Bi-Level Optimization Scheduling Strategy for PIES Considering Uncertainties of Price-Based Demand Response

Abstract

The asymmetry-induced uncertainty in both sources and loads is a crucial and continuously spotlighted issue within modern power systems. Applying optimization scheduling method to deal with this asymmetry is a feasible solution. Accordingly, this paper proposes a bi-level park-level integrated energy system (PIES) optimization strategy considering uncertainties of price-based load demand response (PLDR). Firstly, a model for characterizing the uncertainties of the PLDR is developed based on fuzzy theory. Secondly, a bi-level two-stage PIES optimization model that includes multiple device models is established. In the first stage, the dynamic pricing optimization is carried out with the aim of maximizing user satisfaction. In the second stage, the PIES scheduling strategy optimization is performed with the aim of minimizing the operation costs of PIES. Finally, multiple scenarios are set to conduct comparative validation, which demonstrates that the proposed method not only improves the renewable energy integration capacity of the system, optimizes the load profiles, and enhances the economic and low-carbon performance, but also increases user satisfaction, thus providing a reference for the dispatch and operation of the park-level integrated energy system.

1. Introduction

To achieve the “dual carbon” goals, alleviate energy supply–demand asymmetry and improve energy utilization, integration of multiple complementary resources by applying the optimization method has become a significant direction for future energy revolution [1]. Park-level integrated energy systems, which are a modern power system characterized by coupling multiple energy resources and achieving cascaded energy utilization, play a crucial role in this process and are also one of the key trends in the field of energy development. Within PIES, on one hand, there are multiple flexible energy conversion devices, and on the other hand, there are many potential sources of flexibility. Demand response on the consumer side is one particularly important form of flexibility resource. Regarding demand response, both domestic and foreign governments have introduced several incentive-based support policies, thus laying a solid foundation for the participation of demand response mechanisms in ancillary service markets [2,3,4]. This approach, which incentivizes users to change their consumption behaviors by providing them with economic compensation, can partially alleviate the supply–demand imbalance during peak load periods. It provides an available approach for demand-side resources in PIES strategy optimization.

Recently, extensive research on strategy optimization problems of PIES has been conducted. The concept of an Energy Hub (EH) was introduced in [5] and a standardized modeling of PIES was presented for planning and scheduling studies. Literature [6] proposed an IES scheduling method considering energy-carbon comprehensive pricing model. It establishes an energy scheduling model using a Stackelberg game approach to maximize profits. This method can enhance economic efficiency and reduce carbon emissions. Literature [7] proposes a two-stage coordinated optimization method with long-term and short-term scheduling strategy for PIES. The results show that under long-term operating conditions, two-stage scheduling strategy of PIES can acquire more energy revenue. This two-stage scheduling strategy determines the optimum capacity for long-term scheduling while ensuring effective integration with power grid, thereby cutting down decision-making complexity. Literature [8] proposes a comprehensive planning strategy considering the coupling relationship of electricity, natural gas, and thermal load. In the aforementioned literature, researchers have studied system optimization problems from various perspectives, including optimization scheduling methods, equipment model modeling, and solution algorithms. However, none of these studies considered the influences of demand response on optimization process. Indeed, in practical operation of integrated energy systems, system operators can guide users to actively adjust their energy consumption and participate in demand response programs, which can improve system’s economic and low-carbon performance. Given this, ref. [9] analyzes the implementation of integrated energy demand response based on cooling, heating, and electricity loads. It examines how demand response can enhance the system economy and flexibility. Literature [10] explores an implementation of demand response in real-time electricity markets. It demonstrates that demand response can maximize the profit return of energy loads and alleviate the supply–demand imbalance of IES. Literature [11] establishes an intra-day optimization scheduling strategy for regional IES considering LDR. The results demonstrate that this scheduling strategy mitigates the intra-day supply–demand imbalances of renewable resources and loads, enhances system stability, and further reduces operational costs.

