Two-Stage capacity allocation optimization method for user-level integrated energy systems considering user satisfaction and thermal inertia

0 Introduction

The energy sector is vital to modern society because it supplies the power required for daily activities, industries,and economic development.However, continued reliance on fossil fuels has resulted in considerable environmental problems.Research on alternative, sustainable-energy sources has gained urgency with the rapidly increasing energy needs of the global population.Widespread integration of renewable-energy sources has introduced several novel challenges.The coupling of conventionalenergy grids with intermittent renewable-energy sources results in energy wastage and power-system instability.The independent operation of different, energy subnetworks makes energy conversion and coping with renewable-energy fluctuations difficult, thus constraining large-scale, renewable-resource integration.Integratedenergy systems (IESs) [1,2] have garnered widespread attention as solutions with tremendous potential, with advantages such as multienergy complementarity and cascading energy utilization[3].IESs serve as a foundation for realizing the energy internet and pervasive power IoT,involving the conversion, distribution, and coordination of various forms of energy, including heating, cooling,electricity, and gas [4].The energy Internet comprehensively uses advanced power electronics technology, etc.,with the power system as the center, and interconnects a large number of energy nodes such as new power networks composed of distributed energy storage devices and various types of loads, so as to realize the ‘‘multi-source complementarity” of electricity, gas, heat, and renewable energy.The introduction of IESs can lead to higher energy efficiency and effectively address fluctuations in renewableenergy sources, thereby enhancing the stability and sustainability of the entire, energy supply chain.

To enhance energy-supply efficiency and meet diverse,energy demands, IESs are classified into cross-regional,regional, and user levels, based on geography and energy-demand characteristics[5].The smallest spatial unit of IESs are the user-level IESs (UIESs), the fundamental components of regional and cross-regional IESs; they facilitate energy exchange and directly cater to specific end-user energy requirements [6].With the improvement of relevant operational mechanisms and technology,UIESs can realize energy self-sufficiency and will be key to the development of IESs; large, commercial buildings,schools, and hospitals (i.e., buildings or building groups of a certain scale) will function as units.Consequently,improving the user-level energy-integration efficiency,promoting renewable-energy integration,and balancing development between economic and environmental objectives are the current, crucial challenges.

Currently, researchers worldwide are focusing on improving system energy efficiency and operational cost effectiveness.Many scholars are exploring renewableenergy-integration mechanisms and operational economics, primarily from a demand perspective.By investigating demand-response mechanisms and emphasizing close interactions with end users,they aim to achieve more intelligent and flexible, energy scheduling.Reference [7]utilized triangular membership functions to express the uncertainty in various, flexible, load-response levels and studied the relationship between incentive levels and fluctuations in the user-demand response.This significantly enhances the system flexibility and economic viability.Reference [8] introduces a novel, integrated-energy, retailbundling mechanism for demand-response management.The effectiveness of this mechanism was validated by constructing a dual-layer optimization model and tailoring packages with varying response requirements and discounts for different consumers.Reference [9] proposed a method for analyzing the potential for demand response on the user side by considering the coupling relationships among different, energy sources.The goal is to optimize the operational costs of user-side energy, for substantial economic benefits.

The cited literature predominantly focuses on optimizing systems through pricing strategies in the energy market from the demand-response side.This approach aims to incentivize users to actively engage in demand response,thereby achieving supply-demand equilibrium and effi-cient energy distribution.However,it is crucial to consider user satisfaction in addition to incentivizing participation.User satisfaction is expected to result in proactive user involvement.Hence,researchers have reached a consensus regarding user satisfaction.User dissatisfaction is incorporated as a constraint by adjusting the energy-device output and production-equipment operating load to establish a collaborative optimization model for IESs [10].Reference[11] utilized a comprehensive, user-satisfaction approach integrating subjective and objective weights.The objective is to minimize the operating costs of energy systems,maximize the utilization of demand-response potential, and simultaneously determine the optimal scheduling scheme.Reference [12] presented a multi-objective optimization model for incentive-driven demand response in IESs.This model considers the user satisfaction from diverse perspectives.

