CN103257298B - Based on the combining inverter island detection method of parameter adaptive Sandia frequency deviation method - Google Patents

Abstract

The invention discloses a kind of based on parameter adaptive Sandia frequency deviation method (Sandia Frequency Shift, SFS) combining inverter island detection method, this method utilizes the phase angle between digital correlation principle detection point of common coupling voltage and inverter output current, makes the initial copped wave coefficient cf in SFS method according to the phase angle detected ₀automatically adjust with inverter frequency metrical error, the positive feedback gain K in SFS method can be made to make Adaptive Modulation with the difference of local loaded quality factor simultaneously.The present invention had both overcome the shortcoming that dilution effect that traditional SFS method produces because of frequency detecting error under multi-inverter grid-connected conditions can cause islanding detect failure; solve again local loaded quality factor very high time islanding detect difficulty even cannot measure the problem of isolated island; under the condition ensureing distributed generation system power supply quality, complete islanding detect and island protect fast.

Description

Based on the combining inverter island detection method of parameter adaptive Sandia frequency deviation method

Technical field

The invention belongs to the islanding detect technical field of distributed grid-connected electricity generation system, be specifically related to a kind of combining inverter island detection method based on parameter adaptive Sandia frequency deviation method.

Background technology

Along with the aggravation of energy crisis and the enhancing of environmental consciousness, the distributed generation system based on the regenerative resource such as sun power, wind energy is subject to people and more and more pays close attention to.These regenerative resources, are first converted to electric energy usually, then are transported to electrical network by combining inverter.Island effect is a kind of phenomenon that distributed grid-connected electricity generation system may occur.So-called island phenomenon, refer to electrical network for some reason interruption of power supply time inverter still to electrical grid transmission electric energy, and local load forms a uncontrollable self-energizing isolated island of public electric wire net system.The generation of isolated island can threaten the safety of electrical network maintenance personal, affects the protection switch operation program of distribution system, may cause damage when reclosing to consumer.So islanding detect is the prerequisite function of combining inverter.

Distributed grid-connected electricity generation system island detection method based on combining inverter is mainly divided into passive type and active two classes.Passive type islanding detect method comprised/under-voltage (OVR/UVR) Protection Code, mistake/under-frequency (OFR/UFR) Protection Code, voltage harmonic detection method, voltage-phase sudden change method etc.Active detecting method comprises power disturbance method, frequency disturbance method, phase shift method etc.Passive type detection method is easy to realize, the quality of power supply of system and stability are not all affected, but the threshold value of these class methods is more difficult to be determined, and whether the output power of inverter is mated with the power of load have strict demand, there is larger check frequency (Non-Detection Zone NDZ), detection time is longer.Active detection method by adding corresponding disturbance in inverter control signal, the amplitude of the rear voltage of isolated island generation or frequency is made to shift out threshold range fast, thus overcome the shortcoming of passive type method, reduce islanding detect blind area, accelerate the islanding detect time.

In active alone island detection technique, Sandia frequency deviation method (Sandia Frequency Shift, SFS) because of simple to operate, check frequency is little is widely applied.But this method is under the condition that multiple stage inverter is simultaneously grid-connected, dilution effect phenomenon can be produced because inverter there is frequency detecting error, finally cause islanding detect failure.In addition, be ensure distributed generation system power supply quality and system stability, the positive feedback gain K in Sandia frequency deviation method can not be too large, is 2.5 to adjust usually by local loaded quality factor.So after local loaded quality factor is more than 2.5, inverter usually can examine the generation not measuring isolated island, makes island state sustainable existence.

Summary of the invention

The present invention seeks to the weak point existed for traditional Sandia frequency deviation method, a kind of combining inverter island detection method based on parameter adaptive Sandia frequency deviation method is provided, the shortcoming that dilution effect that traditional Sandia frequency deviation method produces because of frequency detecting error under multi-inverter grid-connected conditions can cause islanding detect failure can be overcome, solve again local loaded quality factor very high time islanding detect difficulty even cannot measure the problem of isolated island, under the prerequisite not affecting distributed generation system power supply quality, complete islanding detect and island protect fast, and there is the little advantage in islanding detect blind area.

