Stability judgment method and device applied to virtual inertia control system

Abstract

The invention discloses a stability judgment method and device applied to a virtual inertia control system. The method comprises the following steps: constructing a state space model of the virtual inertia control system; converting the state space model into a multivariable system transfer function matrix G (s), wherein s is a Laplace operator; drawing a Nyquist diagram with a Gerer round belt of the system transfer function matrix G (s); and if the virtual inertia control system meets the use condition of the combined criterion based on the Gerer round belt, judging the stability of the virtual inertia control system by using the combined criterion. According to the method, the calculation complexity is remarkably reduced, a direct and visual reference is provided for optimal selection of key parameters such as a virtual inertia coefficient, and the applicability and efficiency in engineering practice are greatly improved.

Description

Technical Field

[0001] This invention relates to the field of new energy power generation and grid connection technology, and in particular to a stability determination method and device for a virtual inertia control system. Background Technology

[0002] In the process of evolving from traditional power systems to new power systems, traditional generating units are gradually being replaced by new energy generating units, resulting in a continuous decline in system inertia. Under low inertia, active power surge events are becoming increasingly severe, posing a serious challenge to the frequency stability of the power system. Therefore, improving the inertia support capability of new power systems has become a key research topic for ensuring their safe and stable operation.

[0003] Currently, there has been some research on methods to improve system inertia on the power supply side. However, the exploration and utilization of inertia resources on the load side are still insufficient. Flexible loads, as a type of inertia resource on the load side, have good energy storage-like characteristics and can interact bidirectionally with grid-side energy. Therefore, new types of loads with dual characteristics of "source" and "load," such as electric vehicles and energy storage, can alleviate abnormal frequency fluctuations in the grid and improve the system inertia level after being connected to the grid.

[0004] Virtual inertia control is a core technology for providing inertia support for flexible loads. However, the virtual inertia control system constructed from this is usually a high-order, strongly coupled multi-input multi-output system. The traditional single-variable Nyquist stability criterion is difficult to apply directly to such complex systems, while the classic multivariable Nyquist criterion, although theoretically feasible, involves complex analysis and massive computation, posing significant inconvenience in practical engineering applications and hindering the efficient assessment of system stability. Summary of the Invention

[0005] This invention provides a method and apparatus for determining the stability of a virtual inertia control system, which solves the problems of complex and inefficient system stability analysis in the prior art, which is not convenient for engineering applications, and realizes efficient evaluation of the stability of the virtual inertia control system.

[0006] This invention provides a stability determination method for a virtual inertia control system, comprising: Construct a state-space model of the flexible load grid-connected system; The state-space model is transformed into a multivariable system transfer function matrix G(s), where s is the Laplace operator; Plot the Nyquist plot of the system transfer function matrix G(s) with Gaelic circles; If the virtual inertia control system meets the usage conditions based on the joint criterion of the Gaelic circle, then the stability of the virtual inertia control system is determined using the joint criterion.

[0007] According to the stability determination method for a virtual inertia control system provided by the present invention, the step of constructing the state-space model of the virtual inertia control system includes: Construct the state-space model of the filter module; Construct a state-space model of the DC / DC converter and its control module; Construct a state-space model of a DC / AC inverter and its control module; The state space model of the virtual inertia control system is constructed based on the filter state space model, the DC / DC converter state space model, and the DC / AC inverter state space model. The state space models of the DC / DC converter and its control module, the DC / AC inverter and its control module, and the filter are sequentially coupled in series; and the filter state space model and the DC / AC inverter and its control module state space model form a feedback coupling.

[0008] According to the stability determination method for a virtual inertia control system provided by the present invention, the construction of the state-space model of the filter module specifically includes: Constructed using the following small signal model: ;

[0009] in, The differential representing the change in the d-axis component of the inverter port output current; This represents the change in the q-axis component of the boost inductor current on the DC / AC inverter side; This represents the change in the q-axis component of the grid connection point voltage; This represents the change in the d-axis component of the grid-connected current; The change in the q-axis component of the grid-connected current; Indicates the filter resistor; Indicates the filter inductance; Indicates the system's angular frequency; Indicates the filter capacitor; Indicates the equivalent inductance of the transmission line; Indicates the equivalent resistance of the transmission line; This represents the proportional gain of the DC / AC inverter current loop controller. This represents the integral coefficient of the DC / AC inverter current loop controller; This represents the integral coefficient of the voltage loop controller in a DC / AC inverter. This represents the proportional gain of the DC / AC inverter voltage loop controller. This indicates the change in the d-axis input of the DC / AC inverter current loop controller; This indicates the change in the q-axis input of the DC / AC inverter current loop controller; This represents the change in the d-axis input of the DC / AC inverter voltage loop controller; This represents the change in voltage across the DC link capacitor. This represents the q-axis component of the output current at the DC / AC inverter port. This represents the d-axis component of the output current at the DC / AC inverter port. Indicates the virtual inertia coefficient; Represents the q-axis component of the grid-connected current; This represents the d-axis component of the grid-connected current.

[0010] According to the stability determination method for a virtual inertia control system provided by the present invention, the construction of the state-space model of the DC / DC converter and its control module specifically includes: Constructed using the following small signal model:

[0011] in, This indicates the change in the input quantity of the DC / DC converter current loop controller; This indicates the change in the input quantity of the DC / DC converter voltage loop controller; The table shows the output current variation of the flexible load; This represents the change in DC link voltage. This refers to the change in the reference value of the output current of the flexible load. Inductor for boost circuit; For the output current of the flexible load; This refers to the change in output voltage of the flexible load. This is the reference value for the DC link voltage. d is the DC link voltage, and d is the duty cycle of the boost circuit. This indicates the change in the duty cycle of the boost circuit; For DC link capacitor, This represents the change in DC link current.

