CFG

The output of CFG units is related to coal consumption and power generation efficiency, as shown in Equation (1):

Fig. 1.

System collaborative operation framework.

Where, P_t^CFG is the output of the CFG unit at time t; α^CFG is the efficiency of CFG; O_t^CFG is the coal consumption of CFG units at time t; θ_cola is the lower calorific value of coal.

PV

The output of PV panels depends on the intensity of light radiation, and the relationship between output and radiation intensity is shown in Equation (2):

Where, P_t^PV is the output of the photovoltaic panel at time t; α^PV and S_t^PV is the power generation efficiency and area of photovoltaic panels; F_t^PV is the intensity of light radiation at time t.

WP

The output of WP depends on the wind speed, and the relationship between output and wind speed is shown in Equation (3):

Where, P_t^WP is the output of the WP at time t; P_e^WP is the rated output of the WP; v_t^WP is the wind speed at time t; v_in^WP, v_out^WP, and v_e^WP is the WP’s inlet wind speed, outlet wind speed, and rated wind speed.

GB

The GB is a gas thermal coupling device, and its output model is shown in Equation (4):

Where, P_t^GB is the heat generation of the GB at time t; α^GB is the heat production efficiency of the GB; G_in,t^GB is the natural gas consumed by the GB at time t.

GHP

A typical HP unit comprises a compressor, condenser, evaporator, and thermal expansion valve. It extracts heat from the ground source by consuming electrical energy, recovering low-temperature heat sources to produce high-temperature heat sources. The schematic diagram of the ground source heat pump is shown in Fig. 2.

The output of the GHP is shown in Equation (5):

Where, H_t^HP is the heat generated by the HP at time t; α_com and α_con represents the efficiency of the compressor and condenser, respectively; P_in,t^HP is the electrical energy consumed by the HP at time t.

P2G

The electric-to-gas conversion equipment consists of two stages. The first stage is to generate hydrogen gas by electrolyzing water, and the second stage is to mix hydrogen gas with CO₂ to generate methane, as shown in Equation (6):

Fig. 2.

Structure of GHP.

Based on this, the gas production of P2G equipment is obtained as shown in Equation (7):

Where, G_t^P2G is the gas production of P2G equipment at time t; α_H2 and α_CO2 is the efficiency of the first and second stages of P2G conversion; P_in,t^P2G is the gas production rate of the P2G conversion equipment.

SBA

The battery discharges during peak hours and charges during valley hours, as shown in Equation (8):

Where, Q_t^SBA and Q _−t^SBA₁ is the capacity of the SBA at time t and t-1; α_loss^SBA is the self-loss rate of the SBA; P_cha,t^SBA and P_dis,t^SBA is the charging and discharging power of the SBA at time t; α_cha^SBA and α_dis^SBA is the charging and discharging efficiency of the SBA.

TSE

The TSE releases heat during peak hours and stores heat during valley hours, as shown in Equation (9):

Where, Q_t^TSE and Q _−t^TSE₁ is the capacity of the TSE at time t and t-1; α_loss^TSE is the self-loss rate of the TSE; H_cha,t^TSE and H_dis,t^TSE is the heat storage and release power of the TSE at time t; α_cha^TSE and α_dis^TSE is the heat storage and release efficiency of the TSE.

Carbon Certification Collaborative Mechanism

The carbon certification collaborative mechanism refers to the coordinated participation of heat pump coupling systems in the CET and GCT markets. Below, we will elaborate on the two markets separately and construct a collaborative mechanism.

(1) CET

CET refers to the situation where if the actual CO₂ emissions of an accounting entity exceed the free allocation of carbon emissions, the accounting entity needs to purchase the missing carbon emission rights in the carbon trading market. Otherwise, the excess carbon emissions can be sold in the carbon trading market. This paper uses benchmark values to determine the free carbon emissions, and based on this, the net emissions of the heat pump energy storage coupling system are obtained as shown in Equation (10):

Where, D_co2,t^free , D_co2,t^ac , and D_co2,t^∆ac is the free carbon quota, actual carbon emissions, and net carbon emissions of the coupled system at time t; d_co2^e and d_co2^h is the free carbon quota coefficient for unit electricity and heat energy; d_co2^CFP and H_t^GB is the carbon emissions per unit of CFG and gas-fired boiler output, respectively.

