcost(x),Fcarbon(x))Tsubject toCmax=1100Cz,t\u2264Cmax\u2200zfort\u2208{occupied}OAmin,unocc\u2264OAfrac,t\u2264OAmax,unocct\u2208{unoccupied}OAmin,occ\u2264OAfrac,t\u2264OAmax,occt\u2208{occupied}Tmin,unocc\u2264Tsetp,t\u2264Tmax,unocct\u2208{unoccupied}Tmin,occ\u2264Tsetp,t\u2264Tmin,occt\u2208{occupied}x=(Tsetp,OAfrac)T$$rt$ : electricity rate at time $t$

$ct$ : marginal carbon emission rate at time $t$

$Et$ : HVAC electricity consumption at time $t$

$Cz,t$ : zone $CO2$ concentration

$Cmax$ : upper $CO2$ concentration threshold

$OAmin,unocc$ : minimum unoccupied OA fraction

$OAmax,unocc$ : maximum unoccupied OA fraction

$OAmin,occ$ : minimum occupied OA fraction

$OAmax,occ$ : maximum occupied OA fraction

$Tmin,unocc$ : minimum unoccupied temperature

$Tmax,unocc$ : maximum unoccupied temperature

$Tmin,occ$ : minimum occupied temperature

$Tmax,occ$ : Maximum occupied temperature

$OAfrac$ : OA fraction hourly control schedule

$Tsetp$ : Zone temperature setpoint hourly control schedule

$xsch$ = ($Tsetp$,$OAfrac$) : combined decision vector

EnergyPlus cannot handle equality or inequality constraints directly, so to enforce constraints additional terms within the optimization were created to ensure all solutions adhered to the constraints listed earlier. These terms along with the associated constraints are shown following Eq. (4). All minimum and maximum bounds on the decision variables are configurable and do not necessarily reflect the actual operation, but rather constraints on the search space for the optimizer. For example, $OAmin,unocc$, $OAmin,occ$, and $OAmax,unocc$ are all zero in this study. Nonzero ventilation rates required during occupancy could be accommodated using this framework.

### 2.4 Optimization Parameters

#### 2.4.1 Optimization Horizons.

The two horizons of concern in this study are the planning horizon and the preconditioning horizon. As mentioned in Sec. 2.2.2, all cases take place over one 24-h period; thus, the planning horizon is 24 h. This choice was justified by the findings of Henze et al. who suggested a 24-h horizon when trying to reduce daily energy consumption or cost.

The preconditioning horizon refers to the length of time prior to the planning horizon when the building undergoes a warmup period, similar to the necessary warmup period in EnergyPlus. This was necessary since the initial thermal state of the model cannot be set explicitly. Corbin et al. [18] show that at least 5 days of simulation is necessary for cooling loads to stabilize. They go on to suggest 7 days to account for weekend effects. Seven days was used as the preconditioning horizon throughout this study. The control strategy used during the preconditioning horizon follows the default strategy laid out in Sec. 2.5. This 7-day horizon was mimicked in the DEF and DCV models, which were all simulated in energyplus external from the optimization environment.

Because the case studies are a single day, steady-periodic behavior for the control strategies is not achieved. That would require multiple simulation days, which would create different thermal histories for each of the days. Instead, we enforce the same initial conditions for each strategy and assess the extent to which both incentive signals (price and carbon intensity) trigger a change in building operation.

#### 2.4.2 Optimization Blocks.

The framework is capable of optimizing 24 individual setpoints. This, however, would create an enormous decision space to search. To reduce this space, optimization blocks were used to group hours in the planning horizon. Since this was an exploratory study, resolution was prioritized with optimization efficiency/dimension reduction left for future work.

In the case of the OA optimization, only occupied hours were optimized. This reduces the problem to a 10-h optimization. Both TEMP and DUAL allowed for pre-occupancy cooling, resulting in a higher dimension problem.

