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International High Performance Buildings
Conference School of Mechanical Engineering
2024
Advanced Predictive Rule-based Control for HVAC Cost Reduction Advanced Predictive Rule-based Control for HVAC Cost Reduction
Under Dynamic Electricity Pricing in Residential Buildings Under Dynamic Electricity Pricing in Residential Buildings
Avik Ghosh
University of California San Diego
, avghosh@ucsd.edu
Xing Lu
Paci>c Northwest National Laboratory
, xing.lu@pnnl.gov
Veronica Adetola
Paci>c Northwest National Laboratory
, veronica.adetola@pnnl.gov
Follow this and additional works at: https://docs.lib.purdue.edu/ihpbc
Ghosh, Avik; Lu, Xing; and Adetola, Veronica, "Advanced Predictive Rule-based Control for HVAC Cost
Reduction Under Dynamic Electricity Pricing in Residential Buildings" (2024).
International High
Performance Buildings Conference.
Paper 438.
https://docs.lib.purdue.edu/ihpbc/438
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries.
Please contact epubs@purdue.edu for additional information.
Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at
https://engineering.purdue.edu/Herrick/Events/orderlit.html
3166, Page 1
Advanced Predictive Rule-based Control for HVAC Cost Reduction Under
Dynamic Electricity Pricing in Residential Buildings
Avik GHOSH 1, 2 *, Xing
LU 2,
Veronica ADETOLA 2
1 University
of
California, San Diego, Department
of
Mechanical and Aerospace Engineering,
La
Jolla, CA, USA
avghosh@ucsd.edu
2 Pacific Northwest National Laboratory, Resilient Control Methods Group,
Richland,
WA,
USA
xing.lu@pnnl.gov, veronica.adetola@pnnl.gov
* Corresponding Author
ABSTRACT
Efficient electrification
of
space heating/cooling presents the most viable pathway to GHG emissions reduction, and
heat pumps (HPs) remain the dominant alternative for replacing gas/oil-based space heating systems.
To
achieve
widespread adoption
of
HPs, it is imperative to improve their energy efficiency and operational cost. In this paper,
a scalable and computationally inexpensive advanced predictive rule-based-control (PRBC) strategy for HPs is pre-
sented. The controller is tested on an Energy Plus prototype model
of
a single-family detached house within the building
optimization testing framework (BOPTEST). The HVAC system consists
of
a single-speed
HP,
inclusive
of
a single-
speed
DX
heating coil, a single-speed
DX
cooling coil, and a constant-speed fan. The PRBC model uses the current
indoor air temperature inside the building, day-ahead ambient air temperature, and hourly electricity price (HEP) fore-
casts to preheat/precool a building, with the final goal ofHVAC cost/energy reduction without a noticeable increase
of
indoor thermal discomfort. The ambient air temperature and HEP forecasts are integrated into the PRBC model
by: (i) assigning proportional weight to the forecasted values, prioritizing closer time steps to the present, due to the
intuitive principle that forecasting accuracy diminishes with greater temporal distance from the present, (ii) modulating
the amount
of
precooling/preheating based on weighted ambient air temperature and HEP forecasts to not only shift
HVAC energy usage from high to low HEP periods but also avoid excess precooling/preheating. Results show the
advanced PRBC
of
being able to identify and quickly respond to finer trends in HEP and ambient temperature than
the other controllers resulting in cost/energy savings. The thermal discomfort
of
the advanced PRBC is comparable
to the other controllers, proving the efficacy
of
the proposed PRBC injudiciously preheating/precooling the building.
The advanced PRBC performs significantly better in the cooling season than the heating season, achieving as high as
14%, 9%, and 8% in monthly cost savings, and 11%, 6%, and 8% in monthly HVAC energy savings,
as
compared to
the industry standard, relaxed baseline and literature inspired controllers respectively.
1.
INTRODUCTION
1.1
Motivation and Literature Review
Buildings account for about 30%
of
the global fmal energy consumption and 26%
of
global energy related emissions
(International Energy Agency, 2024). In order to meet satisfactory indoor air environment (i.e, thermal comfort), more
than 50%
of
a residential building's energy need is spent on heating, ventilation and air-conditioning (HVAC) (United
States Environmental Protection Agency, 2009), leading to considerable greenhouse (GHG) gas emissions for HVAC
systems that consume fossil fuels onsite. Efficient electrification
of
space heating/cooling presents the most viable
pathway to GHG emissions reduction, and heat pumps (HPs) remain the dominant alternative for replacing gas/oil-
based space heating systems. The indoor air temperature is a major determining factor in the HVAC energy usage/costs
of
a building (Alimohammadisagvand, Jokisalo, & Siren, 2018). One
of
the most popular techniques for HVAC load
shifting is to precool or preheat the building before peak price periods, while maintaining indoor thermal comfort.
Precooling or preheating the building uses the thermal mass
of
the building to store thermal energy during low price
periods which can be released to maintain the indoor air temperature within the acceptable thermal comfort bounds,
even obviating HVAC equipment usage during the high price periods, thereby saving electricity costs.
