CN103326364A - Method for determining best installation position of passive filter device - Google Patents

Abstract

The invention discloses a method for determining the best installation position of a passive filter device, and belongs to the technical field of installation of the passive filter device. According to the technical scheme, the method for determining the best installation position of the passive filter device comprises the following steps that a harmonic wave target management function is built; a geometric model of the harmonic wave target management function is built, and whether the geometric model meeting the requirements is built or not according to the harmonic wave target management function is judged; the best installation position of the passive filter is obtained. The method for determining the best installation position of the passive filter device is applicable to the electric power department.

Description

Definite method of the optimum installation site of passive filtration unit

Technical field

Definite method of the optimum installation site of passive filtration unit of the present invention is specifically related to definite method of the optimum installation site of a kind of passive filtration unit in power distribution network.

Background technology

Along with the extensive use of the nonlinear-loads such as power electronic equipment in electric power system, the electrical network especially electric harmonic pollution of power distribution network is also day by day serious, the harmonic wave of electric power system and idle problem have caused that people more and more pay close attention to, harmonic wave suppresses to become one of hot issue of electric power system, suppress harmonic pollution and mainly contain two basic ideas: the one, active suppression, namely the nonlinear-loads such as power electronic equipment itself are transformed, solved harmonic problem from the source; The 2nd, passive compensation, namely in the situation that system is come compensation harmonic by harmonic pollution installing harmonic compensation device, adopting at present more harmonic wave inhibition and reactive-load compensation method in the distribution network system is that capacitor and passive filter are installed; When distribution network systems was installed passive filter for the system harmonics inhibition, the correct position that selective filter is installed made filter capacity under the prerequisite that obtains identical compensation effect minimum, thereby can reduce the passive filtration unit input cost.

The passive filtration unit installation mainly is to be installed voluntarily by non-linear customer in the distribution network systems at present, the technical scheme that employing is installed nearby in the nonlinear-load side is come the filtering harmonic wave, consider that from the electrical network angle harmonic wave suppresses relatively less, not from the optimum installation site problem of distribution network systems angle consideration under the identical situation of harmonic wave control effect, when in power distribution network, adopting simultaneously passive filtration unit that harmonic wave is administered, except considering passive filter to the regulation effect of harmonic wave, also to consider the Cost Problems of passive filter.

Summary of the invention

The present invention overcomes the deficiency that prior art exists, and technical problem to be solved is: definite method that the optimum installation site of a kind of passive filtration unit is provided.

For solving the problems of the technologies described above, the technical solution adopted in the present invention is: definite method of the optimum installation site of passive filtration unit said method comprising the steps of:

The first step: set up the harmonic wave target and administer function, suppose total K bar branch road in the distribution network system, main harmonic wave is the h subharmonic, and the passive filter of filtering h subharmonic is installed at the m branch road, sets up each branch road h subharmonic voltage expression formula and is:

$V_{k,\mathrm{new}}^h=V_{k,\mathrm{old}}^h+{\mathrm{\ΔV}}_k^h---\left(1\right)$

${\mathrm{\ΔV}}_k^h=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{Z}_{k,m}^h{I}_m^h---\left(2\right)$

In formula (1) and the formula (2): k represents electrical network branch of a network numbering, and h is harmonic number,

With

Be illustrated respectively in the h subharmonic voltage of m branch road access passive filter front and back k branch road; Wherein,

Be the change in voltage that causes at the k branch road behind the access passive filter,

Be the equiva lent impedance of k branch road for the h subharmonic,

Be the current value of passive filter in the absorption of m branch road, wherein

With

And

Be respectively

With

Real part and imaginary part;

To formula (1) both sides square, the relational expression that obtains h subharmonic voltage and offset current is:

$f\left[I_m^h\right]={\left(V_{k,\mathrm{new}}^h\right)}^2={(V_{k,\mathrm{old}}^h+{\mathrm{\ΔV}}_k^h)}^2---\left(3\right)$

(3) formula is launched and can be got:

$f\left[I_m^h\right]=f[I_m^{h,r},I_m^{h,i}]={(V_{k,\mathrm{old}}^{h,r}+Z_{k,m}^{h,r}{I}_m^{h,r}-Z_{k,m}^{h,i}{I}_m^{h,i})}^2$

