WO2023108769A1 - 平衡点无关的电力系统暂态同步稳定性分析方法及系统 - Google Patents

平衡点无关的电力系统暂态同步稳定性分析方法及系统 Download PDF

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WO2023108769A1
WO2023108769A1 PCT/CN2021/140595 CN2021140595W WO2023108769A1 WO 2023108769 A1 WO2023108769 A1 WO 2023108769A1 CN 2021140595 W CN2021140595 W CN 2021140595W WO 2023108769 A1 WO2023108769 A1 WO 2023108769A1
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power system
synchronization
synchronous
transient
stability
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French (fr)
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刘锋
杨鹏
吴世勇
于沛鑫
沈沉
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清华大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0639—Performance analysis of employees; Performance analysis of enterprise or organisation operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Energy or water supply
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/001—Methods to deal with contingencies, e.g. abnormalities, faults or failures
    • H02J3/00125—Transmission line or load transient problems, e.g. overvoltage, resonance or self-excitation of inductive loads
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H02J3/242—Arrangements for preventing or reducing oscillations of power in networks using phasor measuring units [PMU]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Definitions

  • the present application relates to the field of power system stability analysis and monitoring technology, in particular to a method and system for analyzing the stability of power system transient synchronization regardless of the balance point.
  • the first method calculate the trajectory of the system after the failure by simulation, so as to determine the stability, the obtained result is accurate, and there is no need to know the equilibrium point after the failure, but it often has a large amount of calculation and cannot provide a stability margin other quantitative information;
  • the second method direct method: estimate the stability region of the post-fault equilibrium point by constructing Lyapunov function or energy function, and calculate a certain critical function value, generally called critical energy. If the energy corresponding to the initial value after the fault is smaller than the critical energy, it can be directly determined that the system is stable with large disturbances.
  • the direct method avoids time-consuming simulation calculations and can give quantitative information such as stability margins, so it is favored.
  • the direct method is a stability analysis method for a specific post-failure equilibrium point, that is, a method that is "related" to the equilibrium point.
  • the equilibrium point of the system after the failure needs to be known in advance before the failure.
  • the post-failure equilibrium point is often difficult to predict in advance. There are at least three difficulties in the following aspects: 1) The dynamics of the system are complex and large-scale; 2) The operating point fluctuations caused by the high proportion of new energy; Converge to which equilibrium point. The above problems cause the direct method "correlated" with the equilibrium point to face serious challenges in practical application.
  • This application provides an equilibrium-point-independent analysis method and system for power system transient synchronous stability. Time-consuming simulation calculation, and can provide quantitative information such as stability margin.
  • an equilibrium-point-independent power system transient synchronous stability analysis method including:
  • the transient synchronization stability of the power system is judged according to the initial value of the power system after a fault.
  • the present application before determining the synchronous energy function corresponding to the power system model according to the power system model, it further includes:
  • State variables of the power system are determined from the power system model.
  • the power system model is determined according to the following formula:
  • x 1 and x 2 are the sub-state variables of the power system, is n 1- dimensional Euclidean space, is the n 2- dimensional Euclidean space, z is the algebraic variable of the power system, ⁇ is the phase angle of each node of the power system, V is the voltage amplitude of each node of the power system, col( ⁇ ) is a column vector splicing function, f 1 ( ⁇ ), f 2 ( ⁇ ), g( ⁇ ) are quadratic continuous differentiable functions.
  • the determining the state variables of the power system according to the power system model includes:
  • n n 1 +n 2
  • x is the state variable of the power system
  • x 1 and x 2 are the sub-state variables of the power system.
  • the determining the synchronous energy function corresponding to the power system model according to the power system model includes:
  • the synchronous energy function is determined according to the state variable of the power system and the algebraic variable of the power system; wherein, the synchronous energy function satisfies the following formula at the same time:
  • x is the state variable of the power system
  • z is the algebraic variable of the power system
  • ⁇ ( ), ⁇ ( ) are vector functions
  • ⁇ ( ), ⁇ ( ) and ⁇ ( ) is a K-type function
  • c is a constant not less than
  • h( ) is a set Continuously differentiable functions on ;
  • the continuous differentiable function h( ) is defined as:
  • the collection gather is a connected open set and satisfies the algebraic nonsingularity condition
  • the determining the synchronization convergence domain according to the synchronization energy function includes:
  • the synchronization convergence domain is determined according to the level set.
  • the definition of the level set is:
  • the judging the transient synchronization stability of the power system based on the synchronization convergence domain based on the initial value of the power system after a fault includes:
  • the judging the transient synchronization stability of the power system based on the synchronization convergence domain based on the initial value of the power system after a fault includes:
  • the synchronization energy is greater than the critical energy value, it is determined that the power system is unstable in a transient state.
  • the method proposed in the embodiment of the first aspect of the present application determines the synchronous energy function corresponding to the power system model according to the power system model; determines the synchronous convergence domain according to the synchronous energy function; and based on the synchronous convergence domain, Judging the transient synchronous stability of the power system based on the initial value of the power system after the fault.
  • This application can directly judge the transient synchronous stability of the power system according to the initial value of the power system after the fault without knowing the information of the balance point after the fault. At the same time, it can avoid time-consuming simulation calculations and provide a stability margin. and other quantitative information.
  • an equilibrium-point-independent power system transient synchronous stability analysis system including:
  • a function determination module configured to determine a synchronous energy function corresponding to the power system model according to the power system model
  • a convergence region determination module configured to determine a synchronization convergence region according to the synchronization energy function
  • the stability judging module is used to judge the transient synchronous stability of the power system based on the synchronous convergence domain and according to the initial value of the power system after a fault.
  • the system proposed in the embodiment of the second aspect of the present application uses a function determination module to determine the synchronization energy function corresponding to the power system model according to the power system model; a convergence domain determination module is used to determine the synchronization energy function according to the synchronization energy The function determines the synchronous convergence domain; the stability judging module is used for judging the transient synchronous stability of the power system based on the synchronous convergence domain and according to the initial value of the power system after a fault.
  • This application can directly judge the transient synchronous stability of the power system according to the initial value of the power system after the fault without knowing the information of the balance point after the fault. At the same time, it can avoid time-consuming simulation calculations and provide a stability margin. and other quantitative information.
  • Fig. 1 is the flow chart of a kind of balance point irrelevant power system transient synchronous stability analysis method provided by the embodiment of the present application;
  • FIG. 2 is a schematic structural diagram of an IEEE-9 node power system provided by an embodiment of the present application.
