Modeling method of hybrid admittance model for droop control inverter considering sampling process

Abstract

The present invention relates to the technical field of new energy inverter modeling, and discloses a modeling method for a hybrid admittance model of a droop control inverter considering a sampling process. A small signal block diagram of the hybrid admittance model of the droop inverter is constructed, and based on the obtained small signal block diagram of the hybrid admittance model, a hybrid admittance model of the droop control inverter considering the sampling process is derived. The present invention provides a small signal block diagram of the hybrid admittance model of the droop control inverter considering the sampling process and a transformation formula of the step-invariant z-transform of the zero-order holder; the method fully considers the physical characteristics of the sampling process of the droop control inverter, the discrete characteristics of the controller and the continuous characteristics of the controlled object; the infinite summation form is avoided by the step invariance of the zero-order holder. Compared with the traditional continuous-time model, it has higher model accuracy near and above the Nyquist frequency.

Description

Technical Field

[0001] The present invention relates to the technical field of new energy inverter modeling, and in particular to a modeling method of a hybrid admittance model of a droop control inverter considering a sampling process. Background Art

[0002] In recent years, the penetration of voltage-source converters (VSCs) in power grids has continued to increase, and the large-scale integration of power electronic equipment has raised concerns about stability. State-space and impedance analysis methods are commonly used to analyze the stability of grid-connected inverters. State-space methods require detailed modeling of all components in the system being analyzed, which quickly becomes unmanageable as the system size increases. In contrast, impedance-based analysis methods only require the grid-connected inverter and the power grid to be modeled as independent subsystems, thus avoiding the "curse of dimensionality" problem faced by state-space methods. As a result, impedance-based analysis methods are widely used to analyze the stability of inverter-grid systems.

[0003] Numerous scholars and experts have proposed inverter impedance modeling methods for dq-axis stability analysis. However, the impedance model for dq-axis stability lacks a clear physical meaning. Therefore, the introduced sequence-domain impedance modeling method provides a clear physical meaning for the impedance model. Using harmonic linearization to establish a sequence-domain impedance model for the inverter allows analysis of frequency coupling and its impact on stability. Furthermore, building on the complex-vector modeling method, a unified αβ impedance model for the inverter allows analysis of the frequency coupling effects caused by the asymmetric structure of the phase-locked loop.

[0004] In the above methods, the inverter and its control system are modeled in the continuous domain. However, the inverter's control system is typically implemented on a digital processor that solves discrete time-domain difference equations. As a result, the inverter exhibits characteristics of both continuous and discrete systems, appearing as a hybrid system. Due to the differences between the above modeling methods and the actual system, the established inverter admittance model exhibits errors in the high-frequency portion, especially the true admittance characteristics near and above the Nyquist frequency. This difference is particularly evident when the controller's sampling frequency is low. Another limitation of the above method is that some discrete control algorithms cannot be accurately modeled using continuous-time transfer functions. Summary of the Invention

[0005] In response to the above problems, the purpose of the present invention is to provide a modeling method for the hybrid admittance model of a droop control inverter taking into account the sampling process, which fully considers the signal sampling characteristics of the actual physical system, the continuous characteristics of the inverter controlled object and the discrete characteristics of the actual controller, and can better reflect the admittance characteristics of the droop control inverter near and above the Nyquist frequency.

[0006] The technical solution is as follows:

[0007] A hybrid admittance modeling method for a droop control inverter considering a sampling process includes the following steps:

[0008] Step 1: Based on the typical three-phase droop control inverter topology and its control system, construct the small signal block diagram of the droop inverter hybrid admittance model;

[0009] The closed-loop control implementation process in the small signal block diagram of the hybrid admittance model is as follows: the output voltage Δu' of the PCC point is collected odq and output current Δi' odq Get the output voltage and output current of the inverter sampled in electrical coordinates and The discrete phase angle Δθ is obtained by droop control * The small signal model is obtained by discrete phase angle Δθ * The small signal model is transformed into coordinates to obtain the voltage and current sampling values ​​in the control coordinate system;

