Applied Energy xxx (2015) xxx-xxx

Contents lists available at ScienceDirect

Applied Energy

journal homepage: www.elsevier.com/locate/apenergy

An NSGA-II based multi-objective optimization for combined gas and electricity network expansion planning q

Yuan Hu, Zhaohong Bie *, Tao Ding, Yanling Lin

State Key Laboratory of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an 710049, China

HIGHLIGHTS

• Developed a multi-objective model for the combined natural gas network and electricity network.

• Taken into account the uncertainty and correlations of wind power in the proposed model.

• Presented an improved point-estimation method to solve the combined optimal power and natural gas load flow.

ABSTRACT

With the increasing proportion of natural gas in power generation, natural gas network and electricity network are closely coupled. Therefore, planning of any individual system regardless of such interdependence will increase the total cost of the whole combined systems. Therefore, a multi-objective optimization model for the combined gas and electricity network planning is presented in this work. To be specific, the objectives of the proposed model are to minimize both investment cost and production cost of the combined system while taking into account the N-1 network security criterion. Moreover, the stochastic nature of wind power generation is addressed in the proposed model. Consequently, it leads to a mixed integer non-linear, multi-objective, stochastic programming problem. To solve this complex model, the Elitist Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to capture the optimal Pareto front, wherein the Primal-Dual Interior-Point (PDIP) method combined with the pointestimate method is adopted to evaluate the objective functions. In addition, decision makers can use a fuzzy decision making approach based on their preference to select the final optimal solution from the optimal Pareto front. The effectiveness of the proposed model and method are validated on a modified IEEE 24-bus electricity network integrated with a 15-node natural gas system as well as a real-world system of Hainan province.

© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CCBY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

ARTICLE INFO

Article history:

Received 30 June 2015

Received in revised form 21 October 2015

Accepted 22 October 2015

Available online xxxx

Keywords:

Natural gas network expansion planning Transmission expansion planning Multi-objective

Primal-Dual Interior-Point method Point-estimate method

1. Introduction

Driven by low prices and the increasingly stringent environmental regulations, natural gas accounts for 25% of the world's primary energy production at present. According to the recent projections, worldwide demand for natural gas is estimated to grow at a rate of 2.9-3.2% per year until 2030 [1]. By the end of the next decade, worldwide natural gas consumption is expected

q This work was supported by the Doctoral Program of Higher Education for the Priority Development Areas (20130201130001), the Fundamental Research Funds for the Central Universities, and the Independence research project of State Key Laboratory of Electrical Insulation and Power Equipment in Xi'an Jiaotong University (EIPE14106).

* Corresponding author. Tel.: +86 29 8266 8655; fax: +86 29 8266 5489. E-mail address: zhbie@mail.xjtu.edu.cn (Z. Bie).

to be about 2.2 billion cubic meters (bcm) per day [2]. Owing to the distinct advantages of low cost, low carbon emission and fast response, gas-fired power generation keeps rising in the proportion of the total generating capacity in recent years, which leads to an increasing investment on the natural gas infrastructures. World Energy Outlook 2010 [3] shows that worldwide demand for natural gas in the power sector in 2008 was 4303 TW h, and it is projected to rise to 7600 TW h by 2035. In light of the observation results by the emission monitoring systems of United States, CO2 emissions from U.S. power plants were 23% lower in 2012 than the emission amount in 1977 after replacing large number of fossil-fuel power plants by gas-fired plants [4]. Since the natural gas network is closely coupled with the electricity network by the gas-fired power plants, planning of any energy system regardless of such interdependence will increase the total cost of the entire combined energy

http://dx.doi.org/10.1016/j.apenergy.2015.10.148 0306-2619/® 2015 The Authors. Published by Elsevier Ltd.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

2 Y.Hu et al./Applied Energy xxx (2015) xxx-xxx

Nomenclature

S} set of nodes in gas network

SEP set of existing pipelines

SCP set of candidate pipelines

SEC set of existing compressors

SCC set of candidate compressors

SWS set of gas supplier nodes

SWL set of gas load nodes

S2 set of nodes in electricity network

SEL set of existing transmission lines

SCL set of candidate transmission lines

SG set of generators

SLoad set of electricity demands

C set of gas-electricity combined nodes in gas network

C2 set of gas-electricity combined nodes in electricity network

W set of normal operation and N-1 contingency states Matrices

A pipe-nodal incidence matrix

U compressor node incidence matrix

V gas supplier-node incidence matrix

C gas load-node incidence matrix

D compressor fuel tap incidence matrix

T transmission line-node incidence matrix

G generator-node incidence matrix

W electricity load-node incidence matrix

Parameters

number of gas suppliers number of coal-fired generators number of gas-fired generators number of candidate pipelines and existing pipelines number of candidate compressors and existing compressors

number of gas loads number of generators number of transmission lines number of electricity loads gas purchase cost of supplier i

CarbonCost carbon emission price

PlineCost ClineCosti ElineCosti

ai, bi, Ci

investment cost of installing pipeline i investment cost of installing compressor i investment cost of installing electricity line coefficient of converting net present value to annualized investment cost

coefficients of the operation cost of generator i

n,1, carbon emission coefficient of coal-fired generator and

gas-fired generator respectively ak, bk, yk gas consumption coefficients of compressor k 11, i2, i3 gas fuel rate coefficients of generator i My gas pipeline constant depending on diameter, length,

temperature, friction and gas composition ak compressor constant depending on temperature,

compressor efficiency and heat ratio gas compressibility factor at compressor inlet specific heat ratio compression ratio of compressor k WSimax max and min amount of gas supply at node i

max and min pressure at node i Bk electrical susceptance of transmission line k

Fk maximum capacity of transmission line k

Pgk"1; Pgkax max and min capacity of generator k GHV gas gross heating value

PLm'n, PLmax max and min amount of load demand at node i SMkc binary parameter that is 0 when the transmission line

kis outage under state c and, 1 otherwise WLi natural gas load at node i PLk real power load at node k

Variables Xi

Pi, Pj WSi fCk

Sk flk

hfr(k), hto(k)

nC nC hfr(k), hto(k)

binary decision variable, 1 if pipeline i is installed, and 0 otherwise.

binary decision variable, 1 if compressor i is installed, and 0 otherwise

binary decision variable, 1 if electricity line i is installed,

and 0 otherwise

natural gas flow of pipeline

pressures at nodeiand, respectively

natural gas injection of gas supplier i

gas flow rate at compressor k

power for compressor k

amount of gas tapped by compressor k

power flow on transmission line k

voltage angle at "from" and ''to" buses of transmission line k

real power supply from generator k

amount of load curtailment at node i

power flow on transmission line k under state c

voltage angle at ''from" and ''to" buses of transmission line k under state c

systems. Therefore, it urgently calls for an effective planning method for the Combined Natural Gas Network and Electricity Network (CGEN) [5].

