Networking converter impedance modeling method based on hybrid synchronous control

Abstract

The invention discloses a hybrid synchronous control-based impedance modeling method for a grid-forming converter, which comprises the following steps of: injecting positive sequence small signal voltage disturbance into output voltage v of the converter, and converting time domain expressions of the output voltage v and output current i of the converter into frequency domain expressions; converting a time domain expression of a trigonometric function in the Park transformation formula into a frequency domain expression; obtaining frequency domain expressions of d-axis and q-axis components of the output voltage and the output current of the converter; frequency domain expressions of active power and reactive power of the converter are obtained through calculation; obtaining a frequency domain expression of the output voltage of the reactive voltage loop, the output phase angle of the hybrid synchronous control loop and the trigonometric function thereof; obtaining frequency domain expressions of d-axis and q-axis modulation voltages of the converter; frequency domain expressions of the A-phase modulation voltage of the converter and the A-phase voltage output by the inverter bridge are obtained; and obtaining expressions of the positive sequence impedance and the negative sequence impedance of the converter. The method can be effectively applied to the small signal stability research of the new energy power generation grid-connected system.

Description

Technical Field

[0001] The invention relates to the technical field of small signal stability analysis of a grid-connected converter, and in particular to an impedance modeling method of a grid-connected converter based on hybrid synchronous control. Background Art

[0002] In the existing technology, with the acceleration of the construction of new power systems, the penetration rate of new energy power generation continues to increase, and the "double high" characteristics of high-proportion power electronic converters and high-proportion new energy access in new power systems are becoming more and more prominent, resulting in the grid showing significant characteristics such as low inertia, low damping, and weak voltage support, which brings huge challenges to the safe and stable operation of the grid. Therefore, grid-forming converters with active voltage and frequency support capabilities have received widespread attention.

[0003] The grid-type converter can not only provide voltage and frequency support for the power grid, but also simulate the inertia and damping characteristics of the synchronous generator, and provide inertia and damping support for the power grid together with the energy storage battery. The grid-type converter is equivalent to a voltage source to the outside, so it has good small-signal stability under weak power grids. However, the conventional grid-type converter represented by droop control and virtual synchronous machine has limited overcurrent capacity, and its transient stability faces severe challenges under large signal disturbances. In order to improve the transient stability of the grid-type converter, in 2021, some scholars proposed a grid-type converter based on hybrid synchronous control that combines the advantages of grid-following control and grid-type control. By introducing the phase-locked loop (PLL) of the synchronous control unit in the grid-following control into the power synchronization loop of the grid-type control, the power setting is equivalently reduced or the damping is increased, while retaining the advantages of the grid-type converter, its transient stability is improved.

[0004] For the grid-connected converter based on hybrid synchronous control, the existing research points out its transient stability advantage, but the understanding of its small signal stability is still insufficient. Since PLL is one of the direct causes of the small signal stability problem of the grid-connected converter under weak power grid, it is of great significance to study the small signal stability of the grid-connected converter and the grid when PLL is added. For the small signal stability problem of the grid-connected converter based on hybrid synchronous control, the relevant research team of Sichuan University established a state space model of the grid-connected system of the converter for analysis. However, the state space model is relatively complex in the stability analysis process, and it is difficult to intuitively reveal the frequency range and instability cause of the system's instability. As a simple and intuitive small signal stability analysis method, the impedance model has been widely used in the stability analysis of renewable energy power generation grid connection. Therefore, for the grid-connected converter based on hybrid synchronous control, it is of great significance to establish an accurate output impedance model considering its multi-loop control dynamics such as hybrid synchronous control loop, reactive voltage loop, virtual impedance, voltage control loop and current control loop. Summary of the invention

[0005] The purpose of the present invention is to provide a grid-connected converter impedance modeling method based on hybrid synchronous control, which can analyze the stability of small signals more accurately and can be effectively applied to the small signal stability research of new energy power generation grid-connected systems.

[0006] To achieve the above object, the present invention provides a method for impedance modeling of a grid-connected converter based on hybrid synchronous control, comprising the following steps:

[0007] S1, inject frequency f into the converter output voltage v p The abc three-phase positive sequence small signal voltage disturbance is calculated, and the time domain expressions of the converter output voltage v and output current i are converted into frequency domain expressions according to Fourier transform;

[0008] S2, substituting the output phase angle of the hybrid synchronous control loop into the Park transform, linearizing the Park transform, and converting the time domain expression of the trigonometric function in the Park transform formula into a frequency domain expression according to the Fourier transform;

[0009] S3, sampling and Park transforming the three-phase output voltage and output current of the converter, and obtaining frequency domain expressions of the d-axis and q-axis components of the output voltage and output current of the converter based on the convolution theorem;

[0010] S4. Based on the frequency domain expressions of the three-phase output voltage and output current of the converter, the frequency domain expressions of the active power and reactive power in the converter control loop are calculated;

[0011] S5. Substituting the frequency domain expression of the converter reactive power into the reactive voltage loop to obtain the frequency domain expression of the output voltage of the reactive voltage loop;

[0012] S6. Substituting the frequency domain expressions of the converter active power and the q-axis component of the output voltage into the hybrid synchronous control loop, obtaining the frequency domain expression of the output phase angle of the hybrid synchronous control loop and its trigonometric function;