#### 2.4.3 Schedule Constraints.

An additional input that can drastically reduce the search space for the optimizer is schedule constraints. Both the temperature and OA fraction values have physical constraints. For example, the upper bound for zone temperature setpoints during occupancy is 23.89 $\u2218$C (75 $\u2218$F)—much tighter than ASHRAE Standard 55-2017, Thermal Environmental Conditions for Human Occupancy, which states that indoor temperatures between 19.44 and 27.78 $\u2218$C (67–82 $\u2218$F) are satisfactory for comfort [49]. The bounds for an OA fraction are physically constrained to 0.0–1.0. Final unoccupied and occupied bounds for schedules are discussed in Sec. 3.

### 2.5 Default Building Energy Model.

The baseline or default building energy model used throughout this analysis will be referred to as the DEF model. The ventilation is controlled with a fixed minimum OA flowrate based on design conditions. The zone temperature cooling setpoints (henceforth referred to as CLG Setpoint) follow a simple nighttime setback strategy in which the setpoint is $23.89\u2218$ C ($75\u2218$ F) starting 2 h before occupancy and off outside of occupancy. This represents the “business-as-usual” operation of the actual building.

A constant OA $CO2$ concentration of 400 ppm is used for this study. Outdoor concentrations can vary considerably depending on the location of the OA intake and should be based on measurements when implementing actual control of a building. A summary of the DEF model’s temperature and ventilation strategies is shown in Fig. 4. Zone $CO2$ concentrations shown throughout this article will always represent the maximum daily zone concentration, and ventilation will be expressed as an OA flow fraction. The OA fraction is the ratio of the OA flowrate to the supply air flowrate.

### 2.6 Demand-Controlled Ventilation Model.

The DCV baseline model is identical to the DEF model, with the exception of its ventilation control. Instead of a fixed minimum OA flowrate, the DCV model controls the OA intake via the IAQP from ASHRAE Standard 62.1 [50].

A ventilation rate of 7.5 L/s per person has been found to dilute odors from human bioeffluents to levels that will satisfy a substantial majority (about 80%) of visitors to a space and thus has been used as the basis for ventilation in many cases [51–55]. Based on that dilution rate and the activity level of office workers (1.2 met units corresponding to 0.31 L/min of $CO2$ generation), a $CO2$ concentration differential of 700 ppm above ambient ($\u2248$400 ppm) will manifest itself in the space. Accordingly, in the DCV model, the constant $CO2$ setpoint schedule was set to 1100 ppm, and the $CO2$ controller was enabled for all hours of all days. For all models, $CO2$ is stored only in air and no surface interactions were considered. A summary of the DCV model’s temperature and ventilation strategies is shown in Fig. 5. The ventilation strategy can be simply described as ensuring the minimum OA flowrate necessary to keep the indoor $CO2$ concentration below the set threshold.

### 2.7 Outdoor Air Optimization Case (OA).

The goal of a ventilation optimization is to optimally determine the amount of OA to bring in and when all while maintaining acceptable IAQ. Analogous to tapping into the thermal storage of a building, ventilation optimization taps into the storage medium of indoor $CO2$ concentration. Although much more transient, it is hypothesized that this medium also offers the potential to shed and shift electric load throughout the day.

The model for the OA optimization is the same as the DEF model except for the OA control. Ventilation is controlled via the “Controller:OutdoorAir” class in EnergyPlus. The controller has several optional fields with a complex hierarchy of precedence. The “Controller:OutdoorAir” class in the OA model was modified to take a single compact schedule capable of modulating the OA intake of the building on an hourly basis. This was accomplished by setting the “Minimum and Maximum Fraction of Outdoor Air Schedule” to the same schedule guaranteeing the OA fraction to be exactly the scheduled value. This enables the optimization environment to replace a single unique identifier, representing the OA fraction schedule, with values from the optimal decision vector.