[0010] Through voltage and current dual loop control, the modulation wave signal is obtained The small signal model of the electrical coordinates is obtained by inverse coordinate change. Small signal model; after the delay module z -1 The voltage value of the inverter port of the main circuit is obtained by the zero-order holder, and the voltage and current values ​​of the circuit output are obtained by Kirchhoff's law, thereby realizing closed-loop control;

[0011] Step 2: Based on the obtained small signal block diagram of the hybrid admittance model, the physical characteristics of the sampling process of the droop control inverter, the discrete characteristics of the controller and the continuous characteristics of the controlled object are considered separately. The infinite summation form is avoided through the step invariance of the zero-order holder, and the hybrid admittance model of the droop control inverter considering the sampling process is derived.

[0012] Furthermore, the step 2 is specifically as follows:

[0013] Step 2.1 According to the small signal block diagram of the hybrid admittance model, the expression of the inverter output voltage is:

[0014]

[0015] Where, is the reference voltage, is the output voltage sampling value under the control coordinate, is the sampling value of the inductor current under the control coordinate, C f is the AC side filter capacitor, L f is the AC side filter inductance, Δθ * Discrete phase angle calculated for droop control, mdq0 is the steady-state value of the modulation wave voltage; z -1 Y is the delay module, representing the PWM delay of one beat; L (s) is the inductance transfer function, Z C (s) is the capacitance transfer function, G V (z) is the voltage PI controller transfer function, G C (z) is the current PI controller transfer function; G h (s) is the transfer function of the zero-order holder;

[0016] Output voltage sampling value and the inductor current sampling value The small signal model of is expressed as:

[0017]

[0018] Where, is the output voltage sampled by the inverter in electrical coordinates; u dq0 is the inverter output voltage value in steady state; is the inverter inductor current in electrical coordinates; i Ldq0 is the inductor current value of the inverter in steady state; j is the imaginary unit;

[0019] According to Kirchhoff's current law, the sampling current satisfies the following formula:

[0020]

[0021] Where, is the output current sampled by the inverter in electrical coordinates;

[0022] Step 2.2 Considering the discrete process of droop control, the small signal model of the reference voltage and phase angle is obtained as:

[0023]

[0024] in, is the conjugate component of the inverter output voltage sampled in electrical coordinates, is the conjugate component of the inverter output current sampled in electrical coordinates; A1(z), B1(z), C1(z), D1(z), A2(z), B2(z), C2(z), and D2(z) are intermediate quantities, specifically:

[0025]

[0026] in, and i odq0 are the conjugate component value of the output current in steady state and the value of the output current in steady state respectively; and u odq0are the conjugate component value of the output voltage in steady state and the value of the output voltage in steady state respectively; n and m are the active power droop coefficient and reactive power droop coefficient respectively; j is the imaginary unit; T is the sampling time;

[0027] Substituting formulas (2), (3), and (4) into (1), we obtain:

[0028]

[0029] Among them, M(z,s), N(z,s), E(z,s), and L(z,s) are intermediate quantities, specifically:

[0030]

[0031] The sampled output voltage used by the discrete-time controller is obtained by sampling both sides of equation (7); the sampling result of the final output voltage is expressed as:

[0032]

[0033] Among them, the step invariant transfer function M(z,s) of the zero-order holder is * =z -1 [G h (s)Y L (s)Z C (s)] * ,E(z,s) * 、N(z,s) * and L(z,s) * By replacing M(z,s) in E(z,s), N(z,s) and L(z,s) with M(z,s) * get;

[0034] The sampling of the transfer function with a zero-order holder is equal to its z-domain impulse transfer function, i.e.

