Optimal Low-Carbon Economic Environmental Dispatch of Hybrid Electricity-Natural Gas Energy Systems Considering P2G

Abstract

Power to gas facilities (P2G) could absorb excess renewable energy that would otherwise be curtailed due to electricity network constraints by converting it to methane (synthetic natural gas). The produced synthetic natural gas can power gas turbines and realize bidirectional energy flow between power and natural-gas systems. P2G, therefore, has significant potential for unlocking inherent flexibility in the integrated system, but also poses new challenges of increased system complexity. A coordinated operation strategy that manages power and natural-gas network constraints together is essential to address such challenges. In this paper, a novel low-carbon economic environmental dispatch strategy is presented considering all the constraints in both systems. The multi-objective black-hole particle swarm optimization algorithm (MOBHPSO) is adopted. In addition to P2G, a gas demand management strategy is proposed to support gas flow balance. A new solving approach that combines the effective redundancy method, trust region method, and Levenberg-Marquardt method is proposed to address the complex coupled constraints. Case studies that use an integrated IEEE 39-bus power and Belgian high-calorific 20-node gas system demonstrate the effectiveness and scalability of the proposed model and optimization method. The analysis of dispatch results illustrates the benefit of P2G for the wind power accommodation, and low-carbon, economic, and environmental improvement of integrated system operation.

1. Introduction

With further acceleration of the low-carbon energy process, as well as the energy crisis, environmental pollution, and other issues, the capacity of renewable energy sources has increased continuously. Due to the intermittency and uncertainty of wind power as well as the lack of peak load regulation of power system, it is likely that more and more wind power generation will have to be curtailed in order to maintain the power system reliability [1]. To solve this problem, much research is carried out to explore practical means to reduce the curtailment of wind power generation. The growing interdependence of the power system and natural-gas system and the development of power to gas technologies [2,3,4,5,6,7,8] creates operational interactions between the power system and natural-gas system, which could obtain additional benefits for both systems, including reducing the curtailed wind power generation. On the one hand, the power system tends to require more flexible power energy from the natural-gas system to shift peak load compared with the gas-fired units [3], which is conductive to the accommodation of wind power. On the other hand, the natural-gas system absorbs methane or hydrogen produced by P2G to guarantee the continuity of gas supply and the wind power energy will be stored and transported in the existing natural-gas system for generating low-carbon electricity or heat later [9,10,11], which uses the curtailed wind power directly. Therefore, the integrated electricity-natural gas energy systems with P2G have become one of the effective forms to reduce the curtailment of wind power generation.

The diagram of integrated electricity-natural gas energy systems with P2G is shown in Figure 1. It can be seen that the power system and the natural-gas system exchange the energy between P2G and gas-fired units. When the curtailed wind power is converted to hydrogen or methane through power to hydrogen facilities (P2H) or power to methane facilities (P2M), P2G which includes P2H and P2M is the load of power system and the gas source of natural-gas system. Meanwhile, the gas-fired units are the load of natural-gas system and the generators of power system. Obviously, operation parameters of P2G, power system and natural-gas system are interrelated and interactive which can affect the operation cost, CO₂ emissions, reliability, and stability of both systems. Therefore, how to deal with the interactive relationship between power system and natural-gas system and how to achieve coordinated optimal operation with economic environmental benefits are the key issues for the integrated power system and natural-gas system.

