CN104810826A - Bidirectional iteration parallel probability load flow calculation method combining Latin hypercube sampling - Google Patents

Abstract

The invention discloses a bidirectional iteration parallel probability load flow calculation method combining Latin hypercube sampling. The method includes: using a Latin hypercube sampling method to sample new energy power generating power variables according to the accumulation distribution function of the new energy power generating power variables, and building the sample matrix of the new energy power generating power variables; aiming at the partitionable feature of a power grid, using a branch cutting and node tearing method to concentrate the power grid into meshes, and building a bidirectional iteration parallel load flow calculation model; using the sample matrix of the new energy power generating power variables as the input variable of the bidirectional iteration parallel load flow calculation model to perform probability load flow calculation so as to obtain the discrete result of output variables, and using kernel density estimation to fit the discrete result of the output variables to obtain the probability density function of the output variables. The method has the advantages that the Latin hypercube sampling is combined with the bidirectional iteration parallel load flow algorithm based on the concentrated meshes, sampling number is reduced, and parallel probability load flow calculation is achieved.

Description

Bidirectional iteration in conjunction with Latin Hypercube Sampling walks abreast probability load flow calculation method

Technical field

The invention belongs to power system analysis field, be specifically related to a kind of bidirectional iteration in conjunction with Latin Hypercube Sampling and walk abreast probability load flow calculation method.

Background technology

Generation of electricity by new energy such as wind power generation, photovoltaic generation receive publicity gradually due to the increasingly mature and huge environmental effect of its generation technology, but due to the randomness of itself, if access electrical network in a large number, by the uncertainty of aggravation electrical network, bring risk to the safe operation of electrical network.Traditional certainty tidal current computing method can only reflect the steady operation situation of electric power system under certain determines operating mode, can not be used for the analysis taking into account uncertain factor scene, and probability load flow calculation method is the effective tool addressed this problem.

Probability load flow calculation method is proposed in 1974 by Borkowska at first, and probabilistic load flow essence solves the power flow equation containing random parameter.Wherein, inputting stochastic variable is the meritorious and reactive power (its uncertainty derives from the stoppage in transit of the fluctuation of load, the fluctuation of generated output of renewable energy source and generator) that network configuration and node inject.Export stochastic variable and comprise State-output stochastic variable (i.e. node voltage amplitude and phase angle) and Branch Power Flow.The process of separating Probabilistic Load Flow equation is exactly determine to export expectation of a random variable, variance or probability distribution according to input expectation of a random variable, variance or probability distribution.

At present, probability load flow calculation method is roughly divided into point estimations, analytic method and simulation.Point estimations is a kind of approximate method for solving, although speed is fast, the expectation and variance precision of output variable is high, and the High Order Moment error of output variable is comparatively large and be difficult to the probability distribution obtaining output variable; Analytic method comprises fast Fourier transform method, Cumulants method and FOSM, although computational speed is fast, but precision is high less than simulation, the representative of simulation is Monte Carlo simulation approach, traditional Monte Carlo simulation approach utilizes random sampling technology to extract the sample of input variable, obtain the probability distribution of output variable after carrying out repeatedly certainty Load flow calculation, precision is very high, but consuming time quite long.

Therefore, how while guarantee computational accuracy, improving computational speed, is the required problem solved of current probability load flow calculation method.

Summary of the invention

Goal of the invention: provide a kind of bidirectional iteration in conjunction with Latin Hypercube Sampling to walk abreast probability load flow calculation method, to solve the problems referred to above that prior art exists.

Technical scheme: a kind of bidirectional iteration in conjunction with Latin Hypercube Sampling walks abreast probability load flow calculation method, comprises the steps:

Step 1, cumulative distribution function according to generation of electricity by new energy power and variable, utilize Latin hypercube to sample to generation of electricity by new energy power and variable, set up the sample matrix of generation of electricity by new energy power and variable;

Step 2, can the feature of subregion for electrical network, utilize Branch cutting and node tearing algorithm that electrical network is condensed into grid, set up bidirectional iteration parallel load flow algorithm model;

Step 3, the sample matrix of described generation of electricity by new energy power and variable is carried out probabilistic load flow as the input variable of bidirectional iteration parallel load flow algorithm model, obtain the discrete results of output variable, utilize Density Estimator to carry out matching to the discrete results of output variable, obtain the probability density function of output variable.