[0035]

[0036] in, is the inverse Laplace transform, Z{·} is the z transform;

[0037] Combining the same terms, (6) and (8) can be written more concisely as:

[0038]

[0039]

[0040] Among them, a, b, c, d, e, f, g, and h are intermediate quantities, specifically:

[0041]

[0042] Considering the conjugate components of formula (11):

[0043]

[0044] in, are the above variables e, f, g, h, N(z,s) respectively * The conjugate component of ; Solving equations (11) and (13) yields and Substituting into formula (10) we get:

[0045]

[0046] Among them, A1, A2, A3, A4, A5 and A6 are intermediate quantities, specifically:

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] Step 2.3 Use the Poisson summation formula to convert the output voltage sampled by the inverter in electrical coordinates and its conjugate components Output current sampled by the inverter in electrical coordinates and its conjugate components Each discrete sample value is represented as an infinite sum of continuous values;

[0054]

[0055] Where x * (s) is the frequency domain expression of the sampled signal, s is the Laplace operator, ω s =2π / T sa is the sampling angular frequency;

[0056] The hybrid admittance model of the droop control inverter considering the sampling process is:

[0057]

[0058] Among them, Δi oαβ (s) and Δu oαβ(s) are the output voltage and current sampled by the inverter respectively; and is the admittance element, specifically:

[0059]

[0060] in, and is an intermediate quantity, specifically:

[0061]

[0062]

[0063]

[0064]

[0065] The beneficial effects of the present invention are as follows: the present invention provides a small signal block diagram of a hybrid admittance model of a droop control inverter considering a sampling process and a transformation formula of a step-invariant z-transform of a zero-order holder. The method fully considers the physical characteristics of the sampling process of the droop control inverter, the discrete characteristics of the controller and the continuous characteristics of the controlled object, and avoids the form of infinite summation through the step invariance of the zero-order holder; compared with the traditional continuous-time model, the model has higher model accuracy near and above the Nyquist frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is the droop inverter topology and control system corresponding to the present invention.

[0067] Figure 2 It is a small signal block diagram of the hybrid admittance model of the droop inverter designed by the present invention.

[0068] Figure 3 This is a comparison between the continuous admittance model and the mixed admittance model corresponding to the present invention.

[0069] Figure 4 This is the frequency sweep result of the hardware-in-the-loop experiment corresponding to the present invention. DETAILED DESCRIPTION

[0070] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0071] This paper proposes an admittance model for a droop-controlled inverter based on a complex vector and sampling process. This model takes into account the signal sampling characteristics of the actual physical system, the continuous characteristics of the inverter controlled object, and the discrete characteristics of the actual controller. This method avoids the infinite summation caused by sampling, achieved through a step-invariant z-transform of the ZOH. This hybrid admittance model effectively reflects the admittance characteristics of a droop-controlled inverter near and above the Nyquist frequency.

[0072] A typical three-phase droop control inverter is as follows Figure 1 As shown in the figure, L f is the AC side filter inductor, C f is the AC side filter capacitor, L g is the AC side line inductance; u oαβ is the output voltage of the inverter, i oαβ is the output current of the inverter; and inverter control is divided into power control and dual-loop control.

[0073] Specifically, droop control is used as a power controller. The phase obtained from the active power droop is used for dq conversion. The voltage amplitude obtained from the reactive power droop is used as the d-axis voltage reference, which is expressed as The dual-loop control operates in a dq framework, which utilizes a voltage proportional-integral (PI) controller (G V ) and current proportional integral (PI) controller (G C ) to generate a modulation signal and sinusoidal pulse width modulation (SPWM) to obtain a pulse signal to drive each switch tube.

[0074] The specific modeling process is as follows:

[0075] Figure 2 First, the output voltage Δu' of the PCC point is collected. odq and output current Δi' odq Get the output voltage and output current of the inverter sampled in electrical coordinates and Secondly, the discrete phase angle Δθ is obtained by droop control * The small signal model of the control coordinate system can be obtained by performing coordinate transformation on the model, such as Then, through the voltage and current dual loop control, the modulation wave signal can be obtained The small signal model of the electrical coordinate can be obtained by changing the inverse coordinate. The small signal model is finally passed through the delay module z -1The voltage value of the inverter port of the main circuit can be obtained by the zero-order holder, and the voltage and current values ​​of the circuit output can be obtained through Kirchhoff's law, thereby realizing closed-loop control.

