Abstract
In this paper, a novel multi-objective optimization model of integrated energy systems (IESs) is proposed based on the ladder-type carbon emission trading mechanism and refined load demand response strategies. First, the carbon emission trading mechanism is introduced into the optimal scheduling of IESs, and a ladder-type carbon emission cost calculation model based on rewards and penalties is established to strictly control the carbon emissions of the system. Then, according to different response characteristics of electric load and heating load, a refined load demand response model is built based on the price elasticity matrix and substitutability of energy supply mode. On these basis, a multi-objective optimization model of IESs is established, which aims to minimize the total operating cost and the renewable energy source (RES) curtailment. Finally, based on typical case studies, the simulation results show that the proposed model can effectively improve the economic benefits of IESs and the utilization efficiency of RESs.
DUE to the rapid development of economy, the utilization of fossil energy has resulted in many serious problems such as the depletion of traditional energy resources and the deterioration of global climate [
As an important carrier of RES utilization, there have been a lot of research on multi-energy systems. In [
Carbon emission trading mechanism can make carbon emission rights become a schedulable resource with economic value, so as to realize the economic and low-carbon development of the energy system. In [
Load demand response (LDR) can effectively promote the adjustment of energy consumption behaviors of users through the energy price and economic incentive mechanism [
In view of the above problems, this paper proposes a novel multi-objective optimization model of IESs, which considers both the ladder-type carbon emission trading mechanism and the refined LDR strategies. The main contributions are summarised as follows.
1) The carbon emission trading mechanism is introduced into the optimal scheduling of IESs. The impacts of each device on carbon emissions are fully considered, and a ladder-type carbon emission cost calculation model based on reward and penalty is built to strictly control the carbon emissions and reduce the carbon trading cost of IESs.
2) According to different flexible characteristics and scheduling potential of load, a refined LDR model based on the price elasticity matrix and the mutual conversion of electric load and heating load on the energy consumption side is established, so as to fully utilize the regulation role of flexible resources.
3) A multi-objective optimization model of IES is established to minimize the total operating cost and the RES curtailment. And the simulation results of the examples verify the effectiveness and superiority of the model proposed in this paper.
The remainder of this paper is organized as follows. The structure of IES is introduced and the mathematical models are established in Section II. Section III builds the multi-objective optimization model of IES and the solution method is also introduced. Case studies are presented in Section IV. Finally, the main conclusions are drawn in Section V.
The IES can achieve complementarity and coordination of multiple energy sources and ensure continuous and reliable energy supply. The structure of the IES in this paper is shown in