Model predictive control (MPC) based HVAC system controllers can be effectively used to exploit the thermal mass
of
a building in reducing/shifting HVAC costs and energy. However, an MPC based HVAC controller requires a lower
order model for the system to be controlled, which increases computational complexity on top
of
being tedious to model
(Clauss, Stinner, Sartori, & Georges, 2019). Moreover, Goyal, Ingley, and Barooah (2013); Goyal, Barooah, and Mid-
8th International High Performance Buildings Conference at Purdue, July 15-18, 2024
3166,
Page2
delkoop (2015) showed that well designed rule based controllers (RBC) are as effective as MPC based controllers,
defeating the purpose
of
the added complexity in the MPC. Data driven Machine Leaming (ML) based controllers can
simplify the modeling complexity
of
the MPC, but suffers from the requirement
of
high quality training data, which
reduces scalablity (Stoffel, Maier, Kumpel, Schreiber, & Muller, 2023). Instead, predictive rule based controllers
(PRBC) can be used to reduce/shift the HVAC cost/load with simpler, highly interpretable and computationally in-
expensive implementation, and can still be effective. Thus, we limit our discussion to studies on rule based control
(RBC) methods, with a specific focus on predictive RBC (PRBC) methods, to provide guidelines in choosing an ap-
propriate control scheme that strikes a balance between computational complexity and benefit in the form
of
HVAC
cost and energy savings. PRBC methods differ from non-predictive RBC in considering predictions about weather,
hourly electricity price (HEP) etc., rather than being completely momentary (Gwerder, M., Todtli,
J.
and Gyalistras,
D., 2010).
In PRBC, based on the forecasts, for example
of
HEP, simple pre-decided rules are implemented, which can take the
form
of
setting different temperature setpoints for the building directly (Alimohammadisagvand et al., 2017), or heat
pump (HP) ON/OFF signals (Clausset al., 2019), or both (Alimohammadisagvand et al., 2018). Alimohammadisagvand
et al. (2018), presented improvements
of
two DR based control algorithms already published in their earlier works
(Alimohammadisagvand, Jokisalo, Kilpelainen, Ali, & Siren, 2016; Alimohammadisagvand et al., 2017)
of
a combined
water based space heating (SH) and domestic hot water (DHW) system. Alimohammadisagvand et al. (2016, 2017)
calculated the future HEP trend by the blocking maximum subarray method (which calculates the largest sum
of
a
contiguous subarray within the HEP forecast array), while (Alimohammadisagvand et al., 2018) implemented the more
dynamic sliding maximum subarray (which is updated more frequently than blocking maximum subarray method), and
moving average algorithm to control the HP and temperature setpoint signals. The sliding maximum subarray method
outperformed as compared to the other existing control methodologies with respect to heating cost savings.
Clausset al. (2019) controlled the HP ON/OFF signals
of
an air-source HP connected to a water storage tank for both SH
and
DHW
requirements. The authors used different temperature setpoint references at different levels (height)
of
the
water storage tank to ascertain the HP ON/OFF decision signals. The reference temperatures are varied according to the
day-ahead HEP
by
ascertaining three HEP regions -below low price threshold, higher than high price threshold and in
between. Additionally, the increasing/decreasing trend
of
HEP is ascertained in a sliding-horizon method for a 2 hour
horizon and is taken into account for setting the reference temperature setpoints. Results showed the method only saves
costs in markets where there is a high fluctuation in HEP, whereas in markets where there are marginal fluctuations
of
HEP, there is a net increase in heating energy imports which outweighed the cost savings due to heating action shift
from high to low price periods. Lu, Fu, and O'Neill (2023) compared the rule-based ASHRAE Guideline 36 (GDL36)
based HVAC controller with an intelligent optimization based controller (OBC) and a deep reinforcement learning
(DRL) based controller for a five-zone variable air volume
(VAY)
cooling system virtual testbed. Results showed the
rule based method to have similar energy performance under both high and mild cooling seasons
as
compared to the
DRL, while having comparable and slightly worse energy performance under high and mild cooling load respectively
as compared to the OBC. Goyal et al. (2013) carried out simulations and verified them through experiments in (Goyal
et al., 2015) which showed that occupancy and temperature feedback based PRBC can reduce HVAC energy usage as
effectively as MPC based strategies without any reduction in thermal comfort or indoor air quality.
An
important limitation
of
(Alimohammadisagvand et al., 2018; Clauss et al., 2019; Alimohammadisagvand et al.,
2017, 2016;
Lu
et al., 2023) is the applicability
of
each RBC based method either during heating or cooling season,
which affects its implementation year around for climatic zones which has both heating and cooling seasons. In addition
(Lu et al., 2023; Goyal et al., 2013, 2015) only considered energy savings without consideration for costs which is the
primary motivation for consumers to participate in DR. A criticism
of RBC
based methods used in practice, highlighted
by Wang, Tang, and Song (2022) for precooling operation states that, such methods do not effectively adapt to changing
conditions, and vary slightly as to when and how much precooling takes place during low price periods to take complete
advantage
of
variable HEP to reduce costs, as compared to a baseline (no precooling) strategy. Additionally, (Wang et
al., 2022) critiques that most
of
the existing RBC methods for reducing on-peak HVAC equipment operation, use time-
of-day schedule to reset the indoor air temperature set point when time-of-use (TOU) rate is in place, which hinders
efficient adaptation
of
the RBC methods to electricity markets which vary more dynamically.