In the prior-at work, research that focuses on CGEN can be categorized into: (a) operation optimization and (b) expansion planning. Regarding the operation optimization of CGEN, the integrated optimal load flow problem for combined natural gas and electric power transmission networks has been analyzed in [6,7]. Specifically, in [6], a combined natural gas and electric optimal power flow is carried out to analyze the impact of the natural gas price variation on the optimal operation for CGEN; while in [7], an integrated load flow of CGEN has been presented considering the effect of temperature on the natural gas system operation. To improve the accuracy of the CGEN model, a

multi-period CGEN optimization model has been developed in [8], where the natural gas storage, line-pack of pipeline, and power ramping characteristics of generators have been taken into account. In contrast, a mixed-integer linear program for the security-constrained optimal power and natural gas flow has been introduced in [9] to help system operators quickly respond to N-1 contingencies. Also, the natural gas network constraints are incorporated into the security-constrained unit commitment problem [10-12]. Compared to the CGEN operation optimization, CGEN expansion planning has become a hot research topic in recent years as many problems remain unsolved. Although [13] develops a long-term, multi-area and multi-stage planning model of CGEN, it only focuses on the system value chain as well as the optimal operation of existing

Y. Hu et al./Applied Energy xxx (2015) xxx-xxx

and new facilities, and most of the important elements of CGEN are simplified. In [5], a detailed CGEN optimization model is then proposed to achieve a low carbon integrated energy system, and the expansion decisions of the future CGEN, such as adding new natural gas pipes, compressors, and storage facilities of natural gas network and new transmission lines of electricity network, can be determined. Ref. [14] presents a multi-period integrated framework for generation, transmission and natural gas network expansion planning, but the modeling of compressor is neglected and the new method to solve natural gas load flow is only applicable to radical natural gas networks. Considering the uncertainties brought by an increasing utilization of natural gas in the power system, Ref. [15] presents an integrated expansion planning framework for CGEN with the aim to maximize the benefit-cost ratio by evaluating benefits in operation reduction, carbon emission reduction and reliability improvement against the increase in investment costs.

In recent years, wind energy is one of the rapidly growing renewable energies [16]. Unlike the traditional controllable power energy supplied by fossil fuel-based power plants, generation by wind energy is volatile due to the fluctuation of wind speeds, which brings about a great challenge to the operation and planning in power systems [17]. On the other hand, the natural gas network is closely coupled with the electricity network, which should be relevant to implement the research of CGEN expansion planning taking into account the uncertainty of wind power. Ref. [18] develops a CGEN model to investigate the impact of a large amount of wind energy on the British natural gas network. The results show that gas-fired generation can be used to compensate the wind energy variability, and the natural gas storage facilities as well as gas-fired plants with dual-fuel capability are suggested to mitigate the variability of wind energy. Ref. [19] proposes a robust optimization approach to analyze the interde-pendency among natural gas, coal and electricity infrastructures considering their operation constraints and wind energy uncertainties. However, there are few papers addressing CGEN expansion planning with the consideration of wind energy uncertainties.

For transmission network expansion planning, it is very important to take into account the ''N—1" network security criterion [20]. The conventional process of conducting ''N—1" network security criteria is that firstly optimizing a scheme without accounting for any component failure, and then checking the ''N—1" security for the obtained scheme. If it is not satisfied, expanding the scheme further until the ''N—1" deterministic security criterion is met [21].

In light of the above issues, this paper presents a multi-objective optimization model for the CGEN expansion planning considering uncertain wind power generation as well as the ' 'N—1" network security criterion. The objective of the proposed model is to minimize the total investment cost and production cost by expanding appropriate pipelines, compressors and electricity lines, while satisfying the future load growth and additional security and operational constraints. In fact, the proposed model is a multi-objective, mixed integer non-linear stochastic problem, which cannot be easily solved by classical mathematical techniques. In this paper, the Elitist Non-dominated Sorting Genetic Algorithm II (NSGA-II) [22] is applied to the proposed model, and the Primal-Dual Interior-Point (PDIP) method combined with the point-estimation method is adopted to evaluate the objective functions and capture the final optimal Pareto front. Finally, decision makers can use a fuzzy decision-making approach based on their preference to select the final optimal solution from the optimal Pareto front.

The main contributions of this paper are suggested as follows:

(1) A multi-objective model is developed to simultaneously minimize the investment cost and production cost of the CGEN. Most importantly, the N— 1 electricity network security criterion is considered in the optimization process.

(2) The primal-dual interior-point method combined with the improved point-estimation method is proposed to solve the combined optimal power and natural gas load flow.

(3) The NSGA-II method is deployed to capture the Pareto front of the proposed multi-objective model and furthermore, the final planning scheme can be selected based on the preference of decision-maker.

The rest of the paper is organized as follows. Section 2 presents the mathematical formulation of the multi-objective CGEN model considering wind power uncertainties. Section 3 shows the NSGA-II method for capturing the Pareto set of proposed model. The numerical results are presented in Section 4, where the impact of wind power uncertainties on the CGEN planning scheme is also discussed. Finally, conclusions are drawn in Section 5.

2. Mathematical formulation of the CGEN expansion planning model

2.1. Deterministic CGEN expansion planning model

A natural gas network includes gas producers, pipelines, gas compressors, interconnection points, storage facilities and gas consumers. In this paper, only three basic types of entities, pipelines, compressor stations and interconnection points are considered for the modeling of natural gas network. It is assumed that all the compressors are driven by gas energy, and the natural gas is tapped from the inlet node of each compressor. The electricity network is represented by a DC power flow model, so the reactive power and voltage amplitude are neglected. Natural gas network and electricity network are closely linked by gas-fired generators, which can be treated as energy converters between these two energy systems. To natural gas network, gas-fired generators are treated as natural gas loads, while for electricity network they are considered as power supplies.

