CN103166224B - Method for optimizing output inductance of three-phase four-wire system parallel active power filter - Google Patents

Abstract

Disclosed is a method for optimizing output inductance of a three-phase four-wire system parallel active power filter. Based on value optimization goals of the output inductance of the bridge arms of the three-phase four-wire system parallel active power filter, constraint conditions of output inductance values of bridge arms are obtained by calculation according to a unified mathematical model and the output capacity of the bridge arms; and a value optimization design method for the output inductance of the bridge arms is given based on the constraint conditions. The value optimization design method is applicable to the three-phase four-wire system parallel active power filter with various topological structures and switching control strategies, fewer data are needed and easily acquired, and an important reference and practical method is provided for improving the design level and the practical level of the three-phase four-wire system parallel active power filter.

Description

A kind of three-phase four-wire system Shunt outputting inductance optimization method

Technical field

The present invention relates to the three-phase four-wire system parallel connection type active electric filter technical field for three-phase four-wire system harmonic compensation, particularly a kind of three-phase four-wire system Shunt outputting inductance optimization method.

Background technology

The parallel connection type active electric filter (APF) that is applicable to three-phase four-wire system harmonic compensation mainly contains separation structure in four bridge arm structures and three brachium pontis electric capacity.The major parameter that affects three-phase four-wire system parallel connection type APF harmonic compensation performance comprises that AC output connects inductance, DC bus capacitor and DC voltage, and the value that wherein each brachium pontis output connects inductance is the most key on the impact of three-phase four-wire system parallel connection type APF harmonic compensation performance.

The main method of the three-phase four-wire system parallel connection type APF brachium pontis outputting inductance value proposing at present comprises Theoretical Design, according to experimental result, designs and rule of thumb formula design etc., and what also have carries out combination by said method.It is basis that theoretical design method be take the Mathematical Modeling set up conventionally, and comparison of computational results is accurate.But current method for designing is carried out for a certain specific topological structure conventionally, during topologies change, need to redesign, and do not consider the impact of different switch-control strategies, versatility is poor.The data volume needing during design is larger, and some data are difficult to directly obtain, and have limited the practicality of the method; According to experimental result design, can overcome the inaccurate problem of design result that in actual motion, various uncertain factors cause, the data volume needing is few, but this method need to be carried out many experiments, design process is complicated, workload is larger, and design result is often only applicable to specific loading condition.When design is output as the outputting inductance of sinusoidal inverter, conventionally adopt following empirical method: the perunit value of selecting outputting inductance is 10%～20% of inverter capacity.Some research directly applies to this empirical method the design of three-phase four-wire system parallel connection type APF brachium pontis outputting inductance, but often comprises a large amount of harmonic components in APF brachium pontis output current, directly applies the method and will occur larger error.

If therefore can be on the basis of the unified Mathematical Modeling of three-phase four-wire system parallel connection type APF and each brachium pontis fan-out capability index, proposition has the optimization value method for designing of the brachium pontis outputting inductance of versatility, to be applicable to the three-phase four-wire system parallel connection type APF of different topology structure and different switch-control strategies, desired data is few and easily obtain, and can provide reliable foundation and method for improve compensation performance and the degree of being practical of three-phase four-wire system parallel connection type APF from parameter designing angle.

Summary of the invention

The object of the present invention is to provide a kind of optimization value method for designing of three-phase four-wire system Shunt outputting inductance.The method makes to be applicable to the three-phase four-wire system parallel connection type APF of different topology structure and different switch-control strategies, and desired data is few and easily obtain, and for improve the compensation performance of three-phase four-wire system parallel connection type APF from parameter designing angle, provides foundation.

Technical scheme of the present invention is a kind of three-phase four-wire system Shunt outputting inductance optimization method, described three-phase four-wire system Shunt DC side consists of the DC capacitor of 4 series connection, A, B, C brachium pontis forms phase three-wire three full-bridge inverter; N brachium pontis is single-phase semi-bridge structure, the tie point of access DC bus capacitor; A, B, it is L that the output of C brachium pontis connects inductance value _s, it is L that the output of N brachium pontis connects inductance value _n, carry out outputting inductance optimization and comprise the following steps,

Step 1, in the situation that ignoring system zero sequence voltage and affecting, by A, B, the voltage u of C brachium pontis mid point to system mid point n _an, u _bn, u _cnthe maximum of absolute value separately | u _an| _max, | u _bn| _max, | u _cn| _maxbe defined as the A of three-phase four-wire system parallel connection type APF, B, the fan-out capability of C brachium pontis, by A, B, C brachium pontis mid point is to N brachium pontis mid-point voltage u _aN, u _bN, u _cNthe maximum of zero-sequence component absolute value | u _f0| _maxbe defined as the fan-out capability of N brachium pontis;

Step 2, obtains respectively A, B, C, the upper limit constraints 1 of the outputting inductance value of N brachium pontis, upper limit constraints 2, A while adopting the fixing control method of switching frequency, B, C, the lower limit constraints 1 of the outputting inductance value of N brachium pontis, lower limit constraints 2, and A while adopting the unfixed control method of switching frequency, B, C, the lower limit constraints 1' of the outputting inductance value of N brachium pontis, lower limit constraints 2';

The obtain manner of described upper limit constraints 1 is, requires A, B, and the fan-out capability of C brachium pontis meets following formula,

$\frac{(k+2)-k(1-m)/2}{k+3}E\≥u_{\mathrm{jn}}+L_S\frac{{\mathrm{di}}_{\mathrm{Fj}}}{\mathrm{dt}},j=A,B,C$

Wherein, k is A, B, and the ratio of the reactance of C brachium pontis and N brachium pontis inductance value, m is the relevant coefficient of the topological structure of three-phase four-wire system Shunt, E is DC voltage; u _jnfor AC system side phase voltage, i _fjfor A, B, C brachium pontis output current; The maximum of formula one right-hand member, calculates according to the main Types of three-phase four-wire system Shunt institute compensation harmonic load;

The obtain manner of described upper limit constraints 2 is to require the fan-out capability of N brachium pontis | u _f0| _maxmeet following formula,

$\frac{3}{2}(m+1)E\≥L_S(1+3/k)\frac{{\mathrm{di}}_{\mathrm{Fn}}}{\mathrm{dt}}$

Wherein, i _fnfor N brachium pontis output current;