For the integrated electricity-natural gas energy systems, the initial research is focused on optimal power flow [12,13,14,15], unit commitment [16], optimal dispatch [17,18,19], steady-state analysis [20], and system planning [21]. For the calculation of optimal power flow, the total operation cost is usually considered as optimal objective and the dual interior point method [12], the Monte Carlo method [13] and the point estimation method [14] are adopted frequently. Some studies introduce an energy hub to deal with the translation of different energies in the hybrid electricity-natural gas energy systems [13,17]. For the optimization of system operation, the operation of power system and the operation of natural-gas system are mostly optimized separately using the deterministic optimization methods or stochastic optimization methods [18]. For the steady-state analysis of the hybrid electricity-natural gas energy systems, based on the steady-state analysis of power system, the analysis model of natural-gas system is realized by analogy analysis between power system and natural-gas system, and then the comprehensive steady-state analysis model of hybrid electricity-natural gas energy systems is given [20]. For the optimal system planning, a chance constrained programing approach is presented to minimize the investment cost of the integrated energy systems [21]. In these studies, P2G is not considered. As the coupling operation link of the power system and natural-gas system, P2G plays a more and more important role in wind power accommodation with broad prospects and potential for energy development [22,23,24]. Therefore, it is necessary to carry out the research on optimal operation of integrated electricity-natural gas energy systems considering P2G. The early studies on P2G are mainly focused on technology implementation and security application [6,25,26,27,28]. Recently, although some achievements about optimal operation of integrated electricity-natural gas energy systems considering P2G have been achieved [6,7,8,24,29,30,31,32,33,34,35,36,37,38], it still seems to be in the exploratory stage from the following aspects.

(1) Optimal objectives: The minimum total operation cost is mostly adopted [6,24,29,30,31,32,37]. In only a few studies, the maximum wind power accommodation [33], the minimum energy purchase cost [34], or net power demand smoothness [38] is also considered as the objective. However, environmental benefit is rarely considered. As we know, the low-carbon and emission reduction requirements become more and more important. Therefore, it is necessary to take environmental benefit into consideration.

(2) Optimal models: The operation model of power system and operation model of natural-gas system are mainly established separately based on the two-level optimal power flow structure [6,30,31,32]. It seems that rare consideration is given to coordinated optimization between the two energy systems.

(3) Optimal algorithms: Generally, the traditional algorithms are adopted in most studies, such as the mix-integer linear programming method [3,24], mixed-integer quadratic programming method [37], and interior point method [35]. However, the intelligent optimization algorithms with high global search ability and fast convergence speed are rarely used.

(4) Constraints handling methods: The constraints handling methods affect the operation results directly. Few articles give full details about the constraints handling methods, especially for the complicated dynamic nodal balance constraint and volume limits of gas storage in the natural-gas system.

On the above premises, this paper establishes the optimal operation model of the hybrid electricity-natural gas energy systems considering operation cost, natural-gas cost reduction due to P2G, CO₂ emissions, and SO_x emissions to achieve low-carbon, economic, and environmental benefits. The multi-objective black-hole particle swarm optimization algorithm (MOBHPSO) [39,40,41,42] is adopted. The power flow is calculated using the Newton-Raphson method. The non-linear gas flow equations are solved by the trust region method [43,44] and Levenberg-Marquardt (L-M) method [45,46], respectively. The gas demand management strategy is proposed to balance the gas flow. Moreover, the detailed handling methods of inequality constraints in natural-gas system are also given in this paper. Several case studies are carried out on a hybrid IEEE 39-bus power system and Belgian high-calorific 20-node gas system in a period of 24 h to investigate the low-carbon, economic and environmental benefits of P2G in terms of cost reduction ($6.165 × 10⁵), rate decline of wind curtailment (from 24.85% to 4.04%), CO₂ emissions reduction (3630 tons), and SO_x emissions reduction (0.254 ton).

2. Problem Formulation

The optimal low-carbon economic environmental dispatch problem of hybrid electricity-natural gas energy systems with P2G is a complicated non-convex, coupled, non-linear, multi-objective, and multi-constraint optimization problem. It contains three parts: The first one is the optimization of power system; the second one is the optimization of natural-gas system; and the last one is the coordination of the hybrid electricity-natural gas energy systems. The flow chart of this optimization problem is shown in Figure 2. Each part of the flow chart will be described in detail.

