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Adaptive Energy Optimization Toward Net-Zero

Energy Building Clusters

Article in Journal of Mechanical Design · April 2016

DOI: 10.1115/1.4033395

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 ADAPTIVE ENERGY OPTIMIZATION TOWARDS
NET-ZERO ENERGY BUILDING CLUSTERS

Philip Odonkor
Graduate Research Assistant, Department of Mechanical and Aerospace Engineering
University at Buffalo-SUNY
Buffalo, NY 14260
podonkor@buffalo.edu

Kemper Lewis∗
Professor, Department of Mechanical and Aerospace Engineering
University at Buffalo-SUNY
Buffalo, NY 14260
kelewis@buffalo.edu

Jin Wen
Associate Professor, Civil, Architectural, and Environmental Engineering Department
Drexel University
Philadelphia, PA 19104
jinwen@drexel.edu

Teresa Wu
Professor, School of Computing, Informatics, Decision Systems Engineering
Arizona State University
Tempe, AZ 85287-5906
teresa.wu@asu.edu

ABSTRACT
Traditionally viewed as mere energy consumers, buildings have adapted, capitalizing on smart grid technologies
and distributed energy resources to efficiently use and trade energy, as evident in net-zero energy buildings. In
this paper, we examine the opportunities presented by applying net-zero to building communities (clusters). This
paper makes two main contributions: one, it presents a framework for generating Pareto optimal operational
strategies for building clusters; two, it examines the energy tradeoffs resulting from adaptive decisions in response
to dynamic operation conditions. Using a building cluster simulator, the proposed approach is shown to adaptively
and significantly reduce total energy cost.

NOMENCLATURE
ηconv AC/DC converter efficiency (%)
ηinv AC/DC inverter efficiency (%)
ηmj Chilled water distribution percentage (%)

∗ Corresponding Author.
MD-15-1676 1 Lewis
fNZB,m Net-zero cost energy balance for building m ($/day)
Hk Number of hours in operation mode k
j Time (1 − 24 hours)
k Operation mode
m Building number
m
Pbat, Battery charge/discharge energy consumption (kWh)
j
Pbch, j Base chiller power consumption at time j (kWh)
Pdch, j Dedicated chiller power consumption at time j (kWh)
m
Pload, Gross non-cooling electrical load (kWh)
j
m
Pnc, j Non-cooling electrical consumption (kWh)
m
Pp, Energy purchased at time j by building m (kWh)
j
m
PPV, Energy generated by PV at time j for building m (kWh)
j
Ps,mj Energy sold at time j by building m (kWh)
Psc, j Shared cooling power consumption (kWh)
Qmj Chilled water demand from building m at time j (Btu/hr)
Qmax, j Maximum chiller capacity at operation time j (Btu/hr)
Rmp, j Energy purchase price at time j for building m ($/kWh)
Rms, j Energy sold at time j by building m (kWh)
m
Sbat, State of Battery
j
Sis, j State of Ice Storage
m
SPV, State of PV Panel
j
SOCbat, j Battery state of charge at time j for building m
SOCbat,max Maximum battery state of charge
SOCbat,min Minimum battery state of charge
SOCis, j Ice storage state of charge at time j
SOCis,max Maximum ice storage state of charge
SOCis,min Minimum ice storage state of charge
Tlbm Lower indoor set-point limit (◦ F)
m
Tsp, j Temperature-setpoint (◦ F) at time j for building m
m
Tsp, j Temperature Set-point
m
Tub Upper indoor set-point limit (◦ F)

1 INTRODUCTION

The current drive towards energy sustainability has played witness to rising interests in the mitigation of energy use

within the building sector. With estimates placing electricity use as high as 74% of the total electricity production in the

United States (US) [1], the need for a new approach to energy management has become urgent, if not critical. This has in

part led to a radical rethink of the role buildings play in the energy ecosystem. Traditionally relegated to the spectator role

in terms of negotiating for energy and actively controlling energy consumption, buildings have now assumed a pivotal role.

They are increasingly expected to achieve high efficiency and comfort standards [2], while maintaining economic feasibility.

With the promise of smart grid and on-site energy generation technologies, the opportunity for buildings to assume the

mantle of maintaining energy security, efficiency and sustainability for the future has never been greater, and has paved the

way for the potential of net-zero energy buildings (NZEBs) to be fully realized.

Net-zero energy buildings promote the idea of energy self-sufficiency through the cyber-physical interactions of energy

efficient buildings, smart grids and renewable energy generating systems. In this context, net-zero conforms to the “cost

NZEB” definition provided in [3] by focusing on achieving a zero annual energy bill. This process is characterized by a

reduction in energy demand by way of energy optimization, and complimented with renewable energy generation to offset

remaining energy deficits. A review of net-zero energy definitions can be found in [3–5].

MD-15-1676 2 Lewis
 With net-zero energy buildings moving into the national spotlight in recent years, there has been promising signs of rapid

integration into both building design practice and US energy policy and initiatives. The Energy Independence and Security

Act (EISA) [6] for example, passed in 2007, is one of many initiatives authorized by the Department of Energy (DOE) to

foster the development and adoption of net-zero buildings in an effort to make them marketable. Additional energy-related

Federal mandates including Executive Order 13514 and the Energy Policy Act of 2005 (EPACT) - further support Net Zero

strategies, calling for 100% adoption of net-zero in all federal buildings by 2030.

As net-zero becomes widely adopted; the next step in its progression will be to expand its scope. Net-zero energy

building clusters address this by extending the idea of NZEBs beyond single ownership buildings and applying it towards

multiple buildings. The innovativeness of this idea hinges on the shift from individual building systems to a distributed

cyber-physical system capable of exploiting the inter-dependencies present in building communities such as shared energy

storage and collaborative load management. We envision that similar to an ecology system; when individual buildings are

allowed to freely exchange energy and information, the entire building cluster will converge to a state of maximum efficiency.

