CN105811403A - Probabilistic load flow algorithm based on semi invariant and series expansion method - Google Patents

Abstract

The invention discloses a probabilistic load flow algorithm based on a semi invariant and series expansion method. By the probabilistic load flow algorithm, the uncertainty of a system under access of large-scale new energy sources can be reflected, a Monte Carlo sampling technology is introduced based on the analysis of a traditional semi invariant method to calculate the output of a wind power generator set, complicated mathematical analysis and calculation are prevented, and the probabilistic load flow algorithm can be applicable to a new energy output model with arbitrary random distribution; and relatively high adaptability and favorable convergence can be achieved when photovoltaic or other new energy sources are accessed to the system except wind and power.

Description

Probabilistic loadflow algorithm based on cumulant and Series Expansion Method

Technical field

The present invention relates to power system technology, particularly relate to the probabilistic loadflow algorithm based on cumulant and Series Expansion Method.

Background technology

Along with the continuous expansion of wind-powered electricity generation scale, the impact of electrical network is also highlighted by day by day.The access of large-scale wind power is except influential system stability, bringing power quality problem (such as voltage pulsation, flickering, harmonic pollution etc.), also can change the trend distribution of electrical network, increase the probability of voltage out-of-limit and circuit overload, bring many difficulties to the planning of power system and operation.Therefore, setting up rational farm model, the impact after using Load flow calculation quantitative analysis wind power integration, system run is significant.

Conventional Load Flow is when predetermined power system, and voltage or electric current to regulation place are calculated, and its result of calculation also determines that.The randomness that blower fan is exerted oneself and uncertainty cause conventional Load Flow cannot reflect the characteristics of tidal flow that large-scale wind power accesses comprehensively, and probabilistic loadflow can effectively solve the problems referred to above.

Probabilistic loadflow (PLF) can reflect the impact that in power system, system is run by the change at random of various factors.It can consider the various uncertain conditions such as the fault of the random fluctuation of wind power output, the change of load, the forced outage of electromotor and circuit, obtains the probabilistic statistical characteristics of system node voltage and Branch Power Flow.Compared to conventional Load Flow, it greatly reduces amount of calculation.Result of calculation is done suitable process, the evaluation index of the static system such as circuit overload probability, voltage out-of-limit probability safety can be released, in order to find the weak link in electrical network in time, provide valuable information for Power System Planning and decision-maker.The algorithm of current main flow probabilistic loadflow adopts the thought of analytic method mostly, on fireballing basis, updates and optimize to reduce the error of result of calculation.But still ubiquity mathematical principle is excessively complicated, it is slow to calculate speed and the deficiency such as the dependency that cannot consider between stochastic variable.

Summary of the invention

Goal of the invention: the purpose of the present invention is to propose to and a kind of calculate that speed is fast, mathematical principle is simply based on the probabilistic loadflow algorithm of cumulant and Series Expansion Method.

Technical scheme: for reaching this purpose, the present invention by the following technical solutions:

Probabilistic loadflow algorithm based on cumulant and Series Expansion Method of the present invention, comprises the steps:

S1: build the stochastic model of power system, input system initial data and wind energy turbine set related data, calculate data, power load distributing data, the exerting oneself and the reactive power probability density function of forced outage rate, wind energy turbine set historical wind speed, the probability density function of wind speed, the output of wind-driven generator, the active power probability density function of load and load of conventional generator including conventional Load Flow；

S2: with Newton-Laphson method being determined property Load flow calculation, obtain the expected value of node voltage and Branch Power Flow and sensitivity matrix S₀And T₀；

S3: each rank cumulant of calculated load and conventional power generation usage acc power；

S4: adopt the method based on Monte-Carlo step technology to solve each rank cumulant that Wind turbines is exerted oneself；

S5: by each rank cumulant of node generator powerEach rank cumulant with load powerIt is added, tries to achieve each rank cumulant Δ W of node injecting power^(k)；

S6: the character according to cumulant, each rank cumulant of computing node state variable Δ X and Branch Power Flow Δ Z；

S7: application Gram-Charlier series expansion obtains node state variable Δ X and the probability-distribution function of Branch Power Flow Δ Z；

S8: with reference to voltage constraint and the thermally-stabilised limit of line current of node, calculate the out-of-limit probability of each node voltage and Branch Power Flow, and obtain the static security probability of whole system.

