Method for determining impedance of network construction type converter based on complex variables

Abstract

The invention provides a complex variable-based network construction type converter impedance determination method, which comprises the following steps of: adding a disturbance small signal to a common coupling point between a network construction type converter and a power grid, and determining an output voltage and an output current of the network construction type converter in a complex frequency domain based on a coupling condition of the disturbance small signal and a fundamental wave frequency; determining the output phase angle disturbance and the reference voltage disturbance of the network construction type converter in the complex frequency domain based on the output voltage and the output current of the network construction type converter; based on the output voltage and the output current of the network construction type converter in the complex frequency domain and the output phase angle disturbance and the reference voltage disturbance of the network construction type converter in the complex frequency domain, determining the disturbance of a modulation wave for controlling the converter in an alpha-beta coordinate system, and converting the disturbance to the complex frequency domain; and constructing a relational expression of input voltage disturbance and output current disturbance of the network-forming converter based on the disturbance of the modulation wave in the complex frequency domain, determining the input voltage disturbance and the output current disturbance, and dividing the input voltage disturbance by the output current disturbance to obtain the impedance of the network-forming converter.

Description

TECHNICAL FIELD

[0001] The application relates to a power grid impedance determination method, in particular to a complex variable-based grid-connected converter impedance determination method. BACKGROUND

[0002] With the increasing penetration of new energy generation and power electronic equipment in the power grid, grid-connected converters become one of the key technologies to solve the stability of weak power grids due to their voltage source characteristics and active support capability. However, grid-connected converters also cause harmonic oscillation problems when they are integrated into the power grid.

[0003] Impedance analysis is a commonly used method for analyzing the stability of grid-connected converter systems. Due to its clear physical concept, modularity, scalability, and the fact that it does not need to re-establish the model of the entire system when the system structure or parameters change, as in the state space model, its application has become more and more widespread in recent years. According to the coordinate system during modeling, there are mainly impedance models based on dq coordinate system and sequence impedance models based on abc stationary coordinate system. The dq impedance model can use the traditional steady-state DC operating point and linearize around the DC operating point because it is analyzed and modeled in the dq axis. However, there is coupling between the dq axes of the dq axis impedance model, and it is difficult to measure in practice, resulting in low accuracy of the final impedance determination result.

[0004] The sequence impedance model is based on the harmonic linearization method and establishes an impedance model in the abc stationary coordinate system, which has a clear physical meaning and simplified operation through frequency domain convolution. However, the sequence impedance model often has coupling between the positive and negative sequences, and when considering the frequency coupling effect, the impedance appears in matrix form, which requires the application of the generalized Nyquist criterion to judge the system stability, making the stability analysis process complex and inefficient.

[0005] Therefore, in order to solve the above technical problems, it is urgent to propose a new technical means. SUMMARY

[0006] Therefore, the purpose of the present application is to provide a complex variable-based grid-connected converter impedance determination method, which determines the input voltage disturbance and output current disturbance of the grid-connected converter in the complex frequency domain by injecting a disturbance signal at the grid-connected point of the grid-connected converter and considering the frequency coupling characteristics of the disturbance signal and the fundamental signal, thereby ultimately determining the impedance of the grid-connected converter. This can effectively ensure the accuracy of the final result, and the algorithm is more concise and efficient compared to the prior art, providing accurate data support for subsequent analysis of the harmonic oscillation problem caused by the grid-connected converter accessing the power grid.

[0007] The complex variable-based grid-connected converter impedance determination method provided by the present application comprises the following steps:

[0008] S1. A small disturbance signal is added to the point of common coupling between the grid-connected converter and the power grid, and the output voltage and the output current of the grid-connected converter in the complex frequency domain are determined based on the coupling between the small disturbance signal and the fundamental frequency;

[0009] S2. The output phase angle disturbance and the reference voltage disturbance of the grid-connected converter in the complex frequency domain are determined based on the output voltage and the output current of the grid-connected converter;

[0010] S3. The disturbance of the modulation wave for controlling the converter in the αβ coordinate system is determined based on the output voltage and the output current of the grid-connected converter in the complex frequency domain and the output phase angle disturbance and the reference voltage disturbance of the grid-connected converter in the complex frequency domain, and is converted to the complex frequency domain;

[0011] S4. The input voltage disturbance and the output current disturbance relationship of the grid-connected converter is constructed based on the disturbance of the modulation wave in the complex frequency domain, and the input voltage disturbance and the output current disturbance are determined, and the impedance of the grid-connected converter is obtained by dividing the input voltage disturbance by the output current disturbance.

