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CN107425520B - Active power distribution network three-phase interval state estimation method containing node injection power uncertainty - Google Patents

Active power distribution network three-phase interval state estimation method containing node injection power uncertainty Download PDF

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CN107425520B
CN107425520B CN201710436621.8A CN201710436621A CN107425520B CN 107425520 B CN107425520 B CN 107425520B CN 201710436621 A CN201710436621 A CN 201710436621A CN 107425520 B CN107425520 B CN 107425520B
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interval
phase
node
value
power
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CN107425520A (en
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吴在军
徐俊俊
徐怡悦
窦晓波
顾伟
袁晓冬
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Southeast University
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand

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Abstract

The invention discloses a method for estimating the state of a three-phase interval of an active power distribution network with uncertain node injection power, which comprises the steps of respectively modeling and analyzing uncertainty problems of pseudo measurement of the node injection power and measurement errors of a real-time measurement device by adopting the number of intervals; establishing an active power distribution network three-phase interval state estimation mathematical model considering uncertainty; splitting the established active power distribution network interval state estimation model into two optimization problems containing nonlinear interval constraint conditions; and effectively solving the established three-phase interval state estimation mathematical model of the active power distribution network by combining a linear programming method based on iterative operation and a sparse matrix technology. The method makes up the defects of neglecting the intermittent output of the distributed power supply and the charging of the electric automobile in the current power distribution network state estimation, improves the measurement precision and the solving speed of the algorithm, and provides theoretical support for the next safety evaluation of the active power distribution network.

Description

Active power distribution network three-phase interval state estimation method containing node injection power uncertainty
Technical Field
The invention relates to a three-phase state estimation method for an active power distribution network, in particular to a three-phase interval state estimation method for the active power distribution network with node injection power uncertainty.
Background
The active development of renewable energy power generation grid-connected technology, electric vehicle network-accessing technology and the like is a strategic choice for adjusting energy structures, coping with climate change, changing economic development modes and realizing sustainable development in China. In the future, the power generation grid connection of a high-permeability multi-type distributed power supply, the active loads of electric vehicles and the like and the large-scale access and application of a large number of intelligent terminal devices gradually convert the traditional unidirectional radial power distribution network into an active power distribution network which comprises a multi-energy power supply system and assists in operating in a weak annular topological structure when necessary. Meanwhile, the power distribution network state estimation technology is expected to be capable of further rapidly and accurately sensing the real-time operation state of the system, and provides reliable data for other high-level management software of the active power distribution network, such as a voltage regulation control technology, a distributed power supply output and active load distribution technology, an active power distribution network active/reactive power coordination optimization technology, an intelligent power distribution system self-healing technology and the like.
However, in the future, random charging of large-scale electric vehicles, intermittent power generation grid connection of high-permeability distributed power sources, measurement errors of a large number of intelligent measurement devices and the like cause the state estimation result of the active power distribution network to need to consider more uncertain factors, the traditional method faces a severe challenge, the accuracy of the estimation result cannot meet the scheduling requirement, and how to consider the influence of strong uncertainty on state estimation is an urgent problem to be solved.
Generally speaking, the modeling modes for uncertainty variables in the power distribution network mainly include a probability model, a fuzzy number model and an interval number model. The probability model is to establish different probability models by taking uncertain factors in the network as random variables, then sample the probability distribution function and count the distribution characteristics of the variables. The fuzzy digital model needs to obtain a credibility measure according to a large amount of historical statistical data and establish a corresponding membership function. However, the state estimation based on probability distribution and fuzzy theory must acquire detailed prior probability density functions or membership functions of each uncertain variable in advance, which easily results in increased time complexity of algorithm solution on one hand, and besides, the probability distribution of a conventional power load in an actual power grid can be simply obtained according to a large amount of historical power consumption data, the complete probability density functions of the output of distributed power supplies such as photovoltaic power and wind power are difficult to obtain, and the upper and lower limits of the power fluctuation of the distributed power supplies are only known in most cases.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the defects of the prior art, the active power distribution network three-phase interval state estimation method containing the node injection power uncertainty can meet the requirement that a current power distribution network situation sensing system can quickly and accurately sense the real-time running state of the system after a large-scale electric automobile and a distributed power generation system are connected in a grid.
The technical scheme is as follows: a method for estimating the three-phase interval state of an active power distribution network with node injection power uncertainty comprises the following steps:
(1) modeling and analyzing uncertainty problems of node injection power pseudo measurement of a system containing photovoltaic power generation, wind power generation and electric vehicle charging and measurement errors of a real-time measurement device respectively by using interval numbers;
(2) selecting three-phase voltage amplitude values and phase angles of the nodes as state variables to be solved by the system, and establishing an active power distribution network three-phase interval state estimation mathematical model considering uncertainty;
(3) the established active power distribution network three-phase interval state estimation mathematical model considering uncertainty is split into two optimization problems containing nonlinear interval constraint conditions based on an unknown error but bounded theory, so that analysis and solution are facilitated;
(4) and solving the established active power distribution network three-phase interval state estimation mathematical model considering uncertainty by adopting a linear programming method based on iterative operation and combining a sparse matrix technology.
Further, the step (1) comprises the following steps:
(11) when the uncertainty of the output of the photovoltaic power generation system is characterized by using interval numbers, performing interval modeling on the output of the photovoltaic power generation system by establishing a dual-output neural network model by adopting an upper and lower limit estimation method;
(12) when the uncertainty of the output of the wind power generation system is represented by the interval number, a double-layer neural network wind power prediction model based on an online sequential-extreme learning machine structure is adopted, the wind speed is corrected through an ELM model, and then the wind power generation power is predicted by using a second layer of ELM;
(13) when the interval modeling analysis is carried out on the random charging of the electric automobile, the interval prediction is carried out on the charging load demand of the electric automobile by adopting a Monte Carlo sampling method based on statistical data rules and a mode of combining the interval number.
Further, the step (11) includes:
(a) data preprocessing, partitioning neural network training and testing data
Collecting historical photovoltaic output data and meteorological data at corresponding moments according to a preset sampling interval, and taking the processed data as input of a neural network;
(b) interval prediction optimization algorithm and particle swarm optimization algorithm setting
The interval coverage rate PICP and the interval width PINAW are important factors for measuring the interval prediction performance, and the calculation formulas are respectively shown as the following formulas:
Figure BDA0001318771560000031
where λ is the number of deterministic predictions made, cκ′The evaluation index is the predicted value of the k' th time; suppose there is some predicted value yκ′When is coming into contact with
Figure BDA0001318771560000032
When c is greater thanκ′1 is ═ 1; otherwise, cκ′＝0；
Figure BDA0001318771560000033
And PVPupper and lower bounds for interval prediction, respectively; lambda is the difference between the minimum value and the maximum value of the target predicted value;
the selected interval prediction comprehensive evaluation index function is as follows:
f＝PINAW(1+γ(PICP)e-η(PICP-Ψ))
Figure BDA0001318771560000034
wherein psi is a confidence value and is also an adjusting parameter of f, η is the adjusting parameter of f, and η epsilon [50,100] in the actual engineering;
initializing the scale and inertia constant of the particle swarm, and generating an initial particle swarm, namely an initial interval value of photovoltaic output prediction;
(c) combining a particle swarm optimization algorithm, outputting a photovoltaic processing prediction optimal interval value, and comprising the following steps:
① sets the number of iterations L to 0, and creates an evaluation function value f(L)；
② updating the particle swarm algorithm parameters
Randomly initializing the position and the speed of each particle in a search space, setting the individual optimal position of each particle as the current particle position to obtain a group optimal position, and continuously updating the position and the speed of the particle;
③ creating a new prediction interval and calculating the evaluation function value f(L+1)
Calculating the adaptive value of each particle, and updating the individual optimal position of each particle and the optimal position of the whole population;
④ judging whether f is satisfied(L+1)<fL
If not, let L be L +1, return to step ② to continue searching, if yes, use the evaluation function value f(L+1)Replacing the evaluation function value f of the last iteration(L)；
⑤ judging whether the algorithm termination condition is satisfied
And giving a particle swarm iterative convergence condition as a condition for stopping the algorithm, if the condition is not met, returning to the step ② to continue searching, and if the condition is met, stopping searching and outputting a photovoltaic output prediction optimal interval value.
