Optimally Coordinated Expansion Planning of Coupled Electricity, Heat and Natural Gas Infrastructure for Multi-Energy System

Gas generation and heat storage are playing a prominent role to multi-energy systems (MES), and coordinated planning of integrated electricity, heat and gas infrastructures can highly benefit MES. In this context, a coordinated planning model of MES is proposed to determine the optimal expansion of conventional generators, transmission lines, gas boilers, combined heat and power units, and gas pipelines. In the model, the one-off investment cost of MES devices in the planning phase plus the operation cost and energy not served cost in the operation phase are considered in the objective, while the energy supply reliability, coupled operational security of multiple energy carriers, as well as the electricity, gas, and heat demand balance are comprehensively taken into account as the constraints. Afterwards, the Benders Decomposition method is adopted to solve the proposed expansion planning model in a divide and conquer manner. Finally three case studies on a 14-bus MES are conducted to demonstrate the effectiveness of the proposed expansion planning model. Simulation results indicate that the total cost of the proposed model in case 3 is saved by 9% and 2.8% compared with the separately planning scheme in case 1 and the coordinated planning scheme without candidate gas pipelines in case 2. Therefore, the proposed coordinated expansion model is very effective for MES Infrastructure planning.

With increasing concerns about the energy crisis and environmental pollution issues, multi-energy system (MES) has aroused widespread attention for its capability of effectively accommodating renewable energy resources [1]- [3]. MES could convert wind and solar power, natural gas, geothermal energy, biomass resources etc. into various directly used energy forms such as cooling, heating, electricity through advanced energy conversion technology, and thus improves the economy and environmental friendliness of energy utilization [4]- [5]. At present, some achievements have been made in MES planning field. For example, based on an energy hub model, a MES expansion method was proposed to plan the combined heating and power (CHP) units, gas boilers (GBs) and other energy carriers in [6], [7]. In [8], the CHP units and natural gas distribution network are jointly optimized to ensure the maximization of electricity and heat supply for satisfying flexible customer need. In [9], the electricity distribution network and natural gas network were co-planned to optimize the site and size of micro-gas turbine, resulting in a reduced total investment cost for the integrated system. Authors of [10] proposed an optimal planning model for the interconnected energy centers and multiple energy infrastructures. A long-term, multi-region and multi-stage planning model was also established in [11] to analyze the economy of electricity-gas hybrid networks. The author mainly focused on traditional coal-fired and gas-fired generation units, but the CHP units were not considered. A distributed energy system of combined cooling, heating and power (CCHP) units, photovoltaic and heat pumps was established in [12], [13], and optimization results indicated that CCHP integrated with solar energy has advantages over the single CCHP in terms of both energy saving and CO2 emission reductions. Authors of [14] proposed a multi-stage flexible planning model of integrated electricity-gas system to maximize the social well-being for increased load demands. An energy hub based optimal planning framework was put forward in [15] to optimize the sizing of CCHPs, boilers, electricity and heat storage for an interconnected electricity and natural gas network. A robust scheduling model with consideration of N − 1 contingencies was presented in [16] for co-expanding power transmission lines and natural gas pipelines, and the case studies demonstrated the presented model was quite robust against wind power uncertainty. However, the authors mainly discussed the optimal operation of MES without taking the planning problem into consideration. Shao et al. [17] established a two-level scheduling model for a heat-electricity integrated system considering electric and thermal load demand response, and revealed that the integrated system could flexibly fulfill customers' energy consumption. In [18], [19], the reliability and security constraints are considered in the gas-electricity coupled planning model, and the solutions have ensured the desired power system reliability requirement. The optimal design and operation of distributed energy systems and heating network layouts is investigated in [20], and afterward a mixed integer linear programming model is established to minimize total cost and carbon emissions. In [21] the expansion of power substations, CCHP, GBs and air conditioning equipment are conducted in an active distribution network, and the influence of extreme load scenario on power supply reliability is analyzed. Yu et al. [22] considered the regional geographical resource endowment and put forward the optimal scheme to coordinate energy suppliers and demands in a micro integrated energy system. In [23], a demand response scheme was tailored to coordinate the power to gas devices, heat pumps, storage and flexible loads, subsequently the optimal dispatch solution with considering interactions among multiple energy carriers was achieved. In [24], based on a two-stage stochastic optimization model, Dr. Yang et al. evaluated the effect of uncertain load demands, energy prices and renewable energy intensity on system planning cost. In [25], a mixed integer linear programming model was proposed to optimally design a combined heat and electricity generation system by small-size CHPs, and thereby the benefits of energy saving and CO2 emission reduction were achieved. In [26] various operation schemes are compared and verified that the mutual network coordination and power co-generation have the highest economic and environmental benefits.
To sum up, the references mentioned above have established various models for MES planning and indeed enriched the MES planning theory. However, none of them has addressed the coupling of electricity, gas and heat networks simultaneously with the energy supply reliability requirement. To fill this research gap, a coordinated MES expansion planning model is proposed as a mixed integer linear programming (MILP) problem in this paper. The coupling of electricity-gas-heat networks and energy reliability etc. are taken into account as operation constraint, while device investment cost, MES operation cost and energy not served cost are considered in the objective. Afterwards, Benders decomposition algorithm is adopted to solve the proposed high-dimensional MILP problem. Finally case studies are conducted on a hybrid 14-node MES with extensive discussions to check performance of the proposed model.
The main contributions of this paper are threefold. 1) A long-term coordinated planning model is proposed to determine the optimal expansion plans of generation units, transmission lines, gas boilers, combined heat and power units, and gas pipelines for MES. In the model, the one-off investment cost of MES devices, the operation cost and energy not served cost are considered in the objective, while the energy reliability requirement, the coupled operation constraints among multiple energy carriers, the demand balances of electricity, gas, and heat are taken into account as constraints. 2) Benders decomposition algorithm is tailored to decompose the proposed high-dimension model into a master problem for optimizing investment cost and sub-problems for optimizing operation related costs, and thereby the optimal MES expansion solution is effectively obtained.