[0012] Further, step S1 specifically comprises:

[0013] The expressions of the output voltage and the output current of the grid-connected converter in the αβ coordinate system are:

[0014]

[0015] The output voltage and the output current of the grid-connected converter are determined by formula (1) and formula (2);

[0016] wherein v α and v β represent the output voltage of the α phase and the β phase of the grid-connected converter respectively, i α and i β represent the output current of the α phase and the β phase of the grid-connected converter respectively, V1 represents the fundamental voltage amplitude, I1 represents the fundamental current amplitude, ω1 represents the fundamental angular frequency, the initial phase of the fundamental voltage is 0, and the initial phase of the fundamental current is V p represents the disturbance voltage amplitude, I p1 represents the disturbance current amplitude, I p2 represents the coupling current amplitude, ω p represents the disturbance frequency, and represent the initial phase of the disturbance voltage and the disturbance current respectively, represents the initial phase of the coupling current, and 2ω1-ω p represents the coupling frequency between the small disturbance signal and the fundamental frequency;

[0017] The complex variable forms of the output voltage and the output current in the αβ coordinate system are:

[0018]

[0019] wherein:

[0020] Further, determining the output phase angle disturbance and the reference voltage disturbance of the grid-forming converter in the complex frequency domain based on the output voltage and the output current of the grid-forming converter specifically comprises:

[0021] Determining the active power and the reactive power of the converter output:

[0022]

[0023] wherein: * represents the conjugate operation;

[0024] and determining the active power and the reactive power disturbance of the grid-forming converter output based on formula (5):

[0025]

[0026] wherein: ΔPe(t) and ΔQe(t) respectively represent the active power and the reactive power disturbance of the grid-forming converter output;

[0027] Converting formula (6) and formula (7) to the complex frequency domain is:

[0028]

[0029]

[0030] wherein: ΔPe(s-jω1) and ΔPe(jω1-s) respectively represent the active power disturbance of the grid-forming converter output at ω p -ω1 and ω1-ω p , respectively; ΔQe(s-jω1) and ΔQe(jω1-s) respectively represent the reactive power disturbance of the grid-forming converter output at ω p -ω1 and ω1-ω p , respectively;

[0031] Inputting the active power and the reactive power of the grid-forming converter into the power loop of the grid-forming converter to obtain the phase angle disturbance and the reference voltage disturbance of the grid-forming converter:

[0032]

[0033] wherein: Δθ(s-jω1) and Δθ(jω1-s) respectively represent the output phase angle disturbance of the grid-forming converter at ω p -ω1 and ω1-ωp perturbation at two frequencies, ΔE m (s-jω1) and ΔE m (jω1-s) respectively represent the reference voltage of the grid-forming converter at ω p -ω1 and ω1-ω p perturbation at two frequencies;

[0034]

[0035] wherein: k p represents the active loop primary frequency modulation coefficient of the grid-forming converter, k q represents the reactive loop primary frequency modulation coefficient of the grid-forming converter, J and D respectively represent the virtual inertia and virtual damping of the active loop of the grid-forming converter, ω n represents the rated angular frequency of the grid-forming converter, taking the value of 50*2π.

[0036] Further, step S4 specifically comprises:

[0037] determining the bridge arm potential of the grid-forming converter at ω p -ω1 and ω1-ω p perturbation at two frequencies, ΔE dq (s-jω1) and ΔE dq (jω1-s):

[0038]

[0039] wherein: G i (s) and G v (s) respectively represent the transfer function of the PI controller of the current loop and the voltage loop of the grid-forming converter, G i (s) = k pi +k ii / s; G i (s) = k pv +k iv / s; wherein: k pi , k ii respectively represent the proportional coefficient and the integral coefficient of the current loop PI controller of the grid-forming converter, k pv , k iv respectively represent the proportional coefficient and the integral coefficient of the voltage loop PI controller of the grid-forming converter, C f represents the filter capacitance of the grid-forming converter, L f represents the filter inductance of the grid-forming converter;

