Due to its characteristic of “power determined by heat,” CHP has its operating curve as shown in Figure 2.

CHP is the main device for power generation and heat generation inside the IES. The block diagram of its thermoelectric coupling output range is shown in Figure 2. The construction model is E t C H P ≥ U C H P ⋅ E min C H P E t C H P ≥ U C H P ⋅ k d o w n H t C H P − H max C H P + E 0 C H P E t C H P ≤ U C H P ⋅ E max C H P + k u p H t C H P − H max C H P H t C H P ≥ 0 U C H P ∈ 0,1 . (1)

In the formula, E t C H P and H t C H P are the CHP power generation and heat generation power, respectively; E max C H P and E min C H P are the upper and lower limits of CHP power generation, respectively; the minimum value of CHP heat generation power is 0, and the maximum value is H max C H P ; the corresponding generation power of CHP maximum heat generation power is E 0 C H P ; the upper limit slope of the CHP electrothermal coupling interval is k u p , and the lower limit slope is k d o w n ; and U C H P is the switch state identification bit of CHP, which takes 0 and 1.

H t G B = V g a s , t G B ⋅ Q g a s ⋅ η G B / 3.6 e 6 * Δ t H t G B , Y R = H t G B ⋅ 1 − η G B η G B 0 ≤ H t G B ≤ H t G B , max . (2)

In the formula, H t G B is the heat production power of the GB at time t ; V g a s , t G B is the volume of natural gas consumed by the boiler at time t , m³; Q gas is the calorific value of natural gas, k g / m 3 ; η G B is the heat production efficiency of the GB; H t G B , Y R is the waste heat efficiency of the GB; and H t G B , max is the upper limit of the output thermal power of the gas boiler.

A heat pump is a device that transfers heat energy from a low-level heat source to a high-level heat source. The low-level heat energy in the system can be converted into high-grade heat energy that can be utilized by people through the heat pump. The mathematical model is H t H P = η H P ⋅ E t H P 0 ≤ H t H P ≤ H t H P , max Δ H H P min ≤ H H P t − 1 − H H P t ≤ Δ H H P max . (3)

In the formula, E t H P is the power consumption of the HP at time t , H t H P is the output heat power of the HP at time t , η H P is the conversion efficiency of the HP, and H t H P , max is the upper limit of the heat pump output thermal power, and Δ H H P max and Δ H H P min are the heat pump ramp rate constraints.

The Karina regenerative power generation system is a system that can use 100°C low-temperature heat energy to generate electricity. Its advantage is that it can convert low-temperature waste heat into electrical energy. The working fluid of the Karina regenerative power generation system is mostly water and ammonia mixture, and no carbide is used in the production process, which is in line with the concept of low-carbon economy. The Kalina model is E t K L N = η E K L N ⋅ H t K L N H t K L N + H t X H L ≤ H t P V + H t C H P , Y R + H t G B , I R . (4)

In the formula, E t K L N is the power generated by the Kalina system at time t ; H t K L N is the thermal power consumed by the Kalina system at time t ; and η E K L N is the thermoelectric conversion efficiency of the Karina system.

BT, HST, and GST can all be established using similar capacity models, and their operation models can be uniformly expressed as follows. Therefore, this article conducts unified modeling of electric, thermal, and gas energy storage equipment. 0 ≤ P E S , n c h a t ≤ B E S , n c h a t P E S , n max 0 ≤ P E S , n d i s t ≤ B E S , n d i s t P E S , n max P E S , n t = P E S , n c h a t η E S , n c h a − P E S , n d i s t / η E S , n d i s S n t = S n t − 1 + P E S , n t / P E S , n c a p S n 1 = S n T B E S , n c h a t + B E S , n d i s t = 1 S n min ⩽ S n t ⩽ S n max . (5)

In the formula, P E S , n c h a t and P E S , n d i s t are the charging and discharging power of the n energy storage device in period t , respectively; P E S , n max is the maximum single charging and discharging power of the n device; B E S , n c h a and B E S , n d i s are both binary variables, which are the charging and discharging state parameters of the n energy storage device in period t , respectively; B E S , n c h a t = 1, B E S , n d i s t = 0 indicate that it is in the charging state; B E S , n d i s t = 1, B E S , n c h a t = 0 means it is in the state of discharging energy; P ES , n t is the final output power of the n device in period t ; η E S , n c h a and η E S , n d i s are the charging and discharging efficiencies of the n energy storage device, respectively; S n T is the rated capacity of the n energy storage device in period t ; and S n max and S n max 1 are the upper and lower limits of the n device capacity, respectively.