As the natural gas load and electricity load increase in the planning horizon year, the objective of the proposed model is to determine which and where candidate pipelines, compressors and electricity lines should be constructed to achieve the minimum investment cost while satisfying the future energy requirement. Certainly, transmission structures have great impacts on the optimal operation for both natural gas network and electricity network and we also expect to minimize the production cost of natural gas supply and power generation. Meanwhile, to achieve the low-carbon economy, the carbon emission cost of power generation is also considered as a part of the production cost. In addition, the operation and security constraints of CGEN should be strictly considered, so the mathematical formulation of the proposed co-planning model can be expressed as follows:

Min f 1 = InvestmentCost

/NCP NCC NCL \

InvestmentCost = 1 ■ ¡Y^XjPlineCostj + y^y¡ClineCosti + z¡ElineCosti |

\i 1 i 1 i 1 )

Min f2 = ProductionCost + CarbonEmissionCost

Y. Hu et al./Applied Energy xxx (2015) xxx-xxx

ProductionCost = 8760 • Costgasi* WSt + 8760 ^(aiP2gi + biPgi + ci) i=1

CarbonEmissionCost = 8760 • CarbonCost * n1 * Pgi

¡=1 NGG

+ y^8760 • CarbonCost * n2 * Pgi

Subject to:

(1) Natural gas network constraints Gas pipeline constraints

fP2k = sgnsMs(p2 - p) k 2 SEP, i, j 2 S1

-Wk 6 fPk 6 Wk k 2 SEP, i, j 2 S1

+1 Pi > Pj -1 pi < Pj

- M1 (1 -Zk) 6 fP2 - sgn«M«(P2 - P«2) 6 M1 (1 - Zk) k 2 SCP,

8i, j 2 S1

-zfPk 6 fPk 6 zfk k 2 SCP, 8i, j 2 S1 Compressor operation constraints

Hk = Gkfck

jZki(df) - 1

k 2 SE^^JSCC, i, j 2 S1

Sk = cH + bkHk + ak k 2 SEC U SCC

166 Rm

k 2 SE^^jSCC, i, j 2 S1

0 6 pj -1 6 yk*r k 2 SCC, i, j 2 S1

Nodal pressure constraints pmin 6 Pi 6 Pmin 8i 2 S1 Natural gas supply constraints WSmin 6 WSi 6 WSmax 8i 2 SWS

Nodal natural gas flow balance equation

(9) (10) (11) (12)

Y^Ami^ fpi + ^Umr fc, + £VmWSi - £CmiWLi -^miS = 0 i=1 i=1 i=1 i=1 i=1

8m 2 N1 (15)

(2) Electricity network constraints Electricity line power flow constraints

flk = Bk(hfr(k) - hto(k)) 8k 2 SEL hfr(k), hto(k) 2 S2 (16)

-Fk 6 flk 6 Fk 8k 2 SEL (17)

-Mk(1 - zk) 6 flk - Bk(dfr(k) - dto(k)) 6 Mk(1 - Zk) 8k 2 SCL (18)

-zkFk 6 flk 6 zkFk 8k 2 SCL

Generation constraints

PgkD 6 Pgk 6 PST 8k 2 SG (20)

Node balance constraints for electricity network

NL NG ND

Yjmifli + Y,GmiPgi-J2WmiPLi = 0 8m 2 S2 (21)

i=1 i=1 i=1

(3) Equality constraints for joint gas and electricity

WLk = (hP2gi + i2Pgi +ft) /GHV k 2 A, i 2 C (22)

The first objective is the investment costs of selected gas pipelines, compressors and electricity lines. The second objective function is to minimize the production cost including the carbon emission cost under constraints (4)-(22). The production cost and carbon emission cost are represented by Eqs. (2) and (3), respectively. It should be noted that the production cost and the carbon emission cost of coal-fired generators and gas-fired generators are calculated separately.

The constraints of the proposed CGEN optimization model include three parts: (a) constraints (4)-(15) represent the operation and security constraints of natural gas network; (b) constraints (16)-(21) refer to the operation and security constraints of electricity network; and (c) constraint (22) is the energy conversion equality constraint which links the two systems together. To be specific, constraints (4)-(6) represent the operation constrains of existing gas pipelines, and constraints (7) and (8) represent the operation constrains of candidate gas pipelines, where M1, often called ''big M" value, represents a large enough input value. This parameter is applied to guarantee the constraint (7) to be inactive if the pipeline k is not selected. The appropriate value of Mi can be referred to [1]. Constraints (9)-(11) represent the operation constrains of both existing and candidate gas compressors. When the candidate compressor is not selected, the pressure at the inlet node of compressor will be equal to the pressure at outlet node by the constraint (12), and then we can treat the compressor as an interconnection point. Constraints (18) and (19) represent the operation and security constraints of candidate transmission lines, respectively. The effect of Parameter Mk is the same as that of M1, and we set it as 1.2Bk in this paper. The detailed discussion on setting a proper value for Mk can be referred to [23].

2.2. Deterministic CGEN expansion planning model considering N-1 network security criterion

Assuming that the stored natural gas can be used to avoid natural gas load curtailment if a contingency occurs in the natural gas network, we thus only consider the N-1 network security criterion for the electricity network. It should be noted that the outage of the generator is neglected in this paper, so the number of N-1 electricity line contingency states is N. First of all, an NL x (NL + 1) state matrix SM is introduced to represent the normal operation and N-1 contingency states, in which the row number equals to the number of electricity lines and the column number equals to the number of normal operation state plus N-1 contingency states, yielding

1 0 1 1 1 0

NLx(NL+1)

Y. Hu et al./Applied Energy xxx (2015) xxx-xxx

The first column of matrix SM represents the normal operation states, and all the element values are 1 indicating all electricity lines can operate normally. The other columns of the matrix SMrepresent N—1 electricity line contingency states, and each column only has one element with value set as 0 to represent that this electricity is outage. Then, a mixed integer linear programming model with minimizing total load curtailment of electricity network under normal and N— 1 contingency states can be written as:

emission cost and the amount of load curtailment as objectives. The mathematical formulation is as follows

Min LoadSheddingAmount — y^APL,-

Subject to

-Mk(1 - SMkc) 6 flk - Bk(8cfm - ffCo(k)J

6 Mk(1 - SMkc) 8k 2 SEL fr(k), to(k) 2 S2C 2 W

-SMkcFk 6 flk 6 SMkcFk 8k 2 SEL c 2 W

-Mk(2 - Zk - SMkc) 6 flk - Bk( fk) - 0Co(k))

6 Mk (2 - Zk - SMkc) 8k 2 SCL fr(k), to (k) 2 S2 c 2 W

-ZkSMkcTk 6 flk 6 ZkSMkcTk 8k 2 SCL c 2 W

PL"1" 6 APLi 6 PLf

i SLoad

Yjmifli + Y,GmiPgi + Y]WmiAPLi - £WmiPLi — 0 8m 2 S2

(28) (29)

Gas network constraints (4)-(15). Electricity network constraints (20). Gas and electric combined node equality constraints (22). In the above formulation, constraints (25)-(28) represent the operation and security constraints of candidate electricity lines under normal and N— 1 contingency states. Constraints (25) and (26) will become inactive if the value of SMkc is 0, and 1 otherwise. Constraints (27) and (28) only become active when the values of zk and SMkc are set as 1 simultaneously, which means that the electricity line k is selected and it can normally operate. In other situations, both constraints (27) and (28) are inactive constraints.