3) Simulation results and comparisons have validated
the benefits of the proposed coordinated expansion planning model, which can enhance the economic and reliability of a coupled electricity, heat and natural gas system.
The rest of this paper is organized as follows. The MES architecture and its general mathematical formula are introduced in section II. Section III presents the coordinated expansion planning model, and numerical case studies are conducted in Section IV with the conclusion provided in the last Section.

II. GENERAL FORMULATION OF MULTI-ENERGY SYSTEM
MES can effectively improve energy efficiency and is the main supplier in next-era energy paradigm, which is the key transformation medium coupling different energy flow through energy conversion devices. For example the most commonly used CHP and gas boiler (GB) are sources in electricity and heat network but consumers in the natural gas system. Fig. 1 shows the typical structure of a MES.
where η CHP g−e and η CHP g−h are the gas-to-electricity and gasto-heat conversion coefficients of CHPs, and η GB g−h is the gasto-heat coefficient of GBs.

III. PROPOSED MULTI-ENERGY SYSTEM PLANNING MODEL
This section presents the mathematical formulation of the coordinated expansion planning model, which considers the investment and operation costs as well as the coupled operation constraints of electricity, gas and heat system. For proposed long term planning model, the electricity load demand during each year is represented by a total number of h blocks with different load levels as shown Fig.2. The block h is with a load consumption level EL b,h,t and time duration DT h,t , which means that the h th load level (in MW) will last DT h,t hours at bus b in year t, and it will be used to maintain the power balance in Eq. (III-C.1). Similarly, the gas and heat load demand during each planning year is also represented by a total number of h blocks with h load levels.

A. OBJECTIVE FUNCTION
The objective of the proposed coordinated expansion planning model is to minimize MES total cost during the 10-year planning horizon in (4), and the coefficient of present value λ t is calculated as λ t = 1/(1 + τ ) t−1 . Eq. (5) represents the investment cost of generators, transmission lines, CHP, and GBs respectively. Eq. (6) represents the operation costs of generators, CHP, and GBs. The cost of Energy Not Served (ENS) is calculated by multiplying the amount of ENS with the price of lost load (PLL) as in (7).
The coordinated expansion planning model considers investment constraints of generators, transmission lines, CHPs, gas boilers, and gas pipelines. Once a candidate device is installed, its investment state is fixed to 1 for the remaining years (8)- (12). Besides, commissioning time is imposed on a newly installed MES device by (13)- (17). Constraint (18) ensures that the total power generation capacity meets the predicted electricity load demand and reserve requirement.

C. OPERATION CONSTRAINTS
The proposed planning model takes into account the coupled operation constraints of electricity, gas and heat networks as follows.  (24)

2) GAS NETWORK RELATED CONSTRAINTS
The natural gas flow through a pipeline with nodes m and n is stated as a quadratic term of terminal pressure of both ends by (27)-(28), where the sgn( * ) indicates the gas flow direction. When the pressure of node m is larger than n, the gas flows from m to n, otherwise from n to m. Similar to bus voltage limits in power transmission network, the natural gas network has to maintain the nodal pressure within an appropriate range by (29). Gas flow balance constraint (30) describes that the total gas flow injection is equal to the total gas outflow at each node. The gas flow capacity of a pipeline is restricted by (31).

5) RELIABILITY CONSTRAINTS
The ENS calculated in (40) is adopted to measure the amount of electricity not served during each year, and the corresponding system reliability is constrained by (41).