Introducing a tiered carbon price in the CET obtains the carbon trading cost of the heat pump energy storage coupling system, as shown in Equation (11). If D_co2,t^∆ac > 0, the carbon trading cost of the coupling system is −|C_t^CTM|, otherwise, it is |C_t^CTM|.

Where, ū_co2 is the benchmark price for CO₂ trading; g is the range of carbon emissions; γ^cr s the growth rate of carbon emission trading prices.

(2) GCT

GCT refers to the regulation that in order to promote the development of renewable energy, the amount of renewable energy generated in a certain system cannot be less than a certain value. If the number of green certificates in a system is less than the specified value, purchasing the missing green certificates in the GCT market is necessary. If the number of green certificates in the system exceeds the specified value, excess green certificates need to be sold in the GCT market. The green certificate source for the heat pump energy storage coupling system is photovoltaic power generation. The net green certificate number of the coupled system can be obtained as shown in Equation (12):

Where, D_CET,t^ex and D_CET,t^ac represents the number of green certificates specified and actual at time t, respectively; d_CET^ex is the minimum holding amount of green certificates per unit load; D_CET,t^∆ac is the net number of green certificates at time t.

Based on Equation (12), the green certificate transaction cost of the heat pump energy storage coupling system is obtained as shown in Equation (13). If D_CET,t^∆ac > 0 , the green certificate transaction cost is −|C_t^CET|, otherwise it is |C_t^CET|.

Where, ū_t^CET is the unit green certificate price.

(3) Carbon certification collaborative mechanism

Photovoltaic power generation in the coupled system not only calculates free carbon quotas in carbon trading but also calculates the number of green certificates in the GCT mechanism. In order to avoid duplicate calculations, this paper uses the average method to subtract duplicate parts, and the resulting kernel reduction is shown in Equation (14):

Where, C^∆_t ^CGM is the cost reduction under the carbon certification collaborative mechanism.

Analysis of Response Characteristics Based on CEEMDAN-IIR

(1) Analysis framework diagram

In order to match the differences in response characteristics of different devices and reduce the uncertainty between the source and load ends of the coupled system, where the uncertainty at the source end comes from photovoltaic output and the uncertainty at the load end comes from electricity, heat, and natural gas loads. Based on this, this paper decomposes photovoltaic output, electrical load, thermal load, and natural gas load into low-frequency, mid-frequency, and high-frequency components using the CEEMDAN-IIR method.

In optimizing low-frequency components, the low-frequency components are input as basic parameters into the model, and the objective function is to minimize the comprehensive cost to obtain the initial output of GB, GHP, P2G, and CFG units. In optimizing intermediate frequency components, the objective function is to minimize the comprehensive cost and optimize SBA and TSE’s charging and discharging plans. In high-frequency component optimization, the objective is to minimize the overall cost and optimize the charging and discharging adjustment plan for SBA and TSE. The specific optimization framework is shown in Fig. 3.

(2) CEEMDAN-IIR

The empirical mode decomposition (EMD) method, as the most commonly used method for signal decomposition, essentially decomposes the original signal into a series of intrinsic mode functions (IMFs) with different amplitudes by varying the scales of the fluctuations. The Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm is an improved empirical mode decomposition method. The CEEMDAN algorithm can reduce the reconstruction error to almost zero with fewer average iterations by adding a finite number of adaptive white noises at each stage, effectively avoiding the mode aliasing problem of EMD methods.

Fig. 3.

Optimization framework.

However, the number of IMF components obtained by CEEMDAN decomposition is too large, and the frequency distribution of each IMF component does not strictly conform to the time scale divided in the previous text, so it is necessary to reconstruct each fluctuation component. This paper uses an infinite impulse response (IIR) filter to decompose and reconstruct the IMF components in the three frequency bands mentioned above, obtaining the fluctuation components of photovoltaic output, electrical load, thermal load, and natural gas load at three time scales: high frequency (<15 minutes), medium frequency (15-60 minutes), and low frequency (>1 hour). Taking photovoltaic output as an example, a signal decomposition model is constructed, and the signal decomposition steps of the load are consistent with photovoltaic output.

