CN107425520A - A kind of probabilistic active distribution network three-phase section method for estimating state of injecting power containing node - Google Patents

Abstract

The invention discloses a method for estimating the state of three-phase intervals of an active distribution network with uncertainty of node injection power, including the use of interval numbers to perform pseudo-measurement of node injection power and the uncertainty of measurement errors of real-time measurement devices Carry out modeling and analysis respectively; establish a three-phase interval state estimation mathematical model of active distribution network considering uncertainties; split the established active distribution network interval state estimation model into two optimized ones containing nonlinear interval constraints Problem: A linear programming method based on iterative operations combined with sparse matrix technology is used to effectively solve the established mathematical model of the three-phase interval state estimation of the active distribution network. The invention makes up for the shortcomings of ignoring the intermittent output of distributed power sources and the charging of electric vehicles in the state estimation of the current distribution network, improves the accuracy of measurement and the solution speed of the algorithm, and provides theoretical support for the next step of safety evaluation of the active distribution network.

Description

A Three-Phase Interval State Estimation for Active Distribution Networks with Node Injected Power Uncertainty calculation method

technical field

The invention relates to a method for estimating a three-phase state of an active distribution network, in particular to a method for estimating a three-phase interval state of an active distribution network with node injection power uncertainty.

Background technique

Actively developing renewable energy power grid-connected technology and electric vehicle grid-connected technology is a strategic choice for my country to adjust energy structure, cope with climate change, transform economic development mode and achieve sustainable development. In the future, the grid-connected power generation of multi-type distributed power sources with high penetration rate, active loads such as electric vehicles, and the large-scale access and application of a large number of intelligent terminal equipment will gradually transform the traditional one-way radial distribution network into a multi-energy power supply system. , Auxiliary active distribution network operating in a weak ring topology when necessary. At the same time, the distribution network state estimation technology is expected to be able to further quickly and accurately perceive the real-time operating status of the system, and provide other advanced management software for the active distribution network, such as voltage regulation control technology, distributed power output and active load distribution technology, active Distribution network active/reactive power coordination optimization technology and intelligent power distribution system self-healing technology provide reliable data.

However, in the future, the random charging of large-scale electric vehicles, the intermittent power generation of distributed power sources with high penetration rate and the measurement errors of a large number of intelligent measurement equipment will make the state estimation results of active distribution network need to consider more uncertainties. However, traditional methods face severe challenges, and the accuracy of estimation results cannot meet the scheduling requirements. How to consider the impact of strong uncertainty on state estimation is an urgent problem to be solved.

Generally speaking, the modeling methods of uncertain variables in distribution network mainly include probability model, fuzzy number model and interval number model. The probability model is to use the uncertain factors in the network as random variables to establish different probability models, and then sample the probability distribution function and count the distribution characteristics of the variables. The fuzzy number model needs to obtain the credibility measure based on a large amount of historical statistical data, and establish the corresponding membership function. However, the state estimation based on probability distribution and fuzzy theory must obtain the detailed prior probability density function or membership function of each uncertainty variable in advance. On the one hand, it is easy to increase the time complexity of the algorithm solution. In addition to the probability distribution of conventional power loads that can be easily known based on a large amount of historical power consumption data, it is difficult to obtain the complete probability density function of distributed power generation such as photovoltaics and wind power. In most cases, only the upper and lower limits of its power fluctuations are known.

Contents of the invention

Purpose of the invention: In order to solve the deficiencies of the existing technology, provide a system that can meet the requirements of the current distribution network situation awareness system that can quickly and accurately perceive the real-time operating status of the system after large-scale electric vehicles and distributed power generation systems are connected to the grid. Three-phase interval state estimation method for active distribution network with node injected power uncertainty.

Technical solution: A three-phase interval state estimation method for active distribution network with node injection power uncertainty, including the following steps:

(1) Using the interval number to model and analyze the uncertainties of pseudo-measurement of node injection power including photovoltaic power generation, wind power generation and electric vehicle charging system and measurement error of real-time measurement devices;

(2) Select the three-phase voltage amplitude and phase angle of the node as the state variables to be obtained in the system, and establish a three-phase interval state estimation mathematical model of the active distribution network considering uncertainty;

(3) Based on the unknown but bounded error theory, the established mathematical model of active distribution network three-phase interval state estimation considering uncertainty is split into two optimization problems containing nonlinear interval constraints, which is convenient for analysis and solution ;

(4) A linear programming method based on iterative operation combined with sparse matrix technology is used to solve the established mathematical model of active distribution network three-phase interval state estimation considering uncertainty.

Further, step (1) includes:

(11) When using the interval number to characterize the output uncertainty of the photovoltaic power generation system, the upper and lower limit estimation method is used to model the output of the photovoltaic power generation system by establishing a dual-output neural network model;

(12) When interval numbers are used to represent the uncertainty of wind power system output, a two-layer neural network wind prediction model based on the online sequential-extreme learning machine structure is used. First, the wind speed is corrected by the ELM model, and then the second layer is used to ELM predicts wind power generation;

(13) When performing interval modeling analysis on the stochastic charging of electric vehicles, the Monte Carlo sampling method based on the law of statistical data combined with interval numbers is used to forecast the charging load demand of electric vehicles in intervals.

Further, step (11) includes:

(a) Data preprocessing, divide neural network training and test data

Collect historical photovoltaic output data and meteorological data at the corresponding time according to the predetermined sampling interval, and use the processed data as the input of the neural network;

(b) Interval prediction optimization algorithm and particle swarm optimization algorithm settings

Interval coverage rate PICP and interval width PINAW are important factors to measure the performance of interval forecasting, and the calculation formulas are as follows:

In the formula, λ is the number of deterministic predictions, and c _κ' is the evaluation index of the κ'th predicted value; assuming that there is a certain predicted value y _κ' , when , c _κ' = 1; otherwise, c _κ' = 0; and _PPV are the upper limit and lower limit of the interval prediction respectively; Λ is the difference between the minimum value and the maximum value of the target prediction value;

The comprehensive evaluation index function of the selected interval forecast is as follows:

f=PINAW(1+γ(PICP)e -η ^(PICP-Ψ) )

In the formula, Ψ is the confidence value, which is also the adjustment parameter of f; η is the adjustment parameter of f, and in actual engineering, η∈[50,100];

Initialize the size and inertia constant of the particle swarm to generate the initial particle swarm, which is the initial interval value for photovoltaic output prediction;

(c) Combined with the particle swarm optimization algorithm, output the optimal interval value for photovoltaic processing prediction, including:

① set the number of iterations L=0, and create an evaluation function value f ^(L) ;

②Update particle swarm algorithm parameters

Randomly initialize the position and velocity of each particle in the search space, set the individual optimal position of each particle as the current particle position, obtain the optimal position of the group, and continuously update the position and velocity of the particles;

③Create a new prediction interval and calculate the evaluation function value f ^(L+1)

Calculate the fitness value of each particle, and update the individual optimal position of each particle and the optimal position of the entire group;

④Judge whether f ^(L+1) <f ^L is satisfied

If not satisfied, make L=L+1, return to step 2. continue searching; If satisfy, then replace the evaluation function value f (L) of last iteration with evaluation function value f ^{(L+1 )} ;

⑤ Determine whether the algorithm termination condition is satisfied

Given the condition of particle swarm iterative convergence, as the condition for the termination of the algorithm, if not satisfied, return to step ② to continue the search; if satisfied, stop the search, and output the optimal interval value of photovoltaic output prediction.

Further, step (12) includes:

(a) Data preprocessing, the data includes the historical power generation data of the wind power generation system and the corresponding weather forecast data, the vector Θ is used as the network input of the ELM, the formula is as follows:

Θ＝[vv _sin v _cos ρ] ^T

In the formula, v is the wind speed; v _sin and v _cos are the sine and cosine values of the wind direction respectively; ρ is the air density, which is calculated from the temperature, air pressure and air relative humidity; all input data in the ELM network are normalized to [ 0,1] interval;

(b) In the wind speed correction link, the first-layer ELM network is used to simulate and correct the nonlinear relationship between the forecast wind speed and the measured wind speed;

(c) In the link of wind power generation system output interval prediction, the second-layer ELM network is used to predict the interval of wind power generation system output, and the corrected wind speed value, wind direction positive, cosine value and air density value at the current moment are selected as the second-layer ELM network The input value is the upper and lower interval values of the output of the wind power generation system at the current moment output for the network.