There has been significant groundwork towards exploring the benefits of net-zero building clusters. This comes in the

wake of stringent directives from [6] and [7], which by law require the US Army to completely eliminate the use of fossil

fuels in all new and renovated military complexes by 2030. While net-zero energy building clusters offer several promising

opportunities, they also present a host of challenges. Despite being deployed independent of each other and operated under

varying time and space scales, systems within NZEB clusters are expected to synergistically achieve strict energy and comfort

targets. From an operational strategy standpoint, the challenge of leveraging this heterogeneity towards realizing net-zero

goals serves as the motivation for this work.

2 PREVIOUS WORK

The initial study of building operation and control research has focused on building thermal mass [8]. With regards to

reducing operational costs, conventional operational strategies have largely failed to utilize the thermal storage capabilities

of building structures [9]. A growing body of literature highlights this and demonstrates the benefits of strategies such as

pre-cooling, towards reducing peaking cooling loads and energy cost [10–12]. With as much as 20% of building energy

wasted due to poor HVAC control strategies [13], extensive work has also been conducted to optimize HVAC control within

buildings. In [14], the authors demonstrate a 7% cost saving compared with existing control methods by developing a

metaheuristic-evolutionary programming approach to optimize HVAC control. Zaheer-uddin and Zheng [15] also explored

the problem of computing optimal HVAC control strategies for time-scheduled operation, taking into account building sched-

ules and weather forecasts. In more recent work, Ma et. al. [16] demonstrated the effectiveness of adopting an economic

model predictive control approach to reducing HVAC demand costs.

Away from HVAC systems, studies have been reported which investigate the potential of hybrid renewable energy

systems (HRES), along with integrated energy storage systems towards offsetting energy demand and cost. Mazhari et

al. [17] developed simulation tools for HRES sizing and for generating optimal operational decisions with respect to energy

price. Similarly, the authors in [18] present a methodology for the design and optimal operation of HRES. In their paper,

MD-15-1676 3 Lewis
the receding horizon optimization technique is leveraged to allow for the integration of real-time weather forecasting and

demand response (DR). Marano et. al. [19] applied dynamic programming techniques towards the optimal management of

HRES, coupling PV panels and wind turbines with a compressed air energy storage (CAES).

While these emerging efforts present promise, most of them primarily target operational strategies for single subsys-

tems, namely, HVAC, energy storage or energy generation. Considering that net-zero energy building clusters rely on the

cyber-physical interactions of multiple building subsystems, it is imperative to expand this scope to consider multi-system

interactions. To this end, Hu et al. [13] present a decentralized decision framework which models multi-building system

interactions to generate Pareto optimal operational strategies. They demonstrate from an energy efficiency standpoint that

building clusters are notably better than single buildings [8, 13]. The computational performance of the decision framework

was later improved using an augmented multi-objective particle swarm optimization (AMOPSO) algorithm in [8]. With a

similar interest, but with a focus on net-zero energy cost, Odonkor et al. [20] demonstrated how the agent based decision

framework in [13] can be applied towards net-zero building clusters based on an 8 hour operation horizon.

The computational expense posed by the algorithms used in [13, 20] however prohibited the application of hourly op-

erational strategies. Moreover, the frameworks failed to fully appreciate the dynamic environment within which buildings

operate, opting for static profiles for factors such as occupant preferences. To address these shortcomings, this paper makes

two main contributions. The first contribution extends the work in [13] and [20] by developing a bi-level decision frame-

work capable of generating adaptive, hourly operational strategies. Furthermore, its scope is expanded to allow for dynamic

changes in, and response to, energy price, energy consumption and indoor occupant comfort preferences. The second con-

tribution employs the fast elitist multi-objective genetic algorithm (NSGA-II) [21] to identify and examine Pareto optimal

operational strategies and energy cost tradeoffs within the NZEB cluster.

The remainder of the paper is structured as follows. Section 3 introduces the NZEB cluster emulator used in this work.

This is followed by an in-depth look at the adaptive decision model in Section 4. The overall system formulation is presented

in Section 5 and Section 6 combines the results of the various tests performed on the proposed framework. Finally, Section

7 presents our conclusions.

3 NET-ZERO BUILDING CLUSTER EMULATOR

A fundamental precursor to developing the proposed decision framework is the need for a net-zero energy cost building

emulator to allow for energy simulations and operational strategy testing. Selection of a suitable model is based primarily

on the level of detail required, simulation objectives, available knowledge and computational resources [22].

With operational strategy optimization serving as the main focus of this work, a detailed building model was not required.

This is because the optimization process is iterative in nature, requiring several objective function calls. As a result, the

simplified building model developed in [13] was used in this work to simulate the energy flows within a commercial net-zero

building cluster. This model affords us the ability to explore many more solutions in a timely fashion.

Exclusively developed in MATLAB, the model is composed of two distinctly sized buildings (see Table 1) with different

mass levels. Mass level, a property of wall density, represents a building’s ability to utilize its structural mass for thermal

MD-15-1676 4 Lewis
storage. As seen in Table 1, the heavy mass building is associated with denser walls.

The emulator is composed of five main subsystem models; (i) building consumption model; (ii) chiller model; (iii) ice

storage model; (iv) battery model; and a (v) photovoltaic model. In addition, three input parameters are required to fully

initialize the model, namely, dry/wet bulb temperature, solar radiation on inclined surfaces, and real-time energy pricing

rates. Table 2 provides a summary of the models and parameters used to develop the emulator. These models and parameters

were sourced from relevant literature, industry practices, and validation experiments.

Each building within the cluster is equipped with a photovoltaic (PV) system to allow for energy generation, and a

battery to allow for energy storage. With resource sharing serving as the most fundamental idea in net-zero building clusters,

the two buildings are setup to share a single base chiller and ice storage system. An overall schematic of the emulator is

illustrated in Figure 1.

