CN102253266B - Linear filter-based harmonic current detection method in three-phase four-wire system - Google Patents

Linear filter-based harmonic current detection method in three-phase four-wire system Download PDF

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CN102253266B
CN102253266B CN 201110109158 CN201110109158A CN102253266B CN 102253266 B CN102253266 B CN 102253266B CN 201110109158 CN201110109158 CN 201110109158 CN 201110109158 A CN201110109158 A CN 201110109158A CN 102253266 B CN102253266 B CN 102253266B
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omega
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CN102253266A (en
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邱晓初
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Xihua University
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Abstract

The invention discloses a linear filter-based harmonic current detection method in a three-phase four-wire system. According to the method, a structural characteristic of the three-phase four-wire system is considered; according to the idea of an adaptive notch filter (ANF), a two-dimensional linear sine filter is obtained after rotation transformation on the basis of a minimum variance principle and a gradient decent method; fundamental currents of all phases are respectively separated from an actual measured current by the two-dimensional linear sine filter; and then a symmetrical fundamental wave positive sequence component is obtained by utilizing a modified instantaneous symmetric component calculation method; after calculation of the fundamental wave positive sequence component with the original actual measured current, a harmonic component of a load current, a fundamental negative sequence component and a zero sequence component are drawn off. Compared with the prior art, a technique employed in the linear filter-based harmonic current detection method in the three-phase four-wire system provided of the invention enables the method to have the following advantages that: the method is simple with a small amount of computation and it is not needed to carry out complicated rotation transformation and trigonometric function calculation; the method has a good real-time performance and high detection precision; and a harmonic current and a reactive current and a neutral current in the three-phase four-wire system can be detected on the condition of unsymmetrical nonlinear load and nonideal voltage.

Description

A kind of three-phase four-wire system harmonic current detecting method based on linear filter
Technical field
The present invention relates to field of power, exactly refer to a kind of three-phase four-wire system harmonic current detecting method based on linear filter.
Background technology
At present, along with development and the application of modern power electronics technology, it has been topmost harmonic pollution source in electrical network that power electronic equipment becomes, the safety that is seriously threatening electrical network and consumer.The harmonic wave control of electric system has been subjected to the concern of numerous Chinese scholars.At present, the research that China controls Harmonious Waves in Power Systems mainly concentrates in the three-phase three-wire system system, although some researchs are also arranged in three-phase four-wire system, still has many problems to await furtheing investigate.
In low-voltage distribution system, the three-phase four-wire power supply mode is topmost power supply mode, is used widely in industry spot and covil construction.Symmetrical three-phase nonlinear load produces positive sequence harmonic and negative phase-sequence harmonic wave, but be connected to the single-phase nonlinear load in three-phase four-wire system, as being widely used of the household electrical appliance such as personal computer, business automation equipment, convertible frequency air-conditioner, mains lighting supply and uninterrupted power source etc., to produce a large amount of neutral harmonic currents in electrical network, although their separate unit power is less, but huge because of its quantity, the harmonic pollution that brings is extremely serious.Neutral harmonic current (being mainly 3 subharmonic currents) is stack mutually on center line, the large electric current up to 1.73 times of phase currents may occur, and this just makes the Harmonic Conditions in current in middle wire extremely serious.The center line harmonic current makes current in middle wire substantially exceed its design load on the one hand, easily causes the center line fault; Make on the other hand transformer overheated, cause insulation breakdown, also can cause simultaneously the center line potential to ground to promote, have great importance so the harmonic wave in three-phase four-wire system and three-phase imbalance are compensated.
It is the prerequisite of harmonic wave control that quick harmonic wave in three-phase four-wire system detects.At present, main detection method is based on fast Fourier transform (FFT) with based on the large class of instantaneous reactive power theory two of red wooden Thai language.Adopt fft algorithm can detect rapidly the harmonic wave of analyzed signal, but need the sampled data of one-period due to fft algorithm, therefore have larger time-delay, and computing is comparatively complicated, real-time is relatively poor.The instantaneous reactive power theory that red wooden Thai language proposes, for detecting, the quick harmonic wave of electric system provides theoretical foundation, greatly promoted the development of active power filtering practical research, but asymmetric or when containing harmonic wave when supply voltage, the precision that harmonic wave detects will be greatly affected, mainly be applicable to directly to apply in three-phase four-wire system in the three-phase three-wire system system of balance.For this reason, Chinese scholars is improved instantaneous reactive power theory, and it is generalized in three-phase four-wire system.In addition, utilize wavelet analysis to carry out harmonic wave and detect, although obtained better effects, its operand is larger, and real-time is relatively poor, and the selection of wavelet basis simultaneously is also a relatively hard problem.
Summary of the invention
For defects, the technical matters that the present invention solves is to provide a kind of three-phase four-wire system harmonic current detecting method based on linear filter, method is simple, operand is little, need not to carry out complicated rotational transform and the calculating of trigonometric function, real-time is good, and accuracy of detection is high, can detect harmonic current, reactive current, current in middle wire in three-phase four-wire system under unbalanced nonlinear loads and nonideal voltage condition.
In order to solve above technical matters, the three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention comprises the steps:
(a) utilize the design feature of three-phase four-wire system, regard as mutually its each three independently single-phase, the unbalanced three-phase load current i a, i b, i c, each uses a two-dimensional linear wave filter to extract fundamental current; If the fundamental frequency of electrical network is f, its angular frequency is ω, and the electric power signal of wave filter input is i (t), has:
State variable is chosen as x (t)=[x 1(t) x 2(t)] T:
The estimated value of i (t) Can be expressed as: i ^ ( t ) = x 1 ( t ) · sin ωt + x 2 ( t ) · cos ωt - - - ( 3 )
The evaluated error of signal equals: e ( t ) = i ( t ) - i ^ ( t ) - - - ( 4 )
According to minimum variance thought, the definition cost function is: J ( x ) = 0.5 e 2 ( t ) = 0.5 ( i ( t ) - i ^ ( t ) ) 2 - - - ( 5 )
According to gradient descent method, have:
x · = - N ∂ J ( x ) ∂ x - - - ( 6 )
Matrix Ν regulates x (t) and converges to the speed of optimal value and the stability of algorithm.Make μ 1, μ 2>0, select:
N = μ 1 0 0 μ 2 - - - ( 7 )
Thus, can obtain the periodic coefficient linear dynamic system:
Wherein: x · = x · 1 ( t ) x · 2 ( t ) T , x=[x 1(t)?x 2(t)] T
A = - μ 1 sin 2 ωt - μ 1 sin ωt · cos ωt - μ 2 sin ωt · cos ωt - μ 2 cos 2 ωt B = μ 1 sin ωt μ 2 cos ωt
Do rotational transform, order
y ( t ) = y 1 ( t ) y 2 ( t ) = sin ωt cos ωt cos ωt - sin ωt · x 1 ( t ) x 2 ( t ) - - - ( 9 )
Known the estimated value of i (t) by formula (1) and formula (3) For:
i ^ ( t ) = y 1 ( t ) = x 1 ( t ) sin ωt + x 2 ( t ) cos ωt - - - ( 10 )
With formula (9) substitution formula (8), have:
y · 1 ( t ) y · 2 ( t ) = - μ 1 sin 2 ωt - μ 2 cos 2 ωt ω - ω 0 · y 1 ( t ) y 2 ( t ) +
μ 1 sin 2 ωt + μ 2 cos 2 ωt ( μ 1 - μ 2 ) sin ωt · cos ωt · i ( t ) - - - ( 11 )
Make μ 12=μ, η=ω obtains the two-dimensional linear filtering algorithm:
y · 1 ( t ) y · 2 ( t ) = - μ η - η 0 · y 1 ( t ) y 2 ( t ) + μ 0 · i ( t ) - - - ( 12 )
Wherein: y (t)=[y 1(t) y 2(t)] TBe state variable; μ, η are the parameter of wave filter, all greater than zero real constant; y 1(t) be wave filter output, in its expression input signal, contained angular frequency is the sinusoidal component of ω, is also the fundametal compoment of input signal, y 2(t) be and y 1(t) quadrature and leading homogenous frequency signal;
If starting condition y 1(0)=0, y 2(0)=0 is got i (t) and is input, y 1(t) be output, the transport function of two-dimensional linear wave filter is
H ( s ) = μs s 2 + μs + η 2 - - - ( 13 )
Make s=j ω, have:
H ( jω ) = jωμ ( jω ) 2 + jωμ + η 2 - - - ( 14 )
Its amplitude versus frequency characte and phase-frequency characteristic are respectively:
| H ( jω ) | = ωμ ( η 2 - ω 2 ) 2 + ω 2 μ 2 - - - ( 15 )
arg [ H ( jω ) ] = π 2 - arctan ωμ η 2 - ω 2 - - - ( 16 )
When getting μ=0.5, during η=ω=314rad/s, have:
| H ( jω ) | = ωμ ( η 2 - ω 2 ) 2 + ω 2 μ 2 = 1 - - - ( 17 )
arg [ H ( jω ) ] = π 2 - arctan ωμ η 2 - ω 2 = 0 - - - ( 18 )
(b) unbalanced fundamental current i af, i bf, i cfCalculate by instantaneous symmetrical components, obtain symmetrical fundamental positive sequence current component i afp, i bfp, i cfpIf the unbalanced three-phase load current instantaneous value is:
Wherein: i a(t), i b(t), i c(t) be respectively the three-phase current instantaneous value; I am, I bm, I cmBe respectively the amplitude of three-phase current; Be respectively the initial phase of three-phase current;
If with three-phase current i a(t), i b(t), i c(t) corresponding rotating phasor is respectively Have:
Known phasor by formula (20) The imaginary part coefficient be the three-phase current instantaneous value, as long as can determine its real part, just can determine these rotating phasors; If the instantaneous value of a phase current can be expressed as:
Also namely:
Therefore have:
Again because:
Can get after arrangement:
In like manner can get:
In formula (25)~(27) substitution formula (20), consist of instantaneous rotating phasor, unbalanced three-phase load electric current positive-sequence component value is:
i ap ( t ) i bp ( t ) i cp ( t ) = Im { 1 3 1 a a 2 a 2 1 a a a 2 1 · I · a I · b I · c } - - - ( 28 )
Wherein: Im{) for asking the imaginary-part operation of plural number; A=e J2 π/3, a 2=e -j2 π/3, 1+a+a 2=0;
(c) with former load current computing after, can isolate harmonic current components i ah, i bh, i ch
Three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention, design feature for three-phase four-wire system, thought according to adaptive notch filter (ANF), according to minimum variance principle and Gradient Descent method, obtain the two-dimensional linear sinusoidal filter through rotational transform, separation of phases fundamental current from measured current respectively, recycle improved instantaneous symmetrical components computing method, obtain symmetrical fundamental positive sequence, with the harmonic component and first-harmonic negative sequence component and the zero-sequence component that extract load current after former measured current computing.Compared with prior art, three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention, method is simple, operand is little, need not to carry out complicated rotational transform and the calculating of trigonometric function, real-time is good, and accuracy of detection is high, can detect harmonic current, reactive current, current in middle wire in three-phase four-wire system under unbalanced nonlinear loads and nonideal voltage condition.
Description of drawings
Fig. 1 is based on the detection principle schematic of the three-phase four-wire system harmonic current detecting method of linear filter in the present invention;
Fig. 2 is the harmonic wave testing result figure under desirable principal voltage in embodiment 1;
Fig. 3 is that in embodiment 1, the current in middle wire under desirable principal voltage is eliminated and reactive-load compensation figure as a result;
Fig. 4 is the harmonic wave testing result figure under non-equilibrium principal voltage in embodiment 2;
Fig. 5 is that in embodiment 2, the current in middle wire under non-equilibrium principal voltage is eliminated and reactive-load compensation figure as a result;
Fig. 6 is the harmonic wave testing result figure under balance distortion principal voltage in embodiment 3;
Fig. 7 is that in embodiment 3, the current in middle wire under balance distortion principal voltage is eliminated and reactive-load compensation figure as a result;
Fig. 8 is the harmonic wave testing result figure under non-equilibrium distortion principal voltage in embodiment 4;
Fig. 9 is that in embodiment 4, the current in middle wire under non-equilibrium distortion principal voltage is eliminated and reactive-load compensation figure as a result.
Embodiment
For those skilled in the art can understand technical scheme provided by the present invention better, set forth below in conjunction with specific embodiment.
See also Fig. 1, this figure is based on the detection principle schematic of the three-phase four-wire system harmonic current detecting method of linear filter in the present invention
Three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention comprises the steps:
(a) utilize the design feature of three-phase four-wire system, regard as mutually its each three independently single-phase, the unbalanced three-phase load current i a, i b, i c, each uses a two-dimensional linear wave filter to extract fundamental current; If the fundamental frequency of electrical network is f, its angular frequency is ω, and the electric power signal of wave filter input is i (t), has:
State variable is chosen as x (t)=[x 1(t) x 2(t)] T:
The estimated value of i (t) Can be expressed as: i ^ ( t ) = x 1 ( t ) · sin ωt + x 2 ( t ) · cos ωt - - - ( 3 )
The evaluated error of signal equals: e ( t ) = i ( t ) - i ^ ( t ) - - - ( 4 )
According to minimum variance thought, the definition cost function is: J ( x ) = 0.5 e 2 ( t ) = 0.5 ( i ( t ) - i ^ ( t ) ) 2 - - - ( 5 )
According to gradient descent method, have:
x · = - N ∂ J ( x ) ∂ x - - - ( 6 )
Matrix Ν regulates x (t) and converges to the speed of optimal value and the stability of algorithm, makes μ 1, μ 2>0, select:
N = μ 1 0 0 μ 2 - - - ( 7 )
Thus, can obtain the periodic coefficient linear dynamic system:
Wherein: x · = x · 1 ( t ) x · 2 ( t ) T , x=[x 1(t)?x 2(t)] T
A = - μ 1 sin 2 ωt - μ 1 sin ωt · cos ωt - μ 2 sin ωt · cos ωt - μ 2 cos 2 ωt B = μ 1 sin ωt μ 2 cos ωt
Do rotational transform, order
y ( t ) = y 1 ( t ) y 2 ( t ) = sin ωt cos ωt cos ωt - sin ωt · x 1 ( t ) x 2 ( t ) - - - ( 9 )
Known the estimated value of i (t) by formula (1) and formula (3) For:
i ^ ( t ) = y 1 ( t ) = x 1 ( t ) sin ωt + x 2 ( t ) cos ωt - - - ( 10 )
With formula (9) substitution formula (8), have:
y · 1 ( t ) y · 2 ( t ) = - μ 1 sin 2 ωt - μ 2 cos 2 ωt ω - ω 0 · y 1 ( t ) y 2 ( t ) +
μ 1 sin 2 ωt + μ 2 cos 2 ωt ( μ 1 - μ 2 ) sin ωt · cos ωt · i ( t ) - - - ( 11 )
Make μ 12=μ, η=ω obtains the two-dimensional linear filtering algorithm:
y · 1 ( t ) y · 2 ( t ) = - μ η - η 0 · y 1 ( t ) y 2 ( t ) + μ 0 · i ( t ) - - - ( 12 )
Wherein: y (t)=[y 1(t) y 2(t)] TBe state variable; μ, η are the parameter of wave filter, all greater than zero real constant; y 1(t) be wave filter output, in its expression input signal, contained angular frequency is the sinusoidal component of ω, is also the fundametal compoment of input signal, y 2(t) be and y 1(t) quadrature and leading homogenous frequency signal;
If starting condition y 1(0)=0, y 2(0)=0 is got i (t) and is input, y 1(t) be output, the transport function of two-dimensional linear wave filter is
H ( s ) = μs s 2 + μs + η 2 - - - ( 13 )
Make s=j ω, have:
H ( jω ) = jωμ ( jω ) 2 + jωμ + η 2 - - - ( 14 )
Its amplitude versus frequency characte and phase-frequency characteristic are respectively:
| H ( jω ) | = ωμ ( η 2 - ω 2 ) 2 + ω 2 μ 2 - - - ( 15 )
arg [ H ( jω ) ] = π 2 - arctan ωμ η 2 - ω 2 - - - ( 16 )
When getting μ=0.5, during η=ω=314rad/s, have:
| H ( jω ) | = ωμ ( η 2 - ω 2 ) 2 + ω 2 μ 2 = 1 - - - ( 17 )
arg [ H ( jω ) ] = π 2 - arctan ωμ η 2 - ω 2 = 0 - - - ( 18 )
(b) unbalanced fundamental current i af, i bf, i cfCalculate by instantaneous symmetrical components, obtain symmetrical fundamental positive sequence current component i afp, i bfp, i cfpIf the unbalanced three-phase load current instantaneous value is:
Wherein: i a(t), i b(t), i c(t) be respectively the three-phase current instantaneous value; I am, I bm, I cmBe respectively the amplitude of three-phase current; Be respectively the initial phase of three-phase current;
If with three-phase current i a(t), i b(t), i c(t) corresponding rotating phasor is respectively Have:
Known phasor by formula (20) The imaginary part coefficient be the three-phase current instantaneous value, as long as can determine its real part, just can determine these rotating phasors; If the instantaneous value of a phase current can be expressed as:
Also namely:
Therefore have:
Again because:
Can get after arrangement:
In like manner can get:
In formula (25)~(27) substitution formula (20), consist of instantaneous rotating phasor, unbalanced three-phase load electric current positive-sequence component value is:
i ap ( t ) i bp ( t ) i cp ( t ) = Im { 1 3 1 a a 2 a 2 1 a a a 2 1 · I · a I · b I · c } - - - ( 28 )
Wherein: Im{} is the imaginary-part operation of asking plural number; A=e J2 π/3, a 2=e -j2 π/3, 1+a+a 2=0;
(c) with former load current computing after, can isolate harmonic current components i ah, i bh, i ch
In order to verify the three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention, use the electric system tool box of Matlab-Simulink to set up the three-phase four-wire system electric power system model of four brachium pontis, adopt the load of three phase rectifier bridge-type as the threephase load of symmetry, two single-phase bridge rectification loads contain the uneven phase current and the current in middle wire that contains zero-sequence component of harmonic current and reactive current as non-equilibrium load with generation.The harmonic wave of active filter detects the algorithm that adopts this paper to propose, and four-leg inverter adopts stagnant ring control mode, connecting system when 0.15s, and a single-phase load is connected to the B phase when 0.3s, with the dynamic perfromance of Study system.By carry out simulation study in desirable balance principal voltage, uneven principal voltage, balance distortion principal voltage and four kinds of situations of uneven distortion principal voltage, verify correctness and the validity of institute's put forward the methods.The systematic parameter that emulation is used is as shown in table 1.
The systematic parameter that table 1 emulation is used
Parameter Value
Power supply ?
Voltage 220V
Frequency 50Hz
Impedance 10mΩ,50μH
Four bridge-arm active filters ?
Dc terminal voltage 800V
DC terminal electric capacity 1500μF
Exchange the end filter inductance 0.1Ω,1mH
Load ?
Threephase load 12Ω,20mH
Single-phase load 15Ω,1mH,470μF
Wave filter ?
Center-frequency parameters 314rad/s
The speed of convergence parameter 1.8(t<0.01s),0.5(t>0.01s)
Embodiment 1
Desirable balance principal voltage situation: Fig. 2 and Fig. 3 have shown the simulation result of system in the three phase sine principal voltage situation of perfect symmetry.Provided respectively principal voltage waveform V in Fig. 2 abc(a), load current waveform i Labc(b), source current waveform i Sabc(c), the fundamental waveform i of each phase source current of two-dimensional linear wave filter output Fabc(d) and the current first harmonics positive-sequence component waveform i of symmetrical components after calculating Fpabc(e).Fig. 3 has provided the compensation situation of current in middle wire and reactive current.Current in middle wire iln (a) before compensation, the current in middle wire isn (b) after compensation, the waveform Vsa of A phase voltage electric current before compensation, ila (c), the voltage current waveform Vsa after compensation, isa (d).Load current, source current, current in middle wire and percent harmonic distortion thereof (Total Harmonic Distortion, the THD) value of system in desirable principal voltage situation is as shown in table 2.Simulation result shows, the three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention has been issued to good effect in desirable principal voltage situation.
Load current, source current and THD under the desirable principal voltage of table 2
Embodiment 2
Unbalanced sinusoidal principal voltage situation: unbalanced sinusoidal principal voltage is provided by following formula:
v a=380sinωt+38sinωt
v b=380sin(ωt-120°)+38sin(ωt+120°)
v c=380sin(ωt+120°)+38sin(ωt-120°)
The simulation result of system in unbalanced three phase sine principal voltage situation as shown in Figure 4 and Figure 5, in figure, the implication of each waveform is identical with Fig. 2 and Fig. 3.
Simulation result shows, under nonequilibrium sinusoidal voltage effect, comparatively serious imbalance has appearred in the load current of A, B, C three-phase, has occurred very large harmonic current on center line.When after 0.15s access AFP, the three-phase supply electric current reaches balance, the THD of B phase current is between 0.15s and 0.3s, drop to 1.14% by original 39.34%, the time greater than 0.3s after, THD drops to 1.27% by original 51.55%, simultaneously, current in middle wire also drops to respectively 0.44A and 0.48A by original 40.27A and 80.4A, sees table 3 for details.As seen, three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention is in nonequilibrium principal voltage situation, the harmonic component of system be can detect exactly, harmonic current and current in middle wire in three-phase four-wire system effectively eliminated.
Load current, source current and THD under the non-equilibrium principal voltage of table 3
Embodiment 3
Balance distortion principal voltage situation: in order to study the system performance under balance distortion principal voltage, the three-phase supply that is constructed as follows:
v a=380sinωt+4.56sin3ωt+22.8sin(5ωt-120°)+
5.7sin7ωt+3.8sin(11ωt-120°)
v b=380sin(ωt-120°)+4.56sin3ωt+22.8sin5ωt+
5.7sin(7ωt-120°)+3.8sin11ωt
v c=380sin(ωt+120°)+4.56sin3ωt+
22.8sin(5ωt+120°)+5.7sin(7ωt+120°)+
3.8sin(11ωt+120°)
The simulation result of system in unbalanced three phase sine principal voltage situation as shown in Figure 6 and Figure 7, in figure, the implication of each waveform is identical with Fig. 2 and Fig. 3.
Simulation result shows, under the effect of balance distortion principal voltage, serious distortion and imbalance have appearred in load current and source current, the THD of current in middle wire is 70.81%, after 0.15s access APF, the harmonic wave in source current is suppressed well, and imbalance is compensated, current in middle wire is also reduced to respectively 0.63A and 0.59A by original 14.7A and 29.37A, has improved source current and current in middle wire characteristic.Load current, source current, current in middle wire and the THD value thereof of system in distortion principal voltage situation is as shown in table 4.As seen, the three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention has good performance in the situation that the distortion principal voltage can detect each phase harmonic wave well.
Load current, source current and THD under table 4 balance distortion principal voltage
Embodiment 4
Uneven distortion principal voltage situation: in order to study the system performance under non-equilibrium distortion principal voltage, the three-phase supply that is constructed as follows:
v a=380sinωt+38sinωt+4.56sin3ωt+
22.8sin(5ωt-120°)+5.7sin7ωt+
3.8sin(11ωt-120°)
v b=380sin(ωt-120°)+38sin(ωt+120°)+
4.56sin3ωt+22.8sin5ωt+5.7sin(7ωt-120°)+
3.8sin11ωt
v c=380sin(ωt+120°)+38sin(ωt-120°)+
4.56sin3ωt+22.8sin(5ωt+120°)+
5.7sin(7ωt+120°)+3.8sin(11ωt+120°)
Simulation result such as the Fig. 8 and shown in Figure 9 in unbalanced three-phase distortion principal voltage situation of system.In figure, the implication of each waveform is identical with Fig. 2 and Fig. 3.
This non-sinusoidal, unbalanced power supply simulation work state are near the working condition of practical power voltage, and simulation result shows, the algorithm of carrying still can detect harmonic wave in system well, balance source current, compensating reactive power.APF is after the 0.15s connecting system, and the THD of source current reduces greatly, and three-phase imbalance is inhibited, and reactive current is compensated, and current in middle wire is limited in the 0.6A left and right.Although the THD of source current will be before several situations slightly high, but still in national approval standard scope.Load current, source current, current in middle wire and the THD value thereof of system in distortion principal voltage situation is as shown in table 5.As seen, the three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention has good performance in the situation that non-equilibrium distortion principal voltage also can detect each phase harmonic wave well.
Load current, source current and THD under the non-equilibrium distortion principal voltage of table 5
by in balance ideal sinusoidal principal voltage situation, uneven sinusoidal principal voltage situation, emulation in balance distortion principal voltage situation and uneven distortion principal voltage situation, result verification validity and the correctness of the three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention, system has good sound performance, utilize the three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention and four brachium pontis parallel A PF, can realize the harmonic compensation of asymmetric three-phase four-wire system in the situations such as non-equilibrium distortion principal voltage, reactive-load compensation, the balance of load current and the inhibition of current in middle wire.
Compared with prior art, three-phase four-wire system harmonic current detecting method based on linear filter provided by the invention, method is simple, operand is little, need not to carry out complicated rotational transform and the calculating of trigonometric function, real-time is good, and accuracy of detection is high, can detect harmonic current, reactive current, current in middle wire in three-phase four-wire system under unbalanced nonlinear loads and nonideal voltage condition.
To the above-mentioned explanation of the disclosed embodiments, make this area professional and technical personnel can realize or use the present invention.Multiple modification to these embodiment will be apparent concerning those skilled in the art, and General Principle as defined herein can be in the situation that do not break away from the spirit or scope of the present invention, realization in other embodiments.Therefore, the present invention will can not be restricted to these embodiment shown in this article, but will meet the widest scope consistent with principle disclosed herein and features of novelty.

Claims (1)

1. the three-phase four-wire system harmonic current detecting method based on linear filter, is characterized in that, comprises the steps:
(a) utilize the design feature of three-phase four-wire system, regard as mutually its each three independently single-phase, the unbalanced three-phase load current i a, i b, i c, each uses a two-dimensional linear wave filter to extract fundamental current; If the fundamental frequency of electrical network is f, its angular frequency is ω, and the electric power signal of wave filter input is i (t), has:
State variable is chosen as x (t)=[x 1(t) x 2(t)] T:
The estimated value of i (t) Can be expressed as:
The evaluated error of signal equals:
According to minimum variance thought, the definition cost function is:
According to gradient descent method, have:
Matrix Ν regulates x (t) and converges to the speed of optimal value and the stability of algorithm, makes μ 1, μ 2>0, select:
Thus, can obtain the periodic coefficient linear dynamic system:
Wherein: X=[x 1(t) x 2(t)] T
Do rotational transform, order
Known the estimated value of i (t) by formula (1) and formula (3) For:
With formula (9) substitution formula (8), have:
Make μ 12=μ, η=ω obtains the two-dimensional linear filtering algorithm:
Wherein: y (t)=[y 1(t) y 2(t)] TBe state variable; μ, η are the parameter of wave filter, all greater than zero real constant; y 1(t) be wave filter output, in its expression input signal, contained angular frequency is the sinusoidal component of ω, is also the fundametal compoment of input signal, y 2(t) be and y 1(t) quadrature and leading homogenous frequency signal;
If starting condition y 1(0)=0, y 2(0)=0 is got i (t) and is input, y 1(t) be output, the transport function of two-dimensional linear wave filter is
Make s=j ω, have:
Its amplitude versus frequency characte and phase-frequency characteristic are respectively:
When getting μ=0.5, during η=ω=314rad/s, have:
(b) unbalanced fundamental current i af, i bf, i cfCalculate by instantaneous symmetrical components, obtain symmetrical fundamental positive sequence current component i afp, i bfp, i cfpIf the unbalanced three-phase load current instantaneous value is:
Wherein: i a(t), i b(t), i c(t) be respectively the three-phase current instantaneous value; I am, I bm, I cmBe respectively the amplitude of three-phase current; Be respectively the initial phase of three-phase current;
If with three-phase current i a(t), i b(t), i c(t) corresponding rotating phasor is respectively Have:
Known phasor by formula (20) The imaginary part coefficient be the three-phase current instantaneous value, as long as can determine its real part, just can determine these rotating phasors; If the instantaneous value of a phase current can be expressed as:
Also namely:
Therefore have:
Again because:
Can get after arrangement:
In like manner can get:
In formula (25)~(27) substitution formula (20), consist of instantaneous rotating phasor, unbalanced three-phase load electric current positive-sequence component value is:
Wherein: Im{} is the imaginary-part operation of asking plural number; A=e J2 π/3, a 2=e -j2 π/3, 1+a+a 2=0;
(c) with former load current computing after, can isolate harmonic current components i ah, i bh, i ch
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