CN112883627B - Power distribution network state estimation method and system based on pseudo Monte Carlo particle filtering - Google Patents

Power distribution network state estimation method and system based on pseudo Monte Carlo particle filtering Download PDF

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CN112883627B
CN112883627B CN202110217889.9A CN202110217889A CN112883627B CN 112883627 B CN112883627 B CN 112883627B CN 202110217889 A CN202110217889 A CN 202110217889A CN 112883627 B CN112883627 B CN 112883627B
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张文
张婷婷
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Abstract

The utility model provides a power distribution network state estimation method and system based on pseudo-Monte Carlo particle filtering, which comprises the following steps: generating sampling points which are subjected to uniform distribution by adopting a pseudo Monte Carlo sampling method; randomizing the sampling points which are subjected to uniform distribution; according to the prior probability density function, the random sampling points are placed in a sample space to generate particles required by a particle filter algorithm; based on Bayes theory, the three-phase state estimation of the power distribution network is carried out by using the particles generated by the randomized pseudo-Monte Carlo sampling method and adopting particle filtering, and the estimated value of the running state of the power distribution network is obtained. The method is based on the Bayesian theory, exerts the advantage of high convergence speed of fitting errors of a pseudo Monte Carlo sampling method, takes into account the state transition process of the power distribution network, fully utilizes historical state information and current measurement information, and can adopt fewer particles to achieve the same estimation precision as standard particle filtering, thereby effectively reducing the calculated amount of power distribution network estimation and realizing high-precision estimation of the power distribution network.

Description

Power distribution network state estimation method and system based on pseudo Monte Carlo particle filtering
Technical Field
The disclosure relates to the technical field of power distribution network state estimation, in particular to a power distribution network state estimation method and system based on pseudo Monte Carlo particle filtering.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
With the increasing power demand and the increasingly prominent contradiction of fossil energy shortage, the active power distribution system becomes a new trend of the development of modern power distribution systems. The system integrates multiple technologies such as information communication, big data and power systems, and aims to coordinate renewable energy sources and other controllable resources in the system through flexible and effective active control and management means, so that the system has certain capability of actively adjusting and optimizing internal running states. In order to realize the function, the primary task is to comprehensively and accurately control the running state of the system.
The power distribution system state estimation is an effective means for sensing the system running state and is a core function of a power distribution management system. The redundancy of the measurement information can be utilized to improve the data accuracy, error information caused by random interference is automatically eliminated, the running state of the system is estimated or forecasted, and a data basis is provided for other high-level applications. Accurate and efficient state estimation is crucial to realizing real-time perception of the operating state of the power distribution system.
The inventor finds that the power distribution system state estimation method has the following problems:
(1) The traditional estimation method based on weighted least square only adopts current measurement information for estimation, but fails to utilize prior state information, and may not meet the requirement of estimation precision when the load of the power distribution network is greatly changed. Although the dynamic estimation method based on the kalman filter takes the state transition process into account, the dynamic estimation method is difficult to be applied to the actual situation of ubiquitous non-gaussian noise due to the assumed condition of gaussian noise.
(2) Although particle filtering is suitable for processing the state estimation problem of a nonlinear and non-gaussian system, the particle filtering has high computational complexity and long time consumption, and the real-time requirement of online state estimation is difficult to meet.
Disclosure of Invention
In order to solve the above problems, the present disclosure provides a power distribution network state estimation method based on pseudo-monte carlo particle filtering, and a pseudo-monte carlo sampling method based on a Sobol' low difference sequence is adopted, so that on the premise of ensuring estimation accuracy, fewer particles are adopted for estimation, thereby reducing the calculation amount of power distribution network state estimation and improving estimation efficiency.
In order to achieve the purpose, the following technical scheme is adopted in the disclosure:
one or more embodiments provide a power distribution network state estimation method based on pseudo-Monte Carlo particle filtering, which includes the following steps:
generating sampling points which are subjected to uniform distribution by adopting a pseudo Monte Carlo sampling method;
randomizing the uniformly distributed sampling points to convert the original deterministic sampling points into random sampling points;
according to a prior probability density function, placing the random sampling points in a sample space to generate particles required by a particle filtering algorithm;
based on Bayesian theory, the particles generated by the randomized pseudo-Monte Carlo sampling method are used for calculating the state transition process of the power distribution network, historical state information and current measurement information are obtained, particle filtering is adopted for three-phase state estimation of the power distribution network, and an estimated value of the running state of the power distribution network is obtained.