[0013] S7, substituting the frequency domain expression of the reactive voltage loop output voltage, the frequency domain expressions of the d-axis and q-axis components of the converter output voltage and output current into the converter virtual impedance, voltage and current double closed-loop control structure, and obtaining the frequency domain expressions of the converter d-axis and q-axis modulation voltages;

[0014] S8. Substitute the frequency domain expressions of the converter d-axis and q-axis modulation voltages and the frequency domain expressions of the trigonometric functions of the output phase angle of the hybrid synchronous control loop into Park -1 Transform the formula to obtain the modulation voltage of phase A of the converter at the positive sequence voltage disturbance frequency f p Frequency domain expression at ;

[0015] S9, use the delay function to mathematically model the PWM modulation and the three-phase inverter bridge, and set the A-phase modulation voltage of the converter at the positive sequence voltage disturbance frequency f p The frequency domain expression at is multiplied by the delay function to obtain the A-phase voltage output by the inverter bridge at the positive sequence voltage disturbance frequency f p Frequency domain expression at ;

[0016] S10, the A phase voltage output by the inverter bridge is adjusted to the positive sequence voltage disturbance frequency f p Substitute the frequency domain expression at into the main circuit equation to calculate the frequency f p The ratio between the positive sequence voltage disturbance and the positive sequence current response is obtained to obtain the expression of the converter positive sequence impedance.

[0017] S11. According to the relationship between the positive-sequence impedance and the negative-sequence impedance of the converter, the imaginary unit j in the positive-sequence impedance is replaced by -j to obtain an expression for the negative-sequence impedance of the converter.

[0018] Preferably, in S1, a small positive-sequence voltage disturbance v of the three-phase abc is injected into the converter output voltage v pa (t), v pb (t) and v pc (t):

[0019]

[0020] Among them, V p 、f p and Represent the amplitude, frequency and phase of the positive sequence voltage disturbance respectively;

[0021] After superimposing the positive sequence small signal voltage disturbance, the output voltage of phase a of the converter is expressed as:

[0022]

[0023] Where V1 and f1 represent the amplitude and frequency of the fundamental component of the output voltage, respectively, and V p Much smaller than V1;

[0024] Because under the action of fundamental voltage and disturbance voltage, the output current response of the converter will be mainly based on the fundamental current and disturbance current response. Taking phase a as an example, the output current of the converter is expressed as:

[0025]

[0026] In the formula, I1 and is the amplitude and phase of the output current of the converter at f1; I p and Represents the positive sequence voltage disturbance at fp The amplitude and phase of the positive sequence current response caused by

[0027] Convert the time domain expressions of phase A output voltage and output current into frequency domain expressions, and we can get v a (t) and i a The frequency domain expression of (t) is V a [f] and I a [f] are:

[0028]

[0029] Where V1 = V1 / 2, f represents frequency;

[0030] Similarly, the output voltage V of the converter phase b and phase c is b [f] and V c [f], and the output currents of phase b and phase c, I b [f] and I c The frequency domain expression of [f] is:

[0031]

[0032] Wherein, j represents the imaginary number symbol.

[0033] Preferably, in S2, the Park transformation formula T(θ) and Park -1 Transformation formula T -1 (θ) is:

[0034]

[0035] Where θ is Park and Park -1 The angle of transformation;

[0036] Park and Park grid-connected converters based on hybrid synchronous control loop -1 The transformed angle is derived from the output θ of the hybrid synchronous control loop v ; The phase response of the hybrid synchronous control loop caused by the positive sequence voltage disturbance is expressed as Δθ v , then θ v =θ1+Δθ v ;in, θ1 represents the phase response caused by the fundamental voltage, represents the power angle of the converter, s is the Laplace operator, and s = j2πf, θ v =θ1+Δθ v Substituting into equation (6) converts the Park transform into:

[0037]

[0038] Following the linearization rule, cos(Δθ v )≈1, sin(Δθ v )≈Δθ v ;

[0039] According to Fourier transform, the time domain expression of the trigonometric function in T(θ1) is converted into the frequency domain, and we get:

[0040]

[0041] Preferably, in S3, equations (4) and (5) are sampled and substituted into equation (7). According to the convolution theorem, we get:

[0042]

[0043] Where, ω1 is the fundamental angular frequency, ω1=2πf1; V d1 [f] and V q1 [f] respectively v d and v q The frequency domain expressions of the d-axis and q-axis voltages obtained after sampling and T(θ1) transformation; V d [f] and V q [f] respectively v d and v q After sampling and T(θ v ) The frequency domain expressions of the d-axis and q-axis voltages obtained after transformation;

[0044]

[0045] In the formula, I d1 [f] and I q1 [f] are i d and i q The frequency domain expressions of the d-axis and q-axis currents obtained after sampling and T(θ1) transformation; I d [f] and I q [f]] are i d and i q After sampling and T(θ v ) The frequency domain expressions of the d-axis and q-axis currents obtained after transformation;

[0046] In S4, based on the frequency domain expressions of the three-phase output voltage and output current of the converter shown in equations (4) and (5), the frequency domain expressions of the active power Pe and reactive power Qe in the converter control loop are calculated as follows:

[0047]

[0048] Where V1 * and I1* Represent the conjugate complex numbers of V1 and I1 respectively.