1.2 Objective
of
the work and novelty
The present work develops a advanced PRBC for HP applications in residential buildings under highly dynamic elec-
tricity pricing to reduce HVAC electricity costs/energy. The advanced PRBC uses the current indoor air temperature
8th International High Performance Buildings Conference at Purdue, July 15-18, 2024
3166,
Page3
inside the conditioned space, and day ahead predictions
of
HEP and ambient temperature to determine the preheating or
precooling actions to reduce HVAC costs without noticeable increase
of
indoor thermal discomfort with respect to the
predefmed ideal range
of
indoor air temperature. The novelty
of
the proposed advanced PRBC is as follows:
• A computationally inexpensive yet novel methodology that incorporates future trend in HEP and ambient tem-
perature is presented. The proposed method assigns proportional weight to forecasted values, prioritizing closer
time steps to the present, due to the intuitive principle that forecasting accuracy diminishes with greater temporal
distance from the present.
To
the best
of
the authors' knowledge such a methodology has never been used before
in the context
of
rule-based control.
•
By
utilizing weighted ambient air temperature forecast in addition to HEP, the proposed preheating/precooling
strategy enables efficient shifting
of
energy use from high to low HEP periods and prevents unnecessary over-
cooling/overheating, even during low HEP periods, a problem that has nullified PRBC benefits in the past liter-
ature (Clauss et al., 2019).
• The adaptability
of
the advanced RBC is improved over literature, as the same control framework can be applied
for both the cooling and heating seasons.
• Consideration
of
not only HVAC energy but also costs, which is the primary incentive for consumers to partici-
pate in DR.
2. RESIDENTIAL BUILDING HEAT PUMP VIRTUAL TESTBED
In this research, the EnergyPlus prototype model
of
a single-family detached house in a new residential construction
was leveraged, aligned with the 2021 version
of
the International Energy Conservation Code (IECC) (Mendon &
Taylor, 2014).
We
based our study on the Pasco-TriCities TMY3 weather data, specific to Climate 5A. The EnergyPlus
model was then reformulated into the Spawn-of-EnergyPlus (Spawn) model (Wetter, Benne, & Ravache, 2021). In
this process, HVAC and control elements from the original EnergyPlus model were swapped out for ones based on
the Spawn framework in Modelica. The Spawn framework allows for accurate modeling
of
control sequences and
equipment behavior, which is crucial for this research. This Spawn model was compiled into functional mockup units
(FMUs) and executed within the Building optimization testing framework (BOPTEST) (Blum et al., 2021), a platform
designed for testing, and benchmarking building control algorithms. Within the BOPTEST framework, external signals
could override either the heating/cooling temperature setpoints or the
HP
signal, which we leverage for implementing
our control algorithms via Python. The residential HVAC system is a single-speed heat pump, comprising
of
a single-
speed DX heating coil, a supplementary electric resistance heating coil, a single-speed
DX
cooling coil, and a constant
speed fan. The HP's rated Coefficient
of
Performance (COP) is 3 for cooling and 2.75 for heating.
3. HVAC CONTROL ALGORITHMS
3.1 Overview
of
controllers and conditions for thermal comfort
The baseline and literature inspired controllers are based on controlling the indoor air temperature setpoints directly,
while the proposed PRBC based method is based on directly controlling the
HP
ON/OFF signal. For acceptable indoor
thermal comfort, the minimum and maximum predicted mean vote (PMV) value
of
-0
.5
and O
.5
respectively is chosen,
based on ASHRAE Standard
55
(2020). Alimohammadisagvand et al. (2017) formulated linear relationships between
maximum and minimum PMV and indoor air temperature
(T subscript a,ind),
given in equation (1), which is used to derive the
acceptable range
of
indoor air temperature.
(1)
The acceptable range
of
indoor air temperature is found to be between
T subscript comfort,lower
and
T subscript comfort,upper
of21.5 Cand 24.5
Crespectively from equation (1). The temperature deadband
(T subscript db)
for the controllers described in Section 3.2 and 3.3
(baseline and literature inspired controllers) is 0.5 C. The temperature deadband for the controllers help avoid rapid
cycling
of
the HP which adversely affects HP lifespan in addition to causing noise pollution, disturbing the user. In
Section 3.4 (proposed controller), the HP ON/OFF signal is controlled directly, and rapid cycling
of
the HP is avoided
by persisting with previous control signals which indirectly mimics a situation similar to having a deadband
of
T subscript db
for
a fair comparison with controllers in Section 3.2 and 3.3. In this study, we ensured that the
HP
does not simultaneously
operate in both heating and cooling mode within a specific season. The discouragement for the
HP
to switch between
heating and cooling mode intra-season is to ensure lifespan longevity
of
the
HP.
However, the control framework in
itself does not prohibit switching between heating and cooling modes, and the user might choose it for more operational
flexibility.