One or more embodiments provide a power distribution network state estimation system based on pseudo-monte carlo particle filtering, comprising:
a deterministic sampling point determination module: configured for generating sampling points subject to uniform distribution using a pseudo-monte carlo sampling method;
a sampling point randomization module: the sampling points are configured to be subjected to randomization processing, so that original deterministic sampling points are converted into random sampling points;
a particle determination module: the random sampling points are arranged in a sample space according to a prior probability density function so as to generate particles required by a particle filter algorithm;
a state estimation module: the method is configured for calculating the state transition process of the power distribution network by using the particles generated by the randomized pseudo-Monte Carlo sampling method based on the Bayes theory, acquiring historical state information and current measurement information, and performing three-phase state estimation of the power distribution network by using particle filtering to acquire an estimated value of the running state of the power distribution network.
An electronic device comprising a memory and a processor and computer instructions stored on the memory and executed on the processor, the computer instructions, when executed by the processor, performing the steps of the above method.
A computer readable storage medium storing computer instructions which, when executed by a processor, perform the steps of the above method.
Compared with the prior art, this disclosed beneficial effect does:
the method is based on the Bayesian theory, adopts the particle filtering method to estimate the three-phase state of the power distribution network, can take the state transition process of the power distribution network into account, fully utilizes historical state information and current measurement information, and effectively solves the problem of state estimation of a nonlinear and non-Gaussian system, thereby realizing high-precision estimation of the power distribution network. The pseudo Monte Carlo sampling method has the advantage of high convergence rate of fitting errors, and can achieve the same estimation precision as standard particle filtering by adopting fewer particles, thereby effectively reducing the calculation amount of power distribution network estimation and improving the estimation efficiency.
Advantages of additional aspects of the disclosure will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the disclosure.
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The accompanying drawings, which are included to provide a further understanding of the disclosure, illustrate embodiments of the disclosure and together with the description serve to explain the disclosure and do not constitute a limitation thereof.
Fig. 1 is a flowchart of a state estimation method of embodiment 1 of the present disclosure;
fig. 2 is a wiring diagram of an IEEE33 node three-phase power distribution network system provided by an example of embodiment 1 of the present disclosure;
FIG. 3 is a pseudo-Monte Carlo particle filter algorithm (QMC-PF) and a standard particle filter (MC-PF) voltage amplitude Root Mean Square Error (RMSE) for an IEEE33 node three-phase power distribution network system provided by an example of embodiment 1 of the present disclosure V Comparing the images;
FIG. 4 is a pseudo-Monte Carlo particle filter algorithm (QMC-PF) and a standard particle filter (MC-PF) voltage phase angle Root Mean Square Error (RMSE) for an IEEE33 node three-phase power distribution network system provided by an example of embodiment 1 of the present disclosure θ Compare the figures.
The specific implementation mode is as follows:
the present disclosure is further illustrated by the following examples in conjunction with the accompanying drawings.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present disclosure. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise. It should be noted that, in the case of no conflict, the embodiments and features in the embodiments in the present disclosure may be combined with each other. The embodiments will be described in detail below with reference to the accompanying drawings.
Example 1
In one or more embodiments, as shown in fig. 1, a power distribution network state estimation method based on pseudo monte carlo particle filtering includes the following steps:
generating sampling points which are subjected to uniform distribution by adopting a pseudo Monte Carlo sampling method;
and (2) randomizing the sampling points to convert the original deterministic sampling points into random sampling points.
And (3) placing the random sampling points in a sample space according to a prior probability density function to generate particles required by a particle filter algorithm.
And (4) on the basis of Bayesian theory, calculating the state transition process of the power distribution network by using the particles generated by the random pseudo-Monte Carlo sampling method, acquiring current measurement information and historical state information, and performing three-phase state estimation on the power distribution network by using particle filtering to obtain an estimated value of the running state of the power distribution network.
