CN115632401B - SAPF parameter design method considering load and power grid impedance influence - Google Patents

Abstract

The invention discloses a SAPF parameter design method considering load and power grid impedance influences, and belongs to the technical field of alternating current-direct current conversion under a new energy power grid. Firstly, obtaining an optimal proportional coefficient expression of proportional link gains of a fundamental current loop and a power grid current loop controller under passive guidance according to a power grid current response equation of an SAPF double-loop current control system and correcting the optimal proportional coefficient expression; and selecting LCL filter parameters and calculating the gain of a proportional link of a power grid current loop/fundamental current loop controller according to a power grid current response equation, the corrected optimal proportional coefficient and the given minimum control bandwidth of a power grid current loop, and finally designing a proportional gain coefficient of a PCC power grid voltage feedforward term meeting the passivity requirement to ensure that the output admittance of the SAPF system is completely passive in the Nyquist range. The invention can ensure that the SAPF system is not influenced by the impedance fluctuation of a power grid and switching load, and has strong robustness.

Description

SAPF parameter design method considering load and power grid impedance influence

Technical Field

The invention belongs to the technical field of alternating current-direct current conversion under a new energy power grid, and particularly relates to an SAPF parameter design method considering load and power grid impedance influences.

Background

With the development of new power systems, more and more power electronics devices are used on the generation and demand sides, making the grid characteristics increasingly complex. The rectifier, especially the uncontrolled rectifier, brings serious power quality problems to the power grid, and the introduced harmonic current can cause power grid voltage distortion, generate extra line loss, accelerate the aging of power transmission and transformation equipment, and even cause the misoperation of a relay protection device. The parallel active power filter is used as a typical electric energy quality control device, has the characteristics of flexible compensation of harmonic current, quick response and the like, and can effectively relieve harmonic pollution in a power grid.

In order to suppress the inverter switching harmonics, an L-type or LCL-type filter is required to be provided at the output terminal thereof. Of these, LCL type filters are widely used due to their better harmonic attenuation capability. However, the inherent resonance characteristics of LCL type filters, coupled with the inevitable control delays in discrete control systems, pose a risk of instability in SAPF systems. In addition, the power grid environment of the SAPF grid-connected point can be changed due to the fluctuation of the power grid impedance and the switching of the load, and the system oscillation can be caused by the change of the power grid environment when the LCL filter and the controller are improperly designed or have poor robustness.

Disclosure of Invention

In view of the above, the present invention provides an SAPF parameter design method considering load and grid impedance influences, which takes passivity as a guide, obtains proportional link gain parameters of a fundamental current loop and a grid current loop controller and LCL filter parameters on the premise of simultaneously satisfying current loop control bandwidth and stability margin of an SAPF dual-loop current control system, and finally makes output admittance of an SAPF system completely passive by adjusting a proportional gain coefficient of a common coupling Point (PCC) grid voltage feedforward. The invention can ensure that the SAPF system still ensures the passivity of the LCL filter when the parameters of the LCL filter fluctuate, so that the three-phase LCL type SAPF system can stably operate when the impedance and the load of a power grid fluctuate.

The invention adopts the following technical scheme:

an SAPF parameter design method considering load and power grid impedance influences is provided, wherein SAPF parameters comprise proportional link gain of a fundamental current loop and a power grid current loop controller, LCL filter parameters and proportional gain coefficients of a PCC power grid voltage feedforward term;

the parameter design method comprises the following steps:

(1) Obtaining the optimal proportional coefficient expression of the proportional link gain of a fundamental current loop controller and the proportional link gain of a power grid current loop controller under passive guidance according to the real part information of the system output admittance when PCC voltage feedforward is not applied in the power grid current response equation of the SAPF double-loop current control system;

(2) Calculating a correction factor of the optimal proportionality coefficient expression in the step (1) according to the maximum negative deviation of the inductance value and the capacitance value of the inverter side in the LCL filter to obtain a corrected optimal proportionality coefficient expression;

(3) Obtaining an inequality equation set of LCL filter parameter values according to the corrected optimal proportionality coefficient expression, the stable condition of the power grid current response equation of the SAPF double-loop current control system and the given minimum control bandwidth of the power grid current loop, and selecting the LCL filter parameters in a feasible area surrounded by the inequality equation set;

(4) Substituting the LCL filter parameter value selected in the step (3) into the optimal proportional coefficient expression modified in the step (2) to obtain a modified optimal proportional coefficient, and obtaining the proportional link gain of the grid current loop controller and the proportional link gain of the fundamental current loop controller according to the modified optimal proportional coefficient, the selected minimum grid current loop control bandwidth and the grid side inductance value of the LCL filter;

(5) And (5) designing a proportional gain coefficient of a voltage feedforward term of the PCC power grid, which meets the passivity requirement, under the condition of the proportional link gain of the power grid current loop controller and the proportional link gain of the fundamental current loop controller obtained in the step (4).

Further, the SAPF dual-loop current control system comprises:

the bus voltage loop takes direct-current bus voltage and a direct-current bus voltage reference value as input, and obtains the amplitude of the fundamental current loop reference value after being adjusted by a bus voltage controller; obtaining a phase angle of a fundamental wave current loop reference value after the phase-locked loop is used for carrying out phase locking on the PCC network voltage; obtaining a fundamental current loop reference value according to the amplitude and the phase angle;

the fundamental current loop takes a fundamental current loop reference value and inverter side feedback current as input, and obtains output quantity after passing through the fundamental current loop controller;

the power grid current loop takes power grid current as input and obtains output quantity after passing through a power grid current loop controller;

the PCC power grid voltage feedforward item takes the PCC power grid voltage as input, and obtains output quantity after low-pass filtering and multiplying by a proportional gain coefficient;

and adding the output quantities of the fundamental wave current loop, the grid current loop and the PCC grid voltage feedforward item, modulating by SPWM to obtain a switching signal, and acting the switching signal on the three-phase voltage source inverter to obtain the output voltage of the inverter.

