CN105811403B - Probabilistic loadflow algorithm based on cumulant and Series Expansion Method - Google Patents
Probabilistic loadflow algorithm based on cumulant and Series Expansion Method Download PDFInfo
- Publication number
- CN105811403B CN105811403B CN201610165113.6A CN201610165113A CN105811403B CN 105811403 B CN105811403 B CN 105811403B CN 201610165113 A CN201610165113 A CN 201610165113A CN 105811403 B CN105811403 B CN 105811403B
- Authority
- CN
- China
- Prior art keywords
- mrow
- msub
- mtd
- mtr
- power
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 35
- 238000009826 distribution Methods 0.000 claims abstract description 19
- 238000005516 engineering process Methods 0.000 claims abstract description 10
- 238000004364 calculation method Methods 0.000 claims description 15
- 239000011159 matrix material Substances 0.000 claims description 12
- 230000003068 static effect Effects 0.000 claims description 11
- 238000000205 computational method Methods 0.000 claims description 8
- 238000005315 distribution function Methods 0.000 claims description 8
- 238000010248 power generation Methods 0.000 claims description 8
- 230000001186 cumulative effect Effects 0.000 claims description 4
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 2
- 239000013256 coordination polymer Substances 0.000 claims description 2
- 238000004458 analytical method Methods 0.000 abstract description 5
- 230000005611 electricity Effects 0.000 abstract description 4
- 230000005684 electric field Effects 0.000 description 3
- 239000004744 fabric Substances 0.000 description 3
- 230000010354 integration Effects 0.000 description 3
- 238000004445 quantitative analysis Methods 0.000 description 2
- 230000035945 sensitivity Effects 0.000 description 2
- 235000006508 Nelumbo nucifera Nutrition 0.000 description 1
- 240000002853 Nelumbo nucifera Species 0.000 description 1
- 235000006510 Nelumbo pentapetala Nutrition 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
Classifications
-
- 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
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected 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]
Abstract
The invention discloses a kind of probabilistic loadflow algorithms based on cumulant and Series Expansion Method.The present invention can reflect the uncertainty of the lower system of extensive new energy access, Monte-Carlo step technology is introduced on the basis of the analysis of traditional Cumulants method to contribute to calculate Wind turbines, avoid complicated mathematical analysis and calculating, it can adapt to the new energy output model with arbitrary random distribution, there is well adapting to property in the case of also having photovoltaic or the access of other new energy in system in addition to wind-powered electricity generation, and with good convergence.
Description
Technical field
The present invention relates to power system technologies, are calculated more particularly to the probabilistic loadflow based on cumulant and Series Expansion Method
Method.
Background technology
With the continuous expansion of wind-powered electricity generation scale, the influence to power grid is also increasingly prominent.The access of large-scale wind power except
It can influence system stability, bring power quality problem (such as voltage fluctuation, flickering, harmonic pollution) outside, can also change power grid
Trend distribution, increase the probability of voltage out-of-limit and circuit overload, many difficulties brought to the planning and operation of electric system.Cause
This, establishes rational farm model, has weight with the influence to system operation after Load flow calculation quantitative analysis wind power integration
Want meaning.
Conventional Load Flow is under the conditions of predetermined electric system, and the voltage or electric current of required location are calculated,
What its result of calculation was also to determine.The randomness and uncertainty that wind turbine is contributed cause conventional Load Flow that can not reflect comprehensively on a large scale
The characteristics of tidal flow of wind power integration, and probabilistic loadflow can effectively solve the above problems.
Probabilistic loadflow (PLF) can reflect influence of the random variation of various factors in electric system to system operation.It can
It is various not to consider the failure of the forced outage of the variation of the random fluctuation of wind power output, load, generator and circuit etc.
Certain situation obtains the probabilistic statistical characteristics of system node voltage and Branch Power Flow.Compared to conventional Load Flow, it is greatly reduced
Calculation amount.Proper treatment is done to result of calculation, the static systems such as circuit overload probability, voltage out-of-limit probability safety can be released
To find the weak link in power grid in time, valuable letter is provided for Power System Planning and decision-maker for evaluation index
Breath.The algorithm of mainstream probabilistic loadflow uses the thought of analytic method mostly at present, on the basis of fireballing, continuously improve and optimizes
To reduce the error of result of calculation.But still generally existing mathematical principle is excessively complicated, calculating speed is slow and can not consider random
The deficiencies of correlation between variable.
The content of the invention
Goal of the invention：The purpose of the present invention is to propose to a kind of calculating speed is fast, mathematical principle is simply based on cumulant
With the probabilistic loadflow algorithm of Series Expansion Method.
