﻿ 基于混沌遗传算法和物元可拓的特高压输电线路评估 Evaluation of UHV Transmission Lines Based on Chaotic Genetic Algorithm and Element Extension

Pure Mathematics
Vol. 13  No. 07 ( 2023 ), Article ID: 69715 , 9 pages
10.12677/PM.2023.137218

Evaluation of UHV Transmission Lines Based on Chaotic Genetic Algorithm and Element Extension

Haolun Li, Heli Duan, Qiyuan Sun, Jinzhi Fan, Zijie Xia, Kang Zhao

School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha Hunan

Received: Jun. 17th, 2023; accepted: Jul. 21st, 2023; published: Jul. 28th, 2023

ABSTRACT

With the growth of the national economy, China’s demand for electricity is increasing. In order to reduce the loss of transmission lines and save precious land resources, the UHV network is developing continuously. This project considers the small and medium scale weather, terrain elevation obstacle, transmission tower layout factors, uses the chaotic genetic algorithm preliminary line planning, reuses the initial comprehensive benefit assessment of the optimal line, to get the UHV transmission line optimization path and feasibility analysis, and adds time factor for problems such as engineering delay, to provide effective reference for actual engineering implementation.

Keywords:UHV Transmission, Chaos Genetic Algorithm, Chaos Disturbance, Perturbation Factor, Comprehensive Benefit Evaluation, Time Factor, Improve the Topology of Objects

1. 引言

2. 初步线路规划

${\xi }_{i+1,j}=4{\xi }_{ij}\left(1-{\xi }_{ij}\right)$ (1)

$\eta \left(i,j\right)=\eta \mathrm{min}\left(j\right)+\left(\eta \mathrm{max}\left(j\right)-\eta \mathrm{min}\left(j\right)\right)×\xi \left(i,j\right)$ (2)

${\eta }_{ij}={a}_{0}+\left({b}_{0}-{a}_{0}\right){\xi }_{ij}$ (3)

3. 线路综合效益评估

3.1. 特高压输电线路综合效益指标构架

1) 输送效果。传统输电的大部分只考虑输电能力和输电效率，本文选取输电量、输电损耗率、能量不可利用率等指标对输电能力进行整体评价。

2) 经济效益。项目的盈利能力和偿还债务的能力是反映项目整体经济效益的两个重要的参考因素，因此本文综合选取偿债覆盖率和投资回收年限两个指标对特高压输电项目进行经济效益评估。

3) 环境效益。当前，加快建设特高压电网，充分发挥特高压远距离、大容量、低损耗、少占地的优势，建设“资源节约型、环境友好型”社会，促进经济、社会、环境可持续发展，已成为各方的广泛共识。因此本文综合考虑了清洁能源的输送。

4) 社会效益。由于特高压输电电网需要进行大规模的建设，因此前期需要投入大量的资金和人力、物力，对社会有着较大的影响，与此同时也存在着诸多不确定的因素。因此特高压输电工程项目的社会效益需要详细讨论，其中对人民生活效果的影响是一个重要的指标。

3.2. 特高压输电线路综合效益评价模型

3.2.1. 贝叶斯最优最劣方法

1) 根据特高压输电线路综合效益评价指标 $\left\{{d}_{1},{d}_{2},\cdots ,{d}_{n}\right\}$ ，来确定最优指标 ${d}_{B}$ 和最劣指标 ${d}_{W}$

2) 将 ${d}_{B}$ 与其他指标 ${d}_{j}$ 进行两两之间的对比，用数字1~9来表示 ${d}_{B}$ 与其他指标之间的重要程度，其中1表示 ${d}_{B}$${d}_{j}$ 重要程度等同，9表示 ${d}_{B}$ 重要程度远高于 ${d}_{j}$ ，最优比较向量可表示为：

${A}_{B}=\left({a}_{B1},{a}_{B2},\cdots ,{a}_{Bn}\right)$

3) 将最劣指标 ${d}_{W}$ 与其他指标 ${c}_{j}$ 两两对比，其中1表示 ${d}_{j}$${d}_{W}$ 重要程度等同，9表示 ${d}_{j}$ 重要程度远高于 ${d}_{W}$ ，最劣比较向量可表示为：

${A}_{W}=\left({a}_{1W},{a}_{2W},\cdots ,{a}_{nW}\right)$

4) 确定最优指标权重值 $\left({w}_{1}^{*},{w}_{2}^{*},\cdots ,{w}_{n}^{*}\right)$ ，当然这个过程也可以转化成最优化问题，即：