To guarantee the final scheme satisfy the N— 1 network security criterion for the electricity network, we treat the amount of load curtailment as a penalty term and add it to the first two objectives. Then the new objectives are as follows:

Min f 1 = In v estmentCost + Penalty 1 • LoadSheddingAmount (31) Min f2 = ProductionCost + CarbonEmissionCost + Penalty 2

• LoadSheddingAmount

where Penalty1 and Penalty2 are the coefficients of penalty term, and both of them are set as 1000.

2.3. Stochastic CGEN expansion planning model considering N—1 network security criterion

The wind energy is intermittent and uncertain, so the value of the second objective becomes a stochastic variable. Taking into account the uncertain wind energy, we establish a multi-objective stochastic model for the CGEN expansion planning with the investment cost and the expected production cost, carbon

Minf 1 — InvestmentCost + penaltyi • 1 LoadSheddingAmount Min f 2 = IpECost + Penalty2 • 1 LoadSheddingAmount

1 LoadSheddingAmount E

^APLij

Subject to constraints (4)-(15), (20), (22), (26)-(30).

/NWS NCG

IpECost — E ]T8760 • Costgasi* WSi + 8760 ^ (aiP2^ + biPgi + c^ i 1 i 1

i 1 NCG

i 1 NGG

+ 8760 • CarbonCost * n1 * Pgi + J_^8760 • CarbonCost

*Í2 * Pgi)

Subject to constraints (4)-(22).

In order to remove the binary variable sgnij in Eq. (6) and make this model solvable by the optimization tool IPOPT, we introduce two new continuous variables sk and tk , and make the following transformation for constraints (4) and (6).

fPk = (1 — 2sk) ■ tk (37)

t4= M2( p2 — p/)2 (38)

—Msk <= p — Pj < = M(1 — sk) (39)

sk(1 — sk) = 0 (40)

where M is a large value, and we set it as 10,000 in this paper. Then, all the proposed models only include three binary decision variables for candidate pipelines, compressors and electricity lines. This transformation will facilitate the proposed algorithm introduced in the next section.

3. NSGA-II based multi-objective optimization model

In the traditional network expansion planning study, the natural gas network and electricity network are implemented independently. For each of them, the optimization model is a mixed integer non-linear programming problem (MINLP). However, when these two models are combined together by a series of nonlinear energy conversion equation constraints, it becomes a CGEN co-planning model which is complex and difficult to solve. To address this problem, we employ a heuristic algorithm Elitist Non-dominated Sorting Genetic Algorithm" (NSGA II) [22] combined with the IPOPT (Interior Point Optimizer) to solve the proposed model.

It should be noted that the integer decision variables of the proposed model including three parts: candidate pipelines, candidate compressors and candidate electricity lines, and the decimal coding is adopted in the proposed algorithm. Based on the NSGA-II for multi-objective optimization problem, the whole procedure for solving the proposed model, which is shown in Fig. 1, can be summarized as follows:

Step 1: Set iteration counter t = 0, a population P(t) with predefined size randomly generated, in which each individual represents a scheme to add candidate pipelines, compressors and electricity lines on the base CGEN.

Step 2: The objective functions of each scheme can be evaluated as shown in the red box of Fig. 1, and then according to

Y. Hu et al./Applied Energy xxx (2015) xxx-xxx

Input wind data and planning data of gas network and electricity network

Randomly initialize the population POP

Run the OPF solved by the improved 2m+1 pointestimate method

Determine investment cost for each individual Determine the expected value of production cost for each individual Determine th value of the load curtailm indiv e expected amount of ent for each dual

Assign non-dominated rank and distance rank for each individual in POP

Iteration count t=1

Select individuals from POP by tournament selection to form parent population (P1)

Generate the offspring population (P2) by manipulating crossover and mutation on P1, and evaluate the objective functions for each individual as the circle (!)

Combine P2 and original POP, and create the new POP according to the assigned non-dominated rank and distance rank for each individual

Using the decision making analysis to chose the final solution from the final optimal Pareto front

Fig. 1. Flowchart of the proposed algorithm.

\ Solutions with larger crowding-distance

First Front with non donminated solutions

Solutions with smaller crowding-distance

Third Front Second Front

Fig. 2. Population classified by non-dominated sorting technique.

non-domination ranks and crowding-distance values, all schemes are classified into a number of non-dominated fronts as shown in Fig. 2. The detailed process to achieve objective functions of each scheme will be introduced in the section 3.1. Step 3: Apply a binary tournament selection on P(t) to form the parent population S(t), where schemes with lower non-domination rank or larger crowding distance value, as presented in Fig. 2, have more chance to be selected. Step 4: Manipulate crossover and mutation operators on parent population S(t), so new schemes can be reproduced to create

offspring population Q(t). And then calculate objective functions for each scheme in Q(t).

Step 5: Combine population P(t) with population Q(t) to develop R(t), and carry out non-dominated sorting on R(t), then a new population P(t) is generated from R(t). The detailed forming process is shown in Fig. 3. It can be seen that the schemes, belonging to the lower front or with larger crowding-distance, have a higher priority of being selected for reproduction. Therefore, candidate gas pipelines, gas compressor and transmission lines with larger contribution to attain desirable objective functions are selected.

Step 6: Set t = t + 1, and verify whether the value of iteration count reaches the maximum number of predefined iterations. If it is not satisfied, go back to Step 3; otherwise, stop the iterative search and output the optimal Pareto front of the planning schemes.

Step 7: To obtain the final planning scheme from the optimal Pareto front, a fuzzy satisfying method is adopted to help the planner make the final decision.

However, there are two issues that should be addressed in section 3.1 and 3.2.

3.1. Evaluation of objective functions

Because the value of candidate pipelines, compressors and electricity lines is known for each scheme, the first objective (investment cost) of each scheme in population can be easily obtained. Meanwhile, when solving the second objective, the original MINLP model becomes a non-linear programming problem which can be solved by the IPOPT solver. So the difficult problem is how to tackle the uncertainty and correlations of wind power.