The purpose of the OA optimization is to evaluate the HVAC electric expense and carbon emissions savings associated with the optimal control of a building’s ventilation using OA fraction setpoints as decision variables. A secondary goal was to determine whether the standard $CO2$-based DCV strategy can be improved upon if given knowledge of external influences like day-ahead energy and carbon emission rates. In addition to comparing to the DEF case, the OA optimized model will also be compared to a model featuring standard $CO2$-based DCV. Importantly, both DEF and DCV have no awareness of hourly grid energy prices or carbon emission rates. The optimizer was initially given the DCV strategy as a seed for the OA optimization. As stated in Sec. 2.4.1, the planning horizon was 24 h and the preconditioning horizon was 7 days. These horizons were constant across all optimizations.

### 2.8 Temperature Optimization Case (TEMP).

The purpose of the TEMP optimization is to evaluate the HVAC electric expense and carbon emission savings associated with the optimal control of a building’s thermal mass using cooling setpoints as decision variables.

Similar to the OA model, the model for the temperature setpoint optimization is the same as the DEF model with the exception of the cooling temperature setpoint schedule. The ventilation control is identical to that of the DEF model. Unlike the OA optimization, it is advantageous to allow the TEMP model to cycle on the HVAC system before occupancy. This functionality enables the optimizer to choose a solution similar to the well-established precooling and subcooling strategies discussed in Sec. 1.1.

### 2.9 Temperature and Outdoor Air Optimization Case (DUAL).

The temperature and ventilation optimized model, or DUAL model, is a combination of the two previous models. It features the ventilation control and the night cycle features necessary for the OA and TEMP optimization, respectively. The DUAL model is capable of manipulating both the cooling setpoint schedule and the OA fraction schedule. This allows the optimizer to consider the effects of changing both schedules simultaneously and presents the opportunity to explore synergistic effects between the two schedules.

The goal of a DUAL optimization is to optimally determine the zone temperatures and the ventilation, all while maintaining acceptable IAQ and thermal comfort. One objective of this work was to identify the extent of any synergistic effect through simultaneous optimization of both schedules. Synergistic effects in this case will refer to a result in which the DUAL optimization produces greater savings when compared to a solution from a model with the sequential optimization of temperature and OA. If the DUAL model increases savings in either of the two objectives, this indicates that a connection between ventilation and temperature control that is advantageous for HVAC electric expense and/or carbon reduction.

### 2.10 Evaluating Synergy Cases ($SeqTO$ and $SeqOT$).

To evaluate whether the simultaneous optimization of two schedules produces synergistic effects, two additional models were created and optimized. The first model will take the solution from the TEMP optimization, hard code the temperature setpoint schedule, and thereafter perform an OA optimization. The second model will take the solution from the OA optimization, hard code the OA fraction setpoint schedule, and thereafter perform a TEMP optimization. These two cases will represent two sequential optimizations. The sequential optimization of temperature followed by OA will be referred to as $SeqTO$, and the sequential optimization of OA followed by temperature will be referred to as $SeqOT$.

## 3 Results and Discussion

All results presented in this section will include absolute HVAC energy use, HVAC electric expense, and marginal carbon emissions capturing SCUC. All percentages are calculated from the default operation (DEF) model. The DEF and conventional DCV cases are shown first, followed by each single schedule optimization, and finally, the DUAL optimization and the evaluation of synergy. All results are representative of a single optimal solution chosen from a Pareto front. The diversity of the Pareto front and the decision-making for the represented optimal solutions are discussed in Sec. 3.3.3.

Important to the following results, all models include a chiller sequencing strategy that encourages chillers to be loaded according to the part load performance characteristics. The optimization implicitly optimizes chiller loading by changing the total chilled water plant load as a function of time. While only the zone temperature and outdoor air fraction setpoints are considered decision variables, these parameters indirectly impact the chiller loading. Savings accrue from preferentially operating the chilled water plant closer to optimum part load and avoiding operation at inferior part load performance. Given the region and time of year of this simulation study, chiller usage dominates the fluctuations in HVAC total power, and thus, the graphs shown below of HVAC total power are highly correlated to chiller power. Power near or below 1200 kW is indicative of a single chiller in use and anything above that is indicative of two chillers in use.

### 3.1 DEF and Demand-Controlled Ventilation Results.

Figure 6 visualizes the results of both the DEF and DCV models.

