AHO virtual oscillation controller stabilization method and adaptive inertia method

Abstract

The invention belongs to the technical field of virtual oscillator control of power electronic inverters, and particularly discloses an AHO virtual oscillation controller stabilization method and an adaptive inertia method. The stabilization method comprises the following steps: establishing a nonlinear model of a GFM inverter in a single-inverter grid-connected and multi-inverter interconnection mode; acquiring a balance point by using a numerical analysis method, linearizing the balance point, extracting a linearized Jacobian matrix, and further designing a multi-target fitness function taking eigenvalue real part minimization as a core; and in combination with a particle swarm intelligent search algorithm, parameters influencing the stability in the AHO virtual oscillation controller are optimized, and the dynamic stability of the power system under the wide working condition is ensured. The AHO-VOC controller using the particle swarm optimization method can ensure stability under switching of various working conditions; compared with inertia-free and fixed inertia methods, the adaptive inertia method shows better transient characteristics.

Description

Technical Field

[0001] The present application belongs to the technical field of virtual oscillator control of power electronic inverters, and more specifically, relates to an AHO virtual oscillation controller stabilization method and an adaptive inertia method. Background Art

[0002] Against the backdrop of a global push for energy transformation and surging demand for clean energy, distributed energy sources such as solar photovoltaics and wind power are experiencing widespread adoption and rapid growth due to their renewable, pollution-free, and decentralized nature. Many of these distributed energy resources are connected to the power system via inverters, creating a distributed energy grid. However, while this trend optimizes the energy mix, it also poses significant challenges to the stable operation of the power system. The output power of distributed energy resources is significantly intermittent and fluctuating, influenced by natural factors such as sunlight intensity and wind speed. As the key interface between distributed energy resources and the power grid, the control strategy and dynamic characteristics of inverters significantly impact power system stability. Traditional power system control methods struggle to adapt to these new changes, resulting in frequent stability issues such as large voltage fluctuations, significant frequency excursions, and severe power oscillations, which can even lead to system failures.

[0003] The Andronov-Hopf Virtual Oscillation Controller (AHO-VOC) is based on the important nonlinear dynamics theory of the Andronov-Hopf bifurcation. This theory precisely describes the process of transitioning from a stable equilibrium point to periodic oscillations when system parameters change, and is closely related to power system stability. By introducing a virtual oscillation mechanism, the AHO-VOC controller enables the inverter to simulate the dynamic characteristics of a synchronous generator, effectively enhancing the inertia and damping of the distributed energy grid-connected system and improving system stability. In actual operation, the AHO-VOC controller can flexibly adjust the inverter output current and voltage based on the real-time system status, ensuring stable operation under complex operating conditions and effectively suppressing power oscillations and voltage fluctuations. However, this controller also has limitations in its application. Parameter design requires comprehensive consideration of the system's dynamic characteristics under various operating conditions, which is a complex process. Furthermore, instability can occur under certain circumstances, leading to reduced system performance.

[0004] Currently, AHO-VOC controller parameter design primarily relies on traditional trial-and-error methods, empirical approaches, or optimization methods based on linearized models. Trial-and-error methods require numerous iterations, are cumbersome, and inefficient, making it difficult to guarantee optimal controller performance under all operating conditions. Empirical methods lack scientific accuracy and precision, making them inadequate for complex and changing power system conditions. Optimization methods based on linearized models fail to adequately account for system nonlinearities, making the controller prone to instability when the system enters the nonlinear region.

[0005] Therefore, how to solve the problem that the stability parameters of the traditional Andronov-Hopf (AHO) virtual oscillation controller rely on experience-based tuning and the fixed inertia is difficult to adapt to changes in working conditions is currently in urgent need of research. Summary of the Invention

[0006] In view of the shortcomings of the prior art, the purpose of this application is to provide an AHO virtual oscillation controller stabilization method and an adaptive inertia method, which can ensure the dynamic stability of the power system under a wide range of operating conditions.

[0007] To achieve the above objectives, in a first aspect, the present application provides an AHO virtual oscillation controller stabilization method, comprising the following steps: S10, establish the nonlinear model of GFM inverter in single grid-connected mode and multi-grid interconnected mode; S20, using numerical analysis to obtain the equilibrium point, linearize the equilibrium point, extract the linearized Jacobian matrix, and then design a multi-objective fitness function with the minimization of the real part of the eigenvalue as the core; S30, combined with the particle swarm intelligent search algorithm, optimizes the parameters affecting stability in the AHO virtual oscillation controller to ensure the dynamic stability of the power system under a wide range of operating conditions.

