Optimization configuration strategy for regional energy systems based on multiple uncertainties and demand response

With the opening of the power market and the development of the energy Internet, the optimal allocation of regional energy systems has become the key to achieving energy efficiency and economic balance. The article studies how to achieve this balance by optimizing the allocation of regional energy systems under the influence of price fluctuations and load demand uncertainty in the electricity market. This study introduces a real-time electricity price adjustment mechanism to stimulate user participation in energy adjustments and improve energy utilization efficiency. By constructing an optimization model based on multiple uncertainties and comprehensive demand response, uncertainty factors such as energy market price fluctuations and climate change were considered, and user demand response was integrated. The research results indicate that electricity price fluctuations have a significant impact on system operation, while CSP power plant thermal storage fluctuations have a relatively small impact. After the introduction of demand response, the electricity load can be reduced to zero during specific periods, and the adjustment of electricity prices stimulates user participation and improves the consumption rate of renewable energy. The total revenue of the system increased by 54.147 million yuan, demonstrating the potential of optimized configuration in reducing costs and improving efficiency. This study provides important references for building more efficient and sustainable energy systems.


Introduction
The optimization of regional energy system configuration and operation, critical components of future energy systems, is at the forefront of addressing these challenges (Wei et al. 2022).Nevertheless, due to the intricate interplay of regional factors, diverse energy sources, and environmental and economic considerations, achieving optimal configuration under different scenarios remains complex.This study introduces an innovative approach to address these challenges by integrating multiple uncertainties and demand response strategies (Kumar 2020;Abdul-Wahab et al. 2020).Diverging from conventional energy system studies that often focus on specific variables, this research incorporates various uncertainties, including wind power output, electricity prices, and gas prices, for a more comprehensive understanding of their impact on system configuration and operation.Additionally, it integrates an adaptive demand response strategy, allowing the system to flexibly adjust energy supply and consumption based on actual demand, enhancing adaptability in diverse scenarios (Jiale 2020;Agrawal and Yücel 2022).By considering uncertainty factors, researchers can provide a more scientifically grounded evaluation of the system's performance in various environments, offering valuable insights for practical applications.Simultaneously, the integrated demand response strategy empowers the energy system to respond effectively to changing energy demands at different times, ultimately enhancing system reliability and efficiency.
The study contains four parts, the first part is a summary of the research on integrated demand response and district energy systems.The second part is the design of the optimization model based on uncertainty and demand response.The third part is the analysis of the optimized energy system, and the fourth part is the summary of the whole paper.

Related works
Amidst the renewable energy boom and technological advancements, the power system is shifting towards decentralization, complexity, and intelligence.Demand response, a flexible energy management strategy, has garnered the attention of researchers.For instance, Chen et al. (2020) introduced the Relief algorithm to tackle the impact of rising residential electricity consumption on global climate by reducing the load characteristic index.They also developed an analytical model of residential electricity consumption behavior using the DBSCAN algorithm.Similarly, Sultana et al. (2020) addressed challenges like power shortages, electricity billing, fault management, and home automation to optimize spectrum utilization.Their work demonstrated the superior performance of FLSTM-CSOA, achieving metrics such as a bit error rate of 10-1, throughput of 200 kbps, and a latency of 10 ms.Selvan (2020) aimed to create an intelligent residential power distribution system by optimizing appliance scheduling to minimize electricity bills through demand response.Trovato (2021) explored the role of High Voltage Direct Current (HVDC) links in managing local frequency dynamics and optimizing their scheduling for power allocation and fast frequency services.Furthermore, Ghasemi et al. (2021) developed a novel framework to enhance power system resilience and security by involving data centers in providing efficient and rapid frequency response.
Numerous scholars have explored optimizing energy system sizing for diverse sectoral energy needs.Abdellatif et al. (2023) focused on standalone hybrid renewable energy systems, employing linear planning techniques like Bender's decomposition, lexicon optimization, and epsilon constraints.In pursuit of sustainable development goals, Sharma et al. (2023) devised a sizing methodology for optimizing grid-connected Hybrid Renewable Energy Systems (HRES), particularly relevant for countries like India.Li et al. (2023) developed power management strategies (PMS) to enhance the longevity of energy storage devices and reduce system costs.Their approach involved a mathematical model with hysteresis bands for controlling energy flow and minimizing the degradation of fuel cells and electrolyzers.Addressing the challenge of aligning production and energy system objectives, Leenders et al. (2023) formulated a two-tier problem using mixed-integer decision variables, showcasing its effectiveness.Meanwhile, Liu et al. (2023) tackled uncertainties in energy supply and demand, along with the temporal coupling of storage systems, by creating a scenario-based operational optimization model for a hydrogen-based multi-energy system.This model was then converted into a mixedinteger linear programming problem, facilitating efficient solutions.Comparative analysis between existing literature and this study is shown in Table 1.
As shown in Table 1, despite extensive research on demand response and energy allocation, ongoing challenges persist, such as managing uncertainties, integrating demand response, and optimizing region-specific factors.This study aims to enhance regional energy systems by improving efficiency, cutting costs, and promoting environmentally friendly energy sources.