Described lower limit constraints 1 is as follows,

${\mathrm{\α}}_{\mathrm{abc}}\×\frac{\left[\frac{(k+2)-k(1-m)/2}{k+3}\right]E}{I_1\×2\mathrm{\π}\×f_{\mathrm{sw}}\×{\mathrm{\λ}}_{\mathrm{abc}}}\≤L_S$

Wherein, α _abcfor the coefficient relevant with modulation ratio and carrier wave ratio, I ₁for the specified first-harmonic effective value of load current, f _swfor switching frequency, λ _abcfor preset ratio;

Described lower limit constraints 2 is as follows,

$\frac{{\mathrm{\α}}_n\×\left[\frac{3[1+m]}{2}\right]E}{I_N\×2\mathrm{\π}\×f_{\mathrm{sw}}\×{\mathrm{\λ}}_n}\≤L_S(3+1/k)$

Wherein, α _nfor the coefficient relevant with modulation ratio and carrier wave ratio, I _nfor system center line allows the electric current passing through, λ _nfor preset ratio;

Described lower limit constraints 1' is as follows,

$\frac{[k+2-k(1-m)/2]E}{(k+3)\×{\mathrm{\λ}}_{\mathrm{abc}}\×I_1}\×\frac{T_{\mathrm{sw}}}{2\sqrt{3}}\≤L_S$

Wherein, T _swthe sampling period adopting for control method;

Described lower limit constraints 2' is as follows,

$\frac{3(1+m)E}{2\×{\mathrm{\λ}}_n\×I_N}\×\frac{T_{\mathrm{sw}}}{2\sqrt{3}}\≤L_S(1+3/k)$

Step 3, according to the harmonic content analysis result of the topological structure of three-phase four-wire system Shunt, load current, when three-phase four-wire system Shunt adopts the fixing control method of switching frequency, utilize step 2 gained upper limit constraints 1, upper limit constraints 2, lower limit constraints 1 and lower limit constraints 2, determine the span of each brachium pontis outputting inductance; When three-phase four-wire system Shunt adopts the unfixed control method of switching frequency, utilize step 2 gained upper limit constraints 1, upper limit constraints 2, lower limit constraints 1' and lower limit constraints 2', determine the span of each brachium pontis outputting inductance.

And, while carrying out the obtaining of upper limit constraints 1, according to the main Types of three-phase four-wire system Shunt institute compensation harmonic load, calculate maximum implementation as follows,

(1) situation that load is mainly rectifier bridge shunt capacitance is calculated as follows,

${(u_{\mathrm{jn}}+L_S\frac{{\mathrm{di}}_{\mathrm{Fj}}}{\mathrm{dt}})}_{\max }=\sqrt{2}\×V_S+L_S\×2\sqrt{2}\mathrm{\π}{f}_1\×h\×I_{\mathrm{abc}\left(h\right)}$

Wherein, h is A, and B needs to have in offset current the number of times of the harmonic wave of maximum rate of change, I in C brachium pontis _{abc (h)}for the effective value of corresponding h primary current, f ₁for fundamental frequency, V _sfor AC system side phase voltage u _an, u _bn, u _cneffective value;

(2) situation that load is mainly rectifier bridge series inductance is calculated as follows,

${(u_{\mathrm{jn}}+L_S\frac{{\mathrm{di}}_{\mathrm{Fj}}}{\mathrm{dt}})}_{\max }=L_S\underset{h=1}{\overset{h=H}{\mathrm{\Σ}}}(2\sqrt{2}\mathrm{\π}{f}_1\×h\×I_{\mathrm{abc}\left(h\right)})$

Wherein, H needs the high reps of compensation harmonic for design.

And, while carrying out the obtaining of upper limit constraints 2, calculate as follows maximum current slew rate,

${\left(\frac{{\mathrm{di}}_{\mathrm{Fn}}}{\mathrm{dt}}\right)}_{\max }=\underset{h=1}{\overset{h=H}{\mathrm{\Σ}}}(2\sqrt{2}\mathrm{\π}{f}_1\×h\×I_{n\left(h\right)})$

Wherein, I _{n (h)}the effective value of the h subharmonic current that need compensate for N brachium pontis.

And, according to A, B, the ratio k of the reactance of C brachium pontis and N brachium pontis inductance value, is 3 regions by the span Further Division of each brachium pontis outputting inductance of step 3 gained, further optimizes respectively the value that output connects inductance in corresponding region.

And 3 regions of division are k<1, k>10,1≤k≤10.

Can see, the Optimization Design of the three-phase four-wire system Shunt outputting inductance value proposing can be applicable to different topological structures and switch-control strategy, needed data are few and easily obtain, span computational methods are simple, for improve the compensation performance of three-phase four-wire system parallel connection type APF from parameter designing angle, provide foundation.

Accompanying drawing explanation

Fig. 1 is the systematic schematic diagram that in prior art, three-phase four-wire system parallel connection type APF carries out harmonic compensation.

Fig. 2 is the unified topological structure schematic diagram of three-phase four-wire system parallel connection type APF in prior art.

Fig. 3 is that the reference current of the embodiment of the present invention is the schematic diagram of 0 o'clock N brachium pontis output current wave.

Fig. 4 is the Simulation Calculation schematic diagram of the embodiment of the present invention.

Fig. 5 is that the outputting inductance that is subject to upper limit constraints limit of the embodiment of the present invention can value areal map, and outputting inductance when wherein Fig. 5 (a) is m=1 can value areal map, and outputting inductance when Fig. 5 (b) is m=0 can value areal map.

Fig. 6 is that the outputting inductance that is subject to lower limit constraints limit of the embodiment of the present invention can value areal map, and outputting inductance when wherein Fig. 6 (a) is m=1 can value areal map, and outputting inductance when Fig. 6 (b) is m=0 can value areal map.

Fig. 7 is that the outputting inductance that is subject to bound constraints limit of the embodiment of the present invention can value areal map, and outputting inductance when wherein Fig. 7 (a) is m=1 can value areal map, and outputting inductance when Fig. 7 (b) is m=0 can value areal map.

Fig. 8 is the simulation result oscillogram of the embodiment of the present invention, wherein Fig. 8 (a) is AC system phase current THD oscillogram, Fig. 8 (b) is AC system current in middle wire effective value oscillogram, each brachium pontis output current ripple shape figure when Fig. 8 (c) is unloaded.

