Transient stability evaluation method for multi-virtual synchronous machine grid-connected system based on energy function

Abstract

The invention relates to a transient synchronous stability evaluation method for a multi-virtual synchronous machine grid-connected system. The method comprises the following steps: constructing a system nonlinear reduced-order mathematical model suitable for transient synchronous stability analysis; considering active and reactive power control dynamic strong coupling and multi-virtual synchronous machine dynamic interaction, and analyzing an energy function of the construction system; 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 the fault is removed through a nearest unstable equilibrium point method and an optimization method; taking the minimum value of the two values to obtain a critical energy value for ensuring the transient stability of the system; calculating the track of the system during the fault through numerical integration to obtain the state of the system at the fault removal moment; the state of the system at the fault clearing moment is substituted into an energy function, and an energy function value of the system at the fault clearing moment is calculated; and evaluating the transient synchronization stability of the system.

Description

Technical Field

[0001] The invention belongs to the field of transient stability analysis of power electronic power systems. Aiming at the problem of transient synchronization stability of a multi-virtual synchronous machine grid-connected system under power grid faults, the invention proposes a transient synchronization stability evaluation method of a multi-virtual synchronous machine grid-connected system based on energy function. Background Art

[0002] With the development of new energy, grid-following converters with power output as the goal are gradually replacing traditional synchronous generators, resulting in a gradual weakening of the grid's forced inertia and short-circuit capacity. [1]-[2] To address this problem, academia and industry have proposed a variety of network control technologies, among which virtual synchronous generator (VSG) is a very promising solution. [3] VSG simulates a synchronous generator and behaves as a voltage source externally, with 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 time scales of the active and reactive loops in VSG control are similar, and the coupling of active and reactive control will seriously affect the transient synchronization characteristics of the system. [6] In addition, due to the weak current carrying capacity of the converter, a current limiting strategy process will be designed in the converter, which makes the VSG system become a switching system. [7]-[8] The differences in these two aspects make the transient characteristics of the multi-VSG grid-connected system more complicated, and the energy function method applicable to the transient stability analysis of the traditional synchronous machine system may no longer be applicable. Therefore, it is necessary to analyze the transient synchronous stability of the multi-VSG grid-connected system under the strong coupling of current limitation and active and reactive control.

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

[10] -

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

[12] -

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

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

[15] -

[16] derived the power angle curves of VSGs under voltage control mode and current control mode, revealed the transient synchronous 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 pointed out 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

[17] -

[18] pointed out that this assumption is not valid 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 synchronous stability problem of multi-VSC grid-connected systems.

[0005] For multi-VSG grid-connected systems, the interaction between VSGs will not only affect the input active and reactive power of VSGs, but also affect the output current of VSGs, thereby affecting the switching conditions of the current limiter, making the transient synchronization stability analysis of multi-VSG grid-connected systems more complicated. For multi-VSG systems, there are currently only a few references such as

[19] -

[23] that analyze the transient synchronization stability of the system under multi-machine interaction without considering the influence of current limiting. References

[19] -

[20] ignore the influence of active and reactive control coupling, that is, consider the reactive loop as a constant voltage output, and draw on the energy function method used in multi-synchronous machine systems to quantitatively analyze the transient synchronization stability of the system. In order to further reduce the conservatism of the analysis results, reference

[21] proposed a damping energy approximation method to quantitatively describe the damping energy. However, the above studies did not consider the influence of active and reactive control coupling. Considering the influence of active and reactive control coupling, references

[22] -

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

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

[23] considers active and reactive control coupling, numerically constructs the Lyapunov function of a two-VSG system based on the TS method, and quantitatively analyzes the transient synchronization stability of the system. However, the calculation time of the TS method is exponentially related to the number of system nonlinearities, so it is difficult to apply it to the transient synchronization stability analysis of a grid-connected system with N VSGs. In general, considering the influence of active and reactive control coupling and multi-machine interaction, the methods proposed in the above studies are difficult to quantitatively analyze the transient synchronization stability of a grid-connected system with N VSGs. More importantly, references

[19] -

[23] also do not consider the influence of current limiting.