The literature introduces significant subjectivity when assessing overall user satisfaction using mathematical models.When considering user interests and satisfaction as the optimization objectives, inherent system connections are neglected.Consequently, the system is more likely to prioritize user satisfaction at the expense of energy efficiency.Defining user satisfaction based on user perception of external temperature changes,in conjunction with the speed of system-response to thermal changes,and accounting for system thermal-inertia constraints,strengthens system integration and better addresses energy-transmission fluctuations, ultimately reducing energy consumption and costs [13,14].Furthermore, current research predominantly relies on single-stage optimization and neglects the adoption of two-stage,capacity-allocation optimization [15].Leveraging the synergy between lower-level, operational optimization and upper-level, capacity allocation can improve the lifecycle performance of IESs.

To summarize, this study proposed a two-stage, optimization method for capacity allocation in comprehensive,energy systems.This method considered both user satisfaction and thermal inertia.The specific contributions of this study are as follows:

(1) A two-stage, capacity-configuration, optimization model was proposed.Through long-term planning,the first stage optimizes the cost targets for annual,investment and construction, operation and maintenance,and environmental costs of the system.Based on the feasible solutions obtained in the first stage,the second stage focused on the details and fine adjustments with the optimization goal of minimizing the operation and maintenance costs of the system.The most cost-effective solution was identified in the first stage and the cost-effectiveness was further optimized in the second stage to ensure the effective resource utilization.

(2) User thermal satisfaction was defined based on their perception of external temperature changes, users were placed at the center, active user participation was promoted, and strategies and services were better adjusted.Combined with the system response speed, stability to heat changes, and the system thermal-inertia constraint, high thermal inertia was found to reduce energy waste.By combining the thermal energy-storage capacity, we could reduce the output of some units and further increase the renewable-energy consumption.Using a residential building as an example, we determined the optimal operating plan for the system on typical days.

1 UIES modeling

The specific structure of the UIES is shown in Fig.1.The system consists of a power-generation unit, energystorage unit, and an energy-consumption unit.The distributed, photovoltaic (PV) system, natural-gas system,and energy-storage unit comprise the energy coupling between the power, gas, and heat grids.

1.1 PV power plants

In the IES studied here,the heat load primarily refers to the heating requirements.The domestic-water heat load was not considered; only the PV power-generation equipment was considered for the system power supply.The PV power-generation device uses solar energy to generate electricity, and its output characteristic PPV is

where PPV t is the amount of electricity that the PV panel can produce at time t;APV is the area of the PV panel,in m2;ηPV is the efficiency of the PV panel,and It is the quantity of solar energy that can be utilized per unit area of the PV panel at time t in kW m2.

The total rated power EPV r of a PV plant is related to the total installed area APV as follows:

where s is the conversion factor between output power and area per unit area of a PV panel at a solar-radiation level of 1 kW m2.The above equation can be converted to:

Considering the limitations of the actual site space on the top floor of residential buildings, there is a maximum capacity limit for PV equipment:

Fig.1.Structure of a user-level IES with renewable energy.

where EPV r max is the total value of the capacity of the PV equipment.

1.2 Combined cooling, heating, and power (CCHP)

(1) Gas-turbine and waste-heat recovery models

Gas-fired units usually use natural gas as fuel, which is fully combusted to produce high-temperature hot gas that pushes the rotor to do work to generate electricity; this provides residents with their daily electricity needs.The relationship between power PGT and input natural gas V GT is as follows:

where ηGT is the gas-turbine power-generation efficiency and L indicates the low calorific value of natural gas,which is 9.73 km h m3.The CO2 emission coefficient of the gas turbine is taken as 0.52 in this article.

The waste-heat boiler acted as a link between the gas turbine and absorption chiller.It produced hightemperature steam by harnessing energy from the hightemperature exhaust smoke discharged from the gas turbine after electricity generation and directed it to the absorption chiller.The heat input to the waste-heat boiler is as follows:

where η1 is the heat-loss coefficient.

The heating power of the waste-heat boiler is as follows:

where Uoph is the heating factor, and ηh is the flue-gas recovery rate.

(2) Gas boiler

In user-level energy systems, standard gas and electric boilers are used; they have low investment costs, are flexible in operation,easy to maintain,and can convert a variety of energy sources.Electric boilers are environmentfriendly because they do not produce harmful gases.Their output is related to their characteristics and load conditions.

where ηGB EB is the heating efficiency of the gas boiler;V GB is the amount of natural gas fed into the gas boiler,in m3;PEB is the input electric-boiler power,kW;HGB EB indicates the heat output of the gas/electric boiler.The CO2 emission coefficient of gas boilers is taken as 0.505 in this article.

