Power distribution network interval state evaluation method based on Bayesian inference

Abstract

The invention discloses a power distribution network interval state evaluation method based on Bayesian inference, and relates to a method for estimating the operation state of a power distribution network. The method comprises the following steps: S1, according to a physical model and measurement data of the power distribution network, establishing prior probability distribution of the state of the power distribution network; s2, researching a fusion method of a global Bayesian framework and multi-type measurement data of the power distribution network, and deducing an expression mode of Bayesian evidence; s3, establishing a power distribution network state posterior model under a Bayesian framework in combination with the prior information and the measurement data of the system state; and S4, in a weakly observable system, realizing complete description of the non-Gaussian total statistics of the system state, and providing a more accurate and comprehensive power distribution network interval state estimation result.

Description

Technical Field

[0001] The distribution network interval state evaluation method based on Bayesian inference of the present invention relates to a method for estimating the operating state of the distribution network. Background Art

[0002] In the distribution network, the traditional state estimation algorithm is affected by model uncertainty, measurement uncertainty and distributed generation output uncertainty, making it difficult to accurately estimate the operating state through point estimation. The interval state estimation method can comprehensively consider the impact of different types of uncertainty and give the system state operating range.

[0003] The existing technologies include the following solutions: Reference [1], “A Review of Distribution Network State Estimation” published in “Electrical Engineering” in September 2019;

[0004] Reference [2] In the prior art, the “Distributed Interval State Estimation of Distribution Network Incorporating Multi-source Measurement Data” published in the Proceedings of the CSEE in 2022;

[0005] Reference [3] In the prior art, the “Distribution Network Section State Estimation with Time-Delay Fusion in Multi-Source Measurement Environment” published in “Automation of Electric Power Systems” in February 2024;

[0006] Reference [4] In the prior art, “Deep learning-assisted regional AC / DC distribution network interval state estimation” is recorded in “Automation of Electric Power Systems”.

[0007] Among them, the Krawczyk operator (KO) method mentioned in reference [1] was first used to solve the interval state estimation problem.

[0008] Subsequently, in addition to the method based on the Krawczyk operator, reference [2] implemented the interval state estimation of regional AC / DC distribution networks based on deep learning; reference [3] implemented the distribution network prediction auxiliary interval state estimation based on deep neural networks to address the problem of uncertainty in the distribution of real-time measurement errors in regional AC / DC distribution networks. However, these methods only give the range of the state interval and do not quantify the probability density of each state. Reference [4] proposed a three-stage interval state estimation method to filter the measurement data in the distribution network with high penetration of distributed generation, and used a mixed integer nonlinear programming method to solve the three-stage interval optimization problem.

[0009] In summary, the traditional interval estimation algorithm is subject to the constraints of the interval algorithm, and the existing research on observability analysis and enhancement still has the following shortcomings: First, the existing interval state estimation algorithms are based on the Krawczyk operator and related derivative algorithms, which can only provide the upper and lower bounds of the state but cannot give the specific state probability distribution density, and cannot reflect the full statistics of the state. In addition, the traditional interval state estimation algorithm is subject to the limitations of the centralized algorithm, does not have strong scalability, and is difficult to apply to large-scale distribution networks. Therefore, the distributed interval state estimation algorithm for the new distribution system needs further research. Summary of the invention

[0010] The present invention aims to solve the problem of distribution network state estimation considering uncertainty, and provides distribution network interval state estimation results considering multi-source uncertainty through a Bayesian method.

[0011] In order to solve the limitations that point estimation cannot characterize the complete information of the potential state distribution, and that traditional interval state estimation can only provide the upper and lower boundaries of the state but cannot give the posterior probability density of the state, the present invention proposes a distribution network interval state estimation method based on Bayesian inference.

[0012] The steps of the distribution network interval state assessment method based on Bayesian inference of the present invention are as follows:

[0013] S1 establishes the prior probability distribution of the distribution network state based on the physical model and measurement data of the distribution network;

[0014] S2 studies the fusion method of the global Bayesian framework and multi-type measurement data of the distribution network, and derives the expression of Bayesian evidence;

[0015] S3 combines the prior information of the system state with the measurement data to establish a posterior model of the distribution network state under the Bayesian framework;

[0016] In a weakly observable system, S4 achieves a complete characterization of the non-Gaussian full statistics of the system state and provides more accurate and comprehensive distribution network interval state estimation results.

[0017] Specifically, in step S1, under the Bayesian framework, assumptions are made on the specific forms of the prior distribution and likelihood function; wherein the Bayesian inference formula is as follows:

[0018]

[0019] Where P(A|B) is the posterior probability of event A occurring given evidence B. P(B|A) is

[0020] The probability of observing evidence B when A occurs is called likelihood; P(A) and P(B) are the belief in event A and the probability of event B occurring, respectively.

[0021] Furthermore, in step S1, in order to improve the accuracy of state estimation and reduce the state distribution scale of interval state estimation, the state estimator used will combine multiple types of measurement data in the distribution network, and the multiple types of measurement data include: voltage amplitude, phase angle, active power and reactive power.