Fig. 1 Structure of IES.
The ES is an important part of the IES. In [
(1) |
(2) |
where is the power consumption of the battery during charging process in time period , which is equivalent to the charging loss; is the power consumption of the battery during discharging process in time period , which is equivalent to the sum of actual discharging power and discharging loss; is the state of charge (SOC) of the battery; is the internal resistance of the battery; is the battery polarization constant that can be calculated according to the manufacturer’s data; and are the rated capacity and rated voltage of the battery, respectively; and and are the charging and discharging power of the battery, respectively.
Thus, the SOC of the battery can be represented as:
(3) |
(4) |
where is the maximum ES capacity of the battery.
Besides, the actual output power of the battery is:
(5) |
The maintenance cost of the battery can be expressed by a linear function of its charging and discharging power consumption [
(6) |
where is the unit maintenance cost of the battery consumption.
When the heat energy generated by CHP and GB cannot be fully absorbed, it can be temporarily stored in HS and released when the heating demand is high, which realizes the transfer of heat energy in time and raises the utilization of heat energy. Similarly, the excess natural gas generated by P2G can be stored into the GS. The mathematical models of HS and GS can be represented as:
(7) |
(8) |
where and are the stored heat energy of HS and the stored natural gas of GS, respectively; and are the heat storing power and heat releasing power of HS, respectively; and are the heat storing efficiency and heat releasing efficiency of HS, respectively; and are the gas storing power and gas releasing power, respectively; and and are the input efficiency and output efficiency of GS, respectively.
From above, the actual output power of HS and GS can be represented as:
(9) |
(10) |
The carbon emission trading mechanism refers to the establishment of legal carbon emission rights and allowing them to be traded on the carbon market, which is intended to control carbon emissions. The free carbon emission credits are allocated to the carbon emission sources of energy suppliers by the government firstly. If the carbon emission credits are exceeded by the carbon emissions in the actual production process, the energy suppliers need to buy additional carbon emission credits in the carbon trading market. If the carbon emissions of energy suppliers are lower than their existing emission credits, according to the carbon trading price of the day, i.e., unit carbon emission price, the excess carbon emission credits can be sold on the carbon market, so as to gain certain benefits.
In this paper, the distribution of initial carbon emission credits in IES consists of three parts: electricity purchased from external power grid, CHP, and GB. CHP can generate electric power and heat power by MT and HRB, respectively. According to the “Shanghai 2016 Carbon Emission Allocation Scheme”, the electricity generated by CHP can be transformed into equivalent heat. Based on this, the carbon emission credit allocation of CHP is determined by the equivalent heat generation. Therefore, the expression of free carbon emission credits of IES is:
(11) |
(12) |
(13) |
(14) |
(15) |
where is the initial carbon emission credit; , , and are the carbon emission credits of CHP, GB, and electricity purchased from the power grid, respectively; is the electric power purchased from the grid; is the carbon emission credit per unit of electricity supply; and are the electric power generated by MT and the heat power recovered by HRB, respectively; is the transformation coefficient from electricity to heat of CHP; is the recovery efficiency of HRB; is the electricity generation efficiency of MT; is the carbon emission credit per unit of heat supply; and is the heat power output by GB.
In the actual energy supply process, the consumptions of electricity and natural gas decide the carbon emissions of the whole energy system. Besides, for P2G, CO2 is required to be used as raw materials in the process of converting electricity to gas. And we think that CO2 consumed by P2G also participates in the carbon trading. Therefore, the actual carbon emissions of IES can be expressed as:
(16) |
(17) |
(18) |
(19) |
where is the actual carbon emission; and are the unit carbon emission coefficients of electricity consumption and natural gas consumption, respectively; is the gas consumed by MT; is the calorific value of natural gas; is the gas consumed by GB; is the heat production efficiency of GB; is the gas absorbed by P2G; is the electric power consumed by P2G; and is the electricity-gas conversion efficiency of P2G.
On the basis of the conventional carbon emission trading mechanism, this paper proposes a ladder-type carbon emission cost calculation model based on rewards and penalties. Based on initial carbon emission credits, several emission ranges are divided. When , the incentive factor is introduced. It means that in addition to selling excess carbon emission credits on the carbon trading market for profit, the government will also give some incentives to energy suppliers. And the smaller the carbon emission range corresponding to carbon emissions, the more incentives the government will give and the more benefits can be obtained. Conversely, when , the greater the emission range corresponding to carbon emissions, the higher the carbon trading price, which means that more carbon emission cost penalties are imposed on energy suppliers. These policies on the division of carbon emission ranges are formulated by the government. The ladder-type carbon emission trading cost of IES can be calculated by:
(20) |
where is the carbon price in carbon emission trading market; is the incentive factor; is the interval length of carbon emission range; is the target value of carbon reduction; and is the extent of carbon price growth for each ladder. It should be mentioned that when the proposed carbon emission cost calculation model is applied to practice, the government can establish the standard of carbon emission interval length according to the actual situation and demand, so as to realize the goal of carbon emission reduction.
Through the ladder-type carbon emission trading mechanism, the high-emission energy suppliers need to pay higher carbon emission costs, which encourages them to reduce emissions and promotes a shift towards low-carbon and environmentally friendly development models. At the same time, the energy suppliers with low emissions can reduce operating costs and have an advantage in the market. Therefore, the ladder-type carbon emission trading mechanism has attracted the attention of many academic researchers. Even if the ladder-type carbon emission trading mechanism has not been widely applied in current carbon trading market, its wide popularization is an inevitable trend in the future.
The traditional LDR model usually only considers the demand response of electric load, for example, changing the user’s electricity consumption habits by adjusting the price of electricity. However, in IES, there are other load forms. So not only electric load can be involved in LDR, but also the heating load can participate in LDR regulation. Therefore, the LDR model proposed in this paper considers the demand response of both electric and heating loads, so as to fully utilize flexible resources. In view of the load characteristics of the user side, the loads in IES can be divided into uncontrollable load (UL) and controllable load (CL). And the LDR in this paper divides CL into price dependent load (PDL) and energy fungible load (EFL).
