Active filtering method for network-forming converter based on selective overcurrent limitation

Abstract

The invention belongs to the technical field of power distribution, and particularly relates to a selective over-current limitation-based active filtering method for a network-forming converter, which comprises the following steps of: S1, performing state space modeling on a VSC: (i) VSC; (ii) a main controller of the VSC (Virtual Synchronous Generator), which is realized by a virtual synchronous generator (VSG); (iii) an AHF function implemented by direct harmonic voltage control; (iv) selective harmonic overcurrent protection; s2, performing preliminary calculation on the gain of the controller; s3, linearizing the nonlinear state space model of the system provided in the step S1 near a balance point, and evaluating a characteristic value; and S4, determining a stable range of each control parameter so as to set a final control gain. According to the invention, the current component can be selectively limited under the condition that the VSC is overloaded, so that a stable AHF function is provided for the VSC.

Description

Technical Field

[0001] The present invention relates to the technical field of power distribution, and in particular to an active filtering method of a grid-type converter based on selective overcurrent limitation. Background Art

[0002] The growth of electricity demand, the increase of environmental pressure and the promotion of scientific and technological progress have made great progress in the application of renewable energy and power electronic equipment in power systems. The scale of renewable energy such as wind power and photovoltaic power in the new power sources has exceeded that of traditional fossil energy, becoming the main force to meet the growing demand for electricity. The vast majority of renewable energy is connected to the grid through power electronic interfaces, which has promoted the widespread application of power electronic equipment in power systems. It is worth noting that this situation may bring new technical challenges. With the continuous increase in the scale of new energy installed capacity, the number of conventional synchronous generators has been relatively reduced, and the rotational inertia and rotating reserve inertia in system operation have been reduced, thereby weakening the ability of the power grid to cope with load disturbances. As the system inertia decreases, the frequency and voltage deviations of the power grid will increase, thus affecting the safe and reliable operation of the power system. This change comes with the transformation of the demand side, and traditional electromechanical loads are being replaced by power electronic equipment. These nonlinear loads improve performance, efficiency and flexibility, but also introduce harmonic currents, which inevitably affect the quality of power output during the grid connection process.

[0003] At present, the main method used for harmonic control is to install passive filters, active filters or hybrid filters near large nonlinear loads, but this method will bring additional investment. Converter interfaced generators (CIGs) can also reduce harmonic distortion through appropriate control measures. Adding resonant controllers tuned to target harmonics to current or voltage control loops can improve the performance of existing harmonic controllers. In addition, VSCs may reach the output threshold of rated current and voltage during active harmonic filtering (AHF). In existing research, current limiting control strategies based on VSC can be divided into three categories: direct current limiting control, indirect current limiting control and hybrid current limiting control. It should be noted that the goal of these current limiting measures is to limit the total current and do not distinguish between different components of the current. At present, the limitation of AHF capability under VSC overload conditions has been studied in the current controller of the active power filter. However, the limitation of AHF capability under VSC overcurrent conditions under direct harmonic voltage tracking has not been studied. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is: how to selectively limit the current of the VSC in the case of an overload, so as to provide a stable AHF function.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] A grid-type converter active filtering method based on selective overcurrent limitation comprises the following steps:

[0007] S1. State space modeling of VSC: (i) VSC; (ii) main controller of VSC implemented by virtual synchronous generator (VSG); (iii) AHF function implemented by direct harmonic voltage control; (iv) selective harmonic overcurrent protection;

[0008] S2. Perform a preliminary calculation of the controller gain;

[0009] S3, linearizing the nonlinear state space model of the system proposed in step S1 near the equilibrium point to evaluate the eigenvalue;

[0010] S4. Determine the stable range of each control parameter to set the final control gain.

[0011] Preferably, in step S1, the VSC is a three-phase three-wire device connected to the grid via an LCL coupling filter, the filter also having a physical damping resistor in series with a capacitor. The grid is modeled as a series inductive impedance (R g and L g ) is an AC voltage source. VSC is at an angle θ with VSG vsg The differential equations in the synchronized dq rotating reference frame are given below:

[0012]

[0013] Among them, L t and L s They are the filter inductors on the VSC side and the grid side, R t and Rs is the corresponding resistance, C f is the filter capacitor, R d is the damping resistor, v t,dq =[v td ,v tq ] is the terminal voltage of VSC, v m,dq =[v md ,v mq ] is the voltage between the capacitor and the damping resistor, v c,dq =[v cd ,v cq ] is the capacitor voltage, v s,dq =[v sd ,v sq ] is the voltage of POI, v g,dq =[vgd ,v gq ] is the grid voltage, i t,dq =[i td ,i tq ] is the inductor current on the VSC side, i s,dq =[i sd ,i sq ] is the grid-side inductor current, ω vsg is the angular frequency of VSG.

[0014] Considering the above equations, the model of the grid-connected VSC will add six state variables x to the state space equations: f .

[0015] x f =[i td ,i tq ,i sd ,i sq ,v cd ,v cq ] (6)

[0016] Preferably, in step S1, the VSG selected to provide networking capacity is composed of an outer control loop (Outer Control Loop, OCL) and an inner control loop (Inner Control Loop, ICL).

[0017] The OCL consists of two parallel proportional-integral (PI) controllers for active and reactive power, respectively. Figure 1 The active power controller modifies the virtual rotor angle θ vsg To achieve synchronization with the power grid. The reactive power controller calculates the amplitude E of the virtual electromotive force. Therefore, OCL can be described by the following equation:

[0018]

[0019] Among them, ξ p is the integral of the active power error, p is the active power of the POI, and p ＊ is the reference active power, ω 0 is the rated frequency, k pp and k ip are the proportional and integral gains of the PI active power controller, ξ q is the integral of the reactive power error, q is the reactive power of the POI, and q ＊ is the reference reactive power, E 0 is the rated electromotive force, k pq and k iq are the proportional and integral gains of the PI reactive power controller.

[0020] The active and reactive powers p and q of the POI can be described by the following equations in the dq coordinate system:

[0021]

[0022] like Figure 2 As shown, the direction of the electromotive force is consistent with the direction of the q axis. Therefore, the electromotive force in the dq coordinate is always equal to e dq =[0,-E]. On the other hand, assuming that the grid voltage is at rated frequency ω 0 rotation. This means that the grid voltage is considered as a disturbance that does not add any dynamics to the system. Therefore, the grid voltage V can be defined as g The phase difference between the electromotive force E is ψ, such as Figure 2 As shown, the grid voltage V g Dynamic changes according to VSG angle:

[0023]

[0024] This approach allows replacing θ with ψ in (7) vsg , keeping the dynamic characteristics of the VSG but adding the grid angular frequency ω to the model 0 impact.

[0025] The ICL consists of a single PI current controller implemented in the dq axis. The current reference is determined by the electromotive force e dq , POI voltage v s,dq And virtual admittance Yv = Gv-jB v In addition, before these reference currents are introduced into the current controller, they are also low-pass filtered (LPF) to provide reference values ​​with low harmonic content. and It can be expressed as:

[0026]

[0027] Among them, τ lpf is the time constant of the low-pass filter, is the filtered reference current.

[0028] Finally, the PI current controller equation including the cross-coupling cancellation term and the feed-forward term is:

[0029]

[0030] Among them, ξ id and iq is the current error integral on the dq axis, k pi and k iiThey are the proportional gain and integral gain of the PI current controller respectively.

[0031] According to (7)-(13), the VSG control loop model adds seven new state variables to the state space equations:

[0032]

[0033] Preferably, in step S1, the selected AHF function implemented by direct harmonic voltage control is implemented by a set of resonant controllers included on each target harmonic. Its goal is to track the harmonic voltage reference value in the αβ coordinate system, This corresponds to the POI harmonic voltage. Note that the resonant controllers are implemented in the αβ coordinate system, not in the dq coordinate system, because each harmonic needs to be compensated in its corresponding sequence. These resonant controllers generate a new current reference value, Before adding it to the VSG fundamental reference current (13), it needs to be converted into the dq coordinate system, such as Figure 1 shown.

