Sampling process-considered droop control inverter hybrid admittance model modeling method

Abstract

The invention relates to the technical field of new energy inverter modeling, and discloses a droop control inverter hybrid admittance model modeling method considering a sampling process. And constructing a small signal block diagram of the hybrid admittance model of the droop inverter, and deducing the hybrid admittance model of the droop control inverter considering the sampling process based on the obtained small signal block diagram of the hybrid admittance model. According to the method, a small signal block diagram of a droop control inverter hybrid admittance model considering a sampling process and a transformation formula of step invariant z transformation of a zero-order retainer are given; according to the method, physical characteristics of a droop control inverter sampling process, discrete characteristics of a controller and continuous characteristics of a controlled object are fully considered; and the form of infinite summation is avoided through the step invariance of the zero-order retainer. Compared with a traditional continuous time model, the method has higher model precision 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 taking a sampling process into consideration. Background Art

[0002] In recent years, the penetration of voltage-source converters (VSCs) in the power grid has continued to increase, and the large-scale access of power electronic devices to the grid has caused concerns about stability. When analyzing the stability of grid-connected inverters, state-space methods and impedance analysis methods are usually used. The state-space method requires detailed modeling of all components in the system being analyzed, which quickly becomes unmanageable as the size of the system increases. In contrast, the impedance-based analysis method only needs to establish an impedance model for the grid-connected inverter and the power grid as independent subsystems, thus avoiding the "curse of dimensionality" problem faced by the state-space method. Therefore, the impedance analysis-based method is widely used to analyze the stability of inverter grid systems.

[0003] Many scholars and experts have proposed inverter impedance modeling methods under the dq axis for stability analysis. However, the impedance model under the dq axis lacks a clear physical meaning. Based on this, the introduced sequence domain impedance modeling method provides a clear physical meaning for the impedance model. The frequency coupling and its impact on stability can be analyzed by establishing the sequence domain impedance model of the inverter using the harmonic linearization method. In addition, based on the complex vector modeling method, the frequency coupling effect caused by the asymmetric structure of the phase-locked loop can be analyzed by establishing a unified αβ impedance model of the inverter.

[0004] In the above methods, the inverter and its control system are modeled in the continuous domain. However, the control system of the inverter is usually implemented on a digital processor that solves discrete time-domain difference equations. Therefore, the inverter exhibits the characteristics of continuous and discrete systems and appears as a hybrid system. Due to the difference between the above modeling method and the actual system, the established inverter admittance model has errors in the high-frequency part, especially the real admittance characteristics near and above the Nyquist frequency. This difference is particularly obvious when the sampling frequency of the controller 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 view of the above problems, the purpose of the present invention is to provide a modeling method of a 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 method for modeling a hybrid admittance model of a droop control inverter considering a sampling process comprises 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 implementation process of closed-loop control 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 sampled by the inverter under 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 transformation. 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 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 step invariance of the zero-order holder is used to avoid the infinite summation form, 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] In the formula, 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 is expressed as:

[0017]

[0018] In the formula, 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 inverter inductor current value in steady state; j is an imaginary unit;

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

[0020]

[0021] In the formula, 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 reference voltage and phase angle is obtained as:

[0023]

[0024] in, is the conjugate component of the inverter sampled output voltage in electrical coordinates, is the conjugate component of the inverter sampled output current 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 droop coefficient and reactive 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 of the zero-order holder is M(z,s) * =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 pulse transfer function, i.e.

[0035]

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

[0037] By 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), we have:

[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] In the formula, 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] Then 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 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 It 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] The present invention proposes a droop control inverter admittance model based on complex vector and sampling process. The 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. The method can avoid the infinite summation form caused by sampling, which is achieved by the step-invariant z-transform of ZOH. The hybrid admittance model can better reflect the admittance characteristics of the droop control 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 active power droop is used for dq conversion. The voltage amplitude obtained from reactive power droop is used as the d-axis voltage reference, 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 a 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 sampled by the inverter under electrical coordinates and Secondly, the discrete phase angle Δθ is obtained by droop control * The small signal model of can be used to transform the coordinates of the model to obtain the voltage and current sampling values ​​in the control coordinate system, 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 system can be obtained by inverse coordinate transformation. 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 small signal block diagram of the hybrid admittance model, the expression of the inverter output voltage can be derived as:

[0077]

[0078] In the formula, 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] In the formula, 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 inverter inductor current value in steady state; j is an imaginary unit.

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

[0083]

[0084] In the formula, 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 sampled output current 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 two sampled discrete variables. The same rule applies to the product of continuous variables and discrete variables. However, the sampling of the product of two continuous variables cannot be separated into the form of 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 by difference, and the transformation between z domain and s domain is performed by identity. The transformation between z domain and s domain is expressed as:

[0097]

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

[0099] The sampling of the transfer function with ZOH is equal to its z-domain impulse transfer function, that is,

[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 of the transfer function with ZOH can avoid 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] Considering the conjugate component of (12), we have

[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 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] In the formula, 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] Through Laplace transform and Poisson's summation theorem, we can get the infinite summation of the sampled signal:

[0122]

[0123] In the formula, 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 sampled value of voltage, current and its conjugate components as an infinite sum of continuous values.

[0125] In addition, since it has little impact on the modeling accuracy, the n≠0 component generated by the image can be safely discarded. Therefore, 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 model 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 frequency range of 100 to 4000 Hz. The amplitude difference of Y2(s) and Y3(s) is small, but the phase difference increases with the increase of frequency. In the frequency range of 4000~10000Hz, the phase difference and amplitude difference of coupling admittance increase with the increase of frequency.

[0135] In order to further verify the accuracy of the hybrid admittance model, a test was conducted on the HIL experimental platform based on RT-Box of PLECS. On this platform, the TMS320F28379D of Texas Instruments was used as the digital controller, and the three-phase droop control inverter was simulated on the RT-Box. The main parameters of the simulation model are shown in Table 1.

[0136] Table 1 Main experimental parameters

[0137]

[0138] The frequency scan results are as follows: Figure 4 As shown. The results show that the proposed hybrid admittance model is in good agreement with the frequency sweep results. Especially in the frequency range near and above the Nyquist frequency, the established theoretical model is in good agreement with the experimental frequency sweep results, indicating that the established analytical model not only reflects the frequency coupling effect of the droop control inverter, but also accurately describes the high-frequency admittance characteristics of the droop control 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 implementation process of closed-loop control 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 sampled by the inverter under 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 transformation. 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 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 step invariance of the zero-order holder is used to avoid the infinite summation form, and the hybrid admittance model of the droop control inverter considering the sampling process is derived.

2. The hybrid admittance modeling method for droop control inverter considering sampling process according to claim 1 is 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: In the formula, 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 is expressed as: In the formula, 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 inverter inductor current value in steady state; j is an imaginary unit; According to Kirchhoff's current law, the sampling current satisfies the following formula: In the formula, 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 reference voltage and phase angle is obtained as: in, is the conjugate component of the inverter sampled output voltage in electrical coordinates, is the conjugate component of the inverter sampled output current 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 droop coefficient and reactive 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 of the zero-order holder is M(z,s) * =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 pulse transfer function, namely: in, is the inverse Laplace transform, Z{·} is the z-transform; By 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), we have: 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; In the formula, 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; Then 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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