[0049] Preferably, in S5, the frequency domain expression Q of the reactive output power of the converter shown in formula (11) is e Substituting [f] into the reactive voltage loop, the frequency domain expression of the reactive voltage loop output voltage Ev is obtained as follows:

[0050]

[0051] Remember N i (s)=3G p (s)K q V1 * G v (dry jω1), N v (s)=3G p (s)K q I1 * G i (dry jω1), then at the frequency ±(f p -f1) at E v The expression of [f] is:

[0052]

[0053] Preferably, in S6, according to the hybrid synchronous control loop structure of the grid-type converter, the expression of its output phase is obtained as follows:

[0054]

[0055] Substitute the active power frequency domain expression (11) into the hybrid synchronous control loop output phase expression (14), and record M(s) = 1 / (Js2+Dps), The frequency domain expression of the output phase of the hybrid synchronous control loop is further obtained as:

[0056]

[0057] From this we get Δθ v The frequency domain expression of is:

[0058]

[0059] V in formula (9) q [f] at frequency ±(f p Substituting the expression at -f1) into equation (16), further simplifying it to obtain Δθ v The expression of [f] is:

[0060]

[0061] remember Then Δθ v The expression of [f] is further expressed as:

[0062]

[0063] Known cosθ v =cos(θ1+Δθ v )=cosθ1cos(Δθ v )-sinθ1sin(Δθ v ), according to the convolution theorem, the multiplication in the time domain corresponds to the convolution in the frequency domain, cosθ v The frequency domain expression of is:

[0064] cosθ v [f]=cosθ1[f]-sinθ1[f]*Δθ v [f] (19);

[0065] In the formula, the symbol “*” represents the convolution operation;

[0066] Substituting equation (8) and equation (18) into equation (19), we get cosθ v The expression of [f] is:

[0067]

[0068] Then get

[0069] Preferably, in S7, according to the voltage-current dual closed-loop control structure of the grid-type converter, the frequency domain expressions of the d-axis and q-axis modulation voltages are obtained as follows:

[0070]

[0071] Set the frequency ±(f p -f1) at E v [f], I d [f], I q [f], V d [f] and V q Substituting the expression of [f] into equation (21), we get V md [f] and V mq [f] at frequency ±(f p -f1) is:

[0072]

[0073] In the formula, Z v =R v ±jω N L v, F d (s) and F q (s) are:

[0074]

[0075] Write the frequency domain equation of the main circuit according to the LCL filtering link. Taking phase A as an example, the output voltage V oa [f] and the inverter A phase output voltage V a [f], inverter A phase output current I a The relationship between [f] is:

[0076]

[0077] Let P1(s) = L1L2s 2 / [R1+1 / (sC1)]+s(L1+L2), P2(s)=L1s / [R1+1 / (sC1)]+1, then V oa [f]=P1(s)I a [f]+P2(s)V a [f];

[0078] Using the delay function G for PWM modulation and three-phase inverter bridge d (s) = e -s1.5Ts Describe, that is, V o [f] = V mabc [f]G d (s); where T s =1 / f s represents the switching time constant, f s is the switching frequency, V mabc [f] and V o [f] are the three-phase modulation voltages v of abc respectively mabc and the inverter bridge output voltage v o Frequency domain expression of ;

[0079] According to the fundamental frequency signal relationship of the converter, calculate V md [f] and V mq [f] Expression V at frequency f = 0 md [0] and V mq [0], V md [0] and V mq [0] Substitute the Park value shown in equation (6) into -1 Transformation formula, according to the convolution theorem, is:

[0080] V oa [f1]={V md [0]*cosθ1[f1]-V mq[0]*sinθ1[f1]}·G d (jω1) (24);

[0081] Where V oa [f1], cosθ1[f1], sinθ1[f1] represent the expressions of the output voltage of phase A of the converter, cosθ1, sinθ1 at the frequency f1 respectively;

[0082] V oa Substituting [f1] into the main circuit frequency domain equation shown in equation (23), we can derive V md [0]±jV mq The expression of [0] is:

[0083]

[0084] remember Then V md [0]±jV mq [0] = V m0 .

[0085] Preferably, in S8, according to the convolution theorem, the A phase modulation voltage v is obtained. ma At frequency ±f p The frequency domain expression V ma [f] is:

[0086]

[0087] Substituting equations (20), (22) and (25) into equation (26), we get V ma [f] at frequency ±f p The specific expression is:

[0088]

[0089] In S9, due to the PWM modulation and the three-phase inverter bridge, the delay function G d (s) = e -s1.5Ts Description, the A phase voltage of the inverter bridge output is obtained at the positive sequence voltage disturbance frequency ±f p The frequency domain expression at is:

[0090]

[0091] Preferably, in S10, based on formula (27), formula (28) is substituted into formula (23) to obtain:

[0092]

[0093] Based on equation (29), the converter positive sequence impedance Z p The expression of (s) is:

[0094]

[0095] Preferably, in S11, according to the relationship between the positive-sequence impedance and the negative-sequence impedance of the converter, the imaginary unit j in the positive-sequence impedance shown in formula (30) is replaced by -j, and the expression of the negative-sequence impedance Zn(s) of the converter is obtained as follows:

[0096]

[0097] In the formula, and F d (s), F q (s) and V m0 Get, expressed as:

[0098]

[0099] Therefore, the present invention adopts the above-mentioned grid-connected converter impedance modeling method based on hybrid synchronous control, which can analyze the stability of small signals more accurately and can be effectively applied to the small signal stability research of new energy power generation grid-connected systems.