[0034] In the Laplace domain, the resonant controller in the αβ coordinate system can be expressed as:

[0035]

[0036] Among them, h,αβ =[ò hα ,ò hβ ] represents the harmonic voltage error, v s,αβ =[v sα ,v sβ ] represents the harmonic voltage of POI, and k rh , δ h and ω h represent the gain, damping and tuned harmonic frequency of the hth harmonic resonant controller, respectively. However, it is necessary to transform equation (15) into the dq coordinate system, considering the derived grid-connected VSC and VSG models.

[0037]

[0038] Among them, h,dq =[ò hd ,ò hq ] represents the harmonic voltage error, represents the reference harmonic current, and represents the reference harmonic voltage. Finally, the time domain expression of equation (16) is as follows:

[0039]

[0040] Among them, γ h,dq=[γ hd ,γ hq ] is a new state variable, representing the Points:

[0041]

[0042]

[0043] It should be noted that for the reference harmonic current Perfect tracking of requires the use of resonant controllers tuned for each harmonic, just like the controller for the harmonic voltages. However, it is also possible to use only a conventional PI controller in combination with a resonant voltage controller, providing a high bandwidth to track the reference harmonic currents. In this way, the computational cost of the harmonic function is greatly reduced.

[0044] Harmonic voltage control introduces four new differential equations (17)-(18) for each target harmonic h, and their corresponding state variables:

[0045]

[0046] Preferably, in step S1, the selected selective harmonic overcurrent protection is used to achieve a perfect sinusoidal POI voltage, and the harmonic voltage reference The default setting is zero. An ideal resonant controller injects additional harmonic currents to ensure that the harmonic voltage is zero. However, if these current terms are not limited, this may lead to overloading of the VSC. To avoid this, we add an algebraic virtual harmonic impedance Z h =R h +jX h , which modifies the default harmonic voltage reference in the dq reference frame as follows:

[0047]

[0048] Parameter R h and X h It can be defined independently for each harmonic, depending on the limits imposed by the existing grid code. Larger virtual harmonic impedances can be associated with harmonics with higher permissible limits. For this purpose, different harmonic weighting factors σ are used. h , to define virtual harmonic impedances relative to a reference value, as follows:

[0049] R h +jX h =σ h (R b +jL b ω h ) (twenty two)

[0050] Among them, R b and L b In this way, the compensation of each harmonic can be selectively reduced to avoid the VSC overcurrent condition.

[0051] Table I shows the maximum harmonic voltage amplitude and weighting factor values ​​allowed by the EN 50160 standard:

[0052]

[0053] Table I

[0054] Table I defines a set of harmonic weighting factors taking into account the voltage harmonic limits specified in standard EN 50160. Note that the lowest harmonic weighting factor is assigned to the harmonic with the lowest limit, i.e. the sixth harmonic, while the other factors are assigned according to their relative amplitude A. h Zoomed:.

[0055]

[0056] In order to prevent the VSC from overloading, the reference virtual harmonic impedance is dynamically adjusted according to the VSC current. According to (21) and (22), the reference virtual harmonic impedance can be expressed as a function of harmonic voltage, harmonic current and fundamental current. This patent proposes an adaptive method in which the reference virtual harmonic impedance is adjusted when the VSC current is greater than the rated current I rat Considering that the reference virtual harmonic impedance is defined as a piecewise linear function, a hysteresis band ±H is added. Is to limit impedance changes. The band is around a rat The current I hys And setting, such as Figure 3 If the POI current I s Below I rat , then the reference virtual harmonic impedance is set to zero, that is, A sinusoidal POI voltage can be achieved. However, if I s Greater than I rat , the overcurrent limit is activated by linearly increasing the base virtual harmonic impedance as shown below:

[0057]

[0058] Among them, m r and m l are the rates of change of the reference virtual harmonic resistance and inductance, respectively, and Δt is the sampling time of the controller. Therefore, due to the reduction of harmonic current, the VSC current decreases to I hysFrom this point on, the reference virtual harmonic impedance remains constant. Once the VSC current drops to the threshold I hys -H Is Below this value, the base virtual harmonic impedance decreases. This results in an increase in the injected harmonic current. If the VSC current reaches I hys and the base virtual harmonic impedance is not zero, the VSC current will be limited to this value, such as Figure 3 If I hys However, the base virtual harmonic impedance is zero, which allows the VSC current to increase to I hys Above, as long as it does not exceed I rat . About the component R of the reference virtual harmonic impedance b and L b The impact on the control algorithm is discussed in Section III.

[0059] The differential equations in the previous four parts (1)-(23) can be combined into a unique state-space model that integrates the system and control dynamics:

[0060]

[0061] Preferably, in S2, Figure 1 The preliminary calculation of the control gain of the VSG outer control loop OCL is as follows: The active power control loop is based on a PI controller. The integral gain k ip is calculated to obtain a given inertial response, and the proportional gain k pp These gains are initially calculated according to the following formula:

[0062]

[0063] Where H is the inertia constant, V g is the peak value of the grid voltage, and X v =1 / Y v is the virtual impedance. Similarly, the gain of the reactive power control loop is preliminarily calculated as:

[0064]

[0065] Among them, S n is the rated power of the VSC.

[0066]

[0067] Preferably, in S2, Figure 1 The initial calculation of the control gain of the VSG internal control loop ICL is as follows: Virtual admittance Y v is defined as a pure inductive impedance and is set to 10% of the VSC base impedance, while the time constant τ of the low-pass filter LPF islpf is set to 1.6 milliseconds. The proportional and integral gains of the current control loop are initially calculated as follows:

[0068]

[0069] Among them, M p is the phase margin, ω c is the cutoff filter frequency. They are usually set to π / 3 and 20% of the maximum compensated harmonic frequency, respectively. The reference virtual harmonic impedance is initially set to zero to achieve full voltage harmonic compensation at the POI.

[0070] Preferably, in S3, the stability analysis is performed by 0 The linearized state space equations are then analyzed by small signal model. By solving (25) we can obtain and the equilibrium point for a given input vector u. The analysis has taken into account the preliminary controller gains calculated in S1, detailed in Table II, and the calculated VSC characteristics in Table III. The input u has been set to the case where the VSC injection power is equal to 9kW and 4.5kvar. Regarding the AHF function, the target harmonics are the 5th and 7th harmonics, and the reference virtual harmonic impedance is zero.

[0071] Table II shows the initial value, range and final value of the controller gain:

[0072]

[0073] Table II

[0074] Table III shows the system parameters used for stability analysis and experimental verification:

[0075]

[0076] Table III

[0077] The linearization of the system is performed as follows:

[0078]

[0079] Get the small signal model:

[0080]

[0081] Matrix A 0 and B 0 are the linearization matrices of matrices A and B respectively.

[0082] The stability of the system can be evaluated by analyzing the eigenvalues ​​of A0 near the equilibrium point, such as Figure 4As shown, preliminary values ​​of the controller gains are given. All eigenvalues ​​have non-zero real parts, which means that the system is linearized around a hyperbolic equilibrium point. According to the Hartman-Grobman theorem, the system is structurally stable, so at this equilibrium point the linearized system represents a nonlinear system. It is worth noting that the AHF function introduces non-conjugate eigenvalues. In particular, the 5th harmonic compensation is related to +400πrad / s(λ 18 ,λ 19 ) and -600πrad / s(λ 16 ,λ 17 ) is related to the eigenvalue at +600πrad / s(λ). 20 ,λ 21 ) and -800πrad / s(λ 15 ,λ 16 ) place.