2.1. Optimal Economic Environmental Dispatch of Power System

2.1.1. Objectives

(1) Minimum Fuel Cost of the Power System

$$\begin{array}{cc}\mathrm{Min}& F_p={\displaystyle \sum _{i=1}^{N_G}{\displaystyle \sum _{t=1}^T{a}_i{P}_{Gi}^{}{(t)}^2+b_i{P}_{Gi}(t)+c_i}}\end{array}$$

(1)

(2) Minimum SO_x Pollutant Emissions of the Power System

$$\begin{array}{cc}\mathrm{Min}& E_{S{O}_x}={\displaystyle \sum _{i=1}^{N_G}{\displaystyle \sum _{t=1}^T({\alpha }_i+{\beta }_i{P}_{Gi}(t)+{\gamma }_i{P}_{Gi}{(t)}^2+{\delta }_i{e}^{{\lambda }_i{P}_{Gi}(t)})}}\end{array}$$

(2)

(3) Minimum Load Loss Rate of the Power System

$$\begin{array}{cc}\mathrm{Min}& L_p=\frac{{\displaystyle \sum _{t=1}^T\left[P_L(t)+{\displaystyle \sum _{k=1}^{N_{P2G}}{P}_{P2G,k}(t)}-{\displaystyle \sum _{i=1}^{N_{\mathrm{G}}}{P}_{\mathrm{G}i}(t)}\right]}}{{\displaystyle \sum _{t=1}^T{P}_L(t)}}\end{array}$$

(3)

where F_p is the fuel cost of power system; N_G is the number of power generations; T is the number of time periods; P_Gi (t) is the power generation output at time t; a_i, b_i, c_i are coefficient of the fuel cost; E_SOx is the pollutant emission of SO_x; α_i, β_i, γ_i, δ_i, λ_i are coefficient of the pollutant emission; L_p is the load loss rate presenting the reliability of power supply; N_P2G is the number of P2G; P_L(t) is the power load at time t; P_P2G (t) is the power supplied to the P2G facilities at time t.

The power output of gas-fired units is calculated by the product of the gas flow injected to the gas-fired units Q_GT(t), higher heating value of natural gas HHV_g and the energy conversion efficiency η_GT(t). In this paper, the last objective is converted into a constraint by being less than a given value ε.

2.1.2. Constraints

(1)

Power Output Limits

$$P_{\mathrm{G}i}^{\min }\le P_{\mathrm{G}i}(t)\le P_{Gi}^{\max }$$

(4)

where $P_{Gi}^{\min }$ and $P_{Gi}^{\max }$ represent the minimum power output and maximum power output of unit i, respectively.

(2)

Ramp Rate Limits

$$\{\begin{array}{l}{P}_{Gi}(t)\ge \max \left\{P_{Gi}^{\min },P_{Gi}(t-1)-\Delta P_{Gi}^{down}\right\},\begin{array}{cc}& \end{array}{P}_{Gi}(t)\le P_{Gi}(t-1)\\ P_{Gi}(t)\le \min \left\{P_{Gi}^{\max },P_{Gi}(t-1)+\Delta P_{Gi}^{up}\right\},\begin{array}{cc}& \end{array}{P}_{Gi}(t)\ge P_{Gi}(t-1)\end{array}$$

(5)

where $\mathsf{\Delta }{P}_{Gi}^{up}$ and $\mathsf{\Delta }{P}_{Gi}^{down}$ represent the ramp up rate and the ramp down rate of unit i, respectively.

(3)

Line Capacity Limit

$$S_l(t)\le S_l^{\max }$$

(6)

where $S_l^{\max }$ is the maximum capacity of line l.

2.2. Optimal Low-Carbon Economic Dispatch of Natural-Gas System Considering P2G

2.2.1. Objectives

(1) Minimum the Operational Cost of Natural-Gas System

$$\begin{array}{cc}\mathrm{Min}& C_{well}+C_{gs}+C_{P2G}-S_{P2G}\end{array}$$

(7)

$$C_{well}={\displaystyle \sum _{n=1}^{N_w}{\displaystyle \sum _{t=1}^T{Q}_{wn}^{}(t)u_{wn}(t)}}$$

(8)

$$C_{gs}={\displaystyle \sum _{m=1}^{N_{gs}}{\displaystyle \sum _{t=1}^T{Q}_{gs,m}(t)u_{gs,m}(t)}}$$

(9)

$$C_{P2G}={\displaystyle \sum _{k=1}^{N_{P2G}}{\displaystyle \sum _{t=1}^T{P}_{P2G,k}(t)}}{u}_{P2G,k}$$

