Energy-function-based transient stability evaluation method for grid-connected system including multiple virtual synchronous generators

Abstract

The present invention relates to an energy-function-based transient synchronization stability evaluation method for a grid-connected system including multiple virtual synchronous generators, the method comprising the following steps: constructing a system non-linear reduced-order mathematical model suitable for transient synchronization stability analysis; taking into consideration dynamic strong coupling of active power control and reactive power control and dynamic interaction of multiple virtual synchronous generators, analyzing and constructing an energy function of the system; by means of the closest unstable equilibrium point method and an optimization method, respectively calculating a maximum energy value for ensuring system stability and a maximum energy value for ensuring that the system does not trigger current amplitude limiting under the condition that the system does not trigger current amplitude limiting after fault removal; taking the smaller value of the two to obtain a critical energy value for ensuring transient stability of the system; calculating a trajectory of the system during the fault by means of numerical integration to obtain the state of the system at the moment of fault removal; substituting the state of the system at the moment of fault removal into the energy function to calculate an energy function value of the system at the moment of fault removal; and evaluating transient synchronization stability of the system.

Description

Transient stability assessment method for grid-connected systems with multiple virtual synchronous machines based on energy function Technical Field

[0001] This invention belongs to the field of transient stability analysis of power electronic power systems. It proposes a transient synchronization stability evaluation method based on energy function for multi-virtual synchronous machine grid-connected systems under grid faults to address the transient synchronization stability problem of multi-virtual synchronous machine grid-connected systems. Background Technology

[0002] With the development of new energy sources, grid-connected converters, which are designed for power output, are gradually replacing traditional synchronous generators, resulting in a gradual reduction in grid forced inertia and short-circuit capacity. [1]-[2] To address this problem, academia and industry have proposed various network-based control technologies, among which the virtual synchronous generator (VSG) is a promising solution. [3] VSG, by simulating a synchronous generator, exhibits voltage source characteristics externally, possessing voltage and frequency support capabilities. [4] However, similar to synchronous machines, VSGs also face the risk of transient synchronization instability under large disturbances such as faults. [5] .

[0003] Unlike synchronous machines, the active and reactive power loops in VSG control have similar time scales. The coupling of active and reactive power control can severely affect the transient synchronization characteristics of the system. [6] Furthermore, due to the converter's weak current withstand capability, a current limiting strategy is designed into the converter, which transforms the VSG system into a switching system. [7]-[8] These two differences make the transient characteristics of multi-VSG grid-connected systems more complex, and the energy function method, which is suitable for transient stability analysis of traditional synchronous machine systems, may no longer be applicable. Therefore, it is necessary to analyze the transient synchronization stability of multi-VSG grid-connected systems under strong coupling of current limiting and active and reactive power control.

[0004] Most existing studies focus on single-grid converter systems. Specifically, reference [9] uses the equal area method to reveal the influence mechanism of active and reactive power control coupling on the transient synchronization stability of the system. References

[0010] -

[0011] analyze and construct the energy function of the system, propose transient synchronization stability criteria, and characterize the transient stability boundary of the system. In order to reduce the conservatism of stability assessment, references

[0012] -

[0013] use numerical methods, such as the phase trajectory method and the iterative equal area method, to quantitatively analyze the transient synchronization stability of a single-grid system under the action of active and reactive power control coupling. The above studies ignore the influence of the VSG current limiting control link on the transient stability of the system. Reference

[0014] points out that under severe faults, the VSG will trigger current limiting, thereby switching from voltage control mode to current control mode, which makes the system a switching system and the transient characteristics more complex. References

[0015] -

[0016] derived the power angle curves of VSGs under voltage control mode and current control mode, and revealed the transient synchronization instability mechanism of the system under switching dynamics based on the equal area rule, and analyzed the influence of different current limiting angles on the acceleration and deceleration areas. It should be noted that most of the above studies assume that the control mode switching occurs at the intersection of the power angle curve under normal voltage control mode and the power angle curve under current limiting control mode. References

[0017] -

[0018] pointed out that this assumption does not hold in general, and derived the conditions for system mode switching, and analyzed the influence of system parameters on the switching conditions. However, the above studies only considered a single VSG and did not consider the interaction between multiple VSGs. Therefore, the proposed model and analysis method cannot solve the transient synchronization stability problem of multi-VSC grid-connected systems.