[0076] according to Figure 2 The hybrid admittance model small signal block diagram, the expression of the inverter output voltage can be derived as:

[0077]

[0078] Where, is the output voltage sampling value, is the inductor current sampling value, Δθ * Discrete phase information calculated for droop control, m dq0 is the steady-state value of the modulation wave voltage, z -1 is the delay module, Δu' odq is the output voltage, Δi' odq is the output current, Y L (s) is the inductance transfer function, Z C (s) is the capacitance transfer function, G V (z) is the voltage PI controller, G C (z) is the current PI controller.

[0079] The small signal model of output voltage and current sampling is expressed as:

[0080]

[0081] Where, is the output voltage sampled by the inverter in electrical coordinates; u dq0 is the inverter output voltage value in steady state; is the output current sampled by the inverter in electrical coordinates; i Ldq0 is the inductor current value of the inverter in steady state; j is the imaginary unit.

[0082] According to Kirchhoff's current law, the sampling current satisfies the following formula

[0083]

[0084] Where, is the output current sampled by the inverter in electrical coordinates;

[0085] Considering the discrete process of droop control, the small signal model of reference voltage and phase angle is obtained as follows:

[0086]

[0087] in, is the conjugate component of the inverter output voltage sampled in electrical coordinates, is the conjugate component of the inverter output current sampled in electrical coordinates; A1(z), B1(z), C1(z), D1(z), A2(z), B2(z), C2(z), and D2(z) are intermediate quantities, specifically:

[0088]

[0089] Substituting formulas (2), (3), and (4) into (1), we can obtain:

[0090]

[0091] Among them, M(z,s), N(z,s), E(z,s), and L(z,s) are intermediate quantities, specifically:

[0092]

[0093] Sampling both sides of (6) yields the sampled output voltage used by the discrete-time controller. According to discrete control theory, the sampling of the product of two discrete variables can be expressed as the product of the two sampled discrete variables. The same rule applies to the product of a continuous variable and a discrete variable. However, the sampling of the product of two continuous variables cannot be separated into the form of a sample product. Therefore, the sampling result of the final output voltage can be expressed as:

[0094]

[0095] Among them, M(z,s) * =z -1 [G h (s)Y L (s)Z C (s)] * ; and the intermediate variable E(z,s) * ,N(z,s) * and L(z,s) * This can be done by replacing M(z,s) with M(z,s) in E(z,s), N(z,s) and L(z,s) * get.

[0096] The controller is discretized using difference, and the transformation between the z domain and the s domain is performed using the identity. The transformation between the z domain and the s domain is expressed as:

[0097]

[0098] Where z = exp(sT sa ).

[0099] The sampled transfer function with ZOH is equal to its z-domain impulse transfer function, i.e.

[0100]

[0101] in is the inverse Laplace transform, and Z{·} is the z-transform. This result is equivalent to the step-invariant z-transform of YL(s)ZC(s). Therefore, sampling the transfer function with ZOH avoids the infinite sum form caused by sampling.

[0102] By combining the same terms, (6) and (8) can be written more concisely as

[0103]

[0104]

[0105] in,

[0106]

[0107] Consider the conjugate component of (12)

[0108]

[0109] in, are the conjugate components of the above variables e, f, g, h, and N(z,s)* respectively;

[0110] Solving (12) and (14) yields and Substituting into formula (11) we get

[0111]

[0112] Among them, A1, A2, A3, A4, A5 and A6 are intermediate quantities, specifically:

[0113]

[0114]

[0115]

[0116]

[0117] The left side of formula (15) is the inverter output voltage Δu' odq , which is a continuous variable. In contrast, the right side includes not only the output voltage sampled by the inverter and its conjugate components Also includes the sampled output current and its conjugate components They are all discrete variables.

