CN107145707A - 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 - Google Patents

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 Download PDF

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CN107145707A
CN107145707A CN201710215832.9A CN201710215832A CN107145707A CN 107145707 A CN107145707 A CN 107145707A CN 201710215832 A CN201710215832 A CN 201710215832A CN 107145707 A CN107145707 A CN 107145707A
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CN107145707B (en
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杨楠
李宏圣
黎索亚
王璇
董邦天
黄禹
叶迪
周峥
崔家展
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China Three Gorges University CTGU
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06313—Resource planning in a project environment
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G16Z—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS, NOT OTHERWISE PROVIDED FOR
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    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Abstract

The present invention, which is proposed, a kind of considers that distributed energy is exerted oneself the distribution transforming planing method of uncertain and overall life cycle cost, belongs to distribution network planning field.First, it is considered to the uncertainty of exerting oneself of distributed photovoltaic power generation, it is proposed that a kind of distribution transforming risk constant volume method theoretical based on chance constraint；On this basis, the distribution Probabilistic Load Flow after distributed photovoltaic power generation access is calculated using three point estimations, while building the object function based on overall life cycle cost, and finally proposes the uncertain plan model of the distribution transforming based on life cycle theory.Simulation Example result shows, compared to traditional deterministic distribution transforming planing method, set forth herein method all costs in equipment life cycle management can not only be carried out to become more meticulous measurement, and accurately calculate the uncertain influence for equipment constant volume type selecting of distributed power source, it compensate for the boundary of distribution transforming constant volume and type selecting, so as to effectively improve the economy of distribution transforming planning, method more science proposed by the invention.

Description

It is a kind of to count and photovoltaic is exerted oneself the power distribution network transformation of uncertain and overall life cycle cost Device planing method
Technical field
The present invention is a kind of to be counted and photovoltaic is exerted oneself the power distribution network transformer planing method of uncertain and overall life cycle cost, Belong to containing distributed power source (Distributed Generation, DG) distribution network planning field.
Background technology
In recent years, with environmental pollution and the continuous exacerbation of energy shortage problem, distributed generation technology is further by weight Depending on.In power distribution network, distributed power source, especially distributed photovoltaic power generation (Photovoltaic Generation, PVG) Permeability is increased rapidly, in this context, how to carry out the power equipment investment decision of science, builds reliable and economic Power distribution network is the study hotspot of current planning field.
Distribution transformer (distribution transforming) is important power equipment in power distribution network, and usage amount is big, when having a wide range of application, running Between it is long, energy-saving potential is huge.For a long time, initial outlay or interim cost are paid close attention in distribution transforming investment planning, are ignored and are set The standby potential expense in the whole military service cycles such as later stage operation, retired disposal, so as to cause the selection of its capacity and model to lack The weary overall viewing angle through equipment life cycle management, easily forms overly conservative or radical programme, causes larger throwing Money is wasted.In consideration of it, the distribution transforming investment decision method based on life cycle theory (Life Cost Cycle, LCC) is Gradually recognized and applied, its mainly on the basis of planning reliability is ensured, by accurately calculate distribution transforming from purchasing, Operation, maintenance and the retired value characteristic changing rule for reclaiming (i.e. life cycle management) in the whole military service cycle, are realized to distribution The constant volume type selecting of science.Study and find simultaneously, though the accurate assessment to distribution transforming LCC costs is realized in distribution transforming planning at present, But still there are some problems：On the one hand, the uncertain factor influence in power distribution network is not considered during planning, and with big Uncertain influence factor during amount distributed power source access power distribution network, distribution network planning further increases, this based on true The distribution transforming planning of qualitative LCC costs is accurately assessed because of the influence that it can not be to uncertain factor, has been difficult to meet existing There is the actual demand planned containing distributed power distribution network；On the other hand, most of distribution transformings only under fixed capacity at present Selection issue, is to isolate distribution transforming constant volume and type selecting to be respectively calculated for two questions of independence, this has in planning process The inherence that the former may be ignored for distribution transforming type selecting influences, so as to influence the computational accuracy of plan model.
At present, the accurate planing method for considering uncertain factor has been obtained in power source planning, circuit rack planning field Application to a certain extent.Using chance constraint, robust optimize etc. uncertainties model method, build meter and not Certainty factor influence plan model so that solve distributed power source access after power network a series of planning problems, for Become planning problem research and provide good reference and reference.
The content of the invention
Distribution transforming planning problem after being accessed for distributed photovoltaic power generation, the present invention proposes a kind of meter and photovoltaic is exerted oneself not The power distribution network transformer planing method of certainty and overall life cycle cost, it is first, theoretical based on chance constraint, build distribution transforming The risk model of calculation of capacity, determines the optimal capacity of distribution transform under different confidential intervals, proposes to estimate based on 3 points on this basis The power distribution network probability load flow calculation method of meter method, and bring plan model into as constraints, then consider to match somebody with somebody Varying capacity selects the influence to cost of investment and operating cost, proposes the mathematical expression mode of distribution transforming LCC costs, final to set up Uncertainty of objective distribution transforming plan model is turned to LCC cost minimizations.
The technical scheme that the present invention takes is：
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, including with Lower step：
Step 1：Based on the capacity of distribution transform planning that chance constraint is theoretical.
Step 1.1：According to actual conditions, determine that planning region photovoltaic is exerted oneself probabilistic model and load fluctuation probabilistic model；
Step 1.2：According to platform area actual load data, the platform area capacity of distribution transform plan model based on chance constraint is set up.