[0083] Preferably, in S4, the stability range of the system is evaluated using a small signal model, taking into account possible variations of the controller gain and the grid impedance. To this end, the evolution of the eigenvalues ​​in the complex plane is analyzed when these parameters are modified within the ranges detailed in Table II. The results are presented using two graphs, focusing on the eigenvalues ​​of the VSG dynamics (left side) and the AHF function (right side). The arrows in these figures indicate the direction of the change of the eigenvalues ​​as the analyzed parameters evolve.

[0084] Preferably, in S4, the small signal of the VSG active power control loop is evaluated as follows: According to (26), the integral gain k ip is inversely proportional to the inertia constant H. Considering that H is in the interval [0.01,20]s, the results are as follows Figure 4 For very small inertia constants (H < 1s), the system is unstable. Larger H can stabilize the system because the real part of the eigenvalues ​​decreases. Therefore, H is adjusted to the desired VSC inertia response, but greater than 1s to ensure system stability. As for the eigenvalues ​​of AHF, as shown in the upper right figure, these are almost unaffected by changes in this parameter. pp , if increased, it will endanger the stability of the system, such as Figure 4 This effect is shown in the lower left figure. pp >10 -3 rad / (sW) further intensifies, when k pp =10 -3 When 4 and λ 10 The damping of is significantly reduced from 0.8 to almost zero, both of which are related to the VSG dynamics. The effect on the AHF eigenvalue is asymmetric, such as Figure 4The eigenvalues ​​at negative frequencies are uniformly damped, while the eigenvalues ​​at positive frequencies gradually separate from each other and tend toward the imaginary axis.

[0085] Preferably, in S4, the small signal of the VSG reactive power control loop is evaluated as follows: The impact of such a control loop is usually ignored in small signal analysis. Figure 5 It shows that as k pq and k iq This assumption is further strengthened by the increase in the eigenvalue. pq The increase of , the characteristic value is significantly affected, but it does not reduce the stability of the system. Therefore, this gain is selected according to the required VSC reactive power injection under a given POI voltage change. On the other hand, the integral gain k iq There is almost no impact on dynamics, such as Figure 5 Shown at bottom.

[0086] Preferably, in S4, the small signal evaluation of the VSG virtual admittance is as follows: Figure 6 The effect of virtual conductance and susceptance is shown. Virtual conductance G v It has little effect on the system dynamics, and as its value increases, the eigenvalues ​​will only shift slightly. Virtual Susceptance B v When it decreases, the damping of most eigenvalues ​​decreases slightly. Considering the virtual conductance G v It has little effect on the system dynamics, so the virtual admittance is set to a pure inductance Y v =-jB v .

[0087] Preferably, in S4, the small signal evaluation of the VSG LPF time constant is as follows: The LPF time constant is zero, that is, a controller without LPF will lead to system instability, where λ 2,10 =472.92±j10889π. Figure 7 As shown on the left, as τ lpf The increase of eigenvalue λ 3 , 4 , 10 and λ 11 The natural frequency of is reduced through a constant damping path until it reaches a value consisting only of negative real parts. As for the eigenvalue λ 2 and λ 12 , they move to the left, increasing the stability of the system. On the contrary, the eigenvalue λ 1 and λ 13To the right, which may lead to system instability. On the other hand, the eigenvalues ​​related to AHF hardly move to the left when the LPF bandwidth is reduced. From this analysis, it can be seen that considering that the goal of the LPF is to provide a reference current with the lowest possible harmonic content without affecting the dynamics of the current control loop, the LPF time constant is set to τ lpf =1.6ms.

[0088] Preferably, in S4, the small signal evaluation of the VSG current controller is as follows: The gain of the PI current controller is limited by the minimum time constant of 1 ms, so the maximum value is k pi =5 and k ii =157. Figure 8 Describes the pi and k ii The change of eigenvalues ​​in the range. pi As the value of increases, the damping of VSG and AHF increases. As expected, the wider the PI controller bandwidth, the better the system performance. ii The impact on system stability is not obvious. However, k ii Depends on the resistance of the coupling filter, as shown in (28). This patent assumes that the quality factor of the inductor is equal to 10. However, considering that the resistance is prone to large changes in practice (manufacturing tolerance, temperature, material degradation, wiring, etc.), k ii The final value of is adjusted through some experimental tests so that the closed-loop time constant τ of the current controller i =1ms.

[0089] Preferably, in S4, the small signal of AHF is evaluated as follows: The AHF function only works on the 5th and 7th harmonics. For simplicity, it is assumed that k r5 =k r7 =k rh and δ 5 =δ 7 =δ h .like Fig. 9 As shown, increasing δ h This will increase the damping of the AHF and thus affect the performance, but will not have any effect on the VSG dynamics. h = 0 for the best performance, but this will lead to stability limitations, which depend mainly on the external damping source. Again, δ h It is a balance between providing enough AHF capability and sufficient damping. On the other hand, the resonant gain k rh The VSG and AHF dynamics are greatly affected, especially for values ​​above 100. The natural frequencies of the AHF eigenvalues ​​are greatly affected, especially those corresponding to negative sequences. rhA low value is taken so that AHF affects the VSG performance as little as possible. It is worth noting that the bandwidth of the harmonic voltage controller, involving the series operation of the resonant and PI current controllers, is 2931.1 rad / s according to the final value of the controller gain summarized in Table II. This controller bandwidth is sufficient to reduce the 5th and 7th harmonic voltages without adding an additional resonant controller in the VSG current control.

[0090] Preferably, in S4, the small signal evaluation of the overcurrent protection is as follows: Fig.10 The effect of the resistive and inductive terms of the fundamental virtual harmonic impedance on stability is shown. The VSG eigenvalue is almost unaffected, while the AHF eigenvalue has a significant effect on R b and L b The resistance term causes the eigenvalue to shift to the left and the damping to increase. In contrast, the inductance term L b When it is greater than 80μH, the system becomes unstable. Therefore, the fundamental virtual harmonic impedance must be purely resistive.

[0091] Preferably, in S4, the small signal of the grid impedance is evaluated as follows: R g and L g Various values ​​of have been extensively studied. The higher the resistance, the higher the damping for all eigenvalues. Even if R g The value of is zero, and the system remains stable. The eigenvalue of the average frequency, such as λ 3 , 4 , 10 and λ 11 , tends to move to the right, thus making weak grids (such as island grids) unstable. g increases, the eigenvalue moves toward the imaginary axis. g For values ​​above 1mH and an R / X ratio of 0.07, the system becomes unstable. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 Schematic diagram of the proposed control scheme of the present invention with AHF and overcurrent protection VSC;

[0093] Figure 2 It is the schematic diagram of the grid voltage VSG electromotive force in the αβ and dq frames;

[0094] Figure 3 Overview of the hysteresis band for selective overload reduction. ;

[0095] Figure 4 Schematic diagram of the change of eigenvalue when the gain changes in the active power control loop (H∈[0.01,20]s, k pp ∈[10 -4 ,10-2 ]);

[0096] Figure 5 Schematic diagram of the change of characteristic value when the gain changes in the reactive power control loop (k pq ∈[10 -4 ,10 -2 ]V / W,k iq ∈[10 -3 ,10 -1 ]V / W);

[0097] Figure 6 Schematic diagram of the change of eigenvalue when the VSG virtual admittance changes (G v =[0,125]S,B v ∈[0.125,125]S);

[0098] Figure 7 Schematic diagram of the change of characteristic value when the LPF time constant changes (τ lpf ∈[0.16,3.2]ms, bandwidth BW lpf ∈[1000,50]Hz);

[0099] Figure 8 Schematic diagram of the change of characteristic value when the PI current controller changes (k pi ∈[1,5]V / A and k ii ∈[1.8,157]V / A);

[0100] Fig. 9 The schematic diagram of the change of the characteristic value when the AHF resonant controller changes (δ h ∈[0,10 -3 ],k rh ∈[1,50]A / V);

[0101] Fig.10 Schematic diagram of the change of characteristic value when the basic virtual harmonic impedance changes (R b ∈[0,0.3]Ω,L b ∈[0,0.15]mH);

[0102] Fig.11 The schematic diagram of the change of characteristic value when the grid impedance changes (R g ∈[0,1]Ω,,L g ∈[0,1]mH);

[0103] Fig.12 is a flow chart in an embodiment; DETAILED DESCRIPTION

[0104] In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. Unless otherwise defined, the technical terms or scientific terms used herein should be the common meaning understood by people with general skills in the field to which the present invention belongs.