Optimization model design based on uncertainty and demand response
This chapter focuses on the optimal configuration and operation analysis of RIES under multiple uncertainties, integrating demand response.It introduces a two-tier optimal configuration model, utilizing a multivariate universe-interval linear programming method to construct an integrated electricity-heat demand response model.

RISE optimized configuration based on multiple uncertainties
The study utilizes a two-tier optimization model to maximize both gross and net operating revenue.The upper layer generates equipment capacity, while the lower layer uses this capacity to constrain equipment output, incorporating net operating revenue into the upper layer's objective function (Fang et al. 2022).The upper-level planning model is defined in Eq. (1).
In Eq. (1), F tot ,F ope , and C in denote the gross return, the net return, and the total invest- ment cost of the system equipment, respectively, over the operating life of the system.The second planning is shown in Eq. (2).
In Eq. ( 2), C cchp denotes the investment cost of the CCHP unit, S chp denotes the con- figured capacity of the CCHP unit, C gb and S gb denote the investment cost and the con- figured capacity of the GB unit, C ec and S ec denote the unit investment cost and the configured capacity of the EC unit, C PtG and S PtG denote the investment cost and the configured capacity of the PtG unit, and C cool ,S cool ,C heat ,S heat ,C gas , and S gas denote the unit investment cost of the cooling unit, the heating unit, and the configured capacity of the gas storage unit, respectively.The lower level model aims to maximize the net operating return of RISE, specifying unit outputs as in Eq. (3).
(1) Provides new methods for data centers to participate in frequency response Not directly related to regional energy system optimization configuration In Eq. ( 3), N and r denote the planned operating life and discount rate of the sys- tem, θ s denotes the proportion of the s season in a year, and F sale , C buy ,C ope , and C curt_c denote the total revenue from energy sales, the total cost of electricity and gas purchases, and the total cost of operation and maintenance for each device, respectively.The charging and discharging power of the energy storage device is shown in Eq. ( 4 , P GB s,t , P EC s,t denotes the power of CCHP, GB, and EC units under typical seasons of category s, respectively; and p cur_c denotes the cost of car- bon emission penalty per unit power.In an energy system, a balance between generating and consuming the four forms of energy is crucial, including cold energy, as shown in Eq. ( 6).
In Eq. ( 6), x ope cchp,t , x ope gb,t , x ope ec,t , x ope ptg,t denotes a variable of the system state, characteristic, or performance of the CCHP, GB, EC, and PtG units, respectively, during the operation of the system or process, and x ope cchp,t , x ope gb,t , x ope ec,t , x ope ptg,t ∈ [0, 1] , P CCHP max , P GB max , P EC max , P PtG max , P CCHP min , P GB min , P EC min , P PtG min denote the upper and lower power limits of the CCHP, GB, EC, and PtG units, respectively.The energy storage constraints are shown in Eq. ( 7).
In Eq. ( 7), P ψ cha,t , P ψ dis,t denotes the charging and discharging power of energy storage devices, x ope cha_ψ , x ope dis_ψ denotes the variable of the state of ψ energy storage devices dur- ing charging and discharging, and (5) size of ψ energy storage devices in t and t − 1 time periods, respectively; η ψ cha , η ψ dis denotes the efficiency of the energy conversion of ψ energy storage devices during charging and discharging, and t denotes the time period of the scheduling.These subproblems are efficiently solved using Yalmip and Gurobi solvers (Mandel et al. 2019), as illustrated in Fig. 1.
The MVO algorithm emulates matter transfer between universes via wormholes, resembling white holes to black holes.WEP (0-1) indicates wormhole probability for inter-universe data exchange.TDR controls travel distance, with higher values expanding exploration and lower values limiting searches (Lehner et al. 2020).See Fig. 2 for details.
The conceptual model of MVO algorithm can be divided into three assumptions for elaboration (Roelich and Giesekam 2019).The first one is that objects in high expansion rate universes always converge to objects in low expansion rate universes; the second one is that objects are transferred between neighboring universes through the white/black hole mechanism and the updating of the cosmic position is carried out as shown in Eq. ( 8).In Eq. ( 8), x j i denotes the j th variable for the i th universe, r 1 denotes any number between [0, 1] , NI(U i ) denotes the rate of expansion of the i th universe, which is usually expressed by the Hubble constant, and x j k denotes the value of the j th variable for the k th universe selected from multiple universes using the roulette wheel selection mechanism.The third assumption involves object transfer and universe position updating through wormhole tunneling, as shown in Eq. ( 9).
In Eq. ( 9), X j denotes the first j variable of the optimal universe, ub j , lb j denotes the maxi- mum and minimum values of the j variable respectively, r 2 , r 3 , r 4 is any number between [0, 1] , and WEP denotes the probability of whether there is a wormhole between neighbor- ing universes.TDR denotes the travel distance rate, which is used to control the distance of matter jumping between universes in the MVO algorithm.