Indeed, it is evident that the optimal planning problem for integrated energy systems has gained significant attention from the academic community both domestically and internationally. Among these research efforts, there is a particular focus on fully exploiting the potential of demand-side response to improve economic and stability. This area of research is becoming a key hotspot in PIES. Although existing research has made preliminary explorations in this area, there are still some issues that need to be addressed. Firstly, most research efforts predominantly focus on deterministic demand response programs without considering the potential impact of various uncertainties that may exist in practical applications. However, for non-direct control demand response programs (such as demand response based on real-time price), users need to adjust their energy consumption plans based on real-time market signals. The inherent differences in users’ lifestyle habits, rationality, and behavioral preferences create a high degree of uncertainty in their demand response capabilities. Therefore, disregarding the uncertainty impact of demand response would result in planning solutions that are not truly globally optimal in nature. In addition, in existing research, stochastic optimization or robust optimization methods are commonly used to model uncertainty factors. Stochastic optimization involves extracting statistical characteristics of uncertain factors from a large amount of reliable historical data and generating expected scenarios based on the obtained probability distribution functions. However, for this study, the acquisition of demand-side classified time-of-use data is limited owing to simultaneous involvement of energy consumption timing and type of energy consumption [12] in demand response under integrated energy systems. As a result, acquiring and analyzing demand response data becomes challenging, making it difficult to obtain reliable probability distributions for user response parameters. Furthermore, user response behavior often exhibits randomness and fuzziness [13,14], which is difficult to effectively describe using fixed probability distribution functions. Therefore, these reasons present significant obstacles for the application of stochastic optimization methods in this study. On the other hand, traditional robust optimization approaches typically focus on the most unfavorable uncertain scenarios for achieving system objectives, leading to conservative solution outcomes that may not satisfy the planning requirements for system economics effectively.

To address the asymmetry of sources and loads in modern power systems, this paper proposes a bi-level PIES optimization scheduling method considering the uncertainties of PLDR. This paper focuses on demand response programs based on dynamic pricing as an example. By taking into account both the configuration of PIES and demand-side management strategies in a comprehensive way, the proposed model aims to optimize the configuration of PIES. Additionally, the impact of uncertainty in demand response is described by using fuzzy theory. Finally, the validity of the proposed method is verified by means of setting multiple scenarios.

2. Park-Level Integrated Energy System

The PIES is a multi-input and multi-output system integrating multiple energy conversion facilities, energy resources, and loads [15]. Different types of energy flows are conducted in PIES and multiple load demands are satisfied. In the PIES designed in this paper, wind power, photovoltaics, electric boilers (EB), gas boilers (GB), battery energy storage devices, and combined heat and power (CHP) are included. Additionally, energy storage devices, under different operating conditions, can store excess energy, thereby enhancing the system’s capacity to accommodate renewable energy and forming beneficial interactions with the grid.

3. Uncertainties of PLDR

In PLDR, users voluntarily adjust their energy consumption based on dynamic prices provided by the system operator. Due to subjective factors, demand response exhibits a certain level of volatility. This paper takes into account the uncertainty of demand response by using fuzzy theory. From the perspective of demand characteristics, the loads in PIES can be approximately classified into four types: essential loads, reducible loads, transferable loads, and substitutable loads [16,17]. The following section discusses the modeling of these types of loads.

3.1. Essential Loads (Els)

ELs refer to loads that could not be interrupted under a specific time period. They possess fixed and uninterrupted characteristics, meaning they do not respond to dynamic electricity or gas prices. With the presence of ELs in PIES, their operating characteristics of ELs can be represented by Equations (1) and (2).

$$P_{el,t}={\gamma }_{el,t}{P}_t$$

(1)

$$P_{hl,t}={\gamma }_{hl,t}{P}_t$$

(2)

where P_t represents the total load value, P_el,t represents the value of essential electric load, P_hl,t represents the value of essential thermal load, γ_el,t represents the ratio of essential electric load to total load value, and γ_hl,t represents the ratio of essential thermal load to total load value at time t.

3.2. Reducible Loads and Transferable Loads

Reducible loads are defined as the loads that users can voluntarily reduce according to their own interests and needs without sacrificing the fulfillment of their own demand. These loads have a certain degree of flexibility and can respond to dynamic electricity and natural gas prices. Common reducible loads include some air conditioning equipment, household appliances, and certain types of lighting fixtures used in residential buildings. Transferable loads are the loads whose supply periods can be changed according to a schedule. Within a certain time frame, the total amount of power supplied remains constant, but the specific hours of supply can be adjusted without significantly impacting the users. Transferable loads exhibit strong controllability. Common examples of transferable loads include washing machines and water heaters. Considering the existence of these reducible and transferable loads in PIES, this paper aims to establish a mapping relationship between the reducible load quantity, transferable load quantity, and dynamic electricity and natural gas prices (ENGPs). This mapping relationship is described as follows:

1. Dynamic ENGPs are positively correlated with the reducible load quantity. This means that as the ENGPs increase, the reduction rate of load at a given time also increases. Similarly, during periods with higher ENGPs, the load tends to be shifted to periods with lower prices. In other words, as the ENGPs increase, the transfer rate of load at a given time also increases;

2. The reduction rate and transfer rate of the load range between zero and one. As the electricity and natural gas prices increase, these rates tend to approach one, while they tend to approach zero when the prices are lower;

3. In an ideal scenario, assuming that user behavior follows a normal distribution pattern, the reduction rate and transfer rate of the load are symmetric about a center point of electricity and natural gas prices.