[0006] Considering the influence of current limitation, the current literature

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

[24] ignores the influence of active and reactive control coupling. In fact, active and reactive control coupling will deteriorate the transient synchronization stability of the system. Therefore, for the transient synchronization stability problem of the multi-grid converter grid-connected system, the influence of active and reactive control coupling must be taken into account.

[0007] Related Literature:

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[0016] [9]Z.Shuai,C.Shen,X.Liu,et al,"Transient Angle Stability ofVirtualSynchronous Generators Using Lyapunov’s Direct Method,"IEEE Trans.Smart Grid,vol.10,no.4,pp.4648-4661,July 2019.

[0017]

[10] S.Tang,X.Fu,Z.Tian,et al,"Third-Order Energy Function ModellingApproach for Grid-Forming Converters,"2024 IEEE 10th International PowerElectronics and Motion Control Conference(IPEMC2024-ECCEAsia),Chengdu,China,2024,pp.4038-4041.

[0018]

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

[0019]

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

[0020]

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

[0021]

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

[0022]

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

[0023]

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

[0024]

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

[0025]

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

[0026]

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

[0027]

[20] L.Chen,J.Tang,X.Qiao,et al,"Investigation on Transient StabilityEnhancement of Multi-VSG System Incorporating Resistive SFCLs Based on DeepReinforcement Learning,"IEEE Trans.IndustryApplications,vol.60,no.1,pp.1780-1793,Jan.-Feb.2024.

[0028]

[21] 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]

[22] 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]

[23] 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]

[24] 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 the present invention is to disclose a method for quantitatively evaluating the transient synchronization stability of a multi-virtual synchronous machine grid-connected system under a power grid fault. First, the multi-virtual synchronous machine grid-connected system under a power grid fault is reasonably simplified, and a nonlinear reduced-order mathematical model of the system is established; then, considering the dynamic strong coupling of active and reactive control and the dynamic interaction of multiple virtual synchronous machines, the energy function of the multi-virtual synchronous machine grid-connected system is analytically constructed. Then, the maximum energy value that ensures the stability of the system without triggering the current limit and the maximum energy that ensures that the system does not trigger the current limit are calculated respectively through the nearest unstable equilibrium point method and the optimization method. The minimum value of the two is taken to obtain the critical energy value that ensures 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 transient synchronization stability of a multi-virtual synchronous machine grid-connected system comprises the following steps:

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

[0035] Step 2: Considering the dynamic strong coupling of active and reactive control and the dynamic interaction of multiple virtual synchronous machines, the energy function of the grid-connected system of multiple virtual synchronous machines is analytically constructed;

[0036] Step 3: By using the nearest unstable equilibrium point method and optimization method, the maximum energy value that ensures system stability and the maximum energy value that ensures that the system does not trigger current limiting are calculated respectively under the condition that the multi-virtual synchronous machine grid-connected system does not trigger current limiting after fault removal; the minimum value of the two is taken 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 by numerical integration to obtain the state of the system at the time of fault removal; bring the state of the multi-virtual synchronous machine grid-connected system at the time of fault removal into the energy function to calculate the energy function value of the multi-virtual synchronous machine grid-connected system at the time of fault removal;

[0038] Step 5: Compare the energy function value of the multi-virtual synchronous machine grid-connected system at the moment of fault removal with the critical energy value obtained in the third step, and 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:

[0040]

[0041] Where δi and ω i Respectively represent VSG i The difference between the output phase angle and angular frequency and the infinite grid voltage phase angle and angular frequency; P refi ,J i , and D i VSG i Active power reference value, virtual inertia and damping coefficient; U i ,Q refi ,U refi ,D qi and K qi are the voltage amplitude of node i, VSG i Reactive power reference value, voltage reference value, QV droop coefficient and integral gain; B ij is the transfer susceptance from node i to node j, B ig is the transfer susceptance from node i to the infinite bus node; N is the number of virtual synchronous machines;