The sensitivity of different types of load to energy price signal is different. Therefore, PDL can be further divided into time transferable load (TTL) and quantity reducible load (QRL).
TTL means that the users take the time-sharing energy price as the signal, some loads during peak period of energy consumption are shifted to low peak period, and the total TTL remains unchanged during the scheduling cycle. According to the ratio of time-sharing energy price to initial energy price, the TTL characteristics can be described by price demand elasticity matrix :
(21) |
(22) |
where is the element of the price demand elasticity matrix of TTL; is the initial TTL in time period ; is the initial energy price in time period ; is the variation of TTL after LDR in time period ; and is the variation of energy price after LDR in time period .
Thus, the variation of TTL can be further represented as:
(23) |
To ensure the total TTL remains unchanged before and after LDR, the following condition should be met:
(24) |
QRL represents that in order to relieve scheduling pressure, the load is reduced in peak period of energy consumption. And the price demand elasticity matrix of QRL is represented as diagonal matrix :
(25) |
(26) |
where is the element of the price demand elasticity matrix of QRL; and and are the initial QRL and the variation of QRL after LDR, respectively.
Therefore, the variation of QRL can be calculated by:
(27) |
EFL means that part of the load can be substituted by the load of other energy forms. And it is considered that the electric load and the heating load can substitute each other in this paper. The substitution relationship between them is expressed as:
(28) |
(29) |
where and are the alternative electric EFL and corresponding heating EFL, respectively; is the electrothermal substitution coefficient; and are the utilization efficiencies of electric energy and heat energy, respectively; and and are the calorific values of electric energy and heat energy, respectively.
The multi-objective optimization model of IES considering LDR under carbon emission trading mechanism aims to achieve the best economy and maximize the utilization of RES. The objective functions are established with the objectives of minimizing the total operating cost and the RES curtailment of IES.
The objective function of the minimum total operating cost can be expressed as:
(30) |
where is the total operating cost; is the cost of energy purchase; is the cost of device maintenance; is the cost of pollutant treatment; and is the cost of carbon emission trading.
(31) |
where and are the purchase prices of electricity and natural gas, respectively.
(32) |
where the values of represent WT, PV, CHP, GB, P2G, HS, GS, respectively; is the output power of device ; and is the maintenance cost coefficient of device .
In the operation process of IES, some pollutants will be produced, such as SO2, NOx, and inhalable particulate matter PM2.5. The pollutant emissions mainly come from CHP, GB, and power purchase. The pollutant treatment cost can be expressed as:
(33) |
where , , and are the pollutant treatment costs per unit active power of electricity purchase, CHP, and GB, respectively.
The RES curtailment in IES is expressed by the difference between the maximum predicted output of RES and the actual RES accommodated by the system:
(34) |
where and are the wind power curtailment and PV power curtailment, respectively; and are the maximum predicted outputs of wind power and PV power, respectively; and and are the wind power and PV power accommodated by the system, respectively.
The energy balance constraints intend to ensure the balance between energy supply and consumption, as shown in (35)-(37).
(35) |
where is the electric load of users; and , , and are the electric power variations of TTL, QRL, and EFL after LDR, respectively.
(36) |
where is the heating load of users; and , and are the heat power variations of TTL, QRL, and EFL after LDR, respectively.
The equipment operating constraints are used to ensure the safe and stable operation of each device, as shown in (38)-(52).
(38) |
(39) |
where is the upper limit output of MT; and is the maximum ramp rate of MT. It should be mentioned that (15) shows the relationship between electric power and heat power generated by CHP. Constraint (38) limits the upper/lower electric power output of MT. According to (15) and (38), the upper/lower limits of the heat power output of HRB can also be determined. Similarly, according to (15) and (39), the ramping up/down limits of HRB can also be determined.
(40) |
(41) |
where is the upper limit output of GB; and is the maximum ramp rate of GB.
(42) |
(43) |
where is the maximum power of P2G; and is the maximum ramp rate of P2G.
(44) |
(45) |
where and are the maximum and minimum ES capacities of the battery, respectively; and is the maximum output power of the battery.
Besides, to prevent the battery from being charged and discharged simultaneously, the following condition should be met:
(46) |
(47) |
(48) |
(49) |
(50) |
where and are the maximum and minimum HS capacities, respectively; and are the maximum and minimum GS capacities, respectively; and and are the maximum output power of HS and GS, respectively.
In addition, HS and GS both cannot release energy and store energy at the same time, thus the following constraints should also be satisfied:
(51) |
(52) |
The tie line constraints limit the maximum power exchange between the system and the grid.
(53) |
where is the maximum electricity purchased from the power grid.
The LDR model constraints are used to ensure users’ basic energy demands and enhance their satisfaction with energy use.
(54) |
(55) |
(56) |
where , , and are the upper limits of TTL, QRL, and EFL, respectively.
It should be mentioned that in this paper, we mainly consider the influence of ladder-type carbon emission trading mechanism and refined LDR strategies on IES operation. For the uncertainties of RES and load, since the IES in this paper is connected to the external power grid, some uncertainties of RES output and load demand can be smoothed through the power exchange between IES and power grid. In addition, the refined LDR model is considered in the optimal scheduling of IES. When the fluctuations of RES generation and load demand occur, the LDR model can transfer, reduce, or replace part of the load, so as to fully utilize RES and satisfy the energy demand of users. Thus the partial adverse influence of the uncertainties can also be eliminated by the LDR model.
In multi-objective optimization problems, each objective function conflicts with each other, and it is impossible to achieve optimal results for multiple objectives simultaneously. So the optimal solution of multi-objective optimization problem is a set of solutions in which the value of any objective function cannot be further optimized without deteriorating other objective functions, i.e., the Pareto optimal solution set.
In this paper, the niche multi-objective particle swarm optimization (NMOPSO) algorithm is applied to solve the multi-objective problem of IES. The algorithm uses niche sharing mechanism to update the position of particles and maintain the diversity of solutions and the uniformity of distribution. And the chaotic mutation is introduced to disturb some non-dominant particles in a small range, which improves the global search ability of the algorithm and avoids falling into local optimization. Compared with other multi-objective optimization algorithms, the NMOPSO algorithm has been verified to have better performance in terms of computational efficiency and accuracy [