The sigmoid function has the properties of monotonicity, a constrained range, and symmetry, which are in line with the aforementioned mapping relationship. Given the complexity of this mapping relationship, a non-standard type of sigmoid function is used for modeling [18]. Additionally, considering the uncertainty in user behavior, most users are sensitive to benefits, but the sensitivity varies among individuals. Moreover, non-benefit factors such as psychological factors and unexpected events can also influence user behavior. As a result, there is significant fluctuation in the reduction rate and transfer rate of the load. In general, when prices are lower, the benefits are smaller, and subjective factors play a dominant role. This leads to higher uncertainty in user behavior, resulting in larger fluctuations in the reduction rate and transfer rate of the load. Conversely, when prices are higher, the benefits are greater, and the influence of benefits becomes dominant. This leads to lower uncertainty in user behavior, resulting in smaller fluctuations in the reduction rate and transfer rate of the load. This paper utilizes triangular fuzzy numbers to characterize this uncertainty. Therefore, the modeling of the reduction rate, transfer rate, and their uncertainties is as follows:

$${\lambda }_{xc,t}={\displaystyle \frac{1}{1+e^{-{\alpha }_{x1}(x_{xc,t}-{\beta }_{x1})}}}+{\epsilon }_{xc,t}$$

(3)

$${\lambda }_{xs,t{t}^{\prime }}={\displaystyle \frac{1}{1+e^{-{\alpha }_{x2}(x_{xs,t{t}^{\prime }}-{\beta }_{x2})}}}+{\epsilon }_{xs,t{t}^{\prime }}$$

(4)

$$\left\{\begin{array}{c}{\epsilon }_{xc,t}=\left(-d_{xc,t},0,d_{xc,t}\right)\\ d_{xc,t}=\left\{\begin{array}{c}{k}_{x1},x_{xc,t}\le 0\\ k_{x1}{e}^{-k_{x2}{x}_{xc,t}},x_{xc,t}\ge 0\end{array}\right.\end{array}\right.$$

(5)

$$\left\{\begin{array}{c}{\epsilon }_{xs,t{t}^{\prime }}=\left(-d_{xs,t{t}^{\prime }},0,d_{xs,t{t}^{\prime }}\right)\\ d_{xs,t{t}^{\prime }}=\left\{\begin{array}{c}{k}_{x3},x_{xs,t{t}^{\prime }}\le 0\\ k_{x3}{e}^{-k_{x4}{x}_{xc,t{t}^{\prime }}},x_{xs,t{t}^{\prime }}\ge 0\end{array}\right.\end{array}\right.$$

(6)

where α_x1, α_x2, β_x1, β_x2 are the parameters of the sigmoid functions, λ_xc,t represents the reduction rate of the xth type of load (electrical or thermal loads) at time t, λ_xs,tt′ represents the transfer rate of the xth type of load from t to t′, x_xc,t represents the price difference between electricity or natural gas prices and the baseline electricity or natural gas price, x_xs,tt′ represents the price difference between electricity or natural gas prices and electricity or natural gas prices, ε_xc,t represents the uncertainty error in the reducible load of the xth type, ε_xs,tt′ represents the uncertainty error in transfer rate of the xth type of load from time t to t′, k_x1, k_x2, k_x3, k_x4 are proportional coefficients, d_xc,t represents the maximum error in the reduction rate of the xth type of load at time t, d_xs,tt′ represents the maximum error in the transfer rate of the xth type of load from time t to t′;

Taking all the above formulas into consideration, we can obtain the values of electricity/thermal load after reduction and transfer for each period, as shown below.

$$P_{xc,t}=\left(1-{\lambda }_{xc,t}\right){\gamma }_{xc,t}{P}_t$$

(7)

$$P_{xs,t}=(1-{\displaystyle \sum _{t^{\prime }\in T,t^{\prime }\ne t}{\lambda }_{xs,t{t}^{\prime }}}){\gamma }_{xs,t}{P}_t+{\displaystyle \sum _{t^{\prime }\in T,t^{\prime }\ne t}{\lambda }_{xs,t^{\prime }t}}{\gamma }_{xs,t^{\prime }}{P}_{t^{\prime }}$$

(8)

where P_xc,t represents the value of the xth type of load after reduction at time t, P_xs,t represents value of the xth type of load after transfer, γ_xc,t represents the ratio of the value of the xth type of load that can be reduced to the total load value, γ_xs,t represents the ratio of the value of the xth type load that can be transferred to the total load value.