In a further embodiment, the process setting up the sample matrix of generation of electricity by new energy power and variable in step 1 is further:

Step 1.1, according to the cumulative distribution function of generation of electricity by new energy power and variable, layering is carried out to generation of electricity by new energy power and variable;

Step 1.2, each subinterval are after separating the layers selected mid point or get a point at random as sample point;

Step 1.3, sample point to be sorted, set up the sample matrix of generation of electricity by new energy power and variable.

Described step 3 is further:

Step 3.1, the sample matrix of described generation of electricity by new energy power and variable is carried out cycle calculations as the input variable of described bidirectional iteration parallel load flow algorithm model, each cycle calculations extracts a certain column vector of generation of electricity by new energy power and variable sample matrix as input variable;

Step 3.2, set up the sample matrix of output variable according to the result of the output variable of cycle calculations gained;

Step 3.3, utilize the probability density function of Density Estimator matching output variable.

Described step 2 is further:

According to Branch cutting principle, electrical network is divided into several subnets, each subnet is associated by interconnection, according to node tearing algorithm, interconnection node tearing is become two child nodes, one of them child node merger is in interconnection side, and another child node merger is in corresponding subnet;

Through above-mentioned process, namely each subnet is summed up as the node interactive relation tearing out from ancestor node to its externalities; By the limit of interconnection as grid, subnet forms a concentrated grid as the node of grid, and each subnet forms the computing node in a grid.

Beneficial effect: can the feature of subregion for electrical network, Latin Hypercube Sampling combines with the bidirectional iteration parallel flow algorithm based on concentrated grid by the present invention, reduces sampling number and realizes parallel probabilistic load flow.

Accompanying drawing explanation

Fig. 1 is the general flow chart of computational methods of the present invention.

Fig. 2 is that the bidirectional iteration in conjunction with Latin Hypercube Sampling of the present invention walks abreast probability load flow calculation method flow chart.

Embodiment

As depicted in figs. 1 and 2, the bidirectional iteration in conjunction with Latin Hypercube Sampling of the present invention walks abreast probability load flow calculation method, comprises the following steps:

1) according to the cumulative distribution function of generation of electricity by new energy power and variable, utilize Latin hypercube to sample to generation of electricity by new energy power and variable, set up the sample matrix of generation of electricity by new energy power and variable.

Suppose stochastic variable X ₁, X ₂... X _kfor K generation of electricity by new energy power and variable, for stochastic variable X _k(k=1,2 ..., K), its cumulative distribution function is F _k(x).

(1) sample

First to stochastic variable X _kcumulative distribution function F _kx the interval [0,1] of () carries out N decile, generate N number of subinterval (s=1,2 ..., N), then in each subinterval (s=1,2 ..., N) select mid point or get a point at random last according to stochastic variable X _kcumulative distribution function F _kthe inverse function of (x) calculate the value of the corresponding x of r by x _k.ras subinterval sample point.The initial sample matrix of generation of electricity by new energy power and variable is generated after all stochastic variables are sampled all according to the method described above

(2) sort

To the initial sample matrix of generation of electricity by new energy power and variable carry out randomly ordered or sort with the sort method that other improve, generating sample matrix X _{k × N}.

2) can the feature of subregion for electrical network, utilize Branch cutting and node tearing algorithm that electrical network is condensed into grid, set up bidirectional iteration parallel load flow algorithm model;

Select rational interconnection that electrical network is divided into several subnets according to Branch cutting principle, each subnet is associated by interconnection, and interconnection node is (B ₁, B ₂..., B _u), according to node tearing algorithm by interconnection Node B _k(k=1,2 ..., u) tear into two sub-Node B 1 _kand B2 _k, a sub-Node B 1 _kmerger in interconnection side, another child node B2 _kmerger is in corresponding subnet.

