阅读说明：本技术 大扰动下同步发电机/构网型逆变器交互振荡机理分析方法 (Method for analyzing interaction oscillation mechanism of synchronous generator/network-constructing type inverter under large disturbance ) 是由 叶华 裴玮 马腾飞 张国宾 王天昊 于 2021-07-28 设计创作，主要内容包括：一种大扰动下同步发电机/构网型逆变器交互振荡机理分析方法,首先建立同步发电机和构网型逆变器组成的孤岛系统非线性动力学模型,其次推导出能够有效表达振荡特性的孤岛系统时变参数二阶振荡器,再次采用多尺度法提取时变自然频率并分析影响时变频率的主要因素,最后通过不稳定判据揭示同步发电机和构网型逆变器交互振荡的物理机理。(A method for analyzing interactive oscillation mechanism of a synchronous generator/a network-forming type inverter under large disturbance includes the steps of firstly establishing an island system nonlinear dynamic model formed by the synchronous generator and the network-forming type inverter, secondly deducing a time-varying parameter second-order oscillator of the island system capable of effectively expressing oscillation characteristics, thirdly adopting a multi-scale method to extract time-varying natural frequency and analyze main factors influencing the time-varying frequency, and finally revealing the physical mechanism of interactive oscillation of the synchronous generator and the network-forming type inverter through instability criterion.)

1. A method for analyzing an interactive oscillation mechanism of a synchronous generator/network-forming type inverter under large disturbance is characterized by comprising the following steps: the method for analyzing the interactive oscillation mechanism of the synchronous generator/network-forming type inverter comprises the steps of firstly establishing an island system nonlinear dynamic model formed by the synchronous generator and the network-forming type inverter, secondly deducing an island system time-varying parameter second-order oscillator capable of effectively expressing oscillation characteristics, thirdly extracting time-varying natural frequency by adopting a multi-scale method and analyzing main factors influencing the time-varying frequency, and finally revealing the physical mechanism of the interactive oscillation of the synchronous generator and the network-forming type inverter through unstable criteria;

the method comprises the following steps:

step 1: establishing a grid-forming inverter dynamic differential equation containing a droop controller, and establishing a synchronous generator dynamic differential equation;

step 2: establishing a nonlinear oscillator dynamic model of a hybrid island system comprising a network-forming inverter and a synchronous generator;

and step 3: extracting time-varying natural frequency by adopting a multi-scale perturbation method, and revealing a parametric oscillation physical mechanism of a nonlinear oscillator of a hybrid island system containing a network-forming inverter and a synchronous generator;

and 4, step 4: and deducing parametric oscillation stability criterion for inducing the interactive oscillation according to the interactive oscillation physical mechanism of the synchronous generator and the network-forming inverter.

2. The method for analyzing the mutual oscillation mechanism of the synchronous generator/grid-connected inverter according to claim 1, wherein: in the step 1, the dynamic differential equation of the grid-connected inverter with the droop controller is established by considering the quick adjustment characteristic of the grid-connected inverter as follows:

in equations (1) to (3), where points on the variables represent derivatives, i represents a grid-type inverter node, ω_refIs a reference value of angular frequency; omega_iIs a grid-type inverter angular frequency, delta_iRepresenting the phase angle of the grid-type inverter relative to a reference value; m is_PiFor droop control coefficient, P, of network-forming inverter_eiIs the active power output, V, of the network-forming inverter_iAnd V_jRespectively is the voltage amplitude of the port of the grid-connected inverter and the internal voltage amplitude of the synchronous generator; the network-building inverter and the synchronous generator hybrid system are equivalent by adopting a Kron simplification method, and G is_iiIs the equivalent local conductance load, | Y_ijI and beta_ijAre each Y_ijAbsolute value and phase angle of (Y)_ijIs the connection admittance between the network-building inverter and the synchronous generator.