Optimized configuration of RISE with integrated demand response
The study enhanced the CSP power plant's RIES with integrated demand response.Loads were categorized as electrical, thermal, and cooling and gas.Conventional loads remained stable, while curtailable and substitutable loads adjusted based on real-time tariffs.Different load types were mathematically modeled, with electric and thermal load models adapting to demand response.See Fig. 3 for details.
Uncontrollable Load (UL) modeling consists of modeling the regular, unregulated electrical loads in the grid.The expression for conventional electrical load is shown in Eq. ( 10).
In Eq. ( 10), L UL ele,t denotes the electric load demand of conventional loads under Real-Time Pricing (RTP), γ UL−e t denotes the proportion of conventional loads in the total electric load demand, and L ele,t denotes the total amount of electric energy required by the entire energy system under a fixed standard tariff.
(8) In Eq. ( 11), L ECL ele,t RTP denotes the amount of energy required by Energy Curtailable Load (ECL) under real-time tariffs, γ ECL t denotes the proportion of ECL in the total load demand of the whole system, ε ECL denotes the price inelasticity coefficient of ECL which is a measure of the load's sensitivity to changes in tariffs, p ele RTP,t is a pricing mechanism whereby tariffs fluctuate in accordance with real-time supply and demand, and denotes a fixed constant.A pricing mechanism that fluctuates based on real-time supply and demand, p ele denotes a fixed constant.
In Eq. ( 12), L EFL ele,t denotes the amount of electrical energy required by substitutable loads in a real-time tariff environment, γ EFL−e t denotes the proportion of substitutable loads in the total electrical load demand of the entire system, and ε EFL heat denotes the thermal load substitution price elasticity coefficient is a measure of the sensitivity of thermal loads to changes in their substitution prices.Equation ( 13) depicts the electric load model after IDR participation.Equation ( 14) represents the conventional heat load model for unadjustable, fundamental heating demands in the energy system.
In Eq. ( 14), L UL heat,t denotes the heat load energy required by conventional loads in the case of real-time tariff, γ UL−h t denotes the proportion of conventional loads in the total heat load demand of the whole system, and L heat,t denotes the total heat load demand of the whole system in the case of baseline tariff.The substitutable electric load is shown in Eq. ( 15).
In Eq. ( 15), L EFL heat,t denotes the heat load demand of alternative loads under real-time tariffs, γ EFL−h t denotes the proportion of alternative loads in the total heat load demand of the whole system, and δ EFL e−h denotes the electric-heat conversion efficiency of alternative loads which is the proportion of energy lost in the process of converting electric energy to heat energy.Equation ( 16) represents the heat load model after integrated electric-thermal demand response (DIR) implementation in the two-tier optimization model (Li et al. 2021) decision-making process for optimizing the configuration of regional energy systems is shown in Fig. 4. As shown in Fig. 4, the study proposes a process for optimizing the allocation of regional energy systems.Firstly, the objectives are to ensure economic efficiency and reliability.Secondly, the uncertainty factors such as market price fluctuations, climate change, and demand randomness are analyzed.A two-layer optimization model has been constructed, with the upper layer making production capacity and cost decisions, and the lower layer pursuing maximum operational benefits.The key model parameters include system operating years, discount rate, and electricity price, and the optimal solution is obtained through a solver.Further through result analysis and market adaptability assessment, adjust strategies to respond to changes, and ultimately form systematic optimization configuration suggestions, providing efficient and sustainable decision-making support for regional energy systems.