[0118] The concept of signal sampling is introduced. Sampling a continuous signal x(t) is equivalent to a pulse modulation model. In pulse modulation, the input signal is modulated by an infinite series of Dirac functions, where the modulation function is an ideal unit pulse sequence. The output expression of the sampled signal is:

[0119]

[0120] Where x * (t) is the time domain expression of the sampled signal, T sa is the sampling period, k is the number of sampling times, t is the time in the time domain; δ(·) is the Dirac function.

[0121] The infinite summation term of the sampled signal is obtained through Laplace transform and Poisson's summation theorem:

[0122]

[0123] Where x * (s) is the frequency domain expression of the sampled signal, s is the Laplace operator, ω s =2π / T sa is the sampling angular frequency.

[0124] In order to derive the inverter admittance model that describes the mathematical relationship between current and voltage, the Poisson summation formula (17) is used to express each discrete sample value of voltage, current and its conjugate components as an infinite sum of continuous values.

[0125] In addition, since the n≠0 component generated by the image can be safely discarded due to its little impact on the modeling accuracy, the hybrid admittance model of the droop control inverter considering the sampling process is:

[0126]

[0127] Among them, Δi oαβ (s) and Δu oαβ (s) are the output voltage and current sampled by the inverter; Y1 s (s), Y3 s (s) and is the admittance element, specifically:

[0128]

[0129] in, and is an intermediate quantity, specifically:

[0130]

[0131]

[0132]

[0133]

[0134] Figure 3 The frequency and phase characteristics of the analytical models obtained by the continuous model and the hybrid model are given, and the parameters are shown in Table 1. It can be seen that in the frequency range below 100 Hz, the proposed hybrid admittance model is consistent with the continuous model. In the frequency range above 100 Hz, the amplitude and phase of Y1(s) and Y4(s) are consistent with There is a slight deviation compared to the above. In the frequency range of 100~4000Hz, the admittance element The amplitude difference between Y2(s) and Y3(s) is small, but the phase difference increases with increasing frequency. In the frequency range of 4000 to 10000 Hz, the phase difference and amplitude difference of the coupling admittance increase with increasing frequency.

[0135] To further verify the accuracy of the hybrid admittance model, we conducted tests on a PLECS-based RT-Box HIL experimental platform. A three-phase droop control inverter was simulated on this platform using the Texas Instruments TMS320F28379D as the digital controller. The main parameters of the simulation model are shown in Table 1.

[0136] Table 1 Main experimental parameters

[0137]

[0138] Frequency scan results are as follows Figure 4 The results show that the proposed hybrid admittance model agrees well with the frequency sweep results. In particular, within the frequency range near and above the Nyquist frequency, the established theoretical model agrees well with the experimental frequency sweep results, demonstrating that the established analytical model not only reflects the frequency coupling effect of the droop-controlled inverter but also accurately describes the high-frequency admittance characteristics of the droop-controlled inverter.

Claims

1. A hybrid admittance modeling method for a droop control inverter considering a sampling process, characterized in that: The following steps are involved: Step 1: Based on the typical three-phase droop control inverter topology and its control system, construct the small signal block diagram of the droop inverter hybrid admittance model; The closed-loop control implementation process in the small signal block diagram of the hybrid admittance model is as follows: the output voltage Δu' of the PCC point is collected odq and output current Δi' odq Get the output voltage and output current of the inverter sampled in electrical coordinates and The discrete phase angle Δθ is obtained by droop control * The small signal model is obtained by discrete phase angle Δθ * The small signal model is transformed into coordinates to obtain the voltage and current sampling values ​​in the control coordinate system; Through voltage and current dual loop control, the modulation wave signal is obtained The small signal model of the electrical coordinates is obtained by inverse coordinate change. Small signal model; after the delay module z -1 The voltage value of the inverter port of the main circuit is obtained by the zero-order holder, and the voltage and current values ​​of the circuit output are obtained by Kirchhoff's law, thereby realizing closed-loop control; Step 2: Based on the obtained small signal block diagram of the hybrid admittance model, the physical characteristics of the sampling process of the droop control inverter, the discrete characteristics of the controller and the continuous characteristics of the controlled object are considered separately. The infinite summation form is avoided through the step invariance of the zero-order holder, and the hybrid admittance model of the droop control inverter considering the sampling process is derived.