An improved Point Estimate Method (PEM) proposed in [24] is extended to calculate the expected value of second objective (production cost and amount of load curtailment). Comparing to the traditional commonly used methods, such as the Monte Carlo Simulation, the employed method can significantly reduce the computational time especially for large-scale optimization model. Assuming that there are m wind farms, the approximation of expected value of second objective can be obtained only by calculating 2m + 1 times deterministic optimal power and natural gas load flow via IPOPT.

Unlike PEM that requires uncorrelated random variables, the improved PEM can take the effects of the correlations among wind farm outputs into consideration, by using an orthogonal transformation. Therefore, the correlated input variables are converted into variables with independent distribution, and the traditional PEM can be deployed.

The improved PEM method to calculate the expected value of second objective is divided into two stages. The first stage is to achieve correlated outputs of wind farms as input data, and the second stage is applying this input data to evaluate the expected objective value.

3.1.1. Obtaining correlated wind farm output

In this paper, the commonly used Weibull distribution [25] is chosen to simulate the volatile wind speed, and the correlations among wind speeds of different wind farms can be represented by a correlation matrix [24] as:

CW = (Pij) =

(Pll Pl2 p21 p22

\Pn1 Pn2

Pln\ P2n

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Front 1 Front 2

Front 3

P(t+1)

Non-dominated sorting on R(t)

Front 4

Crowding-distance sorting on Front 3

Larger Crowding -distance

Smaller Crowding -distance

■ Rejected

Fig. 3. Forming process of new population.

where Pj is the correlation coefficient between wind speed variable Vt and wind speed variable Vj.

Given the Weibull distribution parameters and the correlation matrix of wind speeds, the method of generating the correlated wind speeds can be referred to [26]. And then the correlated outputs of wind farms can be obtained by Eq. (42).

Pw = { Prate(V - Vci)/(Vrate - Vd)

V < Vd, V > Vco Vci 6 V < Vrate Vrate 6 V 6 Vco

where Prate is the rated power of wind turbine, Vci, Vrate and Vco are the cut-in, rated, cut-out wind speed, respectively. After obtaining a large number of simulated wind power data, the first four statistical moments of each wind farm can be easily calculated by mathematical statistics analysis method [26]. Meanwhile, the variance-co-variance matrix, which represents the correlations among the wind power outputs, can also be easily obtained from correlation matrix CW.

Certainly, if enough data of measured weed speed is known to planner, it can be directly applied to calculate the first four statistical moments and variance-covariance matrix as input data of wind farms.

3.1.2. Evaluating the second objective by the Improved PEM

Let vector X represent the correlated output of m wind farms and Y be the second objective function, and the detailed procedure of applying the improved PEM is summarized as follows to evaluate the expected objective value:

m , , 4 kzl,4 = ft- J kxr,4 dxr l = 1, •• •

(4) Calculate the concentrations ((zlk, mlyk), k = 1,2 ,3 l = 1,... m) in the transformed independent space according to Eqs. (47)-(51).

+ (-1)3

Ô 3 = 0

Xl k =

nl,k(nl, 1 - Îl,2) '

kzl 4--7 k

k = 1,2

k = 1,2

ml 3 =---

' m kzl ,4 - k

zl,k = Izi + il,k ■ dzl, k = 1,2

(5) Construct the 3m transformed points in the form

(Zk = (1Z1; 1Z2; ...zl,k, ... ,1zm) k= 1,2 ,3l = 1; and

convert these points into the original space by applying the inverse transformation, that is, Xlk LZlk k 1 2 3 l 1 ...m.

(6) Solve 3m times deterministic optimal power and natural gas load flow (Yk = H(Xk) k = 1,2 , 3 l = 1,... m), and then the expected value of Y can be obtained as follows:

(1) Input the first four statistical moments of the m wind farms outputs, including column vectors of the means iX, standard deviations dX, skewness kX3 and kurtosis kX4, as well as the variance-covariance matrix CX.

(2) Obtain inferior triangular matrix L by decomposing CX through Cholesky decomposition, CX = LLT.

(3) Calculate the first four central moments of vector Z with independent variables (corresponding to correlated vector X ) as follows:

1y = ËÎ2°}l.k x H(X'k)

1 L ßx

Cz = L-1Cx (L-1)T = I

m t \3

kzl, 3 = \L-J ÀXr, 3 dxr l= 1, •••'

It should be noted that m of 3 m points are at the same point (lX1, iX2 ,... iXk,..., 1Xm), so in fact only 2m + 1 iterations are need to yield the approximation of the expected value of Y.

3.2. Final deterministic decision-making

Obviously, the result of multi-objective optimization problems should be a Pareto set. To obtain the final planning scheme, a fuzzy satisfying method using the distance metric method is adopted to help the planner make the final decision [27].

Firstly, map all the schemes in the final optimal Pareto front into fuzzy sets. The fuzzy sets are defined by a linear membership function as follows:

Y. Hu et al./Applied Energy xxx (2015) xxx-xxx

f (x) =

( 0 fi(x) > fmax

fmf fmin 6 f(x) 6 ¡m

fi(x) < fr

where /Jnax and /J"1" denote the maximum and minimum value of objective function i in the final optimal Pareto front, respectively. The membership value ranges from 0 to 1, representing the satisfied degree of membership in a fuzzy set.

Secondly, obtain the final planning scheme according to the preference of decision maker. After determining the membership function to each objective function of every scheme, the decision maker needs to define the desirable level idi for each objective, and the final solution can be obtained by solving the following optimization problem:

X 2 Solutionset

Y\ldi~ 1fi(x)\

where the value of idiranges from 0 to 1, and it reflects the degree of attention to the objective function i. For example, if we have enough investment budget and aim to minimize the production cost, the values of id1 and id2 can be set to 0 and 1 respectively.

