CN103326364B

CN103326364B - Method for determining best installation position of passive filter device

Info

Publication number: CN103326364B
Application number: CN201310242731.2A
Authority: CN
Inventors: 刘永刚; 王新彦; 杨亚奇; 刘海艳; 赵莉华; 张亚超; 雷晶晶
Original assignee: LULIANG POWER SUPPLY Co OF SHANXI ELECTRIC POWER Co; State Grid Corp of China SGCC
Current assignee: LULIANG POWER SUPPLY Co OF SHANXI ELECTRIC POWER Co; State Grid Corp of China SGCC
Priority date: 2013-06-18
Filing date: 2013-06-18
Publication date: 2015-05-27
Anticipated expiration: 2033-06-18
Also published as: CN103326364A

Abstract

The method for determining the optimal installation position of the passive filter device of the present invention belongs to the technical field of passive filter device installation; the technical problem to be solved is: to provide a method for determining the optimal installation position of the passive filter device; the adopted technical solution is : Including the following steps: the first step: establish the harmonic governance objective function, the second step: establish the geometric model of the harmonic governance objective function, judge whether the geometric model satisfying the conditions can be established according to the harmonic governance objective function, the third step: Find the optimal installation position of the passive filter; the invention is applicable to the power sector.

Description

The Method of Determining the Optimum Installation Position of Passive Filter Device

技术领域technical field

本发明无源滤波装置最优安装位置的确定方法，具体涉及一种无源滤波装置在配电网中的最优安装位置的确定方法。The method for determining the optimal installation position of the passive filter device of the present invention specifically relates to a method for determining the optimal installation position of the passive filter device in a power distribution network.

背景技术Background technique

随着电力电子装置等非线性负荷在电力系统中的广泛应用，电网尤其是配电网的电力谐波污染也日益严重，电力系统的谐波和无功问题引起了人们越来越多的关注，谐波抑制成为电力系统的热点问题之一，抑制谐波污染主要有两个基本思路：一是主动抑制，即对电力电子装置等非线性负荷本身进行改造，从源头解决谐波问题；二是被动补偿，即在系统已经被谐波污染的情况下装设谐波补偿装置来补偿谐波，目前配电网系统中采用较多的谐波抑制和无功补偿方法是安装电容器和无源滤波器；在配网系统安装无源滤波器用于系统谐波抑制时，选择滤波器安装的合适位置，使滤波装置在获得相同补偿效果的前提下容量最小，从而可减小无源滤波装置投入成本。With the wide application of nonlinear loads such as power electronic devices in the power system, the power harmonic pollution of the power grid, especially the distribution network, is becoming more and more serious. The harmonic and reactive power problems of the power system have attracted more and more attention. , Harmonic suppression has become one of the hot issues in the power system. There are two basic ideas for suppressing harmonic pollution: one is active suppression, that is, to transform the nonlinear load itself such as power electronic devices, and solve the harmonic problem from the source; two. It is passive compensation, that is, install a harmonic compensation device to compensate harmonics when the system has been polluted by harmonics. At present, more harmonic suppression and reactive power compensation methods are used in the distribution network system to install capacitors and passive compensation. Filter; when installing a passive filter in the distribution network system for system harmonic suppression, choose a suitable location for filter installation so that the filter device has the smallest capacity under the premise of obtaining the same compensation effect, thereby reducing the investment in passive filter devices cost.

目前配网系统中无源滤波装置安装主要是由非线性用户自行安装，采用在非线性负荷侧就近安装的技术方案来滤除谐波，从电网角度考虑谐波抑制相对较少，没有从配网系统角度考虑在谐波治理效果相同的情形下的最优安装位置问题，同时在配电网中采用无源滤波装置对谐波进行治理时，除了要考虑无源滤波器对谐波的治理效果，还要考虑无源滤波器的成本问题。At present, the installation of passive filtering devices in the distribution network system is mainly installed by the nonlinear users themselves, and the technical solution installed on the nonlinear load side is used to filter out the harmonics. Considering the harmonic suppression from the perspective of the power grid, there is relatively little harmonic suppression, and there is no such thing as a distribution network. From the perspective of the network system, consider the optimal installation location under the same harmonic control effect. At the same time, when using passive filter devices to control harmonics in the distribution network, in addition to considering the control of harmonics by passive filters effect, but also consider the cost of passive filters.