Example analysis of the energy system after optimization of the allocation results
The study's optimized configuration results facilitate the assessment of RIES system performance with integrated electric-thermal demand response in different scenarios.Detailed analyses of these examples can reveal how system configuration and operation patterns change when considering numerous uncertainties.

Arithmetic analysis under optimal configuration of RIES considering multiple uncertainties
The study analyzed the CSP power plant's RIES system using typical seasonal data, including wind power, solar thermal energy, and load information.This analysis considered a 24-h dispatch cycle with varying time-of-day tariffs (RMB 0.367/KW h at valley time, RMB 1.253/KW h at peak time, and RMB 0.866/KW h on weekdays).Natural gas price was set at RMB 2.37/m3.The electricity sales price was RMB 0.785/KW h, and the system had a planned 10-year operational life with a 5 percent discount rate (Fig. 5).
MVO algorithm optimally allocates resources for summer days.Wind turbines generate excess power during 1-8 and 23-24, converted to natural gas to reduce waste.7-19 relies on wind, PV, and CSP, with CCHP units and purchased power as backup.Electric chillers are essential from 9-22, reducing CCHP cooling output, while CCHP units and thermal storage meet heat demand without a gas boiler.The optimal scheduling results for typical winter weather are shown in Fig. 6.

Fig. 4
Decision process for optimizing the configuration of regional energy systems Figure 6 presents the optimal winter day schedule.In Fig. 5a, excess wind and solar power is stored as natural gas during 1-7 and 23-24, and grid power is purchased during 8-22 to meet higher demand.Figure 5b depicts cooling by CCHP units with cold storage for efficiency, and in Fig. 5c, gas boilers supply winter thermal energy with limited thermal storage and occasional heat release during specific periods.The impact of a single uncertain factor on system configuration is shown in Fig. 7.
In Fig. 7, uncertainties in wind power output, CSP power plant heat storage unit output, load, electricity price, and gas price are examined using fluctuation ratios (± 3 to ± 15%).The study concludes that increasing fluctuation ratios lead to more significant fluctuations in the capacity configurations of CCHP units, GB units, and gas storage devices.The impact of a single uncertain factor on system efficiency is shown in Fig. 8.