[0105] The words "first", "second" and similar words used in the patent application specification and claims of the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, unless the context clearly indicates otherwise, the singular forms of "a", "an" or "the" and other similar words do not indicate a quantitative limitation, but indicate the existence of at least one. Words such as "include" or "comprise" mean that the elements or objects appearing before "include" or "comprise" cover the features, wholes, steps, operations, elements and / or components listed after "include" or "comprise", and do not exclude the existence or addition of one or more other features, wholes, steps, operations, elements, components and / or their collections. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0106] S1. State space modeling of VSC: (i) VSC; (ii) main controller of VSC implemented by virtual synchronous generator (VSG); (iii) AHF function implemented by direct harmonic voltage control; (iv) selective harmonic overcurrent protection;.

[0107] In specific implementation, the process of state space modeling can be expressed as follows:

[0108] In step S1, the VSC is a three-phase three-wire device connected to the grid through an LCL coupling filter, which also has a physical damping resistor in series with a capacitor. The grid is modeled as a series inductive impedance (R g and L g ) is an AC voltage source. VSC is at an angle θ with VSG vsg The differential equations in the synchronized dq rotating reference frame are given below:

[0109]

[0110] Among them, Lt and L s They are the filter inductors on the VSC side and the grid side, R t and Rs is the corresponding resistance, C f is the filter capacitor, R d is the damping resistor, v t,dq =[v td ,v tq ] is the terminal voltage of VSC, v m,dq =[v md ,v mq ] is the voltage between the capacitor and the damping resistor, v c,dq =[v cd ,v cq ] is the capacitor voltage, v s,dq =[v sd ,v sq ] is the voltage of POI, v g,dq =[v gd ,v gq ] is the grid voltage, i t,dq =[i td ,i tq ] is the inductor current on the VSC side, i s,dq =[i sd ,i sq ] is the grid-side inductor current, ω vsg is the angular frequency of VSG.

[0111] Considering the above equations, the model of the grid-connected VSC will add six state variables x to the state space equations: f .

[0112] x f =[i td ,i tq ,i sd ,i sq ,v cd ,v cq ] (37)

[0113] In step S1, the VSG selected to provide networking capacity is composed of an outer control loop (Outer Control Loop, OCL) and an inner control loop (Inner Control Loop, ICL).

[0114] The OCL consists of two parallel proportional-integral (PI) controllers for active and reactive power, respectively. Figure 1 The active power controller modifies the virtual rotor angle θ vsg To achieve synchronization with the power grid. The reactive power controller calculates the amplitude E of the virtual electromotive force. Therefore, OCL can be described by the following equation:

[0115]

[0116] Among them, ξ p is the integral of the active power error, p is the active power of the POI, and p ＊ is the reference active power, ω 0 is the rated frequency, k pp and k ip are the proportional and integral gains of the PI active power controller, ξ q is the integral of the reactive power error, q is the reactive power of the POI, and q ＊ is the reference reactive power, E 0 is the rated electromotive force, k pq and k iq are the proportional and integral gains of the PI reactive power controller.

[0117] The active and reactive powers p and q of the POI can be described by the following equations in the dq coordinate system:

[0118]

[0119] like Figure 2 As shown, the direction of the electromotive force is consistent with the direction of the q axis. Therefore, the electromotive force in the dq coordinate is always equal to e dq =[0,-E]. On the other hand, assuming that the grid voltage is at rated frequency ω 0 rotation. This means that the grid voltage is considered as a disturbance that does not add any dynamics to the system. Therefore, the grid voltage can be defined as V g The phase difference between the electromotive force E is ψ, such as Figure 2 As shown, the grid voltage V g Dynamic changes according to VSG angle:

[0120]

[0121] This approach allows replacing θ with ψ in (7) vsg , keeping the dynamic characteristics of the VSG but adding the grid angular frequency ω to the model 0 impact.

[0122] The ICL consists of a single PI current controller implemented in the dq axis. The current reference is determined by the electromotive force e dq , POI voltage v s,dq And virtual admittance Yv = Gv-jB v In addition, before these reference currents are introduced into the current controller, they are also low-pass filtered (LPF) to provide reference values ​​with low harmonic content. and It can be expressed as:

[0123]

[0124] Among them, τ lpf is the time constant of the low-pass filter, is the filtered reference current.

[0125] Finally, the PI current controller equation including the cross-coupling cancellation term and the feed-forward term is

[0126]

[0127] Among them, ξ id and iq is the current error integral on the dq axis, k pi and k ii They are the proportional gain and integral gain of the PI current controller respectively.

[0128] According to (7)-(13), the VSG control loop model adds seven new state variables to the state space equations:

[0129]

[0130] In step S1, the selected AHF function implemented by direct harmonic voltage control is implemented by a set of resonant controllers included on each target harmonic. Its goal is to track the harmonic voltage reference value in the αβ coordinate system, This corresponds to the POI harmonic voltage. Note that the resonant controllers are implemented in the αβ coordinate system, not in the dq coordinate system, because each harmonic needs to be compensated in its corresponding sequence. These resonant controllers generate a new current reference value, Before adding it to the VSG fundamental reference current (13), it needs to be converted into the dq coordinate system, such as Figure 1 shown.

[0131] In the Laplace domain, the resonant controller in the αβ coordinate system can be expressed as:

[0132]

[0133] Among them, h,αβ =[ò hα ,ò hβ ] represents the harmonic voltage error, v s,αβ =[v sα ,v sβ ] represents the harmonic voltage of POI, and k rh , δ h and ω hrepresent the gain, damping and tuned harmonic frequency of the hth harmonic resonant controller, respectively. However, it is necessary to transform equation (15) into the dq coordinate system, considering the derived grid-connected VSC and VSG models.

[0134]

[0135] Among them, h,dq =[ò hd ,ò hq ] represents the harmonic voltage error, represents the reference harmonic current, and represents the reference harmonic voltage. Finally, the time domain expression of equation (16) is as follows:

[0136]

[0137] Among them, γ h,dq =[γ hd ,γ hq ] is a new state variable, representing the Points:

[0138]

[0139]

[0140] It should be noted that for the reference harmonic current Perfect tracking of requires the use of resonant controllers tuned for each harmonic, just like the controller for the harmonic voltages. However, it is also possible to use only a conventional PI controller in combination with a resonant voltage controller, providing a high bandwidth to track the reference harmonic currents. In this way, the computational cost of the harmonic function is greatly reduced.

[0141] Harmonic voltage control introduces four new differential equations (17)-(18) for each target harmonic h, and their corresponding state variables:

[0142]

[0143] In step S1, the selected selective harmonic overcurrent protection is used to achieve a perfect sinusoidal POI voltage. The harmonic voltage reference The default setting is zero. An ideal resonant controller injects additional harmonic currents to ensure that the harmonic voltage is zero. However, if these current terms are not limited, this may lead to overloading of the VSC. To avoid this, we add an algebraic virtual harmonic impedance Z h =R h +jX h, which modifies the default harmonic voltage reference in the dq reference frame as follows:

[0144]

[0145] Parameter R h and X h It can be defined independently for each harmonic, depending on the limits imposed by the existing grid code. Larger virtual harmonic impedances can be associated with harmonics with higher permissible limits. For this purpose, different harmonic weighting factors σ are used. h , to define virtual harmonic impedances relative to a reference value, as follows:

[0146] R h +jX h =σ h (R b +jL b ω h ) (53)

[0147] Among them, R b and L b In this way, the compensation of each harmonic can be selectively reduced to avoid the VSC overcurrent condition.