(3) Absorption chillers, Electric chillers

Absorption and electric chillers, as essential coupling devices for the UIES cooling energy, can convert different qualities of power, and their equivalent models can be described by (10).

where Pα in and Pα out are respectively the input and output powers of intermediate conversion device α.

1.3 Energy-storage device model

Energy-storage devices play a crucial role in the development of IESs and facilitation of multi-energy synergistic operations.In this study, we designate a power-storage device and heat-storage device as the energy-storage equipment within the UIESs.This choice substantially improved the flexibility of the system scheduling plan within the permissible-capacity range.The general expressions are as follows:

To ensure flexibility in scheduling various cycles, the capacity of the energy-storage device remained consistent at both the initial and final moments.

where t1 and tn denote the scheduling-cycle start and end moments, respectively.n depends on the resolution of the selected time scale [16].

2 Heating-system characteristics of the UIES

Heating systems use materials like hot water or steam which are slow in propagating heat and consequently have large thermal inertia[17];it takes time for heat to be transferred from the heat source to the heat load in user buildings.The temperature-change process depends on the building structure, outdoor temperature, and other factors; in this process there is hysteresis.This thermalenergy-storage effect depends on the thermal inertia [18].Therefore, building units with thermal inertia can be regarded as resources with scheduling flexibility.The heat load has a degree of elasticity in space and time, and thermal inertia can be used in cooperative optimization of electric-thermal scheduling.

The heat network can be regarded as a distinctive form of an energy-storage device,owing to the time delay in the heat-transfer process and the resulting hot-water temperature disparity between the pipeline inlet and outlet for the duration of the delay.Existing heat-supply systems primarily regulate quality, quantity, or both when the heattransfer medium is hot water.Ignoring the small, flowrate changes in the supply and return pipelines due to the water-temperature difference, and regulating the quality of the heat network [19] the supply- and return-water temperatures at time t are Tg t , Th t.The auto-regressive and moving average (ARMA) time-series model [20]describes the relationship between indoor and outdoor temperatures Th in t ,Th out t in buildings,during heating,as:

where the coefficients αj , βj , γj , θ1 , φ1, and ω1 are the physical parameters of the thermal inertia of the heating system that can be obtained by parameter identification using the measured data,and the order reflects the thermal inertia of the heating system.The above equation describes the multitemporal relationship between thermal inertia and indoor temperatures in a heated building.

In the event of a heat-network failure, the indoor temperature does not immediately reach the outdoor temperature.Users are a little uncertain about their external environment.When integrated with user thermal comfort,the heating/cooling load shifts from a fixed to an adaptable value.This adjustment enhances the energy-storage capacity of the heating/cooling system [21].

The predicted-mean vote(PMV)index describes human comfort based on factors such as ambient temperature,relative humidity, air-flow rate, human-metabolic rate, and user clothing [22].The 7-point heat-sensation scale of the American society of heating, refrigerating, and airconditioning engineers is shown in the Table 1 below and ranges from 3 to + 3.

Table 1
Human-comfort indicators.

PMV index Comfort level 3 freezing 2 cold 1 cool 0 moderate 1 warmish 2 balmy 3 blistering

The existing Chinese design code for heating, ventilation and air conditioning [23] stipulates that for general,indoor, environmental, thermal-comfort the standard PMV index ranges from 1 to+1.This satisfies the winter thermal-comfort requirements of indoor users.ISO-7730 stipulates that a PMV index between 0.5 and 0.5 is more appropriate, corresponding to in-door temperatures of 24.7-26.5 oC.γPMV is the value of the PMV index, and its mathematical equation [24] is:

where X and Y represent the energy-metabolic rate of the body and the generated mechanical power,respectively,in W m2.Pa refers to the partial pressure of water vapor around the human body, in Pa.The Scl is the ratio of the area of the body covered with clothing to that of the exposed body, in m2.hc is the surface heat-transfer coeffi-cient, in W m2 K.Ta, Tcl, and Tr represent the air temperature surrounding the human body, the outergarment surface temperature,and the average radiant temperature, respectively, in ℃.This study primarily addressed heat supply, with indoor, thermal comfort intuitively perceived through temperature; therefore, except for the air temperature around the human body Ta, it is assumed that all other parameters are given values.

3 Solutions for UIES capacity allocation and scheduling strategy

The optimal capacity allocation scenario changes as the operational strategy changes, and the results of the twotier model affect each other.This study used a two-stage,optimization approach to plan a UIES.A mixed-integer linear-programming model was established from the a mathematical-planning perspective to find an optimal solution, and the process is shown in Fig.2.