Arithmetic analysis of RISE optimized configurations incorporating integrated demand response
The baseline tariff of the study is set at $0.785/KW h, which is in line with the total electric and thermal loads of the system; the upper limit of the real-time tariff is set at $1.5/ KW h, and the lower limit at $0.3/KW h; the price self-elasticity coefficient of the curtailable load is − 1.75; the substitution price elasticity coefficient of the thermal load is − 0.19; and the electric-heat conversion efficiency of the substitutable loads (EFLs) is 0.8.The distribution of electricity and heat load over time is shown in Table 2.
As shown in Table 2, the integrated consideration of integrated electricity-heat demand response becomes an important means to improve the efficiency and economy of the system.The study achieves the coordination and optimization of multi-energy supply of electricity, heat, cooling, and gas by integrating the optimal configuration of renewable integrated energy system (RIES) with integrated demand response.The adaptation of electrical and thermal loads after IDR is shown in Fig. 9.
In Fig. 9, we observe changes in various electrical and thermal loads with the introduction of IDR. Figure 8a reveals that curtailable electric loads disappear entirely in time periods 1-6, 10, and 18-24, and decrease in time periods 7, 9, and 11-17.Figure 8b displays a contrasting trend, with a gradual increase in replaceable thermal loads across all time periods under IDR.Notably, heat loads gradually supplant a significant portion of electric loads, primarily influenced by the lower cost of heat, as users opt for more  Figure 10 shows the baseline tariff and optimal real-time tariff curves.High tariffs in periods 1-6, 9-10, and 18-24 encourage load reduction and wind power conversion.In 7-8 and 11-17, tariffs are higher and variable, promoting electricity use and enhancing renewable energy consumption.The comparison of the optimal configuration results for RIES with and without IDR is shown in Table 3.
Table 3 compares RIES configurations with and without IDR.CCHP unit capacity is due to its high initial cost.IDR increases thermal load demand, reduces electrical load demand, and leads to larger configurations for GB units, PtG units, and gas storage units.EC units, cold storage units, and heat storage units show minimal changes in both scenarios.The cost-effectiveness comparison of benefits with and without IDR is shown in Table 4.   Table 4 shows that IDR reduces energy sales revenue but cuts user energy costs.Energy purchase, O&M, and equipment investments decrease significantly.While energy sales revenue drops, both net and gross operating revenues rise, resulting in a $541.47 million total revenue increase.The analysis of the benefits of optimizing the allocation of regional energy systems is shown in Table 5.
Table 5 shows that the optimization measures significantly reduced energy consumption in various scenarios, with urban commercial complexes saving 16.5%, hightech industrial parks achieving a savings rate of 16.9%, and residential new areas and multifunctional shopping centers reducing 14.2% and 13.0%, respectively.In terms of economic benefits, urban commercial complexes and high-tech industrial parks increased by 501,000 yuan and 685,000 yuan respectively, and other scenarios also showed varying degrees of income improvement.The reduction in carbon emissions is between 27 and 205 tons, indicating the positive impact of configuration on environmental benefits.The sensitivity analysis in this article delves into the key parameters that affect energy system optimization, including carbon tax prices, renewable energy subsidies, energy efficiency improvements, technology cost reduction, population growth rate, and GDP growth rate.The results are shown in Table 6.
As shown in Table 6 analysis, the fluctuation of carbon tax prices has moderate sensitivity to the model prediction results, with a sensitivity coefficient ranging from -0.5 to 0.9.The adjustment of renewable energy subsidies has a significant impact on the model output, with sensitivity coefficients ranging from -0.83 to 1.25, highlighting the crucial role of subsidy policies in promoting renewable energy technologies.The improvement of energy efficiency has a positive impact on the model output, with sensitivity coefficients ranging from 0.67 to 1.33, indicating that improving energy efficiency is crucial for reducing energy consumption.The reduction of