发明内容Contents of the invention

本发明克服现有技术存在的不足，所要解决的技术问题是：提供一种无源滤波装置最优安装位置的确定方法。The invention overcomes the deficiencies in the prior art, and the technical problem to be solved is to provide a method for determining the optimal installation position of a passive filtering device.

为解决上述技术问题，本发明所采用的技术方案是：无源滤波装置最优安装位置的确定方法，所述方法包括以下步骤：In order to solve the above-mentioned technical problems, the technical solution adopted in the present invention is: a method for determining the optimal installation position of a passive filtering device, said method comprising the following steps:

第一步：建立谐波目标治理函数，假设配电网系统中共有K条支路，主要谐波为h次谐波，在m支路安装滤除h次谐波的无源滤波器，建立各支路h次谐波电压表达式为：The first step: establish the harmonic target governance function, assuming that there are K branches in the distribution network system, and the main harmonic is the h-order harmonic, install a passive filter to filter the h-order harmonic in the m branch, and establish The expression of the hth harmonic voltage of each branch is:

${V V}_{k k,, new new}^{h h} = = {V V}_{k k,, old old}^{h h} + + Δ Δ {V V}_{k k}^{h h} - - - - - - ((11))$

$Δ Δ {V V}_{k k}^{h h} = = {Z Z}_{k k,, m m}^{h h} {I I}_{m m}^{h h} - - - - - - ((22)),,$

公式(1)和公式(2)中：k表示电网网络支路编号，h为谐波次数，和分别表示在m支路接入无源滤波器前后第k支路的h次谐波电压；其中，为接入无源滤波器后在k支路引起的电压变化，为k支路对于h次谐波的等效阻抗，为无源滤波器在m支路的吸收的电流值，其中和以及分别为和的实部和虚部；In formula (1) and formula (2): k represents the branch number of the grid network, h is the harmonic order, and respectively represent the hth harmonic voltage of the kth branch before and after the m branch is connected to the passive filter; where, is the voltage change caused by the k branch after the passive filter is connected, is the equivalent impedance of the k branch for the h harmonic, is the current value absorbed by the passive filter in the m branch, where and as well as respectively and The real and imaginary parts of ;

对公式(1)两边平方，得到h次谐波电压和补偿电流的关系式为：Square the two sides of the formula (1), and the relationship between the hth harmonic voltage and the compensation current is obtained as:

$f f [[{I I}_{m m}^{h h}]] = = {(({V V}_{k k,, new new}^{h h}))}^{22} = = {(({V V}_{k k,, old old}^{h h} + + Δ Δ {V V}_{k k}^{h h}))}^{22} - - - - - - ((33))$

(3)式展开可得：(3) can be expanded to get:

$\begin{matrix} f f [[{I I}_{m m}^{h h}]] = = f f [[{I I}_{m m}^{h h,, r r},, {I I}_{m m}^{h h,, i i}]] = = {(({V V}_{k k,, old old}^{h h,, r r} + + {Z Z}_{k k,, m m}^{h h,, r r} {I I}_{m m}^{h h,, r r} - - {Z Z}_{k k,, m m}^{h h,, i i} {I I}_{m m}^{h h,, i i}))}^{22} \\ + + {(({V V}_{k k,, old old}^{h h,, i i} + + {Z Z}_{k k,, m m}^{h h,, r r} {I I}_{m m}^{h h,, i i} - - {Z Z}_{k k,, m m}^{h h,, i i} {I I}_{m m}^{h h,, r r}))}^{22} \\ = = {(({V V}_{k k,, old old}^{h h,, r r}))}^{22} + + {(({V V}_{k k,, old old}^{h h,, i i}))}^{22} \\ + + 22 {I I}_{m m}^{h h,, r r} (({V V}_{k k,, old old}^{h h,, r r} {Z Z}_{k k,, m m}^{h h,, r r} + + {V V}_{k k,, old old}^{h h,, i i} {Z Z}_{k k,, m m}^{h h,, i i})) \\ + + 22 {I I}_{m m}^{h h,, i i} (({V V}_{k k,, old old}^{h h,, i i} {Z Z}_{k k,, m m}^{h h,, r r} - - {V V}_{k k,, old old}^{h h,, r r} {Z Z}_{k k,, m m}^{h h,, i i})) \\ + + [[{(({I I}_{m m}^{h h,, r r}))}^{22} + + {(({I I}_{m m}^{h h,, i i}))}^{22}]] [[{(({Z Z}_{k k,, m m}^{h h,, r r}))}^{22} + + {(({Z Z}_{k k,, m m}^{h h,, i i}))}^{22}]] \end{matrix} - - - - - - ((44))$

