CN105588982A - Measurement and calculation method of harmonic impedance of power system - Google Patents
Measurement and calculation method of harmonic impedance of power system Download PDFInfo
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Abstract
The invention discloses a measurement and calculation method of harmonic impedance of a power system. A complex least square method is introduced into harmonic impedance calculation of a power system and the phasor real and imaginary parts like a measured voltage and a measured current and the like are used as an organic integrated part to carry out calculation, so that an optimized least square solution is obtained. According to the invention, the data processing process is introduced and original data are screened by using a relative-complex-residual-sorting-based method, so that the influence on a regression coefficient by an abnormal point can be effectively eliminated. On the basis of screening of the original data, circulated regressive calculation is carried out by employing a complex field repeated weighting method, so that the influence on the regression coefficient by the strong influence point can be effectively reduced and the regression robustness is enhanced.
Description
Technical field
The present invention relates to the measurement computational methods of harmonic impedance computational methods design field, particularly a kind of Harmonious Waves in Power Systems impedance.
Background technology
Harmonious Waves in Power Systems impedance is to POWER SYSTEM STATE assessment and to access the design of new power equipment very important, plays a part indispensable in the configuration of the electric devices such as power system modeling, emulation and route protection. Simultaneously, along with the development of domestic and international Power Electronic Technique, formed by electronic power switch in a large number, the consumer with nonlinear characteristic is widely used in the demand fields such as metallurgy, iron and steel, traffic, chemical industry, as electrolysis unit, electric locomotive, rolling mill, coreless induction furnace etc., cause Harmonic in Power System problem day by day serious, to harmonic wave relevant issues, if the research of harmonic trend calculating, harmonic wave divisions of responsibility, harmonic emission level, harmonic source identification etc. is the problem that power industry is paid close attention to always. And the Measurement accuracy of system harmonic impedance is research harmonic wave relevant issues basis.
At present, harmonic impedance measurement method of estimation is mainly divided into " intervention formula " and " non-intervention formula " two large classes. " intervention formula " method is mainly to produce disturbance by artificial mode, as to system harmonic electric current or a harmonic current, or carries out the measurement of system side harmonic impedance by a certain branch road of the system of cut-offfing. This disturbance may normally move generation adverse influence to power system, and therefore these class methods can not be used widely. " non-intervention formula " method is to utilize the disturbance of system or harmonic-producing load itself, carries out correlation computations by measurable parameter, can not have influence on safety, the stable operation of system, thereby becomes the main stream approach of current relevant subject study. Typically " non-intervention formula " method has undulate quantity method and linear regression method. Linear regression method is occupying critical role aspect harmonic emission level assessment, is the core of " non-intervention formula " method. Traditional linear regression method comprises binary regression method, robustness regression method and PLS, these methods all do not have the preprocessing process of data, its essence is all that phasor real part, imaginary component are isolated, and utilizes least square method to carry out respectively solving of regression coefficient in real number field. This processing method has been ignored phasor has the entirety of specific physical significance to exist as one, and its solution procedure is not simple addition and the combination of real part, imaginary part result.
Summary of the invention
The object of the invention is to provide a kind of measurement computational methods of Harmonious Waves in Power Systems impedance.
For achieving the above object, the present invention implements according to following technical scheme:
Measurement computational methods for Harmonious Waves in Power Systems impedance, comprise the following steps:
Step 1: gather the busbar voltage instantaneous value of points of common connection and the current instantaneous value of user's injected system, obtain harmonic voltage and harmonic wave electric current phasor data sequence by Fourier transformation, and set up the multiple regression equation of harmonic voltage and harmonic wave electric current phasor;
Step 2: the harmonic voltage that step 1 is obtained and harmonic wave electric current phasor data sequence are carried out Preliminary screening, gets rid of the impact of abnormity point on regression coefficient;
Step 3: on Preliminary screening basis, solving system harmonic impedance regression coefficient; Obtain optimum tax power regression coefficient, and obtain the value of harmonic impedance.