[0042]

[0043] Furthermore, in the second step, the energy function of the multi-virtual synchronous machine grid-connected system is considered to be the sum of the energy of all VSGs and the energy corresponding to the interaction between converters, which is specifically expressed as follows:

[0044]

[0045] Where V ki For VSG i Kinetic energy of virtual rotor; V pi For VSG i Potential energy; V inter is the energy of interaction between converters; V ki ,V pi and V inter The expressions are as follows:

[0046]

[0047] Furthermore, the method of the third step is as follows:

[0048] (1) According to the nearest unstable equilibrium point method, the maximum energy value V that ensures system stability without triggering current limiting after fault removal cr The calculation is as follows:

[0049]

[0050] Where x=[δ1,ω1,U1,...,δ N ,ω N ,U N], represents the state variables of the multi-virtual synchronous machine grid-connected system; suppose the dimension of the state space of the multi-virtual synchronous machine grid-connected system is n=3N; set M is the set of all equilibrium points of the multi-virtual synchronous machine grid-connected system;

[0051] (2) The maximum energy value V that ensures that the system does not trigger current limiting after the fault is removed cL By solving the following optimization problem:

[0052] V cL = min V(δ,ω,U)

[0053]

[0054] Where I Mi For VSG i Maximum allowable current amplitude, I ti For VSG i The injected current

[0055] (3) Obtain the critical energy value V that guarantees the transient stability of the system after fault removal c , as shown below;

[0056] V c =min{V cr ,V cL}

[0057] Furthermore, the energy function value of the multi-virtual synchronous machine grid-connected system at the time of fault removal is designed and calculated as V(x c ); In the fifth step, by comparing the energy function value V(x c ) and critical energy value V c The relationship between the magnitudes of and is used to evaluate the transient synchronous stability of the system, as shown below;

[0058] V(x c )≤V c

[0059] If the above equation is true, it means that the system can maintain transient synchronous stability; if the above equation is not true, it means that the system may be transiently unstable.

[0060] The beneficial effects of the present invention are as follows:

[0061] 1) The active power control and reactive power control characteristics of VSG are retained, while the voltage control and current control dynamics with faster response speed are ignored. A reduced-order mathematical model of a multi-converter grid-connected system is established under grid faults, taking into account the active and reactive control coupling and transient interaction between multiple VSGs. This greatly reduces the complexity of transient synchronous stability analysis of a multi-VSG grid-connected system under grid faults.

[0062] 2) A quantitative evaluation method for the transient synchronization stability of a multi-virtual synchronous machine grid-connected system based on an energy function is proposed, based on which the transient synchronization stability of the system after fault removal can be analyzed. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 Topology diagram of multi-VSG grid-connected system

[0064] Figure 2 (a)VSG i Control structure diagram; (b) Active and reactive power control structure

[0065] Figure 3 Schematic diagram of phase-priority limiter

[0066] Figure 4 Schematic diagram of the system not entering current limiting mode after a fault

[0067] Figure 5 System energy change curve under Case 1

[0068] Figure 6 Simulation results of Case 1: (a) trajectory of VSG1; (b) trajectory of VSG2

[0069] Figure 7 System energy change curve under Case 2

[0070] Figure 8 Simulation results of Case 2: (a) trajectory of VSG1; (b) trajectory of VSG2 DETAILED DESCRIPTION

[0071] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0072] (I) Reduced-order model of multi-grid converter grid-connected system under fault

[0073] 1. System Description

[0074] The multi-VSG grid-connected system topology involved in the embodiment of the present invention is as follows: Figure 1 As shown, the system includes N VSGs, and the i-th VSG is denoted as VSG i , where i = 1, 2, ..., NL fi and C fi It is VSG i The inductance and capacitance of the filter; U i ∠θ i and U g ∠θ g VSG i Output voltage and infinite bus voltage; X i and X gVSG i The equivalent reactance between the filter and the point of common coupling (PCC) and between the PCC and the infinite bus.