Fig. 2 Flow chart of NMOPSO algorithm.
The data of electric and heating loads and the wind and PV power output come from a typical day of Northeast China. The simulation parameters are listed in
Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|
0.413 | 280 | 0.5 | |||
424 g/kWh | 60 V | 0.25 | |||
6 MJ/kWh | 210 kWh | 0.7 | |||
0.102 t/GJ | 100 kg | 0.9 | |||
968 g/kWh | 0.35 | 0.85 | |||
220 g/ | 0.85 | 0.9 | |||
9.78 kWh/ | 0.9 | 0.85 |
Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|
100 kW | 100 kW | 60 kW | |||
100 kW | 100 kW | 50 kW | |||
200 kWh | 400 kWh | 150 kWh | |||
40 kWh | 300 kW | 5 kW/min | |||
15 kW/min | 10 kW/min |

Fig. 3 Predicted electric load, heating load, and the maximum outputs of wind power and PV power.

Fig. 4 Time-sharing price of electricity purchased from power grid.
The Pareto frontier solution set calculated by NMOPSO algorithm is shown in

Fig. 5 Pareto frontier solution set.
It can be observed from
In order to determine the scheme that is closest to the optimal level, i.e., both objective functions are minimized, the technique for order preference by similarity to an ideal solution (TOPSIS) decision-making method is used to select the only compromise scheme. By TOPSIS decision-making method, the proximity index between each solution and the optimal level can be obtained, and sorted in descending order. And the greater the proximity index, the closer to the optimal level [
For the Pareto frontier solution sets in various scenarios, the operating costs and RES curtailment are assumed to have the same weight in this paper. And the first six solutions of Pareto set determined by TOPSIS decision-making method are shown in
Order | Total cost () | RES curtailment (kWh) | Proximity index |
---|---|---|---|
1 | 3273.96 | 110.536 | 0.62070 |
2 | 3235.83 | 112.419 | 0.61189 |
3 | 3225.65 | 112.812 | 0.61107 |
4 | 3338.55 | 108.356 | 0.61083 |
5 | 3255.40 | 111.811 | 0.61014 |
6 | 3228.82 | 112.773 | 0.60972 |
In order to research the impacts of LDR and carbon emission trading mechanism built in this paper, this part sets up four different scenarios. Similarly, for the Pareto frontier solution set in each scenario, the TOPSIS decision-making method is adopted to determine the only compromise scheme.
Scenario 1: the unified carbon emission cost calculation model [
Scenario 2: the unified carbon emission cost calculation model is used in the optimal scheduling of IES, and LDR is also considered.
Scenario 3: the ladder-type carbon emission cost calculation model based on rewards and penalties is used in the optimal scheduling of IES, but LDR is not considered.
Scenario 4: the ladder-type carbon emission cost calculation model based on rewards and penalties is used in the optimal scheduling of IES, and LDR is also considered.
The simulation results of the four scenarios are shown in
Scenario | Total operating cost () | Device maintenance cost () | Energy purchase cost () | Carbon trading cost () | Carbon emission (kg) | Pollution treatment cost () | RES curtailment (kWh) | Rate of RES curtailment (%) |
---|---|---|---|---|---|---|---|---|
1 | 3502.62 | 369.18 | 2437.72 | 252.20 | 2337.85 | 443.52 | 268.486 | 2.63 |
2 | 3352.14 | 348.24 | 2337.65 | 237.76 | 2285.74 | 428.49 | 115.351 | 1.13 |
3 | 3415.43 | 368.32 | 2420.86 | 195.71 | 2238.23 | 430.54 | 248.180 | 2.41 |
4 | 3273.96 | 352.16 | 2316.52 | 188.17 | 2201.46 | 417.11 | 110.536 | 1.08 |
It can also be observed from