(10)

$$S_{P2G}={\displaystyle \sum _{k=1}^{N_{P2G}}{\displaystyle \sum _{t=1}^T{Q}_{P2G,k}(t)}}{u}_{ave}(t)$$

(11)

where C_well, C_gs, and C_P2G represent the operation cost of gas wells, the operation cost of gas storage, and the operation cost of P2G, respectively. S_P2G is the saved natural-gas cost due to the P2G. N_w, N_gs represent the number of gas wells and the number of gas storage, respectively; Q_wn(t) is the gas flow of gas well n; u_wn(t) is the gas price of gas well n at time t; Q_gs,m(t) is the gas flow of gas storage m at time t (It is positive for inflow and negative for outflow); u_gs,m(t) is the storage price for gas storage m at time t; u_P2G,k is the operation cost of P2G k; Q_P2G,k(t) is the gas flow of P2G k at time t; u_ave(t) is the average gas price (In this paper, it is the average price of gas wells).

(2) Minimum CO₂ Emissions of the Natural-Gas System

$$\begin{array}{cc}\mathrm{Min}& E_{C{O}_2}={\displaystyle \sum _{n=1}^{N_w}{\displaystyle \sum _{t=1}^T{E}_{wn}^{}(t)}}+{\displaystyle \sum _{m=1}^{N_{gs}}{\displaystyle \sum _{t=1}^T{E}_{gs,m}^{}(t)}-}{\displaystyle \sum _{k=1}^{N_{\mathrm{P}2\mathrm{G}}}{\displaystyle \sum _{t=1}^T{E}_{P2G,k}^{}(t)}}\end{array}$$

(12)

where E_CO2 represents CO₂ emissions of the natural-gas system; E_wn(t), E_gs,m(t) are the CO₂ emissions of gas well n, gas storage m at time t, respectively; E_P2G,k(t) is the amount of CO₂ absorbed by the methanation process of P2G k at time t.

2.2.2. Constraints

(1) Gas Flow Limits of Gas Wells

$$Q_{wn}^{\min }\le Q_{wn}(t)\le Q_{wn}^{\max }$$

(13)

where $Q_{wn}^{\min }$, $Q_{wn}^{\max }$ represent the minimum gas flow and the maximum gas flow of gas well n, respectively.

(2) Gas Pressure Limits of Gas Nodes

$$M_i^{\min }\le M_i(t)\le M_i^{\max }$$

(14)

where M_i(t) represents gas pressure of gas node i at time t. $M_i^{\min }$ and $M_i^{\max }$ are the minimum and maximum gas pressure of gas node i.

(3) Gas Flow Equation of Pipelines

The natural-gas system satisfies the mass conservation law of fluid dynamics and Bernoulli equation in the operation. The relationship between gas flow of pipelines and gas pressure of gas nodes can be modeled as follows [12,35].

$$Q_{ij}(t)\left|Q_{ij}(t)\right|=C_{ij}\left(M_i{(t)}^2-M_j{(t)}^2\right)$$

(15)

$$Q_{ij}(t)=\frac{Q_{ij}^{in}(t)+Q_{ij}^{out}(t)}{2}$$

(16)

where Q_ij(t) is the average gas flow of pipeline ij (Pipeline ij is the pipeline between gas node i and gas node j); $Q_{ij}^{in}$(t) and $Q_{ij}^{out}$(t) are the injection and withdrawal gas flow of pipeline ij, respectively; C_ij is a constant related to the length, diameter, temperature and compressibility factor of pipeline ij.

(4) Line Pack Equation

Due to the compressibility of natural gas, the injection gas flow and the withdrawal gas flow of the same pipeline would be different. Some excess natural gas can be stored in the pipelines, which is called line pack. The line pack of pipeline ij is related to the average pressure and its own parameters of pipelines, which can be modeled as below [12,15].

$$L_{ij}(t)={\omega }_{ij}{M}_{ij}(t)$$

(17)

$$M_{ij}(t)=\frac{M_i(t)+M_j(t)}{2}$$

(18)

$$L_{ij}(t)=L_{ij}(t-1)+Q_{ij}^{in}(t)-Q_{ij}^{out}(t)$$

(19)

where L_ij(t) is the line pack of pipeline ij at time t; ω_ij is a constant related to pipeline parameters, gas constant, compressibility factor, gas density, and gas temperature.