[0005] For multi-VSG grid-connected systems, the interaction between VSGs not only affects the input active and reactive power of the VSGs but also their output current, thus influencing the switching conditions of the current limiter and making the transient synchronization stability analysis of multi-VSG grid-connected systems more complex. Currently, only a few studies, such as

[0019] -

[0023] , have analyzed the transient synchronization stability of systems with multi-machine interaction while neglecting the influence of current limiting. References

[0019] -

[0020] neglect the influence of active and reactive power control coupling, i.e., considering the reactive power loop as a constant voltage output, and quantitatively analyze the transient synchronization stability of the system by referencing the energy function method used in multi-synchronous machine systems. To further reduce the conservatism of the analysis results, reference

[0021] proposes a damping energy approximation method to quantitatively describe the damping energy. However, none of the above studies have considered the influence of active and reactive power control coupling. Considering the influence of active and reactive power control coupling, references

[0022] -

[0023] analyze the transient stability of the system from the perspectives of mechanism analysis and quantitative evaluation, respectively. Reference

[0022] takes into account the effects of active and reactive power control coupling and multi-machine interaction, and establishes a nonlinear mathematical model of a multi-VSG grid-connected system. It uses the equal area method to reveal the transient synchronization instability mechanism of the system under fault conditions. Reference

[0023] considers active and reactive power control coupling, and numerically constructs the Lyapunov function of a two-VSG system based on the TS method, quantitatively analyzing the transient synchronization stability of the system. However, the computation time of the TS method is exponentially related to the number of nonlinearities in the system, making it difficult to apply to the transient synchronization stability analysis of a N-VSG grid-connected system. In summary, considering the effects of active and reactive power control coupling and multi-machine interaction, the methods proposed in the above studies are insufficient for quantitatively analyzing the transient synchronization stability of a N-VSG grid-connected system. More importantly, references

[0019] -

[0023] also do not consider the effect of current limiting.

[0006] Considering the impact of current limiting, current literature

[0024] uses the energy function method to analyze the transient synchronization stability of multi-VSG grid-connected systems. However, literature

[0024] neglects the influence of active and reactive power control coupling. In fact, active and reactive power control coupling can worsen the transient synchronization stability of the system. Therefore, for the transient synchronization stability problem of multi-VSG grid-connected converter systems, the influence of active and reactive power control coupling must be taken into account.

[0007] Related literature:

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[0017]

[0010] S.Tang,X.Fu,Z.Tian,et al,"Third-Order Energy Function Modelling Approach for Grid-Forming Converters,"2024 IEEE 10th International Power Electronics and Motion Control Conference(IPEMC2024-ECCE Asia),Chengdu,China,2024,pp.4038-4041.

[0018]

[0011] Y.Fan,M.Han,S.Wang,et al,"Transient Stability Analysis of Grid-Forming Converter in Current Limiting Mode Based on Hamiltonian Theory,"IEEE Trans.Power Delivery,Early Access.

[0019]

[0012] M.Chen,D.Zhou,F.Blaabjerg,"Enhanced Transient Angle Stability Control of Grid-Forming Converter Based on Virtual Synchronous Generator,"IEEE Trans Industrial Electronics,vol.69,no.9,pp.9133-9144,Sept.2022.

[0020]

[0013] X.Li,C.Shen,X.Liu,et al,"Transient Stability Analysis for Grid-Tied VSG Considering High-Order Nonlinear Interactions Between Active and Reactive Power Control Loops,"IEEE Trans.Power Electronics,vol.39,no.6,pp.6974-6988,June 2024.

[0021]

[0014] H.Xin,L.Huang,L.Zhang,et al,"Synchronous Instability Mechanism of P-f Droop-Controlled Voltage Source Converter Caused by Current Saturation,"IEEE Trans.Power Systems,vol.31,no.6,pp.5206-5207,Nov.2016.

[0022]

[0015] K.G.Saffar,S.Driss,F.B.Ajaei,"Impacts of Current Limiting on the Transient Stability of the Virtual Synchronous Generator,"IEEE Trans.Power Electronics,vol.38,no.2,pp.1509-1521,Feb.2023.

[0023]

[0016] E.Rokrok,T.Qoria,A.Bruyere,et al,"Transient Stability Assessment and Enhancement of Grid-Forming Converters Embedding Current Reference Saturation as Current Limiting Strategy,"IEEE Trans.Power Systems,vol.37,no.2,pp.1519-1531,March 2022.

