﻿ 基于改进PSO算法的分布式能源供应链配置研究
 上海理工大学学报  2021, Vol. 43 Issue (4): 393-399 PDF

Distributed energy supply chain configuration based on improved PSO algorithm
PAN Fengchao, LIU Qinming, YE Chunming, LI Guanlin
Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: The energy crisis caused by the shortage of traditional energy reserves makes distributed energy share higher and higher in the energy network. The highly efficient and environmentally friendly distributed energy supply chain has laid the foundation for energy Internet plus intelligent energy, and has solved the distributed block allocation problem on the supply side of distributed energy supply chain. Taking the economic and environmental problems of each distributed module in the distributed energy supply chain as the objective function, relevant models were establishes creatively. The distributed wind energy, distributed solar energy and distributed natural gas modules were analyzed, and the optimal allocation of the supply side of the distributed energy supply chain was studied. The PSO algorithm was improved by combining with simulated annealing algorithm to form an improved PSO algorithm. Compared with the standard PSO algorithm, the improved algorithm was used to solve the model. The feasibility of the model, the superiority of the algorithm and the effective solution of the distributed energy supply chain configuration problem were verified through the analysis of an example.
Key words: PSO algorithm     configuration optimization     distributed energy     supply chain

1 问题描述

 图 1 分布式能源系统框架 Fig. 1 Framework of distributed energy system

2 目标函数 2.1 环保性目标

 ${C_{\rm{1}}} = {g_{\rm{a}}}{e_{\rm{a}}} + {g_{\rm{b}}}{e_{\rm{b}}}$ (1)

2.2 经济性目标

 ${C_2} = {C_{\rm{d}}} + {C_{\rm{e}}} + {C_{\rm{f}}}$ (2)

 ${C_{\rm{d}}} = {C_{{\rm{w0}}}} + {C_{{\rm{l0}}}} + {C_{{\rm{g0}}}} + {C_{{\rm{s0}}}} + {C_{{\rm{t0}}}}$ (3)

 ${C_{\rm{e}}} = {C_{{\rm{w1}}}} + {C_{{\rm{l1}}}} + {C_{{\rm{g1}}}} + {C_{{\rm{s1}}}} + {C_{{\rm{t1}}}}$ (4)

 ${C_{\rm{e}}} = {C_{{\rm{w}}2}} + {C_{{\rm{l2}}}} + {C_{{\rm{g2}}}} + {C_{{\rm{s2}}}} + {C_{{\rm{t2}}}}$ (5)

 $C = {C_1} + {C_2}$ (6)
3 约束条件

 $\begin{split}{P_{\rm{l}}}\left( t \right) +& {P_{\rm{a}}}\left( t \right) + {P_{\rm{c}}}\left( t \right) =\\ &{P_{\rm{w}}}\left( t \right) + {P_{\rm{s}}}\left( t \right) + {P_{\rm{g}}}\left( t \right) + {P_{\rm{d}}}\left( t \right) + {P_{\rm{b}}}\left( t \right)\end{split}$ (7)

 ${N_{{\rm{Wmin}}}} \leqslant {N_{\rm{W}}} \leqslant {N_{{\rm{Wmax}}}}$ (8)
 ${N_{{\rm{Lmin}}}} \leqslant {N_{\rm{L}}} \leqslant {N_{{\rm{Lmax}}}}$ (9)
 ${N_{{\rm{Gmin}}}} \leqslant {N_{\rm{G}}} \leqslant {N_{{\rm{Gmax}}}}$ (10)
 ${N_{{\rm{Smin}}}} \leqslant {N_{\rm{S}}} \leqslant {N_{{\rm{Smax}}}}$ (11)

 $L = \mathop \sum \limits_{t = 1}^T {P_{\rm{b}}}\left( t \right)\Biggr/\mathop \sum \limits_{t = 1}^T {P_{\rm{l}}}\left( t \right)$ (12)
 $L< {L}_{\rm{set}}$ (13)

 ${S_{{\rm{min}}}} < {\rm{S}} < {S_{{\rm{max}}}}$ (14)

4 数学模型

 $P = \eta {P_{\rm{m}}}$ (15)
 ${P_{\rm{m}}} = \frac{1}{2}{C_{\rm{p}}}\rho \text{π} {R^3}{v^2}$ (16)
 ${P_{{\rm{WT}}}} = \left\{ {\begin{array}{*{20}{l}} {0}, & {0 \leqslant v \leqslant {v_{{\rm{ci}}}},v > {v_{{\rm{co}}}}}\\ {P_{\rm{r}}}\dfrac{{v - {v_{{\rm{ci}}}}}}{{{v_{{\rm{cr}}}} - {v_{{\rm{ci}}}}}},&{v_{{\rm{ci}}}} \leqslant v \leqslant {v_{{\rm{cr}}}}\\ {P_{\rm{r}}},&{v_{{\rm{cr}}}} \leqslant v \leqslant {v_{{\rm{co}}}} \end{array}} \right.$ (17)