$+{(V_{k,\mathrm{old}}^{h,i}+Z_{k,m}^{h,r}{I}_m^{h,i}-Z_{k,m}^{h,i}{I}_m^{h,r})}^2$

$={\left(V_{k,\mathrm{old}}^{h,r}\right)}^2+{\left(V_{k,\mathrm{old}}^{h,i}\right)}^2$

$+{2I}_m^{h,r}(V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,r}+V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,i})---\left(4\right)$

$+{2I}_m^{h,i}(V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,r}-V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,i})$

$+[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2][{\left(Z_{k,m}^{h,r}\right)}^2+{\left(Z_{k,m}^{h,i}\right)}^2]$

Be defined as follows:

$A_{k,m}^h={\left(V_{k,\mathrm{old}}^{h,r}\right)}^2+{\left(V_{k,\mathrm{old}}^{h,i}\right)}^2$

$B_{k,m}^h=2(V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,r}+V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,i})$

$C_{k,m}^h=2(V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,r}-V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,i})$

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

Will

Substitution formula (4) can get:

$\begin{array}{c}f[I_m^{h,r},I_m^{h,i}]=A_{k,m}^h+B_{k,m}^h{I}_m^{h,r}+C_{k,m}^h{I}_m^{h,i}\\ +D_{k,m}^h[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2]\end{array}---\left(5\right)$

Should satisfy the requirement of single harmonic component aberration rate according to the h subharmonic for the k branch road, Prescribed Properties:

$\left|\frac{V_k^{\mathrm{<figure-callout\; id="1"\; label="h\; V\; k"\; filenames="130618105219.png"\; state="\{\{state\}\}">h</figure-callout>}}}{V_k^{}}\right|\&le;\mathrm{VL}---\left(6\right)$

In the formula (6) Expression k branch road fundamental voltage, Expression k branch road h subharmonic voltage;

If VL≤3% item satisfies the single harmonic component standard limit, then the harmonic current value minimum of passive filter absorption system is:

$\mathrm{MIN}[f(I_m^{h,r},I_m^{h,i})={\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2]---\left(7\right)$

Draw according to formula (7): when the m branch road satisfied formula (7), namely the passive filter Absorption Current was minimum, and capacity is minimum, then was the optimum installation site of filter, thereby can draws k bar branch road, and the target function that the h subharmonic is administered is:

$\begin{array}{c}f[I_m^{h,r},I_m^{h,i}]=A_{k,m}^h+B_{k,m}^h{I}_m^{h,r}+C_{k,m}^h{I}_m^{h,i}\\ +D_{k,m}^h[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2]\&le;{\mathrm{VL}}_k^2\end{array}---\left(8\right)$

Enter second step;

Second step: the geometrical model of setting up the harmonic wave control target function, judge whether to set up the geometrical model that satisfies condition according to the harmonic wave control target function, if can, then entered for the 3rd step, if cannot, show that this branch road is not the filter best position, then returns the first step, reselect the branch road that passive filter is installed, rebulid the harmonic wave control target function;

Formula (8), in the formula:

With

It is known,

With Be about

With

Function, formula (8) be one about With

Circle, above-mentioned K bar branch road, then corresponding constraint circle number is K, draws K constraint round in coordinate system;

If any two constraint circles all have the general constraint part, then entered for the 3rd step, if any two constraint circles do not have the general constraint part, then return the first step, reselect the branch road that passive filter is installed, rebulid the harmonic wave target and administer function;

The 3rd step: the optimum installation site of obtaining passive filter: at first, construct the related circle relevant with feasible area; Secondly, find out the boundary line of feasible area; At last, find out on the feasible area boundary line from the nearest point of the origin of coordinates, judge whether closest approach is included in the related circle, if should be in association is round, then the branch road at this closest approach place be passive filter optimum installation site; If this is not in the association circle, then the branch road from the nearest some place of initial point is the optimum installation site of passive filter in the intersection point.

The beneficial effect that the present invention compared with prior art has is: the inventive method is by setting up the harmonic wave control target function, adopt method of geometry to find the solution target function, determine the optimum installation site of passive filter, can accurately calculate the installation site of passive filtration unit optimum, have tight science and logicality; Adopt how much method that target function is found the solution, avoided complicated deduce mathematical and calculating, simplify computational process, visual result is reliable.