The arrows in Figure 1denote the flow of energy between system components, with arrows originating from the shared

cooling block representing the flow of chilled water, and arrows originating from the power grid and both buildings repre-

senting electricity flow. Compared to the electricity demands of the shared cooling system, the combined electricity output of

the PV and battery systems are relatively small. As such, their role within the model is limited to only satisfying non-cooling

building loads. The PV system can alternatively sell electricity to the power grid or charge the battery if needed. While both

systems can be sized up to meet the higher electricity demands of shared cooling, this process introduces system scaling

challenges which however extend beyond the scope of this work. As a result, the shared cooling system in this paper draws

its full electricity load from the energy grid, as illustrated in Figure 1. Figure 1 also shows the flow control valves and on/off

control valves used to control the flow of energy within the building cluster. In all, there are a total of 15 control valves. The

operational strategies developed by the proposed decision model will be responsible for controlling the operation of these

valves on an hourly basis. The adaptive decision model, which is examined in the next section, is tasked with finding the

best configuration for each of these valves in order to minimize energy costs while maintaining an acceptable comfort level.

Comfort level is measured using the Predicted Percentage Dissatisfied (PPD) metric, with an acceptable level being anything

below 10%. This metric is explored further in section 4.2.

4 ADAPTIVE BUILDING DECISION MODEL

One of the main objectives of this work is the ability to adaptively respond to dynamic changes in energy price, energy

consumption and indoor occupant comfort preferences. Should there be any fluctuations in energy price, the model is

capable of reconstructing its operational strategies in order to realize new energy cost savings. Moreover, being able to

handle varying energy prices allows the model to accommodate multiple energy pricing plans within the same building

cluster. The following section provides further insights into the dynamic pricing model used.

4.1 Dynamic Energy pricing

The energy pricing structure used for this work was obtained from the Salt River Project (SRP) Company website [23].

Two energy plans were considered, with energy plan 1 representing an SPR EZ-3 plan and energy plan 2 representing a

MD-15-1676 5 Lewis
Time-of-Use (TOU) energy plan. Table 3 provides an overview of the energy plans used. Having multiple energy plans

allows us to not only test the decision model’s ability to handle variations in energy price, but also examine its ability to

leverage these variations towards energy cost savings.

The next area of interest is dynamic occupant comfort preferences. This focuses on the changing tolerances of building

occupants to indoor temperature. In both [13] and [20], comfort preference was assumed to be static. Realistically though,

we know this is not the case. Our model addresses this by allowing preferences to be changed on a daily basis. The following

section highlights the the method by which occupant preferences were modelled and allowed to vary within the model.

4.2 Dynamic Occupant Comfort Preferences

Variations in thermal comfort within a building can be attributed to changes in occupant comfort preferences and indoor

temperature, both of which are functions of thermal comfort as shown in Eqn. 1.

Thermal Comfort= f(Temperature Set-point,Occupant Preference) (1)

Thermal comfort is measured using Predicted Percentage of Dissatisfied (PPD) [24], a metric which establishes a quan-

titative prediction of the percentage of occupants that will be dissatisfied with thermal conditions within a given space. PPD

is formulated in Eqn.2 as

h  i
PPDmj = 100 − 95 × exp − 0.03353 × PMV jm )4 + 0.3179 × PMV jm )2 (2)

where predicted mean vote (PMV) is a function of temperature set-point, mean radiant temperature, relative humidity, air

velocity, thermal clothing resistance and metabolic rate. Details regarding the calculation of PMV is provided in Fanger [25].

For the purpose of introducing dynamism in occupant comfort preferences, we leverage two variables from Fanger’s

PMV model which lend themselves well for our purposes; the dynamic predictive clothing level (influenced primarily by

outdoor temperatures) and the activity level of building occupants (influenced by building function, time of day, etc.).

Dynamic predictive clothing level allows us to vary the clothing level of building occupants within the simulation, which

in turn varies their preferences towards indoor temperature. Activity level on the other hand allows us to vary the activity

levels of building occupants within the simulation. As with the clothing level, different levels of activity elicit different

tolerances to indoor temperature. Varying both of these values allows us to simulate the dynamic and unpredictable nature

of occupant preferences within the simulation.

Table 4 shows the different levels associated to three clothing types typically worn during the summer months depending

on the outdoor temperature. Typically, a static clothing level value is used to represent the clothing level for an entire season.

However, in this work, selection of the clothing level was done based on outdoor temperature.

Table 5 catalogs the metabolic rates corresponding to typical activities performed in office buildings. Instead of using

a single static value, the decision framework selects a value based on the activity occurring within the building. This works

well for buildings with varying activity levels based on set schedules or time of day. The ability to adapt to different activity

levels enables the optimizer to maintain comfort in light of changing occupant preferences and behavior.

Finally, dynamic non-cooling loads allow us to test the model’s performance in light of fluctuating energy demands.

MD-15-1676 6 Lewis
Although the non-cooling loads used in [13] and [20] varied on an hourly basis, the profile shape remained static for every

simulation. This was done out of necessity in order to maintain the same non-cooling consumption across all simulations.

The current model allows for this as well, but it does so while varying the shape of the consumption profile, requiring the

model to adapt. The next section provides insights into the consumption model used to generate the non-cooling profiles

used in this work.

4.3 Dynamic Non-Cooling Energy Consumption

Non-cooling loads are primarily composed of plug loads, which refer to all the energy consumed by various equipment

plugged into electrical outlets within the building. The decision to incorporate non-cooling loads within the model is sup-

ported by previous work, with Metzger et al. in [26] noting the importance of plug loads with respect to energy efficiency,

and highlighting the need for plug load reduction strategies. While active plug load management is beyond the scope of

this work, we expect the decision model to be capable of leveraging the flexible schedules of energy storage and renewable

systems to ensure that non-cooling demands are fully met in a cost effective fashion. Using a scale-down non-cooling load

model derived from [27], two distinct non-cooling profiles based on Energy Plan 1 were generated as illustrated in Figure 2.

The total energy consumed in both profiles is equal, measured at 25.89 kW each. In addition, the energy consumed

during peak periods in both profiles is also equal, measured at 8.86 kW each. A point worth noting is that 25.89 kW

represents the total non-cooling load, not the total energy consumption of the building.