3.3. Substitutable Loads

A substitutable load refers to a load where users have the flexibility to choose the form of energy based on their specific needs. Common examples of substitutable loads are heating equipment, kitchen appliances, and certain air conditioning systems. In PIES, these loads exist, and users can adaptively choose the form of energy according to different electricity and natural gas prices during different time periods. Therefore, it is essential to establish a model for the substitution rate of the load with respect to price. In an ideal scenario, if the electricity price is high, users choose natural gas as the energy source, while if the electricity price is low, they choose electricity as the energy source. However, apart from considering the benefits, users are also influenced by subjective factors and can voluntarily choose the energy supply method. Taking all these considerations into account, the mapping relationship between the substitution rate of the electricity load (denoted as λ_et) and the difference between ENGPs (denoted as x_eh) can be described as follows:

1. The substitution rate of the electricity load is positively correlated with the differences between ENGPs. The larger the price difference, the closer the substitution rate of the electricity load is to one, and the smaller the price difference, the closer it is to xero.

2. In the substitutable load category, assuming that electricity and natural gas are interchangeable and users have no preference in usage, user behavior follows a normal distribution pattern. When x_eh equals 0, λ_et equals 0.5, and the mapping relationship λ_et is symmetric about the center (0, 0.5), with its rate of change being symmetric about the y-axis. In other words, the derivative of the substitution rate of the electricity load is an even function.

3. When x_eh approaches zero, the user’s benefit is small, indicating strong subjectivity and high uncertainty. When x_eh approaches infinity, the user’s benefit is large, indicating weak subjectivity and low uncertainty. Therefore, the uncertainty model is an even function with a monotonically increasing and then decreasing trend.

Based on the above relationships, this paper adopts the arctangent function to describe the relationship between λ_et and x_eh. The uncertainty is modeled using a Gaussian function. The modeling is as follows:

$${\lambda }_{\mathit{et},t}={\displaystyle \frac{1}{\pi }}\left(\arctan x_{eh,t}+{\displaystyle \frac{\pi }{2}}\right)+{\epsilon }_{eh,t}$$

(9)

$$\left\{\begin{array}{c}{\epsilon }_{eh,t}=\left(-d_{eh,t},0,d_{eh,t}\right)\\ d_{eh,t}=a{e}^{-{\displaystyle \frac{x_{eh,t}^2}{2c^2}}}\end{array}\right.$$

(10)

where a and c are parameters of Gaussian function, ε_eh,t represents the uncertainty error in the substitution rate of electricity load, d_eh,t represents maximum error in the substitution rate of electricity load.

Taking all the above formulas into consideration, we can obtain the values of electricity/thermal load after substitution for each period, as shown below.

$$P_{et,t}=\left(1-{\lambda }_{\mathit{et},t}\right)\left({\gamma }_{et,t}+{\gamma }_{ht,t}\right)P_t$$

(11)

$$P_{ht,t}={\lambda }_{\mathit{et},t}\left({\gamma }_{et,t}+{\gamma }_{ht,t}\right)P_t$$

(12)

where P_et,t, P_ht,t represent the values of electricity/thermal load after substitution, γ_et,t, γ_ht,t represent the ratio of substitutable electricity/thermal load to total load value.

3.4. The System’s Total Load Demand Considering Dynamic Pricing

Considering the dynamic pricing and user uncertainty based on Equations (1)–(12), the values of electricity/thermal load at time t, denoted as P_e,t and P_h,t, are as follows:

$$P_{e,t}=P_{el,t}+P_{ec,t}+P_{es,t}+P_{et,t}$$

(13)

$$P_{h,t}=P_{hl,t}+P_{hc,t}+P_{hs,t}+P_{ht,t}$$

(14)

4. Bi-Level Optimization Scheduling Model for PIES

In this section, a bi-level optimization scheduling strategy for PIES is put forward, taking into account the diverse interests and demands of different user groups. The model considers both supply and user side while addressing the uncertainties associated with price-based load demand response.

4.1. The Upper-Level Price Decision Model

On the user side, it is desirable to adjust the response quantity of electricity and thermal load based on dynamic pricing to achieve economic benefits while ensuring a certain level of energy comfort. The target is constructed as

$$\max C_1=C_m+C_{pr}$$

(15)

$$C_m={\displaystyle \frac{{\displaystyle \sum _{t\in T}\left|P_{pr,t}\right|}}{{\displaystyle \sum _{t\in T}{P}_t}}}$$

(16)

$$C_{pr}=1-{\displaystyle \frac{{\displaystyle \sum _{t\in T}\left(P_{e,t}{x}_{e,t}+P_{h,t}{x}_{h,t}\right)}}{{\displaystyle \sum _{t\in T}\left(P_{e,t}^{\prime }{x}_{e,0}+P_{h,t}^{\prime }{x}_{h,0}\right)}}}$$

(17)

where C_m represents the user’s satisfaction with electricity usage, C_pr represents the user’s satisfaction with the economic benefits, P_pr,t is load response quantity, P′_e,t, P′_h,t represent electricity/thermal load values before the response at time t, x_e,0/x_h,0 is baseline electricity/natural gas prices, x_e,t/x_h,t is dynamic electricity/natural gas prices.