Further, the step (12) includes:
(a) preprocessing data, wherein the data comprise historical generated power data of a wind power generation system and corresponding meteorological forecast data, a vector theta is used as network input of the ELM, and the formula is as follows:
Θ＝[v vsinvcosρ]T
wherein v is the wind speed; v. ofsin、vcosThe sine value and the cosine value of the wind direction are respectively; rho is air density and is calculated by temperature, air pressure and air relative humidity; all input data in the ELM network are normalized to [0,1 ]]An interval;
(b) in the wind speed correction step, a first-layer ELM network is adopted to simulate and correct the nonlinear relation between the predicted wind speed and the actually measured wind speed;
(c) in the section prediction link of the output of the wind power generation system, a second-layer ELM network is adopted to predict the section of the output of the wind power generation system, a corrected wind speed value, a wind direction correction value, a cosine value and an air density value at the current moment are selected as input values of the second-layer ELM network, and the upper and lower section values of the output of the wind power generation system at the current moment are taken as input values of the second-layer ELM network
Figure BDA0001318771560000041
Is output by the network.
Further, the step (13) includes:
(a) setting the number M of electric vehicles*＝0
(b) Let M*＝M*+1
(c) Determining an initial charging time T according to T and f (T)S
The user behavior is mainly determined by the daily driving mileage d of the electric automobile and the starting time t of the charging process, and probability statistical rules of d and t are obtained by combining a maximum likelihood estimation method according to survey data of a family trip survey item in the whole united states and are respectively shown as the following formula:
Figure BDA0001318771560000042
Figure BDA0001318771560000043
in the formula, mud＝3.2，σd＝0.88，μt＝17.6，σt3.4; f (t) is a probability density function of the initial moment of the charging process; and obtaining an initial charging time T according to f (T)S；
(d) According to the charge state of the sampling initial battery, calculating the required charging time TCAnd determining the end time T of chargingEWherein T isE＝TS+TC；
The battery SOC of the electric automobile and the daily driving mileage d thereof also approximately satisfy the linear relation, and then the charging time length T of the electric automobileCEstimated as:
Figure BDA0001318771560000051
in the formula, W100Is the average power consumption of electric automobile in hundred kilometers, PCA charging power for the EV;
(e) calculating a sample t0Charging power P (t) at time0)
In the optimized peak-valley electricity price time period, the electric automobile generally adopts an orderly charging mode, and then a single electric automobile is in t0The charging power demand at a time is expressed as:
Figure BDA0001318771560000052
in the formula: p (t)0) Is t0Power requirements of a single electric vehicle on a time section; pC(t0) Is t0Charging power of a single EV on a time section; zetaC(t0) Is t0The probability of the charging power of a single electric vehicle on a time section, and psi (-) is a probability density function of the initial charging time of the electric vehicle;
(f) accumulation [ T ]S，TE]Time interval EV charging load
Assuming that a certain region has M electric vehicles, and the total charging load of the electric vehicles can be obtained by accumulating the single electric vehicles one by one in one day, the tth0The total electric vehicle charging load in this region of time section is:
Figure BDA0001318771560000053
wherein, Pγ′(t0) Represents t0Charging load of the gamma' th electric vehicle on the time section;
(g) judging whether the number of the electric vehicles exceeds a preset value
If M is*<If M is established, returning to the step (b) and continuing to calculate;
if M is*<And if M is not satisfied, acquiring the standard deviation of the charging load requirements of all the electric vehicles, and outputting the optimal interval value of the charging prediction.
In addition, since the formula in step (e) is difficult to derive the analytical solution, the total charging requirement of the electric vehicle on each time section in a certain day is respectively sampled by using a monte carlo method based on a large amount of historical statistical data, and the total charging requirement is approximately subjected to normal distribution, the expected value and the standard deviation of the total charging requirement are respectively muEVAnd σEVTherefore, the charging requirement of the electric automobile can be expressed by the number of the available intervals:
Figure BDA0001318771560000061
in the formula, upsilon is a radius adjusting parameter of interval number and can be set according to actual conditions.
Further, the step (2) comprises the following steps:
(21) taking into account the uncertainty of the injected power of the node
Figure BDA0001318771560000062
The phase of the mixture is shown as phase,
Figure BDA0001318771560000063
the injected active/reactive power can be expressed as:
Figure BDA0001318771560000064
in the formula,
Figure BDA0001318771560000065
respectively representing the constant expressed by the number of intervalsThe active information of the rule load demand, the distributed power supply output and the electric automobile charging;
Figure BDA0001318771560000066
respectively representing the conventional load demand and the reactive power information of the distributed power supply output which are depicted by the interval number; similar to the node injection power, the branch active/reactive power measurement and the branch current amplitude measurement interval number can also be expressed as
Figure BDA0001318771560000067
Where i and k denote nodes i, k is 1,2, …, and n, the measurement vector [ z ] in the interval state estimation model]Can be expressed as:
Figure BDA0001318771560000068
three-phase voltage amplitude of node i
Figure BDA0001318771560000069
Angle of sum
Figure BDA00013187715600000610
As the state variable x to be solved by the systemiThen there is
Figure BDA00013187715600000611
The active power distribution network three-phase interval state estimation is that state variable information of a system is determined according to upper and lower bound information of a measurement vector and a nonlinear mapping relation, and is described as follows by a mathematical relation:
Figure BDA00013187715600000612
wherein X' (. cndot.) represents the uncertainty set of the system state variables, X represents the state variables to be solved, h (X) represents the nonlinear mapping relationship between the measurement vector and the state variables,zrepresents the lower limit of the interval measurement vector, and
Figure BDA00013187715600000613
the upper limit of the interval measurement vector is represented, M is a system measurement set, and Z' (·) represents an uncertainty set of the system measurement vector, specifically:
Figure BDA0001318771560000071
in the formula,
Figure BDA0001318771560000072
is a certain actual measurement vector, zjRepresenting the measurement of the jth quantity, jzrepresents a lower limit value of the jth quantity measurement,
Figure BDA0001318771560000073
represents the upper limit of the jth quantity measurement, M' is the base of the system measurement set M;
if the correlation between the distributed power sources and the loads is not considered, the three-phase interval state estimation specific model of the active power distribution network containing the uncertainty of the multi-type distributed power sources and the loads is expressed as the following formula:
Figure BDA0001318771560000074
in the formula,
Figure BDA0001318771560000076
gamma is any one of a phase, b phase and c phase;
Figure BDA0001318771560000077
for node i to be solved
Figure BDA0001318771560000078
The amplitude of the phase voltage is,
Figure BDA0001318771560000079
being node i
Figure BDA00013187715600000710
Information on the upper limit of the amplitude of the phase voltage,
Figure BDA00013187715600000711
being node i
Figure BDA00013187715600000712
Information on the lower limit of the amplitude of the phase voltage,
Figure BDA00013187715600000713
for node i to be solved
Figure BDA00013187715600000714
The amplitude of the phase voltage is,
Figure BDA00013187715600000715
being node i
Figure BDA00013187715600000716
Information on the upper limit of the phase angle of the phase voltage,
Figure BDA00013187715600000717
being node i
Figure BDA00013187715600000718
Information on the lower limit of the phase angle of the phase voltage,
Figure BDA00013187715600000719
is on branch ik
Figure BDA00013187715600000720
The lower limit value of the phase active power,
Figure BDA00013187715600000721
is on branch ik
Figure BDA00013187715600000722
The upper limit value of the phase active power,
Figure BDA00013187715600000723
is on branch ik
Figure BDA00013187715600000724
The lower limit value of the phase reactive power,
Figure BDA00013187715600000725
is on branch ik
Figure BDA00013187715600000726
The upper limit value of the phase reactive power,
Figure BDA00013187715600000727
is on branch ik
Figure BDA00013187715600000728
The lower limit value of the amplitude of the phase current,
Figure BDA00013187715600000729
is on branch ik
Figure BDA00013187715600000730
An upper limit value of the magnitude of the phase current,
Figure BDA0001318771560000081
injecting for node i
Figure BDA0001318771560000082
The lower limit information of the phase active power,
Figure BDA0001318771560000083
injecting for node i
Figure BDA00013187715600000824
The upper limit information of the phase active power,
Figure BDA0001318771560000084
injecting for node i
Figure BDA00013187715600000825
Information on the lower limit of the phase reactive power,
Figure BDA0001318771560000085
injecting for node i
Figure BDA00013187715600000826
Upper limit information of the phase reactive power,
Figure BDA0001318771560000086
the gamma phase voltage phase angle at node i,
Figure BDA0001318771560000087
is on node i
Figure BDA00013187715600000827
The phase angle difference between the phase and the gamma phase,
Figure BDA0001318771560000088
between node i and node k (or d)
Figure BDA00013187715600000828
The phase angle difference between the phase and the gamma phase,
Figure BDA0001318771560000089
and
Figure BDA00013187715600000810
are the corresponding elements in the three-phase node admittance matrix,
Figure BDA00013187715600000811
the gamma phase voltage phase angle at node k,
Figure BDA00013187715600000812
the gamma phase voltage amplitude at node i,
Figure BDA00013187715600000813
the gamma phase voltage magnitude at node k.