[0100] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 It is a schematic diagram of the main circuit and control circuit structure of a grid-forming converter based on hybrid synchronous control;

[0102] Figure 2 It is a step diagram of a method for modeling impedance of a grid-type converter based on hybrid synchronous control of the present invention;

[0103] Figure 3 1 is a comparison diagram of the positive and negative sequence impedance models and the measurement results of the present invention, wherein (a) is a comparison diagram of the positive sequence impedance model and the positive sequence measurement results, and (b) is a comparison diagram of the negative sequence impedance model and the negative sequence measurement results. DETAILED DESCRIPTION

[0104] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0105] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "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] Embodiment 1

[0107] The main circuit and control circuit structure of the grid-connected converter based on hybrid synchronous control is as follows: Figure 1 As shown, in the main circuit, L1, C1, and L2 form an LCL filter, and R1 is its damping resistor; v o and v c are the inverter bridge output voltage and capacitor branch voltage of the converter respectively; v and i are the three-phase output voltage and output current of the converter respectively. The control circuit mainly includes a hybrid synchronous control loop, a reactive voltage loop, a virtual impedance and a voltage-current double closed loop. The controlled signals of the control circuit include v d 、v q 、i d 、i q And the active power P calculated and filtered by them e and reactive power Q e , where v d and v q are the d-axis and q-axis components of the output voltage obtained after sampling and Park transformation, i d and i q are the d-axis and q-axis components of the output current obtained after sampling and Park transformation, G v (s) and G i (s) represent the equivalent voltage sampling function and current sampling function, G p (s) represents the power filter. As shown in the figure, the hybrid synchronous control loop is composed of a virtual synchronous generator (VSG) active synchronous loop and a PLL. The loop converts the q-axis voltage component v of the output voltage into q The synchronous characteristics of the grid-connected converter are adjusted by proportional regulation and superimposing it on the angular frequency output by the VSG active synchronous loop. N is the active power given, Pe is the active power output by the converter, ω N is the given angular frequency, J is the virtual inertia, D p is the active damping coefficient, K pll is the proportional coefficient of the PLL, ω v1 and ω v2 are the angular frequencies of the VSG active synchronization loop output and the PLL output, ω v and θ v are the angular frequency and phase angle of the hybrid synchronous control output respectively; in the reactive voltage loop, Q N and V N Respectively, reactive power setting and voltage amplitude setting, K q is the reactive power droop coefficient, E v is the voltage amplitude of the reactive loop output; R v and L v Represent virtual resistance and virtual inductance respectively, v vd and v vq They represent the d-axis and q-axis virtual voltages generated by the virtual impedance respectively. The voltage and current double closed loop is controlled by a proportional integral (PI) controller in the dq coordinate system, and its d-axis and q-axis voltages are given by E v and 0,H v (s) and H i (s) represent the voltage loop PI controller and the current loop PI controller, respectively, v md and v mq They represent the d-axis and q-axis modulation voltages respectively. After Park-1 transformation, the modulation voltages are converted into the abc three-phase modulation voltage v mabc The three-phase modulated voltage is output through the PWM modulator as a switching signal m abc To control the inverter bridge of the converter.

[0108] According to the principle of harmonic linearization, the transformer impedance modeling is performed in the frequency domain. Figure 2 As shown, the present invention provides a grid-type converter impedance modeling method based on hybrid synchronous control, comprising the following steps:

[0109] S1. Inject a three-phase positive sequence small signal voltage disturbance of abc with a frequency of fp into the converter output voltage v, and convert the time domain expressions of the converter output voltage v and output current i into frequency domain expressions according to Fourier transform.

[0110] Inject abc three-phase positive sequence small signal voltage disturbance v into the converter output voltage v pa (t), v pb (t) and v pc (t):

[0111]

[0112] Among them, V p 、f p and They represent the amplitude, frequency and phase of the positive sequence voltage disturbance respectively.

[0113] After superimposing the positive sequence small signal voltage disturbance, the output voltage of phase a of the converter is expressed as:

[0114]

[0115] Where V1 and f1 represent the amplitude and frequency of the fundamental component of the output voltage, respectively, and V p Much smaller than V1.

[0116] Because under the action of fundamental voltage and disturbance voltage, the output current response of the converter will be mainly based on the fundamental current and disturbance current response. Taking phase a as an example, the output current of the converter is expressed as:

[0117]

[0118] In the formula, I1 and is the amplitude and phase of the output current of the converter at f1; I p and Represents the positive sequence voltage disturbance at f p The amplitude and phase of the positive sequence current response caused by

[0119] Convert the time domain expressions of phase A output voltage and output current into frequency domain expressions, and we can get v a (t) and i a The frequency domain expression of (t) is V a [f] and I a [f] are:

[0120]

[0121] Where V1 = V1 / 2, f stands for frequency.

[0122] Similarly, the output voltage V of the converter phase b and phase c is b [f] and V c [f], and the output currents of phase b and phase c, I b [f] and I c The frequency domain expression of [f] is:

[0123]

[0124] Wherein, j represents the imaginary number symbol.

[0125] S2. Substitute the output phase angle of the hybrid synchronous control loop into the Park transform, and linearize the Park transform. According to the Fourier transform, the time domain expression of the trigonometric function in the Park transform formula is converted into a frequency domain expression.

[0126] Given the Park transformation formula T(θ) and Park -1 Transformation formula T -1 (θ) is:

[0127]

[0128] Where θ is Park and Park -1 The angle of transformation.