(5) Nodal Gas Flow Balance Equation

For each gas node, the gas flows into the node must equals the gas flows out of the node.

$$\begin{array}{l}{\displaystyle \sum _{n\in i}{Q}_{wn}(t)}+{\displaystyle \sum _{m\in i}{Q}_{gs,m}^{}(t)}+{\displaystyle \sum _{k\in i}{Q}_{P2G,k}(t)}-{\displaystyle \sum _{j\in Set\_I(i)}{Q}_{ij}^{in}(t)}\\ +{\displaystyle \sum _{j\in Set\_O(i)}{Q}_{ij}^{out}(t)}-Q_{GT,i}(t)-Q_{Li}(t)=0\end{array}$$

(20)

where, the first three items are the gas flow of gas wells, gas storage, and P2G located at gas node i at time t, respectively; Q_GT,i(t) and Q_Li(t) indicate the gas flow injected to gas-fired units and the gas load at gas node i at time t, respectively; Set_I(i) is the set of pipeline ij which lets gas node i as the input node; Set_O(i) is the set of pipeline ij which lets gas node i as the output node.

(6) Gas Flow Limits and Capacity Limits of Gas Storage

$$Q_{gs,m}^{\min }\le Q_{gs,m}^{}(t)\le Q_{gs,m}^{\max }$$

(21)

$$V_m^{\min }\le V_m(t)\le V_m^{\max }$$

(22)

$$V_m(t)=V_m(t-1)+Q_{gs,m}^{}(t)$$

(23)

where $Q_{gs,m}^{\min }$ and $Q_{gs,m}^{\max }$ are the minimum and maximum gas flow of gas storage m, respectively; V_m(t), $V_m^{\min }$, $V_m^{\max }$ are the capacity of gas storage m at time t, the minimum and maximum capacity of gas storage m, respectively. When the gas is injected to the gas storage, Q_gs,m(t) is positive, otherwise it is negative.

(7) Compressor

The compressors are used to boost the pressure of the natural-gas network, which can help the natural gas transporting to each gas load. In this paper, the energy consumed by the compressors is calculated by using natural gas flow through the compressors. The consumed gas flow of compressor r, $Q_{cr}^{consume}$(t), is calculated as presented below [15].

$$Q_{cr}^{consume}(t)={\beta }_{cr}{P}_{cr}(t)$$

(24)

$$P_{cr}(t)=\frac{Q_{cr}(t)}{{\eta }_{cr}\cdot \tau }\cdot \left({\left(\frac{M_{or}(t)}{M_{ir}(t)}\right)}^{\tau }-1\right)$$

(25)

where β_cr is energy conversion coefficient of compressor r; P_cr(t) is the consumed energy by compressor r; Q_cr(t) is the gas flow flowing through compressor r at time t; η_cr is the efficiency of compressor r; τ = (α − 1)/α and α is variability index of compressors; M_or(t) and M_ir(t) are the pressure of output node and input node of compressor r, respectively.

(8) Gas Flow Limit of P2G

$$Q_{P2G,k}^{\min }\le Q_{P2G,k}^{}(t)\le Q_{P2G,k}^{\max }$$

(26)

where $Q_{P2G,k}^{\min }$ and $Q_{P2G,k}^{\max }$ are the minimum and maximum gas flow of P2G k, respectively.

2.3. Gas Demand Management Strategy to Coordinate the Two Energy Systems

When the pressure of some gas nodes is higher than the maximum pressure or lower than the minimum pressure, which means the gas demand and the gas supply is not balanced on these gas nodes, then the gas demand management strategy is used. The main idea is to adjust the gas flow of gas turbines to achieve the gas demand balance, which means changing the power output of gas-fired units. Then, the power output of units in power system will be adjusted.

2.4. Constraints Handling Methods

The constraints of power system are handled using the methods presented in Reference [39]. In this paper, the constraints of natural-gas system are handled by the proposed method as shown below.