IV. SOLUTION METHODS
The proposed optimization model (4)-(41) is a mixed integer linear programming (MILP) problem with a large number of coupling variables. In this paper, the Benders decomposition is adopted to solve the MILP. General steps of using Benders Decomposition method for solving this problem are demonstrated in Fig. 3. By using the Benders decomposition method, the proposed MILP model can be decomposed into an investment planning master problem and an optimal operation sub-problem. The master problem sends the solved planning variables to the sub-problem, while sub-problem feedback the dual variables to master problem for generating Benders cut, and these two procedures execute iteratively until reach the convergence criterion. VOLUME 8, 2020 For the proposed MES model, the master problem comprises the objective (42)-(43) and constraints (8)- (18).
and H * hl,h,t are the optimal solutions obtained from the sub-problem; u * t , υ * t , and ω * t are the corresponding Lagrange multipliers. The master problem is solved to obtain the upper bound (UB) of the original MILP model, i.e. the optimal value of α, and its optimal solution x * p,t are transferred to the sub-problem.
It should be noted that the variables x i,t , x l,t , x c,t , x g,t , x p,t in constraints (22)(23), (26), (31), (35-36) and (39) should be replaced by the investment variables x * p,t optimized from the master problem. By solving the sub-problem, the solutions The master problem and sub-problem are solved iteratively until the termination condition is satisfied that the gap of master and sub-problem objective is smaller than a threshold, i.e. Benders decomposition is an exact algorithm for the MILP problem, and thus they could guarantees solution optimality for large-scale MILP model as discussed in [27]. The effectiveness of the same strategy has been verified in [18], [19] and will also be validated by the three case studies in Section V. With a flowchart shown in Fig. 4, the main steps of using Benders decomposition to solve the proposed model are described as follows.
Step 1: System initialization. Input system parameters including electricity supply and load, natural gas supply and load, heat load demand and network data.
Step 2: Solve the master problem (8)- (18) and (42)-(43), afterward update the UB of the original MILP model as well as transfer the solution x * i,t , x * l,t , x * c,t , x * g,t , x * p,t to the sub-problem.
Step 4: Stop Benders decomposition loop and go to Step 5 if the termination condition (|UB − LB| ≤ ε) is satisfied; otherwise, add feasible cut to the master problem and go to Step 2.
Step 5: The optimal planning scheme is obtained.

V. CASE STUDIES A. PARAMETER DESCRIPTION OF TEST SYSTEM
The proposed coordinated expansion planning model was validated by a MES network as showed in Fig. 5. The electricity network comprises 14 buses, 5 generators and 20 transmission lines, while 6 candidate generators and 10 candidate transmission lines are considered for expansion. Heat and natural gas systems are composed of 14 nodes, 4 GBs, 11 gas pipelines, and 3 natural gas suppliers. 3 candidate GBs and 4 candidate CHPs are considered to enhance the heat and natural gas system. Parameters of all the candidate generators, lines, GBs and CHPs are provided in Tables 1-5. A 10-year planning horizon is applied for the following case studies, and each candidate device is considered for installing at the beginning of each year. The annual electricity load demand is divided into 3 load blocks to represent     the base, medium, and peak load level according to Fig. 2. The electricity peak load of the first year is 178.8 MW with an average annual growth rate of 3% for the next 9 years. The spinning reserve requirement of electricity load is 5% [22]. The investment discount rate is 5% and the PLL is 10000$/MWh [13]. The heat and gas peak loads are 120.3 MW and 88.5 MW with an annual growth rate of 2% and 5% respectively. VOLUME 8, 2020

B. SIMULATION RESULTS AND DISCUSSIONS
Three cases are tested and compared here to illustrate the effectiveness of the proposed model.
Case 1: the electricity, gas, and heat systems are planned separately. Electricity loads are supplied by generators, while heating loads are supplied by gas boilers.
Case 2: the coordinated expansion planning of coupled electricity, gas, and heat system is considered, but gas pipelines are not considered to be installed during the 10-year planning horizon [20].
Case 3: the coordinated expansion planning of coupled electricity, heat and natural gas systems is considered with a full set of candidate devices including generators, transmission lines, GBs, CHPs and gas pipelines.

1) CASE 1
In this case, electricity, heat and gas systems are planned separately. As shown in Fig.6, four candidate generators including CG1, CG2, CG5 and CG6 are constructed at year 1, 3, 6, and 9 to meet the growing electricity load demand, and three transmission lines including CTL4, CTL7, CTL8 are built at year 6, 8, 10 respectively to enhance the electricity transferring capacity. It can be seen that the planed generators and transmission lines have a positive correlation with the growing electricity load demand. For the planning of heat and gas system, three gas boilers CGB2, CGB1 and CGB3 are developed at year 3, 6, 7, and two gas pipelines CGP1 and CGP3 are established at year 6 and 9 respectively. At the end of the planning horizon, a total of 3 transmission lines and 96 MW generators are installed at buses 2, 3 14 for the electricity network, while 3 gas boilers are installed at nodes 5, 12 and 13 for the natural gas-heating system. The total cost of decoupled planning of the electricity, gas, and heat system to supply the increasing load is 11.082 × 10 6 $ for 10 years.