Embodiment

Below in conjunction with drawings and Examples, describe technical solution of the present invention in detail.

Accompanying drawing 1 is the systematic schematic diagram that three-phase four-wire system parallel connection type APF carries out harmonic compensation.The principle and the method that due to the harmonic current that adopts parallel connection type APF to produce nonlinear-load, compensate have been ripe technology, below only briefly introduce harmonic compensation principle.When three phase and four wire circuit system is powered to nonlinear load, the current i on four supply lines of load _la, i _lb, i _lc, i _lnmiddlely will comprise a large amount of harmonic currents, if do not take control measures, these harmonic currents are by the current i appearing on four supply lines of AC system side _sa, i _sb, i _sc, i _snin, thereby the operation of AC system, equipment etc. are impacted.By node a, b, c, n, adding after three-phase four-wire system parallel connection type APF the current i that it is sent by controlling APF _fa, i _fb, i _fcin harmonic content and i _la, i _lb, i _lcin identical, and the current i that it is sent _fnwith i _lnidentical, AC system side phase current i so _sa, i _sb, i _scto be first-harmonic sinusoidal quantity, while current in middle wire i _snbe 0, realized the object of harmonic compensation.

Accompanying drawing 2 is the unified topological structure of three-phase four-wire system parallel connection type APF, is characterized in: DC side consists of the DC capacitor of 4 series connection, and each capacitance is followed successively by C from top to bottom _a, C _b, C _b, C _a, total DC voltage is V _o+O-=E.A, B, C brachium pontis forms phase three-wire three full-bridge inverter, and N brachium pontis is single-phase semi-bridge structure, and the tie point of access DC bus capacitor, as the J in accompanying drawing 2 and K point.A, B, it is L that the output of C brachium pontis connects inductance value _s, it is L that the output of N brachium pontis connects inductance value _n.

Definition:

$\frac{C_a}{C_a+C_b}=m,0\&le;m\&le;1---\left(1\right)$

Coefficient m that can be relevant with topological structure by definition.By document [1] " happy strong; Jiang Qirong; Han Ying's tongued bell (LE Jian; JIANG Qi-rong; HAN Ying-duo). the performance evaluation of the three-phase and four-line Shunt based on uniform mathematical model (Performance Analysis of Three-phase Four-wire Shunt APF Based on the Unified Mathematic Model). Proceedings of the CSEE (Proceedings of the CSEE); 2007,27 (7): 108-114. " analysis in is known, works as C _a/ C _b=∞, during m=1, topological structure now develops into common four bridge arm topologicals; Work as C _b/ C _a=∞, during m=0, topological structure now develops into the output of N brachium pontis with in three brachium pontis electric capacity of reactance minutes topologys.

Definition:

k＝L _S/L _N (2)

K is A, B, the ratio of C brachium pontis inductance value and N brachium pontis inductance value.

Document [1] utilizes DC voltage E, A, B, C brachium pontis inductance and the ratio k of N brachium pontis inductance value and with topological structure relevant Coefficient m, calculated A in the situation that ignoring system zero sequence voltage and affecting, B, the voltage u of C brachium pontis mid point to system mid point n _an, u _bn, u _cn, and by its maximum of absolute value separately | u _an| _max, | u _bn| _max, | u _cn| _maxbe defined as the A of three-phase four-wire system parallel connection type APF, B, the fan-out capability of C brachium pontis, shown in (3), to weigh A, B, the harmonic compensation performance of C brachium pontis.

${\left|u_{\mathrm{jn}}\right|}_{\max }=\frac{(k+2)-k(1-m)/2}{k+3}\&times;E,j=A,B,C---\left(3\right)$

U _jnindicate the voltage of j brachium pontis mid point to system mid point n.

Document [1] has calculated A in the situation that ignoring system zero sequence voltage and affecting, B, and C brachium pontis mid point is to N brachium pontis mid-point voltage u _aN, u _bN, u _cNzero-sequence component u _f0, by the maximum of its absolute value | u _f0| _maxbe defined as the fan-out capability of the N brachium pontis of three-phase four-wire system parallel connection type APF, shown in (4), to weigh the harmonic compensation performance of N brachium pontis

${\left|u_{F0}\right|}_{\max }=\frac{1}{2}(m+1)\&times;E---\left(4\right)$

Wherein, E is DC voltage.

The present invention utilizes A defined above, B, and C, N brachium pontis fan-out capability is carried out the optimal design that each brachium pontis output of three-phase four-wire system parallel connection type APF connects reactance value.

The optimal design target that the embodiment of the present invention is set each brachium pontis output connection reactance value of three-phase four-wire system parallel connection type APF is: (a) make parallel connection type APF have good harmonic wave and AC system current in middle wire compensation ability, have good response speed.(b) make the higher harmonic content in parallel connection type APF brachium pontis output current be less than set point, there is good control precision.

The present invention is according to AC system phase voltage u _an, u _bn, u _cnand A, B, the output current i of C brachium pontis _fa, i _fb, i _fccalculate A, B, the fan-out capability of C brachium pontis | u _an| _max, | u _bn| _max, | u _cn| _maxmust satisfied constraints.In the situation that load mostly is rectifier bridge shunt capacitance, can compensate to calculate this constraints to thering is the harmonic wave of maximum current slew rate when AC system phase voltage has maximum; In the situation that load mostly is rectifier bridge series inductance, with need compensation individual harmonic current, there is maximum rate of change simultaneously and calculate this constraints, thereby can obtain A, B, C, the upper limit constraints 1 of the outputting inductance value of N brachium pontis.In the situation that ignoring system zero sequence voltage and affecting, according to the output current i of N brachium pontis _fncalculate the fan-out capability of N brachium pontis | u _f0| _maxmust satisfied constraints.Due to N brachium pontis output current i _fnrate of change and AC system independent from voltage, with need compensation individual harmonic current, there is maximum rate of change simultaneously and calculate this constraints, thereby can obtain A, B, C, the upper limit constraints 2 of the outputting inductance value of N brachium pontis.

