﻿ 一种基于 FBD 的改进谐波检测算法分析与研究
 舰船科学技术  2017, Vol. 39 Issue (9): 54-58 PDF

An improved harmonic analysis and research detection algorithm based on FBD
MA Tao, YU Meng-hong, ZHANG Chun-lai
School of Electronic and Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: In order to detect the the fundamental and harmonic current quickly and accurately for drilling ship power supply system, this paper presents an improved algorithm of harmonic detection based on FBD. The algorithm use fully move window algorithm to replace the traditional FBD low-pass filter, ananysising two corenstrate that improved speed and accuracy in FBD harmonic current detection. In order to verify the effectof improved algorithm in drillship grid, but also showed good results, adding a dynamic load FBD demonstrate the improved algorithm. Use Matlab simulation experimentsin steady-state and dynamic loads on the positive sequence current distortion and DC componentssimulate each time,conclude that the algorithm has a good dynamic response, high precision, easy to implement and so on. Finally, the feasibility of improved FBD current detection with PR control mode for drilling rigs compenaste complex power system, we can see the improved effect by observing the harmonic current compensation harmonic current distortion improving verification of FBD.
Key words: drilling ship     move windows     dynamic load     harmonic detection     current compensation
0 引 言

FBD 法是基于时域中的谐波电流检测算法，没有复杂的矩阵变换，原理简单明了并且实时性好[2]。目前在其他电力系统中得到广泛应用，但在钻井船领域还没有得到推广。FBD 法中低通滤波器（LPF）对检测精度及动态响应速度起着决定性作用，很多国内外学者对 LPF 问题研究探讨[3]。本文以钻井船电网为背景，提出了一种基于 FBD 算法的谐波电流检测方法，用移动窗代替了 LPF，利用移动窗加法器求均值检测出电流谐波。

1 FBD 法谐波电流实时检测分析

FBD 法的根本理论：把电路中的各相负载用等值电导进行等效，电路中的功率消耗都来自于等值电导，其他的能量没有改变[4]。电力系统需要补偿的电流分量等于等值电导的值与锁相环（PLL）生成的参考电压（式（1））之积[5]。在电流检测环节电压幅值不受限制，说明了电压畸变对 FBD 的电流检测不产生影响，因此该算法应该在钻井船复杂的电力系统中得到推广，用于检测出基波电流正序分量、负序分量以及零序分量（式（2）），从而对电流进行有效补偿。FBD 原理如图 1 所示。

 图 1 FBD 检测原理图 Fig. 1 FBD detection theory

 $\left[ \begin{array}{l}{e_a}\\{e_b}\\{e_c}\end{array} \right] = \left( \begin{array}{l}\sin \omega t\\\sin (\omega t - 120^\circ )\\\sin (\omega t + 120^\circ )\end{array} \right)\text{。}$ (1)

 $\begin{array}{l}{i_a} = \sum\limits_{n = 1}^\infty {\left[ {{I_{1n}}\sin (n\omega t + {\varphi _{1n}}) + {I_{2n}}\sin (n\omega t + {\varphi _{2n}}) + } \right.} \\[3pt]\qquad\left. {{I_{0n}}\sin (n\omega t + {\varphi _{0n}})} \right]\text{，}\\{i_b} = \sum\limits_{n = 1}^\infty {\left[ {{I_{1n}}\sin (n\omega t + {\varphi _{1n}} - 120^\circ ) + } \right.} \\[3pt]\qquad{I_{2n}}\sin (n\omega t + {\varphi _{2n}} - 120^\circ ) + \\[3pt]\left.\qquad {{I_{0n}}\sin (n\omega t + {\varphi _{0n}} - 120^\circ )}\right]\text{，} \\{i_c} = \sum\limits_{n = 1}^\infty {\left[ {{I_{1n}}\sin (n\omega t + {\varphi _{1n}} + 120^\circ ) + } \right.} \\[3pt]\qquad{I_{2n}}\sin (n\omega t + {\varphi _{2n}} + 120^\circ ) + \\[3pt]\left. \qquad{{I_{0n}}\sin (n\omega t + {\varphi _{0n}} + 120^\circ )} \right]\text{。}\end{array}$ (2)

