CN112310959A - Power distribution network low voltage comprehensive treatment method considering uncertainty factors and correlation thereof - Google Patents

Power distribution network low voltage comprehensive treatment method considering uncertainty factors and correlation thereof Download PDF

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CN112310959A
CN112310959A CN202011092716.0A CN202011092716A CN112310959A CN 112310959 A CN112310959 A CN 112310959A CN 202011092716 A CN202011092716 A CN 202011092716A CN 112310959 A CN112310959 A CN 112310959A
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formula
cost
correlation
value
model
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姚俊伟
代璐
杨星磊
邓玲
田立勃
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Yichang Power Supply Co of State Grid Hubei Electric Power Co Ltd
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Yichang Power Supply Co of State Grid Hubei Electric Power Co Ltd
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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
    • H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand
    • 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
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/466—Scheduling the operation of the generators, e.g. connecting or disconnecting generators to meet a given demand
    • 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]
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/22—The renewable source being solar energy
    • H02J2300/24—The renewable source being solar energy of photovoltaic origin
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/40—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation wherein a plurality of decentralised, dispersed or local energy generation technologies are operated simultaneously
    • 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
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B10/00—Integration of renewable energy sources in buildings
    • Y02B10/10—Photovoltaic [PV]
    • 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
    • Y02E10/50—Photovoltaic [PV] energy
    • Y02E10/56—Power conversion systems, e.g. maximum power point trackers
    • 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
    • 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
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation

Abstract

The comprehensive low-voltage treatment method for the power distribution network, which takes uncertainty factors and the relevance thereof into consideration, takes line transformation, reactive compensation, transformer voltage regulation and newly-built transformer substations as decision variables, and constructs a comprehensive low-voltage treatment model based on the life cycle cost; considering load fluctuation, uncertainty of wind power output and correlation of the uncertainty, and constructing a low-voltage comprehensive treatment robust planning model based on an information gap decision theory IGDT; modeling uncertainty of load and wind power output; establishing a robust model by an IGDT method, converting random samples with correlation into mutually independent random samples based on a Cholesky decomposition method, and determining a worst scenario based on the random samples; and solving the model by using an order optimization algorithm. The decision scheme obtained by the method has better robustness, reduces the whole life cycle cost of the system, can resist larger load fluctuation and wind power output fluctuation, and improves the economy of low-voltage comprehensive treatment and the fine planning level of planning.

Description

Power distribution network low voltage comprehensive treatment method considering uncertainty factors and correlation thereof
Technical Field
The invention relates to the technical field of power system planning research, in particular to a comprehensive treatment method for low voltage of a power distribution network, which considers uncertainty factors and the relativity of the uncertainty factors.
Background
With the rapid development of economy and the increasing improvement of the living standard of people, on one hand, the low voltage phenomenon at the tail end of a line is frequent due to the rapid increase of load. On the other hand, because the wind power output has stronger intermittency, volatility and randomness, the large-scale wind power grid connection also brings new uncertain factors for the power system. Therefore, how to formulate a reasonable low-voltage problem planning scheme under an uncertain environment has important theoretical and practical significance for improving the electricity utilization quality of residents and improving the operation economy of the power distribution network.
In the process of researching the power distribution network planning, the method for improving the accuracy of the power distribution network planning by considering the uncertainty of load, wind power output, photovoltaic output or other variables comprises an Information Gap Decision Theory (IGDT) method, and can obtain a Decision scheme of the maximum allowable fluctuation range of uncertain parameters when the result is not worse than the expected target, so that the overall coordination of the economy and the robustness of the Decision scheme is realized, and the method is more economical than a robust optimization method. However, the existing research on uncertain factors focuses on the research on the problems of power loss load recovery, scheduling, power transmission network planning and the like under the power distribution network fault, and the problem of low-voltage comprehensive treatment of the power distribution network is not reported yet. Against this problem, it still has the following problems:
1: the conventional IGDT method only considers a single uncertainty factor. In fact, in the problem of low-voltage comprehensive treatment, various uncertain factors including wind power, photovoltaic output, load prediction errors and the like often exist, and the uncertain factors are not mutually independent and have a certain degree of probabilistic correlation. This means that the worst case scenarios of these uncertainty factors are generally difficult to come together. However, according to the conventional IGDT concept, these uncertainty factors with correlation are treated as independent uncertainty factors, and the worst scenario of the uncertainty factors is simply linearly superimposed to form the final worst scenario for planning, so that the final result of the planning is inevitably too conservative.
2: at present, the planning method based on IGDT mostly simply considers the investment and operation costs of planning, however, the costs of the planning method in the whole life cycle of the equipment include not only the investment and operation costs, but also various costs such as failure and retirement. Meanwhile, the capital and time values of these costs are also a factor to be considered, so that it is difficult to ensure the economy of the planning scheme by only using the IGDT planning method based on the investment and operation costs.
Therefore, the research of the low-voltage comprehensive treatment method comprehensively considering the load fluctuation and wind power output uncertainty factors and the correlation thereof has important significance for planning the power distribution network of the power system.
Disclosure of Invention
The invention provides a power distribution network low-voltage comprehensive treatment method considering uncertainty factors and correlation thereof, which considers life cycle cost factors and various uncertainty factors such as wind power, photovoltaic output, load prediction errors and the like and carries out modeling calculation on the power distribution network low-voltage comprehensive treatment. The decision scheme obtained by the method has better robustness, the whole life cycle cost of the system is reduced, larger load fluctuation and wind power output fluctuation can be resisted, and the economy of low-voltage comprehensive treatment and the fine planning level of planning are improved.
The technical scheme adopted by the invention is as follows:
the comprehensive treatment method for the low voltage of the power distribution network considering the uncertainty factors and the correlation thereof comprises the following steps:
step 1: constructing a low-voltage comprehensive treatment model based on the life cycle cost by taking line transformation, reactive compensation, transformer voltage regulation and newly-built transformer substations as decision variables;
step 2: considering load fluctuation, uncertainty of wind power output and correlation of the uncertainty, and constructing a low-voltage comprehensive treatment robust planning model based on an information gap decision theory IGDT;
and step 3: modeling uncertainty of load and wind power output;
and 4, step 4: establishing a robust model by an IGDT method, converting random samples with correlation into mutually independent random samples based on a Cholesky decomposition method, and determining a worst scenario based on the random samples;
and 5: and solving the robust model established by the IGDT by using an order optimization algorithm.