[0024]

[0017] B.Fan,X.Wang,"Fault Recovery Analysis of Grid-Forming Inverters With Priority-Based Current Limiters,"IEEE Trans.Power Systems,vol.38,no.6,pp.5102-5112,Nov.2023.

[0025]

[0018] Y.Li,Y.Lu,J.Yang,et al.,"Transient Stability of Power Synchronization Loop Based Grid Forming Converter,"IEEE Trans.Energy Conversion,vol.38,no.4,pp.2843-2859,Dec.2023.

[0026]

[0019] M.Choopani,S.H.Hosseinian,B.Vahidi,"New Transient Stability and LVRT Improvement of Multi-VSG Grids Using the Frequency of the Center of Inertia,"IEEE Trans.Power Systems,vol.35,no.1,pp.527-538,Jan.2020.

[0027]

[0020] L.Chen,J.Tang,X.Qiao,et al,"Investigation on Transient Stability Enhancement of Multi-VSG System Incorporating Resistive SFCLs Based on Deep Reinforcement Learning,"IEEE Trans.Industry Applications,vol.60,no.1,pp.1780-1793,Jan.-Feb.2024.

[0028]

[0021] Q. Qu, X. Xiang, J. Lei, et al., "Transient Stability Analysis for Paralleled System of Virtual Synchronous Generators Based on Damping Energy Visualization and Approximation," IEEE Trans. Power Electronics, vol. 39, no. 12, pp. 15785 - 15799, Dec. 2024.

[0029]

[0022] J. Wang, X. Zhang, M. Li, "Transient Stability Analysis and Improvement of Mult - paralleled Virtual Synchronous Generators Grid - Connected System," IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 12, no. 4, pp. 4094 - 4105, Aug. 2024.

[0030]

[0023] H. Cheng, Z. Shuai, C. Shen, et al., "Transient Angle Stability of Paralleled Synchronous and Virtual Synchronous Generators in Islanded Microgrids," IEEE Trans. Power Electronics, vol. 35, no. 8, pp. 8751 - 8765, Aug. 2020.

[0031]

[0024] Y. Li, Y. Lu, J. Yang, et al., "Synchronization Stability of Multiple VSGs Embedded Power System With Controller Limits," IEEE Trans. Power Systems, Early Access. Summary of the Invention

[0032] The purpose of this invention is to disclose a quantitative evaluation method for the transient synchronization stability of a multi-virtual synchronous machine (MPSM) grid-connected system under grid fault conditions. First, the MPSM grid-connected system under grid fault conditions is reasonably simplified, and a nonlinear reduced-order mathematical model of the system is established. Then, considering the strong dynamic coupling of active and reactive power control and the dynamic interaction of the multiple MPSMs, the energy function of the MPSM grid-connected system is analytically constructed. Next, using the nearest unstable equilibrium point method and optimization methods, the maximum energy value that guarantees system stability without triggering current limiting and the maximum energy value that guarantees system stability without triggering current limiting are calculated, respectively. The minimum of these two values ​​is taken to obtain the critical energy value that guarantees the transient stability of the system. Based on this, a transient synchronization stability criterion is proposed. The technical solution is as follows:

[0033] A method for evaluating the transient synchronization stability of a multi-virtual synchronizer grid-connected system includes the following steps:

[0034] Step 1: Ignore the fast-time-scale dynamics of the virtual synchronous machine, including voltage control and current control, and consider the strong coupling of active and reactive power control dynamics and the dynamic interaction of multiple virtual synchronous machines. Construct a nonlinear reduced-order mathematical model of the multi-virtual synchronous machine grid-connected system suitable for transient synchronization stability analysis.

[0035] Step 2: Consider the dynamic strong coupling of active and reactive power control and the dynamic interaction of multiple virtual synchronous machines, and analyze the energy function of the grid-connected system with multiple virtual synchronous machines.

[0036] Step 3: Using the nearest unstable equilibrium point method and optimization method, calculate the maximum energy value that ensures system stability and the maximum energy value that ensures system stability without triggering current limiting in the multi-virtual synchronous machine grid-connected system after fault clearing; take the minimum of the two values ​​to obtain the critical energy value that ensures system transient stability.