Step 2：Uncertain distribution transforming type selecting modeling based on life cycle theory.
Step 2.1：Set up the distribution transforming type selecting object function based on life cycle theory；
Step 2.2：Consider that photovoltaic is exerted oneself and the probabilistic distribution transforming operating cost of load fluctuation becomes more meticulous analysis.
Step 3：Probabilistic Load Flow model solution method based on three point estimations.
By above-mentioned steps, completion is counted and photovoltaic is exerted oneself, and the uncertain power distribution network transformer with overall life cycle cost is advised Draw.
The present invention proposes a kind of count and the exert oneself power distribution network transformer of uncertain and overall life cycle cost of photovoltaic is advised The method of drawing, technique effect is as follows：
1)：Compared to conventional electrical distribution transformer constant volume selection method, carry and being exerted oneself while considering photovoltaic generation in the present invention A kind of overall life cycle cost of probabilistic influence and distribution transforming, it is proposed that probabilistic LCC planing methods, effectively keeps away So as not to going out the programme guarded or advanced rashly, the level that becomes more meticulous of planning is improved.
2)：Compared to conventional electrical distribution transformer constant volume selection method, take into full account capacity of distribution transform selection to distribution transforming type selecting The influence of middle cost of investment and operating cost, realizes the unification of distribution transforming constant volume and selection issue, improves planning and becomes more meticulous water It is flat.
Brief description of the drawings
Fig. 1 is the Probabilistic Load Flow model solution flow chart of the invention based on three point estimations.
Fig. 2 is iteration convergence curve map of the embodiment of the present invention.
Fig. 3 is the different forecast model predicated error probability density contrast matched curve figures of the present invention.
Fig. 4 is distribution transforming LCC cost figures under different comprehensive type selecting modes under method 1.
Embodiment
A kind of to count and photovoltaic is exerted oneself the power distribution network transformer planing method of uncertain and overall life cycle cost, its is specific Embodiment is as follows
Step 1：Based on the capacity of distribution transform planning that chance constraint is theoretical：
Step 1.1：According to actual conditions, determine that planning region photovoltaic is exerted oneself probabilistic model and load fluctuation probabilistic model.
Generally the intensity of illumination in certain period of time is approximately described using Beta distributions：
In formula：I is intensity of illumination, IrRepresent maximum intensity of illumination in the period；α and β is two ginsengs that Beta is distributed Number；Γ () is gamma function.
The relation that PVG exerts oneself between intensity of illumination can using approximate representation as：
In formula：PPVGExerted oneself active power size for photovoltaic；For photovoltaic unit rated capacity.
According to the function Distribution Theorem of stochastic variable, the general of photovoltaic unit output is derived in combination with formula (1), formula (2) Rate density function is：
In formula：QPVGThe reactive component exerted oneself for light；It is expressed as photovoltaic power of the assembling unit factor size.
Load fluctuation characteristic is approximately generally described using normal distribution：
In formula：PLFor the active component of load；μP、σPExpectation and standard deviation for load active component；QLFor the nothing of load Work(component；θ is expressed as the power factor angle of load.
Step 1.2：The foundation of platform area capacity of distribution transform plan model based on chance constraint：
The uncertainty exerted oneself after bounding theory of improving the occasion processing photovoltaic access load side, platform area higher level's power network is provided Active-power PNWith photovoltaic active power output PPVGSum is less than active-power P needed for platform areaLProbability should be put no more than given Reliability e：
f{PN+λPPVG≤PL}≤e (5)
In formula：F { } represents the probability that event is set up in { }；λ represents that photovoltaic Firsthand Users are exerted oneself and accounts for the ratio of gross capability Example；Confidence level e artificially gives according to regional real economy Social Development State.
Simultaneous formula (3) and (5) can be obtained：
Active-power P needed for known platform area loadL, the network for the load P under given confidence level is can determine that by above formulaN, set simultaneously The growth of platform area load is all by PNTo undertake, distribution transforming attaching capacity can determine that according to formula (7)：
In formula：Represent the active power that t higher level's power network is provided；δ is average annual load growth rate；T becomes for distribution Depressor plans the maximum service life (MSL) time limit；Represent that power distribution network j-th strip branch road is appeared on the stage area's capacity of distribution transform in life cycle T；η For distribution transforming Economic load rate；NbranchRepresent power distribution network branch road sum；ξjRepresent that j-th strip branch road area's load of appearing on the stage accounts for the distribution institute The ratio of You Tai areas total load, kjAppeared on the stage area's load simultaneity factor for j-th strip branch road.
Step 2：Uncertain distribution transforming type selecting modeling based on life cycle theory：
Step 2.1：The foundation of type selecting object function：
The object function of distribution transforming type selecting plan model is as follows：
minCT=CI+CW+CO+CF+CR (8)
In formula：CTFor distribution transforming LCC costs in cycle T；CIFor distribution transforming initial outlay cost；CWFor the operating cost of distribution transforming；CO To become the repair and maintenance cost of distribution transforming；CFFor the failure cost of distribution transforming；CRFor the retired cost of disposal of distribution transforming.
