An analytical method considering the impact of uncertainty on the dynamic process of power system

Abstract

The present invention provides an analysis method that considers the influence of uncertainty on the dynamic process of the power system, and relates to the field of simulation analysis technology. The method expands the Brownian motion term in the random differential-algebraic equation by the Brownian motion expansion method, and then orderly analyzes the influence of each frequency band in the frequency domain corresponding to the Brownian motion on the transient stability of the system, and finds the frequency band that has the most serious influence on the instability of the power system. The proposed framework has the advantages of not needing to linearize the system, effectively retaining the nonlinearity of the system, and being close to engineering applications, and can project the uncertainty of continuous random excitation over the entire simulation time to the start time of the simulation, reducing the complexity of the simulation calculation, and the obtained analysis results can provide a basis for improving the transient stability of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of simulation analysis, and in particular to an analysis method that takes into account the influence of uncertainty on the dynamic process of a power system. Background Art

[0002] In recent years, with the rapid development of social economy and science and technology, the proportion of new energy power generation such as wind power and photovoltaics and new loads such as electric vehicles in the power system has continued to increase. The strong randomness introduced by them can no longer be ignored. The traditional dynamic power system analysis method often regards generator output and load as constants, which cannot effectively quantify the uncertainty in the system. Therefore, it cannot meet the steady-state and dynamic operation control requirements in the process of transition from the current power grid to a new power system, posing a major challenge to the safe and stable operation of the system.

[0003] The dynamic simulation of the power system is carried out by simulating the system in the form of a set of differential-algebraic equations, taking the steady-state flow calculation results as the initial values, calculating the initial values ​​of the generator state variables, and then using numerical calculation methods such as the implicit trapezoidal method to solve the differential-algebraic equations to obtain system state variables, such as generator power angle, speed, and algebraic variables, such as node voltage amplitude and phase angle. The simulation is to measure the evolution of these variables over a period of time. In the scenario of considering uncertainty, the dynamic characteristics of the power system are transformed from ordinary differential equations to stochastic differential equations based on Brownian motion, which have complex characteristics and difficult to solve. The relationship between the dynamic response of the system and the introduced uncertainty is even more difficult to quantify, and the cause of system instability is difficult to analyze. Traditional analysis methods usually perform a large number of simulations based on the Monte Carlo method, and finally perform statistics and analysis on all the simulation curves and results. However, if continuous random excitation causes system instability, some simulations are forced to terminate at some point in the simulation process, such as power angle instability, voltage collapse, etc. Traditional Monte Carlo simulation is difficult to analyze the internal causes and mechanisms that lead to its instability, and can only observe the instability phenomenon. Traditional stability analysis methods find it difficult to deal with Brownian motion terms in stochastic differential-algebraic equations.

[0004] Most traditional power system dynamic simulation methods are deterministic modeling and do not take uncertainty into consideration. Therefore, they usually need to perform massive sampling of random variables, and then observe and summarize the changes in the simulation curves, that is, perform multiple simulations in a Monte Carlo manner, and finally obtain the probability characteristics of system state variables and algebraic variables after statistical analysis, such as moments of various orders, probability distribution, etc., but they cannot analyze and verify the causes of system instability. Some studies have theoretically analyzed the system instability mechanism caused by generalized forced oscillations, but such studies are usually based on the linearization assumption of the model and cannot retain the nonlinear characteristics of the actual power system, while the nonlinearity of the system is one of the important characteristics of large power grids. In addition, the existing methods cannot deeply analyze the mechanism of random processes affecting the dynamic response of the system under the condition of retaining the original high-order model of the system, and have the disadvantages of being difficult to provide guidance for improving the transient stability of the system for the actual power system. Summary of the invention

[0005] In view of this, the present invention provides an analysis method that considers the impact of uncertainty on the dynamic process of the power system. The method expands the Brownian motion term in the stochastic differential-algebraic equation through the Brownian motion expansion method, and then orderly analyzes the impact of each frequency band in the frequency domain corresponding to the Brownian motion on the transient stability of the system, and finds the frequency band that has the most serious impact on the instability of the power system. The proposed framework has the advantages of not needing to linearize the system, effectively retaining the nonlinearity of the system, and being close to engineering applications. It can also project the uncertainty of continuous random excitation over the entire simulation time to the start time of the simulation, reducing the complexity of the simulation calculation, and the obtained analysis results can provide a basis for improving the transient stability of the system.