[0075] VSG i Control structure Figure 2 As shown. VSG i The control includes active power control (APL), reactive power control (DRPL) and voltage and current inner loop control. i The active power control simulates the swing equation of the synchronous machine and generates the angular frequency ω vsgi and phase angle θ vsgi . VSG i The phase angle θ vsgi The phase angle difference between the infinite bus voltage and the power angle δ is defined as i , as shown in formula (2).

[0076] δ i =θ vsgi -θ g =∫(ω vsgi -ω g )dt (1)

[0077] Consider VSG i The rated angular frequency ω0 and the angular frequency ω of the infinite bus voltage g equal, that is, ω0=ω g Then we can get VSG i The active power control dynamics are as follows:

[0078]

[0079] Where P refi ,J i , and D i VSG i Active power reference value, virtual inertia and damping coefficient.

[0080] VSG i The reactive power control adopts droop control to generate the voltage internal potential U vsgi , its dynamic equation can be described as follows:

[0081]

[0082] Where Q refi ,U refi ,D qi and k qi VSG i Reactive power reference value, voltage reference value, QV droop factor and integral gain;

[0083] VSG i The control objectives of the voltage inner loop and current inner loop of VSG are to achieve i The output voltage U i ∠θ i Tracking the θ generated by the active control loop and the reactive control loop vsgi and U vsgi To avoid VSG i Overcurrent, usually a current limiter is used to limit the q-axis and q-axis current reference generated by the voltage inner loop. The present invention uses a phase angle priority limiter, which can be mathematically expressed as formula (4).

[0084]

[0085] Where x = x d +jx q , I Mi For VSG i The maximum current amplitude allowed, It is the customized current phase angle.

[0086] When the magnitude of the current reference value generated by the voltage control loop is greater than I Mi When the limiter is triggered, VSG i Enter current limiting mode. It should be noted that when VSG i When entering the current limiting mode, the voltage control loop and the reactive power control loop will not work. Therefore, in the current limiting mode, the reactive power outer loop and the voltage inner loop are locked, that is, k qi =0, the integral coefficient of the voltage inner loop is equal to zero.

[0087] 2. Nonlinear price reduction mathematical model

[0088] Focusing on the synchronous stability problem, considering that the voltage and current inner loop dynamics of VSG are usually much faster than those of APL and DRPL, the following assumptions are considered to simplify the analysis:

[0089] 1) Ignore LC filters and AC network electromagnetic transients;

[0090] 2) Ignore the dynamics of the current inner loop, that is, assume that the VSG injection current can approximately track the current reference value in real time;

[0091] 3) In normal operation (limiter not triggered), ignoring the voltage inner loop dynamics, U vsgi ∠θ vsgi ≈U i ∠θ i

[0092] Based on the above assumptions, we can get VSG iThe equivalent circuit model of is shown below. Obviously, in normal operation mode, VSG i is considered as a controllable voltage source. In current limiting mode, VSG i becomes a controllable current source.

[0093] According to the network equation, VSG can be calculated i The injected current I ti , the expression is as follows.

[0094]

[0095] Get I ti After that, by comparing I ti with I Mi The size relationship is used to judge VSG i Whether to enter current limiting mode.

[0096] Assume that there are Nk VSGs in the system in normal operation mode, and define their set as ν. Then there will be k VSGs in the system in current limiting mode, and define their set as τ. Then, according to the superposition theorem, we can get VSG i The output voltage U i , the expression is as follows.

