CN107039981A - One kind intends direct current linearisation probability optimal load flow computational methods - Google Patents
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Classifications
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- 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
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- H02J3/386—
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- 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]
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/70—Wind energy
- Y02E10/76—Power conversion electric or electronic aspects
Abstract
Intend direct current linearisation probability optimal load flow computational methods the invention discloses one kind, on the basis of former probability optimal load flow model, linearization process is carried out to conventional probability optimal load flow model by approximate method for simplifying, simultaneously wind-powered electricity generation scene generation is carried out using Latin Hypercube Sampling, technology is cut down based on scene and obtains the larger a small number of wind-powered electricity generation scenes of probability measure, is finally solved using simplified interior point method.Probability optimal load flow, which is calculated, belongs to NONLINEAR CALCULATION, and as system scale increases, difficulty in computation is greatly increased, and computational efficiency is low, it is difficult to meets power system and analyzes requirement in line computation.For containing large-scale wind power power system, Simulation Example result shows that precision of the present invention is high, and the calculating time is short, strong applicability.
Description
Technical field
Intend direct current linearisation probability optimal load flow computational methods the present invention relates to one kind, belong to Power System Analysis and calculating
Field.
Background technology
With the development of power industry, fossil energy is because being large-scale developed and utilized positive increasingly depleted, energy crisis and ring
Border problem turns into the Tough questions that countries in the world face, and wind-powered electricity generation is used as a kind of regenerative resource, it has also become with fastest developing speed in the world
Green energy resource.Wind-powered electricity generation has an intermittent, fluctuation, and large-scale wind-electricity integration is by the safe and stable operation band to power system
Carry out stern challenge.Optimal load flow (optimal power flow, OPF) is the important hand of power system Real time optimal dispatch
Section, OPF is by the control variable in regulating system, in the case where meeting relevant constraint, desired value can be made to reach most
It is excellent.Traditional OPF is calculated based on deterministic models, but the power system moment containing large-scale wind power is random by wind-powered electricity generation
Property, the influence of fluctuation.Therefore, research considers that the optimal power flow problems of enchancement factor are significant.
The optimal load flow research to considering enchancement factor is broadly divided into two major classes, i.e. random optimum trend at present
(stochastic optimal power flow, SOPF) and probability optimal load flow (probabilistic optimal
power flow,POPF).POPF has important effect in the security analysis of electric power system containing large-scale wind power, is one
Individual typical nonlinear programming problem.It is traditional with the continuous expansion and the increasingly raising of power network complexity of system scale
POPF models carry out complicated NONLINEAR CALCULATION because needing, and can not meet power system in terms of real-time and applicability
Safety on line calculates analysis and required.DC Model is current most widely used inearized model, and its solution efficiency is high, but meter
Calculate precision low, and can not calculate node voltage magnitude, this intrinsic not enough application for significantly limiting DC Model pushes away
Extensively.
The content of the invention
Goal of the invention：The technical problems to be solved by the invention are in power system for conventional probability optimal load flow model
Analysis is difficult to meet to analyze in line computation with calculating degree field to be required, and the probability optimal load flow model accuracy based on once-through principle
Situation poor, poor for applicability.
Technical scheme：The present invention is adopted the following technical scheme that：
The present invention intends direct current linearisation probability optimal load flow computational methods to be a kind of, in a computer successively according to the following steps
Realize：
(1) wind-powered electricity generation scene is generated using Latin Hypercube Sampling method.
(2) the wind-powered electricity generation scene of generation is cut down using synchronous back substitution null method.
(3) other electrical network parameters in addition to wind-powered electricity generation are obtained.
(4) linearization process is carried out to conventional probability optimal load flow model by approximate method for simplifying, sets up linearisation general
Rate optimal load flow model.
(5) complementary clearance G ap is calculated, judges whether it meets required precision, if meeting, optimal solution is exported, terminates to follow
Ring, otherwise, continues；
(6) Jacobian matrix is calculatedHessian matrix
And each constant term Lx′、Ly、Lw、And Δ x, Δ y, Δ u, Δ w are solved according to below equation：
Wherein：Δ x, Δ y, Δ u, Δ w are respectively variable x, y, u, w correction；
(7) variable and the step-length α of Lagrange multiplier are calculated according to following formulap、αd, and more new variables multiplies with Lagrange
The value of son.
(8) judge whether iterations reaches maximum, do not restrained if then calculating, if it is not, iterations adds 1 return to walk
Suddenly (5), continue.