2. The hybrid admittance modeling method for a droop control inverter considering a sampling process according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2.1 According to the small signal block diagram of the hybrid admittance model, the expression of the output voltage of the collected PCC point is: Where, is the reference voltage, is the output voltage sampling value under the control coordinate, is the sampling value of the inductor current under the control coordinate, C f is the AC side filter capacitor, L f is the AC side filter inductance, Δθ * Discrete phase angle calculated for droop control, m dq0 is the steady-state value of the modulation wave voltage; z -1 Y is the delay module, representing the PWM delay of one beat; L (s) is the inductance transfer function, Z C (s) is the capacitance transfer function, G V (z) is the voltage PI controller transfer function, G C (z) is the current PI controller transfer function; G h (s) is the transfer function of the zero-order holder; Output voltage sampling value under control coordinates And the inductor current sampling value under the control coordinate The small signal model of is expressed as: Where, is the output voltage sampled by the inverter in electrical coordinates; u dq0 is the inverter output voltage value in steady state; is the inverter inductor current in electrical coordinates; i Ldq0 is the inductor current value of the inverter in steady state; j is the imaginary unit; According to Kirchhoff's current law, the sampling current satisfies the following formula: Where, is the output current sampled by the inverter in electrical coordinates; Step 2.2 Considering the discrete process of droop control, the small signal model of the reference voltage and phase angle is obtained as: in, is the conjugate component of the inverter output voltage sampled in electrical coordinates, is the conjugate component of the inverter output current sampled in electrical coordinates; A1(z), B1(z), C1(z), D1(z), A2(z), B2(z), C2(z), and D2(z) are intermediate quantities, specifically: in, and i odq0 are the conjugate component value of the output current in steady state and the value of the output current in steady state respectively; and u odq0 are the conjugate component value of the output voltage in steady state and the value of the output voltage in steady state respectively; n and m are the active power droop coefficient and reactive power droop coefficient respectively; j is the imaginary unit; T is the sampling time; Substituting formulas (2), (3), and (4) into (1), we obtain: Among them, M(z,s), N(z,s), E(z,s), and L(z,s) are intermediate quantities, specifically: The sampled output voltage used by the discrete-time controller is obtained by sampling both sides of equation (7); the sampling result of the final output voltage is expressed as: Among them, the step invariant transfer function M(z,s) of the zero-order holder is * =z -1 [G h (s)Y L (s)Z C (s)] * , intermediate variable E(z,s) * 、N(z,s) * and L(z,s) * By replacing M(z,s) in E(z,s), N(z,s) and L(z,s) with M(z,s) * get; The sampled transfer function with a zero-order holder is equal to its z-domain impulse transfer function, namely: in, is the inverse Laplace transform, Z{·} is the z transform; Combining the same terms, (6) and (8) can be written more concisely as: Among them, a, b, c, d, e, f, g, and h are intermediate quantities, specifically: Considering the conjugate components of formula (11): in, are the above variables e, f, g, h, N(z,s) respectively * The conjugate component of ; Solving equations (11) and (13) yields and Substituting into formula (10) we get: Among them, A1, A2, A3, A4, A5 and A6 are intermediate quantities, specifically: Step 2.3 Use the Poisson summation formula to convert the output voltage sampled by the inverter in electrical coordinates and its conjugate components Output current sampled by the inverter in electrical coordinates and its conjugate components Each discrete sample value is represented as an infinite sum of continuous values; Where x * (s) is the frequency domain expression of the sampled signal, s is the Laplace operator, ω s =2π / T sa is the sampling angular frequency; The hybrid admittance model of the droop control inverter considering the sampling process is: Among them, Δi oαβ (s) and Δu oαβ (s) are the output voltage and current sampled by the inverter respectively; and is the admittance element, specifically: in, and is an intermediate quantity, specifically:

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