  • FIG. 3 is a schematic diagram of the synchronous convergence domain provided by the embodiment of the present application and the system trajectory starting from two initial points of the power system after a fault;
  • FIG. 4 is a schematic diagram of waveforms of voltages and phase angles of each node corresponding to the first track provided by the embodiment of the present application;
  • FIG. 5 is a schematic diagram of waveforms of voltages and phase angles of each node corresponding to the second track provided by the embodiment of the present application, and the phase angle changes with time;
  • FIG. 6 is a schematic structural diagram of an equilibrium point-independent power system transient synchronous stability analysis system provided by an embodiment of the present application.
  • the direct method transforms the transient stability problem into a Lyapunov asymptotic stability problem of the equilibrium point.
  • any solution starting from its stable domain will asymptotically converge to this equilibrium point. Therefore, if the post-fault equilibrium point is asymptotically stable, and the post-fault initial value is within its stable domain, it can be judged that the system is transiently stable after a disturbance.
  • the real stable domain of the equilibrium point is often difficult to accurately describe, it is generally by finding the inner approximation of the stable domain to obtain a conservative temporary stability judgment.
  • the existing direct methods such as the dominant unstable equilibrium point BCU method based on the stable domain boundary theory, the potential energy boundary surface PEBS method, etc., first construct a suitable Lyapunov function or energy function based on the system model, The stable region is then estimated by the level set of the function.
  • the existing direct method needs to know the equilibrium point after the fault, and the stable domain studied is only valid for this equilibrium point, and the result obtained is only the estimation of the stable domain of a single equilibrium point, that is, it can only judge whether the system trajectory after the fault is Converge to a single equilibrium point determined in advance. Therefore, the direct method is an equilibrium point-dependent method and cannot be used when the equilibrium point after a fault is unknown or when there are multiple possible equilibrium points after a fault.
  • the synchronous state refers to a state in which the voltage phasor amplitude of each node in the power system is constant and rotates synchronously at the same frequency.
  • the synchronous state is the state that all AC power systems should have when they operate stably. The synchrony itself has nothing to do with the equilibrium point.
  • FIG. 1 is a flow chart of an equilibrium-point-independent power system transient synchronization stability analysis method provided by an embodiment of the present application.
  • an equilibrium-point-independent power system transient synchronization stability analysis method includes the following steps:
  • Step 101 determining a synchronous energy function corresponding to the power system model according to the power system model
  • Step 102 determining the synchronization convergence domain according to the synchronization energy function
  • Step 103 based on the synchronization convergence domain, judge the transient synchronization stability of the power system according to the initial value of the power system after the fault.
  • the state variables of the power system are determined according to the power system model.
  • the power system model is determined according to the following formula:
  • x 1 and x 2 are the sub-state variables of the power system, is n 1- dimensional Euclidean space, is the n 2- dimensional Euclidean space, z is the algebraic variable of the power system, ⁇ is the phase angle of each node of the power system, V is the voltage amplitude of each node of the power system, col( ⁇ ) is a column vector splicing function, f 1 ( ⁇ ), f 2 ( ⁇ ), g( ⁇ ) are quadratic continuous differentiable functions.
  • the solution of the structure-preserving model of the power system is (x(t,x 0 ,z 0 ),z(t,x 0 , z 0 )), when the initial value is clear, the solution of the structure-preserving model of the power system is abbreviated as (x(t),z(t)).
  • the structure preserving model of the power system satisfies the algebraic nonsingularity condition.
  • Algebraic singularity corresponds to the short-term voltage collapse problem of the power system, which does not belong to the scope of consideration of the embodiments of the present application.
  • algebraic nonsingularity guarantees a certain regularity of differential algebraic equations, which is called the index-1 property.
  • algebraic variables can be represented locally as functions of state variables, and the derivatives of algebraic variables are well-defined.
  • the collection gather is a connected open set and satisfies the algebraic nonsingularity condition, that is, for any in, for The closure of , det( ⁇ ) is the matrix determinant.
  • the set of equilibrium points satisfying the algebraic non-singularity condition of the power system is determined according to the following formula:
  • power system transient synchronization refers to the frequency synchronization and voltage convergence of all nodes in the power system network, which is defined mathematically as for any t ⁇ 0, hour,
  • the power system after the fault returns to the synchronous state, that is, when the transient synchronous state is stable, it is defined mathematically as for any t ⁇ 0, And when t ⁇ ,
  • the state variables of the power system are determined according to the power system model, including:
  • n n 1 +n 2
  • x is the state variable of the power system
  • x 1 and x 2 are the sub-state variables of the power system.
  • the synchronization energy function corresponding to the power system model is determined according to the power system model, including:
  • x is the state variable of the power system
  • z is the algebraic variable of the power system
  • ⁇ ( ), ⁇ ( ) are vector functions
  • ⁇ ( ), ⁇ ( ) and ⁇ ( ) is a K-type function
  • c is a constant not less than
  • h( ) is a set Continuously differentiable functions on ;
  • the continuous differentiable function h( ) is defined as:
  • the collection gather is a connected open set and satisfies the algebraic nonsingularity condition
  • the synchronization energy function middle, and, any
  • the synchronization convergence domain is determined according to the synchronization energy function, including:
  • the domain of synchronization convergence is determined according to the level set.
  • determining the critical energy value Also, make sure The larger the critical energy value l, the lower the conservatism.
  • level set is:
  • the transient synchronization stability of the power system is judged according to the initial value of the power system after a fault, including:
  • the transient synchronization stability of the power system is judged according to the initial value of the power system after a fault, including:
  • the synchronous energy corresponding to the initial value of the power system after the fault is determined
  • the synchronization energy is greater than the critical energy value, it is judged that the transient synchronization of the power system is unstable.
  • FIG. 2 is a schematic structural diagram of an IEEE-9 node power system provided by an embodiment of the present application.
  • nodes 1 and 2 are connected to synchronous generators
  • node 3 is connected to a power electronic power supply
  • nodes 5, 7 and 9 are constant power loads.
  • the power system transient synchronization stability analysis method provided by the embodiment of the present application specifically includes the following steps:
  • Step 201 obtain the dynamics of node 1; assume that the synchronous generator connected to node 1 has a strong excitation control so that the internal potential is approximately constant during the transient process, and a speed controller is used to restore the system frequency. Then determine the dynamics of the synchronous generator connected to node 1 according to the following formula:
  • M 1 is the inertia of the synchronous generator connected to node 1 and M 1 >0
  • D 1 is the damping of the synchronous generator connected to node 1 and D 1 >0
  • u( ⁇ ) is the PI control of the frequency deviation
  • the PI control of the frequency deviation is determined according to the following formula:
  • the PI control of the frequency deviation can be equivalent to the following differential form:
  • E is the internal potential of the synchronous generator connected to node 1 and E>0
  • x′ d1 is the d-axis transient reactance
  • V 1 ⁇ 1 is the terminal voltage of node 1.
