A method for impedance modeling of grid-connected converters based on hybrid synchronous control

Abstract

The present invention discloses a hybrid synchronous control-based impedance modeling method for a grid-type converter. The method involves injecting a positive-sequence small-signal voltage disturbance into the converter output voltage v, converting the time-domain expressions of the converter output voltage v and output current i into frequency-domain expressions; converting the time-domain expressions of the trigonometric functions in the Park transform formula into frequency-domain expressions; obtaining frequency-domain expressions for the d-axis and q-axis components of the converter output voltage and output current; calculating frequency-domain expressions for the converter's active power and reactive power; obtaining frequency-domain expressions for the reactive voltage loop output voltage and the hybrid synchronous control loop output phase angle and their trigonometric functions; obtaining frequency-domain expressions for the converter's d-axis and q-axis modulation voltages; obtaining frequency-domain expressions for the converter's A-phase modulation voltage and the inverter bridge output A-phase voltage; and obtaining expressions for the converter's positive- and negative-sequence impedances. The present invention employs the above-mentioned method and can be effectively applied to small-signal stability research in grid-connected renewable energy power generation systems.

Description

Technical Field

[0001] The present 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] With the acceleration of new power system construction and the increasing penetration of renewable energy generation, the "double high" characteristics of these systems—a high proportion of power electronic converters and a high proportion of renewable energy access—are becoming increasingly prominent. This results in grids exhibiting significant characteristics such as low inertia, low damping, and weak voltage support, posing significant challenges to the safe and stable operation of the grid. Consequently, grid-connected converters with active voltage and frequency support capabilities have garnered 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 overcurrent capacity of conventional grid-type converters represented by droop control and virtual synchronous machines is limited, and their 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, thereby improving its transient stability while retaining the advantages of the grid-type converter.

[0004] Existing research on grid-connected converters based on hybrid synchronous control has highlighted their transient stability advantages, but their small-signal stability is still underdeveloped. Because PLL is one of the direct causes of small-signal stability issues in grid-connected converters under weak grid conditions, studying the small-signal stability of grid-connected converters with PLL integration is of great significance. A research team at Sichuan University analyzed the small-signal stability of grid-connected converters based on hybrid synchronous control by establishing a state-space model of the converter's grid-connected system. However, the state-space model is complex in the stability analysis process and cannot intuitively reveal the frequency range and causes of system instability. Impedance models, as a simple and intuitive small-signal stability analysis method, have been widely used in the stability analysis of renewable energy generation grid connections. Therefore, it is important to establish an accurate output impedance model for grid-connected converters based on hybrid synchronous control, taking into account the dynamics of multiple control loops, including the 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 more accurately analyze the stability of small signals and can be effectively applied to the small signal stability research of renewable energy power generation grid-connected systems.

[0006] To achieve the above object, the present invention provides a method for impedance modeling of a grid-type 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. Substitute the output phase angle of the hybrid synchronous control loop into the Park transform, linearize the Park transform, and convert the time domain expression of the trigonometric function in the Park transform formula into a frequency domain expression based on the Fourier transform;

[0009] S3. Sampling and Park transforming the three-phase output voltage and output current of the converter are performed. Based on the convolution theorem, frequency domain expressions of the d-axis and q-axis components of the output voltage and output current of the converter are obtained.

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

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

[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, obtain the frequency domain expression of the hybrid synchronous control loop output phase angle and its trigonometric function;

[0013] S7. Substituting 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, obtain 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 hybrid synchronous control loop output phase angle trigonometric functions 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, mathematically model the PWM modulation and three-phase inverter bridge using the delay function, and modulate the converter A phase modulation voltage 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 with -j to obtain the expression of the negative-sequence impedance of the converter.

[0018] Preferably, 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):

[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] Where 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 Frequency domain expression of (t) 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] Where 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 Transformation angle;

[0036] Park and Park grid-connected converters based on hybrid synchronous control loop -1 The transformed angle is derived from the output of the hybrid synchronous control loop θ 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] are v d and v q Frequency domain expressions of d-axis and q-axis voltages obtained after sampling and T(θ1) transformation; V d [f] and V q [f] are 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] Where, I d1 [f] and I q1 [f] are i d and i q Frequency domain expressions of 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 converter's three-phase output voltage and output current shown in equations (4) and (5), the frequency domain expressions of the converter's active power Pe and reactive power Qe in the 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 converter reactive output power 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] Note 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), we can further simplify 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 equations (8) and (18) into equation (19), we can obtain 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 formula (21), we get V md [f] and V mq [f] at frequency ±(f p -f1) is:

[0072]

[0073] Where 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 of phase A of the inverter bridge is V oa [f] and the output voltage V of the converter phase A 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] The 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 The 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, and sinθ1 at frequency f1, respectively;

[0082] V oa Substituting [f1] into the frequency domain equation of the main circuit shown in formula (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 frequencies ±f p Frequency domain expression V ma [f] is:

[0086]

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

[0088]

[0089] In S9, due to the PWM modulation and the three-phase inverter bridge delay function G d (s)=e -s1.5Ts Description, the A-phase voltage output by the inverter bridge is 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 formula (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 converter negative-sequence impedance Zn(s) is obtained as follows:

[0096]

[0097] Where, 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 more accurately analyze the stability of small signals 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 This is a schematic diagram of the main circuit and control circuit structure of a grid-type converter based on hybrid synchronous control;

[0102] Figure 2 This is a step diagram of a method for modeling impedance of a grid-type converter based on hybrid synchronous control according to 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 with reference to the accompanying drawings and embodiments.