 $\begin{array}{l}{{G}_{P}}({t}) = \displaystyle\frac{{\left\langle {u,i} \right\rangle }}{{\left\langle {u,u} \right\rangle }} = \frac{{{P_{\sum {} }}}}{{{{\left\| u \right\|}^2}}} = \displaystyle\frac{{{e_a}{i_a} + {e_b}{i_b} + {e_c}{i_c}}}{{e_a^2 + e_b^2 + e_c^2}}\text{，}\\[10pt]{{G}_{q}}({t}) = \displaystyle\frac{{\left\langle {{u^*},i} \right\rangle }}{{\left\langle {{u^*},u} \right\rangle }} = \frac{{{P_{\sum {} }}}}{{{{\left\| {{u^*}} \right\|}^2}}} = \displaystyle\frac{{{e_a}^*{i_a} + {e_b}^*{i_b} + {e_c}^*{i_c}}}{{{{\left( {e_a^*} \right)}^2} + {{\left( {e_b^*} \right)}^2} + {{(e_c^*)}^2}}}\text{。}\end{array}$ (3)

 $\begin{array}{l}{G_P} = \overline {{G_P}(t)} = {G_P}(t){I_{11}}\cos {\varphi _{11}}\text{，}\\[5pt]{G_q} = \overline {{G_q}(t)} = {G_q}(t){I_{11}}\sin {\varphi _{11}}\text{。}\end{array}$ (4)

 $\begin{array}{l}{i_{a1p}} = {G_P}{e_a} = {I_{11}}\cos {\varphi _{11}}\sin \omega t\text{，}\\{i_{b1p}} = {G_P}{e_b} = {I_{11}}\cos {\varphi _{11}}\sin (\omega t - 120^\circ )\text{，}\\{i_{c1p}} = {G_P}{e_c} = {I_{11}}\cos {\varphi _{11}}\sin (\omega t + 120^\circ )\text{。}\end{array}$ (5)

 $\begin{array}{l}{i_{a1q}} = {G_q}{e_a} = {I_{11}}\sin {\varphi _{11}}\cos \omega t\text{，}\\{i_{b1q}} = {G_q}{e_b} = {I_{11}}\sin {\varphi _{11}}\cos (\omega t - 120^\circ )\text{，}\\{i_{c1q}} = {G_q}{e_c} = {I_{11}}\sin {\varphi _{11}}\cos (\omega t + 120^\circ )\text{。}\end{array}$ (6)

 $\begin{array}{l}{i_{a1}} = {i_{a1p}} + {i_{a1q}}\text{，}\\{i_{b1}} = {i_{b1p}} + {i_{b1q}}\text{，}\\{i_{c1}} = {i_{c1p}} + {i_{c1q}}\text{。}\end{array}$ (7)

2 改进 FBD 的移动窗数据积分法

 图 2 移动窗结构图 Fig. 2 Structure chart of move window
 $y(k) = \frac{1}{N}\sum\limits_{N = 0}^{N - 1} {x(k - n) = \frac{1}{N}} \left[ {x(k - n + 1) + ... + x(k)} \right]\text{，}$ (8)

 图 3 改进 FBD 的移动窗数据积分法原理图 Fig. 3 Structure theory chart of move window based on FBD

 图 4 移动窗模块原理图 Fig. 4 Modules of move window theory
3 改进 FBD 算法仿真与分析

 图 5 改进前基波正序电流图 Fig. 5 Fundamental positive sequence current before improving

 图 6 改进后基波正序电流图 Fig. 6 Fundamental positive sequence current after improving

 图 7 改进前基波正序电流畸变率图 Fig. 7 Fundamental positive sequence current distortion before improving

 图 8 改进后基波正序电流畸变率图 Fig. 8 Fundamental positive sequence current distortion after improving

 图 9 改进前电流直流分量响应图 Fig. 9 DC component of the current response before improving

 图 10 改进后电流直流分量响应图 Fig. 10 DC component of the current response after improving

 图 11 改进前后电流直流分量响应图 Fig. 11 Compare about the DC component of the current response in improving or not

 图 12 改进前后动态负载电流直流分量响应图 Fig. 12 Compare about the DC component of the current response in improving or not after adding dynamic load

 图 13 电流补偿前三相电流图 Fig. 13 Three-phase current before current compensation

 图 14 电流补偿前三相电流畸变率图 Fig. 14 Three-phase current distortion before current compensation

 图 15 电流补偿后三相电流图 Fig. 15 Three-phase current after current compensation

 图 16 电流补偿后三相电流畸变率图 Fig. 16 Three-phase current distortion after current compensation
4 结 语

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