Technical solution：To reach this purpose, the present invention uses following technical scheme：
Probabilistic loadflow algorithm of the present invention based on cumulant and Series Expansion Method, includes the following steps：
S1：The stochastic model of electric system, input system initial data and wind power plant related data are built, including conventional tide
Stream calculation data, power load distributing data, the output of conventional generator and forced outage rate, wind power plant historical wind speed, wind speed it is general
Rate density function, the output power of wind-driven generator, the reactive power of the active power probability density function of load and load are general
Rate density function；
S2：With Newton-Laphson method being determined property Load flow calculation, the desired value of node voltage and Branch Power Flow is obtained, with
And sensitivity matrix S0And T0；
S3：Each rank cumulant of calculated load and conventional power generation usage acc power；
S4：Each rank cumulant of Wind turbines output is solved using the method based on Monte-Carlo step technology；
S5：By each rank cumulant of node generator powerWith each rank cumulant of load powerPhase
Add, acquire each rank cumulant Δ W of node injecting power(k)；
S6：According to the property of cumulant, each rank cumulant of calculate node state variable Δ X and Branch Power Flow Δ Z；
S7：The probability point of node state variable Δ X and Branch Power Flow Δ Z is obtained using Gram-Charlier series expansions
Cloth function；
S8：With reference to the voltage constraint of node and the thermostabilization limit of line current, each node voltage and Branch Power Flow are calculated
Out-of-limit probability, and obtain the static security probability of whole system.
Further, the probability density function of the wind speed is calculated using Two-parameter Weibull distribution, such as formula (1) institute
Show：
In formula (1), v is wind speed, and k and c are two parameters of Weibull distributions, and wherein k is form parameter, embodies wind speed
The characteristics of distribution, c are scale parameter, reflect the size of regional mean wind speed；Shown in k and c such as formulas (2)：
In formula (2), Γ is Gamma functions, and μ is mean wind speed, and σ is standard deviation；
The output power P of the wind-driven generatorwFor：
In formula (3), vciTo cut wind speed, vcoFor cut-out wind speed, vrFor rated wind speed, PrFor the specified work(of wind-driven generator
Rate, k1And k2As shown in formula (4)：
The active power probability density function f (P) of the load and the reactive power probability density function f (Q) of load are such as
Shown in formula (5)：
In formula (5), μP、σPThe respectively desired value and mean square deviation of the active power of load, μQ、σQThe respectively nothing of load
The desired value and mean square deviation of work(power, P, Q are respectively as shown in formula (6) and (7)：
In formula (6), PPFor the active power availability of generating set, CPFor the active power rated capacity of generating set；Formula
(7) in, PQFor the reactive power availability of generating set, CQFor the reactive power rated capacity of generating set.
Further, following step is included with the method for Newton-Laphson method being determined property Load flow calculation in the step S2
Suddenly：
S2.1：Each bus admittance matrix Y is formed, if the initial value U of each node voltage and phase angle initial value e also have iteration time
Number initial value is 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 no
Meet, then carry out step S2.3；
S2.3：The each element in Jacobian matrix is calculated, corrects each node voltage, return to step S2.1；
S2.4：Terminate.
Further, in the 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)：
In formula (8), γiFor i rank cumulant, i=1,2 ..., μ are the expectation of load power, and σ is the equal of load power
Variance；
For the load power of discrete distribution, its each rank moment of the orign first is obtained by formula (9)：
In formula (9), αLmFor the m rank moment of the origns of load variation；piFor load values xiProbability,Wherein tiIt is negative
Lotus is equal to xiDuration, T is research cycle；
Then each rank cumulant of each node load power is acquired by the relation of cumulant and moment of the orign.
Further, in the step S3, the computational methods of each rank cumulant of conventional power generation usage acc power are：
First, each rank moment of the orign of the total output power of the N platform conventional generators being equipped at a node is obtained：
αm=P1Cm+P2(2C)m+...+Pi(iC)m+...+PN(NC)m(m=1,2 ...) (10)
In formula (10), αmFor each rank moment of the orign of the total output power of N platform conventional generators, C is the volume of conventional generator
Constant volume, Pi(i=1,2 ..., N) is as shown in formula (11)：
In formula (11), PiTo there is the probability of i platform conventional generator normal operations in N platform conventional generators, P is conventional power generation usage
Machine is operated in the probability of rated capacity C；
Then, each rank cumulant of conventional power generation usage acc power is acquired using the relation of cumulant and moment of the orign.
Further, in the step S4, the computational methods for each rank cumulant that Wind turbines are contributed comprise the following steps：
S4.1：N number of wind is extracted from the function of wind speed for obeying Two-parameter Weibull distribution using Monte-Carlo step technology
Fast sequence { v1,v2,…,vN}；
S4.2：Active power sequence { P is obtained according to the characteristics of output power of Wind turbines1,P2,…,PN}；
S4.3：Under constant power factor control mode, the reactive power of Wind turbines is directly proportional to active power, so as to
To reactive power sequence { Q1,Q2,…,QN}；
S4.4：Each rank moment of the orign that Wind turbines are contributed is calculated, as shown in formula (12)：
In formula (12), αPmAnd αQmThe active power and the m rank moment of the origns of reactive power that respectively Wind turbines are contributed；
S4.5：Each rank cumulant of Wind turbines output is acquired using the relation of cumulant and moment of the orign.