[0037] Step 4: Calculate the trajectory of the multi-virtual synchronous machine grid-connected system during the fault period through numerical integration to obtain the system state at the time of fault clearing; substitute the state of the multi-virtual synchronous machine grid-connected system at the time of fault clearing into the energy function to calculate the energy function value of the multi-virtual synchronous machine grid-connected system at the time of fault clearing.

[0038] Step 5: Compare the energy function value of the multi-virtual synchronous machine grid-connected system at the fault clearing time with the critical energy value obtained in Step 3 to evaluate the transient synchronization stability of the multi-virtual synchronous machine grid-connected system.

[0039] Furthermore, the nonlinear reduced-order mathematical model of the multi-virtual synchronous machine grid-connected system constructed in the first step is expressed as follows: In the formula δ i and ω i They represent VSG respectively iThe difference between the output phase angle and angular frequency and the phase angle and angular frequency of the infinite mains voltage; P refi J i , and D i They are VSG i Active power reference value, virtual inertia and damping coefficient; U i Q refi U refi D qi and K qi These are the voltage magnitudes at node i and VSG, respectively. i The reactive power reference value, voltage reference value, QV droop factor, and integral gain; B ij For the transfer susceptance from node i to j, B ig Let N be the transfer susceptance from node i to the infinite bus node; N is the number of virtual synchronous machines.

[0040] Furthermore, in the second step, the energy function of the multi-virtual synchronous machine grid-connected system is considered as the sum of the energy of all VSGs and the energy corresponding to the interaction between converters, specifically expressed as follows: In the formula V ki For VSG i The kinetic energy of the virtual rotor; V pi For VSG i Potential energy; V inter It is the energy exchanged between converters; V ki V pi and V inter The expressions are as follows:

[0041] Furthermore, the third step is as follows:

[0042] (1) According to the nearest unstable equilibrium point method, the maximum energy value V that ensures system stability under the condition that the system does not trigger current limiting after fault clearance. cr The calculation is as follows: In the formula, x = [δ1,ω1,U1,…,δ N ,ω N U N ] represents the state variables of a multi-virtual synchronous machine grid-connected system; let the dimension of the state space of the multi-virtual synchronous machine grid-connected system be n = 3N; set M is the set of all equilibrium points of the multi-virtual synchronous machine grid-connected system;

[0043] (2) Ensure the maximum energy value V that prevents the system from triggering current limiting after fault clearance. cL The following optimization problem is obtained: V cL =min V(δ,ω,U) In the formula I Mi For VSGi Maximum allowable current amplitude, I ti For VSG i The injected current;

[0044] (3) Obtain the critical energy value V that guarantees the transient stability of the system after fault clearance. c As shown below; V c =min{V cr V cL}

[0045] Furthermore, the energy function value of the multi-virtual synchronous machine grid-connected system at the fault clearing time was calculated to be V(x). c In the fifth step, the energy function value V(x) of the multi-virtual synchronous machine grid-connected system at the fault clearing time is compared. c ) and critical energy value V c The magnitude relationship is used to evaluate the transient synchronization stability of the system, as shown below; V(x) c )≤V c

[0046] If the above equation holds true, it means that the system can maintain transient synchronization and stability; if the above equation does not hold true, it means that the system may be transiently unstable.

[0047] The beneficial effects of this invention are as follows:

[0048] 1) The active and reactive power control characteristics of VSGs are retained, while the dynamics of voltage and current control with faster response times are ignored. A reduced-order mathematical model of a multi-converter grid-connected system considering the coupling of active and reactive power control and transient interactions among multiple VSGs under grid fault conditions is established. This greatly reduces the complexity of transient synchronization stability analysis of multi-VSG grid-connected systems under grid fault conditions.

[0049] 2) A quantitative evaluation method for transient synchronization stability of a multi-virtual synchronous machine grid-connected system based on energy function is proposed, which can be used to analyze the transient synchronization stability of the system after fault clearing. Attached Figure Description

[0050] Figure 1. Topology of a multi-VSG grid-connected system

[0051] Figure 2(a) VSG i (a) Control structure diagram; (b) Active and reactive power control structure

[0052] Figure 3. Schematic diagram of phase angle priority limiter

[0053] Figure 4. Schematic diagram of the system not entering the current limiting mode after a fault.

[0054] Figure 5. System energy change curve under Case 1.