[0022] Furthermore, in step S2, by integrating multiple measurement types of voltage amplitude, phase angle, active power and reactive power, the accuracy and reliability of state estimation are improved. Specifically, the measurement equation is:

[0023] z=h(x)+v

[0024] z is the measured phase quantity, including voltage amplitude, phase angle, line and node active and reactive measurements, etc.; h(x) is the measurement equation, which is a nonlinear or linear function of the state; v is the measurement noise.

[0025] Furthermore, in step S3, the distribution network state posterior model under the Bayesian framework is established by combining the prior information of the system state and the measurement data; after the measurement value vector d is given, the following Bayesian posterior distribution probability density function of the state x' is obtained:

[0026] π post (x'|d)∝π like (d|x')π prior (x')

[0027] In the formula, π post (x'|d) represents the posterior probability of the state after a given measurement, π like (d|x') is the likelihood function, π prior (x') is the prior probability of the state. Here, it is assumed that the prior distribution and noise follow Gaussian distribution.

[0028] An electronic device includes one or more processors for storing one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors execute the aforementioned distribution network interval state assessment method based on Bayesian inference.

[0029] A storage medium stores a computer program, wherein the computer program is configured to execute the aforementioned distribution network interval state assessment method based on Bayesian inference when running.

[0030] Compared with the prior art, the present invention has the following advantages:

[0031] Bayesian inference can provide the posterior probability distribution of the state, which means that the uncertainty degree and distribution characteristics of the state can be obtained, rather than just the upper and lower bounds of the interval. In contrast, the Krawczyk operator can only give the deterministic interval range of the state and cannot reflect the probability information of the state. Therefore, the Bayesian method can more comprehensively describe the potential state of the system and help operators better assess the operation risks of the distribution network.

[0032] Bayesian inference does not require strict assumptions about the distribution form of the state and can adapt to nonlinear and non-Gaussian complex situations. Therefore, the Bayesian algorithm is more robust in the nonlinear and non-Gaussian noise environment that may exist in the distribution network. In contrast, the algorithm based on the Krawczyk operator may face the problem of reduced accuracy when dealing with nonlinear or non-Gaussian characteristics.

[0033] Through Bayesian inference, we can directly obtain statistical information about the system state, such as expected value, variance, and probability distribution characteristics. These statistics can help decision makers understand the uncertainty and fluctuation of the state more clearly. However, the Krawczyk operator can only provide an interval range and lacks a detailed statistical description of the state characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a topology diagram of the IEEE-123 bus system in an embodiment of the distribution network section state assessment method based on Bayesian inference of the present invention.

[0035] Schematic diagram of the workflow.

[0036] Figure 2 This is a diagram of the state estimation result of busbar 13 interval in an embodiment of the distribution network interval state evaluation method based on Bayesian inference of the present invention.

[0037] Figure 3 It is a posterior distribution diagram of the state of bus 13 at a certain moment in an embodiment of the distribution network interval state assessment method based on Bayesian inference of the present invention. DETAILED DESCRIPTION

[0038] The specific implementation plan of this program is as follows:

[0039] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following reference is made to the attached Figure 1-3 It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the protection scope of the present invention.

[0040] Refer to the attached Figure 1-3First, based on the physical model and measurement data of the distribution network, the prior probability distribution of the distribution network state is established. Under the Bayesian framework, assumptions are made on the specific forms of the prior distribution and likelihood function. The Bayesian inference formula is as follows:

[0041]

[0042] Where P(A|B) is the posterior probability of event A occurring given evidence B. P(B|A) is

[0043] The probability of observing evidence B when A occurs is called likelihood. P(A) and P(B) are the belief in event A and the probability of event B occurring, respectively.

[0044] In order to improve the accuracy of state estimation and reduce the state distribution scale of interval state estimation, the state estimator used will combine multiple types of measurement data in the distribution network, such as voltage amplitude, phase angle, active power and reactive power.

[0045] Then, the fusion method of the global Bayesian framework and multi-type measurement data of the distribution network is studied, and the expression of Bayesian evidence is derived. Specifically, by integrating multiple measurement types of voltage amplitude, phase angle, active power and reactive power, the accuracy and reliability of state estimation are improved. Specifically, the measurement equation is:

[0046] z=h(x)+v

[0047] z is the measured phase quantity, including voltage amplitude, phase angle, line and node active and reactive measurements, etc.; h(x) is the measurement equation, which is a nonlinear or linear function of the state; v is the measurement noise.

[0048] Combining the prior information of the system state and the measurement data, a posterior model of the distribution network state under the Bayesian framework is established. After the measurement value vector d is given, the following Bayesian posterior distribution probability density function of the state x' can be obtained:

[0049] π post (x'|d)∝π like (d|x')π prior (x')

[0050] In the formula, π post (x'|d) represents the posterior probability of the state after a given measurement, π like (d|x') is the likelihood function, π prior (x') is the prior probability of the state. Here, it is assumed that the prior distribution and noise follow Gaussian distribution.

