CN100361363C - Low-loss multi-tuned passive power filter - Google Patents

Abstract

The present invention discloses a low-loss multi-tuned passive electric power filter which comprises a frequency selection two-port multi-tuned filter, wherein the multi-tuned filter is formed by the series connection of an LC series resonance branch and one to two LC parallel resonance branches. The present invention is characterized in that a capacitor (C1) in an LC series resonance circuit is formed by the equivalent series connection of two capacitors (C0 and C1'); a damping resistor (R1) is connected in parallel to a two-port network between a series node (a) and the ground of the two equivalent series capacitors (C0 and C1') or between series nodes (b) of LC parallel resonance loops which are mutually connected in series; a loop forms series resonance on a fundamental frequency point is composed of the damping resistor (R1) and the two-port network which is connected in parallel with the damping resistance (R1). The low-loss multi-tuned passive electric power filter of the present invention has the obvious technical effect of low electric energy loss of fundamental waves.

Description

Low-loss multi-tuned passive power filter

Technical field:

The present invention relates to the electrotechnics technical field, relate to and a kind ofly only select two-port network as the frequency of network components, specifically relate to a kind of passive harmonic filter, be applicable to and administer the utility network harmonic wave with passive electrical element.

Background technology:

The desirable voltage that utility network provided should be the voltage magnitude of single and fixing frequency and regulation.The appearance of higher harmonic current and harmonic voltage is a kind of pollution to utility network, and it worsens the residing environment of power consumption equipment, communication system around the harm and the equipment that connects with utility network.Installing the ac filter device additional is one of effective measures of administering harmonic pollution in electric power net.Existing ac filter device mainly contains passive harmonic filter, active harmonics filter and mixes harmonic filter.Traditional passive filter,, small investment simple in structure because of it, operational reliability is higher and operating cost is lower, is still the main means that harmonic wave suppresses so far.

The main type of existing passive power filter has single tuned filter and multi-tuned filter.What multi-tuned passive power filter entered practical application mainly contains double-tuned filter and three tuned filters.With regard to its basic circuit, the most frequently used also all is that a LC series arm constitutes with a LC parallel branch or two LC parallel branch series connection of connecting mutually.Fig. 1 (a) and Fig. 1 (b) are respectively undamped double-tuned filter and three tuned filter circuit.In AC network filtering, undamped formula harmonic filter easily with AC system at some harmonic frequency point generation parallel resonance, cause harmonic current seriously to amplify, the element of filter and system transshipped and damage.In order in the filtering of AC network, to suppress the serious amplification phenomenon of harmonic current, normal by the upper electric capacity (capacitor C among Fig. 1 at Fig. 1 (a) and Fig. 1 (b) ₁) method of parallel resistance is come the parallel resonance of damping filter and system, formation Fig. 1 (c) and the damp type double-tuned filter of Fig. 1 (d) and the damp type three tuned filter circuit of Fig. 1 (e)～Fig. 1 (h) on following network or the network element.

The circuit of Fig. 1 (c) double-tuned filter of practical application that is Gezhou Dam to the south bridge DC engineering, the circuit of the another kind of double-tuned filter circuit of Fig. 1 (d) practical application to the DC engineering of Guangzhou that is natural bridge, Fig. 1 (e) a kind of damp type three tuned filters of practical application that are high slope to the DC engineering of Zhaoqing.But the mode of Fig. 1 (c)～Fig. 1 (h) parallel resistance, damping resistance then will produce bigger fundamental energy loss.

Referring to Fig. 1, according to double-tuned filter circuit and its filtering characteristic, the fundamental frequency f of electrical network _F＜filter first frequency filtering the f ₁＜filter L ₂, C ₂The resonance frequency F of parallel resonance branch road ₂＜filter second frequency filtering the f ₂For three tuned filter circuit and its filtering characteristic, the fundamental frequency f of electrical network _F＜filter first frequency filtering the f ₁＜filter L ₂, C ₂The resonance frequency F of parallel resonance branch road ₂＜filter second frequency filtering the f ₂＜filter L ₃, C ₃The resonance frequency F of parallel resonance branch road ₃＜filter the 3rd frequency filtering f ₃In brief, the fundamental frequency of electrical network is less than filter L ₂, C ₂The resonance frequency of parallel resonance branch road is also less than filter L ₃, C ₃The resonance frequency of parallel resonance branch road.According to the electrotechnics principle, for the LC shunt-resonant circuit, when frequency during less than its parallel resonance frequency, its equivalent reactance is the characteristic of inductance.Specific to double-tuned filter shown in Figure 1 and three tuned filters, under fundamental frequency, L ₂, C ₂Parallel resonance branch road and L ₃, C ₃The equivalent reactance of parallel resonance branch road all is the characteristic of inductance.Therefore no matter which kind of mode damping resistance connects with Fig. 1 (c)～Fig. 1 (h), and the equivalent two port circuit in parallel with damping resistance all is inductance characteristic under fundamental frequency.This shows that under fundamental frequency, described damping resistance two ends have fundamental voltage to exist, this fundamental voltage must make damping resistance produce the fundamental energy loss.