As optimization, the Latin Hypercube Sampling method generation wind speed scene in the step 1 includes sampling and two steps of sequence；
It is N number of non-overlapping copies first by [0,1] interval division when being sampled for each independent stochastic variable that the general principle of sampling, which is,
Equidistant interval, now each interval width is 1/N, and N is hits, and is then adopted in each interval random selection one
Sample value, finally takes out substantial amounts of sample from the probability density function of wind speed；Sequence is then that the great amount of samples obtained by sampling is entered
Row Cholesky is decomposed, and reduces the correlation between multiple input variables.
As optimization, it is that great amount of samples is handled that scene in the step 2, which is cut down, finally obtain probability measure compared with
Big a few sample, computation complexity is reduced while preferably reaction stochastic variable fluctuation；Then according to wind speed and wind
The relational expression of power, obtains corresponding scene leeward electricity and exerts oneself.
As optimization, the electrical network parameter in the step 3 includes bus numbering, title, burden with power, load or burden without work, simultaneously
Join compensating electric capacity, branch road number, headend node and the endpoint node numbering of transmission line of electricity, series impedance, shunt admittance, transformer become
Than and impedance, generator output.
Linearizing probability optimal load flow model as optimization, in the step 4, to set up process as follows：
AC power flow interior joint injecting power equation is
In formula：Vi、VjRespectively node i, j voltage magnitude, Gij、BijRespectively the i-th row of bus admittance matrix, jth
The real part and imaginary part of column element；θijFor node i, j phase difference of voltage；
According to the feature of bus admittance matrix, above formula is carried out to deform
In formula：gij、bijRespectively circuit ij conductance and susceptance；
According to approximate formula Vi(Vi-Vjcosθij)≈Vi-Vj, Vi,Vj≈1,V2≈ V and sin θij≈θij,cosθij≈
1, above formula can further deform and obtain lienarized equation
In formula：giiFor yiiReal part, θjFor node j voltage phase angle, B 'ijTo remove the admittance matrix of node self-admittance
The imaginary part of i-th row, jth column element；
Similarly, the injection reactive power equation of node also can approximately be simplified to lienarized equation, replace conventional probability optimal
Corresponding equation in tide model, finally obtains linearisation probability optimal load flow model.
Beneficial effect：The present invention is compared with prior art：Traditional probability optimal load flow computational methods based on once-through principle,
Although computational efficiency is high, misconvergence sex chromosome mosaicism, its computational accuracy is poor, it is impossible to calculate voltage magnitude and circuit is idle, application
Occasion is limited.The present invention establishes a kind of direct current of intending by approximate method for simplifying and linearizes probability optimal load flow model.
Brief description of the drawings
Accompanying drawing 1：The inventive method flow chart.
Embodiment
The calculating of probability optimal load flow is the important means of the power system Real time optimal dispatch containing large-scale wind power.Due to wind
Electricity has natural randomness, intermittent and fluctuation, and most of documents are approximately retouched using two-parameter Weibull distribution is obeyed
Wind speed is stated, wind speed probability density function is：
In formula：V is the wind speed of wind power plant, and k is the distribution shape coefficient of Weibull distribution, and c is scale coefficient.
In steady-state analysis, output of wind electric field depends on wind speed size, its fluctuation with wind speed and change, output of wind electric field
It can be represented with the relation of wind speed with formula (2)：
In formula：PwFor the power output of wind power plant, PrFor the rated output power of wind power plant, vin、voutAnd vrRespectively wind
Incision wind speed, cut-out wind speed and the rated wind speed of group of motors.
Conventional probability optimal load flow is calculated and solved based on AC model, and AC model is a nonlinear model, by
One group of nonlinear equation composition, it can intactly reflect practical problem, and computational accuracy is high.The number of general probability optimal load flow
Model is learned to be made up of object function, equality constraint and inequality constraints.：
1) object function.
Generally, POPF models are with generator expense minimum or the minimum object function of system losses.
2) equality constraint.Predominantly node trend Constraints of Equilibrium:
In formula：QGiFor the reactive power of generator at node i, PWi、QWiRespectively be connected the having of Wind turbines with node i
Work(, it is idle exert oneself, PDi、QDiThe respectively active and reactive load of node i, Pi、QiThe respectively active and reactive injection work(of node i
Rate.