Further, the probability density function of described wind speed adopts Two-parameter Weibull distribution to be calculated, as shown in formula (1):

$f\left(v\right)=\frac{k}{c}\·{\left(\frac{v}{c}\right)}^{k-1}\·\exp \[-{\left(\frac{v}{c}\right)}^k\]---\left(1\right)$

In formula (1), v is wind speed, and k and c is two parameters of Weibull distribution, and wherein k is form parameter, embodies the feature of wind speed profile, and c is scale parameter, the size of reflection area mean wind speed；K and c is as shown in formula (2):

$\left\{\begin{array}{c}k={\left(\frac{\mathrm{\σ}}{\mathrm{\μ}}\right)}^{-1.086}\\ c=\frac{\mathrm{\μ}}{\mathrm{\Γ}(1+\frac{1}{k})}\end{array}\right.---\left(2\right)$

In formula (2), Γ is Gamma function, and μ is mean wind speed, and σ is standard deviation；

The output P of described wind-driven generator_wFor:

$P_w=\left\{\begin{array}{cc}0& v\≤v_{ci}\\ k_{1}v+k_2& v_{ci}\≤v\≤v_r\\ P_r& v_r\≤v\≤v_{co}\\ 0& v_{co}\≤v\end{array}\right.---\left(3\right)$

In formula (3), v_ciFor incision wind speed, v_coFor cut-out wind speed, v_rFor rated wind speed, P_rFor the rated power of wind-driven generator, k₁And k₂As shown in formula (4):

$\left\{\begin{array}{c}{k}_1=\frac{P_r}{v_r-v_{ci}}\\ k_2=-k_1{v}_{ci}\end{array}\right.---\left(4\right)$

Active power probability density function f (P) of described load and reactive power probability density function f (Q) of load are as shown in formula (5):

$\left\{\begin{array}{c}f\left(P\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_p}\exp (-\frac{{(P-{\mathrm{\μ}}_P)}^2}{2{\mathrm{\σ}}_P^2})\\ f\left(Q\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_Q}\exp (-\frac{{(Q-{\mathrm{\μ}}_Q)}^2}{2{\mathrm{\σ}}_Q^2})\end{array}\right.---\left(5\right)$

In formula (5), μ_P、σ_PThe respectively expected value of the active power of load and mean square deviation, μ_Q、σ_QThe respectively expected value of the reactive power of load and mean square deviation, P, Q are respectively as shown in formula (6) and (7):

$P(X=x_i)=\left\{\begin{array}{cc}{P}_P& x_i=C_P\\ 1-P_P& x_i=0\end{array}\right.---\left(6\right)$

$Q(Y=y_i)=\left\{\begin{array}{cc}{P}_Q& y_i=C_Q\\ 1-P_Q& y_i=0\end{array}\right.---\left(7\right)$

In formula (6), P_PFor the active power availability of generating set, C_PActive power rated capacity for generating set；In formula (7), P_QFor the reactive power availability of generating set, C_QReactive power rated capacity for generating set.

Further, described step S2 comprises the following steps by the method for Newton-Laphson method being determined property Load flow calculation:

S2.1: form each bus admittance matrix Y, if the initial value U of each node voltage and phase angle initial value e also has iterations initial value to be 0, calculates the unbalanced power amount of each node；

S2.2: judge whether unbalanced power amount meets the condition of convergence: if it is satisfied, then skip to step S2.4；If be unsatisfactory for, then carry out step S2.3；

S2.3: calculate each element in Jacobian matrix, revises each node voltage, returns step S2.1；

S2.4: terminate.