1) CEEMDAN algorithm

Suppose P is defined as the original sequence of photovoltaic output, and IMF_i(1, 2, , ..., n) and res are the individual fluctuation components and residuals decomposed by the CEEMDAN algorithm. In this case, the relationship is as shown in Equation (15):

Where the magnitude of res is relatively small and can be ignored.

2) IIRF algorithm

Firstly, an IIR low-pass filter separates the low-frequency components from each IMF component.

Where, IMF_i^low and IMF_i^rest represents the low-frequency and residual parts of the IMF component.

Then, an IIR high-pass filter separates the high-frequency components from the remaining parts of each IMF component.

Where, IMF_i^high is the high-frequency part of the i-th IMF component; the remaining IMF_i^mid is the intermediate frequency part of the i-th IMF component.

Finally, reconstruct according to different frequency distributions.

Where, F_high, F_mid and F_low refers to the high-frequency component (<15 minutes), mid-frequency component (15-60 minutes), and low-frequency component (>1 hour) of the net load.

Objective Function

In order to balance economy and environmental protection, the economic aspect is characterized by the minimum total cost of the coupled system, while the environmental aspect is characterized by the maximum renewable energy consumption rate.

(1) Minimize total cost

The cost of a heat pump energy storage coupling system consists of the operating cost of the equipment, carbon certificate trading cost, external interaction cost, penalty cost for wind and solar power curtailment, and energy sales revenue, as shown in Equation (19):

Where, C^total is the total cost of the coupled system; C_t^op, C_t^grid, C_t^pun, and R_t^sale is the operating cost, external interaction cost, wind and solar curtailment penalty cost, and energy sales revenue of the coupled system at time t.

The operating cost of the system is shown in Equation (20):

Where, ū_pv^op , ū_WP^op , ū_SBA^op , ū_CFG^op , ū_GB^op , ū_HP^op , ū_TSE^op , and ū_P2G^op represents the unit operating costs of PV, WP, SBA, CFG, GB, HP, TSE, and P2G, respectively.

The external interaction cost is the cost generated by the interaction between the coupled system and the power grid, heating network, and natural gas network, as shown in Equation (21): Ctgrid = ue tgrid, ( Pbuy,gridt − Psale,gridt ) + uh tgrid, ( Hbuy,gridt − Hsale,gridt )

+ ug,gridt (Gbuy,gridt − Gsale,gridt )

Where, u_e,t^grid , u_h,t^grid , and u_g,t^grid is the interaction cost between the coupled system at time t and the power grid, heating network, and natural gas network; P_buy,t^grid and P_sale,t^grid is the purchase and sales volume of the coupled system at time t on the power grid; H_buy,t^grid and H_sale,t^grid is the purchase and sales volume of the coupled system at the heating network at time t; G_buy,t^grid and G_sale,t^grid is the purchase and sales volume of the coupled system at time t in the natural gas network, respectively.

The cost of wind and solar curtailment penalty is the cost caused by the uncertainty of clean energy output in the coupled system, as shown in Equation (22):

Where, u_re^pun is the uncertainty cost caused by the error in unit clean energy output; P_t^pre,pv and P_t^pre,WP is the predicted output of photovoltaic and wind power generation at time t.

Energy sales revenue refers to the income obtained by the system through the sale of electricity, heat, and natural gas, as shown in Equation (23):

Where, u_sale,tⁱ is the unit income of the i-th energy source.

(2) Maximum renewable energy consumption rate

The clean energy consumption rate is shown in Equation (24):

Where, ℓ is renewable energy consumption rate; _re P_ac,t^PV and P_ac,t^WP is the actual output of PV and WP.

Constraints

The operation of the heat pump energy storage coupling system is subject to constraints such as balance, operation, external interaction, and climbing, among which the system balance constraints include electrical energy, thermal energy, and natural gas balance constraints, as shown in Equation (25):

The operational constraints of the coupled system are shown in Equation (26):

Where, P_min^pv and P_max^pv is the minimum and maximum value of PV output; P_min^WP and P_max^WP is the minimum and maximum value of WP output; P_min^CFG and P_max^CFG is the minimum and maximum value of CFG output; H_min^GB and H_max^GB is the minimum and maximum value of GB output; H_min^HP and H_max^HP is the minimum and maximum value of HP output; G_min^P2G and G_max^P2G is the minimum and maximum value of P2G output.