[0012] According to the stability determination method for a virtual inertia control system provided by the present invention, the construction of the state-space model of the DC / AC inverter and its control module specifically includes: Constructed using the following small signal model:

[0013] in, Indicates the virtual inertia coefficient; This indicates the change in the d-axis input of the DC / AC inverter current loop controller; This indicates the change in the q-axis input of the DC / AC inverter current loop controller; This represents the change in the d-axis input of the DC / AC inverter voltage loop controller; This represents the change in the reference value of the d-axis current at the grid connection point. This represents the change in the reference value of the q-axis current at the grid connection point. This represents the change in the system's angular frequency. This represents the change in the d-axis component of the boost inductor current on the DC / AC inverter side; This represents the change in the q-axis component of the boost inductor current on the DC / AC inverter side; This represents the change in the d-axis component of the grid connection point voltage; This represents the change in the q-axis component of the grid connection point voltage; This represents the change in the d-axis component of the grid-connected current; The change in the q-axis component of the grid-connected current; This represents the change in voltage across the DC link capacitor.

[0014] The phase-locked loop is constructed using the following small-signal model:

[0015] in, The change in the input quantity to the phase-locked loop controller; This represents the change in phase angle.

[0016] According to the stability determination method for a virtual inertia control system provided by the present invention, the step of constructing a state-space model of the virtual inertia control system based on the filter state-space model, the DC / DC converter state-space model, and the DC / AC inverter state-space model specifically includes: By combining the various state-space models, the state-space model of the virtual inertia control system is obtained: ;

[0017] ;

[0018] ;

[0019] in, A represents the state variables; B represents the system state matrix; C represents the system input matrix; and D represents the system output matrix. This represents the change in the output value of the virtual inertia controller. The d-axis component of the grid connection point current The change output by the proportional controller after subtracting the actual value from the reference value; This represents the change in the system's angular frequency. The change in the reference value of the q-axis component of the grid-connected current. The change in the actual value of the q-axis component of the grid connection current difference; The The state variables from the filter state-space model include: This represents the change in the d-axis component of the boost inductor current on the inverter side; This represents the change in the q-axis component of the boost inductor current on the inverter side; This represents the change in the d-axis component of the grid connection point voltage; This represents the change in the q-axis component of the grid connection point voltage; This represents the change in the d-axis component of the grid-connected current; The change in the q-axis component of the grid-connected current; The The state variables derived from the state-space model of the DC / AC inverter and its control module include: This represents the change in the output of the d-axis proportional controller of the current loop in a DC / AC inverter. The change in the output of the q-axis proportional controller of the current loop of the DC / AC inverter; The change in the output of the d-axis proportional controller of the DC / AC inverter voltage loop; The change in the input quantity of the phase-locked loop proportional controller; This refers to the change in the phase angle of the phase-locked loop output. The The state variables from the state space model of the DC / DC converter and its control module include: The change in the input quantity of the proportional controller in the current loop of the DC / DC converter; This indicates the change in the input quantity of the proportional controller in the voltage loop of the DC / DC converter; This refers to the change in output current of the flexible load. This represents the change in voltage across the DC link capacitor.

[0020] According to the stability determination method for a virtual inertia control system provided by the present invention, the conditions for using the joint criterion include: each of the system transfer function matrix G(s) The Gaelic circle does not contain points. Where i is a positive integer; The feedback quantity of the virtual inertia control system includes the virtual inertia coefficient. And the proportional coefficient of the DC / AC inverter current loop controller.

[0021] According to the stability determination method for a virtual inertia control system provided by the present invention, if the virtual inertia control system meets the aforementioned usage conditions, then if each of the aforementioned conditions is met... The Gaelic circle surrounds the point in a clockwise direction. If the sum of the cycles equals -n0, the system is stable in closed loop; otherwise, the system is unstable; where n0 is the number of poles of the system transfer function matrix G(s) in the right half of the complex plane.

[0022] According to the stability determination method for a virtual inertia control system provided by the present invention, if the virtual inertia control system does not meet the usage conditions based on the joint criterion of the Gaelic circle, a static compensator is set. The virtual inertia control system is pseudo-diagonalized, and the system stability is further determined by the joint criterion.

[0023] According to the present invention, a stability determination method for a virtual inertia control system is provided, wherein a static compensator is set. The virtual inertia control system is pseudo-diagonalized by constructing the following objective function. Solve for the optimal real constant matrix : ; ;

[0024] ;

[0025] in, The system transfer function matrix after compensation; For matrix The diagonal elements; This represents the i-th frequency point; j is the imaginary unit; Representation matrix off-diagonal elements; r represents the matrix Which order; represents the weighting coefficient for the i-th frequency point; N represents the number of frequency points.

[0026] This invention also provides a stability determination device for a virtual inertia control system, comprising: The construction module is used to construct the state-space model of the virtual inertia control system; The transformation module is used to transform the state-space model into a multivariable system transfer function matrix G(s), where s is the Laplace operator; A plotting module is used to plot the Nyquist plot of the system transfer function matrix G(s) with Gaelic circles; The determination module is used to determine the stability of the virtual inertia control system by means of the joint criterion based on the Gaelic circle if the virtual inertia control system meets the usage conditions.

[0027] Compared with the prior art, the beneficial effects of the present invention are: This invention constructs a state-space model of a flexible load grid-connected system and transforms it into a system transfer function. It then introduces the Nyquist array theory of Gael's circular bands for joint determination of system stability. This method simplifies the complex stability problem of high-order, multivariable systems to the observation of a series of intuitive Nyquist plots and their Gael's circular bands, ultimately significantly reducing computational complexity. This makes the analysis process not only physically clear and the results accurate and intuitive, but also provides direct and visual references for the optimal selection of key parameters (such as the virtual inertia coefficient), greatly improving its applicability and efficiency in engineering practice.

[0028] This invention designs a compensator for systems that do not meet the conditions of the joint criterion. Once the system meets the criterion, the design problem of the multivariable system can be decomposed into a series of design problems of single-variable subsystems, thereby simplifying the system design. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0030] Figure 1 This is a schematic diagram of Gell's circle theorem according to an embodiment of the present invention.

[0031] Figure 2 This is a flowchart illustrating a stability determination method for a virtual inertia control system according to an embodiment of the present invention.