Further, in described step S3, the computational methods of each rank cumulant of load are:

For the load power of normal distribution, shown in each rank cumulant such as formula (8):

$\left\{\begin{array}{c}{\mathrm{\γ}}_1=\mathrm{\μ}\\ {\mathrm{\γ}}_2={\mathrm{\σ}}^2\\ {\mathrm{\γ}}_3={\mathrm{\γ}}_4={\mathrm{\γ}}_5=...=0\end{array}\right.---\left(8\right)$

In formula (8), γ_iFor i rank cumulant, i=1,2 ..., μ is the expectation of load power, and σ is the mean square deviation of load power；

For the load power of Discrete Distribution, first obtain its each rank moment of the orign by formula (9):

$\begin{array}{cc}{\mathrm{\α}}_{Lm}=\underset{i}{\Σ}{p}_i{x}_i^m& (m=1,2,\mathrm{...})\end{array}---\left(9\right)$

In formula (9), α_LmM rank moment of the orign for load variation；p_iFor load values x_iProbability,Wherein t_iFor load equal to x_iPersistent period, T is research cycle；

Then each rank cumulant of each node load power is tried to achieve by the relation of cumulant and moment of the orign.

Further, in described step S3, the computational methods of each rank cumulant of conventional power generation usage acc power are:

First, obtain a node place equipped with each rank moment of the orign of the total output of N platform conventional generator:

α_m=P₁C^m+P₂(2C)^m+...+P_i(iC)^m+...+P_N(NC)^m(m=1,2 ...) (10)

In formula (10), α_mFor each rank moment of the orign of the total output of N platform conventional generator, C is the rated capacity of conventional generator, P_i(i=1,2 ..., N) as shown in formula (11):

$P_i=C_N^i{P}^i{(1-P)}^{N-i}---\left(11\right)$

In formula (11), P_iFor there being the properly functioning probability of i platform conventional generator in N platform conventional generator, P is the probability that conventional generator is operated in rated capacity C；

Then, the relation utilizing cumulant and moment of the orign tries to achieve each rank cumulant of conventional power generation usage acc power.

Further, in described step S4, the computational methods of each rank cumulant that Wind turbines is exerted oneself comprise the following steps:

S4.1: adopt Monte-Carlo step technology to extract N number of wind series { v from the function of wind speed obeying Two-parameter Weibull distribution₁,v₂,…,v_N}；

S4.2: obtain active power sequence { P according to the characteristics of output power of Wind turbines₁,P₂,…,P_N}；

S4.3: under constant power factor control mode, the reactive power of Wind turbines is directly proportional to active power, thus obtaining reactive power sequence { Q₁,Q₂,…,Q_N}；

S4.4: calculate each rank moment of the orign that Wind turbines is exerted oneself, as shown in formula (12):

$\left\{\begin{array}{c}{\mathrm{\α}}_{Pm}=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{P}_i^m\\ {\mathrm{\α}}_{Qm}=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{Q}_i^m\end{array}\right.---\left(12\right)$

In formula (12), α_PmAnd α_QmActive power that respectively Wind turbines is exerted oneself and the m rank moment of the orign of reactive power；

S4.5: utilize the relation of cumulant and moment of the orign to try to achieve each rank cumulant that Wind turbines is exerted oneself.

Further, in described step S5, each rank cumulant Δ W of node injecting power^(k)Employing formula (13) is calculated:

${\mathrm{\ΔW}}^{\left(k\right)}={\mathrm{\ΔW}}_g^{\left(k\right)}+{\mathrm{\ΔW}}_l^{\left(k\right)}---\left(13\right)$

In formula (13),For each rank cumulant of node generator power, Δ W^(k)Each rank cumulant for load power.

Further, in described step S6, each rank cumulant of node state variable Δ X and Branch Power Flow Δ Z adopts formula (14) to be calculated:

$\left\{\begin{array}{c}{\mathrm{\ΔX}}^{\left(k\right)}=S_0^{\left(k\right)}\·{\mathrm{\ΔW}}^{\left(k\right)}\\ {\mathrm{\ΔZ}}^{\left(k\right)}=T_0^{\left(k\right)}\·{\mathrm{\ΔW}}^{\left(k\right)}\end{array}\right.---\left(14\right)$