Step 2.2：Consider that photovoltaic is exerted oneself detailed with each stepped cost in the probabilistic distribution transforming life cycle management of load fluctuation Thin model
1) distribution transforming initial outlay cost CI：
Distribution transforming initial outlay cost mainly includes distribution transforming purchase commodity CGZWith installation and debugging expense CAZ, it is mainly held by transformer Measure the influence of size and model selection：
In formula：Distribution transforming installation and debugging expense is generally the 6.2% of purchase commodity；Represent the power distribution network j-th strip in life cycle T Branch road appears on the stage area with Variant number；G () is the function that initial outlay cost changes with capacity of distribution transform and model, capacity of distribution transform choosing Select bigger, model selection is better, and initial outlay cost is bigger, specific change matches somebody with somebody variable element with reference to related, sees annex.
2), consider that photovoltaic is exerted oneself and the probabilistic distribution transforming operating cost C of load fluctuationWAnalysis：
Distribution transforming operating cost mainly includes distribution transforming operation energy consumption cost CNHWith Daily Round Check cost CCS。
In formula：For distribution transforming t energy consumption cost；For the routing inspection cost that distribution transforming is annual, the annual daily tour of distribution transforming Laboratory Fee is about 50,000 yuan；R is inflation rate, is usually taken to be 3.5%；R is social discount rate, is usually taken to be 10%；P is comprehensive Close electricity price；△StFor distribution transforming t unit running wastages, its detailed mathematical is expressed as follows：
In formula：WithRespectively distribution transforming t units open circuit loss and unit load are lost；WithRespectively match somebody with somebody Become the unloaded active loss of t units and the unloaded reactive loss of unit, M (), N () are represented respectivelyWith with modification Number and volume change function, can refer to related distribution transforming technical parameter directly calculate try to achieve；WithDistribution transforming t is represented respectively Year unit load active loss and unit load reactive loss；F (), S () are represented respectivelyWith with Variant number, appearance Amount, photovoltaic exert oneself size, load fluctuation change function；K is non-work economic equivalent, i.e., every kilowatt reactive power loss is becoming Active power loss caused by depressor, generally takes K=0.1kW/kvar.
Exerted oneself in view of photovoltaic and load fluctuation uncertainty, it is impossible to directly according to nameplate parameter to distribution transforming run load Loss carries out precisive, in consideration of it, present invention research introduces Probabilistic Load Flow model matches somebody with somebody varying load to power distribution network transformer branch Loss is accurately solved, and Probabilistic Load Flow model is as follows：
In formula：PaAnd QaNode a active power and reactive power injection rate are represented respectively；W represents power distribution network nodes；Va And VbNode a and node b voltage magnitude is represented respectively；rzAnd xzRespectively platform area branch road line resistance and reactance；rbAnd xbPoint Wei not distribution transforming resistance and reactance；GabAnd BabThe real and imaginary parts of bus admittance matrix are represented respectively；δabRepresent node a nodes b Phase angle difference.
3), distribution transforming repair and maintenance cost CO：
Distribution transforming repair and maintenance cost mainly includes the overhaul cost C of distribution transforming operation lifecycleDXWith light maintenance expense CXX, Service life is 20 years~25 years under normal circumstances for distribution transforming, and distribution transforming carries out a light maintenance, entered within the 5th year every year after putting into operation Overhaul of row, carried out an overhaul every 10 years afterwards.This cost is unrelated with capacity of distribution transform sizes and types, and it is calculated Formula is as follows：
In formula：CdxRepresent single overhaul cost；CxxSingle light maintenance expense is represented, U represents overhaul number of times；Floor () is represented Decimal is rounded downwards.
4), distribution transforming failure cost CCF：
Distribution transforming failure cost mainly includes distribution transforming trouble hunting expense and breakdown loss expense.This cost and capacity of distribution transform And model selection is relevant.It can be expressed from the next：
In formula：CcfFor year failure cost；KdMultiple is converted for electricity price, K is typically takend=15；tgDuring annual forced outage Between, tg=ε × 24；ψiRepresent t distribution transforming Rate of average load；ε is distribution transforming year accident rate, and better with Variant number, accident rate is got over It is low； CjxFor trouble hunting expense, the 3% of general taking equipment purchase commodity；ε is distribution transforming year fault rate.
5), the retired cost of disposal C of distribution transformingCD：
The retired cost of disposal of distribution transforming mainly includes distribution transforming scrap cost and remanent value of equipment takes.Its remanent value of equipment takes with transfiguration Amount and model positive correlation.It is expressed as follows：
In formula：CbfFor equipment scrapping cost, the 32% of general taking equipment installation fee；CczTake for remanent value of equipment, generally purchase Put the 5% of expense.
Step 2.3：Constraints：
1), node voltage and branch current constraint
In formula：ViminAnd VmaxThe minimum value and maximum of respectively i-th node voltage amplitude；IjWithFor j-th strip branch The actual value and maximum permissible value of road electric current；NbusFor power distribution network node total number.
2), DG access nodes installed capacity is constrained：
In formula：Si.DGFor i-th of node DG access node installed capacity；Allow for i-th of node DG on installed capacity Limit.
3), constrained with Variant number and capacity discreteness：
If set A is distribution transforming design capacity grade, set B matches somebody with somebody Variant number to be to be selected, there is following constraints：
Step 3：Probabilistic Load Flow model solution method based on three point estimations：
If platform area distribution transforming unit load loss △ SFExerted oneself with photovoltaic as follows with the functional relation of platform area load：
In formula：△SWThe branch road loss where the distribution transforming of platform area；WithRepresent that i-th of node photovoltaic is exerted oneself and load respectively Size；ζ represents the ratio of branch impedance where being accounted for impedance.