For achieving the above object, present invention employs following technical scheme: based on the combining inverter island detection method of parameter adaptive Sandia frequency deviation method.This technical scheme is carried out according to the following procedure:

(1) magnitude of voltage and the inverter output current value that distributed grid-connected electricity generation system is positioned at point of common coupling place is gathered;

(2) the phase angle φ between magnitude of voltage and inverter output current value utilizing digital correlation principle to calculate to be collected by (1), phase angle calculating formula is:

$\mathrm{\φ}=\±\arcsin \sqrt{\frac{2}{N}\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}\{R_{\mathrm{iu}}\left(m\right)-R_{\mathrm{ui}}\left(m\right)-\frac{1}{N}\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}[R_{\mathrm{iu}}\left(m\right)-R_{\mathrm{ui}}\left(m\right)]{\}}^2}$

In formula, φ is the phase angle between the voltage at point of common coupling place and inverter output current, and N is sampling number, R _iu(m) and R _uicross correlation function between m voltage that () is point of common coupling place and inverter output current signal, m is the independent variable in cross correlation function.

(3) the phase angle φ drawn according to step (2) calculates the frequency detecting error f of inverter _e, and according to the concrete condition of frequency detecting error to the initial copped wave coefficient cf in Sandia frequency deviation method ₀carry out self-adaptative adjustment.Initial copped wave coefficient cf ₀adjustment type be:

${\mathrm{cf}}_0={\mathrm{cf}}_0^{,}+K\·f_e$

In formula, cf ₀the initial copped wave coefficient after adjustment, be the initial copped wave coefficient of initial setting, K is positive feedback gain, f _eit is frequency detecting error.

(4) according to the phase angle φ that step (2) draws, under the local loading condition of different quality factor, make self-adaptative adjustment to the positive feedback gain K in Sandia frequency deviation method, the calculating formula that positive feedback gain K adjusts is:

$K>\frac{2\mathrm{\φ}}{\mathrm{\π}(f_g-f)}$

In formula, K is positive feedback gain, and φ is the phase angle between the voltage at point of common coupling place and inverter output current, f _gbe line voltage rated frequency, f is system operating frequency.

(5) according to the initial copped wave coefficient cf that step (3), (4) obtain ₀and positive feedback gain K, the shift frequency initial phase angle obtaining the inverter output current Setting signal needed for islanding detect is:

${\mathrm{\θ}}_{\mathrm{SFS}}=\frac{\mathrm{\π}}{2}\·\mathrm{cf}=\frac{\mathrm{\π}}{2}[{\mathrm{cf}}_0+K(f-f_g)]$

In formula, θ _sFSbe the shift frequency initial phase angle of inverter output current Setting signal, cf is copped wave coefficient, cf ₀be the initial copped wave coefficient after adjustment, K is the positive feedback gain after adjustment.

Compared with traditional Sandia frequency deviation method, beneficial effect of the present invention is embodied in:

1, traditional Sandia frequency deviation method is due to its initial copped wave coefficient cf ₀for fixed value, so under multi-inverter grid-connected conditions, the shift frequency disturbance that each inverter causes it to produce because of frequency detecting error cancels each other, and namely produces so-called dilution effect, can cause islanding detect failure.The inventive method according to the concrete condition of frequency detecting error to initial copped wave coefficient cf ₀automatically adjust, make every platform inverter can the disturbance ability that upwards offsets of sustain pulse frequency after suspension, overcome the adverse effect of dilution effect to islanding detect.

2, traditional Sandia frequency deviation method due to its positive feedback gain K be fixed value, when local loaded quality factor is very high after suspension frequency shift (FS) difficulty, usually because of frequency offset cannot exceed islanding detect setting threshold value cause islanding detect failure.The inventive method aligns feedback gain K according to the difference of local loaded quality factor and makes self-adaptative adjustment, namely during local loaded quality factor height, positive feedback gain K also can improve accordingly, thus the threshold value that guarantee frequency shift (FS) can exceed setting successfully detects isolated island.