[0008] As a further preferred embodiment, step S10 is specifically as follows: S11, construct the state space equation of AHO virtual oscillation controller based on Poincare bifurcation equation; S12, establishing a virtual oscillator grid-connected equation group and a virtual oscillator interconnection equation group based on the state space equation.

[0009] As a further preferred embodiment, in step S11, the state space equation of the AHO virtual oscillation controller is:

[0010] in, 、 are the voltages on the capacitor and inductor in the AHO virtual oscillator respectively; 、 are the derivatives of the voltages on the capacitor and inductor in the AHO virtual oscillator, respectively; It is the nonlinear link in the AHO virtual oscillation controller; 、 It is the input of AHO virtual oscillation controller; is the oscillation frequency of the virtual oscillation controller; C is the virtual capacitance of the virtual oscillation controller.

[0011] As a further preferred embodiment, in step S12, the method for constructing the virtual oscillator grid-connected equation group is as follows: for the first inverter, in a stationary reference coordinate system, according to its current dynamic characteristic equation, a phase angle difference is introduced, where the phase angle difference is determined by the power transmitted by the inverter to the grid; then, by means of a rotation transformation, a dynamic equation of the projected current in a bus voltage coordinate system is obtained, thereby constructing a single inverter grid-connected system equation group; The construction method of the virtual oscillator interconnection equation group is as follows: take the island system composed of three interconnected inverters as the research object, set the local coordinate system of the first inverter as the global coordinate system, and define the j ( j =2,3) The angle difference between the local coordinate system and the global coordinate system of the inverter is ( j =2,3); then analyze the voltage / phase angle characteristics of each inverter, the line current dynamic characteristics, the line current dynamic equation in the global coordinate system, the load current dynamic characteristic equation, and the related algebraic relations, and finally obtain the system equations for the interconnection of multiple inverters.

[0012] As a further preference, in step S30, the parameters affecting stability are selected according to the operation mode of the inverter, the number of inverters and their topology.

[0013] As a further preferred embodiment, when the first inverter is connected to the infinite inertia grid, in the stationary reference coordinate system, the parameters affecting stability are 、 、 ; In an island system consisting of three interconnected inverters, the parameters that affect stability are 、 、 、 、 、 、 、 、 、 and ; in, It is The convergence constant in the AHO virtual oscillation controller determines the convergence speed of AHO; 、 They are AHO controller Filter parameters; and They are the resistance and inductance values ​​of the RL filter respectively.

[0014] As a further preferred embodiment, step S30 is specifically as follows: S31, initialize the particle swarm, including the number of particles, initial position and initial velocity; S32, substitute the current position of the particle into the objective function to evaluate the fitness. The objective function is the inverse of the sum of the absolute values ​​of the real parts of all eigenvalues ​​and a penalty term is added to ensure the stability of the system equation; S33, compare and update the individual optimal and global optimal positions, update the particle speed and position, and perform boundary processing on the positions that are out of range; S34, judge whether the system is stable according to the stability criterion of the equation group, and punish the particles if it is not satisfied; S35, continuously repeating steps S31 to S34 until the maximum number of iterations is reached or the fitness value converges, and finally outputting the global optimal position to obtain the optimized controller parameters.

[0015] In a second aspect, the present application provides an AHO virtual oscillation controller stabilization system, comprising: Nonlinear model building module, used to build nonlinear models of GFM inverters in single grid-connected and multi-grid interconnected modes; The objective function design module is used to obtain the equilibrium point using numerical analysis, linearize the equilibrium point, extract the linearized Jacobian matrix, and then design a multi-objective fitness function with the minimization of the real part of the eigenvalue as the core; The parameter optimization module is used to combine the particle swarm intelligent search algorithm to optimize the parameters affecting the stability of the AHO virtual oscillation controller, thereby ensuring the dynamic stability of the power system under a wide range of operating conditions.

[0016] In a third aspect, the present application provides an AHO virtual oscillation controller, which adopts the above-mentioned AHO virtual oscillation controller stabilization method.

[0017] In a fourth aspect, the present application provides an adaptive inertia method based on the above-mentioned AHO virtual oscillation controller, comprising the following steps: Get the frequency and frequency change rate output by the AHO virtual oscillation controller; The frequency and frequency change rate are formulated to express the inertia requirement of the power system for adaptively adjusting the inertia.