Make unit load that △ S are lostFRepresented with stochastic variable Y, photovoltaic is exerted oneself to be represented with platform area load with stochastic variable X, Formula (12) is reduced to：
Y=ζ × f (X)=ζ × f (X1,X2…,Xn) (20)
In formula：N represents stochastic variable X sum.
It is assumed that the X of each stochastic variablekThe expectation of (k=1,2,3 ... n), standard deviation are respectively μkAnd σk, and choose with Machine variable XkExpectation μkAnd its each a little totally three sampled values in the field of left and right, it is denoted as xk.i(i=1,2,3), its expression formula is such as Under：
xk.i=μk+ξk.iσk(i=1,2,3) (21)
In formula：ξk.iFor the position parameter of k-th of stochastic variable ith sample value.ξk.iIt is represented by：
In formula：λk.3It is expressed as stochastic variable XkThe coefficient of skewness, its absolute value is bigger, then illustrates stochastic variable XkDistribution Just too distribution is deviateing larger with standard；λk.4To weigh stochastic variable XkSteep of the probability density near desired value Coefficient of kurtosis, its absolute value is smaller, and the value of stochastic variable is more concentrated near desired value, λk.4=0, then illustrate stochastic variable XkDistribution have with standardized normal distribution as steepness.XkCoefficient of skewness λk.3With coefficient of kurtosis λk.4Expression formula point It is not：
In formula：E[(Xk-μk)3]、E[(Xk-μk)4] it is stochastic variable XkThree ranks, fourth central square.
Sampled value xk.i(i=1,2,3) the corresponding weight coefficient p of differencek.iFor：
From formula (23)~formula (24), three point estimations are substantially the preceding Fourth-order moments according to input stochastic variable Determine specimen sample value xk.i(i=1,2,3), and using qualitative functional relationship is sampled to each really as shown in formula (25) Value being determined property evaluation.
Yk.i=ζ × f (μ1..., μk-1, xk.i,μk+1..., μn) i=1,2,3 (25)
It is worth noting that, because each stochastic variable contains its desired value μ when samplingk, so wherein It is repetition to have n certainty evaluation, so need to only carry out 2n+1 evaluation to Y.According to above-mentioned conclusion, with reference to sampling The corresponding weight coefficient of point, Y z ranks moment of the orign can be expressed as：
After each rank square for obtaining output variable Y, it is possible to obtain it and expect μYAnd standard deviation sigmaY, Ji Tai areas distribution transforming unit bear Load-loss is expected and variance.
Detailed solution calculation flow chart is as shown in Figure 1.
Embodiment：
The present invention verifies distribution transforming choosing proposed by the invention using amended IEEE33 power distribution networks node system as example The validity and correctness of type constant volume method.L-G simulation test programming realization under Matlab environment.
1), the IEEE33 node systems of modification：
Assuming that a region increases platform area A, B, C, D, corresponding load node 34,35,36 and 37, if each newly-increased platform area load newly A reference value is respectively 50kVA, 70kVA, 90kVA and 110kVA and equal Normal Distribution (is desired for corresponding node load benchmark Value, variance is that 1), the impedance of Ge Tai areas distribution transforming is converted in corresponding branch impedance parameter respectively.If node 5,14,21 and 37 The photovoltaic unit for having 100kW, 150kW, 200kW and 250kW respectively is accessed, and is taken as 0.85, each photovoltaic unit active power output is obeyed Parameter, Beta distribution.Amended IEEE33 power distribution networks node system is as shown in Fig. 1.Voltage class is 12.66kV, benchmark Power is 100MVA, and interconnection switch disconnects.
If the average annual load growth rate in the region is 0.05, novel transformer model to be chosen has SCB10 series, SCB11 systems Row and the serial dry type 10kV transformers of SCB13, transformer detailed technology parameter are shown in annex, and design distribution transforming life cycle is 20 years, Now need to carry out integrating distribution transforming constant volume for platform area A, B, C, D and type selecting is planned.
The IEEE33 node power distributions net such as accompanying drawing 2 of modification.
2), Simulation Example result and analysis：
The correctness and validity of the inventive method are verified, three kinds of methods is utilized respectively and distribution transforming rule is carried out to example of the present invention Draw decision-making：
Method 1：Meter and photovoltaic proposed by the invention is exerted oneself the distribution transforming planning side of uncertain and overall life cycle cost Method, confidence level takes 0.01, and load average growth rate per annum is taken as 0.05.
Method 2：Consider the certainty distribution transforming planing method of distribution transforming operating condition and overall life cycle cost.Now, ignore The uncertainty influence that DG exerts oneself with load fluctuation, therefore when being chosen for capacity of distribution transform, confidence level is taken as 0；Carrying out distribution transforming During type selecting, photovoltaic is exerted oneself and increased newly load point parameter and takes desired value to carry out conventional certainty trend according to respective probability density function Calculate, other specification is set with method 1.
Method 3：Consider the distribution transforming Fuzzy Programming of overall life cycle cost.Now, by distribution transforming operating condition obfuscation Processing, ignores DG and exerts oneself and load fluctuation, when being chosen for capacity of distribution transform, confidence level is taken as 0；When carrying out distribution transforming type selecting, Without reference to calculation of tidal current, distribution transforming LCC is estimated roughly only in accordance with distribution transforming nameplate parameter；Ge Tai areas are not considered simultaneously Influence of the constant volume type selecting result to trend, the independent constant volume of Ge Tai areas progress and type selecting.
①：The simulation result of method 1 and analysis：
Using institute's extracting method of the present invention, the Ge Tai areas capacity of distribution transform of A, B, C, D tetra- is solved in example under different confidential intervals Situation of change as shown in Figure 3.