3, the present invention can be used for the combining inverter comprising wind-power electricity generation, solar electrical energy generation, fuel cell distributed energy unit, comprises and is applied to single-phase distributed grid-connected electricity generation system, three-phase separate cloth grid-connected system, have wide range of applications.Initial copped wave coefficient cf ₀self-adaptative adjustment be mainly used in the grid-connected distributed grid-connected electricity generation system of multi-inverter.The self-adaptative adjustment of positive feedback gain K, then be both applicable to the distributed grid-connected electricity generation system that multi-inverter is grid-connected, is also applicable to the distributed grid-connected electricity generation system that single inverter is grid-connected.

Accompanying drawing illustrates:

Fig. 1 is the combining inverter island detection method algorithm flow that the present invention is based on parameter adaptive Sandia frequency deviation method;

Fig. 2 is the combining inverter island detection method implementing circuit that the present invention is based on parameter adaptive Sandia frequency deviation method;

Fig. 3 is local loaded quality factor Q _fthe test pattern of positive feedback gain K in copped wave coefficient when=1;

Fig. 4 is local loaded quality factor Q _fthe test pattern of positive feedback gain K in copped wave coefficient when=4.5;

Fig. 5 for adopt of the present invention based on parameter adaptive Sandia frequency deviation method at Q _fsimulation waveform when=4.5;

Fig. 6 is for adopting traditional Sandia frequency deviation method at Q _fsimulation waveform when=4.5;

Fig. 7 is initial copped wave coefficient cf ₀the test pattern of adjustment;

Fig. 8 for adopt when there is dilution effect of the present invention based on parameter adaptive Sandia frequency deviation method at Q _fsimulation waveform when=4.5;

Fig. 9 is for adopting traditional Sandia frequency deviation method at Q when there is dilution effect _fsimulation waveform when=1.

Embodiment

See Fig. 1, be carry out according to the following procedure based on the combining inverter island detection method of parameter adaptive Sandia frequency deviation method in the present embodiment:

Step 1, collection distributed grid-connected electricity generation system are positioned at magnitude of voltage and the inverter output current value signal at point of common coupling place;

Step 2, the phase angle between voltage and inverter output current signal utilizing digital correlation principle to calculate to be collected by step 1, concrete grammar is as follows:

First be normalized the voltage gathered and current signal, two signal expressions obtaining the computing of actual participation cross correlation function are:

u＝u ₁+u _h+u _e＝sin(ωt+φ _u)+u _h+u _e

i＝i ₁+i _h+i _e＝sin(ωt+φ _i)+i _h+i _e

In formula, u, i are the above-mentioned voltage and current signal that collect, u ₁=sin (ω t+ φ _u), i ₁=sin (ω t+ φ _i) be useful component after gathered these two kinds of signal normalization process, u _h, i _hfor the harmonic component of above-mentioned voltage and current signal, u _e, i _efor voltage and current signal carry out quantization error when A/D converts.The discrete expression of above-mentioned two kinds of signal cross correlation functions is:

$R_{\mathrm{ui}}\left(m\right)=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}u\left(n\right)i(n+m)=\frac{1}{2}\cos (2\mathrm{\π}\frac{m}{N}+\mathrm{\φ})+R_1$

$R_{\mathrm{iu}}\left(m\right)=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}i\left(n\right)u(n+m)=\frac{1}{2}\cos (2\mathrm{\π}\frac{m}{N}-\mathrm{\φ})+R_2$

In formula, φ is the phase angle (φ=φ between the voltage at point of common coupling place and inverter output current _u-φ _i), N is sampling number, R _iu(m) and R _uicross correlation function between m voltage that () is point of common coupling place and inverter output current signal, R ₁, R ₂for the cross correlation function between signal collected useful component, harmonic component, quantization error component.