The invention relates to a power distribution network low voltage comprehensive treatment method considering uncertainty factors and relativity thereof, which has the following beneficial effects: (I): if the decision is made on the low-voltage comprehensive treatment with the aim of lowest initial investment cost only from the perspective of investment cost, although the initial investment cost of the target power grid can be reduced to a certain extent, the initial investment cost is at the expense of loss reduction benefit of the target power grid. In contrast, the invention comprehensively considers the cost factor of the whole life cycle in the planning process, can effectively ensure the refinement level of the planning, and improves the economical efficiency of the low-voltage comprehensive treatment.
(II): if the correlation between the load and the wind power processing is not considered, the maximum and minimum values are directly selected, the operation cost generated by the worst scene obtained through simple linear superposition is high, and the economy of the planning scheme is influenced. And the correlation between the load and the wind power output is fully considered, and the extreme scenes which cannot appear can be eliminated in the decision process, so that the planning reduces the whole life cycle cost while ensuring the system robustness.
(III): compared with the traditional method, the decision scheme calculated by the low-voltage comprehensive treatment method considering the life cycle cost and the correlation has better robustness and can resist larger load fluctuation and wind power output fluctuation.
Drawings
FIG. 1(a) is a Flat type OPC graph;
FIG. 1(b) is a U-shaped OPC plot;
FIG. 1(c) is a Neutral type OPC graph;
FIG. 1(d) is a Bell-type OPC plot;
fig. 1(e) is a Steep-type OPC graph.
FIG. 2 is a flow diagram of a solution based on order optimization.
Fig. 3 is a diagram of an IEEE 33 node power distribution system.
FIG. 4 is an OPC graph resulting from a sequence optimization algorithm.
Fig. 5 is a diagram of a preferred embodiment network topology.
Detailed Description
The comprehensive treatment method for the low voltage of the power distribution network considering the uncertainty factors and the correlation thereof comprises the following steps:
step 1: constructing a low-voltage comprehensive treatment model based on the life cycle cost by taking line transformation, reactive compensation, transformer voltage regulation and newly-built transformer substations as decision variables;
step 2: considering load fluctuation, uncertainty of wind power output and correlation of the uncertainty, and constructing a low-voltage comprehensive treatment robust planning model based on an information gap decision theory IGDT;
and step 3: modeling uncertainty of load and wind power output;
and 4, step 4: establishing a robust model by an IGDT method, converting random samples with correlation into mutually independent random samples based on a Cholesky decomposition method, and determining a worst scenario based on the random samples;
and 5: and solving the robust model established by the IGDT by using an order optimization algorithm.
In the step 1, the low-voltage comprehensive treatment model is constructed as follows:
1): constructing an objective function as shown in formula (1):
Figure 100002_3
in the formula: x is a line reconstruction decision variable, and when x is 1, the line is replaced, and when x is 0, the line is not replaced;
y is a single group of reactive compensationA capacitance decision variable of the compensation capacitor; z is a decision variable of a voltage regulating gear of the transformer; w is a number decision variable of the newly-built transformer substation;
Figure BDA0002722688090000032
is the predicted value of the load in the t-th year,
Figure BDA0002722688090000033
the predicted values of the wind power output in the t year are one of the parameters of the cost, and the determined values need to be explained in the following way that the parameters of the indexes not only comprise
Figure BDA0002722688090000034
And
Figure BDA0002722688090000035
but for the sake of embodiment
Figure BDA0002722688090000036
And
Figure BDA0002722688090000037
the influence on the model is separately reflected in the model. Due to the fact that
Figure BDA0002722688090000038
And
Figure BDA0002722688090000039
is a definite value, so at this time, CcThe life cycle cost of the target power grid under the deterministic environment;
Figure BDA00027226880900000310
initial investment cost of a target power grid under a deterministic environment;
Figure BDA0002722688090000041
the operation cost of a target power grid under a deterministic environment is obtained;
Figure BDA0002722688090000042
for targets in a deterministic environmentThe maintenance cost of the power grid;
Figure BDA0002722688090000043
a cost of fault handling for the target grid in the deterministic environment;
Figure BDA0002722688090000044
and (4) the decommissioning disposal cost of the target power grid in a deterministic environment.
Converting the annual operating, maintenance, fault disposal and decommissioning waste disposal costs into a cost CcThe model of (2) can be modified as shown in formula (2):
Figure BDA0002722688090000045
wherein:
Figure BDA0002722688090000046
in the formula:
Figure BDA0002722688090000047
the current value of the operation cost in the t year under the deterministic environment;
Figure BDA0002722688090000048
the current value of the overhaul and maintenance cost in the t year under the deterministic environment is obtained;
Figure BDA0002722688090000049
the current value of the fault handling cost in the t year under the deterministic environment;
Figure BDA00027226880900000410
the current value of the retired disposal cost in the t year under the deterministic environment; PV (photovoltaic)sumThe current value sum of the annual investment cost is obtained; t is the planning year limit; r is the discount rate.
Initial investment cost
Figure BDA00027226880900000411
The initial investment cost is mainly the sum of the line modification cost, the reactive power compensation device installation cost, the transformer tap adjustment cost and the new substation (including the new line) cost in the planning years, and the formula is as follows:
Figure BDA00027226880900000412
wherein:
Aq＝pqLq (5)
in the formula: daIs a set of lines to be transformed; dbIs a set of reactive compensation devices to be installed; dcIs a set of gears to be regulated; ddSetting a position set of a transformer substation to be newly built; a. theqThe initial investment cost of the line to be transformed; a. thehInvestment cost per unit capacity of reactive compensation device to be installed; a. thekThe unit gear shifting cost for adjusting the tap joint of the transformer; a. thegThe unit initial investment cost (including the new line cost) of the transformer substation to be newly built is calculated; p is a radical ofqInitial investment cost for unit length to be reconstructed; l isqThe length of the line to be modified.
xqA decision variable representing the line q to be modified, when xqWhen 1, it indicates a line is replaced, and when xqWhen the value is 0, the circuit is not replaced; y ishRepresenting a capacity decision variable of the node h single group reactive compensation capacitor; z is a radical ofkA voltage regulating gear decision variable of a unit transformer tap; w is agAnd (4) determining variables for the number of newly built substations of a unit.
q is a line to be modified; h is a single node; k is the unit gear shifting of the transformer tap; and g is a unit transformer substation to be newly built.