  • Step 202 obtain the dynamics of node 2; determine the dynamics of the synchronous generator connected to node 2 according to the following formula:
  • M 2 is the inertia of the synchronous generator connected to node 2 and M 2 >0
  • D 2 is the damping of the synchronous generator connected to node 2 and D 2 >0
  • T′ d0 is the d-axis open-circuit transient time constant and T′ d0 >0
  • E′ q is the q-axis transient voltage
  • x d2 is the d-axis synchronous reactance of the synchronous generator connected to node 2
  • x ′d2 is the node 2 d-axis transient reactance of the connected synchronous generator.
  • x q2 is the q-axis synchronous reactance of the synchronous generator connected to node 2
  • V 2 ⁇ 2 is the terminal voltage of node 2.
  • Step 203 obtain the dynamics of node 3; since node 3 is a power source device of the power electronics interface, the output power can be adjusted by droop control according to the node voltage, and the specific dynamic equation is as follows:
  • ⁇ 1 and ⁇ 2 are time constants and ⁇ 1 and ⁇ 2 >0
  • d 1 and d 2 are droop coefficients and d 1 and d 2 >0
  • P 3 is the active power output by node 3
  • Q 3 is the node 3 Output reactive power
  • V 3 ⁇ 3 is the voltage of node 3
  • the superscript ref indicates the set value of the corresponding variable.
  • Step 204 determine the power system model and the state variables of the power system; make each node satisfy the power balance constraint to form an algebraic equation group, wherein the algebraic equation group is determined according to the following formula:
  • P i is the net injected active power of node i
  • Q i is the net injected reactive power of node i
  • G ij and B ij are the network admittance of the power system elements in the matrix.
  • the power system model is determined according to the node 1, node 2 and node 3 dynamics.
  • the state variables of the power system can be obtained as
  • Step 205 construct a synchronous energy function; determine the synchronous energy function corresponding to the IEEE-9 node power system provided by the embodiment of the present application according to the following formula:
  • level set is an 8-dimensional submanifold in a 26-dimensional Euclidean space, projecting it onto the 2-dimensional plane of ⁇ - ⁇ 1 , an elliptical projection can be obtained, as shown in Figure 3.
  • Step 207 judging the transient synchronous stability; if the initial value of the power system after the fault is within the estimated synchronous convergence region, then judging the transient synchronous stability of the power system.
  • the simulation calculates the system trajectories starting from the two initial points (-0.15,-1) and (0.15,1) of the power system after the fault respectively, and the projection on the ⁇ - ⁇ 1 plane. As shown in Figure 3, the first and second trajectories located within the estimated simultaneous convergence region are obtained. According to the method provided in the embodiment of the present application, it can be directly judged that the two power systems after the fault can recover the synchronous state, that is, the transient state is synchronously stable.
  • simulation results are used to verify the effectiveness of the methods provided in the embodiments of the present application.
  • the method provided by the embodiment of the present application does not depend on or be limited to a certain balance point after a fault, and can solve the stability analysis problem when the balance point is unknown; and can adapt to the situation where there are multiple balance points and the balance point is not isolated situation, which can solve the problem of stability analysis in more complex situations.
  • the waveforms of the node voltages and phase angles changing with time corresponding to the first track are shown in Figure 4; the waveforms of the node voltages and phase angles changing with time corresponding to the second track are shown in Figure 5.
  • the power system after the fault corresponding to the first trajectory and the second trajectory can recover to the state of frequency synchronization and voltage convergence.
  • the waveforms corresponding to the first trajectory and the second trajectory finally converge to different phase angle values and voltage values, indicating that the equilibrium points after the fault corresponding to the first trajectory and the second trajectory are not the same.
  • the method proposed in the embodiment of this application determines the synchronous energy function corresponding to the power system model according to the power system model; determines the synchronous convergence domain according to the synchronous energy function; System Transient Synchronous Stability.
  • This application can directly judge the transient synchronous stability of the power system according to the initial value of the power system after the fault without knowing the information of the balance point after the fault. At the same time, it can avoid time-consuming simulation calculations and provide a stability margin.
  • Quantitative information such as quantitative information, can be adapted to various types of dynamic equipment and lossy networks, with wider application and stronger engineering practicability.
  • the present application also proposes an equilibrium-point-independent power system transient synchronization stability analysis system.
  • FIG. 6 is a schematic structural diagram of an equilibrium point-independent power system transient synchronous stability analysis system provided by an embodiment of the present application.
  • an equilibrium-point-independent power system transient synchronous stability analysis system includes:
  • a function determination module 601 configured to determine a synchronous energy function corresponding to the power system model according to the power system model
  • a convergence domain determination module 602 configured to determine a synchronization convergence domain according to a synchronization energy function
  • the stability judging module 603 is configured to judge the transient synchronous stability of the power system based on the initial value of the power system after a fault based on the synchronization convergence domain.
  • the system proposed in the embodiment of the present application uses the function determination module to determine the synchronization energy function corresponding to the power system model according to the power system model; the convergence domain determination module is used to determine the synchronization convergence domain according to the synchronization energy function; The stability judgment module is used for judging the transient synchronization stability of the power system based on the synchronization convergence domain and the initial value of the power system after a fault.
  • This application can directly judge the transient synchronous stability of the power system according to the initial value of the power system after the fault without knowing the information of the balance point after the fault. At the same time, it can avoid time-consuming simulation calculations and provide a stability margin.
  • Quantitative information such as quantitative information, can be adapted to various types of dynamic equipment and lossy networks, with wider application and stronger engineering practicability.
  • each part of the present application may be realized by hardware, software, firmware or a combination thereof.
  • various steps or methods may be implemented by software or firmware stored in memory and executed by a suitable instruction execution system.
  • a suitable instruction execution system For example, if implemented in hardware, as in another embodiment, it can be implemented by any one or combination of the following techniques known in the art: Discrete logic circuits, ASICs with suitable combinational logic gates, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.
  • each functional unit in each embodiment of the present application may be integrated into one processing module, each unit may exist separately physically, or two or more units may be integrated into one module.
  • the above-mentioned integrated modules can be implemented in the form of hardware or in the form of software function modules. If the integrated modules are implemented in the form of software function modules and sold or used as independent products, they can also be stored in a computer-readable storage medium.
  • the storage medium mentioned above may be a read-only memory, a magnetic disk or an optical disk, and the like.