做如下定义：Do the following definition:

${A A}_{k k,, m m}^{h h} = = {(({V V}_{k k,, old old}^{h h,, r r}))}^{22} + + {(({V V}_{k k,, old old}^{h h,, i i}))}^{22}$

${B B}_{k k,, m m}^{h h} = = 22 (({V V}_{k k,, old old}^{h h,, r r} {Z Z}_{k k,, m m}^{h h,, r r} + + {V V}_{k k,, old old}^{h h,, i i} {Z Z}_{k k,, m m}^{h h,, i i}))$

${C C}_{k k,, m m}^{h h} = = 22 (({V V}_{k k,, old old}^{h h,, i i} {Z Z}_{k k,, m m}^{h h,, r r} - - {V V}_{k k,, old old}^{h h,, r r} {Z Z}_{k k,, m m}^{h h,, i i}))$

${D D.}_{k k,, m m}^{h h} = = {(({Z Z}_{k k,, m m}^{h h,, r r}))}^{22} + + {(({Z Z}_{k k,, m m}^{h h,, i i}))}^{22}$

将代入式(4)可得：Will Substitute into formula (4) to get:

$\begin{matrix} f f [[{I I}_{m m}^{h h,, r r},, {I I}_{m m}^{h h,, i i}]] = = {A A}_{k k,, m m}^{h h} + + {B B}_{k k,, m m}^{h h} {I I}_{m m}^{h h,, r r} + + {C C}_{k k,, m m}^{h h} {I I}_{m m}^{h h,, i i} \\ + + {D D.}_{k k,, m m}^{h h} [[{(({I I}_{m m}^{h h,, r r}))}^{22} + + {(({I I}_{m m}^{h h,, i i}))}^{22}]] \end{matrix} - - - - - - ((55))$

根据对于第k支路的h次谐波应满足单次谐波畸变率要求，有约束条件：According to the h-th harmonic of the k-th branch should meet the single-order harmonic distortion rate requirements, there are constraints:

$| | \frac{{V V}_{k k}^{h h}}{{V V}_{k k}^{11}} | | \leq \leq VL VL - - - - - - ((66))$

公式(6)中表示k支路基波电压，表示k支路第h次谐波电压；In formula (6) Indicates the k-branch fundamental wave voltage, Indicates the hth harmonic voltage of the k branch;

若VL≤3％则满足单次谐波限值标准，则无源滤波器吸收系统的谐波电流值最小为：If VL≤3%, the single harmonic limit standard is met, and the minimum harmonic current value of the passive filter absorption system is:

$MIN MIN [[f f (({I I}_{m m}^{h h,, r r},, {I I}_{m m}^{h h,, i i})) = = {(({I I}_{m m}^{h h,, r r}))}^{22} + + {(({I I}_{m m}^{h h,, i i}))}^{22}]] - - - - - - ((77))$

根据公式(7)得出：当m支路满足公式(7)时，即无源滤波器吸收电流最小，容量最小，则为滤波器的最优安装位置，从而可得出对第k条支路，第h次谐波治理的目标函数为：According to the formula (7), it can be concluded that when the m branch satisfies the formula (7), that is, the passive filter absorbs the minimum current and the minimum capacity, then it is the optimal installation position of the filter, so that the kth branch can be obtained Road, the objective function of the hth harmonic control is:

$\begin{matrix} f f [[{I I}_{m m}^{h h,, r r},, {I I}_{m m}^{h h,, i i}]] = = {A A}_{k k,, m m}^{h h} + + {B B}_{k k,, m m}^{h h} {I I}_{m m}^{h h,, r r} + + {C C}_{k k,, m m}^{h h} {I I}_{m m}^{h h,, i i} \\ + + {D D.}_{k k,, m m}^{h h} [[{(({I I}_{m m}^{h h,, r r}))}^{22} + + {(({I I}_{m m}^{h h,, i i}))}^{22}]] \leq \leq {VL VL}_{k k}^{22} \end{matrix} - - - - - - ((88))$

进入第二步；Enter the second step;