[0148] Table I defines a set of harmonic weighting factors taking into account the voltage harmonic limits specified in standard EN 50160. Note that the lowest harmonic weighting factor is assigned to the harmonic with the lowest limit, i.e. the sixth harmonic, while the other factors are assigned according to their relative amplitude A. h Zoomed:.

[0149]

[0150] In order to prevent the VSC from overloading, the reference virtual harmonic impedance is dynamically adjusted according to the VSC current. According to (21) and (22), the reference virtual harmonic impedance can be expressed as a function of harmonic voltage, harmonic current and fundamental current. This patent proposes an adaptive method in which the reference virtual harmonic impedance is adjusted when the VSC current is greater than the rated current I rat Considering that the reference virtual harmonic impedance is defined as a piecewise linear function, a hysteresis band ±H is added. Is to limit impedance changes. The band is around a rat The current I hys And setting, such as Figure 3 If the POI current I s Below I rat , then the reference virtual harmonic impedance is set to zero, that is, A sinusoidal POI voltage can be achieved. However, if Is Greater than I rat , the overcurrent limit is activated by linearly increasing the base virtual harmonic impedance as shown below:

[0151]

[0152] Among them, m r and m l are the rates of change of the reference virtual harmonic resistance and inductance, respectively, and Δt is the sampling time of the controller. Therefore, due to the reduction of harmonic current, the VSC current decreases to I hys From this point on, the reference virtual harmonic impedance remains constant. Once the VSC current drops to the threshold I hys -H Is Below this value, the base virtual harmonic impedance decreases. This results in an increase in the injected harmonic current. If the VSC current reaches I hys and the base virtual harmonic impedance is not zero, the VSC current will be limited to this value, such as Figure 3 If I hys However, the base virtual harmonic impedance is zero, which allows the VSC current to increase to I hys Above, as long as it does not exceed I rat . About the component R of the reference virtual harmonic impedance b and L b The impact on the control algorithm is discussed in Section III.

[0153] The differential equations in the previous four parts (1)-(23) can be combined into a unique state-space model that integrates the system and control dynamics:

[0154]

[0155] S2. Perform a preliminary calculation of the controller gain.

[0156] In specific implementation, in S2, Figure 1 The preliminary calculation of the control gain of the VSG outer control loop OCL is as follows: The active power control loop is based on a PI controller. The integral gain k ip is calculated to obtain a given inertial response, and the proportional gain k pp These gains are initially calculated according to the following formula:

[0157]

[0158] Where H is the inertia constant, V g is the peak value of the grid voltage, and X v =1 / Y vis the virtual impedance. Similarly, the gain of the reactive power control loop is preliminarily calculated as:

[0159]

[0160] Among them, S n is the rated power of the VSC.

[0161]

[0162] In S2, Figure 1 The initial calculation of the control gain of the VSG internal control loop ICL is as follows: Virtual admittance Y v is defined as a pure inductive impedance and is set to 10% of the VSC base impedance, while the time constant τ of the low-pass filter LPF is lpf is set to 1.6 milliseconds. The proportional and integral gains of the current control loop are initially calculated as follows:

[0163]

[0164] Among them, M p is the phase margin, ω c is the cutoff filter frequency. They are usually set to π / 3 and 20% of the maximum compensated harmonic frequency, respectively. The reference virtual harmonic impedance is initially set to zero to achieve full voltage harmonic compensation at the POI.

[0165] S3. Linearize the nonlinear state space model of the system proposed in step S1 near the equilibrium point to evaluate the eigenvalues.

[0166] In the specific implementation, in S3, the stability analysis is performed by 0 The linearized state space equations are then analyzed by small signal model. By solving (25) we can obtain and the equilibrium point for a given input vector u. The analysis has taken into account the preliminary controller gains calculated in S1, detailed in Table II, and the calculated VSC characteristics in Table III. The input u has been set to the case where the VSC injection power is equal to 9kW and 4.5kvar. Regarding the AHF function, the target harmonics are the 5th and 7th harmonics, and the reference virtual harmonic impedance is zero.

[0167] The linearization of the system is performed as follows:

[0168]

[0169] Get the small signal model:

[0170]

[0171] Matrix A 0 and B 0are the linearization matrices of matrices A and B respectively.

[0172] The stability of the system can be evaluated by analyzing the eigenvalues ​​of A0 near the equilibrium point, such as Figure 4 As shown, preliminary values ​​of the controller gains are given. All eigenvalues ​​have non-zero real parts, which means that the system is linearized around a hyperbolic equilibrium point. According to the Hartman-Grobman theorem, the system is structurally stable, so at this equilibrium point the linearized system represents a nonlinear system. It is worth noting that the AHF function introduces non-conjugate eigenvalues. In particular, the 5th harmonic compensation is related to +400πrad / s(λ 18 ,λ 19 ) and -600πrad / s(λ 16 ,λ 17 ) is related to the eigenvalue at +600πrad / s(λ). 20 ,λ 21 ) and -800πrad / s(λ 15 ,λ 16 ) place.

[0173] In S4, the stability range of the system is evaluated using a small signal model, taking into account possible variations of the controller gains and the grid impedance. To this end, the evolution of the eigenvalues ​​in the complex plane is analyzed when these parameters are modified within the ranges detailed in Table II. The results are presented using two graphs, focusing on the eigenvalues ​​of the VSG dynamics (left side) and the AHF function (right side). The arrows in these graphs indicate the direction of the eigenvalue changes as the analyzed parameters evolve.

[0174] S4. Determine the stable range of each control parameter to set the final control gain.

[0175] In specific implementation, in S4, the small signal evaluation of the VSG active power control loop is as follows: According to (26), the integral gain k ip is inversely proportional to the inertia constant H. Considering that H is in the interval [0.01,20]s, the results are as follows Figure 4 For very small inertia constants (H < 1s), the system is unstable. Larger H can stabilize the system because the real part of the eigenvalues ​​decreases. Therefore, H is adjusted to the desired VSC inertia response, but greater than 1s to ensure system stability. As for the eigenvalues ​​of AHF, as shown in the upper right figure, these are almost unaffected by changes in this parameter. pp , if increased, it will endanger the stability of the system, such as Figure 4 This effect is shown in the lower left figure. pp >10 -3rad / (sW) further intensifies, when k pp =10 -3 When 4 and λ 10 The damping of is significantly reduced from 0.8 to almost zero, both of which are related to the VSG dynamics. The effect on the AHF eigenvalue is asymmetric, such as Figure 4 The eigenvalues ​​at negative frequencies are uniformly damped, while the eigenvalues ​​at positive frequencies gradually separate from each other and tend toward the imaginary axis.

[0176] In S4, the small signal evaluation of the VSG reactive power control loop is as follows: The impact of this control loop is usually ignored in small signal analysis. Figure 5 It shows that as k pq and k iq This assumption is further strengthened by the increase in the eigenvalue. pq The increase of , the characteristic value is significantly affected, but it does not reduce the stability of the system. Therefore, this gain is selected according to the required VSC reactive power injection under a given POI voltage change. On the other hand, the integral gain k iq There is almost no impact on dynamics, such as Figure 5 Shown at bottom.

[0177] In specific implementation, in S4, the small signal evaluation of VSG virtual admittance is as follows: Figure 6 The effect of virtual conductance and susceptance is shown. Virtual conductance G v It has little effect on the system dynamics, and as its value increases, the eigenvalues ​​will only shift slightly. Virtual Susceptance B v When it decreases, the damping of most eigenvalues ​​decreases slightly. Considering the virtual conductance G v It has little effect on the system dynamics, so the virtual admittance is set to a pure inductance Y v =-jB v .