For the sake of ease of implementation, provide embodiment to ask for upper limit constraints specific implementation as follows:

Consider above-mentioned optimal design target (a), according to AC system A, B, the phase voltage u of C phase _jnand A, B, the output current i of C brachium pontis _fj, convolution (3), requires A, B, and the fan-out capability of C brachium pontis meets:

$\frac{(k+2)-k(1-m)/2}{k+3}E\&GreaterEqual;u_{\mathrm{jn}}+L_S\frac{{\mathrm{di}}_{\mathrm{Fj}}}{\mathrm{dt}},j=A,B,C---\left(5\right)$

Wherein: u _jnfor AC system side phase voltage; i _fjfor A, B, C brachium pontis output current, it is distinguished as shown in Figure 1 with reference to positive direction, represent current i _fjdifferential.

Formula (5) right-hand member is according to the actual value that on system voltage and inductance, voltage calculates, and left end is the maximum that brachium pontis can be exported.When the output of design brachium pontis connects inductance value, need to know the maximum of formula (5) right-hand member, can calculate according to the main Types of three-phase four-wire system parallel connection type APF institute compensation harmonic load, that is:

(1) load mostly is the situation of rectifier bridge shunt capacitance.Now maximum current slew rate usually occurs near the maximum of AC system side voltage.Therefore the peaked computational methods of formula (5) right-hand member are: when AC system side phase voltage VS has maximum, can compensate having the harmonic wave of maximum current slew rate:

${(u_{\mathrm{jn}}+L_S\frac{{\mathrm{di}}_{\mathrm{Fj}}}{\mathrm{dt}})}_{\max }=\sqrt{2}\&times;V_S+L_S\&times;2\sqrt{2}\mathrm{\&pi;}{f}_1\&times;h\&times;I_{\mathrm{abc}\left(h\right)}---\left(6\right)$

Wherein: h is A, B, needs to have in offset current the number of times of the harmonic wave of maximum rate of change in C brachium pontis; I _{abc (h)}effective value for corresponding h primary current; f ₁for fundamental frequency; V _sfor AC system side phase voltage u _an, u _bn, u _cneffective value.

(2) load mostly is the occasion of rectifier bridge series inductance.Now each primary current rate of change is all larger, and needs the maximum rate of change of offset current to usually occur in AC system side phase voltage hour.Therefore the peaked computational methods of formula (5) right-hand member are: ignore AC system side voltage, and think that individual harmonic current has maximum rate of change simultaneously, that is:

${(u_{\mathrm{jn}}+L_S\frac{{\mathrm{di}}_{\mathrm{Fj}}}{\mathrm{dt}})}_{\max }=L_S\underset{h=1}{\overset{h=H}{\mathrm{\&Sigma;}}}(2\sqrt{2}\mathrm{\&pi;}{f}_1\&times;h\&times;I_{\mathrm{abc}\left(h\right)})---\left(7\right)$

Wherein: H needs the high reps of compensation harmonic for design;

According to the type of actual compensating load, can be by formula (6) or (7) substitution to formula (5), thus obtain A, B, C, the upper limit constraints 1 of the outputting inductance value of N brachium pontis.

Consider above-mentioned optimal design target (a), when ignoring output and connect affecting of inductance AC system side phase voltage zero-sequence component, according to N brachium pontis, output connects the current i that inductance flows through _fn, convolution (4), requires the fan-out capability of N brachium pontis | u _f0| _maxmeet:

$\frac{3}{2}(m+1)E\&GreaterEqual;L_S(1+3/k)\frac{{\mathrm{di}}_{\mathrm{Fn}}}{\mathrm{dt}}---\left(8\right)$

Wherein: i _fnfor N brachium pontis output current, it with reference to positive direction as shown in Figure 1.

Due to N brachium pontis output current rate of change and AC system side independent from voltage, can carry out according to the form of similar formula (7) maximum current slew rate of calculating formula (8) right-hand member:

${\left(\frac{{\mathrm{di}}_{\mathrm{Fn}}}{\mathrm{dt}}\right)}_{\max }=\underset{h=1}{\overset{h=H}{\mathrm{\&Sigma;}}}(2\sqrt{2}{f}_1\&times;h\&times;I_{n\left(h\right)})---\left(9\right)$

Wherein: I _{n (h)}the effective value of the h subharmonic current that need compensate for N brachium pontis.

By formula (9) substitution formula (8), thereby obtain A, B, C, the upper limit constraints 2 of the outputting inductance value of N brachium pontis.

Consider above-mentioned optimal design target (b), for example, while adopting the fixing control method (pulse width modulation) of switching frequency, the frequency of the high order harmonic component of each brachium pontis output current content maximum equals switching frequency, and the content of this subharmonic of conventionally usining does not exceed a threshold value as constraints.And for example, for the unfixed control method of switching frequency (current hysteresis comparison control), the number of times of the high order harmonic component in each brachium pontis output current is unfixing, the current ripples of now conventionally usining does not exceed a threshold value as constraints.To adopting the fixing control method of switching frequency as pulse width modulation (PWM), require A, B, C brachium pontis output current i _fa, i _fb, i _fcin high order harmonic component be not more than load first-harmonic rated current I ₁a ratio lambda _abc, the factor alpha that utilization is relevant with modulation ratio and carrier wave ratio _abc, load rating current first harmonics effective value I ₁, APF control method switching frequency f _sw, DC voltage E, A, B, the reactance of C brachium pontis and the ratio k of N brachium pontis reactance value and with topological structure relevant Coefficient m, solve A while obtaining adopting the fixing control method of switching frequency, B, C, the lower limit constraints 1 of the outputting inductance value of N brachium pontis.To N brachium pontis, require brachium pontis output current i _fnin high order harmonic component be not more than AC system center line and allow by a ratio lambda of electric current _n, the factor alpha that utilization is relevant with modulation ratio and carrier wave ratio _n, system center line allows the electric current I of passing through _n, N brachium pontis mid point is to having the effective value V of the harmonic component of switching frequency in system mid-point voltage _{fn (fsw)}, APF control method switching frequency f _sw, DC voltage E, A, B, the reactance of C brachium pontis and the ratio k of N brachium pontis reactance value and with topological structure relevant Coefficient m, solve A while obtaining adopting the fixing control method of switching frequency, B, C, the lower limit constraints 2 of the outputting inductance value of N brachium pontis.To adopting the unfixed control method of switching frequency to control as stagnant ring, first utilize A, B, C, N brachium pontis output current i _fa, i _fb, i _fc, i _fnwith reference value i separately _{fa (ref)}, i _{fb (ref)}, i _{fc (ref)}, i _{fc (ref)}calculate a stagnant ring control cycle T _swinterior A, B, C, the ripple Δ I of N brachium pontis output current _fa, Δ I _fb, Δ I _fc, Δ I _fn.Require A, B, C brachium pontis output current i _fa, i _fb, i _fcripple Δ I _fa, Δ I _fb, Δ I _fcbe not more than respectively load first-harmonic rated current I ₁a ratio lambda _abc, A while obtaining adopting the unfixed control method of switching frequency, B, C, the constraints of the outputting inductance value of N brachium pontis, proportion of utilization coefficient lambda _abc, load first-harmonic rated current I ₁, DC voltage E, A, B, the reactance of C brachium pontis and the ratio k of N brachium pontis reactance value and relevant Coefficient m solves A while obtaining adopting the unfixed control method of switching frequency, B, C, the constraints 1' of the outputting inductance value of N brachium pontis with topological structure; Require N brachium pontis output current i _fnripple Δ I _fnbe not more than AC system center line and allow to pass through electric current I _na ratio lambda _n, A while obtaining adopting the unfixed control method of switching frequency, B, C, the constraints of the outputting inductance value of N brachium pontis, proportion of utilization coefficient lambda _n, system center line allows the electric current I of passing through _n, DC voltage E, A, B, C brachium pontis inductance and the ratio k of N brachium pontis inductance value and relevant Coefficient m solves A while obtaining adopting the unfixed control method of switching frequency, B, C, the constraints 2' of the outputting inductance value of N brachium pontis with topological structure.