[0032] Figure 3 This is a schematic diagram of the topology of a flexible load system based on virtual inertia control according to an embodiment of the present invention.

[0033] Figure 4 This is a schematic block diagram of a DC / DC converter and its control module according to an embodiment of the present invention.

[0034] Figure 5 This is a schematic block diagram of a DC / AC inverter and its control module according to an embodiment of the present invention.

[0035] Figure 6This is a block diagram of the virtual inertia and current loop control circuit after adding an additional controller according to an embodiment of the present invention.

[0036] Figure 7 This is a calculation example diagram of a virtual inertia control system that satisfies the joint criteria and is stable according to an embodiment of the present invention.

[0037] Figure 8 This is a calculation example diagram of a virtual inertia control system according to an embodiment of the present invention that does not satisfy the joint criterion.

[0038] Figure 9 This is a calculation example diagram of the virtual inertia control system with an added static compensator according to an embodiment of the present invention.

[0039] Figure 10 This is a flowchart illustrating the stability determination and pseudo-diagonalization method according to an embodiment of the present invention.

[0040] Figure 11 This is a schematic diagram of the stability determination device for a virtual inertia control system according to an embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0042] Before delving into the specific implementation of the embodiments of the present invention, a brief introduction to the terminology in the system will be provided to better understand its working principle and innovations.

[0043] Define the Geer's circle and the Geer's circle zone: Suppose there is a complex matrix H, as shown in formula (1), whose eigenvalues ​​satisfy formula (2), that is, the eigenvalues ​​of the complex matrix H lie in a family of... The circle whose center is and whose radius is the expression on the right-hand side of the inequality is called a Gell-Kühler circle. Figure 1 As shown. For all the data of the frequency response, the envelope of a series of Gell circles can form a Gell circle band.

[0044] ;

[0045] ;

[0046] In the formula: These are the eigenvalues ​​of the complex matrix H; is the diagonal element of the complex matrix H; n is the order of the complex matrix H.

[0047] like Figure 2 As shown, this invention provides a stability determination method for a virtual inertia control system, applicable to a flexible load grid-connected system based on virtual inertia control, comprising the following steps: Step 200: Construct the state-space model of the virtual inertia control system.

[0048] Step 201: Transform the state-space model into a multivariable system transfer function matrix G(s), where s is the Laplace operator.

[0049] Step 202: Draw the Nyquist plot of the system transfer function matrix G(s) with Gaelic circles.

[0050] Step 203: If the virtual inertia control system meets the usage conditions based on the joint criterion of the Gaelic circle, then the stability of the virtual inertia control system is determined using the joint criterion.

[0051] Specifically, an example of a complete virtual inertia control system is as follows: Figure 3 As shown, the flexible load grid-connected system based on virtual inertia control (hereinafter referred to as the virtual inertia control system) includes: a flexible load module, a DC-DC converter and its control module, a DC-AC inverter and its control module (abc-dq conversion module, virtual inertia control module and phase-locked loop PLL), a filter module, a transmission line and equivalent load module, and a power grid. Figure 3 The parameters in the table are the system values ​​in the dq coordinate system, where... , Output voltage and current for flexible loads; Inductor for boost circuit; , For the DC link capacitor voltage and current; , The inverter output voltage and filter current; , , For filter inductors, resistors, and capacitors; Indicates the equivalent load. Indicates the equivalent resistance of the transmission line, Indicates the equivalent inductance of the transmission line; , For grid connection point voltage and current; , For grid voltage and current, Represents the q-axis component of the grid-connected current. Represents the d-axis component of the grid-connected current. Represents the q-axis component of the grid connection point voltage. Represents the d-axis component of the grid connection point voltage. Indicates the angular frequency of the power grid. Indicates the power grid frequency. Reference value for power grid frequency.

[0052] In step 200 above, the system state can be as described above. Figure 3 The state of multiple modules in, for example, by , , The states of the filter circuit, the DC / DC converter, and its control module are all considered. For a flexible load system based on virtual inertia control, which is a high-order, multivariable, and strongly coupled complex system, constructing a state space is essential for characterizing the system's dynamic characteristics and is a prerequisite for obtaining the system's transfer function, thus laying the foundation for system stability analysis. For ease of analysis, independent state-space models can be established for each module of the system.

[0053] Optionally, constructing the state-space model of the flexible load grid-connected system includes: constructing a filter module state-space model; constructing a DC / DC converter and its control module state-space model; constructing a DC / AC inverter and its control module state-space model; and constructing the state-space model of the flexible load grid-connected system based on the filter state-space model, the DC / DC converter state-space model, and the DC / AC inverter state-space model. The DC / DC converter and its control module state-space model, the DC / AC inverter and its control module state-space model, and the filter state-space model are sequentially series-coupled; and the filter state-space model and the DC / AC inverter and its control module state-space model form a feedback coupling.

[0054] from Figure 3 As can be seen, feedback coupling is the process by which the grid connection point voltage / phase information measured by the filter state-space model through a phase-locked loop (PLL) is fed back to the control module of the DC / AC inverter.

[0055] The following provides an illustrative example of how to construct various state-space models.

[0056] (1) Construct the state-space model of the filter module Constructing a small-signal model for the filter stage: ; In the formula: represents the change in the variable. This represents the differential of the change in the d-axis component of the inverter port output current. This represents the change in the q-axis component of the boost inductor current on the inverter side. This represents the change in the q-axis component of the grid connection point voltage; This represents the change in the d-axis component of the grid-connected current; The change in the q-axis component of the grid-connected current. Indicates the filter resistor. Indicates the filter inductance. Represents the system's angular frequency. Indicates the filter capacitor. Indicates the equivalent inductance of the transmission line. Indicates the equivalent resistance of the transmission line. This represents the proportional gain of the inverter current loop controller. This represents the integral coefficient of the inverter current loop controller. This represents the integral coefficient of the inverter voltage loop controller. This represents the proportional gain of the inverter voltage loop controller. This represents the change in the d-axis input of the inverter current loop controller. This represents the change in the q-axis input of the inverter current loop controller. This represents the change in the d-axis input of the inverter voltage loop controller. This represents the change in voltage across the DC link capacitor; * indicates a reference value for the variable. This represents the q-axis component of the inverter port output current. This represents the d-axis component of the inverter port output current. Represents the virtual inertia coefficient. Represents the q-axis component of the grid-connected current. This represents the d-axis component of the grid-connected current.

