## 考虑经济性与碳排放的电-气综合能源系统多目标规划

1.国网山东省电力公司潍坊供电公司, 山东 潍坊 261000

2.山东大学 电气工程学院, 济南 250061

3.丹麦科技大学 电气工程学院,丹麦 灵比 2800

## Multi-Objective Planning of Power-Gas Integrated Energy System Considering Economy and Carbon Emission

ZHU Hainan,1, WANG Juanjuan1, CHEN Bingbing1, ZHANG Houwang2, CHEN Jian2, WU Qiuwei3

1. State Grid Weifang Power Supply Company, Weifang 261000, Shandong, China

2. School of Electrical Engineering, Shandong University, Jinan 250061, China

3. Department of Electrical Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark

 基金资助: 国网山东省电力公司科技项目(520604200003)国家重点研发计划(2018YFA0702200)

Received: 2021-12-16   Revised: 2022-01-6   Accepted: 2022-02-7

Abstract

In order to accelerate the rapid and economic low-carbon transformation of the power-gas system, a multi-objective stochastic optimization programming model for the whole equipment of the power-gas system was established, which comprehensively considered the economic cost and carbon emissions. First, the mathematical model of the electric-gas network and related equipment was established, and the uncertainty characteristics of the electric and gas loads and photovoltaic output were analyzed by using the scenario method. Next, a mixed-integer quadratically constrained programming (MIQCP) model considering the economic cost and carbon emissions of the system was established. An overall planning was made for power feeders, gas network pipelines, substations, gas distribution stations, gas units, power-to-gas devices, photovoltaic, and energy storage devices. Finally, a numerical example was built to verify the feasibility and effectiveness of the model. The results show that the model can fully consider the coupling relationship between power-gas network lines and a variety of comprehensive energy equipment under different weight choices of objective function, and obtain the overall optimal planning scheme.

Keywords： integrated energy; multi-objective; expansion planning; low-carbon transformation

ZHU Hainan, WANG Juanjuan, CHEN Bingbing, ZHANG Houwang, CHEN Jian, WU Qiuwei. Multi-Objective Planning of Power-Gas Integrated Energy System Considering Economy and Carbon Emission[J]. Journal of Shanghai Jiaotong University, 2023, 57(4): 422-431 doi:10.16183/j.cnki.jsjtu.2021.513

## 1 数学模型

#### 1.1.1 燃气机组

$Pi,d,hgt=∑g∈TgPg,i,d,hgt$
$Qi,d,hgt=∑g∈TgηgPg,i,d,hgt$
$Fm,d,hgt=∑g∈TgPg,i,d,hgtζgHgas$
$0≤Pg,i,d,hgt≤∑g∈TgZg,igtPgmax$
$∑g∈TgZg,igt≤1$

#### 1.1.2 电转气装置

$Pi,d,hp2g=∑p∈TpgPp,i,d,hp2g$
$Fm,d,hp2g=∑p∈TpgζpPp,i,d,hp2gHgas$
$0≤Pp,i,d,hp2g≤∑p∈TpgZp,ip2gPpmax$
$∑p∈TpgZp,ip2g≤1$

#### 1.1.3 储能装置

$∑e∈TeZe,iessEemin≤Ei,d,hess≤∑e∈TeZe,iessEemax$
$0≤Pi,d,hess,cha≤∑e∈TeZe,iessPemax$
$0≤Pi,d,hess,dis≤∑e∈TeZe,iessPemax$
$Ei,d,hess=Ei,d,h-1ess+μPi,d,hess,cha-Pi,d,hess,dis/μ$
$Ei,d,24ess=Ei,d,0ess$
$∑e∈TeZe,iess≤1$

#### 1.1.4 分布式光伏

$∑v∈TvZv,ipv≤1$
$0≤Pi,d,hpv≤∑v∈TvZv,ipvPvmaxP^d,hpv$

#### 1.2.1 变电站

$(Pi,d,hsub)2+(Qi,d,hsub)2≤∑s∈TsZs,isub(Ssmax)2$
$Zs,isub=Zn,s,isub+Zc,s,isub$
$∑s∈TsZs,isub≤1$

#### 1.2.2 配电网潮流

$Vi,d,h-Vj,d,h=∑c∈Tc(rcPc,ij,d,hcod+xcQc,ij,d,hcod)LijVref+bij,d,h$
$Vmin≤Vi,d,h≤Vmax$
$∑ji∈BePji,d,hbra+Pi,d,hgt+Pi,d,hpv+Pi,d,hess,dis=∑ij∈BePij,d,hbra+Pi,d,hp2g+Pi,d,hess,cha+PiloadS^d,h$
$∑ji∈NeQji,d,hbra-∑ij∈NeQij,d,hbra+Qi,d,hgt+QiloadS^d,h=0$
$Pij,d,hbra=∑c∈TcPc,ij,d,hcod$
$Qij,d,hbra=∑c∈TcQc,ij,d,hcod$
$Pc,ij,d,hcod≤Zc,ijcodPcod,cmax$
$Qc,ij,d,hcod≤Zc,ijcodQcod,cmax$
$bij,d,h≤(Vmax-Vmin)(1-∑c∈TcZc,ijcod)$
$Zc,ijcod=Zn,c,ijcos+Zc,c,ijcod$
$∑c∈TcZc,ijcod≤1$