[0051] This model can fully characterize the probability distribution of the system state, overcoming the shortcomings of the traditional Krawczyk operator-based method that only provides point estimates or upper and lower bounds of the interval. On the contrary, the proposed posterior model can give the full probability distribution of the system state, and the average value of the maximum posterior state interval can be considered as the final state point estimate result.

[0052] Finally, in a weakly observable system, this method achieves a complete characterization of the non-Gaussian full statistics of the system state, providing a more accurate and comprehensive distribution network interval state estimation result than the traditional method. This technical solution not only solves the limitations of the existing technology, but also provides new ideas and methods for distribution network state estimation, which has important practical application value.

[0053] In the embodiment of the present invention, the specific implementation steps are as follows:

[0054] 1. Initialization: Select the initial state variable value, set the number of iterations and algorithm parameters.

[0055] 2. Iterative sampling:

[0056] 2.1 Candidate state generation: Based on the current state, a new candidate state is generated using the proposed distribution.

[0057] 2.2 Acceptance probability calculation: Calculate the probability of a candidate state being accepted, taking into account the impact of prior information and measurement data on the state.

[0058] 2.3 State update: According to the acceptance probability, decide whether to accept the candidate state. If accepted, update the current state to the candidate state; otherwise, keep the current state unchanged.

[0059] 3. Result collection: Repeat the above process until the preset number of iterations is reached and collect the sampling results of the state variables.

[0060] By using the MH algorithm to obtain a large number of posterior samples, we can statistically calculate the various statistical characteristics of the state variables. For example, we can calculate the mean and variance of each state variable, as well as the interval estimate under a specified confidence level. These statistics can fully reflect the distribution characteristics of the state variables and characterize the uncertainty of the state.

[0061] The present invention is Figure 1 In the IEEE-123 bus system shown in FIG. 1 , the time-sharing state interval of bus 13 is estimated according to the above principle, as shown in FIG. Figure 2 As shown, the state posterior distribution diagram of the busbar 13 at a single moment is given, such as Figure 3 Experiments show that this method can not only give a reasonable state estimation interval, but also give a specific state distribution, which can better reflect the actual possible state and provide more detailed data information for the operator.

Claims

1. A distribution network interval state assessment method based on Bayesian inference, characterized in that: Here are the steps: S1 establishes the prior probability distribution of the distribution network state based on the physical model and measurement data of the distribution network; S2 studies the fusion method of the global Bayesian framework and multi-type measurement data of the distribution network, and derives the expression of Bayesian evidence; S3 combines the prior information of the system state with the measurement data to establish a posterior model of the distribution network state under the Bayesian framework; In a weakly observable system, S4 achieves a complete characterization of the non-Gaussian full statistics of the system state and provides more accurate and comprehensive distribution network interval state estimation results.

2. The distribution network interval state assessment method based on Bayesian inference according to claim 1 is characterized in that: In step S1, under the Bayesian framework, assumptions are made on the specific forms of the prior distribution and likelihood function; wherein the Bayesian inference formula is as follows: Where P(A|B) is the posterior probability of event A occurring given evidence B; P(B|A) is The probability of observing evidence B when A occurs is called likelihood; P(A) and P(B) are the belief in event A and the probability of event B occurring, respectively.

3. The distribution network interval state assessment method based on Bayesian inference according to claim 2 is characterized in that: In step S1, in order to improve the accuracy of state estimation and reduce the state distribution scale of interval state estimation, the state estimator used will combine multiple types of measurement data in the distribution network, including: voltage amplitude, phase angle, active power and reactive power.

4. The distribution network interval state assessment method based on Bayesian inference according to claim 1 is characterized in that: In step S2, the accuracy and reliability of state estimation are improved by integrating multiple measurement types of voltage amplitude, phase angle, active power and reactive power; the measurement equation is: z=h(x)+v z is the measured phase quantity, including voltage amplitude, phase angle, line and node active and reactive measurements, etc.; h(x) is the measurement equation, which is a nonlinear or linear function of the state; v is the measurement noise.

5. The distribution network interval state assessment method based on Bayesian inference according to claim 1 is characterized in that: In step S3, the distribution network state posterior model under the Bayesian framework is established by combining the prior information of the system state and the measurement data; after the measurement value vector d is given, the following Bayesian posterior distribution probability density function of the state x' is obtained: π post (x'|d)∝π like (d|x')π prior (x') In the formula, π post (x'|d) represents the posterior probability of the state after a given measurement, π like (d|x') is the likelihood function, π prior (x') is the prior probability of the state; here, the prior distribution and noise are assumed to follow Gaussian distribution.

6. An electronic device comprising one or more processors for storing one or more programs, characterized in that: When the one or more programs are executed by the one or more processors, the one or more processors execute the aforementioned distribution network interval state assessment method based on Bayesian inference.

7. A storage medium storing a computer program, wherein: The computer program is configured to execute the aforementioned distribution network interval state assessment method based on Bayesian inference when running.

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