Further, step (13) includes:

(a) Set the number of electric vehicles M ^* = 0

(b) Let M ^* =M ^* +1

(c) Determine the initial charging time T _S according to t and f(t)

User behavior is mainly determined by the daily mileage d of the electric vehicle and the starting time t of the charging process. According to the survey data of the national household travel survey project, combined with the maximum likelihood estimation method, the probability and statistical laws of d and t are respectively shown in the following formula :

In the formula, μ _d = 3.2, σ _d = 0.88, μ _t = 17.6, σ _t = 3.4; f(t) is the probability density function of the initial charging process; and the initial charging time T _S is obtained according to f(t);

(d) Sampling the initial state of charge of the battery according to d, calculating the required charging time T _C , and determining the charging end time T _E , where T _E =T _S +T _C ;

The battery SOC of an electric vehicle and its daily mileage d also approximately satisfy a linear relationship, then the charging time T _C of an electric vehicle is estimated as:

In the formula, W ₁₀₀ is the average power consumption per 100 kilometers of electric vehicles, and P _C is the charging power of EVs;

(e) Calculate the charging power P(t ₀ ) at sampling time t ₀

During the optimized peak and valley electricity price period, electric vehicles generally adopt an ordered charging mode, and the charging power demand of a single electric vehicle at time t ₀ is expressed as:

In the formula: P(t ₀ ) is the power demand of a single electric vehicle on the t ₀ time section; P _C (t ₀ ) is the charging power of a single EV on the t ₀ time section; ζ _C (t ₀ ) is t ₀ The probability of the charging power of a single electric vehicle on the time section, Ψ( ) is the probability density function of the initial charging time of the electric vehicle;

(f) Accumulate EV charging load during [T _S , T _E ] period

Assuming that there are M electric vehicles in a certain area, the total charging load in one day can be obtained by accumulating single electric vehicles one by one, then the total charging load of electric vehicles in this area at time _t0 is:

Among them, P _γ′ (t ₀ ) represents the charging load of the γ′th electric vehicle on the t ₀ time section;

(g) Judging whether the number of electric vehicles exceeds a predetermined value

If M ^* < M is established, return to step (b) and continue the calculation;

If M ^* < M is not established, then obtain the standard deviation of charging load demand of all electric vehicles, and output the optimal interval value of charging prediction.

In addition, since the formula in step (e) is difficult to derive its analytical solution, it is necessary to use the Monte Carlo method to sample the total charging demand of electric vehicles on each time section in a day based on a large amount of historical statistical data, and approximate It obeys a normal distribution, and its expected value and standard deviation are μ _EV and σ _EV , respectively, so the available interval numbers can express the charging demand of electric vehicles:

In the formula, υ is the radius adjustment parameter of the interval number, which can be set according to the actual situation.

Further, step (2) includes:

(21) Considering the uncertainty factor of node injection power pseudo-measurement, node i’s Mutually, The injected active power/reactive power can be expressed as:

In the formula, Respectively represent the conventional load demand expressed by the interval number, the distributed power output and the active information of electric vehicle charging; It represents the conventional load demand described by the interval number and the reactive power information of the distributed power output; similar to the node injection power, the branch active/reactive power measurement and the branch current amplitude measurement interval number can also be represented separately for In the formula, i,k represent nodes i,k=1,2,...,n, then the measurement vector [z] in the interval state estimation model can be expressed as:

Take the three-phase voltage amplitude of node i and phase angle As the state variable x _i to be demanded by the system, there is The three-phase interval state estimation of the active distribution network is to determine the state variable information of the system according to the upper and lower bound information of the measurement vector and the nonlinear mapping relational expression, which is described by the mathematical relational expression as:

In the formula, X′(·) represents the uncertainty set of system state variables, x represents the state variable to be obtained, h(x) represents the nonlinear mapping relationship between the measurement vector and the state variable, z represents the interval measurement The lower bound of the vector, while Indicates the upper limit of the interval measurement vector, M is the system measurement set, Z′(·) represents the uncertainty set of the system measurement vector, specifically:

In the formula, is an actual measurement vector, z _j represents the jth quantity measurement, z _j represents the lower limit value of the jth quantity measurement, Indicates the upper limit value of the jth quantity measurement, m' is the cardinality of the system measurement set M;

If the correlation between distributed power and load is not considered, the specific model expression of the three-phase interval state estimation of active distribution network with multi-type distributed power and load uncertainty is as follows:

In the formula, γ is any one of the three phases a, b and c respectively; for the node i to be sought phase voltage amplitude, for node i The upper limit information of the phase voltage amplitude, for node i The lower limit information of the phase voltage amplitude, for the node i to be sought phase voltage amplitude, for node i upper limit information of the phase voltage phase angle, for node i The lower limit information of the phase voltage phase angle, on branch road ik The lower limit of phase active power, on branch road ik Upper limit of phase active power, on branch road ik The lower limit of phase reactive power, on branch road ik upper limit of phase reactive power, on branch road ik The lower limit value of the phase current amplitude, on branch road ik The upper limit value of the phase current amplitude, Inject for node i The lower limit information of phase active power, Inject for node i Upper limit information of phase active power, Inject for node i Lower limit information of phase reactive power, Inject for node i upper limit information of phase reactive power, is the γ-phase voltage phase angle of node i, for node i Phase angle difference between phase and γ phase, between node i and node k (or d) in The phase angle difference between phase and γ phase, with is the corresponding element in the three-phase node admittance matrix, is the γ-phase voltage phase angle of node k, is the γ-phase voltage amplitude of node i, is the amplitude of the γ-phase voltage at node k.

Furthermore, in step (3), the original problem is split into two optimization problems containing nonlinear interval constraints, and the upper and lower bounds of the variables to be sought are obtained respectively, then the established active power distribution considering uncertainty The grid three-phase interval state estimation model is briefly described as:

In the formula represents the uncertain interval value of node i state variable x _i , and x _i , Then represent the confidence lower bound and upper bound of node i state variable x _i fluctuation.

Further, step (4) includes:

(a) Obtain the original parameters of the network. The original parameters of the network include the pseudo-measurement interval value of the node injection power of the branch impedance, the load and the distributed power supply, and the real-time measurement interval value of the branch power and current amplitude;

(b) Generate the node three-phase admittance matrix Y _B and the measurement vector [z] in the interval state estimation model, where,

In the formula, are the corresponding elements in the three-phase admittance matrix, i,k=1,...,n, Inject active and reactive power interval values for nodes respectively, Respectively, the number of intervals for real-time measurement of branch active power, reactive power and current amplitude;

(c) Set the initial value of the system state variable to be requested

Select the system state variable to be sought, and set the intermediate value of the initial interval approximate solution of the state variable as the initial value of the system state variable to be sought Select the three-phase voltage amplitude and phase angle of the network nodes as the state variables to be obtained in the system, then we have

(d) Set the number of iterations S=0;

(e) Obtain the corresponding elements in the correction equations, including △ z ⁿ , △ z ^mn ,

Will Substituting △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and △[I ¹² ] in the revised equations, and calculating the corresponding elements △ z ⁿ , △ z ^mn , Among them, △ z ⁿ represents the first n rows of matrix data of △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and the lower limit of △[I ¹² ], Represents the first n rows of matrix data of △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and the upper limit of △[I ¹² ]; while △ z ^mn represents △[P ¹ ], △ [Q ¹ ], △[P ¹² ], △[Q ¹² ] and the remaining mn row matrix data of the lower limit of △[I ¹² ], Then represent the remaining mn row matrix data of △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and the upper limit of △[I ¹² ]; the correction equations can be expressed in matrix form as :

In the formula, △[P ¹ ], △[Q ¹ ] represent the unbalanced amount of active and reactive power injected into the node interval, respectively, and △[P ¹² ], △[Q ¹² ] represent the unbalanced amount of active and reactive power injected into the branch interval, respectively. △[I ¹² ] represents the imbalance of the current amplitude in the branch section, H ^* , N ^* , K ^* , L ^* , F ^* and S ^* are auxiliary matrices generated in the correction equations, △U, △ θ respectively represent the unbalance of node voltage amplitude and phase angle;

(f) Calculate and decompose the measurement Jacobian matrix J ^m to obtain the corresponding elements J ⁿ and J ^mn

use Calculate each element in the measurement Jacobian, the measurement function h(x) in The first-order Taylor expansion is carried out at , and the measurement Jacobian matrix J ^m is obtained after ignoring the high-order terms, and the corresponding J ⁿ and J ^mn are obtained; among them,

(g) Invert J ⁿ and calculate elements (J ⁿ ) ^-1 and J ^mn (J ⁿ ) ^-1 ;

(h) Obtain each row element a ⁱ in the (J ⁿ ) ^-1 matrix, and perform a linear programming operation;

(i) Obtain the interval value of the correction amount And calculate the initial interval value of the new iterative state quantity Combining △ z ⁿ , △ z ^mn , And the corresponding elements in J ^mn (J ⁿ ) ^-1 are respectively substituted into the following formulas:

△ x _i = min a ⁱ · △ z ⁿ

In the formula, △ x _i represent the upper and lower limits of the unbalance of the state variable to be sought on node i respectively, and △ z ⁿ represents the unbalance of the first n rows of elements in the measurement vector matrix;

Obtain the interval value of the system voltage correction amount by executing the linear programming operation program Then obtain the new initial interval value of the system node voltage state quantity

(j) Check whether the iteration converges

Use the predetermined convergence criteria to judge whether the iteration has converged, and the criterion for algorithm convergence is:

In the formula, S is the number of iterations, ε is a given arbitrary decimal;

(k) If it does not converge, update the iterative state quantity, and set replace As the initial approximate solution of the new equation, let S=S+1, return to step (e) and enter the next iteration until the convergence criterion is reached, and output the optimal estimated value of the three-phase interval state estimation of the active distribution network ;

If it converges, directly output the best estimated interval value of the system state quantity.

Beneficial effect: compared with the prior art, the method of the present invention has the following advantages:

(1) The present invention can make up for the shortcomings of ignoring the randomness of electric vehicle charging and the intermittent output of distributed power sources in the current distribution network situation awareness system, and provide theoretical support for the next step of safety assessment of active distribution networks.