Further, in the step S5, each rank cumulant Δ W of node injecting power(k)It is counted using formula (13)
It calculates：
In formula (13),For each rank cumulant of node generator power, Δ W(k)For each rank half of load power
Invariant.
Further, in the step S6, each rank cumulant of node state variable Δ X and Branch Power Flow Δ Z use formula
(14) calculated：
In formula (14), Δ X(k)For each rank cumulant of node state variable Δ X, Δ Z(k)For each of Branch Power Flow Δ Z
Rank cumulant, Δ W(k)For each rank cumulant of load power,WithRespectively matrix S0And T0K times of middle element
The matrix that power is formed for arbitrary element (i, j), has：
Further, in the step S7, node state variable Δ X and Branch Power Flow based on Gram-Charlier series
The probability-distribution function computational methods such as formula (16) of Δ Z, (17) are shown：
In formula (16), (17), F (x) be standardization node state variable or Branch Power Flow cumulative distribution function, f (x)
For the node state variable of standardization or the probability density function of Branch Power Flow,For stochastic variable node state variable Δ X or branch
The standardized random variable of road trend Δ Z,For standardized normal distribution density function, HiFor Hermite multinomials, giFor
The polynomial coefficients of Hermite.
Further, in the step S8, the static security method for calculating probability of whole system is：Obtain node state variable
After the probability-distribution function of Δ X and Branch Power Flow Δ Z, with reference to the voltage constraint of node and the thermostabilization limit of line current, meter
The out-of-limit probability of each node voltage and Branch Power Flow is calculated, is denoted as p1,p2,…,pn；Then the static security probability of whole system is：
Advantageous effect：Compared with prior art, the beneficial effects of the present invention are：
The present invention can reflect the uncertainty of the lower system of extensive new energy access, in the base of traditional Cumulants method analysis
Monte-Carlo step technology is introduced on plinth to contribute to calculate Wind turbines, avoids complicated mathematical analysis and calculating, Neng Goushi
There should be the new energy output model of arbitrary random distribution, when also having what photovoltaic or other new energy accessed in system except wind-powered electricity generation in addition to
In the case of there is well adapting to property, and with good convergence.
Description of the drawings
Fig. 1 is the algorithm steps block diagram of the present invention；
Fig. 2 is IEEE-30 node systems；
Fig. 3 is the CDF curves of the voltage magnitude of node 10 obtained by PLF-CM and MCS；
Fig. 4 is the CDF curves of the voltage magnitude of node 24 obtained by PLF-CM and MCS；
Fig. 5 is the CDF curves of the active power of branch 19-20 obtained by PLF-CM and MCS；
Fig. 6 is the CDF curves of the active power of branch 27-30 obtained by PLF-CM and MCS.
Specific embodiment
The present invention is further described with attached drawing With reference to embodiment.
The invention discloses a kind of probabilistic loadflow algorithm based on cumulant and Series Expansion Method, as shown in Figure 1, including
Following steps：
S1：The stochastic model of electric system, input system initial data and wind power plant related data are built, including conventional tide
Stream calculation data, power load distributing data, the output of conventional generator and forced outage rate, wind power plant historical wind speed, fan characteristic,
The probability density function of wind speed, the output power of wind-driven generator, the active power probability density function of load and the nothing of load
Work(power probability density function；
S2：With Newton-Laphson method being determined property Load flow calculation, the desired value of node voltage and Branch Power Flow is obtained, with
And sensitivity matrix S0And T0；
S3：Each rank cumulant of calculated load and conventional power generation usage acc power；
S4：Each rank cumulant of Wind turbines output is solved using the method based on Monte-Carlo step technology；
S5：By each rank cumulant of node generator powerWith each rank cumulant of load powerPhase
Add, acquire each rank cumulant Δ W of node injecting power(k)；
S6：According to the property of cumulant, each rank cumulant of calculate node state variable Δ X and Branch Power Flow Δ Z；
S7：The probability point of node state variable Δ X and Branch Power Flow Δ Z is obtained using Gram-Charlier series expansions
Cloth function；
S8：With reference to the voltage constraint of node and the thermostabilization limit of line current, each node voltage and Branch Power Flow are calculated
Out-of-limit probability, and obtain the static security probability of whole system.
Below by taking IEEE-30 node systems as an example, it is random that the electric system containing wind power plant is worked out by Matlab R2010b
Flow calculation program analyzes influence of the enchancement factors such as wind power integration, load fluctuation to system load flow, gives each node electricity
Press the static systems index of security assessment such as out-of-limit probability.