In formula (14), Δ X^(k)For each rank cumulant of node state variable Δ X, Δ Z^(k)For each rank cumulant of Branch Power Flow Δ Z, Δ W^(k)For each rank cumulant of load power,WithRespectively matrix S₀And T₀The matrix that the k power of middle element is constituted, for arbitrary element (i, j), has:

$\left\{\begin{array}{c}{S}_0^{\left(k\right)}(i,j)={\[S_0(i,j)\]}^k\\ T_0^{\left(k\right)}(i,j)={\[T_0(i,j)\]}^k\end{array}\right.---\left(15\right).$

Further, in described step S7, shown in the probability-distribution function computational methods such as formula (16) of node state variable Δ X and Branch Power Flow Δ Z of Gram-Charlier progression, (17):

In formula (16), (17), F (x) is the cumulative distribution function of standardized node state variable or Branch Power Flow, and f (x) is the probability density function of standardized node state variable or Branch Power Flow,For the standardized random variable of stochastic variable node state variable Δ X or Branch Power Flow Δ Z,For standard normal distribution density function, H_iFor Hermite multinomial, g_iFor the polynomial coefficient of Hermite.

Further, in described step S8, the static security method for calculating probability of whole system is: after obtaining the probability-distribution function of node state variable Δ X and Branch Power Flow Δ Z, voltage with reference to node retrains the thermally-stabilised limit with line current, calculate the out-of-limit probability of each node voltage and Branch Power Flow, be designated as p₁,p₂,…,p_n；Then the static security probability of whole system is:

$p_s=\underset{i=1}{\overset{n}{\Π}}(1-p_i)---\left(18\right).$

Beneficial effect: compared with prior art, the beneficial effects of the present invention is:

The present invention can reflect that extensive new forms of energy access the uncertainty of lower system, the basis of tradition Cumulants method analysis introduces Monte-Carlo step technology calculate Wind turbines and exert oneself, avoid mathematical analysis and the calculating of complexity, can adapt to have the new forms of energy of any random distribution exert oneself model, when system also having except wind-powered electricity generation photovoltaic or other new forms of energy have, when accessing, well adapting to property, and there is good convergence.

Accompanying drawing explanation

Fig. 1 is the algorithm steps block diagram of the present invention；

Fig. 2 is IEEE-30 node system；

Fig. 3 is the CDF curve of the voltage magnitude of PLF-CM and MCS gained node 10；

Fig. 4 is the CDF curve of the voltage magnitude of PLF-CM and MCS gained node 24；

Fig. 5 is the CDF curve of the active power of PLF-CM and MCS gained branch road 19-20；

Fig. 6 is the CDF curve of the active power of PLF-CM and MCS gained branch road 27-30.

Detailed description of the invention

Below in conjunction with detailed description of the invention and accompanying drawing, the present invention is further described.

The invention discloses a kind of probabilistic loadflow algorithm based on cumulant and Series Expansion Method, as it is shown in figure 1, comprise the steps:

S1: build the stochastic model of power system, input system initial data and wind energy turbine set related data, calculate data, power load distributing data, the exerting oneself and the reactive power probability density function of forced outage rate, wind energy turbine set historical wind speed, fan characteristic, the probability density function of wind speed, the output of wind-driven generator, the active power probability density function of load and load of conventional generator including conventional Load Flow；

S2: with Newton-Laphson method being determined property Load flow calculation, obtain the expected value of node voltage and Branch Power Flow and sensitivity matrix S₀And T₀；

S3: each rank cumulant of calculated load and conventional power generation usage acc power；

S4: adopt the method based on Monte-Carlo step technology to solve each rank cumulant that Wind turbines is exerted oneself；

S5: by each rank cumulant of node generator powerEach rank cumulant with load powerIt is added, tries to achieve each rank cumulant Δ W of node injecting power^(k)；

S6: the character according to cumulant, each rank cumulant of computing node state variable Δ X and Branch Power Flow Δ Z；

S7: application Gram-Charlier series expansion obtains node state variable Δ X and the probability-distribution function of Branch Power Flow Δ Z；

S8: with reference to voltage constraint and the thermally-stabilised limit of line current of node, calculate the out-of-limit probability of each node voltage and Branch Power Flow, and obtain the static security probability of whole system.