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3166, Page 4
3.2 Baseline controllers: Fixed indoor air temperature setpoint control
Two fixed baseline indoor air temperature set-point controllers are devised, with only one
of
the heating or cooling set
points applied at a time to avoid intra season HP switching between heating/cooling modes. Baseline controller (A)
is
the industry standard baseline controller which aims to maintain the indoor air temperature at
th
e average
of
upper
and lower comfort limits given
in
equation (2). The controller starts heating/cooling once the indoor air temperature
drops/rises below/above the setpoint. Baseline controller (B) is the relaxed baseline controller which permits the in-
door air temperature to deviate further from the average setpoint before heating or cooling begins, while still remaining
within the thermal comfort bounds. The setpoints for the Baseline controller (B) are given in equation (3).
(2)
(3)
3.3 Literature inspired controller
The literature inspired controller is a PRBC control algorithm based on the sliding maximum subarray problem de-
scribed
in
(Alimohammadisagvand et al., 2018, Section 4.2.2). The model uses the current HEP and trend
of
future
HEP to determine the decision and extent
of
preheating and precooling in the heating and cooling seasons respectively.
The flowchart for the literature inspired control algorithm during the heating season is given
in
Fig. la. First, the cur-
rent HEP
is
compared to a threshold limiting price (LP). The LP
is
set as the daily median HEP for the heating season.
The daily median HEP can
be
set at the start
of
the simulation
of
each day as it is quite common for electricity markets
to announce prices day ahead (Alimohammadisagvand et al., 2018). The model only considers preheating
if
the HEP is
below the LP, to avoid unnecessary preheating costs during high HEP times. The heating setpoint is decided depending
on the trend
of
the HEP
in
the forecast horizon (considered 5 h in this study). The rising/falling/constant trend
of
the
HEP is decided from the sliding horizon maximum subarray problem, which calculates the increase/decrease/leveling
out
of
the largest sum
of
a contiguous subarray
of
HEP forecast in the forecast horizon window. The trend
of
HEP
between two adjacent horizons is thus dependent on only the first HEP entry from the first horizon, which is replaced
by the last HEP entry
of
the second horizon (as the HEP entries
in
between are still the same), which makes the method
in (Alimohammadisagvand et al., 2018) blind to finer trends in HEP. In the present case, as HEP entries are positive
numbers, the sliding maximum subarray sum
is
simply the sum
of
all the HEP entries
in
the forecast horizon win-
dow.
If
the trend
of
HEP increases
(delta HEP subscript max,subarray
> 0), the heating setpoint
is
set high to preheat more -as future
HEP will increase, leading to increasing HVAC costs
if
heating
is
delayed. Similarly,
if
the trend
of
HEP decreases
(delta HEP subscript max,subarray < 0), the heating setpoint is set low (discouraging heating), as it is economical to heat later when
HEP decreases.
If
delta HEP subscript max,subarray
= 0, indicating constant trend
of
the HEP, the heating setpoint
is
moderate.
Figure
1:
Literature inspired controller flowchart for the (a) heating season, (b) cooling season
The flowchart for the literature inspired algorithm during cooling season
is
given
in
Fig. 1 b, and follows the same
control framework as for heating season, with the LP set as the daily
75th
percentile HEP.
3.4 Proposed controller
The proposed control algorithm directly controls the HP ON/OFF signals, as opposed to setting the indoor air heating
and cooling setpoints as
in
Sections 3.2 and 3.3. The convention
of
time t followed for this controller is such that HP
action at time (t -1) causes a observable change in T subscript a,ind at time t. The flowchart for the proposed control algorithm
during the heating season is given
in
Fig. 2. The Cooling Coil signal is always OFF during the heating season, while
the Heating Coil
is
always OFF during the cooling season.
Figure 2a shows the first control layer, where, depending on the indoor air temperature, and the Heating Coil signal
from the last time step, it
is
decided whereas the controller should go into FLEX mode. Being
in
FLEX mode
is
the
first check for considering preheating. The goal is to preheat the room during low HEP times to avoid HP usage during
high HEP times
(i
.e
.,
flexibly shifting HP energy usage).
If
the indoor air temperature
is
in
the thermal comfort zone
8
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(6)
(4c)
3166, Page 5
(i.e., between T subscript comfort,lower and T subscript comfort,upper), the controller can go into FLEX mode except when indoor air temperature
is
between T subscript comfort,lower and T subscript comfort,lower +
T subscript db
and Heating Coil
(t-
l)
=ON.Persisting with the heating at time t when
the Heating Coil
(t
-
1)
= ON, and the indoor air temperature
is
between T subscript comfort,lower and T subscript comfort,lower +
T subscript db,
is
an
indirect way
of
mimicking the controller to respond similar to literature/baseline with a deadband on heating setpoint.
The same method
of
checking Heating Coil signal at the previous time step is also followed
in
the FLEX mode
of
the
proposed controller for a fair comparison with literature/baseline controllers.
Figure
2:
Proposed control flowchart for the heating season with the (a) primary, and (b) FLEX control layers.