Summary of the invention:

In view of having the problem that there is above-mentioned fundamental energy loss in damp type multi-tuned filter technology now, technical problem to be solved by this invention is to reduce the fundamental energy loss of damp type multi-tuned passive power filter damping resistance in parallel.

The technical solution that the present invention solves the problems of the technologies described above is:

A kind of low-loss multi-tuned passive filter, comprise the two port multi-tuned filter of selecting as the frequency of network element with passive electrical element, this multi-tuned filter is in series by a LC series resonance branch road and 1～2 LC parallel resonance branch road and constitutes, and it is characterized in that the capacitor C in the described LC series resonance branch road is composed in series by two capacitor equivalents; Series connection node between the two equivalent series electric capacity over the ground or to being parallel with damping resistance on the two-port network between the series connection node of the two LC parallel resonance branch roads of connecting, the two-port network in parallel with this damping resistance constitutes a loop in the fundamental frequency series resonance.

Because technique scheme comprises the series connection node of two equivalent series electric capacity to being parallel with the technical scheme of damping resistance on the two-port network between the series connection node of the LC parallel resonance branch road of mutual series connection.In this scheme, next stage LC parallel branch then is a undamped LC parallel branch.And under some specific system condition, need further to increase the damping of filter, therefore technical solutions according to the invention are at the series connection node of the two LC parallel resonance branch roads of connecting mutually another damping resistance in parallel over the ground, to improve the effect that suppresses parallel resonance between damping filter and the system.

Below in conjunction with accompanying drawing technical solutions according to the invention and prior art are analyzed comparison, fully understand the technique effect that the present invention can reach in the hope of the public.

The technical problem to be solved in the present invention is to reduce the fundamental energy loss that the damp type multi-tuned filter plays the damping resistance in parallel of damping action, and the key that solves this technical problem is: realize two-port network under fundamental frequency the series resonance in parallel with damping resistance, in the hope of the terminal voltage that is implemented in damping resistance in parallel under the first-harmonic condition is zero, and damping resistance fundamental energy promptly in parallel loss is zero purpose.With Fig. 1 (d) damp type double-tuned filter is example, because under fundamental frequency, the network in parallel with damping resistance R is perception, so the fundamental energy loss is inevitable.If with the capacitor C among Fig. 1 (d) ₁Capacitor C with two equivalent series ₀And C ₁' replace, and make damping resistance R by the mode of Fig. 2 circuit ₁Be connected across capacitor C ₀And C ₁' node a and ground d between, be a kind of fundamental type of technical scheme of the present invention just.Under the first-harmonic condition, capacitor C ₁' with by inductance L ₁, L ₂And capacitor C ₂After the equivalent inductance series connection of the two ends of forming to network, by parameter matching, just can be in series resonance under the fundamental frequency.

Fig. 2 the right resistance R ₁With the left side by inductance L ₁, L ₂And capacitor C ₁', C ₂In the resonant tank of forming, make resistance R ₁The fundamental voltage at two ends is that zero unique possible condition is that the left side is by inductance L ₁, L ₂And capacitor C ₂, C ₁The two ends of ' composition are 0 to the fundamental reactance of network, promptly $X_{L_1{C}_1^{\′}{L}_2{C}_2}(\mathrm{\ω}={\mathrm{\ω}}_F)={\mathrm{\ω}}_F{L}_1+\frac{{\mathrm{\ω}}_F{L}_2}{1-{\mathrm{\ω}}_F^2/{\mathrm{\ω}}_2^2}-\frac{1}{{\mathrm{\ω}}_F{C}_1^{\′}}=10$ ω in the formula _FBe the first-harmonic angular frequency, ω ₂Be L ₂, C ₂The parallel resonance angular frequency.Before address because ω _F＜ω ₂So preceding two of this formula is positive number under fundamental frequency, back one is negative.Therefore, suitably select the described inductance L of technical solution of the present invention ₁, L ₂And capacitor C ₂, C ₁' component parameters, under the first-harmonic condition, can make damping resistance R ₁The fundamental voltage at two ends is zero, reaches to make the fundamental energy loss near zero technique effect.Consider the variation of the parameter error and the mains frequency of inductance, electric capacity in actual applications, and the interior resistance of inductance, capacitor element (resistance is very little in this), although whole filter still has some fundamental energy losses, electric energy loss is quite little, and energy-saving effect is still fairly obvious.