第二步：建立谐波治理目标函数的几何模型，判断是否根据谐波治理目标函数能建立满足条件的几何模型，如果可以，则进入第三步，如果不可以，表明该支路不是滤波器最佳安装位置，则返回第一步，重新选择安装无源滤波器的支路，重新建立谐波治理目标函数；Step 2: Establish the geometric model of the harmonic control objective function, and judge whether a geometric model that satisfies the conditions can be established according to the harmonic control objective function. If yes, go to the third step. If not, it indicates that the branch is not a filter If the best installation position is found, return to the first step, re-select the branch where the passive filter is installed, and re-establish the harmonic control objective function;

公式(8)，式中：和已知，和是关于和的函数，公式(8)为一个关于和的圆，上述K条支路，则对应的约束圆个数为K个，在坐标系中画出K个约束圆；Formula (8), where: and A known, and its about and function, formula (8) is a function about and For the above K branches, the number of corresponding constrained circles is K, and K constrained circles are drawn in the coordinate system;

如果任意两个约束圆均有公共约束部分，则进入第三步，如果任意两个约束圆没有公共约束部分，则返回第一步，重新选择安装无源滤波器的支路，重新建立谐波目标治理函数；If any two constraint circles have a common constraint part, go to the third step, if any two constraint circles have no common constraint part, then return to the first step, re-select the branch where the passive filter is installed, and re-establish the harmonics target governance function;

第三步：求出无源滤波器的最优安装位置：首先，构造与可行性区域相关的关联圆；其次，找出可行性区域的边界线；最后，找出可行性区域边界线上离坐标原点最近的点，判定最近点是否包含在关联圆中，如果该点在关联圆中，则这个最近点所在的支路即为无源滤波器最优安装位置；如果该点不在关联圆中，则交点中离原点最近的点所在的支路为无源滤波器最优安装位置。Step 3: Find the optimal installation position of the passive filter: first, construct the associated circle related to the feasibility region; second, find out the boundary line of the feasibility region; finally, find out the boundary line of the feasibility region away from The point closest to the origin of the coordinates determines whether the nearest point is included in the associated circle. If the point is in the associated circle, the branch where the nearest point is located is the optimal installation position of the passive filter; if the point is not in the associated circle , then the branch where the point closest to the origin in the intersection is located is the optimal installation position of the passive filter.

本发明与现有技术相比具有的有益效果是：本发明方法通过建立谐波治理目标函数，采用几何方法求解目标函数，确定无源滤波器最优安装位置，能够准确计算出无源滤波装置最优的安装位置，具有严密的科学性和逻辑性；采用几何的方法对目标函数进行求解，避免了复杂的数学公式推导和计算，简化计算过程，结果直观可靠。Compared with the prior art, the present invention has the beneficial effects that: the method of the present invention establishes the harmonic control objective function, solves the objective function by geometrical methods, determines the optimal installation position of the passive filter, and can accurately calculate the passive filter The optimal installation position is rigorously scientific and logical; the objective function is solved using geometric methods, which avoids the derivation and calculation of complex mathematical formulas, simplifies the calculation process, and the results are intuitive and reliable.

附图说明Description of drawings

下面结合附图对本发明做进一步详细的说明：Below in conjunction with accompanying drawing, the present invention is described in further detail:

图1是本发明的流程图；Fig. 1 is a flow chart of the present invention;

图2是配电系统电路图；Figure 2 is a circuit diagram of the power distribution system;

图3是三个约束圆图形；Fig. 3 is three constraint circle graphics;

图4是两圆相交图形；Fig. 4 is the intersecting figure of two circles;

图5是多圆相交图形；Fig. 5 is multi-circle intersection figure;

图6是约束圆求解图形；Fig. 6 is a graph for solving a constrained circle;

具体实施方式Detailed ways

如图1所示，本发明无源滤波装置最优安装位置的确定方法，其特征在于：所述方法包括以下步骤：As shown in Figure 1, the method for determining the optimal installation position of the passive filtering device of the present invention is characterized in that: the method includes the following steps:

第一步：建立谐波治理目标函数，图2所示为一个典型的配网系统，假设系统中共有K条支路，各支路中含有非线性负载，主要谐波为h次谐波，在m支路安装滤除h次谐波的无源滤波器，建立各支路h次谐波电压表达式为：The first step: establish the objective function of harmonic control. Figure 2 shows a typical distribution network system. It is assumed that there are K branches in the system, each branch contains nonlinear loads, and the main harmonic is the h-th harmonic. Install a passive filter to filter out the h-order harmonic in the m branch, and establish the expression of the h-order harmonic voltage of each branch as:

公式(1)和公式(2)中：k表示网络支路编号，h为谐波次数，和分别表示在m支路接入无源滤波器前后第k支路的h次谐波电压；其中，为接入无源滤波器后在k支路引起的电压变化，为k支路对于h次谐波的等效阻抗，为无源滤波器在m支路的吸收的电流值；In formula (1) and formula (2): k represents the network branch number, h is the harmonic order, and respectively represent the hth harmonic voltage of the kth branch before and after the m branch is connected to the passive filter; where, is the voltage change caused by the k branch after the passive filter is connected, is the equivalent impedance of the k branch for the h harmonic, is the current value absorbed by the passive filter in the m branch;

(3)式展开可得：(3) can be expanded to get:

做如下定义：Do the following definition:

将代入式(4)可得：Will Substitute into formula (4) to get:

无源滤波器吸收的谐波电流最小时，滤波电容的安装容量最小，滤波器的投资成本最少，此时滤波器的安装位置可以认为是最佳安装位置。根据标准规定，对于第k支路的h次谐波应满足单次谐波畸变率要求，有约束条件：When the harmonic current absorbed by the passive filter is the smallest, the installation capacity of the filter capacitor is the smallest, and the investment cost of the filter is the least. At this time, the installation position of the filter can be considered as the best installation position. According to the standard, the h-order harmonic of the k-th branch should meet the requirements of the single-order harmonic distortion rate, and there are constraints:

根据国家标准：若VL≤3％能满足单次谐波限值标准，则无源滤波器吸收系统的谐波电流值最小，即：According to the national standard: if VL≤3% can meet the single harmonic limit standard, the harmonic current value of the passive filter absorption system is the smallest, namely:

根据公式(7)得出：当m支路满足公式(7)时，即为无源滤波器的最优安装位置，得出对第k条支路，第h次谐波治理目标函数为：According to the formula (7), it can be concluded that when the m branch satisfies the formula (7), it is the optimal installation position of the passive filter. It is obtained that for the kth branch, the hth harmonic control objective function is:

然后进入第二步；从式(8)可以看出，谐波治理目标函数为二次凸函数，解决问题的关键就是选择适当的方法对目标治理函数进行求解。Then enter the second step; from formula (8), it can be seen that the objective function of harmonic governance is a quadratic convex function, and the key to solving the problem is to choose an appropriate method to solve the objective governance function.

第二步：建立谐波治理目标函数的几何模型，判断是否根据谐波治理目标函数能建立满足条件的几何模型，如果可以，则进入第三步，如果不可以，则返回第一步，重新选择安装无源滤波器的支路，重新建立谐波目标治理函数；Step 2: Establish the geometric model of the objective function of harmonic control, judge whether a geometric model satisfying the conditions can be established according to the objective function of harmonic control, if yes, go to the third step, if not, return to the first step, and re Select the branch where the passive filter is installed, and re-establish the harmonic target governance function;

如果任意两个约束圆均有公共约束部分，则进入第三步，如果任意两个约束圆没有公共约束部分，则返回第一步，重新选择安装无源滤波器的支路，重新建立谐波治理目标函数。If any two constraint circles have a common constraint part, go to the third step, if any two constraint circles have no common constraint part, then return to the first step, re-select the branch where the passive filter is installed, and re-establish the harmonics Governance objective function.

本发明方法通过建立谐波治理目标函数，采用几何方法解决无源滤波器的最优安装位置，能够准确的计算出无源滤波装置最优的安装位置，具有严密的科学性和逻辑性。The method of the invention solves the optimal installation position of the passive filter by establishing the objective function of harmonic wave control, adopts a geometric method, can accurately calculate the optimal installation position of the passive filter device, and has strict scientificity and logic.

从上述公式(8)可以看出，在几何上目标函数为一簇受约束的圆，本方法采用几何图形方法来求解目标函数，本具体实施方式以系统含有3条支路的情况为例进行分析。As can be seen from the above formula (8), the objective function is a cluster of constrained circles geometrically, and the method adopts a geometric figure method to solve the objective function. The specific implementation mode takes the situation that the system contains 3 branches as an example. analyze.