Price-based demand response mainly functions during peak energy consumption periods and aims to influence users’ energy consumption patterns through price factors, that is, users can voluntarily choose whether to reduce energy consumption at this time by comparing prices before and after demand response.

In price-based demand response, the demand price elasticity coefficient is the key coefficient, which describes the sensitivity of the electric load demand participating in the demand response to the adjustment of the system energy price, as shown in the following equation: m = Δ L L Δ c p c p − 1 . (6)

In the formula, m represents the price elasticity coefficient of electricity load demand; c p and Δ c p are the difference between the peak and valley electricity price and its fixed electricity price; and L and Δ L are the electricity consumption and load response volume before load response, respectively. According to the load level, the complete cycle is divided into three periods of peak and valley according to the dispatch period. The electric load can cross-response between the three periods. The electric load demand price elasticity coefficient matrix can be obtained as follows: N e = N 11 N 12 ⋯ N 21 N 22 ⋯ ⋮ ⋮ ⋱ N n 1 N n 2 ⋯ N 1 m N 2 m ⋮ N n m , (7) N i i = Δ L i L i Δ c p i c p i − 1 , (8) N i j = Δ L i L i Δ c p j c p j − 1 . (9)

In the formula: N i i is the self-elasticity coefficient; N e is the electricity price elasticity matrix; L i and Δ L i are the user’s electricity quantity and its change amount in the i period; N i j is the cross elasticity coefficient; and c p i , Δ c p i and c p j , Δ c p j are the i period and j period of electricity prices and changes in electricity prices, respectively.

According to the electricity price elasticity matrix N e , the user load response can be obtained as Δ L e t = L e , 0 , f 0 0 0 L e , 0 , p 0 0 0 L e , 0 , g ⋅ N e Δ c e , p f / c e , p 0 , f Δ c e , p p / c e , p 0 , p Δ c e , p g / c e , p 0 , g . (10)

In the formula: L e , 0 , f , L e , 0 , p , and L e , 0 , g represent the electricity consumption during the peak, valley, and normal periods before the price incentive, respectively; Δ L e t is the electricity transfer amount after the price incentive; and c e , p 0 , f , c e , p 0 , p , and c e , p 0 , g and Δ c e , p f , Δ c e , p p , and Δ c e , p g represent the difference between the fixed electricity price and the time-of-use electricity price, respectively.

Since gas energy has the same commodity attributes as electric energy, gas load can be adjusted based on the published time-of-use gas price. Therefore, the price elasticity matrix method can also be used to model the gas load IDR model. By analogy with the electricity price IDR model, the gas load changes with the time-of-use gas price as shown in Eq. 10, which is expressed as follows: Δ L g t = L g , 0 , f 0 0 0 L g , 0 , p 0 0 0 L g , 0 , g ⋅ N g Δ c g , p f / c g , p 0 , f Δ c g , p p / c g , p 0 , p Δ c g , p g / c g , p 0 , g . (11)

In the formula: Δ L g t is the gas load transfer amount after the gas price incentive; L g , 0 , f , L g , 0 , p , and L g , 0 , g respectively represent the gas consumption during the peak, valley and normal periods before the price incentive; c g , p 0 , f , c g , p 0 , p , and c g , p 0 , g and Δ c g , p f , Δ c g , p p , and Δ c g , p g represent the difference between the fixed gas price and the time-based gas price respectively. Represents the gas price and gas volume elasticity matrix.