Dispatched from the factory design capacity in view of SCB10 series, SCB11 series and the serial platform area's distribution transformings of SCB13 under actual conditions, It is as shown in table 1 that different confidential interval Xia Getai areas capacity of distribution transform selected results can be provided according to accompanying drawing 3.
Distribution transforming constant volume result under the Ge Tai areas of table 1 difference confidence
From accompanying drawing 3, table 1, distribution transforming planned capacity is negatively correlated with fiducial probability, and its reason is in Uncertain environments Under, confidence level value is lower, it is meant that taken risks during systems organization smaller, thus the capacity of distribution transform chosen is bigger, by This visible the inventive method can realize the measurement that becomes more meticulous to system operation risk in capacity of distribution transform selection course；And match somebody with somebody Varying capacity selection can also be influenceed by system loading, and system loading is bigger, and distribution transforming planned capacity is bigger.
Assuming that confidence level value 0.01, then can determine that put into effect area's A, B, C, D capacity of distribution transform is set to respectively according to table 1 250kVA、315kVA、400kVA、500kVA.Based on this, can be with using distribution transforming type selecting planing method (method 1) of the present invention Obtain platform area A, B, C, D LCC totle drilling costs corresponding under 81 kinds of different synthesis distribution transforming type selecting modes as shown in Figure 4.
By Fig. 4 it can be found that：The distribution transforming of 42nd Zhong Tai areas integrates type selecting mode (platform area A：SCB11, platform area B：SCB11, platform Area C：SCB11, platform area D：SCB13 LCC totle drilling costs that) will be following 20 years Shi Tai areas A, B, C, D reach minimum, now comprehensive Type selecting result is closed to be optimal.
, for the influence of distribution transforming type selecting result, according to the method described above, confidence level value area is made for further research confidence level Between be 0.01~0.2, step-length takes 0.01, under the same conditions to four Ge Tai areas carry out integrate distribution transforming constant volume and type selecting, obtain not Distribution transforming constant volume is integrated with the Ge Tai areas of A, B, C, D under confidential interval tetra- and type selecting result is as shown in table 2：
Distribution transforming under the different confidence levels of table 2 integrates constant volume type selecting result
By table 2 it can be found that the Capacity Selection and model selection result of difference confidence level Xia Tai area's distribution transformings constantly occur Change, while feature that gradually increase in first drop afterwards rise of the optimal LCC costs with confidence level.Confidential interval [0.01~ 0.06] in, four Ge Tai areas distribution transforming LCC totle drilling costs reduce as confidence level integrally increases；And in confidence level [0.07~0.2] Interval in, LCC costs then increase as confidence level increases, and growth rate is more and more faster.In example of the present invention, when When confidence level is taken as 0.07, distribution transforming LCC costs reach minimum, and the distribution transforming of Ge Tai areas integrates constant volume and type selecting is optimal.
The main cause for this phenomenon occur is：In confidential interval [0.01~0.06], capacity of distribution transform is selected relatively Greatly, model selection is relatively preferable, and distribution transforming running wastage is relatively low, with the increase of risk, and distribution transforming is saved on capacity and model selection Cost of investment about is more more than the operating cost of growth；And in the interval of confidence level [0.07~0.2], with capacity of distribution transform Selection is less and less, and model is selected worse and worse, and the impedance of distribution transforming in itself gradually increases, and growth rate is increasing, distribution transforming Running wastage is larger, causes the cost of investment saved to be difficult to the operating cost for balancing out distribution transforming sharp increase.
2. mode 2, the simulation result of mode 3 and comparative analysis：
Under the same terms, the Ge Tai areas of A, B, C, D tetra- carry out distribution transforming synthesis in 3 pairs of examples of the present invention of Land use systems 2 and mode Constant volume and type selecting, and contrasted with method 1, as a result as shown in table 3.
Distribution transforming constant volume type selecting result under under the different planing methods of table 3
It is can be found that by table 3：1. under method 2, platform area B and platform area C adds 85kVA and 100kVA respectively compared with method 1, It is more excellent with Variant number that platform area B and platform area D is selected, and LCC totle drilling costs add 6.1647 ten thousand yuan.Its main cause is：Side Distribution transforming planning confidence level under method 2 is taken as 0, it is meant that any risk is not risked in the constant volume type selecting of distribution transforming, so as to cause to match somebody with somebody Varying capacity chooses overall larger compared with method 1 time, and model selection is overall preferable, and then influences distribution transforming initial outlay cost also therewith Increase, while in the whole life cycle of distribution transforming, advantage of the programme in operating cost under method 2 can not make up it Inferior position in initial outlay, causes LCC totle drilling costs bigger compared with method 1.2. the Xia Getai areas capacity of distribution transform program results of method 3 It is identical with method 2, but in distribution transforming type selecting, platform area A, B, C selection are more excellent, and LCC totle drilling costs add 21.2029 ten thousand yuan. Its main cause is：In capacity of distribution transform selection, being determined property is determined all in the case where confidence level is 0 for method 3 and method 2 Content regulation is drawn, and causes capacity selection result the same, and in distribution transforming type selecting mode, method 3 does not consider the actual trend operation of power distribution network As a result, LCC accounting directly is carried out using the load loss demarcated on distribution transforming nameplate, frequently can lead to adjust result than actual Situation is bigger, so that the operating cost virtual height calculated, and then cause distribution transforming type selecting more to be guarded compared with method 2.