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Abstract

一种平衡点无关的电力系统暂态同步稳定性分析方法及系统，属于电力系统稳定分析和监测技术领域。其中，平衡点无关的电力系统暂态同步稳定性分析方法，包括：根据电力系统模型确定与电力系统模型对应的同步能量函数（101）；根据同步能量函数确定同步收敛域（102）；基于同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性（103）。在无需知道故障后平衡点的信息的前提下，根据故障后电力系统初值，直接判断电力系统暂态同步稳定性，同时，可以避免耗时的仿真计算，并且能提供稳定裕度等定量信息。

Description

平衡点无关的电力系统暂态同步稳定性分析方法及系统
相关申请的交叉引用
本申请基于申请号为202111553917.0、申请日为2021年12月17日的中国专利申请提出，并要求该项中国专利申请的优先权，将该项中国专利申请的全部内容在此引入本申请作为参考。
技术领域
本申请涉及电力系统稳定分析和监测技术领域，尤其涉及一种平衡点无关的电力系统暂态同步稳定性分析方法及系统。
背景技术
现有技术采用以下两种方法分析电力系统暂态稳定性：
第一种方法，时域仿真法：通过仿真计算得出系统故障后的轨迹，从而判定稳定性，所得结果精确，不需要知道故障后平衡点，但往往计算量大，且不能提供稳定裕度等定量信息；
第二种方法，直接法：通过构造李雅普诺夫函数或能量函数来估计故障后平衡点的稳定域，并计算某个临界函数值，一般称为临界能量。若故障后初值对应的能量比临界能量小，则可直接判定系统大扰动稳定。直接法避免了耗时的仿真计算，并且能给出稳定裕度等定量信息，备受青睐。
然而，直接法是针对特定故障后平衡点的稳定性分析方法，即与平衡点“相关”的方法。应用该方法，需要在故障前事先知道故障后系统的平衡点。但是，故障后平衡点往往很难在事前预知。至少有以下三个方面的困难：1)系统动 态复杂、规模庞大；2)高比例新能源造成的工作点波动；3)故障后系统平衡点不唯一甚至非孤立，难以事先预知故障后轨迹会收敛到哪一个平衡点。上述问题导致与平衡点“相关”的直接法在实际应用中面临严峻挑战。随着大量新能源和电力电子设备的接入，电力系统的暂态稳定性问题愈发棘手，而新能源的波动和系统动态的复杂化却使得故障后平衡点的预知愈发困难。在这样的背景下，如何在不知道故障后平衡点具体信息的情况下判断系统的暂态同步稳定性是亟需解决的问题。
发明内容
本申请提供了一种平衡点无关的电力系统暂态同步稳定性分析方法及系统，主要目的在于在不知道故障后平衡点具体信息的情况下判断系统的暂态同步稳定性，同时，可以避免耗时的仿真计算，并且能提供稳定裕度等定量信息。
根据本公开的一方面，提供了一种平衡点无关的电力系统暂态同步稳定性分析方法，包括：
根据电力系统模型确定与所述电力系统模型对应的同步能量函数；
根据所述同步能量函数确定同步收敛域；
基于所述同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性。
在一些实施例中，在本申请的一个实施例中，在所述根据电力系统模型确定与所述电力系统模型对应的同步能量函数之前，还包括：
确定电力系统模型；
根据所述电力系统模型确定电力系统的状态变量。
在一些实施例中，在本申请的一个实施例中，根据下式确定所述电力系统 模型：
Figure PCTCN2021140595-appb-000001
Figure PCTCN2021140595-appb-000002
Figure PCTCN2021140595-appb-000003
其中，x 1、x 2为电力系统的子状态变量，
Figure PCTCN2021140595-appb-000004
为n 1维欧式空间，
Figure PCTCN2021140595-appb-000005
为n 2维欧式空间，z为电力系统的代数变量，θ为电力系统各节点的相角，V为电力系统各节点的电压幅值，col(·)为列向量拼接函数，f 1(·)、f 2(·)、g(·)为二次连续可微函数。
在一些实施例中，在本申请的一个实施例中，所述根据所述电力系统模型确定电力系统的状态变量，包括：
根据电力系统的子状态变量确定电力系统的状态变量，其中，根据下式确定电力系统的状态变量：
Figure PCTCN2021140595-appb-000006
n＝n 1+n 2
Figure PCTCN2021140595-appb-000007
其中，x为电力系统的状态变量，x 1、x 2为电力系统的子状态变量。
在一些实施例中，在本申请的一个实施例中，所述根据电力系统模型确定与所述电力系统模型对应的同步能量函数，包括：
根据电力系统的状态变量以及电力系统的代数变量确定所述同步能量函数；其中，所述同步能量函数同时满足以下公式：
Figure PCTCN2021140595-appb-000008
Figure PCTCN2021140595-appb-000009
||h(x，z)||≤c||η(x，z)||
其中，
Figure PCTCN2021140595-appb-000010
为连续可微的同步能量函数，x为电力系统的状态变量，z为电力系统的代数变量，η(·)、ξ(·)为向量函数，α(·)、β(·)和γ(·)为K类函数，c为不小于0的常数，h(·)为集合
Figure PCTCN2021140595-appb-000011
上的连续可微函数；
其中，连续可微函数h(·)定义为：
Figure PCTCN2021140595-appb-000012
其中，集合
Figure PCTCN2021140595-appb-000013
集合
Figure PCTCN2021140595-appb-000014
为一个连通的开集，并满足代数非奇异条件；
其中，K类函数为[0,k)→[0,∞)的单调递增的连续函数，且K(0)＝0。
在一些实施例中，在本申请的一个实施例中，所述根据所述同步能量函数确定同步收敛域，包括：
确定所述同步能量函数的临界能量值；
确定所述同步能量函数的临界能量值的水平集；
根据所述水平集确定所述同步收敛域。
在一些实施例中，在本申请的一个实施例中，所述水平集的定义为：
Figure PCTCN2021140595-appb-000015
其中，
Figure PCTCN2021140595-appb-000016
为水平集，l为临界能量值，
Figure PCTCN2021140595-appb-000017
为同步能量函数，x为电力系统的状态变量，z为电力系统的代数变量，G为满足代数约束0＝g(x 2,z)的点的集合，
Figure PCTCN2021140595-appb-000018
为n维欧式空间，
Figure PCTCN2021140595-appb-000019
为m维欧式空间。
在一些实施例中，在本申请的一个实施例中，所述基于所述同步收敛域， 根据故障后电力系统初值判断电力系统暂态同步稳定性，包括：
若所述故障后电力系统初值位于所述同步收敛域内，则判断电力系统暂态同步稳定；
反之，则判断电力系统暂态同步不稳定。
在一些实施例中，在本申请的一个实施例中，所述基于所述同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性，包括：