According to the related properties of cross correlation function and the relevant calculating formulas of trigonometric function, the expression formula that can obtain calculating phase angle between above-mentioned voltage and current signal is:

$\mathrm{\φ}=\±\arcsin \sqrt{\frac{2}{N}\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}\{R_{\mathrm{iu}}\left(m\right)-R_{\mathrm{ui}}\left(m\right)-\frac{1}{N}\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}[R_{\mathrm{iu}}\left(m\right)-R_{\mathrm{ui}}\left(m\right)]{\}}^2}$

Step 3, the phase angle drawn according to step 2, calculate the frequency detecting error of inverter, and according to the concrete condition of frequency detecting error to the initial copped wave coefficient cf in SFS algorithm ₀automatically adjust.To contain the simultaneously grid-connected distributed generation system of 2 inverters shown in Fig. 2, cf is described ₀self-adjusting method.

If line voltage rated frequency f _g=50Hz, assuming that inverter 1 does not have frequency detecting error, there is the negative frequency detecting error of 0.2Hz in inverter 2, then system with the stable operation of line voltage rated frequency and net state, the electric voltage frequency at the point of common coupling place that two inverters detect is respectively: f ₁=f _g=50Hz, f ₂=f _g-0.2=49.8Hz.Assuming that two inverter initial copped wave coefficient cf ₀all be set as 0.01 at first, positive feedback gain K is all by local loaded quality factor Q _f=2.5 adjust, K=0.07 after adjusting, then inverter 1 is respectively with the shift frequency phase angle of inverter 2 output current:

From result of calculation, inverter 1 output current phase place is ahead of point of common coupling voltage-phase, has upwards shift frequency effect after suspension, and inverter 2 output current phase place then lags behind point of common coupling voltage-phase, has downward shift frequency effect after suspension.So the disturbance of two inverter shift frequencies is cancelled out each other, and namely there is dilution effect phenomenon, islanding detect failure can be caused.For this reason, can adjust having the initial copped wave coefficient of the inverter 2 of frequency detecting error.

First the frequency detecting error f of inverter is calculated by step 2 gained phase angle φ _e:

$f_e=\frac{\mathrm{\φ}-{\mathrm{\φ}}_0}{K}\·\frac{1}{90}$

In formula, φ is the phase angle between the magnitude of voltage at point of common coupling place and inverter output current value, φ ₀be the phase angle between the magnitude of voltage at point of common coupling place when not having frequency detecting error and inverter output current value, K is positive feedback gain.

Again according to frequency detecting error f _ecalculate the initial copped wave coefficient cf after adjustment ₀:

${\mathrm{cf}}_0={\mathrm{cf}}_0^{,}+K\·f_e$

In formula, cf ₀the initial copped wave coefficient after adjustment, be the initial copped wave coefficient of initial setting, K is positive feedback gain, f _eit is frequency detecting error.

In this example, get 0.01, K and get setting valve 0.07 in advance, due to φ ₀with the shift frequency phase angle theta of inverter output current when not having a frequency detecting error _sFSa pair opposite number, so calculate φ ₀=-0.9 °.In inverter 2, the measured value of phase angle φ is 0.36 °, then f _ecan calculate is 0.2Hz, calculate thus adjustment after initial copped wave coefficient be: cf ₀=0.01+0.07 × 0.2=0.024.After adjustment, the shift frequency phase angle of inverter 2 output current is:

Result of calculation shows, inverter 2 is at initial copped wave coefficient cf ₀after automatic adjustment, regaining upwards shift frequency ability, islanding detect failure after suspension, can not be caused because of cancelling out each other with the disturbance of inverter 1 shift frequency.

For preventing cf ₀frequent adjustment adverse effect is caused to system stability, in the present invention, every 10 voltage cycles are to cf ₀adjustment once, because frequency detecting error is a metastable value, adjusts rear cf ₀substantially remain unchanged.In addition, for inverter after guarantee suspension can produce initial shift frequency disturbance, cf ₀minimum value be set as 0.01.

