CN104682387A - Probability load flow calculation method based on multi-zone interactive iteration - Google Patents

Abstract

The invention discloses a probability load flow calculation method based on multi-zone interactive iteration. The probability load flow calculation method comprises the following steps: firstly, sampling new energy electricity generation power variable by using an improved Latin hypercube sampling method, and establishing a sample matrix of the new energy electricity generation power variable; partitioning a power grid by using a node tearing method, and establishing a multi-zone interactive iteration calculation model; finally performing probability load flow calculation. According to the probability load flow calculation method disclosed by the invention, the tail characteristics of random variable probability distribution can be considered, and the new energy electricity generation power variable is sampled by using the improved Latin hypercube sampling method, so that the validity of samples is improved; as the power grid is partitioned by using the node tearing method, and the multi-zone interactive iteration calculation model is established, parallel computing can be achieved, Jacobian matrix dimensions of load flow calculation can be reduced, and multi-zone probability load flow calculation can be achieved.

Description

A kind of probability load flow calculation method based on multi-regional interactive iteration

Technical field

The invention belongs to power system analysis field, be specifically related to a kind of probability load flow calculation method based on multi-regional interactive iteration.

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, 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, the probability distribution of output variable is obtained after carrying out repeatedly certainty Load flow calculation, precision is very high, but it is consuming time quite long, based on the improvement Monte Carlo simulation approach of Latin Hypercube Sampling based on the principle of stratified 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.How while guarantee computational accuracy, to improve computational speed, be the required problem solved of current probability load flow calculation method.

Summary of the invention

The invention provides a kind of probability load flow calculation method realizing the multi-regional interactive iteration of parallel computation.

Probability load flow calculation method based on multi-regional interactive iteration of the present invention, comprises the following steps:

1) according to cumulative distribution function and the probability density function of generation of electricity by new energy power and variable, utilize improvement 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;

2) can the feature of subregion for electrical network, utilize node tearing algorithm to carry out subregion to electrical network, set up multi-regional interactive iterative computation model;

3) using 1) sample matrix of gained generation of electricity by new energy power is as 2) input variable of multi-regional interactive iterative computation model set up carries out probabilistic load flow, utilize Density Estimator to carry out matching to probabilistic load flow result, obtain probability density function and the cumulative distribution function of node voltage and Branch Power Flow.

In a preferred version of the inventive method, step 1) in the sample matrix of generation of electricity by new energy power and variable set up set up in such a way:

First 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; Then each subinterval after separating the layers according to the maximum point of the probability density function select probability density value of generation of electricity by new energy power and variable as sample point; Finally sample point is carried out randomly ordered, set up the sample matrix of generation of electricity by new energy power and variable.

In a preferred version of the inventive method, step 3) idiographic flow for: first using 1) sample matrix of gained generation of electricity by new energy power and variable is as 2) input variable of multi-regional interactive iterative computation model set up carries out cycle calculations, each cycle calculations extracts a certain column vector of generation of electricity by new energy power and variable sample matrix as input variable; Then the sample matrix of output variable is set up according to the result of the output variable of cycle calculations gained; Finally utilize the probability density function of Density Estimator matching output variable.

The present invention compared with prior art, has the following advantages:

The present invention is directed to the tail feature that traditional Latin hypercube is difficult to consider probability distribution, propose improvement Latin hypercube to sample to stochastic variable, the point that in each subinterval, select probability density value is maximum after separating the layers, as sample point, improves the validity of sample and has taken into full account the tail feature of probability distribution; Can the feature of subregion for electrical network, propose and utilize node tearing algorithm to carry out subregion to electrical network, set up the computation model of multi-regional interactive iteration, while realizing parallel computation, decrease the Jacobian matrix dimension of Load flow calculation.

Accompanying drawing explanation

Fig. 1 is the probabilistic load flow flow chart that the present invention is based on multi-regional interactive iteration.

Embodiment

Below in conjunction with Figure of description and embodiment, the present invention is further described.

See accompanying drawing 1, the probability load flow calculation method based on multi-regional interactive iteration of the present invention, comprises the following steps:

1) according to cumulative distribution function and the probability density function of generation of electricity by new energy power and variable, utilize improvement 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 probability density function is f _kx (), 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 $[\frac{s-1}{N},\frac{s}{N}](s=\mathrm{1,2},...,N),$ Then to each subinterval $[\frac{s-1}{N},\frac{s}{N}](s=\mathrm{1,2},...,N)$ Carry out m decile, generate m interval $[\frac{s-1}{N}+\frac{r-1}{N\·m},\frac{s-1}{N}+\frac{r}{N\·m}](r=\mathrm{1,2},...,m),$ And then according to stochastic variable X _kcumulative distribution function F _kthe inverse function of (x) calculate interval $[\frac{s-1}{N}+\frac{r-1}{N\·m},\frac{s-1}{N}+\frac{r}{N\·m}]$ $(r=\mathrm{1,2},...,m)$ The value of the corresponding x in border $x_{k.s.r-1}=F_k^{-1}(\frac{s-1}{N}+\frac{r-1}{N\·m}),x_{k.s.r}=F_k^{-1}(\frac{s-1}{N}+\frac{r}{N\·m}),$ Last according to probability density function f _kx () calculates x _k.s.r-1and x _k.s.rprobability density value f _k(x _k.s.r-1), f _k(x _k.s.r), the maximum x of select probability density value is as 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 node tearing algorithm to carry out subregion to electrical network, set up multi-regional interactive iterative computation model;

Selection portion partial node (B in electrical network ₁, B ₂..., B _u) tear, electrical network is divided into T region.Node B _k(k=1,2 ..., u) being torn is two Node B 1 _kand B2 _k, represent that these tear node respectively with set B 1, B2.