The method is based on the Bayesian theory, adopts a particle filtering method to carry out three-phase state estimation on the power distribution network, can take the state migration process of the power distribution network into account, fully utilizes historical state information and current measurement information, and effectively solves the problem of state estimation of a nonlinear and non-Gaussian system, so that high-precision estimation of the power distribution network is realized. The method has the advantages that the pseudo-Monte Carlo sampling method is high in fitting error convergence speed, and the same estimation accuracy as standard particle filtering can be achieved by adopting fewer particles, so that the calculation amount of power distribution network estimation is effectively reduced, and the estimation efficiency is improved.
Optionally, in step 1, the method for generating sampling points obeying uniform distribution by using the pseudo-monte carlo sampling method comprises the following steps of generating a hypercube [0,1 ] in s-dimensional unit based on Sobol' low difference sequence s The sampling points that are generated and obeyed uniform distribution are deterministic sampling points, which may be specifically as follows:
for the ith dimension space, a primitive polynomial can be constructed as follows:
p i (x)＝X q +a 1,i X q-1 +…+a q-1,i X+1
wherein q is the order of the primitive polynomial, and the coefficient a of each order of the primitive polynomial j,i Satisfies a j,i ∈{0，1}，j＝1,…,q-1。
For the ith dimension space, the number of defined directions is:
v c,i ＝d c,i /2 c ＝(0.v 1 v 2 …) 2
wherein a group satisfying 0 is selected<d c,i <2 k C is not less than 1 and not more than q, when c is an odd number>When q is, d c,i This can be given in a recursive manner by:
Figure BDA0002954630350000061
wherein the content of the first and second substances,
Figure BDA0002954630350000062
representing a bitwise exclusive-or operation.
Wherein v is j Is v is c,i The number at the j-th bit in binary representation. Sobol' sequence t of unit subspace of i dimension for any natural number alpha i The alpha-th element can be selected fromThe formula is given as:
Figure BDA0002954630350000063
wherein alpha is 0 ,…,α r-1 Binary expansion for α: α = α 0 +2α 1 +…+2 r-1 α r-1 The corresponding coefficients. Whereby an s-dimensional unit hypercube [0, 1) s The sequence of Sobol' can be represented as t = { t = } 0 ,t 1 ,…,t s }。
In the step (2), a linear matrix scrambling method is adopted to convert the deterministic sampling points obtained in the step (1) into random sampling points.
The linear matrix scrambling method comprises the following steps:
(1) using a random matrix L to count the direction v in the step (1) c And (4) scrambling. After the scrambling, the number v 'in the i-dimensional space direction' c Can be calculated from the following formula:
Figure BDA0002954630350000064
wherein l i,j Is a vector with 2 as a base number, consisting of i,j Formed matrix L i ＝[l i,1 ,l i,2 ,…]Is a random independent non-singular lower triangular matrix.
(2) The deterministic sampling point in each Sobol' is compared with a random vector e with the base number of 2 i Adding the random vectors to obtain a scrambled sampling point which is a random sampling point, wherein the random vector e i Are independent of each other. For an arbitrary natural number α, the ith dimension of a sampling point in the scrambled Sobol' sequence can be represented by the following formula:
Figure BDA0002954630350000071
wherein, g 1 (α)g 0 And (alpha) is a Gray code expression of alpha-1.
In the step (3), each Sobol' point coordinate is used as an accumulated probability value, and a corresponding quantile point is obtained based on given prior probability density distribution and used as a particle adopted in a particle filter algorithm for power distribution network state estimation.
And solving corresponding quantile points based on the given prior probability density distribution, and converting Sobol' sampling points obeying uniform distribution into sampling points obeying state quantity prior probability density functions. For the first N Sobol ' points of the Sobol ' sequence, taking the coordinates of each Sobol ' point as an accumulated probability value, and solving a corresponding quantile point based on a given prior probability density distribution, wherein the quantile point is used as a particle adopted in a particle filter algorithm and is used for state estimation.