Fig. 6 Initial and time-sharing energy prices. (a) Initial and time-sharing electricity prices. (b) Initial and time-sharing heat prices.
The electric load curve and heating load curve before and after considering LDR and the corresponding changes of various types of loads are shown in

Fig. 7 Variations of load before and after considering LDR. (a) Variations of electric load. (b) Variations of heating load.
As can be observed that part of the electric TTL in the high electricity price period, i.e., 10:00-12:00 and 20:00-22:00, is transferred to the low electricity price period. And part of the heating TTL in the high heat price period, i.e., 11:00-14:00 and 20:00-22:00, is transferred to the low heat price period. Meanwhile, it also can be observed that some electric QRL is reduced in the high electricity price period, i.e., 10:00-12:00 and 20:00-22:00. And some heating QRL is also reduced in the high heat price period, i.e., 13:00-14:00. Besides, part of electric EFL is converted into heating load in high electricity price period, i.e., 10:00-12:00 and 20:00-22:00, and low heat price period, i.e., 08:00-10:00, 15:00-19:00, and 23:00-24:00. In low electricity price period, i.e., 15:00-19:00, and high heat price period, i.e., 11:00-12:00 and 20:00-22:00, part of the heating EFL is converted into electric load. So by considering LDR, the energy load are effectively adjusted to make the overall daily load curve of users consistent with the output of RES.
Figures

Fig. 8 Electric power balance in scenario 4.

Fig. 9 Heat power balance in scenario 4.
Figures

Fig. 10 Electric power balance in scenario 3.

Fig. 11 Heat power balance in scenario 3.

Fig. 12 Comparison of RES accommodation in scenarios 3 and 4.
In the above research, the proportion of all kinds of loads involved in LDR is assumed to be fixed. But in practical application, due to different electricity and heat consumption habits of users, the impact of LDR on the IES operation is also different. In order to research the above effects, three scenarios are set as follows.
Scenario 5: LDR is acted by PDL alone.
Scenario 6: LDR is acted by EFL alone.
Scenario 7: LDR is jointly acted by PDL and EFL.
It is assumed that the proportions of UL and CL in the total load are fixed in the following analysis, both 50% and 50%. And for PDL, the ratio of TTL to QRL is 1:1. The effects of LDR under different load types on IES operation are shown in
Scenario | Total cost () | Improvement rate of total cost (%) | RES curtailment (kWh) | Improvement rate of RES curtailment (%) |
---|---|---|---|---|
5 | 3317.15 | 2.88 | 135.28 | 45.49 |
6 | 3366.36 | 1.43 | 172.58 | 30.46 |
7 | 3273.96 | 4.14 | 110.54 | 55.46 |
From
In addition, in order to study the influence of electric LDR and heating LDR in IES, three other scenarios are set as follows:
Scenario 8: LDR is acted on by electric load alone.
Scenario 9: LDR is acted on by heating load alone.
Scenario 10: LDR is jointly acted by electric load and heating load.
The effects of LDR under different load forms on IES operation are shown in
Scenario | Total cost () | Improvement rate of total cost (%) | RES curtailment (kWh) | Improvement rate of RES curtailment (%) |
---|---|---|---|---|
8 | 3343.41 | 2.11 | 129.83 | 47.68 |
9 | 3382.62 | 0.96 | 156.88 | 36.78 |
10 | 3273.96 | 4.14 | 110.54 | 55.46 |
In order to promote the development of low-carbon economy and the utilization of RES in multi-energy coupling systems, an innovative multi-objective optimization model of IES considering the ladder-type carbon emission trading mechanism and the refined LDR strategies is proposed. According to the simulation results, the conclusions are as follows.
1) On the premise of guaranteeing the economic operation of IES, considering LDR can improve the utilization efficiency of RES and play a positive role in environmental protection.
2) Compared with the unified carbon emission cost calculation model, the ladder-type carbon emission cost calculation model based on rewards and penalties can significantly reduce the carbon emissions and carbon trading cost, and has a better effect on the economy of IES.
3) The contributions of LDR to IES are influenced by many factors. Under the same conditions, the more diversified the load types and load forms involved in LDR, the better the effect of implementing LDR.
In the future work, the uncertainties of renewable energy and load demand will be considered in system operation via some methods such as scenario-based stochastic programming and adaptive dynamic programming. Besides, we plan to establish detailed models of power, heat, and gas system based on the characteristics and coupling relationships of different energy networks, and consider their network models and flow constraints in the optimal operation.
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