This article comprehensively considers the mutual substitution among the three loads of electricity, heat, and gas. Users can choose the type of energy that meets their needs for the same energy quality based on the relative price relationship between energy sources. The alternative demand response mathematical model is as follows. When constructing a multi-energy alternative demand response mathematical model, the substitution direction between energy sources needs to be considered. This paper sets the following direction as the positive direction: the electric load is replaced by gas and heat load, and the heat load is replaced by gas load substitution; in addition, the effective value conversion coefficient between energy sources is based on the energy source being replaced. Δ P e , A E t = − θ e g Δ P e g t − θ e h Δ P e h t Δ P g , A E t = θ e g μ e g Δ P e g t + θ h g μ h g Δ P h g t Δ P h , A E t = θ e h μ e h Δ P e h t − θ h g Δ P h g t 0 ≤ Δ P i j t ≤ Δ P i j t , max , Δ P i j t > 0 0 ≤ μ Δ P i j t ≤ Δ P i j t , max , Δ P i j t < 0 0 ≤ Δ P i , A E t ≤ Δ P i , A E t , max . (12)

In the formula, i , j ∈ e , h , h , i ≠ j ; Δ P e , A E t are the total change of the load after the substitution-type IDR at time t ; Δ P e g t , Δ P e h t , and Δ P h g t are the substitution amount between the two energy sources at time t ; when the value is positive, it means that the former energy is replaced by the latter energy, and if the value is negative, vice versa; and θ e g , θ h g , and θ h g represent the substitution state between two energy sources. When the load substitution direction is positive, we take 1; otherwise, we take −1; μ e g , μ e h , and μ h g are the conversion coefficients of effective value between energy sources, taking 1.5, 2.8, and 0.625, respectively, and Δ P i j t and Δ P i j t , max are the load to be replaced and the upper limit of the replacement amount, respectively.

According to the actual needs of the IES, the allowable load adjustment amount of IDR is constrained; that is, the adjustable load ratio range is given as follows: P i , I D R t = P i , 0 t + Δ P i , C L t P − Δ P i , S L t − Δ P i , A E t P i , I D R t , min ≤ P i , I D R t ≤ P i , I D R t , max , i ∈ e , g , h . (13)

In the formula, P i , I D R t is the load after taking into account the comprehensive IDR at time t ; P i , I D R t , max and P i . I D R t , min are the upper and lower limits of the load after taking into account the comprehensive IDR, respectively, the electrical and gas loads are taken as [0.8 P i , 0 t , 1.2 P i , 0 t ], and the thermal load is taken as [0.9 P i , 0 t , 1.1 P i , 0 t ].

Similar to the carbon trading mechanism, the GCT mechanism also utilizes trading to leverage the market’s role in optimizing resource allocation. The calculation formula for the transaction cost of green certificates can be expressed as D P = δ P ∑ t = 1 T L e t D S = ε L Z ∑ t = 1 T P W T t + P P V t . F G C T = c G C T D S − D P (14)

In the formula, δ P is the quota coefficient of the number of green certificates allocated in the IES; ε L Z is the conversion coefficient of WT power, PV power generation into the number of green certificates, and one green certificate corresponds to the WT settlement amount of 1 MWh; L e t is the actual power demand of the user; P W T t and P P V t are the output electric power of WT, respectively; D P is the quota for the number of green certificates held by the IES; D S is the number of green certificates obtained for IES new energy power generation; c G C T is the green certificate transaction price; and F G C T is the green certificate transaction cost of the IES.

This article is based on the Cournot trading model of quantity competition to characterize the green certificate trading price. According to the Cournot model formula, the green certificate trading price model can be expressed as c GCT = α GCT ′ − χ GCT ′ D c . (15)

In the equation, α GCT ′ and χ GCT ′ are the two positive parameters of the inverse price function in the Cournot trading model, respectively. D c is the number of green certificates sold for the IES.