[0040] Converting formula (12) and formula (13) to the αβ coordinate system obtains the bridge arm potential of the grid-forming converter at ω p-ω1 and ω1-ω p Disturbance of output current I αβ (s) and ΔE αβ (j2ω1-s) :

[0041]

[0042]

[0043] The disturbance relationship of input voltage and output current of the grid-connected converter is constructed as follows:

[0044]

[0045] The formula (14) and the formula (15) are substituted into the formula (16), and the grid-connected converter at ω p -ω1 and ω1-ω p Disturbance of output current I p (s) and I p (j2ω1-s) ;

[0046] The self-impedance Z S (s) and the companion impedance Z A (s) :

[0047]

[0048] Wherein: V p (s) represents the input voltage disturbance of the grid-connected converter, Z L (s) represents the impedance of the filter inductance branch, Z L (s) = R L +sL f , R L represents the parasitic resistance of the filter inductance, Y C (s) represents the admittance of the filter capacitance branch, R c represents the damping resistance of the filter capacitance C f .

[0049] Advantages of the present application: through the present application, by injecting a disturbance signal at the grid-connected point of the grid-connected converter, and considering the frequency coupling characteristics of the disturbance signal and the fundamental signal, the input voltage disturbance and the output current disturbance of the grid-connected converter are determined in the complex frequency domain, so that the impedance of the grid-connected converter is finally determined, which can effectively ensure the accuracy of the final result, and the algorithm is more simple and efficient compared with the prior art, and accurate data support is provided for subsequent analysis of the harmonic oscillation problem caused by the grid-connected converter accessing the power grid. BRIEF DESCRIPTION OF DRAWINGS

[0050] The application will be further described below in conjunction with the accompanying drawings and embodiments.

[0051] Figure 1 is a flow chart of the application.

[0052] Figure 2 is a main circuit structure and control block diagram of the grid-forming converter in the application;

[0053] Figure 3 is a control block diagram of the power loop in the application;

[0054] Figure 4 is a control block diagram of the voltage and current loop in the application;

[0055] Figure 5 is a small-signal transfer function structure block diagram of the full system in complex variable form including the main circuit and control loop in the application;

[0056] Figure 6 is a theoretical curve and sweep curve of the self-impedance of the grid-forming converter in the application;

[0057] Figure 7 is a theoretical curve and sweep curve of the companion impedance of the grid-forming converter in the application. DETAILED DESCRIPTION

[0058] The application will be further described below in conjunction with the accompanying drawings and embodiments:

[0059] The application provides a grid-forming converter impedance determination method based on complex variable, including the following steps:

[0060] S1. A small disturbance signal is added at the point of common coupling between the grid-forming converter and the power grid, and the output voltage and output current of the grid-forming converter in the complex frequency domain are determined based on the disturbance small signal and the fundamental frequency coupling condition; as shown in the following formula: Figure 2 The main circuit topology of the grid-forming converter includes a DC power supply, a three-phase converter, an LC filter and a line impedance;

[0061] S2. The output phase angle disturbance and reference voltage disturbance of the grid-forming converter in the complex frequency domain are determined based on the output voltage and output current of the grid-forming converter;

[0062] S3. The disturbance of the modulation wave in the αβ coordinate system for controlling the converter is determined based on the output voltage and output current of the grid-forming converter in the complex frequency domain and the output phase angle disturbance and reference voltage disturbance of the grid-forming converter in the complex frequency domain, and is converted to the complex frequency domain;

[0063] S4. Construct the input voltage disturbance and output current disturbance relationship of the grid-connected converter based on the disturbance of the modulation wave in the complex frequency domain, and determine the input voltage disturbance and output current disturbance, and the impedance of the grid-connected converter is obtained by dividing the input voltage disturbance by the output current disturbance. Through the present application, by injecting a disturbance signal at the grid-connected point of the grid-connected converter, and considering the frequency coupling characteristics of the disturbance signal and the fundamental signal, the input voltage disturbance and the output current disturbance of the grid-connected converter are determined in the complex frequency domain, so as to finally determine the impedance of the grid-connected converter, which can effectively ensure the accuracy of the final result, and the algorithm is more concise and efficient compared with the prior art, and provides accurate data support for subsequent analysis of the harmonic oscillation problem caused by the grid-connected converter accessing the power grid.

