The operation cost of TP, WT (Yang et al., 2017), photovoltaic power (PV) (Liu et al., 2020), CCHP, gas boiler (GB), EH, P2G, EC, absorption refrigerator (AR), electricity storage (ES), thermal storage (TS), cooling storage (CS), and gas storage (GS) at time t are shown in (7)–(19): C T P , t = d P T P , t 2 + f P T P , t + g (7) C W T , t = Y W T P W T , t (8) C P V , t = Y P V P P V , t (9) C C C H P , t = Y C C H P P C C H P , t (10) C G B , t = Y G B P G B , t (11) C E H , t = Y E H P E H , t (12) C P 2 G , t = Y P 2 G P P 2 G , t (13) C E C , t = Y E C P E C , t (14) C A R , t = Y A R P A R , t (15) C E S , t = C e d P e d , t + C e c P e c , t (16) C T S , t = C t d P t d , t + C t c P t c , t (17) C C S , t = C c d P c d , t + C c c P c c , t (18) C G S , t = C g d P g d , t + C g c P g c , t , (19) where P T P , t , P W T , t , P P V , t , P C C H P , t , P G B , t , P E H , t , P P 2 G , t , P E C , t , and P A R , t are the output of TP, WT, PV, CCHP, GB, EH, P2G, EC, and AR at time t, respectively; d, f, and g represent the coal consumption cost coefficients of TP; Y W T , Y P V , Y C C H P , Y G B , Y E H , Y P 2 G , Y E C and Y A R , respectively, represent the cost coefficient of WT, PV, CCHP, GB, EH, P2G, EC, and AR; P e c , t , P t c , t , P c c , t , and P g c , t are the charging power of ES, RS, CS, and GS, respectively, at time t; P e d , t , P t d , t , P c d , t , and P g d , t , respectively, represent the discharging power of ES, RS, CS, and GS at time t; C e d , C t d , C c d , and C g d , respectively, represent the discharging cost coefficient of ES, RS, CS, and GS at time t; C e c , C t c , C c c , and C g c , respectively, represent the charging cost coefficient of ES, RS, consisting CS and GS at time t.

The equipment operation cost of the IES at time t can be expressed as follows: C Y , t = C T P , t + C P V , t ⋯ + C G S , t (20) C Y ( P T P , t , P P V , t , ⋯ P Ω , t ) = ∑ t = 1 T C Y , t , (21) where Ω represents various equipment in the IES, including TP, WT, PV, CCHP, and GB on the production side, EH, P2G, EC, AR, and ESD on the network side; P Ω , t is the output of the equipment Ω.

In order to maintain the balance of energy supply and load demand, the IES operator needs to purchase electricity and natural gas from the PG and NGN. Thus, the energy purchasing cost of the IES includes the electricity purchasing cost and the gas purchasing cost. The energy purchasing cost of the IES at time t can be written as follows: C G , t = ρ e l e , t P e l e , t + ρ g a s , t P g a s , t (22) C G ( P e l e , t , P g a s , t ) = ∑ t = 1 T C G , t , (23) where ρ e l e , t and ρ g a s , t , respectively, represent the electricity price and natural gas price at time t; P e l e , t is the amount of electricity and natural gas purchased by the IES from the PG at time t; and P g a s , t is the amount of natural gas purchased by the IES from the NGN at time t.

The calculation of the carbon emission cost can be divided into three steps: 1) determining the carbon emission quota; 2) calculating the actual carbon emissions; 3) calculating the carbon emission cost.

On the production side of the IES, there are GB, CCHP, and other energy production equipment that convert primary energy into secondary energy, and the purchased electricity of the IES which is generated from TP. For the aforementioned equipment, the carbon emission quota and the actual carbon emissions corresponding to its output need to be determined. In addition, the carbon emission quota of PV and WT also needs to be calculated.

The network side of the IES mainly involves the conversion process of various secondary energy sources. Carbon emissions are rarely generated during this process, and only the carbon emissions absorbed by P2G need to be determined.

Since the GL on the load side is mainly used as fuel for combustion, it is also necessary to calculate the carbon emission quota and actual carbon emissions of the GL.

1) Carbon Emission Quota

The calculation method for the carbon emission quota is based on the output of each piece of equipment. The initial carbon emission quota is proportional to the output of each piece of equipment. Taking TP and CCHP for example, The carbon emission quota of TP is determined by its power generation, the more the output of TP, the more the carbon emission quota it gains; The carbon emission allowance of CCHP depends on its output of electrical, thermal, and cooling energy, different types of energy corresponding to different carbon emission quota factors. The more the output of CCHP, the more will be the carbon emission quota it gains.