基于所述同步能量函数，确定故障后电力系统初值对应的同步能量；
若所述同步能量不大于所述临界能量值，则判断电力系统暂态同步稳定；
若所述同步能量大于所述临界能量值，则判断电力系统暂态同步不稳定。
综上，本申请第一方面实施例提出的方法，通过根据电力系统模型确定与所述电力系统模型对应的同步能量函数；根据所述同步能量函数确定同步收敛域；基于所述同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性。本申请可以在无需知道故障后平衡点的信息的前提下，根据故障后电力系统初值，直接判断电力系统暂态同步稳定性，同时，可以避免耗时的仿真计算，并且能提供稳定裕度等定量信息。
根据本申请的另一方面，提供了一种平衡点无关的电力系统暂态同步稳定性分析系统，包括：
函数确定模块，用于根据电力系统模型确定与所述电力系统模型对应的同步能量函数；
收敛域确定模块，用于根据所述同步能量函数确定同步收敛域；
稳定性判断模块，用于基于所述同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性。
综上，本申请第二方面实施例提出的系统，通过函数确定模块，用于根据 电力系统模型确定与所述电力系统模型对应的同步能量函数；收敛域确定模块，用于根据所述同步能量函数确定同步收敛域；稳定性判断模块，用于基于所述同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性。本申请可以在无需知道故障后平衡点的信息的前提下，根据故障后电力系统初值，直接判断电力系统暂态同步稳定性，同时，可以避免耗时的仿真计算，并且能提供稳定裕度等定量信息。
本申请附加的方面和优点将在下面的描述中部分给出，部分将从下面的描述中变得明显，或通过本申请的实践了解到。
附图说明
本申请上述的和/或附加的方面和优点从下面结合附图对实施例的描述中将变得明显和容易理解，其中：
图1为本申请实施例所提供的一种平衡点无关的电力系统暂态同步稳定性分析方法的流程图；
图2为本申请实施例所提供的IEEE-9节点电力系统的结构示意图；
图3为本申请实施例所提供的同步收敛域以及从两个故障后电力系统初值点出发的系统轨迹的示意图；
图4为本申请实施例所提供的第一条轨迹对应的各节点电压、相角随时间变化的波形示意图；
图5为本申请实施例所提供的第二条轨迹对应的各节点电压、相角随时间变化的波形示意图；
图6为本申请实施例所提供的一种平衡点无关的电力系统暂态同步稳定性分析系统的结构示意图。
具体实施方式
下面详细描述本申请的实施例，所述实施例的示例在附图中示出，其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施例是示例性的，仅用于解释本申请，而不能理解为对本申请的限制。相反，本申请的实施例包括落入所附加权利要求书的精神和内涵范围内的所有变化、修改和等同物。
需要说明的是，在数学上，目前的电力系统的暂态稳定性问题通过李雅普诺夫稳定性理论框架进行研究。在该理论框架下，首先将故障后的电力系统建模为一组常微分方程组(ODEs)或微分代数方程组(DAEs)。该方程组的平衡点对应着故障后电力系统的平衡点。
根据一些实施例，直接法将暂态稳定性问题转化为平衡点的李雅普诺夫渐近稳定(Asymptotical Stability)问题。根据相关的数学结论，对于渐近稳定的平衡点，任何从其稳定域出发的解都会渐近收敛到该平衡点。因此，如果故障后平衡点是渐近稳定的，并且故障后初值在其稳定域内，则可判断系统受扰后暂态稳定。在具体应用时，由于平衡点真实的稳定域往往难以准确刻画，所以一般是通过寻找稳定域的内近似，从而得出保守的暂稳判断。
在一些实施例中，现有的直接法，例如基于稳定域边界理论的主导不稳定平衡点BCU法、位能边界曲面PEBS法等，先基于系统模型构造合适的李雅普诺夫函数或者能量函数，然后通过函数的水平集来估计稳定域。但是现有直接法需要知道故障后的平衡点，研究的稳定域也是仅对该平衡点有效的稳定域，所得结果也只是对单个平衡点的稳定域估计，即只能判断故障后系统轨迹是否收敛到事先确定的单个平衡点。因此，直接法是一种平衡点相关的方法，当故障后平衡点未知或者当故障后存在多个可能的平衡点时不能使用。
需要说明的是，同步态指的是电力系统全网各节点电压相量幅值恒定并以相同的频率同步旋转的一种状态。同步态是所有交流电力系统稳定运行时应该具备的状态。同步态本身与平衡点无关。
下面结合具体的实施例对本申请进行详细说明。
图1为本申请实施例所提供的一种平衡点无关的电力系统暂态同步稳定性分析方法的流程图。
如图1所示，本申请实施例提供的一种平衡点无关的电力系统暂态同步稳定性分析方法，包括以下步骤：
步骤101，根据电力系统模型确定与电力系统模型对应的同步能量函数；
步骤102，根据同步能量函数确定同步收敛域；
步骤103，基于同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性。
在本申请实施例中，在根据电力系统模型确定与电力系统模型对应的同步能量函数之前，还包括：
确定电力系统模型；
根据电力系统模型确定电力系统的状态变量。
在本申请实施例中，根据下式确定电力系统模型：
Figure PCTCN2021140595-appb-000020
Figure PCTCN2021140595-appb-000021
Figure PCTCN2021140595-appb-000022
其中，x 1、x 2为电力系统的子状态变量，
Figure PCTCN2021140595-appb-000023
为n 1维欧式空间，
Figure PCTCN2021140595-appb-000024
为n 2维欧式空间，z为电力系统的代数变量，θ为电力系统各节点的相角，V为电力系统各节点的电压幅值，col(·)为列向量拼接函数，f 1(·)、f 2(·)、g(·)为二次连续可微函数。
在一些实施例中，若电力系统所有的子状态变量都出现在代数约束0＝g(x 2,z)中，则
Figure PCTCN2021140595-appb-000025
在一些实施例中，根据下式确定满足代数约束0＝g(x 2,z)的点的集合：
Figure PCTCN2021140595-appb-000026
对任意的故障后电力系统初值(x 0,z 0)∈G，此时，电力系统的结构保留模型的解为(x(t,x 0,z 0),z(t,x 0,z 0))，当初值明确时，电力系统的结构保留模型的解简记为(x(t),z(t))。
在一些实施例中，电力系统的结构保留模型满足代数非奇异条件。代数奇异时对应电力系统的短时电压崩溃问题，不属于本申请实施例的考虑范畴。
需要说明的是，代数非奇异保证了微分代数方程组的某种正则性，称为index-1性质。在非奇异的点处，根据隐函数定理，代数变量可以局部的表示为状态变量的函数，并且代数变量的导数具有良好定义。
在一些实施例中，集合
Figure PCTCN2021140595-appb-000027
集合
Figure PCTCN2021140595-appb-000028
为一个连通的开集，并满足代数非奇异条件，即对任意
Figure PCTCN2021140595-appb-000029
其中，
Figure PCTCN2021140595-appb-000030