[0178] In specific implementation, in S4, the small signal evaluation of the VSG LPF time constant is as follows: The LPF time constant is zero, that is, the controller without LPF will cause system instability, where λ 2,10 =472.92±j10889π. Figure 7 As shown on the left, as τ lpf The increase of eigenvalue λ 3 , 4 , 10 and λ 11 The natural frequency of is reduced through a constant damping path until it reaches a value consisting only of negative real parts. As for the eigenvalue λ 2 and λ 12, they move to the left, increasing the stability of the system. On the contrary, the eigenvalue λ 1 and λ 13 To the right, which may lead to system instability. On the other hand, the eigenvalues ​​related to AHF hardly move to the left when the LPF bandwidth is reduced. From this analysis, it can be seen that considering that the goal of the LPF is to provide a reference current with the lowest possible harmonic content without affecting the dynamics of the current control loop, the LPF time constant is set to τ lpf =1.6ms.

[0179] In specific implementation, in S4, the small signal evaluation of the VSG current controller is as follows: The gain of the PI current controller is limited by the minimum time constant of 1ms, so the maximum value is k pi =5 and k ii =157. Figure 8 Describes the pi and k ii The change of eigenvalues ​​in the range. pi As the value of increases, the damping of VSG and AHF increases. As expected, the wider the PI controller bandwidth, the better the system performance. ii The impact on system stability is not obvious. However, k ii Depends on the resistance of the coupling filter, as shown in (28). This patent assumes that the quality factor of the inductor is equal to 10. However, considering that the resistance is prone to large changes in practice (manufacturing tolerance, temperature, material degradation, wiring, etc.), k ii The final value of is adjusted through experimental tests so that the closed-loop time constant τ of the current controller i =1ms.

[0180] In specific implementation, in S4, the small signal of AHF is evaluated as follows: The AHF function only works on the 5th and 7th harmonics. For simplicity, it is assumed that k r5 =k r7 =k rh and δ 5 =δ 7 =δ h .like Fig. 9 As shown, increasing δ h This will increase the damping of the AHF and thus affect the performance, but will not have any effect on the VSG dynamics. h = 0 for the best performance, but this will lead to stability limitations, which depend mainly on the external damping source. Again, δ h It is a balance between providing enough AHF capability and sufficient damping. On the other hand, the resonant gain k rhThe VSG and AHF dynamics are greatly affected, especially for values ​​above 100. The natural frequencies of the AHF eigenvalues ​​are greatly affected, especially those corresponding to negative sequences. rh A low value is taken so that AHF affects the VSG performance as little as possible. It is worth noting that the bandwidth of the harmonic voltage controller, involving the series operation of the resonant and PI current controllers, is 2931.1 rad / s according to the final value of the controller gain summarized in Table II. This controller bandwidth is sufficient to reduce the 5th and 7th harmonic voltages without adding an additional resonant controller in the VSG current control.

[0181] In specific implementation, in S4, the small signal evaluation of overcurrent protection is as follows: Fig.10 The effect of the resistive and inductive terms of the fundamental virtual harmonic impedance on stability is shown. The VSG eigenvalue is almost unaffected, while the AHF eigenvalue has a significant effect on R b and L b The resistance term causes the eigenvalue to shift to the left and the damping to increase. In contrast, the inductance term L b When it is greater than 80μH, the system becomes unstable. Therefore, the fundamental virtual harmonic impedance must be purely resistive.

[0182] In specific implementation, in S4, the small signal evaluation of the grid impedance is as follows: R g and L g Various values ​​of have been extensively studied. The higher the resistance, the higher the damping for all eigenvalues. Even if R g The value of is zero, and the system remains stable. The eigenvalue of the average frequency, such as λ 3 , 4 , 10 and λ 11 , tends to move to the right, thus making weak grids (such as island grids) unstable. g increases, the eigenvalue moves toward the imaginary axis. g For values ​​above 1mH and an R / X ratio of 0.07, the system becomes unstable.

[0183] In summary, this paper stabilizes the AHF capability by introducing a direct harmonic voltage controller that implements selective current limitation under VSC overload conditions. Specifically, a selective current limitation strategy is proposed to adjust the AHF capability of the VSC to prevent VSC overload. The strategy feeds the harmonic voltage reference (obtained as a function of the injected VSC current and virtual harmonic impedance) into a set of resonant controllers whose frequencies are tuned to the target harmonic frequencies. The outputs of these controllers are added to the reference current of the VSG current control loop. The value of the virtual harmonic impedance for each harmonic is selected based on the relative importance of each harmonic in existing power quality standards such as EN 50160. This allows for the priority to be given to reducing the VSC harmonic current under overload conditions. The dynamic performance and stability of the controllers, as well as the impact of each controller gain, are evaluated through sensitivity analysis based on a small signal model based on state-space equations. The analysis shows that tuning the proportional gain in the VSG active power control loop, the proportional gain of the PI current controller, the LPF of the current controller, and the virtual harmonic reactance in the overload protection are key to achieving system stability. It is worth noting that inhibiting the use of LPF and using virtual harmonic reactance may lead to system instability. In addition, the analysis also shows that the proposed VSG with AHF function is stable for various grid impedances.

[0184] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the technical solution. Those skilled in the art should understand that those modifications or equivalent substitutions of the technical solution of the present invention that do not depart from the purpose and scope of the technical solution should be included in the scope of the claims of the present invention.

Claims

1. A grid-type converter active filtering method based on selective overcurrent limitation, characterized in that: The following steps are involved: S1. State space modeling of VSC: (i) VSC; (ii) main controller of VSC implemented by virtual synchronous generator (VSG); (iii) AHF function implemented by direct harmonic voltage control; (iv) selective harmonic overcurrent protection; S2. Perform a preliminary calculation of the controller gain; S3, linearizing the nonlinear state space model of the system proposed in step S1 near the equilibrium point and evaluating the eigenvalues; S4. Determine the stable range of each control parameter to set the final control gain.