Step 4, the phase angle drawn according to step 2, under the local loading condition of different quality factor, make self-adaptative adjustment to the positive feedback gain K in SFS algorithm, and the calculating formula that positive feedback gain K adjusts is derived as follows:

Eliminate the check frequency under any loading condition, inequality below must be met:

$\frac{{\mathrm{d\&phi;}}_{\mathrm{load}}}{\mathrm{df}}{|}_{f_0}<\frac{{\mathrm{d\&theta;}}_{\mathrm{SFS}}}{\mathrm{df}}{|}_{f_0}---\left(1\right)$

Due to inverter shift frequency phase angle theta _sFSgeneral type is:

${\mathrm{\&theta;}}_{\mathrm{SFS}}=\frac{\mathrm{\&pi;}}{2}\&CenterDot;\mathrm{cf}=\frac{\mathrm{\&pi;}}{2}\&lsqb;c{f}_0+K(f-f_g)]---\left(2\right)$

Consider that inverter generally adopts the current control mode of unity power factor, the phase angle φ between suspension moment point of common coupling place voltage and inverter output current is a very little value, therefore meets tan ^-1(φ) ≈ φ, again because local load is RLC shunt load, after can obtaining suspension, following formula is set up:

$\mathrm{\&phi;}\&ap;Q_f(\frac{f_0}{f}-\frac{f}{f_0})---\left(3\right)$

In formula, f ₀local load resonant frequency, Q _fit is local loaded quality factor.

(1), (2), (3) Shi Ke get above comprehensive:

$K>\frac{{4Q}_f}{{\mathrm{\&pi;f}}_0}---\left(4\right)$

(3) formula variation is considered suspension moment f ≈ f ₀, then have

$Q_f\&ap;\frac{0.5f_0}{f_0-f}\mathrm{\&phi;}---\left(5\right)$

(4), (5) two formulas and local load resonant frequency f according to above ₀with line voltage rated frequency f _gapproximately equal, can obtain

$K>\frac{2\mathrm{\&phi;}}{\mathrm{\&pi;}(f_g-f)}---\left(6\right)$

(6) formula is the calculating formula that positive feedback gain K adjusts.According to the phase angle φ detected in real time and f value, by this formula to the adjustment automatically of K value, the islanding detect failure that the quality factor of local load height causes can be avoided.

By (6) formula, when distributed generation system be incorporated into the power networks and frequency stabilization at f _gtime neighbouring, K value will be very large, and this will cause adverse effect to the quality of power supply, and be unfavorable for system stability.So in the present invention, K value Adjustment principle is: first by loaded quality factor Q _f=2.5 whole defining K values, when frequency shift (FS) is no more than 0.1Hz, K value is the same with traditional SFS algorithm to immobilize; Frequency shift (FS) more than after 0.1Hz, then adjusts K value by (6) formula, to meet the needs of the local load islanding detect of high quality factor.

Step 5, the initial copped wave coefficient cf obtained according to step 3 and step 4 ₀and positive feedback gain K, the shift frequency phase angle obtaining the inverter output current Setting signal needed for islanding detect is:

${\mathrm{\&theta;}}_{\mathrm{SFS}}=\frac{\mathrm{\&pi;}}{2}\&CenterDot;\mathrm{cf}=\frac{\mathrm{\&pi;}}{2}[{\mathrm{cf}}_0+K(f-f_g)]$

Using the initial phase angle of this shift frequency phase angle as combining inverter output current Setting signal, thus shift frequency disturbance can be implemented to the frequency of point of common coupling place voltage after suspension.

In the present embodiment, method is adapted to distributed grid-connected electricity generation system is single-phase distributed grid-connected electricity generation system, three-phase separate cloth grid-connected system, is below the instantiation carrying out islanding detect for the distributed grid-connected electricity generation system containing 2 single-phase inverters shown in Fig. 2:

This example relevant parameters arranges as follows: line voltage 220V/50Hz; Inverter direct-flow side busbar voltage is 600V; Two inverters all adopt the current control mode of unity power factor, and inverter output current amplitude is 20A, and inverter output end filter inductance is 5mH, resistance 0.4 Ω; Local load is RLC load in parallel, its rated voltage 220V, rated frequency 50Hz, the active-power P that load absorbs _l=4kw, i.e. its resistive component R _l=12.1 Ω.