Further, the harmonic voltage that step 1 is obtained and harmonic wave electric current phasor data sequence are carried out Preliminary screening, and described Preliminary screening adopts the method based on residual error sorts relatively again, the multiple residual error column vector of definition，e=[e1,e2,e3…en] ＇, wherein，Refer to not pass through the estimated value of process of data preprocessing regression parameter, Y is the column vector of harmonic voltage phasor data sequence composition, and X is the augmented matrix of harmonic current phasor data sequence composition,For the associate matrix of X; Definition is residual error relatively again，（i=1,2，…，n），ejBe i multiple residual values, YjBe i harmonic voltage phasor, the number that n is column vector; By eriAscending sequence, obtains residual sequence { e relatively againri, delete in the relatively multiple irregular e of afterbody 5%riCorresponding harmonic voltage and harmonic current data, and remaining harmonic voltage and harmonic wave electric current phasor are designated as to Y95%、X95%。
Concrete, described solving system harmonic impedance regression coefficient, adopts Ramsay influence function to compose the robustness regression method of the multiple least square of weighting repeatedly of power; Concrete steps are:
A) select remaining harmonic voltage X95%With harmonic current Y95%, according to formula, calculate regression parameter；For X95%Associate matrix;
B) by formula, calculate multiple residual error f=[f1,f2,f3,…,fm] ＇, i.e. f={fj}，（i=1,2,3…，m，m=0.95n）；
C) by formulaCalculate Ramsay influence function independent variable, wherein,=1.5med（）；med（) beMedian; By formula, calculate the tax weight function based on Ramsay influence function, wherein a is the adjustment factor of adjusting Ramsay influence function shape;
D) get tax weight functionValue=(i=1,2,3 ..., m), note weight diagonal matrix is W=diag(），（i=1,2,3…，m，m=0.95）；
E) by the multiple least-squares calculation formula of weighting:; Calculate the regression parameter of the power of tax,；
F) calculate, calculate the difference of adjacent twice regression parameter; Wherein j representative returns computation cycles number of times, and its initial value is 0, in the time of j=0,Be the regression parameter that step a obtains, andIt is the regression parameter that step e obtains;WithIt is all plural number;
G) calculateWithMould valueWith, and judge max{，}<Whether set up, if set up, perform step h; Otherwise, order=, return to step b;
H) byCan obtain harmonic impedance。
Compared with prior art, beneficial effect of the present invention:
To answer least square method and introduce Calculation of Harmonic Impedances of Power Systems problem, and the phasor real parts such as measuring voltage, measurement electric current and imaginary part be calculated as an organic whole, thereby obtain optimum least square solution. Meanwhile, the present invention introduces data handling procedure, adopts the method based on residual error sequence relatively again to screen original harmonic voltage current data, effectively gets rid of the impact of abnormity point on regression coefficient. On the basis of this original harmonic voltage and harmonic current data screening, adopt complex field repeatedly the method for weighting circulate to return and calculates, effectively reduce the strong impact of point on regression coefficient that affect, increase the robustness of recurrence.
Brief description of the drawings
Fig. 1 is system and user's equivalent circuit schematic diagram of the measurement computational methods of a kind of Harmonious Waves in Power Systems impedance provided by the invention;
Fig. 2 is the Calculation of Harmonic Impedances of Power Systems flow chart of the measurement computational methods of a kind of Harmonious Waves in Power Systems impedance provided by the invention;
Fig. 3 is the IEEE14 node standard testing system of the measurement computational methods of a kind of Harmonious Waves in Power Systems impedance provided by the invention;
Fig. 4 is the 5 subwave electric currents that the harmonic source HL1 of the measurement computational methods of a kind of Harmonious Waves in Power Systems impedance provided by the invention injects; Wherein, a is 5 subharmonic current real parts; B is 5 primary current imaginary parts;
Fig. 5 is bus 11 place's 5 subharmonic voltage virtual value curves of the measurement computational methods of a kind of Harmonious Waves in Power Systems impedance provided by the invention;
Fig. 6 is the 5 subharmonic current virtual value curves that the harmonic source HL1 of the measurement computational methods of a kind of Harmonious Waves in Power Systems impedance provided by the invention injects bus 11.
Detailed description of the invention
Below in conjunction with specific embodiment, the invention will be further described, is used for explaining the present invention in illustrative examples and the explanation of this invention, but not as a limitation of the invention.