Further, in the step (3), the original problem is split into two optimization problems including nonlinear interval constraint conditions, and upper and lower bounds of variables to be solved are respectively solved, so that the established active power distribution network three-phase interval state estimation model considering uncertainty is briefly described by a formula:
Figure BDA00013187715600000814
Figure BDA00013187715600000815
in the formula
Figure BDA00013187715600000816
Representing the state variable x of a node iiIs not determined by the interval value of ix,
Figure BDA00013187715600000817
Then the state variable x of node i is representediThe confidence lower and upper bounds of the fluctuation.
Further, the step (4) comprises the following steps:
(a) acquiring network original parameters, wherein the network original parameters comprise branch impedance, load and node injection power pseudo measurement interval values of a distributed power supply and branch power and current amplitude real-time measurement interval values;
(b) generating a node three-phase admittance matrix YBAnd a measurement vector [ z ] in the interval state estimation model]Wherein
Figure BDA00013187715600000818
Figure BDA00013187715600000819
in the formula,
Figure BDA00013187715600000820
the corresponding elements in the three-phase admittance matrix, i, k ═ 1, …, n,
Figure BDA00013187715600000821
Figure BDA00013187715600000822
interval values of active power and reactive power are respectively injected into the nodes,
Figure BDA00013187715600000823
the interval number of the real-time measurement of the active amplitude, the reactive amplitude and the current amplitude of the branch circuit is respectively;
(c) setting initial value of state variable of system to be solved
Figure BDA0001318771560000091
Selecting a system state variable to be solved, and setting the intermediate value of the approximate solution of the initial interval of the state variable as the initial value of the system state variable to be solved
Figure BDA0001318771560000092
Selecting three-phase voltage amplitude and phase angle of network node as state variable to be solved by system, and obtaining the three-phase voltage amplitude and phase angle
Figure BDA0001318771560000093
(d) Setting the iteration number S to be 0;
(e) obtaining corresponding elements of the correction equation set, including △z n,
Figure BDA0001318771560000094
△z m-n,
Figure BDA0001318771560000095
Will be provided with
Figure BDA0001318771560000096
Substitution into △ [ P ] in the correction equation set1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]And find the corresponding element △z n,
Figure BDA0001318771560000097
△z m-n,
Figure BDA0001318771560000098
Wherein, △z nRepresents △ [ P ]1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]The first n rows of matrix data of the lower limit,
Figure BDA00013187715600000913
represents △ [ P ]1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]Upper limit of the first n rows of matrix data, and △z m-nRepresents △ [ P ]1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]The remaining m-n rows of matrix data of the lower limit,
Figure BDA0001318771560000099
then represents △ [ P1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]The remaining m-n rows of matrix data of the upper bound; the correction equation set can be expressed in a matrix form as:
Figure BDA00013187715600000910
in the formula, △ [ P ]1]、△[Q1]Respectively representing the amount of unbalance between the active and the reactive injected in the node interval, △ [ P ]12]、△[Q12]Representing the amount of unbalance between active and reactive injected in the branch interval, △ [ I12]Representing the unbalance of the current amplitudes in the branch interval, H*、N*、K*、L*、F*And S*The auxiliary matrixes are generated in a correction equation set, and △ U and △ theta respectively represent the unbalance amount of the node voltage amplitude and the phase angle;
(f) computing and decomposing a measured jacobian matrix JmObtaining the corresponding element JnAnd Jm-n
By using
Figure BDA00013187715600000911
Calculating each element in the measured Jacobian, and setting the measurement function h (x) in
Figure BDA00013187715600000912
Performing first-order Taylor expansion, and neglecting high-order terms to obtain a measured Jacobian matrix JmAnd obtaining the corresponding JnAnd Jm-n(ii) a Wherein,
Figure BDA0001318771560000101
Figure BDA0001318771560000102
Figure BDA0001318771560000103
(g) to JnInvert, and calculate element (J)n)-1And Jm-n(Jn)-1；
(h) Obtaining (J)n)-1Each row element a in the matrixiAnd performing linear programming operation;
(i) obtaining interval value of correction quantity
Figure BDA0001318771560000104
And calculating new initial interval value of iteration state quantity
Figure BDA0001318771560000105
Bond △z n,
Figure BDA0001318771560000106
△z m-n,
Figure BDA0001318771560000107
And Jm-n(Jn)-1The corresponding elements are respectively substituted into the following formulas:
△ ix＝min ai·△zn
Figure BDA0001318771560000108
Figure BDA0001318771560000109
Figure BDA00013187715600001010
in the formula,
Figure BDA00013187715600001011
△ ixrespectively representing the upper and lower limits of the unbalance of the state variable to be determined on node i, △ znRepresenting the unbalance amount of the first n rows of elements in the measurement vector matrix;
calculating the interval value of the system voltage correction quantity by executing a linear programming calculation program
Figure BDA0001318771560000111
Further, the new initial interval value of the system node voltage state quantity is obtained
Figure BDA0001318771560000112
(j) Checking whether iteration converges
And judging whether the iteration is converged by using a preset convergence standard, wherein the criterion of algorithm convergence is as follows:
Figure BDA0001318771560000113
in the formula, S is iteration times, and epsilon is any given decimal number;
(k) if not, the iteration state quantity is updated, and
Figure BDA0001318771560000114
instead of the former
Figure BDA0001318771560000115
The initial approximate solution is used as a new equation, S is made to be S +1, the step (e) is returned to, the next iteration is started, until the convergence criterion is reached, and the optimal estimated value of the state estimation of the three-phase interval of the active power distribution network is output;
and if the state quantity is converged, directly outputting the optimal estimation interval value of the system state quantity.
Has the advantages that: compared with the prior art, the method has the following advantages:
(1) the method can make up the defects that the charging randomness of the electric automobile and the output intermittence of the distributed power supply are ignored in the current power distribution network situation perception system, and provides theoretical support for the next safety evaluation of the active power distribution network.
(2) Compared with the existing power distribution network state estimation based on the optimal estimation criterion, the active power distribution network three-phase interval state estimation provided by the invention has higher engineering application value, and can provide effective system state quantity 'boundary' information for scheduling personnel under the condition of containing node injection power uncertainty.
(3) The linear programming method based on iterative operation can realize effective solving of the active power distribution network three-phase interval state estimation mathematical model, and compared with the traditional interval optimization solving method, the efficiency is higher, so that the real-time performance of active power distribution network three-phase interval state estimation can be further improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a flow chart of a photovoltaic power generation system interval prediction algorithm;
FIG. 3 is a flow chart of a wind power generation system interval prediction algorithm;
FIG. 4 is a flowchart of an electric vehicle charging load interval prediction algorithm;
FIG. 5 is a schematic diagram of a simple active power distribution network and a measurement system thereof;
fig. 6 is a flowchart of solving the active power distribution network three-phase interval state estimation model.
Detailed Description
The technical solution of the present invention is described in detail below, but the scope of the present invention is not limited to the embodiments.
As shown in fig. 1, the method for estimating the state of the three-phase interval of the active power distribution network including uncertainty of node injection power of the present invention includes the following steps:
step 1: and quantitatively describing uncertainty of system measurement such as pseudo measurement of injection power of network nodes containing photovoltaic power generation, wind power generation and electric vehicle charging, real-time branch measurement and the like by using the interval number.