[0097]

[0098] Where X ij ,K ij ,K i ,I Mj The expression is as follows:

[0099]

[0100]

[0101] K i =X g / (X g +X VT ) (9)

[0102]

[0103] Where X VT and X VTj The expression is as follows:

[0104]

[0105]

[0106] According to the power flow equation, VSG i Output active power P iand reactive power Q i It can be expressed as follows:

[0107]

[0108] Where δ ij =δ i -δ j ,B ij is the transfer susceptance from node i to node j, B ig is the transfer susceptance from node i to the infinite bus node.

[0109] Combining equations (2) to (13), we can get VSG i The nonlinear mathematical model of (i=1,...,N) is shown in formula (14):

[0110]

[0111] Where P ci and Q ci Represents the interaction between converters VSG i Dynamic influence, expressed as formula (15); K qi The expressions of and are shown in equation (16) and equation (17) respectively:

[0112]

[0113]

[0114] ΔQ refi =(U refi -U i ) / D qi +Q refi (17)

[0115] (II) Transient synchronization stability analysis of multi-grid converter grid-connected system

[0116] The present invention considers the problem of whether the multi-VSG grid-connected system can maintain transient synchronous stability after fault removal based on the energy function method. The key to using the energy function method to analyze the transient stability of the system is: 1) constructing the energy function of the system after fault removal; 2) determining the critical energy value. Then, the transient synchronous stability of the system is directly evaluated by comparing the energy value at the time of system fault removal with the critical energy value.

[0117] Firstly, considering the strong dynamic coupling of active and reactive control and the dynamic interaction of multiple VSGs, the energy function of the system is analytically constructed when the current limiting is not triggered after the fault is removed. Then, considering the current limiting constraint, the critical energy value that ensures that the system does not enter the current limiting mode and can maintain transient synchronous stability after the fault is removed is given based on the nearest unstable equilibrium point theory.

[0118] 1. Energy function considering the strong coupling of active and reactive control and the dynamic interaction of multiple VSGs

[0119] From equation (14), we can see that the mathematical model of the multi-VSG and single-VSG grid-connected systems has 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 all VSGs i The sum of the energy of and the energy corresponding to the power coupling term, the specific expression is as shown in formula (18).

[0120]

[0121] Where V ki For VSG i Kinetic energy of virtual rotor; V pi For VSG i potential energy.

[0122] For VSG i , considering the dynamic coupling of active and reactive control, the kinetic energy and potential energy functions can be constructed as follows:

[0123] V ki =J i ω i 2 (19)

[0124]

[0125] According to the first integration method, the energy function V corresponding to the interaction term between converters is inter The following conditions must be met:

[0126]

[0127] According to formula (21), we can get V inter The expression of is shown in formula (22).

[0128]

[0129] Combining equations (18) to (22), the energy function V(δ, ω, U) of the system under the dynamic coupling of active and reactive control and the interaction of multiple VSGs can be obtained as follows:

[0130]

[0131] 2. Calculation of critical energy of multi-VSG grid-connected system under the influence of current limitation

[0132] 1) Critical energy to ensure transient synchronous stability of the system without triggering current limiting after fault removal

[0133] If the system does not trigger current limiting after the fault is removed, the multi-VSG system is an autonomous system. According to the nearest unstable equilibrium point method, the critical energy value V under the condition that the system does not trigger current limiting after the fault is removed is cr It can be calculated as follows:

[0134]

[0135] Where x=[δ1,ω1,U1,...,δ N ,ω N ,U N ] represents the state variable of the system; n = 3N represents the dimension of the system state space; the 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 2N nonlinear equations as shown in formula (25).

[0136]

[0137] 2) Critical energy to ensure that the system does not trigger current limiting after fault removal

[0138] As long as the system trajectory is not at an equilibrium point, the energy function will be strictly decreasing along the system trajectory. Therefore, if the energy V(x c ) is less than the minimum energy V that will trigger the current limit after the fault is removed. cL , then the system will definitely not trigger current limiting after the fault is removed.

[0139] Next, sufficient conditions are given to ensure that the system does not enter the current limiting mode after the fault is removed.