Further, the grid current response equation of the SAPF double-loop current control system is as follows:

wherein the content of the first and second substances,i _g (s)、u _g (s)、i _Lh (s) Harmonic current sources equivalent to the power grid current, the power grid voltage and the nonlinear load respectively;G _L (s) Is a closed loop transfer function from the non-linear load current to the grid current;Y _oa (s) For the total output admittance of the system,Y _mL (s) The admittance generated for the nonlinear load input admittance coupling to the system,Y _oc (s) For the system output admittance when applying the PCC voltage feed-forward,Y _oca (s) To the output admittance when no PCC voltage feed-forward is applied,Y _ocf (s) For the PCC voltage feed-forward effect equivalent admittance,Z _g (s) Is the grid impedance.

Further, the expression of the corrected optimal proportionality coefficient in step (2) is as follows:

wherein, the first and the second end of the pipe are connected with each other,K _OPT in order to optimize the scaling factor before the correction,K _MOPT in order to obtain the optimum scaling factor after the modification,

in order to correct the factor(s),ω _s in order to sample the angular frequency of the signal,ω _r being the resonance angular frequency of the LCL filter,

is the ratio of the inverter side inductance value and the grid side inductance value in the LCL filter.

Further, the correction factor is:

wherein the content of the first and second substances,

the inductance and the capacitance of the inverter side in the LCL filter are respectively the maximum negative deviation from the factory parameters.

Further, the inequality equation set of the LCL filter parameter values in step (3) includes the following constraint conditions:

the first constraint condition is:

the second constraint condition is as follows:

the third constraint condition is as follows:

wherein the content of the first and second substances,ω _cmin for a given minimum control bandwidth of the grid current loop,T _s is the sampling time.

Further, in the step (4), a calculation formula of the proportional link gain of the grid current loop controller and the proportional link gain of the fundamental current loop controller is as follows:

wherein the content of the first and second substances,ω _cmin for a given minimum control bandwidth of the grid current loop,K _pf is the proportional link gain of the fundamental current loop controller,K _ph the proportional link gain of the current loop controller of the power grid is obtained,L ₂ is the grid side inductance value in the LCL filter.

Further, the step (5) is specifically as follows:

and (3) according to the value range of the proportional gain coefficient of the PCC power grid voltage feedforward term, the gain of the proportional link of the power grid current loop controller obtained in the step (5) and the gain of the proportional link of the fundamental current loop controller, obtaining the frequency response of the system output admittance when the PCC voltage feedforward is applied, and selecting the proportional gain coefficient of the PCC power grid voltage feedforward term as a design result in the range that the frequency response meets the passivity requirement.

Compared with the prior art, the invention has the following beneficial effects:

the invention provides a three-phase SAPF controller considering load fluctuation and power grid impedance influence and an LCL filter parameter design method. And then, proportional link gain parameters of fundamental waves and a power grid current loop controller are designed by utilizing an admittance model and taking passivity as guidance, and parameters of an LCL filter are obtained. And finally, adjusting a proportional gain coefficient of a PCC (point-to-point capacitor) power grid voltage feedforward link to ensure that the output admittance of the SAPF system is completely passive within the Nyquist range. The parameters designed by the invention can enable the SAPF system to simultaneously meet the requirements of control bandwidth and stability margin, so that the SAPF system not only has strong robustness on the impedance of a power grid on the basis of ensuring good harmonic wave treatment capability, but also can resist the influence brought by load fluctuation, and the application scenes of the SAPF are greatly expanded.

Drawings

FIG. 1 is a block diagram of a three-phase LCL type SAPF dual-loop current control system;

FIG. 2 is an equivalent transfer function control block diagram of a three-phase LCL model SAPF dual-loop current control system;

FIG. 3 is an equivalent circuit diagram of the SAPF dual-loop current control system, the grid, and the non-linear load;

FIG. 4 shows the current bandwidthω _cmin Defined by three inequality constraints when chosen as 2000rad/s

Andω _r a feasible region map of (a);

FIG. 5 is a graph of current bandwidthω _cmin 1000rad/s and 3000rad/s respectively, and is formed by three inequality constraint conditions

Andω _r a feasible region map of (a);

in FIG. 6, (a) to (h) are as

And

when wave motion occurs, adoptK _OPT Parameter ofL ₁ AndC _f fluctuating admittance imaginary part

A feasible domain variation graph of (1);

in FIG. 7, (a) to (d) are

And

when fluctuation occurs, adoptK _MOPT Parameter ofL ₁ AndC _f fluctuating admittance imaginary part

A feasible domain variation graph of (1);

fig. 8 shows the values of the LCL parameters of filter I and filter II;

fig. 9 (a) to (c) are graphs of SAPF grid current loop open-loop transfer functions Bode under three sets of parameters corresponding to the filter I and the filter II, respectively;

in fig. 10, (a) to (c) are three sets of parameters corresponding to the filter I and the filter II, respectively, whenL ₁ AndC _f SAPF output admittance when parameter fluctuation occursY _oca (s) A frequency response characteristic map of (a);

FIG. 11 shows the case of applying the corresponding parameters of filter II

Bode diagram of (1);

FIG. 12 (a) is a graph showing the absence of PCC voltage feed-forward term adjustmentY _oca (jω) AndY _mL (jω) Phasor diagram of interaction, fig. 12 (b) is after adjustment by the PCC voltage feed forward termY _oc (jω) And withY _mL (jω) A phasor diagram of the interactions;

FIG. 13 is a schematic view of

Has a frequency response ofK _ff A varying three-dimensional surface map;

FIG. 14 is a drawing showingY _oc (s) Frequency response plot of (a);

fig. 15 (a) to (b) are respectively the power grid current waveform and Total Harmonic Distortion (THD) of the SAPF system using the parameters designed according to the present invention, when the power grid impedance is not applied;

FIG. 16 shows the system resonating after the grid impedance is applied without applying PCC voltage feed forward using the design parameters of the present invention; after the load is put into operation, the resonance is inhibited, and the waveform of the a-phase PCC voltage and the waveform of the power grid current are obtained;

fig. 17 (a) to (b) show the waveform and Total Harmonic Distortion (THD) of the current in the power grid, which are still stable after the system is stabilized after the impedance of the power grid is applied and the load is removed, respectively, in the SAPF system using the parameters designed according to the present invention.