[0018] The beneficial effects of this application are as follows: In view of the many shortcomings of existing AHO-VOC controller stabilization methods and the higher requirements of power systems for stability and reliability, this application innovatively proposes an Andronov-Hopf virtual oscillation controller stabilization method and an adaptive inertia control method based on a particle swarm algorithm. The above method utilizes the optimization capability of the particle swarm algorithm to deeply optimize the design of the AHO-VOC controller parameters and realizes adaptive intelligent adjustment of the parameters. At the same time, adaptive inertia is used to solve the different inertia requirements of the power system under different working conditions, thereby comprehensively improving the stability and comprehensive performance of the distributed energy grid-connected system and providing strong technical support for the safe, reliable and efficient operation of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a flow chart of the AHO virtual oscillation controller stabilization method provided by an embodiment of the present application; Figure 2 Schematic diagram of the AHO virtual oscillation controller stabilization method provided in an embodiment of the present application; Figure 3 This is a single AHO-VOC inverter grid-connected structure provided in a specific embodiment of the present application; Figure 4 The specific embodiment of this application provides a parallel structure based on multiple AHO-VOC inverters; Figure 5 This is a flow chart of the AHO virtual oscillation controller stabilization method based on the particle swarm algorithm provided in a specific embodiment of the present application; Figure 6 This is a waveform diagram of a single AHO-VOC inverter under different working conditions provided by a specific embodiment of the present application; Figure 7 These are waveform diagrams of the AHO-VOC inverters with no inertia, fixed inertia, and adaptive inertia under different working conditions, provided in the specific embodiments of the present application. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of this application.

[0021] After research, this applicant discovered that the Particle Swarm Optimization (PSO) algorithm, a highly efficient optimization algorithm based on swarm intelligence, simulates the foraging behavior of bird flocks or fish schools. In the PSO algorithm, each particle represents a potential solution. Based on its own and the group's historical optimal positions, it dynamically updates its flight direction and speed within the search space to find the global optimal solution. The PSO algorithm is simple in principle, easy to implement, and converges quickly. In particular, it possesses powerful global search capabilities, enabling it to quickly locate solutions close to the global optimal solution in complex solution spaces. Furthermore, the algorithm does not require the differentiation of the objective function and can effectively handle complex nonlinear optimization problems. Given these advantages, the PSO algorithm has great potential for application in power system control. In the stable design of the AHO-VOC controller, the PSO algorithm can fully utilize its optimization capabilities to scientifically optimize key controller parameters, improve controller performance and stability, and achieve adaptive dynamic adjustment of controller parameters, enabling it to better adapt to the complex and changing operating conditions of the power system.

[0022] Therefore, to solve the problem that the stability parameters of the existing Andronov-Hopf (AHO) virtual oscillation controller rely on experience tuning and the fixed inertia is difficult to adapt to changes in working conditions, this application provides an AHO virtual oscillation controller stabilization method, such as Figure 1 and 2 As shown, the following steps are included: Step S10: establishing a nonlinear model of the GFM inverter (grid-connected inverter) in single-unit grid-connected mode and multiple-unit interconnected mode.

[0023] In this embodiment, step S10 can be implemented by using steps S11 and S12 as follows: Step S11: Based on the Poincare bifurcation equation, the state space equation of the AHO virtual oscillation controller is constructed, and its expression is:

[0024] in, It is the nonlinear link in the AHO virtual oscillator control.

[0025]

[0026] Where, 、 are the voltages on the capacitor and inductor in the AHO virtual oscillator respectively; 、 are the derivatives of the voltages on the capacitor and inductor in the AHO virtual oscillator, respectively; is a constant that determines the speed of convergence to the quasi-steady-state periodic state; is the voltage gain constant; It is the input of AHO virtual oscillation controller; is the oscillation frequency of the virtual oscillation controller; C is the virtual capacitance of the virtual oscillation controller.

[0027]

[0028] Where, is the reference current, is the actual current, is the current gain constant, The angle is Rotational inertia.

[0029]

[0030] The controller studied is able to control the active power and reactive power set points and These set points are The coordinate system is converted into a current instruction, that is, the reference current , The resulting expression is as follows:

[0031] make and , Afterwards

[0032] in , is the voltage gain, is the current gain.