Description of drawings

The present invention will be further described in detail below in conjunction with accompanying drawing:

Fig. 1 is flow chart of the present invention;

Fig. 2 is the distribution system circuit diagram;

Fig. 3 is three constraint circle diagram shapes;

Fig. 4 is that two circles intersect figure;

Fig. 5 is that many circles intersect figure;

Fig. 6 is that the constraint circle is found the solution figure;

Embodiment

As shown in Figure 1, definite method of the optimum installation site of passive filtration unit of the present invention is characterized in that: said method comprising the steps of:

The first step: set up the harmonic wave control target function, Figure 2 shows that a typical distribution network systems, total K bar branch road in the supposing the system, contain nonlinear load in each branch road, main harmonic wave is the h subharmonic, the passive filter of filtering h subharmonic is installed at the m branch road, is set up each branch road h subharmonic voltage expression formula and be:

$V_{k,\mathrm{new}}^h=V_{k,\mathrm{old}}^h+{\mathrm{\&Delta;V}}_k^h---\left(1\right)$

${\mathrm{\&Delta;V}}_k^h=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{Z}_{k,m}^h{I}_m^h---\left(2\right),$

In formula (1) and the formula (2): k represents the branch of a network numbering, and h is harmonic number,

With

Be illustrated respectively in the h subharmonic voltage of m branch road access passive filter front and back k branch road; Wherein,

Be the change in voltage that causes at the k branch road behind the access passive filter, Be the equiva lent impedance of k branch road for the h subharmonic,

Be the current value of passive filter in the absorption of m branch road;

To formula (1) both sides square, the relational expression that obtains h subharmonic voltage and offset current is:

$f\left[I_m^h\right]={\left(V_{k,\mathrm{new}}^h\right)}^2={(V_{k,\mathrm{old}}^h+\mathrm{\&Delta;}{V}_k^h)}^2---\left(3\right)$

(3) formula is launched and can be got:

$f\left[I_m^h\right]=f[I_m^{h,r},I_m^{h,i}]={(V_{k,\mathrm{old}}^{h,r}+Z_{k,m}^{h,r}{I}_m^{h,r}-Z_{k,m}^{h,i}{I}_m^{h,i})}^2$

$+{(V_{k,\mathrm{old}}^{h,i}+Z_{k,m}^{h,r}{I}_m^{h,i}-Z_{k,m}^{h,i}{I}_m^{h,r})}^2$

$={\left(V_{k,\mathrm{old}}^{h,r}\right)}^2+{\left(V_{k,\mathrm{old}}^{h,i}\right)}^2$

$+{2I}_m^{h,r}(V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,r}+V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,i})---\left(4\right)$

$+{2I}_m^{h,i}(V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,r}-V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,i})$

$+[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2][{\left(Z_{k,m}^{h,r}\right)}^2+{\left(Z_{k,m}^{h,i}\right)}^2]$

Be defined as follows:

$A_{k,m}^h={\left(V_{k,\mathrm{old}}^{h,r}\right)}^2+{\left(V_{k,\mathrm{old}}^{h,i}\right)}^2$

$B_{k,m}^h=2(V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,r}+V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,i})$

$C_{k,m}^h=2(V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,r}-V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,i})$

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

Will

Substitution formula (4) can get:

$\begin{array}{c}f[I_m^{h,r},I_m^{h,i}]=A_{k,m}^h+B_{k,m}^h{I}_m^{h,r}+C_{k,m}^h{I}_m^{h,i}\\ +D_{k,m}^h[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2]\end{array}---\left(5\right)$

The harmonic current that passive filter absorbs hour, the installed capacity of filter capacitor is minimum, the cost of investment of filter is minimum, this moment, best position can be thought in the installation site of filter.According to standard code, should satisfy the requirement of single harmonic component aberration rate, Prescribed Properties for the h subharmonic of k branch road:

$\left|\frac{V_k^{\mathrm{<figure-callout\; id="1"\; label="h\; V\; k"\; filenames="130618105219.png"\; state="\{\{state\}\}">h</figure-callout>}}}{V_k^{}}\right|\&le;\mathrm{VL}---\left(6\right)$