Detailed Description

In order to more specifically describe the present invention, the following detailed description is provided for the technical solution of the present invention with reference to the accompanying drawings and the specific embodiments.

As shown in FIG. 1, in the SAPF dual-loop current control strategy, the grid currenti _g Side current of inverteri _inv Dc bus voltageu _dc And PCC point voltageu _pcc Is sampled as a control variable. Wherein for the network current loop, the goal is to convert the network currenti _g Harmonic component ofi _gh The control is zero. Considering that a Proportional Resonant (PR) controller employed by a grid current loop controller has a high gain at a specific subharmonic frequency, the grid currenti _g Harmonic waves do not need to be extracted, and the harmonic waves can be directly used as the input of a power grid current loop controller. For the fundamental current loop, the control objective is to keep the bus voltage stable. For this purpose, the inverter side currenti _inv Tracking a reference current by a Proportional Resonant (PR) controller of a fundamental current loopi _{f, ref} . Reference current of fundamental current loopi _{f, ref} By means of a Phase Locked Loop (PLL) with a PCC voltageu _pcc The phase of (2) remains synchronized. In this embodiment, in order not to introduce the influence of the PLL, the bandwidth thereof may be set to be low, for example, 25Hz. PCC grid voltageu _pcc Passing through a low pass filterG _ff (s) Post-multiplying by a proportional gain factorK _ff As a feedforward term, the feedforward term is superposed with the output of a power grid current loop controller and a fundamental current loop controller, a switching signal is obtained after SPWM modulation, the switching signal acts on a three-phase Voltage Source Inverter (VSI), and finally the output voltage of the inverter is obtainedu _inv 。u _inv Obtaining output current after filtering by LCLi _out ，i _out Harmonic component in and non-linear load currenti _L And the harmonic content in the power grid current is reduced by offsetting.

The principles and process flow of the present invention are described below.

(1) Using the rest shown in figure 2

The transfer function control block diagram under the coordinate system establishes an admittance model of the SAPF system, and the detailed discussion is as follows:

the dual loop current control block diagram of FIG. 1 may be equivalent to the quiescent state of FIG. 2

And controlling the block diagram of the transfer function under the coordinate system. As shown in fig. 2, which is a sampled-data system, there are continuous and discrete time signals, and the sampled discrete variables are represented by the corresponding continuous variables with marks. By means of sampling switches between continuous and discrete signals (with sampling period ofT _s ) And zero order keeperG _h (s) And (6) performing conversion. For a continuous signaliCorresponding to a sampled discrete signal ofi ^* The relationship between the two can be expressed in the frequency domain as:

wherein the content of the first and second substances,

in order to sample the angular frequency of the signal,sin order to be the laplacian operator,jis a symbol of an imaginary number,kthe values are integers. The above expression shows that the sampled signal is introduced into the image andω _s is a period.

The zero order keeper (ZOH) in fig. 2 is used to equate to a pulse width modulation Process (PWM), and its corresponding transfer function can be expressed as follows:

through ZOH, discrete voltage signalsu ^* _inv Can be converted into actual voltage signalsu _inv . In addition, the introduction of the discrete control is inevitableThe calculation delay, which is dependent on the configuration of the control system, is typically one sampling period, i.e.D(z) = z ^-1 ，z = exp(sT _s ). In the present embodiment, for the fundamental current reference valuei _{f, ref} And grid current harmonic component reference valuei _{gh, ref} Controller for realizing zero-error tracking and power grid current loopG _ch (s) And fundamental current loop controllerG _cf (s) All adopt PR controller, the resonance (R) unit of PR controller issThe domain can be expressed as:

wherein the content of the first and second substances,K _rn is as followsnThe resonant gain of the sub-harmonics,

and are respectively the secondnThe corresponding compensation angle of the sub-R unit and the resonance angular frequency. The proportional gains of the fundamental current loop and the grid current loop controller are respectively controlled byK _pf AndK _ph and (4) showing.G _ch (z) AndG _cf (z) Are respectively composed ofG _ch (s) AndG _cf (s) Dispersing to obtain the product.G _ff (s) Is a low-pass filter which is discrete toG _ff (z)。K _ff The value of the proportional gain coefficient is 0~1. Due to the DC bus voltageu _dc Is controlled to be a constant value, and the corresponding control link is omitted in fig. 2.

For an LCL filter, its frequency characteristics can be expressed as the following admittance:

a mixed output admittance model can be obtained by utilizing the inteswample modeling method, and the method can be used for solving the problem that the traditional method is not suitable for the traditional methodz = exp(sT _s ) And realizing unification. From fig. 2, the relationship between all variables in the sapf control system can be expressed as:

according to the above equation and ignoring the effect of the image introduced during sampling, byu _pcc (s) The closed loop response under the SAPF dual loop current control framework as input can be derived as follows:

wherein the content of the first and second substances,G _i (s)，G _L (s) Respectively corresponding input-to-output closed loop transfer functions,Y _oc (s) To output admittance, it can be expressed as:

wherein the content of the first and second substances,Y _c1 (z)，Y _c2 (z)，Y _o1 (z)，Y _o2 (z) Can be respectively obtained by the dispersion of the zero-order keeper by the corresponding continuous domain admittance.