IEEE-30 node systems are as shown in Fig. 2, system has 6 generators, 30 nodes, 41 branches.Specific node
See annex with line parameter circuit value.For convenience of calculation, it is assumed that between each stochastic variable independently of each other, the output of generator obeys 0-1 points
Cloth, the equal Normal Distribution of load, using IEEE-30 node systems load value as average, standard deviation is the 20% of average.In example
The wind power plant capacity used is 5 × 2MW, and wind turbine is divided into two rows in wind power plant, and row's spacing is 120m, and unit is with constant power factor control
Mode processed is run, power factor 0.75.Assuming that atmospheric density is 1.2245kg/m in wind power plant3, the swept area of wind turbine is
1840m2, two parameters of the Weibull distributions of wind speed.
Optional node 10, node 24, branch 19-20 and branch 27-30 are research object, using based on cumulant and grade
The probabilistic loadflow algorithm of the number method of development carries out probabilistic loadflow calculating.
The algorithm key is to solve for each rank cumulant value of each state variable, first can be with according to the content of step S3
The voltage magnitude of node and each rank cumulant of branch active power are taken before obtaining wind power plant access, as shown in table 1.
Each rank cumulant of part of nodes voltage magnitude and branch active power before the access of 1 wind power plant of table
According to step S4 after node 25 accesses wind power plant, pass through Monte-Carlo step technology proposed by the present invention (sampling
Number), the first seven rank cumulant of output of wind electric field is calculated, as shown in table 2
Each rank cumulant of 2 Power Output for Wind Power Field of table (active and idle)
Each rank cumulant of the output of wind electric field acquired is added with each rank cumulant of each node original loads, i.e.,
Obtain each rank cumulant of each node injecting power, according to step S5 can be obtained wind power plant access after each state variable it is each
Rank cumulant value, as shown in table 3
Each rank cumulant of part of nodes voltage magnitude and branch active power after the access of 3 wind power plant of table
Finally, the first seven rank cumulant value is taken according to step S6, S7 and combines the side of Gram-Charlier series expansions
Method obtains the probability density function and 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 subjected to quantitative analysis, herein our sides of introducing
The root average (Average Root Mean Square, ARMS) of poor sum is weighed between the present invention and traditional algorithm (MCS)
Error.Table 4 gives the ARMS values of respective nodes voltage magnitude and branch active power.
The ARMS of 4 part of nodes voltage magnitude of table and branch active power
As can be seen that the ARMS value very littles of the corresponding state amount of selected node and branch, are respectively less than 1%, illustrate the present invention
Algorithm and MCS result of calculation it is basically identical, have higher precision.Wherein, the ARMS values of 10 voltage magnitude of node are remote small
In 24 corresponding value of node, this is because node 10 compared to node 24 apart from wind power plant access point farther out, by output of wind electric field ripple
Dynamic influence is smaller, and calculation error also can be relatively reduced.
By cumulative distribution function (CDF) curve, node voltage and the active out-of-limit probability of branch can easily be obtained, such as
MCS and inventive algorithm acquired results are set forth shown in table 5, in table.
The out-of-limit probability of 5 part of nodes voltage magnitude of table and branch active power
The method of applying step S8 counts the voltage out-of-limit and power of all nodes and circuit in IEEE-30 node systems
Out-of-limit probability can obtain the static security probability of whole system, as shown in table 6：
6 static system safe probability index of table
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 notable on the time is calculated
Advantage, and take it is unrelated with sample size, system scale it is larger, need online power flow calculating in the case of, have wide
Application prospect.
The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the technical principles of the invention, several improvement and deformation can also be made, these are improved and deformation
Also it should be regarded as protection scope of the present invention.
Claims (10)
1. the probabilistic loadflow algorithm based on cumulant and Series Expansion Method, it is characterised in that：Include the following steps：
S1：The stochastic model of electric system, input system initial data and wind power plant related data are built, including conventional Load Flow meter
Count evidence, power load distributing data, the output of conventional generator and forced outage rate, wind power plant historical wind speed, the probability of wind speed is close
The reactive power probability for spending function, the output power of wind-driven generator, the active power probability density function of load and load is close
Spend function；
S2：With Newton-Laphson method being determined property Load flow calculation, the desired value of node voltage and Branch Power Flow, Yi Jiling is obtained
Sensitive matrix S0And T0；
S3：Each rank cumulant of calculated load and conventional power generation usage acc power；
S4：Each rank cumulant of Wind turbines output is solved using the method based on Monte-Carlo step technology；
S5：By each rank cumulant of node generator powerWith each rank cumulant of load powerIt is added,
Acquire each rank cumulant Δ W of node injecting power(k)；
S6：According to the property of cumulant, each rank cumulant of calculate node state variable Δ X and Branch Power Flow Δ Z；
S7：The probability distribution letter of node state variable Δ X and Branch Power Flow Δ Z are obtained using Gram-Charlier series expansions
Number；
S8：With reference to the voltage constraint of node and the thermostabilization limit of line current, calculate each node voltage and Branch Power Flow more
Probability is limited, and obtains the static security probability of whole system.
