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Citation: Liu, Y.; Liu, C.; Tao, J.; Liu,
S.; Wang, X.; Zhang, X. Corrective
Evaluation of Response Capabilities
of Flexible Demand-Side Resources
Considering Communication Delay
in Smart Grids. Electronics 2024,13,
2795. https://doi.org/10.3390/
electronics13142795
Academic Editor: François Auger
Received: 7 June 2024
Revised: 10 July 2024
Accepted: 14 July 2024
Published: 16 July 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
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4.0/).
electronics
Article
Corrective Evaluation of Response Capabilities of Flexible
Demand-Side Resources Considering Communication Delay in
Smart Grids
Ying Liu 1,2, Chuan Liu 1,3, Jing Tao 1, Shidong Liu 1, Xiangqun Wang 1and Xi Zhang 1,4,*
1State Grid Smart Grid Research Institute Co., Ltd., Nanjing 210003, China; liuying@geiri.sgcc.com.cn (Y.L.);
liuchuan@geiri.sgcc.com.cn (C.L.); taojing@geiri.sgcc.com.cn (J.T.); liushidong@geiri.sgcc.com.cn (S.L.);
wangxiangqun@geiri.sgcc.com.cn (X.W.)
2State Grid Laboratory of Electric Power Communication Network Technology, Nanjing 210003, China
3School of Cyber Science and Engineering, Huazhong University of Science and Technology,
Wuhan 430074, China
4Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK
*Correspondence: x.zhang14@imperial.ac.uk
Abstract: With the gradual increase in the proportion of new energy sources in the power grid, there
is an urgent need for more flexible resources to participate in short-term regulation. The impact of
communication network channel quality will continue to magnify, and factors such as communication
latency may directly affect the efficiency and effectiveness of resource regulation. In this context of a
large number of flexible demand-side resources accessing the grid, this article proposes a bidirectional
channel delay measurement method based on MQTT (Message Queuing Telemetry Transport). It can
effectively evaluate the real-time performance of communication links, considering that resources
mainly access the grid through the public network. Subsequently, focusing on two typical types
of resources on the demand side, namely, split air conditioners and central air conditioners, this
article proposes an assessment method for correcting the response capabilities of air conditioning
resources considering communication latency. Experimental simulations are conducted, and the
results demonstrate that under given communication conditions, this method can more accurately
estimate the response capability of air conditioners. This provides a basis for formulating more
reasonable scheduling strategies, avoiding excessive or insufficient resource regulation caused by
communication issues, and aiding the power grid in achieving precise scheduling.
Keywords: flexible demand-side resources; communication latency; response capability; MQTT;
air conditioning
1. Introduction
1.1. Background
In the context of the profound transformation of the current energy structure and the
flourishing development of smart grids, flexible demand-side resources such as distributed
energy, smart homes, and electric vehicle charging stations are gradually becoming an
indispensable part of the power system due to their characteristics of flexible deploy-
ment, environmental friendliness, and proximity to consumer terminals [
1
,
2
]. In contrast
to the past reliance on dedicated network connections for large-scale power plants and
centralized loads, these emerging distributed resources tend to interact with the power
grid through public communication networks [
3
–
5
]. This shift has greatly promoted the
universal accessibility and utilization efficiency of resources, but it has also introduced new
challenges, especially considering the openness, dynamic changes, and channel instability
of such network environments [
6
–
8
], which are more prominent against the backdrop of
the continuous increase in the penetration rate of new energy sources. With the increasing
Electronics 2024,13, 2795. https://doi.org/10.3390/electronics13142795 https://www.mdpi.com/journal/electronics
Electronics 2024,13, 2795 2 of 21
share of wind and solar energy in the power grid, there is a need for frequent and precise
scheduling of a larger number of small-scale resources scattered across different locations
to effectively respond to supply and demand fluctuations within short periods [
9
–
11
]. In
this scenario, the performance of the communication channels, particularly the issue of
latency, has become a major constraint determining scheduling efficiency and system stabil-
ity
[12,13]
. Latency not only affects the transmission and execution of control commands,
reducing the timeliness of adjustments, but also increases the complexity and uncertainty
of system control, impacting the dynamic balance of the power grid and the quality of
electrical energy. Therefore, the evaluation of communication link performance, especially
the measurement of communication latency, has become a core issue in current research
and technological innovation.
1.2. Literature Review
Information communication plays a crucial role in energy management. For instance,
through Grid-to-Vehicle (G2V) and Vehicle-to-Grid (V2G) protocols, communication sys-
tems can facilitate data exchange, making the interaction between electric vehicles and the
grid more intelligent. Additionally, communication technology is equally important in pho-
tovoltaic (PV) systems and energy storage (ES). It can monitor and control the generation,
storage, and distribution of energy in real time, ensuring maximum energy utilization and
grid stability [
14
]. However, to achieve these goals, the measurement and management of
communication latency are essential. Communication latency directly affects the timeliness
of data transmission and the responsiveness of the system.
The most commonly used methods for measuring network latency are based on the
Internet Control Message Protocol (ICMP), such as the ping method [
15
] and the tracer-
oute method, the latter of which primarily functions to test the routing information from
the source to the destination. NetPerf [
16
] is also a common network measurement tool
based on the Transmission Control Protocol (TCP) and User Datagram Protocol (UDP).
sFlow [
17
], developed through collaboration among InMon, HP, and FoundryNetworks, is
a representative example of sampled measurement technology that requires embedding
in hardware devices. NetFlow measurement technology [
18
,
19
], developed by Cisco, uses
flow-switching technology and is mainly utilized in Cisco’s own routing and switching
devices. TCPProbe introduces a network performance measurement tool based on op-
timized probing methods, utilizing legitimate TCP datagrams as probe messages [
20
].
Meanwhile, one study in the literature [
21
] uses the Precision Time Protocol (PTP) for
measuring message latency, estimating it as the delay of user data. Traditional one-way
delay measurement based on PTP is proposed in the literature [
22
], where the delay of
the network path is calculated by measuring the round-trip delay of the link. Active
measurement-based precise parallel flow monitoring methods are presented in the liter-
ature [
23
]; these methods aggregate measurement samples of other flows into the same
flow sample, utilizing clustering algorithms from machine learning to improve measure-
ment accuracy. A theoretical model of the transfer function for power line communication
channels based on transfer parameters is discussed in the literature [
24
], considering the
impact of electric appliances on the channel’s transfer function. Additionally, a segmented
delay measurement method for Wide-Area Measurement Systems (WAMS) is proposed
in the literature [
25
], effectively measuring the delays at various stages of the WAMS data
transmission process, providing an analytical basis for ensuring the real-time currency
and accuracy of WAMS data. The network latency measurement methods proposed in
the abovementioned domestic and international literature primarily rely on controllable
communication network environments. In uncontrollable environments such as the public
Internet, the direct application of these methods may be limited. As flexible-resource access
mainly occurs through open public communication networks, there is a higher demand
for precise measurement of network latency. Therefore, there is an urgent need to propose
solutions to the problem of uncontrollable network latency when facing a large number of
flexible demand-side resources accessing the network [26,27].
Electronics 2024,13, 2795 3 of 21
In addition, currently, flexible resources mainly participate in various flexibility mar-
kets through demand-side management. With technological advancements and policy
support, more and more businesses and household users will have the opportunity to
actively participate in these markets through smart devices and energy management sys-
tems [
28
,
29
]. A study in the literature [
30
] discusses a demand-side management strategy
aimed at minimizing the daily peak power of electric vehicle charging stations. Another
study [
31
] proposes an energy optimization strategy for micro-grids that accounts for
demand-side management, achieving reliable and economical operation of micro-grids. A
study [
32
] establishes a bi-level optimization model for the aggregation of demand-side
resources participating in peak shaving, providing effective guidance for retail market
entities to develop strategies for participating in peak-shaving auxiliary services. Finally,
one study [
33
] proposes a robust clearing model and pricing method for capacity markets
considering flexible adjustment demand, which helps flexible resources to provide capacity
to meet the system’s flexible adjustment needs. These are the basis for the participation of
flexible demand-side resources in regulation.
When flexible resources participate in short-term regulation services, the response
capability of resources will exhibit significant value degradation due to latency. By studying
the evaluation method of distributed resources’ response capability, it is possible to scien-
tifically quantify the adjustment ability and contribution of various types of distributed
resources at different time scales. This provides strong support for formulating reason-
able resource planning schemes and improving the efficiency and stability of the power
system [
34
–
36
]. One article in the literature [
37
] proposes an evaluation method for the
response capability of household electric heating load based on temperature forecasts and
a load cluster control strategy. Another article [
38
] presents a framework for evaluating
the response capability and interaction of air conditioning temperature control loads par-
ticipating in distributed photovoltaic integration in the electricity market environment,
based on data-driven and deep belief networks. One published study [
39
] constructs
a two-stage adjustable capacity evaluation model for electric vehicles for peak-shaving
and valley-filling auxiliary services from a physical and economic perspective. Another
study [
40
] proposes an analysis and evaluation method for assessing the response capability
of industrial loads supporting the operation of isolated industrial park networks. A differ-
ent study [
41
] analyzes the participation and characteristics of industrial loads in primary
frequency regulation as a specific type of adjustable load. One article [
42
] established an
aggregated response capability evaluation model that includes response time and duration,
which is used to assess the overall response capability of aggregated resources in a virtual
power plant. Another article [
43
] designs a potential assessment method for response based
on user response characteristics under differentiated subsidy prices and establishes a user
ranking sequence based on response potential. Finally, one study in the literature [
44
]
presents an adjustable capacity evaluation method based on multi-objective optimization,
establishing an aggregate model considering demand response and economic constraints
to demonstrate the adjustable capacity of integrated energy systems. The abovementioned
literature mainly focuses on the application scenarios and technical means to study the
response capability of resources, with less consideration given to the impact of communica-
tion factors, especially latency, in the assessment of response capability. As more flexible
resources participate in smaller-scale regulation, the response capability of resources needs
to be recalculated after considering the actual communication network environment in
order to more accurately reflect the availability of resources and ensure the reliability of
decision making.
1.3. Innovations and Contributions
•
In the context of large-scale flexible-resource integration scenarios, a method for ef-
ficient communication-network delay measurement based on the MQTT protocol
is proposed to address potential challenges faced by traditional communication ar-
chitectures. The MQTT protocol, known for its lightweight nature, low bandwidth
Electronics 2024,13, 2795 4 of 21
consumption, and Quality of Service (QoS) guarantee mechanism, is suitable for re-
liable communication in resource-constrained environments and unstable network
conditions. It provides a solid foundation for precise delay measurement in demand-
side resource integration.
•
By collecting a large quantity of network latency data through practical deployment
and testing, then further analyzing and transforming it, the data are quantified as a
high-latency rate indicator to accurately reflect the impact of network conditions on
the transmission of resource scheduling commands. Building upon this foundation,
the article delves into how to incorporate latency factors into the evaluation model of
flexible resources, especially air conditioning response capabilities. By introducing
latency constraints, an innovative method for assessing resource response capabilities
considering network latency is proposed. This method can more accurately predict and
evaluate the actual adjustment capabilities of flexible resources such as air conditioning
when facing rapidly changing energy demands.
1.4. Structure
The subsequent sections of this paper are structured as follows. Section 2introduces
the method of bidirectional channel latency measurement based on MQTT. Section 3
proposes an air conditioning response capability evaluation method considering latency. In
the fourth part, the proposed methods are tested through case studies. Finally, in Section 5,
the article provides a summary.
2. A Method for Measuring Bidirectional Channel Delay Based on MQTT
Due to the diverse types of data sources, numerous participating users, novel appli-
cation functionalities, and high future scalability requirements involved in an aggregated
control network for flexible resources, its overall architecture often adopts a layered design
approach. Through system layering, different layers’ functionalities address corresponding
issues at each level. As shown in Figure 1, the typical architecture of an aggregated control
network for flexible resources is illustrated.
Electronics 2024, 13, 2795 4 of 23
proposed to address potential challenges faced by traditional communication archi-
tectures. The MQTT protocol, known for its lightweight nature, low bandwidth con-
sumption, and Quality of Service (QoS) guarantee mechanism, is suitable for reliable
communication in resource-constrained environments and unstable network condi-
tions. It provides a solid foundation for precise delay measurement in demand-side
resource integration.
• By collecting a large quantity of network latency data through practical deployment
and testing, then further analyzing and transforming it, the data are quantified as a
high-latency rate indicator to accurately reflect the impact of network conditions on
the transmission of resource scheduling commands. Building upon this foundation,
the article delves into how to incorporate latency factors into the evaluation model of
flexible resources, especially air conditioning response capabilities. By introducing
latency constraints, an innovative method for assessing resource response capabili-
ties considering network latency is proposed. This method can more accurately pre-
dict and evaluate the actual adjustment capabilities of flexible resources such as air
conditioning when facing rapidly changing energy demands.
1.4. Structure
The subsequent sections of this paper are structured as follows. Section 2 introduces
the method of bidirectional channel latency measurement based on MQTT. Section 3 pro-
poses an air conditioning response capability evaluation method considering latency. In
the fourth part, the proposed methods are tested through case studies. Finally, in Section
5, the article provides a summary.
2. A Method for Measuring Bidirectional Channel Delay Based on MQTT
Due to the diverse types of data sources, numerous participating users, novel appli-
cation functionalities, and high future scalability requirements involved in an aggregated
control network for flexible resources, its overall architecture often adopts a layered de-
sign approach. Through system layering, different layers’ functionalities address corre-
sponding issues at each level. As shown in Figure 1, the typical architecture of an aggre-
gated control network for flexible resources is illustrated.
Power t rading pla tform
Optical fiber private network
IEC61850
IEC61970
Dispatching clo ud VPP pla tform
EV
Terminal
(wireles s)
PV ES
VPPA
RS485、HPLC ZigBee、LoRA
DER
aggregatio n
coordination
control
Terminal
(wireles s)
AC Triple
generation
VPPB
RS485、HPLC ZigBee、LoRA
Industrial
load
Status i nformation
Real-time measurement
Control execution
Terminal
230M private network,
4/5G network
Wirele ss base
station
Clearing result
Sett lement
info rmati on
IEC62746
DL/T1867
IEC62325
Deck l ayer
Backbon e layer
Access layer
Perce ptu al lay er
(Terminal layer)
Power plant
Figure 1. A flexible-resource aggregation control network.
Figure 1. A flexible-resource aggregation control network.
Electronics 2024,13, 2795 5 of 21
The four-layer architecture of a flexible-resource aggregation and control network,
including the perception layer, access layer, backbone layer, and platform layer, aligns with
the architecture of the Internet of Things (IoT), which consists of cloud, management, edge,
and end devices. This indicates that the flexible-resource aggregation and control network
is a typical IoT architecture.
In terms of delay measurement for the control network, it is typically divided into two
modes: out-of-band measurement and in-band measurement. Out-of-band measurement
technology simulates business data packets indirectly and periodically sends packets to
measure and analyze the end-to-end performance of the network path. In contrast, in-band
measurement technology marks real business data packets to measure and analyze the
performance of actual business flows [
45
–
47
]. The mainstream communication protocols for
resource aggregation and control have significant differences in packet formats. If in-band
measurement is adopted, the protocol needs to be modified according to the measurement
requirements. However, due to the large number of third-party assets in the massive
flexible resources and considering cost and security, it is not feasible to achieve large-scale
protocol modifications. Therefore, out-of-band measurement methods can be employed for
large-scale delay measurement of flexible resources. An out-of-band measurement system
can generally be designed as a two-layer structure, consisting of measurement probes and
a master measurement station.
•
Measurement Probes: These are primarily responsible for capturing data on key
network links. They are deployed on various critical links within the network and
typically function as complete network measurement devices with measurement
and communication capabilities. Each probe is equipped with a local database for
temporary storage of captured data packets and for timely uploading based on the
settings of the master measurement station. It also ensures that test data are not lost in
case of network congestion.
•
Master Measurement Station: This serves as the core component of the measurement
system and has two main functions: node management and data analysis. It typi-
cally employs server clusters and large databases. The master measurement station
manages all the collection nodes and controls the invocation, configuration, status
monitoring, and upgrades of the measurement probes. It can issue user commands
and measurement parameter requirements to the measurement probes.
A flexible-resource aggregation and control network that accesses the public network
is classified as a typical uncontrolled network. The deployment range of measurement
probes is relatively limited. Due to cost and security considerations regarding the deploy-
ment of measurement probes, they can be deployed within controlled aggregation control
units. They can be extended to perform the functions of the master measurement station
within the edge state perception system of the cloud network. This forms the out-of-band
measurement architecture as shown in Figure 2.
In the selection of an out-of-band measurement protocol, one needs to consider
the characteristics of the flexible-resource aggregation and control network. MQTT is
a “lightweight” communication protocol based on the publish/subscribe pattern, and it
is built on top of TCP/IP (Internet Protocol). Similar protocols include TCP, UDP, and
HTTP (Hypertext Transfer Protocol). Table 1shows a comparison of the four protocols in
terms of lightweightness, reliability, secure communication, bidirectional communication,
continuous connection, stateful sessions, and support for large-scale IoT.
From the table, it can be seen that MQTT possesses characteristics and functionalities
specific to the requirements of the Internet of Things. Therefore, for the out-of-band
network measurement needs of a flexible-resource aggregation and control network, using
this protocol provides significant advantages. Additionally, in contrast to other common
IoT protocols such as Constrained Application Protocol (CoAP), CoAP uses UDP/IP, which
makes it more efficient when running on resource-constrained devices but sacrifices a
certain degree of reliability. Resource-management business systems mostly use TCP to
transmit data; therefore, using MQTT for measurement is more aligned with the latency of
Electronics 2024,13, 2795 6 of 21
real business systems. CoAP adopts a request/response model, which is a more traditional
client–server interaction pattern. In our measured business system, a platform connects
multiple edge devices, and using the publish/subscribe model in MQTT can improve
measurement efficiency. On the other hand, Advanced Message Queuing Protocol (AMQP),
as a more general and complex message queue protocol, provides more advanced features,
which may increase system complexity and resource consumption.
Electronics 2024, 13, 2795 6 of 23
Figure 2. Out-of-band measurement in a flexible-resource aggregation control network.
In the selection of an out-of-band measurement protocol, one needs to consider the
characteristics of the flexible-resource aggregation and control network. MQTT is a “light-
weight” communication protocol based on the publish/subscribe paern, and it is built on
top of TCP/IP (Internet Protocol). Similar protocols include TCP, UDP, and HTTP (Hyper-
text Transfer Protocol). Table 1 shows a comparison of the four protocols in terms of light-
weightness, reliability, secure communication, bidirectional communication, continuous
connection, stateful sessions, and support for large-scale IoT.
Table 1. Comparison of the four protocols.
Peculiarity TCP UDP HTTP MQTT
Lightweightness × Relatively heavy ✔ Relatively light-
weight × Relatively heavy
✔ Extremely light-
weight, suitable for de-
vices with limited re-
sources
Reliability ✔ Ver y reliable × No guarantee, may
experience packet loss
✔ Transport layer relia-
bility, no additional relia-
bility mechanisms at the
application layer
✔ Based on TCP, with
QoS mechanism en-
hancing reliability
Secure communi-
cation
× Does not provide on
its own, needs to be
combined with Secure
Sockets Layer/Transport
Layer Security
× Does not provide on
its own, needs to be
combined with Secure
Sockets Layer/Transport
Layer Security
✔ Supports HTTPS (Hy-
pertext Transfer Protocol
Secure)
✔ Supports Secure
Sockets
Layer/Transport Layer
Security
Bidirectional
communication
✔ Supports bidirec-
tional communication,
connection-oriented
✔ Supports, but ses-
sion management is re-
quired at the applica-
tion layer
✔ Supports mechanisms
such as HTTP/2 server
push
✔ Supports the pub-
lish/subscribe model
Continuous con-
nection
✔ Long-lasting connec-
tions, continuous until
closed
× No connection, does
not maintain state
× HTTP/1.1 uses short-
lived connections
✔ Typically uses long-
lasting connections and
continuous sessions
Stateful sessions × Does not maintain ap-
plication layer state on × No connection state
× Stateless, but can be
managed through cook-
ies/sessions
✔ Supports session
state retention and re-
covery
Figure 2. Out-of-band measurement in a flexible-resource aggregation control network.
Table 1. Comparison of the four protocols.
Peculiarity TCP UDP HTTP MQTT
Lightweightness ×Relatively heavy ✔Relatively lightweight ×Relatively heavy
✔Extremely lightweight,
suitable for devices with
limited resources
Reliability ✔Very reliable ×No guarantee, may
experience packet loss
✔Transport layer
reliability, no additional
reliability mechanisms at
the application layer
✔
Based on TCP, with QoS
mechanism enhancing
reliability
Secure communication
×Does not provide on its
own, needs to be
combined with Secure
Sockets Layer/Transport
Layer Security
×Does not provide on its
own, needs to be
combined with Secure
Sockets Layer/Transport
Layer Security
✔Supports HTTPS
(Hypertext Transfer
Protocol Secure)
✔
Supports Secure Sockets
Layer/Transport Layer
Security
Bidirectional
communication
✔Supports bidirectional
communication,
connection-oriented
✔Supports, but session
management is required at
the application layer
✔Supports mechanisms
such as HTTP/2
server push
✔Supports the
publish/subscribe model
Continuous connection
✔Long-lasting
connections, continuous
until closed
×No connection, does
not maintain state
×HTTP/1.1 uses
short-lived connections
✔Typically uses
long-lasting connections
and continuous sessions
Stateful sessions
×Does not maintain
application layer state on
its own, but has
connection state
×No connection state
×Stateless, but can be
managed through
cookies/sessions
✔Supports session state
retention and recovery
Support for
large-scale IoT
×Available, but
managing a large number
of connections is complex
×Suitable for simple
transmission, lacks
advanced functionality
×Relatively low
efficiency
✔Specifically designed,
efficient, and flexible
×means this peculiarity is not present, ✔means this peculiarity is present.
Consequently, for the latency measurement requirements of a flexible-resource aggrega-
tion and control network, the MQTT approach was selected for the data interaction between
Electronics 2024,13, 2795 7 of 21
the flexible resources and the master station. Meanwhile, the system on the main site in-
cludes a data validation module that provides prompts and corrections for format errors and
abnormal values in the data. The data interaction architecture is shown in Figure 3.
Electronics 2024, 13, 2795 7 of 23
its own, but has connec-
tion state
Support for large-
scale IoT
× Available, but manag-
ing a large number of
connections is complex
× Suitable for simple
transmission, lacks ad-
vanced functionality
× Relatively low effi-
ciency
✔ Specifically de-
signed, efficient, and
flexible
× means this peculiarity is not present, ✔ means this peculiarity is present.
From the table, it can be seen that MQTT possesses characteristics and functionalities
specific to the requirements of the Internet of Things. Therefore, for the out-of-band net-
work measurement needs of a flexible-resource aggregation and control network, using
this protocol provides significant advantages. Additionally, in contrast to other common
IoT protocols such as Constrained Application Protocol (CoAP), CoAP uses UDP/IP,
which makes it more efficient when running on resource-constrained devices but sacri-
fices a certain degree of reliability. Resource-management business systems mostly use
TCP to transmit data; therefore, using MQTT for measurement is more aligned with the
latency of real business systems. CoAP adopts a request/response model, which is a more
traditional client–server interaction paern. In our measured business system, a platform
connects multiple edge devices, and using the publish/subscribe model in MQTT can im-
prove measurement efficiency. On the other hand, Advanced Message Queuing Protocol
(AMQP), as a more general and complex message queue protocol, provides more ad-
vanced features, which may increase system complexity and resource consumption.
Consequently, for the latency measurement requirements of a flexible-resource ag-
gregation and control network, the MQTT approach was selected for the data interaction
between the flexible resources and the master station. Meanwhile, the system on the main
site includes a data validation module that provides prompts and corrections for format
errors and abnormal values in the data. The data interaction architecture is shown in Fig-
ure 3.
Figure 3. Data interaction architecture based on MQTT.
The MQTT protocol only implements the format for message transmission and does
not restrict the user protocol to follow a specific style. Therefore, on top of the MQTT pro-
tocol, it is necessary to define our own communication protocol. Since any supported type
can be represented using JSON, such as strings, numbers, objects, arrays, etc., the syntax
rules are as follows: objects represent key–value pairs, data are separated by commas, ob-
jects are enclosed in curly braces, and arrays are enclosed in square brackets. The JSON
hierarchical structure is concise and clear, making it easy to read and write, facilitating
machine parsing and generation, and effectively improving network transmission
Figure 3. Data interaction architecture based on MQTT.
The MQTT protocol only implements the format for message transmission and does
not restrict the user protocol to follow a specific style. Therefore, on top of the MQTT
protocol, it is necessary to define our own communication protocol. Since any supported
type can be represented using JSON, such as strings, numbers, objects, arrays, etc., the
syntax rules are as follows: objects represent key–value pairs, data are separated by commas,
objects are enclosed in curly braces, and arrays are enclosed in square brackets. The JSON
hierarchical structure is concise and clear, making it easy to read and write, facilitating
machine parsing and generation, and effectively improving network transmission efficiency.
Therefore, the combination of MQTT and JSON is the optimal solution. After setting up an
MQTT broker server on the platform server, bidirectional channel latency measurement is
conducted using the process depicted in Figure 4.
Electronics 2024, 13, 2795 8 of 23
efficiency. Therefore, the combination of MQTT and JSON is the optimal solution. After
seing up an MQTT broker server on the platform server, bidirectional channel latency
measurement is conducted using the process depicted in Figure 4.
Figure 4. Bidirectional channel latency measurement scheme based on MQTT.
Taking a measurement task as an example, the master station initiates a latency meas-
urement task, assembles the request message, and timestamps it as t1. The message is then
pushed to the agreed topic delay_req on the message broker service (hereinafter referred
to as broker). Each terminal consumes messages from the topic delay_req, records the
message arrival time (t2), and calculates the downstream communication latency of the
message as delayDown = t2 − t1. Subsequently, each terminal sends a response message
to the topic delay_resp, carrying delayDown and the sending time (t3) data. The master
station consumes the upstream message from the topic delay_resp, records the arrival
time (t4), parses the message to obtain delayDown and t3, and calculates the upstream
latency as delayUp = t4 − t3. The master station program writes the measured values of
the upstream and downstream latency, delayUp/delayDown, into the database, complet-
ing this round of the latency measurement task. After waiting for a measurement cycle,
the next measurement task is executed. If the edge device experiences a disconnection, the
main site will not receive the response message, resulting in an infinite delay.
The request message initiated by the master station for calculating the delay is shown
in Table 2.
Table 2. Request message for calculating the delay.
Subject MQTT Message
/ltd/device/delay/req
{
“rid”: “23445678”,
“id”: “233534535”,
“addr”: “192.168.100.1”,
“curSec”: “662256002”,
“curUsec”: “122228”
}
After receiving the request message, the terminal responds with a message as shown
in Table 3.
Figure 4. Bidirectional channel latency measurement scheme based on MQTT.
Taking a measurement task as an example, the master station initiates a latency
measurement task, assembles the request message, and timestamps it as t1. The message
is then pushed to the agreed topic delay_req on the message broker service (hereinafter
referred to as broker). Each terminal consumes messages from the topic delay_req, records
Electronics 2024,13, 2795 8 of 21
the message arrival time (t2), and calculates the downstream communication latency of the
message as delayDown = t2
−
t1. Subsequently, each terminal sends a response message
to the topic delay_resp, carrying delayDown and the sending time (t3) data. The master
station consumes the upstream message from the topic delay_resp, records the arrival
time (t4), parses the message to obtain delayDown and t3, and calculates the upstream
latency as delayUp = t4
−
t3. The master station program writes the measured values of the
upstream and downstream latency, delayUp/delayDown, into the database, completing
this round of the latency measurement task. After waiting for a measurement cycle, the
next measurement task is executed. If the edge device experiences a disconnection, the
main site will not receive the response message, resulting in an infinite delay.
The request message initiated by the master station for calculating the delay is shown
in Table 2.
Table 2. Request message for calculating the delay.
Subject MQTT Message
/ltd/device/delay/req
{
“rid”: “23445678”,
“id”: “233534535”,
“addr”: “192.168.100.1”,
“curSec”: “662256002”,
“curUsec”: “122228”
}
After receiving the request message, the terminal responds with a message as shown
in Table 3.
Table 3. Response message.
Subject MQTT Message
/ltd/device/delay/resp
{
“rid”: “23445678”,
“id”: “233534535”,
“addr”: “192.168.100.1”,
“delaySec”: ”0”,
“delayUsec”: ”12222”,
“curSec”: ”662256002”,
“curUsec”: ”145478”,
“status”: 1
}
The field definitions are as shown in Table 4.
Table 4. Field definitions.
Field Type Description
rid string Request number
id string Terminal ID
addr string Terminal IP address
curSec string Time the message is sent, seconds part
curUsec string Time the message is sent, microseconds part
delaySec string Seconds part of the delay value
delayUsec string Microseconds part of the delay value
status int
Result of the terminal’s calculation of downstream latency: if the latency is greater than 0, the
status is 1; if the latency equals 0, the status is 2; if the latency is less than 0, the status is 3
Electronics 2024,13, 2795 9 of 21
3. Evaluation Method for the Tunable Potential of Split Air Conditioning Groups
Considering Delay
From the perspective of response, devices may fail to participate in a certain regulation
due to certain uncertain factors, among which communication delay is one of the factors
that need to be considered. Defining a delay higher than a certain set value as high latency,
in this case, user refusal to respond constitutes a response failure. In response to this
situation, it is necessary to assess the reliability of device response.
3.1. Response Reliability Evaluation
The measured delay data are introduced into the assessment of resource response
capability in the form of a metric called high-latency rate. The high-latency rate represents
the probability of control failure due to high latency in the communication link of response
devices (such as air conditioners, energy storage systems, electric vehicle charging stations,
etc.). It is defined as the ratio of the duration of high latency to the total measurement
time within a certain period. The ratio of the duration of high latency,
δdelay
, is expressed
as follows:
δdelay =
I
∑
i=1
tdelay,i
I
∑
i=1
ttotal,i
·100% (1)
where
ttotal,i
represents the duration of delay collection for the i-th device,
tdelay,i
represents
the duration of high latency for the i-th device, and Irepresents the total number of devices.
Uncertainty factors are represented using a response degree indicator, where response
degree refers to the ratio of a device’s response capacity to its controllable capacity. The
degree of responsiveness ηres is expressed as follows:
ηres =Pres
Pcon (2)
where
Pres
is the response capacity of the device and
Pcon
is the controllable capacity of
the device.
As shown in Figure 5, (a) represents the user’s original equivalent load curve, while
(b) represents the user’s equivalent load curve considering the delay factor.
Electronics 2024, 13, 2795 10 of 23
where
,total i
t
represents the duration of delay collection for the i-th device, ,delay i
t repre-
sents the duration of high latency for the i-th device, and I represents the total number of
devices.
Uncertainty factors are represented using a response degree indicator, where re-
sponse degree refers to the ratio of a device’s response capacity to its controllable capacity.
The degree of responsiveness res
η
is expressed as follows:
res
res
con
P
P
η
=
(2)
where res
P
is the response capacity of the device and con
P
is the controllable capacity of
the device.
As shown in Figure 5, (a) represents the user’s original equivalent load curve, while
(b) represents the user’s equivalent load curve considering the delay factor.
(a) Original equivalent load curve (b) Equivalent load curve considering the delay
Figure 5. Equivalent load curves before and after considering the delay.
Based on historical data within a certain period, the user’s equivalent load curve Ψ(P)
can be obtained, where the horizontal axis represents the user’s load power and the verti-
cal axis represents the duration of the load. T denotes the time period, and any point on
the curve indicates that the duration for which the user’s load is greater than or equal to
P is t, with Pmax representing the maximum value of the user’s load. The response capa-
bility of a certain device is denoted as ∆P. When the device is in a state of high latency, the
user’s equivalent load curve can be represented as Ψ(P − ∆P), which is equivalent to shift-
ing the continuous load curve to the right by ∆P of load.
If the high-latency rate of this device is denoted as
(1)
delay
δ
, then the continuous load
curve of the user will become
(1)
delay
δ
in the figure; its calculation formula is as follows.
(1) (1) (1)
() (1 ) () ( )
delay delay
PPPP
ψψδδψ
⋅+⋅−Δ=−
(3)
Based on the above equation, the variation of the user’s continuous load curve
(1)
()P
ψ
under different
(1)
delay
δ
values can be obtained, as shown in Figure 6.
Figure 5. Equivalent load curves before and after considering the delay.
Based on historical data within a certain period, the user’s equivalent load curve
Ψ
(P)
can be obtained, where the horizontal axis represents the user’s load power and the vertical
axis represents the duration of the load. Tdenotes the time period, and any point on the
curve indicates that the duration for which the user’s load is greater than or equal to Pis t,
Electronics 2024,13, 2795 10 of 21
with Pmax representing the maximum value of the user’s load. The response capability of
a certain device is denoted as
∆
P. When the device is in a state of high latency, the user ’s
equivalent load curve can be represented as
Ψ
(P
−∆
P), which is equivalent to shifting the
continuous load curve to the right by ∆P of load.
If the high-latency rate of this device is denoted as
δ(1)
delay
, then the continuous load
curve of the user will become δ(1)
delay in the figure; its calculation formula is as follows.
ψ(1)(P) = (1−δ(1)
delay)·ψ(P) + δ(1)
delay·ψ(P−∆P)(3)
Based on the above equation, the variation of the user’s continuous load curve
ψ(1)(P)
under different δ(1)
delay values can be obtained, as shown in Figure 6.
Electronics 2024, 13, 2795 11 of 23
Figure 6. User load curves under different high-latency rates.
In Figure 5b, (1)
S
represents the area enclosed by the initial user equivalent load
curve and the equivalent load curve considering the high latency rate of this device. Its
physical meaning is the reduction in the response capacity of the user’s load due to high
latency. The calculation formula is as follows.
max
(1) (1)
0
(() ())
PP
ST P PdP
ψψ
+Δ
=−
(4)
The total responsive capacity of the user’s device is S
all
:
max
0
(( ) ())
PP
all
ST PPP Pd
ψψ
+Δ
=Δ−−
(5)
This can be used to calculate the corrected actual responsive capacity value S
real
for
the user.
(1)
real all
SSS=−
(6)
Assuming the user’s responsiveness under a certain stimulus is res
η
, according to
the corrected actual responsive capacity value, the trustworthy response level cre
η
of the
user considering the delay impact is obtained as shown in the following equation.
real res
cre
all
S
S
η
η
⋅
=
(7)
Based on the above reliability assessment of response, tailored resource response ca-
pability correction models for split air conditioning and central air conditioning, two typ-
ical adjustable resources, are proposed, and their trustworthy response capabilities are
calculated. The Response reliability evaluation algorithm is shown in Algorithm 1.
Figure 6. User load curves under different high-latency rates.
In Figure 5b,
S(1)
represents the area enclosed by the initial user equivalent load curve
and the equivalent load curve considering the high latency rate of this device. Its physical
meaning is the reduction in the response capacity of the user’s load due to high latency.
The calculation formula is as follows.
S(1)=T
Pmax+∆P
Z
0
(ψ(1)(P)−ψ(P))dP (4)
The total responsive capacity of the user’s device is Sall :
Sall =T
Pmax+∆P
Z
0
(ψ(P−∆P)−ψ(P))dP (5)
This can be used to calculate the corrected actual responsive capacity value S
real
for
the user.
Sreal =Sall −S(1)(6)
Assuming the user’s responsiveness under a certain stimulus is
ηres
, according to the
corrected actual responsive capacity value, the trustworthy response level
ηcre
of the user
considering the delay impact is obtained as shown in the following equation.
ηcre =Sreal ·ηres
Sall
(7)
Electronics 2024,13, 2795 11 of 21
Based on the above reliability assessment of response, tailored resource response
capability correction models for split air conditioning and central air conditioning, two
typical adjustable resources, are proposed, and their trustworthy response capabilities are
calculated. The Response reliability evaluation algorithm is shown in Algorithm 1.
Algorithm 1 Response reliability evaluation
Input:tdelay,tt otal ,ψ(P),Pmax
Initialization: ∆P,I,T,ηres
Procedure:
Calculate δdelay of I devices with tdelay and ttotal according to (1)
Determine equivalent load curve ψ(1)(P)with Pand ∆Paccording to (3)
Access reduction in responsiveness S(1)with Pmax according to (4)
Calculate total responsive capacity Sall according to (5)
Adjust actual responsive capacity value Sreal with Sal l and S(1)according to (6)
Fixed the degree of trusted response ηcre with ηres,Sreal and Sall according to (7)
Results: ηcre
3.2. Adjustment of Air Conditioning Response Capability
For the modeling of split air conditioning (AC), refer to the method proposed in [
48
].
The physical model input parameters for participation in response include the control
signal, outdoor temperature, indoor temperature setpoint, and indoor temperature at time
t, with the outputs being the air conditioning power and the indoor temperature for the
next time period. In addition, the model should consider the air conditioning unit’s own
parameters and the parameters of the building volume. For ease of calculation, these
parameters are set as constants based on statistical results. The architecture of the split air
conditioning load model is shown in Figure 7.
Electronics 2024, 13, 2795 12 of 23
Algorithm 1 Response reliability evaluation
Input: delay
t, total
t, ()
P
ψ
, max
P
Initialization: PΔ, I, T, res
η
Procedure:
Calculate delay
δ
of I devices with delay
t and total
t according to (1)
Determine equivalent load curve
(1) ()P
ψ
with P and PΔ according to (3)
Access reduction in responsiveness (1)
S with max
P according to (4)
Calculate total responsive capacity all
S according to (5)
Adjust actual responsive capacity value real
S with all
S and (1)
S according to (6)
Fixed the degree of trusted response cre
η
with res
η
, real
S and all
S according to (7)
Results: cre
η
3.2. Adjustment of Air Conditioning Response Capability
For the modeling of split air conditioning (AC), refer to the method proposed in [48].
The physical model input parameters for participation in response include the control sig-
nal, outdoor temperature, indoor temperature setpoint, and indoor temperature at time t,
with the outputs being the air conditioning power and the indoor temperature for the next
time period. In addition, the model should consider the air conditioning unit’s own pa-
rameters and the parameters of the building volume. For ease of calculation, these param-
eters are set as constants based on statistical results. The architecture of the split air con-
ditioning load model is shown in Figure 7.
Figure 7. Split air conditioning load model architecture diagram.
The actual power of the air conditioning unit at time t
A
C
t
P is calculated by the fol-
lowing equation:
Figure 7. Split air conditioning load model architecture diagram.
The actual power of the air conditioning unit at time t
PAC
t
is calculated by the
following equation:
PAC
t=PAC·SAC
t(8)
SAC
t+1=
0, TAC
t+1≤TAC
min
1, TAC
t+1≥TAC
max
SAC,TAC
min ≤TAC
t≤TAC
max
(9)
where
PAC
is the rated power of the air conditioning unit;
SAC
t
is the operational status of
the air conditioning unit, with 1 indicating “on” and 0 indicating “off”;
TAC
min
represents the
minimum indoor set temperature; and
TAC
max
represents the maximum indoor set tempera-
ture.
SAC
t+1
indicates the air conditioner’s working state at time t+ 1. The indoor temperature
for the next time period t+ 1, TAC
t+1, can be calculated using the following equation.
Electronics 2024,13, 2795 12 of 21
TAC
t+1=TAC
t+Gt
∆c·∆t+SAC
t·GAC
∆c·∆t(10)
where
TAC
t
represents the indoor temperature at time t;
Gt
is the indoor–outdoor heat
exchange value;
∆c
represents the indoor temperature coefficient, indicating the heat
required for every 10
◦
C increase in indoor temperature;
GAC
represents the air conditioning
heat capacity; and
∆t
represents the time interval. After linearization, the following
equation is shown.
TAC
t+1=TAC
t+0.4 +0.8SAC
t,SAC
t=1 (11)
TAC
t+1=TAC
t+0.4, SAC
t=0 (12)
The response capability of air conditioning equipment,
Pu,AC
t
, is expressed as follows:
Pu,AC
t=SAC
t·Pu,AC
t(13)
The minimum adjustable physical capacity, Pd,AC
t, is expressed as follows:
Pd,AC
t=SAC
t·Pd,AC
t(14)
Taking into account the user ’s trusted response level, one can calculate the air condi-
tioner’s trusted response capability, Pc f ,AC
t.
Pc f ,AC
t=(Pu,AC
t+Pd,AC
t)
2·ηcre (15)
According to the calculation methods proposed in [
49
,
50
], the calculation results of
the confidence interval for the adjustment capability, [Pd,c f ,AC
t,Pu,c f ,AC
t], are as follows:
Pd,c f ,AC
t=Pd,AC
t·ηcre + (Pc f ,AC
t−Pd,AC
t·ηcre )(1−Z
√6)(16)
Pu,c f ,AC
t=Pu,AC
t·ηcre −(Pu,AC
t·ηcre −Pc f ,AC
t)(1−Z
√6)(17)
where
Pc f ,AC
t
represents the most trusted adjustment capacity,
Pu,c f ,AC
t
represents the upper
limit of trusted response capability,
Pd,c f ,AC
t
represents the lower limit of trusted response
capability, and Zis the critical value related to the confidence level.
For the central air conditioning (CAC), assuming that the central air conditioning
system in the building operates in cooling mode during the summer, one operational
cycle includes the cooling and shutdown periods. During the cooling period, the chiller
unit processes the chilled water to provide cooling, and the chilled water absorbs indoor
heat through the evaporator coils, thereby reducing the indoor temperature. During the
shutdown period, the chiller unit ceases operation, and the indoor temperature generally
shows an increasing trend.
The change in indoor heat can be obtained by the difference between the heat entering the
indoor environment over a period of time and the heat reduced by the central air conditioning
load. Based on this principle, the time-varying curve of the building’s indoor temperature can
be derived for the central air conditioning system, as shown in the following equation:
Tin
t=
Tc,in
t=θ3−QP
θ2−(θ3−QP
θ2−Tc,in
0)·e−θ2
θ1t
Ts,in
t=θ3
θ2+θ4
α·θ1−θ2·e−αt−(θ4
α·θ1−θ2+θ3
θ2−Ts,in
0)·e−θ2
θ1t(18)
where
Tin
t
represents the indoor temperature of the central air conditioning system at time
t,
Tin
t
represents the indoor temperature of the central air conditioning system at time
Electronics 2024,13, 2795 13 of 21
tduring the cooling period,
Tin
t
represents the initial indoor temperature of the period,
Ts,in
t
represents the indoor temperature of the central air conditioning system at time t
during the shutdown period,
Ts,in
0
represents the initial indoor temperature of the period,
QP
represents the rated cooling capacity of the central air conditioning system, and
α
represents the temperature change parameter of the chilled water. The parameters
θ1
,
θ2
,
θ3
, and
θ4
are determined by the building parameters, as shown in the following equations:
θ1=ρa·ca·Vk+ks·Si n
wall (19)
θ2=α·(kr·Sr+kw·Sw)(20)
θ3=θ2·Tout +Qer (21)
θ4=a·mz·cw·(Tw−out −Tw−in)(22)
where
ρa
and
ca
represent the air density and the specific heat capacity of air, respectively;
Vk
represents the indoor volume;
ks
represents the heat storage coefficient of the interior walls;
Sin
wall
represents the interior wall area;
kr
and
kw
represent the heat conduction coefficients
of the house roof and walls, respectively;
Sr
represents the roof area;
Sw
represents the
wall area;
Qer
represents the total heat dissipation load from interior equipment, lighting,
and personnel;
Tout
represents the outdoor temperature;
mz
represents the mass of chilled
water;
cw
represents the specific heat capacity of chilled water;
Tw−in
and
Tw−out
represent
the inlet and outlet water temperatures of the chilled water; and αis set to 1.8.
Based on Equation (18), a schematic diagram of indoor temperature variation is shown
in Figure 8, with the indoor temperature set at
Tset
; the range of indoor temperature
variation is in the range [Tset−,Tset−].
Electronics 2024, 13, 2795 15 of 23
conduction coefficients of the house roof and walls, respectively; r
S represents the roof
area; w
S represents the wall area; er
Q represents the total heat dissipation load from
interior equipment, lighting, and personnel; out
T represents the outdoor temperature;
z
m represents the mass of chilled water; w
c represents the specific heat capacity of
chilled water; win
T− and w out
T− represent the inlet and outlet water temperatures of the
chilled water; and
α
is set to 1.8.
Based on Equation (18), a schematic diagram of indoor temperature variation is
shown in Figure 8, with the indoor temperature set at
s
et
T; the range of indoor tempera-
ture variation is in the range [
s
et
T−
,
s
et
T−
].
Figure 8. Temperature change curve of room with central air conditioning.
The corresponding operating power of the central air conditioning system is shown
in Figure 9, with the operating power switching between the rated power and zero. The
durations for which the central air conditioning system is in the cooling and shutdown
states are denoted as tc and ts, respectively.
Figure 9. Operating status and power of central air conditioning.
One can calculate the average cooling power
CAC
t
P of the central air conditioning
system over one cycle based on the above figure.
Figure 8. Temperature change curve of room with central air conditioning.
The corresponding operating power of the central air conditioning system is shown
in Figure 9, with the operating power switching between the rated power and zero. The
durations for which the central air conditioning system is in the cooling and shutdown
states are denoted as tc and ts, respectively.
Electronics 2024, 13, 2795 15 of 23
conduction coefficients of the house roof and walls, respectively; r
S represents the roof
area; w
S represents the wall area; er
Q represents the total heat dissipation load from
interior equipment, lighting, and personnel; out
T represents the outdoor temperature;
z
m represents the mass of chilled water; w
c represents the specific heat capacity of
chilled water; win
T− and w out
T− represent the inlet and outlet water temperatures of the
chilled water; and
α
is set to 1.8.
Based on Equation (18), a schematic diagram of indoor temperature variation is
shown in Figure 8, with the indoor temperature set at
s
et
T; the range of indoor tempera-
ture variation is in the range [
s
et
T−
,
s
et
T−
].
Figure 8. Temperature change curve of room with central air conditioning.
The corresponding operating power of the central air conditioning system is shown
in Figure 9, with the operating power switching between the rated power and zero. The
durations for which the central air conditioning system is in the cooling and shutdown
states are denoted as tc and ts, respectively.
Figure 9. Operating status and power of central air conditioning.
One can calculate the average cooling power
CAC
t
P of the central air conditioning
system over one cycle based on the above figure.
Figure 9. Operating status and power of central air conditioning.
Electronics 2024,13, 2795 14 of 21
One can calculate the average cooling power
PCAC
t
of the central air conditioning
system over one cycle based on the above figure.
PCAC
t=Rt2
t1Ptdt
t2−t1
=tc
tc+ts·Pe(23)
From this, the credible response capability of the central air conditioning system
Pc f ,CAC
tis expressed.
Pc f ,CAC
t=(Pd,CAC
t+Pu,CAC
t)·ηcre
2(24)
The confidence interval for the regulatory capacity is [Pd,c f ,av
t,Pu,c f ,av
t].
Pd,c f ,CAC
t=Pd,CAC
t·ηcre + (Pc f ,C AC
t−Pd,CAC
t·ηcre )(1−Z
√6)(25)
Pu,c f ,CAC
t=Pu,CAC
t·ηcre + (Pu,C AC
t·ηcre −Pc f ,CAC
t)(1−Z
√6)(26)
where
Pc f ,CAC
t
represents the most credible response capability of the central air condition-
ing system,
Pu,c f ,CAC
t
represents the upper limit of the credible response capability of the
central air conditioning system, and
Pu,c f ,CAC
t
represents the lower limit of the credible
response capability of the central air conditioning system.
The following takes split air conditioning as an example and gives the pseudo-code of
the algorithm as shown in Algorithms 2 and 3.
Algorithm 2 Split air conditioning power
Input: PAC,TAC
min,TAC
max
Initialization: TAC
t,SAC
t
Procedure:
Calculate the indoor temperature for the next time period TAC
t+1
Electronics 2024, 13, 2795 16 of 23
2
1
21
t
t
t
CAC c
te
cs
Pdt t
P
P
tt tt
==⋅
−+
(23)
From this, the credible response capability of the central air conditioning system
,cf CAC
t
P is expressed.
,,
,()
2
dCAC uCAC
cf CAC ttcre
t
PP
P
η
+⋅
= (24)
The confidence interval for the regulatory capacity is [
,,dcf av
t
P,
,,ucf av
t
P].
,, , , ,
()1
6
d cf CAC d CAC cf CAC d CAC
ttcrettcre
Z
PP PP
ηη
=⋅+ −⋅−（）
(25)
,, , , ,
()1
6
u cf CAC u CAC u CAC cf CAC
t t cre t cre t
Z
PP P P
ηη
=⋅+ ⋅− −（）
(26)
where
,cf CAC
t
P represents the most credible response capability of the central air condi-
tioning system,
,,ucf CAC
t
P represents the upper limit of the credible response capability
of the central air conditioning system, and
,,ucf CAC
t
P represents the lower limit of the
credible response capability of the central air conditioning system.
The following takes split air conditioning as an example and gives the pseudo-code
of the algorithm as shown in Algorithm 2 and Algorithm 3.
Algorithm 2 Split air conditioning power
Input:
A
C
P, mi n
A
C
T, ma x
A
C
T
Initialization:
A
C
t
T,
A
C
t
S
Procedure:
Calculate the indoor temperature for the next time period 1
A
C
t
T+
If 1
AC
t
S= then
according to (11)
Else if 0
AC
t
S= then
according to (12)
Determine the operational status 1
A
C
t
S+
If 1min
A
CAC
t
TT
+≤ then
10
AC
t
S+=
Else if 1max
A
CAC
t
TT
+≥ then
11
AC
t
S+=
Else
1
AC
tAC
SS
+=
Calculate the air conditioning actual power
A
C
t
P according to (8)
Results:
A
C
t
P, 1
A
C
t
T+
Determine the operational status SAC
t+1
Electronics 2024, 13, 2795 16 of 23
2
1
21
t
t
t
CAC c
te
cs
Pdt t
P
P
tt tt
==⋅
−+
(23)
From this, the credible response capability of the central air conditioning system
,cf CAC
t
P is expressed.
,,
,()
2
dCAC uCAC
cf CAC ttcre
t
PP
P
η
+⋅
= (24)
The confidence interval for the regulatory capacity is [
,,dcf av
t
P,
,,ucf av
t
P].
,, , , ,
()1
6
d cf CAC d CAC cf CAC d CAC
ttcrettcre
Z
PP PP
ηη
=⋅+ −⋅−（）
(25)
,, , , ,
()1
6
u cf CAC u CAC u CAC cf CAC
t t cre t cre t
Z
PP P P
ηη
=⋅+ ⋅− −（）
(26)
where
,cf CAC
t
P represents the most credible response capability of the central air condi-
tioning system,
,,ucf CAC
t
P represents the upper limit of the credible response capability
of the central air conditioning system, and
,,ucf CAC
t
P represents the lower limit of the
credible response capability of the central air conditioning system.
The following takes split air conditioning as an example and gives the pseudo-code
of the algorithm as shown in Algorithm 2 and Algorithm 3.
Algorithm 2 Split air conditioning power
Input:
A
C
P, mi n
A
C
T, ma x
A
C
T
Initialization:
A
C
t
T,
A
C
t
S
Procedure:
Calculate the indoor temperature for the next time period 1
A
C
t
T+
If 1
AC
t
S= then
according to (11)
Else if 0
AC
t
S= then
according to (12)
Determine the operational status 1
A
C
t
S+
If 1min
A
CAC
t
TT
+≤ then
10
AC
t
S+=
Else if 1max
A
CAC
t
TT
+≥ then
11
AC
t
S+=
Else
1
AC
tAC
SS
+=
Calculate the air conditioning actual power
A
C
t
P according to (8)
Results:
A
C
t
P, 1
A
C
t
T+
Calculate the air conditioning actual power PAC
taccording to (8)
Results: PAC
t,TAC
t+1
Electronics 2024,13, 2795 15 of 21
Algorithm 3 Responsiveness correction
Input: SAC
t,Pd,AC
t,Pu,AC
t,ηcre,Z
Procedure:
Update responsiveness Pu,AC
twith SAC
taccording to (13)
Updated minimum adjustable physical capability Pd,AC
twith SAC
taccording to (14)
Computes trusted response capability Pc f ,AC
twith ηcre according to (15)
Confidence interval of adjusted ability [Pd,c f ,AC
t,Pu,c f ,AC
t] with Z according to (16) and (17)
Results: Pc f ,AC
t,Pu,c f ,AC
t,Pd,c f ,AC
t
4. Example Analysis
4.1. Fixed Responsiveness of Resident Users
Taking residential users as an example, according to the method proposed in this paper,
the calculation flowchart of the trusted response capability for these users is provided, as
shown in Figure 10.
Electronics 2024, 13, 2795 17 of 23
Algorithm 3 Responsiveness correction
Input:
AC
t
S
,
,dAC
t
P
,
,uAC
t
P
, cre
η
, Z
Procedure:
Update responsiveness
,uAC
t
P with
AC
t
S according to (13)
Updated minimum adjustable physical capability
,dAC
t
P
with
AC
t
S
according to (14)
Computes trusted response capability
,cf AC
t
P with
cre
η
according to (15)
Confidence interval of adjusted ability [
,,dcf AC
t
P
,
,,ucf AC
t
P
] with Z according to (16)
and (17)
Results:
,cf AC
t
P
,
,,ucf AC
t
P
,
,,dcf AC
t
P
4. Example Analysis
4.1. Fixed Responsiveness of Resident Users
Taking residential users as an example, according to the method proposed in this
paper, the calculation flowchart of the trusted response capability for these users is pro-
vided, as shown in Figure 10.
Figure 10. Calculation flowchart for trusted response capability of residential users.
In the given residential area, there are a total of 2285 households and 10,000 split air
conditioners. The rated power of a single air conditioner follows a random distribution
within the interval [1.6 kW, 2 kW]. The minimum indoor temperature setpoint is 24 °C,
and the maximum is 26 °C. All air conditioners are operating stably within the set tem-
perature range before responding. The time interval is set to 1 h.
The calculated power values of the air conditioner group in the residential area at
different outdoor temperatures are shown in Table 5.
Table 5. Aggregate power of air conditioners at different outdoor temperatures.
Outdoor temperature (℃) 28 30 32
Aggregate power (MW) 1.97 3.26 4.55
As can be seen from the above table, when the outdoor temperature is 32 °C, the
aggregate power of the air conditioner is the maximum, and the aggregate power is the
minimum at 28 °C. The aggregate power of the air conditioner load increases with the
Figure 10. Calculation flowchart for trusted response capability of residential users.
In the given residential area, there are a total of 2285 households and 10,000 split air
conditioners. The rated power of a single air conditioner follows a random distribution
within the interval [1.6 kW, 2 kW]. The minimum indoor temperature setpoint is 24
◦
C, and
the maximum is 26
◦
C. All air conditioners are operating stably within the set temperature
range before responding. The time interval is set to 1 h.
The calculated power values of the air conditioner group in the residential area at
different outdoor temperatures are shown in Table 5.
Table 5. Aggregate power of air conditioners at different outdoor temperatures.
Outdoor temperature (°C) 28 30 32
Aggregate power (MW) 1.97 3.26 4.55
As can be seen from the above table, when the outdoor temperature is 32
◦
C, the
aggregate power of the air conditioner is the maximum, and the aggregate power is the
minimum at 28
◦
C. The aggregate power of the air conditioner load increases with the
increase of the outdoor temperature. This is because when the outdoor temperature is high,
the indoor–outdoor temperature difference is large, and the outdoor heat is transferred
into the room at a faster rate. The aggregate power of air conditioners at different set
temperature ranges and different outdoor temperatures is calculated below, as shown in
Table 6.
Electronics 2024,13, 2795 16 of 21
Table 6. Aggregate power of air conditioners with different set temperature ranges and different
outdoor temperatures.
Outdoor temperature (◦C) 28 30 32
Set temperature range of air conditioner (◦C) [20, 22] [22, 24] [24, 26]
Aggregate power (MW) 4.76 4.76 4.76
It can be seen from the above table that when the difference between the outdoor
temperature and the set temperature of the air conditioner is the same, the aggregate power
of the air conditioner is the same.
The load aggregation power of a typical daytime split air conditioner group in summer
in a set temperature range of [24 ◦C, 26 ◦C] is calculated, as shown in Figure 11.
Electronics 2024, 13, 2795 18 of 23
increase of the outdoor temperature. This is because when the outdoor temperature is
high, the indoor–outdoor temperature difference is large, and the outdoor heat is trans-
ferred into the room at a faster rate. The aggregate power of air conditioners at different
set temperature ranges and different outdoor temperatures is calculated below, as shown
in Table 6.
Table 6. Aggregate power of air conditioners with different set temperature ranges and different
outdoor temperatures.
Outdoor temperature (°C) 28 30 32
Set temperature range of air conditioner (°C) [20, 22] [22, 24] [24, 26]
Aggregate power (MW) 4.76 4.76 4.76
It can be seen from the above table that when the difference between the outdoor
temperature and the set temperature of the air conditioner is the same, the aggregate
power of the air conditioner is the same.
The load aggregation power of a typical daytime split air conditioner group in sum-
mer in a set temperature range of [24 °C, 26 °C] is calculated, as shown in Figure 11.
Figure 11. Air conditioning load power.
As shown in the figure above, the trend of the power load of the air conditioner group
is basically the same as the trend of the outdoor temperature. When the temperature rises
during the day, the frequency of air conditioner use increases, leading to a significant rise
in power. When the temperature drops at night, the power also decreases accordingly.
Although the power of a single air conditioner load is limited, considering the aggregation
of air conditioner loads, the overall response capability of the residential area is relatively
large.
By sorting the load of a household user in the residential area based on historical
data, the original responsive load curve of the user without considering delay is obtained,
as shown in Figure 12. It represents the total load of the household, with the response
probability indicating the success rate of the response. The horizontal axis represents the
user load, and the vertical axis represents the response probability.
024681012141618202224
0
1
2
3
4
5
6
7
8
Power(MW)
Time(h)
Figure 11. Air conditioning load power.
As shown in the figure above, the trend of the power load of the air conditioner group is
basically the same as the trend of the outdoor temperature. When the temperature rises during
the day, the frequency of air conditioner use increases, leading to a significant rise in power.
When the temperature drops at night, the power also decreases accordingly. Although the
power of a single air conditioner load is limited, considering the aggregation of air conditioner
loads, the overall response capability of the residential area is relatively large.
By sorting the load of a household user in the residential area based on historical
data, the original responsive load curve of the user without considering delay is obtained,
as shown in Figure 12. It represents the total load of the household, with the response
probability indicating the success rate of the response. The horizontal axis represents the
user load, and the vertical axis represents the response probability.
Electronics 2024, 13, 2795 19 of 23
Figure 12. Residential users can respond to load curves.
The responsive load of a certain split air conditioner for this user is 2.5 kW. When this
split air conditioner experiences high latency, it is equivalent to the device having a re-
sponse capability of 0 and thus being unable to participate in the current response. The
user’s responsive load curve at this time is shown in Figure 13.
Figure 13. User response load curve considering delay.
Considering the impact of high latency on the demand response capability of air con-
ditioners, the continuous load curves of this split air conditioner under different high-
latency rates can be obtained. At this time, the user’s response level under a certain incen-
tive is 0.35. Based on this, the trusted response levels of the user under different high-
latency rates are calculated, as shown in Table 7.
Table 7. Consider the degree to which users can be trusted to respond with high latency.
High Latency 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Degree of trusted response 0.329 0.297 0.260 0.238 0.184 0.165 0.122 0.063 0.034
From Table 7, it can be seen that with the increase in high-latency rates, the degree of
user trusted response significantly decreases. When the high-latency rate is low (0.1–0.3),
even a small delay can have a noticeable impact on response capability. At a high-latency
Figure 12. Residential users can respond to load curves.
Electronics 2024,13, 2795 17 of 21
The responsive load of a certain split air conditioner for this user is 2.5 kW. When
this split air conditioner experiences high latency, it is equivalent to the device having a
response capability of 0 and thus being unable to participate in the current response. The
user’s responsive load curve at this time is shown in Figure 13.
Electronics 2024, 13, 2795 19 of 23
Figure 12. Residential users can respond to load curves.
The responsive load of a certain split air conditioner for this user is 2.5 kW. When this
split air conditioner experiences high latency, it is equivalent to the device having a re-
sponse capability of 0 and thus being unable to participate in the current response. The
user’s responsive load curve at this time is shown in Figure 13.
Figure 13. User response load curve considering delay.
Considering the impact of high latency on the demand response capability of air con-
ditioners, the continuous load curves of this split air conditioner under different high-
latency rates can be obtained. At this time, the user’s response level under a certain incen-
tive is 0.35. Based on this, the trusted response levels of the user under different high-
latency rates are calculated, as shown in Table 7.
Table 7. Consider the degree to which users can be trusted to respond with high latency.
High Latency 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Degree of trusted response 0.329 0.297 0.260 0.238 0.184 0.165 0.122 0.063 0.034
From Table 7, it can be seen that with the increase in high-latency rates, the degree of
user trusted response significantly decreases. When the high-latency rate is low (0.1–0.3),
even a small delay can have a noticeable impact on response capability. At a high-latency
Figure 13. User response load curve considering delay.
Considering the impact of high latency on the demand response capability of air
conditioners, the continuous load curves of this split air conditioner under different high-
latency rates can be obtained. At this time, the user ’s response level under a certain
incentive is 0.35. Based on this, the trusted response levels of the user under different
high-latency rates are calculated, as shown in Table 7.
Table 7. Consider the degree to which users can be trusted to respond with high latency.
High Latency 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Degree of trusted response
0.329 0.297 0.260 0.238 0.184 0.165 0.122 0.063 0.034
From Table 7, it can be seen that with the increase in high-latency rates, the degree of
user trusted response significantly decreases. When the high-latency rate is low (0.1–0.3),
even a small delay can have a noticeable impact on response capability. At a high-latency
rate of around 0.5, the trusted response degree begins to decline rapidly, which can be
considered a critical point. Beyond this critical point, the response capability deteriorates
sharply, and other regulatory measures need to be considered as a supplement. When
latency rates are high (0.7–0.9), the trusted response degree drops to an extremely low
value, making it almost impossible to provide effective load response.
In this residential area, the high-latency rates of split air conditioners for 2285 house-
holds are distributed within the range of (0–1). With a confidence level of 95%, the Zis
1.645 [
42
,
43
]. The trusted adjustable potential for participating in the response over a 12-h
period is calculated, and the results are shown in Table 8.
As shown in the table above, at 12:00, the total responsive power for this residential
area is 3754.074 kW, with the responsive capability of the split air conditioner group being
3304.169 kW. The confidence interval provides statistical confidence in the trusted response
potential. The 95% confidence interval is [3270.087, 4238.061], indicating that in 95% of
cases, the response capability will fluctuate within this range.
The response degree reflects the enthusiasm of residential users to participate in load
adjustment at various times. It can be seen that from 3:00 to 5:00, the response potential
is almost zero, which is related to the daily routines of residential users. The response
potential gradually increases during the morning period as devices begin to be used
gradually. From 10:00 to 12:00, residential electricity consumption is relatively high, and
Electronics 2024,13, 2795 18 of 21
the potential for load adjustment is also at its maximum. During this time, residential users
are most likely to participate in load adjustment.
Table 8. Residential user credible response potential.
Time
(h) Credible Response Potential (kW) Response Potential Confidence Interval
(kW) Response Degree
1 371.094 [353.035, 389.142] 0.083
2 106.055 [101.171, 110.938] 0.027
3 21.901 [21.129, 22.694] 0.006
4 0 [0, 0] 0
5 0 [0, 0] 0
6 76.068 [71.275, 80.850] 0.018
7 208.241 [195.041, 221.442] 0.047
8 389.880 [365.024, 414.736] 0.088
9 584.678 [547.278, 622.079] 0.15
10 3342.069 [3127.222, 3556.906] 0.785
11 3430.005 [3044.948, 3815.062] 0.793
12 3754.074 [3270.087, 4238.061] 0.921
Based on the calculated trusted response capability and confidence interval, these
figures can provide a basis for quickly mobilizing the load of residential users in emergency
situations. This helps in setting more reliable response targets in emergency plans and
improves the scientific accuracy and market competitiveness of trading decisions in the
electricity market.
4.2. Discussions
The research outcomes presented in this paper are not confined solely to the application
scope of air conditioning systems. This set of solutions can be widely applied to the
management of diverse flexible energy resources, such as distributed photovoltaics, energy
storage systems, and electric vehicle charging networks. For other types of flexible demand
resources, it is only necessary to adjust the corresponding models and parameter settings
according to their specific characteristics and operating modes. In addition, depending
on the layered architecture, with the increase in the number of intelligent devices, the
system is scalable. To avoid affecting the computing speed, the data processing capacity
can be allocated to the edge through edge computing, effectively reducing the burden on
the central server. This paper primarily focuses on the impact of delay as an uncertain
communication factor, while current research on communication uncertainty may rely
more on mathematical models [
51
,
52
]. In contrast, this paper utilizes actual measured
data, which can more accurately reflect the delay conditions in real environments. We
also recognize the necessity to introduce more uncertainty factors, such as user response
willingness mentioned in [
53
,
54
], to enhance the applicability and robustness of the model.
5. Conclusions
The core of this study lies in addressing the response latency issues encountered when
integrating demand-side flexible resources into the energy management system. The article
innovatively proposes a bidirectional communication latency measurement technique
based on the MQTT protocol, which accurately measures and analyzes network latency
characteristics. This not only strengthens the system’s real-time perception of network
conditions but also provides a scientific basis for optimizing communication processes and
reducing unnecessary data delays, as well as offering real-time data support for subsequent
resource regulation strategies. Furthermore, a resource responsiveness adjustment model
considering network delay is proposed. The highlight of this model is the creative inclusion
of latency reliability assessment indicators, enabling accurate prediction and evaluation
of the actual response of air conditioning systems even in the presence of communication
Electronics 2024,13, 2795 19 of 21
delays. This effectively mitigates the negative effects of latency, ensuring timely execution
of control commands. This undoubtedly provides a guarantee for enhancing the efficiency
of flexible resource utilization and the precision of regulation.
This paper assumes that high latency uniformly affects all devices. In the future, we
will explore the impact of factors such as device type and location on delay.
Author Contributions: Conceptualization, Y.L. and C.L.; methodology, Y.L. and C.L.; software,
Y.L. and J.T.; validation, J.T. and S.L.; formal analysis, S.L.; investigation, X.W.; resources, J.T.; data
curation, C.L.; writing—original draft preparation, Y.L. and C.L.; writing—review and editing, J.T.
and S.L.; visualization, X.Z. and X.W.; supervision, Y.L.; project administration, C.L. All authors have
read and agreed to the published version of the manuscript.
Funding: This work was supported by the National Key R&D Program of China (No. 2021YFB2401200).
Data Availability Statement: The data presented in this study are available on request from the
corresponding author. The data are not publicly available due to privacy.
Conflicts of Interest: Authors Ying Liu, Chuan Liu, Jing Tao, Shidong Liu, Xiangqun Wang and
Xi Zhang were employed by the company State Grid Smart Grid Research Institute Co., Ltd. The
remaining authors declare that the research was conducted in the absence of any commercial or
financial relationships that could be construed as a potential conflict of interest.
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