[0033] Step S12: establishing a virtual oscillator grid-connected equation group and a virtual oscillator interconnection equation group based on the state-space equation.

[0034] In this embodiment, the AHO-VOC equations and grid-connected equations are established: For the first inverter (No. ), in the stationary reference frame ( Coordinate system), according to its current dynamic characteristic equation:

[0035] Since the inverter voltage and bus voltage (the voltage across the AC filter) has a different reference frame, and the angle difference is defined as , the angle difference is determined by the power transmitted by the inverter to the grid. According to the inverter phase angle formula, the angle dynamic equation is:

[0036] Among them, the above equation and is the inverter current in its own local coordinate system. It can be found that the current in the busbar coordinate system is two system state quantities; by converting these currents between the two coordinate systems through rotation transformation, the dynamic equation of the projected current in the busbar voltage coordinate system can be obtained:

[0037]

[0038] in and is the projected current in the bus voltage coordinate system. Their dynamic equations can be obtained by converting the current dynamic equations to the bus voltage coordinate system, and the expressions are:

[0039] Therefore, according to the above derivation, the system equations of a single inverter grid-connected system are obtained, and the system vector .

[0040] Establish the AHO-VOC interconnection equations: The study object is an island system consisting of three interconnected inverters, which are connected to each other through the filter / line shown in the figure and power two passive loads (Load 1 and Load 2) at the same time.

[0041] The local coordinate system of the first inverter is set as the global coordinate system. Therefore, the angle difference between the local coordinate system of the first inverter and the global coordinate system is expressed and defined as , No. j ( j =2,3) The angle difference between the local coordinate system and the global coordinate system of the inverter is ( j =2,3). Since the local coordinate system of the first inverter is actually the global coordinate system, the angle is always zero, i.e. , and there is no dynamic change.

[0042] Then the voltage / phase angle characteristics of each inverter, the line current dynamic characteristics, the line current dynamic equation in the global coordinate system, the load current dynamic characteristic equation and the related algebraic relations are analyzed.

[0043] Specifically, the voltage / phase angle characteristics of each inverter can be described as:

[0044] Please note that in the above equation and It is in its own reference coordinate system and needs to be transformed into the global coordinate system.

[0045]

[0046] The first inverter and grid connection point The current dynamic characteristics of the connection are:

[0047] Together with the dynamic characteristics of the first inverter current:

[0048] Among them use This is because the coordinate system of the first inverter is the global coordinate system. and are the voltages at bus 1 and bus 2 respectively.

[0049] In addition, the dynamic equation of the line current in the global coordinate system is as follows:

[0050] The dynamic characteristic equation of the load current can be written as:

[0051] in . and They are j In addition to the dynamic characteristics derived above, the following algebraic relationship is obtained:

[0052] Therefore, according to the above derivation, the system equations of multiple inverters interconnected are obtained, and the system vector .

[0053] In step S20, a numerical analysis method is used to obtain an equilibrium point, the equilibrium point is linearized, the linearized Jacobian matrix is ​​extracted, and a multi-objective fitness function with minimization of the real part of the eigenvalue as the core is designed.

[0054] In this embodiment, the system optimization goal is to stabilize the system equations, that is, to ensure that the real parts of the eigenvalues ​​of the linearized system of equations are all less than zero at the equilibrium point. Therefore, the objective function is designed to be the inverse of the sum of the absolute values ​​of the real parts of all eigenvalues. The goal is to make the real parts of the eigenvalues ​​as negative as possible and as far away from the imaginary axis. Furthermore, a penalty term is added to ensure that the real part of each eigenvalue is negative. Each real part of each eigenvalue adds a penalty term to the objective function.

[0055] According to the actual use of the RL filter parameters, it is necessary to take into account the filtering, power, and response. According to the switching frequency of the inverter and the cut-off frequency required for filtering, the resistance range of the RL filter is initially determined to be (0.01 , 5 ), the inductance range is (0.05 , 30 ). At the same time, for the convergence constant The range is (0, 50).

[0056] In step S30 , the parameters affecting the stability of the AHO virtual oscillation controller are optimized in combination with a particle swarm intelligent search algorithm to ensure the dynamic stability of the power system under a wide range of operating conditions.

[0057] In this embodiment, the parameters affecting stability are selected according to the operation mode of the inverter, the number of inverters and their topology.