[0006] The technical purpose of the present invention is achieved in this way:

[0007] The present invention provides an analysis method considering the influence of uncertainty on the dynamic process of the power system, comprising the following steps:

[0008] S1: Collect the generator parameters, network parameters and load parameters in the power system, model the random disturbances, and construct the original stochastic differential-algebraic equation model of the power system;

[0009] S2: Based on BME, the Brownian motion term in the original stochastic differential-algebraic equation model is transformed to obtain a set of weighted standard independent Gaussian random variables and as BME terms;

[0010] S3: Set the scenario to system stability maintenance and set the initial BME expansion order n1;

[0011] S4: Expand the BME terms according to the current BME expansion order, insert them into the original stochastic differential-algebraic equation model, perform dynamic simulation of the power system, analyze the simulation results, and obtain analysis results;

[0012] S5: increasing the BME expansion order in sequence and going to step S4;

[0013] S6: Repeat steps S4-S5 until the analysis results meet the requirements and obtain the final BME expansion order n2;

[0014] S7: Set the scenario to system instability and set the BME expansion order to n2;

[0015] S8: Orderly remove m BME items to obtain new BME items, expand the new BME items according to the BME expansion order n2, insert them into the original stochastic differential-algebraic equation model, perform R times of power system dynamic simulation, and obtain the number of instability trajectories of the power system;

[0016] S9: Compare and analyze the number of unstable trajectories of the power system to obtain the BME items that affect the dynamic stability of the power system. The corresponding frequency bands in the frequency domain are the key frequency bands that affect the stability of the power system.

[0017] On the basis of the above technical solution, preferably, in step S8, the m BME items that are orderly removed are BME items of different expansion orders, so as to obtain the number of instability trajectories of the power system when removing BME items of different expansion orders.

[0018] Based on the above technical solution, preferably, step S8 includes:

[0019] S81: Expand the complete BME terms according to the BME expansion order n2, and substitute them into the original stochastic differential-algebraic equation model to perform power system simulation and record the dynamic response of the initial power system;

[0020] S82: Sort the BME items from high to low according to the expansion order;

[0021] S83: Select a BME item to remove and update the BME item configuration;

[0022] S84: according to the current BME item configuration, expand it according to the BME expansion order n2, perform R simulations, and record the dynamic response of the R power system;

[0023] S85: repeating steps S83-S84 until m BME items are removed, and obtaining the dynamic responses of the power system when 1 to m BME items are removed respectively;

[0024] S86: Statistically analyze the dynamic responses of the power system when 1 to m BME items are removed and the dynamic responses of the initial power system to obtain the number of unstable trajectories under each BME item configuration.

[0025] On the basis of the above technical solution, preferably, in step S6, the analysis result meets the requirements means that the difference between the mean and standard deviation of the random variables before and after the expansion in the simulation results reaches a predetermined threshold.

[0026] On the basis of the above technical solution, preferably, in step S1, the mathematical expression of the original stochastic differential-algebraic equation model of the power system is:

[0027]

[0028] 0=g(x(t),y(t),u(t),ζ(t))

[0029] Where x(t) is the c-dimensional state vector; y(t) is the k-dimensional algebraic variable; u(t) is the discrete control variable; f(·) is the c-dimensional differential equation describing the system dynamics; g(·) is the k-dimensional algebraic equation describing the system steady state; ζ(t) is the n-dimensional random variable.