② running cost
Figure BDA0002722688090000051
The operation cost mainly comprises the expense generated by the network loss of the system, and the formula is as follows:
Figure BDA0002722688090000052
in the formula: pLBtThe network loss value of the system in the t year after the planning scheme is implemented; t ismaxThe number of hours of maximum load utilization; epsilon is the price of electricity purchase. T is the planning year limit;
Figure BDA0002722688090000053
the current value of the operation cost in the t year under the deterministic environment; PV (photovoltaic)sumThe current value sum of the annual investment cost is obtained; r is the discount rate; t is year t.
Thirdly, maintenance cost
Figure BDA0002722688090000054
The overhaul and maintenance cost mainly comes from the maintenance cost and the maintenance cost generated by equipment faults, and the formula is as follows:
Figure BDA0002722688090000055
in the formula: a istAnd the maintenance coefficient is the overhaul maintenance coefficient of the t year.
Figure BDA0002722688090000056
The current value of the overhaul and maintenance cost in the t year under the deterministic environment is obtained;
Figure BDA0002722688090000057
is the initial investment cost of the target power grid in a deterministic environment.
Fourthly, failure disposal cost
Figure BDA0002722688090000058
The failure handling costs include losses due to equipment failures and unplanned power outages. The value is equal to the selling price multiplied by the expected value of the power shortage, and the formula is as follows:
Figure BDA0002722688090000059
in the formula: EENStSampling the expected value of the power shortage in the t year by adopting a non-sequential Monte Carlo simulation method; and χ is the price of electricity sold.
Figure BDA00027226880900000510
Is the current value of the fault handling cost in the t year under a deterministic environment.
Fifthly, retirement treatment cost
Figure BDA00027226880900000511
The retired disposal cost comprises a disposal cost for equipment retired and a residual income of the equipment, and the formula is as follows:
Figure BDA0002722688090000061
in the formula: b is the ratio coefficient of the scrap asset management cost; and c is the residual value rate.
Figure BDA0002722688090000062
The current value of the retired disposal cost in the t year under the deterministic environment; and b is the ratio coefficient of the management cost of the scrapped assets.
2): the constraint conditions in the low-voltage comprehensive treatment model are as follows:
(1) node voltage constraint:
Figure BDA0002722688090000063
in the formula:
Figure BDA0002722688090000064
the voltage amplitude of the node i in the t year under the deterministic environment is shown; vi,maxAnd Vi,minThe upper limit and the lower limit of the voltage of the node i are respectively set; wherein the content of the first and second substances,
Figure BDA0002722688090000065
the solution is obtained by equation (11).
Figure BDA0002722688090000066
In the formula:
Figure BDA0002722688090000067
active power injected for the node i in a deterministic environment,
Figure BDA0002722688090000068
Reactive power injected for a node i in a deterministic environment; vi c、
Figure BDA0002722688090000069
The voltage amplitudes of the node i and the node j under the deterministic environment are respectively; gij、BijRespectively the real part and the imaginary part of the admittance matrix;
Figure BDA00027226880900000610
is the phase angle difference between node i and node j.
(2) And (3) output limit of the wind turbine generator:
Figure BDA00027226880900000611
in the formula: pW,tThe actual output of the wind turbine generator is obtained,
Figure BDA00027226880900000612
and
Figure BDA00027226880900000613
respectively representing the upper limit and the lower limit of the output of the wind turbine generator.
(3) And (3) branch current constraint:
Figure BDA00027226880900000614
in the formula:
Figure BDA00027226880900000615
the current flowing through the branch m under the deterministic environment is adopted; i ism,maxTo allow an upper limit value of the current to flow through branch m.
(4) And (3) reactive compensation capacitor switching capacity constraint:
Figure BDA00027226880900000616
in the formula:
Figure BDA00027226880900000617
a single group of reactive compensation capacity is set for the node h under the deterministic environment; y ish,maxAnd the maximum capacity of reactive compensation is singly set for the node h.
(5) And (3) restricting the on-load tap changing transformer tap:
Figure BDA00027226880900000618
in the formula:
Figure BDA0002722688090000071
the gear of the on-load tap changing transformer tap joint under the deterministic environment; z is a radical ofk,maxAnd zk,minRespectively an upper limit and a lower limit of a tap joint of the on-load tap changing transformer.
(6) Newly building transformer substation constraints:
Figure BDA0002722688090000072
in the formula:
Figure BDA0002722688090000073
for newly-built substations in deterministic environmentsThe number of the particles; w is ag,maxThe number of the transformer substations is the upper limit of the newly built transformer substations.
In the step 2, the constructed low-voltage comprehensive treatment robust planning model is expressed in the following form:
Figure BDA0002722688090000074
in the formula: f is an objective function; cuThe target value is the target value of the life cycle cost of the target power grid under the uncertain environment; x is a decision variable and belongs to { X, y, z, w }; xi is an uncertain parameter; h and G represent equality and inequality constraints, respectively.
x is a line reconstruction decision variable, and when x is 1, the line is replaced, and when x is 0, the line is not replaced; y is a capacity decision variable of the single group of reactive compensation capacitors; z is a decision variable of a voltage regulating gear of the transformer; and w is a newly-built substation quantity decision variable.
In the step 3, the actual load and the wind power output in the power distribution network fluctuate up and down according to the predicted quantity, so that the actual output value can be represented by an information gap model:
Figure BDA0002722688090000075
Figure BDA0002722688090000076
in the formula: alpha and beta respectively represent fluctuation amplitudes of the load and the wind power output; pL,tActual value of year t load;
Figure BDA0002722688090000077
is PL,tA set of values; pW,tThe actual value of the wind power output in the t year is obtained;
Figure BDA0002722688090000078
is PW,tA set of values.
Figure BDA0002722688090000079
Load prediction value of the t year;
Figure BDA00027226880900000710
and (5) predicting the wind power output value in the t year.
