CN-122020952-A - Small-interference stability analysis method suitable for flexible direct-current asymmetric working condition

Abstract

The invention relates to the technical field of electric power systems and automation thereof, in particular to a small-interference stability analysis method suitable for flexible direct current asymmetric working conditions, which comprises the following steps of S1, establishing an MMC-HVDC nonlinear periodic time-varying state space model, S2, solving a steady-state periodic track of the MMC-HVDC system and calculating a jacobian matrix time sequence, and S3, solving a state transfer matrix and carrying out eigenvalue decomposition based on the Floquet theorem. The method solves the technical problems of high model order and large calculated amount in the MMC-HVDC system small interference stability analysis under the asymmetric working condition.

Inventors

• LIU HANG
• ZHAO PEILIN
• CHEN QIAN
• Liao Fangqun
• HUANG YILONG
• ZHANG PEIRAN
• ZOU YANSHENG
• ZHANG NAN
• Hong Quanwei
• HUANG YUNFENG

Assignees

• 中国南方电网有限责任公司超高压输电公司电力科研院

Dates

Publication Date

20260512

Application Date

20251205

Claims (10)

1. 1. The small-interference stability analysis method suitable for the flexible direct-current asymmetric working condition is characterized by comprising the following steps of: step S1, establishing an MMC-HVDC nonlinear period time-varying state space model; constructing a nonlinear periodic time-varying state space model of a modularized multi-level converter-high-voltage direct current system suitable for asymmetric working conditions, and determining the relation between a system state variable and an input variable; S2, solving a steady-state periodic track of the MMC-HVDC system and calculating a Jacobian matrix time sequence; Solving a steady-state periodic track of the system by adopting a Newton-Krylov algorithm, and solving a periodic time sequence of a Jacobian matrix at the track; Step S3, solving a state transition matrix based on the Floquet theorem and decomposing the characteristic values; and taking the basic solution system as an initial condition, solving a state transition matrix through numerical integration, decomposing the characteristic value of the state transition matrix to obtain a Floquet multiplier, and judging the system stability.
2. 2. The method for analyzing the stability of small interference suitable for the asymmetric working condition of flexible direct current according to claim 1, wherein the step S1 comprises: step S1.1, defining an MMC main loop topological structure; Defining main components and parameters of the system according to MMC power circuit topology; s1.2, deducing a mathematical model equation of an MMC-HVDC system; based on kirchhoff's law and the working principle of the converter, a nonlinear periodic time-varying state space equation of the MMC-HVDC system is established: (1) the above formula (1) can be expressed as: (2); wherein: representing a vector of system state variables, Representing a vector made up of the inputs to the system, Representing a vector field.
3. 3. The method for analyzing the stability of small interference suitable for the asymmetric working condition of flexible direct current according to claim 1, wherein the step S2 comprises: S2.1, solving a steady-state periodic track by applying a Newton-Krylov algorithm; And S2.2, calculating the periodic time sequence of the jacobian matrix.
4. 4. A method for analyzing stability of small disturbance applied to asymmetric flexible DC conditions as set forth in claim 3, wherein step S2.1 comprises obtaining steady-state periodic trajectory of formula (1) by Newton-Krylov algorithm 。
5. 5. The method for analyzing the small interference stability suitable for the flexible direct current asymmetric working condition according to claim 4, wherein the step S2.2 comprises the following steps of linearizing at a steady-state periodic track to obtain a linear periodic time-varying system equation for describing the small interference stability of the system: (3); wherein: representing vectors of system state variables due to Has a periodically time-varying nature, and therefore Is a matrix of periodic coefficients with period t=0.02 s for MMC systems.
6. 6. The method for analyzing the stability of small interference suitable for the asymmetric working condition of flexible direct current according to claim 1, wherein the step S3 comprises: S3.1, establishing a basic solution matrix differential equation; S3.2, solving a state transition matrix through numerical integration; and S3.3, characteristic value decomposition and stability criterion.
7. 7. The method for analyzing the stability of small interference suitable for the asymmetric working condition of flexible direct current according to claim 6, wherein in the step S3.1, a basic solution matrix of the formula (2) is obtained according to the Floquet theorem: (4); wherein: For the base solution matrix of the system, For a period of Is a function of (a) and (b), Is a non-singular steady matrix, Is an identity matrix.
8. 8. The method for analyzing the stability of small disturbance applied to a flexible DC asymmetric mode according to claim 7, wherein in step S3.2, said differential equation set is applied in a single period Numerical integration is carried out to obtain State transition matrix at time: (5); in step S3.3, in formula (5) The solution is obtained by numerical integration of the following differential equation set: (6); Definition of the definition Is one of the characteristic values of , Is a matrix Is called as Is a Floquet multiplier, Is Floquet index, pair Decomposing the characteristic values to obtain n And Wherein n is the system order, when any one 0 Or When 1, the system is unstable, when any one Not more than 0 or And (2) when the temperature is less than or equal to 1, the system stability or critical stability is ensured, so that the system stability criterion can be obtained as follows: (7); the stability of the system is analyzed by calculating the Floquet multiplier of the LTP system.
9. 9. A data processing apparatus, comprising: A memory for storing a computer program; A processor for implementing the steps of a method for small disturbance stability analysis applicable to a flexible direct current asymmetric operating mode according to any one of claims 1 to 8 when executing the computer program.
10. 10. A computer readable storage medium, characterized in that the computer readable storage medium has stored thereon a computer program which, when executed by a processor, implements the steps of a method for small disturbance stability analysis applicable to flexible direct current asymmetric operating conditions according to any of claims 1 to 8.