[0030] On the basis of the above technical solution, preferably, the n-dimensional random variable ζ(t) is described by constructing a stochastic differential equation:

[0031]

[0032] Where a and b are both n-dimensional vectors, drift term and divergence term respectively; ξ(t) is n-dimensional Gaussian white noise; It is the Hadamard product, which is the multiplication of elements in corresponding positions in two matrices of the same dimension.

[0033] On the basis of the above technical solution, preferably, n-dimensional Gaussian white noise ξ(t) defines Brownian motion:

[0034] ξ(t)dt=dB(t)

[0035] Where B(t) is n b Brownian motion.

[0036] Based on the above technical solution, preferably, the mathematical expressions of the drift term and the divergence term are as follows:

[0037] a(ζ(t))=-α(ζ(t)-μ)

[0038]

[0039] Where α is the autocorrelation coefficient; μ is the mean of the random variable; σ is the standard deviation of the random variable.

[0040] Based on the above technical solution, preferably, in step S2, the differential form of the BME term is:

[0041]

[0042] Where B(t) is n b Brownian motion; i are independent standard Gaussian distributed random variables; p i (t) is the orthogonal polynomial basis; P is the expansion order.

[0043] On the basis of the above technical solution, preferably, the orthogonal polynomial basis p i (t) Calculated using orthogonal trigonometric functions:

[0044]

[0045] Where i represents the current expansion order, T is the fixed time, and t is the current time.

[0046] The method of the present invention has the following beneficial effects compared with the prior art:

[0047] (1) The present invention adopts the Brownian motion expansion method, which can effectively convert the uncertainty of continuous random excitation into probabilistic random uncertainty, and effectively convert the uncertainty in the entire simulation period into the uncertainty at the initial moment of the simulation, thereby reducing the complexity of the simulation calculation;

[0048] (2) The present invention can analyze the impact of different random process frequency bands on the transient response of the power system and obtain accurate conclusions while completely retaining the nonlinearity of the system. This can provide a basis for improving the transient stability of the system and has the advantage of being close to engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0050] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0051] Figure 2 A topological diagram of a power system according to an embodiment of the present invention;

[0052] Figure 3 is a mean comparison diagram of the simulation results of an embodiment of the present invention;

[0053] Figure 4 A standard deviation comparison diagram of the simulation results of an embodiment of the present invention;

[0054] Figure 5P is the voltage collapse in the simulation result of the embodiment of the present invention. L7 Change trajectory diagram;

[0055] Figure 6 The diagram is a trajectory diagram of voltage amplitude changes at each node when voltage collapse occurs in the simulation results of an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] Terminology explanation:

[0058] Dynamic simulation of power system: English name: dynamic simulation of power system, refers to the simulation and simulation of the system transient process by solving differential algebraic equations through mathematical methods and applying computers and other simulation tools in order to study the transient process of the power system.

[0059] Continuous stochastic excitation: English name: continuous stochastic excitation. In the present invention, it means that the value of random excitation is changing at every moment, and it is necessary to use random process theory for mathematical modeling.

[0060] Uncertainty: English name: uncertainty. In the present invention, it refers to the uncertainty corresponding to the fluctuation of load in the system, which can affect the dynamic response of the power system.

[0061] Brownian motion expansion method: English name: Brownian motion expansion method (BME).

[0062] like Figure 1 As shown, the present invention provides an analysis method considering the influence of uncertainty on the dynamic process of the power system, comprising the following steps:

[0063] S1: Collect the generator parameters, network parameters and load parameters in the power system, model the random disturbances, and construct the original stochastic differential-algebraic equation model of the power system;

[0064] S2: Based on BME, the Brownian motion term in the original stochastic differential-algebraic equation model is transformed to obtain a set of weighted standard independent Gaussian random variables and as BME terms;

[0065] S3: Set the scenario to system stability maintenance and set the initial BME expansion order n1;