The actual load value P is calculated from the equations (18) and (19)L,tActual output P of wind powerW,tRespectively expressed as:
Figure BDA00027226880900000711
Figure BDA00027226880900000712
when uncertainty is not considered, namely alpha is 0 and beta is 0, the formula (17) is a definite low-voltage comprehensive treatment model, and the total life cycle cost at the moment can be obtained and is marked as C0。
In the step 4, the IGDT method calculates the comprehensive uncertainty γ by establishing a robust model, the uncertainty maximum fluctuation degree indicating that the possible maximum target value is still within the acceptable range is indicated within the acceptable range, and the larger the γ value is, the better the robustness of the decision scheme is indicated, and the less the uncertainty is. Therefore, a robust model can be built based on IGDT as shown in equation (22):
Figure BDA0002722688090000081
in the formula: ccIs a desired target value; delta is a deviation coefficient, namely the deviation degree between the expected target and the optimal solution of the deterministic model, and the expected cost target value C is used for ensuring the robustness of the decision schemecHigher than C0Thus δ>0, set to 0.01 in this model.
The robust model converts the deterministic optimization model into C with the target value not lower than (1+ delta)0Under the premise of (1), the fluctuation degree of the uncertain parameters is maximized, namely a decision value X in the model is obtained, and when the load and the wind power output fluctuate randomly in the range, the target value is ensured not to exceed C all the timec. It should be noted that, during calculation, the worst scenario may be sought first, and then the model is solved;
the solution for the worst scenario is as follows:
the method comprises the following specific steps:
1) respectively constructing probability density functions of wind power and load based on non-parameter kernel density estimation;
2) generating random samples by utilizing Latin hypercube sampling;
3) and converting the random samples with correlation into mutually independent random samples by adopting a Cholesky decomposition method, and determining the worst scene on the basis of the random samples.
In step 4, the specific process of solving the worst scenario is as follows:
s4.1: modeling probability density function of uncertainty factor:
the probability density function of the load and the wind power output is constructed based on the non-parameter kernel density estimation method and is shown as the following formula:
Figure BDA0002722688090000082
Figure BDA0002722688090000091
in the formula: phi (P)L) And phi (P)W) Respectively expressed as a load probability density function and an wind power output probability density function based on non-parametric kernel density estimation; n is the number of samples; pLmThe m-th sample value in the load sample is obtained; pWmThe mth sample value in the wind power output sample is obtained; l is the bandwidth.
S4.2: latin hypercube sampling:
random variables were sampled using latin hypercube sampling. Let the sampling scale be N, Ym＝Fm(Xm) Denotes the m-th random variable XmIs determined. The specific sampling process is as follows: will be interval [0,1]Equally dividing the sampling value into N equal parts, selecting the middle value of each subinterval, and obtaining the sampling value through the inverse function of the middle value
Figure BDA0002722688090000092
And obtaining a sample matrix after sampling is completed.
S4.3: cholesky decomposition of the correlation coefficient matrix:
the method is characterized in that the correlation between the load and the wind power is described by using a correlation coefficient matrix, and a sample matrix obtained by Latin hypercube sampling is set as W ═ W1,w2,…,wl]TThe matrix of correlation coefficients is CW：
Figure BDA0002722688090000093
Figure BDA0002722688090000094
Represents the matrix of correlation coefficients as CWRow i and column j in (1), which means specifically an input sample variable wiAnd wjThe correlation coefficient between them is calculated by equation (26).
Wherein:
Figure BDA0002722688090000095
in the formula:
Figure BDA0002722688090000096
and
Figure BDA0002722688090000097
are respectively an input variable wiAnd wjStandard deviation of (d); cov(wi,wj) As an input variable wiAnd wjThe covariance of (a). Processing the correlation coefficient matrix by adopting Cholesky decomposition methodThe formula is as follows:
CW＝GGT (27)
in the formula: g is a lower triangular matrix, where the elements can be found by equation (28):
Figure BDA0002722688090000101
gkkdiagonal elements (elements of the k-th row) in the lower triangular matrix G,
Figure BDA0002722688090000102
is a diagonal element in the correlation coefficient matrix of equation (25); gkmThe diagonal-line-divided elements (the mth row elements) in the kth row in the lower triangular matrix G; gikAll elements except diagonal elements (i-th row and k-th row elements) in the lower triangular matrix G;
Figure BDA0002722688090000103
all elements of diagonal elements in the correlation coefficient matrix of equation (25); gimThe other elements in the ith row of the lower triangular matrix G except the last two elements of each row are shown, i.e. starting from the third row (row i, row m elements).
S4.4: derivation of orthogonal transformation matrix:
in order to convert an input random variable matrix W having correlation into an uncorrelated random variable matrix Y, an orthogonal matrix B is provided, which includes:
Y＝BW (29)
in the formula: y ═ Y1,y2,…,yn]T
Correlation coefficient matrix C due to uncorrelated random variable matrix YYIs an identity matrix I, and thus:
CY＝ρ(Y,YT)＝ρ(BW,WTBT)＝Bρ(W,WT)BT＝BCWBT＝I (30)
CYis notA correlation coefficient matrix of the correlation random variable matrix Y; rho is a correlation coefficient; y isTA transposed matrix which is an uncorrelated random variable matrix Y; cWA correlation coefficient matrix which is an input random variable matrix W with correlation; i is an identity matrix; b is an orthogonal matrix which is supposed to exist; b isTWhich is the transpose of the orthogonal matrix B.
Further, it can be obtained from the formula (27):
CY＝BCWBT＝BGGTBT＝(BG)(BG)T＝I (31)
further, it can be deduced that:
B＝G-1 (32)
by substituting formula (32) for formula (29), it is possible to obtain:
Y＝G-1W (33)
on the premise of inputting uncertain quantity W with correlation, the uncertain quantity W can be changed into independent random variable Y through orthogonal transformation, the correlation of the uncertain quantity is eliminated, and then worst scene S is obtainedworstNamely:
Figure BDA0002722688090000111
in the formula: sworstIs a worst scene set;
Figure BDA0002722688090000112
and
Figure BDA0002722688090000113
and the actual load value and the actual wind-power output value under the worst scene are respectively.
Equation (22) can be modified to:
Figure BDA0002722688090000114
and (3) recovering: gamma is the integrated uncertainty; alpha represents the fluctuation degree of the load(ii) a Beta represents the fluctuation amplitude of the wind power output; pL,PWRespectively a load value and an electric power output value; ccIs a desired target value; cuThe target value is the target value of the life cycle cost of the target power grid under the uncertain environment; delta is a deviation coefficient, i.e. the degree of deviation between the desired target and the optimal solution of the deterministic model; when uncertainty is not considered, i.e., α is 0 and β is 0, the full life cycle cost is recorded as C0；SworstIs the worst scenario set.