[0129] according to Figure 1 The control circuit structure shown is based on the hybrid synchronous control loop of the grid-type converter Park and Park -1 The transformed angle is derived from the output θ of the hybrid synchronous control loop v Assume that the phase response of the hybrid synchronous control loop caused by the positive sequence voltage disturbance is expressed as Δθ v , then θ v =θ1+Δθ v ;in, θ1 represents the phase response caused by the fundamental voltage, represents the power angle of the converter, s is the Laplace operator, and s = j2πf. v =θ1+Δθ v Substituting into equation (6) converts the Park transform into:

[0130]

[0131] Following the linearization rule, cos(Δθ v )≈1, sin(Δθ v )≈Δθ v .

[0132] According to Fourier transform, the time domain expression of the trigonometric function in T(θ1) is converted into the frequency domain, and we can get:

[0133]

[0134] S3. According to Figure 1 The control circuit structure shown in FIG. 4 samples and performs Park transformation on the three-phase voltage and current of the converter shown in equations (4) and (5), and based on the convolution theorem, obtains the frequency domain expressions of the d-axis and q-axis components of the converter output voltage and output current.

[0135] Sampling equations (4) and (5) and substituting them into equation (7), according to the convolution theorem, we can get:

[0136]

[0137] Where, ω1 is the fundamental angular frequency, ω1=2πf1; V d1 [f] and V q1 [f] respectively v d and v q The frequency domain expressions of the d-axis and q-axis voltages obtained after sampling and T(θ1) transformation; V d [f] and V q [f] respectively v d and v q After sampling and T(θ v ) The frequency domain expressions of the d-axis and q-axis voltages obtained after transformation;

[0138]

[0139] In the formula, I d1 [f] and I q1 [f] are i d and i q The frequency domain expressions of the d-axis and q-axis currents obtained after sampling and T(θ1) transformation; I d [f] and I q [f]] are i d and i q After sampling and T(θ v ) are the frequency domain expressions of the d-axis and q-axis currents obtained after transformation.

[0140] S4. Based on the frequency domain expressions of the three-phase output voltage and output current of the converter, the frequency domain expressions of the active power and reactive power in the converter control loop are calculated.

[0141] Based on the frequency domain expressions of the converter three-phase output voltage and output current shown in equations (4) and (5), the active power P in the converter control loop can be calculated: e and reactive power Q e The frequency domain expression of is:

[0142]

[0143] Where V1 * and I1 * Represent the conjugate complex numbers of V1 and I1 respectively.

[0144] S5. Substitute the frequency domain expression of the converter reactive power into the reactive voltage loop to obtain the frequency domain expression of the output voltage of the reactive voltage loop.

[0145] according to Figure 1The structure shown in the figure is transformed into the frequency domain expression Q of the converter reactive output power shown in equation (11) e Substituting [f] into the reactive voltage loop, the frequency domain expression of the reactive voltage loop output voltage Ev is obtained as follows:

[0146]

[0147] Remember N i (s)=3G p (s)K q V1 * G v (dry jω1), N v (s)=3G p (s)K q I1 * G i (dry jω1), then at the frequency ±(f p -f1) at E v The expression of [f] is:

[0148] E v [f] = mjN i (s)I p G i (s±jω1)±

[0149] Jb v (s)V p G v (s±jω1),f=±(f p -f1) (13).

[0150] S6. Substitute the frequency domain expressions of the converter active power and the q-axis component of the output voltage into the hybrid synchronous control loop to obtain the frequency domain expression of the hybrid synchronous control loop output phase angle and its trigonometric function.

[0151] according to Figure 1 The hybrid synchronous control loop structure shown in the figure can be expressed as follows:

[0152]

[0153] Substitute the active power frequency domain expression (11) into the hybrid synchronous control loop output phase expression (14), and record M(s) = 1 / (Js 2 +D p s), The frequency domain expression of the output phase of the hybrid synchronous control loop is further obtained as:

[0154]

[0155] From this, we can get Δθv The frequency domain expression of is:

[0156]

[0157] V in formula (9) q [f] at frequency ±(f p Substituting the expression at -f1) into equation (16), further simplifying it, we can get Δθ v The expression of [f] is:

[0158]

[0159] remember Then Δθ v The expression of [f] is further expressed as:

[0160]

[0161] Known cosθ v =cos(θ1+Δθ v )=cosθ1cos(Δθ v )-sinθ1sin(Δθ v ), according to the convolution theorem, multiplication in the time domain corresponds to convolution in the frequency domain, so cosθ v The frequency domain expression of is:

[0162] cosθ v [f]=cosθ1[f]-sinθ1[f]*Δθ v [f] (19);

[0163] In the formula, the symbol “*” represents the convolution operation.

[0164] Substituting equation (8) and equation (18) into equation (19), we get cosθ v The expression of [f] is:

[0165]

[0166] Then get

[0167] S7. Substitute the frequency domain expression of the reactive voltage loop output voltage, and the frequency domain expressions of the d-axis and q-axis components of the converter output voltage and output current into the converter virtual impedance, voltage and current dual closed-loop control structure to obtain the frequency domain expression of the converter d-axis and q-axis modulation voltage.