$\left\{\begin{array}{l}\mathrm{min}{\mathrm{max}}_{j}\left\{|\frac{{w}_{B}}{{w}_{j}}-{a}_{Bj}|,|\frac{{w}_{j}}{{w}_{W}}-{a}_{jW}|\right\}\\ \text{s}\text{.t}.\left\{\begin{array}{l}\underset{j}{\sum }{w}_{j}=1\\ {w}_{j}\ge 0,j=1,2,\cdots ,n\end{array}\end{array}$ (4)

$\left\{\begin{array}{l}\mathrm{min}\sigma \\ |\frac{{w}_{B}}{{w}_{j}}-{a}_{Bj}|\le \sigma \\ |\frac{{w}_{j}}{{w}_{W}}-{a}_{jW}|\le \sigma \\ \underset{j}{\sum }{w}_{j}=1\\ {w}_{j}\ge 0,j=1,2,\cdots ,n\end{array}$ (5)

5) 根据式(5)计算一致性比率(concordance ratio, CR)。其中一致性比率越接近0，一致性越高。

${\chi }_{CR}=\sigma /{\chi }_{CI}$ (6)

3.2.2. 改进物元可拓方法步骤

${R}_{j}=\left({P}_{j},{D}_{j},{G}_{ij}\right)=\left[\begin{array}{ccc}{P}_{j}& {d}_{1}& {g}_{1j}\\ & {d}_{2}& {g}_{2j}\\ & ⋮& ⋮\\ & {d}_{n}& {g}_{nj}\end{array}\right]=\left[\begin{array}{ccc}{P}_{j}& {d}_{1}& 〈{a}_{1j},{b}_{1j}〉\\ & {d}_{2}& 〈{a}_{2j},{b}_{2j}〉\\ & ⋮& ⋮\\ & {d}_{n}& 〈{a}_{nj},{b}_{nj}〉\end{array}\right]$ (7)

${R}_{p}=\left(P,{D}_{i},{G}_{ij}\right)=\left[\begin{array}{ccc}{P}_{j}& {d}_{1}& {g}_{1p}\\ & {d}_{2}& {g}_{2p}\\ & ⋮& ⋮\\ & {d}_{n}& {g}_{np}\end{array}\right]=\left[\begin{array}{ccc}{P}_{j}& {d}_{1}& 〈{a}_{1p},{b}_{1p}〉\\ & {d}_{2}& 〈{a}_{2p},{b}_{2p}〉\\ & ⋮& ⋮\\ & {d}_{n}& 〈{a}_{np},{b}_{np}〉\end{array}\right]$ (8)

${R}_{0}=\left({P}_{0},{D}_{i},{G}_{i}\right)=\left[\begin{array}{ccc}{P}_{0}& {d}_{1}& {g}_{1}\\ & {d}_{2}& {g}_{2}\\ & ⋮& ⋮\\ & {d}_{n}& {g}_{n}\end{array}\right]$ (9)

$D\left({g}^{\prime }\right)=|{g}^{\prime }-\frac{{{a}^{\prime }}_{ij}+{{b}^{\prime }}_{ij}}{2}|-\frac{{{b}^{\prime }}_{ij}-{{a}^{\prime }}_{ij}}{2}$ (10)

$K=1-\frac{1}{k\left(k+1\right)}\underset{i=1}{\overset{n}{\sum }}D{w}_{i}$ (11)

${K}_{j}\left({p}_{0}\right)=1-\frac{1}{k\left(k+1\right)}\underset{i=1}{\overset{n}{\sum }}{D}_{j}\left({g}_{i}\right){w}_{i}\left(X\right)$ (12)

3.3. 添加时间因子

${A}_{B}\left(\tau \right)=\left({a}_{B1}\left(\tau \right),{a}_{B2}\left(\tau \right),\cdots ,{a}_{Bn}\left( \tau \right) \right)$

${A}_{W}\left(\tau \right)=\left({a}_{1W}\left(\tau \right),{a}_{2W}\left(\tau \right),\cdots ,{a}_{nW}\left( \tau \right) \right)$

${{R}^{\prime }}_{j}\left(\tau \right)=\left({P}_{j}\left(\tau \right),{D}_{i},{{G}^{\prime }}_{ij}\left(\tau \right)\right)=\left[\begin{array}{ccc}{P}_{j}\left(\tau \right)& {d}_{1}& {{g}^{\prime }}_{1j}\left(\tau \right)\\ & {d}_{2}& {{g}^{\prime }}_{1j}\left(\tau \right)\\ & ⋮& ⋮\\ & {d}_{n}& {{g}^{\prime }}_{nj}\left(\tau \right)\end{array}\right]=\left[\begin{array}{ccc}{P}_{j}\left(\tau \right)& {d}_{1}& 〈\frac{{a}_{1j}\left(\tau \right)}{{b}_{1p}\left(\tau \right)},\frac{{b}_{1j}\left(\tau \right)}{{b}_{1p}\left(\tau \right)}〉\\ & {d}_{2}& 〈\frac{{a}_{2j}\left(\tau \right)}{{b}_{2p}\left(\tau \right)},\frac{{b}_{2j}\left(\tau \right)}{{b}_{2p}\left(\tau \right)}〉\\ & ⋮& ⋮\\ & {d}_{n}& 〈\frac{{a}_{nj}\left(\tau \right)}{{b}_{np}\left(\tau \right)},\frac{{b}_{nj}\left(\tau \right)}{{b}_{np}\left(\tau \right)}〉\end{array}\right]\text{}$ , (14)