[0055] Figure 6 Simulation results for Case 1: (a) Trajectory of VSG1; (b) Trajectory of VSG2

[0056] Figure 7. System energy variation curve under Case 2.

[0057] Figure 8 Simulation results for Case 2: (a) Trajectory of VSG1; (b) Trajectory of VSG2 Detailed Implementation

[0058] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0059] (I) Reduced-order model of multi-network converter grid-connected system under fault conditions

[0060] 1. System Description

[0061] The multi-VSG grid-connected system topology involved in this embodiment of the invention is shown in Figure 1. The system contains N VSGs, and the i-th VSG is denoted as VSG. i where i = 1, 2, ..., NL fi and C fi It's VSG i The filter's inductance and capacitance; U i ∠θ i and U g ∠θ g VSG i Output voltage and infinite bus voltage; X i and X g VSG i The equivalent reactance between the filter and the point of common coupling (PCC) and between the PCC and the infinite bus.

[0062] VSG i The control structure is shown in Figure 2. VSG i The control system includes active power control (APL), reactive power control (DRPL), and voltage-current inner loop control. VSG i The swing equation of the active control analog synchronous machine generates the angular frequency ω. vsgi and phase angle θ vsgi VSG i phase angle θ vsgi The phase angle difference between the voltage of the infinite bus and the voltage of the infinite bus is defined as the power angle δ. i As shown in equation (2).

[0063] δ i =θ vsgi -θ g =∫(ω vsgi -ω g)dt (1)

[0064] Consider VSG i The rated angular frequency ω0 and the angular frequency ω of the infinite bus voltage g They are equal, that is, ω0 = ω g Therefore, VSG can be obtained. i The active power control dynamics are as follows:

[0065] In the formula P refi J i , and D i They are VSG i The active power reference value, virtual inertia and damping coefficient.

[0066] VSG i The reactive power control adopts droop control to generate an internal voltage potential U. vsgi Its dynamic equation can be described as follows:

[0067] Q refi U refi D qi and k qi They are VSG i The reactive power reference value, voltage reference value, QV droop factor and integral gain;

[0068] VSG i The control objectives of the voltage inner loop and current inner loop are to achieve VSG. i Output voltage U i ∠θ i θ is generated by tracking the active power control loop and the reactive power control loop. vsgi and U vsgi To avoid VSG i Overcurrent is typically addressed by using a current limiter to restrict the q-axis and q-axis current reference generated by the voltage inner loop. This invention employs a phase angle-priority limiter, which can be mathematically expressed as equation (4).

[0069]

[0070] In the formula, x = x d +jx q , For VSG i Maximum allowable current amplitude This is a custom current phase angle.

[0071] When the amplitude of the current reference value generated by the voltage control loop is greater than I Mi At that time, the limiter was triggered, VSG iEntering rate limiting mode. It should be noted that when VSG... i When entering current-limiting mode, the voltage control loop and reactive power control loop will not function. Therefore, in current-limiting mode, the reactive power outer loop and voltage inner loop are locked, i.e., k qi =0, the integral coefficient of the voltage inner loop is equal to zero.

[0072] 2) Nonlinear price reduction mathematical model

[0073] Focusing on the synchronization stability problem, considering that the voltage and current inner loop dynamics of the VSG are usually much faster than the dynamics of the APL and DRPL, the following assumptions are made to simplify the analysis:

[0074] 1) Ignore the electromagnetic transients of the LC filter and AC network;

[0075] 2) Ignore the dynamics of the inner current loop, that is, assume that the VSG injected current can track the current reference value approximately in real time;

[0076] 3) During normal operation (limiter not triggered), ignore the voltage inner loop dynamics, U vsgi ∠θ vsgi ≈U i ∠θ i

[0077] Based on the above assumptions, we can obtain VSG i The equivalent circuit model is shown below. Clearly, in normal operating mode, the VSG can be... i It is considered a controllable voltage source. In current-limiting mode, VSG i It becomes a controllable current source.

[0078] Based on the network equations, VSG can be calculated. i Injection current I ti The expression is as follows.

[0079] Get I ti Then, by comparing I ti with I Mi Judging VSG by size relationship i Should we enter traffic limiting mode?

[0080] Suppose there are Nk VSGs in the system operating normally, and we define their set as ν. Then there will be k VSGs in the system operating in current-limited mode, and we define their set as τ. Then, according to the superposition theorem, we can obtain the VSG... i Output voltage U i The expression is as follows.

