Impedance-based virtual synchronous machine multi-machine system stability analysis method

Abstract

The application discloses a kind of virtual synchronous machine multi-machine parallel system stability analysis methods based on impedance, it is first equivalent to the small signal model of voltage source system as voltage source, obtain the current of load in the small signal model of voltage source, the stability of the voltage source system is judged by the current of load;Then equivalent to the small signal model of current source system as current source, obtain the voltage of load in the small signal model of current source, the stability of the current source system is judged by the voltage of load;Finally, it is judged that virtual synchronous machine multi-machine parallel system is voltage source system or current source system, virtual synchronous machine multi-machine parallel system is equivalent to corresponding small signal model, obtain corresponding voltage or current to judge the stability of virtual synchronous machine multi-machine parallel system.The application can quickly locate the source or load causing instability problem, and provide the basis for solving the problem.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power system stability, and particularly relates to a method for analyzing stability of a multi-machine parallel system of virtual synchronous machines based on impedance. BACKGROUND

[0002] With the rapid development of new energy technology, the penetration rate of new energy power generation in the power system is rapidly increasing, however, new energy power generation lacks inertia and damping characteristics, which has a negative impact on the stable operation of the power grid. Therefore, the virtual synchronous generator technology emerges as the times require, and the virtual synchronous technology introduces the rotational inertia and damping characteristics of the synchronous generator, which improves the stability of the power system. At the same time, the stability analysis of the virtual synchronous generator cluster connected to the power grid has also become a problem to be studied.

[0003] The existing method for analyzing the stability of the power system can be roughly divided into two categories, namely the time domain method based on the state space model and the frequency domain method based on the impedance model. In the state space model method, the source and the independent load can be combined into a whole system model, and the stability and other dynamic characteristics of the system can be analyzed by the whole model. This method is suitable for systems with determined parameters and infrequently changing parameters, such as traditional public power systems, because the capacity of the load is relatively small, the influence of the load on the stability of the system can be reflected by its steady-state or static model when analyzing the stability of the system. For AC distributed power systems, the load has a significant impact on the stability of the system, and when the load is added or removed, the system needs to be re-modeled, making it difficult to effectively use the state space model method in AC distributed power systems. In the impedance-based stability analysis method, the characteristics of the source and the load are reflected by their input impedance or output impedance, and the stability of the whole system can be analyzed by applying the Nyquist stability criterion to the output impedance of the source and the input impedance of the load. When the load changes, there is no need to re-model the whole system, which is suitable for stability analysis of AC distributed power systems.

[0004] However, the existing virtual synchronous generator cluster connected to the power grid has the disadvantage that the stability of the power system is difficult to measure, therefore, a method for analyzing the stability of the virtual synchronous generator parallel system based on impedance-based stability analysis method is needed. SUMMARY

[0005] The purpose of the present application is to provide a method for analyzing the stability of a multi-machine parallel system of virtual synchronous machines based on impedance, thereby overcoming the disadvantage that the stability of the power system is difficult to measure after the existing virtual synchronous generator cluster is connected to the power grid.

[0006] To achieve the above-mentioned purpose, the present application provides a method for analyzing the stability of a multi-machine parallel system of virtual synchronous machines based on impedance, comprising the following steps:

[0007] The voltage source system is equivalent to a small signal model of a voltage source, the current of the load in the small signal model of the voltage source is obtained, and the stability of the voltage source system is determined by the current of the load, wherein the expression of the current of the load is an impedance-based expression;

[0008] The current source system is equivalent to a small signal model of a current source, the voltage of the load in the small signal model of the current source is obtained, and the stability of the current source system is determined by the voltage of the load, wherein the expression of the voltage of the load is an impedance-based expression;

[0009] The virtual synchronous machine multi-machine parallel system is determined to be a voltage source system or a current source system, the virtual synchronous machine multi-machine parallel system is equivalent to a corresponding small signal model, and the stability of the virtual synchronous machine multi-machine parallel system is determined by the corresponding voltage or current.

[0010] Preferably, the small signal model of the current source system equivalent to a current source specifically includes: the current source is represented as a Norton equivalent circuit, the equivalent circuit includes a current source and an output admittance of the current source in parallel, and one output admittance represents a load.