The operational constraints of SBA and TSE are shown in Equations (27) and (28), respectively:

Where, P_min^SBA and P_max^SBA represents the minimum and maximum values of SBA charging and discharging power; Q₁^SBA and Q₂₄^SBA is the capacity of SBA at the 1st and 24th moments; Q_min^SBA and Q_max^SBA is the minimum and maximum values of SBA capacity; H_min^TSE and H_max^TSE represents the minimum and maximum values of TSE charging and discharging power; Q₁^TSE and Q₂₄^TSE is the capacity at the 1st and 24^th moments of TSE; Q_min^TSE and Q_max^TSE represents the minimum and maximum values of TSE capacity.

The specific external interaction constraints are shown in Equation (29):

Optimization Result Analysis

(1) Signal decomposition results

The signal decomposition of wind power output, photovoltaic output, electricity load demand, heat load demand, and natural gas load demand based on Equations (15) - (18) is shown in Fig. 6.

Fig. 6 shows that in terms of fluctuation amplitude, the low-frequency component>the mid-frequency component>the high-frequency component. Based on the decomposition results of the photovoltaic output, the fluctuation amplitudes of low-frequency, mid-frequency, and high-frequency components are within the range of [01000kW], [-400400] kW, and [-100100] kW. This indicates that the amplitude of low-frequency component fluctuations is relatively large, which can effectively match the operating characteristics of equipment such as GB, GHP, P2G, and CFG units. The high-frequency components oscillate periodically and have small fluctuation amplitudes, which is in line with the charging and discharging characteristics of SBA and TSE. It can reduce the operating state of energy storage devices that are overcharged or overdischarged in a short period of time and improve the utilization rate of energy storage devices. From the comparison of the fluctuation amplitudes of various types of wind power generation and photovoltaic power generation, it can be seen that the fluctuation amplitude of wind power generation is greater than that of photovoltaic power generation, indicating that the volatility brought by wind power generation needs to be given special attention.

Fig. 4.

Predictive output of WP and PV.

Fig. 5.

Load demand.

(2) System operation optimization results

Optimize and analyze the electrical, thermal, and natural gas subsystems of the heat pump energy storage coupling system based on the signal decomposition results. The operation optimization results of the electric energy subsystem are shown in Fig. 7.

From Fig. 7, it can be seen that wind power output and photovoltaic output have complementary characteristics. From 23:00 to 3:00, photovoltaic output was 0, but WP is in a high incidence stage. During 12:00-14:00, photovoltaic output peaked, while wind power output was relatively low. From 22:00 to 5:00, due to the high frequency of wind power generation, there is less demand for electricity load. After meeting the system’s energy demand, the excess electricity supply is stored in the SBA. During the time period of 1:00-3:00, after reaching the maximum storage capacity of the battery, the coupling system sells excess electricity to the external power grid. During 18:00- 20:00, photovoltaic output was almost zero, and energy consumption peaked. Wind power alone cannot meet the system’s energy demand, so coal-fired power generation units are started for energy supply.

The operation optimization results of the heat energy subsystem are shown in Fig. 8.

As shown in Fig. 8, the heat load demand of the heat pump energy storage coupling system is mainly met by the HP and the GB, with the heat generated by the heat pump being greater than that of the GB. This is mainly because HP’s conversion efficiency is higher than that of GB. The TSE played a role in various time periods, including 15:00-17:00, 23:00-24:00, and 4:00. The TSE stores heat, and during these time periods, there is a sufficient supply of electrical energy. Part of the remaining electrical energy is converted into thermal energy through an HP and stored in the TSE. During the rest of the time, the heat storage equipment releases heat, especially from 1:00 to 3:00. The heat load demand is high, and even after the heat pump operates at full power, it still cannot meet the heat load demand. It is necessary to use the TSE and externally purchased heat energy to meet the shortfall in heat demand. This indicates that the TSE effectively realizes the coupling between the electrical energy subsystem and the heat energy system.

Fig. 6.

Signal decomposition results.