[0081]

[0082] In the formula X ij,K ij ,K i ,I Mj The expression is as follows:

[0083]

[0084]

[0085] K i =X g / (X g +X VT (9)

[0086]

[0087] In the formula X VT and X VTj The expression is as follows:

[0088]

[0089]

[0090] According to the power flow equation, VSG i Output active power P i and reactive power Q i It can be represented as follows:

[0091] In the formula δ ij =δ i -δ j B ij For the transfer susceptance from node i to j, B ig Let be the transfer susceptance from node i to the infinite bus node.

[0092] Combining equations (2) to (13), we can obtain VSG. i The nonlinear mathematical model for (i = 1, ..., N) is shown in equation (14).

[0093]

[0094] In the formula P ci and Q ci This indicates the interaction between converters via VSG. i The dynamic effect is expressed as in equation (15); K qi The expressions for and are shown in equations (16) and (17) respectively:

[0095]

[0096]

[0097] ΔQ refi =(U refi -U i ) / D qi +Q refi (17)

[0098] (II) Transient Synchronization Stability Analysis of Multi-Grid Converter Grid-Connected Systems

[0099] This invention addresses the question of whether a multi-VSG grid-connected system can maintain transient synchronization stability after fault clearing, based on the energy function method. The key to analyzing system transient stability using the energy function method lies in: 1) constructing the system's energy function after fault clearing; and 2) determining the critical energy value. Then, the transient synchronization stability of the system is directly evaluated by comparing the energy value at the time of fault clearing with the critical energy value.

[0100] First, considering the strong dynamic coupling of active and reactive power control and the dynamic interaction of multiple VSGs, the energy function of the system is analytically constructed when current limiting is not triggered after fault clearing. Then, considering the current limiting constraint, the critical energy value is given based on the nearest unstable equilibrium point theory to ensure that the system does not enter the current limiting mode and can maintain transient synchronization stability after fault clearing.

[0101] 1. Consider the energy function of dynamic strong coupling between active and reactive power control and dynamic interaction of multiple VSGs.

[0102] As can be seen from equation (14), the mathematical models of multi-VSG and single-VSG grid-connected systems have the same form. The only difference is that the multi-VSG system has an additional power coupling term P. ci and Q ci Therefore, for a multi-VSG system, its energy function V(δ,ω,U) can be considered as the sum of all VSGs. i The sum of the energy and power coupling terms is expressed as in equation (18).

[0103]

[0104] In the formula V ki For VSG i The kinetic energy of the virtual rotor; V pi For VSG i Potential energy.

[0105] For VSG i Considering the dynamic coupling of active and reactive power control, its kinetic and potential energy functions can be constructed as follows:

[0106] V ki =Ji ω i 2 (19)

[0107]

[0108] According to the first integration method, the energy function V corresponding to the inter-converter interaction term is... inter The following conditions must be met:

[0109]

[0110] According to equation (21), we can then obtain V. inter The expression for is shown in equation (22).

[0111]

[0112] Combining equations (18) to (22), the energy function V(δ,ω,U) of the system under dynamic coupling of active and reactive power control and multiple VSG interactions can be obtained as follows:

[0113]

[0114] 2. Critical Energy Calculation of Multi-VSG Grid-connected Systems under Current Limiting

[0115] 1) Critical energy to ensure transient synchronization and stability of the system under the condition that the system does not trigger current limiting after fault clearance.

[0116] If the system does not trigger current limiting after fault clearing, then the multi-VSG system is an autonomous system. Based on the nearest unstable equilibrium point method, the critical energy value Vc under the condition that the system does not trigger current limiting after fault clearing is... cr The following can be calculated:

[0117]

[0118] In the formula, x = [δ1,ω1,U1,…,δ N ,ω N U N ] represents the state variables of the system; n = 3N represents the dimension of the system state space; set M is the set of equilibrium points of the multi-VSG grid-connected system (14); the equilibrium points of the multi-VSG grid-connected system can be obtained by solving the 2N nonlinear equations shown in equation (25).

[0119]

[0120] 2) The critical energy that ensures the system does not trigger current limiting after fault clearance.

[0121] As long as the system's trajectory is not located at the equilibrium point, the energy function will strictly decrease along the system's trajectory. Therefore, if the fault is cleared, the system's energy V(x) will decrease. c The energy V that will trigger current limiting after the fault is cleared is less than the minimum energy V. cL If the fault is cleared, the system will definitely not trigger the current limiting.