[0011] Preferably, the expression of the voltage of the load is:

[0012]

[0013] In the above formula, V(s) is the voltage of the load, I(s) is the current output by the current source, Y l (s) is the input admittance, Y s (s) is the output admittance.

[0014] Preferably, the expression of the voltage of the load is changed to:

[0015]

[0016] In the above formula, V(s) is the voltage of the load, I(s) is the current output by the current source, Y l (s) is the input admittance, Y s (s) is the output admittance, Z l (s) is the load input impedance, Z s (s) is the power source output impedance.

[0017] Preferably, the stability of the current source system is determined by the voltage of the load, which includes:

[0018] When the small signal model of the current source is empty, that is, the load is short-circuited, the current source system is stable;

[0019] When the current source is powered by an ideal current source, the load is stable, and the current source system is stable.

[0020] When the ratio of the load input impedance to the power supply output impedance meets the Nyquist criterion, the current source system is stable.

[0021] Preferably, determining whether the virtual synchronous machine multi-machine parallel system is a voltage source system or a current source system comprises: a commonly used power grid model is a series connection of an ideal voltage source and a power grid impedance, the power grid impedance is replaced by an inductance and a resistance in series equivalent; the virtual synchronous machine is represented as a parallel connection of a current source and an output impedance, therefore, the equivalent small signal equivalent circuit model of the virtual synchronous machine-power grid system is an improved small signal model of the current source, and the virtual synchronous machine-power grid system is a virtual synchronous machine multi-machine parallel system.

[0022] Preferably, the output current of the virtual synchronous machine in the small signal equivalent circuit model is represented as:

[0023]

[0024] In the above formula, I(s) is the output current of the virtual synchronous machine, I c (s) is the current source output current, Z0(s) is the virtual synchronous machine output impedance, Z g (s) is the power supply input impedance, V g (s) is the power supply voltage.

[0025] Preferably, according to the stability of the virtual synchronous machine multi-machine parallel system, it is indicated that the virtual synchronous machine should have a high output impedance to stably operate under a wide range of power grid conditions.

[0026] Preferably, the stability requirement of the current source system is opposite to that of the voltage source system.

[0027] Compared with the prior art, the present application has the following beneficial effects:

[0028] 1. The impedance-based virtual synchronous machine multi-machine parallel system stability analysis method provided by the application first equivalently converts a voltage source system into a small signal model of a voltage source, obtains the current of the load in the small signal model of the voltage source, and determines the stability of the voltage source system through the current of the load; then equivalently converts a current source system into a small signal model of a current source, obtains the voltage of the load in the small signal model of the current source, and determines the stability of the current source system through the voltage of the load; finally, determines whether the virtual synchronous machine multi-machine parallel system is a voltage source system or a current source system, equivalently converts the virtual synchronous machine multi-machine parallel system into a corresponding small signal model, and obtains the corresponding voltage or current to determine the stability of the virtual synchronous machine multi-machine parallel system. That is, the virtual synchronous machine multi-machine parallel system stability analysis method of the application can quickly locate the source or load causing the instability problem and provide a basis for solving the problem.

[0029] 2. When the output impedance of the source and the input impedance of the load are known, the virtual synchronous machine multi-machine parallel system is equivalently converted into a corresponding small signal model, which is easy to obtain and can be expressed in the form of a linear impedance network. When analyzing the stability of the virtual synchronous machine multi-machine parallel system at a certain operating point, only the equivalent impedances of the source and the load at the operating point need to be calculated by applying linear theory.

[0030] 3. When a source or a load is added or removed in the virtual synchronous machine multi-machine parallel system, or the operating mode of any of them changes, only a certain impedance element in the impedance network of the virtual synchronous machine multi-machine parallel system is affected, and the model of the entire system is not greatly affected.

[0031] 4. When the impedance model of a source or a load in the virtual synchronous machine multi-machine parallel system cannot be obtained or is difficult to establish, the input or output impedance thereof can be obtained through experiments or a large number of simulations, and the mathematical model thereof can be obtained by curve fitting the response of the impedance.