The measurement computational methods of a kind of Harmonious Waves in Power Systems impedance as shown in Figure 1 and Figure 2, comprise the following steps:
Step 1: gather the busbar voltage instantaneous value of points of common connection and the current instantaneous value of user's injected system, obtain harmonic voltage and harmonic wave electric current phasor data sequence by Fourier transformation, and set up the multiple regression equation of harmonic voltage and harmonic wave electric current phasor;
Step 2: the harmonic voltage that step 1 is obtained and harmonic wave electric current phasor data sequence are carried out Preliminary screening, gets rid of the impact of abnormity point on regression coefficient;
Step 3: on Preliminary screening basis, solving system harmonic impedance regression coefficient; Obtain optimum tax power regression coefficient, and obtain the value of harmonic impedance.
The harmonic voltage that step 1 is obtained and harmonic wave electric current phasor data sequence are carried out Preliminary screening, and described Preliminary screening adopts the method based on residual error sorts relatively again, the multiple residual error column vector of definition，e=[e1,e2,e3…en] ＇, wherein，Refer to not pass through the estimated value of process of data preprocessing regression parameter, Y is the column vector of harmonic voltage phasor data sequence composition, and X is the augmented matrix of harmonic current phasor data sequence composition,For the associate matrix of X; Definition is residual error relatively again，（i=1,2，…，n），ejBe i multiple residual values, YjBe i harmonic voltage phasor, the number that n is column vector; By eriAscending sequence, obtains residual sequence { e relatively againri, delete in the relatively multiple irregular e of afterbody 5%riCorresponding harmonic voltage and harmonic current data, and remaining harmonic voltage and harmonic wave electric current phasor are designated as to Y95%、X95%。
Solving system harmonic impedance regression coefficient, adopts Ramsay influence function to compose the robustness regression method of the multiple least square of weighting repeatedly of power; Concrete steps are:
A) select remaining harmonic voltage X95%With harmonic current Y95%, according to formula, calculate regression parameter；For X95%Associate matrix;
B) by formula, calculate multiple residual error f=[f1,f2,f3,…,fm] ＇, i.e. f={fj}，（i=1,2,3…，m，m=0.95n）；
C) by formulaCalculate Ramsay influence function independent variable, wherein,=1.5med（）；med（) beMedian; By formula, calculate the tax weight function based on Ramsay influence function, wherein a is the adjustment factor of adjusting Ramsay influence function shape;
D) get tax weight functionValue=(i=1,2,3 ..., m), note weight diagonal matrix is W=diag(），（i=1,2,3…，m，m=0.95）；
E) by the multiple least-squares calculation formula of weighting:; Calculate the regression parameter of the power of tax,；
F) calculate, calculate the difference of adjacent twice regression parameter; Wherein j representative returns computation cycles number of times, and its initial value is 0, in the time of j=0,Be the regression parameter that step a obtains, andIt is the regression parameter that step e obtains;WithIt is all plural number;
G) calculateWithMould valueWith, and judge max{，}<Whether set up, if set up, perform step h; Otherwise, order=, return to step b;
H) byCan obtain harmonic impedance。
Fig. 3 is the IEEE14 node standard testing system of the measurement computational methods of a kind of Harmonious Waves in Power Systems impedance provided by the invention. In Fig. 3, G is generator, and C is phase modifier,Be two-winding transformer, utilize IEEE14 node standard testing system, algorithm proposed by the invention is carried out to simulating, verifying, this test macro is made up of 2 generators, 3 synchronous capacitors, 14 buses, 15 transmission lines of electricity and 3 transformers. Select bus 11 for paying close attention to bus, HL1 and L2 are connect load by bus 11, and wherein HL1 is nonlinear-load, represents Harmonics source customer, and L2 is linear load. Taking bus 11 as public junction bus, load HL1 is considered as separately to user's side, the network remainder of removing load HL1 is considered as to the system side of this simulation example, the system harmonics of the harmonic wave producing while normally work using system side during as problem analysis, this is identical with equivalent circuit shown in Fig. 1. The present invention carries out simulating, verifying as an example of 5 subharmonic example.
One minute 1 sample point in the 5 subharmonic current curves of harmonic source HL1, one day corresponding 1440 point, as shown in Figure 4. Measure bus 11 place's harmonic voltage virtual value curves and harmonic source HL1 inject bus 11 harmonic current virtual value curves respectively as 5 and Fig. 6 as shown in.