(2) Compared with the existing distribution network state estimation based on the best estimation criterion, the three-phase interval state estimation of the active distribution network proposed by the present invention has more engineering application value. In the case of node injection power uncertainty The following can provide dispatchers with effective system state quantity "boundary" information.

(3) The linear programming method based on iterative operation used in the present invention can effectively solve the mathematical model of the three-phase interval state estimation of the active distribution network, which is more efficient than the traditional interval optimization solution method, so it can be further improved Improve the real-time performance of three-phase interval state estimation in active distribution network.

Description of drawings

Fig. 1 is the flowchart of the inventive method;

Figure 2 is a flow chart of the interval prediction algorithm for the photovoltaic power generation system;

Fig. 3 is a flow chart of the interval prediction algorithm of the wind power generation system;

Figure 4 is a flowchart of the electric vehicle charging load interval prediction algorithm;

Figure 5 is a schematic diagram of a simple active distribution network structure and its measurement system;

Fig. 6 is a flow chart for solving the three-phase interval state estimation model of the active distribution network.

detailed description

The technical solutions of the present invention will be described in detail below, but the protection scope of the present invention is not limited to the embodiments.

As shown in Figure 1, the method for estimating the three-phase interval state of the active distribution network with node injection power uncertainty of the present invention includes the following steps:

Step 1: Quantitatively describe the uncertainty of system measurements such as pseudo-measurement of injected power of network nodes and real-time measurement of branches including photovoltaic power generation, wind power generation and electric vehicle charging by using interval numbers.

At present, most short-term power prediction models of photovoltaic power generation systems use deterministic point prediction, that is, to give a certain power value of photovoltaic output at a certain time in the future. Obviously, this point-value power prediction method ignores the uncertainty of photovoltaic output. The error is large. In order to improve the prediction results, as shown in Figure 2, the present invention uses the upper and lower limit estimation method to perform interval prediction on the output of the photovoltaic power generation system by establishing a dual-output neural network model. The main implementation steps of the algorithm are as follows:

(1) Data preprocessing, divide neural network training and test data

Photovoltaic output is related to many factors, such as the intensity of light radiation, the area of the photovoltaic array, and the ambient temperature. According to a certain sampling interval, the historical photovoltaic output data and the meteorological data at the corresponding time are collected, and the processed data is used as the input of the neural network.

(2) Interval prediction optimization algorithm and particle swarm optimization algorithm settings

The important factors to measure interval prediction performance are interval coverage (prediction intervals coverage probability, PICP) and interval width (prediction intervals normalized averaged width, PINAW), and the calculation formulas are as follows:

In the formula, λ is the number of deterministic predictions, and c _κ' is the evaluation index of the κ'th predicted value; assuming that there is a certain predicted value y _κ' , when , c _κ' = 1; otherwise, c _κ' = 0; and _PPV are the upper limit and lower limit of the interval prediction respectively; Λ is the difference between the minimum value and the maximum value of the target prediction value.

The comprehensive evaluation index function of the selected interval forecast is as follows:

In the formula, Ψ is the confidence value, which is also the adjustment parameter of f; η is also the adjustment parameter of f, and in actual engineering, η∈[50,100].

Initialize the parameters such as the size of the particle swarm and the inertia constant to generate the initial particle population, which is the initial interval value of the photovoltaic output prediction.

(3) Combined with the particle swarm optimization algorithm, output the optimal interval value for photovoltaic processing prediction. The specific optimization steps are:

① set the number of iterations L=0, and create an evaluation function value f ^(L) ;

②Update particle swarm algorithm parameters

The position and velocity of each particle are randomly initialized in the search space, the individual optimal position of each particle is set as the current particle position, and the group optimal position is obtained; and the position and velocity of the particles are continuously updated.

③Create a new prediction interval and calculate the evaluation function value f ^(L+1)

Calculate the fitness value of each particle, and update the individual optimal position of each particle and the optimal position of the entire population.

④Judge whether f ^(L+1) <f ^L is satisfied

If not satisfied, set L=L+1, return to step ② to continue searching; if satisfied, replace the evaluation function value f (L) of the previous iteration with the evaluation function value f ^{(L+1 )} .

⑤ Determine whether the algorithm termination condition is satisfied

Given the condition for particle swarm iterative convergence (the maximum number of iterations can be set as the convergence condition) as the condition for algorithm termination, if not satisfied, return to step ② to continue searching; if satisfied, stop searching and output the optimal interval for photovoltaic output prediction value.

The uncertainty of wind power generation system is mainly affected by wind speed and wind direction. At present, the methods of wind power ultra-short-term/short-term forecasting can be roughly divided into physical analysis methods, statistical analysis methods, and physical-statistical hybrid methods. The physical analysis method is a method that comprehensively considers the geographical information of wind farms and the characteristics of wind turbines for detailed analysis, mathematical modeling and prediction. This method does not require historical data, but requires high model accuracy. As shown in Figure 3, on the basis of existing research, the present invention adopts a double-layer neural network wind force forecasting model based on an online sequential-extreme learning machine (online sequential-extreme learning machine, OS-ELM) structure, first through the ELM model The wind speed is corrected, and then the second-layer ELM is used to predict the wind power generation power. The main implementation steps are as follows:

(1) Data preprocessing. Including the historical power generation data of the wind power system and the corresponding weather forecast data, such as wind speed, wind direction and temperature, etc., consider the vector Θ in formula (3) as the network input of ELM:

Θ＝[vv _sin v _cos ρ] ^T (3)

In the formula, v is the wind speed; v _sin and v _cos are the positive and cosine values of the wind direction respectively; ρ is the air density, which can be calculated from the temperature, air pressure and air relative humidity. All input data in the ELM network needs to be normalized to the [0,1] interval.

(2) Wind speed correction link. According to the power output characteristic curve of common wind turbines, it is easy to know that in the process of cut-in wind speed to rated wind speed, small changes in wind speed will cause obvious changes in the output power of wind turbines, so the wind speed forecast data needs to be corrected to a certain extent. The first layer of ELM network can be used to simulate the nonlinear relationship between the corrected forecast wind speed and the measured wind speed.

(3) The output interval prediction link of wind turbines. The second-layer ELM network is used to predict the interval of wind turbine output, and the corrected wind speed value, positive and cosine value of wind direction, and air density value at the current moment are selected as the input value of the second-layer ELM network, and the upper and lower intervals of wind turbine output at the current moment are used. value output for the network.

Since the charging of electric vehicles is a highly uncertain process, the factors that affect the charging load include the driving characteristics of the car owner, the choice of charging, the duration of charging, the characteristics of the battery, and the current grid electricity price, etc. Modeling and analysis of the prediction of electric vehicle charging load demand. In order to improve the rationality and accuracy of the electric vehicle charging load interval prediction model, on the basis of the existing relevant research, as shown in Figure 4, the present invention adopts the Monte Carlo sampling method based on the law of statistical data combined with the interval number The method is used to predict the charging load demand of electric vehicles. Proceed as follows:

(1) Set the number of electric vehicles M ^* = 0

(2) Let M ^* =M ^* +1

(3) Determine the initial charging time T _S according to t, where T _S can be obtained according to the probability density function formula f(t) at the beginning of the charging process described below.

User behavior is mainly determined by the daily mileage d of the electric vehicle and the starting time t of the charging process (assuming that the user starts charging immediately after the last trip), according to the survey data of the Nationwide Household Travel Survey (NHTS2009), Combined with the maximum likelihood estimation method, the probability and statistical laws of d and t can be roughly obtained, as shown in formula (4) and formula (5):

In the formula, μ _d =3.2, σ _d =0.88, μ _t =17.6, σ _t =3.4.

(4) Sampling the initial state of charge (State of Charge, SOC) of the battery according to d, calculating the required charging time T _C , and determining the charging end time T _E , where T _E =T _S +T _C .

The battery SOC of an electric vehicle and its daily mileage d also approximately satisfy a linear relationship, then the charging time T _C of an electric vehicle can be estimated as:

In the formula, W ₁₀₀ is the average power consumption per 100 kilometers of electric vehicles (unit: kW h/100km); P _C is the charging power of EVs (unit: kW).

(5) Calculate the charging power P(t ₀ ) at sampling time t ₀

During the optimized peak-valley electricity price period, electric vehicles generally adopt an orderly charging mode, so the charging power demand of a single electric vehicle at time t ₀ can be expressed as:

In the formula: P(t ₀ ) is the power demand of a single electric vehicle on the t ₀ time section; P _C (t ₀ ) is the charging power of a single EV on the t ₀ time section; ζ _C (t ₀ ) is t ₀ The probability of the charging power of a single electric vehicle on the time section, Ψ(·) is the probability density function of the initial charging time of the electric vehicle, that is, formula (5).

(6) Accumulate EV charging load during [T _S , T _E ] period

Assuming that there are M electric vehicles in a certain area, the total charging load in one day can be obtained by accumulating single electric vehicles one by one, then the total charging load of electric vehicles in this area at time _t0 is:

(7) Judging whether the number of electric vehicles exceeds the predetermined value

If M ^* < M holds true, return to step (2) and continue the calculation.

If M ^* < M is not established, then obtain the standard deviation of charging load demand of all electric vehicles, and output the optimal interval value of charging prediction.