3.1 Capacity allocation model

3.1.1 Objective function

To determine the optimal capacity configuration for various system components and schedules on an hourly basis, the optimal economic performance of the system must be ensured during energy supply.The model aimed to minimize the annual IES operating, comprising investment and construction, operation and maintenance, and environmental expenses.This can be mathematically expressed as follows:

Fig.2.Optimizing process of UIES.

where Cy b , Cy r, and Cy env respectively denote the annual investment, operation and maintenance, and environmental costs.

(1) Annual investment cost

The investment and construction cost Cy b is the cost of equipment purchase and installation.When optimizing the capacity configuration,it is crucial to account for the varying lifespans of energy devices such as PV-power systems,energy-storage-battery systems,and gas turbines.By utilizing the net-present-value method to convert the initial investment costs into equivalent annual values, the influence, of different,equipment lifecycles on investment decisions, is mitigated.The mathematical expression is as follows:

where i is the serial number of the type of equipment in the system; Ccap i is the capacity limit for each piece of equipment; Ui is the acquisition cost per unit capacity of each piece of equipment; r is the discount rate for the equipment; and k indicates the age of the equipment.

(2) Annual operation and maintenance costs

The annual operation and maintenance costs (denoted as Cy r) arising from equipment wear and tear, maintenance, and manual inspections are contingent on factors such as equipment type, capacity, frequency of use, and mode of operation.These costs are calculated using the following formula:

where λ is the annual operation and maintenance costs of the system equipment as a proportion of the initial investment costs; this study used a value of 0.85.

(3) Annual environmental cost

The environmental cost was indexed by the annual carbon-emission cost Cy env, which was added to the multi-objective optimization model as the optimization objective for minimization.The formula is as follows:

where θCO2 is the cost per unit of CO2 emissions factors.Pbuy and Gbuy are the amount of electricity purchased from the grid and the amount of gas purchased from the gas network,respectively;Pi represents the power of equipment in category i(gas turbines,gas boilers).ωgrid gas i CO2 are unitemission factors due to purchased electricity and gas, and unit output, respectively.

3.1.2 Restrictive condition

The operational constraints in the UIES include energy balance, equipment operation, and energy-storage limitations, which ensure both energy supply and system safety.

(1) System electrical, thermal, cooling, and air balance constraints.

where Le t ,Lh t ,and Lc t are,respectively,the electrical,thermal,and cooling loads on the consumer side,at time t.Pnet t is the power exchanged with the larger grid at time t;Pcha t and Pdis t are the charging and discharging power of the electric-energy storage at moment t.PEC t and PEB t are the input powers of the electric refrigerator and boiler at time t; Hcha t , and Hdis t are the charging and discharging powers of the heat-storage device at time t, respectively.

(2) Equipment power constraint

(3) Energy-storage constraints

The electrical and thermal energy-storage constraints are similar to those in Section 2.3, and are repeated here owing to space constraints.

3.2 Typical-day selection

As the main gathering place of energy consumption in the city, the energy demand of residential buildings includes electricity,heat and cooling,and the load characteristics of the user demand side have little difference in spatial scope, but the timing is obvious.This timing change varies daily and seasonally; and is likely to be nearly the same over a period of a few days.In the absence of sudden weather changes, the energy demand increases,but the time-sequence characteristics are approximately steady.For such a load, a typical, residential-customerside, energy-demand scenario can be established using cluster analysis [25].

Based on the above considerations,this study employed the K-means clustering algorithm to analyze customer demand-side data for electricity, heat, and cooling loads[26].The K-means clustering algorithm, which is a partitioning method, assigns objects to a finite number of clusters to minimize the distance between the cluster centers and objects [27].The K-means clustering algorithm has extensive applications in load clustering, demonstrating superior efficiency in scenarios involving large datasets compared to other algorithms [28].Due to space constraints, this study does not delve further into this topic.

3.3 Optimized scheduling model

3.3.1 Objective function

Consider the operating costs of the system (including the cost of purchased and sold electricity Cgrid,cost of purchased gas Cgas, and cost of running the equipment Com)on a typical day (spring, summer, autumn, and winter):

In this formula, the system uses time-sharing electricity and gas-pricing mechanisms.Cgrid buy sell t is the tarifffor electricity purchased and sold by the system from the external grid,Pbuy sell t is the real-time power purchase/sale of the system on a single day, Cgas t is the real-time cost of gas purchased for the system, Gbuy t is the real-time gas purchase volume of the for a single day,Ci is the unit operation and maintenance cost of equipment in i;and Pi is the operating power of equipment in i.