4.2. The Lower-Level Park Energy Supply Decision Model

The objective of the park energy supply side is to meet the user’s energy demand at the lowest cost:

$$\min C_2=C_{ma}+C_b+C_{wpv}+C_{dr}$$

(18)

$$\left\{\begin{array}{c}{C}_{ma}={\displaystyle \sum _{i\in I}{R}_i{W}_i}\\ C_b={\displaystyle \sum _{t\in T}\left({\alpha }_{e,t}{P}_{eb,t}+{\alpha }_{h,t}{P}_{hb,t}\right)}\\ C_{wpv}={\displaystyle \sum _{t\in T}\left({\beta }_w{P}_{qw,t}+{\beta }_{pv}{P}_{qpv,t}\right)}\\ C_{dr}={\displaystyle \sum _{t\in T}\left(\begin{array}{l}\left(P_{e,t}{x}_{e,t}+P_{h,t}{x}_{h,t}\right)-\\ \left(P_{e,t}^{\prime }{x}_{e,0}+P_{h,t}^{\prime }{x}_{h,0}\right)\end{array}\right)}\end{array}\right.$$

(19)

where C_ma is PIES annual maintenance cost, C_b is PIES annual energy procurement cost, C_wpv is annual penalty cost for curtailed wind and solar power, C_dr is PIES annual demand response cost, i represents equipment category, I represents the set of equipment types, R_i represents the capacity of equipment i, W_i is annual maintenance cost per unit capacity for equipment i, α_e,t/α_h,t represents the price of electricity/natural gas, P_eb,t/P_hb,t represents the amount of purchased electricity/natural gas, β_w/β_pv represents the penalty cost of curtailed wind/solar power per unit at time t, P_qw,t/P_qpv,t represents curtailed wind/solar power at time t.

4.3. Constraints

(1)

Pricing constraints

Due to the influence of objective factors, the electricity price and natural gas price should satisfy certain upper and lower limits.

$$x_{e,t}^{\min }\le x_{e,t}\le x_{e,t}^{\max }$$

(20)

$$x_{h,t}^{\min }\le x_{h,t}\le x_{h,t}^{\max }$$

(21)

(2)

User constraints

Considering the user’s own interests, the satisfaction with the electricity usage and the economic benefits should meet certain threshold values.

$$\left\{\begin{array}{c}{C}_m\le C_m^{\max }\\ C_{pr}\ge C_{pr}^{\min }\end{array}\right.$$

(22)

(3)

Load transfer rate constraint

The sum of the transfer rates of transferable loads from a specific time to other times should be less than one.

$${\displaystyle \sum _{t^{\prime }\in T,t^{\prime }\ne t}{{\lambda }_{xs,t{t}^{\prime }}}^{\prime }}\le 1$$

(23)

(4)

Constraints on energy supply

The constraints on the energy supply side of the PIES mainly consist of wind and photovoltaic power output constraints, gas boiler constraints, electric boiler constraints, and energy storage constraints.

4.4. Evaluation Indicators

Based on the above bi-level optimization scheduling model, this paper can effectively evaluate the economic performance and user satisfaction of the system from the perspectives of the total cost and user satisfaction with the electricity usage. The PIES as an important direction of the future energy revolution is evaluated for its low-carbon performance and peak shaving ability with the help of two indicators, namely carbon emissions and peak-valley difference rate. This evaluation is performed considering the achievement of dual carbon goals and stable operation of the power grid.

(1)

Total cost: calculated by (18).

$$C=C_2$$

(24)

(2)

User satisfaction: user satisfaction is a comprehensive evaluation formed by users based on their actual experience after using the electric heating and gas services.

$$C_{yh}=1-{\displaystyle \frac{{\displaystyle \sum _{t\in T}\left|P_{pr,t}\right|}}{{\displaystyle \sum _{t\in T}{P}_t}}}$$

(25)

(3)

Carbon emission

Assuming that external electricity purchases are all from coal-fired power units, the main carbon emissions sources include coal-fired power units, CHP, GB. The formula for calculating carbon emissions is as follows:

$$\left\{\begin{array}{c}E=E_{buy}+E_{cg}\\ E_{buy}={\displaystyle \sum _{t=1}^T\left(a+b{P}_{eb,t}+c{P_{eb,t}}^2\right)}\\ E_{cg}={\displaystyle \sum _{t=1}^{T}d\left(Q_{CHP}+Q_{GB}\right)}\end{array}\right.$$

(26)

where E, E_buy, E_cg represent, respectively, total carbon emissions, carbon emissions from external electricity purchases, and carbon emissions from CHP and GB; a, b, c represent the carbon emission coefficients of external electricity purchasing; d is carbon emission coefficient for natural gas-consuming devices; Q_CHP and Q_GB are, respectively, the gas consumption of CHP and GB.