After adopting such process, each subnet just can be summed up as the node interactive relation tearing out from ancestor node to its externalities.By the limit of interconnection as grid, subnet forms a concentrated grid as the node of grid, and each subnet forms the computing node in a grid.Introduce virtual current what represent interconnection tears Node B 1 _kand B2 _kbetween the relation that influences each other.

The power flow equation of computing node is

$\left[\begin{array}{c}\mathrm{\Δ}{\stackrel{\·}{S}}_a\\ \mathrm{\Δ}{\stackrel{\·}{S}}_b\end{array}\right]=J_{\mathrm{ab}}\left[\begin{array}{c}\mathrm{\Δ}{\stackrel{\·}{U}}_a\\ \mathrm{\Δ}{\stackrel{\·}{U}}_b\end{array}\right]+\left[\begin{array}{c}0\\ {\stackrel{\·}{U}}_b\end{array}\right]{\mathrm{\Δ}\stackrel{\·}{I}}_b---\left(1\right)$

Wherein, a is the internal node of subnet, and b is that merger tears node at the interconnection of sub-network side, for complex power, J _abfor the Jacobian matrix of computing node, for voltage, Δ is departure, wherein for the complex power departure of internal node, for the voltage deviation amount of internal node; for tearing the complex power departure of node, for tearing the voltage deviation amount of node, for tearing the magnitude of voltage of node; for virtual current departure.

Linear transformation is carried out to formula (1)

$\mathrm{\Δ}{\stackrel{\·}{I}}_b=\stackrel{\·}{K}\mathrm{\Δ}{\stackrel{\·}{U}}_b+\stackrel{\·}{C}---\left(2\right)$

Wherein, for the coefficient of linear relationship, for the constant of linear relationship.

The power flow equation of grid is

$\mathrm{\Δ}{\stackrel{\·}{S}}_c=J_c\mathrm{\Δ}{\stackrel{\·}{U}}_b+{\stackrel{\·}{U}}_b\mathrm{\Δ}{\stackrel{\·}{I}}_b---\left(3\right)$

Wherein, c is that merger tears node at the interconnection of grid side, J _cfor the Jacobian matrix of grid.

Power flow equation (1) according to computing node obtains virtual current departure with tear node voltage departure relation (2), then this relation is substituted into the power flow equation (3) of grid side, calculates the voltage deviation amount of tearing node and virtual current departure and then obtain new tearing node voltage value and new virtual current value node voltage value is torn in new and new virtual current value the power flow equation (1) substituting into computing node carries out next iteration calculating, bidirectional iteration like this, stops being masked as of iteration with enough little, what last iterative computation gone out tears node voltage value and virtual current value be updated to computing node and carry out Load flow calculation;

3) using 1) sample matrix of gained generation of electricity by new energy power is as 2) input variable of bidirectional iteration parallel load flow algorithm model set up carries out probabilistic load flow, utilize Density Estimator to carry out matching to probabilistic load flow result, obtain the probability density function of output variable.

By generation of electricity by new energy power and variable sample matrix X _{k × N}carry out cycle calculations as input variable, for n-th cycle calculations, extract sample matrix X _{k × N}the n-th row column vector as 2) input variable of bidirectional iteration parallel load flow algorithm model set up carries out Load flow calculation, obtains the result Z of output variable ⁿ, n=n+1 is set, carries out cycle calculations next time, until X _{k × N}all column vectors all participated in calculate after end loop.

According to the result Z of output variable ⁿ(n=1,2 ..., N) and set up the sample matrix of output variable:

Z＝[Z ¹,Z ²,…,Z ^N] (4)

Utilize Density Estimator matching output variable probability density function:

$\hat{f}\left(z\right)=\frac{1}{\mathrm{Nh}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}K\left(\frac{z-Z_i}{h}\right)---\left(5\right)$

Wherein, N is the discrete data number of output variable, and h is window width, Z _ifor the discrete data of output variable, i ∈ 1,2, N, K () they are kernel function.