The operation optimization results of the natural gas system are shown in Fig. 9.

As shown in Fig. 9, during the time periods of 2:00- 3:00 and 5:00-7:00, it is necessary to supply both natural gas load demand and GB. Therefore, during these time periods, the natural gas generated by P2G equipment cannot meet the system’s demand, and the system needs to interact with the external natural gas network to purchase the missing natural gas. At the two time points of 1:00 and 7:00, there is an excess supply of natural gas, and the heat pump energy storage coupling system sells natural gas to the external natural gas network.

Fig. 7.

Optimization results of electric energy subsystem operation.

Fig. 8.

Optimization results of heat energy subsystem operation.

Effectiveness Analysis

This article’s three innovative points are: the construction of a heat pump energy storage coupling system, the carbon certification collaborative mechanism, and the uncertainty decomposition of the CEEMDAN algorithm. It also analyzes the effectiveness of these three aspects.

(1) Effectiveness analysis of heat pump energy storage coupling system

In order to verify the effectiveness of the heat pump energy storage coupling system, three scenarios were set up, as shown in Table 5.

Based on the three scenarios set in Table 5, the operating costs and external interaction costs of the heat pump energy storage coupling system in the three scenarios are shown in Table 6.

According to Table 6, although the operating cost of Scenario 2 increased by 11.21 yuan compared to Scenario 1, the external interaction cost decreased by 428.89 yuan, with a reduction rate of 22.50%. This is because scenario 2 adds a thermal storage device based on scenario 1, increasing the operating cost of the TSE. However, through the thermal storage device’s peak heat release and valley heat storage mechanism, it is possible to reduce the system’s high-priced purchase of thermal energy during peak hours and lower the system’s external interaction costs. Compared with Scenario 2, Scenario 3 has reduced operating costs by 469.44 yuan, with a reduction rate of 6.14%, and the external interaction costs are consistent. This is because scenario 3 is based on scenario 1, and the economic efficiency of heat generation through HP units is higher than that of GB, which can reduce the system’s heat production cost.

Fig. 9.

Optimization results of natural gas subsystem operation.

(2) Analysis of the effectiveness of carbon certification collaboration mechanism

In order to verify the effectiveness of the carbon certification collaborative mechanism, the following three scenarios were set up:

Scenario 1: The coupled system only considers the CET;

Scenario 2: The coupled system only considers the GCT;

Scenario 3: The coupling system considers the carbon certification collaborative mechanism.

On this basis, the clean energy consumption rate and carbon dioxide emissions for the three scenarios are shown in Fig. 10.

According to Fig. 10, Scenario 1 has higher carbon dioxide emissions of 20.48kg and a lower clean energy consumption rate of 1.32% compared to Scenario 3. This is because Scenario 1 did not consider the GCT mechanism, resulting in a decrease in the driving force of the heat pump energy storage coupling system to absorb wind and photovoltaic power, leading to a decrease in the clean energy consumption rate. Under the condition of fixed load demand in the coupled system, the proportion of WP and PV output decreases while the proportion of CFP increases accordingly. Scenario 2 shows a 79.71% increase in carbon dioxide emissions and a 0.64% decrease in clean energy consumption rate compared to Scenario 3. This is because Scenario 2 did not consider the carbon trading mechanism, and the coupled system, from an economic perspective, will increase the output of coal-fired power generation units, increasing the system’s carbon emissions. This indicates that the carbon certification collaborative mechanism can not only reduce carbon emissions but also increase the consumption rate of clean energy.

(3) CEEMDAN algorithm

To verify the effectiveness of the CEEMDAN algorithm in signal decomposition, it was compared with the EMD algorithm and the ensemble EMD (EEMD) algorithm using the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) as comparison metrics, as shown in Equation (30):

Fig. 10.

Clean energy consumption rate and carbon dioxide emissions in three scenarios.

Where, U_t^after is the decomposed signal value at time t; U_t^ac is the actual signal value at time t.

Based on Equation (30), the comparative results are shown in Table 7.