Taking a one-dimensional Sobol 'sequence as an example, the coordinate of the 1 st Sobol' point is 0.3804, and assuming that the prior probability density function obeys the standard normal distribution, the corresponding sample point obeying the prior probability density distribution should be-0.3044.
In the step (4), the state transition process of the power distribution network is calculated by using the particles generated in the step (3) based on the Bayesian theory, the current measurement information is collected, and the three-phase state estimation of the power distribution network is performed by using particle filtering.
The current measurement information comprises real-time measurement and pseudo measurement information, wherein the implementation measurement information comprises a voltage amplitude value of a node, a branch current amplitude value and branch power, and the pseudo measurement information comprises node injection power. Mainly comprises the following steps:
(41) Establishing a three-phase state estimation model based on a discrete time state space model of the power distribution network, namely the state transition equation and the measurement equation are as follows:
x k ＝f(x k-1 ,u k )+ξ k
z k ＝h(x k ,u k )+υ k
wherein x is k Is a state variable matrix of the system at time k, u k For the system input variable matrix, z k A matrix is measured for the system quantity. f (-) and h (-) are nonlinear and non-Gaussian state transition equations and measurement equations respectively; xi shape k System process noise matrix, upsilon k To measure the noise matrix. System processNoise matrix xi k Respectively, is P k Measuring the noise matrix upsilon k Has an error covariance matrix of R k And the accuracy of the system model is reflected.
(42) A prediction stage: and aiming at each particle obtained from the running state of the power distribution network at the previous moment, solving the state prediction value at the current moment based on the state transition equation of the power distribution network.
And aiming at each particle at the k-1 th time, a state predicted value at the k-1 th time is obtained based on a state transition equation.
Optionally, for each particle at the k-1 th time, predicting a state value at the k time for each particle based on a power flow calculation formula by using the load predicted value at the k time, that is:
Figure BDA0002954630350000081
wherein, J k-1 To use the state value x at the time k-1 k A calculated Jacobian matrix. Δ u k The node load change value between the k moment and the k-1 moment is obtained based on the load predicted value of the k moment.
(43) And a filtering stage: and calculating a normalization weight based on a current moment measurement value aiming at the predicted particles, copying the particles with high weight and eliminating the particles with low weight by adopting a sampling-importance-resampling method to realize filtering, and obtaining an estimated value of the running state of the power distribution network based on the normalization weight and the corresponding resampled particles.
(43.1) calculating a measurement estimation h (x) for each predicted particle by a measurement equation k ) Thereby obtaining the measurement residual error delta z k ＝z k -h(x k ) And according to a given measurement error probability distribution function p (Δ z) k |x k ) Calculating the importance weight w of the particles based on Bayes theory k And normalized to obtain
Figure BDA0002954630350000091
The particle importance weight calculation formula is as follows:
w k ＝w k-1 p(Δz k |x k )
wherein, w k-1 And w k The importance weights for the particle at time k-1 and time k, respectively.
(43.2) in order to solve the problem of particle degradation in particle filtering, a sampling-importance-resampling method is adopted, resampling is carried out according to the normalized weight of each particle, and the particles with high weight are copied and the particles with low weight are eliminated, so that degradation is inhibited, and estimation accuracy is guaranteed.
Optionally, the weight w is normalized by each particle after resampling k Can be set to 1/N, wherein N is the number of particles.
(43.3) weighting and summing the resampled particles by using the normalized weights of the particles to obtain a state estimation value at the k moment, wherein a calculation formula of the state estimation value is as follows:
Figure BDA0002954630350000092
wherein the content of the first and second substances,
Figure BDA0002954630350000093
is an estimated value of the state at the moment k.
The effects of the method of the present embodiment are not described, and a specific example will be described below.
Table 1 ieee33 node three-phase unbalanced distribution network measurement configuration:
Figure BDA0002954630350000094
Figure BDA0002954630350000101
fig. 2 shows a system structure diagram of an IEEE33 node three-phase unbalanced distribution network, which is used for simulation verification of the proposed method, and the measurement configuration is shown in table 1. Respectively at 14 nodes, phase A and section 23The point C phase and the 30 node B phase are respectively accessed to a network with an area of 300m 2 And the photoelectric conversion efficiency is 13.44 percent.