2. the probabilistic loadflow algorithm according to claim 1 based on cumulant and Series Expansion Method, it is characterised in that：Institute
The probability density function for stating wind speed is calculated using Two-parameter Weibull distribution, as shown in formula (1)：
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mi>k</mi>
<mi>c</mi>
</mfrac>
<mo>&CenterDot;</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mi>v</mi>
<mi>c</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>&CenterDot;</mo>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mi>v</mi>
<mi>c</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mi>k</mi>
</msup>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (1), v is wind speed, and k and c are two parameters of Weibull distributions, and wherein k is form parameter, embodies wind speed profile
The characteristics of, c is scale parameter, reflects the size of regional mean wind speed；Shown in k and c such as formulas (2)：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>k</mi>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mi>&sigma;</mi>
<mi>&mu;</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1.086</mn>
</mrow>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>c</mi>
<mo>=</mo>
<mfrac>
<mi>&mu;</mi>
<mrow>
<mi>&Gamma;</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mi>k</mi>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (2), Γ is Gamma functions, and μ is mean wind speed, and σ is standard deviation；
The output power P of the wind-driven generatorwFor：
<mrow>
<msub>
<mi>P</mi>
<mi>w</mi>
</msub>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mi>v</mi>
<mo>&le;</mo>
<msub>
<mi>v</mi>
<mrow>
<mi>c</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>k</mi>
<mn>1</mn>
</msub>
<mi>v</mi>
<mo>+</mo>
<msub>
<mi>k</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mi>c</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&le;</mo>
<mi>v</mi>
<mo>&le;</mo>
<msub>
<mi>v</mi>
<mi>r</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>P</mi>
<mi>r</mi>
</msub>
</mtd>
<mtd>
<mrow>
<msub>
<mi>v</mi>
<mi>r</mi>
</msub>
<mo>&le;</mo>
<mi>v</mi>
<mo>&le;</mo>
<msub>
<mi>v</mi>
<mrow>
<mi>c</mi>
<mi>o</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mi>c</mi>
<mi>o</mi>
</mrow>
</msub>
<mo>&le;</mo>
<mi>v</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (3), vciTo cut wind speed, vcoFor cut-out wind speed, vrFor rated wind speed, PrFor the rated power of wind-driven generator, k1
And k2As shown in formula (4)：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>k</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>P</mi>
<mi>r</mi>
</msub>
<mrow>
<msub>
<mi>v</mi>
<mi>r</mi>
</msub>
<mo>-</mo>
<msub>
<mi>v</mi>
<mrow>
<mi>c</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>k</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>k</mi>
<mn>1</mn>
</msub>
<msub>
<mi>v</mi>
<mrow>
<mi>c</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
The active power probability density function f (P) of the load and the reactive power probability density function f (Q) such as formula (5) of load
It is shown：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>P</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msqrt>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</msqrt>
<msub>
<mi>&sigma;</mi>
<mi>P</mi>
</msub>
</mrow>
</mfrac>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>P</mi>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mi>P</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mrow>
<mn>2</mn>
<msubsup>
<mi>&sigma;</mi>
<mi>P</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>Q</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msqrt>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</msqrt>
<msub>
<mi>&sigma;</mi>
<mi>Q</mi>
</msub>
</mrow>
</mfrac>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>Q</mi>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mi>Q</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mrow>
<mn>2</mn>
<msubsup>
<mi>&sigma;</mi>
<mi>Q</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (5), μP、σPThe respectively desired value and mean square deviation of the active power of load, μQ、σQThe respectively reactive power of load
Desired value and mean square deviation, P, Q are respectively as shown in formula (6) and (7)：
<mrow>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>X</mi>
<mo>=</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msub>
<mi>P</mi>
<mi>P</mi>
</msub>
</mtd>
<mtd>
<mrow>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>C</mi>
<mi>P</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>P</mi>
<mi>P</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>Q</mi>
<mrow>
<mo>(</mo>
<mi>Y</mi>
<mo>=</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msub>
<mi>P</mi>
<mi>Q</mi>
</msub>
</mtd>
<mtd>
<mrow>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>C</mi>
<mi>Q</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>P</mi>
<mi>Q</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (6), PPFor the active power availability of generating set, CPFor the active power rated capacity of generating set；Formula (7)
In, PQFor the reactive power availability of generating set, CQFor the reactive power rated capacity of generating set.