Once the controller is
in
FLEX mode, Fig. 2b shows that, similar to literature, it
is
first checked whether HEP
is
below
the
LP,
to consider preheating. The rationale behind preheating ( even when the room air temperature is
in
the thermal
comfort zone)
is
to increase the indoor air temperature when the HEP
is
low (but has an increasing trend), resulting
in
thermal energy being stored in the indoor air. The stored thermal energy can be released during high HEP times, to
keep the indoor air temperature comfortable even when the HP
is
turned
off
. Note that the LP
is
same for proposed
and literature inspired controller (median daily HEP for heating season). Next, it is checked whether the indoor air
temperature is below the preheat temperature setpoint T subscript preheat(t) with consideration
of
deadband
(T subscript db).
The current
preheat temperature is decided based on the weighted ambient temperature
(T subscript a,amb,W)
and price (HEPw) forecasts over
the 5 h ahead forecast horizon window. The 5 h forecast window
is
evenly divided into N discrete time steps, with
the time index being denoted by k. With the intuitive assumption that near-future forecasts will
be
more accurate than
distant-future forecasts, the weighing factors
(W subscript k)
are formulated as
(4a)
Also the weighing factors sum up to 1, implying
(4b)
Putting Eqs. 4a and 4b together, the constant
of
proportionality p
is
formulated as
The weighted ambient temperature and price forecasts are formulated as
(5a)
(5b)
The current preheat temperature
is
formulated with HEP
subscript HT
= percentile(HEP
subscript daily,
25) as
Equation (6) shows that
if
the
HEP subscript w
is
low, the T subscript preheat
is
set higher (for the same
T subscript a,amb,w)
to take advantage
of
preheating the room during low HEP. The T subscript preheat is set lower for higher
T subscript a,amb,W
to avoid unnecessary preheating costs
as the higher ambient air temperature can in itself increase the indoor air temperature. T subscript preheat is set considering a trade
8
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3166, Page 6
off
between taking advantage
of low
HEP periods without over heating,
as
PRBC studies in the past have encountered
problems
of
the energy savings due to load shifting from high to low HEP periods being outweighed by increase in
electricity use due to overheating leading to increasing HVAC costs (Clauss et al., 2019).
In order to incorporate the trend
of
the HEP (F), the 5 h ahead forecast horizon
is
divided evenly into 3 sub-horizons,
of
3 h each. The first, second and third sub-horizons cover hours 0 -
3,
1 - 4 and 2 - 5 respectively. Each sub-horizon
is
evenly divided into n discrete time steps, with each time step covering 3 / n hours, being indexed by k.
With
the
same intuitive assumption as near-future forecasts being more accurate than distant-future forecasts, we define the 3h
subhorizon weighting factors as w subscript k = q / k, for all k = { 1, 2, 3,
...
,
n},
where q = 1 The weighted HEP over the
(1+1/2+1/3+ ...3/4).
first
(F subscript 1
), second (F subscript 2), and third
(F subscript 3)
sub-horizons are defined
as
7)
Dividing the 5 h horizon into 3 sub-horizons
is
able to capture finer trends
of
HEP, contrary to the literature inspired
controller which is unable to see finer trends
of
HEP.
If
the indoor air temperature
is
below the preheat temperature
setpoint with consideration
of
deadband, the trend
of
the HEP
is
checked by comparing F subscript 1 with
F subscript 2,
and F subscript 1 with F subscript An
immediately increasing HEP
(F subscript 2
>
F subscript 1)
or a momentarily decreasing/leveled out HEP
(F subscript 2
less than or equal to
F subscript 1)
followed by a major
increase
of
HEP
(F subscript 3
>
F subscript 1)
warrants preheating to be done now to avoid future high HVAC costs
if
heating is delayed.
A decreasing HEP
(F subscript 2
less than or equal to
F subscript 1 AND F subscript 3 < F subscript 1) turns off the HP, as it is more economical to heat later when HEP reduces.
The two remaining control conditions
in
Fig. 2b makes sure that the proposed controller incorporates the deadband
consistent with literature/baseline.
3.
The flowchart for the proposed control algorithm during the cooling season is given in Fig. 3. The algorithmic frame-
work for the proposed controller during cooling season
is
same as that
of
the heating season, with preheating being
replaced
by
precooling. Note that the LP is set as the daily
75th
percentile HEP for the cooling season, similar to the
literature inspired controller.
Figure
3:
Proposed control flowchart for the cooling season with the (a) primary, and (b) FLEX control layers.
The current precool temperature is formulated with HEP subscript ct
= percentile(HEP subscript daily, 50) as
-
(8)
4. DATA AND PERFORMANCE METRICS
We
run simulations for 2 heating (January and February), and 2 cooling season months (July and August) for the
climatic conditions
of
Pasco-Tri Cities under highly dynamic hourly electricity price (HEP) to test the performance
of
our proposed controller with the baseline and literature inspired controllers.
We
assume perfect knowledge
of
ambient
air temperature (T subscript a,amb) and HEP for this study. It is to be noted that day-ahead HEP forecast is required for setting
the LP for each day at the start
of
the day. However, for calculating the trend
of
HEP (F), and weighted forecasts
of
ambient temperature
(T subscript a,amb,w)
and HEP (HEP subscript w), a 5 h ahead forecast window is used.