The reasoning behind setting the energy consumptions in both profiles equal to each other is because a truly adaptable

system should theoretically be capable of realizing avenues for profile specific energy cost savings, despite both profiles

having equal consumptions. Furthermore, with energy costs serving as the main measure of energy cost savings in this work,

it is necessary to ensure that the proportion of energy used during peak time, when energy is most expensive, is maintained

across both profiles. This condition is however not required for pre-peak and off-peak time periods across both profiles since

energy price during both periods are identical. To account for the size difference between the buildings in the cluster, the

magnitude of the energy demand applied to the heavy mass building is taken to be twice as large. In other words, the heavy

mass building non-cooling load is taken to be 51.78 kW. Having examined the main dynamic variables in the model, the next

section introduces the decision variables of interest in this work.

4.4 Decision Variables

In formulating the decision model, five decision variables were considered. These variables were selected due to their
m ,a
significant impacts on total energy consumption as demonstrated in [13]. The first of which is temperature set-point, Tsp, j

continuous variable constrained between 72◦ F and 81◦ F, representing the indoor building temperature. The subscript sp is

short for ”set-point” and j refers to the time of day, while the superscript m refers to the building number. This variable can
m
be independently varied for each building to minimize energy costs. In addition, with reference to Eqn. 1, we note that Tsp, j

has a direct effect on thermal comfort.

The second decision variable considered in this work relates to the distribution of chilled water within the building

MD-15-1676 7 Lewis
cluster. The variable ηmj is used to quantify the distribution of chilled water (used for cooling) from the ice storage unit to

each building within the cluster. The subscript j refers to the time of day, while the superscript m refers to the building

number. As with the temperature set-point, this is a continuous variable, and has a range between 0% and 100%. The
m , Sm , and Sm
last three variables under consideration; Sis, j bat, j PV, j are related to the operation states of the ice storage, battery

and photovoltaic systems respectively. The subscripts is, bat and PV represent ”ice-storage”, ”battery” and ”photovoltaic”

respectively, while j refers to the time of day, and the superscript m refers to the building number. These variables are

discrete in nature, employing integer values between 0-3 to represent actual system states as shown in Table 6. Collectively,

these decision variables (summarized in Table 6) can be used to develop optimized operational strategies in NZEB clusters.

The envisioned idea behind NZEB clusters allows for the possibility of having multiple buildings with unique functions

and owners within one cluster. In such a scenario, it may be infeasible to subject the entire cluster to the same operational

strategy. As such, it makes sense to allow each building to make customized operational decisions to suit their respective

needs in light of the overarching net-zero goals. This is achieved by separating decision variables into two main groups:

coupled and decoupled variables. Decoupled variables represent the collective group of variables which are independently

controlled by each building. Variables such as temperature set-point are unique to each building, and hence can be regarded

as decoupled variables.

Coupled variables on the other hand refer to the collective group of variables which are jointly controlled by at least

two or more buildings within the cluster. These variables cannot be altered without some level of cooperation between the

associated buildings. The state of ice storage’ is an example of a coupled variable because the ice storage system is shared

among all the buildings within the cluster. This same classification system can be extended to the system constraints. System

constraints can be decomposed into coupled or decoupled constraints, with decoupled constraints being building specific

while coupled constraints affect the entire building cluster.

4.5 Bi-Level Decision Framework

By separating decision variables based on scope, this decomposition approach allows for a bi-level decision framework

to be developed. This approach is heavily influenced by some of the hierarchical optimization architectures used in multi-

disciplinary design optimization (MDO) [28–30]. The decomposition structure for example draws influence from the Con-

current Subspace Optimization architecture (CSSO) [31], as well as the Bi-level Integrated Systems Synthesis (BLISS) [32]

architecture.

Each level within the framework is tailored to work on a specific decision problem, namely (i) the minimization of

energy consumption on the individual building level and (ii) the minimization of energy consumption of the entire building

cluster. The resulting two-tiered decision framework is illustrated in Figure 3.

4.5.1 Building Agents

Level 1 is composed of heuristic optimization engines referred to as building agents. Building agents are responsible

for independently minimizing energy consumption at the individual building level through the optimization of decoupled

MD-15-1676 8 Lewis
decision variables. However, of the three decoupled decision variables, only two are considered at this level, namely (i) state
m , and (ii) state of PV panel, Sm . Temperature set-point, T m , is reserved for level 2 because it requires a
of battery, Sbat, j PV, j sp, j

response from the cooling system (a coupled system), which is beyond the scope of the building agents.

The building agent objective function is expressed as a minimization of the building’s non-cooling load. The building
m (kW h), lends itself well to be used for this purpose because it represents the building’s total energy
non-cooling load, Pnc, j

consumption, excluding energy used towards the cooling of the building. Lighting loads and plug loads factor into it, in

addition to energy acquired from the energy grid specifically for charging the building’s battery system.

Mathematically, the non-cooling load of building m at time j can be expressed as shown in Eqn. (3).

m m m m m m m m m m
Pnc, j = max(Pload, j − Pbat, j ηconv BIbat, j (2) − PPV, j ηinv BIPV, j (2), 0) + max(Pbat, j BIbat, j (1) − PPV, j BIPV, j (1), 0)/ηconv (3)

This equation captures the energy flow occurring at the building level. To evaluate the non-cooling load, two max

function terms are used. The first term compares the difference between the gross building non-cooling load for building m,
m
at time j (Pload, m m
j (kW h)) as well as the amount of load satisfied by both the battery (Pbat, j ηconv BIbat, j (2)) and PV system
m η BI m (2), 0) of building m, at time j, to zero. This term assumes the larger of the two values. Similarly, the second
(PPV, j inv PV, j
m BI m (1)) and
term compares the difference between the total load used to charge the battery of building m, at time j (Pbat, j bat, j
m BI m (1), 0)/η
the proportion of the said battery charging load satisfied using PV energy from building m, at time j (PPV, j PV, j conv )

to zero. This term also assumes the larger value of the two. The two terms are then added together to find the non-cooling
m . BI is a notation used to indicate the state of a system. For example, BI m (1) represents a charging state of
load, Pnc, j bat, j

building m0 s battery at time j.