It should be mentioned that since it is difficult to derive its analytical solution for formula (7), it is necessary to use the Monte Carlo method to sample the total charging demand of electric vehicles on each time section in a certain day based on a large amount of historical statistical data. And approximately obey the normal distribution, its expected value and standard deviation are μ _EV and σ _EV respectively, so the interval number can be used to express the charging demand of electric vehicles:

In the formula, υ is the radius adjustment parameter of the interval number, which can be set according to the actual situation.

Step 2: Select the three-phase voltage amplitude and phase angle of the node as the state variables to be obtained in the system, and establish a three-phase interval state estimation mathematical model of the active distribution network considering uncertainty.

As shown in Figure 5, a simple active distribution network and its measurement system. Before establishing the three-phase interval state estimation model of the active distribution network, the interval number [a] is defined as a non-empty real number set that satisfies in a represent the upper and lower boundary information of the interval number [a], especially, when When , interval numbers degenerate into real numbers. Assuming that there are n nodes in the network as shown in Figure 5, after considering the uncertain factors, the node i's Mutually Injected active/reactive work can be expressed as:

In the formula, Respectively represent the conventional load demand described by the interval number, the distributed power output and the active information of electric vehicle charging; Respectively represent the conventional load demand described by the interval number and the reactive information of the distributed output. What needs to be mentioned is that most conventional loads and distributed power sources use constant power factor control in the process of steady-state analysis of the active distribution network. Correspondingly calculate the reactive power of conventional loads, photovoltaic output and fan output; and for electric vehicles, the unit power factor control is adopted, and the reactive power demand for charging is zero.

In addition, in the actual distribution network, power measurement and current amplitude measurement devices are only installed at the root of the feeder or at the switch, and the measurement error generated by the measurement device during the measurement process is unavoidable. Therefore, through data acquisition and monitoring control (Supervisory control and data acquisition, SCADA) system uploaded to the dispatching center branch power and the true value of the branch current amplitude measurement also need to be considered as an interval number (that is, the measurement error is bounded), similar to the node injection power, The number of intervals for branch active/reactive power measurement and branch current amplitude measurement can also be expressed as In the formula, i, k are nodes, i, k=1, 2,..., n, then the measurement vector [z] in the interval state estimation model can be expressed as:

Take the three-phase voltage amplitude of node i and phase angle As the state variable x _i to be demanded by the system, there is The three-phase interval state estimation of the active distribution network is to determine the state variable information of the system according to the upper and lower bound information of the measurement vector and the nonlinear mapping relational expression, which is described by the mathematical relational expression as:

In the formula, X′(·) represents the uncertainty set of system state variables, x represents the state variable to be obtained, h(x) represents the nonlinear mapping relationship between the measurement vector and the state variable, z represents the interval measurement The lower bound of the vector, while Indicates the upper limit of the interval measurement vector, M is the system measurement set, and Z′(·) represents the uncertainty set of the system measurement vector. Specifically:

In the formula, is an actual measurement vector, z _j represents the jth quantity measurement, z _j represents the lower limit value of the jth quantity measurement, Indicates the upper limit of the jth quantity measurement, and m' is the base of the system measurement set M.

Furthermore, if the correlation between distributed power sources and loads is not considered, the specific model for three-phase interval state estimation of active distribution networks with multi-type distributed power and load uncertainties can be expressed as shown in formula (14) :

In the formula, γ is any one of the three phases a, b and c respectively; Indicates the voltage amplitude of node i to be sought ( Mutually), Represents the upper limit information of node i voltage amplitude ( Mutually), Represents the lower limit information of node i voltage amplitude ( Mutually), The voltage amplitude of node i to be sought ( Mutually), Represents the upper limit information of node i voltage phase angle ( Mutually), Represents the lower limit information of node i voltage phase angle ( Mutually), Indicates the lower limit of active power on branch ik ( Mutually), Indicates the upper limit of active power on branch ik ( Mutually), Indicates the lower limit of reactive power on branch ik ( Mutually), Indicates the upper limit of reactive power on branch ik ( Mutually), Indicates the lower limit of the current amplitude on branch ik ( Mutually), Indicates the upper limit of the current amplitude on the branch ik ( Mutually), Represents the lower limit information of active power injected by node i ( Mutually), Represents the upper limit information of active power injected by node i ( Mutually), Represents the lower limit information of reactive power injected by node i ( Mutually), Represents the upper limit information of reactive power injected by node i ( Mutually), Represents the voltage phase angle (γ phase) of node i, for node i Phase angle difference between phase and γ phase, between nodes i and k(d) in The phase angle difference between phase and γ phase, with is the corresponding element in the three-phase node admittance matrix, Represents the voltage phase angle (γ phase) of node k, Represents the voltage amplitude (γ phase) of node i, Represents the voltage amplitude of node k (γ phase).

Step 3: Based on the unknown-but-bounded error (UBBE) theory, the established active distribution network interval state estimation model is split into two optimization problems containing nonlinear interval constraints, It is convenient to adopt the appropriate solution method for analysis and solution.

Since the dimension of the measurement vector is larger than the dimension of the system state variables, analyzing this kind of problem from a mathematical point of view belongs to the modeling and solution of interval overdetermined equations, and there is a nonlinear mapping relationship h(x), resulting in the state The geometry of the set X′(·) and the measurement set Z′(·) is very complex, and it is difficult to establish a unified analytical expression and standard analysis method at present. Applied mathematician A.Bargiela based on the theory that the error (noise) is unknown but bounded An effective analysis method for this kind of problem is given, that is, the original problem is divided into two optimization problems containing nonlinear interval constraints, and the upper and lower bounds of the variables to be sought are obtained respectively. Drawing lessons from this kind of thought, then the interval state estimation model established by the present invention can be briefly described as:

In the formula can represent the uncertain interval value of the state variable of node i, and x _i , Then can represent the confidence limits (confidence limits) of the fluctuation of the state variable of node i.

Step 4: Use a linear programming method based on iterative operations combined with sparse matrix technology to effectively solve the established mathematical model of the three-phase interval state estimation of the active distribution network.

The process flow of the algorithm for solving the three-phase interval state estimation of the active distribution network based on the linear programming algorithm proposed by the present invention is shown in Figure 6, and the main implementation steps are as follows:

(1) Obtain the original parameters of the network. The original parameters of the network include pseudo-measurement interval values of node injection power such as branch impedance, load and distributed power supply, and real-time measurement interval values of branch power and current amplitude.

(2) Generate the node three-phase admittance matrix Y _B and the measurement vector [z] in the interval state estimation model. in,

In the formula, are the corresponding elements in the three-phase admittance matrix, i,k=1,...,n, The interval values of active and reactive power are injected into the nodes respectively. The interval values of injected power of photovoltaic, wind power and electric vehicles can be obtained according to the modeling method introduced in the previous chapter. The interval values of conventional load injected power can be added on the basis of day-ahead prediction A certain number of fluctuation intervals. They are respectively the number of intervals for real-time measurement of branch active power, reactive power, and current amplitude. It is only necessary to add a smaller number of fluctuation intervals on the basis of the measured true value.

(3) Set the initial value of the system state variable to be requested

Select the system state variable to be sought, and set the intermediate value of the initial interval approximate solution of the state variable as the initial value of the system state variable to be sought The present invention selects the three-phase voltage amplitude and phase angle of the network node as the state variable to be sought by the system, then there are

(4) Set the number of iterations S=0.

(5) Obtain the corresponding elements in the correction equations, including △ z ⁿ , △ z ^mn ,

Will Substituting △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and △[I ¹² ] in the revised equations, and calculating the corresponding elements △ z ⁿ , △ z ^mn , Among them, △ z ⁿ represents the first n rows of matrix data of △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and the lower limit of △[I ¹² ], Represents the first n rows of matrix data of △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and the upper limit of △[I ¹² ]; while △ z ^mn represents △[P ¹ ], △ [Q ¹ ], △[P ¹² ], △[Q ¹² ] and the remaining mn row matrix data of the lower limit of △[I ¹² ], Then represent the remaining mn row matrix data of △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and △[I ¹² ] upper limit; the correction equations can be expressed in matrix form as :

In the formula, △[P ¹ ], △[Q ¹ ] represent the unbalanced amount of active and reactive power injected into the node interval, respectively, and △[P ¹² ], △[Q ¹² ] represent the unbalanced amount of active and reactive power injected into the branch interval, respectively. △[I ¹² ] represents the imbalance of the current amplitude in the branch section, H ^* , N ^* , K ^* , L ^* , F ^* and S ^* are auxiliary matrices generated in the correction equations, △U, △ θ respectively represent the unbalanced amount of node voltage amplitude and phase angle.

(6) Calculate and decompose the measurement Jacobian matrix J ^m to obtain the corresponding elements J ⁿ and J ^mn

use Calculate each element in the measurement Jacobian, the measurement function h(x) in The first-order Taylor expansion is carried out at , and the measurement Jacobian matrix J ^m is obtained after ignoring the high-order items, and the corresponding J ⁿ and J ^mn are obtained. in,

(7) Calculate the inverse of J ⁿ and calculate elements (J ⁿ ) ^-1 and J ^mn (J ⁿ ) ^-1 .

(8) Obtain the element a ⁱ of each row in the (J ⁿ ) ^-1 matrix, and perform a linear programming operation.

(9) Obtain the interval value of the correction amount And calculate the initial interval value of the new iterative state quantity Combining △ z ⁿ , △ z ^mn , And the corresponding elements in J ^mn (J ⁿ ) ^-1 are respectively substituted into the following formulas:

In the formula, △ x _i represent the upper and lower limits of the unbalance of the state variable to be obtained on node i respectively, and △ z ⁿ represents the unbalance of the first n rows of elements in the measurement vector matrix.