[0122] Next, we will provide sufficient conditions to ensure that the system does not enter the rate limiting mode after the fault is cleared.

[0123] Theorem 1: If the energy V(x) of the system after fault clearing is... c If equation (26) is satisfied, then none of the converters in the system will enter the current limiting mode after the fault is cleared.

[0124] V(x c )≤V cL (26)

[0125] In the formula V cL This represents the minimum energy required to trigger current limiting in the system after a fault is cleared. (V) cL The solution can be obtained by solving the following optimization problem, as shown in Figure 4.

[0126]

[0127] Combining equations (24) and (26), the following criterion can be obtained to ensure that the system does not enter the current limiting mode and can maintain transient synchronization stability after the fault is cleared, where V c The critical energy of the system

[0128] V(x c )≤V c =min{V cr V cL} (28)

[0129] If equation (28) is satisfied, that is, the energy value of the system after fault clearing is less than the critical energy, it means that the system can definitely remain stable after fault clearing; otherwise, transient synchronous instability may occur. Obviously, the larger the energy value of the system after fault clearing, the lower the stability margin of the system. Therefore, the stability coefficient η is defined to reflect the stability margin of the system, and its expression is as shown in equation (28).

[0130] η = V c / V(x c (29)

[0131] Clearly, the larger η is, the stronger the stability margin of the system. If η≥1, it indicates that the system can maintain transient synchronous stability after the fault is cleared; otherwise, the system may become transiently unstable.

[0132] Based on the above analysis, the following algorithm is proposed for calculating the stability coefficient of a multi-VSG grid-connected system based on the energy function method, referred to as Algorithm 1.

[0133] To verify the effectiveness of the transient synchronous stability assessment method proposed in this invention, a simulation example of two VSG grid-connected systems was built on the PSCAD / EMTDC simulation platform. Detailed parameters are shown in Table 1. Two operating conditions, Case 1 and Case 2, are considered. The fault setting for both conditions is that the grid voltage drops to 0.14 pu within 1 second. The fault clearing times for Case 1 and Case 2 are 100 ms and 132 ms, respectively.

[0134] Table 1 System Parameters

[0135] For Case 1, Algorithm 1 shows that the system's stability coefficient is 1.16 > 1, indicating that the system's energy is less than the critical energy value after the fault is cleared. Figure 5 shows the curves of the system's potential energy, kinetic energy, and total energy during the transient process. It can also be seen from the figure that at the moment of fault clearing, the system's total energy does not exceed the critical energy. Therefore, after the fault is cleared, the system will not trigger current limiting and can maintain transient synchronous stability.

[0136] Figure 6 shows the transient simulation results of the system under Case 1. As can be seen from the figure, both VSG1 and VSG2 entered current-limiting mode during the fault. After the fault was cleared, both VSG1 and VSG2 returned to normal operation and maintained transient synchronization and stability. The simulation results shown in the figure are consistent with the theoretical analysis, verifying the effectiveness of the proposed method.

[0137] For Case 2, using Algorithm 1, the system stability coefficient is calculated to be 0.71 < 1, indicating that the system energy exceeds the critical energy value after the fault is cleared. Figure 7 shows the curves of the system's potential energy, kinetic energy, and total energy during the transient process. It can be seen from the figure that at the moment of fault clearing, the system's total energy is greater than the critical energy. Therefore, the system may experience transient synchronous instability after the fault is cleared.

[0138] Figure 8 shows the transient simulation results of the system under Case 2. As can be seen from Figure 8, after the fault is cleared, VSG1 and VSG2 switch between current limiting mode and normal mode, and the system transiently becomes unstable, which further verifies the effectiveness of the proposed method.

[0139] In addition, the red curves in Figures 6 and 8 represent the results of the nonlinear mathematical model (14) of the system under Case 1 and Case 2 conditions, respectively. As can be seen from the figures, the simulation results based on the detailed model highly overlap with the nonlinear mathematical model (14) established in this invention, verifying the effectiveness of the mathematical model.