Description of drawings:

Fig. 1 is the circuit theory diagrams of existing passive double-tuned filter and three tuned filters.Wherein: (a) figure is undamped basic double-tuned filter, (b) figure is undamped basic three tuned filters, (c) figure is a kind of damp type double-tuned filter, (d) figure is another kind of damp type double-tuned filter, (e) figure is a kind of damp type three tuned filters, (g) figure is another kind of damp type three tuned filters, and (h) figure is another damp type three tuned filter;

Fig. 2 is a kind of double-tuned filter circuit theory diagrams of the present invention;

Fig. 3 is a kind of three tuned filter circuit theory diagrams of the present invention;

Fig. 4 is a kind of three tuned filter circuit theory diagrams of the present invention;

Fig. 5 is a kind of three tuned filter circuit theory diagrams of the present invention;

Fig. 6 is the impedance frequency characteristic curve chart of following embodiment 1;

Fig. 7 is the impedance frequency characteristic curve chart of following embodiment 2;

Fig. 8 is the impedance frequency characteristic curve chart of following embodiment 3;

Fig. 9 is the impedance frequency characteristic curve chart of following embodiment 4.

Embodiment:

Describe the specific embodiment of the present invention in detail below in conjunction with drawings and Examples, but the present invention is not limit by described specific embodiment.

Example 1

Referring to Fig. 2, the low-loss type double-tuned filter circuit of present embodiment is to form like this: C ₀, C ₁', L ₁Series connection back and L ₂, C ₂Parallel branch is in series, then in capacitor C ₀, C ₁' series connection node a and ground node d between a damping resistance R in parallel ₁Design condition is: fundamental frequency f _F=50Hz, rated voltage U=230kV requires single group three-phase reactive compensation capacity Q=100Mvar, and the filter filtering frequency is f ₁=150Hz, f ₂=1800Hz.

It is very simple that circuit shown in Figure 2 seems, but will according to given condition to carry out designing and calculating but very complicated and loaded down with trivial details, so the present invention also adopts the common way of those skilled in the art, promptly bypasses damping resistance R earlier ₁, and suppose actual frequency filtering equal design condition given frequency filtering, promptly $f_1^t=f_1,$ $f_2^t=f_2,$ At first with reference to each component parameters L that calculates of the basic double-tuned filter circuit of Fig. 1 (a) ₁, C ₁, L ₂, C ₂(concrete calculation of parameter derivation is seen: ' Algorithm for Parameters of Double TunedFilter ', by Xiao Yao, proceedings of the 8 ^ThInternational conference on harmonicsand quality of power, Volume 1, October 14-16,1998, Atherns, Greece, pp 154～157).Then with reference to Fig. 2 with C ₁Equivalence is split into C ₀, C ₁' after, select the damping resistance R of different resistances again for use ₁Calculate, draw out under different resistances, the impedance frequency characteristic curve of filter, the resistance of the harmonic impedance comparison filter of coupling system frequency characteristic and damping are revised then, through comparing and optimizing and determine damping resistance R ₁Resistance value, check and calculate the error between the given frequency filtering of actual frequency filtering and design condition at last, if this error exceeds the design specification allowed band, turn around again to revise, calculate, till the error of frequency filtering is in the design specification allowed band.

Below be described in detail each element computation of electrical, selection course in the present embodiment, so that the public grasps concrete enforcement means of the present invention better.

At first calculate L with reference to Fig. 1 (a) ₁, C ₁, L ₂, C ₂Parameter.