[0066] S4: Expand the BME terms according to the current BME expansion order, insert them into the original stochastic differential-algebraic equation model, perform dynamic simulation of the power system, analyze the simulation results, and obtain analysis results;

[0067] S5: increasing the BME expansion order in sequence and going to step S4;

[0068] S6: Repeat steps S4-S5 until the analysis results meet the requirements and obtain the final BME expansion order n2;

[0069] S7: Set the scenario to system instability and set the BME expansion order to n2;

[0070] S8: Orderly remove m BME items to obtain new BME items, expand the new BME items according to the BME expansion order n2, insert them into the original stochastic differential-algebraic equation model, perform R times of power system dynamic simulation, and obtain the number of instability trajectories of the power system;

[0071] S9: Compare and analyze the number of unstable trajectories of the power system to obtain the BME items that affect the dynamic stability of the power system. The corresponding frequency bands in the frequency domain are the key frequency bands that affect the stability of the power system.

[0072] The present invention proposes a novel method for analyzing the dynamic response of power systems based on Brownian motion expansion. The method expands the Brownian motion term in the stochastic differential-algebraic equation by the Brownian motion expansion method, and then analyzes the influence of each frequency band in the frequency domain corresponding to the Brownian motion on the transient stability of the system in an orderly manner, and finds the frequency band with the most serious impact on the instability of the system. The proposed framework has the advantages of not requiring linear processing of the system, effectively retaining the nonlinearity of the system, and being close to engineering applications. It can also project the uncertainty of continuous random excitation over the entire simulation time to the start time of the simulation, reducing the complexity of the simulation calculation, and the obtained analysis results can provide a basis for improving the transient stability of the system.

[0073] The Brownian motion expansion method is a method that can effectively decompose the Brownian motion terms in random differential-algebraic equations. It is currently rarely used in the field of dynamic simulation of power systems taking into account continuous random excitations. It can expand the Brownian motion terms into the sum of a set of weighted Gaussian random variables. Since its weights can be expanded into the sum of trigonometric functions, the decomposed Brownian motion can be converted to the frequency domain for analysis, and the impact of each frequency band of each random process on the system stability can be quantitatively analyzed.

[0074] Specifically, in one embodiment of the present invention, the generator parameters, network parameters and load parameters of the power system are first collected, wherein the generator parameters include the inertia constant, damping coefficient, synchronous reactance, transient reactance, etc. of the generator, and the generator parameters determine the basic characteristics of the generator in the dynamic behavior of the power system; the network parameters include the impedance (resistance and reactance) of the transmission line, the parameters of the transformer, the topological structure of the system, etc., and the network parameters are the basis for power flow calculation and system stability analysis; the load parameters include the size, type (such as constant impedance load, constant current load, constant power load, etc.) and change characteristics of the load, and the dynamic change of the load has a direct impact on the stability of the system.

[0075] Afterwards, the collected generator parameters, network parameters and load parameters of the power system are input into the simulation software to model the random disturbances. The random disturbances of the power system include: random load fluctuations, random changes in load; fluctuations in the output of new energy, and random output changes in wind and solar power generation.

[0076] In one embodiment of the present invention, the process of constructing the original stochastic differential-algebraic equation model of the power system is as follows:

[0077] 1. Continuous random excitation is described by constructing stochastic differential equations:

[0078]

[0079] Where a and b are both n-dimensional vectors, drift term and divergence term respectively; ξ(t) is n-dimensional Gaussian white noise; It is the Hadamard product, which is the multiplication of elements in corresponding positions in two matrices of the same dimension.

[0080] Brownian motion is defined by Gaussian white noise ξ(t) as follows:

[0081] ξ(t)dt=dB(t) (2)

[0082] Where B(t) is n b Brownian motion.

[0083] However, the random processes in actual power systems are usually bounded. If the form of the drift term and the divergence term is not constrained, the random process ζ will diverge with the growth of time. Therefore, the Ornstein-Uhlenbeck process (OUP) is used to model the fluctuation of random load and renewable energy output. OUP defines the drift term and divergence term in equation (1):

[0084]

[0085] Where α is the autocorrelation coefficient; μ is the mean of the random variable; σ is the standard deviation of the random variable.