#### 1.2.3 放射状拓扑

$yij+≥0, yij-≥0$
$yij++yij-≤1$
$∑c∈TcZc,ijcod=yij++yij-$
$∑ki∈Beyki++∑ij∈Beyij-=1-∑s∈TsZs,isub≤1, ∀i∈Ns$
$∑ki∈Beyki++∑ij∈Beyij-=1, ∀i∈Ne-Ns$

#### 1.3.1 配气站

$0≤Fm,d,hgat≤∑a∈TaFamaxZa,mgat$
$Za,mgat=Zn,a,mgat+Zc,a,mgat$
$∑a∈TaZa,mgat≤1$

#### 1.3.2 天然气网

$∑mn∈BtFmn,d,hbra+Fm,d,hp2g=∑nm∈BtFmn,d,hbra+Fm,d,hgt+FmloadF^d,h$
$Ff,mn,d,hpip≤Zf,mnpipFfmax$
$Fmn,d,hbra=∑f∈TfFf,mn,d,hpip$
$Zf,mnpip=Zn,f,mnpip+Zc,f,mpip$
$∑f∈TfZf,mnpip≤1$

#### 1.3.3 放射状拓扑

$ymn+≥0, ymn-≥0, ∀mn∈Bt$
$∑f∈TfZf,mnpip=ymn++ymn-, ∀mn∈Bt$
$ymn++ymn-≤1, ∀mn∈Bt$
$∑lm∈Btylm++∑mn∈Btymn-=1-∑a∈TaZa,mgat,∀m∈Na$
$∑lm∈Btylm++∑mn∈Neymn-=1, ∀m∈Nt-Na$

## 2 规划模型

### 2.1 目标函数

$f1、f2$的具体表达形式如下:

$f1=Cinv+Cope$

$Cinv=∑mn∈Bt∑f∈Tfκ(Cf,npipLmnZn,f,mnpip+Cf,cpipLmnZc,f,mnpip)+$

$∑ij∈Be∑c∈Tcκ(Cc,ncodLijZn,c,ijcod+Cc,ccodLijZc,c,ijcod)+$

$∑m∈Nt∑a∈Taκ(Ca,ngatZn,a,mgat+Ca,cgatZc,a,mgat)+$

$∑i∈Ns∑s∈Tsκ(Cs,nsubZn,s,isub+Cs,csubZc,s,isub)+$

$∑i∈Ng∑g∈TgκCggtZg,igt+∑i∈Npg∑p∈TpgκCpp2gZp,ip2g+$

$∑i∈Nv∑v∈TvκCvpvZv,ipv+∑i∈Nes∑e∈TeκCeessZe,iess$
$Cope=Ce∑i∈Ns∑d(nd∑hPi,d,hsub)+Ca∑m∈Na∑d(nd∑hFm,d,hgat)$
$f2=Wcηc∑i∈Ns∑d(nd∑hPi,d,hsub)+Wgt∑i∈Ng∑d(nd∑hPi,d,hgt)-Wp2g∑i∈Npg∑d(nd∑hPi,d,hp2g)$
$κ=r1-(1+r)-T$

$minω1f1-f1,minf1,max-f1,min+ω2f2-f2,minf2,max-f2,min$

## 3 算例分析

### 图1

Fig.1   Integrated power and natural gas system[13]

Tab.1  Parameters of alternate feeder

(元·km-1)
$Cc,ncod$/
(元·km-1)
$Pcod,cmax$/MW$Qcod,cmax$/Mvarrc/(Ω·km-1)xc/(Ω·km-1)
111.526.443.390.822 30.567
211.52×10422.26×10413.67.160.4110.283 5

Tab.2  Parameters of alternate piping

(元·km-1)
$Cf,npip$/
(元·km-1)
$Ffmax$/(m3·h-1)
114.88420
235.65×10437.14×1042 600

Tab.3  Parameters of alternate transformer substation

1198.0×10410
2185.7×104297.1×10415
3267.3×104445.7×10420

Tab.4  Parameters of alternate gas distributing station

1399.0×1043 200
2331.4×104533.7×1044 200
3468.0×104668.5×1045 200

Tab.5  Parameters of alternate gas generator

10.350.3440.24×1041.08
20.400.3483.46×1042.62

Tab.6  Parameters of alternate power to gas device

10.60666.4×1041
20.621 928.0×1043

Tab.7  Parameters of alternate PV

1102 704×1042、4、11
2154 056×1042、4、11
3205 406×1042、4、11

Tab.8  Parameters of alternate energy storage device

(MW·h)
$Pemax$/
MW
$Ceess$/
Nesμ
151.75883.2×1042、4、110.95
272.451 236.0×1042、4、110.95
3103.51 766.0×1042、4、110.95

### 图2

Fig.2   Curves of normalized electrical load

### 图3

Fig.3   Curves of normalized gas load

### 图4

Fig.4   Variation curves of photovoltaic output per unit capacity

### 3.2 结果分析

Tab.9  Equipment selection of each case

### 图5

Fig.5   Expansion planning results of cases

Tab.10  Cost of each case

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