(1) selects L ₂, C ₂Parallel resonance frequency F ₂

The front is by the agency of, F ₂Must be between the actual frequency filtering f of filter ₁ ^tAnd f ₂ ^tBetween, must avoid between filter and the system at F ₂Serious harmonic wave takes place near the frequency amplify, harmonic source is at F simultaneously ₂Near the harmonic wave of the generation of frequency is very little.Select F in this example ₂=176Hz.

Then, according to the actual frequency filtering f of the supposition of filter ₁ ^tAnd f ₂ ^t, and L ₂, C ₂Parallel branch resonance frequency F ₂, calculate L ₁, C ₁The series resonance frequency of branch road

$F_1=\frac{f_1^t{f}_2^t}{F_2}=\frac{150\×1800}{176}=1534.09\mathrm{Hz}.$

(2) harmonic number of the harmonic number filter filtering frequency of calculating filter frequency filtering and each series, parallel resonance branch road resonance frequency:

$h_1=f_1^t/f_F=150/50=3,$ $h_2=f_2^t/f_F=1800/50=36;$

The harmonic number of each resonance branch road of filter:

L ₁With C ₁The harmonic number of series resonance branch road: H ₁=F ₁/ f _F=1534.09/50=30.6818,

L ₂With C ₂The harmonic number of parallel resonance branch road: H ₂=F ₂/ f _F=165/50=3.52.

(3) calculate L ₁, C ₁, L ₂, C ₂Parameter

Can extrapolate according to Fig. 1 (a) and electrotechnics principle:

$C_1=-\{{\left(\frac{H_2}{h_1{h}_2}\right)}^2-1+\frac{(h_1^2+h_2^2-H_2^2)H_2^2-h_1^2{h}_2^2}{h_1^2{h}_2^2(H_2^2-1)}\}\frac{Q}{{\mathrm{\ω}}_F{U}^2}---(\mathrm{eq}.1)$

$C_2=\frac{H_1^2}{h_1^2+h_2^2-H_1^2-H_2^2}\×C_1---(\mathrm{eq}.2)$

$L_1=\frac{1}{{\left(2\mathrm{\π}{H}_1{f}_F\right)}^2{C}_1}---(\mathrm{eq}.3)$

$L_2=\frac{1}{{\left(2\mathrm{\π}{H}_2{f}_F\right)}^2{C}_2}---(\mathrm{eq}.4)$

Calculate the first-harmonic angular frequency of system by given design condition _F=2 π f _F=314.16rad/s is with ω _FThe result of value and above-mentioned steps (1) and (2) gets among substitution following formula (eq.1), (eq.2), (eq.3), (eq.4) respectively: C ₁=5.8232 μ F, C ₂=15.5428 μ F, L ₁=1.8504mH, L ₂=52.5524mH.

(4) calculate C ₀And C ₁'

Calculating L by Fig. 1 (a) ₁, C ₁, L ₂, C ₂The basis on, refer again to Fig. 2, with capacitor C ₁Resolve into two equivalent capacity C ₀And C ₁' series connection, and with the resistance parallel connection node a with between the d.Make by L ₁, C ₁', L ₂And C ₂The circuit of being formed (referring to Fig. 2) produces series resonance under fundamental frequency, its total impedance must equal 0, promptly ${\mathrm{\ω}}_F{L}_1-\frac{1}{{\mathrm{\ω}}_F{C}_1^{\′}}+\frac{{\mathrm{\ω}}_F{L}_2}{1-{\mathrm{\ω}}_F^2{L}_2{C}_2}=0,$ The L that above-mentioned steps (3) is calculated ₁, C ₁, L ₂, C ₂The value substitution promptly gets C ₁'=17.13 μ F.

Because capacitor C ₀With C ₁' series connection, and be equivalent to C ₁, therefore $\frac{1}{C_1}=\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="C20051010155400201.png,C20051010155400211.png"\; state="\{\{state\}\}">C</figure-callout>}}_0}+\frac{1}{C_1^{\&prime;}},$ Substitution C ₁, C ₁' result of calculation solve C ₀=6.0281 μ F.

(5) R ₁Parameter determine

Select different damping resistance R ₁Parameter, connect according to Fig. 2, the impedance frequency characteristic curve (see figure 6) of filter is calculated and is drawn out in pointwise, then the resistance of coupling system harmonic impedance comparison filter frequently characteristic and damping revise, determine damping resistance R ₁Resistance value.This routine described correction, determine that principle is harmonic current multiplication factor≤3 of inflow system.In the present embodiment, damping resistance R ₁Resistance value finally be defined as 2000 Ω.