2. The active filtering method of a grid-type converter based on selective overcurrent limitation according to claim 1 is characterized in that: In step S1, the VSC is a three-phase three-wire device connected to the grid through an LCL coupling filter, which also has a physical damping resistor in series with a capacitor. The grid is modeled as a series inductive impedance (R g and L g ) is an AC voltage source. VSC is at an angle θ with VSG vsg The differential equations in the synchronized dq rotating reference frame are given below: Among them, L t and L s They are the filter inductors on the VSC side and the grid side, R t and Rs is the corresponding resistance, C f is the filter capacitor, R d is the damping resistor, v t,dq =[v td ,v tq ] is the terminal voltage of VSC, v m,dq =[v md ,v mq ] is the voltage between the capacitor and the damping resistor, v c,dq =[v cd ,v cq ] is the capacitor voltage, v s,dq =[v sd ,v sq ] is the voltage of POI, v g,dq =[v gd ,v gq ] is the grid voltage, i t,dq =[i td ,i tq ] is the inductor current on the VSC side, i s,dq =[i sd ,i sq ] is the grid-side inductor current, ω vsg is the angular frequency of VSG. Considering the above equations, the model of the grid-connected VSC will add six state variables x to the state space equations: f . x f =[i td ,i tq ,i sd ,i sq ,v cd ,v cq ] (6) In step S1, the VSG selected to provide networking capacity is composed of an outer control loop (Outer Control Loop, OCL) and an inner control loop (Inner Control Loop, ICL). The OCL consists of two parallel proportional-integral (PI) controllers for active and reactive power, respectively, as shown in Figure 1. The active power controller modifies the virtual rotor angle θ vsg To achieve synchronization with the power grid. The reactive power controller calculates the amplitude E of the virtual electromotive force. Therefore, OCL can be described by the following equation: Among them, ξ p is the integral of the active power error, p is the active power of the POI, and p ＊ is the reference active power, ω0 is the rated frequency, k pp and k ip are the proportional and integral gains of the PI active power controller, ξ q is the integral of the reactive power error, q is the reactive power of the POI, and q ＊ is the reference reactive power, E0 is the rated electromotive force, k pq and k iq are the proportional and integral gains of the PI reactive power controller. The active and reactive powers p and q of the POI can be described by the following equations in the dq coordinate system: As shown in Figure 2, the direction of the electromotive force is consistent with the direction of the q axis. Therefore, the electromotive force in the dq coordinate is always equal to e dq =[0,-E]. On the other hand, it is assumed that the grid voltage rotates at the rated frequency ω0. This means that the grid voltage is considered to not add any dynamic disturbance to the system. Therefore, the grid voltage V can be defined as g The phase difference between the grid voltage and the electromotive force E is ψ, as shown in Figure 2. V g Dynamic changes according to VSG angle: This approach allows replacing θ with ψ in (7) vsg , the dynamic characteristics of VSG are maintained but the influence of grid angular frequency ω0 is added to the model. The ICL consists of a single PI current controller implemented in the dq axis. The current reference is determined by the electromotive force e dq , POI voltage v s,dq And virtual admittance Yv = Gv-jB v In addition, before these reference currents are introduced into the current controller, they are also low-pass filtered (LPF) to provide reference values ​​with low harmonic content. and It can be expressed as: Among them, τ lpf is the time constant of the low-pass filter, is the filtered reference current. Finally, the PI current controller equation including the cross-coupling cancellation term and the feed-forward term is: Among them, ξ id and iq is the current error integral on the dq axis, k pi and k ii They are the proportional gain and integral gain of the PI current controller respectively. According to (7)-(13), the VSG control loop model adds seven new state variables to the state space equations: In step S1, the selected AHF function implemented by direct harmonic voltage control is implemented by a set of resonant controllers included on each target harmonic. Its goal is to track the harmonic voltage reference value in the αβ coordinate system, This corresponds to the POI harmonic voltage. Note that the resonant controllers are implemented in the αβ coordinate system, not in the dq coordinate system, because each harmonic needs to be compensated in its corresponding sequence. These resonant controllers generate a new current reference value, Before adding it to the VSG fundamental reference current (13), it needs to be transformed into the dq coordinate system, as shown in Figure 1. In the Laplace domain, the resonant controller in the αβ coordinate system can be expressed as: in, Represents harmonic voltage error, v s,αβ =[v sα ,v sβ ] represents the harmonic voltage of POI, and k rh , δ h and ω h represent the gain, damping and tuned harmonic frequency of the hth harmonic resonant controller, respectively. However, it is necessary to transform equation (15) into the dq coordinate system, considering the derived grid-connected VSC and VSG models. in, represents the harmonic voltage error, represents the reference harmonic current, and represents the reference harmonic voltage. Finally, the time domain expression of equation (16) is as follows: Among them, γ h,dq =[γ hd ,γ hq ] is a new state variable, representing the Points: It should be noted that for the reference harmonic current Perfect tracking of requires the use of resonant controllers tuned for each harmonic, just like the controller for the harmonic voltages. However, it is also possible to use only a conventional PI controller in combination with a resonant voltage controller, providing a high bandwidth to track the reference harmonic currents. In this way, the computational cost of the harmonic function is greatly reduced. Harmonic voltage control introduces four new differential equations (17)-(18) for each target harmonic h, and their corresponding state variables: In step S1, the selected selective harmonic overcurrent protection is used to achieve a perfect sinusoidal POI voltage. The harmonic voltage reference The default setting is zero. An ideal resonant controller injects additional harmonic currents to ensure that the harmonic voltage is zero. However, if these current terms are not limited, this may lead to overloading of the VSC. To avoid this, we add an algebraic virtual harmonic impedance Z h =R h +jX h , which modifies the default harmonic voltage reference in the dq reference frame as follows: Parameter R h and X h It can be defined independently for each harmonic, depending on the limits imposed by the existing grid code. Larger virtual harmonic impedances can be associated with harmonics with higher permissible limits. For this purpose, different harmonic weighting factors σ are used. h , to define virtual harmonic impedances relative to a reference value, as follows: R h +jX h =s h (R b +jL b oh h ) (22) Among them, R b and L b In this way, the compensation of each harmonic can be selectively reduced to avoid the VSC overcurrent condition. Table I defines a set of harmonic weighting factors taking into account the voltage harmonic limits specified in standard EN 50160. Note that the lowest harmonic weighting factor is assigned to the harmonic with the lowest limit, i.e. the sixth harmonic, while the other factors are assigned according to their relative amplitude A. h Zoomed:. In order to prevent the VSC from overloading, the reference virtual harmonic impedance is dynamically adjusted according to the VSC current. According to (21) and (22), the reference virtual harmonic impedance can be expressed as a function of harmonic voltage, harmonic current and fundamental current. This patent proposes an adaptive method in which the reference virtual harmonic impedance is adjusted when the VSC current is greater than the rated current I rat Considering that the reference virtual harmonic impedance is defined as a piecewise linear function, a hysteresis band ±H is added. Is to limit impedance changes. The band is around a rat The current I hys And set as shown in Figure 3. If the POI current I s Below I rat , then the reference virtual harmonic impedance is set to zero, that is, A sinusoidal POI voltage can be achieved. However, if I s Greater than I rat , the overcurrent limit is activated by linearly increasing the base virtual harmonic impedance as shown below: Among them, m r and m l are the rates of change of the reference virtual harmonic resistance and inductance, respectively, and Δt is the sampling time of the controller. Therefore, due to the reduction of harmonic current, the VSC current decreases to I hys From this point on, the reference virtual harmonic impedance remains constant. Once the VSC current drops to the threshold I hys -H Is Below this value, the base virtual harmonic impedance decreases. This results in an increase in the injected harmonic current. If the VSC current reaches I hys and the reference virtual harmonic impedance is not zero, the VSC current will be limited to this value, as shown in Figure 3. hys However, the base virtual harmonic impedance is zero, which allows the VSC current to increase to I hys Above, as long as it does not exceed I rat . About the component R of the reference virtual harmonic impedance b and L b The impact on the control algorithm is discussed in Section III. The differential equations in the previous four parts (1)-(23) can be combined into a unique state-space model that integrates the system and control dynamics:

3. The active filtering method of a grid-type converter based on selective overcurrent limitation according to claim 2 is characterized in that: In step S2, the initial calculation of the control gain of the VSG outer control loop OCL in Figure 1 is as follows: The active power control loop is based on a PI controller. The integral gain k ip is calculated to obtain a given inertial response, and the proportional gain k pp These gains are initially calculated according to the following formula: Where H is the inertia constant, V g is the peak value of the grid voltage, and X v =1 / Y v is the virtual impedance. Similarly, the gain of the reactive power control loop is preliminarily calculated as: Among them, S n is the rated power of the VSC. In S2, the initial calculation of the control gain of the VSG internal control loop ICL in Figure 1 is as follows: Virtual admittance Y v is defined as a pure inductive impedance and is set to 10% of the VSC base impedance, while the time constant τ of the low-pass filter LPF is lpf is set to 1.6 milliseconds. The proportional and integral gains of the current control loop are initially calculated as follows: Among them, M p is the phase margin, ω c is the cutoff filter frequency. They are usually set to π / 3 and 20% of the maximum compensated harmonic frequency, respectively. The reference virtual harmonic impedance is initially set to zero to achieve full voltage harmonic compensation at the POI.