At present, most photovoltaic power generation system short-term power prediction models adopt deterministic point prediction, namely, a power value determined by photovoltaic output at a certain time in the future is given, obviously, the point value power prediction method ignores the uncertainty of the photovoltaic output, and meanwhile, the prediction error is large. In order to improve the prediction result, as shown in fig. 2, the method adopts an 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, and the algorithm mainly comprises the following implementation steps:
(1) data preprocessing, partitioning neural network training and testing data
Photovoltaic output is related to a number of factors, such as illumination radiation intensity, photovoltaic array area, and ambient temperature. And collecting historical photovoltaic output data and meteorological data at corresponding moments according to a certain sampling interval, and taking the processed data as the input of a neural network.
(2) Interval prediction optimization algorithm and particle swarm optimization algorithm setting
Important factors for measuring the interval prediction performance are interval coverage (PICP) and interval width (PINAW), and the calculation formulas are respectively shown as follows:
Figure BDA0001318771560000121
where λ is the number of deterministic predictions made, cκ′The evaluation index is the predicted value of the k' th time; suppose there is some predicted value yκ′When is coming into contact with
Figure BDA0001318771560000122
When c is greater thanκ′1 is ═ 1; otherwise, cκ′＝0；
Figure BDA0001318771560000123
And PVPupper and lower bounds for interval prediction, respectively; and lambda is the difference between the minimum value and the maximum value of the target predicted value.
The selected interval prediction comprehensive evaluation index function is as follows:
Figure BDA0001318771560000131
where Ψ is the confidence value and is also the tuning parameter for f, η is also the tuning parameter for f, and η ∈ [50,100] in real engineering.
Initializing parameters such as the scale and inertia constant of the particle swarm, and generating an initial particle swarm, namely an initial interval value of photovoltaic output prediction.
(3) And (3) outputting a photovoltaic processing prediction optimal interval value by combining a particle swarm optimization algorithm, wherein the optimization method comprises the following specific steps:
① sets the number of iterations L to 0, and creates an evaluation function value f(L)；
② updating the particle swarm algorithm parameters
Randomly initializing the position and the speed of each particle in a search space, setting the individual optimal position of each particle as the current particle position, and obtaining a group optimal position; and the position and velocity of the particles are continuously updated.
③ creating a new prediction interval and calculating the evaluation function value f(L+1)
And calculating the adaptive value of each particle, and updating the individual optimal position of each particle and the optimal position of the whole population.
④ judging whether f is satisfied(L+1)<fL
If not, let L be L +1, return to step ② to continue searching, if yes, use the evaluation function value f(L+1)Replacing the evaluation function value f of the last iteration(L)。
⑤ judging whether the algorithm termination condition is satisfied
And (3) giving a particle swarm iterative convergence condition (the maximum iterative times can be set as the most convergence condition) as a condition for stopping the algorithm, if the condition is not met, returning to the step ② to continue searching, and if the condition is met, stopping searching and outputting a photovoltaic output prediction optimal interval value.
The uncertainty of a wind power generation system is mainly influenced by the wind speed and the wind direction. At present, methods for ultra-short term/short term prediction of wind power are roughly classified into physical analysis methods, statistical analysis methods and physical-statistical hybrid methods. The physical analysis method is a method for performing detailed analysis, mathematical modeling and prediction by comprehensively considering information such as geographic information of a wind power plant, characteristics of a wind turbine generator and the like, does not need historical data, and has a high requirement on model precision. As shown in fig. 3, the invention adopts a double-layer neural network wind power prediction model based on an online sequential-extreme learning machine (OS-ELM) structure based on the existing research, firstly corrects the wind speed through an ELM model, and then predicts the wind power generation power by using a second layer ELM, and the main implementation steps are as follows:
(1) and (4) preprocessing data. The method comprises the historical generated power data of the wind power system and corresponding meteorological forecast data such as wind speed, wind direction, temperature and the like, and the vector theta in the formula (3) is considered as the network input of the ELM:
Θ＝[v vsinvcosρ]T(3)
wherein v is the wind speed; v. ofsin、vcosRespectively are the sine and cosine values of the wind direction; 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 need to be normalized to [0,1 ]]An interval.
(2) And (5) a wind speed correction link. According to a common wind turbine power output characteristic curve, in the process of cutting-in wind speed to rated wind speed, obvious wind turbine output power change can be caused by small wind speed change, and therefore wind speed forecast data needs to be corrected to a certain degree. The first-layer ELM network may be used to simulate and correct the non-linear relationship between the predicted wind speed and the measured wind speed.
(3) And (3) a wind turbine generator output interval prediction link. Adopting a second-layer ELM network to predict the interval of the wind turbine generator output, selecting a corrected wind speed value, a wind direction normal value, a cosine value and an air density value at the current moment as input values of the second-layer ELM network, and taking the upper and lower interval values of the wind turbine generator output at the current moment
Figure BDA0001318771560000141
Is output by the network.
Because the charging of the electric vehicle is a strong uncertainty process, factors influencing the charging load of the electric vehicle include the driving characteristics of a vehicle owner, the selection mode of the charging, the charging duration, the battery characteristics, the power grid price at the current moment and the like, so that the modeling analysis of the prediction of the charging load requirement of the electric vehicle from the mechanism direction is difficult to perform. In order to improve the rationality and accuracy of the electric vehicle charging load interval prediction model, on the basis of the existing related research, as shown in fig. 4, the method adopts a monte carlo sampling method based on a statistical data rule and an interval number combined mode to predict the electric vehicle charging load demand. The method comprises the following steps:
(1) setting the number M of electric vehicles*＝0
(2) Let M*＝M*+1
(3) Determining an initial charging time T according to TSWherein T isSMay be obtained according to the probability density function formula f (t) at the starting time of the charging process described below.
The user behavior is mainly determined by the daily driving mileage d of the electric vehicle and the starting time t (assuming that the charging is started immediately after the last trip of the user is finished) in the charging process, and according to national household trip Survey item (NHTS 2009) Survey data, the probability statistical rules of d and t can be roughly obtained by combining a maximum likelihood estimation method, and are respectively shown as the following formulas (4) and (5):
Figure BDA0001318771560000151
Figure BDA0001318771560000152
in the formula, mud＝3.2，σd＝0.88，μt＝17.6，σt＝3.4。
(4) According to the State of Charge (SOC) of the sampling initial battery, calculating the required charging time TCAnd determining the end time T of chargingEWherein T isE＝TS+TC。
The battery SOC of the electric automobile and the daily driving mileage d thereof also approximately satisfy the linear relation, and then the charging time length T of the electric automobileCCan be estimated as:
Figure BDA0001318771560000153
in the formula, W100The average power consumption of the electric automobile is hundred kilometers (unit: kW.h/100 km); pCThe charging power (unit: kW) of the EV.
(5) Calculating a sample t0Charging power P (t) at time0)
In the optimized peak-valley electricity price time period, the electric automobile generally adopts an orderly charging mode, and then a single electric automobile is in t0The charging power demand at a time may be expressed as:
Figure BDA0001318771560000154
in the formula: p (t)0) Is t0Power requirements of a single electric vehicle on a time section; pC(t0) Is t0Charging power of a single EV on a time section; zetaC(t0) Is t0Time breakThe probability of charging power of a single electric vehicle on the surface, Ψ (·), is a probability density function of the initial charging time of the electric vehicle, i.e., equation (5).
(6) Accumulation [ T ]S，TE]Time interval EV charging load
Assuming that a certain region has M electric vehicles, and the total charging load of the electric vehicles can be obtained by accumulating the single electric vehicles one by one in one day, the tth0The total electric vehicle charging load in this region of time section is:
Figure BDA0001318771560000161
(7) judging whether the number of the electric vehicles exceeds a preset value
If M is*<And (5) if M is established, returning to the step (2) and continuing to calculate.
If M is*<And if M is not satisfied, acquiring the standard deviation of the charging load requirements of all the electric vehicles, and outputting the optimal interval value of the charging prediction.
It should be noted that, because the analytic solution of equation (7) is difficult to derive, the total charging requirement of the electric vehicle on each time section in a certain day is respectively sampled by using the monte carlo method based on a large amount of historical statistical data, and the total charging requirement is approximately subjected to normal distribution, and the expected value and the standard deviation are respectively μEVAnd σEVTherefore, the charging requirement of the electric automobile can be expressed by the number of the available intervals:
Figure BDA0001318771560000162
in the formula, upsilon is a radius adjusting parameter of interval number and can be set according to actual conditions.