对于含有3条支路的系统，其目标函数对应3个约束圆，如图3所示，图中的每个圆对应一条支路，显然，无源滤波器最小吸收电流应受所有约束圆的约束，图中的阴影部分为所有约束圆共同约束部分，则无源滤波器的最小吸收电流应在图中的阴影部分，其大小为坐标原点到阴影部分最近点的距离，即图3中的T1点，如果系统含有K条支路，则对应的约束圆个数为K个，无源滤波器的最小吸收电流应为K个约束圆共同约束部分中离坐标原点最近点的距离。For a system with 3 branches, its objective function corresponds to 3 constrained circles, as shown in Figure 3, each circle in the figure corresponds to a branch, obviously, the minimum absorbed current of the passive filter should be limited by the constraints of all constrained circles Constraints, the shaded part in the figure is the common constraint part of all the constraint circles, then the minimum absorption current of the passive filter should be in the shaded part of the figure, and its size is the distance from the coordinate origin to the nearest point of the shaded part, that is, in Figure 3 At point T1, if the system contains K branches, the number of corresponding constrained circles is K, and the minimum absorbed current of the passive filter should be the distance from the nearest point of the coordinate origin in the common constrained part of the K constrained circles.

在建立目标函数几何模型时，需要注意以下几点：When establishing the geometric model of the objective function, the following points should be paid attention to:

一、为了使求解简单，应尽量减少约束圆个数，如果有大圆包含小圆的情况，可忽略大圆；1. In order to make the solution simple, the number of constrained circles should be reduced as much as possible. If there is a situation where a large circle contains a small circle, the large circle can be ignored;

二、当无源滤波器安装于某一支路时，如果有任意两个约束圆没有公共约束部分，说明该支路不符合安装要求，不能在此支路安装无源滤波器，需选择别的支路安装；2. When the passive filter is installed on a certain branch, if any two constraint circles have no common constraint part, it means that the branch does not meet the installation requirements, and the passive filter cannot be installed on this branch. branch installation;

三、把符合安装要求的约束圆按照一定的顺序排列(半径从小到大或者从大到小)，从半径最大(或者最小)的两个圆开始计算，求出任意两个圆的交点，如图3中的A、B、C、D、E、F；3. Arrange the constraining circles that meet the installation requirements in a certain order (radius from small to large or from large to small), start calculation from the two circles with the largest (or smallest) radius, and find the intersection point of any two circles, such as A, B, C, D, E, F in Fig. 3;

四、对半径最大的圆检查其上所有的交点，找到满足所有的约束圆的点，如图3中的D、E，如果交点不存在，则说明该约束圆代表的支路不是无源滤波器的最优安装支路，需考虑选择别的支路。4. Check all the intersections on the circle with the largest radius, and find the points that satisfy all the constraint circles, as shown in D and E in Figure 3. If the intersection does not exist, it means that the branch represented by the constraint circle is not a passive filter If the optimal installation branch of the switch is selected, another branch should be considered.

根据以上的化解原则对目标函数所对应的约束圆进行化简后，可求出无源滤波器的最小吸收电流值，步骤如下：According to the above resolution principle, after simplifying the constraint circle corresponding to the objective function, the minimum absorption current value of the passive filter can be obtained, the steps are as follows:

一、构造与可行性区域相关的关联圆；从图3可以看出，各约束圆共同的阴影部分为求解最优注入电流的可行性区域，要直接从这个区域求出最优电流解比较困难，所以构造一个与可行性区域相关联的圆，以方便求解；下面详细讨论有两个约束圆相交时和有多个约束圆相交时该关联圆的构造过程：1. Construct the associated circle related to the feasibility region; as can be seen from Figure 3, the common shaded part of each constraint circle is the feasibility region for solving the optimal injection current, and it is difficult to directly obtain the optimal current solution from this region , so a circle associated with the feasibility region is constructed to facilitate the solution; the following discusses in detail the construction process of the associated circle when two constraint circles intersect or when there are multiple constraint circles intersect:

图4所示为有两个约束圆相交构造关联圆的情况，可分为两种情况，一是两圆相交的弦JK的中点P位于两圆圆心连线的延长线上，如图4(a)，则小圆即是所要找的关联圆，二是弦JK的中点P位于两圆圆心的连线上，如图4(b)，这时以点P为圆心，弦JK为直径构造一个圆即为所要找的关联圆；Figure 4 shows the situation where two constrained circles intersect to construct an associated circle, which can be divided into two situations. One is that the midpoint P of the chord JK where the two circles intersect is located on the extension line of the line connecting the centers of the two circles, as shown in Figure 4 (a), then the small circle is the associated circle you want to find, and the second is that the midpoint P of the chord JK is located on the connecting line between the centers of the two circles, as shown in Figure 4(b). At this time, the point P is the center of the circle, and the chord JK is Constructing a circle with the diameter is the associated circle you are looking for;

