Integrated Natural Gas , Heat , and Power Dispatch Considering Wind Power and Power-toGas

A large amount of wind power has to be curtailed due to the inflexibility of the combined heat and power (CHP) system in the heating season in northern China. The power-to-gas (P2G) technology, which uses electricity to produce hydrogen or synthetic natural gas, has become a promising energy conversion option for the utilization of surplus power energy. In this paper, an integrated natural gas, heat, and power dispatch (INGHPD) model which balances natural gas, heat, and power demand considering wind power and a P2G unit, is proposed. A natural gas network and P2G are modeled and integrated into the dispatch model. To demonstrate the effectiveness of the proposed model, an integrated energy system consisting of a six-bus power system, a six-node natural gas system, and a district heating system is simulated. The benefits of P2G are investigated in terms of reducing wind power curtailment, as well as system operation cost and CO2 emissions. The results in the deterministic model show that with the introduction of 40 MW P2G, the wind power curtailment rate decreases from 24.0% to 9.7%. The daily wind power energy consumed by P2G reaches 256 MWh and the daily CO2 emissions reduction reaches 46,080 kg. Additionally, the impact of the power and heat demand on the gas production of P2G and of the P2G capacity on the wind power curtailment are also investigated. P2G tends to generate more natural gas when the power demand is low and the heat demand is high.


Introduction
Wind energy has achieved a great development all over the world in recent years.In China, the gross installed capacity of wind power reached 97 GW by the end of 2014, representing 27% of the global installed capacity.Moreover, eight wind power generation bases have been planned, mainly located in northern China, each of which is planned to have an installed capacity of more than 10 GW by 2020 [1].Combined heat and power (CHP) is a technology which can simultaneously satisfy heat and power requirements with a high efficiency.Compared to the separated generation of heat and power by pure heating and power technologies, the efficiency can improve the performance by 10-40% in CHP units [2].CHP units play an important role in northern China.For example, in the Jilin Province, over 70% of the heat demand is supplied by CHP units [3].However, in the winter, when the heat demand is high and the power demand is low, CHP units have to meet the heat demand and then generate a considerable amount of electricity, leaving little room for wind power integration.This leads to a high wind power curtailment.
The natural gas-fired units (NGFU) and combined heat and power units, due to their high efficiency, low investment cost, operational flexibility, and low environmental pollution in comparison with conventional coal plants, have grown dramatically in the last decade and play an important role in the power system [4].Gas-fired units establish the interdependence of the power system and natural gas system [5,6], while CHP units provide the linkage between the heating system and power system [7].The economy and security of the three different systems would affect each other.For example, the natural gas supply could influence the dispatch and operation of gas-fired power units and CHP units.The operation of CHP units would then affect the heat supply.The rapid development of natural gas-fired plants strengthens the interdependence of gas, heat, and electricity.Thus, it is significant to investigate the operation optimization of the integrated natural gas, heat, and power system considering their operational constraints.
Power-to-gas (P2G) is a technology which uses electricity to produce hydrogen or synthetic natural gas that can be later utilized for re-electrification or heating [8][9][10][11][12].Surplus wind power can be utilized in this method and stored in the natural gas system [13,14].P2G provides the bidirectional energy flow between a power and natural gas system, which can largely increase the efficiency of energy utilization.It provides an important flexibility option for the CHP system in northern China and needs to be further studied.
In this paper, an integrated natural gas, heat, and power dispatch (INGHPD) model which balances the natural gas load, heat load, and power load is proposed, with a consideration of the constraints of the three systems.The benefits of P2G in the integrated energy system are evaluated in terms of reducing the wind power curtailment, system operation cost, and CO 2 emissions.
The main contributions of this paper are illustrated as follows: (1) A novel framework of an integrated energy system considering wind power and P2G is proposed (as depicted in Figure 1), in which a natural gas system, heating system, and power system are included.The INGHPD model, aimed at minimizing the system operation cost, is proposed.(2) A natural gas network is modeled and its system constraints are taken into account in the optimal dispatch model.(3) P2G is integrated into the dispatch model and its benefits in reducing the wind power curtailment, system operation cost, and CO 2 emissions are evaluated.Factors influencing the performance of P2G are also investigated.
This paper is organized as follows: The related work is briefly reviewed in Section 2. The key components of the integrated natural gas, heat, and power system are modeled in Section 3. The INGHPD model considering wind power and P2G is formulated in Section 4. In Section 5, a case study is simulated to demonstrate the effectiveness of the proposed method.Conclusions are drawn in Section 6.