[0058] Specifically, the parameters that affect stability are: When the first inverter is connected to the infinite inertia grid, in the stationary reference coordinate system, 、 、 Variables have a significant impact on system stability. In an island system consisting of three interconnected inverters, 、 、 、 、 、 、 、 、 、 and Many variables are closely related to system stability. It is The convergence constant in the AHO controller determines the convergence speed of AHO. 、 They are AHO controller Filter parameters.

[0059] In this embodiment, step S30 can be specifically implemented by the following steps: first, the particle swarm is initialized, including determining the number of particles, particle positions (ensuring that each component is within the specified parameter range), and particle speed; then, the current position of the particle is substituted into the objective function to evaluate the fitness, and the individual optimal and global optimal positions are updated by comparison; then, the particle speed and position are updated according to a specific formula, and the position out of range is processed at the boundary; after the update is completed, the stability criterion of the equation group is checked, and if it is not satisfied, the particle is penalized; the above steps are repeated until the maximum number of iterations is reached or the fitness value converges, and finally the global optimal position is output.

[0060] Based on the same inventive concept, the present application also provides an AHO virtual oscillation controller stabilization system and an AHO virtual oscillation controller.

[0061] The AHO virtual oscillation controller stabilization system provided in this embodiment includes a nonlinear model establishment module, an objective function design module, and a parameter optimization module.

[0062] In this embodiment, the nonlinear model establishment module is used to establish nonlinear models for the GFM inverter in both single-unit grid-connected and multi-unit interconnected modes. The objective function design module uses numerical analysis to determine the equilibrium point, linearizes the equilibrium point, extracts the linearized Jacobian matrix, and then designs a multi-objective fitness function centered on minimizing the real part of the eigenvalue. The parameter optimization module combines a particle swarm intelligent search algorithm to optimize stability-affecting parameters in the AHO virtual oscillation controller, ensuring the dynamic stability of the power system under a wide range of operating conditions.

[0063] It should be noted that the functions of the modules provided in this embodiment can be found in the detailed description of the embodiment of the AHO virtual oscillation controller stabilization method, and will not be described in detail in this embodiment.

[0064] The AHO virtual oscillation controller provided in this embodiment adopts the aforementioned AHO virtual oscillation controller stabilization method.

[0065] Furthermore, this application also discovered that existing AHO-VOC controller stabilization methods are mostly based on fixed-parameter designs and lack adaptive adjustment capabilities. When power system operating conditions undergo significant changes, such as fluctuations in distributed energy output power, load variations, and grid failures, fixed-parameter controllers are unable to adjust their control strategies in a timely manner, resulting in decreased system stability. Furthermore, AHO-VOC controller stabilization design typically involves multi-objective optimization, such as improving system stability, reducing power loss, and improving power quality. However, existing methods are limited in their ability to handle multi-objective optimization problems and struggle to simultaneously meet the stringent requirements of multiple objectives.

[0066] At the same time, fixed inertia has many drawbacks in power systems. Because its inertia parameters are constant, it cannot be adjusted according to the system's real-time operating status. This makes it difficult to effectively respond to changes in operating conditions, such as the massive access of new energy sources and drastic load fluctuations. Fixed inertia cannot quickly adjust the system frequency after a disturbance, which can easily lead to large frequency overshoot and long recovery times, and in severe cases, even cause system instability. Furthermore, under fixed inertia control, energy storage devices frequently participate in system frequency regulation, making them prone to deep overcharging and over-discharging, significantly shortening their service life. Furthermore, fixed inertia is difficult to match the system's differentiated inertia requirements under different operating conditions, limiting the flexibility and reliability of power system operation and failing to meet the complex and ever-changing operational requirements of modern power systems.

[0067] In this regard, the present application also provides an adaptive inertia method for an AHO virtual oscillation controller, comprising the following steps: obtaining the frequency and frequency change rate output by the AHO virtual oscillation controller; formulating the frequency and frequency change rate to express the inertia requirement of the power system for adaptively adjusting the inertia.

[0068] The adaptive inertia method provided in this embodiment is applicable to the peripheral inertia controller link of the AHO-VOC controller. A link for obtaining the frequency and frequency change rate of the AHO-VOC controller is added to the inertia controller to adjust the virtual inertia of the inertia controller.

