CN109038603A - A kind of idle and harmonic compensation method with Local sensitivity analysis function - Google Patents
A kind of idle and harmonic compensation method with Local sensitivity analysis function Download PDFInfo
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- CN109038603A CN109038603A CN201810838850.7A CN201810838850A CN109038603A CN 109038603 A CN109038603 A CN 109038603A CN 201810838850 A CN201810838850 A CN 201810838850A CN 109038603 A CN109038603 A CN 109038603A
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- boost
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
- H02J3/1821—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/30—Reactive power compensation
Abstract
A kind of idle and harmonic compensation method with Local sensitivity analysis function solves the harmonic wave Cross-coupling issues that each even-order harmonic modulation item generates in duty ratio, makes to modulate difficulty significant decrease by establishing the frequency-domain model of system.Derive the reactive compensation electric current of device and the quantitative relationship of individual harmonic current and duty ratio, it is proposed Sensitivity Analysis Method, be compensated the general corresponding relationship of each harmonic and each harmonic modulation item of duty ratio in electric current, using the closed loop control algorithm based on synchronous reference coordinate theory allow system in real time, quickly and accurately compensating reactive power and harmonic current.Compared with existing device and its control method, Local sensitivity analysis method proposed by the present invention preferably solves the idle and harmonic wave compensation precision limitation problem of Boost AC chopping type D-CAP, and response speed faster, compensates more accurate.
Description
Technical field
The present invention relates to power quality control technology fields, and in particular to a kind of with the idle of Local sensitivity analysis function
And harmonic compensation method.
Background technique
AC chopping type vibrating capacitor (D-CAP) is a kind of novel dynamic reactive and harmonic compensation device, is fabricated to
Originally quite with Static Var Compensator (SVC), but its response speed is faster, and dynamic compensation ability is stronger；It is filtered with parallel connection type active
Wave device (APF) is compared with static synchronous compensator (STATCOM), has similar performance, but its cost is less expensive, reliability is more
Height, and it does not need the electrolytic capacitor using large capacity as energy storage device, and lifetime of system is longer, application and maintenance cost
It is lower, wide market.
By literature search, some D-CAP are theoretical according to virtual orthographic source, topological using Buck type alternating-current chopper circuit,
Reactive compensation and harmonics restraint can be achieved at the same time by the control to Buck alternating-current chopper circuit using ac capacitor in secondary side
Function；Some D-CAP propose that active impedance is theoretical, and the inductance or capacitor of secondary side, Jin Erxiang are controlled by alternating-current chopper circuit
Power grid injects controllable perception or capacitive reactive power compensation electric current.The above method is used using single-phase Buck type D-CAP as research object
Direct Current Closed-loop Control Strategy, can accurately obtain duty ratio and idle and harmonic current relational expression, but its compensation range by
Limit；And Boost and Buck-Boost etc. other topology relational expressions be difficult to obtain.Existing research is using open loop compensated setpoint electricity
Stream method obtains rough quantitative calculated result using numerical computation method.Though using closed loop control method in experiment,
A large amount of uncontrollable harmonic currents are generated in control process, do not obtain good control effect.China Patent No.
CN102570473A discloses AC chopping formula Static Var Compensator design scheme, in design process without using reactor, from
Body is without harmonic wave, though being not directed to harmonic controling scheme, the design scheme of its two-way switch has reference to the present invention.
Summary of the invention
Realize that idle and harmonic current quickly accurately compensates to overcome the above deficiencies, the invention provides a kind of
The idle and harmonic compensation method with Local sensitivity analysis function.