3. The method for analyzing the mutual oscillation mechanism of the synchronous generator/grid-connected inverter according to claim 1, wherein: the nonlinear oscillator dynamic model of the grid-type inverter and synchronous generator hybrid island system established in the step 2 is as follows:

in the formula, delta_ijIs a relative phase angle, beta, of a network-structured inverter and a synchronous generator_ijIs the phase angle of the connection admittance between the grid-forming inverter and the synchronous generator, F is the amplitude of the pumping function, P_disIs an equivalent disturbance function, D₀＝ω_refm_PiV_iV_j|Y_ijI and D₀cos(δ_ij+β_ij) Defined as the equivalent damping coefficient, while ω_nReferred to as natural oscillation frequency:

in the formula, ω_nIs the natural frequency of oscillation, omega_refIs a reference value of angular frequency, M_jIs the inertia time constant of the synchronous generator, V_iAnd V_jRespectively, the voltage amplitude of the port of the grid-connected inverter and the internal voltage amplitude, | Y, of the synchronous generator_ijIs Y |)_ijAbsolute value of (A) and Y_ijIs a connection admittance between a network-forming inverter and a synchronous generator; the pump function F sin (2 δ) in equation (8) takes into account the coupling effect of active and reactive power control_ij+2β_ij) Of amplitude ofWherein coefficient c_i＝ω_refm_Pik_im_QiWherein k is_iIs the gain, m, of the grid-forming inverter integral controller_QiIs the reactive voltage droop coefficient, and the equivalent disturbance P in equation (8)_disComprises the following steps:

in the formula (10), B_iiIs a grid-type inverter side local susceptance, P_disIs an equivalent disturbance function, ω_refIs a reference value of angular frequency, M_jIs the inertia time constant of the synchronous generator, V_iAnd V_jRespectively, the voltage amplitude of the port of the grid-connected inverter and the internal voltage amplitude, G, of the synchronous generator_iiAnd G_jjIs the equivalent local conductance load, | Y_ijI and beta_ijAre each Y_ijAbsolute value and phase angle of (Y)_ijIs the connection admittance, delta, between the grid-forming inverter and the synchronous generator_ijIs a relative phase angle, beta, of a network-structured inverter and a synchronous generator_ijThe phase angle of the connection admittance between the network-building inverter and the synchronous generator.

4. The method for analyzing the mutual oscillation mechanism of the synchronous generator/grid-connected inverter according to claim 1, wherein: in the step 3, the physical mechanism of the parametric oscillation of the nonlinear oscillator of the hybrid island system comprising the network-structured inverter and the synchronous generator is as follows:

in the formula:

whereinh represents a parametric resonance factor, ε is compared to ω_nA smaller amount;

equation (15) introduces the term hcos (2 ω) of two times the natural frequency_nt); the existence of the two times of natural frequency terms plays a crucial role in triggering parametric oscillation;

deriving the above equation as approximationWherein the inertia of the system is M ═ M_j(1+hcos(2ω_nt)) and varies periodically with twice the natural frequency;

further to the explanation of the mechanism of parametric oscillation caused by two times of the natural frequency, external energy is applied to the system by the pumping function of equation (14) so that the kinetic energy isPeriodic variation of amplitude thereofAnd (4) increasing. When energy is accumulated in the form of potential energy, i.e.The total energy increases and accordingly triggers a parametric oscillation.

5. The method for analyzing the mutual oscillation mechanism of the synchronous generator/grid-connected inverter according to claim 1, wherein: in the step 4, the parameter oscillation stability criterion for inducing the interactive oscillation is derived based on the interactive oscillation physical mechanism of the synchronous generator and the network-forming inverter as follows:

in the above equation, ε represents a small parameter, the presence of a range of ε means that the system satisfies the instability condition, and the range of ε decreases as the damping ratio ξ increases. In order to ensure the stability of the system, the value range of epsilon needs to be reduced or even eliminated; omega_nIs called natural oscillation frequency, h represents parametric resonance factor;

the nonlinear factor is an intrinsic cause of parametric oscillation, which is analytically derived from equations (14), (15) and (18) with the nonlinear factor being twice the natural frequency. Amplification or attenuation of parametric oscillations depends on h²And 16 ξ²The balance between, however, h and ξ are both time-varying parameters; when the damping is relatively low, i.e. h²＞16ξ²The parametric resonance is a possible factor causing the oscillation instability of the grid-structured inverter and the synchronous generator hybrid island system.