为
Figure PCTCN2021140595-appb-000031
的闭包，det(·)为矩阵行列式。
根据一些实施例，根据下式确定电力系统满足代数非奇异条件的平衡点集：
Figure PCTCN2021140595-appb-000032
Figure PCTCN2021140595-appb-000033
需要说明的是，电力系统暂态同步指的是电力系统全网各节点的频率同步、电压收敛，在数学上定义为对任意的t≥0，
Figure PCTCN2021140595-appb-000034
时，
Figure PCTCN2021140595-appb-000035
根据一些实施例，故障后的电力系统恢复到同步态，即暂态同步稳定时，在数学上定义为对任意的t≥0，
Figure PCTCN2021140595-appb-000036
并且当t→∞时，
Figure PCTCN2021140595-appb-000037
Figure PCTCN2021140595-appb-000038
在本申请实施例中，根据电力系统模型确定电力系统的状态变量，包括：
根据电力系统的子状态变量确定电力系统的状态变量，其中，根据下式确定电力系统的状态变量：
Figure PCTCN2021140595-appb-000039
n＝n 1+n 2
Figure PCTCN2021140595-appb-000040
其中，x为电力系统的状态变量，x 1、x 2为电力系统的子状态变量。
在本申请实施例中，根据电力系统模型确定与电力系统模型对应的同步能量函数，包括：
根据电力系统的状态变量以及电力系统的代数变量确定同步能量函数；其中，同步能量函数同时满足以下公式：
Figure PCTCN2021140595-appb-000041
Figure PCTCN2021140595-appb-000042
||h(x，z)||≤c||η(x，z)||
其中，
Figure PCTCN2021140595-appb-000043
为连续可微的同步能量函数，x为电力系统的状态变量，z为 电力系统的代数变量，η(·)、ξ(·)为向量函数，α(·)、β(·)和γ(·)为K类函数，c为不小于0的常数，h(·)为集合
Figure PCTCN2021140595-appb-000044
上的连续可微函数；
其中，连续可微函数h(·)定义为：
Figure PCTCN2021140595-appb-000045
其中，集合
Figure PCTCN2021140595-appb-000046
集合
Figure PCTCN2021140595-appb-000047
为一个连通的开集，并满足代数非奇异条件；
其中，K类函数为[0,k)→[0,∞)的单调递增的连续函数，且K(0)＝0。
在一些实施例中，
Figure PCTCN2021140595-appb-000048
在一些实施例中，在同步能量函数
Figure PCTCN2021140595-appb-000049
中，
Figure PCTCN2021140595-appb-000050
并且，任意的
Figure PCTCN2021140595-appb-000051
在一些实施例中，在向量函数η(·)中，
Figure PCTCN2021140595-appb-000052
在一些实施例中，在向量函数ξ(·)中，
Figure PCTCN2021140595-appb-000053
在本申请实施例中，根据同步能量函数确定同步收敛域，包括：
确定同步能量函数的临界能量值；
确定同步能量函数的临界能量值的水平集；
根据水平集确定同步收敛域。
在一些实施例中，确定临界能量值
Figure PCTCN2021140595-appb-000054
同时，确定
Figure PCTCN2021140595-appb-000055
临界能量值l越大，则保守性越低。
在本申请实施例中，水平集的定义为：
Figure PCTCN2021140595-appb-000056
其中，
Figure PCTCN2021140595-appb-000057
为水平集，l为临界能量值，
Figure PCTCN2021140595-appb-000058
为同步能量函数，x为电力系统的状态变量，z为电力系统的代数变量，G为满足代数约束0＝g(x 2,z)的点的集合，
Figure PCTCN2021140595-appb-000059
为n维欧式空间，
Figure PCTCN2021140595-appb-000060
为m维欧式空间。
在本申请实施例中，基于同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性，包括：
若故障后电力系统初值位于同步收敛域内，则判断电力系统暂态同步稳定；
反之，则判断电力系统暂态同步不稳定。
在本申请实施例中，基于同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性，包括：
基于同步能量函数，确定故障后电力系统初值对应的同步能量；
若同步能量不大于临界能量值，则判断电力系统暂态同步稳定；
若同步能量大于临界能量值，则判断电力系统暂态同步不稳定。
在一些实施例中，若
Figure PCTCN2021140595-appb-000061
则(x 0,z 0)位于同步收敛域
Figure PCTCN2021140595-appb-000062
之内，此时判断电力系统暂态同步稳定；若
Figure PCTCN2021140595-appb-000063
则(x 0,z 0)不位于同步收敛域
Figure PCTCN2021140595-appb-000064
之内，此时判断电力系统暂态同步不稳定。
以一种场景举例，图2为本申请实施例提供的IEEE-9节点电力系统的结构示意图。如图2所示，节点1和节点2接有同步发电机，节点3接有电力电子型电源，节点5、节点7和节点9为恒功率负荷。本申请实施例提供的电力系统暂态同步稳定性分析方法，具体包括以下步骤：
步骤201，获取节点1动态；假设节点1所连同步发电机带有较强的励磁控制使得内电势在暂态过程中近似为常数，并带有调速控制器用以恢复系统频 率。则根据下式确定节点1所连同步发电机的动态：
Figure PCTCN2021140595-appb-000065
其中，M 1为节点1所连同步发电机的惯量且M 1>0，D 1为节点1所连同步发电机的阻尼且D 1>0，
Figure PCTCN2021140595-appb-000066
为输入功率，
Figure PCTCN2021140595-appb-000067
受PI调速控制，即
Figure PCTCN2021140595-appb-000068
Figure PCTCN2021140595-appb-000069
为固定的机械输入功率，u(·)为对频率偏差的PI控制；
其中，根据下式确定对频率偏差的PI控制：
Figure PCTCN2021140595-appb-000070
引入状态变量ζ，可将对频率偏差的PI控制等价为以下微分形式：
Figure PCTCN2021140595-appb-000071
因此，节点1所连同步发电机输出的有功功率
Figure PCTCN2021140595-appb-000072