[0168] according to Figure 1 The voltage and current dual closed-loop control structure shown in the figure can obtain the frequency domain expressions of the d-axis and q-axis modulation voltages as follows:

[0169]

[0170] Set the frequency ±(f p -f1) at E v [f], I d [f], I q [f], V d [f] and V q Substituting the expression of [f] into equation (21), we get V md [f] and V mq [f] at frequency ±(f p -f1) is:

[0171]

[0172] In the formula, Z v =R v ±jω N L v , F d (s) and F q (s) are:

[0173]

[0174] Write the frequency domain equation of the main circuit according to the LCL filtering link. Taking phase A as an example, the output voltage V oa [f] and the inverter A phase output voltage V a [f], inverter A phase output current I a The relationship between [f] is:

[0175]

[0176] Let P1(s) = L1L2s 2 / [R1+1 / (sC1)]+s(L1+L2), P2(s)=L1s / [R1+1 / (sC1)]+1, then V oa [f]=P1(s)I a [f]+P2(s)V a [f];

[0177] Using the delay function G for PWM modulation and three-phase inverter bridge d (s) = e -s1.5Ts Describe, that is, V o [f] = V mabc [f]G d (s). Among them, T s =1 / f s represents the switching time constant, f s is the switching frequency, V mabc [f] and Vo [f] are the three-phase modulation voltages v of abc respectively mabc and the inverter bridge output voltage v o The frequency domain expression of .

[0178] According to the fundamental frequency signal relationship of the converter, calculate V md [f] and V mq [f] Expression V at frequency f = 0 md [0] and V mq [0], V md [0] and V mq [0] Substitute the Park value shown in equation (6) into -1 Transformation formula, according to the convolution theorem, we know:

[0179] V oa [f1]={V md [0]*cosθ1[f1]-V mq [0]*sinθ1[f1]}·G d (jω1) (24);

[0180] Where V oa [f1], cosθ1[f1], sinθ1[f1] represent the expressions of the inverter A phase output voltage, cosθ1, sinθ1 at frequency f1 respectively.

[0181] V oa Substituting [f1] into the main circuit frequency domain equation shown in equation (23), we can derive V md [0]±jV mq The expression of [0] is:

[0182]

[0183] remember Then V md [0]±jV mq [0] = V m0 .

[0184] S8. Substitute the frequency domain expressions of the converter d-axis and q-axis modulation voltages and the frequency domain expressions of the trigonometric functions of the output phase angle of the hybrid synchronous control loop into Park -1 Transform the formula to obtain the modulation voltage of phase A of the converter at the positive sequence voltage disturbance frequency f p The frequency domain expression of .

[0185] According to the convolution theorem, the A phase modulation voltage v ma At frequency ±f p The frequency domain expression V ma [f] is:

[0186]

[0187] Substituting equations (20), (22) and (25) into equation (26), we can get V ma [f] at frequency ±f p The specific expression is:

[0188]

[0189] S9, use the delay function to mathematically model the PWM modulation and the three-phase inverter bridge, and set the A-phase modulation voltage of the converter at the positive sequence voltage disturbance frequency f p The frequency domain expression at is multiplied by the delay function to obtain the A-phase voltage output by the inverter bridge at the positive sequence voltage disturbance frequency f p The frequency domain expression of .

[0190] Due to PWM modulation and the three-phase inverter bridge, the delay function G d (s) = e -s1.5Ts Therefore, the A-phase voltage of the inverter bridge output can be obtained at the positive sequence voltage disturbance frequency ±f p The frequency domain expression at is:

[0191]

[0192] S10, the A phase voltage output by the inverter bridge is adjusted to the positive sequence voltage disturbance frequency f p Substitute the frequency domain expression at into the main circuit equation to calculate the frequency f p The ratio between the positive-sequence voltage disturbance and the positive-sequence current response is obtained, and the expression of the converter positive-sequence impedance is obtained.

[0193] Based on formula (27), substituting formula (28) into formula (23) yields:

[0194]

[0195] Based on formula (29), the positive sequence impedance Z of the converter is p The expression of (s) is:

[0196]

[0197] S11. According to the relationship between the positive-sequence impedance and the negative-sequence impedance of the converter, the imaginary unit j in the positive-sequence impedance is replaced by -j to obtain an expression for the negative-sequence impedance of the converter.

[0198] According to the relationship between the positive-sequence impedance and the negative-sequence impedance of the converter, the imaginary unit j in the positive-sequence impedance shown in equation (30) is replaced by -j to obtain the negative-sequence impedance Z of the converter. n The expression of (s) is:

[0199]

[0200] In the formula, and F d (s), F q (s) and V m0 Get, expressed as:

[0201]

[0202] like Figure 3 As shown in Figure 2, the above model was simulated and verified, where Figure 3 (a) and (b) are the impedance measurement results and impedance models of the positive sequence impedance and negative sequence impedance respectively. It can be seen that the model is basically consistent with the impedance measurement results, which proves the accuracy of the constructed model.

[0203] Therefore, the present invention adopts the above-mentioned grid-connected converter impedance modeling method based on hybrid synchronous control, which can analyze the stability of small signals more accurately and can be effectively applied to the small signal stability research of new energy power generation grid-connected systems.