4. Numerical results

4.1. Results analysis on the test system

The proposed model is tested on a combined energy system consisting of the IEEE 24-bus test system [28] and a 15-node natural gas network [6] to analyze the impact of wind power uncertainty on the CGEN expansion planning. These two networks are coupled via eight natural gas-fired generators as shown in Fig. 5. The natural gas network includes two sources, five gas loads (excluding the combined nodes), twelve gas pipelines and four compressors, where all compressors are treated as candidate infrastructures and node #1 serves as the reference node in the gas network. In addition, it is assumed that new pipelines can be added into each path of the gas network, and the maximum expansion number is two. The parameters of the candidate pipelines are the same as the existing ones on each path. The gas supply sources and gas demand will increase 1.5 times compared to the base year. The IEEE 24-bus system has thirty-eight existing lines, eight gas-fired generators and twenty-three coal-fired generators. Assuming that the system will be expanded for the future, the generation and load demand level equals to 2.2 times of their original values in the planning year. The candidate lines can be added into thirty-four existing corridors and seven new corridors 1-8, 2-8, 6-7, 13-14, 14-23, 16-23 and 19-23. Up to three candidate lines can be installed for these corridors. The carbon emission coefficient of gas-fired generator is assumed to be 0.549 ton/MWh and coal-fired generator 0.976 ton/MW h. The carbon price is $23/ton. The annualized investment cost for each gas compressor is $2 000 000.The annualized investment costs of electricity line and gas pipeline are $100 000/km and $150 000/km, respectively. All the detailed input data of the test system can be available from Appendices A and B.

The test is performed on a PC consisting of a 3.0-GHz processor and 2 GB of RAM. The proposed algorithm initializes the population size to be 80, and the probabilities of crossover and mutation to be 0.8 and 0.1, respectively.

To investigate the effects of the wind energy uncertainty on the integrated energy system, the generators on Bus-7, Bus-13 and Bus-23 are replaced by three wind farms A, B and C. The capacity of the three wind farms A, B, C is set to be 360 MW, 360 MW and 1000 MW, and the other generations are controlled by traditional

thermal generators. The input data of wind farms are shown in Table 1. Furthermore, the effect of correlations among wind farms on the optimal Pareto front is studied on two cases: the correlation among wind farms is 0.8 in Case 2, while in Case 1 it is assumed that the outputs of the three wind farm are independent.

The results obtained by the proposed method are shown in Fig. 4, where it can be observed that the optimal Pareto front of case 1 is located in the front of Case 2. The reason is that the correlations among wind farms are positive and the variations of wind energy become stronger when the correlations are taken into consideration. Therefore, it will need more backup coal-fired or gas-fired generators and thus the total production cost increases in Case 2.

Furthermore, taking the Case 2 as an example, we consider four different desirable levels of two objectives by the fuzzy satisfying method on the optimal Pareto front. Tables 2 and 3 present the detailed expansion results of the natural gas network planning and electricity network planning. It should be noted that the desirable level is determined upon the attention level of the planner to the objective. In Table 4, total planning costs of the four schemes are presented. It can be seen that with the increase of the desirable level on investment cost, the investment cost is decreasing and the production cost is increasing, which reflects that the production cost of CGEN is closely related to the investment cost.

Moreover, the comparison of results of co-planning and separated planning (se-planning) of CGEN under the same desirable levels is shown in Tables 4 and 5, where it can be observed that the investment costs of se-planning is lower than that of co-planning, but the production cost is significantly higher. Loosely speaking, the total cost of co-planning is lower than that of se-planning. For all the four schemes, the total cost of co-planning is saved more than 10% than that of se-planning.

Choose the Scheme 3 for illustration, and the co-planning result is shown in Fig. 5. In the gas network, it can be observed that 12 new gas pipelines and two compressors are installed. Firstly, to

Table 1

Input data of wind farms.

Wind farm Scale Shape Vci (m/ Vrate Vco (m/

bus parameter parameter s) (m/s) s)

7 5.90 1.51 3 12 25

13 5.93 2.03 3 12 25

23 5.12 1.99 3 12 25

1560 1540 1520 1500 1480

□ Chosen Scheme O Case 1 ♦ Case 2

3© 1+

0000 oc o o

900 1000 1100 1200 1300 1400 15! Investment Cost (MS)

Fig. 4. Comparison of optimal Pareto fronts between Casel and Case 2.

Y. Hu et al./Applied Energy xxx (2015) xxx-xxx

Table 2

Expansion results of the natural gas network on the four schemes.

Candidate pipelines Scheme 1 Scheme 2 Scheme 3 Scheme 4

From node To node

1 3 2 2 2 2

2 4 2 2 1 2

3 4 0 0 0 0

3 5 2 2 2 1

4 7 1 1 2 1

6 9 2 2 2 0

8 11 2 2 1 2

10 13 2 2 1 2

12 14 2 2 1 2

13 14 0 0 0 0

13 15 1 1 0 0

14 15 1 1 0 1

Candidate compressors Scheme 1 Scheme 2 Scheme 3 Scheme 4

Inlet node Outlet node

5 6 0 0 1 0

7 8 0 0 1 0

9 10 1 0 0 1

11 12 0 0 0 0

Table 3

Expansion results of the electricity network on the four schemes.

Candidate electricity lines

Scheme 1 Scheme 2 Scheme 3 Scheme 4

From bus To bus

1 2 0 0 0 0

1 3 0 0 1 0

1 5 3 1 0 1

1 8 0 0 0 0

2 4 0 0 0 0

2 6 0 0 0 0

2 8 0 0 0 0

3 9 1 1 0 0

3 24 1 1 1 1

4 9 0 0 2 0

5 10 0 0 0 0

6 7 0 0 0 0

6 10 3 3 1 3

7 8 2 2 1 1

8 9 0 0 0 0

8 10 1 1 1 1

9 11 1 1 1 1

9 12 1 1 0 1

10 11 1 1 0 1

10 12 0 0 1 0

11 13 0 0 1 0

11 14 0 0 2 0

12 13 0 0 1 0

12 23 0 0 0 0

13 14 0 0 0 0

13 23 1 1 0 1

14 16 1 1 2 1

14 23 0 0 0 0

15 16 0 0 0 0

15 21 0 0 0 0

15 24 1 1 0 0

16 17 1 1 2 1

16 19 2 0 0 2

16 23 0 0 0 0

17 18 0 0 1 0

17 22 0 0 0 0

18 21 0 0 1 0

19 20 0 0 0 0

19 23 0 0 0 0

20 23 1 1 0 1

21 22 0 0 0 0

ensure the natural gas to be sent out, all the gas pipelines connected gas suppliers and compressors are strengthened. Secondly, we can find that few gas pipelines connected to node #15 are expanded. The reason is that pressures at node #13 and #14 are improved by two compressors, respectively, so the pressure differences between #13-#15 and #14-#15 are capable of delivering enough natural gas to meet the gas demand WL5. As for the electricity network, transmission lines are mostly added around the gas-fired generators. The reason is that both the production cost and carbon emission cost of gas-fired generators are lower than coal-fired generators, so as the capacity of electricity lines around gas-fired plants are improved, the cleaner power energy with lower price can be delivered as much as possible to meet the electricity demands. In addition, around the electricity nodes connected with wind farms (i.e., node #7, #13 and #23), lots of electricity lines are expected to be expanded because the total transmission capacity of the existing electricity lines is insufficient to ensure the wind energy, gas-fired generation and coal-fired generation to be fully sent out.