As seen from Figure 6, the impedance frequency characteristic curve has formed two impedance low spots near frequency is 150Hz and 1800Hz, and near the most of harmonic current this Frequency point will be bypassed by filter.

(6) calculate error between the given frequency filtering of actual frequency filtering and design condition

Find out the minimizing Frequency point of impedance from impedance frequency characteristic figure (Fig. 6), the frequency of this point is the actual frequency filtering f of filter ₁ ^t, f ₂ ^tCalculate actual frequency filtering f ₁ ^t, f ₂ ^tFrequency filtering f with designing requirement ₁And f ₂Between error: $\mathrm{\&Delta;}{f}_1=f_1-f_1^t,$ $\mathrm{\&Delta;}{f}_2=f_2-{f_2}^t.$ If | Δ f ₁|＜ε, and | Δ f ₂|＜ε, the frequency filtering that design is described is in the error allowed band, and filter can meet the demands.This example is set ε=2Hz by design specification.If | Δ f ₁|＞ε or | Δ f ₂|＞ε, illustrate that the frequency filtering of design exceeds the error allowed band, therefore need by revising original frequency value f ₁ ^t, f ₂ ^t, come back to step (1) then and calculate, until | Δ f ₁| and | Δ f ₂| all less than till the ε.

(7) performance of filter is checked

Impedance frequency characteristic curve chart (Fig. 6) according to filter, check every index of filter, especially after passing through filtering, the percent value of harmonic voltage and fundamental voltage will meet the regulation of standard GB/T14549-93 " quality of power supply electric power system harmonic wave ".

Calculate the fundamental wave reactive power compensation power Q=100.39Mvar of present embodiment, filter damping resistance R through checking ₁The fundamental power loss be 0.13104W.Because reactor, capacitor have internal resistance, so filter also has power loss in a small amount, but very little.

Fig. 2 circuit is to develop according to Fig. 1 (d), if according to the circuit shown in Fig. 1 (d) (this circuit is to use one of more double-tuned filter circuit in the prior art), calculating its first-harmonic loss under the condition of same circuit parameter is 48.7989kW.This shows that present embodiment compared with prior art can significantly reduce the fundamental energy loss.

Example 2

The three tuned filter design conditions that present embodiment is given are: fundamental frequency f _F=50Hz, rated voltage U=525kV, single group reactive compensation capacity Q=140Mvar, frequency filtering is f ₁=150Hz, f ₂=1200Hz, f ₃=1800Hz.

Referring to Fig. 3, present embodiment is a kind of three tuning passive harmonic filters, compares with example 1, just at L ₂, C ₂A L has connected under the parallel resonance branch road ₃, C ₃Therefore the parallel resonance branch road need utilize under the fundamental frequency and damping resistance R ₁Oscillating circuit total impedance in parallel $Z(\mathrm{\&omega;}={\mathrm{\&omega;}}_F)=\mathrm{j\&omega;}{L}_1-\frac{j}{\mathrm{\&omega;}{C}_1^{\&prime;}}+\frac{{\mathrm{j\&omega;L}}_2}{1-{\mathrm{\&omega;}}^2{L}_2{C}_2}+\frac{\mathrm{j\&omega;}{L}_3}{1-{\mathrm{\&omega;}}^2{L}_3{C}_3}=0$ Condition calculate C ₀And C ₁'.The basic process of calculation of parameter is: bypass damping resistance R earlier ₁, and suppose actual frequency filtering equal design condition given frequency filtering (promptly $f_1^t=f_1,$ $f_2^t=f_2,$ $f_3^t=f_3$ ), calculate each component parameters L with reference to the basic three tuned filter circuit of Fig. 1 (b) ₁, C ₁, L ₂, C ₂, L ₃, C ₃(concrete calculation of parameter derivation is seen: the inventor is in " south electric network technical research ", 2005 the 3rd phases, " calculation method of parameters of three tuned filters " literary composition of delivering on pp.43～46); Then with reference to Fig. 3, with C ₁Be split into C ₀, C ₁' after, select the damping resistance R of different resistances again for use ₁Connect, calculate and draw out the impedance frequency characteristic curve of filter under different resistances, and the resistance of the harmonic impedance comparison filter of coupling system frequently characteristic and damping revise, through relatively and optimize and determine damping resistance R ₁Resistance value, check and calculate the error between the given frequency filtering of actual frequency filtering and design condition at last, if this error exceeds the design specification allowed band, turn around again to revise, calculate, till the error of frequency filtering is in the design specification allowed band.