[0032] 5. When the virtual synchronous machine multi-machine parallel system has an instability problem, the impedance-based stability analysis method can quickly locate the source or load causing the instability problem and provide a basis for solving the problem. BRIEF DESCRIPTION OF DRAWINGS

[0033] In order to more clearly illustrate the technical solutions of the application, the drawings needed in the following embodiment description will be briefly introduced. Obviously, the drawings in the following description are only one embodiment of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0034] Figure 1is a flow chart of a method for analyzing stability of a multi-machine parallel system of virtual synchronous machines based on impedance according to the present application;

[0035] Figure 2 is a structural schematic diagram of a small signal model of a voltage source system according to the present application;

[0036] Figure 3 is a structural schematic diagram of a small signal model of a current source system according to the present application;

[0037] Figure 4 is an equivalent small signal equivalent circuit model of a virtual synchronous machine-grid system according to the present application. DETAILED DESCRIPTION

[0038] The technical solutions in the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0039] As shown in Figure 1 , the method for analyzing stability of a multi-machine parallel system of virtual synchronous machines based on impedance according to the present application comprises the following steps:

[0040] S1, equivalent the voltage source system to a small signal model of a voltage source, obtain the current of the load in the small signal model of the voltage source, and determine the stability of the voltage source system by the current of the load, wherein the expression of the current of the load is an expression based on impedance;

[0041] Specifically, the stability of the voltage source system is analyzed by using the impedance stability principle, comprising the following steps:

[0042] The voltage source system is represented as a Thevenin equivalent circuit of an ideal voltage source and output impedance in series, and the load subsystem is represented by its input impedance. Since many power electronic circuits are nonlinear, this linear representation is only valid for small signal analysis. Therefore, as shown in Figure 2 , the small signal model of the voltage source system, and thus the current of the voltage source flowing to the load is:

[0043]

[0044] The formula (1) is changed to obtain:

[0045]

[0046] In formula (2), I(s) is the current of the voltage source flowing to the load, V s (s) is the voltage of the power source, and Z l(s) is the power supply output impedance, Z s (s) represents the load input impedance.

[0047] To facilitate stability analysis of the voltage source system, we can assume that the power supply voltage is stable under no-load conditions and the load current is stable when powered by an ideal power source. In this case, V s (s) and It is stable; the stability of the current depends on the second term H(s) on the right-hand side of equation (2):

[0048]

[0049] The stability principle based on impedance depends on equation (3), which is similar to the closed-loop transfer function of a system with negative feedback control, where the feedforward gain is 1 and the feedback gain is Z. s (s) / Z l (s) represents the ratio of the power supply output impedance to the load input impedance. According to linear control theory, only Z... s (s) / Z l H(s) satisfies the Nyquist criterion, and H(s) is stable.

[0050] When applying the impedance stability principle described above, it is important to note that the power source is assumed to be a stable voltage source under no-load conditions. Since many real-world power sources are voltage sources and stable under no-load conditions, this assumption is often overlooked. However, when a virtual synchronous machine is connected to the grid, the inverter is typically controlled as a current source, injecting a certain amount of current into the grid; the inverter behaves as a current source rather than a voltage source. Therefore, its stability cannot be analyzed using existing impedance methods.

[0051] S2. Equivalent the current source system to a small-signal model of the current source, obtain the load voltage in the small-signal model of the current source, and determine the stability of the current source system using the load voltage. The expression for the load current is based on impedance. Specifically, this includes the following steps:

[0052] Similarly, it begins with a small-signal model similar to a voltage source, such as... Figure 3 The small-signal model of the current source system shown specifically includes: representing the current source as a Norton equivalent circuit, wherein the equivalent circuit includes the output admittance of the current source connected in parallel with the current source, and one output admittance indicates one load.

[0053] In the small-signal model of the current source system, the load voltage is:

[0054]

[0055] In equation (4), V(s) is the load voltage, I(s) is the current output by the current source, and Y... l(s) is the input admittance, Y s (s) represents the output admittance;

[0056] Transform equation (4):

[0057]

[0058] In equation (5), V(s) is the load voltage, I(s) is the current output by the current source, and Y... l (s) is the input admittance, Y s (s) is the output admittance, Z l (s) is the load input impedance, Z s (s) represents the power supply output impedance.

[0059] Similar to the voltage source system, it is assumed that the current source is stable under no-load conditions (the admittance is infinite when the load is short-circuited), and the load is stable when powered by an ideal voltage source. Based on this assumption, I(s) and Both are stable; the stability of V(s) depends on the second term on the right-hand side of equation (5). Note that it is similar to the closed-loop transfer function of a negative feedback control system, with a feedforward gain of 1 and a feedback gain of Y. s (s) / Y l (s).