The zone temperature and cooling setpoints for the DCV case are identical to the DEF model as seen by the overlapping plots. The zone $CO2$ concentration starts the same but diverges from DEF at the start of occupancy because the DCV model keeps the OA fraction at zero and allows the zone concentration to rise at the maximum rate. At 2 p.m., the model slows the rise of $CO2$ by allowing some OA to enter the air loop. The fraction modulates to maintain a concentration below $Cmax=1100$ ppm until the end of occupancy. The practical effect of DCV is to avoid the expense of over-ventilating the building. More specifically, by not having to condition 30–34 $\u2218$C OA air down to 23.89 $\u2218$C in the middle of the day, the building was able to reduce the use of the less efficient chiller 2 and increase the use and optimal loading of the more efficient chiller 1. The optimal part load ratio (PLR) of chiller 1 and 2 are 1.0 and 0.5, respectively. The dispatch of chillers was not a direct decision variable, but merely a product of the optimizations.

The values shown in Table 3 represent the HVAC energy use, expense, and carbon emissions of a nongrid-interactive building using standard $CO2$-based DCV.

DEF | DCV | % from DEF | |
---|---|---|---|

Energy (kWh) | 21,867.94 | 19,069.73 | $\u221212.80$ |

Expense ($) | 1,295.58 | 1,120.58 | $\u221213.51$ |

Carbon (tons) | 40.23 | 35.48 | $\u221211.80$ |

DEF | DCV | % from DEF | |
---|---|---|---|

Energy (kWh) | 21,867.94 | 19,069.73 | $\u221212.80$ |

Expense ($) | 1,295.58 | 1,120.58 | $\u221213.51$ |

Carbon (tons) | 40.23 | 35.48 | $\u221211.80$ |

Though not informed by hourly energy prices or carbon emission rates, the DCV model still accomplishes significant savings when compared to the DEF model. It was able to decrease HVAC energy use by 12.80%, HVAC electric expense by 13.51%, and carbon emissions by 11.80%. This result highlights how powerful basic DCV can be in overventilated buildings.

### 3.2 OA Results.

This case represents a grid-connected building where OA optimization is informed by day-ahead energy prices and carbon emission rates—an improvement on standard DCV.

As stated in Sec. 2.7, the OA model only allowed for the optimization of OA setpoints within normal occupancy hours. This decision was based on two defining characteristics of the study and model. Since this took place in the middle of summer, there was no opportunity for economizing in the early morning and the ambient temperature never got below the zone temperature. Also, due to overnight infiltration, zone $CO2$ concentrations were at their lowest in the early morning. Allowing more OA into the air loop at this time of day has marginal effects as the concentration approaches ambient levels. With these considerations in mind, the optimization blocks for this case were defined such that the first 7 h were blocked together and not optimized, the next 10 h were individually blocked and optimized, and the last 7 h were blocked and not optimized. All nonoptimized hours were set to the minimum schedule value constraint, 0.0. As stated in Sec. 2.7, the initial maximum bound on the OA schedule was 1.0. After reviewing the strategies of DEF, DCV, and a great number of OA results, it was clear that any near-optimal strategy would almost certainly stay below an OA fraction of 0.3. With this in mind, the upper bound was lowered to 0.3, and the search space was reduced by 70%.

The OA optimization results outperformed the DCV model on all metrics. Many optimizations terminated with only one optimal solution, suggesting that optimal solutions within these constraints are fairly unique. The optimizer also found these solutions in early generations, suggesting the minimum was easy to find. The results are compiled and displayed in Fig. 7.

The OA solution is very similar to the DCV solution in that it keeps the OA fraction at zero for the morning hours and only allows OA in when necessary to keep the $CO2$ concentration below 1100 ppm. The results of the OA optimization are compared with the DCV model and summarized in Table 4.