In the formula (6)

Expression k branch road fundamental voltage,

Expression k branch road h subharmonic voltage;

According to national standard: if VL≤3% can satisfy the single harmonic component standard limit, then the harmonic current value of passive filter absorption system is minimum, that is:

$\mathrm{MIN}[f(I_m^{h,r},I_m^{h,i})={\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2]---\left(7\right)$

Draw according to formula (7): when the m branch road satisfies formula (7), be the optimum installation site of passive filter, draw k bar branch road, h subharmonic management goal function is:

$\begin{array}{c}f[I_m^{h,r},I_m^{h,i}]=A_{k,m}^h+B_{k,m}^h{I}_m^{h,r}+C_{k,m}^h{I}_m^{h,i}\\ +D_{k,m}^h[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2]\&le;{\mathrm{VL}}_k^2\end{array}---\left(8\right)$

Then enter second step; Can find out from formula (8), the harmonic wave control target function is the secondary convex function, and the key of dealing with problems is exactly to select suitable method that target is administered function to find the solution.

Second step: the geometrical model of setting up the harmonic wave control target function, judge whether to set up the geometrical model that satisfies condition according to the harmonic wave control target function, if can, then entered for the 3rd step, if cannot, then return the first step, reselect the branch road that passive filter is installed, rebulid the harmonic wave target and administer function;

Formula (8), in the formula:

With

It is known,

With

Be about With

Function, formula (8) be one about

With

Circle, above-mentioned K bar branch road, then corresponding constraint circle number is K, draws K constraint round in coordinate system;

If any two constraint circles all have the general constraint part, then entered for the 3rd step, if any two constraint circles do not have the general constraint part, then return the first step, reselect the branch road that passive filter is installed, rebulid the harmonic wave control target function.

The 3rd step: the optimum installation site of obtaining passive filter: at first, construct the related circle relevant with feasible area; Secondly, find out the boundary line of feasible area; At last, find out on the feasible area boundary line from the nearest point of the origin of coordinates, judge whether closest approach is included in the related circle, if should be in association is round, then the branch road at this closest approach place be passive filter optimum installation site; If this is not in the association circle, then the branch road from the nearest some place of initial point is the optimum installation site of passive filter in the intersection point.

The inventive method adopts the optimum installation site of method of geometry solution passive filter by setting up the harmonic wave control target function, can calculate accurately the installation site of passive filtration unit optimum, has tight science and logicality.

Can find out from above-mentioned formula (8), target function is the affined circle of cluster on how much, and this method adopts geometric method to find the solution target function, and this embodiment contains 3 branch roads take system situation is analyzed as example.

For the system that contains 3 branch roads, corresponding 3 the constraint circles of its target function, as shown in Figure 3, corresponding branch road of each circle among the figure, obviously, passive filter minimal absorption electric current should be subjected to the constraint of institute's Constrained circle, dash area among the figure is the common constraint portions of institute's Constrained circle, the dash area that then the minimal absorption electric current of passive filter should be in the drawings, its size arrives the distance of dash area closest approach for the origin of coordinates, i.e. the point of T1 among Fig. 3 is if system contains K bar branch road, then corresponding constraint circle number is K, and the minimal absorption electric current of passive filter should be in K the round common constraint portions of constraint the distance from origin of coordinates closest approach.

When setting up the target function geometrical model, should be noted that following some:

One, to find the solution simply in order making, should to reduce constraint circle number as far as possible, if there is great circle to comprise the situation of roundlet, can ignore great circle;

Two, when passive filter is installed on a certain branch road, if there are any two constraint circles not have the general constraint part, illustrate that this branch road does not meet installation requirement, can not passive filter be installed at this branch road, need to select other branch road to install;

Three, the constraint circle that meets installation requirement is arranged in a certain order (radius from small to large or from big to small), begin to calculate from two circles of radius maximum (perhaps minimum), obtain the intersection point of any two circles, such as the A among Fig. 3, B, C, D, E, F;

Four, the circle of pair radius maximum checks all intersection points on it, find the point that satisfies all constraint circles, such as the D among Fig. 3, E, if intersection point does not exist, the branch road that this constraint circle representative then is described is not that the optimum of passive filter is installed branch road, needs to consider to select other branch road.