[0057] It should be noted that the current loop controller and voltage loop controller in the embodiments of the present invention can be proportional-integral (PI) controllers.

[0058] (2) Construct the state-space model of the DC / DC converter and its control module like Figure 4 As shown, its circuit equations and control equations are as follows: ;

[0059] ;

[0060] In the formula: This is a reference value for the output current of a flexible load. For boost circuit inductance, The output current is the flexible load current, and t is time. For flexible load output voltage, This is the reference value for the DC link voltage. d is the DC link voltage, and d is the duty cycle of the boost circuit. This refers to the proportional coefficient of the converter voltage loop controller; The integral coefficient of the converter voltage loop controller; This refers to the proportional coefficient of the converter current loop controller; The integral coefficient of the converter current loop controller; For DC link capacitor, Let be the DC link current, and s be the Laplace operator.

[0061] Figure 4 The final output d of the module acts on Figure 3 Switching transistors in and .

[0062] in, It can be canceled out from the small-signal model using the following power equation and represented using state variables.

[0063] ;

[0064] In the formula, This is the DC link voltage. The d-axis component of the grid connection point voltage. Let d be the d-axis component of the grid connection point current. The grid connection point voltage q-axis component, This represents the q-axis component of the grid connection point current.

[0065] Linearizing equations (4)-(6) above, we can obtain the small-signal model of the DC / DC converter:

[0066] In the formula: The change in the input quantity of the PI controller for the converter current loop; The table shows the changes in the input of the converter voltage loop PI controller; The table shows the change in output current of the flexible load. This represents the change in DC link voltage.

[0067] (3) Construct the state-space model of the DC / AC inverter and its control module The small-signal model of the inverter and control module is as follows, and the control block diagram is as follows. Figure 5 As shown.

[0068]

[0069] In the formula: This is the virtual inertia coefficient; This represents the change in the d-axis input of the inverter current loop controller; This represents the change in the q-axis input of the inverter current loop controller; This represents the change in the d-axis input of the inverter voltage loop controller; This represents the change in the reference value of the d-axis current at the grid connection point. This represents the change in the reference value of the q-axis current at the grid connection point. This represents the change in the system's angular frequency.

[0070] Phase-locked loop:

[0071] In the formula: The change in the input quantity of the phase-locked loop PI controller; This represents the change in phase angle.

[0072] Entering the current loop, compared to the actual q-axis current. The comparison generates a control signal, which is then modulated by PWM to drive the inverter switching transistors, ultimately changing the active power injected into the grid.

[0073] By combining the state-space equations obtained in parts (1) to (3) above, the complete state-space model of the virtual inertia control system is obtained. The integrated overall state-space equations are shown below:

[0074] ;

[0075] ;

[0076] in, Let A be the state variable; let B be the system state matrix, which is formed by combining the differential equations of the three state-space models of the filter, the DC / DC converter and its control module, and the DC / AC inverter and its control module after linearization; let C be the system input matrix; and let D be the system output matrix. This represents the change in the output value of the virtual inertia controller. for The change output by the proportional controller after subtracting the actual value from the reference value; This represents the change in the system's angular frequency. This represents the change in the d-axis component of the boost inductor current on the inverter side; This represents the change in the q-axis component of the boost inductor current on the inverter side; This represents the change in the d-axis component of the grid connection point voltage; This represents the change in the q-axis component of the grid connection point voltage; This represents the change in the d-axis component of the grid-connected current; The change in the q-axis component of the grid-connected current; This represents the change in the output of the d-axis proportional controller of the inverter current loop. This represents the change in the output of the inverter current loop q-axis proportional controller. This represents the change in the output of the inverter voltage loop d-axis proportional controller. The change in the input quantity of the phase-locked loop proportional controller; This refers to the change in the phase angle of the phase-locked loop output. The change in the input quantity of the proportional controller in the current loop of the DC / DC converter; This indicates the change in the input quantity of the proportional controller in the voltage loop of the DC / DC converter; This refers to the change in output current of the flexible load. This is the voltage of the DC link capacitor; The change in the reference value of the q-axis component of the grid-connected current. The change in the actual value of the q-axis component of the grid connection current difference.

[0077] Therefore, the state-space equation has 15 state variables (see Equation 11) and 2 inputs. 2 outputs The selection of these 15 state variables comprehensively covers the entire dynamic process from flexible loads, DC / DC conversion, DC links, inverter control to grid interfaces, and conforms to the minimum realization principle. This modeling accuracy forms the basis for subsequent stability analysis and compensator design using Nyquist array theory, ensuring the reliability of the criteria. and As input, it represents two main control actions. As outputs, they represent the core controlled target and coupled observation points. Based on their central role in system dynamics and the practical needs of stability analysis, they are chosen as inputs and outputs to ensure that the model can accurately capture key control loops, simplify stability determination of multivariable systems, and facilitate engineering applications.

[0078] In step 201 above, by performing a Laplace transform on formula (10), the system transfer function G(s) is obtained as follows: ;

[0079] Wherein: the inputs to the system transfer function matrix G(s) are: DC link voltage change. and The outputs are the changes in the system's angular frequency. The change after subtracting the q-axis current C is the system output matrix, I is the identity matrix, A is the system state matrix, and B is the system input matrix.

[0080] The matrix form of G(s) is:

[0081] In the formula: , , , It is a sub-transfer function that constitutes the system transfer function matrix G(s). , used to describe right The impact (virtual inertia control path). , used to describe right Impact (current loop control path); off-diagonal elements and This directly reflects the coupling between the two control loops. Therefore, according to Figure 5 The virtual inertia coefficient can be obtained. and current loop proportionality coefficient The feedback quantities y1 and y2 of the virtual inertia control system are used as the basis for stability determination.