As shown in Table 7, the EEMD algorithm reduces MAE, MAPE, and RMSE by 9.56%, 19.96%, and 7.13%, respectively, compared to the EMD algorithm. This is because EMD has a weaker ability to handle noise and mode mixing problems and is easily affected by signal noise. EEMD introduces random perturbations based on EMD and decomposes the original signal by adding different white noise multiple times to reduce random errors. The CEEMDAN algorithm reduces MAE, MAPE, and RMSE by 25.48%, 11.40%, and 35.76%, respectively, compared to the EEMD algorithm. This is because although EEMD solves some problems in EMD, there may still be modal aliasing issues. CEEMDAN can more effectively suppress false modes and improve the stability and accuracy of decomposition. This algorithm performed well in denoising and modal decomposition tasks, effectively eliminating mode aliasing problems.

Applicability and Limitations Analysis

(1) Scenario expansion analysis

In order to expand the application scenarios of the model in this article, the CEEMDAN algorithm was used to solve it. The optimization scheduling model of the heat pump energy storage coupling system, considering the synergy and response characteristics of carbon certificates, was extended to typical days in different seasons throughout the year, where spring and autumn are collectively referred to as transition seasons. The scenario settings are shown in Table 8. The effectiveness analysis of the heat pump energy storage coupling system has fully verified that configuring energy storage devices can significantly reduce the system’s external interaction costs. Therefore, energy storage devices are configured in all scenarios in the expansion analysis.

Based on the scenarios set in Table 8, Fig. 11 shows the total cost and clean energy consumption rate of typical days in the transition season, summer, and winter under different scenarios. The negative total cost represents the system’s revenue.

Fig. 11 shows that in each season, the proposed optimization scheduling model for the heat pump energy storage coupling system considering carbon certification synergy and response characteristics (Scenario 6) has the lowest total cost and the highest clean energy consumption rate compared to other scenarios. The total cost of Scenario 6 during the transition season, summer, and winter, is -8524.37 yuan, -33671.25 yuan, and -25900.96 yuan, respectively. Compared to the other five scenarios, the average total cost is reduced by 0.93%, 0.89%, and 0.95%. From the perspective of clean energy consumption rate, Scenario 6 had clean energy consumption rates of 95.31%, 91.22%, and 89.39% in the transition season, summer, and winter, respectively. Compared with the other five scenarios, the clean energy consumption rates increased by 1.36%, 1.17%, and 2.54%, respectively. This indicates that the model proposed in this article applies to typical daily scenarios throughout the year and can effectively improve the regional systems’ revenue and clean energy consumption rate.

Fig. 11.

Total cost and clean energy consumption rate on different typical days throughout the year.

Fig. 12.

Sensitivity analysis results.

(2) Sensitivity analysis

In order to enhance the applicability of the model proposed in this article, sensitivity analysis was conducted by selecting the CO₂ trading benchmark price, unit green certificate price, internal unit electricity sales revenue, internal unit heat sales revenue, internal unit gas sales revenue, external unit electricity exchange price, external unit heat exchange price, and external gas exchange price as sensitivity factors. Record these sensitive factors as d1, d2, d3, d4, d5, d7, d8, and d9, respectively, and explore whether the variation range of sensitive factors within [-20%, 20%] affects the applicability of the model proposed in this paper, and analyze the limitations of the model proposed in this paper. The sensitivity analysis results are shown in Fig. 12.

As shown in Fig. 12, from the perspective of the impact of various factors on the system’s net income, the changes in d1, d2, d3, d4, d5, d8, and d9 are all positively correlated with the net income of the system, while the external unit electricity exchange price (d7) is negatively correlated with the net income of the system. This is mainly because the interaction cost between the heat pump energy storage coupling system and the external power grid is positive. When the exchange price of external unit electricity increases, the interaction cost between the system and the external power grid also increases, resulting in a decrease in the system’s net income of the system. From the perspective of the impact of various factors on the net income of the system, the internal unit sales revenue (d3) has the greatest impact on the net income of the system, with a sensitivity coefficient of 1.09, mainly because the internal sales revenue of the system accounts for the largest proportion. This indicates that in order to ensure the stability of revenue, the heat pump energy storage coupling system needs to meet the electricity demand of internal users, and the system also needs to prevent and control the impact of unstable wind and photovoltaic power supply on the system in real time. If the system’s power supply is unstable, it will cause a sharp decline in its net profit.