Among them, α GCT ′ and χ GCT ′ , respectively, represent the following: α GCT ′ = c GCT , 0 χ GCT ′ = 1 − ε GCT ′ c GCT , 0 δ Q ∑ t = 1 T L e t . (16)

In the formula, c GCT , 0 is the basic transaction price of the green certificate and ε GCT ′ is the GCT transaction price ratio calculated based on historical data.

The carbon emission sources of the IES are mainly divided into three categories: power purchase from higher authorities, GB, and CHP. At present, the quota method mainly adopted is free quota, and it is believed that the power purchased by the superior comes from the coal-fired unit power generation. E I E S = E e , b u y + E C H P + E G B E e , b u y = χ e ∑ t = 1 24 P e , b u y t E C H P = χ g ∑ t = 1 24 P C H P , e t + P C H P , h t E G B = χ g ∑ t = 1 24 P G B , h t . (17)

In the formula, E I E S , E e , b u y , E C H P , and E G B are the carbon emission right quotas of the IES, superior power purchase, CHP, and GB, respectively; χ e and χ g are the carbon emission right quotas of unit electricity consumption of coal-fired units and natural gas consumption of natural gas units, respectively; P e , b u y t is time t of superior power purchase; and P G B , h t is the thermal energy output by GB during period t .

Since the coal-fired units, CHP and GB, are not linear in the output process, the actual output model is E I E S , a = E e , b u y , a + E t o t a l , a E e , b u y , a = ∑ t = 1 24 a 1 + b 1 P e , b u y t + c 1 P e , b u y 2 t E t o t a l , a = ∑ t = 1 T a 2 + b 2 P t a t a l t + c 2 P total 2 t P t o t a l t = P C H P , e t + P C H P , h t + P G B , h t . (18)

In the formula, E I E S , a and E e , b u y , a are the actual carbon emissions of the IES and superior power purchase, respectively; E t o t a l , a is the total actual carbon emissions of CHP and GB; P t o t a l t is the equivalent output power of CHP and GB during period t ; and a 1 , b 1 , and c 1 and a 2 , b 2 , and c 2 are the coal-fired units and carbon emission calculation parameters for natural gas-consuming energy supply equipment (Mehrjerdi, et al., 2022).

We obtain the carbon emission quota and actual carbon emission of the IES and then obtain the carbon emission transaction amount that actually participates in the carbon emission market. E I E S , t = E I E S , a − E I E S . (19)

In the formula, E I E S , t is the carbon emission trading amount of the IES.

The traditional carbon trading cost is the difference between the actual carbon emissions and the carbon quota allocated without compensation multiplied by the carbon trading price in the market, but its carbon trading price is fixed. Its mathematical model is W C O 2 = ∑ t = q 24 c E I E S , t . (20)

In the formula, c is the unit carbon trading price and W C O 2 is the system carbon trading cost.

Due to the fact that the carbon reduction of new energy supply can be calculated (Dong and Shi, 2019), green certificate carbon joint trading can be achieved through the green certificate linkage carbon trading mechanism and green certificate trading mechanism. Generally speaking, after considering the green certificate trading mechanism, in the assessment of carbon emission rights, some carbon emissions can be offset by the carbon reduction behind new energy supply, thereby affecting the carbon trading mechanism. At this point, green certificates can participate in both carbon trading and green certificate trading mechanisms and achieve joint interaction between both parties through market guidance on factors such as trading price and demand. The specific steps of the green certificate carbon joint trading mechanism are as follows:

Step 1

Calculating the carbon emissions of the IES: According to Eqs 21–24, we calculate the CO₂ emissions of coal-fired and gas-fired units in the IES during use.

Step 2

Analyzing the carbon reduction emissions of the green certificate: Due to the high proportion of coal-fired power generation in China, this article compares the CO₂ emissions equivalent generated by coal-fired power generation with new energy power generation to obtain the carbon reduction behind the green certificate. The calculation formula is as follows: F green = E coal − E green . (21)

In the formula, F green is the carbon reduction allocated for new energy generation. E green and E coal represent the C O 2 emission equivalents of new energy supply and coal-fired power supply in their respective industry chain lifecycles, respectively.