Using a genetic algorithmic-driven optimization engine, the building agent explores the combination of various opera-

tional decisions such as different times of the day for charging/discharging the battery system, buying/selling energy to the

grid or powering the building with PV energy. Through this process, it is able to explore the design space to find the most

energy efficient operational strategies for the PV and battery systems. Once these decisions have been made, the building

agent passes this data to the facilitator agent. The following section provides an in-depth analysis of the facilitator agent.

4.5.2 Facilitator Agent

The facilitator agent is responsible for solving the coupled objective function which aims to minimize the energy con-

sumption of the shared systems within the building cluster. It is also responsible for optimizing the overall system objective

function. In order to optimize the coupled objective, it explores the design space to find the best values for the tempera-
m ), ice storage distribution (ηm ), and state of ice storage (S ). The facilitator agent objective function is
ture set-point (Tsp, j j is, j

expressed as a minimization of the shared cooling electricity consumption, Psc, j (kW h).

The shared cooling electricity consumption is expressed as the summation of two power consumption as shown in Eqn.

(4), with Pdch, j (kW h) representing the power consumption of the dedicated chiller at time j, and Pbch, j (kW h) being the

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power consumption of the base chiller at time j.

Psc, j = Pdch, j + Pbch, j (4)

The energy consumption of the base and dedicated chillers are determined from their respective operation states. The

dedicated chiller demands energy from the power grid only if it is in a charging state, and distributes chilled water to the

building cluster only when it is in a discharging state. On the other hand, the base chiller is only active in the event where

the dedicated chiller is unable to meet the cooling demand of the building cluster. Besides handling the coupled objective

function, the facilitator agent is also responsible for optimizing the total energy cost of the entire building cluster. For this,

an overall system formulation is required, which is presented in the next section.

5 OVERALL SYSTEM FORMULATION

With the coupled and decoupled objective functions defined, an overall net-zero energy cost balance can be formulated

for the building cluster. Since the goal of this work is net-zero, the overall system objective function is presented as a

minimization problem, taking into account the total energy demanded by the building cluster, as well as the energy generated

through on-site renewable systems.

5.1 General Formulation

To mathematically model the overall net-zero formulation, we let fNZB,m be the net-zero energy cost balance for building

m (m = 1, , M), where M represents the total number of buildings within the cluster, k (k = 1, , K) represents the building

operation mode(1=pre-peak, 2=peak and 3=post peak), and Hk is the number of hours spent in the kth operation mode. In

addition, let Rmp, j and Rm

s, j represent the purchasing and selling price respectively, at time j, for building m, measured in terms
m and Pm to represent the energy purchased from the grid and the energy sold to the
of $/kW h. We also define variables Pp, j s, j

grid respectively by building m, at time j, measured in kW h. The subscripts p and s denote a shorthand representation of

the terms ”purchase” and ”selling” respectively. The difference between the total cost of energy purchased from, and the

total cost of energy sold to the energy grid equates to the total net-zero energy cost balance. This is captured as the objective

function to be minimized in the problem formulation of Eqns. (5 - 12).

Minimize

M Hk
fNZB = ∑ ∑ (Rmp, j Pp,m j − Rms, j Ps,mj ) (5)
m=1 j=1
subject to

Tlbm ≤ T jm ≤ Tub
m
(6)

M
∑ Qmj ≤ Qmax, j (7)
m=1

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 1 ≤ max(0, SOCbat,max − SOCbat, j ) (8)

1 ≤ max(0, SOCbat, j − SOCbat,min ) (9)

1 ≤ max(0, SOCis,max − SOCis, j ) (10)

1 ≤ max(0, SOCis, j − SOCis,min ) (11)

m m
BIPV, j (1) = BIbat, j (1) (12)

5.2 System Constraints

As with most optimization problems, the net-zero energy cost balance is governed by a set of constraints aimed at

maintaining feasibility. The indoor temperature constraint (Eqn. 6) limits the feasible range within which the optimizer is
m represents the
allowed to set the building temperature set-point. The lower constraint bound is represented as Tlbm , while Tub

upper constraint bound. The variable T jm represents the actual temperature set-point of building m at time j. Another notable

system constraint, the base chiller constraint (Eqn. 7), ensures that the load placed on the base chiller does not exceed its

rated capacity. The variable Qmax, j represents the maximum chiller capacity at operation time j, while Qmj represents the

chiller demand of chilled water coming from building m at time j.

To ensure that the battery system does not experience over-charging/discharging, battery storage constraints, as shown

in Eqn. (8) and Eqn. (9), are developed, with SOCbat,max and SOCbat,min representing the maximum and minimum state of

charge respectively, and SOCbat, j representing the initial state of charge of the system at time k. In a similar fashion, the

ice storage constraints shown in Eqn. (10) and Eqn.(11), actively prevent scenarios of over-charging / discharging, with

SOCis,max and SOCis,min representing the maximum and minimum state of charge respectively, and SOCis, j representing the

initial state of charge of the ice-storage system at time j.

The last system constraint considered focuses on the PV systems. In order for the PV system to provide energy to the
m (2)). Failure to satisfy this
battery system for the purpose of charging, the battery has to be in the charging state (BIbat, j

requirement will result in unnecessary energy loss. To prevent this, the PV system constraint is used, as shown in Eqn. (12).

In this work, we employ the fast elitist multi-objective genetic algorithm (NSGA-II) [21] to optimize the operational

strategies on both levels of the decision framework. This was influenced in part by Nguyen et al. [33] and Nassif et al. [24]

whose respective research work elucidated the suitability of GAs towards building studies. Furthermore, the literature also

illustrates the efficacy of applying advanced optimization techniques towards energy related design problems. Kwong et

al [34] for example used NSGA-II to study the energy generation to noise propagation trade-off problem posed by wind farm

layout design, while Lu et al. [35] employ a multidisciplinary decomposition algorithm to allow for optimal design in hybrid

power generation systems (HPGSs). We incorporated the bi-level decision framework into a NSGA-II optimization scheme

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to develop an overall optimization scheme for the decision framework as illustrated in Figure 4.