Below for IEEE-30 node system, the Probabilistic Load Flow calculation procedure containing wind energy turbine set is worked out by MatlabR2010b, analyze the impact on system load flow of the random factor such as wind power integration, load fluctuation, give the static system index of security assessments such as each out-of-limit probability of node voltage.

IEEE-30 node system as in figure 2 it is shown, system has 6 electromotors, 30 nodes, 41 branch roads.Concrete node and line parameter circuit value are shown in annex.For convenience of calculation, it is assumed that separate between each stochastic variable, the obedience 0-1 distribution of exerting oneself of electromotor, the equal Normal Distribution of load, with IEEE-30 node system load value for average, standard deviation is the 20% of average.The wind energy turbine set capacity adopted in example is 5 × 2MW, and in wind energy turbine set, blower fan is divided into two rows, and trestle column is 120m, and unit runs with constant power factor control mode, and power factor is 0.75.In false wind electric field, atmospheric density is 1.2245kg/m³, the swept area of blower fan is 1840m2, two parameters of the Weibull distribution of wind speed.

Optional node 10, node 24, branch road 19-20 and branch road 27-30 are object of study, adopt the probabilistic loadflow algorithm based on cumulant and Series Expansion Method to carry out probabilistic loadflow calculating.

This algorithm, it is crucial that solve each rank cumulant value of each state variable, the content according to step S3, first can obtain the voltage magnitude of taken node before wind energy turbine set accesses and each rank cumulant of branch road active power, as shown in table 1.

Table 1 wind energy turbine set accesses each rank cumulant of forward part node voltage amplitude and branch road active power

According to step S4 after node 25 accesses wind energy turbine set, by the Monte-Carlo step technology (frequency in sampling) that the present invention proposes, calculate the first seven rank cumulant of output of wind electric field, as shown in table 2

Each rank cumulant of table 2 Power Output for Wind Power Field (meritorious and idle)

Each rank cumulant of the output of wind electric field tried to achieve is added with each rank cumulant of each node original loads, namely each rank cumulant of each node injecting power is obtained, each rank cumulant value of each state variable after wind energy turbine set accesses can be obtained, as shown in table 3 according to step S5

Table 3 wind energy turbine set accesses each rank cumulant of rear section node voltage amplitude and branch road active power

Finally, take the first seven rank cumulant value the method in conjunction with Gram-Charlier series expansion according to step S6, S7, obtain probability density function and the cumulative distribution function of respective nodes voltage and Branch Power Flow, as shown in figures 3 to 6.

In order to embody the accuracy of acquired results of the present invention, its error is carried out quantitative analysis, here we introduce the root average (AverageRootMeanSquare, ARMS) of variance sum and weigh the error between the present invention and traditional algorithm (MCS).Table 4 gives the ARMS value of respective nodes voltage magnitude and branch road active power.

The ARMS of table 4 part of nodes voltage magnitude and branch road active power

It can be seen that the ARMS value of the corresponding state amount of selected node and branch road is only small, it is respectively less than 1%, illustrates that the algorithm of the present invention is basically identical with the result of calculation of MCS, there is higher precision.Wherein, the ARMS value of node 10 voltage magnitude is much smaller than the value of node 24 correspondence, and this is owing to node 10 compares node 24 apart from wind energy turbine set access point farther out, and the impact by output of wind electric field fluctuation is less, and calculating error also can be relatively reduced.

By cumulative distribution function (CDF) curve, it is possible to obtain the out-of-limit probability that node voltage and branch road are meritorious easily, as shown in table 5, table sets forth MCS and inventive algorithm acquired results.

The out-of-limit probability of table 5 part of nodes voltage magnitude and branch road active power

The method of applying step S8, adds up voltage out-of-limit and the out-of-limit probability of power of all nodes and circuit in IEEE-30 node system, it is possible to obtain the static security probability of whole system, as shown in table 6:

Table 6 static system safe probability index

Finally, table 7 compares the calculating time of two kinds of probabilistic loadflow algorithms,

The calculating time of 7 two kinds of probabilistic loadflow algorithms of table compares

There it can be seen that compared with tradition immediately power flow algorithm MCS, inventive algorithm has significant advantage on the calculating time, and consuming time unrelated with sample size, relatively big at system scale, when needing online power flow to calculate, have broad application prospects.