Step 3

Calculating the CET cost after offsetting carbon emissions with new energy. Based on equations Eqs 19–27, since new energy supply offsets a portion of carbon emissions, the actual carbon emissions of the IES can be rewritten as E IES , t = E I E S , a − E I E S − D P F green . (22)

Compared with the traditional carbon trading pricing mechanism, in order to further limit carbon emissions, this paper uses a stepped carbon trading pricing mechanism. The ladder-type pricing mechanism divides multiple purchase intervals. As more carbon emission rights need to be purchased, the purchase price in the response interval is higher. The step-by-step carbon trading cost is W C O 2 = λ E I E S , a λ 1 + α E I E S , t − l + λ l λ 1 + 2 α E I E S , t − 2 l + λ 2 + α l λ 1 + 3 α E I E S , t − 3 l + λ 3 + 3 α l λ 1 + 4 α E E S , t − 4 l + λ 4 + 6 α l . (23)

In the formula, W C O 2 is the step-wise carbon trading cost; λ is the base price of carbon trading; l is the interval length of carbon emissions; and α is the price growth rate.

According to the aforementioned model, the relationship between carbon emissions and carbon trading prices is intuitively expressed in Figure 4.

This paper comprehensively considers the energy purchase cost W b u y , ladder carbon transaction cost W C O 2 , CHP unit switching cost W o n o f f C H P , wind abandonment cost W W T , solar power abandonment cost W P V , and operation and maintenance cost of the IES W w h and optimizes with the lowest total cost as the goal. The objective function of the IES can be expressed as W I E S = W b u y + W C O 2 + W W T + W P V + W w h + F G C T + W o n o f f C H P . (24)

The problem addressed in this article is a mixed integer linear programming problem. First, price-based demand response and substitution-based demand response are analyzed to obtain the load curve after demand response. Then, a ladder-type carbon trading mechanism is introduced, and the carbon trading cost under the carbon trading mechanism is as a component of the objective function; finally, under the conditions of satisfying wind power output constraints, energy balance constraints, equipment energy conversion constraints, energy storage equipment constraints, and user satisfaction constraints on electricity consumption, the CPLEX solver is called based on the MATLAB platform to solve the problem. The solution flow chart is shown in Figure 5.

In order to verify the rationality of the proposed comprehensive IDR model, this paper makes a comparative analysis of the following four scenarios; we set the price-based IDR to account for 15% of the total load and alternative IDR 5% of total load.

Scenario 1: The IES did not introduce a carbon trading mechanism and a demand response mechanism.

Scenario 2: The IES introduces a comprehensive demand response mechanism.

Scenario 3: The IES introduces a comprehensive demand response mechanism and a traditional carbon trading mechanism.

Scenario 4: The IES introduces a comprehensive demand response mechanism and a tiered carbon trading mechanism.

Scenario 5: The IES introduces a comprehensive demand response mechanism and a green certificate carbon trading mechanism.

(1) Comparative analysis of Scenario 1 and Scenario 2

From Table 4, it can be seen that compared to Scenario 2 and Scenario 1, the total cost and carbon emissions of the IES have decreased by 3.8% and 6.9%, respectively. This is because Scenario 1 does not consider demand response strategies, and users cannot adjust their energy consumption load independently. As a result, the IES will bear higher energy purchase costs during periods of high energy consumption, leading to an increase in operating costs. Due to the fact that the load in Scenario 1 has not been transferred or reduced, the carbon emissions in Scenario 1 are also relatively high compared to other scenarios.

The composition of electricity, heat, and gas loads in Scenario 2 is shown in Figure 7. From Figure 7, it can be seen that compared to the obvious peak valley flat distribution of the original load, the electricity price demand response reduces part of the load during the high electricity price period and transfers part of the load from the high-electricity price period to the low-electricity price period, achieving peak shaving and valley filling of the load, reducing the load during the peak electricity price period, and adding the load during the low electricity price period, making the load curve smoother and increasing the security of the power grid. Alternative demand response can convert some electrical loads into heat or gas loads, while conversely, during peak gas price periods, it can convert electrical or heat loads into gas loads, reducing system operating costs. The combination of price-based demand response and alternative demand response makes the load curve smoother, improves the security of the power grid, and achieves peak shaving and valley filling of the system.