和无功功率
Figure PCTCN2021140595-appb-000073
为：
Figure PCTCN2021140595-appb-000074
其中，E为节点1所连同步发电机的内电势且E>0，x′ d1为d轴暂态电抗，V 1∠θ 1为节点1的机端电压。
步骤202，获取节点2动态；根据下式确定节点2所连同步发电机的动态：
Figure PCTCN2021140595-appb-000075
其中，M 2为节点2所连同步发电机的惯量且M 2>0，D 2为节点2所连同步发电机的阻尼且D 2>0，
Figure PCTCN2021140595-appb-000076
为恒定的输入机械功率且
Figure PCTCN2021140595-appb-000077
为恒定的励磁电压且
Figure PCTCN2021140595-appb-000078
T′ d0为d轴开路暂态时间常数且T′ d0>0，E′ q为q轴暂态电 压，x d2为节点2所连同步发电机的d轴同步电抗，x ′d2为节点2所连同步发电机的d轴暂态电抗。
因此，节点2所连同步发电机输出的有功功率
Figure PCTCN2021140595-appb-000079
和无功功率
Figure PCTCN2021140595-appb-000080
为：
Figure PCTCN2021140595-appb-000081
Figure PCTCN2021140595-appb-000082
其中，x q2为节点2所连同步发电机的q轴同步电抗，V 2∠θ 2为节点2的机端电压。
步骤203，获取节点3动态；由于节点3为电力电子接口的功率源设备，可以根据节点电压采用下垂控制的方式调整输出功率，具体动态方程如下：
Figure PCTCN2021140595-appb-000083
其中，τ 1、τ 2为时间常数且τ 1、τ 2>0，d 1、d 2为下垂系数且d 1、d 2>0，P 3为节点3输出的有功功率，Q 3为节点3输出的无功功率，V 3∠θ 3为节点3的电压，上标ref表示相应变量的设定值。
步骤204，确定电力系统模型以及电力系统的状态变量；令各节点满足功率平衡约束，形成代数方程组，其中，根据下式确定代数方程组：
Figure PCTCN2021140595-appb-000084
其中，P i为节点i的净注入有功功率，Q i为节点i的净注入无功功率， θ ij＝θ i-θ 2为相角差，G ij、B ij为电力系统的网络导纳矩阵中的元素。
基于代数方程组，根据节点1、节点2和节点3动态，确定电力系统模型。
根据电力系统模型，可得电力系统的状态变量为
x＝col(ζ,ω 1,δ 1,ω 2,δ 2,E′ q,P 3,Q 3)
步骤205，构造同步能量函数；根据下式确定本申请实施例提供的IEEE-9节点电力系统对应的同步能量函数：
Figure PCTCN2021140595-appb-000085
Figure PCTCN2021140595-appb-000086
步骤206，确定同步收敛域；取临界能量值l＝4的水平集
Figure PCTCN2021140595-appb-000087
作为同步收敛域的估计。水平集
Figure PCTCN2021140595-appb-000088
是一个26维欧式空间中的8维子流形，将其投影到ζ-ω 1的2维平面上，可以得到一个椭圆形投影，如图3所示。
步骤207，判断暂态同步稳定性；如果故障后电力系统初值位于估计的同步收敛域内，则判断电力系统暂态同步稳定。仿真计算分别从两个故障后电力系统初值点(-0.15,-1)、(0.15,1)出发的系统轨迹，并且，在ζ-ω 1平面上的投影。如图3所示，得到位于估计的同步收敛域内的第一条轨迹和第二条轨迹。根据本申请实施例所提供的方法，可直接判断这两个故障后的电力系统可以恢复同步态，即暂态同步稳定。
在一些实施例中，用仿真结果验证本申请实施例所提供的方法的有效性。如图3所示，第一条轨迹、第二条轨迹均收敛到同步态，即ω 1＝0；但是这两 条轨迹最终收敛到的平衡点并不相同。说明本申请实施例所提供的方法不依赖也不局限于某一个故障后的平衡点，可以解决平衡点未知情况下的稳定性分析问题；并且可以适应存在多个平衡点以及平衡点非孤立的情况，可以解决更复杂情况下的稳定性分析问题。
进一步的，第一条轨迹对应的各节点电压、相角随时间变化的波形如图4所示；第二条轨迹对应的各节点电压、相角随时间变化的波形如图5所示。如图4、图5所示，第一条轨迹、第二条轨迹对应的故障后的电力系统均能恢复到频率同步、电压收敛的状态。但是，第一条轨迹、第二条轨迹对应的波形最后收敛到的相角值和电压值并不相同，说明第一条轨迹、第二条轨迹对应的故障后的平衡点并不相同。
综上，本申请实施例提出的方法，通过根据电力系统模型确定与电力系统模型对应的同步能量函数；根据同步能量函数确定同步收敛域；基于同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性。本申请可以在无需知道故障后平衡点的信息的前提下，根据故障后电力系统初值，直接判断电力系统暂态同步稳定性，同时，可以避免耗时的仿真计算，并且能提供稳定裕度等定量信息，可以适应多种类型的动态设备以及有损网络，适用面更广，工程实用性更强。
为了实现上述实施例，本申请还提出一种平衡点无关的电力系统暂态同步稳定性分析系统。
图6为本申请实施例提供的一种平衡点无关的电力系统暂态同步稳定性分析系统的结构示意图。
如图6所示，一种平衡点无关的电力系统暂态同步稳定性分析系统，包括：
函数确定模块601，用于根据电力系统模型确定与电力系统模型对应的同步能量函数；
收敛域确定模块602，用于根据同步能量函数确定同步收敛域；
稳定性判断模块603，用于基于同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性。
综上，本申请实施例提出的系统，通过函数确定模块，用于根据电力系统模型确定与电力系统模型对应的同步能量函数；收敛域确定模块，用于根据同步能量函数确定同步收敛域；稳定性判断模块，用于基于同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性。本申请可以在无需知道故障后平衡点的信息的前提下，根据故障后电力系统初值，直接判断电力系统暂态同步稳定性，同时，可以避免耗时的仿真计算，并且能提供稳定裕度等定量信息，可以适应多种类型的动态设备以及有损网络，适用面更广，工程实用性更强。
需要说明的是，在本申请的描述中，术语“第一”、“第二”等仅用于描述目的，而不能理解为指示或暗示相对重要性。此外，在本申请的描述中，除非另有说明，“多个”的含义是两个或两个以上。
流程图中或在此以其他方式描述的任何过程或方法描述可以被理解为，表示包括一个或更多个用于实现特定逻辑功能或过程的步骤的可执行指令的代码的模块、片段或部分，并且本申请的优选实施方式的范围包括另外的实现，其中可以不按所示出或讨论的顺序，包括根据所涉及的功能按基本同时的方式或按相反的顺序，来执行功能，这应被本申请的实施例所属技术领域的技术人员所理解。