2.4.1. Equality Constraints Handling Method

In this paper, the set of non-linear constraints Equations (15)–(20) of the natural-gas system are solved by the trust region algorithm [43,44] and Levenberg-Marquardt algorithm (L-M) [45,46]. Trust region and L-M methods are both simple and powerful tools for solving systems of nonlinear equations and large-scale optimization problems. They have the advantages of guaranteeing a solution whenever it exists [43,44,45,46]. In this paper, the trust region method and L-M method are used to solve the gas flow non-linear equations, respectively. The optimization results are compared in the case studies.

2.4.2. Inequality Constraints Handling Method

For the inequality constraints (13)–(14), (21)–(22), (26), the gas flow is the minimum when it is lower than the minimum value and the gas flow is the maximum when it is over the maximum value. For the gas storage volume constraint, the effective redundancy method is proposed in this paper. The details of this method are as below.

a)

For gas storage m at time t;

b)

If V_m(t) ≤ $V_m^{min}$, calculate ΔV = $V_m^{min}$ − V_m(t);

c)

For ii = 1:t, calculate the gas flow redundancy of gas storage m at time ii. ΔQ_gs(ii) = min{$Q_{gs,m}^{max}$ − Q_gs,m(ii), $V_m^{max}$ − V_gs,m(ii)}. If the gas node where the gas storage m is connected with P2G, ΔQ_P2G(ii) = $Q_{P2G}^{max}$ − Q_P2G(ii), the effective redundancy ΔQ(ii) = min{ΔQ_gs(ii), ΔQ_P2G(ii)}; else, ΔQ(ii) = ΔQ_gs(ii). Then, arrange ΔQ in descending order;

d)

According to the descending order, Q_P2G(ii) and Q_gs,m(ii) are adjusted successively until V_m(t) ≥ $V_m^{min}$;

e)

Update V_m(t);

f)

If V_m(t) ≥ $V_m^{max}$, calculate ΔV = V_m(t) − $V_m^{max}$;

g)

For ii = 1:t, calculate the gas flow redundancy of gas storage m at time ii. ΔQ_gs(ii) = min{Q_gs,m(ii) – $Q_{gs,m}^{min}$, V_gs,m(ii) − $V_m^{min}$}. If the gas node where the gas storage m is connected with P2G, ΔQ_P2G(ii) = Q_P2G(ii) − $Q_{P2G}^{min}$, the effective redundancy ΔQ(ii) = min{ΔQ_gs(ii), ΔQ_P2G(ii)}; else, ΔQ(ii) = ΔQ_gs(ii). Then, arrange ΔQ in descending order;

h)

According to the descending order, Q_P2G(ii) and Q_gs,m(ii) are adjusted successively until V_m(t) ≤ $V_m^{max}$;

i)

Update V_m(t).

3. Case Studies Application

3.1. Description of Case Studies

The hybrid electricity-natural gas energy systems shown in Figure 3 are composed by the revised IEEE 39-bus power system [35] and Belgian high-calorific 20-node gas system [3]. The IEEE 39-bus power network has 46 branches, five coal-fired units, three gas-fired units and two wind power units, where the capacity of wind power units accounts for 35% of the total installed capacity of 3903 MW. The Belgian high-calorific 20-node gas system has 24 pipelines, two gas wells, three gas storages and two compressors. The parameters of the power system are from References [35,40] and the parameters of natural gas system are from Reference [3]. The revised parameters are shown in

Table 1. Parameters of power units.

Power Units	Pmax/MW	Pmin/MW	Ramp Up Rate/MW/h	Ramp Down Rate/MW/h
Coal-fired unit 1	470	150	80	80
Coal-fired unit 2	470	135	80	80
Coal-fired unit 3	340	73	80	80
Coal-fired unit 4	300	60	50	50
Coal-fired unit 5	243	73	50	50
Gas-fired unit 1	260	0	260	260
Gas-fired unit 2	230	0	230	230
Gas-fired unit 3	220	0	220	220
Wind power unit 1	750	0	750	750
Wind power unit 2	620	0	620	620

and

Table 2. Parameters of gas storage.