Related Work
The integration of a power system and natural gas system has recently been investigated [15][16][17][18][19].A mixed-integer linear programing security-constrained optimal power and gas flow is formulated in [16].A coordinated stochastic model is proposed in [19] for studying the interdependence of electricity and natural gas transmission networks.In [20], the security-constrained unit commitment is modeled considering natural gas transmission constraints.Reference [21] explores the impact of the electricity demand response in the integrated electricity and natural gas network.Firming the variability of wind power is analyzed in [22], with the consideration of interdependent power and natural gas infrastructures.
However, P2G is not taken into consideration in the aforementioned studies.The impacts of P2G on reducing the operation cost and CO 2 emissions, and relieving electricity and natural gas congestions, are evaluated in [23].Reference [24] analyzes the optimal capacity and spatial distribution of P2G plants in an 85% renewable energy scenario.Reference [25] assesses the potential of P2G with the integration of gas seasonal storage in terms of gas production from renewable energy, as well as its impact on natural gas prices.Reference [26] focuses on a steady-state analysis of the integrated natural gas and power system considering P2G.A unified energy flow formulation is developed to describe the nodal balance and branch flow in both systems.However, the heat supply is not considered and its impact on P2G is not investigated in previous studies.
The combined operation of integrated electricity and heat systems is also investigated in the recent papers.In [27], heat storage tanks and electric boilers are introduced into the CHP system to increase the wind power integration.In [28], the energy storage capability of a district heating network is investigated to improve the overall efficiency of the integrated heat and power system.In [29], the electric heat pump and building thermal inertia are considered to decouple the strong linkage of electric power and heat supplies in the CHP system.
In contrast to the previous work, we jointly optimize the natural gas, heat, and power supplies to promote wind power integration with the consideration of P2G.This work is a beneficial supplement for the previous works.

Structure of Integrated Natural Gas, Heat, and Power System
The structure of an integrated natural gas, heat, and power system is depicted in Figure 1.Natural gas is provided for the CHP units, NGFUs, and residential gas loads.The power load is satisfied by the CHP units, NGFUs, and wind power, while the heat load is satisfied by the CHP units.Surplus power energy can be utilized to produce hydrogen or synthetic natural gas by power-to-gas plants, which is then inputted into the natural gas network.It should be noted that other heat sources such as a gas-fired boiler and heat storage could also be introduced to the system, but they are not the focus of this paper and are not modeled here.The combined operation of integrated electricity and heat systems is also investigated in the recent papers.In [27], heat storage tanks and electric boilers are introduced into the CHP system to increase the wind power integration.In [28], the energy storage capability of a district heating network is investigated to improve the overall efficiency of the integrated heat and power system.In [29], the electric heat pump and building thermal inertia are considered to decouple the strong linkage of electric power and heat supplies in the CHP system.
In contrast to the previous work, we jointly optimize the natural gas, heat, and power supplies to promote wind power integration with the consideration of P2G.This work is a beneficial supplement for the previous works.

Structure of Integrated Natural Gas, Heat, and Power System
The structure of an integrated natural gas, heat, and power system is depicted in Figure 1.Natural gas is provided for the CHP units, NGFUs, and residential gas loads.The power load is satisfied by the CHP units, NGFUs, and wind power, while the heat load is satisfied by the CHP units.Surplus power energy can be utilized to produce hydrogen or synthetic natural gas by power-to-gas plants, which is then inputted into the natural gas network.It should be noted that other heat sources such as a gas-fired boiler and heat storage could also be introduced to the system, but they are not the focus of this paper and are not modeled here.

CHP Unit
A typical feasible operation region [30] of the CHP is shown in Figure 2. The heat and power productions of the CHP are restricted by the boundary curve ABCD.The power and heat production of the CHP unit are constrained by three operational limits: minimum fuel consumption, maximum fuel consumption, and maximum heat extraction [31].The corners of the operating region are called the extreme characteristic points of the CHP unit.The power production, heat production, and gas cost of each point within the feasible operation region can be represented by the convex combination of extreme characteristic points [32].The relationship can be presented by:

CHP Unit
A typical feasible operation region [30] of the CHP is shown in Figure 2. The heat and power productions of the CHP are restricted by the boundary curve ABCD.The power and heat production of the CHP unit are constrained by three operational limits: minimum fuel consumption, maximum fuel consumption, and maximum heat extraction [31].The corners of the operating region are called the extreme characteristic points of the CHP unit.The power production, heat production, and gas cost of each point within the feasible operation region can be represented by the convex combination of extreme characteristic points [32].The relationship can be presented by: It should be noted that the dispatch of one CHP unit may have an impact on the remaining capacity of the heat pipelines and electrical lines, and thus have an influence on the feasible region of other CHP units.In this paper, it is assumed that the capacities of the heat pipelines and electrical lines are large enough and the impact is not considered.
Sustainability 2017, 9, 602 4 of 16 It should be noted that the dispatch of one CHP unit may have an impact on the remaining capacity of the heat pipelines and electrical lines, and thus have an influence on the feasible region of other CHP units.In this paper, it is assumed that the capacities of the heat pipelines and electrical lines are large enough and the impact is not considered.

Natural Gas Network
The main components of a natural gas system include natural gas wells, transmission pipelines, and natural gas loads.In this paper, the model of a natural gas system is presented by using the steady-state mathematical model.
Natural gas supply: In general, natural gas suppliers are gas wells, which are seen as positive gas injections at related nodes.The gas supplies are restricted by their upper and lower limits: Natural gas loads: The gas loads are seen as negative injections at related nodes.Natural gas loads can be classified into residential, commercial, and industrial loads.Natural gas-fired units are the industrial load.The gas loads are restricted by their upper and lower limits: Pipelines: The pipelines are used to transmit natural gas from the gas wells to gas customers.The pipelines can be classified into active pipelines and passive pipelines.The active pipelines are comprised of compressors, which are equipped to increase the gas pressure of the pipelines and thus

Natural Gas Network
The main components of a natural gas system include natural gas wells, transmission pipelines, and natural gas loads.In this paper, the model of a natural gas system is presented by using the steady-state mathematical model.
Natural gas supply: In general, natural gas suppliers are gas wells, which are seen as positive gas injections at related nodes.The gas supplies are restricted by their upper and lower limits: Natural gas loads: The gas loads are seen as negative injections at related nodes.Natural gas loads can be classified into residential, commercial, and industrial loads.Natural gas-fired units are the industrial load.The gas loads are restricted by their upper and lower limits: Pipelines: The pipelines are used to transmit natural gas from the gas wells to gas customers.The pipelines can be classified into active pipelines and passive pipelines.The active pipelines are comprised of compressors, which are equipped to increase the gas pressure of the pipelines and thus increase the transmission capacity.In this paper, we only consider the passive pipelines.The natural gas flow in the pipelines can be modeled by the Weymouth equation [33]: where C mn is the pipeline constant which depends on the temperature, length, friction, diameter, and natural gas compositions.The function of sgn(π m ,π n ) represents the direction of the gas flow through the pipeline.When the pressure of node m is higher than node n, it is equal to one; otherwise, it is −1.
The pressure of each node should be maintained within a certain interval, as depicted in (5).
Then, in the optimization model, the pressure variable of each node can be defined by p m = π 2 m , which could eliminate the nonlinearity on the right side of the equation.Moreover, the quadratic term on the left side of Equation ( 6) can be piecewise-linearly approximated, as shown in (7).
Natural gas flow conservation: With respect to node m, the gas injected into the node should be equal to the gas extracted from the node.Thus, natural gas flow conservation can be depicted as: The first term represents the gas supply from the gas suppliers to node m.The second term represents the gas load at node m.The third term represents the gas flow rate in the pipelines which are connected with node m.

Power to Gas
The power-to-gas technology utilizes surplus power energy from renewable energy to produce hydrogen by the process of electrolysis.The produced hydrogen can be injected into the natural gas network or further converted to synthetic natural gas by additional methanation combined with carbon dioxide.However, the amount of hydrogen injected into the natural gas system should be limited, since blending hydrogen into the natural gas network will reduce the energy density of the gas and have a bad effect on the pipeline material.In the UK, the maximal level of hydrogen in the natural gas network is currently limited to 0.1% (by volume) [25].Therefore, in this paper, we assume that all of the produced hydrogen is converted to natural gas.The conversion from power to natural gas production has a 60-65% efficiency [35].
In this paper, a power-to-gas plant is modeled to covert the power to natural gas with a certain efficiency [36], as demonstrated in (9).The volumetric quantity of natural gas can be converted by Equation (10).The P2G power is restricted by its installed power capacity, as shown in (11).The incremental power consumption of P2G is restricted by its maximum ramping rate, as depicted in (12).
3.5.Natural Gas-Fired Unit NGFUs consume gas to generate power according to the flexible gas contracts and can be regarded as gas loads in the natural gas network.The power production derived from natural gas consumption is modeled in (13).Then, the natural gas consumption cost can be represented as (14).

Formulation of INGHPD Model
In this section, the INGHPD model is formulated considering wind power and P2G, which seeks the optimal dispatch of natural gas, power, and heat sources, while satisfying the physical and security constraints of the natural gas, heat, and power system.It is assumed that the power units remain on during the scheduling horizon.

Objective Function
The objective of the dispatch model is to minimize NGFUs, the operating cost of the CHP units, and the revenue of the natural gas produced by P2G over the scheduling horizon, which can be expressed as:

Constraints
(1) Power balance constraints: The power demand is satisfied by NGFUs, CHP units, and wind power.
(2) Heat balance constraints: The heat demand is satisfied by the CHP units only.
(3) Power output constraints of NGFUs: The power outputs of the NGFUs are constrained by their technical limits.
(4) Ramping rate constraints of NGFUs and CHP units: The incremental power outputs of the power generation units are restricted by their maximum ramping rates.
(5) Power output constraints of wind farms: The integrated wind power should not exceed its forecasted wind power.0 ≤ p w i,t ≤ p fore i,t i ∈ Ω WP (20) (6) Spinning reserve constraints: A certain level of spinning reserve capacity is required to deal with the system contingencies.∑ The other constraints are expressed in ( 1)-( 14).

Robust Optimization Model
When uncertainty is taken into consideration, the optimization model can be formulated by using stochastic optimization, interval optimization, or robust optimization.In this paper, a robust optimization model is formulated to verify the feasibility of the proposed method when the uncertainties of wind power, power demand, and heat demand are considered.The objective of the robust optimization model is to minimize the worst-case total cost.The objective function can be formulated as: where u represents the decision variables, ∼ p w , ∼ p Load , ∼ q Load are the uncertain parameter vectors that represent the available wind power, power demand, and heat demand, respectively.
The uncertainty sets define the range of the uncertain wind power, power demand, and heat demand: The constraints in the robust optimization model are the same as those in the deterministic model, expect that the certain parameters are substituted by the uncertain parameters.

System Description
The six-bus power system [28,30], as shown in Figure 3, consists of a CHP unit, two NGFUs, a P2G plant, and a wind farm.All of the three generation units are gas-fired units.The natural gas price is 30 $/MWh [23].
The six-node natural gas system, as depicted in Figure 4, includes two gas wells, five pipelines, and six gas loads.NGFU1, NGFU2, and the CHP unit are connected to node 1, 2, and 3, respectively.
The main parameters of the power generation units are listed in Table 1 and the feasible operation region of the CHP unit is shown in Figure 5.The other three gas loads (L4, L5, L6) are fixed residential gas loads.The detailed parameters of the power and natural gas networks can be found in [21].The difference is the parameters of the natural gas supplier and residential gas load, and they are listed in Table 2.A 40 MW P2G plant is connected to node 5.The efficiency of P2G is set to 65% for natural gas production.
The profiles of power, heat demand, and forecasted wind power are shown in Figure 6.The heat demand can be increased or decreased by 10% of the original heat load.The district heating control of individual heat consumption is not considered in this paper.The simulations are considered for the hourly generation dispatch over 24 h.All of the simulations were implemented in MATLAB R2013a and solved by Gurobi 6.5 on a computer with two Inter Core i5 CPU (2.5 GHz) and 4.0 GB RAM.

System Description
The six-bus power system [28,30], as shown in Figure 3, consists of a CHP unit, two NGFUs, a P2G plant, and a wind farm.All of the three generation units are gas-fired units.The natural gas price is 30 $/MWh [23].
The six-node natural gas system, as depicted in Figure 4, includes two gas wells, five pipelines, and six gas loads.NGFU1, NGFU2, and the CHP unit are connected to node 1, 2, and 3, respectively.The main parameters of the power generation units are listed in Table 1 and the feasible operation region of the CHP unit is shown in Figure 5.The other three gas loads (L4, L5, L6) are fixed residential gas loads.The detailed parameters of the power and natural gas networks can be found in [21].The difference is the parameters of the natural gas supplier and residential gas load, and they are listed in Table 2.A 40 MW P2G plant is connected to node 5.The efficiency of P2G is set to 65% for natural gas production.
The profiles of power, heat demand, and forecasted wind power are shown in Figure 6.The heat demand can be increased or decreased by 10% of the original heat load.The district heating control of individual heat consumption is not considered in this paper.The simulations are considered for the hourly generation dispatch over 24 h.All of the simulations were implemented in MATLAB R2013a and solved by Gurobi 6.5 on a computer with two Inter Core i5 CPU (2.5 GHz) and 4.0 GB RAM.Table 2. Parameters of the natural gas supplier and residential gas load.

Scenarios
To demonstrate the feasibility and effectiveness of the proposed model, three scenarios are presented: Scenario 1: Dispatch model is formulated without considering the natural gas system constraints and P2G.
Scenario 2: Dispatch model is formulated considering the natural gas system constraints, but the P2G process is not integrated.Scenario 3: Both the natural gas system constraints and P2G process are integrated to the dispatch model.

Necessity of Considering Natural Gas System Constraints
The hourly power dispatch results of the CHP unit and NGFU1 in Scenario 1 and Scenario 2 are shown in Figure 7.It can be observed that the power outputs of the CHP unit in the first eight hours are the same in the two scenarios, but at other times, the power outputs in Scenario 2 are less than those in Scenario 1.However, for NGFU1, the results are the opposite and the outputs increase, even in the off-peak hour (at 6:00).The power outputs of NGFU2 have not changed, but the wind power curtailment rate increases from 23.1% to 24.0%.The reason for this lies in the power outputs of the CHP unit between 9:00 and 24:00 in Scenario 2, which are restricted by natural gas transmission and supply constraints.This part of the power is substituted by NGFU1, which has a wider natural gas transmission and supply margin.Additionally, the increased power outputs of NGFU1 hinder part of the wind power integration.
The daily operation costs in these two scenarios are $351,360 and $352,730, respectively.The reason for this lies in the fact that NGFU1 is more frequently dispatched in Scenario 2, but it costs more compared with the CHP unit.The substituted power production by NGFU1 increases the total fuel cost.
Thus, it can be concluded that the natural gas system constraints influence the operation results and must be taken into account in the dispatch model.The daily operation costs in these two scenarios are $351,360 and $352,730, respectively.The reason for this lies in the fact that NGFU1 is more frequently dispatched in Scenario 2, but it costs more compared with the CHP unit.The substituted power production by NGFU1 increases the total fuel cost.
Thus, it can be concluded that the natural gas system constraints influence the operation results and must be taken into account in the dispatch model.

Effect of P2G on Wind Power Curtailment, Fuel Cost, and CO 2 Emission
The power dispatch results of the wind power and P2G in Scenario 2 and 3 are depicted in Figure 8.It can be seen that in Scenario 2, the wind power is largely curtailed during the periods when the power demand is low and the heat demand is high.In Scenario 3, the integration of P2G largely promotes the wind power accommodation, decreasing the curtailment rate of the wind power from 24.0% to 9.7%.The reason for this is that the P2G utilizes the surplus wind power to produce natural gas, creating an extra margin for wind accommodation in the off-peak hours.
A comparison of the dispatch results in these two scenarios is summarized in Table 3.It can be observed that the operation cost of the integrated energy system decreases from Scenario 2 to 3. The P2G plant utilizes the free wind power to produce natural gas which can be used later for re-electrification, thereby decreasing the total fuel cost.The daily wind power energy consumed by P2G reaches 256 MWh.Moreover, according to [23], the CO 2 emission reduction factor is 180 kg/MWh.Thus, the daily CO 2 emission reduction reaches 46,080 kg.
Therefore, it can be indicated that the introduction of P2G will promote wind power integration, and reduce the fuel cost and CO 2 emissions of the integrated energy system.The power dispatch results of the wind power and P2G in Scenario 2 and 3 are depicted in Figure 8.It can be seen that in Scenario 2, the wind power is largely curtailed during the periods when the power demand is low and the heat demand is high.In Scenario 3, the integration of P2G largely promotes the wind power accommodation, decreasing the curtailment rate of the wind power from 24.0% to 9.7%.The reason for this is that the P2G utilizes the surplus wind power to produce natural gas, creating an extra margin for wind accommodation in the off-peak hours.A comparison of the dispatch results in these two scenarios is summarized in Table 3.It can be observed that the operation cost of the integrated energy system decreases from Scenario 2 to 3. The P2G plant utilizes the free wind power to produce natural gas which can be used later for re-electrification, thereby decreasing the total fuel cost.The daily wind power energy consumed by P2G reaches 256 MWh.Moreover, according to [23], the CO2 emission reduction factor is 180 kg/MWh.Thus, the daily CO2 emission reduction reaches 46,080 kg.
Therefore, it can be indicated that the introduction of P2G will promote wind power integration, and reduce the fuel cost and CO2 emissions of the integrated energy system.In order to explore the impact of power and heat demand on P2G, the natural gas production of P2G under different power and heat demand levels is investigated.As shown in Figure 9, P2G tends to generate more natural gas when the power demand is lower and the heat demand is higher.It can be attributed to the energy storage capability of P2G: when the heat demand is high and the power demand is low, the heat and power production of the CHP units are deeply coupled.This leads to a high wind energy curtailment.By means of P2G, the surplus wind power will be utilized to produce gas fuel that can be stored in the existing natural gas networks and then be injected back into the

Impact of Power and Heat Demand on P2G
In order to explore the impact of power and heat demand on P2G, the natural gas production of P2G under different power and heat demand levels is investigated.As shown in Figure 9, P2G tends to generate more natural gas when the power demand is lower and the heat demand is higher.It can be attributed to the energy storage capability of P2G: when the heat demand is high and the power demand is low, the heat and power production of the CHP units are deeply coupled.This leads to a high wind energy curtailment.By means of P2G, the surplus wind power will be utilized to produce gas fuel that can be stored in the existing natural gas networks and then be injected back into the power system through gas-fired generators.Thus, it can be indicated that P2G has the potential to increase the flexibility of the integrated energy system.Sustainability 2017, 9, 602 12 of 16 power system through gas-fired generators.Thus, it can be indicated that P2G has the potential to increase the flexibility of the integrated energy system.

Impact of P2G Capacity on Wind Power Integration
The impact of different P2G capacities on wind power integration is investigated in Scenario 3. P2G capacities varying from 0 MW to 70 MW are integrated to the integrated energy system to accommodate the otherwise curtailed wind power.The effects of P2G in reducing the wind curtailment rate are investigated at three different heat demand levels: 90%, 95%, and 100% of the original heat demand.As shown in Figure 10, the wind curtailment rate declines with the increasing capacity of P2G, independent of the heat demand level.However, there exhibits a declining marginal effect of increased P2G capacity on reducing wind power curtailments.The reason for this

Impact of P2G Capacity on Wind Power Integration
The impact of different P2G capacities on wind power integration is investigated in Scenario 3. P2G capacities varying from 0 MW to 70 MW are integrated to the integrated energy system to accommodate the otherwise curtailed wind power.The effects of P2G in reducing the wind curtailment rate are investigated at three different heat demand levels: 90%, 95%, and 100% of the original heat demand.As shown in Figure 10, the wind curtailment rate declines with the increasing capacity of P2G, independent of the heat demand level.However, there exhibits a declining marginal effect of increased P2G capacity on reducing wind power curtailments.The reason for this lies in the fact that when the P2G capacity increases, the available free wind power is nearly used up, resulting in a declining benefit.The impact of different P2G capacities on wind power integration is investigated in Scenario 3. P2G capacities varying from 0 MW to 70 MW are integrated to the integrated energy system to accommodate the otherwise curtailed wind power.The effects of P2G in reducing the wind curtailment rate are investigated at three different heat demand levels: 90%, 95%, and 100% of the original heat demand.As shown in Figure 10, the wind curtailment rate declines with the increasing capacity of P2G, independent of the heat demand level.However, there exhibits a declining marginal effect of increased P2G capacity on reducing wind power curtailments.The reason for this lies in the fact that when the P2G capacity increases, the available free wind power is nearly used up, resulting in a declining benefit.

Robust Optimization Result
In this section, the uncertainties of the wind power, power demand, and heat demand are considered.For simplicity, the maximum downward/upward deviation levels from the forecasted values are set to ±5%, ±2%, and ±2% for wind power, power demand, and heat demand, respectively.The robust optimization result is shown in Table 4.

Robust Optimization Result
In this section, the uncertainties of the wind power, power demand, and heat demand are considered.For simplicity, the maximum downward/upward deviation levels from the forecasted values are set to ±5%, ±2%, and ±2% for wind power, power demand, and heat demand, respectively.The robust optimization result is shown in Table 4. Compared to the deterministic result, the fuel cost increases while the wind power consumed by P2G decreases, which is attributed to the uncertainties of the wind power, power demand, and heat demand.However, the fuel cost in Scenario 3 is still less than that in Scenario 2. This result reveals the feasibility of the proposed method when the uncertainties are considered.

Conclusions
In this paper, an INGHPD model that balances natural gas, heat, and power demands with energy sources including a CHP unit, NGFUs, wind power, and P2G unit is proposed.The natural gas system constraints are introduced to the dispatch model and the results show that the security constraints of the natural gas system influence the dispatch results and should be taken into account in the operation optimization.
P2G is used as a power load to consume surplus wind power and convert electricity to natural gas for a later use.The effects of P2G in the integrated natural gas, heat, and power system are investigated and the results show that P2G could largely promote wind power accommodation, as well as reduce the fuel cost and CO 2 emissions.With the introduction of 40 MW P2G in the deterministic model, the wind power curtailment rate decreases from 24.0% to 9.7%.The daily wind power energy consumed by P2G reaches 256 MWh.Moreover, the daily fuel cost and CO 2 emissions reduction reach 516$ and 46,080 kg in integrated energy system, respectively.In addition, the impact of the power and heat demand on the output of P2G and the impact of P2G capacity on the wind power curtailment are also investigated.P2G tends to generate more natural gas when the power demand is low and the heat demand is high.With the increase of P2G capacity, the wind curtailment rate declines, but exhibits a declining marginal effect.
Based on the proposed INGHPD model, many interesting issues could be further investigated.For instance, P2G facility can be used to relieve the power transmission limitations by consuming the power at certain nodes and transforming the energy by the natural gas system.Additionally, P2G can be utilized to produce natural gas at vulnerable nodes in the natural gas system, which could reduce the natural gas congestions.Utilizing the produced natural gas to directly generate heat and help decouple the heat and power production of CHP will also be analyzed in our future work.

Figure 1 .
Figure 1.Structure of an integrated natural gas, heat, and power system.

Figure 1 .
Figure 1.Structure of an integrated natural gas, heat, and power system.

Figure 2 .
Figure 2. Feasible operation region of a typical CHP unit.

Figure 2 .
Figure 2. Feasible operation region of a typical CHP unit.

( 7 )
Power transmission constraints: Transmission flow should not exceed the transmission capacity.

Figure 5 .
Figure 5. Feasible operation region of the CHP unit.

Figure 5 .
Figure 5. Feasible operation region of the CHP unit.

Figure 5 .
Figure 5. Feasible operation region of the CHP unit.

Figure 5 .
Figure 5. Feasible operation region of the CHP unit.

Figure 6 .
Figure 6.Profiles of power, heat demand, and forecasted wind power.

Figure 6 .
Figure 6.Profiles of power, heat demand, and forecasted wind power.

Figure 7 .
Figure 7. Power dispatch results of (a) the CHP unit and (b) NGFU1.Figure 7. Power dispatch results of (a) the CHP unit and (b) NGFU1.

Figure 7 .
Figure 7. Power dispatch results of (a) the CHP unit and (b) NGFU1.Figure 7. Power dispatch results of (a) the CHP unit and (b) NGFU1.

Figure 8 .
Figure 8. Power dispatch results of the wind power and P2G in (a) Scenario 2 and (b) Scenario 3.

Figure 8 .
Figure 8. Power dispatch results of the wind power and P2G in (a) Scenario 2 and (b) Scenario 3.

Figure 9 .
Figure 9. Impact of the power and heat demand on the gas production of P2G.

Figure 9 .
Figure 9. Impact of the power and heat demand on the gas production of P2G.

Figure 9 .
Figure 9. Impact of the power and heat demand on the gas production of P2G.

Table 1 .
Main parameters of the power generation units.

Table 2 .
Parameters of the natural gas supplier and residential gas load.

Table 1 .
Main parameters of the power generation units.

Table 3 .
Comparison of the dispatch results under different scenarios.

Table 3 .
Comparison of the dispatch results under different scenarios.

Table 4 .
Comparison of robust dispatch results under different scenarios.

Table 4 .
Comparison of robust dispatch results under different scenarios.