[0086] OUP is a mean reversion model. The random process ζ(t) will be more likely to stabilize within the range of μ±3σ as t increases. Its boundedness is more consistent with the changes of random variables in actual systems, and ζ(t) obeys a Gaussian distribution with a mean of μ and a standard deviation of σ.

[0087] 2. The dynamic model of the power system under continuous random excitation can be described by the following stochastic differential algebraic equation:

[0088]

[0089] Where x(t) is the c-dimensional state vector, such as generator power angle, speed, etc.; y(t) is the k-dimensional algebraic variable, such as node voltage amplitude, phase angle, etc.; u(t) is the discrete control variable, such as generator ratio, etc.; f(·) is the c-dimensional differential equation describing the system dynamics; g(·) is the k-dimensional algebraic equation describing the system steady state; ζ(t) is the n-dimensional random variable, such as random load, new energy output, etc., and its definition is shown in equations (1) and (3).

[0090] 3. Brownian motion expansion:

[0091] For any fixed time T>0, assuming p i (t), i = 1, 2, ..., is a set of orthogonal polynomial bases, then based on p i (t) Define the Ito integral as follows:

[0092] ξ i =∫0 T p i (t)dB(t) (5)

[0093] In the formula, ξ i are independent standard Gaussian distribution random variables. Then the Brownian motion B(t) can be expanded into the following form:

[0094]

[0095] where p i (t) takes the form of the following orthogonal trigonometric functions:

[0096]

[0097] Where i represents the current expansion order, T is the fixed time, and t is the current time.

[0098] Further, we get the differential form of Brownian motion:

[0099]

[0100] Where B(t) is n bBrownian motion; i are independent standard Gaussian distributed random variables; p i (t) is the orthogonal polynomial basis; P is the expansion order. That is, ξ i p i (t) is a BME item, is a set of BME items.

[0101] Thus, the Brownian motion is transformed into the sum of a series of independent standard Gaussian distributed random variables and their weights. These Gaussian random variables represent the sources of uncertainty in the system dynamics, such as load fluctuations or random changes in generator output. i The value taken at the beginning of the simulation will remain unchanged, so the original continuous random excitation scenario is converted into a probabilistic random excitation scenario, that is, the uncertainty in the entire simulation duration is projected to the initial moment of the simulation.

[0102] Then the single-dimensional formula (1) can be transformed into:

[0103]

[0104] Since the weight of BME is p i (t) is a trigonometric function, so it can be directly converted to the frequency domain to study the impact of different frequency bands on the stability of the power system. That is, the dynamic uncertainty source in the power system, namely the Gaussian random variables, is converted to the frequency domain. These random variables represent different frequency bands. A frequency band is a specific area in the frequency domain, which contains a series of specific frequencies.

[0105] After constructing the model and converting the Brownian motion into differential form, simulation analysis of the power system can be carried out.

[0106] Firstly, in the scenario where the system is not instability, the Brownian motion terms containing random process variables are expanded through the given BME expansion order and brought into the original stochastic differential-algebraic equation. Multiple power system dynamic simulations are performed, such as 1000 times. The simulation results are analyzed and summarized, and the mean and standard deviation of the simulation results of random process variables before and after the expansion are compared.

[0107] The BME expansion order is continuously increased, and the simulation is repeated many times until the mean and standard deviation of the random process variables before and after the expansion in the simulation results are similar.

[0108] Specifically, system stability refers to the state in which the power system operates normally without large-scale instability or failure. This includes the ability of the power system to cope with small to medium-sized random disturbances without frequency or voltage collapse. Appropriate initial conditions are selected, such as the initial power output of generators, load demand, and network configuration, which should reflect the actual power system state under normal operating conditions.