应当理解，本申请的各部分可以用硬件、软件、固件或它们的组合来实现。 在上述实施方式中，多个步骤或方法可以用存储在存储器中且由合适的指令执行系统执行的软件或固件来实现。例如，如果用硬件来实现，和在另一实施方式中一样，可用本领域公知的下列技术中的任一项或他们的组合来实现：具有用于对数据信号实现逻辑功能的逻辑门电路的离散逻辑电路，具有合适的组合逻辑门电路的专用集成电路，可编程门阵列(PGA)，现场可编程门阵列(FPGA)等。
本技术领域的普通技术人员可以理解实现上述实施例方法携带的全部或部分步骤是可以通过程序来指令相关的硬件完成，所述的程序可以存储于一种计算机可读存储介质中，该程序在执行时，包括方法实施例的步骤之一或其组合。
此外，在本申请各个实施例中的各功能单元可以集成在一个处理模块中，也可以是各个单元单独物理存在，也可以两个或两个以上单元集成在一个模块中。上述集成的模块既可以采用硬件的形式实现，也可以采用软件功能模块的形式实现。所述集成的模块如果以软件功能模块的形式实现并作为独立的产品销售或使用时，也可以存储在一个计算机可读取存储介质中。
上述提到的存储介质可以是只读存储器，磁盘或光盘等。
在本说明书的描述中，参考术语“一个实施例”、“一些实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本申请的至少一个实施例或示例中。在本说明书中，对上述术语的示意性表述不一定指的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。
尽管上面已经示出和描述了本申请的实施例，可以理解的是，上述实施例 是示例性的，不能理解为对本申请的限制，本领域的普通技术人员在本申请的范围内可以对上述实施例进行变化、修改、替换和变型。

Claims (10)

  1. 一种平衡点无关的电力系统暂态同步稳定性分析方法，其特征在于，所述方法包括：
    根据电力系统模型确定与所述电力系统模型对应的同步能量函数；
    根据所述同步能量函数确定同步收敛域；
    基于所述同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性。
  2. 如权利要求1所述的方法，其特征在于，在所述根据电力系统模型确定与所述电力系统模型对应的同步能量函数之前，还包括：
    确定电力系统模型；
    根据所述电力系统模型确定电力系统的状态变量。
  3. 如权利要求2所述的方法，其特征在于，根据下式确定所述电力系统模型：
    Figure PCTCN2021140595-appb-100001
    Figure PCTCN2021140595-appb-100002
    Figure PCTCN2021140595-appb-100003
    其中，x 1、x 2为电力系统的子状态变量，
    Figure PCTCN2021140595-appb-100004
    为n 1维欧式空间，
    Figure PCTCN2021140595-appb-100005
    为n 2维欧式空间，z为电力系统的代数变量，θ为电力系统各节点的相角，V为电力系统各节点的电压幅值，col(·)为列向量拼接函数，f 1(·)、f 2(·)、g(·)为二次连 续可微函数。
  4. 如权利要求3所述的方法，其特征在于，所述根据所述电力系统模型确定电力系统的状态变量，包括：
    根据电力系统的子状态变量确定电力系统的状态变量，其中，根据下式确定电力系统的状态变量：
    Figure PCTCN2021140595-appb-100006
    n＝n 1+n 2
    Figure PCTCN2021140595-appb-100007
    其中，x为电力系统的状态变量，x 1、x 2为电力系统的子状态变量。
  5. 如权利要求4所述的方法，其特征在于，所述根据电力系统模型确定与所述电力系统模型对应的同步能量函数，包括：
    根据电力系统的状态变量以及电力系统的代数变量确定所述同步能量函数；其中，所述同步能量函数同时满足以下公式：
    α(||η(x，z)||)≤v(x，z)≤β(||ξ(x，z)||)
    v(x，z)≤-γ(||ξ(x，z)||)
    ||h(x，z)||≤c||η(x，z)||
    其中，v(x，z)为连续可微的同步能量函数，x为电力系统的状态变量，z为电力系统的代数变量，η(·)、ξ(·)为向量函数，α(·)、β(·)和γ(·)为K类函数，c为不小于0的常数，h(·)为集合
    Figure PCTCN2021140595-appb-100008
    上的连续可微函数；
    其中，连续可微函数h(·)定义为：
    Figure PCTCN2021140595-appb-100009
    其中，集合
    Figure PCTCN2021140595-appb-100010
    集合
    Figure PCTCN2021140595-appb-100011
    为一个连通的开集，并满足代数非奇异条件；
    其中，K类函数为[0,k)→[0,∞)的单调递增的连续函数，且K(0)＝0。
  6. 如权利要求5所述的方法，其特征在于，所述根据所述同步能量函数确定同步收敛域，包括：
    确定所述同步能量函数的临界能量值；
    确定所述同步能量函数的临界能量值的水平集；
    根据所述水平集确定所述同步收敛域。
  7. 如权利要求6所述的方法，其特征在于，所述水平集的定义为：
    Figure PCTCN2021140595-appb-100012
    其中，
    Figure PCTCN2021140595-appb-100013
    为水平集，l为临界能量值，v(x，z)为同步能量函数，x为电力系统的状态变量，z为电力系统的代数变量，G为满足代数约束0＝g(x 2,z)的点的集合，
    Figure PCTCN2021140595-appb-100014
    为n维欧式空间，
    Figure PCTCN2021140595-appb-100015
    为m维欧式空间。
  8. 如权利要求1所述的方法，其特征在于，所述基于所述同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性，包括：
    若所述故障后电力系统初值位于所述同步收敛域内，则判断电力系统暂态同步稳定；
    反之，则判断电力系统暂态同步不稳定。
  9. 如权利要求6所述的方法，其特征在于，所述基于所述同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性，包括：
    基于所述同步能量函数，确定故障后电力系统初值对应的同步能量；
    若所述同步能量不大于所述临界能量值，则判断电力系统暂态同步稳定；
    若所述同步能量大于所述临界能量值，则判断电力系统暂态同步不稳定。
  10. 一种平衡点无关的电力系统暂态同步稳定性分析系统，其特征在于， 所述系统包括：
    函数确定模块，用于根据电力系统模型确定与所述电力系统模型对应的同步能量函数；
    收敛域确定模块，用于根据所述同步能量函数确定同步收敛域；
    稳定性判断模块，用于基于所述同步收敛域，根据故障后电力系统初值判断电力系统暂态同步稳定性。
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