The electrical, thermal, and gas outputs of each device in Scenario 2 are shown in Figure 8. From Figure 8, it can be seen that during the low-electricity price period, the system mainly relies on wind power, photovoltaic output, and purchasing electricity from the superior power grid to meet the needs of heat pumps, batteries, and electrical loads, in order to maintain the balance of the system’s electrical power. The system’s thermal load is mainly supplied by heat pumps, gas boilers, and heat storage pipes, achieving the user’s thermal load demand. During the peak electricity price period, the system mainly relies on wind and photovoltaic output, CHP output, and battery discharge to meet user needs, while the heat load is directly obtained by heat storage, heat pump, and CHP. During peak price periods, the system responds to demand by converting a portion of the gas load into electrical or thermal loads, reducing the operating costs of the system.

During the low-electricity price period, the operation and maintenance costs of wind power and photovoltaic power are relatively low. The system prioritizes the selection of wind power and photovoltaic output. When wind power and photovoltaic power cannot meet the system’s electricity load demand during this period and the electricity price is low, the cost of purchasing electricity from the superior power grid is lower than the cost of purchasing gas from the superior gas grid. On the other hand, the heating efficiency of heat pumps is higher than that of gas boilers and CHP units, so the system is limited in choosing heat pumps for heating. When the heat pumps cannot meet the system’s heat load demand and the CHP unit output is insufficient, the system uses gas boilers for heating.

During the peak electricity price period, the electricity price is relatively high, and the price of purchasing gas from the superior power grid is more economical than purchasing electricity from the superior power grid. Therefore, at this time, the system mainly meets the system’s electrical and thermal loads through CHP units and gas boilers.

(2) Comparative analysis of scenarios 2, 3, and 4

From Table 4, it can be seen that compared to Scenario 2, the total operating cost of Scenario 3 has decreased by 11.9%, and the carbon emissions have decreased by 12.1%. The specific reason is that Scenario 3 introduces traditional carbon trading costs in the optimization model, and the IES only optimizes the unit output with the goal of maximizing its own interests. The total system cost of Scenario 4 has decreased by 15.3% compared to Scenario 2, and the system carbon emissions have decreased by 12.6%. As shown in Figure 11, during the peak or flat periods of electricity prices from 23:00 to 06:00 and 13:00 to 18:00, the cost of purchasing electricity from the external power grid is lower than that of generating electricity through gas turbines, resulting in a large amount of carbon emissions. For Scenario 4, due to the introduction of carbon trading costs in the optimization model, the IES can sell the surplus carbon quota in the carbon trading market due to its high output of gas turbines. As a result, the IES can obtain certain carbon trading benefits and choose to increase the output power of gas turbines with lower carbon emissions, such as CHP and GB, effectively reducing the total carbon emissions of the system. The system can coordinate the output modes of various units by comparing energy prices at different time periods, thus selecting a more economical and low-carbon operation mode, effectively coordinating the economic and low-carbon operation of the system.

(3) Comparative analysis of Scenario 5 and Scenario 4

Compared to Scenario 4, Scenario 5 further considers the mutual influence between the green certificate trading mechanism and carbon trading; that is, in the assessment of carbon emission rights, carbon emissions can be offset by the carbon reduction behind new energy supply, thereby affecting the carbon trading mechanism. Therefore, it further reduces the carbon emissions of the IES and enhances the enthusiasm of the IES to purchase green certificates, reflecting the low-carbon economy of carbon trading and green certificate joint trading strategies. From the table, it can be seen that compared to Scenario 4, the total cost and carbon emissions of the IES in Scenario 5 have decreased by 1.35% and 12.56%, respectively, verifying the effectiveness of the green certificate carbon joint trading mechanism proposed in this article.