Technical Field

The invention relates to a synchronous generator/network-constructing-type inverter interactive oscillation mechanism analysis method.

Background

At present, a power system capable of effectively resisting large disturbance in a complex environment is constructed, and the method has important significance for realizing safe and reliable power supply and guaranteeing social and economic development. When the power system encounters scenes such as blackouts caused by extreme abnormal weather, the power system can operate in a plurality of island modes. At this time, the restoration and continuous power supply capability of the island power system can be supported by a grid type inverter (GFI) and conventional Synchronous Generators (SGs). However, when the grid-structured inverter and the conventional synchronous generator run in parallel in the island system, the response speed of the grid-structured inverter after large disturbance is high, and the dynamic response of the conventional synchronous generator is low, so that the oscillation instability phenomenon which may occur by interaction of the grid-structured inverter and the conventional synchronous generator threatens the safe and stable operation of the island power system.

In order to improve the restoring force and the safety stability of an island power system, a stabilizing mechanism of synchronous generator/grid-structured inverter interactive oscillation needs to be disclosed urgently. For an island micro-grid containing a synchronous generator and a grid-forming inverter, a small signal model is generally adopted to calculate multiple modes, so that a dominant oscillation mode is identified, but the small signal model cannot account for the influence of nonlinear factors under large disturbance. On the other hand, the Lyapunov function is generally used for large-disturbance stability analysis, however, the Lyapunov method cannot effectively and clearly reveal the oscillation instability mechanism. In general, under the condition of large disturbance, the large disturbance can periodically change system parameters, so that the interaction between the synchronous generator and the grid-type inverter is actually influenced by the time-varying parameters of the system.

Disclosure of Invention

The invention aims to overcome the defect that the existing small signal model and Lyapunov function analyze the large disturbance oscillation stability mechanism, and provides a method for analyzing the interaction oscillation mechanism of a synchronous generator/network-forming type inverter under large disturbance. The invention considers the problem of large-disturbance oscillation nonlinear dynamics, tries to solve the problem that the traditional subsynchronous/supersynchronous oscillation analysis method, such as a small-signal analysis method, is difficult to be directly applied, and can solve the problems of real-time monitoring of power grid oscillation and wave recording data loss.

The invention relates to an analysis method for interactive oscillation mechanism of a synchronous generator/a network-forming type inverter under large disturbance, which comprises the steps of firstly establishing an island system nonlinear dynamics model formed by the synchronous generator and the network-forming type inverter, secondly deducing an island system time-varying parameter second-order oscillator capable of effectively expressing oscillation characteristics, thirdly adopting a multi-scale method to extract time-varying natural frequency and analyze main factors influencing the time-varying frequency, and finally disclosing the physical mechanism of interactive oscillation of the synchronous generator and the network-forming type inverter.

The method comprises the following specific steps:

step 1: and establishing a dynamic differential equation of the grid-structured inverter with the droop controller, and establishing a dynamic differential equation of the synchronous generator.

In order to better simulate the quick adjustment characteristic of the grid-structured inverter, the delay effect of the active power measurement link of the converter is not considered, namely the grid-structured inverter-power grid dynamic differential algebraic equation with the droop effect only considered is expressed as follows:

in order to analyze the oscillation mechanism conveniently, a general dynamic differential algebraic equation of the synchronous generator is established by considering the slow response characteristic of the speed regulator of the synchronous generator compared with a current converter as follows:

in the formulas (1) to (6), points on the variables represent derivatives, i and j represent a grid-type inverter port node and a synchronous generator internal node, respectively, and ω_refIs a reference value for the angular frequency. Symbol omega_iAnd ω_jRespectively the angular frequency of the grid-connected inverter and the angular frequency of the synchronous generator, delta_iAnd delta_jRepresenting the phase angle of the grid inverter relative to a reference value and the phase angle of the synchronous generator relative to a reference value. Defining the relative angular velocity and phase angle as ω_ij＝ω_i-ω_jAnd delta_ij＝δ_i-δ_j，m_PiFor droop control coefficient, M, of network-forming inverter_jIs the synchronous generator inertia time constant. P_eiAnd P_ejIs the active power output of the network-forming inverter and the active power output of the synchronous generator, V_iAnd V_jRespectively, the internal voltage amplitude of the grid-connected inverter and the internal voltage amplitude of the synchronous generator. Consider the network-forming inverter and synchronous generator hybrid system equivalent circuit, G, in FIG. 2_iiAnd G_jjIs the equivalent local conductance load, | Y_ijI and beta_ijAre each Y_ijAbsolute value and phase angle of, and Y_ijIs the connection admittance between the network-building inverter and the synchronous generator.

Step 2: and establishing a nonlinear oscillator dynamic model of a hybrid island system comprising a network-forming inverter and a synchronous generator.

Subtracting formula (4) from formula (1), subtracting formula (5) from formula (2), and combining the formulas to obtain:

in the formula, delta_ijIs the relative phase angle of the network-structured inverter and the synchronous generator,for the second derivation of the relative phase angles, omega, of the network-forming inverter and synchronous generator_refIs a reference value of angular frequency, m_PiFor droop control coefficient, P, of network-forming inverter_eiAnd P_ejActive power output of a network-forming inverter and of a synchronous generator, M_jIs the synchronous generator inertia time constant. Formula (3) and formula (6) are used instead of formula (7)And P_ejThen, rearranging to obtain a new equation, namely a nonlinear oscillator:

in the formula (I), the compound is shown in the specification,for the second derivation of the relative phase angles of the grid-connected inverter and the synchronous generator, beta_ijIs the phase angle of the connection admittance between the grid-forming inverter and the synchronous generator, D₀＝ω_refm_PiV_iV_j|Y_ijI and D₀ cos(δ_ij+β_ij) Which may be defined as an equivalent damping coefficient. While F is the amplitude of the pumping function, P_disIs an equivalent disturbance function, ω_nReferred to as natural oscillation frequency:

in the formula (9), the time constant M is dependent on the inertia_jOf natural frequency ω_nAnd is increased. In addition, the equivalent damping coefficient D₀And natural vibrationOscillation frequencyDepending on the grid operating conditions. Taking the increased load as the disturbance of the system, taking into account the coupling effect of the active and reactive power control, the pumping function Fsin (2 δ) in equation (8)_ij+2β_ij) Of amplitude of Wherein coefficient c_i＝ω_refm_Pik_im_QiWherein k is_iIs the gain, m, of the grid-forming inverter integral controller_QiIs the reactive voltage droop coefficient. In addition, the equivalent disturbance P in the equation (8)_disComprises the following steps:

in the formula (10), B_iiIs a grid-type inverter side local susceptance, P_disIs an equivalent disturbance function, ω_refIs a reference value of angular frequency, M_jIs the inertia time constant of the synchronous generator, V_iAnd V_jRespectively, the voltage amplitude of the port of the grid-connected inverter and the internal voltage amplitude, G, of the synchronous generator_iiAnd G_jjIs the equivalent local conductance load, | Y_ijI and beta_ijAre each Y_ijAbsolute value and phase angle of (Y)_ijIs the connection admittance, delta, between the grid-forming inverter and the synchronous generator_ijIs a relative phase angle, beta, of a network-structured inverter and a synchronous generator_ijThe phase angle of the connection admittance between the network-building inverter and the synchronous generator.

Since r/x ≠ 0 in an island microgrid, the grid-structured inverter reactive voltage droop control loop has an influence on the active power of the injection system, and the influence of the reactive power on the active power can be expressed as energy transfer in the form of a pump function.

And step 3: a multi-scale perturbation method is adopted to extract time-varying natural frequency, main factors influencing the time-varying frequency are analyzed, and a physical mechanism of parametric oscillation of a nonlinear oscillator of a hybrid island system comprising a network-forming inverter and a synchronous generator is disclosed.

