CN103326364B - 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

The defining method of best installation position of passive filter device

Technical field

The defining method of best installation position of passive filter device of the present invention, is specifically related to the defining 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 electric harmonic pollution of electrical network especially power distribution network is also day by day serious, the harmonic wave of electric power system and idle problem cause people and more and more pay close attention to, one of harmonics restraint hot issue becoming electric power system, harmonic inhabitation pollutes and mainly contains two basic ideas: one is active suppression, namely the nonlinear-loads such as power electronic equipment itself are transformed, solve harmonic problem from source; Two is passive compensation, is namely installed harmonic compensation device when harmonic pollution in system and carrys out compensation harmonic, adopts more harmonics restraint and reactive-load compensation method to be install capacitor and passive filter in current distribution network system; When distribution network systems installs passive filter for system harmonics suppression, the correct position that selective filter is installed, makes filter capacity under the prerequisite obtaining identical compensation effect minimum, thus can reduce passive filtration unit input cost.

In current distribution network systems, passive filtration unit is installed and is mainly installed voluntarily by non-linear customer, the technical scheme of installing in nonlinear-load side is adopted to carry out filtering harmonic wave nearby, consider that harmonics restraint is relatively less from electrical network angle, do not consider the optimum installation site problem when harmonic wave control effect is identical from distribution network systems angle, when adopting passive filtration unit to administer harmonic wave in power distribution network simultaneously, except the regulation effect of passive filter to harmonic wave will be considered, the Cost Problems of passive filter also to be considered.

Summary of the invention

The present invention overcomes the deficiency that prior art exists, and technical problem to be solved is: the defining method providing a kind of best installation position of passive filter device.

For solving the problems of the technologies described above, the technical solution adopted in the present invention is: the defining method of best installation position of passive filter device, said method comprising the steps of:

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

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

$\mathrm{\Δ}{V}_k^h=Z_{k,m}^h{I}_m^h---\left(2\right),$

In formula (1) and formula (2): k represents electricity grid network branch number, and h is harmonic number, with be illustrated respectively in the h subharmonic voltage of kth branch road before and after m branch road access passive filter; Wherein, for the change in voltage caused at k branch road after access passive filter, for k branch road is for the equiva lent impedance of h subharmonic, for passive filter is at the current value of 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 obtaining h subharmonic voltage and offset current is:

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

(3) formula is launched to obtain:

$\begin{array}{c}f\left[I_m^h\right]=f[I_m^{h,r},I_m^{h,i}]={(V_{k,\mathrm{old}}^{h,r}+Z_{k,m}^{h,r}{I}_m^{h,r}-Z_{k,m}^{h,i}{I}_m^{h,i})}^2\\ +{(V_{k,\mathrm{old}}^{h,i}+Z_{k,m}^{h,r}{I}_m^{h,i}-Z_{k,m}^{h,i}{I}_m^{h,r})}^2\\ ={\left(V_{k,\mathrm{old}}^{h,r}\right)}^2+{\left(V_{k,\mathrm{old}}^{h,i}\right)}^2\\ +2I_m^{h,r}(V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,r}+V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,i})\\ +2I_m^{h,i}(V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,r}-V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,i})\\ +[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2][{\left(Z_{k,m}^{h,r}\right)}^2+{\left(Z_{k,m}^{h,i}\right)}^2]\end{array}---\left(4\right)$

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 obtain:

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

The requirement of single harmonic component aberration rate should be met, Prescribed Properties according to the h subharmonic for kth branch road:

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

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

If VL≤3%, meet single harmonic component standard limit, then the harmonic current value of passive filter absorption system is minimum 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 m branch road meets formula (7), namely passive filter Absorption Current is minimum, and capacity is minimum, be then the optimum installation site of filter, thus can draw kth bar branch road, the target function that h subharmonic is administered is:

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

Enter second step;

Second step: the geometrical model setting up harmonic wave control target function, judge whether set up the geometrical model satisfied condition according to harmonic wave control target function, if passable, then enter the 3rd step, if cannot, show that this branch road is not filter best position, then return the first step, reselect the branch road installing passive filter, re-establish harmonic wave control target function;

Formula (8), in 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 restrained circle number is K, draws K restrained circle in a coordinate system;

If any two restrained circle all have general constraint part, then enter the 3rd step, if any two restrained circle do not have general constraint part, then return the first step, reselect the branch road installing passive filter, re-establish harmonic wave target and administer function;

3rd step: the optimum installation site obtaining passive filter: first, constructs associate relevant to feasible area and justifies; Secondly, the boundary line of feasible area is found out; Finally, find out point nearest from the origin of coordinates on feasible area boundary line, judge whether closest approach is included in association circle, if this point is in association circle, then the branch road at this closest approach place is the optimum installation site of passive filter; If this point is not in association circle, then in intersection point from the branch road at the nearest some place of initial point be the optimum installation site of passive filter.