有多个约束圆相交构造关联圆的情况如图5所示，图5中给出了三个约束圆，假设三个约束圆相交，构造关联圆时，先从半径最大的两个约束圆开，根据两个约束圆相交的情况，找到其关联圆，如图5(a)中粗线标出的圆B1，再用圆B1与第三个圆(即圆1)依据两个约束圆相交的情况找到所需要的圆B2，B2即为所要找的关联圆，如图5(b)，多于三个约束圆时，采用类似方法即可。The situation where multiple constrained circles intersect to construct an associated circle is shown in Figure 5. Three constrained circles are given in Figure 5. Assuming that the three constrained circles intersect, when constructing an associated circle, start with the two constrained circles with the largest radii. , according to the intersection of two constraint circles, find its associated circle, such as the circle B1 marked by the thick line in Figure 5(a), and then use circle B1 to intersect with the third circle (circle 1) according to the two constraint circles Find the required circle B2 in the case of , and B2 is the associated circle to be found, as shown in Figure 5(b). When there are more than three constrained circles, a similar method can be used.

二、找出可行性区域的边界线；所有的交点都包含在关联圆中，并满足所有的约束圆，为可行性区域的拐点，这样，就确定了可行性区域的边界，如图5所示，图5的阴影部分即为可行性区域边界线。2. Find out the boundary line of the feasibility region; all the intersection points are included in the associated circle, and all the constraint circles are satisfied, which is the inflection point of the feasibility region, thus, the boundary of the feasibility region is determined, as shown in Figure 5 The shaded part in Figure 5 is the boundary line of the feasibility region.

三、无源滤波器最优安装位置的确定，根据得到的可行性区域边界线，按照以下方法确定无源滤波器的最优安装位置：找出可行性区域边界线上离坐标原点最近的点，如图6中的点T1，判定最近点是否包含在关联圆中，如果该点在关联圆中，则这个最近点所在的支路即为无源滤波器最优安装位置；如果该点不在关联圆中，则交点中离原点最近的点所在的支路为无源滤波器最优安装位置，图6中，T1点所在的支路是无源滤波器的最优安装位置。3. Determination of the optimal installation position of the passive filter, according to the obtained boundary line of the feasibility area, determine the optimal installation position of the passive filter according to the following method: Find the point closest to the coordinate origin on the boundary line of the feasibility area , as shown in point T1 in Figure 6, determine whether the nearest point is included in the associated circle, if the point is in the associated circle, then the branch where the nearest point is located is the optimal installation position of the passive filter; if the point is not in In the correlation circle, the branch where the point closest to the origin in the intersection is located is the optimal installation position of the passive filter. In Figure 6, the branch where the point T1 is located is the optimal installation position of the passive filter.

本发明采用几何的方法对目标函数进行求解，避免了复杂的数学公式推导和计算，简化计算过程，结果直观可靠。The invention adopts a geometric method to solve the objective function, avoids the derivation and calculation of complex mathematical formulas, simplifies the calculation process, and the result is intuitive and reliable.

Claims

1. The method for determining the optimal installation position of the passive filter device is characterized by comprising the following steps: the method comprises the following steps:

the first step is as follows: establishing a harmonic target governing function, assuming that a power distribution network system has K branches, wherein the main harmonic is h-th harmonic, a passive filter for filtering the h-th harmonic is arranged on the m branch, and the voltage expression of the h-th harmonic of each branch is established as follows:

in formula (1) and formula (2): k represents the number of the branch of the power grid network, h is the harmonic frequency,andrespectively representing h-order harmonic voltages of k-th branches before and after the m branch is connected to the passive filter; wherein,in order to introduce the voltage change caused in the k branch after the passive filter,for the equivalent impedance of the k branch for the h harmonic,current value absorbed by the passive filter in the m branch, whereinAndandare respectively asAndthe real and imaginary parts of (c);

and (3) squaring two sides of the formula (1) to obtain a relation between the h-th harmonic voltage and the compensation current as follows:

(3) the formula is developed to obtain:

\begin{matrix} f [I_{m}^{h}] = f [I_{m}^{h, r}, I_{m}^{h, i}] = {(V_{k, old}^{h, r} + Z_{k, m}^{h, r} I_{m}^{h, r} - Z_{k, m}^{h, i} I_{m}^{h, i})}^{2} \\ + {(V_{k, old}^{h, i} + Z_{k, m}^{h, r} I_{m}^{h, i} - Z_{k, m}^{h, i} I_{m}^{h, r})}^{2} \\ = {(V_{k, old}^{h, r})}^{2} + {(V_{k, old}^{h, i})}^{2} \\ + 2 I_{m}^{h, r} (V_{k, old}^{h, r} Z_{k, m}^{h, r} + V_{k, old}^{h, i} Z_{k, m}^{h, i}) \\ + 2 I_{m}^{h, i} (V_{k, old}^{h, i} Z_{k, m}^{h, r} - V_{k, old}^{h, r} Z_{k, m}^{h, i}) \\ + [{(I_{m}^{h, r})}^{2} + {(I_{m}^{h, i})}^{2}] [{(Z_{k, m}^{h, r})}^{2} + {(Z_{k, m}^{h, i})}^{2}] \end{matrix} - - - (4)

as defined below:

A_{k, m}^{h} = {(V_{k, old}^{h, r})}^{2} + {(V_{k, old}^{h, i})}^{2}

B_{k, m}^{h} = 2 (V_{k, old}^{h, r} Z_{k, m}^{h, r} + V_{k, old}^{h, i} Z_{k, m}^{h, i})

C_{k, m}^{h} = 2 (V_{k, old}^{h, i} Z_{k, m}^{h, r} - V_{k, old}^{h, r} Z_{k, m}^{h, i})

D_{k, m}^{h} = {(Z_{k, m}^{h, r})}^{2} + {(Z_{k, m}^{h, i})}^{2}

will be provided withCan be substituted by the formula (4):

\begin{matrix} f [I_{m}^{h, r}, I_{m}^{h, i}] = A_{k, m}^{h} + B_{k, m}^{h} I_{m}^{h, r} + C_{k, m}^{h} I_{m}^{h, i} \\ + D_{k, m}^{h} [{(I_{m}^{h, r})}^{2} + {(I_{m}^{h, i})}^{2}] \end{matrix} - - - (5)

according to the condition that the h-th harmonic of the kth branch should meet the requirement of the single harmonic distortion rate, the method has the following constraint conditions:

in the formula (6)The fundamental voltage of the k-branch is shown,representing the h-th harmonic voltage of the k branch;

if VL is less than or equal to 3%, the single harmonic limit standard is met, and the minimum harmonic current value of the passive filter absorption system is as follows:

MIN [f (I_{m}^{h, r}, I_{m}^{h, i}) = {(I_{m}^{h, r})}^{2} + {(I_{m}^{h, i})}^{2}] - - - (7)

from equation (7) it follows: when the m branch satisfies formula (7), that is, the passive filter has the minimum absorbed current and the minimum capacity, the optimal mounting position of the filter is obtained, and therefore, for the kth branch, the objective function for the h-th harmonic treatment is as follows:

entering a second step;

the second step is that: establishing a geometric model of a harmonic wave treatment target function, judging whether the geometric model meeting the conditions can be established according to the harmonic wave treatment target function, if so, entering a third step, if not, indicating that the branch is not the optimal installation position of the filter, returning to the first step, reselecting the branch for installing the passive filter, and reestablishing the harmonic wave treatment target function;

formula (8), wherein:andin the known manner, it is known that,andis aboutAndis a function of (8) is a function ofAndthe number of the corresponding constraint circles of the K branches is K, and K constraint circles are drawn in a coordinate system;

if any two constraint circles have a common constraint part, entering a third step, if any two constraint circles have no common constraint part, returning to the first step, reselecting a branch for installing a passive filter, and reestablishing a harmonic target governance function; the third step: and (3) solving the optimal installation position of the passive filter: firstly, constructing an association circle related to a feasibility region; secondly, finding out a boundary line of a feasibility region; finally, finding out a point closest to the origin of coordinates on the boundary line of the feasibility region, and judging whether the closest point is contained in the association circle, wherein if the point is in the association circle, the branch where the closest point is located is the optimal installation position of the passive filter; and if the point is not in the associated circle, the branch where the point closest to the origin in the intersection point is located is the optimal installation position of the passive filter.