Fig. 3 and fig. 4 are comparison conditions of three-phase state estimation of a power distribution network based on standard particle filtering and pseudo-monte carlo sampling particle filtering, wherein fig. 3 is comparison of root mean square error of node voltage amplitude values, and fig. 4 is comparison of root mean square error of node voltage phase angles.
As can be seen from FIGS. 3 and 4, when the voltage amplitude and the phase angle mean root mean square error reach 1.21 × 10 -4 And 0.74X 10 -4 In this case, the pseudo-monte carlo particle filter only needs 1000 particles, and the standard particle only needs 2000 particles. After the pseudo Monte Carlo particle filtering is adopted, the corresponding average estimated time is reduced to 99.71 seconds from 195.97 seconds, and the calculation efficiency is improved by 49.12%. Under the condition that the estimation accuracy is the same, the calculation efficiency of the phase angle standard particle filter of the pseudo-Monte Carlo particle filter is higher, and due to the pseudo-Monte Carlo sampling method, the sampling points can cover the state space more uniformly, so that the given probability distribution function can be fitted better. The convergence rate of the fitting error of the pseudo Monte Carlo sampling along with the number of samples is O (N) -1 ) While the rate of convergence of the pseudo-Monte Carlo sampling fitting error with the number of samples is about O (N) -1/2 ) Therefore, the error convergence rate of the particle filter based on the pseudo-monte carlo sampling is higher than that of the standard particle filter based on the monte carlo sampling, and the number of particles required by the pseudo-monte carlo particle filter is far smaller than that of the standard particle filter when the same estimation precision is achieved, so that the calculation amount is reduced, the estimation time is shortened, and the calculation efficiency of the particle filter is improved.
Example 2
Based on embodiment 1, this embodiment provides a power distribution network state estimation system based on pseudo monte carlo particle filtering, including:
a deterministic sampling point determination module: configured for generating sampling points subject to uniform distribution using a pseudo-monte carlo sampling method;
a sampling point randomization module: the sampling points are configured to be subjected to randomization processing, so that original deterministic sampling points are converted into random sampling points;
a particle determination module: configured to place the random sampling points in a sample space according to a prior probability density function to generate particles required by a particle filter algorithm;
a state estimation module: the method is configured for calculating the state transition process of the power distribution network by using the particles generated by the randomized pseudo-Monte Carlo sampling method based on the Bayes theory, acquiring historical state information and current measurement information, and performing three-phase state estimation of the power distribution network by using particle filtering to acquire an estimated value of the running state of the power distribution network.
Example 3
The present embodiment provides an electronic device comprising a memory and a processor, and computer instructions stored on the memory and executed on the processor, wherein the computer instructions, when executed by the processor, perform the steps of the method of embodiment 1.
Example 4
The present embodiment provides a computer readable storage medium for storing computer instructions which, when executed by a processor, perform the steps of the method of embodiment 1.
The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure, and various modifications and changes may be made to the present disclosure by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present disclosure should be included in the protection scope of the present disclosure.
Although the present disclosure has been described with reference to specific embodiments, it should be understood that the scope of the present disclosure is not limited thereto, and those skilled in the art will appreciate that various modifications and changes can be made without departing from the spirit and scope of the present disclosure.

Claims (8)

1. The power distribution network state estimation method based on the pseudo Monte Carlo particle filtering is characterized by comprising the following steps of:
generating sampling points which are subjected to uniform distribution by adopting a pseudo Monte Carlo sampling method; the method specifically comprises the following steps: based on Sobol' low difference sequence insDimension unit hypercube [0, 1) s Generating sampling points which are subjected to uniform distribution;
randomizing the uniformly distributed sampling points to convert the original deterministic sampling points into random sampling points;
according to the prior probability density function, the random sampling points are placed in a sample space to generate particles required by a particle filter algorithm;
based on a Bayesian theory, particles generated by the randomized pseudo-Monte Carlo sampling method are used, the state migration process of the power distribution network is calculated, historical state information and current measurement information are obtained, particle filtering is adopted to carry out three-phase state estimation on the power distribution network, and an estimated value of the running state of the power distribution network is obtained; the method comprises the following steps:
establishing a three-phase state estimation model of the power distribution network based on a discrete time state space model of the power distribution network;
aiming at each particle obtained from the running state of the power distribution network at the previous moment, solving a state prediction value at the current moment based on a power distribution network state transition equation in the three-phase state estimation model;
and calculating a normalization weight aiming at the predicted particles, copying the particles with high weight and eliminating the particles with low weight by adopting a sampling-importance-resampling method to realize filtering, and obtaining an estimated value of the running state of the power distribution network based on the normalization weight and the corresponding resampled particles.