In summary, because the inventive method is in the same of uncertain and load fluctuation progress precisive of being exerted oneself to photovoltaic When, the influence that capacity of distribution transform is selected its model has also been taken into full account, thus the programme drawn is compared with conventional method Speech, with higher economy, so as to effectively improve the level that becomes more meticulous of distribution network planning.
The present invention is illustrated according to the preferred embodiment, but above-described embodiment does not limit the present invention in any form, all The technical scheme obtained using the form of equivalent substitution or equivalent transformation, in the range of all falling within technical solution of the present invention.

Claims (1)

  1. A kind of power distribution network transformer planing method of uncertain and overall life cycle cost 1. meter and photovoltaic are exerted oneself, its feature exists In comprising the following steps：
    Step 1：Based on the capacity of distribution transform planning that chance constraint is theoretical：
    Step 1.1：Determine that planning region photovoltaic is exerted oneself probabilistic model and load fluctuation probabilistic model, generally by certain period of time Intensity of illumination approximately described using Beta distributions：
    <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>I</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>&amp;alpha;</mi> <mo>+</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msup> <mrow> <mo>(</mo> <mfrac> <mi>I</mi> <msub> <mi>I</mi> <mi>r</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>&amp;alpha;</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mi>I</mi> <msub> <mi>I</mi> <mi>r</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>&amp;beta;</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    In formula：I is intensity of illumination, IrRepresent maximum intensity of illumination in the period；α and β is two parameters that Beta is distributed；Γ () is gamma function；
    The relation that PVG exerts oneself between intensity of illumination can using approximate representation as：
    <mrow> <msub> <mi>P</mi> <mrow> <mi>P</mi> <mi>V</mi> <mi>G</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>P</mi> <mi>V</mi> <mi>G</mi> </mrow> <mi>r</mi> </msubsup> <mfrac> <mi>I</mi> <msub> <mi>I</mi> <mi>r</mi> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <mi>I</mi> <mo>&amp;le;</mo> <msub> <mi>I</mi> <mi>r</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>P</mi> <mrow> <mi>P</mi> <mi>V</mi> <mi>G</mi> </mrow> <mi>r</mi> </msubsup> </mtd> <mtd> <mrow> <mi>I</mi> <mo>&gt;</mo> <msub> <mi>I</mi> <mi>r</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    In formula：PPVGExerted oneself active power size for photovoltaic；For photovoltaic unit rated capacity；
    According to the function Distribution Theorem of stochastic variable, derive that the probability of photovoltaic unit output is close in combination with formula (1), formula (2) Spending function is：
    In formula：QPVGThe reactive component exerted oneself for light；It is expressed as photovoltaic power of the assembling unit factor size；
    Load fluctuation characteristic is approximately described using normal distribution：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>q</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;&amp;sigma;</mi> <mi>P</mi> </msub> </mrow> </msqrt> </mfrac> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>&amp;mu;</mi> <mi>P</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <msup> <msub> <mi>&amp;sigma;</mi> <mi>P</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mi>L</mi> </msub> <mo>=</mo> <msub> <mi>P</mi> <mi>L</mi> </msub> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>&amp;theta;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    In formula：PLFor the active component of load；μP、σPExpectation and standard deviation for load active component；QLFor idle point of load Amount；θ is expressed as the power factor angle of load；
    Step 1.2：The foundation of platform area capacity of distribution transform plan model based on chance constraint, bounding theory of improving the occasion processing photovoltaic The uncertainty exerted oneself after access load side, the active-power P that platform area higher level's power network is providedNWith photovoltaic active power output PPVGIt With less than active-power P needed for platform areaLProbability should be no more than given confidence level e：
    f{PN+λPPVG≤PL}≤e (5)
    In formula：F { } represents the probability that event is set up in { }；λ represents that photovoltaic Firsthand Users are exerted oneself and accounts for the ratio of gross capability；Put Reliability e artificially gives according to regional real economy Social Development State；
    Simultaneous formula (3) and (5) can be obtained：
    <mrow> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mfrac> <mrow> <msub> <mi>P</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> </mrow> <mi>&amp;lambda;</mi> </mfrac> </msubsup> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>P</mi> <mi>V</mi> <mi>G</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>d</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>P</mi> <mi>V</mi> <mi>G</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;le;</mo> <mi>e</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    Active-power P needed for known platform area loadL, the network for the load P under given confidence level is can determine that by above formulaN, while setting platform area The growth of load is all by PNTo undertake, distribution transforming attaching capacity can determine that according to formula (7)：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mi>N</mi> <mi>t</mi> </msubsup> <mo>=</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mi>t</mi> </msup> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>...</mo> <mi>T</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>S</mi> <mi>T</mi> <mi>j</mi> </msubsup> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>P</mi> <mi>N</mi> <mi>i</mi> </msubsup> <mo>/</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;theta;</mi> </mrow> <mrow> <msqrt> <mn>3</mn> </msqrt> <mi>&amp;eta;</mi> </mrow> </mfrac> <msub> <mi>&amp;xi;</mi> <mi>j</mi> </msub> <msub> <mi>k</mi> <mi>j</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>N</mi> <mrow> <mi>b</mi> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>c</mi> <mi>h</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    In formula：Represent the active power that t higher level's power network is provided；δ is average annual load growth rate；T is distribution transformer Plan the maximum service life (MSL) time limit；Represent that power distribution network j-th strip branch road is appeared on the stage area's capacity of distribution transform in life cycle T；η is distribution transforming Economic load rate；NbranchRepresent power distribution network branch road sum；ξjRepresent that j-th strip branch road area's load of appearing on the stage accounts for all areas of the distribution The ratio of total load, kjAppeared on the stage area's load simultaneity factor for j-th strip branch road；