The present invention overcomes the technical solution used by its technical problem to be:
A kind of idle and harmonic compensation method with Local sensitivity analysis function, includes the following steps:
A) pass through formulaAnd formulaEstablish the mathematics of Boost AC chopper
Model, wherein μcIt (t) is the output voltage of Boost AC chopper, icIt (t) is the compensation electric current of Boost AC chopper, μs
It (t) is supply voltage, iL(t) electric current on the capacitor C to flow through Boost AC chopper, d (t) are Boost AC chopper
Two-way switch K1Duty ratio, 1-d (t) be Boost AC chopper two-way switch K2Duty ratio；
B) when duty ratio d (t) is constant constant D0When, pass through formulaAnd formulaThe reactive compensation mathematical model of Boost AC chopping type D-CAP is established, wherein UsFor power grid electricity
Pressure amplitude value, ω are fundamental wave frequency, and C is idle supplement capacitance, and t is time variable；
C) when even-order harmonic modulation item EHM is added to duty ratio d (t), pass through formula
The even-order harmonic modulation mathematical model for establishing Boost AC chopping type D-CAP, wherein 0≤D0+D2+D4+···+Dn≤
1, DnFor the amplitude of n-th even-order harmonic modulation item,For the initial phase angle of n-th even-order harmonic modulation item；
D) pass through formulaAndEstablish Boost friendship
Flow the frequency-domain model of chopper-type D-CAP, YRLFor the series admittance square of filter inductance L in Boost AC chopper and dead resistance R
Battle array, ZcFor the impedance matrix of capacitor C in Boost AC chopper, wherein
Y11(n, n)=Y22(n, n)=real (yRL(n))
Y12(n, n)=- Y21(n, n)=imag (yRL(n))
Z11(n, n)=Z22(n, n)=real (Zc(n))
Z12(n, n)=- Z21(n, n)=imag (Zc(n))
yRL(n)=1/ (R+j2 π 50nL), yRL(n) series admittance for being L and R, j is complex unit, Zc(n)=- j/2 π
50nC), Zc(n) impedance for being C；
E) pass through formulaCalculate voltage on line side μ
(ω t), a in formula0For constant term, anFor Fourier space sine term coefficient, bnFor Fourier space cosine term coefficient, by net side
Voltage byOne-dimensional matrix expression is carried out, wherein U1...UnRespectively voltage on line side Fourier
The cos item and sin amplitude coefficients of expansion, pass through formulaComputing system
Reactive compensation electric currentE is unit matrix in formula, and T is the corresponding matrix of alternating-current chopper circuit, and T is transposition symbol,For
The transposition of voltage on line side matrix；
F) according to formula
The Sensitivity Analysis of Boost AC chopping type D-CAP is established, wherein x=[2C, 2S, 4C, 4S], C is cosine
, S is sine term, DxFor Fourier expansion formula coefficient.
The beneficial effects of the present invention are: solving each even-order harmonic modulation in duty ratio by the frequency-domain model for establishing system
The harmonic wave Cross-coupling issues that item generates make to modulate difficulty significant decrease.Derive device reactive compensation electric current and each time it is humorous
The quantitative relationship of wave electric current and duty ratio proposes Sensitivity Analysis Method, is compensated each harmonic and duty ratio in electric current
The general corresponding relationship of each harmonic modulation item uses the closed loop control algorithm based on synchronous reference coordinate theory to make system can be with
In real time, quickly and accurately compensating reactive power and harmonic current.It is proposed by the present invention compared with existing device and its control method
Local sensitivity analysis method, the idle and harmonic wave compensation precision for preferably solving Boost AC chopping type D-CAP, which is limited, asks
Topic, response speed faster, compensate more accurate.
Detailed description of the invention
Fig. 1 is each component of degree n n of compensation electric current of the invention and second of even-order harmonic modulation item relational graph；
Fig. 2 is each component of degree n n of compensation electric current of the invention and the 4th even-order harmonic modulation item relational graph；
Fig. 3 is cos sensitivity analysis figures of second of even-order harmonic modulation item of the invention；
Fig. 4 is sin sensitivity analysis figures of second of even-order harmonic modulation item of the invention；
Specific embodiment
1 the present invention will be further described with reference to the accompanying drawing.
A kind of idle and harmonic compensation method with Local sensitivity analysis function, includes the following steps:
A) pass through formulaAnd formulaEstablish the mathematics of Boost AC chopper
Model, wherein μcIt (t) is the output voltage of Boost AC chopper, icIt (t) is the compensation electric current of Boost AC chopper, μs
It (t) is supply voltage, iL(t) electric current on the capacitor C to flow through Boost AC chopper, d (t) are Boost AC chopper
Two-way switch K1Duty ratio, 1-d (t) be Boost AC chopper two-way switch K2Duty ratio.