Fig. 3, Fig. 4 are local loaded quality factor Q respectively _f=1 and Q _fthe test pattern of positive feedback gain K in copped wave coefficient when=4.5, as seen from Figure 3, before suspension, K value immobilizes, and its size presses Q by (6) formula _f=2.5 adjust is 0.07.Disconnect at 0.2 second moment main electrical network, due to the saltus step of suspension instantaneous phase difference, all there is of short duration increase, subsequently because of Q in the K value of two inverters _fbe less than 2.5, the K value of two inverters all drops to less than 0.07.And Fig. 4 is because Q _fexceed 2.5, so K value is all obviously greater than 0.07 after suspension.Fig. 3, Fig. 4 illustrate that K value can along with local loaded quality factor Q after suspension _fvary in size and automatically change, thus can Q be detected _fthe generation of isolated island in > 2.5 situation.The minimum value that can set K in practical application is 0.07, can detect isolated island as early as possible like this after suspension.

Fig. 5 be adopt of the present invention based on parameter adaptive Sandia frequency deviation method at Q _fthe change waveform of power network current, two inverter output current and point of common coupling electric voltage frequency before and after the suspension recorded when=4.5.After there is suspension at 0.1 second; electric voltage frequency moves on continuing; overfrequency setting threshold value 50.5Hz after about 0.37 second, successfully detect isolated island and implement island protect, the islanding detect time meets the time requirement detecting isolated island within 2 seconds that GB GB/T19939-2005 propose.

In contrast, Fig. 6 gives and adopts traditional SFS method at Q _fthe waveform correlation detected when=4.5.As seen from the figure because positive feedback gain K keeps 0.07 constant, fail automatically to adjust with loading condition, the downward shift frequency effect of high quality factor load impedance angle seriously constrains SFS method shift frequency phase angle theta _sFSthe effect of upwards shift frequency, cause frequency upper shift in 2 seconds to fail to exceed detection threshold, islanding detect failure.

Fig. 7 is initial copped wave coefficient cf ₀the test pattern of adjustment.Cf in emulation ₀first be set as 0.01, like this according to previous step 3, the shift frequency phase angle not having combining inverter during frequency detecting error is 0.9 °, the voltage delay namely detected in the phase angle of electric current be-0.9 °; If inverter exists the negative frequency detecting error of 0.2Hz, can calculate the phase angle that voltage is ahead of electric current is-(0.01-0.07 × 0.2) × 90=0.36 °.As seen from Figure 7, inverter 1 does not have frequency of occurrences metrical error, and the phase differential of its voltage and electric current remains-0.9 °, so its cf ₀value does not adjust; And inverter 2 exists the negative frequency detecting error of 0.2Hz, so the phase angle of its voltage and electric current starts to be 0.36 °, after 0.2 second, inverter detects the numerical value of frequency detecting error, by cf ₀automatically be adjusted to 0.024, make the phase angle of its voltage and electric current drop to about-0.9 °, thus the upwards shift frequency ability of inverter after maintaining suspension.In addition, the cf of inverter 2 ₀after adjustment, its output current wave Dead Time is identical with the electric current of inverter 1, so cf ₀adjustment can not impact distributed generation system power supply quality.

Fig. 8, Fig. 9 are the frequency detecting error for providing in Fig. 7 respectively, adopt the waveform carrying out isolated island test based on parameter adaptive Sandia frequency deviation method and traditional SFS method that the present invention proposes.Wherein, Fig. 8 is at local load Q _fthe test case based on parameter adaptive Sandia frequency deviation method is adopted when=4.5.Due to the cf of inverter 2 ₀made Adaptive Modulation, two inverters all have upwards shift frequency ability, even if loaded quality factor is very high, but inverter successfully detects isolated island respectively through 0.46 second and 0.8 second after suspension, meets the Standard of islanding detect detection time; Fig. 9 is at local load Q _fthe test waveform of traditional SFS method is adopted when=1.If there is no the dilution effect phenomenon that frequency detecting error causes, by Q _f=2.5 adjust after positive feedback gain K can shift out threshold range by electric voltage frequency easily.But owing to there is dilution effect, after suspension, inverter 2 shift frequency effect downwards counteracts the upwards shift frequency effect of inverter 1, and in 2 seconds, frequency upper shift is less than 0.1Hz, thus makes isolated island sustainable existence, islanding detect failure.