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3166, Page 7
The metrics used to compare the proposed controller with the baseline and literature inspired controller are HVAC
energy usage
(E subscript HVAC),
HVAC cost
(C subscript HVAC)
which is the dot product
of
E subscript HVAC
and
HEP,
nominal thermal discomfort
(psi
subscript nom),
and HP cycles (Heating/Cooling Coil signal change from OFF to ON to OFF). The nominal thermal discomfort
defmes the cumulative deviation
of
the indoor air temperature from the upper and lower indoor air comfort limits. The
nominal thermal discomfort is formulated, with delta tbeing the granularity
of
the control actions (considered 5 min) as
(9)
HP
subscript signal
=
1,
when the Heating/Cooling
Coil=
ON, and HP
subscript signal
=
0,
when the Heating/Cooling
Coil=
OFF. The net
HVAC coefficient
of
performance is formulated as COP(t) =
(T(t))/(P(t))
where
T is
the thermal heating/cooling rate due to
the
HP,
and P is the electrical power usage.
5.
RESULTS AND DISCUSSIONS
5.1 Heating season
5 .1.1 Timeseries analysis on a representative day: The timeseries analyses
of
the four controllers for a representative
day in the heating season (January 2, represented as 24 -48 h
of
the year) is shown in Fig.
4.
Figures 4b and 4c show
that both the baseline controllers (A) and (B) tries to maintain the indoor air temperature above their respective heating
setpoints (with consideration for deadband), regardless
of
the
HEP.
As the ambient temperature during the start
of
the
day is low (see Fig. 4a) until about 36 h (i.e., 35:59 h), both the baseline controllers undergo cycling as HP has to
frequently
tum
on. The baseline controllers avoid heating during the high HEP hours between 40 -
43
h (i.e., 40:00
h to 42:59 h), as the ambient temperature also had a rise just before the high HEP hours, allowing sufficient thermal
storage in the building envelope to ride
off
the peak HEP without heating. However, one can easily imagine a
(HEP-
ambient temperature) combination where the baseline controllers continuously have to keep operating during high HEP
periods.
For both the literature inspired and the proposed controller, the LP is important for determining when the preheating
occurs. The hours when the HEP is below the LP are 24 -29 h, 36 -39 h, and 44 -48 h. The literature inspired
controller seeing the rising trend
of
the HEP until 29 h (see Fig. 4a), has a higher heating setpoint than the proposed
controller leading to more HVAC energy usage (compare Figs. 4h and 4i until 29 h). The heating setpoint choices
for the literature inspired controller (see Fig. 4d) in this study are 24 C,
23
C and 22 Cwhen the HEP rises, levels
out and decreases respectively. Although the preheat temperature choices for the proposed controller are same as that
of
the literature, the proposed controller (see Fig. 4e) is able to modulate its preheat temperature setpoint depending
on the weighted forecast
of
the HEP, leading to the decrease
of
T subscript preheat
of
the proposed controller from 24 C to
23
Cat 27 h, whereas for the literature inspired controller
T subscript heat,set
remains 24 Cuntil 29 h. The reduction
of
T subscript preheat
of
the proposed controller from 24 Cto
23
Cat 27 h prevents excess preheating, which can undermine the benefits
of
preheating. After 29 h, the HEP becomes higher than the
LP,
and both the literature and the proposed controller tries
to minimize use
of
the
HP.
Note that the
T subscript preheat
for the proposed controller is only active when in the FLEX mode and
HEP
less than or equal to
LP (indicated by absence
of
T subscript preheat
in Fig. 4e between 29 -36 h).
Between
36-39
h,
HEP<
LP, and the trend
of
the HEP rises, with the literature inspired controller setting
T subscript heat,set
to 24
C, leading to overheating (which is redundant) as the ambient temperature increases until about 38
h.
The proposed
controller leverages the knowledge
of
the ambient temperature forecast through T
subscript w and
HEP forecast through HEP subscript w,
to set
T subscript preheat
to 22 and
23
C, preventing the need for heating. The excess energy usage
of
the literature inspired
controller as compared to the proposed controller between 36 -39 h can be seen on comparing Figs. 4h and 4i from
36 -39 h. Between 39 -44 h, as HEP > LP, both the literature inspired and the proposed controller avoid using the
HP,
leveraging the thermal storage to keep the indoor air temperature in the thermal comfort zone.