${{R}^{\prime }}_{0}\left(\tau \right)=\left({P}_{0}\left(\tau \right),{D}_{i},{{G}^{\prime }}_{i}\left(\tau \right)\right)=\left[\begin{array}{ccc}{P}_{0}\left(\tau \right)& {d}_{1}& \frac{{g}_{1}\left(\tau \right)}{{b}_{1p}\left(\tau \right)}\\ & {d}_{2}& \frac{{g}_{2}\left(\tau \right)}{{b}_{2p}\left(\tau \right)}\\ & ⋮& ⋮\\ & {d}_{n}& \frac{{g}_{n}\left(\tau \right)}{{b}_{np}\left(\tau \right)}\end{array}\right]$ (15)

${K}_{j}^{*}\left(\tau \right)=1-\frac{1}{k\left(k+1\right)}\underset{i=1}{\overset{n}{\sum }}{D}_{j}\left(\tau \right){w}_{i}\left(\tau \right)$ (16)

$\stackrel{¯}{\omega }\left(\tau \right)=\underset{{t}_{1}}{\overset{{t}_{2}}{\int }}\omega \left(t\right)\text{d}t$ (17)

${\tau }^{*}=\underset{j=1,2,\cdots ,{n}^{\prime }}{\mathrm{inf}}\left\{mE\left[{\varpi }_{i}\left({\tau }_{j}\right)\le {M}_{i}^{{\tau }_{j}}\right]\right\}$ (18)

4. 实证分析

1) 设定经典域classical field

${R}_{1}=\left[\begin{array}{ccc}{P}_{1}& {D}_{1}& <0,90>\\ & {D}_{2}& <0,42>\\ & {D}_{3}& <8,10>\\ & {D}_{4}& <0.5,1>\\ & {D}_{5}& <0,1>\\ & {D}_{6}& <0,9>\end{array}\right]$ , ${R}_{2}=\left[\begin{array}{ccc}{P}_{2}& {D}_{1}& <90,170>\\ & {D}_{2}& <40,77>\\ & {D}_{3}& <8,11>\\ & {D}_{4}& <0.3,0.4>\\ & {D}_{5}& <1,1.5>\\ & {D}_{6}& <10,16>\end{array}\right]$ .

${R}_{3}=\left[\begin{array}{ccc}{P}_{3}& {D}_{1}& <177,266>\\ & {D}_{2}& <80,123>\\ & {D}_{3}& <6,12>\\ & {D}_{4}& <0.13,0.22>\\ & {D}_{5}& <1.6,2>\\ & {D}_{6}& <16,20>\end{array}\right]$ , ${R}_{4}=\left[\begin{array}{ccc}{P}_{4}& {D}_{1}& <260,353>\\ & {D}_{2}& <121,160>\\ & {D}_{3}& <3.6,6>\\ & {D}_{4}& <0.11,0.16>\\ & {D}_{5}& <1.2,3.2>\\ & {D}_{6}& <20,33>\end{array}\right]$ , ${R}_{5}=\left[\begin{array}{ccc}{P}_{5}& {D}_{1}& <356,444>\\ & {D}_{2}& <160,205>\\ & {D}_{3}& <0,3.6>\\ & {D}_{4}& <0,0.2>\\ & {D}_{5}& <3,11>\\ & {D}_{6}& <30,50>\end{array}\right]$ .

2) 设定节域和待评价物元

${R}_{p}=\left[\begin{array}{ccc}{P}_{}& {D}_{1}& <0,444>\\ & {D}_{2}& <0,205>\\ & {D}_{3}& <0,12>\\ & {D}_{4}& <0,1>\\ & {D}_{5}& <0,11>\\ & {D}_{6}& <0,50>\end{array}\right]$ , ${R}_{0}=\left[\begin{array}{cc}{P}_{0}& 178.33\\ & 91.02\\ & 4.5\\ & 0.16\\ & 0.56\\ & 12.33\end{array}\right]$ .