The carbon emission quota of the IES is composed of the carbon emission quota of the production side, the carbon emission quota of the network side, and the carbon emission quota of the load side.

The carbon emission quota of the production side at time t can be calculated as follows: E p , t ∗ = ∑ i λ p P i , t , (24) where E p , t ∗ is the carbon emission quota of production side at time t; λ p is the carbon emission quota factor for unit power output; and P i , t is the output of production-side equipment i at time t, i include TP, WT, PV, CCHP, and GB.

The carbon emission quota of the load side at time t can be expressed as follows: E l , t ∗ = λ l P G L , t , (25) where E l , t ∗ is the carbon emission quota of load side at time t; λ l is the carbon emission quota factor for unit natural gas consumption; and P G L , t represents GL at time t.

Thus, the carbon emission quota of the IES at time t can be calculated as follows: E t ∗ = E p , t ∗ + E l , t ∗ , (26)

2) Actual Carbon Emissions

The actual carbon emissions of the IES are composed of the carbon emissions of the production side, the carbon emissions of the network side, and the carbon emissions of the load side. The actual carbon emissions of the production side at time t can be shown as follows: E p , t = ∑ i a i P i , t 2 + b i P i , t + c i , (27) where E p , t is the actual carbon emissions of production side at time t; a _i , b _i , and c _i represent the carbon emission factor of production side equipment i.

The actual carbon emissions of the network side at time t can be expressed as follows: E n , t = ψ P P 2 G e , t , (28) where E n , t is the amount of CO₂ consumed by the network side at time t; ψ is the carbon absorption factor of P2G; and P P 2 G e , t is the electricity consumed by P2G at time t. E l , t = ς P G L , t , (29) where E l , t is the carbon emissions of the load side at time t and ς is the carbon emission factor of GL.

The actual carbon emissions of the IES at time t can be calculated as follows: E t = E p , t − E n , t + E l , t . (30)

3) Carbon Emission Cost

According to the CEUC model based on the DRPPM proposed in Section 2, the carbon emission cost model of the IES can be constructed as follows: C T ( P T P , t , P P V , t , ⋯ P P 2 G , t ) = { ∑ t = 1 T [ a κ 2 + b κ + c ] ( E t − E t ∗ )     , E t > E t ∗             0                   , E t = E t ∗ ∑ t = 1 T [ − a ( 2 − κ ) 2 − b ( 2 − κ ) − c ] ( E t − E t ∗ ) , E t < E t ∗ , (31) When E t > E t ∗ , the carbon emissions of the IES at time t are higher than its carbon emission quota. At this time, the system needs to be penalized, and the carbon emission cost of the system is positive; when E t < E t ∗ , the carbon emissions of the IES at time t is less than its carbon emission quota. At this time, the system needs to be rewarded, and the carbon emission cost of the system is negative; when E t = E t ∗ , the carbon emission cost of the system is zero at time t.

The operational constraints of TP, WT, PV, CCHP, GB, EH, P2G, EC, AR, and ESD are given in (32)-(40):

1) Operation Constraints of TP

The rated power constraint and ramping constraint of TP are given as follows: { P TP , min ≤ P TP , t ≤ P TP , max D TP , max ≤ P TP , t − P TP , t − 1 ≤ U TP , max , (32) where P TP , min is the rated minimum power of TP; P TP , max is the rated maximum power of TP; and D TP , max and U TP , max are the maximum ramping constraints of TP.

2) Operation Constraints of WT and PV

The rated power constraint of WT and PV are constructed as follows: { 0 ≤ P W T , t ≤ P W T 0 ≤ P P V , t ≤ P P V , (33) where P W T and P P V are the rated power of WT and PV, respectively.

3) Operation Constraints of CCHP

The rated power constraint, ramping constraint, and power balance constraint of GB can be expressed as follows: { P GB , min ≤ P GB , t ≤ P GB , max D GB , max ≤ P GB , t − P GB , t − 1 ≤ U GB , max P G B , t = η G B P G B g , t , (35) where P GB , min is the rated minimum power of GB; P GB , max is the rated maximum power of GB; D GB , max and U GB , max are the maximum ramping constraints of GB; P G B g , t is the natural gas consumed by GB; and η G B is the efficiency factor of GB.