In a word, the present invention is based on the principle of improvement Monte Carlo simulation approach based on stratified sampling of Latin Hypercube Sampling, extract the probability characteristics that less sample can meet stochastic variable, speed, faster than traditional Monte Carlo simulation approach, can ensure computational accuracy simultaneously.

More than describe the preferred embodiment of the present invention in detail; but the present invention is not limited to the detail in above-mentioned execution mode, within the scope of technical conceive of the present invention; can carry out multiple equivalents to technical scheme of the present invention, these equivalents all belong to protection scope of the present invention.It should be noted that in addition, each the concrete technical characteristic described in above-mentioned embodiment, in reconcilable situation, can be combined by any suitable mode.In order to avoid unnecessary repetition, the present invention illustrates no longer separately to various possible compound mode.In addition, also can carry out combination in any between various different execution mode of the present invention, as long as it is without prejudice to thought of the present invention, it should be considered as content disclosed in this invention equally.

Claims (4)

1. to walk abreast a probability load flow calculation method in conjunction with the bidirectional iteration of Latin Hypercube Sampling, it is characterized in that, comprise the steps:

Step 1, cumulative distribution function according to generation of electricity by new energy power and variable, utilize Latin hypercube to sample to generation of electricity by new energy power and variable, set up the sample matrix of generation of electricity by new energy power and variable;

Step 2, can the feature of subregion for electrical network, utilize Branch cutting and node tearing algorithm that electrical network is condensed into grid, set up bidirectional iteration parallel load flow algorithm model;

Step 3, the sample matrix of described generation of electricity by new energy power and variable is carried out probabilistic load flow as the input variable of bidirectional iteration parallel load flow algorithm model, obtain the discrete results of output variable, utilize Density Estimator to carry out matching to the discrete results of output variable, obtain the probability density function of output variable.

2. to walk abreast probability load flow calculation method in conjunction with the bidirectional iteration of Latin Hypercube Sampling as claimed in claim 1, it is characterized in that, the process setting up the sample matrix of generation of electricity by new energy power and variable in step 1 is further:

Step 1.1, according to the cumulative distribution function of generation of electricity by new energy power and variable, layering is carried out to generation of electricity by new energy power and variable;

Step 1.2, each subinterval are after separating the layers selected mid point or get a point at random as sample point;

Step 1.3, sample point to be sorted, set up the sample matrix of generation of electricity by new energy power and variable.

3. to walk abreast probability load flow calculation method in conjunction with the bidirectional iteration of Latin Hypercube Sampling as claimed in claim 1, it is characterized in that, described step 3 is further:

Step 3.1, the sample matrix of described generation of electricity by new energy power and variable is carried out cycle calculations as the input variable of described bidirectional iteration parallel load flow algorithm model, each cycle calculations extracts a certain column vector of generation of electricity by new energy power and variable sample matrix as input variable;

Step 3.2, set up the sample matrix of output variable according to the result of the output variable of cycle calculations gained;

Step 3.3, utilize the probability density function of Density Estimator matching output variable.

4. to walk abreast probability load flow calculation method in conjunction with the bidirectional iteration of Latin Hypercube Sampling as claimed in claim 1, it is characterized in that, described step 2 is further:

According to Branch cutting principle, electrical network is divided into several subnets, each subnet is associated by interconnection, according to node tearing algorithm, interconnection node tearing is become two child nodes, one of them child node merger is in interconnection side, and another child node merger is in corresponding subnet;

Through above-mentioned process, namely each subnet is summed up as the node interactive relation tearing out from ancestor node to its externalities;

By the limit of interconnection as grid, subnet forms a concentrated grid as the node of grid, and each subnet forms the computing node in a grid.