3) 规格化处理

${R}_{1}=\left[\begin{array}{ccc}{P}_{1}& {D}_{1}& <0,0.2>\\ & {D}_{2}& <0,0.2>\\ & {D}_{3}& <1,1.1>\\ & {D}_{4}& <0.3,1.1>\\ & {D}_{5}& <0,0.2>\\ & {D}_{6}& <0.6,1>\end{array}\right]$ , ${R}_{2}=\left[\begin{array}{ccc}{P}_{2}& {D}_{1}& <0.2,0.5>\\ & {D}_{2}& <0.2,0.4>\\ & {D}_{3}& <0.8,0.9>\\ & {D}_{4}& <0.3,0.4>\\ & {D}_{5}& <0.1,0.13>\\ & {D}_{6}& <0.3,0.6>\end{array}\right]$ ,

${R}_{3}=\left[\begin{array}{ccc}{P}_{3}& {D}_{1}& <0.4,0.6>\\ & {D}_{2}& <0.4,0.6>\\ & {D}_{3}& <0.6,0.8>\\ & {D}_{4}& <0.16,0.2>\\ & {D}_{5}& <0.15,0.2>\\ & {D}_{6}& <0.2,0.3>\end{array}\right]$ , ${R}_{4}=\left[\begin{array}{ccc}{P}_{4}& {D}_{1}& <0.6,0.9>\\ & {D}_{2}& <0.6,0.8>\\ & {D}_{3}& <0.4,0.6>\\ & {D}_{4}& <0.1,0.15>\\ & {D}_{5}& <0.2,0.3>\\ & {D}_{6}& <0.1,0.2>\end{array}\right]$ ,

${R}_{5}=\left[\begin{array}{ccc}{P}_{5}& {D}_{1}& <0.8,1>\\ & {D}_{2}& <0.8,1.1>\\ & {D}_{3}& <0,0.33>\\ & {D}_{4}& <0,0.1>\\ & {D}_{5}& <0.3,1>\\ & {D}_{6}& <0,0.1>\end{array}\right]$ , ${R}_{0}=\left[\begin{array}{ccc}{P}_{0}& {D}_{1}& 0.42\\ & {D}_{2}& 0.44\\ & {D}_{3}& 0.44\\ & {D}_{4}& 0.15\\ & {D}_{5}& 0.05\\ & {D}_{6}& 0.25\end{array}\right]$ .

4) 确定指标权重

Table 1. The best and worst criteria determined by five invited experts

${\text{A}}_{best}^{1:5}=\left[\begin{array}{cccccc}\text{1}& \text{2}& \text{4}& \text{3}& \text{5}& \text{3}\\ \text{1}& \text{2}& \text{3}& \text{3}& \text{5}& \text{4}\\ \text{1}& \text{2}& \text{3}& \text{3}& \text{6}& \text{4}\\ \text{1}& \text{2}& \text{3}& \text{4}& \text{7}& \text{4}\\ \text{2}& \text{1}& \text{3}& \text{2}& \text{5}& \text{4}\end{array}\right]$ , ${\text{A}}_{worst}^{1:5}=\left[\begin{array}{cccccc}8& 7& 5& 6& 4& 6\\ 7& 7& 6& 5& 4& 5\\ 8& 7& 6& 6& 3& 5\\ 8& 7& 6& 5& 2& 5\\ 8& 8& 6& 7& 5& 4\end{array}\right]$

Table 2. Weights of each indicator

5) 计算贴进度及等级评定

${K}_{1}\left({p}_{0}\right)=1-\frac{1}{6×\left(6+1\right)}\underset{i=1}{\overset{6}{\sum }}{D}_{j}\left({g}_{i}\right){w}_{i}=0.99915$

${K}_{\text{2}}\left({p}_{0}\right)=1-\frac{1}{6×\left(6+1\right)}\underset{i=1}{\overset{6}{\sum }}{D}_{j}\left({g}_{i}\right){w}_{i}=0.99\text{8}1\text{6}$

${K}_{\text{3}}\left({p}_{0}\right)=1-\frac{1}{6×\left(6+1\right)}\underset{i=1}{\overset{6}{\sum }}{D}_{j}\left({g}_{i}\right){w}_{i}=0.999\text{33}$

${K}_{\text{4}}\left({p}_{0}\right)=1-\frac{1}{6×\left(6+1\right)}\underset{i=1}{\overset{6}{\sum }}{D}_{j}\left({g}_{i}\right){w}_{i}=0.99\text{869}$

${K}_{\text{5}}\left({p}_{0}\right)=1-\frac{1}{6×\left(6+1\right)}\underset{i=1}{\overset{6}{\sum }}{D}_{j}\left({g}_{i}\right){w}_{i}=0.9991\text{8}$

5. 总结

Evaluation of UHV Transmission Lines Based on Chaotic Genetic Algorithm and Element Extension[J]. 理论数学, 2023, 13(07): 2111-2119. https://doi.org/10.12677/PM.2023.137218

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