For the sake of ease of implementation, provide embodiment to ask for lower limit constraints specific implementation as follows:

(1) while adopting the fixing control method of switching frequency.Require A, B, the high order harmonic component I in C brachium pontis output current _{fj (fsw)}be no more than load first-harmonic rated current I ₁a ratio lambda _abc(while specifically implementing, can be preset as required by user, generally get 2%～5%):

$\frac{I_{\mathrm{Fj}\left(\mathrm{fsw}\right)}}{I_1}=\frac{V_{\mathrm{Fj}\left(\mathrm{fsw}\right)}}{I_1\&times;2\mathrm{\&pi;}\&times;f_{\mathrm{sw}}\&times;L_S}\&le;{\mathrm{\&lambda;}}_{\mathrm{abc}},j=A,B,C---\left(10\right)$

Wherein: I ₁for the specified first-harmonic effective value of load current; f _swfor switching frequency; V _{fj (fsw)}for A, B, C brachium pontis is to having switching frequency f in system mid-point voltage _swthe effective value of harmonic component; I _{fj (fsw)}for thering is the effective value of the harmonic component of switching frequency in j brachium pontis output current.Convolution (3) can obtain:

${\mathrm{\&alpha;}}_{\mathrm{abc}}\&times;\frac{\left[\frac{(k+2)-k(1-m)/2}{k+3}\right]E}{I_1\&times;2\mathrm{\&pi;}\&times;f_{\mathrm{sw}}\&times;{\mathrm{\&lambda;}}_{\mathrm{abc}}}\&le;L_S---\left(11\right)$

To N brachium pontis, require the high order harmonic component V in output current _{fn (fsw)}be not more than AC system center line and allow to pass through electric current I _na ratio lambda _n(while specifically implementing, can be preset as required by user, generally get 5%～8%):

$\frac{V_{\mathrm{Fn}\left(\mathrm{fsw}\right)}}{I_N\&times;2\mathrm{\&pi;}\&times;f_{\mathrm{sw}}\&times;L_S(3+1/k)}\&le;{\mathrm{\&lambda;}}_n---\left(12\right)$

Wherein: I _nfor AC system center line allows the electric current passing through.V _{fn (fsw)}for N brachium pontis mid point is to having the effective value of the harmonic component of switching frequency in AC system mid-point voltage.Convolution (4) abbreviation can obtain:

$\frac{{\mathrm{\&alpha;}}_n\&times;\left[\frac{3(1+m)}{2}\right]E}{I_N\&times;2\mathrm{\&pi;}\&times;f_{\mathrm{sw}}\&times;{\mathrm{\&lambda;}}_n}\&le;L_S(3+1/k)---\left(13\right)$

α in formula (11) _abcand α in formula (13) _nfor the coefficient relevant with modulation ratio and carrier wave ratio, can obtain by current mature harmonic analysis method.Formula (11) and formula (13) are the lower limit constraints 1 and 2 of three-phase four-wire system parallel connection type APF outputting inductance value while adopting the fixing control method of switching frequency.

(2), while adopting the unfixed control method of switching frequency, require the current ripples Δ I of each brachium pontis output current _fjdo not exceed a threshold value.The ripple of output current is defined as:

${\mathrm{\&Delta;I}}_{\mathrm{Fj}}=\sqrt{\frac{1}{T_{\mathrm{sw}}}{{\&Integral;}_0^{T_{\mathrm{sw}}}(i_{\mathrm{Fj}\left(\mathrm{ref}\right)}-i_{\mathrm{Fj}})}^2\mathrm{dt}},j=a,b,c,n---\left(14\right)$

Wherein: i _{fj (ref)}for j brachium pontis output current i _fjreference value, be A, B, C, N brachium pontis output current i _fa, i _fb, i _fc, i _fnreference value i _{fa (ref)}, i _{fb (ref)}, i _{fc (ref)}, i _{fc (ref)}, can be according to mature harmonic wave extraction algorithm by load current i _la, i _lb, i _lc, i _lnobtain.T _swthe sampling period adopting for control method.

Require A, B, the ripple Δ I of C brachium pontis output current _fj(j=a, b, c, n) is no more than load first-harmonic rated current I ₁a ratio lambda _abc(while specifically implementing, can be preset as required by user, generally get 2%～5%):

ΔI _Fj≤λ _abc×I ₁，j＝a,b,c,n (15)

Wherein: λ _abcfor proportionality coefficient; I ₁for the specified first-harmonic effective value of load current.