Step 2: and selecting the three-phase voltage amplitude and the phase angle of the node as state variables to be solved by the system, and establishing an active power distribution network three-phase interval state estimation mathematical model considering uncertainty.
As shown in fig. 5, a simple active power distribution network and its measurement system are provided. Before establishing an estimation model of three-phase interval states of an active power distribution network, definingNumber of intervals [ a ]]Is a non-empty real number set, satisfies
Figure BDA0001318771560000168
Wherein
Figure BDA0001318771560000169
aRespectively represent the number of intervals [ a]Upper and lower boundary information of, in particular, when
Figure BDA00013187715600001610
The number of intervals degenerates to a real number. Assuming that the network shown in FIG. 5 has n nodes, the node i takes the uncertainty into consideration
Figure BDA0001318771560000166
Phase (C)
Figure BDA0001318771560000167
The injected active/reactive power can be expressed as:
Figure BDA0001318771560000163
in the formula,
Figure BDA0001318771560000164
respectively representing the active information of the conventional load demand, the distributed power supply output and the electric automobile charging which are depicted by the interval number;
Figure BDA0001318771560000165
the reactive information of the conventional load demand and the distributed output which are described by the interval number is respectively represented. It should be mentioned that, in the steady state analysis process of the active power distribution network, the conventional load and the distributed power supply mostly adopt a constant power factor control mode, and the invention uses such a processing mode for reference, namely, the reactive power of the conventional load, the photovoltaic output and the fan output can be correspondingly calculated according to the given power factor; and for the electric automobile, the reactive power requirement of charging is zero by adopting unit power factor control.
In addition, only the power measurement and current amplitude measurement devices are installed at the root of the feeder line or at the switch in the actual power distribution network, and measurement errors generated by the measurement devices in the measurement process are inevitable, so that branch power and branch current amplitude measurement truth values uploaded to a dispatching center through a supervisory control and data acquisition (SCADA) system are also considered as interval numbers (that is, measurement errors are bounded), and similarly to node injection power, branch active/reactive power measurement and branch current amplitude measurement interval numbers can be respectively expressed as interval numbers
Figure BDA0001318771560000171
Where i and k are nodes, and i and k are 1,2, …, n, then the measurement vector [ z ] in the interval state estimation model]Can be expressed as:
Figure BDA0001318771560000172
three-phase voltage amplitude of node i
Figure BDA0001318771560000173
Angle of sum
Figure BDA0001318771560000174
As the state variable x to be solved by the systemiThen there is
Figure BDA0001318771560000175
The active power distribution network three-phase interval state estimation is that state variable information of a system is determined according to upper and lower bound information of a measurement vector and a nonlinear mapping relation, and is described as follows by a mathematical relation:
Figure BDA0001318771560000176
wherein X' (. cndot.) represents the uncertainty set of the system state variables, X represents the state variables to be solved, h (X) represents the nonlinear mapping relationship between the measurement vector and the state variables,zrepresents the lower limit of the interval measurement vector, and
Figure BDA0001318771560000177
represents the upper limit of the interval measurement vector, M is the system measurement set, and Z' (. cndot.) represents the uncertainty set of the system measurement vector. The method specifically comprises the following steps:
Figure BDA0001318771560000178
in the formula,
Figure BDA0001318771560000179
is a certain actual measurement vector, zjRepresenting the measurement of the jth quantity, jzrepresents a lower limit value of the jth quantity measurement,
Figure BDA00013187715600001710
represents the upper limit of the jth quantity measurement, and M' is the base of the system measurement set M.
Further, if the correlation between the distributed power sources and the loads is not considered, the specific model for estimating the three-phase interval state of the active power distribution network with the multiple types of distributed power and load uncertainties can be expressed as shown in formula (14):
Figure BDA0001318771560000181
in the formula,
Figure BDA0001318771560000182
gamma is any one of a phase, b phase and c phase;
Figure BDA0001318771560000183
represents the voltage amplitude of the node i to be solved (
Figure BDA0001318771560000184
Phase) of the two phases,
Figure BDA0001318771560000185
upper limit information representing the magnitude of the voltage at node i: (
Figure BDA0001318771560000186
Phase) of the two phases,
Figure BDA0001318771560000187
lower limit information representing the magnitude of the voltage at node i: (
Figure BDA0001318771560000188
Phase) of the two phases,
Figure BDA0001318771560000189
the voltage amplitude of the node i to be solved (
Figure BDA00013187715600001810
Phase) of the two phases,
Figure BDA00013187715600001811
upper limit information representing the voltage phase angle of node i: (
Figure BDA00013187715600001812
Phase) of the two phases,
Figure BDA00013187715600001813
information representing the lower limit of the voltage phase angle of node i: (
Figure BDA00013187715600001814
Phase) of the two phases,
Figure BDA00013187715600001815
lower limit value (representing the active power on branch ik)
Figure BDA00013187715600001816
Phase) of the two phases,
Figure BDA00013187715600001817
upper limit value (representing the active power on branch ik)
Figure BDA00013187715600001818
Phase) of the two phases,
Figure BDA00013187715600001819
represents the lower limit of the reactive power on branch ik (
Figure BDA00013187715600001820
Phase) of the two phases,
Figure BDA00013187715600001821
represents the upper limit of the reactive power on branch ik (
Figure BDA00013187715600001822
Phase) of the two phases,
Figure BDA00013187715600001823
lower limit value representing the amplitude of the current on branch ik: (
Figure BDA00013187715600001824
Phase) of the two phases,
Figure BDA00013187715600001825
represents the upper limit value of the current amplitude on the branch ik (
Figure BDA00013187715600001826
Phase) of the two phases,
Figure BDA00013187715600001827
information of lower limit representing active power injected by node i: (
Figure BDA00013187715600001828
Phase) of the two phases,
Figure BDA00013187715600001829
upper limit information (f) representing active power injected by node i
Figure BDA00013187715600001830
Phase) of the two phases,
Figure BDA00013187715600001831
information representing the lower limit of reactive power injected by node i: (
Figure BDA00013187715600001832
Phase) of the two phases,
Figure BDA00013187715600001833
upper limit information representing reactive power injected by node i: (
Figure BDA00013187715600001834
Phase) of the two phases,
Figure BDA00013187715600001835
representing the voltage phase angle (gamma phase) at node i,
Figure BDA00013187715600001836
is on node i
Figure BDA00013187715600001837
The phase angle difference between the phase and the gamma phase,
Figure BDA00013187715600001838
between nodes i and k (d)
Figure BDA00013187715600001844
The phase angle difference between the phase and the gamma phase,
Figure BDA00013187715600001839
and
Figure BDA00013187715600001840
are the corresponding elements in the three-phase node admittance matrix,
Figure BDA00013187715600001841
representing the voltage phase angle (gamma phase) of node k,
Figure BDA00013187715600001842
representing the voltage magnitude (gamma phase) of node i,
Figure BDA00013187715600001843
representing the voltage magnitude (gamma phase) of node k.
And step 3: the established active power distribution network interval state estimation model is divided into two optimization problems containing nonlinear interval constraint conditions based on an unknown-noise-bound (UBBE) theory, and a proper solving method is convenient to analyze and solve.
Because the dimension of the measurement vector is larger than that of the system state variable, the problem is analyzed from the mathematical angle and belongs to modeling and solving of an interval over-determined equation set, and in addition, a nonlinear mapping relation h (X) exists, so that the geometric shapes of a state set X '(-) and a measurement set Z' (-) are very complex, a unified analytical expression and a standard analytical method are difficult to establish at present, and a mathematician A.Bargilla gives an effective analytical method for the problem on the basis of an error (noise) unknown but bounded theory, namely the original problem is split into two optimization problems comprising nonlinear interval constraint conditions, and the upper and lower bounds of the variable to be solved are respectively solved. By taking such ideas as reference, the interval state estimation model established by the invention can be briefly described as follows by using a formula:
Figure BDA0001318771560000191
in the formula
Figure BDA0001318771560000192
Can represent the uncertain interval value of the state variable of the node i, and ix,
Figure BDA0001318771560000193
a confidence limit (confidence limits) for the fluctuation of the state variable of the node i may be indicated.
And 4, step 4: and effectively solving the established three-phase interval state estimation mathematical model of the active power distribution network by combining a linear programming method based on iterative operation and a sparse matrix technology.