At first calculate L with reference to Fig. 1 (b) ₁, C ₁, L ₂, C ₂, L ₃, C ₃Parameter.

(1) first step will be selected L ₂, C ₂And L ₃, C ₃The resonance frequency of parallel resonance branch road

By the front selected principle of by the agency of: L ₂, C ₂Parallel branch resonance frequency F ₂At f ₁ ^tWith f ₂ ^tBetween, L ₃, C ₃Parallel branch resonance frequency F ₃At f ₂ ^tWith f ₃ ^tBetween, get F in this example ₂=164.7Hz, F ₂=1418.5Hz.

Then according to the actual frequency filtering f of the supposition of filter ₁ ^t, f ₂ ^t, f ₃ ^t, and F ₂And F ₃Value, calculate L ₁, C ₁The series resonance frequency of branch road $F_1=\frac{f_1^t{f}_2^t{f}_3^t}{F_2{F}_3}$

(2) then calculate the filter times of three frequency filterings of filter

$h_1=f_1^t/f_F,$ $h_2=f_2^t/f_F,$ $h_3=f_3^t/f_F$

And the harmonic number of the resonance frequency of each series and parallel resonance branch road

H ₁＝F ₁/f _F，H ₂＝F ₂/f _F，H ₃＝F ₃/f _F

(3) calculate L ₁, C ₁, L ₂, C ₂, L ₃, C ₃Parameter

In order to obtain L ₁, C ₁, L ₂, C ₂, L ₃, C ₃Each parameter at first with reference to Fig. 1 (b), and according to the electrotechnics principle, obtains each following component parameters computing formula:

$C_1=\frac{-Q}{{\mathrm{\&omega;}}_F{U}^2}[\frac{1}{H_1^2}-1+\frac{A_2}{H_1^2(H_2^2-1)}+\frac{A_3}{H_1^2(H_3^2-1)}]---(\mathrm{eq}.5)$

$C_2=\frac{H_1^2{C}_1}{A_2}---(\mathrm{eq}.6)$

$C_3=\frac{H_1^2{C}_1}{A_3}---(\mathrm{eq}.7)$

$L_1=\frac{1}{{\left(2\mathrm{\&pi;}{H}_1{f}_F\right)}^2{C}_1}---(\mathrm{eq}.8)$

$L_2=\frac{1}{{\left(2\mathrm{\&pi;}{H}_2{f}_F\right)}^2{C}_2}---(\mathrm{eq}.9)$

$L_3=\frac{1}{{\left(2\mathrm{\&pi;}{H}_3{f}_F\right)}^2{C}_3}---(\mathrm{eq}.10)$

In (eq.5), (eq.6), (eq.7),

$b_1=h_1^2+h_2^2+h_3^2-H_1^2-H_2^2-H_3^2---(\mathrm{eq}.11)$

$b_2=h_1^2{h}_2^2+h_2^2{h}_3^2+h_1^2{h}_3^2-H_1^2{H}_2^2-H_2^2{H}_3^2-H_1^2{H}_3^2---(\mathrm{eq}.12)$

$A_2=\frac{b_1{H}_2^2-b_2}{H_2^2-H_3^2}---(\mathrm{eq}.13)$

$A_3=\frac{b_2-b_1{H}_3^2}{H_2^2-H_3^2}---(\mathrm{eq}.14)$

Calculate the first-harmonic angular frequency of system by given design condition _F=2 π f _F=314.16rad/s is with ω _FThe result of value and above-mentioned steps (1) and (2) gets among substitution following formula (eq.1), (eq.2), (eq.3), (eq.4) respectively: C ₁=1.579 μ F, C ₂=7.3132 μ F, C ₃=9.3524 μ F, L ₁=8.3413mH, L ₂=127.6873mH, L ₃=1.346mH.