Description

Small-interference stability analysis method suitable for flexible direct-current asymmetric working condition Technical Field The invention relates to the technical field of power systems and automation thereof, in particular to a small-interference stability analysis method suitable for a flexible direct-current asymmetric working condition. Background The modularized multi-level converter (modular multilevel converter, MMC) is used as an advanced voltage source type converter, has the remarkable advantages of good output waveform quality, low switching loss, high fault handling capacity, high scalability and the like, and becomes core equipment of a high-voltage direct current (high voltage direct current, HVDC) power transmission system. With the increase of new energy grid-connected requirements and the intelligent upgrading of an electric power system, a modularized multi-level converter-high-voltage direct current technology (MMC-HVDC for short) is widely applied in the fields of inter-regional power grid interconnection, concentrated new energy transmission and the like, the voltage level and the capacity of the system are continuously improved, and higher requirements are provided for system stability control. However, MMC-HVDC systems face severe stability challenges in practical operation. Because the power electronic degree is high, the control link is complex, and the access proportion of new energy is improved, the system presents complex dynamic characteristics such as broadband resonance, multi-mode coupling and the like. In engineering practice, high-frequency resonance accidents are observed for many times, namely, the national power grid Yu-Hui direct current engineering generates harmonic resonance of 700Hz and 1800Hz, the world first flexible direct current power grid Zhang Bei engineering generates high-frequency oscillation of about 1500Hz in the alternating current side charging process of the Kangbao station, and the southern power grid Lu-West back-to-back flexible direct current engineering generates 1200Hz resonance when being connected into a weak alternating current system. These phenomena not only affect the quality of electric energy, but also may cause the locking of the converter and the system shutdown in severe cases, which constitutes a serious threat to the safe and stable operation of the power grid. For stability analysis of MMC-HVDC systems, the prior art has formed a more sophisticated solution under symmetric conditions. The typical method is based on the harmonic balance principle, the system equivalent with periodic time-varying solution is converted into a linear time-invariant system, and then the small interference stability assessment is realized through eigenvalue analysis. The method can effectively simplify the analysis process under the condition of a symmetrical power grid, but in actual engineering, non-ideal working conditions such as asymmetric three-phase power grid voltage, unbalanced line impedance parameters, bridge arm inductance difference and the like are commonly existed. Under asymmetric working conditions, the MMC converter can generate rich harmonic components, and strong coupling effects exist among different frequency harmonics. At this time, the conventional method based on the harmonic balancing principle needs to consider multiple harmonic frequency components, which causes the system model order to increase along with the number n of harmonics to 2n+1 times, and causes a "dimension disaster". The modeling method is complex in steps and fuzzy in physical meaning, and can also remarkably increase the computational complexity and hardware cost, so that the requirements of rapid analysis and real-time control in engineering application are difficult to meet. Therefore, the high-efficiency small-interference stability analysis method suitable for the asymmetric working conditions is developed, the problem of model order expansion in the traditional technology is avoided, and the method has important theoretical significance and engineering value for improving the safe and stable operation level of an MMC-HVDC system. Disclosure of Invention Aiming at the problems, the small-interference stability analysis method suitable for the flexible direct-current asymmetric working condition is provided, and the technical problems of high model order and large calculated amount in MMC-HVDC system small-interference stability analysis under the asymmetric working condition are solved. In order to solve the problems in the prior art, the invention provides a small-interference stability analysis method suitable for a flexible direct current asymmetric working condition, which comprises the following steps: step S1, establishing an MMC-HVDC nonlinear period time-varying state space model; constructing a nonlinear periodic time-varying state space model of a modularized multi-level converter-high-voltage direct current system suitable for asymmetric work