3) inequality constraints condition：
In formula：Vi、θiThe respectively voltage magnitude and phase angle of node i, PijFor circuit ij effective power flow.nw, n be respectively
Wind-powered electricity generation number of fields and nodes, ●The respectively upper and lower limit of variable.
POPF model nonlinears are concentrated mainly on node power equilibrium equation and the circuit effective power flow side of equality constraint
Cheng Zhong.It can be seen from AC power flow equation, the injecting power equation of node i is
In formula：VjFor node j voltage magnitude, Gij、BijRespectively the i-th row of bus admittance matrix, the reality of jth column element
Portion and imaginary part；θijFor node i, j phase difference of voltage.
The bus admittance matrix of power system be one have special construction matrix, diagonal element be off-diagonal element with
And the admittance sum of node parallel element, as shown in formula (7)：
In formula：YijFor circuit ij bus admittance matrix, yij、yikRespectively circuit ij and circuit ik admittance, yiiFor section
Point i self-admittance.
Formula based on more than, carries out deforming to formula (5)
In formula：gij、bijRespectively circuit ij conductance and susceptance.
It can be obtained by mathematical approach formula：
In formula：ΔVi、ΔVjRespectively node i, the small increment of j voltage magnitudes, its value is about 0.
In most of power systems, the amplitude of node voltage is approximately 1.0pu, and the node voltage phase angle at circuit two ends
The absolute value of difference rarely exceeds 30 degree, and wherein most is within 10 degree.According to such case, can approximately it obtain：
According to formula (7), formula (9) and formula (10), formula (8) can be deformed further, finally obtain the node i of linearisation
Inject active power：
In formula：giiFor yiiReal part, θjFor node j voltage phase angle, B 'ijTo remove the admittance matrix of node self-admittance
The imaginary part of i-th row, jth column element.
Similarly, formula (6) can obtain formula (12) by simplifying change, and conversion process will not be repeated here.
Calculation formula and approximate simplification finally according to Line Flow can draw circuit ij effective power flow：
In formula：T is the no-load voltage ratio of transformer on circuit, when circuit is free of transformer, t=1；θsFor the phase angle of phase shifter,
When circuit is free of phase shifter, θs=0.
The complicated nonlinear equation of traditional POPF models is carried out linearization process by the present invention, in theory than traditional POPF moulds
Type has higher efficiency and convergence, and compared to the POPF models based on DC Model using less simplification and count and
Reactive power influences, with higher precision while Power Flow Information is improved.
The present invention is calculated containing large-scale wind power power system respectively in IEEE-300, Polish-2736 node system
The optimal tide of probability under probability optimal load flow, the optimal load flow based on once-through principle and carried new model based on exchange principle
Stream, is tested.By contrasting the result of calculation of 3 kinds of models, computational methods proposed by the present invention are demonstrated with higher meter
Calculate efficiency and precision, strong applicability.
Embodiments of the invention are described below：
The present invention is tested model calculating method of the present invention by taking IEEE-300, Polish-2736 node system as an example
Card.Two wind power plants are accessed in each test system.Wherein, the total burden with power of system is in IEEE-300 node systems
23526MW, the rated power of 2 wind power plants of system access is Pr=3000MW.System is total in Polish-2736 node systems
Burden with power is 18075MW, and the rated power of 2 wind power plants of system access is Pr=2350MW.Accessed wind power plant is used
Constant power factor is controlled, and assumes that the power factor of each wind power plant is 1.For ease of description, define based on exchange principle
Probability optimal load flow model is model 1, and the optimal load flow model based on once-through principle is model 2, the linearisation that the present invention is carried
Probability optimal load flow is model 3.
Example generates 1000 wind speed scenes by LHS methods first, then cuts down technology using scene and original scene is entered
Row is cut down, and finally obtains 5 scenes to portray the fluctuation of wind speed, the incision wind speed of wind power plant, rated wind speed and cuts out wind
Fast wind Wei not 3m/s, 14m/s, 25m/s.The result that scene is cut down is as shown in table 1.
The wind speed scene of table 1 cuts down result
For ease of observation analysis, the result that example obtains solving model 1 is designated as Cost as benchmark0, solving model 2,
The result that model 3 is obtained is designated as Cost, then model 2, model 3 and the phase of the result of calculation of model 1 can be calculated according to formula (14)
To error.
Δ Cost=| Cost-Cost0|/Cost0× 100% (14)
Table 2, table 3 give each model maximum of relative error, minimum value under each scene in a test system
And desired value.