Each brachium pontis output current reference value is that the ripple of 0 o'clock output current is maximum.When output current reference value is 0, A, B, C brachium pontis output current rate of change is subject to the impact of AC system side voltage, and in two adjacent switch periods, the rising of electric current is different with the speed of decline, but in the sufficiently high situation of switching frequency, can think that the AC system magnitude of voltage in adjacent two switch periods remains unchanged, at the action effect in two adjacent switch cycles, can offset, therefore can derive A, B, C brachium pontis output current ripple is restricted to:

$\frac{[k+2-k(1-m)/2]E}{(k+3)\&times;{\mathrm{\&lambda;}}_{\mathrm{abc}}\&times;I_1}\&times;\frac{T_{\mathrm{sw}}}{2\sqrt{3}}\&le;L_S---\left(16\right)$

Wherein: T _swthe sampling period adopting for control method;

To N brachium pontis, require the ripple Δ I of output current _fnbe not more than AC system center line and allow to pass through electric current I _na ratio lambda _n(while specifically implementing, can be preset as required by user, generally get 5%～10%):

ΔI _Fn≤λ _n×I _N， (17)

Wherein: λ _nfor proportionality coefficient; I _nfor system center line allows the electric current passing through.

Output current reference value be 0 o'clock N brachium pontis output current waveform as shown in Figure 3, wherein abscissa is time t, ordinate is current i, Δ i is a sampling period T _swinterior current change quantity.Can think, at each sampling instant N brachium pontis, a switch motion occur, voltage u in each switch periods _nnbe maximum, with reference to the accompanying drawings 3 and formula (14) can obtain:

${\mathrm{\&Delta;I}}_{\mathrm{Fn}}=\sqrt{f_{\mathrm{sw}}{\&Integral;}_0^{T_{\mathrm{SW}}}{[(t-\frac{1}{2}{T}_{\mathrm{sw}})\&times;\frac{3(1+m)E}{2\&times;L_s(1+3/k)}]}^2\mathrm{dt}}---\left(18\right)$

Wherein: T _sw, f _swthe sampling period and the frequency that adopt for control method;

Simplify above formula, and can obtain according to formula (17):

${\mathrm{\&Delta;I}}_{\mathrm{Fn}}=\frac{3(1+m)F}{2\&times;L_S(1+3/k)}\&times;\frac{T_{\mathrm{sw}}}{2\sqrt{3}}\&le;{\mathrm{\&lambda;}}_n\&times;I_N---\left(19\right)$

Further abbreviation can obtain:

$\frac{3(1+m)E}{2\&times;{\mathrm{\&lambda;}}_n\&times;I_N}\&times;\frac{T_{\mathrm{sw}}}{2\sqrt{3}}\&le;L_S(1+3/k)---\left(20\right)$

Formula (16) and formula (20) are lower limit constraints 1' and the 2' of three-phase four-wire system parallel connection type APF outputting inductance value while adopting the unfixed control method of switching frequency.

According to the harmonic content analysis result of the topological structure of three-phase four-wire system parallel connection type APF, load current, when three-phase four-wire system parallel connection type APF adopts the fixing control method of switching frequency, utilize upper limit constraints 1, upper limit constraints 2, lower limit constraints 1 and the lower limit constraints 2 of resulting brachium pontis outputting inductance value; When three-phase four-wire system parallel connection type APF adopts the unfixed control method of switching frequency, utilize upper limit constraints 1, upper limit constraints 2, lower limit constraints 1' and the lower limit constraints 2' of resulting brachium pontis outputting inductance value, can determine rapidly and accurately that each brachium pontis output connects the span of inductance.In conjunction with concrete condition and economy, considering, can span be 3 regions according to k value Further Division, further optimize respectively the value that output connects inductance in corresponding region.For ease of implementing reference, below further provide the optimization principles of embodiment as follows:

Conventionally the span that is optimized does not comprise the region of k<1.Even if comprise this region, because each restrained boundary curve in this region has larger rate of change, so the slight variation of outputting inductance value all may make constraints be not being met.Therefore generally do not consider the value in k<1 region.

If have, meet the value in k>10 region, when k value is larger, center line outputting inductance will be less, consider manufacturing cost and design factor easily, and k can be taken as to infinity, center line inductance can value be 0.Therefore can be in this region during value, should pay the utmost attention to the value of k=∞.

If only have the value that meets region, 1≤k≤10, can carry out choosing of inductance value according to actual conditions, should make data point be positioned at as far as possible and optimize value regional center position.

Below in conjunction with simulation calculation, be specifically described.

Accompanying drawing 4 is Simulation Calculation.Each branch current direction respectively as shown in FIG..The sample frequency of three-phase four-wire system parallel connection type APF is 10kHz, and 0.1s drops into constantly, adopts Hysteresis Current Control Strategy.APF DC voltage E=600V.When m=0, V _dc1=E/2, V _dc2=0V; When m=1, V _dc2=E/2, V _dc1=0V, V _dc1and V _dc2be respectively three-phase four-wire system parallel connection type APF DC bus capacitor C in accompanying drawing 4 _aand C _bon voltage.

AC system side phase voltage effective value V _s=220V; A phase load is the capacitance-resistance rectifier bridge of output-parallel, and A phase load parameter is: A commutating phase bridge inductance L _la=4mH, A commutating phase bridge shunt load resistance R _la=7 Ω, A commutating phase bridge shunt load capacitor C _la=2200 μ F; B phase load is the capacitance-resistance rectifier bridge of output-parallel, and B phase load parameter is: B commutating phase bridge inductance L _lb=4mH, B commutating phase bridge shunt load resistance R _lb=7 Ω, B commutating phase bridge shunt load capacitor C _lb=2200 μ F; What C phase load was resistance with output-parallel capacitance resistance rectifier bridge is in parallel, and C phase load parameter is: shunt load resistance R _c=5 Ω, C commutating phase bridge inductance L _lc=4mH, C commutating phase bridge shunt load resistance R _lc=7 Ω, C commutating phase bridge shunt load capacitor C _lc=2200 μ F.A, the concrete structure of B phase load and C phase load are similar, for simplifying meter, do not draw A, the concrete structure of B phase load in accompanying drawing 4.

Load is now rectifier bridge shunt capacitor, by the harmonic content analysis result to load, shows: the current changing rate of 3 subharmonic is maximum, according to formula (6) and formula (9), can obtain respectively:

${(u_{\mathrm{jn}}+L_S\frac{{\mathrm{di}}_{\mathrm{Fj}}}{\mathrm{dt}})}_{\max }=311\left(V\right)+L_S\&times;(21.63\mathrm{kA}/s)$

${\left(\frac{{\mathrm{di}}_{\mathrm{Fn}}}{\mathrm{dt}}\right)}_{\max }=56.98\mathrm{kA}/s$

Get m=1 and m=0, separation structure in four brachium pontis and three brachium pontis electric capacity, take k as variable, L _sfor parameter, draw k and L _sbe subject to 2 restrictions of upper limit constraints 1 and upper limit constraints can value region respectively as shown in accompanying drawing 5 (a) and 5 (b).In figure black part be divided into simultaneously meet two upper limit constraintss can value region.