3. the probabilistic loadflow algorithm according to claim 1 based on cumulant and Series Expansion Method, it is characterised in that：Institute
It states in step S2 and is comprised the following steps with the method for Newton-Laphson method being determined property Load flow calculation：
S2.1：Each bus admittance matrix Y is formed, if at the beginning of the initial value U of each node voltage and phase angle initial value e also have iterations
It is worth for 0, calculates the unbalanced power amount of each node, and obtain 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 conditions are not met,
Then carry out step S2.3；
S2.3：The each element in Jacobian matrix is calculated, corrects each node voltage, return to step S2.1；
S2.4：Terminate.
4. the probabilistic loadflow algorithm according to claim 1 based on cumulant and Series Expansion Method, it is characterised in that：Institute
It states in 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)：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&gamma;</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mi>&mu;</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&gamma;</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msup>
<mi>&sigma;</mi>
<mn>2</mn>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&gamma;</mi>
<mn>3</mn>
</msub>
<mo>=</mo>
<msub>
<mi>&gamma;</mi>
<mn>4</mn>
</msub>
<mo>=</mo>
<msub>
<mi>&gamma;</mi>
<mn>5</mn>
</msub>
<mo>=</mo>
<mo>...</mo>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (8), γiFor i rank cumulant, i=1,2 ..., μ are the expectation of load power, and σ is the mean square deviation of load power；
For the load power of discrete distribution, its each rank moment of the orign first is obtained by formula (9)：
<mrow>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>L</mi>
<mi>m</mi>
</mrow>
</msub>
<mo>=</mo>
<munder>
<mo>&Sigma;</mo>
<mi>i</mi>
</munder>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (9), αLmFor the m rank moment of the origns of load variation；piFor load values xiProbability,Wherein tiFor load etc.
In xiDuration, T is research cycle；
Then each rank cumulant of each node load power is acquired by the relation of cumulant and moment of the orign.
5. the probabilistic loadflow algorithm according to claim 1 based on cumulant and Series Expansion Method, it is characterised in that：Institute
It states in step S3, the computational methods of each rank cumulant of conventional power generation usage acc power are：
First, each rank moment of the orign of the total output power of the N platform conventional generators being equipped at a node is obtained：
αm=P1Cm+P2(2C)m+...+Pi(iC)m+...+PN(NC)m(m=1,2 ...) (10)
In formula (10), αmFor each rank moment of the orign of the total output power of N platform conventional generators, C is the specified appearance of conventional generator
Amount, Pi(i=1,2 ..., N) is as shown in formula (11)：
<mrow>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msubsup>
<mi>C</mi>
<mi>N</mi>
<mi>i</mi>
</msubsup>
<msup>
<mi>P</mi>
<mi>i</mi>
</msup>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>P</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mi>i</mi>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (11), PiTo there is the probability of i platform conventional generator normal operations in N platform conventional generators, P is conventional generator work
Make the probability in rated capacity C；
Then, each rank cumulant of conventional power generation usage acc power is acquired using the relation of cumulant and moment of the orign.
6. the probabilistic loadflow algorithm according to claim 1 based on cumulant and Series Expansion Method, it is characterised in that：Institute
It states in step S4, the computational methods for each rank cumulant that Wind turbines are contributed comprise the following steps：
S4.1：N number of wind speed sequence is extracted from the function of wind speed for obeying Two-parameter Weibull distribution using Monte-Carlo step technology
Arrange { v1,v2,…,vN}；
S4.2：Active power sequence { P is obtained according to the characteristics of output power of Wind turbines1,P2,…,PN}；
S4.3：Under constant power factor control mode, the reactive power of Wind turbines is directly proportional to active power, so as to obtain nothing
Work(power sequence { Q1,Q2,…,QN}；
S4.4：Each rank moment of the orign that Wind turbines are contributed is calculated, as shown in formula (12)：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>P</mi>
<mi>m</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>N</mi>
</mfrac>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msubsup>
<mi>P</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>Q</mi>
<mi>m</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>N</mi>
</mfrac>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msubsup>
<mi>Q</mi>
<mi>i</mi>
<mi>m</mi>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (12), αPmAnd αQmThe active power and the m rank moment of the origns of reactive power that respectively Wind turbines are contributed；
S4.5：Each rank cumulant of Wind turbines output is acquired using the relation of cumulant and moment of the orign.
7. the probabilistic loadflow algorithm according to claim 1 based on cumulant and Series Expansion Method, it is characterised in that：Institute
It states in step S5, each rank cumulant Δ W of node injecting power(k)It is calculated using formula (13)：
<mrow>
<msup>
<mi>&Delta;W</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msup>
<mo>=</mo>
<msubsup>
<mi>&Delta;W</mi>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&Delta;W</mi>
<mi>l</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (13),For each rank cumulant of node generator power,It is constant for each rank half of load power
Amount.