B) when duty ratio d (t) is constant constant D0When, pass through formulaAnd formulaThe reactive compensation mathematical model of Boost AC chopping type D-CAP is established, wherein UsFor power grid
Voltage magnitude, ω are fundamental wave frequency, and C is idle supplement capacitance, and t is time variable.Boost AC chopping reactive-load compensator
To the compensation electric current of power grid injection capacitive, it can be regarded as the continuously adjustable vibrating capacitor (D-CAP) of capacitance, due to power grid electricity
Pressure amplitude value Us, fundamental wave frequency ω and reactive compensation capacitor C be steady state value, therefore change duty ratio D0Size i.e. can be changed to
The size of Injection Current in power grid, to realize the idle continuous controllable adjustment of net side.
C) it in order to eliminate the harmonic wave that nonlinear load generates, can be injected into power grid equal in magnitude, square with these harmonic waves
To opposite harmonic current, to realize active power filtering.That single-phase nonlinear load generates is mostly the odd harmonics such as 3,5,7, c)
When even-order harmonic modulation item EHM is added to duty ratio d (t), pass through formula
The even-order harmonic modulation mathematical model for establishing Boost AC chopping type D-CAP, wherein 0≤D0+D2+D4+···+Dn≤
1, DnFor the amplitude of n-th even-order harmonic modulation item,For the initial phase angle of n-th even-order harmonic modulation item.With to duty ratio
For middle addition n-th even-order harmonic modulation item, at this point, duty ratio d (t) are as follows:It flows through
Electric current such as formula on capacitorIt is shown, compensation electricity
Stream such as formulaIt is shown.It knows in duty ratio
When n-th EHM is added, multiple odd harmonic components are contained in the electric current that system is injected to power grid, the harmonic wave electricity generated due to each EHM
Cross-coupling can occur for stream, this undoubtedly increases modulation difficulty.Due to the nonlinear characteristic of Boost alternating-current chopper circuit, moreover,
In electric current calculation formula, duty ratio is located at denominator position and is variable, when multiple EHM are added, to obtain obtaining iC(t)
Fourier analysis formula is more difficult, and the present invention establishes the frequency-domain model of system and utilizes Local sensitivity analysis method, accurately
Ground obtains the corresponding relationship of EHM Yu each odd harmonic.
D) in order to accurately analyze duty ratio and idle and individual harmonic current corresponding relationship, pass through formulaAndEstablish the frequency domain of Boost AC chopping type D-CAP
Model, YRLFor the series admittance matrix of filter inductance L in Boost AC chopper and dead resistance R, ZcIt is cut for Boost exchange
The impedance matrix of capacitor C in wave device, wherein
Y11(n, n)=Y22(n, n)=real (yRL(n))
Y12(n, n)=- Y21(n, n)=imag (yRL(n))
Z11(n, n)=Z22(n, n)=real (Zc(n))
Z12(n, n)=- Z21(n, n)=imag (Zc(n))
yRL(n)=1/ (R+j2 π 50nL), yRL(n) series admittance for being L and R, j is complex unit,
Zc(n)=- j/2 π 50nC), Zc(n) impedance for being C.