Claims

1. A method for evaluating the transient synchronization stability of a multi-virtual synchronizer grid-connected system, comprising the following steps: Step 1: Ignore the fast-time-scale dynamics of the virtual synchronous machine, including voltage control and current control, and consider the strong coupling of active and reactive power control dynamics and the dynamic interaction of multiple virtual synchronous machines. Construct a nonlinear reduced-order mathematical model of the multi-virtual synchronous machine grid-connected system suitable for transient synchronization stability analysis. Step 2: Consider the dynamic strong coupling of active and reactive power control and the dynamic interaction of multiple virtual synchronous machines, and analyze the energy function of the grid-connected system with multiple virtual synchronous machines. Step 3: Using the nearest unstable equilibrium point method and optimization method, calculate the maximum energy value that ensures system stability and the maximum energy value that ensures system stability without triggering current limiting in the multi-virtual synchronous machine grid-connected system after fault clearing; take the minimum of the two values ​​to obtain the critical energy value that ensures system transient stability. Step 4: Calculate the trajectory of the multi-virtual synchronous machine grid-connected system during the fault period through numerical integration to obtain the system state at the time of fault clearing; The state of the multi-virtual synchronous machine grid-connected system at the time of fault clearing is substituted into the energy function to calculate the energy function value of the multi-virtual synchronous machine grid-connected system at the time of fault clearing. Step 5: Compare the energy function value of the multi-virtual synchronous machine grid-connected system at the fault clearing time with the critical energy value obtained in Step 3 to evaluate the transient synchronization stability of the multi-virtual synchronous machine grid-connected system.

2. The method for evaluating the transient synchronization stability of a multi-virtual synchronizer grid-connected system according to claim 1, characterized in that, The nonlinear reduced-order mathematical model of the multi-virtual synchronous machine grid-connected system constructed in the first step is expressed as follows: In the formula δ i and ω i They represent VSG respectively i The difference between the output phase angle and angular frequency and the phase angle and angular frequency of the infinite mains voltage; P refi J i , and D i They are VSG i Active power reference value, virtual inertia and damping coefficient; U i Q refi U refi D qi and K qi These are the voltage magnitudes at node i and VSG, respectively. i The reactive power reference value, voltage reference value, QV droop factor, and integral gain; B ij B is the transfer susceptance from node i to j. ig Let N be the transfer susceptance from node i to the infinite bus node; N is the number of virtual synchronous machines.

3. The method for evaluating the transient synchronization stability of a multi-virtual synchronizer grid-connected system according to claim 2, characterized in that, In the second step, the energy function of the multi-virtual synchronous machine grid-connected system is considered as the sum of the energy of all VSGs and the energy corresponding to the interaction between converters, specifically expressed as follows: In the formula V ki For VSG i The kinetic energy of the virtual rotor; V pi For VSG i Potential energy; V inter It is the energy exchanged between converters; V ki V pi and V inter The expressions are as follows:

4. The transient synchronization stability evaluation method for a multi-virtual synchronizer grid-connected system according to claim 3, characterized in that, The third step is as follows: (1) According to the nearest unstable equilibrium point method, the maximum energy value V that ensures system stability under the condition that the system does not trigger current limiting after fault clearance. cr The calculation is as follows: In the formula, x = [δ1,ω1,U1,…,δ N ,ω N U N ] represents the state variables of a multi-virtual synchronous machine grid-connected system; let the dimension of the state space of the multi-virtual synchronous machine grid-connected system be n = 3N; set M is the set of all equilibrium points of the multi-virtual synchronous machine grid-connected system; (2) Ensure the maximum energy value V that prevents the system from triggering current limiting after fault clearance. cL The following optimization problem was solved to obtain the following result: V cL =min V(δ,ω,U) In the formula I Mi For VSG i Maximum allowable current amplitude, I ti For VSG i The injected current; (3) Obtain the critical energy value V that guarantees the transient stability of the system after fault clearing. c As shown below; V c =min{V cr ,V cL }。 5. The method for evaluating the transient synchronization stability of a multi-virtual synchronizer grid-connected system according to claim 4, characterized in that, The energy function value of the multi-virtual synchronous grid-connected system at the fault clearing time is calculated to be V(x). c In the fifth step, the energy function value V(x) of the multi-virtual synchronous machine grid-connected system at the fault clearing time is compared. c ) and critical energy value V c The magnitude relationship is used to evaluate the transient synchronization stability of the system, as shown below; V(x) c )≤V c If the above equation holds true, it means that the system can maintain transient synchronization and stability; if the above equation does not hold true, it means that the system may be transiently unstable.

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