8. the probabilistic loadflow algorithm according to claim 1 based on cumulant and Series Expansion Method, it is characterised in that：Institute
It states in step S6, each rank cumulant of node state variable Δ X and Branch Power Flow Δ Z are calculated using formula (14)：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mi>&Delta;X</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msup>
<mo>=</mo>
<msubsup>
<mi>S</mi>
<mn>0</mn>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>&CenterDot;</mo>
<msubsup>
<mi>&Delta;W</mi>
<mi>l</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>&Delta;Z</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msup>
<mo>=</mo>
<msubsup>
<mi>T</mi>
<mn>0</mn>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>&CenterDot;</mo>
<msubsup>
<mi>&Delta;W</mi>
<mi>l</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (14), Δ X(k)For each rank cumulant of node state variable Δ X, Δ Z(k)For each rank half of Branch Power Flow Δ Z
Invariant,For each rank cumulant of load power,WithRespectively matrix S0And T0The k power institute of middle element
The matrix of composition for arbitrary element (i, j), has：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>S</mi>
<mn>0</mn>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>S</mi>
<mn>0</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mi>k</mi>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>T</mi>
<mn>0</mn>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>T</mi>
<mn>0</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mi>k</mi>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
9. the probabilistic loadflow algorithm according to claim 1 based on cumulant and Series Expansion Method, it is characterised in that：Institute
It states in step S7, the probability-distribution function of node state variable Δ X and Branch Power Flow Δ Z based on Gram-Charlier series
Shown in computational methods such as formula (16), (17)：
In formula (16), (17), F (x) is the node state variable of standardization or the cumulative distribution function of Branch Power Flow, and f (x) is mark
The node state variable of standardization or the probability density function of Branch Power Flow,For stochastic variable node state variable Δ X or branch tide
The standardized random variable of Δ Z is flowed,For standardized normal distribution density function, HiFor Hermite multinomials, giIt is more for Hermite
The coefficient of item formula.
10. the probabilistic loadflow algorithm according to claim 1 based on cumulant and Series Expansion Method, it is characterised in that：
In the step S8, the static security method for calculating probability of whole system is：Obtain node state variable Δ X and Branch Power Flow Δ
After the probability-distribution function of Z, with reference to the voltage constraint of node and the thermostabilization limit of line current, each node voltage and branch are calculated
The out-of-limit probability of road trend, is denoted as p1,p2,…,pn；Then the static security probability of whole system is：
<mrow>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
<mo>=</mo>
<munderover>
<mo>&Pi;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>18</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610165113.6A CN105811403B (en) | 2016-03-22 | 2016-03-22 | Probabilistic loadflow algorithm based on cumulant and Series Expansion Method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610165113.6A CN105811403B (en) | 2016-03-22 | 2016-03-22 | Probabilistic loadflow algorithm based on cumulant and Series Expansion Method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN105811403A CN105811403A (en) | 2016-07-27 |
| CN105811403B true CN105811403B (en) | 2018-05-22 |
Family
ID=56454745
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610165113.6A Active CN105811403B (en) | 2016-03-22 | 2016-03-22 | Probabilistic loadflow algorithm based on cumulant and Series Expansion Method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105811403B (en) |
Families Citing this family (14)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106911140A (en) * | 2017-04-14 | 2017-06-30 | 新奥科技发展有限公司 | A kind of energy storage planing method |
| CN107451680A (en) * | 2017-07-12 | 2017-12-08 | 河海大学 | A kind of electrical interconnection system random optimum trend heuristic calculation methods |
| CN107968409A (en) * | 2017-11-08 | 2018-04-27 | 中国电力科学研究院有限公司 | A kind of probability load flow calculation method and system for considering imbalance power distribution |
| CN108549752B (en) * | 2018-03-27 | 2021-11-05 | 南京航空航天大学 | Modeling method for functional level model of doubly salient electro-magnetic generator |
| CN108365640A (en) * | 2018-03-29 | 2018-08-03 | 国网江苏省电力有限公司电力科学研究院 | Unit leading phase operation management method between a kind of power grid low-load period |
| CN108711851B (en) * | 2018-06-05 | 2020-06-16 | 国网上海市电力公司 | Method for evaluating safety of medium-voltage distribution network closed-loop operation |
| CN111262248B (en) * | 2018-11-30 | 2023-11-03 | 中国电力科学研究院有限公司 | Random power flow analysis and calculation method and system |
| CN109687431B (en) * | 2018-12-04 | 2020-07-14 | 中国电力科学研究院有限公司 | Active power distribution network probability equivalence modeling method considering new energy randomness |
| CN109740962A (en) * | 2019-01-18 | 2019-05-10 | 国网安徽省电力有限公司 | Voltage stabilization probability evaluation method of failure based on scene subregion and cumulant |