2. The power distribution network state estimation method based on the pseudo-monte carlo particle filtering as claimed in claim 1, wherein: the method for randomizing the sampling points which are subjected to uniform distribution comprises the following steps: and converting the generated sampling points which are subjected to uniform distribution into random sampling points by adopting a linear matrix scrambling method.
3. The method for estimating the state of the power distribution network based on the pseudo-monte carlo particle filter as claimed in claim 2, wherein: the linear matrix scrambling method comprises the following steps:
scrambling the direction numbers, which are generated based on the Sobol' sequence and obey uniformly distributed deterministic sampling points, by adopting a random matrix;
and adding each deterministic Sobol' sampling point and a random vector with 2 as a base number to obtain a scrambled sampling point, namely a random sampling point subject to uniform distribution.
4. The power distribution network state estimation method based on the pseudo-monte carlo particle filtering as claimed in claim 1, wherein: solving corresponding quantile points based on given prior probability density distribution, and converting Sobol' sampling points obeying uniform distribution into sampling points obeying state quantity prior probability density functions: sobol' sequence frontNAnd taking the coordinates of all Sobol' points as cumulative probability values, solving corresponding quantile points based on given prior probability density distribution, and taking the quantiles as particles adopted in a particle filter algorithm for state estimation.
5. The power distribution network state estimation method based on the pseudo-monte carlo particle filtering as claimed in claim 1, wherein:
aiming at the predicted particles, the method for calculating the normalized weight comprises the following steps: and calculating a measurement estimation value through a measurement equation so as to obtain a measurement residual error, and calculating and normalizing the importance weight of the particles based on a Bayesian theory according to a given measurement error probability distribution function.
6. Power distribution network state estimation system based on pseudo Monte Carlo particle filtering is characterized by comprising the following steps:
a deterministic sampling point determination module: is configured for generating sampling points subject to uniform distribution by adopting a pseudo Monte Carlo sampling method; the method comprises the following specific steps: based on Sobol' low difference sequence insDimension unit hypercube [0, 1) s Generating sampling points which are subjected to uniform distribution;
a sampling point randomization module: the sampling points are configured to be subjected to randomization processing, so that original deterministic sampling points are converted into random sampling points;
a particle determination module: configured to place the random sampling points in a sample space according to a prior probability density function to generate particles required by a particle filter algorithm;
a state estimation module: the particle filtering method is used for obtaining historical state information and current measurement information by taking the state transition process of the power distribution network into account, performing three-phase state estimation on the power distribution network by adopting particle filtering and obtaining an estimated value of the running state of the power distribution network based on Bayesian theory and the particles generated by the randomized pseudo-Monte Carlo sampling method; the method comprises the following steps:
establishing a three-phase state estimation model of the power distribution network based on a discrete time state space model of the power distribution network;
aiming at each particle obtained from the running state of the power distribution network at the previous moment, solving a state prediction value at the current moment based on a power distribution network state transition equation in the three-phase state estimation model;
and calculating a normalization weight aiming at the predicted particles, copying the particles with high weight and eliminating the particles with low weight by adopting a sampling-importance-resampling method to realize filtering, and obtaining an estimated value of the running state of the power distribution network based on the normalization weight and the corresponding resampled particles.
7. An electronic device comprising a memory and a processor and computer instructions stored on the memory and executable on the processor, the computer instructions when executed by the processor performing the steps of any of the methods of claims 1-5.
8. A computer-readable storage medium storing computer instructions which, when executed by a processor, perform the steps of the method of any one of claims 1 to 5.
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