After 44 h, the
HEP<
LP, with the trend
of
the HEP falling until 47 h in the literature inspired controller. After 47 h,
the trend
of
the HEP rises in the literature inspired controller due to increases in HEP based on the early hour forecasts
(after 52 h)
of
January 3 (not shown in figures). This increasing trend
of
HEP is manifested in
T subscript heat,set
rising to 24 C
after 47 h (see Fig. 4d). The rise
of
T subscript preheat
to 24 C after 47
his
unnecessary as the immediate decreases in HEP (until
49 h) is ignored by the literature inspired controller (as it only looks at the two extreme HEP entries in two adjacent
horizons), and the HEP in the early hours
of
January 3 is still quite low (not shown in figures), obviating the need for
preheating from so early. In the proposed controller, the thermal energy stored (by preheating) before 44 h was less
than in literature, resulting in the
T subscript a,ind
dropping below 21.5 C sooner, necessitating some cycling
of
HP after 44
h. Note that, although after 44 h, the controller goes in the FLEX mode with
HEP less than or equal to
LP from time to time (indicated
8th International High Performance Buildings Conference at Purdue, July 15-18, 2024
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3166, Page 8
by intermittent T subscript preheat after 44 h in Fig. 4e), preheating
is
never activated
as
F subscript 2
< F subscript 1 AND F subscript 3 < F subscript 1, indicating the
overriding decreasing trend
of
HEP (especially between 47 -49 h) - a fine trend in HEP which the literature inspired
controller missed out on. Figures
4f
, 4g, 4h , and 4i, show that the cumulative cost and electric energy
is
the least for the
proposed controller, without significant thermal discomfort,
as
T subscript a,ind still remained within the thermal comfort band
of
21.5-24.5 C.
Figure
4:
Performance comparison between the four controllers for a representative day in the heating season: (a)
Ambient air temperature and hourly electricity price, (b,t) Baseline controller (A), (c,g) Baseline controller (B), (d,h)
Literature inspired controller, and ( e,i) Proposed controller. The blue filled patch denotes the thermal comfort zone.
5.1.2 Monthly analysis: Table 1 shows that for January the proposed controller outperforms the Baseline controller (A)
by
12%
, and the literature inspired controller
by
5%, while having almost similar performance
to
the Baseline controller
(B) with respect to the
HVAC
cost. The Baseline controller (B) despite having
no
predictive capability performs
as
well
as
the proposed controller with respect to the
HVAC
cost because
of
the increase
of
ambient temperature before
highest HEP periods ( see Fig. 4a and Section 5 .
1.1
), thereby storing enough thermal energy in the building envelope
to
ride off the peak HEP without heating. However, such a
(HEP-
ambient temperature) combination
is
not general,
and the Baseline controller (B) can lead to heating during high HEP periods
in
a situation where ambient temperature
falls just before the high HEP period, because
of
the lack
of
predictive capability, which may lead
to
higher
HVAC
costs. The proposed controller has lower nominal thermal discomfort than the Baseline (A) and literature inspired
controllers. Although, the nominal thermal discomfort
of
the proposed controller
is
quantitatively four times that
of
the Baseline controller (B), the differences are marginal and mathematical,
as
relaxed thermal discomfort, calculated
using
an
additional slack
of plus-minus
0.5 C
in
(9)
is
O
Kh
for both the Baseline (B) and proposed controller, which however are
greater than O for the Baseline (A) and literature inspired controller. The total thermal heating energy demand (Heating
in
Table
1)
of
the proposed controller
is
lower than Baseline (A) and literature inspired controller while being slightly
more than Baseline (B). The total thermal heating energy demand
of
the Baseline controller (B)
is
lowest because
of
the fixed low heating setpoint
of
22 C throughout, while for the literature inspired and proposed controllers, higher
heating/preheating setpoints
of 23
and 24 °
Care
additionally implemented to take advantage
of
preheating during low
HEP periods. The number
of
HP cycles are least for the literature inspired controller, while being the most for the
proposed controller -indicating the quicker response
of
the proposed controller to finer trends
in
HEP and ambient
temperature unlike the other controllers. The average monthly COP (COP)
is
almost identical for all the controllers,
resulting
in
HVAC
energy trend being
in
general similar to the thermal heating energy demand trend.
8
th
International High Performance Buildings Conference at Purdue, July 15-18, 2024
3166, Page 9
The results and trends for February are almost identical to January, with respect to
HVAC
energy/Heating and HP
cycles/COP.
HVAC
cost
is
slightly lower in the Baseline controller (B)
as
compared to the proposed controller. The
biggest difference
is
thermal discomfort -which
is
significantly more for all the controllers in February
as
compared
to January because
of
the higher ambient temperatures in February, leading to the indoor air temperature sometimes
going above the 24.5
C
upper comfort limit -however cooling
is
avoided to prevent intra-season HP mode switching.
Besides the (lucky)
HVAC
cost reduction for the Baseline controller (B) under the specific
HEP-
ambient tempera-
ture combination in this work, the monthly analyses in the heating months in general shows the proposed controller
achieving a tradeoffbetween lower
HVAC
cost and higher
HP
cycles,
as
compared to the Baseline (A) and literature
inspired controllers.