Output admittanceY _oc (s) Phasors can be decomposed into output admittance without applying PCC voltage feed-forwardY _oca (s) Admittance equivalent to PCC voltage feedforward actionY _ocf (s) Namely:

wherein, the first and the second end of the pipe are connected with each other,

the total output admittance of the SAPF control system can be affected by adjusting the PCC voltage feed-forward term, whereinY _ocf (s) For the PCC voltage feed-forward effect equivalent admittance,Y _oca (s) For system output admittance when PCC voltage feed-forward is not applied,Y _oc (s) The system output admittance is fed forward for the application of the PCC voltage.

When the PCC voltage exists at a frequency off _x In harmonic disturbance, neglecting the coupling effect between different subharmonics, the relationship between the harmonic voltage and the current on the ac side of the nonlinear load connected to the PCC point can be expressed as:

wherein the content of the first and second substances,Y _L the amplitude-frequency characteristic of the input admittance of the nonlinear load can be obtained by sweeping frequency to a load port, and the input admittance of the load presents inductance for a three-phase uncontrolled rectifying load with an incoming reactor, which is common in the industry. Thus, the load currenti _L (s) Can be regarded as harmonic current sourcei _Lh (s) Superposition of input admittance model with nonlinear loading:

substituting the above formula into a power grid current response equation of the SAPF closed-loop system to obtain:

wherein the content of the first and second substances,Y _mL (s) = G _L (s)Y _L (s) The admittance generated by the nonlinear load input admittance coupling with the system;G _L (s)=1- G _i (s)，G _L (s) For closed-loop transfer function from non-linear load current to grid currentThe number of the first and second groups is,G _i (s) Is a closed loop transfer function of a power grid current loop. Input admittance of non-linear load can be foundY _L (s) The total output admittance of the PCC port is influenced by the coupling of the SAPF control loop, and the stability of a grid-connected system is further influenced.

The above equation can be expressed as a davinin equivalent circuit, as shown in fig. 3. Will be provided withu _pcc (s)= u _g (s)- i _g (s)Z _g (s) After the formula is substituted, an ideal power grid can be deducedu _g (s) The closed loop system response equation for the input is as follows:

wherein the content of the first and second substances,Y _oa (s) = Y _mL (s) + Y _oca (s) + Y _ocf (s) The total output admittance for the SAPF to the PCC port.

(2) Utilizing SAPF system output admittance when PCC voltage feedforward is not applied as obtained in (1)Y _oca (s) Design of proportional gain of fundamental current loop controllerK _pf Proportional gain to grid current loop controllerK _ph Meanwhile, value constraint conditions of LCL filter element parameters are given, and the specific solving method is as follows:

the stability condition of the SAPF system can be known from the closed-loop system response equation of (1): 1)G _L (s) Gradual stabilization; 2) Loop gainY _oa (s)Z _g (s) The Nyquist stability criterion is satisfied. The condition 1) can be realized by designing parameters of a fundamental current loop and a grid current loop controller, and the sufficient condition for the condition 2) to be satisfied is total output admittanceY _oa (s) From 0 toω _N At a passive origin, i.e. Re, in the range (Nyquist angular frequency) Y _oa (s) Is > 0 or

。

Since the resonant unit of the current controller only has great influence on the amplitude-frequency characteristic near the resonant frequency, the solution is carried outY _oca (s) In the real part, neglecting it, i.e.G _cf (z)≈K _pf ，G _ch (z)≈K _ph . Substitution intos = jω，z = exp(jωT _s ) The following can be obtained:

wherein the content of the first and second substances,

wherein the content of the first and second substances,ωis the angular frequency. When the temperature is higher than the set temperatureωIs less thanω _N Time, always positive, analysisY _oca (s) The real part of (A) is not difficult to find, in the Nyquist frequency range, as long asK _pf AndK _ph satisfies the following conditions:

namely can makeY _oca (s) The real part is greater than zero (only inω = ω _s Zero at/6). Wherein the content of the first and second substances,

a ratio of an inverter-side inductance value and a grid-side inductance value in the LCL filter;ω _r the LCL filter natural resonant angular frequency.

The parameters of the current loop controller are designed under the condition of satisfying the above equation relationG _L (s) And (4) gradually stabilizing. As shown in fig. 2, ignoreu _pcc Andi _L the power grid current loop gain can be obtained as follows:

in general, SAPF grid current loop control bandwidthω _c Much less than the resonant frequency of the LCL filterω _r . Thus at frequencyω _c Nearby, the LCL filter can be approximated as a first order L filter. Likewise, delayD(z) Can be approximately replaced by a first order Taylor expansion, i.e.

. Substitution intoK _pf = K _OPT K _ph Loop gainT _i (s) Can be simplified as follows:

wherein the content of the first and second substances,L = L ₁ +L ₂ the inductance value represents the sum of the inverter-side inductance value and the grid-side inductance value in the LCL filter.

According to the above formula, inω _c ToT _i (s) The amplitude of (d) is:

according to the formula, the proportional gain of the power grid current loop controllerK _ph Determining the control bandwidth of the current loop of the power networkω _c When the network current loop controls the bandwidthω _c After the setting, the user can set the setting,K _ph can be expressed as:

loop gainT _i (s) In thatω _c The phase of (a) is:

wherein the content of the first and second substances,

is the phase margin PM of the system. Will be provided withK _ph After the substitution into the formula (I) is carried out,

can be rewritten as:

as can be seen from the above formula, the PM of the system is the bandwidth set by the systemω _c AndK _OPT and (6) determining. ByK _OPT The expression shows that after LCL filter parameters are designedK _OPT Is uniquely determined. Bandwidth at that timeω _c The size of (b) determines the stability margin of the SAPF control system. Therefore, it is required toω _c And

a compromise is made on the choice of (a) to obtain a larger stability margin with a smaller system bandwidth. Fundamentally, the passivity design goal reduces one degree of freedom in the SAPF dual current loop control, and under the guidance of the design, in order to simultaneously meet the requirements of high bandwidth and larger PM, the LCL filter parameters can be reasonably designed and adjustedK _OPT Is achieved by the value of (c). For the

In other words, since the first-order taylor expansion is used to replace the delay element with a certain conservative property in the phase lag, it can be set to 45 °, and the first constraint on stability can be derived from the above equation:

wherein the content of the first and second substances,ω _cmin for minimum control bandwidth of the grid current loop, because of the grid current loop controllerG _ch (z) Including multiple R units, to avoid an additional 0-dB ride-through,ω _cmin should be greater than the harmonic frequency of the highest order compensation.