For stability analysis, the synchronous generator/grid inverter hybrid system is built as a nonlinear oscillator, as shown in equation (8), and equation (8) is further rewritten to the form of a daphen oscillator by changing the phase angle and approximating the nonlinear term, as follows

Where gamma is xi omega_nF is the amplitude of the pumping function, P_disIs an equivalent disturbance function, ω_nReferred to as the natural oscillation frequency, ξ is the equivalent damping ratio.

In formula (12), M_jIs the inertia time constant of the synchronous generator, m_PiThe droop control coefficient of the network-forming type inverter is disclosed.

The invention adopts a multi-scale perturbation method to solve the formula (11). To reveal the nonlinear parametric oscillation mechanism of daphne oscillator, assume delta_ij(t) contains a perturbation term δ_d(t) and can be expressed by a lower order solution:

δ_ij(t)＝δ₀e^-γtcos(ω_nt)+δ_d(t) (13)

wherein delta₀Is the initial value of the oscillation trajectory, delta, of the system after being disturbed_d(t) is a perturbation term.

Substituting formula (13) for formula (11), recombining with delta_d(t) the associated terms, then ignoring higher order terms, yields:

in the formula

Whereinε is compared to ω_nThe smaller quantity, F ', being the correction value of the amplitude of the pump function, P'_disIs a correction value of the equivalent disturbance function.

Notably, the non-linear term in equation (11)When inserting (13), the term of two times natural frequency is introduced, namely, hcos (2 omega)_nt). The presence of the two times natural frequency term (h ≠ 0) plays a crucial role in the triggering of parametric oscillations. By inserting the formula (9) in the formula (15), the above equation is derived to be approximated asWherein the inertia of the system is M ═ M_j(1+hcos(2ω_nt)) and varies periodically with twice the natural frequency. Further to the explanation of the mechanism of parametric oscillation caused by two times of the natural frequency, external energy is applied to the system by the pumping function of equation (14) so that the kinetic energy isPeriodic variation of amplitude thereofAnd (4) increasing. When energy is accumulated in the form of potential energy, i.e.The total energy increases and accordingly triggers a parametric oscillation.

And 4, step 4: and deducing parametric oscillation stability criterion for inducing the interactive oscillation according to the interactive oscillation physical mechanism of the synchronous generator and the network-forming inverter.

Assuming a lower order solution of equation (14):then, delta is added_d(t) substituting equation (14) and recombining the resulting equations to obtain the relationship of a (t) and b (t) as follows:

in the above formula, the points on the variables represent derivatives, a (t) and b (t) are coefficients of the lower order solution, ω_nThe natural oscillation frequency is the natural oscillation frequency, f is the equivalent damping ratio, and h is the oscillation starting factor of the nonlinear oscillator.

Time-dependent characteristics of a (t) and b (t) can be determined fromIs determined, i.e. isThe characteristic equation obtained from equation (16) is as follows:

in the above formula, λ is a characteristic value variable, λ_iIs the ith characteristic value. Wherein when at least one characteristic value is a positive number, δ_d(t) will increase continuously. Therefore, the parametric amplification condition can be derived from equation (17), i.e., can be used as a destabilization criterion for parametric oscillation:

in the above equation, the presence of the range of ε means that the system satisfies the instability condition, and the range of ε decreases as the damping ratio ξ increases. In order to ensure the stability of the system, the value range of epsilon needs to be reduced or even eliminated.

In summary, the nonlinear factor is regarded as twice the natural frequency, and the nonlinear factor is found through formula analysis and derivation, and is an inherent cause of parametric oscillation. Amplification or attenuation of parametric oscillations depends on h²And 16 ξ²Balance between them; however, h and ξ are both time-varying parameters. When the damping is relatively low, i.e. h²＞16ξ²The parametric resonance may cause instability of oscillation of the grid-tied inverter and synchronous generator hybrid island system.