[0064] In the embodiment, step S1 specifically comprises:

[0065] The expressions of the output voltage and current of the grid-connected converter in the αβ coordinate system are:

[0066]

[0067] The output voltage and output current of the grid-connected converter are determined by formula (1) and formula (2);

[0068] Wherein: v α and v β respectively represent the output voltage of the α phase and the β phase of the grid-connected converter, i α and i β respectively represent the output current of the α phase and the β phase of the grid-connected converter, V1 represents the fundamental voltage amplitude, I1 represents the fundamental current amplitude, ω1 represents the fundamental angular frequency, the initial phase of the fundamental voltage is 0, and the initial phase of the fundamental current is V p represents the disturbance voltage amplitude, I p1 represents the disturbance current amplitude, I p2 represents the coupling current amplitude, ω p represents the disturbance frequency, and respectively represent the initial phase of the disturbance voltage and the disturbance current, represents the initial phase of the coupling current, and 2ω1-ω p represents the coupling frequency between the disturbance small signal and the fundamental;

[0069] The complex variable form of the output voltage and current in the αβ coordinate system is:

[0070]

[0071] Wherein:

[0072] In this embodiment, the output phase angle disturbance and the reference voltage disturbance of the grid-connected converter in the complex frequency domain are determined based on the output voltage and the output current of the grid-connected converter, and specifically include:

[0073] As shown in Figure 3 , the expression of the power calculation is as follows:

[0074]

[0075] In the formula, P e and Q e are the active and reactive power output by the grid-connected inverter respectively. The above power expression is converted into a complex variable form:

[0076] The active power and the reactive power output by the grid-connected converter are determined:

[0077]

[0078] Wherein, * represents the conjugate operation;

[0079] And the active power and the reactive power disturbance output by the grid-connected converter are determined based on formula (5):

[0080]

[0081] Wherein, ΔPe(t) and ΔQe(t) represent the active power and the reactive power disturbance output by the grid-connected converter respectively;

[0082] Formula (6) and formula (7) are converted into the complex frequency domain as follows:

[0083]

[0084] Wherein, ΔPe(s-jω1) and ΔPe(jω1-s) represent the active power disturbance of the grid-connected converter at ω p -ω1 and ω1-ω p respectively, ΔQe(s-jω1) and ΔQe(jω1-s) represent the reactive power disturbance of the grid-connected converter at ω p -ω1 and ω1-ω p respectively;

[0085] The active power and the reactive power of the grid-connected converter are input into the power loop of the grid-connected converter, and the phase angle disturbance and the reference voltage disturbance of the grid-connected converter are obtained:

[0086]

[0087] Wherein, Δθ(s-jω1) and Δθ(jω1-s) represent the output phase angle disturbance of the grid-connected converter at ωp -ω1 and ω1-ω p perturbations at two frequencies, ΔE m (s-jω1) and ΔE m (jω1-s) respectively represent the reference voltage of the grid-forming converter at ω p -ω1 and ω1-ω p perturbations at two frequencies;

[0088]

[0089] wherein: k p represents the active loop primary frequency modulation coefficient of the grid-forming converter, k q represents the reactive loop primary frequency modulation coefficient of the grid-forming converter, J and D respectively represent the virtual inertia and virtual damping of the active loop of the grid-forming converter, ω n represents the rated angular frequency of the grid-forming converter, and is 50*2π.

[0090] In this embodiment, step S4 specifically comprises: as shown in Figure 4 and Figure 5 :

[0091] determining the bridge arm potential of the grid-forming converter in the dq axis coordinates at ω p -ω1 and ω1-ω p perturbations at two frequencies, ΔE dq (s-jω1) and ΔE dq (jω1-s):

[0092]

[0093]

[0094] wherein: G i (s) and G v (s) respectively represent the transfer functions of the PI controllers of the current loop and the voltage loop of the grid-forming converter, G i (s) = k pi +k ii / s; G i (s) = k pv +k iv / s; wherein: k pi , k ii respectively represent the proportional coefficient and the integral coefficient of the current loop PI controller of the grid-forming converter, k pv , k iv respectively represent the proportional coefficient and the integral coefficient of the voltage loop PI controller of the grid-forming converter, C f represents the filter capacitance of the grid-forming converter, L fFiltering inductance of the network-forming converter;