(1) Heating system constraints

The temperature of the heat-transfer-medium in the supply pipe must remain below the upper temperature limit of the heat network to prevent pipe damage from excessive heat.In the heat-transfer-medium return pipe,the temperature of the heat-transfer-medium should be higher than the lower temperature limit to ensure normal operation of the heat-exchange station.It is important to highlight that, owing to heat loss, the highest temperature point within the entire heat network was found at the heatsource water-supply pipe, whereas the lowest temperature point was located at the heat-source return pipe.Hence,it is essential to ensure that the temperature of the heattransfer-medium in the supply and return pipes of the heat source satisfies the specified constraints.This ensures normal operation of the heat network while preventing damage to the pipework caused by the temperature of the heattransfer-medium.

where Tis the maximum water-supply temperature of the heat-network pipework; Tis the minimum return temperature of the heat-network pipework.

where α is the coefficient of the relationship between the boiler heat supply and the supply/return water temperature of the heat network (W/℃), the magnitude of which is related to the flow rate of water in the heat network, β is the PMV-range indicator, and γPMV t is the limit of the PMV-indicator range for the period t.

The remaining constraints were aligned with those outlined in Section 4.1.2, except that the upper limit of the output for each equipment type was a predetermined value.Simultaneously, it is a variable that must be optimized in the capacity-allocation phase.

3.4 Method of solution

During the optimization process, various equipment types were defined using different variable types.For instance, integer variables were employed for PV models,continuous variables were used for battery and thermal storage-tank capacities, and binary variables defined the logical relationships between the subsystem operating modes, such as battery charging or discharging.

The equipment allocation problem investigated in this study was a 0-1 mixed-integer linear-programming problem formulated in the standard form

where x was the variable to be optimized,min F x was the objective function, gi x 0 denoted the equation constraints, hi x 0 denoted the inequality constraint, and xmax and xmin denoted the upper and lower limits of the variable, respectively, and xk indicated that some of the variables are 0-1 binary variables.

4 Example analysis

4.1 Arithmetic scenarios and data

In this study, the example for calculation was based on a residential building in the southern region,where the primary, energy demands included electricity, heating, and cooling loads.The annual light intensity of the community,as depicted in Fig.3,illustrates the seasonal divisions throughout the year: spring (March to May), summer(June to August), autumn (September to November),and winter (December to February).

Fig.3.Annual light intensity.

Table 2
Equipment parameters.

Equipment name Year Cost（¥） Capacity (kW)PV panel 15 2000 2000 Battery 10 1000 650 Gas turbine 15 1000 1650 Gas boiler 15 550 1200 Electric boiler 15 350 550 Waste-heat boiler 10 730 1500 Thermal-energy equipment 10 505 770 Absorption chiller 15 870 700 Electric chiller 10 670 650

The first layer can obtain the UIES capacity configuration and the result of the optimized scheduling of system operation for the entire year by planning and solving,which can satisfy the different types of energy demands of the system and realize the economy.The comprehensive costs obtained by the solution were as follows: annual investment and construction costs - 1.208 million yuan,annual operation and maintenance costs - 1.0268 million yuan, annual environmental costs - 854,500 yuan, and total costs-3.0893 million yuan.The annual costs of operation and maintenance and the environmental costs account for a Ilarge percentage of the total; the energy price is dominated by various types of operational factors,and there is a notable impact on optimization and planning.For example, energy prices affect the preferences for energy-coupling methods.UIES tends to prioritize the selection of periods with high economic energy forms.Simultaneously, varying energy utilization conditions influence the choice of energy equipment, consequently affecting the results of capacity allocation.

The parameters of the UIES capacity configuration equipment are presented in Table 2.Despite the high cost,the planned capacity of the PV power-generation unit is 2000 kW, reflecting the UIES’s emphasis on maximizing the use of renewable-energy sources.The energy-storage component, crucial for coordinating renewable-energy consumption and enhancing system efficiency through peak shaving and valley filling, was well planned.However, owing to the higher unit cost and shorter lifespan of electric-energy-storage devices, their planned capacity was lower than that of thermal storage devices.