Drawings

FIG. 1 is a flow chart of a method for analyzing an interactive oscillation mechanism of a synchronous generator/network-forming inverter under large disturbance;

FIG. 2 is a schematic diagram of an independent microgrid system including a grid-configured inverter and a synchronous generator heterogeneous power source;

FIG. 3 is a multi-stage multi-ring and additional amplitude and phase control frame diagram of the grid type voltage source converter;

FIG. 4 is a schematic diagram of a two-machine four-node microgrid test system;

fig. 5a, 5b, 5c, 5d show the unstable area of resonance and the phase plane trajectory, where the unstable area ξ in fig. 5a is 0.081, the unstable area ξ in fig. 5b is 0.065, and fig. 5c is a damping ratio curve; FIG. 5d is a phase plan view;

FIG. 6a, FIG. 6b, FIG. 6c stability index and simulation results; wherein, fig. 6a is a stability index curve, fig. 6b is a nonlinear oscillator phase angle curve, and fig. 6c is a nonlinear oscillator angular velocity curve; the solid line in the figure is case 1(case 1) with active power recovery and the dashed line is case 2(case2) with active and no power recovery.

Detailed Description

The invention is further described with reference to the following detailed description in conjunction with the accompanying drawings.

The method for analyzing the interactive oscillation mechanism of the synchronous generator/network-constructing-type inverter under the large disturbance comprises the following steps:

step 1: and establishing a dynamic differential equation of the grid-structured inverter with the droop controller, and establishing a dynamic differential equation of the synchronous generator.

In order to better simulate the quick adjustment characteristic of the grid-structured inverter, the delay effect of the active power measurement link of the converter is not considered, namely the grid-structured inverter-power grid dynamic differential algebraic equation with the droop effect only considered is expressed as follows:

in order to conveniently analyze the oscillation mechanism, the response characteristic of the speed regulator can be ignored in consideration of the slow response characteristic of the speed regulator of the synchronous generator compared with the slow response characteristic of the inverter, and a dynamic differential algebraic equation of the synchronous generator is established as follows:

in equations (1) to (6), where points on the variables represent derivatives, i and j represent grid-type inverter internal nodes and synchronous generator internal nodes, respectively, ω_refIs a reference value for the angular frequency. Symbol omega_iAnd ω_jRespectively the angular frequency of the grid-connected inverter and the angular frequency of the synchronous generator, delta_iAnd delta_jRepresenting phase angle of grid-connected inverter with respect to reference value and synchronous power generationThe phase angle of the machine relative to a reference value. Defining the relative angular velocity and phase angle as ω_ij＝ω_i-ω_jAnd delta_ij＝δ_i-δ_j，m_PiFor droop control coefficient, M, of network-forming inverter_jIs the synchronous generator inertia time constant. P_eiAnd P_ejIs the active power output, V, of the network-forming inverter and synchronous generator_iAnd V_jRespectively, the internal voltage amplitude of the grid-connected inverter and the internal voltage amplitude of the synchronous generator.

FIG. 2 shows an equivalent circuit of a hybrid system of a grid-type inverter and a synchronous generator, wherein the grid-type inverter and the synchronous generator are connected by a pi-type equivalent circuit, G_iiAnd G_jjIs the equivalent local conductance load, | Y_ijI and beta_ijAre each Y_ijAbsolute value and phase angle of, and Y_ijIs the connection admittance between the network-building inverter and the synchronous generator. Fig. 3 is a control block diagram of the network-forming inverter, which mainly includes active and reactive power calculations, a filter, a droop control link, an additional control loop, a voltage control loop, a current control loop, and a PWM wave generation link. The active and reactive calculation and filter collects data from the external power distribution network and the port of the network-building type converter, such as the angular speed of a synchronous generator in the external power distribution network, the effective value of the voltage of the port and the like.

Step 2: and establishing a nonlinear oscillator dynamic model of a hybrid island system comprising a network-forming inverter and a synchronous generator.