[0140] Theorem 1: If the energy V(x c ) satisfies equation (26), then all converters in the system will not enter the current limiting mode after the fault is removed.

[0141] V(x c )≤V cL (26)

[0142] Where V cL It indicates the minimum energy of the system that will trigger the current limit after the fault is removed. V cL It can be obtained by solving the following optimization problem, as shown in the schematic diagram Figure 4 shown.

[0143]

[0144] Combining equations (24) and (26), the criterion for ensuring that the system does not enter the current limiting mode and can maintain transient synchronous stability after the fault is removed is as follows: c is the critical energy of the system

[0145] V(x c )≤V c =min{V cr ,V cL} (28)

[0146] If equation (28) is satisfied, that is, the energy value of the system after the fault is removed is less than the critical energy, it means that the system can remain stable after the fault is removed; otherwise, transient synchronous instability may occur. Obviously, the larger the energy value of the system after the fault is removed, the lower the stability margin of the system. Therefore, the stability coefficient η is defined to reflect the stability margin of the system, and the expression is as follows.

[0147] η=V c / V(x c ) (29)

[0148] Obviously, the larger η is, the stronger the stability margin of the system is. If η ≥ 1, it means that the system can maintain transient synchronous stability after the fault is removed, otherwise the system may be transiently unstable.

[0149] Based on the above analysis, the following algorithm for calculating the stability coefficient of the multi-VSG grid-connected system based on the energy function method is proposed, referred to as Algorithm 1.

[0150]

[0151]

[0152] In order to verify the effectiveness of the transient synchronous stability evaluation method proposed in this invention, a simulation example of two VSG grid-connected systems was built on the PSCAD / EMTDC simulation platform. The detailed parameters are shown in Table 1. Considering the two working conditions of Case 1 and Case 2, the fault setting under the two working conditions is: the grid voltage drops to 0.14pu at 1s. The fault clearing time of Case 1 and Case 2 is 100ms and 132ms respectively.

[0153] Table 1 System parameters

[0154]

[0155] For Case 1, the stability coefficient of the system calculated by Algorithm 1 is equal to 1.16>1, indicating that the energy of the system after the fault is removed is less than the critical energy value. Figure 5The curves of the potential energy, kinetic energy and total energy of the system in the transient process are given. It can also be seen from the figure that at the moment of fault removal, the total energy of the system does not exceed the critical energy. Therefore, after the fault is removed, the system will not trigger the current limit and can maintain transient synchronous stability.

[0156] Figure 6 The transient simulation results of the system under Case 1 are given. It can be seen from the figure that both VSG1 and VSG2 enter the current limiting mode during the fault. After the fault is removed, both VSG1 and VSG2 return to the normal operation mode and can maintain transient synchronous stability. The simulation results shown in the figure are consistent with the theoretical analysis, which verifies the effectiveness of the proposed method.

[0157] For Case 2, the stability coefficient of the system calculated by Algorithm 1 is equal to 0.71<1, indicating that the energy of the system exceeds the critical energy value after the fault is removed. Figure 7 The curves of the potential energy, kinetic energy and total energy of the system in the transient process are given. It can be seen from the figure that at the moment of fault removal, the total energy of the system is greater than the critical energy. Therefore, the system may experience transient synchronous instability after the fault is removed.

[0158] Figure 8 The transient simulation results of the system under Case 2 are given. Figure 8 It can be seen from the figure that after the fault is removed, VSG1 and VSG2 switch between the current limiting mode and the normal mode, and the system transient synchronous instability is further verified. The effectiveness of the proposed method is further verified.

[0159] in addition, Figure 6 and Figure 8 The red curves in the figure are the results of the nonlinear mathematical model (14) of the system under Case 1 and Case 2 conditions. It can be seen from the figure that the simulation results based on the detailed model are highly consistent with the nonlinear mathematical model (14) established by the present invention, which verifies the effectiveness of the mathematical model.