[0105] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Words such as "include" or "comprise" mean that the elements or objects preceding the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" 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 object being described changes, the relative positional relationship may also change accordingly.

[0106] Example 1

[0107] The main circuit and control circuit structure of the grid-type 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 consists of a virtual synchronous generator (VSG) active synchronous loop and a PLL. This 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 proportionally adjusting 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 synchronous 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 the proportional integral (PI) controller in the dq coordinate system, and the 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, v md and v mq 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 as a switching signal m by the PWM modulator. abc To control the inverter bridge of the converter.

[0108] According to the principle of harmonic linearization, the converter impedance model 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 small positive-sequence voltage disturbance of the three-phase 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 based on Fourier transform.

[0110] Inject the 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 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] Where 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 Frequency domain expression of (t) 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] Where j represents the imaginary number symbol.

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

[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 conversion angle comes from the output of the hybrid synchronous control loop θ 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 FIG5 samples and performs Park transform on the three-phase voltage and current of the converter shown in Equation (4) and Equation (5). Based on the convolution theorem, the frequency domain expressions of the d-axis and q-axis components of the converter output voltage and output current are obtained.

[0135] Sampling equations (4) and (5) and substituting them into equation (7), we can obtain:

[0136]

[0137] Where ω1 is the fundamental angular frequency, ω1=2πf1; V d1 [f] and V q1 [f] are v d and v q Frequency domain expressions of d-axis and q-axis voltages obtained after sampling and T(θ1) transformation; V d [f] and V q [f] are 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] Where, I d1 [f] and I q1 [f] are i d and i q Frequency domain expressions of 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 are 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 converted into the frequency domain expression Q of the converter reactive output power shown in formula (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] Note 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] JN 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 simplification yields 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 equations (8) and (18) into equation (19), we can obtain 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 formula (21), we get V md [f] and V mq [f] at frequency ±(f p -f1) is:

[0171]

[0172] Where 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 of phase A of the inverter bridge is V oa [f] and the output voltage V of the converter phase A 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). Where, 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] The 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 can 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], and sinθ1[f1] represent the expressions of the converter phase A output voltage, cosθ1, and sinθ1 at frequency f1, respectively.

[0181] V oa Substituting [f1] into the frequency domain equation of the main circuit shown in formula (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 hybrid synchronous control loop output phase angle trigonometric functions 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 frequencies ±f p Frequency domain expression V ma [f] is:

[0186]

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

[0188]

[0189] S9, mathematically model the PWM modulation and three-phase inverter bridge using the delay function, and modulate the converter A phase modulation voltage 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 three-phase inverter bridge delay function G d (s)=e -s1.5Ts Therefore, the A-phase voltage output by the inverter bridge 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 with -j to obtain the expression of 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] Where, 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 model of 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 more accurately analyze the stability of small signals 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 solutions of the present invention rather than to limit the same. 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 solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A grid-type 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. Substitute the output phase angle of the hybrid synchronous control loop into the Park transform, linearize the Park transform, and convert the time domain expression of the trigonometric function in the Park transform formula into a frequency domain expression based on the Fourier transform; S3. Sampling and Park transforming the three-phase output voltage and output current of the converter are performed. Based on the convolution theorem, frequency domain expressions of the d-axis and q-axis components of the output voltage and output current of the converter are obtained. S4. Based on the frequency domain expressions of the three-phase output voltage and output current of the converter, calculate the frequency domain expressions of the active power and reactive power in the converter control loop; S5. Substitute the frequency domain expression of the converter reactive power into the reactive voltage loop to obtain the frequency domain expression of the reactive voltage loop output voltage; 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, obtain the frequency domain expression of the hybrid synchronous control loop output phase angle and its trigonometric function; S7. Substituting 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, obtain 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 hybrid synchronous control loop output phase angle trigonometric functions 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, mathematically model the PWM modulation and three-phase inverter bridge using the delay function, and modulate the converter A phase modulation voltage 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 with -j to obtain the expression of 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: Where 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 Frequency domain expression of (t) 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: Where 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 Transformation angle; Park and Park grid-connected converters based on hybrid synchronous control loop -1 The transformed angle is derived from the output of the hybrid synchronous control loop θ 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] are v d and v q Frequency domain expressions of d-axis and q-axis voltages obtained after sampling and T(θ1) transformation; V d [f] and V q [f] are 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; Where, I d1 [f] and I q1 [f] are i d and i q Frequency domain expressions of 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 converter three-phase output voltage and output current 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 the resulting 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, 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), we can further simplify 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 equations (8) and (18) into equation (19), we can obtain 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, characterized in that: 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: 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 formula (21), we get V md [f] and V mq [f] at frequency ±(f p -f1) is: Where 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 of phase A of the inverter bridge is V oa [f] and the output voltage V of the converter phase A 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] The 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 The 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, and sinθ1 at frequency f1, respectively; V oa Substituting [f1] into the frequency domain equation of the main circuit shown in formula (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, characterized in that: In S8, according to the convolution theorem, the A phase modulation voltage v ma At frequencies ±f p Frequency domain expression V ma [f] is: Substituting equations (20), (22) and (25) into equation (26), we get V ma [f] at frequencies ±f p The specific expression is: In S9, due to the PWM modulation and the three-phase inverter bridge delay function G d (s)=e -s1.5Ts Description, the A-phase voltage output by the inverter bridge is 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, characterized in that: In S10, based on formula (27), substitute formula (28) into formula (23) to obtain: Based on formula (29), the converter positive sequence impedance Z p The expression of (s) is:

10. The impedance modeling method of a grid-type 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: Where, and F d (s), F q (s) and V m0 Get, expressed as:

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