[0082] In step 202 above, after obtaining the system transfer function matrix G(s), its diagonal elements can be plotted. The Nyquist plot is obtained and the corresponding Gaelic circle is superimposed. This is achieved by determining each... Does the Gale circular belt not contain feedback? By identifying points that satisfy the Nyquist enclosure condition, it can be determined whether the system is closed-loop stable. The feedback quantity is designed based on the system stability analysis according to embodiments of the present invention; for example, the feedback quantity can be a virtual inertia coefficient, the proportional gain of the current loop, etc.

[0083] In step 203 above, after obtaining each After superimposing the Gell's circle bands, firstly, it is determined whether the virtual inertia control system meets the usage conditions of the joint criterion based on the Gell's circle bands; secondly, if the usage conditions are met, the system stability is determined by the joint criterion. Specifically, the usage conditions of the joint criterion include: each of the system transfer function matrix G(s)... The Gaelic circle does not contain points. Where i is a positive integer; The feedback quantity of the virtual inertia control system includes the virtual inertia coefficient. And the proportional gain of the DC / AC inverter current loop controller. The joint criterion includes: if the virtual inertia control system meets the aforementioned usage conditions, then if each of the aforementioned... The Gaelic circle surrounds the point in a clockwise direction. If the sum of the cycles equals -n0, the closed-loop system is stable; otherwise, the system is unstable. Here, n0 is the number of poles in the right half of the complex plane of the system's transfer function matrix G(s), which is also the number of poles in the right half of the complex plane of the open-loop system (e.g., n0 = 0). It should be noted that if the virtual inertia control system does not satisfy the conditions of the joint criterion, then... At least one of the Gaelic circular bands contains the corresponding feedback quantity. Then you can set a static compensator. The virtual inertia control system is pseudo-diagonalized, and the system stability is further determined by the joint criterion.

[0084] The reasons for choosing the virtual inertia coefficient and the proportional gain of the current loop as feedback quantities are as follows: The core of virtual inertia control is to provide frequency support for the system by simulating the rotor inertia characteristics of a synchronous generator. Virtual inertia coefficient. This directly determines the system's response speed and damping characteristics to frequency changes: in terms of frequency stability correlation, The larger the value, the stronger the system's response to frequency deviation, but an excessively large value... This could lead to system oscillations or even instability (e.g.) Figure 8 As shown, the uncompensated Gaelic circle contains a critical point; regarding the dominant dynamic characteristics, in the state-space model, The virtual inertia control loop of the inverter voltage loop (see formula (10)) directly affects the system angular frequency. The dynamic response is a key control parameter for frequency stability.

[0085] The current loop acts as the inner loop control, and its proportional gain... The impact on system stability is significant: in the trade-off between response speed and stability margin, Increasing the current loop speed will improve current tracking speed, but may introduce high-frequency oscillations and reduce phase margin. In multivariable systems, the nonlinear coupling effect of the current loop (such as...) and The cross terms will be passed through To magnify the effect, it is necessary to analyze the influence using Gell-Robin circles (e.g.) Figure 7 , Figure 9 Regarding the coupling relationship with virtual inertia, virtual inertia control affects frequency by adjusting active power, while current loop control directly affects the distribution of active / reactive power. The two are linked through the DC link capacitor voltage. and q-axis grid connection point current To form a closed-loop coupling (see formula (12)), select As a feedback quantity, it can directly characterize the stability of this coupling relationship.

[0086] In summary, these two factors, namely frequency response characteristics and internal dynamic coupling, respectively dominate the system and are the most sensitive parameters affecting stability. Analyzing the Gell circumference of the Nyquist array using Nyquist array theory can not only intuitively determine stability but also provide clear guidance for parameter optimization, facilitating the dual requirements of simplicity and accuracy in engineering applications.

[0087] like Figure 7 As shown, The Gaelic circle contains no feedback quantities -1 / y1 and -1 / y2, and the sum of the number of clockwise rotations of the Gaelic circle around each -1 / y1 and -1 / y2 point is 0. The number of poles of the open-loop system in the right half of the complex plane is also 0, and the closed-loop system is stable.

[0088] Conversely, such as Figure 8 As shown, If the Gaelic circle does not contain the feedback quantities -1 / y1 and -1 / y2 respectively, then the virtual inertia control system does not meet the conditions for use of the joint criterion, so a static compensator needs to be further designed.

[0089] Optionally, if the virtual inertia control system does not meet the usage conditions based on the joint criterion of the Gaelic circle, a static compensator can be set. The virtual inertia control system is pseudo-diagonalized, and the system stability is further determined by the joint criterion. For example, this is achieved by setting a static compensator. The virtual inertia control system is pseudo-diagonalized, including: By constructing the following objective function Solve for the optimal real constant matrix : ;

[0090] ;

[0091] ; in, The system transfer function matrix after compensation; For matrix The diagonal elements; This represents the i-th frequency point; j is the imaginary unit; Representation matrix off-diagonal elements; Representation matrix Which order; represents the weighting coefficient for the i-th frequency point; N represents the number of frequency points.

[0092] Specifically, for ease of engineering application, static compensators The simplest design is required, provided the system can meet the joint criterion conditions. Pseudo-diagonalization is essentially achieved by designing a real constant matrix. , so that the compensated matrix The sum of the moduli of all off-diagonal elements at a certain frequency or frequency band should be minimized, that is, the minimum value of the objective function formula (15) should be satisfied.

[0093] ;

[0094] In the formula: Jr is The sum of the moduli of the non-diagonal elements of the row; m represents the matrix. The order of Representation matrix The off-diagonal elements.

[0095] Because J r It is a scalar multivariate function, therefore it can be viewed as an extremum problem of a multivariate function. For several frequency points... The weighting coefficients correspond to The index function and constraint equation for this extreme value problem are shown in formula (14).

[0096] Therefore, the problem can be transformed into an unconditional extremum problem using the Lagrange multiplier method. Finally, the Johnson solution method can be used to transform the problem into a problem of finding the maximum eigenvalue and eigenvector of an m×m real matrix.