From Figure 4 we observe that the decision framework is more procedural than hierarchical. This is because the bi-level

nature of the framework dictates that a subset of the decision variables is constrained to the building agents. Although the

optimization problem of the building agents are not explicitly set as constraints to the overall optimization problem, without

feasible solutions from the building agents, the overall optimization function cannot be evaluated. Thus we can treat this as

a bi-level optimization problem, which inherently fall under the scope of hierarchical optimization problems.

6 SIMULATION RESULTS

The process of testing the adaptive nature of the proposed framework focused on three main test scenarios; energy

cost savings in response to (i) dynamic non-cooling loads, (ii) variations in energy pricing and (iii) customer preferences.

energy cost savings in the context of this paper was measured using energy cost, which represents the dollar amount for the

energy consumed by the building. The simulations made use of real-world weather data, recorded on July 21, 2009 from the

Phoenix, Arizona area, obtained from the National Climatic Data Center (NCDC) [36].

6.1 Adaptive Decisions: Dynamic Non-Cooling Loads

To test for adaptive responses to dynamic non-cooling loads, two simulations were run. In these simulations, the non-

cooling load profiles presented in Figure 2 were used. As noted earlier, both profiles, P1 and P2, have equivalent total

energy consumption and equal peak time energy used (based on energy plan 1). In order to be considered adaptive, the

proposed decision framework is expected to realize avenues for profile specific energy cost savings. This can be achieved by

customizing operational strategies to best suit the demands of each unique consumption profile.

Figure 5 illustrates the hourly energy costs resulting from the two profiles. From the plot, we note clear distinctions.

The energy cost associated with profile P1 after optimization was found to be $5.03/day, while P2 was found to have an

optimized energy cost of $5.10/day. This represents a $0.07/day difference in energy costs, and implies the use of two

different operational strategies in each case. Figure 5 provides data to further support this hypothesis. An indication of the

use of customized strategies is apparent at (time = 14) where the energy cost associated to P2 is near zero, despite the fact

that at (time = 14), the energy consumption associated with P2 is much higher than that of P1 (see Figure 2).

A possible counter argument to the claim of adaptability is to attribute the results to demand shifting. Demand shifting

is an energy cost saving technique used to strategically shift energy demand from peak to off-peak hours. A fundamental

principle is that it realizes energy cost savings without altering energy consumption. This is effective from an energy cost

perspective, but not necessarily from an energy efficiency standpoint. A claim can be made that the variations illustrated

in Figure 5 are purely a result of demand shifts which occurred during the generation of the consumption profiles. While

to some extent this could be true, the key difference between the results obtained in this work and the demand shifting

argument is that the profiles both have equal energy consumption levels during both peak and off peak time periods. For the

cost variations to be a result of demand shifting, we expect to see a difference in the peak time energy demand, which is not

the case. The next section investigates the frameworks’ ability to handle dynamic energy pricing. Adaptiveness in this case

MD-15-1676 12 Lewis
is measured based on the optimizers’ ability to exploit potential energy cost savings across different pricing structures.

6.2 Adaptive Decisions: Dynamic Energy Pricing

Adaptability to variations in energy price is tested by comparing the energy cost response of the proposed model with

that of the model developed in [20], hereinafter referred to as a ”static model”. The main difference between the two models

is that the static model was developed exclusively for Energy Plan 1, while the proposed model, which by design is derived

from the static model, is capable of adapting to varying energy plans.

Figure 6 illustrates the results obtained from this comparison. Step 1 illustrates the response of both models to the use

of Energy Plan 1 (see Table 3). This serves as a baseline for comparison. Step 2 and Step 3 represent the response to the

shift from Energy Plan 1 to Energy Plan 2, with Step 2 representing the static model and Step 3 representing the proposed

adaptive model.

From Figure 6, we can see that the results obtained in Step 3 were significantly better than the results obtained in Step

2. The first nine hours saw Step 3 use an identical operational strategy to that developed in Step 1. Step 2 on the other hand

incurred a marginally smaller cost during this period. Between hours 10-15, Step 3 adopts a new strategy, incurring a greater

cost to that of Steps 1 and 2. One possible explanation for this is that, sensing the oncoming peak price period, the optimizer

decided to delay its reliance on battery resources, hence the higher cost. Moreover, while Step 1 and 2 incurred zero energy

cost for 2 hours (hours 15 and 16), Step 3 only went off the grid at hour 15. This provides further evidence to the notion

that it was strategically managing its battery and/or renewable resources. The most notable cost savings were made between

hours 16-19. During this period, the optimizer in Step 3 was able to use significantly less energy to Step 2. While we cannot

give a definite reason for this without an in-depth analysis of the operational strategy used, we can speculate this to be a

result of a better pre-cooling and renewable utilization strategy. This indicates that the optimizer was indeed able to adjust

its operational strategies to exploit potential energy cost savings across the different pricing structures.

In addition, not only was the optimizer able to perform better than the energy cost in Step 2, it also managed to save

more energy cost than was realized in Step 1. The total energy costs are shown in Table 7.

6.3 Adaptive Decisions: Customer Preferences

Changes in occupant preferences were modeled through hourly variations in occupant activity and clothing levels,

representing an improvement over the daily variations studied in [37]. The static decision model [13] along with the dynamic

model proposed in this work were subjected to the same variations to allow for comparison through PPD analysis. Table 8

summarizes the hourly combinations of clothing level and activity level used.

Figure 7 illustrates the results obtained from both models in terms of average PPD performance. According to ASHRAE

55 [38], PPD for indoor spaces should be maintained below a 10% threshold. This threshold is represented as a black

”dashed” line in Figure 7. The red line represents the performance of the static model. As can be deduced from the figure,

the static model had difficulties in adapting to variations within the comfort model. It failed to maintain a sub 10% PPD level

in 16 out of the 24 hours simulated, managing a total energy cost of $10.82.