[0069] It should be noted that in the study of power system adaptive control, the quasi-resonant controller is the core component for realizing adaptive inertia regulation. Its dynamic characteristics can be rigorously expressed by the state-space equation, which can be written as:

[0070] in is the state variable, and the output variable is , is the resonant frequency, Determine the bandwidth of the quasi-resonant controller and the range of the signal passing through the controller. Set the state variables to be orthogonal sine and cosine quantities, so the amplitude and phase angle of the output variables are Taking the derivative of the amplitude we get:

[0071] Taking the average value of the above within one AC cycle, we can get:

[0072] Considering the AHO equation with the quasi-resonant controller, we get:

[0073] Combined with the classic angle-of-attack swing equation of the synchronous motor, an analytical expression for the system inertia and damping characteristics can be established:

[0074] Through theoretical analysis and mathematical derivation, it is shown that when the system frequency deviates from the rated value, this control mechanism dynamically increases the system inertia based on the frequency deviation and rate of change, enhancing the system's anti-interference capability. As the frequency gradually approaches the rated value, the inertia is adaptively reduced, accelerating the system's response. This adaptive regulation strategy dynamically optimizes the quasi-resonant controller parameters by monitoring the frequency and rate of change of the AHO-VOC controller output in real time, providing effective theoretical support and implementation for power system frequency stability control.

[0075] The beneficial effects of this embodiment are as follows: In view of the many shortcomings of existing AHO-VOC controller stabilization methods and the higher requirements for stability and reliability of power systems, this embodiment innovatively proposes an Andronov-Hopf virtual oscillation controller stabilization method and an adaptive inertia control method based on a particle swarm algorithm. This method utilizes the optimization capabilities of the particle swarm algorithm to deeply optimize the design of AHO-VOC controller parameters and implement adaptive intelligent parameter adjustment. At the same time, adaptive inertia is used to address the different inertia requirements of power systems under different operating conditions, thereby comprehensively improving the stability and overall performance of distributed energy grid-connected systems and providing strong technical support for the safe, reliable, and efficient operation of power systems.

[0076] The present application is described in detail below based on specific embodiments.

[0077] Example 1 takes a distributed energy grid-connected system containing a single inverter as an example to illustrate the implementation process of the AHO virtual oscillation controller stabilization method based on the particle swarm algorithm. The rated power of each inverter in the system is P_rated = 20kW, the switching frequency fs = 10kHz, the cutoff frequency fc = 5kHz, and the RL filter resistor R is initially set to (0.01 , 5 ) range, inductance L in (0.05 , 30 ) range, AHO virtual oscillation controller convergence constant In the range (0,50).

[0078] First, the particle swarm is initialized and the number of particles is set (n = 200). Each particle represents a set of parameter combinations (R, L, ), randomly generate the initial position of the particle, ensuring that each component is within the parameter range. Then evaluate the fitness and substitute the current position of the particle into the objective function:

[0079] is the system eigenvalue, and a penalty term is added if the system is unstable.

[0080] Then update the individual and global optimal, compare the fitness of each particle with the fitness of the individual optimal and global optimal positions, and update the corresponding optimal position if the current particle fitness is better. Then update the particle position and speed, and the speed update formula is:

[0081] Position update formula

[0082] is inertia, which reflects the degree to which a particle depends on its previous state of motion, 、 The weights are individual learning factor and social learning factor respectively. Control particles to their historical optimal position The degree of proximity reflects the particle’s ability to self-recognize; Control particles to the global optimal position The degree of proximity reflects the information sharing and collaboration capabilities between particles. and : It is a random number uniformly distributed in the interval [0,1]. The purpose of introducing random numbers is to increase the randomness and diversity of the algorithm and prevent particles from falling into the local optimal solution too early. Representative i The particle in t The position at the iteration, It is i The optimal position found by a particle in the historical iteration process, It represents the global optimal position found by the entire particle swarm during the historical iteration process. At the same time, it performs boundary processing on positions that exceed the parameter range.

[0083] The stability of the updated system is checked according to the stability criterion of the equation group. If it is unstable, the particles are penalized. The above steps are repeated until the maximum number of iterations is reached or the fitness value converges, and the global optimal position is finally obtained, that is, the optimized controller parameters. Finally, the optimized parameters are applied to the actual system model for simulation. The system responds to load changes, distributed energy output power fluctuations, and inverter off-grid conditions. The results are as follows Figure 6, which shows that the voltage fluctuation of the system is small, the frequency offset is controlled within a small range, and the power oscillation is small, which verifies the effectiveness of this method.