[0109] According to the mathematical characteristics of Brownian motion and the dynamic response characteristics of the power system, select a suitable starting order. Usually, a lower order may not be able to fully capture the dynamic characteristics of the system, while a too high order may lead to a sharp increase in computational complexity. You can start with a lower order, such as n1 = 10 or 20, to ensure the feasibility of the calculation and verify its effectiveness in capturing the system dynamics.

[0110] According to the set BME expansion order n1, the BME terms obtained in step S2 are expanded according to the differential form constructed above, and the expanded BME terms are substituted into the original stochastic differential-algebraic equation model of the power system. Use the stochastic differential equation solver to simulate and collect key data during the simulation process, such as system frequency, voltage level, power flow, etc., which reflect the dynamic behavior of the system. Perform a detailed analysis of the simulation results to evaluate whether the system can remain stable at the current BME expansion order. The analysis includes checking whether the system has excessive fluctuations or behavior that deviates from normal operating conditions.

[0111] Based on the simulation results of step S4, the order of BME expansion is gradually increased. After each increase, step S4 is repeated, that is, the simulation is re-performed and the new results are analyzed. After each increase in the order of BME expansion, the changes in the simulation results are evaluated.

[0112] Continue to repeat steps S4 and S5 until the simulation results show that the simulation of the system behavior is sufficiently accurate, or further increasing the BME expansion order has no significant improvement effect. Meeting the requirements means that the difference between the statistical characteristics (mean, standard deviation) of the key variables (such as voltage, frequency) in the simulation results and the expected target is minimized.

[0113] When the analysis results meet the requirements, the final BME expansion order n2 is obtained.

[0114] Afterwards, based on the BME expansion order n2 obtained in step S6, in the scenario of system instability, some terms in the BME are orderly removed and then introduced into the system stochastic differential-algebraic equation for multiple simulations to obtain the system dynamic response stability results and the number of instability trajectories.

[0115] The number of unstable trajectories of the system dynamic response is compared when different orders of BME items are removed. In the example with the least number of simulated unstable trajectories after removing some BME items, the corresponding frequency band in the frequency domain is obtained according to the order of the removed items, which is the most critical frequency band affecting the transient stability of the system.

[0116] Specifically, the scenario is set to a situation where the system may become unstable. m BME terms are removed in an orderly manner, which are selected from the BME expansion, including terms of different expansion orders. Each time a BME term is removed, the BME expansion is re-performed with the updated BME configuration and simulated in the original stochastic differential-algebraic equation model, with a total of R simulations performed. These simulations help determine the dynamic response of the system in the absence of a specific BME term, especially whether the system will become unstable.

[0117] The number of unstable trajectories obtained from each simulation is statistically analyzed and compared. This includes comparing the number of unstable trajectories after removing different BME items with the initial number of unstable trajectories (when no BME items are removed). Analyze which BME items have the most significant impact on the stability of the system. The frequency bands corresponding to these BME items are considered to be critical frequency bands for power system stability. By identifying these critical frequency bands, we can better understand the system's vulnerabilities in the face of uncertainty and provide guidance for system design and protection.

[0118] Specifically, in one embodiment of the present invention, step S8 includes:

[0119] S81: Expand the complete BME terms according to the BME expansion order n2, and substitute them into the original stochastic differential-algebraic equation model to perform power system simulation and record the dynamic response of the initial power system;

[0120] S82: Sort the BME items from high to low according to the expansion order;

[0121] S83: Select a BME item to remove and update the BME item configuration;

[0122] S84: according to the current BME item configuration, expand it according to the BME expansion order n2, perform R simulations, and record the dynamic response of the R power system;

[0123] S85: repeating steps S83-S84 until m BME items are removed, and obtaining the dynamic responses of the power system when 1 to m BME items are removed respectively;

[0124] S86: Statistically analyze the dynamic responses of the power system when 1 to m BME items are removed and the dynamic responses of the initial power system to obtain the number of unstable trajectories under each BME item configuration.