[0095] Converting formula (12) and formula (13) into αβ coordinate system, the bridge arm potential of the network-forming converter in αβ axis coordinate under ω p -ω1and ω1-ω p Disturbance ΔE αβ (s) and ΔE αβ (j2ω1-s):

[0096]

[0097] According to Kirchhoff's voltage and current law, the complex frequency domain equation of the output bridge arm potential, output voltage and output current of the network-forming converter in αβ coordinate system is as follows:

[0098] E αβ (s) = Z L (s)I p (s) + [1 + Z L (s)Y C (s)]V p (s);

[0099] The input voltage disturbance and output current disturbance relationship of the network-forming converter is constructed as:

[0100]

[0101] Substituting formula (14) and formula (15) into formula (16), the output current disturbance I p -ω1and ω1-ω p of the network-forming converter under ω p (s) and I p (j2ω1-s) at two frequencies can be solved.

[0102] The self-impedance Z S (s) and the companion impedance Z A (s) of the network-forming converter are determined as:

[0103]

[0104] Specifically:

[0105]

[0106] Wherein:

[0107]

[0108]

[0109] Wherein: V p(s) represents the input voltage disturbance of the network-forming converter, Z L (s) represents the impedance of the filter inductor branch, Z L (s) = R L + sL f , R L represents the parasitic resistance of the filter inductor, Y C (s) represents the admittance of the filter capacitor branch, R c represents the damping resistance of the filter capacitor C f .

[0110] To verify the complex variable-based network-forming converter impedance modeling method proposed in the present application, simulation verification is performed in Matlab / Simulink, Figure 6 and Figure 7 are the theoretical curve and the sweep curve of the self-impedance and the companion impedance of the network-forming converter, respectively, and it can be seen from the figure that the impedance sweep result is highly consistent with the established theoretical impedance model, proving the correctness of the complex variable-based network-forming converter impedance modeling method.

[0111] The network-forming converter impedance determination method based on the present application considers the frequency coupling effect of each control loop and system, unifies the positive and negative sequences through the complex variable modeling method, simplifies the modeling process and the stability analysis process, provides a model basis for studying the harmonic oscillation problem caused by the network-forming converter connected to the power grid, and is helpful for promoting the application of the network-forming converter in the power grid.

[0112] Finally, it should be pointed out that the above examples are only used to illustrate the technical solutions of the present application and not to limit it, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced equivalently without departing from the purpose and scope of the technical solutions of the present application, and they should all be covered in the scope of the claims of the present application.

Claims

1. A method for determining the impedance of a network converter based on complex variables, characterized in that: Includes the following steps: S1. A small disturbance signal is added at the common coupling point between the grid converter and the power grid, and the output voltage and output current of the grid converter in the complex frequency domain are determined based on the coupling of the small disturbance signal with the fundamental frequency. S2. Based on the output voltage and output current of the grid converter, the output phase angle disturbance and reference voltage disturbance of the grid converter in the complex frequency domain are determined; S3. Based on the output voltage and output current of the grid converter in the complex frequency domain, as well as the output phase angle disturbance and reference voltage disturbance of the grid converter in the complex frequency domain, the disturbance of the modulation wave used to control the converter in the αβ coordinate system is determined and transformed to the complex frequency domain. S4. Based on the disturbance of the modulation wave in the complex frequency domain, construct the relationship between the input voltage disturbance and the output current disturbance of the grid converter, and determine the input voltage disturbance and the output current disturbance. Divide the input voltage disturbance by the output current disturbance to obtain the impedance of the grid converter.