Now three-phase four-wire system parallel connection type APF has adopted the unfixed Hysteresis Current of switching frequency to control, and gets m=1 and m=0, T _sw=0.1ms, λ _n=10%, I _n=50A calculates lower limit constraints 2'; Get λ _abc=5%, I ₁=100A calculates lower limit constraints 1'.Take k as variable, L _sfor parameter, draw k and L _sbe subject to lower limit constraints 1' and lower limit constraints 2' restriction can value region respectively as shown in accompanying drawing 6 (a) and 6 (b).In figure black part be divided into simultaneously meet two lower limit constraintss can value region.

The bound constraints of output reactance is carried out comprehensively, can obtaining the optimization span of outputting inductance.When m=1, comprehensive accompanying drawing 5 (a) and accompanying drawing 6 (a), can obtain outputting inductance and optimize value region as shown in black part in scheming attached 7 (a).When m=0, comprehensive accompanying drawing 5 (b) and accompanying drawing 6 (b), can obtain outputting inductance and optimize value region as shown in black part in accompanying drawing 7 (b).Conventionally can be in resulting optimization value region value arbitrarily, but proceed from reality, can further optimization value region be divided into three parts according to the size of outputting inductance ratio k:

K<1, as S1 region in accompanying drawing 7 (a) and accompanying drawing 7 (b), conventionally the span that is optimized does not comprise this region, even if comprise this region, because each restrained boundary curve in this region has larger rate of change, so the slight variation of outputting inductance value all may make constraints be not being met.Therefore generally do not consider the value in k<1 region.

K>10, if have, meet the value in this region, as scheme S3 region in attached 7 (a) and accompanying drawing 7 (b), when k value is larger, center line outputting inductance will be less, consider manufacturing cost and design factor easily, k can be taken as to infinity, be that center line inductance can value be 0, as selected k=∞, L in accompanying drawing 7 (a) _s=10mH.Because center line inductance can save, therefore can be in this region during value, should pay the utmost attention to the value of k=∞.

1≤k≤10, meet the value in this region if only have, as scheme S2 region in attached 7 (b), can carry out choosing of inductance value according to actual conditions, should make data point be positioned at as far as possible and optimize value regional center position.As selected k=5, L in accompanying drawing 7 (b) _s=4mH.

Can see, the method computational process proposing is simple, and needed data volume is less, and only need to can obtain by simple simulation calculation, has good practicality.

The schematic diagram that accompanying drawing 8 is simulation result, below illustrates the checking of optimizing value: during m=1, the inductance value that optimal design obtains is k=∞, L _s=10mH.Fig. 8 (a) is the variation of each phase current of AC system THD; Fig. 8 (b) is the variation of AC system current in middle wire effective value; Fig. 8 (c) is the ripple of each brachium pontis output current under idle condition.From Fig. 8 (a), can see, system A after compensation, B, C phase current THD value all drops to and is less than 3%; From Fig. 8 (b), can see, after compensation, system current in middle wire effective value drops to and is less than 1.5A, all meets design performance requirement; From Fig. 8 (c), can see, when reference value is 0, A, B, the output current ripple of C brachium pontis is all less than 1.5A, meets the requirement that is less than 5A (100A * 5%), the output current ripple effective value of N brachium pontis is less than 3A, meets the requirement that is less than 5A (50A * 10%).The above results has illustrated that selected each parameter makes four bridge arm structure parallel connection type APF have good performance.

During m=0, the inductance value k=5 that Parameters Optimal Design obtains, L _s=4mH.Simulation result shows that selected each parameter makes separation structure parallel connection type APF in three brachium pontis electric capacity have good performance equally.Respective waveforms and interpretation of result no longer provide.

Above-mentioned simulation result and analysis verification validity and the accuracy of the method for optimally designing parameters that proposes, also illustrated that the method is all effectively general to various topological structures.

Therefore the output of the three-phase four-wire system parallel connection type APF that the present invention proposes connects the Optimization Design of inductance value.The achievement of studying provides the foundation for improving the performance of three-phase four-wire system parallel connection type APF.The method proposing has versatility to the three-phase four-wire system parallel connection type APF of various topological structures, calculates data volumes simple, that need few and easily obtain, and has certain practical value.

Above embodiment is used for illustrative purposes only, but not limitation of the present invention, person skilled in the relevant technique, without departing from the spirit and scope of the present invention, can also make various conversion or modification, therefore, within all technical schemes that are equal to also should belong to category of the present invention, should be limited by each claim.

Claims (5)

1. a three-phase four-wire system Shunt outputting inductance optimization method, described three-phase four-wire system Shunt DC side consists of the DC capacitor of 4 series connection, A, B, C brachium pontis forms phase three-wire three full-bridge inverter; N brachium pontis is single-phase semi-bridge structure, the tie point of access DC bus capacitor; A, B, it is L that the output of C brachium pontis connects reactance value _s, it is L that the output of N brachium pontis connects reactance value _n, it is characterized in that: carry out outputting inductance optimization and comprise the following steps,

Step 1, in the situation that ignoring system zero sequence voltage and affecting, by A, B, the voltage u of C brachium pontis mid point to system mid point n _an, u _bn, u _cnthe maximum of absolute value separately | u _an| _max, | u _bn| _max, | u _cn| _maxbe defined as the A of three-phase four-wire system parallel connection type APF, B, the fan-out capability of C brachium pontis, by A, B, C brachium pontis mid point is to N brachium pontis mid-point voltage u _aN, u _bN, u _cNthe maximum of zero-sequence component absolute value | u _f0| _maxbe defined as the fan-out capability of N brachium pontis;

Step 2, obtains respectively A, B, C, the upper limit constraints 1 of the outputting inductance value of N brachium pontis, upper limit constraints 2, A while adopting the fixing control method of switching frequency, B, C, the lower limit constraints 1 of the outputting inductance value of N brachium pontis, lower limit constraints 2, and A while adopting the unfixed control method of switching frequency, B, C, the lower limit constraints 1' of the outputting inductance value of N brachium pontis, lower limit constraints 2';