(4) calculate C ₀And C ₁'

Calculating L by Fig. 1 (b) ₁, C ₁, L ₂, C ₂, L ₃, C ₃The basis on, refer again to Fig. 3, with capacitor C ₁Resolve into two equivalent capacity C ₀And C ₁' series connection, and with the resistance parallel connection node a with between the d.Make L ₁, C ₁', L ₂, C ₂, L ₃, C ₃According to producing series resonance under Fig. 3 circuit mode under fundamental frequency, its total impedance must equal 0, promptly $\mathrm{j\&omega;}{L}_1-\frac{j}{\mathrm{\&omega;}{C}_1^{\&prime;}}+\frac{\mathrm{j\&omega;}{L}_2}{1-{\mathrm{\&omega;}}^2{L}_2{C}_2}+\frac{\mathrm{j\&omega;}{L}_3}{1-{\mathrm{\&omega;}}^2{L}_3{C}_3}=0,$ The L that above-mentioned steps (3) is calculated ₁, L ₂, C ₂, L ₃, C ₃The value substitution promptly gets C ₁'=67.539 μ F,

Because capacitor C ₀With C ₁' series connection, and be equivalent to C ₁, therefore $\frac{1}{C_1}=\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="C20051010155400201.png,C20051010155400211.png"\; state="\{\{state\}\}">C</figure-callout>}}_0}+\frac{1}{C_1^{\&prime;}},$ Substitution C ₁, C ₁' result of calculation solve C ₀=1.6168 μ F.

(5) R ₁Parameter determine

Select different damping resistance R ₁Parameter, connect according to Fig. 3, the impedance frequency characteristic curve (see figure 7) of filter is calculated and is drawn out in pointwise, then the resistance of coupling system harmonic impedance comparison filter frequently characteristic and damping revise, determine damping resistance R ₁Resistance value.Described correction, determine that principle is that the harmonic current multiplication factor of inflow system should≤3.In the present embodiment, damping resistance R ₁Resistance value finally be defined as 1900 Ω.

As seen from Figure 7, the impedance frequency characteristic curve is that 150Hz, 1200Hz and 1800Hz place have formed three impedance low spots in frequency, and near the most of harmonic current this Frequency point will be bypassed by filter.

(6) calculate error between the given frequency filtering of actual frequency filtering and design condition

Find out the minimizing Frequency point of impedance from impedance frequency characteristic figure (Fig. 7), the frequency of this point is the actual frequency filtering f of filter ₁ ^t, f ₂ ^t, f ₃ ^tCalculate actual frequency filtering f ₁ ^t, f ₂ ^t, f ₃ ^tFrequency filtering f with designing requirement ₁, f ₂, f ₃Between error: $\mathrm{\&Delta;}{f}_1=f_1-f_1^t,$ $\mathrm{\&Delta;}{f}_2=f_2-{f_2}^t,$ $\mathrm{\&Delta;}{f}_3=f_3-f_3^t.$ If | Δ f ₁|＜ε, | Δ f ₁|＜ε, and | Δ f ₃|＜ε, the frequency filtering that design is described is in the error allowed band, and filter can meet the demands.This example is set ε=2Hz by design specification.If | Δ f ₁|＞ε, or | Δ f ₂|＞ε, or | Δ f ₃|＞ε, illustrate that the frequency filtering of design exceeds the error allowed band, therefore need by revising original frequency value f ₁ ^t, f ₂ ^t, f ₃ ^t, come back to step (1) then and calculate, until | Δ f ₁|, | Δ f ₂| and | Δ f ₃| all less than till the ε.

(7) performance of filter is checked

Impedance frequency characteristic curve chart (Fig. 7) according to filter, check every index of filter, especially after passing through filtering, the percent value of harmonic voltage and fundamental voltage will meet the regulation of standard GB/T14549-93 " quality of power supply electric power system harmonic wave ".

Through check, the fundamental wave reactive power compensation power Q=140.0044Mvar of present embodiment, the fundamental power loss of filter damping resistance is 0kW.Because reactor, capacitor have internal resistance, so filter also has a spot of power loss, but very little, reached purpose of the present invention.

Fig. 3 circuit is to develop according to Fig. 1 (g), if according to the circuit of Fig. 1 (g), and adopts the identical circuit parameter of this example, and then the fundamental energy loss of filter is up to 83.43kW.Both compare, and technique effect of the present invention is very significant.

Example 3

The given design condition of present embodiment is identical with example 2.