E) pass through formulaCalculate voltage on line side μ (ω
T), a in formula0For constant term, anFor Fourier space sine term coefficient, bnFor Fourier space cosine term coefficient, by voltage on line side
ByOne-dimensional matrix expression is carried out, wherein U1...UnRespectively voltage on line side Fourier expansion
The cos item and sin amplitude coefficients of formula, pass through formulaComputing system it is idle
Compensate electric currentE is unit matrix in formula, and T is the corresponding matrix of alternating-current chopper circuit, and T is transposition symbol,For net side electricity
Press the transposition of matrix.By analyzing above it is found that in the case where system determines, matrix UL、YRS、ZCIt can determine, and matrix T exists
The harmonic wave for needing to eliminate also can determine in the case where determining, therefore can obtain compensation current matrix IC, by fundamental wave and each odd times
The cos item of harmonic wave and sin amplitudes are constituted.EHM and each odd harmonic amplitude of system balance electric current have specific to known to
Quantitative relationship.It is mostly odd harmonic since nonlinear load generates harmonic wave, and with the increase of number, harmonic amplitude is smaller, it may be assumed that
Iload((n+2) ω) < Iload(n ω), to obtain maximum adjustable range and 0≤d of duty ratio (t)≤1, Chang Jiang
The D of duty ratio00.5 is taken, the amplitude of each EHM takes the one third of previous item, duty ratio indicated in the matrix form:
D=[D0 D2C D2S D4C D4S...], wherein numerical index indicates that corresponding EHM number, C and S then represent corresponding
Cosine term and sine term.With system shown in table 1, duty ratio is added for 2 EHM, duty ratio d=[0.5 0.05 0.05].
Accurate system balance electric current can be obtained according to formula (13) at this time are as follows:
1 system parameter index of table
The fundamental wave and harmonic amplitude that Fig. 1 and Fig. 2 is the compensation electric current obtained according to frequency-domain model are with D1And D4Variation relation
Curve graph (D at this time0=0.5, D2=0~0.167, D4=0~0.056).It knows with D2Increase, compensates the fundamental wave point of electric current
Amount and each harmonic component increase, and 3 subharmonic amplitudes change greatly, with D2Substantially linear relationship, 7 subharmonic are in D2Value
Amplitude increases rapidly after 0.1, can not ignore in (0.1~0.168) range.5 subharmonic and 9 subharmonic amplitudes are relative to 3
Subharmonic is smaller always.With D4Increase, the harmonic components such as fundametal compoment and 3,7,9,11, which slightly increase, but amplitude is smaller (is less than
1A), 5 subharmonic currents and D4It is in a linear relationship, therefore can be with D4To inhibit 5 subharmonic in power grid.
F) frequency-domain model is compensated the quantitative relationship of electric current each odd harmonic and duty ratio, using local sensitivity point
It analyses each EHM coefficient of technique study and compensates the qualitative relationships of each odd harmonic of electric current.Compensate electric current ICEHM each to duty ratio respectively
Sine and cosine item amplitude derivation, be defined as compensation electric current relative to each EHM of duty ratio cos and sin term coefficient it is sensitive
Degree, according to formula
The Sensitivity Analysis of Boost AC chopping type D-CAP is established, wherein x=[2C, 2S, 4C, 4S ...], C is remaining
String item, S are sine term, DxFor Fourier expansion formula coefficient.Due to 0≤d of duty ratio (t)≤1, row vector d meets:Equally shown in the table 1 for system, duty ratio is added the 2nd time
EHM, and the cos and sin values of EHM are identical (d=[0.5 0.05 0.05]).Fig. 3, Fig. 4 respectively indicate compensation electric current each time
Cos item (D of the harmonic wave relative to the 2nd EHM2C) and sin term coefficient (D2S) susceptibility, the amplitude of column diagram is bigger, shows pair
The harmonic current answered is bigger for the sensitivity of corresponding EHM.The qualitative pass of EHM and harmonic current can be obtained by Fig. 3 and Fig. 4
System.N-th harmonic electric current is most sensitive to the Parameters variation of (n-1)th EHM, therefore in available (n-1)th EHM control compensation electric current
N-th harmonic electric current.And the cos coefficient of n-th harmonic electric current is larger to the cos Coefficient Sensitivity in (n-1)th EHM, n-th
The sin coefficient of subharmonic current is larger to the sin Coefficient Sensitivity in (n-1)th EHM.It is multiple meanwhile when changing a certain EHM
Times harmonic current sensitivity is larger, i.e., cross-coupling can occur between the individual harmonic current in compensation electric current, therefore, change
Any one of duty ratio coefficient can all influence to compensate the multiple harmonic in electric current.Which increase the difficulty of harmonic current control.