DEF | DCV | OA | DCV % from DEF | OA % from DEF | |
---|---|---|---|---|---|

Energy (kWh) | 21,867.94 | 19,069.73 | 18,478.86 | $\u221212.80$ | $\u221215.50$ |

Expense ($) | 1295.58 | 1120.58 | 1070.53 | $\u221213.51$ | $\u221217.37$ |

Carbon (tons) | 40.23 | 35.48 | 33.69 | $\u221211.80$ | $\u221216.24$ |

DEF | DCV | OA | DCV % from DEF | OA % from DEF | |
---|---|---|---|---|---|

Energy (kWh) | 21,867.94 | 19,069.73 | 18,478.86 | $\u221212.80$ | $\u221215.50$ |

Expense ($) | 1295.58 | 1120.58 | 1070.53 | $\u221213.51$ | $\u221217.37$ |

Carbon (tons) | 40.23 | 35.48 | 33.69 | $\u221211.80$ | $\u221216.24$ |

To better illustrate the subtle differences between the DCV and OA cases, their results are overlaid in Fig. 8.

All differences between the DCV and OA results come within the period 2–5 p.m. when both electricity and carbon emission rates are highest. Both strategies succeed in reducing the use of chiller 2 throughout the day, but without external pressures from energy and carbon rates, the conventional DCV strategy overlooks the optimal loading of each chiller in the afternoon. At 2 p.m., the DCV strategy brings on both chillers at around 0.5 PLR. This is optimal for chiller two, but inefficient for the higher COP chiller 1. Conversely, the OA model brings on chiller 1 at a much higher PLR of 0.83 leaving the less efficient chiller 2 to operate at 0.09 PLR. In this hour alone, the difference between chiller loading accounted for a reduction of 205 kW for the OA case in comparison to DCV. A similar scenario occurs at 5 p.m. and results in a 321 kW reduction for the OA case. These subtle differences in chiller loading were the result of intelligently raising the OA above the DCV fraction in key hours.

The OA optimization was able to provide significant savings from DEF and outperform conventional DCV. The OA results shown in Table 4 represent a grid-interactive building with optimal control of its ventilation.

The OA optimization was able to increase savings from DCV in all categories. It decreased energy by 15.50%, HVAC electric expense by 17.37%, and carbon by 16.24% when compared to DEF. Reductions when compared to DCV are much less, which points again to the strength of DCV as a ventilation strategy. From DCV, the OA optimization saved an additional $50 and 1.79 tons of carbon.

### 3.3 TEMP Results.

The TEMP model was meant to act as a business-as-usual strategy for thermal mass control. The optimizer selected a zone temperature setpoint schedule that best met the two objectives. The results are compiled and displayed in Fig. 9.

In anticipation of the hot afternoon hours, the optimizer chose to begin cooling the building at 1 a.m. Differences in the zone $CO2$ concentration are attributed to the building being pressurized earlier due to the precooling period. This resulted in the concentration leveling out for the remaining pre-occupancy hours because no infiltration was coming in and generation of $CO2$ from occupants had not begun. In the HVAC power plot, several intelligent control decisions can be deducted. The building was able to reduce the use of chiller 2 when possible and load chiller 1 at a PLR closer to its optimal. By precooling and intelligently loading chillers, the optimizer was able to shift a significant amount of load out of the high energy and carbon period.

The TEMP model significantly outperformed the DEF model by having knowledge of day-ahead energy and carbon emission rates. The TEMP results shown in Table 5 represent a grid-interactive building with optimal control of its thermal mass.

DEF | TEMP | % from DEF | |
---|---|---|---|

Energy (kWh) | 21,868 | 20,817 | $\u22124.8$ |

Expense ($) | 1296 | 1080 | $\u221216.7$ |

Carbon (tons) | 40.2 | 31.6 | $\u221221.4$ |

DEF | TEMP | % from DEF | |
---|---|---|---|

Energy (kWh) | 21,868 | 20,817 | $\u22124.8$ |

Expense ($) | 1296 | 1080 | $\u221216.7$ |

Carbon (tons) | 40.2 | 31.6 | $\u221221.4$ |

With knowledge of carbon and energy rates as well as having the flexibility to manipulate zone temperature schedules, the TEMP model was able to achieve considerable savings when compared to the DEF model. It decreased HVAC electric expense by 16.7% and carbon by 21.4%. The subtle reduction in consumption was expected, for two reasons. First, site energy use is often a poor surrogate for source economics and carbon emissions. Second, minimizing energy use was not an explicit optimization objective. However, even with significant HVAC energy use in the morning hours due to precooling and subcooling, the model still reduced HVAC energy in comparison with DEF.