The flow of the active power distribution network three-phase interval state estimation solving algorithm based on the linear programming algorithm is shown in fig. 6, and the method mainly comprises the following implementation steps:
(1) and acquiring network original parameters, wherein the network original parameters comprise branch impedance, load, distributed power supply and other node injection power pseudo measurement interval values and branch power and current amplitude real-time measurement interval values.
(2) Generating a node three-phase admittance matrix YBAnd a measurement vector [ z ] in the interval state estimation model]. Wherein,
Figure BDA0001318771560000194
Figure BDA0001318771560000195
in the formula,
Figure BDA0001318771560000201
the corresponding elements in the three-phase admittance matrix, i, k ═ 1, …, n,
Figure BDA0001318771560000202
Figure BDA0001318771560000203
the interval values of active power and reactive power injected into the nodes respectively can be obtained correspondingly according to the modeling method introduced in the above paragraph, and the interval value of the conventional load injection power can be added with a certain fluctuation interval number on the basis of prediction in the day ahead.
Figure BDA0001318771560000204
The interval numbers of active, reactive and current amplitudes of the branch circuit are measured in real time, and only a small fluctuation interval number needs to be added on the basis of a true value measurement.
(3) Setting initial value of state variable of system to be solved
Figure BDA0001318771560000205
Selecting a system state variable to be solved, and setting the intermediate value of the approximate solution of the initial interval of the state variable as the initial value of the system state variable to be solved
Figure BDA0001318771560000206
The invention selects the three-phase voltage amplitude and the phase angle of the network node as the state variable to be solved by the system, if so
Figure BDA0001318771560000207
(4) The iteration number S is set to 0.
(5) Obtaining corresponding elements of the correction equation set, including △z n,
Figure BDA0001318771560000208
△z m-n,
Figure BDA0001318771560000209
Will be provided with
Figure BDA00013187715600002010
Substitution into △ [ P ] in the correction equation set1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]And find the corresponding element △z n,
Figure BDA00013187715600002011
△z m-n,
Figure BDA00013187715600002012
Wherein, △z nRepresents △ [ P ]1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]The first n rows of matrix data of the lower limit,
Figure BDA00013187715600002013
represents △ [ P ]1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]Upper limit of the first n rows of matrix data, and △z m-nRepresents △ [ P ]1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]Residual of lower limitThe remaining m-n rows of matrix data,
Figure BDA00013187715600002014
then represents △ [ P1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]The remaining m-n rows of matrix data of the upper bound; the correction equation set can be expressed in a matrix form as:
Figure BDA00013187715600002015
in the formula, △ [ P ]1]、△[Q1]Respectively representing the amount of unbalance between the active and the reactive injected in the node interval, △ [ P ]12]、△[Q12]Representing the amount of unbalance between active and reactive injected in the branch interval, △ [ I12]Representing the unbalance of the current amplitudes in the branch interval, H*、N*、K*、L*、F*And S*Both are auxiliary matrices generated in the correction equation set, △ U, △ θ represent the amount of imbalance in node voltage magnitude and phase angle, respectively.
(6) Computing and decomposing a measured jacobian matrix JmObtaining the corresponding element JnAnd Jm-n
By using
Figure BDA0001318771560000211
Calculating each element in the measured Jacobian, and setting the measurement function h (x) in
Figure BDA0001318771560000212
Performing first-order Taylor expansion, and neglecting high-order terms to obtain a measured Jacobian matrix JmAnd obtaining the corresponding JnAnd Jm-n. Wherein,
Figure BDA0001318771560000213
Figure BDA0001318771560000214
Figure BDA0001318771560000215
(7) to JnInvert, and calculate element (J)n)-1And Jm-n(Jn)-1。
(8) Obtaining (J)n)-1Each row element a in the matrixiAnd performing a linear programming operation.
(9) Obtaining interval value of correction quantity
Figure BDA0001318771560000216
And calculating new initial interval value of iteration state quantity
Figure BDA0001318771560000217
Bond △z n,
Figure BDA0001318771560000218
△z m-n,
Figure BDA0001318771560000219
And Jm-n(Jn)-1The corresponding elements are respectively substituted into the following formulas:
Figure BDA00013187715600002110
Figure BDA0001318771560000221
in the formula,
Figure BDA0001318771560000222
△ ixrespectively representing the upper and lower limits of the unbalance of the state variable to be determined on node i, △ znRepresenting the unbalance amount of the first n rows of elements in the measurement vector matrix.
By executing linear programming operation program, the system voltage correction is obtainedInterval value of positive quantity
Figure BDA0001318771560000223
Further, the new initial interval value of the system node voltage state quantity is obtained
Figure BDA0001318771560000224
(10) Checking whether iteration converges
And judging whether the iteration is converged by using a preset convergence standard, wherein the criterion of algorithm convergence is as follows:
Figure BDA0001318771560000225
in the formula, S is the iteration number, and epsilon is any given decimal number.
(11) If not, the iteration state quantity is updated, and
Figure BDA0001318771560000226
instead of the former
Figure BDA0001318771560000227
And (4) serving as a new initial approximate solution of an equation, making S equal to S +1, returning to the step (5) and starting to enter the next iteration until a convergence criterion is reached, and outputting an optimal estimated value of the state estimation of the three-phase interval of the active power distribution network.
And if the state quantity is converged, directly outputting the optimal estimation interval value of the system state quantity.

Claims (8)

1. A method for estimating the three-phase interval state of an active power distribution network with node injection power uncertainty is characterized by comprising the following steps:
(1) modeling and analyzing uncertainty problems of node injection power pseudo measurement of a system containing photovoltaic power generation, wind power generation and electric vehicle charging and measurement errors of a real-time measurement device respectively by using interval numbers;
(2) selecting three-phase voltage amplitude values and phase angles of the nodes as state variables to be solved by the system, and establishing an active power distribution network three-phase interval state estimation mathematical model considering uncertainty;
(3) the established active power distribution network three-phase interval state estimation mathematical model considering uncertainty is split into two optimization problems containing nonlinear interval constraint conditions based on an unknown error but bounded theory, so that analysis and solution are facilitated;
(4) and solving the established active power distribution network three-phase interval state estimation mathematical model considering uncertainty by adopting a linear programming method based on iterative operation and combining a sparse matrix technology.
2. The active power distribution network three-phase interval state estimation method containing the node injection power uncertainty as claimed in claim 1, wherein the step (1) comprises:
(11) when the uncertainty of the output of the photovoltaic power generation system is characterized by using interval numbers, performing interval modeling on the output of the photovoltaic power generation system by establishing a dual-output neural network model by adopting an upper and lower limit estimation method;
(12) when the uncertainty of the output of the wind power generation system is represented by the interval number, a double-layer neural network wind power prediction model based on an online sequential-extreme learning machine structure is adopted, the wind speed is corrected through an ELM model, and then the wind power generation power is predicted by using a second layer of ELM;
(13) when the interval modeling analysis is carried out on the random charging of the electric automobile, the interval prediction is carried out on the charging load demand of the electric automobile by adopting a Monte Carlo sampling method based on statistical data rules and a mode of combining the interval number.
3. The active power distribution network three-phase interval state estimation method containing the node injection power uncertainty as claimed in claim 2, wherein the step (11) comprises:
(a) data preprocessing, partitioning neural network training and testing data
Collecting historical photovoltaic output data and meteorological data at corresponding moments according to a preset sampling interval, and taking the processed data as input of a neural network;
(b) interval prediction optimization algorithm and particle swarm optimization algorithm setting
The interval coverage rate PICP and the interval width PINAW are important factors for measuring the interval prediction performance, and the calculation formulas are respectively shown as the following formulas:
Figure FDA0002316425430000021
where λ is the number of deterministic predictions made, cκ′The evaluation index is the predicted value of the k' th time; suppose there is some predicted value yκ′When is coming into contact with
Figure FDA0002316425430000022
When c is greater thanκ′1 is ═ 1; otherwise, cκ′＝0；
Figure FDA0002316425430000023
And PVPupper and lower bounds for interval prediction, respectively; lambda is the difference between the minimum value and the maximum value of the target predicted value;
the selected interval prediction comprehensive evaluation index function is as follows:
f＝PINAW(1+γ(PICP)e-η(PICP-Ψ))
Figure FDA0002316425430000024
wherein psi is a confidence value and is also an adjusting parameter of f, η is the adjusting parameter of f, and η epsilon [50,100] in the actual engineering;
initializing the scale and inertia constant of the particle swarm, and generating an initial particle swarm, namely an initial interval value of photovoltaic output prediction;
(c) combining a particle swarm optimization algorithm, outputting a photovoltaic processing prediction optimal interval value, and comprising the following steps:
① sets the number of iterations L to 0, and creates an evaluation function value f(L)；
② updating the particle swarm algorithm parameters
Randomly initializing the position and the speed of each particle in a search space, setting the individual optimal position of each particle as the current particle position to obtain a group optimal position, and continuously updating the position and the speed of the particle;
③ creating a new prediction interval and calculating the evaluation function value f(L+1)
Calculating the adaptive value of each particle, and updating the individual optimal position of each particle and the optimal position of the whole population;
④ judging whether f is satisfied(L+1)<fL
If not, let L be L +1, return to step ② to continue searching, if yes, use the evaluation function value f(L+1)Replacing the evaluation function value f of the last iteration(L)；
⑤ judging whether the algorithm termination condition is satisfied
And giving a particle swarm iterative convergence condition as a condition for stopping the algorithm, if the condition is not met, returning to the step ② to continue searching, and if the condition is met, stopping searching and outputting a photovoltaic output prediction optimal interval value.