[0084] Example 2 Taking the AHO-VOC inverter with adaptive inertia strategy as an example, a quasi-resonant controller is used as the inertia controller. The state equation of the quasi-resonant controller is:

[0085] in is the state variable, and the output variable is , is the resonant frequency, Determine the bandwidth of the quasi-resonant controller and the range of the signal passing through the controller. Set the state variables to be orthogonal sine and cosine quantities, so the amplitude and phase angle of the output variables are Taking the derivative of the amplitude we get:

[0086] Taking the average value of the above differential equation over one AC cycle, we get:

[0087] Taking into account the AHO equation with the quasi-resonant controller, the droop equation of AHO with respect to reactive voltage and active frequency is obtained:

[0088] Therefore, according to the angle of attack swing equation of the synchronous motor, the system inertia and system damping can be obtained:

[0089] When the frequency is far from the standard value, the inertia is increased, and when the frequency is close to the standard, the inertia is reduced to achieve the purpose of adaptive inertia. That is, the frequency and frequency change rate of the AHO-VOC controller are obtained and expressed in a formula to express the situation when the frequency approaches or deviates from the standard value. The formula expression results are used to adjust the inertia of the quasi-resonant controller.

[0090] like Figure 3 As shown, a single AHO-VOC inverter grid-connected structure of an embodiment of the present application.

[0091] This figure shows a typical grid-connected AHO-VOC inverter structure. It primarily includes the AHO-VOC's virtual electrical components, the inverter, and the RL filter. The AHO-VOC's input is sampled by the digital controller's ADC, and its output transmits switching signals to the inverter via PWM.

[0092] like Figure 4As shown, in one embodiment, based on a parallel structure of multiple AHO-VOC inverters, an island system consisting of three interconnected inverters is considered. These inverters are interconnected through the filters / lines shown in the figure, and power two passive loads (load 1 and load 2) at the same time. There is a filter between the grid connection points connecting load 1 and load 2.

[0093] like Figure 5 The flowchart of a particle swarm optimization-based Andronov-Hopf (AHO) virtual oscillation controller stabilization method is shown. This flowchart illustrates the process for optimizing the parameters of an AHO virtual oscillation controller using the particle swarm algorithm: First, the particle swarm is initialized, setting the particle number, initial position, and initial velocity. Next, the particle's current position is substituted into the objective function to evaluate its fitness. The objective function is the inverse of the sum of the absolute values ​​of the real parts of all eigenvalues, and a penalty term is added to ensure the stability of the system equations (for nonlinear systems, the real parts of the eigenvalues ​​of the linearized system of equations are all less than zero at the equilibrium point). Next, the individual optimal and global optimal positions are compared and updated, and the particle velocities and positions are updated according to specific formulas. Boundary handling is performed for positions that are out of range. The stability criterion for the system of equations is then used to determine whether the system is stable. If not met, the particle is penalized. This process is repeated until the maximum number of iterations is reached or the fitness value converges. Finally, the global optimal position is output, resulting in the optimized controller parameters.

[0094] like Figure 6 As shown, working condition I represents the inverter output power from (0-5kW), working condition II output power from (5-20kW), working condition III inverter carries a load (5kW) in an off-grid state, working condition IV inverter carries a load (10kW) in an off-grid state, and the power, current, voltage and frequency waveforms.

[0095] like Figure 7 As shown, working condition I represents the output power of the inverter with no inertia, fixed inertia and adaptive inertia is (0-10kW), working condition II output power is (10-20kW), working condition III represents the inverter with no inertia, fixed inertia and adaptive inertia carrying a load (5kW) in an off-grid state, and working condition IV represents the frequency waveform of the inverter with a load (10kW) in an off-grid state.

[0096] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A method for stabilizing an AHO virtual oscillation controller, characterized in that: The steps include: S10, establish the nonlinear model of GFM inverter in single grid-connected mode and multi-grid interconnected mode; S20, using numerical analysis to obtain the equilibrium point, linearize the equilibrium point, extract the linearized Jacobian matrix, and then design a multi-objective fitness function with the minimization of the real part of the eigenvalue as the core; S30, combined with the particle swarm intelligent search algorithm, optimizes the parameters affecting stability in the AHO virtual oscillation controller to ensure the dynamic stability of the power system under a wide range of operating conditions.