Claims

1. A method for evaluating transient synchronization stability of a multi-virtual synchronous machine grid-connected system, comprising the following steps: Step 1: Ignoring the fast time scale dynamics of virtual synchronous machines including voltage control and current control, considering the strong coupling of active and reactive control dynamics and the dynamic interaction of multiple virtual synchronous machines, a nonlinear reduced-order mathematical model of the multi-virtual synchronous machine grid-connected system suitable for transient synchronous stability analysis is constructed; Step 2: Considering the dynamic strong coupling of active and reactive control and the dynamic interaction of multiple virtual synchronous machines, the energy function of the multi-virtual synchronous machine grid-connected system is analytically constructed; Step 3: By using the nearest unstable equilibrium point method and optimization method, the maximum energy value that ensures system stability and the maximum energy value that ensures that the system does not trigger current limiting are calculated respectively under the condition that the multi-virtual synchronous machine grid-connected system does not trigger current limiting after fault removal; the minimum value of the two is taken 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 removal; The state of the multi-virtual synchronous machine grid-connected system at the time of fault removal is brought into the energy function, and the energy function value of the multi-virtual synchronous machine grid-connected system at the time of fault removal is calculated; Step 5: Compare the energy function value of the multi-virtual synchronous machine grid-connected system at the moment of fault removal with the critical energy value obtained in the third step, and evaluate the transient synchronization stability of the multi-virtual synchronous machine grid-connected system.

2. The method for evaluating transient synchronization stability of a multi-virtual synchronous machine 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: Where δ i and ω i Respectively represent VSG i The difference between the output phase angle and angular frequency and the infinite grid voltage phase angle and angular frequency; P refi ,J i , and D i VSG i Active power reference value, virtual inertia and damping coefficient; U i ,Q refi ,U refi ,D qi and K qi are the voltage amplitude of node i, VSG i Reactive power reference value, voltage reference value, QV droop coefficient and integral gain; B ij is the transfer susceptance from node i to node j, B ig is the transfer susceptance from node i to the infinite bus node; N is the number of virtual synchronous machines; 3. The method for evaluating transient synchronization stability of a multi-virtual synchronous machine 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 to be the sum of the energy of all VSGs and the energy corresponding to the interaction between converters, which is specifically expressed as follows: Where V ki For VSG i Kinetic energy of virtual rotor; V pi For VSG i Potential energy; V inter is the energy of interaction between converters; V ki ,V pi and V inter The expressions are as follows:

4. The method for evaluating transient synchronization stability of a multi-virtual synchronous machine grid-connected system according to claim 3, characterized in that: The method for the third step is as follows: (1) According to the nearest unstable equilibrium point method, the maximum energy value V that ensures system stability without triggering current limiting after fault removal cr The calculation is as follows: Where x=[δ1,ω1,U1,...,δ N ,ω N ,U N ], represents the state variables of the multi-virtual synchronous machine grid-connected system; suppose the dimension of the state space of the multi-virtual synchronous machine grid-connected system is n=3N; set M is the set of all equilibrium points of the multi-virtual synchronous machine grid-connected system; (2) The maximum energy value V that ensures that the system does not trigger current limiting after the fault is removed cL By solving the following optimization problem: V cL =min V(δ,ω,U) Where 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 removal c , as shown below; V c =min{V cr ,V cL }。 5. The method for evaluating transient synchronization stability of a multi-virtual synchronous machine grid-connected system according to claim 4, characterized in that: The energy function value of the multi-virtual synchronous machine grid-connected system at the time of fault removal is designed and calculated as V(x c ); In the fifth step, by comparing the energy function value V(x c ) and critical energy value V c The relationship between the magnitudes of and is used to evaluate the transient synchronous stability of the system, as shown below; V(x c )≤V c If the above equation is true, it means that the system can maintain transient synchronous stability; if the above equation is not true, it means that the system may be transiently unstable.

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