[0097] The final static compensator designed for the virtual inertia control system is as follows: ;

[0098] Furthermore, in the above steps, if the virtual inertia control system does not meet the conditions of the joint criterion, a corresponding compensator can be designed as an additional controller for the inverter control section, such as... Figure 6 As shown within the dashed box.

[0099] Example of a virtual inertia control system with an added static compensator Figure 9 As shown, after adding static compensator control, G 11 (s) and G 22 The Gaelic bands of (s) do not contain the feedback quantities -1 / y1 and -1 / y2, respectively, and the stability can be further analyzed using the joint criterion.

[0100] Figure 10 The complete process of the entire embodiment is illustrated by way of example. Each step has been described in detail in the above embodiment and will not be repeated here.

[0101] This invention constructs a state-space model of a flexible load grid-connected system and transforms it into a system transfer function. It then introduces the Nyquist array theory of Gell's circle to jointly determine system stability. This method simplifies the complex stability problem of high-order, multivariable systems to the observation of a series of intuitive Nyquist plots and their Gell's circles, significantly reducing computational complexity. This makes the analysis process not only physically clear and the results accurate and intuitive, but also provides direct and visual references for the optimization of key parameters (such as the virtual inertia coefficient), greatly improving the applicability and efficiency of this method in engineering practice. Furthermore, for systems that do not meet the conditions of the joint criterion, a compensator is designed so that once the system meets the criterion, the design problem of the multivariable system can be decomposed into a series of design problems of single-variable subsystems.

[0102] The following describes a stability determination device for a virtual inertia control system provided by the present invention. The stability determination method and device for a virtual inertia control system described below can be referred to in correspondence with the stability determination method for a virtual inertia control system described above.

[0103] like Figure 11 As shown, the present invention provides a stability determination method and apparatus for a virtual inertia control system, comprising the following modules: Module 1100 is used to construct the state-space model of the flexible load grid connection system; The transformation module 1110 is used to transform the state-space model into a multivariable system transfer function matrix G(s), where s is the Laplace operator; The plotting module 1120 is used to plot the Nyquist plot of the system transfer function matrix G(s) with Gaelic circles; The determination module 1130 is used to determine the stability of the flexible load grid connection system by means of the joint criterion if the virtual inertia control system meets the usage conditions based on the joint criterion of the Gale circle.

[0104] According to the present invention, a stability determination device for a virtual inertia control system is provided, wherein constructing the state-space model of the virtual inertia control system includes: Construct the state-space model of the filter module; Construct a state-space model of the DC / DC converter and its control module; Construct a state-space model of a DC / AC inverter and its control module; The state space model of the virtual inertia control system is constructed based on the filter state space model, the DC / DC converter state space model, and the DC / AC inverter state space model. The state space models of the DC / DC converter and its control module, the DC / AC inverter and its control module, and the filter are sequentially coupled in series; and the filter state space model and the DC / AC inverter and its control module state space model form a feedback coupling.

[0105] According to the stability determination device for a virtual inertia control system provided by the present invention, the construction of the state space model of the filter module specifically includes: Constructed using the following small signal model: ;

[0106] in, The differential representing the change in the d-axis component of the inverter port output current; This represents the change in the q-axis component of the boost inductor current on the DC / AC inverter side; This represents the change in the q-axis component of the grid connection point voltage; This represents the change in the d-axis component of the grid-connected current; The change in the q-axis component of the grid-connected current; Indicates the filter resistor; Indicates the filter inductance; Indicates the system's angular frequency; Indicates the filter capacitor; Indicates the equivalent inductance of the transmission line; Indicates the equivalent resistance of the transmission line; This represents the proportional gain of the DC / AC inverter current loop controller. This represents the integral coefficient of the DC / AC inverter current loop controller; This represents the integral coefficient of the voltage loop controller in a DC / AC inverter. This represents the proportional gain of the DC / AC inverter voltage loop controller. This indicates the change in the d-axis input of the DC / AC inverter current loop controller; This indicates the change in the q-axis input of the DC / AC inverter current loop controller; This represents the change in the d-axis input of the DC / AC inverter voltage loop controller; This represents the change in voltage across the DC link capacitor. This represents the q-axis component of the output current at the DC / AC inverter port. This represents the d-axis component of the output current at the DC / AC inverter port. Indicates the virtual inertia coefficient; Represents the q-axis component of the grid-connected current; This represents the d-axis component of the grid-connected current.

[0107] According to the stability determination device for a virtual inertia control system provided by the present invention, the construction of the state-space model of the DC / DC converter and its control module specifically includes: Constructed using the following small signal model: ;

[0108] in, This indicates the change in the input quantity of the DC / DC converter current loop controller; This indicates the change in the input quantity of the DC / DC converter voltage loop controller; The table shows the output current variation of the flexible load; This represents the change in DC link voltage. This refers to the change in the reference value of the output current of the flexible load. Inductor for boost circuit; For the output current of the flexible load; This refers to the change in output voltage of the flexible load. This is the reference value for the DC link voltage. d is the DC link voltage, and d is the duty cycle of the boost circuit. This indicates the change in the duty cycle of the boost circuit; For DC link capacitor, This represents the change in DC link current.

[0109] According to the stability determination device for a virtual inertia control system provided by the present invention, the construction of the state-space model of the DC / AC inverter and its control module specifically includes: Constructed using the following small signal model: ;

[0110] in, Indicates the virtual inertia coefficient; This indicates the change in the d-axis input of the DC / AC inverter current loop controller; This indicates the change in the q-axis input of the DC / AC inverter current loop controller; This represents the change in the d-axis input of the DC / AC inverter voltage loop controller; This represents the change in the reference value of the d-axis current at the grid connection point. This represents the change in the reference value of the q-axis current at the grid connection point. This represents the change in the system's angular frequency. This represents the change in the d-axis component of the boost inductor current on the DC / AC inverter side; This represents the change in the q-axis component of the boost inductor current on the DC / AC inverter side; This represents the change in the d-axis component of the grid connection point voltage; This represents the change in the q-axis component of the grid connection point voltage; This represents the change in the d-axis component of the grid-connected current; The change in the q-axis component of the grid-connected current; This represents the change in voltage across the DC link capacitor.