In the step 5, the concrete steps of model solution based on sequence optimization are as follows:
step 5.1, randomly extracting Q feasible solutions in the feasible domain to form a characterization set thetaQGenerally, Q is 1000. In the robust model established by the IGDT in step 4, the feasible solution refers to a planning scheme that satisfies all constraint conditions of equations (10) to (16) at the same time.
Step 5.2, constructing a rough model:
constructing a rough model based on the formula (4), and evaluating the symptom set by adopting the rough model to perform thetaQSorting all solutions in the set from small to large to obtain an OPC (ordered Performance Curve) curve, and further determining the type of the OPC; the type of optimization problem can be determined with reference to fig. 1(a) to 1 (e).
Step 5.3, determining a selected set S: the first S solutions are taken with reference to equation (36) to determine the selected set S, depending on the type of OPC.
Figure BDA0002722688090000115
In the formula: s is a function of k, g; z0P, m and eta are regression parameters and are determined according to the type of an OPC curve; g is the number of observed good enough solutions, and k is the number of real good enough solutions in g.
And 5.4, accurately evaluating:
and (3) constructing an accurate model based on the formula (2). And accurately evaluating all feasible solutions in the selected set S by using an accurate model, sequencing the feasible solutions from small to large, selecting the first k solutions as real and good enough solutions, and taking the minimum solution in the k solutions as an optimal solution.
Example (b):
example parameter settings were as follows:
simulation analysis was performed using the modified IEEE 33 node power distribution system shown in fig. 3 as an example. 25 switchable parallel capacitor banks are respectively arranged at the nodes 18, 22, 25 and 33, and the cost of unit capacity is 0.013 ten thousand yuan; the unidirectional on-load tap changing transformer comprises 16 (0-15) taps, and the stepping amount is 1.25%; the nodes to be selected of the newly-built transformer substation are 34, 35 and 36, and a wind power plant with installed capacity of 100MW is added to the node 27. The active network loss of an original system is 234kW, the reference voltage is 12.66kV, the reference power is 100MVA, and the upper and lower limits of the per-unit value of the node voltage are set to be 0.93-1.07 pu. The planning age is 10 years.
The target power grid line to be replaced can select three types of wires, namely LGJ-95/15, LGJ-150/35 and LGJ-185/10. In order to meet the power supply reliability, a newly-built transformer substation needs to be connected with an adjacent transformer substation to form a medium-voltage distribution network ring network structure. The construction cost of the transformer substation is 50 ten thousand yuan. The new line can be selected from conductor types LGJ-95/15 or LGJ-150/8, and can be shown in Table 1; the statistics of the parameters of the line to be replaced and the newly-built line are shown in table 2.
TABLE 1 statistical table of newly-built lines
Figure BDA0002722688090000121
Table 2 statistical table of candidate line parameters
Figure BDA0002722688090000122
Figure BDA0002722688090000131
The relevant economic parameters of the target grid are shown in table 3.
TABLE 3 economic parameters table of target power grid
Figure BDA0002722688090000132
The simulation results are as follows:
1): simulation results in deterministic environment:
under the deterministic environment, the voltage amplitude of each node in the first year is taken as the standard. An OPC curve calculated by using the order optimization algorithm for the deterministic planning model (i.e., α is 0 and β is 0) is shown in fig. 4, and as can be seen from fig. 1(b), the corresponding curve type is U-shaped.
Referring to the parameter comparison table of the OPC curve, Z can be known0P, m, η are 8.1200, 1.0044, -1.3695, 9.00 respectively, when k is 1 and g is 10, S is 152 calculated according to formula (36), feasible solutions are sorted in solution set S by formula (2), and the optimal life cycle cost is C0When the expected cost deviation coefficient takes 0.01, the expected cost C is 780.1733c＝787.9750。
2) Simulation results in an uncertain environment:
(1) modeling random variables:
taking historical data of actual load and wind power output of a certain area to perform nonparametric kernel density modeling, and obtaining a probability density function shown in a table 4:
table 4 probability density function table for each random variable
Figure BDA0002722688090000133
(2) Worst scenario:
solving a sample matrix of load and wind power output obtained by Latin hypercube sampling and a sample matrix after the correlation is eliminated by Cholesky decomposition, further solving a worst scene, wherein the comparison result of the worst scene considering the correlation and the worst scene not considering the correlation is shown in a table 5:
TABLE 5 worst scenario comparison Table
Figure BDA0002722688090000141
As can be seen from table 5, the worst scenarios do not occur simultaneously, and the worst scenario values need to be calculated after being subjected to correlation processing and then becoming independent uncertain variables.
(3) Best mode
The total life cycle cost C corresponding to the optimal scheme is calculated according to the low-voltage comprehensive treatment method which comprehensively considers the load fluctuation, the wind power output uncertainty and the correlation thereofuAs 786.0341 ten thousand yuan, C can be seenu≤CcWhen the load and the wind power output can be guaranteed to fluctuate within the range, the planning result can be guaranteed to be within the expected target by the decision scheme, and the robustness of the method is embodied. The network topology connection mode corresponding to the optimal scheme is shown in fig. 5:
comparative analysis is as follows:
in order to verify the correctness and the validity of the invention, the following three methods are set:
the method comprises the following steps: the low-voltage comprehensive treatment method only considers the uncertain influences of load fluctuation and wind power output, but does not consider the correlation of the uncertain influences and only considers the investment cost;
the second method comprises the following steps: the low-voltage comprehensive treatment method considers the uncertain influences of load fluctuation and wind power output, but does not consider the correlation of the uncertain influences, and simultaneously clocks and the whole life cycle cost of the comprehensive treatment method;
the third method comprises the following steps: the invention provides a low-voltage comprehensive treatment method which considers the uncertainty and the correlation of load fluctuation and wind power output and also considers the whole life cycle cost, namely the method provided by the invention.