The obtain manner of described upper limit constraints 1 is, requires A, B, and the fan-out capability of C brachium pontis meets following formula,

$\frac{(k+2)-k(1-m)/2}{k+3}E\&GreaterEqual;u_{\mathrm{jn}}+L_S\frac{{\mathrm{di}}_{\mathrm{Fj}}}{\mathrm{dt}},j=A,B,C$

Wherein, k is A, B, and the ratio of C brachium pontis inductance and N brachium pontis inductance value, m is the relevant coefficient of the topological structure of three-phase four-wire system Shunt, E is DC voltage; u _jnfor AC system side phase voltage, i _fjfor A, B, C brachium pontis output current; The maximum of above formula right-hand member, calculates according to the main Types of three-phase four-wire system Shunt institute compensation harmonic load;

The obtain manner of described upper limit constraints 2 is to require the fan-out capability of N brachium pontis | u _f0| _maxmeet following formula,

$\frac{3}{2}(m+1)E\&GreaterEqual;L_S(1+3/k)\frac{{\mathrm{di}}_{\mathrm{Fn}}}{\mathrm{dt}}$

Wherein, i _fnfor N brachium pontis output current;

Described lower limit constraints 1 is as follows,

$\frac{{\mathrm{\&alpha;}}_{\mathrm{abc}}\&times;\left[\frac{(k+2)-k(1-m)/2}{k+3}\right]E}{I_1\&times;2\mathrm{\&pi;}\&times;f_{\mathrm{sw}}\&times;{\mathrm{\&lambda;}}_{\mathrm{abc}}}\&le;L_S$

Wherein, α _abcfor the coefficient relevant with modulation ratio and carrier wave ratio, I ₁for the specified first-harmonic effective value of load current, f _swfor switching frequency, λ _abcfor preset ratio;

Described lower limit constraints 2 is as follows,

$\frac{{\mathrm{\&alpha;}}_n\&times;\left[\frac{3(1+m)}{2}\right]E}{I_N\&times;2\mathrm{\&pi;}\&times;f_{\mathrm{sw}}\&times;{\mathrm{\&lambda;}}_n}\&le;L_S(3+1/k)$

Wherein, α _nfor the coefficient relevant with modulation ratio and carrier wave ratio, I _nfor system center line allows the electric current passing through, λ _nfor preset ratio;

Described lower limit constraints 1' is as follows,

$\frac{[k+2-k(1-m)/2]E}{(k+3)\&times;{\mathrm{\&lambda;}}_{\mathrm{abc}}\&times;I_1}\&times;\frac{T_{\mathrm{sw}}}{2\sqrt{3}}\&le;L_S$

Wherein, T _swthe sampling period adopting for control method;

Described lower limit constraints 2' is as follows,

$\frac{3(1+m)E}{2\&times;{\mathrm{\&lambda;}}_n\&times;I_N}\&times;\frac{T_{\mathrm{sw}}}{2\sqrt{3}}\&le;L_S(1+3/k)$

Step 3, according to the harmonic content analysis result of the topological structure of three-phase four-wire system Shunt, load current, when three-phase four-wire system Shunt adopts the fixing control method of switching frequency, utilize step 2 gained upper limit constraints 1, upper limit constraints 2, lower limit constraints 1 and lower limit constraints 2, determine the span of each brachium pontis outputting inductance; When three-phase four-wire system Shunt adopts the unfixed control method of switching frequency, utilize step 2 gained upper limit constraints 1, upper limit constraints 2, lower limit constraints 1' and lower limit constraints 2', determine the span of each brachium pontis outputting inductance.

2. three-phase four-wire system Shunt outputting inductance optimization method according to claim 1, it is characterized in that: while carrying out the obtaining of upper limit constraints 1, according to the main Types of three-phase four-wire system Shunt institute compensation harmonic load, calculate maximum implementation as follows,

(1) situation that load is mainly rectifier bridge shunt capacitance is calculated as follows,

${(u_{\mathrm{jn}}+L_S\frac{{\mathrm{di}}_{\mathrm{Fj}}}{\mathrm{dt}})}_{\max }=\sqrt{2}\&times;V_S+L_S\&times;2\sqrt{2}\mathrm{\&pi;}{f}_1\&times;h\&times;I_{\mathrm{abc}\left(h\right)}$

Wherein, h is A, and B needs to have in offset current the number of times of the harmonic wave of maximum rate of change, I in C brachium pontis _{abc (h)}for the effective value of corresponding h primary current, f ₁for fundamental frequency, V _sfor AC system side phase voltage u _an, u _bn, u _cneffective value;

(2) situation that load is mainly rectifier bridge series inductance is calculated as follows,

${(u_{\mathrm{jn}}+L_S\frac{{\mathrm{di}}_{\mathrm{Fj}}}{\mathrm{dt}})}_{\max }=L_S\underset{h=1}{\overset{h=H}{\mathrm{\&Sigma;}}}(2\sqrt{2}\mathrm{\&pi;}{f}_1\&times;h\&times;I_{\mathrm{abc}\left(h\right)})$

Wherein, H needs the high reps of compensation harmonic for design.

3. three-phase four-wire system Shunt outputting inductance optimization method according to claim 1, is characterized in that: while carrying out the obtaining of upper limit constraints 2, calculate as follows maximum current slew rate,

${\left(\frac{{\mathrm{di}}_{\mathrm{Fn}}}{\mathrm{dt}}\right)}_{\max }=\underset{h=1}{\overset{h=H}{\mathrm{\&Sigma;}}}(2\sqrt{2}\mathrm{\&pi;}{f}_1\&times;h\&times;I_{n\left(h\right)})$

Wherein, I _{n (h)}the effective value of the h subharmonic current that need compensate for N brachium pontis.

4. according to three-phase four-wire system Shunt outputting inductance optimization method described in claim 1 or 2 or 3, it is characterized in that: according to A, B, the ratio k of C brachium pontis inductance and N brachium pontis inductance value, by the span Further Division of each brachium pontis outputting inductance of step 3 gained, be 3 regions, in corresponding region, further optimize respectively the value that output connects inductance.

5. three-phase four-wire system Shunt outputting inductance optimization method according to claim 4, is characterized in that: 3 regions of division are k<1, k>10,1≤k≤10.