In contrast, Fig. 6 depicts the results of se-planning for the scheme 3. Unlike the planning results of gas network by co-planning, none of candidate compressors are selected by the se-planning, since the investment cost of compressor is relatively higher than gas pipelines. Thus, the inlet node and outlet node of each compressor becomes a same interconnection point. To ensure the gas to be delivered to each gas load, all the gas pipelines through the path from gas suppliers to the gas demand are expanded. As for the electricity network, transmission lines are only strengthened in the regional parts, such as bus #6, #8, #10 and #16, and the capacity expansion of electricity lines around gas-fired generators is not as strong as the planning results by co-planning.

The comparison between Figs. 5 and 6 shows that the co-planning can strengthen both electricity and gas network (i.e., installing two compressors) to improve the energy transfer capability to deliver more gas for balancing load demand, since the production cost of gas is relatively lower than coal. In contrast, the se-planning mainly strengthens the electricity network, and the production cost of electricity network and the total investment cost are reduced. However, the production cost of the gas network will be greatly increased, so that the total cost including both investment and production cost of CGEN is increased.

4.2. Results analysis on the real-life system

In the future planning year, the predicted power energy of reallife electricity system of Hainan province (China) will be supplied by five types of units, including 8 gas-fired units (2986 MW), 17 coal-fired units (859 MW), 1 nuclear unit (650 MW), 10 hydro units (446 MW) and 3 wind farms (1080 MW). The wind speed data used here is data measured at the real power grid from January 1, 2014 to December 31, 2014 for every 15 min. The total peak load of planning horizon is 4364 MW. The electricity transmission network is mainly operated at two voltage levels, 110 kV and 220 kV, and there are 37 high-voltage substations and 431 existing transmission lines (including transformers). It is assumed that the candidate lines can be added into 27 existing corridors. Up to two candidate lines can be installed on each corridor. The natural gas network consists of two gas sources, eight gas loads (excluding the combined nodes), ten gas pipelines and three compressors, where all compressors are treated as candidate infrastructures and node #1 serves as the reference node in the gas network. In addition, candidate pipelines can be added into each path of the gas network, and the maximum expansion number is two. These two systems are coupled by A, B, C and D four natural gas power plants. The carbon emission coefficient, carbon price and

Y. Hu et al./Applied Energy xxx (2015) xxx-xxx

Table 4

Planning costs of schemes on different desirable levels.

Desirable level

Co-planning

Se-planning

Objective f 1 (M$)

Objective f 2 (M$)

Objective f1 (M$)

Objective f2 (M$)

Scheme 1 Scheme 2 Scheme 3 Scheme 4

0.1 0.3 0.5 0.6

0.9 0.8 0.7 0.6

1420.122 1318.050 1183.724 1113.592

1432.358 1432.366 1439.728 1455.361

1344.194 1231.177 1102.722 1063.295

1848.016 1819.310 1843.762 1821.512

Table 5

Comparison of total planning cost on different desirable levels.

Co-planning total cost (M$)

Se-planning total cost (M$)

Percentage of total cost reduction (%)

Scheme 1 Scheme 2 Scheme 3 Scheme 4

2852.480 2750.416 2623.453 2568.953

3192.210 3050.486 3027.484 2884.807

11.91 10.91 12.31 12.30

Not Added Candidate Compressor <8> Gas-Fired Plant

© Coal-Fired Plant

Added Candidate Compressor Wind farm

Existing Pipeline Existing Electricity Line

Added Pipeline --- Added Electricity Line

Q Gas-Electricity Combined Bus |

Fig. 5. Co-planning scheme (Scheme 3) of combined electricity and gas networks.

Y. Hu et al./Applied Energy xxx (2015) xxx-xxx

W1=WS1

W2=WS2

Not Added Candidate Compressor

Added Candidate Compressor Existing Pipeline Added Pipeline Gas-Electricity Combined Bus

Gas-Fired Plant Coal-Fired Plant Wind farm

Existing Electricity Line Added Electricity Line

Fig. 6. Se-planning scheme (Scheme 3) of combined electricity and gas networks.

the annualized investment cost for each candidate elements are the same as the previous test system. All the data of this system comes from a National High Technology Research and Development Program of China (863 Program).

Fig. 7 depicts the optimal Pareto front of the planning result of the real-life system of Hainan province. Suppose that the budget of investment cost is enough and the aim of the planning project is to minimize the production cost. Thus, the desirable levels for investment cost and production cost can be chosen as 0.1 and 0.9, respectively. The final scheme marked in Fig. 7 will be chosen and the topology of the chosen co-planning result is shown in Fig. 8. Since Hainan province is an island and the middle of it is mountainous areas, the topology of the entire network is a ring structure with only three corridors connecting the East and West. It can be observed that most of the power plants are located in the west, especially for the gas-fired power plants. After adding new transmission lines on the base transmission network, transmission lines around wind farms and most gas-fired plants are strengthened to guarantee that cheaper and cleaner power energy can be sent out. The long distance transmission lines on corridor 1-34, 34-22

1261.6 1261.4 1261.2 1261 1260.8 1260.6 1260.4 1260.2 1260

al Sc he \

* Fin sme

120 140 160 180 200 220 240 260 280 Investment Cost (M$)

Fig. 7. Optimal Pareto front of real-life system.

1259.8

Y. Hu et al./Applied Energy xxx (2015) xxx-xxx

Existing Line New Added Line 171 Hydropower Plant © Thermal Power Plant El Wind Farm ^ Gas Power Plant |Ô1 Nuclear Power Plant @ SOOkV Substation

® 220kV Substation o llOkV Substation

CD Candidate Compressor

M Added Compressor

O Gas-Electricity Combined Bus

--Existing Pipeline

--Added Pipeline

Fig. 8. Co-planning scheme of combined real-life electricity and gas system.

Table 6

Data of coal-fired generators.

Node Number Capacity Cost Cost Cost

(MW) coefficient ai coefficient bi coefficient

($/MW2) ($/MW) Ci

1 2 44 0.01131 12.145 0

1 1 167.2 0.01131 12.145 0

2 2 44 0.01131 12.145 0

2 1 167.2 0.01131 12.145 0

7 1 220 0.0122 17.924 0

13 1 433.4 0.003 20.023 0

14 2 44 0.01131 12.145 0

15 5 26.4 0.0667 9.2706 0

18 1 880 0.0028 5.345 0

22 6 110 0.001 0.5 0

23 1 880 0.00392 8.919 0

and 13-20 are also newly added to enhance the original topology of electricity network. Although these lines have higher investment cost than other candidate lines, it can significantly reduce the

Table 7

Data of gas-fired generators.