2. The method for determining the impedance of a network converter based on complex variables according to claim 1, characterized in that: Step S1 specifically includes: The expressions for the output voltage and current of a grid-type converter in the αβ coordinate system are: The output voltage and output current of the grid converter are determined by formulas (1) and (2); Where: v α and v β i represents the output voltage of phase α and phase β of the grid-type converter, respectively. α and i β Let V1 and I1 represent the output currents of the α-phase and β-phase of the grid-connected converter, respectively. Let V1 represent the fundamental voltage amplitude, I1 represent the fundamental current amplitude, and ω1 represent the fundamental angular frequency. The initial phase of the fundamental voltage is 0, and the initial phase of the fundamental current is... V p I represents the amplitude of the disturbance voltage. p1 I represents the amplitude of the disturbance current. p2 ω represents the magnitude of the coupling current. p Indicates the frequency of the disturbance. and These represent the initial phases of the disturbance voltage and the disturbance current, respectively. Represents the initial phase of the coupling current, 2ω1-ω p This indicates the coupling frequency between the small perturbation signal and the fundamental frequency; In the αβ coordinate system, the complex variable forms of the output voltage and output current are: in:

3. The method for determining the impedance of a network converter based on complex variables according to claim 2, characterized in that: Based on the output voltage and output current of the grid converter, the output phase angle disturbance and reference voltage disturbance of the grid converter in the complex frequency domain are determined, specifically including: Determine the active and reactive power output of the converter: Where: * indicates the conjugate operation; Based on formula (5), the active and reactive power disturbances at the output of the grid converter are determined: Where: ΔPe(t) and ΔQe(t) represent the active power and reactive power disturbances output by the grid-type converter, respectively; Transforming equations (6) and (7) into the complex frequency domain yields: Where: ΔPe(s-jω1) and ΔPe(jω1-s) represent the active power output of the grid-type converter at ω p -ω1 and ω1-ω p The disturbances at the two frequencies, ΔQe(s-jω1) and ΔQe(jω1-s), represent the reactive power output of the grid-type converter at ω. p -ω1 and ω1-ω p Disturbances at two frequencies; The active and reactive power of the grid-connected converter are input into its power loop to obtain the phase angle disturbance and reference voltage disturbance of the grid-connected converter: Where: Δθ(s-jω1) and Δθ(jω1-s) represent the output phase angle disturbance of the grid converter at ω1 and ω2 respectively. p -ω1 and ω1-ω p Disturbances at two frequencies, ΔE m (s-jω1) and ΔE m (jω1-s) represent the reference voltage of the grid-type converter at ω1 and s1 respectively. p -ω1 and ω1-ω p Disturbances at two frequencies; Where: k p k represents the primary frequency regulation coefficient of the active loop in a grid-type converter. q ω represents the primary frequency regulation coefficient of the reactive power loop of the grid-type converter, J and D represent the virtual inertia and virtual damping of the active power loop of the grid-type converter, respectively. n This represents the rated angular frequency of the grid-type converter, with a value of 50*2π.

4. The method for determining the impedance of a network converter based on complex variables according to claim 3, characterized in that: Step S4 specifically includes: Determine the arm potential of the grid converter in ω under the dq axis coordinate system. p -ω1 and ω1-ω p Disturbance ΔE at two frequencies dq (s-jω1) and ΔE dq (jω1-s): Among them: G i (s) and G v (s) represent the transfer functions of the PI controllers for the current loop and voltage loop of the grid converter, respectively, G i (s)=k pi +k ii / s;G i (s)=k pv +k iv / s; where: k pi k ii k represents the proportional and integral coefficients of the current loop PI controller in a grid-connected converter. pv k iv C represents the proportional and integral coefficients of the voltage loop PI controller in a grid-type converter, respectively. f L represents the filter capacitor of a grid-type converter. f This represents the filter inductance of a grid-type converter; Transforming formulas (12) and (13) into the αβ coordinate system, we obtain the arm potential of the grid converter in the αβ axis coordinate system at ω. p -ω1 and ω1-ω p Disturbance ΔE at two frequencies αβ (s) and ΔE αβ (j2ω1-s): The relationship between the input voltage disturbance and the output current disturbance of a grid-type converter is as follows: Substituting equations (14) and (15) into equation (16) yields the solution for the grid-type converter at ω. p -ω1 and ω1-ω p Output current disturbance I at two frequencies p (s) and I p (j2ω1-s); Determine the self-impedance Z of the grid converter S (s) and associated impedance Z A (s): Where: V p (s) represents the input voltage disturbance of the grid-type converter, Z L (s) represents the impedance of the filter inductor branch, Z L (s)=R L +sL f R L Y represents the parasitic resistance of the filter inductor. C (s) represents the admittance of the filter capacitor branch. R c Indicates the filter capacitor C f Damping resistor.

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