The proportion of each type of demand response load affects the implementation effect of system demand response, and the impact of price-based and alternative demand response proportions on system costs is analyzed.

The relationship between the total operating cost and the price-based demand response load ratio is shown in Figure 9.

We set the proportion of price-based demand response to 10%–40% and analyze the impact of price-based demand response on system costs. It can be seen from the figure that as the proportion of price-based demand response increases, the total operating cost of the system decreases; that is, the total operating cost is negatively related to the price-based demand response load. This is because when the total load remains unchanged, increasing the price-based demand response, the proportion of demand response is equivalent to increasing the amount of price-based demand response, which allows users to reduce the load during peak periods of electricity prices and increase the load during trough periods of electricity prices, reducing the system energy purchase cost, thereby reducing the total operating cost of the system.

The relationship between the total operating cost of the system and the proportion of alternative demand response load is shown in Figure 10. It can be seen from the overall figure that when the proportion of price-based demand response is set to 20% and the proportion of substitution-based demand response is increased from 5% to 30%, the total operating cost of the system increases, that is, the total operating cost of the system and the substitution. There is a positive correlation between the load proportion of type demand response, so coordinating the proportion of price-type and substitution-type demand response can help improve operating economy.

Different carbon trading mechanism parameters will affect the internal operation of the IES. Most of the existing literature analyzes the impact of different carbon trading base prices on the total system operation cost, and few articles analyze the impact of price growth rate and price range on the total system operation cost. For this reason, we focus on these three parameter pairs the impact of system carbon emissions and total operating costs.

It can be seen from Figure 11 that when the base price of carbon trading is less than 175 yuan/ton, with the increase in the base price of carbon trading, that is, the greater the weight of the cost of the carbon emission objective function, the greater the role of carbon trading costs, the system will reduce the total amount of carbon emissions by more than. This is to reduce the cost of carbon trading, so carbon emissions are reduced; when the base price of carbon trading is greater than 175 yuan/ton, with the increase in the base price of carbon trading, the total amount of carbon emissions will decrease, and the total operating cost of the system will increase. At this time, the output of each piece of equipment in the system tends to be stable, and the base price of carbon trading increases, resulting in an increase in the total cost of the system.

When the interval length is in the range of (0, 0.75) t, the total operating cost of the system decreases with the increase in the interval length at this time because the system interval length is small at this time, and the carbon transaction cost of the system is very high, so the carbon emission of the system is reduced. When the interval length is greater than 0.75 t, the interval length is relatively large at this time, and the high-order carbon emissions purchased by the system are less, so the carbon transaction cost of the system is smaller. When the carbon trading range is greater than 2.0 t, the carbon trading range has little impact on the carbon emissions of the system, and the carbon emissions tend to be stable. With the increase in the range length, the cost of carbon trading in the system will gradually decrease, and the total cost will stabilize.

When the price growth rate is (0,0.35), at this time, with the increase in the price growth rate, the total carbon emissions of the system will decrease, the carbon trading price will also decrease, and the system will automatically adjust the output of each equipment to reduce carbon emissions, but due to the existence of fixed load in the system, when the price growth rate is (0.35,0.7), the carbon emissions tend to be stable, and the change of carbon emissions also tends to be stable; with the increase in the price growth rate, the carbon transaction cost increases, and the total operating cost of the system increases.

According to the aforementioned analysis, when the base price of carbon trading is 175 yuan/ton, the carbon emission reduction of the IES reaches the minimum. At this time, the price factor will not make the system continue to reduce carbon emissions, but will only increase the total cost of the system. When the interval length is less than or equal to 0.75 t, the carbon emission of the system is the smallest, but when the interval length is greater than 0.75 t, the carbon emission of the system tends to be stable, and the total cost of the system also tends to be stable. Similarly, when the price growth rate is greater than 0.75, the carbon emissions of the system tend to be stable. At this time, increasing the price growth rate will only increase the total operating cost of the system. Therefore, setting appropriate ladder-type carbon trading parameters can reasonably guide the system’s carbon emissions.