5) Operation Constraints of EH

The rated power constraint, ramping constraint, and power balance constraint of EH can be shown as follows: { P EH , min ≤ P EH , t ≤ P EH , max D EH , max ≤ P EH , t − P EH, t − 1 ≤ U EH, max P E H , t = η E H P E H e , t , (36) where P EH , min is the rated minimum power of EH; P EH , max is the rated maximum power of EH; D EH , max and U EH, max are the maximum ramping constraints of EH; P G B g , t is the electricity consumed by EH; and η E H is the efficiency factor of EH.

6) Operation Constraints of EC

The rated power constraint and power balance constraint of EC can be expressed as follows: { 0 ≤ P E C , t ≤ P E C , max P E C , t = η E C P E C e , t , (37) where P E C , max is the rated maximum power of EC; P E C e , t is the electricity consumed by EC; and η E C is the efficiency factor of EC.

7) Operation Constraints of P2G

The rated power constraint and power balance constraint of P2G can be constructed as follows: { 0 ≤ P P 2 G , t ≤ P P 2 G , max P P 2 G , t = η P 2 G P P 2 G e , t , (38) where P P 2 G , max is the rated maximum power of P2G and η P 2 G is the efficiency factor of P2G.

8) Operation Constraints of AR

The rated power constraint and power balance constraint of AR can be expressed as follows: { 0 ≤ P A R , t ≤ P A R , max P A R , t = η A R P A R h , t , (39) where P A R , max is the rated maximum power of AR; P A R h , t is the HEAT consumed by AR; and η A R is the efficiency factor of AR.

9) Operation Constraints of ESD

The operation constraints of ESD include power balance constraint, capacity constraint, charge constraint, and discharge constraint. The operation constraints of ESD can be expressed as follows: { R e s d , t − R e s d , t − 1 = [ ( 1 − μ e s d , t ) P e s d c , t ρ e s d c − μ e s d , t P e s d d , t / ρ e s d d ] Δ t R e s d , min ≤ R e s d , t ≤ R e s d , max 0 ≤ P e s d c , t ≤ ( 1 − μ e s d , t ) P e s d c , max 0 ≤ P e s d d , t ≤ μ e s d , t P e s d d , max , (40) where R e s d , t represents the capacity of the ESD at time t; R e s d , min and R e s d , max represent the minimum and maximum storage capacity of the ESD, respectively; ρ e s d c and ρ e s d d are the charging and discharging efficiency factors of the ESD; μ e s d , t is the 0–1 variable factor that represents the operating state of the ESD, TS, CS, and GS, take the ES for example, μ e s , t = 1 represents the ES works at discharging state and μ e s , t = 0 represents the ES works at charging state; and P e s d c , max and P e s d d , max represent the maximum charging and discharging power of the ESD, respectively.

In the IES, the EL, heat load (HL), cooling load (CL), and GL at time t meet the following power balance constraints: P E L , t = P e l e , t + P TP , t + P W T , t + P P V , t + P C C H P e , t             − P E H e , t − P P 2 G e , t − P E C e , t             + μ e s , t P e d , t − ( 1 − μ e s , t ) P e c , t (41) P H L , t = P G B , t + P E H , t + P C C H P h , t             − P A R h , t             + μ h s , t P h d , t − ( 1 − μ h s , t ) P h c , t (42) P C L , t = P A R , t + P E C , t + P C C H P c , t             + μ c s , t P c d , t − ( 1 − μ c s , t ) P c c , t (43) P G L , t = P g a s , t + P P 2 G , t             − P G B g , t − P C C H P g , t             + μ g s , t P g d , t − ( 1 − μ g s , t ) P g c , t , (44) where P E L , t , P H L , t , P G L , t , and P C L , t , respectively, represent the demand of EL, HL, CL, and GL at time t.

In this section, the relationship between unit power comprehensive cost and output of TP under different CEUC models is, respectively, analyzed. The rated power of TP is 100 MW, and the carbon emissions of TP show a step change when the output is 76 MW. The analysis results are shown in Figure 3.