4. The active filtering method of a grid-type converter based on selective overcurrent limitation according to claim 3 is characterized in that: In step S3, the stability analysis is performed by linearizing the state space equations around the equilibrium point x0 and performing a small signal model analysis. By solving (25) we obtain and the equilibrium point for a given input vector u. The analysis has taken into account the preliminary controller gains calculated in S1, detailed in Table II, and the calculated VSC characteristics in Table III. The input u has been set to the case where the VSC injection power is equal to 9kW and 4.5kvar. Regarding the AHF function, the target harmonics are the 5th and 7th harmonics, and the reference virtual harmonic impedance is zero. The linearization of the system is performed as follows: Get the small signal model: Matrices A0 and B0 are the linearization matrices of matrices A and B respectively. The stability of the system can be assessed near the equilibrium point by analyzing the eigenvalues ​​of A0, given preliminary values ​​of the controller gains, as shown in Figure 4. All eigenvalues ​​have non-zero real parts, which means that the system is around a hyperbolic equilibrium point when linearized. According to the Hartman-Grobman theorem, the system is structurally stable, so at this equilibrium point the linearized system represents a nonlinear system. It is worth noting that the AHF function introduces non-conjugated eigenvalues. In particular, the 5th harmonic compensation is related to +400πrad / s (λ 18 ,λ 19 ) and -600πrad / s(λ 16 ,λ 17 ) is related to the eigenvalue at +600πrad / s(λ). 20 ,λ 21 ) and -800πrad / s(λ 15 ,λ 16 ) place.

5. The active filtering method of a grid-type converter based on selective overcurrent limitation according to claim 4 is characterized in that: In step S4, the stability range of the system is evaluated using a small signal model, taking into account possible variations of the controller gain and the grid impedance. To this end, the evolution of the eigenvalues ​​in the complex plane is analyzed when these parameters are modified within the ranges detailed in Table II. The results are presented using two graphs, focusing on the eigenvalues ​​of the VSG dynamics (left side) and the AHF function (right side). The arrows in these figures indicate the direction of the eigenvalue changes as the analyzed parameters evolve. In S4, the small signal evaluation of the VSG active power control loop is as follows: According to (26), the integral gain k ip is inversely proportional to the inertia constant H. Considering H in the interval [0.01,20]s, the results are shown in the upper left figure of Figure 4. For very small inertia constants (H<1s), the system is unstable. Larger H can make the system stable because the real part of the eigenvalue decreases. Therefore, H is adjusted to the required VSC inertia response, but greater than 1s to ensure system stability. As for the eigenvalues ​​of AHF, as shown in the upper right figure, these are almost unaffected by the change of this parameter. About the proportional gain k pp , if increased, will endanger the stability of the system, as shown in the lower left figure of Figure 4. This effect is pp >10 -3 rad / (sW) further intensifies, when k pp =10 -3 When λ4 and λ 10 The damping of is significantly reduced from 0.8 to almost zero, both of which are related to the VSG dynamics. The effect on the AHF eigenvalues ​​is asymmetric, as shown in the lower right figure of Figure 4. The eigenvalues ​​at negative frequencies are uniformly damped, while the eigenvalues ​​at positive frequencies gradually separate from each other and tend to the imaginary axis. In S4, the small signal evaluation of the VSG reactive power control loop is as follows: The influence of this control loop is usually ignored in small signal analysis. Figure 5 shows the influence of k pq and k iq This assumption is further strengthened by the increase in the eigenvalue. pq The increase of , the characteristic value is significantly affected, but it does not reduce the stability of the system. Therefore, this gain is selected according to the required VSC reactive power injection under a given POI voltage change. On the other hand, the integral gain k iq There is almost no impact on the dynamics, as shown in the bottom of Figure 5. In S4, the small signal evaluation of the virtual conductance of the VSG is as follows: Figure 6 shows the effect of the virtual conductance and susceptance. v It has little effect on the system dynamics, and as its value increases, the eigenvalues ​​will only shift slightly. Virtual Susceptance B v When it decreases, the damping of most eigenvalues ​​decreases slightly. Considering the virtual conductance G v It has little effect on the system dynamics, so the virtual admittance is set to a pure inductance Y v =-jB v . In S4, the small signal evaluation of the VSG LPF time constant is as follows: The LPF time constant is zero, that is, a controller without LPF will lead to system instability, where λ 2,10 =472.92±j10889π. As shown in Figure 7, as τ lpf The increase of eigenvalues ​​λ3, λ4, λ 10 and λ 11 The natural frequency of is reduced through a constant damping path until it reaches a value consisting only of negative real parts. As for the eigenvalues ​​λ2 and λ 12 , they move to the left, increasing the stability of the system. On the contrary, the eigenvalues ​​λ1 and λ 13 To the right, which may lead to system instability. On the other hand, the eigenvalues ​​related to AHF hardly move to the left when the LPF bandwidth is reduced. From this analysis, it can be seen that considering that the goal of the LPF is to provide a reference current with the lowest possible harmonic content without affecting the dynamics of the current control loop, the LPF time constant is set to τ lpf =1.6ms. In S4, the small signal evaluation of the VSG current controller is as follows: The gain of the PI current controller is limited by the minimum time constant of 1ms, so the maximum value is k pi =5 and k ii = 157. Figure 8 describes the pi and k ii The change of eigenvalues ​​in the range. pi As the value of increases, the damping of VSG and AHF increases. As expected, the wider the PI controller bandwidth, the better the system performance. ii The impact on system stability is not obvious. However, k ii Depends on the resistance of the coupling filter, as shown in (28). This patent assumes that the quality factor of the inductor is equal to 10. However, considering that the resistance is prone to large changes in practice (manufacturing tolerance, temperature, material degradation, wiring, etc.), k ii The final value of is adjusted through some experimental tests so that the closed-loop time constant τ of the current controller i =1ms. In S4, the small signal evaluation of AHF is as follows: The AHF function only works on the 5th and 7th harmonics. For simplicity, it is assumed that k r5 =k r7 =k rh and δ5=δ7=δ h As shown in Figure 9, increasing δ h This will increase the damping of the AHF and thus affect the performance, but will not have any effect on the VSG dynamics. h = 0 for the best performance, but this will lead to stability limitations, which depend mainly on the external damping source. Again, δ h It is a balance between providing enough AHF capability and sufficient damping. On the other hand, the resonant gain k rh The VSG and AHF dynamics are greatly affected, especially for values ​​above 100. The natural frequencies of the AHF eigenvalues ​​are greatly affected, especially those corresponding to negative sequences. rh A low value is taken so that AHF affects the VSG performance as little as possible. It is worth noting that the bandwidth of the harmonic voltage controller, involving the series operation of the resonant and PI current controllers, is 2931.1 rad / s according to the final value of the controller gain summarized in Table II. This controller bandwidth is sufficient to reduce the 5th and 7th harmonic voltages without adding an additional resonant controller in the VSG current control. In S4, the small signal evaluation of the overcurrent protection is as follows: Figure 10 shows the effect of the resistance and inductance terms of the fundamental virtual harmonic impedance on the stability. The VSG eigenvalue is almost unaffected, while the AHF eigenvalue has a significant effect on R b and L b The resistance term causes the eigenvalue to shift to the left and the damping to increase. In contrast, the inductance term L b When it is greater than 80μH, the system becomes unstable. Therefore, the fundamental virtual harmonic impedance must be purely resistive. In S4, the small signal evaluation of the grid impedance is as follows: R g and L g Various values ​​of have been extensively studied. The higher the resistance, the higher the damping for all eigenvalues. Even if R g The value of is zero, and the system remains stable. The characteristic value of the average frequency, such as λ3, λ4, λ 10 and λ 11 , tends to move to the right, thus making weak grids (such as island grids) unstable. g increases, the eigenvalue moves toward the imaginary axis. g For values ​​above 1mH and an R / X ratio of 0.07, the system becomes unstable.

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