When designing the control path of individual harmonic current, the cross-coupling between harmonic current to prevent different numbers can be to facing
Close harmonic current designs different time constants, keeps different control path adjustment speeds different.Therefore, faster path can
To compensate the variation that slower path coupling generates.
By establishing the frequency-domain model of system, the harmonic wave cross-coupling that each even-order harmonic modulation item generates in duty ratio is solved
Problem makes to modulate difficulty significant decrease.Derive the reactive compensation electric current of device and quantifying for individual harmonic current and duty ratio
Relationship proposes Sensitivity Analysis Method, is compensated the generality of each harmonic and each harmonic modulation item of duty ratio in electric current
Corresponding relationship compensates system in real time, quickly and accurately using the closed loop control algorithm based on synchronous reference coordinate theory
Idle and harmonic current.Compared with existing device and its control method, Local sensitivity analysis method proposed by the present invention, more
The good idle and harmonic wave compensation precision limitation problem for solving Boost AC chopping type D-CAP, response speed faster, compensate
It is more accurate.
Claims (1)
1. a kind of idle and harmonic compensation method with Local sensitivity analysis function, which comprises the steps of:
A) pass through formulaAnd formulaEstablish the mathematical modulo of Boost AC chopper
Type, wherein μcIt (t) is the output voltage of Boost AC chopper, icIt (t) is the compensation electric current of Boost AC chopper, μs(t)
For supply voltage, iL(t) electric current on the capacitor C to flow through Boost AC chopper, d (t) are Boost AC chopper
Two-way switch K1Duty ratio, 1-d (t) be Boost AC chopper two-way switch K2Duty ratio；
B) when duty ratio d (t) is constant constant D0When, pass through formulaAnd formulaThe reactive compensation mathematical model of Boost AC chopping type D-CAP is established, wherein UsFor power grid electricity
Pressure amplitude value, ω are fundamental wave frequency, and C is idle supplement capacitance, and t is time variable；
C) when even-order harmonic modulation item EHM is added to duty ratio d (t), pass through formula
,
The even-order harmonic modulation mathematical model for establishing Boost AC chopping type D-CAP, wherein 0≤D0+D2+D4+···+Dn≤
1, DnFor the amplitude of n-th even-order harmonic modulation item,For the initial phase angle of n-th even-order harmonic modulation item；
D) pass through formulaAndBoost exchange is established to cut
The frequency-domain model of wave mode D-CAP, YRLFor the series admittance matrix of filter inductance L in Boost AC chopper and dead resistance R,
ZcFor the impedance matrix of capacitor C in Boost AC chopper, wherein
Y11(n, n)=Y22(n, n)=real (yRL(n))
Y12(n, n)=- Y21(n, n)=imag (yRL(n))
Z11(n, n)=Z22(n, n)=real (Zc(n))
Z12(n, n)=- Z21(n, n)=imag (Zc(n))
yRL(n)=1/ (R+j2 π 50nL), yRL(n) series admittance for being L and R, j is complex unit, Zc(n)=- j/2 π 50nC),
Zc(n) impedance for being C；
E) pass through formulaIt calculates voltage on line side μ (ω t),
A in formula0For constant term, anFor Fourier space sine term coefficient, bnFor Fourier space cosine term coefficient, by voltage on line side byOne-dimensional matrix expression is carried out, wherein U1...UnRespectively voltage on line side Fourier expansion formula
Cos item and sin amplitude coefficients, pass through formulaThe idle benefit of computing system
Repay electric currentE is unit matrix in formula, and T is the corresponding matrix of alternating-current chopper circuit, and T is transposition symbol,For net side electricity
Press the transposition of matrix；
F) according to formula
The Sensitivity Analysis of Boost AC chopping type D-CAP is established, wherein x=[2C, 2S, 4C, 4S], C is cosine
, S is sine term, DxFor Fourier expansion formula coefficient.
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| CN114123205A (en) * | 2021-11-01 | 2022-03-01 | 深圳供电局有限公司 | Harmonic compensation system and phase correction method and device thereof |
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Application publication date: 20181218 |