[0125] Specifically, the process identifies and optimizes the stability of the power system under uncertainty by systematically analyzing the impact of different BME terms. Through this analysis, the system can be better designed and adjusted to resist potential stability threats.

[0126] Specifically, in one embodiment of the present invention, step S9 includes:

[0127] By comparing the number of unstable trajectories of the power system before and after removing different BME items, the smaller the number of unstable trajectories, the more critical the BME item is. The frequency band corresponding to the BME item is found in the frequency domain, which is the critical frequency band. The critical frequency band is the frequency band that affects the stability of the system. After finding the critical frequency band, according to the random variables corresponding to the critical frequency band, it can be known which part of the system's random changes will affect the stability of the entire system, so that the power system can be adjusted in a targeted manner.

[0128] For example, due to the fluctuation of random load, the automatic voltage regulator of the generator in the power system will first make one of the automatic voltage regulators work saturated, which will weaken the damping of the remaining automatic voltage regulators and increase the potential instability risk of the system. Some key frequency bands in the random load may cause the automatic voltage regulators that are not saturated to reach saturation during the dynamic process of the system. As the number of automatic voltage regulators working in saturation increases, the system will eventually collapse. By analyzing the key frequency bands, this instability phenomenon can be predicted and avoided.

[0129] The present invention is described with a specific example:

[0130] This embodiment uses the Kundur 2 regional system as an example for simulation and calculation. Its topology diagram is as follows: Figure 2 As shown, the active power P of the node 7 load L7 It is a random process with a mean of the standard value and a standard deviation of 0.4% of the standard value. The total simulation time is 200 seconds, and the simulation times of each order BME and the Monte Carlo (MC) calculation as the standard value are 1000 times.

[0131] The power system is simulated from 5 to 500 orders, and the average value is compared with Figure 3 As shown, the standard deviation is Figure 4 As shown. Figure 3 and Figure 4 It can be seen that the 500th-order BME has good accuracy, and its mean and standard deviation trajectories are basically consistent. Note that the two are not completely consistent, because there is randomness in each step of the random process, so each trajectory is unique, and its mean and variance will also change. Even for the MC algorithm used as a reference, any 1000 trajectories and their mean and variance cannot be completely consistent, so the 500th-order BME has a sufficiently good fitting accuracy.

[0132] Then, the standard deviation of the random process was increased from the standard value of 0.4% to 1% and 1000 simulations were performed. At this time, voltage collapse occurred in some simulations. Taking the simulation result of one voltage collapse as an example, when voltage collapse occurred, P L7 and the voltage amplitude of each node Vm The change trajectory is as Figure 5 , Figure 6 shown.

[0133] Based on the BME algorithm, some items in the 500-order BME are removed in order and 1000 simulations are performed respectively. The number of unstable trajectories in each group of simulations is recorded, and the most critical frequency band affecting the stability of the system dynamic response can be obtained. The results are shown in Table 1.

[0134] Table 1

[0135]

[0136] As can be seen from Table 1, when the 500-order BME is expanded, the number of simulated unstable trajectories is similar to the number of unstable trajectories through the original random process Monte Carlo method. At this time, BME can effectively retain the influence characteristics of Brownian motion on transient response in the original random process. Further remove different orders, and obtain the number of unstable trajectories under the removed orders. It can be seen that when the removed order is 150-170, the corresponding removed frequency band is 0.375-0.425Hz, and the simulated instability number decreases significantly, indicating that this frequency band is the most critical frequency band affecting the transient stability of the system. In the future, the response measures to improve the transient stability of the system can be designed based on the most critical frequency band results obtained by the present invention.