[0111] The phase-locked loop is constructed using the following small-signal model:

[0112] in, The change in the input quantity to the phase-locked loop controller; This represents the change in phase angle.

[0113] According to the present invention, a stability determination device for a virtual inertia control system is provided, wherein constructing the state space model of the virtual inertia control system based on the filter state space model, the DC / DC converter state space model, and the DC / AC inverter state space model specifically includes: By combining the various state-space models, the state-space model of the virtual inertia control system is obtained:

[0114] ; ;

[0115] in, A represents the state variables; B represents the system state matrix; C represents the system input matrix; and D represents the system output matrix. This represents the change in the output value of the virtual inertia controller. The d-axis component of the grid connection point current The change output by the proportional controller after subtracting the actual value from the reference value; This represents the change in the system's angular frequency. The change in the reference value of the q-axis component of the grid-connected current. The change in the actual value of the q-axis component of the grid connection current difference; The The state variables from the filter state-space model include: This represents the change in the d-axis component of the boost inductor current on the inverter side; This represents the change in the q-axis component of the boost inductor current on the inverter side; This represents the change in the d-axis component of the grid connection point voltage; This represents the change in the q-axis component of the grid connection point voltage; This represents the change in the d-axis component of the grid-connected current; The change in the q-axis component of the grid-connected current; The The state variables derived from the state-space model of the DC / AC inverter and its control module include: This represents the change in the output of the d-axis proportional controller of the current loop in a DC / AC inverter. The change in the output of the q-axis proportional controller of the current loop of the DC / AC inverter; The change in the output of the d-axis proportional controller of the DC / AC inverter voltage loop; The change in the input quantity of the phase-locked loop proportional controller; This refers to the change in the phase angle of the phase-locked loop output. The The state variables from the state space model of the DC / DC converter and its control module include: The change in the input quantity of the proportional controller in the current loop of the DC / DC converter; This indicates the change in the input quantity of the proportional controller in the voltage loop of the DC / DC converter; This refers to the change in output current of the flexible load. This represents the change in voltage across the DC link capacitor.

[0116] According to the present invention, a stability determination device for a virtual inertia control system is provided, wherein the conditions for using the joint criterion include: each of the system transfer function matrix G(s) The Gaelic circle does not contain points. Where i is a positive integer; The feedback quantity of the virtual inertia control system includes the virtual inertia coefficient. And the proportional coefficient of the DC / AC inverter current loop controller.

[0117] According to the present invention, a stability determination device for a virtual inertia control system is provided. If the virtual inertia control system meets the aforementioned usage conditions, then if each of the aforementioned conditions is met... The Gaelic circle surrounds the point in a clockwise direction. If the sum of the cycles equals -n0, the system is stable in closed loop; otherwise, the system is unstable; where n0 is the number of poles of the system transfer function matrix G(s) in the right half of the complex plane.

[0118] According to the present invention, a stability determination device for a virtual inertia control system is provided. If the virtual inertia control system does not meet the usage conditions based on the joint criterion of the Gaelic circle, a static compensator is set. The virtual inertia control system is pseudo-diagonalized, and the system stability is further determined by the joint criterion.

[0119] According to the present invention, a stability determination device for a virtual inertia control system is provided, wherein a static compensator is set. The virtual inertia control system is pseudo-diagonalized by constructing the following objective function. Solve for the optimal real constant matrix : ; ;

[0120] ;

[0121] in, The system transfer function matrix after compensation; For matrix The diagonal elements; This represents the i-th frequency point; j is the imaginary unit; Representation matrix off-diagonal elements; r represents the matrix Which order; represents the weighting coefficient for the i-th frequency point; N represents the number of frequency points.

[0122] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0123] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A stability determination method applied to a virtual inertia control system, characterized in that, include: Construct the state-space model of the virtual inertia control system; The state-space model is transformed into a multivariable system transfer function matrix G(s), where s is the Laplace operator; Plot the Nyquist plot of the system transfer function matrix G(s) with Gaelic circles; If the virtual inertia control system meets the usage conditions based on the joint criterion of the Gaelic circle, then the stability of the virtual inertia control system is determined using the joint criterion.

2. The stability determination method for a virtual inertia control system according to claim 1, characterized in that, The construction of the state-space model of the virtual inertia control system includes: Construct the state-space model of the filter module; Construct a state-space model of the DC / DC converter and its control module; Construct a state-space model of a DC / AC inverter and its control module; The state space model of the virtual inertia control system is constructed based on the filter state space model, the DC / DC converter state space model, and the DC / AC inverter state space model. The state space models of the DC / DC converter and its control module, the DC / AC inverter and its control module, and the filter are sequentially coupled in series; and the filter state space model and the DC / AC inverter and its control module state space model form a feedback coupling.

3. The stability determination method for a virtual inertia control system according to claim 2, characterized in that, The construction of the state space model of the filter module specifically includes: Constructed using the following small signal model: ； in, The differential representing the change in the d-axis component of the inverter port output current; This represents the change in the q-axis component of the boost inductor current on the DC / AC inverter side; This represents the change in the q-axis component of the grid connection point voltage; This represents the change in the d-axis component of the grid-connected current; The change in the q-axis component of the grid-connected current; Indicates the filter resistor; Indicates the filter inductance; Indicates the system's angular frequency; Indicates the filter capacitor; Indicates the equivalent inductance of the transmission line; Indicates the equivalent resistance of the transmission line; This represents the proportional gain of the DC / AC inverter current loop controller. This represents the integral coefficient of the DC / AC inverter current loop controller; This represents the integral coefficient of the voltage loop controller in a DC / AC inverter. This represents the proportional gain of the DC / AC inverter voltage loop controller. This indicates the change in the d-axis input of the DC / AC inverter current loop controller; This indicates the change in the q-axis input of the DC / AC inverter current loop controller; This represents the change in the d-axis input of the DC / AC inverter voltage loop controller; This represents the change in voltage across the DC link capacitor. This represents the q-axis component of the output current at the DC / AC inverter port. This represents the d-axis component of the output current at the DC / AC inverter port. Indicates the virtual inertia coefficient; Represents the q-axis component of the grid-connected current; This represents the d-axis component of the grid-connected current.