For SAPF, the resonant frequency of the LCL filter is typically higher due to the higher harmonic frequencies to be compensatedω _r Is generally set higher thanω _s And 6, meeting the requirement of larger current loop bandwidth of the power grid. At this time, for the dual current loop control structure without delay compensation, a pair of open loop instability poles exist. In order for the system to ensure stability, the phase-frequency curve should be only in accordance with the Nyquist stability criterionω _r There is a-180 positive crossing. For this purpose, the loop gainT _i (s) In thatω _s The amplitude at/6 is less than 0dB atω _r The amplitude at (a) should be greater than 0dB. Considering disturbance influence such as parameter fluctuation, the amplitude margin (GM) is generally set to 3dB to improve the system robustness, so the corresponding stability condition can be expressed as

And

the second and third restrictions on stability, respectively, are as follows:

can find that whenω _cmin After determination, the variables of the first, second and third stability constraints are allω _r And

. When LCL filter parametersω _r And

when the three conditions are met, the SAPF system can meet the requirements of bandwidth and stability margin on the premise of ensuring that the output admittance is passive.

The arithmetic example of the present invention shows that the highest harmonic compensation time is 19 ^th Since the power frequency voltage is 50Hz, correspondingly,ω _cmin the value can be 2000rad/s. The boundaries of the three above-mentioned stability constraints are shown in fig. 4 when the sampling frequency is 15kHz, provided that the selection is made in a common region enclosed in fig. 4ω _r And

therefore, the SAPF control system designed by taking passivity as a guide has sufficient stability margin and strong robustness to power grid impedance fluctuation. It can be found that there are countless selection schemes for the LCL filter parameters in the feasible domain defined by the three constraint conditions, and in practice, suitable LCL filter parameters should be designed in the feasible domain according to the power level, reactive capacity constraint, output current ripple limitation, voltage sag limitation, and the like of the SAPF system.

When in useω _cmin When 1000rad/s is taken, a feasible region surrounded by three constraint condition boundaries is shown in (a) in fig. 5, and after the bandwidth of the power grid current loop is increased to 3000rad/s, as shown in (b) in fig. 5, the area of the feasible region is continuously reduced, that is, the selectable range of the LCL filter parameters is smaller and smaller. This means that a very high bandwidth, while improving the response of the system, sacrifices the flexibility of LCL parameter selection, so that the bandwidth is selected to be equal to or greater thanω _cmin That is, when the bandwidth is selected asω _cmin Proportional gain of time-of-flight, grid current loop controllerK _ph The corresponding representation is:

(3) Analysis ofL ₁ AndC _f after the parameters are changed, the SAPF outputs the change rule of admittance frequency response,and pairK _OPT Make a correction to obtainK _MOPT The specific discussion process is as follows:

in practice, the amount of the liquid to be used,L ₁ andC _f the parameters of (a) change after the operation of the SAPF,K _OPT will be changed along with the change of the temperature,K _pf = K _OPT K _ph this condition will no longer be satisfied. At this time, admittanceY _oca (s) Will be in the Nyquist frequency rangeω _s Non-passive regions occur near/6. For the case of the passive region, reference may be made to the document "PassionEnhance for LCL-Filtered observer With Grid Current Control and Capacitor Current Active pointing, xuehua Wang", published in the journal IEEE Transactions on Power Electronics, 2022. In order to compensate the non-passive region, it is necessary to analyze the characteristics of the non-passive region to try to make the region exhibit a consistent inductance or capacitance.

In the invention, all parameters after fluctuation are represented by adding a left-falling part to the upper right corner of the parameter before corresponding fluctuation, for example, by representingL ₁ After the parameters fluctuate. Assuming that the parameters after fluctuation satisfy:

at this time, admittance

The real part of (d) can be expressed as:

after the parameter fluctuates

If the value is still greater than zero, the above formula shows

In thatω _s 6 and

with spacing less than zero, i.e. admittance

Non-passive regions are present.

Further, the admittance in this region was investigated

Positive and negative of imaginary part of will

Substitution into

Taking its imaginary part:

from the above formula, becauseK _OPT > 0，

Always on, therefore, it is true that

Positive or negative of imaginary part depends on

And

relationships between them, as can be seen in FIG. 4ω _r Far greater thanω _s 6, therefore

Should still be greater than

At this time

Is positive, and the admittance exhibits a capacitive property at that frequency.

However,

the imaginary part of (A) cannot be directly deduced intuitively, and the positive and negative parts of the imaginary part deviate along with the fluctuation of the parameter

And

but is changed. To compensate for the passive region of the output admittance,

should be at

And

remains positive throughout the variation, thus admittance

In thatω _s 6 and

the frequency band will exhibit consistent capacitance, requiring only a lagging phase compensation for this region.

Solving for

And an imaginary part ofThe sign is positive, which results in:

wherein the content of the first and second substances,

deviation when parameter fluctuates

And

after determination, the above formula is aboutω _r And

can satisfy the inequality constraint condition to ensure that the current situation is satisfied

And

in the following, the first step is to put the paper into the bag,

the sign of (1) is positive. To obtain following

And

the invention adopts perturbation method to draw the variable trend of the feasible region

And

changing from-15% to 0, and increasing to 15% again

Aboutω _r And

is shown in fig. 6. Fig. 6 is a diagram of the internal stability feasible region of fig. 4, and if there is an intersection between two feasible regions in the fluctuation range of the parameters, it indicates that there is a set of LCL filter parameters that can make the SAPF system in the middle of the time periodL ₁ AndC _f the stability constraint is still satisfied when the change occurs, andω _s 6 and

capacitive non-passive regions occur within the frequency band.