Each model relative error of the IEEE300 node systems of table 2
Each model relative error of the node systems of 3 Polish of table 2 736
As can be seen that being calculated for the optimal load flow containing large-scale wind power Probabilistic, 3 kinds of moulds from table 2, table 3
Type can obtain optimal solution in different scenes, illustrate that each model is feasible effective.In two test systems, different scenes
The maximum relative error of drag 2 close to 3%, minimum relative error still above 2%, and anticipation error 2.5% with
On.With the increase of system, the relative error of model 2 also becomes big, it was demonstrated that system scale is bigger, and the applicability of model 2 is poorer.It is existing
Stage power network development is rapid, and power network scale constantly expands, and model 2 will be unable to meet the power system progress containing large-scale wind power
Safety on line calculates the requirement of analysis.Model 3 is in IEEE300 node systems, and relative error is maintained near 1%, compared to mould
Type 2, computational accuracy improves 57% or so.In the node systems of Polish 2 736, the relative error as little as 0.5% of model 3
Within, compared to model 2, computational accuracy improves more obvious, up to 93% or so.By comparing as can be seen that no matter system is advised
Mould size, model 3 is respectively provided with higher precision than model 2, and applicability is stronger.With the increase of system scale, the calculating of model 3
Precision has significant raising, illustrates that model 3 is adaptive to big system, practicality is stronger, can be very good to apply containing big
The power system safety on line of scale wind power plant is calculated in analysis.
Table 4, table 5 then give in a test system that iterations and calculating time of each model under each scene be most
Big value, minimum value and desired value.
Each model iterations of the IEEE300 node systems of table 4 is with calculating the time
Each model iterations of the node systems of 5 Polish of table 2 736 is with calculating the time
Note：Example shows that the calculating time does not include wind-powered electricity generation scene and generated and the scene reduction time
As can be seen that because model 2, model 3 have carried out linearization process, the calculating effect of two models from table 4, table 5
Rate is all greatly improved compared with model 1, and 2 iterations is less than model 1, it was demonstrated that inearized model is compared with AC model
With bigger advantage.The iterations of model 1 is stronger to the sensitiveness of system scale, with the increase of system, its iteration time
Number increase is more.In more massive practical power systems, because of situations such as overload, line impedance go out than increase
It is existing, easily there is not convergence problem.
In addition, the calculating time of model 1 greatly increases with the increase of system scale, it is difficult to meet containing large-scale wind power
Power system safety on line calculate analysis require, be unfavorable for the safe and stable operation of bulk power grid.Observing and nursing 2, model 3 are calculated
Results, it can be seen that the iterations of the two is influenceed less with the calculating time by system scale, calculating speed is fast, iterations
It is few.Compared with model 1, the calculating time of model 2 reduces 70% -90%, and model 3 then reduces 65% -77%, it is seen that line
The computational efficiency of property model is higher, can more meet the actual requirement for advising the power system touched greatly.Compared with model 2, due to mould
The simplification of type 3 is less, and introduces the influence of reactive power, and the iterations of model 3 is slightly higher, and the calculating time is slightly longer, but compares
In model 1, the computational efficiency of model 3 is still very high, for the practical power systems of large-scale wind power access, and model 3 can be with
Meet the requirement that safety on line calculates analysis.
In summary, for the increasingly huge and complicated power system containing large-scale wind power, AC model can be compared with
Optimal load flow result is precisely calculated, but its computational efficiency is low, convergence is sensitive to system scale, it is difficult to meet meter in real time
The requirement of point counting analysis；DC Model is higher than AC model computational efficiency, but computational accuracy is relatively low, although can meet online meter
The requirement of evaluation time, but calculating deviation is too big, and applicability is low；The present invention carries inearized model compared to AC model, calculates
Hurry up, precision it is high, more conform to power system safety on line and calculate analysis to require, applicability has bigger carry compared with DC Model
It is high.