Table
1:
Monthly performance metrics
of
the four controllers in the heating season months
of
January and February
January February
Controller
E subscript HVAC
C subscript
psi subs
HVAC
cript nom Heating
HP subsc le
E subscrip
COP
ript cyc
t HVAC
C subscript HVAC
psi subscript nom Heating
HP subsc
COP
ript cycle
Baseline (A) 426 kWh $28.7 5.8 Kh
751
kWh 234 1.76 217 kWh $13.8 150.1 Kh 366 kWh
106
1.69
Baseline (B) 375 kWh $25.2 0.2 Kh 672 kWh 230 1.79
177
kWh $11.3 78.4 Kh
301
kWh 98
1.71
Literature 377 kWh $26.4 9.0 Kh
731
kWh
164
1.79 215 kWh $13.2 169.6 Kh 372 kWh 92 1.73
Proposed 383 kWh $25.1 0.8 Kh 687 kWh 266 1.79
188
kWh $11.6 98.2 Kh 324 kWh
126
1.72
5.2 Cooling season
5.2.1 Monthly analysis: Table 2 shows that in the cooling season, the proposed controller outperforms the other con-
trollers with respect to the
HVAC
cost. Note that contrary to the heating season, in the cooling season, the relaxed
Baseline controller (B) without predictive precooling capability
is
left with excess thermal energy in the building en-
velope during high HEP periods, necessitating more cooling demand during high HEP periods
as
compared to the
literature inspired and proposed controller, driving up
HVAC
costs. The nominal thermal discomfort
is
most in the
proposed controller, however the differences are marginal
as
the relaxed thermal discomfort
is
0 Kh for all the con-
trollers. The higher COP
of
the proposed controller along with lower thermal cooling energy demand facilitates lower
HVAC
energy usage. The literature inspired controller cycles most frequently due to excessive overcooling, leading to
indoor air temperature dropping below 21.5
C
frequently -rather than cycling more due to quicker response to fmer
trends in ambient temperature and HEP like the proposed controller. The cooling month analyses show the proposed
controller
of
being able to achieve a better tradeoffbetween lower
HVAC
cost and higher
HP
cycles, than the other
controllers.
Table
2:
Monthly performance metrics
of
the four controllers in the cooling season months
of
July and August
July August
Controller
E subscript HVAC
C subscript HVAC
psi subs
nom
cript
Cooling HP subscr
C
ip
OP
t cycle
E subscript HVAC
C subscript HVAC
psi subs
nom
cript
Cooling
HP subscr
COP
ipt cycle
Baseline (A) 787 kWh $57.0
0Kh
2221 kWh 745 2.86 666 kWh $45.2
0Kh
1945
kWh 750 2.97
Baseline (B) 742 kWh $53.8
0Kh
2122kWh 654 2.89 628 kWh $42.7 0 Kh
1855
kWh 596 2.98
Literature 756 kWh $53.1
0.1
Kh 2203 kWh 906 2.98
641
kWh $42.2
0.1
Kh 1927 kWh 824 3.06
Proposed 699 kWh $49.0 6.2 Kh 2134 kWh 869 3.07
601
kWh $39.8
4.3
Kh 1864 kWh 789
3.11
6. CONCLUSIONS AND FUTURE WORK
We
developed a scalable, computationally inexpensive, yet novel advanced predictive rule based controller (PRBC) for
HP applications in residential buildings under highly dynamically varying hourly electricity pricing (HEP) to reduce
electricity costs. The advanced PRBC uses the current indoor air temperature inside the conditioned space, and day
ahead predictions
of
HEP and ambient temperature to determine the preheating or precooling actions to reduce
HVAC
costs/energy without noticeable increase
of
indoor thermal discomfort. The results
of
the proposed advanced PRBC
are compared with two fixed indoor temperature setpoint baseline controllers ( one industry standard, another more
relaxed, and both without any predictive capability) and a PRBC based literature inspired controller for two heating
season and two cooling season months for the climatic conditions
of
Pasco-Tri Cities, Washington.
The advanced PRBC
is
shown to identify and respond quickly to fmer trends in HEP and ambient temperature than
the other controllers resulting, in general, of HVAC cost and energy reduction, at the expense
of
more heat pump (HP)
ON/OFF cycles. The thermal discomfort
of
the advanced PRBC
is
comparable to the other controllers, proving the
8
th
International High Performance Buildings Conference at Purdue, July 15-18, 2024
3166, Page 10
efficacy
of
the proposed PRBC injudiciously preheating/precooling during low HEP periods to avoid heating/cooling
during high HEP periods. The advanced PRBC performs significantly better in the cooling season than the heating
season, achieving
as
high
as
14%, 9%, and
8%
in monthly cost savings, and
11
%,
6%, and 8% in monthly
HVAC
energy
savings,
as
compared to the industry standard, relaxed baseline and literature inspired controllers respectively.
One
of
the novel features
of
the present work
is
to calculate the future trend
of
the HEP and ambient temperature in a
realistic way by giving proportional weightage to the forecasted values, prioritizing closer time steps to the present, due
to the intuitive principle that forecasting accuracy diminishes with greater temporal distance from the present. However,
for the present work, perfect forecasts
of
HEP and ambient temperature are used. The real benefit
of
the proportional
weightage to forecasted values and its comparison to other controllers (which weights all forecast values equally) will
be manifested under imperfect forecasts (which
is
closer to reality), and will be explored in future works.
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ACKNOWLEDGMENT
The work was supported by the Building Technologies Office
of
the U.S. Department
of
Energy under the contract No.
DEAC05-76RL01830.
8th International High Performance Buildings Conference at Purdue, July 15-18, 2024