$\left\{\begin{array}{c}B{1}_k\∈B1\\ B{2}_k\∈B2\end{array}\right.,k=\mathrm{1,2},...,u---\left(1\right)$

The power flow algorithm in each region adopts iterative computation model, and this model can be expressed as follows:

$J_w^i\·\mathrm{\Δ}{Y}_w^i=\mathrm{\Δ}{X}_w^i,w=\mathrm{1,2},...,T---\left(2\right)$

Wherein, for the Jacobian matrix of i-th iteration in each region, for the departure of i-th the iteration output variable in each region, for the departure of i-th the iteration input variable in each region.

Each region, after i-th iterative computation completes, obtains set B 1, output variable that B2 is new is respectively OB1 ⁱ, OB2 ⁱ:

$\left\{\begin{array}{c}\mathrm{OB}{1}^i=A_1\left(\mathrm{\Δ}{Y}_1^i\right)+A_2\left(\mathrm{\Δ}{Y}_2^i\right)+...+A_T\left(\mathrm{\Δ}{Y}_T^i\right)\\ \mathrm{OB}{2}^i=B_1\left(\mathrm{\Δ}{Y}_1^i\right)+B_2\left(\mathrm{\Δ}{Y}_2^i\right)+...+B_T\left(\mathrm{\Δ}{Y}_T^i\right)\end{array}\right.---\left(3\right)$

By OB1 ⁱand OB2 ⁱafter data exchange mutually, calculating all subregion with

$\left\{\begin{array}{c}{J}_w^{i+1}=C_w\left(\mathrm{OB}{1}^i\right)+D_w\left(\mathrm{OB}{2}^i\right)\\ \mathrm{\Δ}{X}_w^{i+1}=E_w\left(\mathrm{OB}{1}^i\right)+F_w\left(\mathrm{OB}{2}^i\right)\end{array}\right.w=\mathrm{1,2},...,T---\left(4\right)$

Then carry out the i-th+1 time iteration, calculate according to formula (2) converge to mark with each region trend simultaneously and stop iteration.

3) using 1) sample matrix of gained generation of electricity by new energy power is as 2) input variable of multi-regional interactive iterative computation 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 multi-regional interactive iterative computation model set up carries out Load flow calculation, obtains the result Z of output variable ⁿ:

Z ⁿ＝G ₁((ΔY ₁) ⁽ⁿ⁾)+G ₂((ΔY ₂) ⁽ⁿ⁾)+…+G _T((ΔY _T) ⁽ⁿ⁾) n＝1,2,…,N (5)

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] (6)

Utilize Density Estimator matching output variable probability density function:

$\hat{f}\left(z\right)=\frac{1}{\mathrm{Nh}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}K\left(\frac{z-Z_i}{h}\right)---\left(7\right)$

Wherein, N is the discrete data number of output variable, and h is window width, Z _ifor the discrete data of output variable, K () is kernel function.

Above-described embodiment is only the preferred embodiment of the present invention; be noted that for those skilled in the art; under the premise without departing from the principles of the invention; some improvement and equivalent replacement can also be made; these improve the claims in the present invention and are equal to the technical scheme after replacing, and all fall into protection scope of the present invention.

Claims (3)

1. based on a probability load flow calculation method for multi-regional interactive iteration, it is characterized in that, the method comprises the following steps:

1) according to cumulative distribution function and the probability density function of generation of electricity by new energy power and variable, utilize improvement 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;

2) can the feature of subregion for electrical network, utilize node tearing algorithm to carry out subregion to electrical network, set up multi-regional interactive iterative computation model;

3) using 1) sample matrix of gained generation of electricity by new energy power and variable is as 2) input variable of multi-regional interactive iterative computation model set up carries out probabilistic load flow, 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. the probability load flow calculation method based on multi-regional interactive iteration according to claim 1, is characterized in that, the sample matrix of the generation of electricity by new energy power and variable set up in described step 1) is set up in such a way:

First 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; Then each subinterval after separating the layers according to the maximum point of the probability density function select probability density value of generation of electricity by new energy power and variable as sample point; Finally sample point is sorted, set up the sample matrix of generation of electricity by new energy power and variable.

3. the probability load flow calculation method based on multi-regional interactive iteration according to claim 1 and 2, is characterized in that, the idiographic flow of described step 3) is:

First using 1) sample matrix of gained generation of electricity by new energy power and variable is as 2) input variable of multi-regional interactive iterative computation model set up carries out cycle calculations, each cycle calculations extracts a certain column vector of generation of electricity by new energy power and variable sample matrix as input variable; Then the sample matrix of output variable is set up according to the result of the output variable of cycle calculations gained; Finally utilize the probability density function of Density Estimator matching output variable.