 $\begin{split} f\left(G\left(t\right)\right)=& \Gamma \left(\alpha +\beta \right){\left(\frac{G\left(t\right)}{{G}_{\rm{max}}}\right)}^{\alpha -1}\cdot\\ &{\left(1-\frac{G\left(t\right)}{{G}_{\rm{max}}}\right)}^{\beta -1}\Biggr/\Gamma \left(\alpha \right)\left(\beta \right)\end{split}$ (18)

 ${P_{\rm{s}}} = {f_{\rm{s}}}{P_{{\rm{STC}}}}\frac{{{G_{\rm{T}}}}}{{{G_{{\rm{STC}}}}}}\left[ {1 + {\alpha _{\rm{p}}}\left( {{T_{\rm{c}}} - {T_{{\rm{STC}}}}} \right)} \right]$ (19)

 ${F_{\rm{g}}} = \frac{{{\alpha _{\rm{g}}} + {\beta _{\rm{g}}}{P_{\rm{g}}} + {\gamma _{\rm{g}}}{P_{\rm{g}}}^2}}{V}$ (20)

a. 当储能设备充能时，表达式为

 $S=\frac{{P}_{\rm{y}}{\mu }_{\rm{c}}}{{S}_{\rm{e}}(1+\theta )}$ (21)

b. 当储能设备放能时，表达式为

 $S=\frac{{P}_{\rm{u}}}{{S}_{\rm{e}}(1+\theta ){\mu }_{\rm{d}}}$ (22)

5 分布式配置解决方案 5.1 PSO算法

PSO算法（粒子群算法）假设N维空间中有n个无质量、无体积的粒子，向量 ${{\boldsymbol{x}}_i} = ( {x_{i1}}, {x_{i2}}, \cdots ,$ ${x_{iN}} )$ 表示它们的位置，向量 ${{\boldsymbol{v}}_i} = \left( {{v_{i1}},{v_{i2}}, \cdots ,{v_{iN}}} \right)$ 表示它们的移动速度。每个粒子都有其目标函数决定的适度值，粒子在移动中寻找自己最优的位置 ${{\boldsymbol{p}}_i} = \left( {{p_{i1}},{p_{i2}}, \cdots ,{p_{iN}}} \right)$ ，和邻域粒子的最优位置 ${{\boldsymbol{g}}_i} = \left( {{g_{i1}},{g_{i2}}, \cdots ,{g_{iN}}} \right)$ 。粒子通过不断移动，更新迭代得到新的位置参数，它们的速度和位置更新公式为[13]

 $\begin{split}{v_{ij}}\left( {t + 1} \right) =& \omega {v_{ij}}\left( t \right) + {c_1}{r_1}\left( {{p_{iN}}\left( t \right) - {x_{iN}}\left( t \right)} \right) +\\ &{c_2}{r_2}\left( {{g_{iN}}\left( t \right) - {x_{iN}}\left( t \right)} \right)\end{split}$ (23)
 ${x_{ij}}\left( {t + 1} \right) = \omega {v_{ij}}\left( t \right) + {v_{ij}}\left( {t + 1} \right)$ (24)

PSO算法的主要流程如图2所示。

 图 2 PSO算法流程 Fig. 2 Flow chart of PSO algorithm
5.2 改进的PSO算法

PSO算法具有规则简单、优化多维函数速度快、精度高等优点，但也存在一定的局限性。规则简单导致易出现局部最优而结束算法，得出的最终结果存在较大误差。针对此，本文创新地结合模拟退火算法[14]具有跳出局部最优能力的特点，对PSO算法进行改进，得到一个具有全局搜索能力强、精度高、速度快并且可以避免陷入局部最优的改进算法。

 图 3 改进PSO算法流程 Fig. 3 Flow chart of improved PSO algorithm
5.3 算法求解

a. 输入N种分布式能源模块相关参数、风速、光照、温度数据、历史需求数据；

b. 初始化粒子群的速度参数和位置参数，维数为N

c. 通过各分布式模块计算产能总功率和当前时刻符合功率的差值，当差值不为0时，则视为功率不平衡；

d. 根据当前时刻储能设备工作状态、燃气轮机工作情况判断当前时刻供应链是功率过剩还是失负荷；

e. 根据本文研究提出的目标函数，在约束条件下，求解初始参数进行退火操作后的初始解；

f. 对模拟退火算法得出的粗略最优值进行PSO算法迭代操作；

g. 不断迭代直到最大迭代或满足收敛条件，然后输出全局最优值，此时最优位置对应的各维度值即为分布式能源供应链各分布式模块的配置优化结果。

6 算例分析 6.1 算例介绍及参数设置

6.2 结果分析及比较

 图 4 能源分布式配置 Fig. 4 Distributed energy allocation

 图 5 分布式出力组合配置 Fig. 5 Distributed output combination configuration

7 结　论

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