#### 3.3.1 DUAL Results.

The DUAL case is a combination of the decision vectors of both individual schedule optimizations. In an attempt to start the optimizer closer to a potentially optimal solution, an initial seed was made combining the solutions from the TEMP and OA optimizations. This solution represented a pseudo-sequential optimization. This pseudo-sequential model was run externally to obtain HVAC electric expense and carbon emission values for comparison. After these changes were made, a solution was obtained that improved on the pseudo-sequential model, but only in terms of carbon and not cost. The length of the optimization was again the limiting factor. To effectively continue the optimization where it left off, the solution from that optimization was given to a new run as the initial seed. The final optimization terminated again based on the 30,000-s time limit after completing 72 generations. Many of the 72 generations were exactly the same, with little to no improvement between generations. The results from that run were compiled and displayed in Fig. 10.

The DUAL solution closely resembles the TEMP solution due to temperature setpoints having a much larger impact on chiller electricity use. The details of the chiller loading will be discussed in Sec. 3.3.2 where synergy is evaluated. The notable difference in the temperature setpoint portion of the solution is the start time. In the TEMP case, the optimizer chose to lower the setpoint and turn the HVAC system on at 1 a.m., while in the DUAL case, the optimizer waited until 3 a.m. Although these hours have very low energy and carbon rates, 2 h of operation in a building this large adds up quickly. The differences in the OA fraction strategy are much larger when compared to the OA optimization. Instead of waiting until the final hours of the day to ventilate, the optimizer chose to front-load the intake of OA. As a result, the OA fraction was able to be 0.0 during the most costly hour of the day at 4 p.m. Despite this drastic shift in OA scheduling, the model stayed below $Cmax=1100$ ppm, peaking at 1099 ppm.

The DUAL optimization provided the highest savings when compared to the DEF model. The DUAL results shown in Table 6 represent a grid-interactive building with optimal control of its thermal mass and ventilation.

DEF | DUAL | % from DEF | |
---|---|---|---|

Energy (kWh) | 21,868 | 19,339 | $\u221211.6$ |

Expense ($) | 1,296 | 1,005 | $\u221222.5$ |

Carbon (tons) | 40.2 | 29.9 | $\u221225.6$ |

DEF | DUAL | % from DEF | |
---|---|---|---|

Energy (kWh) | 21,868 | 19,339 | $\u221211.6$ |

Expense ($) | 1,296 | 1,005 | $\u221222.5$ |

Carbon (tons) | 40.2 | 29.9 | $\u221225.6$ |

The DUAL optimization was the best-performing solution providing the largest savings in both expense and carbon. It decreased expense by 22.5%, and carbon by 25.6% when compared to DEF. The DUAL case also kept total HVAC energy use below that of the TEMP optimization while performing similar load shifting.

#### 3.3.2 Evaluating Synergy.

Synergy is defined as the interaction or cooperation of two or more agents to produce a combined effect greater than the sum of their separate effects. Using this definition, the DUAL case does not show synergy. This is due to the structure of the study. Since each strategy is being performed on the same building during the same time, the savings associated with one case overlap with the savings from another case. The consequence of this is the sum of their separate effects would effectively double count savings in certain hours. For this reason, the sum of the separate effects represents an unattainable, unrealistic comparison for synergy. This prompted the definition of a new type of synergy when comparing different optimizations of the same building. Synergy in this case is the joint optimization of two strategies producing an effect greater than the *sequential* optimization of the two strategies. In the case of analyzing two strategies, two variations of sequential optimizations are possible. Strategy 1 followed by strategy 2, or strategy 2 followed by strategy 1. These cases are compared to the DUAL case in Figs. 11 and 12.