    Step 2：Uncertain distribution transforming type selecting modeling based on life cycle theory：
    Step 2.1：The foundation of type selecting object function, the object function of distribution transforming type selecting plan model is as follows：
    minCT=CI+CW+CO+CF+CR (8)
    In formula：CTFor distribution transforming LCC costs in cycle T；CIFor distribution transforming initial outlay cost；CWFor the operating cost of distribution transforming；COTo become The repair and maintenance cost of distribution transforming；CFFor the failure cost of distribution transforming；CRFor the retired cost of disposal of distribution transforming；
    Step 2.2：Consider that photovoltaic is exerted oneself and the probabilistic distribution transforming operating cost of load fluctuation becomes more meticulous analysis；
    Distribution transforming operating cost mainly includes distribution transforming operation energy consumption cost CNHWith Daily Round Check cost CCS,
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mi>W</mi> </msub> <mo>=</mo> <msub> <mi>C</mi> <mrow> <mi>N</mi> <mi>H</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>C</mi> <mi>S</mi> </mrow> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>T</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <mo>(</mo> <msubsup> <mi>C</mi> <mrow> <mi>n</mi> <mi>h</mi> </mrow> <mi>t</mi> </msubsup> <mo>+</mo> <msubsup> <mi>C</mi> <mrow> <mi>c</mi> <mi>s</mi> </mrow> <mi>t</mi> </msubsup> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>r</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>R</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>t</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>C</mi> <mrow> <mi>n</mi> <mi>h</mi> </mrow> <mi>t</mi> </msubsup> <mo>=</mo> <msup> <mi>&amp;Delta;S</mi> <mi>t</mi> </msup> <mo>&amp;times;</mo> <mn>8760</mn> <mo>&amp;times;</mo> <mi>p</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    In formula：For distribution transforming t energy consumption cost；For the routing inspection cost that distribution transforming is annual, r is inflation rate, and R is society Discount rate, p is total rate of electricity；△StFor distribution transforming t unit running wastages, its detailed mathematical is expressed as follows：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mi>&amp;Delta;S</mi> <mi>t</mi> </msup> <mo>=</mo> <msubsup> <mi>&amp;Delta;S</mi> <mi>K</mi> <mi>t</mi> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;Delta;S</mi> <mi>F</mi> <mi>t</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;S</mi> <mi>K</mi> <mi>t</mi> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mi>K</mi> <mi>t</mi> </msubsup> <mo>+</mo> <mi>K</mi> <mo>&amp;times;</mo> <msubsup> <mi>Q</mi> <mi>K</mi> <mi>t</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mi>M</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>T</mi> <mi>j</mi> </msubsup> <mo>,</mo> <msubsup> <mi>S</mi> <mi>T</mi> <mi>j</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <mi>K</mi> <mo>&amp;times;</mo> <mi>N</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>T</mi> <mi>j</mi> </msubsup> <mo>,</mo> <msubsup> <mi>S</mi> <mi>T</mi> <mi>j</mi> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;S</mi> <mi>F</mi> <mi>t</mi> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mi>F</mi> <mi>t</mi> </msubsup> <mo>+</mo> <mi>K</mi> <mo>&amp;times;</mo> <msubsup> <mi>Q</mi> <mi>F</mi> <mi>t</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mi>F</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>T</mi> <mi>j</mi> </msubsup> <mo>,</mo> <msubsup> <mi>S</mi> <mi>T</mi> <mi>j</mi> </msubsup> <mo>,</mo> <msubsup> <mi>P</mi> <mrow> <mi>P</mi> <mi>V</mi> <mi>G</mi> </mrow> <mi>j</mi> </msubsup> <mo>,</mo> <msubsup> <mi>P</mi> <mi>L</mi> <mi>j</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <mi>K</mi> <mo>&amp;times;</mo> <mi>S</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>T</mi> <mi>j</mi> </msubsup> <mo>,</mo> <msubsup> <mi>S</mi> <mi>T</mi> <mi>j</mi> </msubsup> <mo>,</mo> <msubsup> <mi>P</mi> <mrow> <mi>P</mi> <mi>V</mi> <mi>G</mi> </mrow> <mi>j</mi> </msubsup> <mo>,</mo> <msubsup> <mi>P</mi> <mi>L</mi> <mi>j</mi> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    In formula：WithRespectively distribution transforming t units open circuit loss and unit load are lost；WithRespectively distribution transforming t The year unloaded active loss of unit and the unloaded reactive loss of unit, M (), N () are represented respectivelyWith with Variant number and appearance The function of change is measured, the directly calculating of related distribution transforming technical parameter is can refer to and tries to achieve；WithRepresent that distribution transforming t units are born respectively Carry active loss and unit load reactive loss；F (), S () are represented respectivelyGo out with Variant number, capacity, photovoltaic Power size, the function of load fluctuation change；K is non-work economic equivalent, i.e., every kilowatt reactive power loss causes in transformer Active power loss；