[0204] 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 it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A grid-connected converter impedance modeling method based on hybrid synchronous control, characterized in that: The following steps are involved: S1, inject frequency f into the converter output voltage v p The abc three-phase positive sequence small signal voltage disturbance is calculated, and the time domain expressions of the converter output voltage v and output current i are converted into frequency domain expressions according to Fourier transform; S2, substituting the output phase angle of the hybrid synchronous control loop into the Park transform, linearizing the Park transform, and converting the time domain expression of the trigonometric function in the Park transform formula into a frequency domain expression according to the Fourier transform; S3, sampling and Park transforming the three-phase output voltage and output current of the converter, and obtaining frequency domain expressions of the d-axis and q-axis components of the output voltage and output current of the converter based on the convolution theorem; S4. Based on the frequency domain expressions of the three-phase output voltage and output current of the converter, the frequency domain expressions of the active power and reactive power in the converter control loop are calculated; S5. Substituting the frequency domain expression of the converter reactive power into the reactive voltage loop to obtain the frequency domain expression of the output voltage of the reactive voltage loop; S6. Substituting the frequency domain expressions of the converter active power and the q-axis component of the output voltage into the hybrid synchronous control loop, obtaining the frequency domain expression of the output phase angle of the hybrid synchronous control loop and its trigonometric function; S7, substituting the frequency domain expression of the reactive voltage loop output voltage, the frequency domain expressions of the d-axis and q-axis components of the converter output voltage and output current into the converter virtual impedance, voltage and current double closed-loop control structure, and obtaining the frequency domain expressions of the converter d-axis and q-axis modulation voltages; S8. Substitute the frequency domain expressions of the converter d-axis and q-axis modulation voltages and the frequency domain expressions of the trigonometric functions of the hybrid synchronous control loop output phase angle into Park -1 Transform the formula to obtain the modulation voltage of phase A of the converter at the positive sequence voltage disturbance frequency f p Frequency domain expression at ; S9, use the delay function to mathematically model the PWM modulation and the three-phase inverter bridge, and set the A-phase modulation voltage of the converter at the positive sequence voltage disturbance frequency f p The frequency domain expression at is multiplied by the delay function to obtain the A-phase voltage output by the inverter bridge at the positive sequence voltage disturbance frequency f p Frequency domain expression at ; S10, the A phase voltage output by the inverter bridge is adjusted to the positive sequence voltage disturbance frequency f p Substitute the frequency domain expression at into the main circuit equation to calculate the frequency f p The ratio between the positive sequence voltage disturbance and the positive sequence current response is obtained to obtain the expression of the converter positive sequence impedance. S11. According to the relationship between the positive-sequence impedance and the negative-sequence impedance of the converter, the imaginary unit j in the positive-sequence impedance is replaced by -j to obtain an expression for the negative-sequence impedance of the converter.

2. The impedance modeling method of a grid-type converter based on hybrid synchronous control according to claim 1 is characterized in that: In S1, the abc three-phase positive sequence small signal voltage disturbance v is injected into the converter output voltage v pa (t), v pb (t) and v pc (t): Among them, V p 、f p and Represent the amplitude, frequency and phase of the positive sequence voltage disturbance respectively; After superimposing the positive sequence small signal voltage disturbance, the output voltage of phase a of the converter is expressed as: Where V1 and f1 represent the amplitude and frequency of the fundamental component of the output voltage, respectively, and V p Much smaller than V1; Because under the action of fundamental voltage and disturbance voltage, the output current response of the converter will be mainly based on the fundamental current and disturbance current response. Taking phase a as an example, the output current of the converter is expressed as: In the formula, I1 and is the amplitude and phase of the output current of the converter at f1; I p and Represents the positive sequence voltage disturbance at f p The amplitude and phase of the positive sequence current response caused by Convert the time domain expressions of phase A output voltage and output current into frequency domain expressions, and we can get v a (t) and i a The frequency domain expression of (t) is V a [f] and I a [f] are: Where V1 = V1 / 2, f represents frequency; Similarly, the output voltage V of the converter phase b and phase c is b [f] and V c [f], and the output currents of phase b and phase c, I b [f] and I c The frequency domain expression of [f] is: Wherein, j represents the imaginary number symbol.

3. The impedance modeling method of a grid-type converter based on hybrid synchronous control according to claim 2 is characterized in that: In S2, the Park transformation formula T(θ) and Park -1 Transformation formula T -1 (θ) is: Where θ is Park and Park -1 The angle of transformation; Park and Park grid-connected converters based on hybrid synchronous control loop -1 The transformed angle is derived from the output θ of the hybrid synchronous control loop v ; The phase response of the hybrid synchronous control loop caused by the positive sequence voltage disturbance is expressed as Δθ v , then θ v =θ1+Δθ v ;in, θ1 represents the phase response caused by the fundamental voltage, represents the power angle of the converter, s is the Laplace operator, and s = j2πf, θ v =θ1+Δθ v Substituting into equation (6) converts the Park transform into: Following the linearization rule, cos(Δθ v )≈1, sin(Δθ v )≈Δθ v ; According to Fourier transform, the time domain expression of the trigonometric function in T(θ1) is converted into the frequency domain, and we get:

4. The impedance modeling method of a grid-type converter based on hybrid synchronous control according to claim 3 is characterized in that: In S3, equations (4) and (5) are sampled and substituted into equation (7). According to the convolution theorem, we get: Where, ω1 is the fundamental angular frequency, ω1=2πf1; V d1 [f] and V q1 [f] respectively v d and v q The frequency domain expressions of the d-axis and q-axis voltages obtained after sampling and T(θ1) transformation; V d [f] and V q [f] respectively v d and v q After sampling and T(θ v ) The frequency domain expressions of the d-axis and q-axis voltages obtained after transformation; In the formula, I d1 [f] and I q1 [f] are i d and i q The frequency domain expressions of the d-axis and q-axis currents obtained after sampling and T(θ1) transformation; I d [f] and I q [f]] are i d and i q After sampling and T(θ v ) The frequency domain expressions of the d-axis and q-axis currents obtained after transformation; In S4, based on the frequency domain expressions of the three-phase output voltage and output current of the converter shown in equations (4) and (5), the active power P in the converter control loop is calculated. e and reactive power Q e The frequency domain expression of is: Where V1 * and I1 * Represent the conjugate complex numbers of V1 and I1 respectively.