The above is only the preferred embodiment of the present invention; it should be pointed out that, for those skilled in the art, under the premise without departing from the technology of the present invention principle; can also making some improvement and deformation, these improve and deformation also should be regarded as protection scope of the present invention.

Claims (10)

1. based on the probabilistic loadflow algorithm of cumulant and Series Expansion Method, it is characterised in that: comprise the steps:

S1: build the stochastic model of power system, input system initial data and wind energy turbine set related data, calculate data, power load distributing data, the exerting oneself and the reactive power probability density function of forced outage rate, wind energy turbine set historical wind speed, the probability density function of wind speed, the output of wind-driven generator, the active power probability density function of load and load of conventional generator including conventional Load Flow；

S2: with Newton-Laphson method being determined property Load flow calculation, obtain the expected value of node voltage and Branch Power Flow and sensitivity matrix S₀And T₀；

S3: each rank cumulant of calculated load and conventional power generation usage acc power；

S4: adopt the method based on Monte-Carlo step technology to solve each rank cumulant that Wind turbines is exerted oneself；

S5: by each rank cumulant of node generator powerEach rank cumulant with load powerIt is added, tries to achieve each rank cumulant Δ W of node injecting power^(k)；

S6: the character according to cumulant, each rank cumulant of computing node state variable Δ X and Branch Power Flow Δ Z；

S7: application Gram-Charlier series expansion obtains node state variable Δ X and the probability-distribution function of Branch Power Flow Δ Z；

S8: with reference to voltage constraint and the thermally-stabilised limit of line current of node, calculate the out-of-limit probability of each node voltage and Branch Power Flow, and obtain the static security probability of whole system.

2. the probabilistic loadflow algorithm based on cumulant and Series Expansion Method according to claim 1, it is characterised in that: the probability density function of described wind speed adopts Two-parameter Weibull distribution to be calculated, as shown in formula (1):

$f\left(v\right)=\frac{k}{c}\·{\left(\frac{v}{c}\right)}^{k-1}\·\exp \[-{\left(\frac{v}{c}\right)}^k\]---\left(1\right)$

In formula (1), v is wind speed, and k and c is two parameters of Weibull distribution, and wherein k is form parameter, embodies the feature of wind speed profile, and c is scale parameter, the size of reflection area mean wind speed；K and c is as shown in formula (2):

$\left\{\begin{array}{c}k={\left(\frac{\mathrm{\σ}}{\mathrm{\μ}}\right)}^{-1.086}\\ c=\frac{\mathrm{\μ}}{\mathrm{\Γ}(1+\frac{1}{k})}\end{array}\right.---\left(2\right)$

In formula (2), Γ is Gamma function, and μ is mean wind speed, and σ is standard deviation；

The output P of described wind-driven generator_wFor:

$P_w=\left\{\begin{array}{cc}0& v\≤v_{ci}\\ k_{1}v+k_2& v_{ci}\≤v\≤v_r\\ P_r& v_r\≤v\≤v_{co}\\ 0& v_{co}\≤v\end{array}\right.---\left(3\right)$

In formula (3), v_ciFor incision wind speed, v_coFor cut-out wind speed, v_rFor rated wind speed, P_rFor the rated power of wind-driven generator, k₁And k₂As shown in formula (4):

$\left\{\begin{array}{c}{k}_1=\frac{P_r}{v_r-v_{ci}}\\ k_2=-k_1{v}_{ci}\end{array}\right.---\left(4\right)$

Active power probability density function f (P) of described load and reactive power probability density function f (Q) of load are as shown in formula (5):

$\left\{\begin{array}{c}f\left(P\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_P}\exp (-\frac{{(P-{\mathrm{\μ}}_P)}^2}{2{\mathrm{\σ}}_P^2})\\ f\left(Q\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_Q}\exp (-\frac{{(Q-{\mathrm{\μ}}_Q)}^2}{2{\mathrm{\σ}}_Q^2})\end{array}\right.---\left(5\right)$