After performing preprocessing tasks, such as identifying and correcting abnormal data in the load, data normalization, and other procedures, the K-means algorithm was employed for clustering, resulting in the identification of four, distinct, typical scenarios.In each season, the typical daily data retained the original data characteristics and were the closest to the overall trend of change within the selected seasons.To simplify the calculations, a representative winter day was used as an example.The outdoor-temperature curves are shown in Fig.4 The electricity, heating, and cooling load curves for the typical days are shown in Fig.5, Fig.6, and Fig.7.The PV-output curve is shown in Fig.8, and the time-of-use electricity-price table is shown in Table 3.The optimization period was 24 h, and the unit optimization time was 1 h.

4.2 Optimization results and analysis

In this study, we aimed to compare and analyze the effects of user comfort and thermal inertia on the optimal operation of a UIES for light abandonment and dissipation.Two scenarios were constructed for comparison: (1)the system did not consider user comfort and thermal inertia, and (2) the system considered user comfort and thermal inertia.

Fig.4.Outdoor-temperature curve.

Fig.5.Typical daily load curve.

Fig.6.Typical daily heat-load curve.

Fig.7.Typical daily cooling-load curve.

Fig.8.PV predicted-output curve.

Table 3
Comparison of optimization results in different scenarios.

Scene Probability of abandoning light (The rate of unused light energy)(%) Operating cost (¥)1 15.88 8740.5217 2 7.98 7623.1746

Fig.9.Electricity-dispatch diagram.

Fig.9 presents the optimization results for the two power-balance scenarios.An electric boiler converted PV energy into heat and stored it in a thermal storage device.At night, the stored heat energy was released from the storage device to reduce the CCHP, electricity, and heat output.Notably,the period from 8:00 to 17:00 experienced a high light intensity.At this time,the Scenario 1-CCHP‘‘heat to set electricity”constraint still maintained a higher level of power generation, leading to the phenomenon of abandoned light.Scenario 1 was constrained by the CCHP heat-to-power ratio;power generation was still maintained at a higher level, and light abandonment occurred.Simultaneously, the photoelectric consumption in Scenario 2,amounting to 472 kW, surpassed that in Scenario 1.This observation suggested that while considering user thermal comfort and building thermal inertia, adjustments to the unit thermal-load pressure can be made without compromising user comfort.Consequently, the electrical-thermal coupling of the system can be alleviated.The adjustment space of the CCHP electric power can be improved to realize considerable fluctuations in the load,and the degree of photoelectricity consumption can be increased.

Fig.10 shows that the amount of abandoned light was considerably reduced when comparing the results of heatbalance optimization in Scenarios 1 and 2.Taking user comfort and building thermal inertia into account and increasing the volatility of the system heat load, the heat-load demand was reduced.The CCHP heat output was reduced to get rid of ‘‘heat to set the power” constraints, for electric-output regulation.The gas boiler primarily supplies space heating, while the electric boiler converts the electric energy stored(in a storage device)into heat.There is no need to add extra expense thus ensuring high economic efficiency by considering the user comfort and building thermal inertia.At night, the electric boiler releases the stored thermal energy, thereby reducing the CCHP heat output and improving PV consumption.

Fig.11 shows the results of the two scenarios of cold balance optimization.When the building thermal inertia and the user comfort are taken into consideration, the thermal load is regulated, the PV-consumption capacity is increased, and the CCHP heat output is decreased.The electric chiller is mainly utilized from 8:00 to 17:00.The electric energy is converted into cold energy.This reduces the cooling cost to the user and substantially improves the system economy.

Fig.10.Heat-dispatch diagram.

Fig.11.Cold-dispatch diagram.

Fig.12.Comparison of PV outputs.

Fig.13.Contrast diagram of indoor temperatures.

Fig.12 shows a comparison between the PV-predicted output and the two scenarios.It can be seen that the PV consumption in Scenario 2 is larger than that in scenario 1.The constraints of user thermal comfort and system thermal inertia can significantly reduce curtailed solar energy and enhance PV-energy absorption.By factoring in the thermal inertia on the user-demand side, during periods of high PV output, heating can be managed using electric boilers, leveraging thermal inertia to maintain indoor temperatures within the range of user comfort for a certain period, which is imperceptible to users.This approach can reduce the heat generation of the units during this period and achieve the goal of absorbing curtailed solar energy.