As shown in fig. 6, when the parameter isL ₁ AndC _f when the value of (A) is reduced, with

And

the intersection area is continuously reduced until disappearing when the concentration is changed from-1% to-15%, which shows that when the concentration is changed to be zeroL ₁ AndC _f when large negative fluctuation occurs, the non-passive area of the output admittance cannot present consistent characteristics, and the characteristics of the non-passive area change suddenly at a certain frequency, so that the inductance is converted into the capacitance, and the design of a phase compensation link is not facilitated. When inL ₁ AndC _f as the value of the parameter increases, with

And

increasing from 1% to 15%, the two regions always coincide, indicating an output admittance factor of the SAPFL ₁ AndC _f the non-passive area generated by the forward fluctuation is always capacitive.

From the above rule, the invention is aimed atK _OPT Making a correction by a factor ofK _MOPT ：

Wherein the content of the first and second substances,

。

and

is composed ofL ₁ AndC _f the maximum negative deviation of the parameter values is, in this embodiment,

=

= -0.15。

after applying the modified coefficients, the output admittance isω _s 6 and

non-passive regions will occur between the frequency bands. As in the analysis described above, it is preferred that,

is always positive, so that

The feasible region of positive sign of (1) is also by perturbation

And

is plotted in fig. 7. As can be seen from FIG. 7, the corrected coefficients are usedK _MOPT After, no matter the parametersL ₁ AndC _f how to fluctuate within a deviation of 15% such that

For the positive parameter robustness feasible region always including the stability feasible region, it should be noted that when the modified coefficient is adoptedK _MOPT Then, the internal stability feasible region in fig. 4 needs to be corrected at the same time, and the internal stability feasible region in fig. 7 is the corrected result.

To verify the correctness of the above passivity-oriented parameter design method, the present embodiment takes a 30kVA SAPF prototype as an example, and the parameters thereof are listed in table 1 below:

TABLE 1 SAPF operating parameters

The two sets of LCL filter parameters are listed in table 2 below:

TABLE 2 LCL Filter parameters

Both sets of parameters were selected within the feasible region obtained from the above analysis, as shown in FIG. 8, where filter I corresponds toω _r Is 24407rad/s,

2.54, located in the corrected feasible region, whichK _MOPT Is 0.0589 whenω _cmin When the amount is set to 2000rad/s, the calculation is performedK _ph Is a high-frequency signal of 2.89 omega,K _pf is 0.17 omega. In order to highlight the effect of the correction method provided by the invention, the filterII corresponds toω _r Is 38730rad/s,

8, located in the overlapping area of the two feasible fields: when not correctedK _OPT Is 0.4804 whenω _cmin When the value is set to 2000rad/s, the calculation can be madeK _ph Is a high-frequency wave of 3.22 omega,K _pf is 1.55 omega; when the correction coefficient is adoptedK _MOPT Is 0.0696, same asω _cmin Then, calculate to obtainK _ph Is a gas flow rate of 2.83 omega,K _pf and is 0.20 omega.

Firstly, the stability of the SAPF closed-loop system is verified, and when the three groups of parameters are adopted, the SAPF power grid current loop open-loop transfer functions Bode diagrams are respectively shown as (a), (b) and (c) in FIG. 9. In accordance with the nyquist stability criterion,N ₊ - N _- should be equal to half the number of open loop instability poles. When in useω _r > ω _s At/6, there are two open-loop instability poles in the system, shown in (a), (b), (c) of FIG. 9N ₊ - N _- All are 1, which indicates that the SAPF system closed loop stability can be ensured by adopting the parameter design method. Further, from Bode fig. 9, the system has PM, GM, and bandwidth that are all large enough. Note that the PM of (b) in fig. 9 is slightly less than 45 °, which is caused by an error introduced by the linearization process of the delay element.

Then analyzing SAPF output admittance under the condition of adopting passive-oriented parameter design methodY _oca (s) The frequency response characteristic of (2) is, as shown in (a), (b) and (c) of fig. 10, as the parameter fluctuates, it is not difficult to find from (a) and (c) of fig. 10, and the corrected passivity coefficient is usedK _MOPT When the parameter fluctuates between-15% and +15%, the output admittance isω _s The non-passive area around/6 presents consistent capacitance; and adopts the original passivity coefficientK _OPT When is coming into contact withL ₁ AndC _f after the parameters have larger negative fluctuation at the same time, the output admittance isω _s The non-passive area near/6 has the capacityThe sex and the sensitivity are difficult to compensate for in a targeted manner, as shown in fig. 10 (b).

(4) Analyzing the influence of the uncontrolled rectifying load on the stability of the SAPF system, wherein the specific analysis process is as follows:

the uncontrolled rectifying load is widely applied in the industry, when the uncontrolled rectifying load is put into operation, harmonic waves can be introduced into a power grid, and meanwhile, the input admittance of the uncontrolled rectifying load is coupled with an SAPF control loop to generate harmonic wavesY _mL (s) From the foregoing analysis, it can be seen that:

after the sampling process has been linearized,Y _mL (s) Can be simplified into a single frequency admittance model

Namely:

wherein the content of the first and second substances,

is a power grid current loop open-loop transfer function under a single-frequency model,G _D (s)=G _h (s)D(z). According to the formula, the compound has the advantages of,

respectively amplitude and phase angle ofY _L (s) And

the decision, can be expressed as follows:

Y _L (s) The expression of input impedance of (a) is:

wherein, the first and the second end of the pipe are connected with each other,Z _dc for dc-side load impedance, it is common in industrial applications to exhibit a resistive characteristic,f ₁ is the fundamental frequency. The expression showsY _L (s) At medium and high frequencies withZ _dc Exhibit the same resistance to inductance. For the

When the LCL parameter of filter II is used, andK _ph is 2.83 the number of the omega is zero,K _pf at 0.20 Ω, the Bode diagram is shown in fig. 11. The equivalent admittance of the SAPF system for the PCC port is as follows, regardless of the PCC voltage feed forward effectY _mL (jω)+Y _oca (jω). At the resonant frequencyf _r Nearby, though

Has a large phase change, but has a large harmonic amplitude value, so that

Has a small amplitude and a relative phasorY _oca (jω) The change of (a) is slight; during the parameter design process, the requirements are always met

And is

Therefore, it is

The value of (A) is positive and real, then always satisfy

Thus, is atω _s Near/6

Is mainly determined byY _L (s). As shown in (a) of FIG. 12, inω _s Near/6 frequency, equivalent phasorY _mL (jω) When the fan-shaped shadow area is positioned, the fan-shaped shadow area can be effectively reduced or even eliminatedY _oca (jω) In thatω _s And a non-passive area near the frequency of 6 improves the robustness of the SAPF system to the power grid impedance fluctuation. However, due to the fluctuation of the load, the passivity of the SAPF output admittance cannot be realized only by depending on the regulation of the load when the load is emptyY _mL (jω) =0 orY _mL (jω) In the non-shaded region of the fourth quadrant,Y _oca (jω) In thatω _s There will still be non-passive regions around the/6 frequency.

(5) Designing PCC voltage feedforward proportional gainK _ff The robustness of the SAPF system is improved, and the specific design process is as follows:

in order to eliminate the influence of the load as much as possible, the load can be reducedY _oca (jω) In thatω _s Phase around/6 frequency, in the present invention byY _ocf (s) To pairY _oca (s) Is adjusted. ByY _oc (s) = Y _oca (s) + Y _ocf (s) Can find out

The expression is as follows:

as can be seen from the above equation, when the first order low pass filterG _ff (z) When a proper cut-off frequency is selected, the frequency can be effectively reducedY _oca (s) Phase in the mid-high frequency band.G _ff (z) Correspond tosOf domainsG _ff (s) The transfer function of (c) can be expressed as follows:

the above equation is a typical first-order low-pass filter,ω _f is the cut-off angular frequency. To reduceY _oca (s) In thatω _s A phase around a/6 frequency, which can be selectedω _f Is (rad/s).

In the present embodiment, drawing is adopted

Is dependent on the phaseK _ff Design parameters with varying frequency response curvesK _ff As shown in fig. 13. As can be seen from figure 13 of the drawings,K _ff main influence of

Frequency characteristics in a low frequency band. In order to ensure that certain feedforward is used for improving the dynamic performance of APF during grid connection and load switching, the selection is carried outK _ff Is 0.8, at this timeY _oc (s) Is plotted in fig. 14, from fig. 14 it can be found thatY _oc (s) The phase of the medium and high frequency band is obviously reduced, and when the 280uH power grid impedance is switched, the system cannot be in resonance instability with the power grid impedance. At this time from (b) in figure 12,Y _mL (jω) The feasible shadow sector area is obviously widened, and at the moment, the load is switched,Y _mL (jω) When the change occurs in the shadow sector, the total output admittance can be effectively ensuredY _oa (s) The passivity of (A).

(1) The experiment verifies as follows:

the experiment adopts the parameters of the LCL filter II in the table 2, and the designed parameters are as follows according to the steps:K _MOPT is a content of 0.0696 (g),ω _c at 2000 (rad/s),K _ph the content of the acid was 2.83,K _pf is 0.20.PCC voltage feedforward linkω _f Is (rad/s),K _ff is 0.8。

With the above parameters, when the grid impedance is not switched, the system steady state performance is as shown in (a) and (b) in fig. 15, where (a) in 15 is abc three-phase grid current waveform, and (b) in 15 is corresponding Total Harmonic Distortion (THD) value. As can be seen from fig. 15, under the control of the SAPF dual-loop current, the THD of the grid current can be reduced to less than 5% by using the parameters in the present embodiment, and the industry standard is satisfied.

In order to verify the effect of the PCC voltage feedforward link, as shown in fig. 16, when the PCC voltage feedforward link is not applied, the grid impedance of 600 uH is applied, the system resonates, and after a load is applied, the resonance is obviously suppressed. The nonlinear load can effectively improve the robustness of the SAPF system to power grid impedance fluctuation to a certain extent, but in practice, the load is switched frequently, and the SAPF system is unstable again after the load is cut off.

After the PCC voltage feed-forward is applied, as shown in (a) of fig. 17, after the grid impedance is applied, the system is stable, and the corresponding grid current THD is 4.3% as shown in (b) of fig. 17, which meets the industry standard; after the load is removed, the system remains stable. The robustness of the SAPF system to the power grid impedance fluctuation is greatly improved after the PCC voltage feedforward is applied, and the whole process is not influenced by load switching.

Experimental results show that the parameter design method can ensure the stable operation of the three-phase LCL type SAPF when the power grid impedance and the load fluctuate, and achieve the ideal harmonic compensation effect.

The embodiments described above are intended to facilitate one of ordinary skill in the art in understanding and using the invention. It will be readily apparent to those skilled in the art that various modifications to the above-described embodiments may be made, and the generic principles defined herein may be applied to other embodiments without the use of inventive faculty. Therefore, the present invention is not limited to the above embodiments, and those skilled in the art should make improvements and modifications to the present invention based on the disclosure of the present invention within the protection scope of the present invention.