4. The active power distribution network three-phase interval state estimation method containing the node injection power uncertainty as claimed in claim 2, wherein the step (12) comprises:
(a) preprocessing data, wherein the data comprise historical generated power data of a wind power generation system and corresponding meteorological forecast data, a vector theta is used as network input of the ELM, and the formula is as follows:
Θ＝[v vsinvcosρ]T
wherein v is the wind speed; v. ofsin、vcosThe sine value and the cosine value of the wind direction are respectively; rho is air density and is calculated by temperature, air pressure and air relative humidity; all input data in the ELM network are normalized to [0,1 ]]An interval;
(b) in the wind speed correction step, a first-layer ELM network is adopted to simulate and correct the nonlinear relation between the predicted wind speed and the actually measured wind speed;
(c) in the output interval prediction link of the wind power generation system, a second-layer ELM network is adopted to carry out wind power generationThe interval prediction of the power system output is carried out by selecting the corrected wind speed value, the wind direction normal value, the cosine value and the air density value at the current moment as the input values of the ELM network of the second layer and taking the upper and lower interval values of the power system output at the current moment
Figure FDA0002316425430000031
Is output by the network.
5. The active power distribution network three-phase interval state estimation method containing the node injection power uncertainty as claimed in claim 2, wherein the step (13) comprises:
(a) setting the number M of electric vehicles*＝0
(b) Let M*＝M*+1
(c) Determining an initial charging time T according to T and f (T)S
The user behavior is mainly determined by the daily driving mileage d of the electric automobile and the starting time t of the charging process, and probability statistical rules of d and t are obtained by combining a maximum likelihood estimation method according to survey data of a family trip survey item in the whole united states and are respectively shown as the following formula:
Figure FDA0002316425430000032
Figure FDA0002316425430000033
in the formula, mud＝3.2，σd＝0.88，μt＝17.6，σt3.4; f (t) is a probability density function of the initial moment of the charging process; and obtaining an initial charging time T according to f (T)S；
(d) According to the charge state of the sampling initial battery, calculating the required charging time TCAnd determining the end time T of chargingEWherein T isE＝TS+TC；
The battery SOC of the electric automobile and the daily driving mileage d thereof also approximately satisfy the linear relation, and then the electric automobileVehicle charging duration TCEstimated as:
Figure FDA0002316425430000041
in the formula, W100Is the average power consumption of electric automobile in hundred kilometers, PCA charging power for the EV;
(e) calculating a sample t0Charging power P (t) at time0)
In the optimized peak-valley electricity price time period, the electric automobile adopts an orderly charging mode, and then a single electric automobile is in t0The charging power demand at a time is expressed as:
Figure FDA0002316425430000042
in the formula: p (t)0) Is t0Power requirements of a single electric vehicle on a time section; pC(t0) Is t0Charging power of a single EV on a time section; zetaC(t0) Is t0The probability of the charging power of a single electric vehicle on a time section, and psi (-) is a probability density function of the initial charging time of the electric vehicle;
(f) accumulation [ T ]S，TE]Time interval EV charging load
Assuming that a certain region has M electric vehicles, and the total charging load of the electric vehicles can be obtained by accumulating the single electric vehicles one by one in one day, the tth0The total electric vehicle charging load in the area on the time section is as follows:
Figure FDA0002316425430000043
wherein, Pγ′(t0) Represents t0Charging load of the gamma' th electric vehicle on the time section;
(g) judging whether the number of the electric vehicles exceeds a preset value
If M is*<If M is established, returning to the step (b) and continuing to calculate;
if M is*<If M is not true, acquiring the standard deviation of all the electric automobile charging load requirements, and outputting the optimal charging prediction interval value;
in addition, since the formula in step (e) is difficult to derive the analytical solution, the total charging requirement of the electric vehicle on each time section in a certain day is respectively sampled by using a monte carlo method based on a large amount of historical statistical data, and the total charging requirement is approximately subjected to normal distribution, the expected value and the standard deviation of the total charging requirement are respectively muEVAnd σEVTherefore, the charging requirement of the electric automobile can be expressed by the number of the available intervals:
Figure FDA0002316425430000051
in the formula, upsilon is a radius adjusting parameter of interval number and can be set according to actual conditions.
6. The active power distribution network three-phase interval state estimation method containing the node injection power uncertainty as claimed in claim 1, wherein the step (2) comprises:
(21) taking into account the uncertainty of the injected power of the node
Figure FDA0002316425430000052
The phase of the mixture is shown as phase,
Figure FDA0002316425430000053
the injected active/reactive power can be expressed as:
Figure FDA0002316425430000054
in the formula,
Figure FDA0002316425430000055
respectively representing the active information of the conventional load demand, the distributed power output and the electric vehicle charging expressed by the interval number;
Figure FDA0002316425430000056
respectively representing the conventional load demand and the reactive power information of the distributed power supply output which are depicted by the interval number; similar to the node injection power, the branch active/reactive power measurement and the branch current amplitude measurement interval number can also be expressed as
Figure FDA0002316425430000057
Where i and k denote nodes i, k is 1,2, …, and n, the measurement vector [ z ] in the interval state estimation model]Can be expressed as:
Figure FDA0002316425430000058
three-phase voltage amplitude of node i
Figure FDA0002316425430000059
Angle of sum
Figure FDA00023164254300000510
As the state variable x to be solved by the systemiThen there is
Figure FDA00023164254300000511
The active power distribution network three-phase interval state estimation is that state variable information of a system is determined according to upper and lower bound information of a measurement vector and a nonlinear mapping relation, and is described as follows by a mathematical relation:
Figure FDA0002316425430000061
wherein X' (. cndot.) represents the uncertainty set of the system state variables, X represents the state variables to be solved, h (X) represents the nonlinear mapping relationship between the measurement vector and the state variables,zrepresents the lower limit of the interval measurement vector, and
Figure FDA0002316425430000062
the upper limit of the interval measurement vector is represented, M is a system measurement set, and Z' (·) represents an uncertainty set of the system measurement vector, specifically:
Figure FDA0002316425430000063
in the formula,
Figure FDA0002316425430000064
is a certain actual measurement vector, zjRepresenting the measurement of the jth quantity, jzrepresents a lower limit value of the jth quantity measurement,
Figure FDA0002316425430000065
represents the upper limit of the jth quantity measurement, M' is the base of the system measurement set M;
if the correlation between the distributed power sources and the loads is not considered, the three-phase interval state estimation specific model of the active power distribution network containing the uncertainty of the multi-type distributed power sources and the loads is expressed as the following formula:
Figure FDA0002316425430000066
Figure FDA0002316425430000067
in the formula,
Figure FDA0002316425430000068
gamma is any one of a phase, b phase and c phase;
Figure FDA0002316425430000069
for node i to be solved
Figure FDA00023164254300000610
The amplitude of the phase voltage is,
Figure FDA00023164254300000611
being node i
Figure FDA00023164254300000612
Information on the upper limit of the amplitude of the phase voltage,
Figure FDA00023164254300000613
being node i
Figure FDA00023164254300000614
Information on the lower limit of the amplitude of the phase voltage,
Figure FDA00023164254300000615
for node i to be solved
Figure FDA00023164254300000616
The amplitude of the phase voltage is,
Figure FDA00023164254300000617
being node i
Figure FDA00023164254300000618
Information on the upper limit of the phase angle of the phase voltage,
Figure FDA00023164254300000619
being node i
Figure FDA0002316425430000071
Information on the lower limit of the phase angle of the phase voltage,
Figure FDA0002316425430000072
is on branch ik
Figure FDA0002316425430000073
The lower limit value of the phase active power,
Figure FDA0002316425430000074
is on branch ik
Figure FDA0002316425430000075
The upper limit value of the phase active power,
Figure FDA0002316425430000076
is on branch ik
Figure FDA0002316425430000077
The lower limit value of the phase reactive power,
Figure FDA0002316425430000078
is on branch ik
Figure FDA0002316425430000079
The upper limit value of the phase reactive power,
Figure FDA00023164254300000710
is on branch ik
Figure FDA00023164254300000711
The lower limit value of the amplitude of the phase current,
Figure FDA00023164254300000712
is on branch ik
Figure FDA00023164254300000713
An upper limit value of the magnitude of the phase current,
Figure FDA00023164254300000714
injecting for node i
Figure FDA00023164254300000715
The lower limit information of the phase active power,
Figure FDA00023164254300000716
injecting for node i
Figure FDA00023164254300000717
The upper limit information of the phase active power,
Figure FDA00023164254300000718
injecting for node i
Figure FDA00023164254300000719
Information on the lower limit of the phase reactive power,
Figure FDA00023164254300000720
injecting for node i
Figure FDA00023164254300000721
Upper limit information of the phase reactive power,
Figure FDA00023164254300000722
the gamma phase voltage phase angle at node i,
Figure FDA00023164254300000723
is on node i
Figure FDA00023164254300000724
The phase angle difference between the phase and the gamma phase,
Figure FDA00023164254300000725
between node i and node k or d
Figure FDA00023164254300000726
The phase angle difference between the phase and the gamma phase,
Figure FDA00023164254300000727
and
Figure FDA00023164254300000728
are the corresponding elements in the three-phase node admittance matrix,
Figure FDA00023164254300000729
the gamma phase voltage phase angle at node k,
Figure FDA00023164254300000730
the gamma phase voltage amplitude at node i,
Figure FDA00023164254300000731
the gamma phase voltage magnitude at node k.