By jointly optimizing both schedules, the DUAL case reacted to the slightly higher $CO2$ concentrations caused by the 3 a.m. start time and modulated its OA intake accordingly. The DUAL case also timed these spikes in ventilation with hours of operation that already required the use of both chillers. By doing this, the DUAL model was lowering its $CO2$ concentration with little to no additional cost. Similar to the TEMP optimization, the DUAL case showed heavy use in the 9 a.m. – 12 p.m. period prior to the higher-priced energy and carbon emission rates. Unlike the TEMP and $SeqOT$ though, the DUAL case completely eliminated the use of chiller 2 during the high-priced 1–6 p.m. period. This was accomplished by optimally loading chillers, leading into the period and dropping the ventilation rates to lower the cooling load on the coils.

The $SeqTO$ came closest to the DUAL strategy. These two cases were the only strategies capable of completely eliminating the use of chiller 2 during the high-cost period. That was the key to optimizing this particular analysis day. If the model had the capability to do some form of precooling and could optimally load the chillers in the middle of the day, it was able to coast through the costly hours. Strategies like this produce their highest use from 9 a.m. to 12 p.m. This poses no issue from an operational standpoint and actually serves to benefit areas with increasing solar PV utilization. This period overlaps well with solar PV generation. Demand curves like those shown in Fig. 12 are exactly what solar generators prefer to see. The results of the DUAL, $SeqOT$, and $SeqTO$ models are summarized and compared in Table 7.

DUAL | $SeqTO$ | $SeqOT$ | $SeqTO$ % from DUAL | $SeqOT$ % DUAL | |
---|---|---|---|---|---|

Energy (kWh) | 19,339 | 19,881 | 17,489 | 2.81 | –9.6 |

Expense ($) | 1005 | 1024 | 1008 | 1.96 | 0.3 |

Carbon (tons) | 29.9 | 30.3 | 32.0 | 1.24 | 7.1 |

DUAL | $SeqTO$ | $SeqOT$ | $SeqTO$ % from DUAL | $SeqOT$ % DUAL | |
---|---|---|---|---|---|

Energy (kWh) | 19,339 | 19,881 | 17,489 | 2.81 | –9.6 |

Expense ($) | 1005 | 1024 | 1008 | 1.96 | 0.3 |

Carbon (tons) | 29.9 | 30.3 | 32.0 | 1.24 | 7.1 |

The DUAL optimization subtly increased savings from both sequential optimizations, thus showing synergistic effects. The DUAL case performed better in all categories against both models except for energy when compared to the $SeqOT$ case. This is expected when comparing two cases where one had little to no precooling, and as stated previously, energy reduction was not an objective. The DUAL case decreased energy by 2.81%, HVAC electric expense by 1.96%, and carbon by 1.24% when compared to $SeqTO$. It decreased HVAC electric expense by 0.3%, and carbon by 7.1% when compared to $SeqOT$. Overall, results improved only marginally from sequential optimizations. However, the DUAL optimization took the best expense reduction from $SeqTO$ and the best carbon reduction from $SeqOT$ and improved on both. This was achieved with a unique ventilation strategy as well, which further points to the synergy between the joint optimization of temperature and ventilation schedules.

#### 3.3.3 Pareto Results.

As mentioned in Sec. 2.3.2, a multiobjective optimization has the potential to produce a Pareto front of solutions showcasing the trade-off between two or more objectives. The Pareto front for the DUAL case is shown in Fig. 13. The DEF solution is included on the graphs for reference. Overall, there was little diversity in Pareto solutions. In this case, diversity refers to the average distance between individual solutions. For example, the TEMP optimization produced 22 unique solutions within less the $1 of cost and two-tenths of a ton of carbon.

The DUAL results also exhibited lack of diversity. The optimal solution and two other unique Pareto solutions are right on top of each other, with the fourth solution having a slightly lower cost at the expense of approximately 1.5 tons of carbon. Optimal solutions were chosen from the Pareto front based on the marginal cost of carbon.