Claims (5)
1. one kind intends direct current linearisation probability optimal load flow computational methods, it is characterised in that press following step successively in a computer
It is rapid to realize：
(1) wind-powered electricity generation scene is generated using Latin Hypercube Sampling method；
(2) the wind-powered electricity generation scene of generation is cut down using synchronous back substitution null method；
(3) other electrical network parameters in addition to wind-powered electricity generation are obtained；
(4) linearization process is carried out to conventional probability optimal load flow model by approximate method for simplifying, sets up linearisation probability most
Excellent tide model；
(5) complementary clearance G ap is calculated, judges whether it meets required precision, if meeting, optimal solution is exported, end loop is no
Then, continue；
(6) Jacobian matrix ▽ is calculatedxh(x)、Hessian matrixAnd
Each constant term L 'x、Ly、Lw、And Δ x, Δ y, Δ u, Δ w are solved according to below equation：
Wherein：Δ x, Δ y, Δ u, Δ w are respectively variable x, y, u, w correction；
(7) variable and the step-length α of Lagrange multiplier are calculated according to following formulap、αd, and more new variables and Lagrange multiplier
Value：
(8) judge whether iterations reaches maximum, do not restrained if then calculating, if it is not, iterations adds 1 return to step
(5), continue.
2. plan direct current linearisation probability optimal load flow computational methods according to claim 1, it is characterised in that the step
Latin Hypercube Sampling method generation wind speed scene in 1 includes sampling and two steps of sequence；The general principle of sampling is for each
It is the equidistant interval of N number of non-overlapping copies, now each area first by [0,1] interval division during independent stochastic variable sampling
Between width be 1/N, N is hits, and then in one sampled value of each interval random selection, finally the probability from wind speed is close
Substantial amounts of sample is taken out in degree function；Sequence is then to carry out Cholesky decomposition to the great amount of samples obtained by sampling, is reduced multiple
Correlation between input variable.
3. plan direct current linearisation probability optimal load flow computational methods according to claim 1, it is characterised in that the step
It is that great amount of samples is handled that scene in 2, which is cut down, finally obtains the larger a few sample of probability measure, is preferably reacting
Reduce computation complexity while stochastic variable fluctuation；Then according to the relational expression of wind speed and wind power, corresponding scene is obtained
Lower wind power output.
4. plan direct current linearisation probability optimal load flow computational methods according to claim 1, it is characterised in that the step
Electrical network parameter in 3 includes bus numbering, title, burden with power, load or burden without work, Shunt compensation capacitor, the branch road of transmission line of electricity
Number, headend node and endpoint node numbering, series impedance, shunt admittance, transformer voltage ratio and impedance, generator output.
5. plan direct current linearisation probability optimal load flow computational methods according to claim 1, it is characterised in that the step
Probability optimal load flow model is linearized in 4, and to set up process as follows：
AC power flow interior joint injecting power equation is
In formula：Vi、VjRespectively node i, j voltage magnitude, Gij、BijRespectively the i-th row of bus admittance matrix, jth row are first
The real part and imaginary part of element；θijFor node i, j phase difference of voltage；
According to the feature of bus admittance matrix, above formula is carried out to deform
In formula：gij、bijRespectively circuit ij conductance and susceptance；
According to approximate formula Vi(Vi-Vjcosθij)≈Vi-Vj, Vi,Vj≈1,V2≈ V and sin θij≈θij,cosθij≈ 1, above formula
It can further deform and obtain lienarized equation
In formula：giiFor yiiReal part, θjFor node j voltage phase angle, B 'ijFor remove node self-admittance the row of admittance matrix i-th,
The imaginary part of jth column element；
Similarly, the injection reactive power equation of node also can approximately be simplified to lienarized equation, replace conventional probability optimal load flow
Corresponding equation in model, finally obtains linearisation probability optimal load flow model.
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| CN107579525A (en) * | 2017-08-18 | 2018-01-12 | 河海大学 | A kind of cold start-up linearisation optimal load flow computational methods for calculating complete Power Flow Information |
| CN109390946A (en) * | 2018-10-08 | 2019-02-26 | 重庆大学 | A kind of optimum probability trend quick calculation method based on multi-parametric programming theory |
| CN110048407A (en) * | 2019-04-12 | 2019-07-23 | 浙江浙能技术研究院有限公司 | Distributed energy power generation plan feasible zone method for optimization analysis |
| CN110224391A (en) * | 2019-05-10 | 2019-09-10 | 广西电网有限责任公司电力科学研究院 | A kind of mixing probability-section optimal load flow method for solving |
| CN111313425A (en) * | 2020-01-15 | 2020-06-19 | 国网重庆市电力公司 | Load flow model linearization error minimization method based on variable space optimal selection |
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| CN110224391B (en) * | 2019-05-10 | 2022-06-24 | 广西电网有限责任公司电力科学研究院 | Method for solving mixed probability-interval optimal power flow |
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