The resulting optimal planning scheme is shown in table 6:
TABLE 6 optimal planning scheme for three methods
Figure BDA0002722688090000142
Figure BDA0002722688090000151
Through calculation, the specific results of the life cycle cost obtained by the three methods are as follows:
(1) validation considering full life cycle cost:
to verify the necessity of considering the full life cycle cost in the low voltage integrated remediation process, methods one and two were compared as shown in table 7 below:
TABLE 7 full Life cycle cost specific results for method one and method two
Figure BDA0002722688090000152
As can be seen from table 7, the first method only considers the investment cost of low-voltage comprehensive treatment, so that the obtained scheme only performs reactive compensation at node 18, and newly establishes a line by using a conductor of model LGJ-95/15 in a L3 line with a short distance, so that the initial investment cost is reduced by 6.75 ten thousand yuan compared with the second method, and the overhaul maintenance cost and the decommissioning treatment cost are positively correlated with the initial investment cost, so that the overhaul maintenance cost and the decommissioning treatment cost of the scheme obtained by the first method are reduced by 0.7245 ten thousand yuan and 0.0054 ten thousand yuan respectively compared with the second method. But because the second method carries out planning decision on the basis of fully considering the whole life cycle cost of low-voltage comprehensive treatment, the second method also carries out reactive compensation on the node No. 22, and selects the L1 line and adopts a conductor of LGJ-95/15 model to establish a new line, thereby directly reducing the network loss of the system, and further reducing the network loss cost (operation cost) by 8.1258 ten thousand yuan compared with the first method. Compared with the first method, the fault handling cost of the scheme obtained by the second method is reduced by 0.0427 ten thousand yuan, and the reason is that the low-voltage comprehensive treatment measures selected by the second method reduce the power shortage amount of the network, so that the fault handling cost is reduced.
From the perspective of the whole life cycle cost, the method two is reduced by 2.614 ten thousand yuan compared with the method one, so that if the decision is made on low-voltage comprehensive treatment with the aim of lowest initial investment cost only from the perspective of investment cost, although the initial investment cost of the target power grid can be reduced to a certain extent, the loss reduction benefit of the target power grid is sacrificed. Therefore, the refinement level of the planning can be ensured only by comprehensively considering the cost factor of the whole life cycle in the planning process.
(2) Validity verification taking into account dependencies
To verify the necessity of considering the correlation in the low voltage comprehensive treatment process, compare method two with method three, as shown in table 8 below:
TABLE 8 full Life cycle cost specific results for method two and method three
Figure BDA0002722688090000161
The analysis of table 8 shows that, according to the third method, not only is the uncertainty of the load and the wind power output considered, but also the probability correlation between the load and the wind power is fully considered, so that an extreme scene that the load and the wind power cannot occur simultaneously in the low-voltage comprehensive treatment process is effectively avoided, the load demand is reduced in the worst scene of the system, the wind power output is increased, the robustness of the system can be guaranteed by selecting a L8 circuit newly-built substation with a short distance, and compared with the second method which only considers the uncertainty but does not consider the correlation, the initial investment cost is reduced by 1 ten thousand yuan, so that the overhaul maintenance cost and the decommissioning disposal cost of the scheme obtained by the third method are respectively reduced by 0.0683 ten thousand yuan and 0.0027 ten thousand yuan. The third method selects a conductor with a model LGJ-150/8 with better performance to establish a new line, so that the network loss of the system is reduced, and therefore, the network loss cost of the obtained scheme is reduced by 0.3895 ten thousand yuan compared with the second method.
In terms of the life cycle cost, compared with the second method, the optimal scheme calculated by the method provided by the invention reduces the life cycle cost by 1.4426 ten thousand yuan. The reason is that if the correlation between the load and the wind power output is not considered, the maximum and minimum values are directly taken, the operation cost generated in the worst scene calculated through simple linear superposition is higher, and the economy of the planning scheme is influenced. And the correlation between the load and the wind power output is fully considered, and an extreme scene which is unlikely to occur can be proposed in the decision process, so that the whole life cycle cost of the planning scheme is reduced while the system robustness is ensured.
(3) Uncertainty analysis of three methods
By calculation, the uncertainties of the three methods are shown in table 9:
TABLE 9 uncertainty of the three methods
Figure BDA0002722688090000171
As can be seen from the analysis of Table 9, compared with the first method and the second method, the uncertainty calculated by the method of the invention is improved by 83.6% and 40.9%, which shows that the decision scheme calculated by the low-voltage comprehensive treatment method considering the whole life cycle cost and the correlation has better robustness, can resist larger load fluctuation and wind power output fluctuation, and verifies the effectiveness.

Claims (7)

1. The comprehensive treatment method for the low voltage of the power distribution network considering the uncertainty factors and the correlation thereof is characterized by comprising the following steps of:
step 1: constructing a low-voltage comprehensive treatment model based on the life cycle cost by taking line transformation, reactive compensation, transformer voltage regulation and newly-built transformer substations as decision variables;
step 2, considering load fluctuation, uncertainty of wind power output and correlation thereof, and constructing a low-voltage comprehensive treatment robust planning model based on an information gap decision theory IGDT;
step 3, modeling uncertainty of load and wind power output;
step 4, establishing a robust model by an IGDT method, converting random samples with correlation into mutually independent random samples based on a Cholesky decomposition method, and determining a worst scene based on the random samples;
and 5, solving the robust model established by the IGDT by using an order optimization algorithm.