Obtain the interval value of the system voltage correction amount by executing the linear programming operation program Then obtain the new initial interval value of the system node voltage state quantity

(10) Check whether the iteration converges

Use the predetermined convergence criteria to judge whether the iteration has converged, and the criterion for algorithm convergence is:

In the formula, S is the number of iterations, and ε is a given arbitrary decimal.

(11) If it does not converge, update the iterative state quantity, and replace As the initial approximate solution of the new equation, let S=S+1, return to step (5) and enter the next iteration until the convergence criterion is reached, and output the optimal estimated value of the three-phase interval state estimation of the active distribution network .

If it converges, directly output the best estimated interval value of the system state quantity.

Claims (8)

1. A method for estimating an active distribution network three-phase interval state containing node injection power uncertainty, is characterized in that, comprises the following steps: (1) Using the interval number to model and analyze the uncertainties of pseudo-measurement of node injection power including photovoltaic power generation, wind power generation and electric vehicle charging system and measurement error of real-time measurement devices; (2) Select the three-phase voltage amplitude and phase angle of the node as the state variables to be obtained in the system, and establish a three-phase interval state estimation mathematical model of the active distribution network considering uncertainty; (3) Based on the unknown but bounded error theory, the established mathematical model of active distribution network three-phase interval state estimation considering uncertainty is split into two optimization problems containing nonlinear interval constraints, which is convenient for analysis and solution ; (4) A linear programming method based on iterative operation combined with sparse matrix technology is used to solve the established mathematical model of active distribution network three-phase interval state estimation considering uncertainty. 2. the active distribution network three-phase interval state estimation method containing node injection power uncertainty according to claim 1, is characterized in that, step (1) comprises: (11) When using the interval number to characterize the output uncertainty of the photovoltaic power generation system, the upper and lower limit estimation method is used to model the output of the photovoltaic power generation system by establishing a dual-output neural network model; (12) When interval numbers are used to represent the uncertainty of wind power system output, a two-layer neural network wind prediction model based on the online sequential-extreme learning machine structure is used. First, the wind speed is corrected by the ELM model, and then the second layer is used to ELM predicts wind power generation; (13) When performing interval modeling analysis on the stochastic charging of electric vehicles, the Monte Carlo sampling method based on the law of statistical data combined with interval numbers is used to forecast the charging load demand of electric vehicles in intervals. 3. the active distribution network three-phase interval state estimation method that contains node injection power uncertainty according to claim 2, is characterized in that, step (11) comprises: (a) Data preprocessing, divide neural network training and test data Collect historical photovoltaic output data and meteorological data at the corresponding time according to the predetermined sampling interval, and use the processed data as the input of the neural network; (b) Interval prediction optimization algorithm and particle swarm optimization algorithm settings Interval coverage rate PICP and interval width PINAW are important factors to measure the performance of interval forecasting, and the calculation formulas are as follows: <mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><mi>P</mi><mi>I</mi><mi>C</mi><mi>P</mi><mo>=</mo><mfrac><mn>1</mn><mi>&amp;lambda;</mi></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><msup><mi>&amp;kappa;</mi><mo>&amp;prime;</mo></msup><mo>=</mo><mn>1</mn></mrow><mi>&amp;lambda;</mi></munderover><msub><mi>c</mi><msup><mi>&amp;kappa;</mi><mo>&amp;prime;</mo></msup></msub></mrow></mtd></mtr><mtr><mtd><mrow><mi>P</mi><mi>I</mi><mi>N</mi><mi>A</mi><mi>W</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mi>&amp;lambda;</mi><mi>&amp;Lambda;</mi></mrow></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><msup><mi>&amp;kappa;</mi><mo>&amp;prime;</mo></msup><mo>=</mo><mn>1</mn></mrow><mi>&amp;lambda;</mi></munderover><mrow><mo>(</mo><mover><msub><mi>P</mi><mrow><mi>P</mi><mi>V</mi></mrow></msub><mo>&amp;OverBar;</mo></mover><mo>-</mo><munder><msub><mi>P</mi><mrow><mi>P</mi><mi>V</mi></mrow></msub><mo>&amp;OverBar;</mo></munder><mo>)</mo></mrow></mrow></mtd></mtr></mtable></mfenced> In the formula, λ is the number of deterministic predictions, and c _κ' is the evaluation index of the κ'th predicted value; assuming that there is a certain predicted value y _κ' , when , c _κ' = 1; otherwise, c _κ' = 0; and _PPV are the upper limit and lower limit of the interval prediction respectively; Λ is the difference between the minimum value and the maximum value of the target prediction value; The comprehensive evaluation index function of the selected interval forecast is as follows: f=PINAW(1+γ(PICP)e -η ^(PICP-Ψ) ) <mrow><mi>&amp;gamma;</mi><mo>=</mo><mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><mn>0</mn><mo>,</mo></mrow></mtd><mtd><mrow><mi>P</mi><mi>I</mi><mi>C</mi><mi>P</mi><mo>&amp;GreaterEqual;</mo><mi>&amp;Psi;</mi></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn><mo>,</mo></mrow></mtd><mtd><mrow><mi>P</mi><mi>I</mi><mi>C</mi><mi>P</mi><mo>&lt;</mo><mi>&amp;Psi;</mi></mrow></mtd></mtr></mtable></mfenced></mrow> 1 In the formula, Ψ is the confidence value, which is also the adjustment parameter of f; η is the adjustment parameter of f, and in actual engineering, η∈[50,100]; Initialize the size and inertia constant of the particle swarm to generate the initial particle swarm, which is the initial interval value for photovoltaic output prediction; (c) Combined with the particle swarm optimization algorithm, output the optimal interval value for photovoltaic processing prediction, including: ① set the number of iterations L=0, and create an evaluation function value f ^(L) ; ②Update particle swarm algorithm parameters Randomly initialize the position and velocity of each particle in the search space, set the individual optimal position of each particle as the current particle position, obtain the optimal position of the group, and continuously update the position and velocity of the particles; ③Create a new prediction interval and calculate the evaluation function value f ^(L+1) Calculate the fitness value of each particle, and update the individual optimal position of each particle and the optimal position of the entire group; ④Judge whether f ^(L+1) <f ^L is satisfied If not satisfied, make L=L+1, return to step 2. continue searching; If satisfy, then replace the evaluation function value f (L) of last iteration with evaluation function value f ^{(L+1 )} ; ⑤ Determine whether the algorithm termination condition is satisfied Given the condition of particle swarm iterative convergence, as the condition for the termination of the algorithm, if not satisfied, return to step ② to continue the search; if satisfied, stop the search, and output the optimal interval value of photovoltaic output prediction. 4. the active distribution network three-phase interval state estimation method that contains node injection power uncertainty according to claim 2, is characterized in that, step (12) comprises: (a) Data preprocessing, the data includes the historical power generation data of the wind power generation system and the corresponding weather forecast data, the vector Θ is used as the network input of the ELM, the formula is as follows: Θ＝[vv _sin v _cos ρ] ^T In the formula, v is the wind speed; v _sin and v _cos are the sine and cosine values of the wind direction respectively; ρ is the air density, which is calculated from the temperature, air pressure and air relative humidity; all input data in the ELM network are normalized to [ 0,1] interval; (b) In the wind speed correction link, the first-layer ELM network is used to simulate and correct the nonlinear relationship between the forecast wind speed and the measured wind speed; (c) In the link of wind power generation system output interval prediction, the second-layer ELM network is used to predict the interval of wind power generation system output, and the corrected wind speed value, wind direction positive, cosine value and air density value at the current moment are selected as the second-layer ELM network The input value is the upper and lower interval values of the output of the wind power generation system at the current moment output for the network. 