Subtracting formula (4) from formula (1) and subtracting formula (5) from formula (2), respectively, and then combining the formulas:

formula (3) and formula (6) are used instead of formula (7)And P_ejThen rearranging to obtain a new equation, namely a nonlinear oscillation oscillator:

in the formula, D₀＝ω_refm_PiV_i0V_j0|Y_ij0I and D₀ cos(δ_ij+β_ij) Which may be defined as an equivalent damping coefficient. At the same time, ω_nReferred to as natural oscillation frequency:

in the formula (9), the time constant M is dependent on the inertia_jOf natural frequency ω_nAnd is increased. In addition, the equivalent damping coefficient D₀And natural oscillation frequencyDepending on the grid operating conditions, the subscript 0 represents the initial values of the corresponding variables after the system has been subjected to large disturbances. Taking the increased load as the disturbance of the system, taking into account the coupling effect of active and reactive power control, the pumping function F sin (2 δ) in equation (8)_ij+2β_ij) The amplitude is:

coefficient of equation c_i＝ω_refm_Pik_im_QiWherein k is_iIs the gain, m, of the grid-forming inverter integral controller_QiIs the reactive voltage droop coefficient, as shown in fig. 3. In addition, the equivalent disturbance P in the equation (8)_disComprises the following steps:

and 4, step 4: and deducing parametric oscillation stability criterion for inducing the interactive oscillation according to the interactive oscillation physical mechanism of the synchronous generator and the network-forming inverter.

Assuming a lower order solution of equation (14):then, delta is added_d(t) substituting equation (14) and recombining the resulting equations to obtain the relationship of a (t) and b (t) as follows:

the time-dependent properties of a (t) and b (t) in the above formula can be represented byIs determined, i.e. isThe characteristic equation obtained from equation (16) is as follows:

wherein when at least one characteristic value is a positive number, δ_d(t) will increase continuously. Therefore, the parametric amplification condition can be derived from equation (17), i.e., can be used as a destabilization criterion for parametric oscillation:

in the above equation, the presence of the range of ε means that the system satisfies the instability condition, and the range of ε decreases as the damping ratio ξ increases. In order to ensure the stability of the system, the value range of epsilon needs to be reduced or even eliminated.

In order to verify the effectiveness of the provided method for analyzing the interactive oscillation mechanism of the synchronous generator/grid-structured inverter and the correctness and rationality of the implementation steps, in the embodiment of the invention, a 4-node two-machine micro-grid system shown in fig. 4 is adopted by means of simulation software Matlab/Simulink/SimPowerSystem, wherein the two machines are respectively a diesel synchronous generator and an energy storage system based on a grid-structured converter.

Assuming that the islanded microgrid performs load recovery, the maximum and minimum values of the natural frequency can be approximately calculated using equation (9), as shown by the dashed lines in fig. 5a and 5 b. Further using the instability criterion in equation (18), the instability region of the system can be obtained, as shown by the shaded area in fig. 5a and 5 b. As the damping ratio decreases, the unstable region increases. As shown in equation (12), the damping ratio ξ (δ)_ij) Is delta_ijIndicating that the unstable region is time-varying. Assume two cases, the first case 1 is to recover 100% of the active power load, and the second case2 is to recover 100% of the active and reactive power. In the latter case, the damping ratio curve is along delta at full load recovery compared to the former case_ijThe shaft negative half-shaft moves as shown in fig. 5 c. When the actual operation value delta_ijMoving to the left and beyond the point, parametric resonance instability may occur. Further using the low-order solution of equation (13), a phase plan of the oscillation trajectory is plotted as shown in fig. 5d, and the result shows that the system has resonance instability under 100% full load recovery with active and reactive power.

To verify the above analysis, a high-order electromagnetic transient simulation model of the system shown in fig. 4 was built in Matlab/Simulink. Adopting instability criterion to obtain h under the two conditions²-16ξ²As shown in fig. 6 a. As can be seen from FIG. 6a, when h is satisfied²-16ξ²And when the condition is more than or equal to 0, the criterion can be used as a prediction index of the instability of the system. In Matlab/Simulink, the relative phase angle and angular frequency between the two generators is shown in fig. 6b and 6 c. For case 1, the system is kept stable, and for case2, the system is unstable in resonance, and the simulation result verifies the effectiveness of the stability criterion provided by the invention.