## 4 Conclusions

Improving the demand flexibility of buildings will become increasingly important over the next decade as intermittent sources of energy such as PV and wind become a larger percentage of the overall electric energy generated. The ability to predictively and efficiently match generation will require advanced HVAC control. Much has been done to optimally control the thermal mass of buildings using zone temperature setpoints as decision variables. Another opportunity to improve the efficiency and expand the flexibility of buildings comes in the form of optimal ventilation control. Ventilation, like zone temperatures, has a considerable effect on the power consumption of a building. This is especially true in the most important hours when utilities set their peak demands and when electric prices and carbon emission rates are at their highest. This opportunity is magnified in a postpandemic world as lower and more variable occupancy means that buildings require more flexibility to meet IAQ objectives with less OA than in the past.

Functionality was added to an existing optimization environment, allowing for a fractional OA schedule to be optimized both individually and jointly with temperature schedules. This led the way for the framework of a novel dual optimization of hourly temperature and OA fraction setpoints to be presented. This case was explored within the context of a multiobjective optimization between HVAC electric expense and carbon emissions.

Two individual optimizations were performed, a zone temperature and OA fraction optimization. Both cases effectively reduced electric expense and carbon emission when compared to both the DEF and DCV strategies. Two sequential optimizations were also performed, zone temperature followed by OA fraction and OA fraction followed by zone temperature. Both cases improved upon the savings of the respective individual optimizations proving that additional control points can result in greater benefits. Given the current optimization framework, if load shifting is of higher importance, it is suggested that zone temperature be optimized first followed by OA to allow the optimizer the most freedom in choosing temperature setpoints.

One dual optimization was performed to evaluate the potential synergy of jointly optimizing zone temperature and OA fraction schedules. When compared to the sequential optimizations of two schedules, the DUAL case outperformed both in each of the objectives. The DUAL case took the best attributes of each strategy and saved the most money and carbon of any optimization. The resulting strategy also created a mid-day peak demand, which happens to align well with common solar PV generation profiles. The DUAL case thus not only reduces the most cost and carbon but also creates a new demand curve suitable for increasing renewable generation, further aiding in use cases such as NY State’s Local Law 97 mentioned in Sec. 2.2.

### 4.1 Future Work.

The ability to optimize an hourly OA ventilation schedule jointly with temperature setpoints allows for countless control strategies to be explored. The full extent to which these strategies can increase the flexibility of buildings has not been completely evaluated. This study took place for 1 day in July to aid in isolating the effects of different optimization techniques. To fully understand the potential of ventilation and dual optimizations, the scale and scope of the study should be increased. Optimizations should be extended to evaluate opportunities on other nonpeak weekdays or weekends. Optimizations should be extended to weeks and months to evaluate the compounding effects of such strategies. The seasons in which these cases are considered should be explored as well. Evaluating ventilation and dual optimizations under these scopes have the potential to shed light on how complex ventilation optimization actually is. If heuristics begin to emerge across certain days of the week, or seasonally, dimensionality has the potential to be decreased yet again by adjusting constraints and parameters based on those time frames. Finally, rules could be extracted from the optimization runs and such enhanced rules can be compared to full optimizations in previously unseen cases [56]. If rule extraction achieves 80% of the benefits for 20% of the effort of full online optimization, the door may be opened to widespread deployment.

## Acknowledgment

G. P. Henze discloses his role as technology advisor and co-founder of QCoefficient, Inc. V. J. Cushing discloses his role as Chief Technology Officer and co-founder of QCoefficient, Inc.

## Funding Data

The Solar Energy Technology Office of the U.S. Department of Energy under Contract No. DE-SC0018855 to QCoefficient, Inc. with a subaward to the University of Colorado Boulder.

## Conflict of Interest

Conflicts of interest have been declared to the Editor and will be included in a Conflict of Interest Declaration section of the final paper.

## Data Availability Statement

Weather and electricity price data supporting the findings of this study are openly available on corresponding public databases [45,46]. Carbon emission data that support the findings of this study are available from the authors upon reasonable request. The building energy model is not available, due to commercial restrictions.