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 In contrast, the blue line represents the proposed model’s response to the same preference variations. With respect to the

static model, the dynamic model adapts very well to the variations, failing to maintain a suitable PPD level in only 4 out of

the 24 hours simulated, at a total energy cost of $12.20. Figure 8 provides a heat map comparison of the static and dynamic

models with regards to temperature set-point. From this figure, it becomes apparent that the dynamic model supported a

lower PPD by maintaining a lower indoor temperature set-point. However, it should be noted that minimizing PPD requires

more than just trivially lowering the temperature set-point, as may be inferred from Figure 8. In fact, reducing temperature

set-point does not always lead to reduced PPD. To illustrate this point, we refer to Figure 8 - focusing on the first three and

last three hours of the day. We observe that the set point for the first 3 hours is much lower than that of the last three hours

of the day. A fair assumption would be to assume a lower PPD level during the first three hours than the last three hours.

However, with reference to Figure 7, we see that PPD was significantly lower during the last three hours.

The real challenge is being able to simultaneously minimize both energy cost and PPD. From the results, we note that

the static model was good at reducing cost, but struggled with PPD. Despite exceeding the allowable PPD on a couple of

occasions, the dynamic model had better control over both cost and comfort. This can be attributed in part to its ability to

control temperature set-point on an hourly basis, and its ability to leverage pre-cooling strategies (as evident in Figure 7).

Having explored the adaptability of the proposed model to variations in energy consumption, energy pricing and occu-

pant preferences, the next step is to explore the holistic effect this has on the total energy consumption of the NZEB cluster.

To explore this, a multi-objective energy minimization problem is modeled based on the NZEB cluster. Each building is

tasked with minimizing its total energy consumption. This poses a trade-off problem due to the presence of shared decision

variables. As a result, the best case scenario for each building might conflict with each other. We refer to this as the “Energy

Cost Vs. Energy Cost” problem. In order to visualize the resulting tradeoffs, Pareto analysis is used. The findings of this

analysis is presented in the next section, with the optimization parameters provided in Table 9.

6.4 Pareto Analysis: Energy Cost Vs. Energy Cost

Figure 9 illustrates the energy cost trade-offs resulting from the simultaneous minimization of the “Energy Cost Vs.

Energy Cost” problem. Three Pareto solutions (A,B,C) are highlighted, with point A representing the best overall energy

cost, point B representing the best case scenario for the light mass building, and point C representing best case scenario for

the heavy mass building. It should be noted that each Pareto solution represent a unique operational strategy.

To fully appreciate the significance of the results obtained by the decision framework, the Pareto plot obtained in Figure

9 is compared to the Pareto plot obtained from previous literature addressing the same trade-off problem [20]. One main dif-

ference between the decision framework employed in this work and the one used in [20] is the use of a memetic optimization

algorithm which leveraged a genetic algorithm for a global search, and simulated annealing for local search. However, the

most significant difference is the fact that the decision model used in [20] is inherently not adaptable to dynamic customer

preferences or dynamic non-cooling loads.

Figure 10 illustrates just how well the current decision framework handles the optimization problem. The best energy

cost obtained in [20] was $14.54, compared to the $11.88 obtained with the current decision model. This represents a 18.2%

MD-15-1676 14 Lewis
reduction in energy cost which corresponds to $2.66/day savings. To put this into perspective, over an annual time frame,

the proposed adaptive model would save approximately $971 over the model used in [20]. Using the $14.54/day benchmark

from [20], this model saves an equivalent of 67 days worth of energy cost.

The drastic difference between the energy costs of the two models begs the question, “Are these cost savings a result of

efficient energy use or simply a result of intelligent demand shifting?” To answer this question, the total consumption profile

of Pareto point A (see Figure 9) was compared to that of the best strategy developed in [20].

From Figure 11, we can see that the current best operational strategy consumes approximately 22kW less energy than

that of previous work. This is in addition to the $2.66/day energy cost savings highlighted in Figure 10. Collectively, these

results highlight the potential of the proposed decision model to significantly impact the energy cost and energy consumption

of building clusters on a 24 hour basis.

To maintain an even tighter control over energy costs, it is imperative to identify the key variables which impact the

Pareto frontier developed in figure 9. There has been attempts in the literature to identify these factors, with [39] notably

performing sensitivity analysis on NZEB macro-parameters. Figure 12 illustrates a set of Pareto frontiers generated from 100

Monte Carlo simulations accounting for uncertainty in three system inputs, namely the dry-bulb temperature, non-cooling

load and the clearness index. Clearness index denotes the proportion of extraterrestrial solar radiation that makes it through

to the earth’s surface, and it has an impact on PV generation. Figure 12 illustrates the possible Pareto frontiers resulting from

the collective effect of these uncertainties. We refer to this as the envelope of optimality. While this plot does not quantify the

sensitivity impacts of individual parameters, it is clear that uncertainty has significantly affects the resulting Pareto frontier

and warrants further investigation. Detailed analysis of the envelope of optimality has however been reserved for future work.

Taking these findings into account in terms of the larger net-zero energy cost picture, we believe that this model has the

potential to significantly bridge the gap between the realizable cost and consumption saving capabilities of current building

systems and the absolute requirements of the net-zero goal. Although the results do not reflect a zero ($0) energy balance, it

is worth noting that net-zero is typically measured over an annual time frame. The work presented here is however limited

to a 24 hour optimization period.

7 CONCLUSION

In this paper, we address the inherent lack of adaptability in operational strategies generated in previous work [20] by

introducing a new adaptive decision model for operational strategies in net-zero building clusters. In addition, the model

leverages pre-cooling strategies to address the lack of thermal storage utilization as noted in [9], and overcomes the compu-

tational difficulties experienced in [13, 20] by adopting an NSGA II driven bi-level decision framework to allow for hourly

operational strategies. The experimental results reveal the potential for energy cost savings using an adaptive model over a

static decision model. The model was shown to be capable of adopting different strategies for exploiting energy cost saving

opportunities on a profile to profile basis.