Referring to Fig. 4, it is damping resistance R that present embodiment is compared different with example 2 (see figure 3)s ₁Be connected in parallel on C ₀With C ₁' series connection node a and L ₂, C ₂With L ₃, C ₃On the series connection node b between two parallel resonance branch roads, promptly be equivalent to the L that under the node d of Fig. 2, connected again ₃With C ₃Parallel branch is still with damping resistance R ₁The circuit of two ends parallel connection is but identical with example 1, therefore calculates C ₀And C ₁' condition identical with method with example 1.According to given design condition and electrotechnics principle, and the design and calculation method of reference example 1 and example 2 to obtain circuit parameter be C ₀=1.6164 μ F, C ₁'=68.005 μ F, C ₂=7.3132 μ F C ₃=9.3524 μ F, L ₁=8.3413mH, L ₂=127.6873mH, L ₃=1.346mH, R ₁=1900 Ω.Draw out the impedance frequency characteristic curve chart and see Fig. 8, it is that 150Hz, 1200Hz and 1800Hz place have formed three impedance low spots in frequency, and near the most of harmonic current this Frequency point will be bypassed by filter.

Check calculates the fundamental wave reactive power compensation power Q=139.997Mvar of present embodiment, and the fundamental power loss of filter resistor is 0kW.Although reactor, capacitor element have internal resistance, filter also has power loss in a small amount, and is very little, also reached purpose of the present invention.

Fig. 4 circuit is to develop according to Fig. 1 (f), if come designing filter according to the circuit shown in Fig. 1 (f), calculating its first-harmonic loss under the condition of same circuit parameter is 81.9427kW.This shows that present embodiment compared with prior art first-harmonic loss significantly reduces.

Example 4

The given design condition of present embodiment is identical with example 2.

Referring to Fig. 5, it is by L that present embodiment is compared different with example 3 (see figure 4)s ₃, C ₃Be parallel with another damping resistance R on the parallel resonance branch road ₂, its objective is the damping that increases filter.Calculate C in this example ₀And C ₁' condition identical with method with example 1, but at definite R ₁Resistance the time to consider R ₂Damping action, R ₁And R ₂Resistance revise, determine by the principle described in the example 1 (be system power multiplication factor should≤3).According to given design condition and electrotechnics principle, and the design and calculation method of reference example 1 and example 3 to obtain circuit parameter be C ₀=1.6164 μ F, C ₁'=68.005 μ F, C ₂=7.3132 μ F, C ₃=9.3524 μ F, L ₁=8.3413mH, L ₂=127.6873mH, L ₃=1.346mH, R ₁=1500 Ω, R ₂=400 Ω; Draw out the impedance frequency characteristic curve chart as shown in Figure 9.As seen from Figure 9, the impedance frequency characteristic curve is that 150Hz, 1200Hz and 1800Hz place have formed three impedance low spots in frequency, and near the harmonic current this Frequency point will be bypassed by filter.

Check calculates the fundamental wave reactive power compensation power Q=139.997Mvar of present embodiment.Although resistance R in this example ₁The fundamental power loss be 0 substantially, but because resistance R ₂Directly and L ₃C ₃Parallel connection, therefore R under fundamental frequency ₂The first-harmonic loss is arranged inevitably, but only be 8.5W.

Fig. 5 circuit is to develop according to Fig. 1 (h), if according to the circuit structure of Fig. 1 (h), under the condition of circuit parameter equally, calculating its first-harmonic loss is 81.95kW.This shows, in the described technical scheme of present embodiment, the first-harmonic loss of damping resistance only former scheme 1% less than.

Claims (2)

1, a kind of low-loss multiple-tuned electric power passive filter, comprise with passive electrical element and select the two port multi-tuned filter as the frequency of network components, this multi-tuned filter is in series by a LC series resonance branch road and 1～2 LC parallel resonance branch road and constitutes, and it is characterized in that the electric capacity (C in the described LC series resonant circuit ₁) by two electric capacity (C ₀And C ₁') the equivalent series composition; Two equivalent series electric capacity (C ₀And C ₁') series connection node (a) (d) or to being parallel with damping resistance (R on the two-port network between the series connection node (b) of the LC shunt-resonant circuit of mutual series connection over the ground ₁), with this damping resistance (R ₁) two-port network formation one loop in the fundamental frequency series resonance in parallel.

2, a kind of low-loss multiple-tuned electric power passive filter according to claim 1 is characterized in that as described two equivalent series electric capacity (C ₀And C ₁') series connection node (a) to being parallel with damping resistance (R on the two-port network between the series connection node (b) of the LC shunt-resonant circuit of mutual series connection ₁) time, the series connection node (b) of the two LC parallel resonance branch roads of connecting mutually is (d) another damping resistance (R in parallel over the ground ₂).

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