[0060] To emphasize its duality with equation (2), admittance is used instead of impedance in equation (5). The analysis can also be based on the power supply output impedance (Z). s ) and load input impedance (Z l Equation (5) becomes:

[0061]

[0062] Therefore, determining the stability of the current source system by the voltage of the load includes:

[0063] (1) When the small-signal model of the current source is unloaded, i.e. the load is short-circuited, the current source system is stable;

[0064] (2) When the current source is an ideal current source, the load is stable, and the current source system is stable.

[0065] (3) When the ratio of the load input impedance to the power supply output impedance satisfies the Nyquist criterion, the current source system is stable.

[0066] That is, the current source system is stable as long as any one of the above three conditions is met.

[0067] Comparing equation (6) and equation (2), to ensure stable operation under multiple loads, the stability requirements of the current source system are opposite to those of the voltage source system: the current source should have a high output impedance (ideally infinite), while the voltage source should have a low impedance (ideally zero). The current source system is more stable when the load impedance is low; the voltage source system is more stable when the load impedance is high.

[0068] S3. Determine whether the virtual synchronous machine multi-machine parallel system is a voltage source system or a current source system. Equivalently transform the virtual synchronous machine multi-machine parallel system into a corresponding small-signal model and obtain the corresponding voltage or current to determine the stability of the virtual synchronous machine multi-machine parallel system.

[0069] Specifically, first, determine whether the virtual synchronous machine multi-machine parallel system is a voltage source system or a current source system. A commonly used power grid model is an ideal voltage source connected in series with the grid impedance, which is equivalently replaced by an inductor and resistor connected in series. The virtual synchronous machine is represented as a current source connected in parallel with the output impedance. Therefore, the equivalent small-signal circuit model of the virtual synchronous machine-power grid system is an improved small-signal model of the current source, such as... Figure 4 As shown, the virtual synchronous machine-grid system is a multi-machine parallel system of virtual synchronous machines.

[0070] The inverter is considered stable when the grid voltage is stable and the grid impedance is zero. The output current of the virtual synchronous machine in the small-signal equivalent circuit model is expressed as:

[0071]

[0072] In equation (7), I(s) is the output current of the virtual synchronous machine, I c Z(s) is the output current of the current source, Z0(s) is the output impedance of the virtual synchronous machine, and Z g (s) is the power supply input impedance, V g (s) represents the power supply voltage.

[0073] Equation (7) can be rewritten as:

[0074]

[0075] Based on equation (8) and the settings for the virtual synchronous machine multi-machine parallel system, if the ratio of the grid impedance to the virtual synchronous machine output impedance satisfies the Nyquist criterion, then the virtual synchronous machine multi-machine parallel system is stable. The stability boundary of the virtual synchronous machine multi-machine parallel system can also be measured using the Nyquist plot. Note that if the virtual synchronous machine multi-machine parallel system is treated as a voltage source system powered by the grid, the same conclusion can be reached.

[0076] Compared to state-space model methods, impedance-based stability analysis methods have the following advantages:

[0077] When the output impedance of the source and the input impedance of the load are known, the equivalent small-signal model of a virtual synchronous machine multi-machine parallel system is relatively easy to obtain and can be represented in the form of a linear impedance network. When analyzing the stability of the virtual synchronous machine multi-machine parallel system at a certain operating point, it is only necessary to apply linear theory to calculate the equivalent impedances of the source and load at that operating point.

[0078] When a source or load is added or removed in a virtual synchronous machine parallel system, or when the operating mode of any of them changes, it only affects a specific impedance element in the impedance network of the virtual synchronous machine parallel system, and will not have a significant impact on the model of the entire system.

[0079] When the impedance model of a source or load in a virtual synchronous machine multi-machine parallel system cannot be obtained or is difficult to establish, its input or output impedance can be obtained through experiments or a large number of simulations, and its mathematical model can be obtained by curve fitting of the impedance response.

[0080] When instability occurs in a multi-machine parallel virtual synchronous machine system, impedance-based stability analysis can be used to quickly locate the source or load causing the instability and provide a basis for solving the problem.