As it can be seen from Figure 3, in case 1, the operator will try to increase the output of TP to 93 MW to get the maximum benefit, but TP also generates huge carbon emissions. In case 2, the unit power comprehensive cost of TP has a segmentation point at 76 MW. When the output of TP is less than 76MW, the comprehensive cost of TP is less than its profit. To make the maximum benefit, the operator will try to increase the output of TP to 76 MW. In addition, to limit the carbon emissions of TP, the operator will try their best to limit the output of TP to less than 76MW, so the carbon emissions in case 2 is less than that in case 1.

In case 3, when the output of TP is less than 75MW, the comprehensive cost of TP is less than its profit. In addition, when the output of TP is higher than 85MW, the comprehensive cost of TP in case 3 is higher than that in case 2. It means that when the load demand is high and the output of TP has to be higher than 75MW, the operator is required to limit the output lower than 85 MW to reduce the carbon emissions in case 3. For example, the operator can replace the output of TP with that of some other low-carbon emission equipment, such as CCHP. It is beneficial for reducing the comprehensive cost. Therefore, under certain conditions, the dispatch model in case 3 has a better ability to limit carbon emissions than that in case 1 and case 2.

The low-carbon economic dispatch results of the aforementioned IES under three cases can be seen in Figure 4:

Compared with case 1, the carbon emission of case 2 was reduced by 29.5t (8.15%). Compared to the carbon emissions of case 1 and case 2, the carbon emission of case 3 is reduced by 52.6t and 23.1t, respectively. In terms of the comprehensive operation cost of the IES, the comprehensive operation cost in case 3 is the highest (295803 Yuan). It is higher than the cost of case 1 and case 2 by 3.79% and 1.32%, respectively. In terms of electricity purchasing cost and gas purchasing cost, case 1 has the highest electricity purchasing cost and the lowest gas purchasing cost. Case 3 has the lowest electricity purchasing cost and the highest gas purchasing cost. The electricity purchasing cost and gas purchasing cost in case 2 are between those in case 1 and case 3. In addition, the carbon emissions in case 1 is the highest, which means that when the constraints of carbon emissions are strengthened, the IES will purchase more natural gas to replace the purchasing of electricity to reduce the penalties when the carbon emissions are too high. Although the energy purchasing cost of the IES will increase in this way, the carbon emissions and the carbon emission cost will be reduced accordingly. Compared with the dispatch model in case 1 and case 2, the dispatch model proposed in this article has a great significance to limit the carbon emissions of the IES, which makes the IES more economically and environment-friendly.

Figures 5–7, respectively, show the operation of electrical load equipment in different cases. Before 6:00, the purchased electricity of the IES in three cases is similar, as well as the output of TP and CCHP. During this period, the system has less demand for EL, but the output of WT and CCHP is high. It results in the overall output of the IES higher than EL. Therefore, the excess electricity is consumed by P2G, which leads to the P2G working at its rated operation state. From 6:00 to 8:00, the purchased electricity of the IES decreases in all three cases, and the P2G still working at rated operation state in case 1, while in case 2 and case 3, the electricity consumption of P2G is significantly reduced, and it decreases more in case 3 than in case 2. Because the CEUC model applied in case 3, the cost of producing natural gas by P2G is higher than the cost of gas purchasing from NGN, thus limiting the output of coal-fired units and power-to-gas equipment. From 9:00 until 15:00, the purchased electricity of the IES and the electricity consumption of P2G are reduced in three cases. Because of the high electricity price during this period, the electricity purchasing cost was also high. The electricity generation equipment only supplies a small amount of its electricity to the P2G. From 16:00 to 21:00, the purchased electricity of the IES and the electricity consumption of P2G are reduced in case 3 due to the high carbon emission cost. The purchased electricity of the IES and the electricity consumption of P2G are increased under the three cases between 22:00 and 24:00. Because of the low electricity price during this period, the operator promotes the output of the P2G by increasing the purchased electricity of IES to meet the system’s demand for natural gas. The comprehensive cost of the IES is relatively lower in this way. And the output of TP in case 1 decreases with the reduction of EL, and the P2G works at the rated operation state. The output of TP in case 3 remains the same, which is different from that in case 1 and case 2.

According to the aforementioned analysis, when the carbon emission cost enhances the restriction for the system, the IES operator will reduces the electricity, which generated by the high-carbon emissions unit and increase the purchase of natural gas, which has relatively low-carbon emissions, in order to limit the carbon emissions and compensate for the reduced output of high-carbon emissions unit by increasing the output of the gas-fired units. So, the proposed method is better in reducing carbon emissions and improving the economy of the IES than the other two methods.