5. The impedance modeling method of a grid-type converter based on hybrid synchronous control according to claim 4 is characterized in that: In S5, the frequency domain expression of the converter reactive output power Q shown in equation (11) is e Substitute [f] into the reactive voltage loop and obtain the reactive voltage loop output voltage E v The frequency domain expression of is: remember Then at the frequency ±(f p -f1) at E v The expression of [f] is:

6. The impedance modeling method of a grid-type converter based on hybrid synchronous control according to claim 5 is characterized in that: In S6, according to the hybrid synchronous control loop structure of the grid-type converter, the expression of its output phase is obtained as follows: Substitute the active power frequency domain expression (11) into the hybrid synchronous control loop output phase expression (14), and record M(s) = 1 / (Js 2 +D p s), The frequency domain expression of the output phase of the hybrid synchronous control loop is further obtained as: From this we get Δθ v The frequency domain expression of is: V in formula (9) q [f] at frequency ±(f p Substituting the expression at -f1) into equation (16), further simplifying it to obtain Δθ v The expression of [f] is: remember Then Δθ v The expression of [f] is further expressed as: Known cosθ v =cos(θ1+Δθ v )=cosθ1cos(Δθ v )-sinθ1sin(Δθ v ), according to the convolution theorem, the multiplication in the time domain corresponds to the convolution in the frequency domain, cosθ v The frequency domain expression of is: cosθ v [f]=cosθ1[f]-sinθ1[f]*Δθ v [f] (19); In the formula, the symbol "*" represents the convolution operation; Substituting equation (8) and equation (18) into equation (19), we get cosθ v The expression of [f] is: Then get 7. The impedance modeling method of a grid-type converter based on hybrid synchronous control according to claim 6 is characterized in that: In S7, according to the voltage and current dual closed-loop control structure of the grid-type converter, the frequency domain expressions of the d-axis and q-axis modulation voltages are obtained as follows: Set the frequency ±(f p -f1) at E v [f], I d [f], I q [f], V d [f] and V q Substituting the expression of [f] into equation (21), we get V md [f] and V mq [f] at frequency ±(f p -f1) is: In the formula, Z v =R v ±jω N L v , F d (s) and F q (s) are: Write the frequency domain equation of the main circuit according to the LCL filtering link. Taking phase A as an example, the output voltage V oa [f] and the inverter A phase output voltage V a [f], inverter A phase output current I a The relationship between [f] is: Let P1(s) = L1L2s 2 / [R1+1 / (sC1)]+s(L1+L2), P2(s)=L1s / [R1+1 / (sC1)]+1, then V oa [f]=P1(s)I a [f]+P2(s)V a [f]; Using the delay function G for PWM modulation and three-phase inverter bridge d (s) = e -s1.5Ts Describe, that is, V o [f] = V mabc [f]G d (s); where T s =1 / f s represents the switching time constant, f s is the switching frequency, V mabc [f] and V o [f] are the three-phase modulation voltages v of abc respectively mabc and the inverter bridge output voltage v o Frequency domain expression of ; According to the fundamental frequency signal relationship of the converter, calculate V md [f] and V mq [f] Expression V at frequency f = 0 md [0] and V mq [0], V md [0] and V mq [0] Substitute the Park value shown in equation (6) into -1 Transformation formula, according to the convolution theorem, is: V oa [f1]={V md [0]*cosθ1[f1]-V mq [0]*sinθ1[f1]}·G d (jω1) (24); Where V oa [f1], cosθ1[f1], sinθ1[f1] represent the expressions of the output voltage of phase A of the converter, cosθ1, sinθ1 at the frequency f1 respectively; V oa Substituting [f1] into the frequency domain equation of the main circuit shown in equation (23), we can derive V md [0]±jV mq The expression of [0] is: remember Then V md [0]±jV mq [0] = V m0 .

8. The impedance modeling method of a grid-type converter based on hybrid synchronous control according to claim 7 is characterized in that: In S8, according to the convolution theorem, the A phase modulation voltage v is obtained ma At frequency ±f p The frequency domain expression V ma [f] is: Substituting equations (20), (22) and (25) into equation (26), we get V ma [f] at frequency ±f p The specific expression is: In S9, due to the PWM modulation and the three-phase inverter bridge, the delay function G d (s) = e -s1.5Ts Description, the A phase voltage of the inverter bridge output is obtained at the positive sequence voltage disturbance frequency ±f p The frequency domain expression at is:

9. The impedance modeling method of a grid-type converter based on hybrid synchronous control according to claim 8 is characterized in that: In S10, based on formula (27), formula (28) is substituted into formula (23) to obtain: Based on equation (29), the converter positive sequence impedance Z p The expression of (s) is:

10. The impedance modeling method of a grid-connected converter based on hybrid synchronous control according to claim 9, characterized in that: In S11, according to the relationship between the positive-sequence impedance and the negative-sequence impedance of the converter, the imaginary unit j in the positive-sequence impedance shown in equation (30) is replaced by -j to obtain the negative-sequence impedance Z of the converter. n The expression of (s) is: In the formula, and F d (s), F q (s) and V m0 Get, expressed as:

Images