[0137] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An analysis method considering the influence of uncertainty on the dynamic process of power system, characterized in that: The steps include: S1: Collect the generator parameters, network parameters and load parameters in the power system, model the random disturbances, and construct the original stochastic differential-algebraic equation model of the power system; S2: Based on BME, the Brownian motion term in the original stochastic differential-algebraic equation model is transformed to obtain a set of weighted standard independent Gaussian random variables and as BME terms; S3: Set the scenario to system stability maintenance and set the initial BME expansion order n1; S4: Expand the BME terms according to the current BME expansion order, insert them into the original stochastic differential-algebraic equation model, perform dynamic simulation of the power system, analyze the simulation results, and obtain analysis results; S5: increasing the BME expansion order in sequence and going to step S4; S6: Repeat steps S4-S5 until the analysis results meet the requirements and obtain the final BME expansion order n2; S7: Set the scenario to system instability and set the BME expansion order to n2; S8: Orderly remove m BME items to obtain new BME items, expand the new BME items according to the BME expansion order n2, insert them into the original stochastic differential-algebraic equation model, perform R times of power system dynamic simulation, and obtain the number of instability trajectories of the power system; S9: Compare and analyze the number of unstable trajectories of the power system to obtain the BME items that affect the dynamic stability of the power system. The corresponding frequency bands in the frequency domain are the key frequency bands that affect the stability of the power system. In step S6, the analysis result meets the requirements when: the difference between the mean and standard deviation of the random variables before and after the expansion in the simulation result reaches a predetermined threshold; In step S1, the mathematical expression of the original stochastic differential-algebraic equation model of the power system is: 0=g(x(t),y(t),u(t),ζ(t)) Where x(t) is the c-dimensional state vector; y(t) is the k-dimensional algebraic variable; u(t) is the discrete control variable; f(·) is the c-dimensional differential equation describing the system dynamics; g(·) is the k-dimensional algebraic equation describing the system steady state; ζ(t) is the n-dimensional random variable; The n-dimensional random variable ζ(t) is described by constructing a stochastic differential equation: Where a and b are both n-dimensional vectors, drift term and divergence term respectively; ξ(t) is n-dimensional Gaussian white noise; is the Hadamard product, which is the multiplication of elements in corresponding positions in two matrices of the same dimension; The n-dimensional Gaussian white noise ξ(t) defines the Brownian motion: ξ(t)dt=dB(t) Where B(t) is n b Dimensional Brownian motion; The mathematical expressions of drift and divergence are as follows: a(ζ(t))=-α(ζ(t)-μ) In the formula, α is the autocorrelation coefficient; μ is the mean of the random variable; σ is the standard deviation of the random variable; In step S2, the differential form of the BME term is: Where B(t) is n b Brownian motion; i are independent standard Gaussian distributed random variables; p i (t) is the orthogonal polynomial basis; P is the expansion order; Orthogonal polynomial basis p i (t) Calculated using orthogonal trigonometric functions: Where i represents the current expansion order, T is the fixed time, and t is the current time.

2. The analysis method considering the influence of uncertainty on the dynamic process of the power system according to claim 1, characterized in that: In step S8, the m BME items that are removed in an orderly manner are BME items of different expansion orders, so as to obtain the number of instability trajectories of the power system when the BME items of different expansion orders are removed.

3. The analysis method considering the influence of uncertainty on the dynamic process of the power system as claimed in claim 2, characterized in that: Step S8 includes: S81: Expand the complete BME terms according to the BME expansion order n2, and substitute them into the original stochastic differential-algebraic equation model to perform power system simulation and record the dynamic response of the initial power system; S82: Sort the BME items from high to low according to the expansion order; S83: Select a BME item to remove and update the BME item configuration; S84: according to the current BME item configuration, expand it according to the BME expansion order n2, perform R simulations, and record the dynamic response of the R power system; S85: repeating steps S83-S84 until m BME items are removed, and obtaining the dynamic responses of the power system when 1 to m BME items are removed respectively; S86: Statistically analyze the dynamic responses of the power system when 1 to m BME items are removed and the dynamic responses of the initial power system to obtain the number of unstable trajectories under each BME item configuration.

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