5. the active distribution network three-phase interval state estimation method that contains node injection power uncertainty according to claim 2, is characterized in that, step (13) comprises: (a) Set the number of electric vehicles M ^* = 0 (b) Let M ^* =M ^* +1 (c) Determine the initial charging time T _S according to t and f(t) User behavior is mainly determined by the daily mileage d of the electric vehicle and the starting time t of the charging process. According to the survey data of the national household travel survey project, combined with the maximum likelihood estimation method, the probability and statistical laws of d and t are respectively shown in the following formula : <mrow><mi>f</mi><mrow><mo>(</mo><mi>d</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>2</mn><mi>&amp;pi;</mi></mrow></msqrt><msub><mi>d&amp;sigma;</mi><mi>d</mi></msub></mrow></mfrac><mi>exp</mi><mo>&amp;lsqb;</mo><mo>-</mo><mfrac><msup><mrow><mo>(</mo><mi>ln</mi><mi></mi><mi>d</mi><mo>-</mo><msub><mi>&amp;mu;</mi><mi>d</mi></msub><mo>)</mo></mrow><mn>2</mi>mn></msup><mrow><mn>2</mn><msubsup><mi>&amp;sigma;</mi><mi>d</mi><mn>2</mn></msubsup></mrow></mfrac><mo>&amp;rsqb;</mo></mrow> 2 <mrow><mi>f</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfenced open = "{" close = ""><mtable><mtr><mtd><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>2</mn><mi>&amp;pi;</mi></mrow></msqrt><msub><mi>&amp;sigma;</mi><mi>t</mi></msub></mrow></mfrac><mi>exp</mi><mo>&amp;lsqb;</mo><mo>-</mo><mfrac><msup><mrow><mo>(</mo><mi>t</mi><mo>-</mo><msub><mi>&amp;mu;</mi><mi>t</mi></msub><mo>)</mo></mrow><mn>2</mn></msup><mrow><mn>2</mn><msubsup><mi>&amp;sigma;</mi><mi>t</mi><mn>2</mn></msubsup></mrow></mfrac><mo>&amp;rsqb;</mo><mo>,</mo><mo>(</mo><msub><mi>&amp;mu;</mi><mi>t</mi></msub><mo>-</mo><mn>12</mn><mo>)</mo><mo>&amp;le;</mo><mi>t</mi><mo>&lt;</mo><mn>24</mn></mtd></mtr><mtr><mtd><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>2</mn><mi>&amp;pi;</mi></mrow></msqrt><msub><mi>&amp;sigma;</mi><mi>t</mi></msub></mrow></mfrac><mi>exp</mi><mo>&amp;lsqb;</mo><mo>-</mo><mfrac><msup><mrow><mo>(</mo><mi>t</mi><mo>+</mo><mn>24</mn><mo>-</mo><msub><mi>&amp;mu;</mi><mi>t</mi></msub><mo>)</mo></mrow><mn>2</mn></msup><mrow><mn>2</mn><msubsup><mi>&amp;sigma;</mi><mi>t</mi><mn>2</mn></msubsup></mrow></mfrac><mo>&amp;rsqb;</mo><mo>,</mo><mn>0</mn><mo>&lt;</mo><mi>t</mi><mo>&amp;le;</mo><mo>(</mo><msub><mi>&amp;mu;</mi><mi>t</mi></msub><mo>-</mo><mn>12</mn><mo>)</mo></mtd></mtr></mtable></mfenced></mrow> In the formula, μ _d = 3.2, σ _d = 0.88, μ _t = 17.6, σ _t = 3.4; f(t) is the probability density function of the initial charging process; and the initial charging time T _S is obtained according to f(t); (d) Sampling the initial state of charge of the battery according to d, calculating the required charging time T _C , and determining the charging end time T _E , where T _E =T _S +T _C ; The battery SOC of an electric vehicle and its daily mileage d also approximately satisfy a linear relationship, then the charging time T _C of an electric vehicle is estimated as: <mrow><msub><mi>T</mi><mi>C</mi></msub><mo>=</mo><mfrac><mrow><mi>d</mi><mo>&amp;CenterDot;</mo><msub><mi>W</mi><mn>100</mn></msub></mrow><mrow><mn>100</mn><msub><mi>P</mi><mi>C</mi></msub></mrow></mfrac></mrow> In the formula, W ₁₀₀ is the average power consumption per 100 kilometers of electric vehicles, and P _C is the charging power of EVs; (e) Calculate the charging power P(t ₀ ) at sampling time t ₀ During the optimized peak and valley electricity price period, electric vehicles generally adopt an ordered charging mode, and the charging power demand of a single electric vehicle at time t ₀ is expressed as: <mfenced open = "{" close = ""><mtable><mtr><mtd><mi>P</mi><mo>(</mo><msub><mi>t</mi><mn>0</mn></msub><mo>)</mo><mo>=</mo><msub><mi>&amp;zeta;</mi><mi>C</mi></msub><mo>(</mo><msub><mi>t</mi><mn>0</mn></msub><mo>)</mo><mo>&amp;times;</mo>mo><msub><mi>P</mi><mi>C</mi></msub><mo>(</mo><msub><mi>t</mi><mn>0</mn></msub><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>&amp;zeta;</mi><mi>C</mi></msub><mo>(</mo><msub><mi>t</mi><mn>0</mn></msub><mo>)</mo><mo>=</mo><mi>&amp;Psi;</mi><mo>(</mo><mi>t</mi><mo><</mo><msub><mi>t</mi><mn>0</mn></msub><mo>,</mo><mi>t</mi><mo>+</mo><msub><mi>T</mi><mi>C</mi></msub><mo>&amp;GreaterEqual;</mo><msub><mi>t</mi><mn>0</mn></msub><mo>)</mo></mtd></mtr><mtr><mtd><mo>+</mo><mi>&amp;Psi;</mi><mo>(</mo><mi>t</mi><mo&gt;&gt;</mo><msub><mi>t</mi><mn>0</mn></msub><mo>,</mo><mi>t</mi><mo>+</mo><msub><mi>T</mi><mi>C</mi></msub><mo>&amp;GreaterEqual;</mo><msub><mi>t</mi><mn>0</mn></msub><mo>+</mo><mn>24</mn><mo>)</mo></mtd></mtr></mtable></mfenced> In the formula: P(t ₀ ) is the power demand of a single electric vehicle on the t ₀ time section; P _C (t ₀ ) is the charging power of a single EV on the t ₀ time section; ζ _C (t ₀ ) is t ₀ The probability of the charging power of a single electric vehicle on the time section, Ψ( ) is the probability density function of the initial charging time of the electric vehicle; (f) Accumulate EV charging load during [T _S , T _E ] period Assuming that there are M electric vehicles in a certain area, the total charging load in one day can be obtained by accumulating single electric vehicles one by one, then the total charging load of electric vehicles in this area at time _t0 is: <mrow><msub><mi>P</mi><mrow><mi>t</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>l</mi></mrow></msub><mrow><mo>(</mo><msub><mi>t</mi><mn>0</mn></msub><mo>)</mo></mrow><mo>=</mo><munderover><mo>&amp;Sigma;</mo><mrow><msup><mi>&amp;gamma;</mi><mo>&amp;prime;</mo></msup><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><msub><mi>P</mi><msup><mi>&amp;gamma;</mi><mo>&amp;prime;</mo></msup></msub><mrow><mo>(</mo><msub><mi>t</mi><mn>0</mn></msub><mo>)</mo></mrow><mo>,</mo><msub><mi>t</mi><mn>0</mn></msub><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>...</mo><mo>,</mo><mn>24</mn></mrow> Among them, P _γ′ (t ₀ ) represents the charging load of the γ′th electric vehicle on the t ₀ time section; (g) Judging whether the number of electric vehicles exceeds a predetermined value If M ^* < M is established, return to step (b) and continue the calculation; If M ^* < M is not established, then obtain the standard deviation of charging load demand of all electric vehicles, and output the optimal interval value of charging prediction. In addition, since the formula in step (e) is difficult to derive its analytical solution, it is necessary to use the Monte Carlo method to sample the total charging demand of electric vehicles on each time section in a day based on a large amount of historical statistical data, and approximate It obeys a normal distribution, and its expected value and standard deviation are μ _EV and σ _EV , respectively, so the available interval numbers can express the charging demand of electric vehicles: <mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><munder><msub><mi>P</mi><mrow><mi>E</mi><mi>V</mi></mrow></msub><mo>&amp;OverBar;</mo></munder><mo>=</mo><msub><mi>&amp;mu;</mi><mrow><mi>E</mi><mi>V</mi></mrow></msub><mo>-</mo><mi>&amp;upsi;</mi><mo>&amp;CenterDot;</mo><msqrt><msub><mi>&amp;sigma;</mi><mrow><mi>E</mi><mi>V</mi></mrow></msub></msqrt></mrow></mtd></mtr><mtr><mtd><mrow><mover><msub><mi>P</mi><mrow><mi>E</mi><mi>V</mi></mrow></msub><mo>&amp;OverBar;</mo></mover><mo>=</mo><msub><mi>&amp;mu;</mi><mrow><mi>E</mi><mi>V</mi></mrow></msub><mo>+</mo><mi>&amp;upsi;</mi><mo>&amp;CenterDot;</mo><msqrt><msub><mi>&amp;sigma;</mi><mrow><mi>E</mi><mi>V</mi></mrow></msub></msqrt></mrow></mtd></mtr></mtable></mfenced> 3 In the formula, υ is the radius adjustment parameter of the interval number, which can be set according to the actual situation. 6. the active distribution network three-phase interval state estimation method that contains node injection power uncertainty according to claim 1, is characterized in that, step (2) comprises: (21) Considering the uncertainty factor of node injection power pseudo-measurement, node i’s Mutually, The injected active power/reactive power can be expressed as: In the formula, Respectively represent the conventional load demand expressed by the interval number, the distributed power output and the active information of electric vehicle charging; It represents the conventional load demand described by the interval number and the reactive power information of the distributed power output; similar to the node injection power, the branch active/reactive power measurement and the branch current amplitude measurement interval number can also be represented separately for In the formula, i,k represent nodes i,k=1,2,...,n, then the measurement vector [z] in the interval state estimation model can be expressed as: Take the three-phase voltage amplitude of node i and phase angle As the state variable x _i to be demanded by the system, there is The three-phase interval state estimation of the active distribution network is to determine the state variable information of the system according to the upper and lower bound information of the measurement vector and the nonlinear mapping relational expression, which is described by the mathematical relational