| CN109861234A (en) * | 2019-02-27 | 2019-06-07 | 浙江大学 | Consider the Power System Reliability judgment method of polymerization air conditioner load spinning reserve |
| CN110189061A (en) * | 2019-06-24 | 2019-08-30 | 合肥工业大学 | A kind of extensive dispersion photovoltaic access planing method based on risk assessment |
| CN110299710A (en) * | 2019-08-02 | 2019-10-01 | 南方电网科学研究院有限责任公司 | A kind of the probabilistic loadflow calculation method and device of wind power plant access power grid |
| CN110797865B (en) * | 2019-10-30 | 2020-06-09 | 山东大学 | Data-driven power supply weak link identification method and system |
| CN113972659B (en) * | 2021-11-04 | 2024-02-02 | 国网冀北电力有限公司经济技术研究院 | Energy storage configuration method and system considering random power flow |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2009195023A (en) * | 2008-02-14 | 2009-08-27 | Toshiba Corp | Method for evaluating overall efficiency for power supply system |
| WO2012161378A1 (en) * | 2011-05-25 | 2012-11-29 | (주)파워이십일 | Method for estimating the status of a power distribution system |
| CN104410069A (en) * | 2014-12-05 | 2015-03-11 | 国家电网公司 | Dynamic probability load flow calculation method taking response correlation into account |
| CN104638644A (en) * | 2015-02-12 | 2015-05-20 | 河海大学 | Acquiring method for dynamic random optimal power flow of power system for wind-containing power field |
-
2016
- 2016-03-22 CN CN201610165113.6A patent/CN105811403B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2009195023A (en) * | 2008-02-14 | 2009-08-27 | Toshiba Corp | Method for evaluating overall efficiency for power supply system |
| WO2012161378A1 (en) * | 2011-05-25 | 2012-11-29 | (주)파워이십일 | Method for estimating the status of a power distribution system |
| CN104410069A (en) * | 2014-12-05 | 2015-03-11 | 国家电网公司 | Dynamic probability load flow calculation method taking response correlation into account |
| CN104638644A (en) * | 2015-02-12 | 2015-05-20 | 河海大学 | Acquiring method for dynamic random optimal power flow of power system for wind-containing power field |
Non-Patent Citations (1)
| Title |
|---|
| 考虑风电场出力随机性的电网静态安全分析;蒋平等;《电力系统自动化》;20131125;第37卷(第22期);第35-40页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN105811403A (en) | 2016-07-27 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN105811403B (en) | Probabilistic loadflow algorithm based on cumulant and Series Expansion Method | |
| CN103259285B (en) | Method for optimizing short running of electric power system comprising large-scale wind power | |
| CN106972481A (en) | Scale electrically-charging equipment accesses the security quantitative estimation method of active power distribution network | |
| CN102709908B (en) | Loss prediction method for large-scale wind power-accessed power grid | |
| CN104156892A (en) | Active distribution network voltage drop simulation and evaluation method | |
| CN103810535B (en) | Power system wind electricity digestion capability appraisal procedure | |
| Sun et al. | Research on ultra-short-term wind power prediction considering source relevance | |
| CN103683326A (en) | Method for calculating optimal admitting ability for wind power multipoint access of regional power grid | |
| CN108306303A (en) | A kind of consideration load growth and new energy are contributed random voltage stability assessment method | |
| CN107968409A (en) | A kind of probability load flow calculation method and system for considering imbalance power distribution | |
| CN106786606B (en) | A kind of calculation method of the Probabilistic Load based on a variety of stochastic variables | |
| CN107145707A (en) | It is a kind of to count and photovoltaic is exerted oneself the power distribution network transformer planing method of uncertain and overall life cycle cost | |
| CN105656084A (en) | Improved stochastic load flow algorithm involved with new energy power generation prediction errors | |
| CN106877336A (en) | A kind of AC and DC power system Continuation power flow for considering wind-powered electricity generation randomness | |
| CN103235984A (en) | Computing method of longitudinal moment probability distribution of power output of wind power station | |
| CN110429637A (en) | A kind of method for visualizing of probability Static Voltage Stability Region | |
| CN107528322A (en) | A kind of Probabilistic Load Flow analysis method of the NATAF conversion based on the Gauss Hermite method of quadratures | |
| CN108054790A (en) | The active method for real-time optimization control of wind light generation cluster based on prediction output Approach by inchmeal | |
| CN107039981A (en) | One kind intends direct current linearisation probability optimal load flow computational methods | |
| CN106611243A (en) | Residual correction method for wind speed prediction based on GARCH (Generalized ARCH) model | |
| CN108565865A (en) | A kind of alternating current-direct current combined hybrid system methods of risk assessment containing wind-powered electricity generation | |
| Sun et al. | Tight semidefinite relaxation for interval power flow model based on multi-dimensional holomorphic embedding method | |
| Zhao et al. | Probabilistic voltage stability assessment considering stochastic load growth direction and renewable energy generation | |
| CN105305485A (en) | Large-scale intermittent energy consuming security constrained economic dispatch method | |
| CN107658878A (en) | A kind of Probabilistic optimal load flow method containing large-scale energy storage device |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |