Demand Response Strategy Optimization Method Based on Differentiated Comprehensive Benefit Model of Air-Conditioning Customers

Abstract

Air-conditioning systems are critical demand response (DR) resources, yet conventional temperature adjustment strategies based on fixed setpoints often neglect users’ heterogeneous economic and comfort requirements. This paper proposes a DR strategy optimization method based on user-specific comprehensive benefit evaluation. Firstly, a quantitative model integrating economic benefits and thermal comfort loss is established through the DR benefit mechanism. Subsequently, a DR strategy optimization model is established with indoor temperature setpoints as variables to maximize comprehensive benefits. Finally, comparative simulations involving 15 customers with varying benefit parameters (basic profitability and labor elasticity coefficients) demonstrate the proposed strategy’s superiority in load reduction and customers’ benefit over traditional fixed setpoint methods. The results indicate the following: (1) the optimized strategy achieves greater load reduction under most scenarios than traditional fixed-setpoint adjustment strategies; (2) all participants obtain enhanced comprehensive benefits compared with traditional strategies; and (3) customers with lower profitability and less dependency on labor show better responsiveness. This study improves DR participation incentives by balancing economic and comfort benefits, providing theoretical support for designing user-specific demand-side management policies in smart building applications.

1. Introduction

With the integration of large-scale intermittent renewable energy, the safe and stable operation of power grids faces growing challenges. Demand response has proven to be an effective solution to alleviate grid pressure, primarily through economic incentives to mobilize demand-side flexible resources for grid regulation requirements. Notably, air conditioning load constitute 40–60% of building energy consumption [1], and its operational adjustment demonstrates significant feasibility, making it a crucial demand response resource. However, differentiated thermal comfort requirements across building types lead to substantial variations in demand response potential. For instance, a regional study revealed that the top 5% of users with high response potential contribute 40% of total adjustable resources [2], indicating their superior regulatory capacity compared to other users. Furthermore, the existing literature consistently highlights that commercial buildings exhibit greater demand response potential than residential buildings [3,4]. Therefore, investigating the demand response characteristics of air-conditioning systems in different building types and developing corresponding control strategies can enhance user participation willingness and optimize the aggregation efficiency of response resources [5].

The potential for air-conditioning demand response is significantly influenced by the differentiated energy consumption needs of air-conditioning users. These needs mainly include thermal comfort and air quality. A few studies have used air pollutants and occupancy to evaluate the need to ventilate [6,7]. Most existing studies directly employ thermal comfort evaluation methods to quantify the energy consumption demands of air-conditioning users [5]. Thermal comfort evaluation methods can be broadly categorized into subjective and objective evaluations. One approach involves using discrete indoor environmental temperatures as objective evaluation indicators [8]. Another approach considers the sensitivity of air-conditioning users to indoor temperatures under different thermal environments [9]. For example, Meimand et al. divided personal thermal sensation against ambient conditions into three categories (uncomfortably cold, comfortable, and uncomfortably warm) and formed individual probability distributions for each class [10]. Su et al. proposed a fast DR optimization method based on user’s personalized thermal comfort temperature range [11]. Based on thermal balance models, relevant subjective evaluation indicators have been constructed [12,13], such as the Predicted Mean Vote (PMV) index. The PMV index takes into account various factors affecting human comfort, including air temperature, mean radiant temperature, relative humidity, air velocity, and the activity level and clothing insulation of individuals [14]. The American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) Standard 55 also selects temperature setpoints based on the PMV [15,16]. For example, Lee et al. used the PMV and the one-time constant to evaluate occupants’ thermal comfort with a DR strategy of increasing the temperature by 2 °C [17]. Li et al. developed thermal comfort PMV models considering the impact of these additional cooling behaviors during residential DR periods [18]. Szczepanik-Scislo et al. used the PMV and PPD to prove that thermal comfort was maintained regardless of changing airflow [19]. However, compared to thermal comfort evaluation metrics themselves, the impact of comfort on users’ benefit for building occupants is more instructive. For example, Amin et al. considered the varying thermal preferences of occupants in various zones as a response of real-time pricing signals [20]. Seppänen et al. developed a quantitative relationship model linking office work performance with temperature [21]. Cui et al. established models for the impact of environmental temperature on occupant activity performance using experimental and regression analysis methods [22]. Nevertheless, most of these studies were limited to straightforward comfort indicators or derived specific thermal comfort models through regression analysis for particular scenarios. The complex impact of thermal comfort on occupant work performance and economic benefits is frequently overlooked, making it challenging to accurately quantify the comprehensive benefit requirements of different DR customers.

The demand response control methods for building air conditioning should take into account the feasibility and DR adjustment objectives and clarify the forms and strategies of regulation. Flexible regulation forms mainly include the following three categories [1,23]. (1) Chiller-side control: this mainly involves adjustments to chilled water temperatures and reducing the number of operating chillers. (2) Energy storage control strategies: these include active energy storage and passive energy storage. (3) End-use control measures: these involve global temperature adjustments, duct static pressure regulation, fan speed adjustments, and supply air temperature adjustments. Flexible regulation methods based on the cold-source side and energy storage have a fast response speed and have received much attention from many studies [24]. However, this method requires professional personnel to carry out regulation. It is only suitable for large-air-conditioning users with a mature energy management system. In contrast, the flexible regulation method based on the air-conditioning terminal is more suitable for promotion among dispersed small users, among which the adjustment of the indoor temperature setpoint is the most convenient and direct means of regulation. The regulation strategies mainly include two modes [25]: rule-based and optimization-based. The rule-based regulation strategy is simple and fast, with a small amount of calculation. However, this strategy is difficult when fully considering the differences in user needs under various scenarios and cannot achieve the optimal regulation effect. The optimization-based regulation strategy mostly takes the maximum load reduction or the optimal economic benefit as the goal and only regards the user’s comfort as a constraint condition [26]. For example, Azuatalam et al. proposed a novel reinforcement learning architecture based on adjusting the zone temperature set point, with the objective of improving energy efficiency and thermal comfort levels [27]. Sun et al. proposed a hierarchical control framework with various objectives (minimizing energy consumption, reducing electricity costs, and lowering carbon emissions), while ensuring thermal comfort [28]. Schierloh et al. constructed a cost function including the cost of electricity bills and the PMV [29]. Most of the demand response regulation methods in existing studies are suitable for centralized regulation systems and mostly take into account load reduction, economic benefit, and thermal comfort as separated metrics. Small-air-conditioning and medium-air-conditioning users are rarely taken into account. And a comprehensive object is lacking, which can conduct a unified evaluation to different DR strategies. The above research defects reduce the enthusiasm of users to participate in demand response.

On the whole, the existing studies related to demand response strategy of air-conditioning load still have the following two problems:

(1)

The existing air-conditioning user demand elasticity model is mostly based on simple regression analysis, ignoring the complex mechanism of economic benefits and thermal comfort on the user’s willingness to participate in the demand response, so it is difficult to accurately quantify the benefit needs of DR control strategies for different air-conditioning users.

(2)

Existing demand response regulation methods ignore the differentiated economic benefits and thermal comfort needs of different users, failing to establish a unified multi-objective coordination mechanism. This results in suboptimal outcomes that do not align with user’s dual requirements for economic benefits and thermal comfort, ultimately diminishing user engagement in demand response initiatives.

To address the above deficiencies, this study takes the office building air-conditioning users participating in summer peak-shaving DR events as an example and establishes an optimization method for DR regulation strategies that takes into account the differentiated benefit needs of air-conditioning users. The main contributions of this work are two-fold:

(1)

A comprehensive benefit quantification model for air-conditioning users that takes into account the DR economic benefits and thermal comfort is established, which aims to accurately quantify the benefit of DR control strategies for different types of air-conditioning users.

(2)

An optimization method for DR regulation strategies is proposed, with the objective of best comprehensive benefits for air conditioning users, which aims to meet the differentiated benefit needs of different users.

The rest of the paper is organized as follows: Section 2 describes the establishment process of the comprehensive benefit quantification model and the optimization method of the DR regulation strategy. Section 3 analyzes the effectiveness of the proposed control strategy optimization method by comparing it with the traditional control strategy of the upward adjustment of fixed indoor temperature setpoints. Section 4 discusses the shortcomings of the comprehensive benefit quantification model and future research directions. Section 5 summarizes this study.

2. Methods

The research adopts a four-step analytical framework consisting of mechanism analysis, model development, algorithm implementation, and validation, as illustrated in Figure 1. Step 1 identifies HVAC users’ demand response (DR) benefit mechanisms and establishes transformation relationships between economic benefits and thermal comfort indicators. Step 2 develops a comprehensive benefit quantification model based on the developed benefit mechanisms, through parameterization of input variables and mathematical formulation of benefit conversion processes. Step 3 constructs the HVAC DR strategy optimization model, which: (1) defines comprehensive benefit maximization as the objective function; (2) selects temperature setpoints per timestep as decision variables; and (3) implements Particle Swarm Optimization (PSO) as the computational algorithm. Step 4 validates model effectiveness using the DOE standard building model as a case study, with a comparative analysis of load reduction performance and user benefit metrics across various DR strategies.

2.1. HVAC Customer’s DR Benefit Mechanism

The satisfaction level of users’ response benefit requirements significantly influences their willingness to participate in demand response (DR) programs [30,31]. This necessitates the establishment of a user demand response benefit mechanism to guide the development of quantitative models for air-conditioning user benefits.

User demand response benefits primarily consist of two components: economic compensation from load reduction and operational losses caused by reduced thermal comfort [32,33]. For profit-driven commercial users, these two elements can be economically equivalent. During summer peak-shaving DR events, the interaction between DR adjustments and benefits manifests differently across phases, which can be seen from

Table 1. DR customers benefit mechanism in different phases.

Phase	DR Incentives	Economic Benefit	Comfort Equivalent Benefit	Profit Function
Response period	✓	Generating economic benefit through load reduction (+)	Operational efficiency losses (−)	Economic benefit + Operational efficiency losses
Pre-response and post-response	✗	Increases energy consumption and electricity costs (−)	Operational efficiency increase (+)	Electricity costs + Operational efficiency increase

.

In the response period, users increase the indoor temperature setpoint to reduce cooling loads, generating economic benefit through load shedding. However, this temperature increase simultaneously degrades thermal comfort, leading to operational efficiency losses. The total benefit during this phase represents the sum of economic benefit and operational losses. While heightened economic incentives motivate users to accept higher temperatures for greater financial returns, such adjustments are constrained by practical limits: insufficient temperature increases yield little economic gains, whereas excessive adjustments risk a decrease in work efficiency and ultimately affect the overall efficiency of the enterprise.

During pre-response and post-response periods, users may lower the indoor temperature setpoint to pre-cool or restore thermal comfort, enhancing operational efficiency through improved environmental conditions. This strategy, however, increases energy consumption and electricity costs. The net benefit during these phases corresponds to the difference between operational gains from comfort improvements and additional electricity expenditures. Temperature reductions are similarly bounded by diminishing benefit—insufficient cooling provides little comfort improvements, while over-cooling disproportionately escalates energy expenses.

The temperature–benefit relationships in both phases exhibit user-specific variations, primarily governed by the sensitivity of operational efficiency to comfort level changes. This theoretical framework underscores the need for a quantitative model enabling precise prediction of user responsiveness and flexibility potential in DR programs. Such a model incorporates user-specific parameters such as comfort thresholds, economic benefit expectations, and external incentive structures.

2.2. Comprehensive Benefit Quantification Model of Air-Conditioning Customers

The transformation model between DR strategy and customer’s DR benefit can be established as shown in Figure 2. The model inputs comprise three categories: temperature setpoint (the baseline temperature and DR regulation temperature), electric parameters (electric price and DR incentive), and customers’ benefit parameters (basic profitability and elasticity coefficient of labor). The output values include customers’ economic benefit, comfort benefit, and comprehensive benefit. For specific DR temperature regulation strategies, the time-step-aligned response temperature sequence and baseline temperature sequence are first input into the building simulation model. Simulation calculations subsequently generate baseline and response load profiles, along with corresponding PMV sequences under baseline and DR-adjusted temperature conditions. Next, the economic benefits under DR strategies are calculated using baseline/response load profiles, electricity prices, and DR incentive signals through the economic benefit calculation model. Concurrently, the comfort equivalent benefits are derived from baseline and response PMV values, customers’ basic profitability, and the elasticity coefficient of labor through the comfort equivalent benefit calculation model. Finally, the total comprehensive benefit under DR strategies is obtained by aggregating economic and comfort equivalent benefits. The following task is to construct the comprehensive benefit calculation model, economic benefit calculation model, and comfort equivalent benefit calculation model.

(1)

Comprehensive benefit composition and calculation model

According to the demand of office building DR customers, the comprehensive benefit calculation model of air conditioner users can be established. The total benefit is the sum of the comprehensive benefits in the pre-cooling period, response period, and recovery period.

$$W_{Total}={\displaystyle {\sum }_{t=1}^{n-pc}}{W}_{pre-cooling}^t+{\displaystyle {\sum }_{t=1}^{n-DR}}{W}_{DR}^t+{\displaystyle {\sum }_{t=1}^{n-rc}}{W}_{recover}^t$$

(1)

where $W_{Total}$ is the total comprehensive benefit of DR customer at all time steps. $W_{pre-cooling}$ and $W_{recover}^t$ are the comprehensive benefits of the pre-cooling and recovery period. $W_{DR}^t$ is the comprehensive benefit of a certain time step in the response period. The user’s benefit is measured in the unit of the electricity price, which is taken in CNY. The time scale of summer peak-shaving demand response events is generally 2 h. Every 15 min in the control system is a regulation time step, and the comprehensive benefit is calculated in each time step. The n-pc, n-DR, and n-rc are the number of time steps in the pre-cooling, response, and recovery periods, which can be set reasonably according to the actual regulation demand and scheduling arrangement of the power grid and the aggregator.

The comprehensive benefit of each time step comprises two elements. The calculation formula is as follows:

$$W_{DR}^t={EC}_{DR}^t+F_{DR}^t$$

(2)

$$W_{pre-cooling}^t={EC}_{pre-cooling}^t+F_{pre-cooling}^t$$

(3)

$$W_{recover}^t={EC}_{recover}^t+F_{recover}^t$$

(4)

where $W_{DR}^t, W_{pre-cooling}^t,W_{recover}^t$ represent the comprehensive benefit of customers at a certain time step in the response, pre-cooling, and recovery period, respectively. ${EC}_{DR}^t,{EC}_{pre-cooling}^t,{EC}_{recover}^t$ represent the economic benefit caused by air conditioning load fluctuation in a certain time step of the response time, pre-cooling, and recovery period. $F_{DR}^t,F_{pre-cooling}^t,F_{recover}^t$ represent the loss of profitability of customers at a certain time step in the response period, pre-cooling period, and recovery period, which is caused by the change in work performance due to the loss of thermal comfort. All values are in CNY.

(2)

Economic benefit calculation model

The economic benefit comprises the electricity economic cost and the DR economic incentive. The calculation formula is as follows:

$${EC}_{DR}^t=\left(P_{base}^t-P_{dr}^t\right)\times \mathrm{t}\times I_{dr}^t-\left(P_{dr}^t\times I_{base}^t-P_{base}^t\times I_{base}^t\right)\times t$$

(5)

$${EC}_{pre-cooling}^t=\left(P_{pre-cooling}^t\times I_{base}^t-P_{base}^t\times I_{base}^t\right)\times t$$

(6)

$${EC}_{recover}^t=\left(P_{recover}^t\times I_{base}^t-P_{base}^t\times I_{base}^t\right)\times t$$

(7)

where $P_{base}^t$ refers to the baseline load of the user at a time step, in kW, which can be calculated according to the baseline of the indoor temperature setpoint, combined with the current meteorological temperature and the building physical model established in the EnergyPlus (v22-2-0) software; $P_{pre-cooling}^t,P_{dr}^t,P_{recover}^t$ refer to the pre-cooling, response, and recovery load of the user at the time step t, in kW, calculated according to the response value of the indoor temperature control point, combined with the current meteorological temperature and the building physical model established in the EnergyPlus software; $I_{base}^t$ refers to the time-of-use electricity price of the grid for office building users at the time step, in CNY; $I_{dr}^t$ refers to the response incentive of the time step, in CNY; and t refers to the length of each control time step.

(3)

Comfort equivalent benefit calculation model

It has been evidenced by research that building infrastructure, sanitary conditions, and thermal environment have significant impacts on employee performance, which subsequently influences the economic benefits of enterprises [34]. The change in equivalent economic benefits caused by the change in the user’s thermal comfort during the DR period is defined as the difference between the benefit at a certain time in the process of pre-cooling, response, and recovery, and the benefit at the baseline temperature, which is calculated as follows:

$$F_{DR}^t=Y_{DR}^t-Y_{base}^t$$

(8)

$$F_{pre-cooling}^t=Y_{pre-cooling}^t-Y_{base}^t$$

(9)

$$F_{recover}^t=Y_{recover}^t-Y_{base}^t$$

(10)

$Y_{DR}^t,Y_{pre-cooling}^t,Y_{recover}^t$ represent the profitability of office building customers at a certain time step in the response period, pre-cooling period, and recovery period, where the unit is CNY. $Y_{base}^t$ is the basic profitability of the same customer at the baseline temperature, in CNY. The profitability discussed in this model is mainly affected by personnel comfort, with a complex transformation mechanism between the two variables. In accordance with the Cobb–Douglas production function [35], the total output value of an enterprise is determined by its production factors as follows:

$$Y\left(t\right)=A\left(t\right){L\left(t\right)}^{\alpha }{K}^{\beta }\mu$$

(11)

Y represents the total output value of the enterprise, which is usually expressed in monetary units. A(t) denotes the level of integrated technology and is a dimensionless parameter. L is the input labor force, which is usually 10,000 people, and sometimes it can also be working hours. K refers to the input capital, usually expressed in monetary units, which is typically defined as net fixed assets. α is the elasticity coefficient of the output of labor; β is the elasticity coefficient of the output of capital; and μ symbolizes the impact of random disturbances. The labor input can be transformed into a product of the basic labor input and labor efficiency, as shown in Equations (12) and (13):

$$L\left(t\right)=l\times KPI\left(t\right)$$

(12)

$$Y\left(t\right)=A\left(t\right)({l\times KPI(t))}^{\alpha }{K}^{\beta }\mu$$

(13)

where l is the amount of basic labor input, and KPI represents the personnel work efficiency affected by thermal comfort, which refers to the percentage of work performance relative to full performance. In the short term, the changes in the net fixed assets, total labor input, capital input, and random interference are very small and can be regarded as a constant, so the above formula can be transformed into:

$$Y\left(t\right)=W\left(t\right)\times {KPI\left(t\right)}^{\alpha }$$

(14)

W represents the basic profitability of an office building, calculated by combining the net fixed asset value, total labor input, invested capital, random interference, and other factors, in CNY. This figure can be used to represent the profitability of office building users when the work performance of personnel is 100% in the target period. The basic profitability W and the labor output elasticity coefficient α require the input value of the user side. Consequently, the two parameters can be adjusted individually in accordance with the operational status of different customers over different time periods.

The work performance percentage KPI here is affected by the environmental thermal comfort. According to GB/T 50785-2012 “Civil Thermal and Humid Environment Evaluation Standard” [36], the Predicted Mean Vote (PMV) is used to characterize the comfort of the indoor environment. The typical model in the existing research is selected to describe the influence of the PMV on employees’ work performance [37], and the calculation expression of KPI is as follows:

$$KPI\left(t\right) = (-0.959\times {PMV\left(t\right)}^2-0.254\times PMV(t)+102.9)/100$$

(15)

The PMV is calculated by building simulation software according to the indoor set temperature of the air-conditioning system in the response period, with consideration of the external environmental parameters, the building’s physical characteristics, and the status of the building’s occupants. As formalized in Equations (1)–(15), the transformation relationship between the DR strategy and office building customers’ comprehensive benefit can be obtained, as shown in Figure 3.

2.3. DR Strategy Optimization Model of Air-Conditioning Customers

Based on the behavior and benefit distribution mechanism of each subject in the demand response event, this section develops an interactive demand response model balancing stakeholder interests and formulates an optimization model for temperature control strategies. The optimization goal is the comprehensive benefit of the air-conditioning user’s response, and the optimization variable is the indoor set temperature at the end of the user’s air-conditioning equipment use in the three stages of pre-cooling, response, and recovery.

2.3.1. Demand Response Implementation Model

The implementation model of the demand response interaction described in this study is shown in Figure 4. First, the load aggregator configures the logic of regulation in the control system, while customers autonomously set benefit parameters via a user-side interface, thus forming a personalized comprehensive benefit calculation model for each office customer. Second, based on building physical information, external environmental parameters, the response DR incentive mechanism, and electricity price, the optimized control algorithm in the control system will evaluate the effect of different control strategies. Finally, the control system will transmit the optimal control strategy signal to the final equipment control device, thereby modifying equipment operation states.

The generated response strategy is the indoor temperature setpoint control that can intuitively characterize the thermal comfort of the environment. The control strategy signal can be made available to an interactive input module of a traditional control system, a user-defined transmission network, or a user interface based on a smart phone application program. Temperature control can be achieved using either simple thermostats or sophisticated building automation control systems [38,39].

2.3.2. User-Side Demand Response Strategy Optimization Process

In the optimization problem discussed in this paper, the optimization variables are discrete indoor temperature setpoint sequences. Due to the long time required for simulation, the optimization algorithm needs to have a fast convergence speed. The Particle Swarm Optimization (PSO) algorithm, chosen for its rapid convergence and optimization efficacy, is finally selected to solve the optimization problem in this paper. The algorithm initializes a population of particles, each representing a candidate solution with a position and velocity in the search space. During iterations, particles evaluate their fitness (objective function value) and dynamically adjust their trajectories by learning from both their own historical best performance and the swarm’s global best solution. By iteratively updating velocities and positions, particles collaboratively explore the solution space, balancing global exploration and local refinement until convergence criteria are met.

To determine the optimal indoor temperature setpoint sequence in this study, the optimization variables, objectives, fitness function, and algorithm parameters of the PSO algorithm are defined as follows. For a single user during a demand response event, the optimization variable corresponds to the temperature setpoint sequence spanning three operational phases (pre-cooling, response, and recovery), with 15 min timesteps. Each particle represents a temperature sequence, where the number of timesteps defines the particle’s dimensionality. The optimization objective is to maximize the comprehensive benefit derived from the temperature sequence. Consequently, the fitness of each particle in PSO quantifies the customer’s comprehensive benefit under a specific temperature sequence. The fitness function, which maps temperature sequences to comprehensive benefits, is implemented via the comprehensive benefit quantification model established in Section 2.2. Algorithm parameters were configured based on preliminary experiments: population sizes of 20–50 particles and iteration limits of 20–50 generations ensured convergence of the comprehensive benefit curves across all users. These ranges will be flexibly adjusted per user to balance computational efficiency and solution quality.

Python (v3.12) is selected as the primary computational tool for mathematical modeling and optimization in this study. EnergyPlus is used for simulation. Furthermore, Python scripting enables automated batch execution of EnergyPlus simulations, effectively invoking the EnergyPlus simulator for iterative computations during optimization processes. This integration streamlines repeated simulation runs by programmatically controlling parameter inputs and output extraction, thereby supporting efficient iterative optimization procedures.

The workflow of the user-side DR indoor temperature setpoints sequence optimization program is set as follows, which is shown in Figure 5.

The controller receives an outdoor temperature signal, an electricity price signal, and a demand response excitation signal.

Users set basic profitability and labor elasticity coefficients.

The PSO algorithm is used to initialize and iterate the users’ indoor temperature setpoints sequence for three periods, pre-cooling, response, and recovery, with the indoor temperature setpoints sequence written into the EnergyPlus input data file through the Python programming language and the response load obtained by simulation calculation.

Calculate comprehensive benefits to customers under different indoor temperature setpoints sequences using the quantification model from Section 2.2.

With the goal of optimizing the comprehensive benefits, judge whether the iterative optimization is completed. When the optimization process is ended, the DR indoor temperature setpoints sequence optimization result is output, and the response load sequence and the customers’ benefit under the optimal temperature sequence are output at the same time.

2.4. Effectiveness Validation Method of the Optimized DR Strategy: A Case Study

Based on a building case and real boundary conditions, this section will verify the feasibility of the air-conditioning DR strategy optimization model proposed in this paper.

2.4.1. Boundary Condition of Building Case

The case study is located in Xiamen, Fujian Province, China, situated in a subtropical zone characterized by a south subtropical monsoon climate. The annual average temperature is 21 °C, while the average temperature in the hottest month (August) is approximately 28 °C, with the potential for the maximum temperature to reach approximately 38 °C. The monitoring data of the power sector in 2014 indicate that on 4 July, during the period of peak temperature, the air-conditioning load accounted for 40% of total electricity consumption in the power grid, reaching a peak in electricity consumption that presented a challenge to the power supply [40]. In January 2023, the Xiamen Development and Reform Commission and the Xiamen Finance Bureau published “The Xiamen Power Demand Response Implementation Plan (2023–2025)”, which specifies participation thresholds, modes, and interaction mechanisms for DR customers [41]. Consequently, air-conditioning users in Xiamen have great DR potential and mature conditions for DR implementation.

The basic electricity price is based on the peak and valley tariff policy announced by the Xiamen grid, which is CNY 0.68/kWh (normal period), CNY 0.955/kWh (peak), and CNY 1.047/kWh (sharp peak). In addition, according to the Xiamen DR policy, the response incentive is set at 4 CNY/kWh. For three different periods of a DR event, the pre-cooling period is 1 timestep, which is 15 min, the DR period is 4 timesteps, and the recovery period is 1 timestep.

The building physical model is selected from the standard building models developed by the U.S. Department of Energy (DOE). The target building is a medium-sized office building with a floor area of 4982.19 m². There are 3 floors in this building, and each floor has four surrounding areas and a core area, which account for 40% and 60% of the floor area, respectively. The building envelope design parameters and occupancy information are shown in Figure 6. To ensure that the model can represent the typical architectural characteristics of China, the building boundary conditions are set according to the building design standards of China. For example, the schedule of personnel occupancy and the anticipated usage of electrical equipment in daily use scenarios are set according to GB 50189-2015 “Design Standard for Energy Efficiency of Public Buildings” [42], Typical Meteorological Year (TMY) data for Xiamen, sourced from EnergyPlus, including temperature, humidity, solar radiation, and wind speed.

2.4.2. Air-Conditioning Customers’ Benefit Parameters Setting

Building users are defined as office customers with a profit motive. As described in Section 2.1, the base profitability W and the labor elasticity coefficient α are the main air-conditioning user characteristics, which are set as shown in

Table 2. Air-conditioning user characteristics setting.

Customer Characteristics	W1 = 10,000 CNY/h	W2 = 20,000 CNY/h	W3 = 30,000 CNY/h	W4 = 40,000 CNY/h	W5 = 50,000 CNY/h
α1 = 0.5	Customer 1	Customer 4	Customer 7	Customer 10	Customer 13
α2 = 1	Customer 2	Customer 5	Customer 8	Customer 11	Customer 14
α3 = 2	Customer 3	Customer 6	Customer 9	Customer 12	Customer 15

.

The basic profitability can be set with reference to the output value of personnel. According to the International Statistical Yearbook 2023 [43], China’s GDP per capita in 2022 was USD 12,720, and the annual working hours were 2080 h, calculated according to 52 weeks, 5 days a week, and 8 h a day, so the GDP per capita per hour was USD 6.12. According to the exchange rate of USD 1 = CNY 7.25, this can be converted to CNY 44.37; The construction area set in this paper is 4982.19 m², the personnel density is 10 m²/person, the total number of people is estimated to be about 500 people, and the total output value is 22,185 CNY/h. Considering that this value is the national average, the per capita output value of other high-income and low-income countries is referred to. Representative values are taken in five output levels of low, lower-middle, middle, upper-middle, and high, respectively. Five basic profitability levels are set as follows: W₁ = 10,000 CNY/h, W₂ = 20,000 CNY/h, W₃ = 30,000 CNY/h, W₄ = 40,000 CNY/h, and W₅ = 50,000 CNY/h.

The labor elasticity coefficient is generally between 0 and 1. For capital-intensive customers, productivity mainly depends on capital input and less on labor input; the labor elasticity coefficient is usually between 0.4 and 0.6. In the knowledge-intensive or service-oriented office building scene, enterprises have a high dependence on labor skills and knowledge, and the contribution of labor input to output is more significant. The elasticity coefficient of labor output is usually higher, which is close to 1. In addition, under special economic circumstances, for example, with labor-intensive office customers, the increase in labor force will significantly affect the productivity of enterprises, and the value of the labor elasticity coefficient may be greater than 1. In summary, this study sets three levels of the labor elasticity coefficient, which are α₁ = 0.5, α₂ = 1, and α₃ = 2.

2.4.3. Control Strategy Setting

Referring to GB 50736-2012 “Design Code for Heating, Ventilation and Air Conditioning in Civil Buildings” [44], the baseline indoor temperature setpoint for air-conditioning users in office buildings is 26 °C. The adjustable range of the indoor temperature setpoint is 24–28 °C, with an adjustment step of 0.5 °C. The indoor temperature setpoint can be optimized in the adjustable range at pre-cooling, response, and recovery periods of DR. The PSO algorithm is used to calculate the optimal indoor temperature setpoint adjustment strategy. Two conventional control strategies are set as control groups, as shown in

Table 3. Control strategies of air-conditioning users.

Control Strategies		Stages
		Pre-Cooling	Response	Recovery
Optimization Strategies		Optimization of the Room Temperature Setting Within the Adjustable Range
Conventional strategies	Strategy A	No pre-cooling	Indoor temperature set point up to 27 °C	Indoor temperature set point down to baseline 26 °C
	Strategy B	No pre-cooling	Indoor temperature set point up to 28 °C	Indoor temperature set point down to baseline 26 °C

. The two conventional strategies have no pre-cooling control, and the end temperature is increased to 27 °C and 28 °C in the response period and then decreased to 26 °C in the recovery period.

The effectiveness of the optimization strategy, compared to baseline strategies, is evaluated using two metrics: grid-side power curtailment and user-side benefit indicators.

(1)

Grid-side power curtailment

For the predefined 1 h demand response period with 15 min timesteps, power curtailment is defined as the average difference between baseline power and response power across four timesteps (t = 2 to 5). Greater curtailment indicates greater alignment with grid-side objectives. The power curtailment for an individual user is calculated according to Formula (16).

$$P_{CUT}={\displaystyle \frac{{\displaystyle {\sum }_{t=2}^5}(P_{DR}^t-P_{BASE}^t)}{4}}$$

(16)

where $P_{CUT}$ denotes the power curtailment of a single user during a response event, $P_{DR}^t$ represents the user’s response power at timestep t, and $P_{BASE}^t$ is the baseline power at timestep t.

(2)

User-side benefits

User benefits are evaluated across six timesteps encompassing pre-cooling, response, and recovery periods. Higher benefits reflect greater user-friendliness of the strategy. The benefits are quantified according to Formulae (17)–(19):

$${EC}_{DR}={\displaystyle {\sum }_{t=1}^6}{EC}_{DR}^t$$

(17)

$$F_{DR}={\displaystyle {\sum }_{t=1}^6}{F}_{DR}^t$$

(18)

$$W_{DR}={\displaystyle {\sum }_{t=1}^6}{W}_{DR}^t$$

(19)

where ${EC}_{DR}$ denotes the total economic benefit, $F_{DR}$ represents the comfort-equivalent benefit, and $W_{DR}$ corresponds to the comprehensive benefit for a user during the response event. The summation spans six timesteps (t = 1 to 6) to capture holistic impacts across all DR periods.

2.4.4. Simulation Verification Process

The effectiveness of the optimization strategy can be validated through the following workflow based on the established boundary conditions, building model, user benefit parameters, and experimental/control group designs for demand response strategies. First, the optimization framework described in Section 2.3 is applied to derive the optimal response temperature adjustment strategies, responsive load profiles, and comprehensive benefits for each customer under 15 distinct benefit parameter combinations, as illustrated in Figure 7. The specific procedure involves three sequential steps: (1) inputting candidate temperature adjustment strategies into EnergyPlus to compute the corresponding air-conditioning load and thermal comfort levels; (2) feeding these results into a Python-based comprehensive benefit calculation model to quantify user benefits; and (3) employing the PSO algorithm implemented in Python to iteratively maximize the comprehensive benefits, ultimately determining the optimal response strategy, load profile, and associated benefits. Subsequently, Strategy A and Strategy B—representing conventional approaches—are directly inputted into the same EnergyPlus building model and Python benefit calculation framework to obtain their respective load profiles and user benefit metrics. Finally, comparative analysis is conducted between the performance of the benefit-optimized strategy and traditional strategies across key response indicators, thereby systematically evaluating the validity and advantages of the proposed methodology.

3. Results

3.1. Optimized DR Temperature Setpoints and Load Sequences

Based on the proposed DR strategy optimization model, the optimal indoor temperature regulation strategy results for 15 users across three periods (pre-cooling, response, and recovery) are calculated. Figure 8 illustrates the optimization results for each user.

(1)

Analysis of optimal temperature setpoints

During the pre-cooling period, most users adopted a strategy of lowering the temperature setpoint to its minimum value. In the response period, significant inter-user differences emerged:

(a)

Customers with smaller labor elasticity coefficients (α) and lower baseline profitability (W) (customers 1, 2, 4, 5, 7, 10, and 13) maintained a constant elevated setpoint of 28 °C.

(b)

Users with larger α and higher W (customers 3, 6, 8, 9, 11, 12, 14, and 15) exhibited fluctuating temperature adjustments, characterized by alternating increases and decreases in setpoints during the response period. During the recovery period, most users reduced their temperature setpoints to a low level.

(2)

Analysis of optimal load sequences

The pre-cooling phase led to an increase in load due to the reduced temperature settings. In the response period, the following occurred:

(a)

Customers with smaller α and W (customers 1, 2, 4, 5, 7, 10, and 13) achieved stable load reductions.

(b)

Customers with larger α and W (customers 3, 6, 8, 9, 11, 12, 14, and 15) displayed intermittent load fluctuations, with temporary load increases corresponding to temperature adjustments. During the recovery period, load levels rose as users readjusted setpoints downward.

The results reveal significant inter-user heterogeneity during the response period, driven by distinct optimal temperature adjustment strategies. Specifically, customers adopting a constant elevated setpoint strategy (e.g., maintaining 28 °C throughout the response period) exhibited load reduction patterns and comprehensive benefits closely aligned with traditional control strategies. In contrast, users implementing dynamic temperature adjustments (characterized by alternating setpoint fluctuations between 24 °C and 28 °C) demonstrated markedly different response effects compared to traditional strategies. This complexity suggests that the observed performance differences arise not merely from setpoint magnitudes, but from time-dependent interactions between thermal storage dynamics and user-specific α/W parameters. A systematic analysis of these transient effects (e.g., through time-series decomposition or sensitivity studies) is required to fully elucidate how dynamic strategies outperform static approaches.

3.2. Effectiveness Analysis of Dynamic Optimal DR Strategy

(1)

Effectiveness of the dynamic optimal strategy for individual customers

Using customer 8 as a representative case, Figure 9 compares the performance of three control strategies: optimized strategy (orange, dynamic optimal temperature adjustments), traditional strategy A (blue, fixed 1 °C temperature increase), and traditional strategy B (green, Fixed 2 °C temperature increase). Figure 9a illustrates load reduction and temperature setpoints, with vertical color blocks demarcating pre-cooling, response, and recovery periods. Figure 9b quantifies economic benefits (upward bars), comfort loss (downward bars), and comprehensive benefits (area plots).

At time steps 1 and 3, the optimized strategy lowered the setpoint temperature, increasing load reduction. Subsequent adjustments at time steps 2 and 4 raised setpoints from lower baseline values, further enhancing economic benefits without significantly compromising comfort. This demonstrates that the optimized strategy leverages the building envelope’s thermal inertia to balance economic gains and comfort preservation. Across all periods, the optimized strategy achieved higher average load reduction and greater comprehensive benefits than traditional strategies, confirming its ability to maximize user-specific trade-offs between economic and comfort benefits.

(2)

Effectiveness of dynamic optimal strategy at the population level

Figure 10 quantifies the optimized strategy’s superiority over traditional methods at the population level using the four metrics defined in Section 2.4.3:

(a)

Load Reduction

As illustrated in Figure 10a, during the response period, the load reduction effect of all samples was superior to strategy A. And the load reduction effect of 61% of samples demonstrated a higher reduction than that of strategy B.

(b)

Economic Benefits

As illustrated in Figure 10b, all air-conditioning users exhibited a greater economic benefit than the baseline.

(c)

Comfort Loss

As illustrated in Figure 10c, the loss of comfort benefits for the 50% of consumers in the sample cluster was less than that of the two traditional strategies. And the loss of comfort benefits for the remaining 50% of consumers was less than that of strategy B and more than that of strategy A.

(d)

Comprehensive Benefits

As illustrated in Figure 10d, the comprehensive benefit of the entire sample population was superior to the two traditional strategies A and B.

3.3. Characteristic Difference Analysis of Culture Customers

Based on the DR strategy optimization model proposed in this paper, different users have different response potentials.

The air conditioner users are more likely to pay attention to the benefits of participating in the DR service. As shown in Figure 11a,b, the equal comprehensive benefit line is approximately perpendicular to the basic profitability coordinates, indicating that the comprehensive benefit of users’ participation in demand response events is mainly related to their basic profitability. In addition, users with low basic profitability have a higher proportion of optimal response income, so this type of user has a higher willingness to respond to demand.

Load aggregators are more likely to pay attention to the load reduction potential of DR customers. As shown in Figure 11c,d, the equal load reduction line is distributed at an angle and more equally, indicating that users with low basic profitability and a low labor elasticity coefficient have greater load reduction potential. Users with low base profitability and a low labor elasticity coefficient have a greater load shedding potential. This is due to the fact that this type of user has a more urgent need for economic gain, while the loss of personnel thermal comfort has a small impact on their efficiency. This type of user is a more ideal DR implementation target.

4. Discussion

The demand response temperature adjustment strategy optimization model for office buildings proposed in this study demonstrates notable innovations. Firstly, it establishes a unified evaluation metric, the comprehensive benefit, to formulate the user-side DR optimization objective. This index effectively balances personalized economic benefit requirements and comfort demands across diverse users. Compared with existing studies that predominantly employ temperature thresholds or thermal comfort indices for strategy evaluation, this approach enables a more precise quantification of user benefits in demand response participation. Secondly, the study develops a three-stage (pre-cooling, response, and recovery) demand response strategy optimization model targeting maximal user comprehensive benefits. This model incorporates differentiated objective functions for users with heterogeneous benefit priorities and extends control periods before and after the response phase to enhance overall performance. Validation results demonstrate that, compared to traditional rule-based control strategies, the optimized strategy not only maintains comparable load reduction effectiveness but also significantly improves user comprehensive benefits. This outcome substantiates the model’s superior capability to address individualized economic and comfort requirements.

This study can be generalized to other types of commercial buildings. The comprehensive benefit assessment method of DR customers proposed in this paper is primarily based on the analysis of office building customers’ economic benefit demand and thermal comfort demand. In addition, to extend the comprehensive benefit model to a range of commercial buildings, the following needs to be conducted: (a) The comprehensive benefit calculation method and economic calculation model can be directly extended to other commercial buildings. (b) The comfort equivalent benefit calculation model can be extended to other commercial buildings after adjusting the KPI, W, and α.

In addition, there are some limitations to this study. The user thermal comfort evaluation model is highly uncertain, and the relationship between thermal comfort and economic benefits is not static. Thermal comfort varies not only among different users but also dynamically with the spatial and temporal environment. For instance, some studies have indicated that a uniform or neutral temperature does not necessarily mean that all individuals are comfortable [45]. Other studies have also shown that user comfort is not only related to the temperature but may also be related to the conditions of temperature change, such as the magnitude, rate, and frequency of temperature changes. What is more, the repeated exposure of occupants to elevated indoor temperatures will ultimately increase their tolerance to these temperatures [9]. This paper focuses only on the thermal comfort demand of occupants in office building scenarios based on static temperature setpoints, and further research considering a more refined transformation relationship between air-conditioning system control parameters and occupant satisfaction is needed.

5. Conclusions

Commercial buildings’ HVAC users participating in demand response (DR) services primarily employ the traditional flexible strategy, which involves raising the indoor temperature set point to a fixed value and then returning it. However, this traditional approach fails to consider the varying thermal comfort requirements of HVAC users with different characteristics. In reality, the willingness of commercial building air-conditioning users to participate in demand response events is influenced by both the economic benefits of DR and the loss of thermal comfort. Moreover, as there is a trade-off between these two factors, DR service organizers need to consider both the economic benefits and the comfort of users and fully enhance the enthusiasm of customers to participate in demand response. Therefore, taking office buildings HVAC users participating in summer peak-shaving demand response events as an example, this paper proposes a demand response strategy optimization method based on the differentiated comprehensive benefit model of HVAC users. Furthermore, the differentiated characteristics of HVAC users adopting the best comprehensive benefits strategy are analyzed, considering both the perspectives of air conditioning users and load aggregators. Additionally, to validate the effectiveness of the proposed optimization strategy, two conventional strategies are utilized for comparative analysis. The principal conclusions are as follows:

(1)

Compared with the two traditional flexible strategies, the optimization strategy effectively improves the load reduction effect and comprehensive benefits. From the perspective of load reduction effect, the load reduction effect of all HVAC users adopting the optimization strategy is higher than that of traditional strategy A (indoor temperature control point increased by 1 °C), and the load reduction effect of 61% of users is higher than that of traditional strategy B (indoor temperature control point increased by 2 °C). From the perspective of comprehensive benefits, the comprehensive benefits of all users adopting the optimization strategy are higher than those of the two traditional strategies.

(2)

The optimization strategy effectively improves the thermal comfort of HVAC users. In total, 50% of customers adopting the optimization strategy have less comfort benefit loss than the two traditional strategies, and the remaining 50% are between the two traditional flexible strategies.

(3)

HVAC users with lower basic profitability and a lower labor elasticity coefficient are better targets for air-conditioning load demand response. Users with lower basic profitability and a lower labor elasticity coefficient have higher load reduction potential and greater comprehensive benefit. In the application scenario involving the optimal scheduling of DR customer clusters, this type of customer should have a higher priority.