While promising, there is still room for improvement with this model. An interesting area for future research could look

at developing an adaptive model to enable the decision model to actively react to changes in weather conditions. Opera-

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tional strategies are normally generated a day in advance using forecasted weather data. Significant differences between the

forecasted weather data and the real-time weather data can result in the inefficient building operation. The ability to alter

operational strategies in response to such changes is hence of interest to us. This is where the full benefits of the envelope

of optimality can be fully realized. It grants us the ability to move from one Pareto front to another with respect to forecast

inaccuracies in order to maintain a tight control on building operation and help minimize avenues for energy inefficiency.

Another interesting area for future research could focus on handling the non-linearity of the optimization problem through

a problem reformulation or decomposition. Investigations into a mixed integer nonlinear programming representation along

with a Bender’s decomposition approach could provide further insights regarding the nature of the optimization problem

along with possible computational savings.

Finally, with NZEB clusters being tightly coupled, the idea of scalability poses quite an interesting challenge. As one

might expect, conditions required for successful scalability are far from trivial. The proposed framework has a plug and

play setup, meaning additional buildings can easily be added to the cluster. However, it currently lacks the ability to inform

on whether cluster expansions will have a beneficial or detrimental effect on the net-zero goal. An area we are currently

exploring is developing a framework for optimizing the size of a building cluster based on building type, function and

available resources.

MD-15-1676 16 Lewis
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List of Tables

1. Parameters related to building model.

2. Surrogate model development.

3. Overview of energy plans used.

4. Clothing level values for occupant preferences.

5. Metabolic rate values for occupant preferences.

6. List of decision variables.

7. Dynamic pricing energy costs.

8. Variations in clothing and activity levels.

9. Optimization parameters used in optimization process.

10. Model Parameters.

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List of Figures

1. Overall schematic of NZEB cluster emulator.

2. Non-cooling load profiles used for testing.

3. Bi-level decision model for building cluster.

4. Proposed decision framework.

5. Energy cost profiles for non-cooling loads.

6. Energy cost profiles for dynamic energy pricing.

7. System response to dynamic preferences.

8. Temperature set-point response to customer preference.

9. Pareto frontier of cost-cost trade-off.

10. Comparing Pareto solutions with previous work

11. Comparison of energy consumption profiles.

12. Pareto Band developed from 100 Monte Carlo simulations.

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 Table 1: Parameters related to building model.

Dimension Wall Density Window to Wall

(LxWxH) ( f t) (lbm/ f t 3 ) ratio
Heavy Mass Building 50x50x10 35 0.2
Light Mass Building 50x30x20 11 0.2

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 Table 2: Surrogate model development.

Model/Parameter Literature Reference

The building cooling load is derived from a building thermal model.
Building consumption model
Non-cooling load data is adopted from [27].
Chiller model The chiller model is adopted from [40].
Ice storage model The ice storage model and scaled parameters is adopted from [41].
Battery model The battery model is adopted from [42].
The PV-panel model adopted from [43]. The angular loss factor
Photovoltaic model
used in [44] is employed to compute the absorbed solar energy.
The total hourly solar irradiance on inclined surfaces with slope angle β and
Solar radiation on inclined surfaces.
surface azimuth angle γ are estimated using the model from [42, 45, 46].
Dry/wet bulb temperature Hourly dry/wet bulb temperatures for Phoenix, AZ USA are obtained from [36].
Real-time energy pricing Obtained from the Salt River Project (SRP) Company website [23].

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 Table 3: Overview of energy plans used.

Pricing Energy Plan 1 Energy Price Energy Plan 2 Energy Price

Period SPR EZ-3 ($/kW h) Time-of-Use (TOU) ($/kW h)
Pre-Peak 12 AM - 1 PM 0.0717 12 AM - 3 PM 0.0788
Peak 2 PM - 8 PM 0.2122 4 PM - 6 PM 0.3507
Off-Peak 9 PM - 12 AM 0.0717 7 PM - 12 AM 0.0788

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 Table 4: Clothing level values for occupant preferences adapted from [47].

Clothing Level
Type of Clothing ◦
m2 WC
Light Clothing (e.g. short sleeved outfit) 0.57
Medium Clothing (e.g. long sleeved outfit) 0.61
Heavy Clothing (e.g. light jacket outfit) 0.96

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 Table 5: Metabolic rate values for occupant preferences adapted from [47].

Metabolic Rate
Type of Activity
(met)
Sedentary Activity (e.g. typing) 1.2
Light Activity (e.g. presentations) 1.4 - 1.7
Medium Activity (e.g lifting/packing) 2.1

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 Table 6: List of decision variables.

Decision Variables Description Type

Decoupled Variables
m
Tsp, Temperature Set-point Continuous parameter
j

m
Integer (0: dormant; 1: charging battery;
SPV, j State of PV Panel
2: powering building; 3: selling to grid)
m
Sbat, State of Battery Integer (0: dormant; 1: charging; 2: discharging)
j

Coupled Variables
ηmj Chilled water distribution Continuous parameter
Sis, j State of Ice Storage Integer (0: dormant; 1: charging; 2: discharging)

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 Table 7: Dynamic pricing energy costs.

Step Energy Cost

1 $5.03/day
2 $5.32/day
3 $4.86/day

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 Table 8: Variations in clothing and activity levels.

Time Range Clothing Activity

12AM - 7AM Medium Sedentary
8AM - 1PM Light Sedentary
2PM - 5PM Light Light
6PM - 12AM Medium Sedentary

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 Table 9: Optimization parameters used in optimization process.

Property Specification
Evaluation Method Black Box Building Emulator
Optimization Algorithm NSGA-II
Population Size 40 individuals
Number of Generations 30
Stopping Criteria Number of generations
Constraints Boundary Constraints
Simulation Period 1 day
Average Run Time 8 hours

MD-15-1676 30 Lewis

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