In formula (5), μ_P、σ_PThe respectively expected value of the active power of load and mean square deviation, μ_Q、σ_QThe respectively expected value of the reactive power of load and mean square deviation, P, Q are respectively as shown in formula (6) and (7):

$P(X=x_i)=\left\{\begin{array}{cc}{P}_P& x_i=C_P\\ 1-P_P& x_i=0\end{array}\right.---\left(6\right)$

$Q(Y=y_i)=\left\{\begin{array}{cc}{P}_Q& y_i=C_Q\\ 1-P_Q& y_i=0\end{array}\right.---\left(7\right)$

In formula (6), P_PFor the active power availability of generating set, C_PActive power rated capacity for generating set；In formula (7), P_QFor the reactive power availability of generating set, C_QReactive power rated capacity for generating set.

3. the probabilistic loadflow algorithm based on cumulant and Series Expansion Method according to claim 1, it is characterised in that: described step S2 comprises the following steps by the method for Newton-Laphson method being determined property Load flow calculation:

S2.1: form each bus admittance matrix Y, if the initial value U of each node voltage and phase angle initial value e also has iterations initial value to be 0, calculates the unbalanced power amount of each node, and obtains Jacobian matrix；

S2.2: judge whether unbalanced power amount meets the condition of convergence: if it is satisfied, then skip to step S2.4；If be unsatisfactory for, then carry out step S2.3；

S2.3: calculate each element in Jacobian matrix, revises each node voltage, returns step S2.1；

S2.4: terminate.

4. the probabilistic loadflow algorithm based on cumulant and Series Expansion Method according to claim 1, it is characterised in that: in described step S3, the computational methods of each rank cumulant of load are:

For the load power of normal distribution, shown in each rank cumulant such as formula (8):

$\left\{\begin{array}{c}{\mathrm{\γ}}_1=\mathrm{\μ}\\ {\mathrm{\γ}}_2={\mathrm{\σ}}^2\\ {\mathrm{\γ}}_3={\mathrm{\γ}}_4={\mathrm{\γ}}_5=...=0\end{array}\right.---\left(8\right)$

In formula (8), γ_iFor i rank cumulant, i=1,2 ..., μ is the expectation of load power, and σ is the mean square deviation of load power；

For the load power of Discrete Distribution, first obtain its each rank moment of the orign by formula (9):

${\mathrm{\α}}_{Lm}=\underset{i}{\Σ}{p}_i{x}_i^m,(m=1,2,...)---\left(9\right)$

In formula (9), α_LmM rank moment of the orign for load variation；p_iFor load values x_iProbability,Wherein t_iFor load equal to x_iPersistent period, T is research cycle；

Then each rank cumulant of each node load power is tried to achieve by the relation of cumulant and moment of the orign.

5. the probabilistic loadflow algorithm based on cumulant and Series Expansion Method according to claim 1, it is characterised in that: in described step S3, the computational methods of each rank cumulant of conventional power generation usage acc power are:

First, obtain a node place equipped with each rank moment of the orign of the total output of N platform conventional generator:

α_m=P₁C^m+P₂(2C)^m+...+P_i(iC)^m+...+P_N(NC)^m(m=1,2 ...) (10)

In formula (10), α_mFor each rank moment of the orign of the total output of N platform conventional generator, C is the rated capacity of conventional generator, P_i(i=1,2 ..., N) as shown in formula (11):

$P_i=C_N^i{P}^i{(1-P)}^{N-i}---\left(11\right)$

In formula (11), P_iFor there being the properly functioning probability of i platform conventional generator in N platform conventional generator, P is the probability that conventional generator is operated in rated capacity C；

Then, the relation utilizing cumulant and moment of the orign tries to achieve each rank cumulant of conventional power generation usage acc power.