(4)

Peak-valley difference rate

$$h_x={\displaystyle \frac{P_x^{\max }-P_x^{\min }}{P_x^{\max }}}$$

(27)

where h_x represents the peak-valley difference rate of the xth load, $P_x^{\max }$/$P_x^{\min }$ represents the maximum/minimum value of the xth load within the scheduling period.

5. Case Study

To validate the effectiveness of the proposed method, a simulation analysis is conducted based on the PIES, as described in [18,19]. The scheduling period is set to a 1 h time step with a total of 24 h per day. Appendix A provides the predicted values of wind, photovoltaic power output, and electricity and thermal load demand within PIES. Specific information regarding energy conversion devices and storage equipment parameters inside the PIES can be found in Appendix B.

5.1. Comparative Analysis Across Multiple Cases

To validate the validity of demand response incentive mechanism in the optimized scheduling model for the PIES, this paper conducts the scheduling strategy analysis in three cases. The case settings are as follows:

Case 1: Without considering demand response optimization.

Case 2: Considering price-based demand response optimization, but without considering uncertainty.

Case 3: Considering price-based demand response optimization while also considering uncertainty.

From

Table 1. Indicators in Cases 1–3.

---	Case 1	Case 2	Case 3
Operating cost (yuan)	26,500	22,246	22,829
Demand response compensation cost (yuan)	0	4152	2046
Wind and solar power curtailment penalties (yuan)	4217	229	9
Total cost (yuan)	30,717	26,627	24,880
Carbon emission (kg)	39,979	32,194	18,391
User satisfaction (%)	-	83.61	86.94

and Figure 1, it can be observed that in Case 2 compared to Case 1, the total cost decreases by 4090 yuan, carbon emissions reduce by 7785 kg, wind and solar power curtailment penalties decrease by 3988 yuan, electricity load peak-to-valley ratio decreases by 2.21%, thermal load peak-to-valley ratio decreases by 14.73%, and the overall load peak-to-valley ratio decreases by 7.92%. This validates the finding that considering price-based demand response mechanisms can reduce the overall cost of the integrated energy system, decrease carbon emissions, lower the load peak-to-valley difference, and smooth out the load curve. In Case 3 compared to Case 2, although there is an increase of 583 yuan in operating costs, the demand response compensation cost decreases by 2110 yuan and wind and solar power curtailment penalties decrease further by 220 yuan, resulting in a decrease of 1747 yuan in total cost. Carbon emissions decrease by 13,803 kg. In terms of user satisfaction, Case 2 has a satisfaction rate of 83.61% while Case 3 has a satisfaction rate of 86.94%, an increase of 3.33%. The electricity load peak-to-valley ratio decreases by 27.47%, the thermal load peak-to-valley ratio decreases by 4.41%, and the overall load peak-to-valley ratio decreases by 14.73%. This validates the finding that the proposed price-based demand response mechanism considering uncertainty can improve user satisfaction while also ensuring the economic efficiency, low-carbon operation, and peak shaving/filling performance of the integrated energy system.

In this paper, we use CPLEX to solve the proposed model. The computing times of Case 1, Case 2 and Case 3 are, respectively, 307.3 s, 422.7 s and 435.1 s. As the uncertainty increases, the computation time becomes longer. The convergence proofs of the proposed method in Case 1, Case 2, and Case 3 are shown in Figure 2. The numbers of iterations in different cases are less than 100.

5.2. Upper-Level Price Decision Analysis

According to the simulation results, it can be observed that significant changes occur in electricity prices during different time periods after implementing demand response, as shown in Figure 3. The high peak electricity prices mainly occur from 9:00 to 21:00, while the low valley electricity prices are concentrated in the range from 22:00 to 8:00. This indicates that during periods of high electricity demand, dynamic prices are often higher than the baseline prices, while during periods of low electricity demand, dynamic prices are often lower than the baseline prices. This economically encourages users to shift their load peaks. Similarly, as shown in Figure 4, during periods of high thermal load demand, dynamic gas prices are higher than the baseline prices, and during periods of low thermal load demand, dynamic gas prices are lower than the baseline prices. This reveals a consistent positive correlation between the overall daily load curve and the price curve under demand response. After the price decision analysis, the results in

Table 2. Indicators before and after price decision.

	Before Price Decision	After Price Decision
average electricity price (yuan)	0.5583	0.5783
average natural gas price (yuan)	0.7	0.6559
user energy purchase cost (yuan)	35,787	33,745
average electricity price (yuan)	0.5583	0.5783

show that the average electricity price increased by 0.02 yuan, the average gas price decreased by 0.0441 yuan, and the user energy purchase cost decreased by 5.71%. This encourages users to cut down load under demand peaking periods and shift loads to low-demand periods, thereby improving system’s ability for peak shaving or filling. Therefore, price-based demand response mechanism allows dynamic prices to be flexibly adjusted based on energy consumption status on demand side, stimulating user response potential.