Node Number Gas fuel rate Gas fuel rate Gas fuel rate

capacity coefficient l1 coefficient l2 coefficient

(MW) (BTU/MW2) (BTU/MW) 13(BTU)

1 1 167.2 0.01131 12.145 0

2 1 167.2 0.01131 12.145 0

7 1 220 0.0122 17.924 0

13 1 833.4 0.003 20.023 0

15 1 341 0.0667 9.2706 0

16 1 341 0.0667 9.2706 0

21 1 880 0.0028 5.345 0

23 1 341 0.00392 8.919 0

production cost and improve the reliability of the whole system by strengthening the connection between the west and the east.

For the gas network, the transmission route between node #3 and node #11 is expanded by adding new pipelines, while on the transmission route between node #4 and node #14, not only the

Y.Hu et al./Applied Energy xxx (2015) xxx-xxx 13

Table 8

Data of load.

Node 1 2 3 4 5 6 7 8 9 10 13 14 15 16 18 19 20

Load (MW) 237 213 396 162 156 299 275 376 385 429 583 426 697 220 732 398 281

Table 9

Data of electricity lines.

From bus To bus Reactance (p.u.) Capacity (MW) Number of existing lines Max. number of expansion Length (km)

1 2 0.0139 175 1 3 3

1 3 0.2112 175 1 3 55

1 5 0.0845 175 1 3 22

1 8 0.1344 175 3 35

2 4 0.1267 175 1 3 33

2 6 0.192 175 1 3 50

2 8 0.1267 175 3 33

3 9 0.119 175 1 3 31

3 24 0.0839 400 1 3 50

4 9 0.1037 175 1 3 27

5 10 0.0883 175 1 3 23

6 7 0.192 175 3 50

6 10 0.0605 175 1 3 16

7 8 0.0614 175 1 3 16

8 9 0.1651 175 1 3 43

8 10 0.1651 175 1 3 43

9 11 0.0839 400 1 3 50

9 12 0.0839 400 1 3 50

10 11 0.0839 400 1 3 50

10 12 0.0839 400 1 3 50

11 13 0.0476 500 1 3 66

11 14 0.0418 500 1 3 58

12 13 0.0476 500 1 3 66

12 23 0.0966 500 1 3 134

13 14 0.0447 500 3 62

13 23 0.0865 500 1 3 120

14 16 0.0389 500 1 3 54

14 23 0.124 500 3 86

15 16 0.0173 500 1 3 24

15 21 0.049 500 3 68

15 24 0.0519 500 1 3 72

16 17 0.0259 500 1 3 36

16 19 0.0231 500 1 3 32

16 23 0.0822 500 3 114

17 18 0.0144 500 1 3 20

17 22 0.1053 500 1 3 146

18 21 0.0259 500 2 3 36

19 20 0.0396 500 2 3 55

19 23 0.0606 500 0 3 84

20 23 0.0216 500 2 3 30

Table 10

Bus data of gas network.

Node Supply capacity Load demand (106 SCF/h) (106 SCF/h)

Minimum Maximum

pressure (psia) pressure (psia)

Table 11

Pipeline branch data of gas network.

1 20.288 - 600 1200 From To Pipeline Number of Max. number of Length

2 20.867 - 600 1200 node node constant existing lines expansion (km)

3 - 1.838 500 1200 1 3 0.0320 1 3 80.5

4 - 1.218 500 1200 2 4 0.0320 1 3 80.3

5 - Gas-fired Plant 400 1200 3 4 0.0128 1 3 55.9

6 - Gas-fired Plant 400 1200 3 5 0.0214 1 3 81.1

7 - Gas-fired Plant 400 1200 4 7 0.0103 1 3 87.9

8 - Gas-fired Plant 400 1200 6 9 0.0199 1 3 93.5

9 - Gas-fired Plant 400 1200 8 11 0.0125 1 3 99.7

10 - Gas-fired Plant 400 1200 10 13 0.0130 1 3 93.5

11 - Gas-fired Plant 400 1200 12 14 0.0060 1 3 97.9

12 - Gas-fired Plant 400 1200 13 14 0.0067 1 3 86.6

13 - 4.263 600 1000 13 15 0.0070 1 3 79.7

14 - 4.274 600 1000 14 15 0.0194 1 3 83.5

15 - 1.501 600 1000

Y. Hu et al./Applied Energy xxx (2015) xxx-xxx

Table 12

Compressor branch data of gas network.

Inlet node

Outlet node

Compressor constant

Gas consumption coefficient a

Gas consumption coefficient ß

Gas consumption coefficient y

5 7 9 11

6 8 10 12

5420.58 5356.05 5420.58 5356.05

0.0305 0.0296 0.0017 0.0017

8.33 8.33 8.33 8.33

transmission capacity is increased, but also a new compressor is installed. The reason is that the transmission distance between node #4 and node #14 is longer than the distance between node #3 and node #11, so a compressor is needed to compensate the pressure loss along this route. It also can be found that after increasing the pressure at the node # 12 by the new added compressor, the natural gas can be sent to the terminate node #14 without investment for a new pipeline between #13 and #14.

5. Conclusions

A multi-objective CGEN co-planning model is developed to search for the optimal scheme of the combined natural gas and electricity network to coordinate different objectives, which can effectively handle the expansion planning problem about which and where natural gas pipes, gas compressors and power transmission lines are expanded in the integrated natural gas network and electricity network. Moreover, the impact of the uncertainties and correlations of the wind farms on the total production cost is revealed that the stochastic wind power may increase the total cost of CGEN. Most importantly, the proposed model is performed on a test system and a real-life system, which achieves a higher social welfare than the design with each separated networks.

Technically, the proposed multi-objective optimization model is solved by the Elitist Non-dominated Sorting Genetic Algorithm II (NSGA-II) to capture the optimal Pareto front. Therein, the combined optimal power and natural gas load flow, served as a subproblem of the original multi-objective optimization model, is tackled by the proposed primal-dual interior-point method combined with the improved point-estimation method. This method is actually a general approach that also can be extended to other research fields with the consideration of different kinds of uncertainties, such as natural gas price, natural gas load and electricity load.

Appendix A. Data of test electricity system

Tables 6-9.

Appendix B. Data of natural gas test system

Tables 10-12.

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