Gas Storage No.	Initial Capacity/Mm3	Max Capacity/Mm3	Min Capacity/Mm3	Max Gas Flow/Mm3/h	Min Gas Flow/Mm3/h
Gas Storage 1	1.5	3.5	0	0.35	-0.20
Gas Storage 2	2.0	4.5	0	0.45	-0.25
Gas Storage 3	1.5	3.5	0	0.35	-0.25

(inflow of gas storage is positive and outflow of gas storage is negative). Gas pressure limits of gas nodes are given in

Table 3. Gas pressure limits of gas nodes.

Node No.	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Mmin/bar	30	30	30	30	10	10	30	30	50	50	30	30	30	30	15	15	25	25	15	15
Mmax/bar	100	100	100	80	80	80	80	70	70	77	70	70	70	70	70	70	70	70	70	70

. Power demand and gas demand are given in

Table 4. Power demand and gas demand.

Time/h	1	2	3	4	5	6	7	8	9	10	11	12
Power demand/MW/h	1272	1188	1104	960	1080	1320	1476	1584	1740	1776	1800	1860
Gas demand/Mm3/h	1.03	0.97	0.92	0.98	0.99	1.03	1.23	1.45	1.79	1.83	1.74	1.61
Time/h	13	14	15	16	17	18	19	20	21	22	23	24
Power demand/MW/h	1680	1560	1320	1104	1416	1680	1800	2040	1860	1632	1344	1116
Gas demand/Mm3/h	1.46	1.42	1.39	1.38	1.39	1.30	1.26	1.19	1.15	1.15	1.12	0.97

. In addition, the theoretical predicted wind power output is given in Figure 4. The efficiency of P2G process is taken as 64% [6]. Wind curtailment cost is set as $100/MWh [47]. The short-term optimal dispatch for this hybrid energy system is studied to illustrate the behavior of the proposed model, the adopted algorithm and the proposed constraints handling methods in several case studies. These case studies are simulated with a low level of initial line pack (0.5 Mm³). In addition, all the case studies are implemented using MATLAB language programming.

3.2. Analysis of Simulation Results

The Newton-Raphson method is used to obtain the power flow. Trust region method and L-M method are used to solve the non-linear equations to obtain the gas flow in natural-gas system, respectively. Furthermore, MOBHPSO [39,40,41,42] is used to optimize the multi-objective dispatch problem of hybrid electricity-natural gas energy systems based on the established models (1–3,7,12), the proposed flow chart (Figure 2), and the proposed constraints handling methods. The optimization results are shown in

Table 5. Optimization results of the power system.

Case Studies	Fuel Cost (M$)	SOx Emission (ton)
Without P2G	1.080	38.193
With P2G	1.084	37.939

and

Table 6. Optimization results of the natural-gas system.

Case Studies	Methods	Cost of Natural-Gas/M$	CO2 Emission/104 ton	Rate of Abandoned Wind Power	Operation Cost of P2G/M$	Absorbed CO2 by the Methanation Process/104 ton	Increased Wind Power by P2G/MWh
Without P2G	Trust Region	0.741	5.791	24.85%	0	0	0
	L-M	0.695	5.790	24.85%	0	0	0
With P2G	Trust Region	0.732	5.727	6.71%	0.106	0.056	5321.66
	L-M	0.685	5.491	4.04%	0.122	0.064	6104.48

. All the constraints are satisfied. The comparisons of power output and gas flow among different case studies are given in Figure 5 and Figure 6, respectively. Moreover, it can be found the different performance of trust region method and L-M method from Figure 7 and Table 6. The wind power absorbed by P2G and the gas flow of P2G are shown in Figure 8. The volume of gas storages is given in Figure 9. The gas pressure of each gas node can be found in Appendix A.

From the obtained results, it can be seen that power output, gas flow of gas wells, gas flow of P2G, gas flow of gas storages, volume of gas storages, and gas pressure of gas nodes all satisfy their respective upper and lower bound constraints. Besides, the nodal gas flow balance equation is satisfied. Moreover, power demand and power supply are balanced which can be drawn from the calculated load loss rate L_p = 6.37 × 10⁻¹⁸. Then, the above results show that all the constraints are satisfied using the proposed constraints handling methods.