By comparing the electricity and gas prices in Figure 5, it can be observed that during the high peak electricity price period from 9:00 to 18:00, the gas price is relatively low. At this time, the electricity load reaches a high peak while the thermal load is at a low valley. However, during the low valley electricity price period from 22:00 to 7:00, the gas price is higher, and the electricity load is at a low valley while the thermal load reaches a high peak. This is because substitutable loads are taken into account when implementing demand response. Therefore, during high peak electricity price periods, part of the electricity load can be replaced by the thermal load, which reduces the peak electricity load and increases the load during the low valley of the thermal load. Similarly, during periods of high peak thermal load, part of the thermal load can be replaced by the electricity load, reducing the peak thermal load and increasing the load during the low valley of the electricity load, further enhancing the system’s ability for peak shaving and filling.

5.3. Load Demand Response and Energy Supply Decision Analysis

Figure 6 compares the three cases in terms of electricity consumption, gas consumption, and carbon emissions. It can be observed that Case 2 significantly reduces electricity consumption by 8708 kWh compared to Case 1, increases gas consumption by 677 cubic meters, and decreases carbon emissions by 7785 kg. In Case 3 compared to Case 2, electricity consumption continues to decrease significantly by 2984 kWh, while gas consumption slightly increases by 155 cubic meters, and carbon emissions decrease significantly by 13,803 kg. This is because price-based demand response reduces the total electricity and thermal load. Meanwhile, the output of gas-consuming devices increases, which leads to a reduction in purchased electricity and lower carbon emission factors for gas-consuming devices, thus decreasing carbon emissions. During high electricity price periods, the load is shifted to low-price periods and periods with high renewable energy output. Additionally, a portion of the load is reduced, resulting in a decrease in operating costs. The reduction in electricity consumption and increase in gas consumption for IES improve the overall energy utilization efficiency as it relies more on natural gas to meet the load demand. Further analysis is conducted on Case 3.

Figure 7 reflects the results of electricity load participation in demand response under Case 3. From the graph, it can be observed that the peak electricity load periods are mainly concentrated from 8:00 to 18:00. After implementing the price-based demand response incentive mechanism, some electricity load is reduced and shifted during the period from 8:00 to 21:00, while the electricity load significantly increases during the time periods of 1:00 to 7:00 and 22:00 to 24:00. Some electricity load during the period from 9:00 to 21:00 is transferred to the low-demand periods of 1:00 to 8:00 and 22:00 to 24:00, resulting in a transfer of 3313 kW of electricity load. After implementing demand response, the high peak electricity price periods mainly occur from 9:00 to 21:00. During this time period, a significant amount of electricity load is reduced, while the low valley electricity prices are mainly concentrated from 22:00 to 8:00, with lesser reduction in electricity load. The total reduction in electricity load amounts to 1560 kW. Additionally, as shown in Figure 4, during the period from 9:00 to 18:00, the electricity price is significantly higher than the natural gas price. Therefore, during this time period, a substantial amount of electricity load is replaced by thermal load. Conversely, during the period from 19:00 to 8:00, the natural gas price is higher than the electricity price, leading to a significant replacement of thermal load with electricity load. The total load substitution amounts to 4343 kW. The electricity load is shifted from daytime high-price periods to nighttime low-price periods, reducing the load during high-price periods. At the same time, the high-price periods are substituted with thermal load, effectively smoothing the electricity load curve and reducing the overall operating costs of the integrated energy system.

Figure 8 reflects the power balance of IES. From the graph, it is observed that there are three time periods with relatively small electricity purchases. The first period is during the high electricity price period, specifically from 9:00 to 18:00. This period is the peak load period before demand response. By transferring and reducing the electricity load, most of electricity load demand is met through CHP, wind power, and photovoltaics, resulting in a decrease in electricity purchases. The second period is during the period of abundant wind resources, specifically from 24:00 to 4:00. This period is a low-demand period before demand response. By transferring and substituting, the electricity load demand increases, and most of it can be met by wind power. If demand response is not implemented, a significant amount of wind resources is wasted. Therefore, this improves the integration capacity of renewable energy consumption. The third period is during the time when electricity prices are similar to natural gas prices, specifically from 19:00 to 21:00. During this time period, natural gas prices are comparable to electricity prices. While meeting the power balance, it also provides a considerable amount of power for thermal balance. This effectively reduces PIES operation costs. Therefore, electricity load demand can be met by relying on renewable energy and CHP. After demand response, electricity load is reduced during these three time periods, smoothing electricity load curve, and improving the economic efficiency and renewable resource integration capacity of the system.