According to above dissolve principle the corresponding constraint circle of target function carried out abbreviation after, can obtain the minimal absorption current value of passive filter, step is as follows:

One, the structure related circle relevant with feasible area; As can be seen from Figure 3, the common dash area of each constraint circle is the feasible area of finding the solution optimum Injection Current, directly obtain relatively difficulty of optimal current solution from this zone, thus construct a circle that is associated with feasible area, conveniently to find the solution; The below discusses two constraint circles in detail when intersecting and should related round construction process when having a plurality of constraints circles to intersect:

Figure 4 shows that two constraint circles intersect the situation of the related circle of structure, can be divided into two kinds of situations, one is that the two mid point P that justify the string JK that intersect are positioned on the extended line of two round heart lines, such as Fig. 4 (a), then roundlet namely is the association circle that will look for, the 2nd, and the mid point P of string JK is positioned on the line of the two round hearts, such as Fig. 4 (b), at this moment take a P as the center of circle, string JK is that circle of diameter structure is the association circle that will look for;

There are a plurality of constraint circles to intersect the related round situation of structure as shown in Figure 5, three constraint circles have been provided among Fig. 5, suppose that three constraint circles intersect, construct related bowlder, open from two constraint circles of radius maximum first, according to two crossing situations of constraint circle, find its related circle, the round B1 that marks such as thick line among Fig. 5 (a), find needed round B2 with circle B1 and the 3rd circle (namely justifying 1) according to the situations that two constraint circles intersect again, it is round that B2 is the association that will look for, such as Fig. 5 (b), more than three constraint bowlders, adopt similar approach to get final product.

Two, find out the boundary line of feasible area; All intersection points are included in the related circle, and satisfy all constraint circles, are the flex point of feasible area, like this, have just determined the border of feasible area, and as shown in Figure 5, the dash area of Fig. 5 is the feasible area boundary line.

Three, the optimum installation site of passive filter determines, according to the feasible area boundary line that obtains, determine in accordance with the following methods the optimum installation site of passive filter: find out on the feasible area boundary line from the nearest point of the origin of coordinates, such as the some T1 among Fig. 6, judge whether closest approach is included in the related circle, if this is in the association circle, then the branch road at this closest approach place is the optimum installation site of passive filter; If this is not in the association circle, then the branch road from the nearest some place of initial point is the optimum installation site of passive filter in the intersection point, and among Fig. 6, the branch road at T1 point place is the optimum installation site of passive filter.

The present invention adopts how much method that target function is found the solution, and has avoided complicated deduce mathematical and calculating, simplifies computational process, and visual result is reliable.

Claims (1)

1. definite method of the optimum installation site of passive filtration unit is characterized in that: said method comprising the steps of:

The first step: set up the harmonic wave target and administer function, suppose total K bar branch road in the distribution network system, main harmonic wave is the h subharmonic, and the passive filter of filtering h subharmonic is installed at the m branch road, sets up each branch road h subharmonic voltage expression formula and is:

$V_{k,\mathrm{new}}^h=V_{k,\mathrm{old}}^h+{\mathrm{\&Delta;V}}_k^h---\left(1\right)$

${\mathrm{\&Delta;V}}_k^h=\underset{k=1}{\overset{k}{\mathrm{\&Sigma;}}}{Z}_{k,m}^h{I}_m^h---\left(2\right)$

In formula (1) and the formula (2): k represents electrical network branch of a network numbering, and h is harmonic number,

With

Be illustrated respectively in the h subharmonic voltage of m branch road access passive filter front and back k branch road; Wherein,

Be the change in voltage that causes at the k branch road behind the access passive filter,

Be the equiva lent impedance of k branch road for the h subharmonic,

Be the current value of passive filter in the absorption of m branch road, wherein

With

And

Be respectively

With

Real part and imaginary part;

To formula (1) both sides square, the relational expression that obtains h subharmonic voltage and offset current is:

$f\left[I_m^h\right]={\left(V_{k,\mathrm{new}}^h\right)}^2={(V_{k,\mathrm{old}}^h+{\mathrm{\&Delta;V}}_k^h)}^2---\left(3\right)$

(3) formula is launched and can be got:

$f\left[I_m^h\right]=f[I_m^{h,r},I_m^{h,i}]={(V_{k,\mathrm{old}}^{h,r}+Z_{k,m}^{h,r}{I}_m^{h,r}-Z_{k,m}^{h,i}{I}_m^{h,i})}^2$

$+{(V_{k,\mathrm{old}}^{h,i}+Z_{k,m}^{h,r}{I}_m^{h,i}-Z_{k,m}^{h,i}{I}_m^{h,r})}^2$

$={\left(V_{k,\mathrm{old}}^{h,r}\right)}^2+{\left(V_{k,\mathrm{old}}^{h,i}\right)}^2$

$+{2I}_m^{h,r}(V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,r}+V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,i})---\left(4\right)$

$+{2I}_m^{h,i}(V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,r}-V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,i})$

$+[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2][{\left(Z_{k,m}^{h,r}\right)}^2+{\left(Z_{k,m}^{h,i}\right)}^2]$

Be defined as follows:

$A_{k,m}^h={\left(V_{k,\mathrm{old}}^{h,r}\right)}^2+{\left(V_{k,\mathrm{old}}^{h,i}\right)}^2$

$B_{k,m}^h=2(V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,r}+V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,i})$

$C_{k,m}^h=2(V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,r}-V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,i})$

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

Will Substitution formula (4) can get:

$\begin{array}{c}f[I_m^{h,r},I_m^{h,i}]=A_{k,m}^h+B_{k,m}^h{I}_m^{h,r}+C_{k,m}^h{I}_m^{h,i}\\ +D_{k,m}^h[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2]\end{array}---\left(5\right)$

Should satisfy the requirement of single harmonic component aberration rate according to the h subharmonic for the k branch road, Prescribed Properties:

$\left|\frac{V_k^h}{V_k^1}\right|\&le;\mathrm{VL}---\left(6\right)$

In the formula (6)

Expression k branch road fundamental voltage,

Expression k branch road h subharmonic voltage;

If VL≤3% item satisfies the single harmonic component standard limit, then the harmonic current value minimum of passive filter absorption system is:

$\mathrm{MIN}[f(I_m^{h,r},I_m^{h,i})={\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2]---\left(7\right)$

Draw according to formula (7): when the m branch road satisfied formula (7), namely the passive filter Absorption Current was minimum, and capacity is minimum, then was the optimum installation site of filter, thereby can draws k bar branch road, and the target function that the h subharmonic is administered is:

$\begin{array}{c}f[I_m^{h,r},I_m^{h,i}]=A_{k,m}^h+B_{k,m}^h{I}_m^{h,r}+C_{k,m}^h{I}_m^{h,i}\\ +D_{k,m}^h[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2]\&le;{\mathrm{VL}}_k^2\end{array}---\left(8\right)$

Enter second step;

Second step: the geometrical model of setting up the harmonic wave control target function, judge whether to set up the geometrical model that satisfies condition according to the harmonic wave control target function, if can, then entered for the 3rd step, if cannot, show that this branch road is not the filter best position, then returns the first step, reselect the branch road that passive filter is installed, rebulid the harmonic wave control target function;

Formula (8), in the formula:

With

It is known,

Be about With

Function, formula (8) be one about With

Circle, above-mentioned K bar branch road, then corresponding constraint circle number is K, draws K constraint round in coordinate system;

If any two constraint circles all have the general constraint part, then entered for the 3rd step, if any two constraint circles do not have the general constraint part, then return the first step, reselect the branch road that passive filter is installed, rebulid the harmonic wave target and administer function; The 3rd step: the optimum installation site of obtaining passive filter: at first, construct the related circle relevant with feasible area; Secondly, find out the boundary line of feasible area; At last, find out on the feasible area boundary line from the nearest point of the origin of coordinates, judge whether closest approach is included in the related circle, if should be in association is round, then the branch road at this closest approach place be passive filter optimum installation site; If this is not in the association circle, then the branch road from the nearest some place of initial point is the optimum installation site of passive filter in the intersection point.

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