2. The AHO virtual oscillation controller stabilization method according to claim 1, wherein: Step S10 is specifically as follows: S11, construct the state space equation of AHO virtual oscillation controller based on Poincare bifurcation equation; S12, establishing a virtual oscillator grid-connected equation group and a virtual oscillator interconnection equation group based on the state space equation.

3. The AHO virtual oscillation controller stabilization method according to claim 2, wherein: In step S11, the state space equation of the AHO virtual oscillation controller is: in, 、 are the voltages on the capacitor and inductor in the AHO virtual oscillator respectively; 、 are the derivatives of the voltages on the capacitor and inductor in the AHO virtual oscillator, respectively; It is the nonlinear link in the AHO virtual oscillation controller; 、 It is the input of AHO virtual oscillation controller; is the oscillation frequency of the virtual oscillation controller; C is the virtual capacitance of the virtual oscillation controller.

4. The AHO virtual oscillation controller stabilization method according to claim 2, wherein: In step S12, the method for constructing the virtual oscillator grid-connected equation group is as follows: for the first inverter, in a stationary reference coordinate system, based on its current dynamic characteristic equation, a phase angle difference is introduced, where the phase angle difference is determined by the power transmitted by the inverter to the grid; then, using a rotation transformation, a dynamic equation of the projected current in the bus voltage coordinate system is obtained, thereby constructing a single inverter grid-connected system equation group; The construction method of the virtual oscillator interconnection equation group is as follows: take the island system composed of three interconnected inverters as the research object, set the local coordinate system of the first inverter as the global coordinate system, and define the j ( j =2,3) The angle difference between the local coordinate system and the global coordinate system of the inverter is ( j =2,3); then analyze the voltage / phase angle characteristics of each inverter, the line current dynamic characteristics, the line current dynamic equation in the global coordinate system, the load current dynamic characteristic equation, and the related algebraic relations, and finally obtain the system equations for the interconnection of multiple inverters.

5. The AHO virtual oscillation controller stabilization method according to claim 1, wherein: In step S30 , parameters affecting stability are selected according to the operation mode of the inverter, the number of inverters and their topology.

6. The AHO virtual oscillation controller stabilization method according to claim 5, characterized in that: When the first inverter is connected to the infinite inertia grid, in the stationary reference coordinate system, the parameters affecting stability are 、 、 ; In an island system consisting of three interconnected inverters, the parameters that affect stability are 、 、 、 、 、 、 、 、 、 and ; in, It is The convergence constant in the AHO virtual oscillation controller determines the convergence speed of AHO; 、 They are AHO controller Filter parameters; and They are the resistance and inductance values ​​of the RL filter respectively.

7. The AHO virtual oscillation controller stabilization method according to claim 1, wherein: Step S30 is specifically as follows: S31, initialize the particle swarm, including the number of particles, initial position and initial velocity; S32, substitute the current position of the particle into the objective function to evaluate the fitness. The objective function is the inverse of the sum of the absolute values ​​of the real parts of all eigenvalues ​​and a penalty term is added to ensure the stability of the system equation; S33, compare and update the individual optimal and global optimal positions, update the particle speed and position, and perform boundary processing on the positions that are out of range; S34, judge whether the system is stable according to the stability criterion of the equation group, and punish the particles if it is not satisfied; S35, continuously repeating steps S31 to S34 until the maximum number of iterations is reached or the fitness value converges, and finally outputting the global optimal position to obtain the optimized controller parameters.

8. An AHO virtual oscillation controller stabilization system, characterized in that: include: Nonlinear model building module, used to build nonlinear models of GFM inverters in single grid-connected and multi-grid interconnected modes; The objective function design module is used to obtain the equilibrium point using numerical analysis, linearize the equilibrium point, extract the linearized Jacobian matrix, and then design a multi-objective fitness function with the minimization of the real part of the eigenvalue as the core; The parameter optimization module is used to combine the particle swarm intelligent search algorithm to optimize the parameters affecting the stability of the AHO virtual oscillation controller, thereby ensuring the dynamic stability of the power system under a wide range of operating conditions.

9. An AHO virtual oscillation controller, characterized in that: The AHO virtual oscillation controller adopts the AHO virtual oscillation controller stabilization method according to any one of claims 1 to 7.

10. An adaptive inertia method based on the AHO virtual oscillation controller according to claim 9, characterized in that: The steps include: Get the frequency and frequency change rate output by the AHO virtual oscillation controller; The frequency and frequency change rate are formulated to express the inertia requirement of the power system for adaptively adjusting the inertia.

Images