4. The stability determination method for a virtual inertia control system according to claim 2, characterized in that, The construction of the state-space model of the DC / DC converter and its control module specifically includes: Constructed using the following small signal model: ； in, This indicates the change in the input quantity of the DC / DC converter current loop controller; This indicates the change in the input quantity of the DC / DC converter voltage loop controller; The table shows the output current variation of the flexible load; This represents the change in DC link voltage. This refers to the change in the reference value of the output current of the flexible load. Inductor for boost circuit; For the output current of the flexible load; This refers to the change in output voltage of the flexible load. This is the reference value for the DC link voltage. d is the DC link voltage, and d is the duty cycle of the boost circuit. This indicates the change in the duty cycle of the boost circuit; For DC link capacitor, This represents the change in DC link current.

5. The stability determination method for a virtual inertia control system according to claim 2, characterized in that, The construction of the state-space model of the DC / AC inverter and its control module specifically includes: Constructed using the following small signal model: ； in, Represents the virtual inertia coefficient; represents the change in the d-axis input of the DC / AC inverter current loop controller; This indicates the change in the q-axis input of the DC / AC inverter current loop controller; This represents the change in the d-axis input of the DC / AC inverter voltage loop controller; This represents the change in the reference value of the d-axis current at the grid connection point. This represents the change in the reference value of the q-axis current at the grid connection point. This represents the change in the system's angular frequency. This represents the change in the d-axis component of the boost inductor current on the DC / AC inverter side; This represents the change in the q-axis component of the boost inductor current on the DC / AC inverter side; This represents the change in the d-axis component of the grid connection point voltage; This represents the change in the q-axis component of the grid connection point voltage; This represents the change in the d-axis component of the grid-connected current; The change in the q-axis component of the grid-connected current; This represents the change in voltage across the DC link capacitor. The phase-locked loop is constructed using the following small-signal model: ； in, The change in the input quantity to the phase-locked loop controller; This represents the change in phase angle.

6. The stability determination method for a virtual inertia control system according to claim 2, characterized in that, The construction of the state space model of the virtual inertia control system based on the filter state space model, the DC / DC converter state space model, and the DC / AC inverter state space model specifically includes: By combining the various state-space models, the state-space model of the virtual inertia control system is obtained: ； ； ； in, A represents the state variables; B represents the system state matrix; C represents the system input matrix; and D represents the system output matrix. This represents the change in the output value of the virtual inertia controller. The d-axis component of the grid connection point current The change output by the proportional controller after subtracting the actual value from the reference value; This represents the change in the system's angular frequency. The change in the reference value of the q-axis component of the grid-connected current. The change in the actual value of the q-axis component of the grid connection current difference; The The state variables from the filter state-space model include: This represents the change in the d-axis component of the boost inductor current on the inverter side; This represents the change in the q-axis component of the boost inductor current on the inverter side; This represents the change in the d-axis component of the grid connection point voltage; This represents the change in the q-axis component of the grid connection point voltage; This represents the change in the d-axis component of the grid-connected current; The change in the q-axis component of the grid-connected current; The The state variables derived from the state-space model of the DC / AC inverter and its control module include: This represents the change in the output of the d-axis proportional controller of the current loop in a DC / AC inverter. The change in the output of the q-axis proportional controller of the current loop of the DC / AC inverter; The change in the output of the d-axis proportional controller of the DC / AC inverter voltage loop; The change in the input quantity of the phase-locked loop proportional controller; This refers to the change in the phase angle of the phase-locked loop output. The The state variables in x from the state-space model of the DC / DC converter and its control module include: The change in the input quantity of the proportional controller in the current loop of the DC / DC converter; This indicates the change in the input quantity of the proportional controller in the voltage loop of the DC / DC converter; This refers to the change in output current of the flexible load. This represents the change in voltage across the DC link capacitor.

7. The stability determination method for a virtual inertia control system according to claim 1, characterized in that, The conditions for using the joint criterion include: each of the system transfer function matrix G(s) The Gaelic circle does not contain points. Where i is a positive integer; The feedback quantity of the virtual inertia control system includes the virtual inertia coefficient. And the proportional coefficient of the DC / AC inverter current loop controller.

8. The stability determination method for a virtual inertia control system according to claim 7, characterized in that, If the virtual inertia control system meets the usage conditions, then if each of the above conditions is met... The Gaelic circle surrounds each of the points in a clockwise direction. If the sum of the cycles equals -n0, the system is stable in closed loop; otherwise, the system is unstable; where n0 is the number of poles of the system transfer function matrix G(s) in the right half of the complex plane. If the virtual inertia control system does not meet the usage conditions based on the joint criterion of the Gaelic circle, then a static compensator is set. The virtual inertia control system is pseudo-diagonalized, and the system stability is further determined by the joint criterion.

9. The stability determination method for a virtual inertia control system according to claim 8, characterized in that, The method of setting a static compensator The virtual inertia control system is pseudo-diagonalized by constructing the following objective function. Solve for the optimal real constant matrix : ； ； ； in, The system transfer function matrix after compensation; For matrix The diagonal elements; This represents the i-th frequency point; j is the imaginary unit; Representation matrix off-diagonal elements; r represents the matrix Which order; represents the weighting coefficient for the i-th frequency point; N represents the number of frequency points.

10. A stability determination device for a virtual inertia control system, characterized in that, include: The construction module is used to construct the state-space model of the virtual inertia control system; The transformation module is used to transform the state-space model into a multivariable system transfer function matrix G(s), where s is the Laplace operator; A plotting module is used to plot the Nyquist plot of the system transfer function matrix G(s) with Gaelic circles; The determination module is used to determine the stability of the virtual inertia control system by means of the joint criterion based on the Gaelic circle if the virtual inertia control system meets the usage conditions.

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