    Introduce Probabilistic Load Flow model accurately to solve power distribution network transformer branch distribution transforming load loss, Probabilistic Load Flow model is such as Shown in lower：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>a</mi> </msub> <mo>=</mo> <msub> <mi>V</mi> <mi>a</mi> </msub> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>b</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>w</mi> </munderover> <msub> <mi>V</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <msub> <mi>cos&amp;delta;</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <msub> <mi>sin&amp;delta;</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mi>a</mi> </msub> <mo>=</mo> <msub> <mi>V</mi> <mi>a</mi> </msub> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>b</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>w</mi> </munderover> <msub> <mi>V</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <msub> <mi>sin&amp;delta;</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <msub> <mi>cos&amp;delta;</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>a</mi> </msub> <mo>=</mo> <msub> <mi>P</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>P</mi> <mi>V</mi> <mi>G</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mi>a</mi> </msub> <mo>=</mo> <msub> <mi>Q</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>Q</mi> <mrow> <mi>P</mi> <mi>V</mi> <mi>G</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>G</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>r</mi> <mi>z</mi> </msub> <mo>+</mo> <msub> <mi>r</mi> <mi>b</mi> </msub> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mi>z</mi> </msub> <mo>-</mo> <msub> <mi>r</mi> <mi>b</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>z</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>b</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>B</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mi>z</mi> </msub> <mo>+</mo> <msub> <mi>x</mi> <mi>b</mi> </msub> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mi>z</mi> </msub> <mo>-</mo> <msub> <mi>r</mi> <mi>b</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>z</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>b</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    In formula：PaAnd QaNode a active power and reactive power injection rate are represented respectively；W represents power distribution network nodes；VaAnd VbPoint Not Biao Shi node a and node b voltage magnitude；rzAnd xzRespectively platform area branch road line resistance and reactance；rbAnd xbRespectively match somebody with somebody Become resistance and reactance；GabAnd BabThe real and imaginary parts of bus admittance matrix are represented respectively；δabRepresent node a nodes b phase angle Difference；
    Step 2.3：Constraints：
    1), node voltage and branch current constraint：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>V</mi> <mrow> <mi>i</mi> <mi>min</mi> </mrow> </msub> <mo>&amp;le;</mo> <msub> <mi>V</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mi>j</mi> </msub> <mo>&amp;le;</mo> <msubsup> <mi>I</mi> <mi>j</mi> <mi>max</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>N</mi> <mrow> <mi>b</mi> <mi>u</mi> <mi>s</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    In formula：ViminAnd VmaxThe minimum value and maximum of respectively i-th node voltage amplitude；IjWithFor j-th strip branch road electricity The actual value and maximum permissible value of stream；NbusFor power distribution network node total number；
    2), DG access nodes installed capacity is constrained：
    <mrow> <msub> <mi>S</mi> <mrow> <mi>i</mi> <mo>.</mo> <mi>D</mi> <mi>G</mi> </mrow> </msub> <mo>&amp;le;</mo> <msubsup> <mi>S</mi> <mrow> <mi>i</mi> <mo>.</mo> <mi>D</mi> <mi>G</mi> </mrow> <mi>max</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
    In formula：Si.DGFor i-th of node DG access node installed capacity；Allow the installed capacity upper limit for i-th of node DG；
    3), constrained with Variant number and capacity discreteness：
    If set A is distribution transforming design capacity grade, set B matches somebody with somebody Variant number to be to be selected, there is following constraints：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>S</mi> <mi>T</mi> <mi>j</mi> </msubsup> <mo>&amp;Element;</mo> <mi>A</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>X</mi> <mi>T</mi> <mi>j</mi> </msubsup> <mo>&amp;Element;</mo> <mi>B</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
    Step 3：Probabilistic Load Flow model solution method based on three point estimations：
    If platform area distribution transforming unit load loss △ SFExerted oneself with photovoltaic as follows with the functional relation of platform area load：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;S</mi> <mi>W</mi> </msub> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <msubsup> <mi>P</mi> <mrow> <mi>P</mi> <mi>V</mi> <mi>G</mi> </mrow> <mi>i</mi> </msubsup> <mo>,</mo> <msubsup> <mi>P</mi> <mi>L</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;S</mi> <mi>F</mi> </msub> <mo>=</mo> <mi>&amp;zeta;</mi> <mo>&amp;times;</mo> <msub> <mi>&amp;Delta;S</mi> <mi>W</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
    In formula：△SWThe branch road loss where the distribution transforming of platform area；WithRepresent that i-th of node photovoltaic is exerted oneself respectively big with load It is small；ζ represents the ratio of branch impedance where being accounted for impedance；
    Make unit load that △ S are lostFRepresented with stochastic variable Y, photovoltaic is exerted oneself to be represented with platform area load with stochastic variable X, formula (12) It is reduced to：
    Y=ζ × f (X)=ζ × f (X1,X2…,Xn) (16)
    In formula：N represents stochastic variable X sum；
    The step of according to traditional three point estimations, which can solve, obtains platform area distribution transforming unit load loss expectation and variance：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>E</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;Delta;S</mi> <mi>F</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;mu;</mi> <mi>Y</mi> </msub> <mo>=</mo> <mi>E</mi> <mrow> <mo>(</mo> <mi>Y</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>D</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;Delta;S</mi> <mi>F</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;sigma;</mi> <mi>Y</mi> </msub> <mo>=</mo> <msqrt> <mrow> <mi>E</mi> <mrow> <mo>(</mo> <msup> <mi>Y</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>E</mi> <mo>(</mo> <mi>Y</mi> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>
    In formula：μYAnd σYExpectation and standard deviation for output variable Y；
    By above-mentioned steps, completion is counted and photovoltaic is exerted oneself, and the uncertain power distribution network transformer with overall life cycle cost is planned.
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