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

Accompanying drawing explanation

Below in conjunction with accompanying drawing, the present invention will be further described in detail:

Fig. 1 is flow chart of the present invention;

Fig. 2 is distribution system circuit diagram;

Fig. 3 is three restrained circle figures;

Fig. 4 is that two circles intersect figure;

Fig. 5 is that many circles intersect figure;

Fig. 6 is that restrained circle solves figure;

Embodiment

As shown in Figure 1, the defining method of best installation position of passive filter device of the present invention, is characterized in that: said method comprising the steps of:

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

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

$\mathrm{\Δ}{V}_k^h=Z_{k,m}^h{I}_m^h---\left(2\right),$

In formula (1) and formula (2): k represents that branch of a network is numbered, and h is harmonic number, with be illustrated respectively in the h subharmonic voltage of kth branch road before and after m branch road access passive filter; Wherein, for the change in voltage caused at k branch road after access passive filter, for k branch road is for the equiva lent impedance of h subharmonic, for passive filter is at the current value of the absorption of m branch road;

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

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

(3) formula is launched to obtain:

$\begin{array}{c}f\left[I_m^h\right]=f[I_m^{h,r},I_m^{h,i}]={(V_{k,\mathrm{old}}^{h,r}+Z_{k,m}^{h,r}{I}_m^{h,r}-Z_{k,m}^{h,i}{I}_m^{h,i})}^2\\ +{(V_{k,\mathrm{old}}^{h,i}+Z_{k,m}^{h,r}{I}_m^{h,i}-Z_{k,m}^{h,i}{I}_m^{h,r})}^2\\ ={\left(V_{k,\mathrm{old}}^{h,r}\right)}^2+{\left(V_{k,\mathrm{old}}^{h,i}\right)}^2\\ +2I_m^{h,r}(V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,r}+V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,i})\\ +2I_m^{h,i}(V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,r}-V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,i})\\ +[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2][{\left(Z_{k,m}^{h,r}\right)}^2+{\left(Z_{k,m}^{h,i}\right)}^2]\end{array}---\left(4\right)$

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 obtain:

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

When the harmonic current that passive filter absorbs is minimum, the installed capacity of filter capacitor is minimum, and the cost of investment of filter is minimum, and now best position can be thought in the installation site of filter.According to standard regulation, the h subharmonic for kth branch road should meet the requirement of single harmonic component aberration rate, Prescribed Properties:

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

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

According to national standard: if VL≤3% can meet 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 m branch road meets formula (7), be the optimum installation site of passive filter, show that, to kth bar branch road, h subharmonic management goal function is:

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

Then second step is entered; As can be seen from formula (8), harmonic wave control target function is secondary convex function, and the key of dealing with problems is exactly select suitable method to administer function to target to solve.

Second step: the geometrical model setting up harmonic wave control target function, judge whether set up the geometrical model satisfied condition according to harmonic wave control target function, if passable, then enter the 3rd step, if cannot, then return the first step, reselect the branch road installing passive filter, re-establish harmonic wave target and administer function;

Formula (8), in 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 restrained circle number is K, draws K restrained circle in a coordinate system;

If any two restrained circle all have general constraint part, then enter the 3rd step, if any two restrained circle do not have general constraint part, then return the first step, reselect the branch road installing passive filter, re-establish harmonic wave control target function.

3rd step: the optimum installation site obtaining passive filter: first, constructs associate relevant to feasible area and justifies; Secondly, the boundary line of feasible area is found out; Finally, find out point nearest from the origin of coordinates on feasible area boundary line, judge whether closest approach is included in association circle, if this point is in association circle, then the branch road at this closest approach place is the optimum installation site of passive filter; If this point is not in association circle, then in intersection point from the branch road at the nearest some place of initial point be the optimum installation site of passive filter.

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

As can be seen from above-mentioned formula (8), be the affined circle of cluster at geometrically target function, this method adopts geometric method to solve target function, and the situation that this embodiment contains 3 branch roads for system is analyzed.

For the system containing 3 branch roads, corresponding 3 restrained circle of its target function, as shown in Figure 3, the corresponding branch road of each circle in figure, obviously, passive filter minimal absorption electric current should by the constraint of all restrained circle, dash area in figure is the common constraint portions of all restrained circle, then the minimal absorption electric current of passive filter should dash area in the drawings, its size is the distance that the origin of coordinates arrives dash area closest approach, namely the T1 point in Fig. 3, if system contains K bar branch road, then corresponding restrained circle number is K, the minimal absorption electric current of passive filter should be the distance from origin of coordinates closest approach in K the common constraint portions of restrained circle.

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

One, solving simply to make, restrained circle number should be reduced as far as possible, if there is great circle to comprise the situation of roundlet, can great circle be ignored;

Two, when passive filter is installed on a certain branch road, if there are any two restrained circle there is no general constraint part, illustrate that this branch road does not meet installation requirement, at this branch road, passive filter can not be installed, other branch road need be selected to install;

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

Four, the circle that pair radius is maximum checks intersection points all on it, find the point meeting all restrained circle, as D, E in Fig. 3, if intersection point does not exist, then illustrate that branch road that this restrained circle represents is not that the optimum of passive filter installs branch road, need consider to select other branch road.