Figure 9 reflects the results of thermal load participation in demand response under Case 3. From the graph, it can be seen that peak thermal load periods are mainly during the nighttime from 1:00 to 5:00. After implementing the PLDR mechanism, thermal load during the peak periods is reduced, and a portion of the thermal load is shifted to the low-demand periods during the daytime. Additionally, during high natural gas price periods, the thermal load is substituted with electricity load. The reduction in thermal load amounts to 399 kW, the transferred thermal load amounts to 636 kW, and substituted thermal load amounts to 4343 kW. This achieves the effect of peak shaving and valley filling, effectively reducing carbon emissions.

Figure 10 reflects the thermal power balance of IES. During the period from 9:00 to 21:00, the thermal load increases after valley filling. During this time period, the electricity price is higher than or close to the natural gas price. Therefore, the cost of electricity generation from CHP is lower than purchasing electricity. Increasing the output of CHP in the energy supply has advantages. From Figure 8, it can also be seen that during this time period, most of the purchased natural gas is supplied to the CHP. From the graph, it can be observed that during the period from 22:00 to 7:00, there are two factors. Firstly, the electricity price is low and wind resources are abundant during this time period. Secondly, the thermal efficiency of gas boilers and electric boilers is higher than that of CHP. As a result, the CHP have minimal output during this time period, while the gas boilers contribute more to the heating supply. Heating is mainly provided by gas boilers and electric boilers during this time period.

In the above study, the proportions of different types of loads in end-demand were assumed to be fixed. However, in reality, the benefits vary due to natural differences in user load composition and usage habits. To reveal the impact of these variations, three additional cases are introduced with different compositions of demand response:

Case 4: Only consider transferable loads.

Case 5: Only consider substitutable loads.

Case 6: Consider both transferable and substitutable loads.

The results obtained from these cases are compared with Case 3, as shown in the table below.

From

Table 3. Indicators in Cases 3–6.

	Case 4	Case 5	Case 6	Case 3
Total cost (yuan)	27,949	29,459	26,951	24,880
Improvement percentage (%)	9.01	4.10	12.26	19.00
User satisfaction (%)	74.16	72.54	81.78	86.94

, it can be observed that the benefits, from highest to lowest, are as follows: Case 3, Case 6, Case 4, and Case 5. In comparison to Case 5, Case 6 reduces the total cost by 2508 yuan and increases user satisfaction by 9.24%. In comparison to Case 6, Case 3 reduces the total cost by 2071 yuan and increases user satisfaction by 5.16%. Therefore, considering a greater variety of load types not only reduces the overall system cost but also improves user satisfaction. The main reason for these results is that in cases where only transferable loads or substitutable loads are considered, the PIES can only transfer or substitute a portion of the load when affected by dynamic price changes. A single type of load is unable to fully utilize the flexible demand response capability. However, when both transferable and substitutable loads are considered, the complementary characteristics of different forms of demand response resources can enable the system to have control over both the timing and form of load energy consumption. This allows for more flexible adjustment of load demand and improved economic efficiency while meeting operational constraints. Case 3 also considers reducible loads, allowing for the reduction in some loads during high-price periods, further enhancing peak shaving capability and economic performance of the system. Therefore, considering demand response with various types of loads can lead to greater benefits and improvements.

6. Conclusions

This paper proposes a bi-level PIES optimization strategy considering the uncertainties of PLDR. The goal is to deal with the asymmetry between sources and loads in modern power systems by applying the optimization scheduling method. The paper focuses on establishing an uncertainty model for PLDR using fuzzy theory, and through the coordinated optimization of park equipment configuration and dynamic pricing on the demand side, it aims to achieve the maximum economic performance of the PIES. Conclusions are drawn as follows:

1. Compared to not taking price decisions into account, the implementation of price decisions can decrease the overall system cost by 13.3%, decrease carbon emissions by 7785 kg, and decrease the peak-to-valley variances in electricity and heat by 2.21% and 14.73%, respectively.

2. Compared to the situation without uncertainties of PLDR, when considering the uncertainties of PLDR, the overall cost is reduced by 6.56%, carbon emissions are decreased by 13,803 kg, and the peak-valley differences in electricity and heat are reduced by 27.41% and 4.41%, respectively. In addition, user satisfaction is increased by 3.33%.

3. The more diverse the types of responsive loads, the more significant the effect of implementing demand response tends to be. Compared to considering only transferable and substitutable loads, the overall system cost is reduced by 7.68% and user satisfaction is improved by 5.16%.

Therefore, the planning solution obtained through the proposed method is effective in dealing with the asymmetry of sources and loads in modern power systems. This research can optimize the scheduling and coordinated control of multiple energy sources within the park to promote the park’s integrated energy system to cope with the uncertainty of demand response.