2) CASE 2
In case 2, we consider a coupling plan of electricity, heat and natural gas systems without taking the gas pipeline expansion into account. Due to the coupling relationship between electricity, heating and gas system, two CHPs are planned to construct at year 3 and 9. With the CHPs installation, fewer generators are built compared with case 1, such as candidate generators CG1, CG2 and CG3 constructed in year 1, 3 and 6 respectively. With the expansion of CG1, CG2 for the growing electricity load demand, the transmission line CTL8 is built in year 4 and the other two transmission lines CTL4 and CTL3 are built in year 6 and 9 respectively to transmit more electricity power. In addition, since CHP can provide electricity and heat simultaneously, fewer gas boilers in terms of CGB1 and CGB2 are constructed at year 1 and 3 in case 2. At the end of the 10-year planning, 72 MW of new generators and three transmission lines are installed for the electricity network, while 46 MW of Gas boilers and two CHPs are constructed for the heat and gas network. The topology of the expanded network at the end of planning horizon is shown in Fig. 9.
In Table 7, though CHPs involved with 0.27 × 10 6 $ investment cost in case 2, the expanded CHPs reduce the operation cost by 0.707 × 10 6 $ compared with that in case 1. This is because the utilization of a high efficient CHP requires less fuel for producing the same amount of energy than that in case 1. In addition, the energy not served cost and total costs are reduced by 0.017×10 6 $ and 0.774×10 6 $ compared with case 1.

3) CASE 3
In this case, new gas pipelines are considered to be installed in the gas network. As shown in Table 6, candidate gas pipelines CGP1 and CGP3 are installed in year 6 and 9 respectively, which would provide extra gas supply capacity. With the construction of these gas pipelines, CHP can convert more natural gas into electricity and heat. As a result, the installation of power generators and gas boilers is delayed compared with case 2 [20]. For example, only generators CG1, CG4, and CG3 are installed in year 1, 5, and 7 respectively, while only the gas boiler CGB2 is installed in year 6. The final MES topology at the end of 10-year planning is shown in Fig. 10. Table 7 also lists the operation cost, investment cost, operation cost, unserved energy cost and total cost in case 3. As indicated by Table 6 and 7, since the gas network congestion is alleviated by the newly expanded gas pipelines CGP1 and CGP6 which enhance the natural gas supply capacity for gas boilers and CHPs, the unserved energy cost in case 3 is reduced by 0.006 × 10 6 $ compared with case 2. This indicates that the coupled planning of electricity, heat and natural gas system can reduce the amount of load lost and thus effectively improve power supply reliability. In case 3, the total cost of the coordinated planning model is 11.052 × 10 6 $ which is the cheapest among these three case studies.
When make detailed comparisons among these three cases according to the results in Table 7, we can clearly observe that: 1) the total cost of case 2 [20] is lower than that of case 1 by 6.4%. This is because the electricity system, natural gas system and heat system are planned independently in case 1, while in case 2 these systems are planned jointly and thus they are coordinated to improve the planning economy. 2) In case 3, due to the installation of candidate gas  pipelines CGP1 and CGP3, its total cost is further reduced by 2.8% compared with case 2, which means new pipelines are effective investment candidates for reducing the total operation cost of interdependent electricity, heat and natural gas infrastructures. Based on these discussions, the proposed coordinated expansion planning model in case 3 is most cost-effective to meet the growing electricity and heat load demand of MES.

VI. CONCLUSION
This paper proposes a long-term coordinated expansion model to determine the optimal planning of candidate generators, transmission lines, gas boilers, CHP, and gas pipelines for MES. The one-off investment cost during the planning phase plus the MES operation coast and energy not served cost during the operation phase are designed in the objective, while the coupled gas, heat and electricity system operation constraints and the reliability requirement are also considered in the model. Consequently, the Benders decomposition algorithm is utilized to solve the proposed coordinated expansion model. Simulation results of the 14-bus electricity, heat and natural gas integrated network have demonstrated that the proposed coordinated planning of MES in case 2 and 3 has a better economy compared with the decoupled planning system in case 1, while the investment of gas pipelines in case 3 can further improve MES energy utilization efficiency and reliability benchmarked with case 2. Therefore, the proposed coordinated model is very effective to optimize the expansion planning of MES.  Institute of  Technology (IIT), Chicago, IL, USA, in 2002, all in electrical engineering. He is currently a Professor with the Electrical and Computer Engineering Department, IIT. His research interests include economic and secure operation of electric power systems, cyber security in smart grid, renewable energy integration, big data analytics, electric demand management of data centers, and power system protection. VOLUME 8, 2020