7. The active power distribution network three-phase interval state estimation method containing the node injection power uncertainty as claimed in claim 1, wherein: in the step (3), the original problem is split into two optimization problems including nonlinear interval constraint conditions, and the upper and lower bounds of the variable to be solved are solved respectively, so that the established active power distribution network three-phase interval state estimation model considering uncertainty is briefly described by a formula:
Figure FDA00023164254300000732
Figure FDA00023164254300000733
in the formula
Figure FDA00023164254300000734
Representing the state variable x of a node iiIs not determined by the interval value of ix,
Figure FDA00023164254300000735
Then the state variable x of node i is representediThe confidence lower and upper bounds of the fluctuation.
8. The active power distribution network three-phase interval state estimation method containing the node injection power uncertainty as claimed in claim 1, wherein the step (4) comprises:
(a) acquiring network original parameters, wherein the network original parameters comprise branch impedance, load and node injection power pseudo measurement interval values of a distributed power supply and branch power and current amplitude real-time measurement interval values;
(b) generating a node three-phase admittance matrix YBAnd a measurement vector [ z ] in the interval state estimation model]Wherein
Figure FDA0002316425430000081
Figure FDA0002316425430000082
in the formula,
Figure FDA0002316425430000083
the corresponding elements in the three-phase admittance matrix, i, k ═ 1, …, n,
Figure FDA0002316425430000084
γ∈{a,b,c}；
Figure FDA0002316425430000085
interval values of active power and reactive power are respectively injected into the nodes,
Figure FDA0002316425430000086
the interval number of the real-time measurement of the active amplitude, the reactive amplitude and the current amplitude of the branch circuit is respectively;
(c) setting initial value of state variable of system to be solved
Figure FDA0002316425430000087
Selecting a system state variable to be solved, and setting the intermediate value of the approximate solution of the initial interval of the state variable as the initial value of the system state variable to be solved
Figure FDA0002316425430000088
Selecting three-phase voltage amplitude and phase angle of network node as state variable to be solved by system, and obtaining the three-phase voltage amplitude and phase angle
Figure FDA0002316425430000089
(d) Setting the iteration number S to be 0;
(e) obtaining corresponding elements of the correction equation set, including △z n,
Figure FDA00023164254300000810
△z m-n,
Figure FDA00023164254300000811
Will be provided with
Figure FDA00023164254300000812
Substitution into △ [ P ] in the correction equation set1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]And find the corresponding element △z n,
Figure FDA00023164254300000813
△z m-n,
Figure FDA00023164254300000814
Wherein, △z nRepresents △ [ P ]1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]The first n rows of matrix data of the lower limit,
Figure FDA00023164254300000815
represents △ [ P ]1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]Upper limit of the first n rows of matrix data, and △z m-nRepresents △ [ P ]1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]The remaining m-n rows of matrix data of the lower limit,
Figure FDA00023164254300000816
then represents △ [ P1]、△[Q1]、△[P12]、△[Q12]And △ [ I ]12]The remaining m-n rows of matrix data of the upper bound; the correction equation set can be expressed in a matrix form as:
Figure FDA00023164254300000817
in the formula, △ [ P ]1]、△[Q1]Respectively representing the amount of unbalance between the active and the reactive injected in the node interval, △ [ P ]12]、△[Q12]Representing the amount of unbalance between active and reactive injected in the branch interval, △ [ I12]Representing the unbalance of the current amplitudes in the branch interval, H*、N*、K*、L*、F*And S*The auxiliary matrixes are generated in a correction equation set, and △ U and △ theta respectively represent the unbalance amount of the node voltage amplitude and the phase angle;
(f) computing and decomposing a measured jacobian matrix JmObtaining the corresponding element JnAnd Jm-n
By using
Figure FDA0002316425430000091
Calculating each element in the measured Jacobian, and setting the measurement function h (x) in
Figure FDA0002316425430000092
Performing first-order Taylor expansion, and neglecting high-order terms to obtain a measured Jacobian matrix JmAnd obtaining the corresponding JnAnd Jm-n(ii) a Wherein,
Figure FDA0002316425430000093
Figure FDA0002316425430000094
Figure FDA0002316425430000095
(g) to JnInvert, and calculate element (J)n)-1And Jm-n(Jn)-1；
(h) Obtaining (J)n)-1Each row element a in the matrixiAnd performing linear programming operation;
(i) obtaining interval value of correction quantity
Figure FDA0002316425430000096
And calculating new initial interval value of iteration state quantity
Figure FDA0002316425430000097
Bond △z n,
Figure FDA0002316425430000098
△z m-n,
Figure FDA0002316425430000099
And Jm-n(Jn)-1The corresponding elements are respectively substituted into the following formulas:
△ ix＝min ai·△zn
Figure FDA0002316425430000101
Figure FDA0002316425430000102
Figure FDA0002316425430000103
in the formula,
Figure FDA0002316425430000104
△ ixrespectively representing the upper and lower limits of the unbalance of the state variable to be determined on node i, △ znRepresenting the unbalance amount of the first n rows of elements in the measurement vector matrix;
calculating the interval value of the system voltage correction quantity by executing a linear programming calculation program
Figure FDA0002316425430000105
Further, the new initial interval value of the system node voltage state quantity is obtained
Figure FDA0002316425430000106
(j) Checking whether iteration converges
And judging whether the iteration is converged by using a preset convergence standard, wherein the criterion of algorithm convergence is as follows:
Figure FDA0002316425430000107
in the formula, S is iteration times, and epsilon is any given decimal number;
(k) if not, the iteration state quantity is updated, and
Figure FDA0002316425430000108
instead of the former
Figure FDA0002316425430000109
The initial approximate solution is used as a new equation, S is made to be S +1, the step (e) is returned to, the next iteration is started, until the convergence criterion is reached, and the optimal estimated value of the state estimation of the three-phase interval of the active power distribution network is output;
and if the state quantity is converged, directly outputting the optimal estimation interval value of the system state quantity.
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