3.2.1. Effects of P2G on the Power System

(1) From Table 5 and Figure 5, it can be seen that the fuel cost of power system with P2G is a little higher than that without P2G. At hour 20, owing to the gas injection from P2G, the pipeline pressure is higher than the maximum value, so the ‘gas demand management strategy’ is used and needs to increase the gas demand by increasing the output of gas-fired units connected with gas node 5 and 14. Then, to guarantee the power load balance, the output of coal-fired units would be reduced. Because the fuel cost of gas-fired units is higher than that of coal-fired units and the SO_x emissions of gas-fired units are lower than that of coal-fired units, it leads to increase of fuel cost and decline of SO_x emissions. The SO_x emissions are reduced by 0.254 ton. In addition, from Figure 8, most abandoned wind power can be absorbed by P2G. During hours 3-5, P2G works at its maximum value when the abandoned wind power is over the maximum capacity of P2G. Owing to the P2G, the wind power output is much smoother and so is the output of coal-fired units, which is propitious to the stability and reliability of the power system.

(2) From Table 6 and Figure 7a, it is obvious that the rate of abandoned wind power is declined from 24.85% to 6.71% (trust region) and from 24.85% to 4.04% (L-M), respectively; The wind power output is increased by 5321.66MWh (trust region) and 6104.48MWh (L-M), respectively.

3.2.2. Effects of P2G on the Natural-gas System

From Figure 6 and Figure 9, it is obvious that the gas flow of gas wells and gas storages is lower when P2G is considered. In addition, the volume of gas storages with P2G is much larger than that without P2G. This is because the economic, clean, and low-carbon energy converted by P2G from wind power has the priority of use compared with that from natural gas network, which creates considerable economic and environmental benefits for the integrated energy systems. The cost benefit of P2G is evaluated in terms of the natural gas cost which it displaces. From Table 6, it can be seen the gas cost is reduced by $9000 (trust region) and $10,000 (L-M), respectively; Moreover, the environmental benefit of P2G in terms of CO₂ reduction and CO₂ absorbed in the P2G methanation process is measured. The total CO₂ emissions are declined by 1200 tons (trust region) and 3630 tons (L-M), respectively.

3.2.3. Total Cost Reduction of the Hybrid Energy Systems

The total cost of the hybrid electricity-natural gas energy systems including the wind power curtailment cost is reduced by $5.372 × 10⁵ (trust region) and $6.165 × 10⁵ (L-M), which can be seen from Figure 7b.

It can be concluded that the proposed model shows that the proposed constraints handling methods are effective and the feasibility of MOBHPSO algorithm for solving the multi-objective optimal dispatch problem of the hybrid electricity-natural gas energy systems is indicated. Moreover, the trust region method and L-M method are effective to solve the non-linear gas flow problem. It also can be seen that the results obtained from L-M method is much better than those obtained from trust region method.

4. Conclusions

This paper presented a multi-objective optimal dispatch model of the hybrid electricity-natural gas energy systems coupled by P2G and gas turbines in order to achieve the maximum of low-carbon economic environmental benefits. The proposed model provides not only enhanced flexibility, as it easily handles bidirectional energy flow and guarantees global optimality, but also considers the compressibility of gas, line pack of pipelines among other complicated system characteristics. The non-linear and non-convex functions of gas flow model are addressed by trust region method and L-M method. The L-M method has much better performance, which can be drawn from the simulation results. Moreover, the case studies simulation results show the feasibility of MOBHPSO algorithm for solving the multi-objective optimal dispatch problem of the hybrid electricity-natural gas energy systems and the effectiveness of proposed constraints handling methods. The obtained results also illustrate that P2G can significantly benefit the operation of both power system and natural gas system in smoothing power output, cutting down gas cost, reducing CO₂ emissions and SO_x emissions as well as avoiding wind curtailment. More specifically, the gas cost is cut down up to $10,000, the total CO₂ emissions are declined up to 3630 tons and the SO_x emissions are reduced by 0.254 ton as well as the wind power curtailment is decreased up to 6104.48 MWh with the rate of abandoned wind power declined from 24.85% to 4.04%. Besides, the total cost including wind power curtailment cost is reduced up to $6.165 × 10⁵.