expression as: <mrow><msup><mi>X</mi><mo>&amp;prime;</mo></msup><mrow><mo>(</mo><mi>M</mi><mo>,</mo><munder><mi>z</mi><mo>&amp;OverBar;</mo></munder><mo>,</mo><mover><mi>z</mi><mo>&amp;OverBar;</mo></mover><mo>)</mo></mrow><mo>:</mo><mo>=</mo><mo>{</mo><mi>x</mi><mo>&amp;Element;</mo><msup><mi>R</mi><mi>n</mi></msup><mo>:</mo><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>&amp;Element;</mo>mo><mi>Z</mi><mrow><mo>(</mo><mi>M</mi><mo>,</mo><munder><mi>z</mi><mo>&amp;OverBar;</mo></munder><mo>,</mo><mover><mi>z</mi><mo>&amp;OverBar;</mo></mover><mo>)</mo></mrow><mo>}</mo></mrow> In the formula, X′(·) represents the uncertainty set of system state variables, x represents the state variable to be obtained, h(x) represents the nonlinear mapping relationship between the measurement vector and the state variable, z represents the interval measurement The lower bound of the vector, while Indicates the upper limit of the interval measurement vector, M is the system measurement set, Z′(·) represents the uncertainty set of the system measurement vector, specifically: <mrow><msup><mi>Z</mi><mo>&amp;prime;</mo></msup><mrow><mo>(</mo><mi>M</mi><mo>,</mo><munder><mi>z</mi><mo>&amp;OverBar;</mo></munder><mo>,</mo><mover><mi>z</mi><mo>&amp;OverBar;</mo></mover><mo>)</mo></mrow><mo>:</mo><mo>=</mo><mo>{</mo><mover><mi>z</mi><mo>^</mo></mover><mo>&amp;Element;</mo><msup><mi>R</mi><msup><mi>m</mi><mo>&amp;prime;</mo></msup></msup><mo>:</mo><munder><msub><mi>z</mi><mi>j</mi></msub><mo>&amp;OverBar;</mo></munder><mo>&amp;le;</mo><msub><mi>z</mi><mi>j</mi></msub><mo>&amp;le;</mo><mover><msub><mi>z</mi><mi>j</mi></msub><mo>&amp;OverBar;</mo></mover><mo>,</mo><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>...</mo><mo>,</mo><mi>m</mi><mo>}</mo></mrow> In the formula, is an actual measurement vector, z _j represents the jth quantity measurement, z _j represents the lower limit value of the jth quantity measurement, Indicates the upper limit value of the jth quantity measurement, m' is the cardinality of the system measurement set M; If the correlation between distributed power and load is not considered, the specific model expression of the three-phase interval state estimation of active distribution network with multi-type distributed power and load uncertainty is as follows: In the formula, γ is any one of the three phases a, b and c respectively; for the node i to be sought phase voltage amplitude, for node i The upper limit information of the phase voltage amplitude, for node i The lower limit information of the phase voltage amplitude, for the node i to be sought phase voltage amplitude, for node i upper limit information of the phase voltage phase angle, for node i The lower limit information of the phase voltage phase angle, on branch road ik The lower limit of phase active power, on branch road ik Upper limit of phase active power, on branch road ik The lower limit of phase reactive power, on branch road ik upper limit of phase reactive power, on branch road ik The lower limit value of the phase current amplitude, on branch road ik The upper limit value of the phase current amplitude, Inject for node i The lower limit information of phase active power, Inject for node i Upper limit information of phase active power, Inject for node i Lower limit information of phase reactive power, Inject for node i upper limit information of phase reactive power, is the γ-phase voltage phase angle of node i, for node i Phase angle difference between phase and γ phase, between node i and node k (or d) in The phase angle difference between phase and γ phase, with is the corresponding element in the three-phase node admittance matrix, is the γ-phase voltage phase angle of node k, is the γ-phase voltage amplitude of node i, is the amplitude of the γ-phase voltage at node k. 7. The method for estimating the three-phase interval state of an active distribution network containing node injection power uncertainty according to claim 1, characterized in that: in step (3), the original problem is split into two intervals containing nonlinear For the optimization problem of constraint conditions, the upper and lower bounds of the variables to be sought are obtained respectively, and the established three-phase interval state estimation model of active distribution network considering uncertainty is briefly expressed as: x _i =min x _i , <mfenced open = "" close = ""><mtable><mtr><mtd><mrow><mi>s</mi><mo>.</mo><mi>t</mi></mrow></mtd><mtd><mrow><mi>x</mi><mo>&amp;Element;</mo><mi>X</mi><mrow><mo>(</mo><mi>M</mi><mo>,</mo><munder><mi>z</mi><mo>&amp;OverBar;</mo></munder><mo>,</mo><mover><mi>z</mi><mo>&amp;OverBar;</mo></mover><mo>)</mo></mrow></mrow></mtd></mtr></mtable></mfenced> In the formula represents the uncertain interval value of node i state variable x _i , and x _i , Then represent the confidence lower bound and upper bound of node i state variable x _i fluctuation. 8. the active distribution network three-phase interval state estimation method that contains node injection power uncertainty according to claim 1, is characterized in that, step (4) comprises: (a) Obtain the original parameters of the network. The original parameters of the network include the pseudo-measurement interval value of the node injection power of the branch impedance, the load and the distributed power supply, and the real-time measurement interval value of the branch power and current amplitude; (b) Generate the node three-phase admittance matrix Y _B and the measurement vector [z] in the interval state estimation model, where, <mrow><msub><mi>Y</mi><mi>B</mi></msub><mo>=</mo><mfenced open = "[" close = "]"><mtable><mtr><mtd><msub><mi>Y</mi><mn>11</mn></msub></mtd><mtd><msub><mi>Y</mi><mn>12</mn></msub></mtd><mtd><mn>...</mn></mtd><mtd><msub><mi>Y</mi><mrow><mn>1</mn><mi>n</mi></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>Y</mi><mn>21</mn></msub></mtd><mtd><msub><mi>Y</mi><mn>22</mn></msub></mtd><mtd><mn>...</mn></mtd><mtd><msub><mi>Y</mi><mrow><mn>2</mn><mi>n</mi></mrow></msub></mtd></mtr><mtr><mtd><mn>...</mn></mtd><mtd><mn>...</mn></mtd><mtd><mn>...</mn></mtd><mtd><mn>...</mn></mtd></mtr><mtr><mtd><msub><mi>Y</mi><mrow><mi>n</mi><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>Y</mi><mrow><mi>n</mi><mn>2</mn></mrow></msub></mtd><mtd><mn>...</mn></mtd><mtd><msub><mi>Y</mi><mrow><mi>n</mi><mi>n</mi></mrow></msub></mtd></mtr></mtable></mfenced><mo>,</mo><msub><mi>Y</mi><mrow><mi>i</mi><mi>k</mi></mrow></msub><mo>=</mo><mfenced open = "[" close = "]"><mtable><mtr><mtd><msubsup><mi>y</mi><mrow><mi>i</mi><mi>k</mi></mrow><mrow><mi>a</mi><mi>a</mi></mrow></msubsup></mtd><mtd><msubsup><mi>y</mi><mrow><mi>i</mi><mi>k</mi></mrow><mrow><mi>a</mi><mi>b</mi></mrow></msubsup></mtd><mtd><msubsup><mi>y</mi><mrow><mi>i</mi><mi>k</mi></mrow><mrow><mi>a</mi><mi>c</mi></mrow></msubsup></mtd></mtr><mtr><mtd><msubsup><mi>y</mi><mrow><mi>i</mi><mi>k</mi></mrow><mrow><mi>b</mi><mi>a</mi></mrow></msubsup></mtd><mtd><msubsup><mi>y</mi><mrow><mi>i</mi><mi>k</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow></msubsup></mtd><mtd><msubsup><mi>y</mi><mrow><mi>i</mi><mi>k</mi></mrow><mrow><mi>b</mi><mi>c</mi></mrow></msubsup></mtd></mtr><mtr><mtd><msubsup><mi>y</mi><mrow><mi>i</mi><mi>k</mi></mrow><mrow><mi>c</mi><mi>a</mi></mrow></msubsup></mtd><mtd><msubsup><mi>y</mi><mrow><mi>i</mi><mi>k</mi></mrow><mrow><mi>c</mi><mi>b</mi></mrow></msubsup></mtd><mtd><msubsup><mi>y</mi><mrow><mi>i</mi><mi>k</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msubsup></mtd></mtr></mtable></mfenced></mrow> In the formula, are the corresponding elements in the three-phase admittance matrix, i,k=1,...,n, Inject active and reactive power interval values for nodes respectively, Respectively, the number of intervals for real-time measurement of branch active power, reactive power and current amplitude; (c) Set the initial value of the system state variable to be requested Select the system state variable to be sought, and set the intermediate value of the initial interval approximate solution of the state variable as the initial value of the system state variable to be sought Select the three-phase voltage amplitude and phase angle of the network nodes as the state variables to be obtained in the system, then we have (d) Set the number of iterations S=0; (e) Obtain the corresponding elements in the correction equations, including △ z ⁿ , △ z ^mn , Will Substituting △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and △[I ¹² ] in the revised equations, and calculating the corresponding elements △ z ⁿ , △ z ^mn , Among them, △ z ⁿ represents the first n rows of matrix data of △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and the lower limit of △[I ¹² ], Representing △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and the upper limit of △[I ¹² ] matrix data; and Representing △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and the remaining mn row matrix data of the lower limit of △[I ¹² ], Then represent the remaining mn row matrix data of △[P ¹ ], △[Q ¹ ], △[P ¹² ], △[Q ¹² ] and the upper limit of △[I ¹² ]; the correction equations can be expressed in matrix form as : <mrow><mfenced open = "[" close = "]"><mtable><mtr><mtd><mrow><mi>&amp;Delta;</mi><mo>&amp;lsqb;</mo><msup><mi>P</mi><mn>1</mn></msup><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>&amp;Delta;</mi><mo>&amp;lsqb;</mo><msup><mi>Q</mi><mn>1</mn></msup><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>&amp;Delta;</mi><mo>&amp;lsqb;</mo><msup><mi>P</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>&amp;Delta;</mi><mo>&amp;lsqb;</mo><msup><mi>Q</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>&amp;Delta;</mi><mo>&amp;lsqb;</mo><msup><mi>I</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow></mtd></mtr></mtable></mfenced><mo>=</mo><mo>-</mo><mfenced open = "[" close = "]"><mtable><mtr><mtd><msup><mi>H</mi><mo>*</mo></msup></mtd><mtd><msup><mi>N</mi><mo>*</mo></msup></mtd></mtr><mtr><mtd><msup><mi>K</mi><mo>*</mo></msup></mtd><mtd><msup><mi>L</mi><mo>*</mo></msup></mtd></mtr><mtr><mtd><msup><mi>F</mi><mo>*</mo></msup></mtd><mtd><msup><mi>S</mi><mo>*</mo></msup></mtd></mtr></mtable></mfenced><mfenced open = "[" close = "]"><mtable><mtr><mtd><mrow><mi>&amp;Delta;</mi><mi>U</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>&amp;Delta;</mi><mi>&amp;theta;</mi></mrow></mtd></mtr></mtable></mfenced></mrow> In the formula, △[P ¹ ], △[Q ¹ ] represent the unbalanced amount of active and reactive power injected into the node interval, respectively, and △[P ¹² ], △[Q ¹² ] represent the unbalanced amount of active and reactive power injected into the branch interval, respectively. △[I ¹² ] represents the imbalance of the current amplitude in the branch section, H ^* , N ^* , K ^* , L ^* , F ^* and S ^* are auxiliary matrices generated in the correction equations, △U, △ θ respectively represent the unbalance of node voltage amplitude and phase angle; (f) Calculate and decompose the measurement Jacobian matrix J ^m to obtain the corresponding elements J ⁿ and J ^mn use Calculate each element in the measurement Jacobian, the measurement function h(x) in The first-order Taylor expansion is carried out at , and the measurement Jacobian matrix J ^m is obtained after ignoring the high-order terms, and the corresponding J ⁿ and J ^mn are obtained; among them, <mrow><msup><mi>J</mi><mi>m</mi></msup><mo>=</mo><mfenced open = "[" close = "]"><mtable><mtr><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>P</mi><mn>1</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>U</mi></mrow></mn>mfrac></mtd><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>P</mi><mn>1</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>&amp;theta;</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>Q</mi><mn>1</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>U</mi></mrow></mfrac></mtd><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>Q</mi><mn>1</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>&amp;theta;</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>P</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>U</mi></mrow></mfrac></mtd><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>P</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>&amp;theta;</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>Q</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>U</mi></mrow></mfrac></mtd><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>Q</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>&amp;theta;</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>I</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>U</mi></mrow></mfrac></mtd><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>I</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>&amp;theta;</mi></mrow></mfrac></mtd></mtr></mtable></mfenced></mrow> <mrow><msup><mi>J</mi><mi>n</mi></msup><mo>=</mo><mfenced open = "[" close = "]"><mtable><mtr><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>P</mi><mn>1</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>U</mi></mrow></mn>mfrac></mtd><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>P</mi><mn>1</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>&amp;theta;</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>Q</mi><mn>1</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>U</mi></mrow></mfrac></mtd><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>Q</mi><mn>1</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>&amp;theta;</mi></mrow></mfrac></mtd></mtr></mtable></mfenced></mrow> <mrow><msup><mi>J</mi><mrow><mi>m</mi><mo>-</mo><mi>n</mi></mrow></msup><mo>=</mo><mfenced open = "[" close = "]"><mtable><mtr><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>P</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>U</mi></mrow></mfrac></mtd><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>P</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>&amp;theta;</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>Q</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>U</mi></mrow></mfrac></mtd><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>Q</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>&amp;theta;</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>I</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>U</mi></mrow></mfrac></mtd><mtd><mfrac><mrow><mo>&amp;part;</mo><mo>&amp;lsqb;</mo><msup><mi>I</mi><mn>12</mn></msup><mo>&amp;rsqb;</mo></mrow><mrow><mo>&amp;part;</mo><mi>&amp;theta;</mi></mrow></mfrac></mtd></mtr></mtable></mfenced></mrow> (g) Invert J ⁿ and calculate elements (J ⁿ ) ^-1 and J ^mn (J ⁿ ) ^-1 ; (h) Obtain each row element a ⁱ in the (J ⁿ ) ^-1 matrix, and perform a linear programming operation; (i) Obtain the interval value of the correction amount And calculate the initial interval value of the new iterative state quantity Combining △ z ⁿ , △ z ^mn , And the corresponding elements in J ^mn (J ⁿ ) ^-1 are respectively substituted into the following formulas: △ x _i = min a ⁱ · △ z ⁿ <mrow><mi>s</mi><mo>.</mo><mi>t</mi><mo>.</mo><mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><mi>&amp;Delta;</mi><msup><munder><mi>z</mi><mo>&amp;OverBar;</mo></munder><mi>n</mi></msup><mo>&amp;le;</mo><msup><mi>&amp;Delta;z</mi><mi>n</mi></msup><mo>&amp;le;</mo><mi>&amp;Delta;</mi><msup><mover><mi>z</mi><mo>&amp;OverBar;</mo></mover><mi>n</mi></msup></mrow></mtd></mtr><mtr><mtd><mrow><mi>&amp;Delta;</mi><msup><munder><mi>z</mi><mo>&amp;OverBar;</mo></munder><mrow><mi>m</mi><mo>-</mo><mi>n</mi></mrow></msup><mo>&amp;le;</mo><msup><mi>J</mi><mrow><mi>m</mi><mo>-</mo><mi>n</mi></mrow></msup><msup><mrow><mo>(</mo><msup><mi>J</mi><mi>n</mi></msup><mo>)</mo></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>&amp;CenterDot;</mo>mo><msup><mi>&amp;Delta;z</mi><mi>n</mi></msup><mo>&amp;le;</mo><mi>&amp;Delta;</mi><msup><mover><mi>z</mi><mo>&amp;OverBar;</mo></mover><mrow><mi>m</mi><mo>-</mo><mi>n</mi></mrow></msup></mrow></mtd></mtr></mtable></mfenced></mrow> <mrow><mi>&amp;Delta;</mi><mover><msub><mi>x</mi><mi>i</mi></msub><mo>&amp;OverBar;</mo></mover><mo>=</mo><mi>max</mi><mi></mi><msup><mi>a</mi><mi>i</mi></msup><mo>&amp;CenterDot;</mo><msup><mi>&amp;Delta;z</mi><mi>n</mi></msup></mrow> <mrow><mi>s</mi><mo>.</mo><mi>t</mi><mo>.</mo><mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><mi>&amp;Delta;</mi><msup><munder><mi>z</mi><mo>&amp;OverBar;</mo></munder><mi>n</mi></msup><mo>&amp;le;</mo><msup><mi>&amp;Delta;z</mi><mi>n</mi></msup><mo>&amp;le;</mo><mi>&amp;Delta;</mi><msup><mover><mi>z</mi><mo>&amp;OverBar;</mo></mover><mi>n</mi></msup></mrow></mtd></mtr><mtr><mtd><mrow><mi>&amp;Delta;</mi><msup><munder><mi>z</mi><mo>&amp;OverBar;</mo></munder><mrow><mi>m</mi><mo>-</mo><mi>n</mi></mrow></msup><mo>&amp;le;</mo><msup><mi>J</mi><mrow><mi>m</mi><mo>-</mo><mi>n</mi></mrow></msup><msup><mrow><mo>(</mo><msup><mi>J</mi><mi>n</mi></msup><mo>)</mo></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>&amp;CenterDot;</mo>mo><msup><mi>&amp;Delta;z</mi><mi>n</mi></msup><mo>&amp;le;</mo><mi>&amp;Delta;</mi><msup><mover><mi>z</mi><mo>&amp;OverBar;</mo></mover><mrow><mi>m</mi><mo>-</mo><mi>n</mi></mrow></msup></mrow></mtd></mtr></mtable></mfenced></mrow> In the formula, △ x _i represent the upper and lower limits of the unbalance of the state variable to be sought on node i respectively, and △ z ⁿ represents the unbalance of the first n rows of elements in the measurement vector matrix; Obtain the interval value of the system voltage correction amount by executing the linear programming operation program Then obtain the new initial interval value of the system node voltage state quantity (j) Check whether the iteration converges Use the predetermined convergence criteria to judge whether the iteration has converged, and the criterion for algorithm convergence is: In the formula, S is the number of iterations, ε is a given arbitrary decimal; (k) If it does not converge, update the iterative state quantity, and set replace As the initial approximate solution of the new equation, let S=S+1, return to step (e) and enter the next iteration until the convergence criterion is reached, and output the optimal estimated value of the three-phase interval state estimation of the active distribution network ; If it converges, directly output the best estimated interval value of the system state quantity.