Fig.13 shows the indoor-temperature variations in the two scenarios.PMV index constraints of 0.6 to 0.6 are selected for the algorithm, and the corresponding indoor temperatures are 24.7C to 27.4C.Scenario 2 incorporated the user comfort and thermal inertia constraints of the building.During the daytime, when the PV output increased, the thermal output of the unit was reduced to regulate the heat load, and the indoor temperature was reduced.However, it remained within the human thermal comfort zone.The PV output was then converted to thermal energy using electric boiler equipment.Subsequently,the converted energy was stored in a thermal energystorage device.At night,the thermal energy-storage device released the stored thermal energy.This process expanded the capacity of gas turbines to regulate their electrical output.Simultaneously,it enhanced the effective utilization of renewable energy and contributed to the reduction of CO2 emissions.

Table 3 presents a comparison of the optimization results under different scenarios.Scenario 1 had a significantly higher discard rate than Scenario 2.The operational costs were higher.However, considering user comfort and system thermal inertia lead to a notable decrease in the discard rates, resulting in reduced operational costs.

5 Conclusions

This study addressed the optimization problem of capacity configuration in UIES and introduces a twostage, capacity-optimization-configuration method for UIES.In the first stage, the optimal capacityconfiguration plan was determined using annual load data.In the second stage, typical, daily, economic and environment-friendly operational considerations were incorporated, introducing system thermal inertia and user satisfaction into the optimization process.Finally,the proposed model and methodology were validated through a UIES case study,demonstrating their ability to ensure user satisfaction while effectively reducing CO2 emissions and promoting the on-site integration of renewable energy.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Shunyu Li, Ying Liu, are currently employed by Guizhou Power Grid Company Ltd;Gang Lv is currently employed by Extra High Voltage Power Transmission Company Guiyang Branch.

Acknowledgments

This work was supported by the science and technology foundation of Guizhou province [2022] general 013, the science and technology foundation of Guizhou province[2022] general 014, the science and technology foundation of Guizhou province GCC [2022] 016-1, and the educational technology foundation of Guizhou province [2022]043.

Appendix A

Table A1
Symbol Description.

Symbol Description Symbol Description PPV t PV-panel electricenergy generation at time t B H,PminB H Upper and lower limits of energystorage capacity APV PV-panel area HinB H t ,HoutB H t 0-1 binary variables ηPV Conversion efficiency of PV panels Pmax Tg t,Th t Supply- and returnwater temperatures of the heating network during time t Tin t,Tout t Indoor and outdoor temperatures of buildings during heating EPV r Total rated power of PV equipment It Solar-energy utilization per unit area of PV panels at time t Tc in t Tc out t Indoor and outdoor temperatures of buildings during cooling supply s Conversion coefficient between output power and area of PV panels QL t Total cooling power during period t V GB Gas-boiler input natural-gas volume PGT Gas-turbine power generation EPV r max Maximum capacity of PV equipment Pα in,Pα out Input and output power of intermediate conversion equipment V GT Gas-turbine input natural-gas volume γPMV PMV-indicator value ηGT Gas-turbine powergeneration efficiency ARMA-model parameters L The low heating value of natural gas αj, βj, γj, θ1,φ1, ω1 ηα Conversion efficiency HinGT Input heat of the waste-heat boiler SB H t The capacity of energy-storage equipment at time t

B H,SminB H Upper and lower limits of energystorage capacity Hout η1 Heat-dissipation coefficient Smax PinB H t ,PoutB H t Charging and discharging power at time t Uoph Heating coefficient QGB Gas-boiler output ηh Flue-gas recovery rate GT Heating power of waste-heat boiler ηGB The heating efficiency of gas boilers

Table A2
PMV parameters of an equation.

Symbol Parameter value X W m2 75 Y W m2 0 Pa Pa 2500 Scl 1.25 hc W m2 K 4.8 Tcl oC 28 Tr oC 26.7

Table A3
ARMA-model coecients of the heating system (J = 2).

j αj βj γj θj φj ωj 0 —— 0.2230 0.3256 ——————1 0.5720 0.0243 0.3168 0.6991 0.1001 0.1998 2 0.0605 0.0104 0.1741 ——————0 —— 0.2230 0.3256 ——————

Table A4
Time-share prices.

Type Time period Price（¥/kWh）peak 07:00-12:00, 19:00-22:00 1.21 flat 13:00-18:00 0.73 valley 23:00-06:00 0.45