[0081] Therefore, based on the stability results of the virtual synchronous machine multi-machine parallel system, it is shown that the virtual synchronous machine should have a high output impedance to operate stably under a wide range of power grid conditions. Thus, the output impedance of the virtual synchronous machine is an important performance indicator, and a simple method for characterizing and comparing different inverters can be designed based on its output impedance.

[0082] The above description only discloses specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or modifications that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A stability analysis method for a multi-machine parallel system based on impedance-based virtual synchronous machines, characterized in that, Includes the following steps: The voltage source system is equivalent to a small-signal model of the voltage source. The current of the load in the small-signal model of the voltage source is obtained. The stability of the voltage source system is determined by the current of the load. The expression for the current of the load is an impedance-based expression. The current source system is equivalent to a small-signal model of the current source. The voltage of the load in the small-signal model of the current source is obtained. The stability of the current source system is determined by the voltage of the load. The expression for the voltage of the load is an impedance-based expression. To determine whether a virtual synchronous machine multi-machine parallel system is a voltage source system or a current source system, the virtual synchronous machine multi-machine parallel system is equivalent to a corresponding small-signal model, and the corresponding voltage or current is obtained to determine the stability of the virtual synchronous machine multi-machine parallel system.

2. The stability analysis method for a multi-machine parallel system based on impedance virtual synchronous machine according to claim 1, characterized in that, The small-signal model that equates a current source system to a current source specifically includes: representing the current source as a Norton equivalent circuit, wherein the equivalent circuit includes the output admittance of the current source connected in parallel with the current source, and one output admittance represents one load.

3. The stability analysis method for a multi-machine parallel system based on impedance-based virtual synchronous machine according to claim 2, characterized in that, The voltage expression for the load is: In the above formula, V(s) is the load voltage, I(s) is the current output by the current source, and Y... l (s) is the input admittance, Y s (s) represents the output admittance.

4. The stability analysis method for a multi-machine parallel system based on impedance virtual synchronous machine according to claim 3, characterized in that, The expression for the load voltage is revised as follows: In the above formula, V(s) is the load voltage, I(s) is the current output by the current source, and Y... l (s) is the input admittance, Y s (s) is the output admittance, Z l (s) is the load input impedance, Z s (s) represents the power supply output impedance.

5. The stability analysis method for a multi-machine parallel system based on impedance-based virtual synchronous machine according to claim 1, characterized in that, Determining the stability of the current source system by measuring the voltage of the load includes: When the small-signal model of the current source is unloaded, i.e. the load is short-circuited, the current source system is stable. When the current source is powered by an ideal current source, the load is stable, and the current source system is stable. A current source system is stable when the ratio of the load input impedance to the power supply output impedance satisfies the Nyquist criterion.

6. The stability analysis method for a multi-machine parallel system based on impedance virtual synchronous machine according to claim 1, characterized in that, Determining whether a virtual synchronous machine multi-machine parallel system is a voltage source system or a current source system includes: the commonly used power grid model is an ideal voltage source connected in series with the power grid impedance, which is equivalently replaced by an inductor and a resistor connected in series; the virtual synchronous machine is represented as a current source connected in parallel with the output impedance. Therefore, the equivalent small-signal circuit model of the virtual synchronous machine-power grid system is an improved small-signal model of the current source, and the virtual synchronous machine-power grid system is a virtual synchronous machine multi-machine parallel system.

7. The stability analysis method for a multi-machine parallel system based on impedance virtual synchronous machine according to claim 6, characterized in that, The inverter is considered stable when the grid voltage is stable and the grid impedance is zero. The output current of the virtual synchronous machine in the small-signal equivalent circuit model is expressed as: In the above formula, I(s) is the output current of the virtual synchronous machine, I c Z(s) is the output current of the current source, Z0(s) is the output impedance of the virtual synchronous machine, and Z g (s) is the power supply input impedance, V g (s) represents the power supply voltage.

8. The stability analysis method for a multi-machine parallel system based on impedance virtual synchronous machine according to claim 1, characterized in that, The results of the stability of the virtual synchronous machine multi-machine parallel system indicate that the virtual synchronous machine should have high output impedance in order to operate stably under a wide range of power grid conditions.

9. The stability analysis method for a multi-machine parallel system based on impedance virtual synchronous machine according to claim 1, characterized in that, The stability requirements for current source systems are the opposite of those for voltage source systems.

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