6. the probabilistic loadflow algorithm based on cumulant and Series Expansion Method according to claim 1, it is characterised in that: in described step S4, the computational methods of each rank cumulant that Wind turbines is exerted oneself comprise the following steps:

S4.1: adopt Monte-Carlo step technology to extract N number of wind series { v from the function of wind speed obeying Two-parameter Weibull distribution₁,v₂,…,v_N}；

S4.2: obtain active power sequence { P according to the characteristics of output power of Wind turbines₁,P₂,…,P_N}；

S4.3: under constant power factor control mode, the reactive power of Wind turbines is directly proportional to active power, thus obtaining reactive power sequence { Q₁,Q₂,…,Q_N}；

S4.4: calculate each rank moment of the orign that Wind turbines is exerted oneself, as shown in formula (12):

$\left\{\begin{array}{c}{\mathrm{\α}}_{Pm}=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{P}_i^m\\ {\mathrm{\α}}_{Qm}=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{Q}_i^m\end{array}\right.---\left(12\right)$

In formula (12), α_PmAnd α_QmActive power that respectively Wind turbines is exerted oneself and the m rank moment of the orign of reactive power；

S4.5: utilize the relation of cumulant and moment of the orign to try to achieve each rank cumulant that Wind turbines is exerted oneself.

7. the probabilistic loadflow algorithm based on cumulant and Series Expansion Method according to claim 1, it is characterised in that: in described step S5, each rank cumulant Δ W of node injecting power^(k)Employing formula (13) is calculated:

${\mathrm{\ΔW}}^{\left(k\right)}={\mathrm{\ΔW}}_g^{\left(k\right)}+{\mathrm{\ΔW}}_l^{\left(k\right)}---\left(13\right)$

In formula (13),For each rank cumulant of node generator power, Δ W^(k)Each rank cumulant for load power.

8. the probabilistic loadflow algorithm based on cumulant and Series Expansion Method according to claim 1, it is characterised in that: in described step S6, each rank cumulant of node state variable Δ X and Branch Power Flow Δ Z adopts formula (14) to be calculated:

$\left\{\begin{array}{c}{\mathrm{\ΔX}}^{\left(k\right)}=S_0^{\left(k\right)}\·{\mathrm{\ΔW}}^{\left(k\right)}\\ {\mathrm{\ΔZ}}^{\left(k\right)}=T_0^{\left(k\right)}\·{\mathrm{\ΔW}}^{\left(k\right)}\end{array}\right.---\left(14\right)$

In formula (14), Δ X^(k)For each rank cumulant of node state variable Δ X, Δ Z^(k)For each rank cumulant of Branch Power Flow Δ Z, Δ W^(k)For each rank cumulant of load power,WithRespectively matrix S₀And T₀The matrix that the k power of middle element is constituted, for arbitrary element (i, j), has:

$\left\{\begin{array}{c}{S}_0^{\left(k\right)}(i,j)={\[S_0(i,j)\]}^k\\ T_0^{\left(k\right)}(i,j)={\[T_0(i,j)\]}^k\end{array}\right.---\left(15\right).$

9. the probabilistic loadflow algorithm based on cumulant and Series Expansion Method according to claim 1, it is characterized in that: in described step S7, shown in the probability-distribution function computational methods such as formula (16) of node state variable Δ X and Branch Power Flow Δ Z of Gram-Charlier progression, (17):

In formula (16), (17), F (x) is the cumulative distribution function of standardized node state variable or Branch Power Flow, and f (x) is the probability density function of standardized node state variable or Branch Power Flow,For the standardized random variable of stochastic variable node state variable Δ X or Branch Power Flow Δ Z,For standard normal distribution density function, H_iFor Hermite multinomial, g_iFor the polynomial coefficient of Hermite.

10. the probabilistic loadflow algorithm based on cumulant and Series Expansion Method according to claim 1, it is characterized in that: in described step S8, the static security method for calculating probability of whole system is: after obtaining the probability-distribution function of node state variable Δ X and Branch Power Flow Δ Z, voltage with reference to node retrains the thermally-stabilised limit with line current, calculate the out-of-limit probability of each node voltage and Branch Power Flow, be designated as p₁,p₂,…,p_n；Then the static security probability of whole system is:

$p_s=\underset{i=1}{\overset{n}{\Π}}(1-p_i)---\left(18\right).$