Discussion
Policy and environmental factors are crucial in optimizing regional energy systems, and these factors are often overlooked in existing research.Policy changes, such as renewable energy subsidies and carbon emission trading systems, have a significant impact on the cost-effectiveness of energy systems.The design of regulatory frameworks, including market access rules and environmental regulations, plays a crucial role in technological innovation and the reliability of energy supply.Meanwhile, environmental factors such as climate change and ecosystem health must be incorporated into energy system planning to reduce environmental footprint and address uncertainties such as extreme weather.
A new optimization model was proposed by introducing real-time electricity price adjustment and comprehensive demand response mechanism, which comprehensively considers multiple uncertainty factors and has been successfully applied to the economic and reliability analysis of regional energy systems.The research results have important theoretical and practical significance for the operation of the actual energy market, providing valuable references for policy makers and energy system operators.
Future research should further explore the following potential directions: considering more uncertain factors such as policy changes and technological progress, enhancing the robustness and adaptability of the model; Extend the model to different types of energy systems, such as distributed energy systems and microgrids, to verify the universality and flexibility of the model; Integrate emerging technologies such as smart grids and energy storage technologies to improve the intelligence level and operational efficiency of energy systems; Using interdisciplinary methods and combining knowledge from fields such as economics, engineering, and environmental science, comprehensively evaluate the socio-economic impact of energy

Conclusion
The study focuses on optimizing regional energy systems while considering multiple uncertainties and integrated demand response, which encompasses various factors like energy market price fluctuations and climate change.The findings reveal that wind turbines meet low electricity demand in summer but require grid electricity in winter.Uncertainty analysis shows significant fluctuations in electricity prices, with minimal impact from CSP power plant heat storage fluctuations ranging from ± 3 to ± 15%.Adjusted real-time tariffs encourage user participation, with high tariffs in certain periods prompting load reduction, greater wind power conversion, and increased thermal energy usage.IDR leads to a slight reduction in system energy sales revenue, lowered user energy costs, increased carbon emission costs due to higher heat load, and substantial reductions in energy purchase, operation and maintenance, and equipment investment costs, resulting in a total revenue increase of $541.47 million.The study's limitations include potential unaccounted factors like policy changes and environmental impacts, which warrant consideration in future research.
However, this study also has some limitations and has not fully considered potential factors such as policy changes and environmental impacts, which require more attention and research in future research.In addition, with the advancement of technology and changes in the market environment, future research can further explore new energy technologies, policy tools, and market mechanisms to achieve more flexible and efficient energy system management.Through continuous technological innovation and policy optimization, we can expect to achieve cleaner, more economical, and more reliable energy supply in the future, making greater contributions to addressing climate change and promoting sustainable development.

Fig. 1
Fig. 1 Two-level optimization model solution relationship

Fig. 3
Fig. 3 Integrated demand response strategy optimization process

Fig. 5 Fig. 6
Fig. 5 Optimal scheduling results for typical days in summer

Fig. 7 Fig. 8
Fig. 7 Influence of single uncertain factor on system configuration

Fig. 9
Fig. 9 Adaptation of electric and thermal loads after IDR

Fig. 10
Fig. 10 Considering the changes of various electric and after IDR

Table 1 Comparative analysis between existing literature and this study Research author Main research content Research method Main findings/contributions Relationship/differences with current research
).

Table 2
Electricity and heat load distribution over time

Table 3
Comparison of RIES optimal configuration results with and without IDR

Table 4
Cost-benefit comparison of RIES with and without IDR

Table 5
Analysis of the benefits of optimizing the allocation of regional energy systems

Application scenario number Application scenario description Energy consumption before optimizing configuration (kWh) Energy consumption after optimized configuration (kWh) Energy saving rate (%) Increase in economic benefits (10,000 yuan) Carbon emission reduction (tons)
Although the changes in population growth rate and GDP growth rate are relatively small, their impact on the model output cannot be ignored.The sensitivity coefficients are 0.14 to 0.35 and 0.35 to 0.55, indicating the indirect effect of macroeconomic indicators on energy demand.

Table 6
Sensitivity analysis results These research directions contribute to achieving a balance between technological, economic, policy, and environmental dimensions in optimizing energy systems, promoting global energy transformation and sustainable development.