2. The comprehensive treatment method for the low voltage of the power distribution network considering the uncertainty factors and the correlation thereof according to claim 1, characterized in that: in the step 1, the low-voltage comprehensive treatment model is constructed as follows:
1): constructing an objective function as shown in formula (1):
Figure 1
in the formula: x is a line reconstruction decision variable, and when x is 1, the line is replaced, and when x is 0, the line is not replaced;
y is a capacity decision variable of the single group of reactive compensation capacitors; z is a decision variable of a voltage regulating gear of the transformer; w is a number decision variable of the newly-built transformer substation;
Figure FDA0002722688080000012
is the predicted value of the load in the t-th year,
Figure FDA0002722688080000013
the predicted value is the wind power output value in the t year;
Ccthe life cycle cost of the target power grid under the deterministic environment;
Figure FDA0002722688080000014
initial investment cost of a target power grid under a deterministic environment;
Figure 2
the operation cost of a target power grid under a deterministic environment is obtained;
Figure FDA0002722688080000016
maintenance cost for overhauling the target power grid in a deterministic environment;
Figure FDA0002722688080000017
for the purpose of a target grid in a deterministic environment(ii) barrier disposal cost;
Figure FDA0002722688080000018
the decommissioning disposal cost of the target power grid under the deterministic environment is obtained;
converting the annual operating, maintenance, fault disposal and decommissioning waste disposal costs into a cost CcThe model of (2) can be modified as shown in formula (2):
Figure 3
wherein:
Figure FDA0002722688080000021
in the formula:
Figure FDA0002722688080000022
the current value of the operation cost in the t year under the deterministic environment;
Figure FDA0002722688080000023
the current value of the overhaul and maintenance cost in the t year under the deterministic environment is obtained;
Figure FDA0002722688080000024
the current value of the fault handling cost in the t year under the deterministic environment;
Figure FDA0002722688080000025
the current value of the retired disposal cost in the t year under the deterministic environment; PV (photovoltaic)sumThe current value sum of the annual investment cost is obtained; t is the planning year limit; r is the discount rate;
initial investment cost
Figure FDA0002722688080000026
The initial investment cost mainly comprises the total cost of line transformation cost, reactive compensation device installation cost, transformer tap adjustment cost and newly-built transformer substation cost within the planning years, and the formula is as follows:
Figure FDA0002722688080000027
wherein:
Aq＝pqLq (5)
in the formula: daIs a set of lines to be transformed; dbIs a set of reactive compensation devices to be installed; dcIs a set of gears to be regulated; ddSetting a position set of a transformer substation to be newly built; a. theqThe initial investment cost of the line to be transformed; a. thehInvestment cost per unit capacity of reactive compensation device to be installed; a. thekThe unit gear shifting cost for adjusting the tap joint of the transformer; a. thegThe unit initial investment cost of the transformer substation to be newly built is calculated; p is a radical ofqInitial investment cost for unit length to be reconstructed; l isqThe length of the line to be modified;
② running cost
Figure FDA0002722688080000028
The operation cost includes the expense generated by the network loss of the system, and the formula is as follows:
Figure FDA0002722688080000029
in the formula: pLBtThe network loss value of the system in the t year after the planning scheme is implemented; t ismaxThe number of hours of maximum load utilization; epsilon is the price of electricity purchase;
thirdly, maintenance cost
Figure FDA00027226880800000210
The repair and maintenance cost comprises maintenance cost and maintenance cost generated by equipment failure, and the formula is as follows:
Figure FDA00027226880800000211
in the formula: a istThe maintenance coefficient is the overhaul maintenance coefficient of the t year;
fourthly, failure disposal cost
Figure FDA0002722688080000031
The cost of failure disposal includes losses due to equipment failure and unplanned outages, which is equal to the selling price multiplied by the expected low battery value, and is given by the formula:
Figure FDA0002722688080000032
in the formula: EENStThe expected value of the power shortage amount in the t year is shown, and chi is the price of power sale;
fifthly, retirement treatment cost
Figure 4
The retired disposal cost comprises a disposal cost for equipment retired and a residual income of the equipment, and the formula is as follows:
Figure FDA0002722688080000034
in the formula: b is the ratio coefficient of the scrap asset management cost; c is the residual value rate;
2): the constraint conditions in the low-voltage comprehensive treatment model are as follows:
(1) node voltage constraint:
Figure FDA0002722688080000035
in the formula:
Figure FDA0002722688080000036
the voltage amplitude of the node i in the t year under the deterministic environment is shown; vi,maxAnd Vi,minThe upper limit and the lower limit of the voltage of the node i are respectively set; wherein the content of the first and second substances,
Figure FDA0002722688080000037
solving the formula (11);
Figure FDA0002722688080000038
in the formula:
Figure FDA0002722688080000039
active power injected for the node i in a deterministic environment,
Figure FDA00027226880800000310
Reactive power injected for a node i in a deterministic environment;
Figure FDA00027226880800000311
the voltage amplitudes of the node i and the node j under the deterministic environment are respectively; gij、BijRespectively the real part and the imaginary part of the admittance matrix;
Figure FDA00027226880800000312
is the phase angle difference between node i and node j;
(2) and (3) output limit of the wind turbine generator:
Figure FDA00027226880800000313
in the formula: pW,tThe actual output of the wind turbine generator is obtained,
Figure FDA00027226880800000314
and
Figure FDA00027226880800000315
respectively representing the upper limit and the lower limit of the output of the wind turbine;
(3) and (3) branch current constraint:
Figure FDA0002722688080000041
in the formula:
Figure FDA0002722688080000042
the current flowing through the branch m under the deterministic environment is adopted; i ism,maxAn upper limit value of current allowed to flow through the branch m;
(4) and (3) reactive compensation capacitor switching capacity constraint:
Figure FDA0002722688080000043
in the formula:
Figure FDA0002722688080000044
a single group of reactive compensation capacity is set for the node h under the deterministic environment; y ish,maxThe maximum capacity of reactive compensation is singly set for the node h;
(5) and (3) restricting the on-load tap changing transformer tap:
Figure FDA0002722688080000045
in the formula:
Figure FDA0002722688080000046
the gear of the on-load tap changing transformer tap joint under the deterministic environment; z is a radical ofk,maxAnd zk,minRespectively an upper limit and a lower limit of an on-load tap changing transformer tap;
(6) newly building transformer substation constraints:
Figure FDA0002722688080000047
in the formula:
Figure FDA0002722688080000048
the number of newly built transformer substations under a deterministic environment is determined; w is ag,maxThe number of the transformer substations is the upper limit of the newly built transformer substations.
3. The comprehensive treatment method for the low voltage of the power distribution network considering the uncertainty factors and the correlation thereof according to claim 1, characterized in that: in the step 2, the constructed low-voltage comprehensive treatment robust planning model is expressed in the following form:
Figure FDA0002722688080000049
in the formula: f is an objective function; cuThe target value is the target value of the life cycle cost of the target power grid under the uncertain environment; x is a decision variable and belongs to { X, y, z, w }; xi is an uncertain parameter; h and G represent equality and inequality constraints, respectively.