Adopt that the present invention proposes based on sane least square method computing system equivalent harmonic wave impedance again, result of calculation is as shown in the table with actual value contrast, symbol "-" represents that this value does not need calculating.
The contrast of table 1 system equivalent harmonic impedance result of calculation
As can be seen from Table 1, steadily and surely least square method can accurate Calculation system equivalent harmonic impedance again.
The emulation experiment of above-mentioned enforcement shows, original harmonic voltage based on residual error sequence relatively again and harmonic current data sequence screening and complex field be the sane least square method again of weighting repeatedly, can effectively eliminate or reduce abnormity point and the impact of strong impact point on regression coefficient, improve system harmonic impedance solving precision.
Technical scheme of the present invention is not limited to the restriction of above-mentioned specific embodiment, and the technology distortion that every technical scheme according to the present invention is made, within all falling into protection scope of the present invention.
Claims (3)
1. measurement computational methods for Harmonious Waves in Power Systems impedance, is characterized in that, comprise the following steps:
Step 1: gather the busbar voltage instantaneous value of points of common connection and the current instantaneous value of user's injected system, obtain harmonic voltage and harmonic wave electric current phasor data sequence by Fourier transformation, and set up the multiple regression equation of harmonic voltage and harmonic wave electric current phasor;
Step 2: the harmonic voltage that step 1 is obtained and harmonic wave electric current phasor data sequence are carried out Preliminary screening, gets rid of the impact of abnormity point on regression coefficient;
Step 3: on Preliminary screening basis, solving system harmonic impedance regression coefficient; Obtain optimum tax power regression coefficient, and obtain the value of harmonic impedance.
2. Calculation of Harmonic Impedances of Power Systems method according to claim 1, it is characterized in that, the harmonic voltage that step 1 is obtained and harmonic wave electric current phasor data sequence are carried out Preliminary screening, and described Preliminary screening adopts the method based on residual error sorts relatively again, the multiple residual error column vector of definition，e=[e1,e2,e3…en] ＇, wherein，Refer to not pass through the estimated value of process of data preprocessing regression parameter, Y is the column vector of harmonic voltage phasor data sequence composition, and X is the augmented matrix of harmonic current phasor data sequence composition,For the associate matrix of X; Definition is residual error relatively again，（i=1,2，…，n），ejBe i multiple residual values, YjBe i harmonic voltage phasor, the number that n is column vector; By eriAscending sequence, obtains residual sequence { e relatively againri, delete in the relatively multiple irregular e of afterbody 5%riCorresponding harmonic voltage and harmonic current data, and remaining harmonic voltage and harmonic wave electric current phasor are designated as to Y95%、X95%。
3. the measurement computational methods of Harmonious Waves in Power Systems impedance according to claim 1, is characterized in that, described solving system harmonic impedance regression coefficient adopts Ramsay influence function to compose the robustness regression method of the multiple least square of weighting repeatedly of power; Concrete steps are:
A) select remaining harmonic voltage X95%With harmonic current Y95%, according to formula, calculate regression parameter；For X95%Associate matrix;
B) by formula, calculate multiple residual error f=[f1,f2,f3,…,fm] ＇, i.e. f={fj}，（i=1,2,3…，m，m=0.95n）；
C) by formulaCalculate Ramsay influence function independent variable, wherein,=1.5med（）；med（) beMedian; By formula, calculate the tax weight function based on Ramsay influence function, wherein a is the adjustment factor of adjusting Ramsay influence function shape;
D) get tax weight functionValue=(i=1,2,3 ..., m), note weight diagonal matrix is W=diag(），（i=1,2,3…，m，m=0.95）；
E) by the multiple least-squares calculation formula of weighting:; Calculate the regression parameter of the power of tax,；
F) calculate, calculate the difference of adjacent twice regression parameter; Wherein j representative returns computation cycles number of times, and its initial value is 0, in the time of j=0,Be the regression parameter that step a obtains, andIt is the regression parameter that step e obtains;WithIt is all plural number;
G) calculateWithMould valueWith, and judge max{，}<Whether set up, if set up, perform step h; Otherwise, order=, return to step b;
H) byCan obtain harmonic impedance。
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Application publication date: 20160518 |