Claims (1)

1., based on a combining inverter island detection method for parameter adaptive Sandia frequency deviation method, it is characterized in that:

(1) magnitude of voltage and the inverter output current value that distributed grid-connected electricity generation system is positioned at point of common coupling place is gathered;

(2) the phase angle φ between magnitude of voltage and inverter output current value utilizing digital correlation principle to calculate to be collected by step (1);

(3) the phase angle φ drawn according to step (2) calculates the frequency detecting error f of inverter _e, and according to frequency detecting error f _econcrete condition to the initial copped wave coefficient cf in Sandia frequency deviation method ₀carry out self-adaptative adjustment;

(4) according to the phase angle φ that step (2) draws, under the local loading condition of different quality factor, self-adaptative adjustment is done to the positive feedback gain K in Sandia frequency deviation method;

(5) according to the initial copped wave coefficient cf that step (3), (4) obtain ₀and positive feedback gain K, obtain the shift frequency initial phase angle θ of the inverter output current Setting signal needed for islanding detect _sFS;

The calculating formula of the phase angle φ between the magnitude of voltage at the described point of common coupling place of step (2) and inverter output current value is:

$\mathrm{\&phi;}=\&PlusMinus;\arcsin \sqrt{\frac{2}{N}\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\{R_{\mathrm{iu}}\left(m\right)-R_{\mathrm{ui}}\left(m\right)-\frac{1}{N}\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}[R_{\mathrm{iu}}\left(m\right)-R_{\mathrm{ui}}\left(m\right)\left]\right\}}^2}$

In formula, φ is the phase angle between the magnitude of voltage at point of common coupling place and inverter output current value, and N is sampling number, R _iu(m) and R _uicross correlation function between m voltage that () is point of common coupling place and inverter output current signal, m is the independent variable in cross correlation function;

The described frequency detecting error f of step (3) _ecalculating formula be:

$f_e=\frac{\mathrm{\&phi;}-{\mathrm{\&phi;}}_0}{K}\text{\&CenterDot;}\frac{1}{90}$

In formula, f _ebe frequency detecting error, φ is the phase angle between the magnitude of voltage at point of common coupling place and inverter output current value, φ ₀be the phase angle between the magnitude of voltage at point of common coupling place when not having frequency detecting error and inverter output current value, K is positive feedback gain;

The described initial copped wave coefficient cf of step (3) ₀adjustment type be:

cf ₀＝cf’ ₀+K·f _e

In formula, cf ₀the initial copped wave coefficient after adjustment, cf ' ₀be the initial copped wave coefficient of initial setting, K is positive feedback gain, f _eit is frequency detecting error;

The calculating formula of step (4) described positive feedback gain K is:

$K>\frac{2\mathrm{\&phi;}}{\mathrm{\&pi;}(f_g-f)}$

In formula, K is positive feedback gain, and φ is the phase angle between the voltage at point of common coupling place and inverter output current, f _gbe line voltage rated frequency, f is distributed generation system frequency of operation;

The shift frequency initial phase angle θ of the described inverter output current Setting signal of step (5) _sFScalculating formula be:

${\mathrm{\&theta;}}_{\mathrm{SFS}}=\frac{\mathrm{\&pi;}}{2}\&CenterDot;\mathrm{cf}=\frac{\mathrm{\&pi;}}{2}[{\mathrm{cf}}_0+K(f-f_g)]$

In formula, θ _sFSbe the shift frequency initial phase angle of inverter output current Setting signal, cf is copped wave coefficient, and other symbol implication is with identical above.