4. The comprehensive treatment method for the low voltage of the power distribution network considering the uncertainty factors and the correlation thereof according to claim 3, characterized in that: in the step 3, the actual load and the wind power output in the power distribution network fluctuate up and down according to the predicted quantity, and the actual output value is represented by an information gap model:
Figure FDA00027226880800000410
Figure FDA00027226880800000411
in the formula: alpha and beta respectively represent fluctuation amplitudes of the load and the wind power output; pL,tActual value of year t load;
Figure FDA0002722688080000051
is PL,tA set of values; pW,tThe actual value of the wind power output in the t year is obtained;
Figure FDA0002722688080000052
is PW,tA set of values;
the actual load value P is calculated from the equations (18) and (19)L,tActual output P of wind powerW,tRespectively expressed as:
Figure FDA0002722688080000053
Figure FDA0002722688080000054
when uncertainty is not considered, namely alpha is 0 and beta is 0, the formula (17) is a definite low-voltage comprehensive treatment model, and the total life cycle cost at the moment can be obtained and is marked as C0。
5. The comprehensive treatment method for the low voltage of the power distribution network considering the uncertainty factors and the correlation thereof according to claim 1, characterized in that: in step 4, a robust model is established based on IGDT as shown in equation (22):
Figure FDA0002722688080000055
in the formula: ccIs a desired target value; delta is a deviation coefficient, namely the deviation degree between the expected target and the optimal solution of the deterministic model, and the expected cost target value C is used for ensuring the robustness of the decision schemecHigher than C0Thus δ>0, set to 0.01 in this model;
the robust model converts the deterministic optimization model into C with the target value not lower than (1+ delta)0Under the premise of (1), the fluctuation degree of the uncertain parameters is maximized, namely a decision value X in the model is obtained, and when the load and the wind power output fluctuate randomly in the range, the target value is ensured not to exceed C all the timec；
The worst scenario solution steps are as follows:
1) respectively constructing probability density functions of wind power and load based on non-parameter kernel density estimation;
2) generating random samples by utilizing Latin hypercube sampling;
3) and converting the random samples with correlation into mutually independent random samples by adopting a Cholesky decomposition method, and determining the worst scene on the basis of the random samples.
6. The comprehensive treatment method for the low voltage of the power distribution network considering the uncertainty factors and the correlation thereof according to claim 5, wherein the comprehensive treatment method comprises the following steps: in step 4, the specific process of solving the worst scenario is as follows:
s4.1: modeling probability density function of uncertainty factor:
the probability density function of the load and the wind power output is constructed based on the non-parameter kernel density estimation method and is shown as the following formula:
Figure FDA0002722688080000061
Figure FDA0002722688080000062
in the formula: phi (P)L) And phi (P)W) Respectively expressed as a load probability density function and an wind power output probability density function based on non-parametric kernel density estimation; n is the number of samples; pLmThe m-th sample value in the load sample is obtained; pWmThe mth sample value in the wind power output sample is obtained; l is a beltWidth;
s4.2: latin hypercube sampling:
sampling a random variable by adopting Latin hypercube sampling; let the sampling scale be N, Ym＝Fm(Xm) Denotes the m-th random variable XmA probability density function of; the specific sampling process is as follows: will be interval [0,1]Equally dividing the sampling value into N equal parts, selecting the middle value of each subinterval, and obtaining the sampling value through the inverse function of the middle value
Figure FDA0002722688080000063
After sampling is finished, a sample matrix of the sampling is obtained;
s4.3: cholesky decomposition of the correlation coefficient matrix:
the method is characterized in that the correlation between the load and the wind power is described by using a correlation coefficient matrix, and a sample matrix obtained by Latin hypercube sampling is set as W ═ W1,w2,…,wl]TThe matrix of correlation coefficients is CW：
Figure FDA0002722688080000064
Wherein:
Figure FDA0002722688080000065
in the formula:
Figure FDA0002722688080000066
and
Figure FDA0002722688080000067
are respectively an input variable wiAnd wjStandard deviation of (d); cov(wi,wj) As an input variable wiAnd wjThe covariance of (a); processing the correlation coefficient matrix by adopting a Cholesky decomposition method, wherein the formula is as follows:
CW＝GGT (27)
in the formula: g is a lower triangular matrix, where the elements can be found by equation (28):
Figure FDA0002722688080000071
s4.4: derivation of orthogonal transformation matrix:
in order to convert an input random variable matrix W having correlation into an uncorrelated random variable matrix Y, an orthogonal matrix B is provided, which includes:
Y＝BW (29)
in the formula: y ═ Y1,y2,…,yn]T
Correlation coefficient matrix C due to uncorrelated random variable matrix YYIs an identity matrix I, and thus:
CY＝ρ(Y,YT)＝ρ(BW,WTBT)＝Bρ(W,WT)BT＝BCWBT＝I (30)
further, it can be obtained from the formula (27):
CY＝BCWBT＝BGGTBT＝(BG)(BG)T＝I (31)
further, it can be deduced that:
B＝G-1 (32)
by substituting formula (32) for formula (29), it is possible to obtain:
Y＝G-1W (33)
on the premise of inputting uncertain quantity W with correlation, the uncertain quantity W can be changed into independent random variable Y through orthogonal transformation, the correlation of the uncertain quantity is eliminated, and then worst scene S is obtainedworstNamely:
Figure FDA0002722688080000072
in the formula: sworstIs a worst scene set;
Figure FDA0002722688080000073
and
Figure FDA0002722688080000074
respectively representing the actual load value and the actual wind-power output value under the worst scene;
equation (22) can be modified to:
Figure FDA0002722688080000075
7. the comprehensive treatment method for the low voltage of the power distribution network considering the uncertainty factors and the correlation thereof according to claim 6, wherein the comprehensive treatment method comprises the following steps: in the step 5, the concrete steps of model solution based on sequence optimization are as follows:
step 5.1, randomly extracting a feasible solution in a feasible domain to form a characterization set thetaQ(ii) a In the model, the feasible solution refers to a planning scheme which simultaneously meets the constraint conditions of all the formulas (10) to (16);
step 5.2, constructing a rough model:
constructing a rough model based on the formula (4), and evaluating the symptom set by adopting the rough model to perform thetaQAll solutions in the set are sorted from small to large to obtain an OPC curve, and then the type of the OPC is determined, and further the type of the optimization problem is determined;
step 5.3, determining a selected set S: according to the type of OPC, taking the first S solutions by referring to a formula (36) to determine a selected set S;
Figure FDA0002722688080000081
in the formula: s is a function of k, g; z0P, m and eta are regression parameters and are determined according to the type of an OPC curve; g is enough for observationThe number of good solutions, k is the number of real enough good solutions in g;
and 5.4, accurately evaluating:
and (3) constructing an accurate model based on the formula (2), accurately evaluating all feasible solutions in the selected set S by using the accurate model, sequencing the feasible solutions from small to large, selecting the first k solutions as real and good enough solutions, and taking the minimum solution in the k solutions as an optimal solution.
CN202011092716.0A 2020-10-13 2020-10-13 Power distribution network low voltage comprehensive treatment method considering uncertainty factors and correlation thereof Pending CN112310959A (en)

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