Dissolve after principle carries out abbreviation to the restrained circle corresponding to target function according to above, can obtain the minimal absorption current value of passive filter, step is as follows:

What one, structure was relevant to feasible area associates circle; As can be seen from Figure 3, the common dash area of each restrained circle is the feasible area solving optimum Injection Current, directly to obtain optimal current solution from this region more difficult, so a structure circle be associated with feasible area, solves to facilitate; Discuss in detail below when two restrained circle intersect with when having multiple restrained circle to intersect this associate circle construction process:

Figure 4 shows that two restrained circle intersect the situation of structure association circle, two kinds of situations can be divided into, one is that the two mid point P justifying the string JK intersected are positioned on the extended line of two circle circle center line connectings, as Fig. 4 (a), then namely roundlet is the association circle that will look for, and two is that the mid point P of string JK is positioned on the line of the two round hearts, as Fig. 4 (b), at this moment with a P for the center of circle, association that string JK will look for for diameter configuration circle is circle;

Multiple restrained circle is had to intersect the situation of structure association circle as shown in Figure 5, three restrained circle are given in Fig. 5, suppose that three restrained circle intersect, structure association bowlder, first open from two restrained circle that radius is maximum, according to the situation that two restrained circle intersect, find its association circle, as the round B1 that thick line in Fig. 5 (a) marks, justify, as Fig. 5 (b) with the association that circle B1 and the 3rd circle (namely round 1) find required round B2, B2 to be will to look for according to the situation that two restrained circle are crossing again, during more than three restrained circle, adopt similar approach.

Two, the boundary line of feasible area is found out; All intersection points are included in association circle, and meet all restrained circle, and be the flex point of feasible area, like this, just determine the border of feasible area, as shown in Figure 5, the dash area of Fig. 5 is feasible area boundary line.

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

The present invention adopts the method for geometry to solve target function, avoids complicated deduce mathematical and calculating, and simplify computational process, visual result is reliable.

Claims (1)

1. the defining method of best installation position of passive filter device, is characterized in that: said method comprising the steps of:

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

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

${\mathrm{\ΔV}}_k^h=Z_{k,m}^h{I}_m^h---\left(2\right)$

In formula (1) and formula (2): k represents electricity grid network branch number, and h is harmonic number, with be illustrated respectively in the h subharmonic voltage of kth branch road before and after m branch road access passive filter; Wherein, for the change in voltage caused at k branch road after access passive filter, for k branch road is for the equiva lent impedance of h subharmonic, for passive filter is at the current value of 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 obtaining 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 to obtain:

$\begin{array}{c}f\left[I_m^h\right]=f[I_m^{h,r},I_m^{h,i}]={(V_{k,\mathrm{old}}^{h,r}+Z_{k,m}^{h,r}{I}_m^{h,r}-Z_{k,m}^{h,i}{I}_m^{h,i})}^2\\ +{(V_{k,\mathrm{old}}^{h,i}+Z_{k,m}^{h,r}{I}_m^{h,i}-Z_{k,m}^{h,i}{I}_m^{h,r})}^2\\ ={\left(V_{k,\mathrm{old}}^{h,r}\right)}^2+{\left(V_{k,\mathrm{old}}^{h,i}\right)}^2\\ +2I_m^{h,r}(V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,r}+V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,i})\\ +2I_m^{h,i}(V_{k,\mathrm{old}}^{h,i}{Z}_{k,m}^{h,r}-V_{k,\mathrm{old}}^{h,r}{Z}_{k,m}^{h,i})\\ +[{\left(I_m^{h,r}\right)}^2+{\left(I_m^{h,i}\right)}^2][{\left(Z_{k,m}^{h,r}\right)}^2+{\left(Z_{k,m}^{h,i}\right)}^2]\end{array}---\left(4\right)$

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 obtain:

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

The requirement of single harmonic component aberration rate should be met, Prescribed Properties according to the h subharmonic for kth branch road:

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

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

If VL≤3%, meet single harmonic component standard limit, then the harmonic current value of passive filter absorption system is minimum 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 m branch road meets formula (7), namely passive filter Absorption Current is minimum, and capacity is minimum, be then the optimum installation site of filter, thus can draw kth bar branch road, the target function that h subharmonic is administered is:

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

Enter second step;

Second step: the geometrical model setting up harmonic wave control target function, judge whether set up the geometrical model satisfied condition according to harmonic wave control target function, if passable, then enter the 3rd step, if cannot, show that this branch road is not filter best position, then return the first step, reselect the branch road installing passive filter, re-establish harmonic wave control target function;

Formula (8), in 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 restrained circle number is K, draws K restrained circle in a coordinate system;

If any two restrained circle all have general constraint part, then enter the 3rd step, if any two restrained circle do not have general constraint part, then return the first step, reselect the branch road installing passive filter, re-establish harmonic wave target and administer function; 3rd step: the optimum installation site obtaining passive filter: first, constructs associate relevant to feasible area and justifies; Secondly, the boundary line of feasible area is found out; Finally, find out point nearest from the origin of coordinates on feasible area boundary line, judge whether closest approach is included in association circle, if this point is in association circle, then the branch road at this closest approach place is the optimum installation site of passive filter; If this point is not in association circle, then in intersection point from the branch road at the nearest some place of initial point be the optimum installation site of passive filter.