Claims (8)

1. An SAPF parameter design method considering load and power grid impedance influence, wherein the SAPF parameters comprise proportional link gain of a fundamental current loop and a power grid current loop controller, LCL filter parameters and a proportional gain coefficient of a PCC power grid voltage feedforward term;

the parameter design method is characterized by comprising the following steps:

(1) Obtaining the optimal proportional coefficient expression of the proportional link gain of a fundamental current loop controller and the proportional link gain of a power grid current loop controller under passive guidance according to the real part information of the system output admittance when PCC voltage feedforward is not applied in the power grid current response equation of the SAPF double-loop current control system;

(2) Calculating a correction factor of the optimal proportionality coefficient expression in the step (1) according to the maximum negative deviation of the inductance value and the capacitance value at the side of the inverter in the LCL filter to obtain a corrected optimal proportionality coefficient expression;

(3) Obtaining an inequality equation set of LCL filter parameter values according to the corrected optimal proportionality coefficient expression, the stable condition of the power grid current response equation of the SAPF double-loop current control system and the given minimum control bandwidth of the power grid current loop, and selecting the LCL filter parameters in a feasible area surrounded by the inequality equation set;

(4) Substituting the LCL filter parameter value selected in the step (3) into the optimal proportionality coefficient expression corrected in the step (2) to obtain a corrected optimal proportionality coefficient, and obtaining the proportional link gain of the power grid current loop controller and the proportional link gain of the fundamental current loop controller according to the corrected optimal proportionality coefficient, the selected minimum power grid current loop control bandwidth and the power grid side inductance value of the LCL filter;

(5) And (5) designing a proportional gain coefficient of a voltage feedforward term of the PCC power grid, which meets the passivity requirement, under the condition of the proportional link gain of the power grid current loop controller and the proportional link gain of the fundamental current loop controller obtained in the step (4).

2. The method of claim 1, wherein the SAPF double-loop current control system comprises:

the bus voltage loop takes direct-current bus voltage and a direct-current bus voltage reference value as input, and obtains the amplitude of the fundamental current loop reference value after being adjusted by a bus voltage controller; obtaining a phase angle of a fundamental wave current loop reference value after the phase-locked loop is used for carrying out phase locking on the PCC network voltage; obtaining a fundamental current loop reference value according to the amplitude and the phase angle;

the fundamental current loop takes a fundamental current loop reference value and inverter side feedback current as input, and obtains output quantity after passing through the fundamental current loop controller;

the power grid current loop takes power grid current as input and obtains output quantity after passing through a power grid current loop controller;

the PCC power grid voltage feedforward item takes the PCC power grid voltage as input, and obtains output quantity after low-pass filtering and multiplication by a proportional gain coefficient;

and the output quantities of the fundamental wave current loop, the grid current loop and the PCC grid voltage feedforward term are added and then are modulated by SPWM to obtain a switching signal, and the switching signal acts on the three-phase voltage source inverter to obtain the output voltage of the inverter.

3. The SAPF parameter design method considering load and grid impedance influences of claim 1, wherein a grid current response equation of the SAPF double-loop current control system is as follows:

wherein the content of the first and second substances,i _g (s)、u _g (s)、i _Lh (s) Harmonic current sources equivalent to the power grid current, the power grid voltage and the nonlinear load respectively;G _L (s) Is a closed loop transfer function from the non-linear load current to the grid current;Y _oa (s) For the total output admittance of the system,Y _mL (s) The admittance generated for the nonlinear load input admittance coupling to the system,Y _oc (s) For the system output admittance when applying the PCC voltage feed-forward,Y _oca (s) To the output admittance when no PCC voltage feed-forward is applied,Y _ocf (s) For the PCC voltage feed-forward effect equivalent admittance,Z _g (s) Is the grid impedance.

4. The method for designing SAPF parameters in consideration of load and grid impedance influences according to claim 1, wherein the modified optimal scaling factor in step (2) is expressed as follows:

wherein the content of the first and second substances,K _OPT in order to optimize the scaling factor before the correction,K _MOPT in order to obtain the optimum scaling factor after the modification,

in order to correct the factor(s),ω _s in order to sample the angular frequency of the signal,ω _r being the resonance angular frequency of the LCL filter,

is the ratio of the inverter side inductance value and the grid side inductance value in the LCL filter.

5. The SAPF parameter design method considering the influence of load and grid impedance of claim 4, wherein the correction factors are:

wherein the content of the first and second substances,

inverter side inductance values in LCL filter andthe maximum negative deviation between the capacitance value and the factory parameters.

6. The SAPF parameter design method considering load and grid impedance influence according to claim 4, wherein the inequality equation set of LCL filter parameter values in step (3) includes the following constraints:

the first constraint condition is:

the second constraint condition is as follows:

the third constraint condition is as follows:

wherein the content of the first and second substances,ω _cmin for a given minimum control bandwidth of the grid current loop,T _s is the sampling time.

7. The SAPF parameter design method considering load and grid impedance influence according to claim 4, wherein in step (4), the calculation formulas of the grid current loop controller proportional link gain and the fundamental current loop controller proportional link gain are as follows:

wherein the content of the first and second substances,ω _cmin for a given minimum control bandwidth of the grid current loop,K _pf is the proportional link gain of the fundamental current loop controller,K _ph the proportional link gain of the current loop controller of the power grid is obtained,L ₂ is LCLGrid side inductance values in the filter.

8. The SAPF parameter design method considering load and grid impedance influence as claimed in claim 1, wherein the step (5) is specifically as follows:

and (3) according to the value range of the proportional gain coefficient of the PCC power grid voltage feedforward term, the gain of the proportional link of the power grid current loop controller obtained in the step (5) and the gain of the proportional link of the fundamental current loop controller, obtaining the frequency response of the system output admittance when the PCC voltage feedforward is applied, and selecting the proportional gain coefficient of the PCC power grid voltage feedforward term as a design result in the range that the frequency response meets the passivity requirement.

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