CN109510189B - Power distribution network planning method based on credibility theory - Google Patents
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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
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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- 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
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Abstract
The invention discloses a distribution network planning method based on a credibility theory, which comprises the following steps of: s1: establishing a power distribution network fuzzy planning model based on a credibility theory; s2: establishing an equivalent model of a given credibility index; s3: and solving the model by adopting fuzzy load flow calculation and a genetic algorithm. The method comprises the steps of establishing a power distribution network planning model based on a credibility theory based on a fuzzy mathematical theory, considering fuzzy uncertainty of loads, introducing a credibility index by taking the minimum fixed investment and fuzzy expected network loss cost of the power distribution network in a planning period as a target function, and processing branch power and node voltage constraints by adopting fuzzy opportunity constraints; secondly, a power distribution network planning model under the credibility index is equivalent to a power distribution network planning model under the interval load by adopting the credibility index equivalence theorem, so that the intercept corresponding to the fuzzy load distribution can be represented by an intuitive interval, the model solving difficulty is reduced by the solving method, and the model solving time is shortened.
Description
Technical Field
The invention relates to the field of power system planning, in particular to a distribution network planning method based on a credibility theory.
Background
The traditional power distribution network planning optimization method is based on determined planning parameters, and a deterministic planning scheme which meets the environmental constraints and is optimal in economic indexes is obtained. The traditional planning method does not consider the influence of uncertain factors in planning, so that the flexibility and the economy of planning the net rack are poor.
Aiming at the treatment of uncertain factors in power distribution network planning, random planning, fuzzy planning, interval planning, a scene analysis method and a risk assessment method are mainly adopted at present. At present, the distribution network planning is less in consideration of the influence of fuzzy uncertainty of loads, the related contents of the distribution network planning are very wide, and a mathematical model of the distribution network planning contains numerous variables and constraints, so that the traditional planning algorithm is difficult to obtain an optimal scheme. The existing uncertain planning models are all based on uncertain planning theory, the models are complex and the solving speed is slow, the obtained schemes are relatively conservative, and mathematical indexes for effectively evaluating the risk level of the system are lacked.
The credibility measure index is one of important indexes in credibility theory, and has self-duality and sub-additivity, so that whether an event occurs or not can be judged, risks can be quantified, and the risks can be controlled by the confidence level of fuzzy opportunity constraint. Therefore, it is necessary to provide a new power distribution network planning method based on the credibility theory to solve the above problems.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a power distribution network planning method based on the credibility theory, which can consider the fuzzy uncertainty of the load, and the established power distribution network fuzzy planning model has low solving difficulty and short solving time.
In order to solve the technical problems, the invention adopts a technical scheme that: the power distribution network planning method based on the credibility theory is provided and comprises the following steps:
s1: establishing a power distribution network fuzzy planning model based on a credibility theory: the method comprises the steps of taking the minimum of fixed investment and fuzzy expected network loss cost of a power distribution network in a planning period as a target function, introducing a reliability index, and processing branch power constraint and node voltage constraint by adopting fuzzy opportunity constraint;
s2: establishing an equivalent model of a given reliability index: the power distribution network planning model under the credibility index is equivalent to the power distribution network planning model under the interval load by adopting the credibility index equivalence theorem, so that the intercept set corresponding to the fuzzy load distribution can be represented by a visual interval;
s3: and solving the model by adopting fuzzy load flow calculation and a genetic algorithm.
In a preferred embodiment of the present invention, in step S1, the objective function is:
minZcost＝Z1+β·Z2 (1)
the branch power constraint and the node voltage constraint are respectively as follows:
wherein,
Pjmaxfuzzy active power of each line and upper limit of allowable line power;
Vimax、Viminfuzzy voltage values and allowable voltage upper and lower limit values of each node are respectively; alpha is an introduced model risk assessment index, namely a reliability index;
respectively, line fuzzy reactive power, node fuzzy active power and reactive power; l is the number of branch circuits of the power distribution network in a certain planning scheme; and N is the number of nodes of the power distribution network in a certain planning scheme.
In a preferred embodiment of the present invention, in step S2, given the confidence level α (≧ 0.5), the equations (1) -6 can be converted into equations (7) -13 for solving:
minZcost＝Z1+β·Z2 (7)
wherein, muξ(y) is a membership function of the fuzzy load; y is fuzzy load
All load values that can be obtained;
the interval expressions corresponding to the fuzzy variables in (expression (1) - (expression (6)) are shown.
In a preferred embodiment of the present invention, the step S3 includes the following steps:
s3.1: inputting net rack original data and basic parameters of a genetic algorithm, including the number of chromosomes of an initial population;
s3.2: randomly generating a binary coded chromosome to carry out connected radiation detection, judging whether the connected radiation requirement is met, and if not, correcting the net rack;
s3.3: sampling fuzzy loads by adopting fuzzy simulation according to the grid structure determined by the chromosome and the distribution of the fuzzy loads, performing deterministic load flow calculation on load data obtained by each sampling, judging whether node voltage fuzzy opportunity constraint and branch load flow fuzzy opportunity constraint are met, and if the constraint is met, taking the load data as an individual in an initial group;
s3.4: repeating steps S3.2-S3.3 until a defined number of chromosomes of the initial population are generated;
s3.5: calculating target function values of all chromosomes, namely expected values of net rack planning year fixed investment and network loss cost, and calculating fitness values of the chromosomes by adopting a penalty function method for a scheme which does not meet node voltage fuzzy opportunity constraints and branch flow fuzzy opportunity constraints;
s3.6: selecting the chromosome with the minimum fitness value in the population by adopting a roulette method;
s3.7: carrying out cross and variation operations on chromosomes in the population to obtain a new generation of chromosomes, and carrying out node voltage fuzzy opportunity constraint and branch flow fuzzy opportunity constraint test on the chromosomes;
s3.8: and (5) repeating the steps S3.5-S3.7 until the chromosome reaches the maximum allowable iteration number, so as to obtain the optimal scheme.
Further, the chromosome number of the initial population is determined according to the scale of the planning grid frame.
Further, the scheme meeting the node voltage fuzzy opportunity constraint and the branch power flow fuzzy opportunity constraint is a scheme for evaluating the risk level by adopting a fuzzy opportunity constraint verification method.
Further, a fuzzy load flow calculation method is adopted for calculating the expected value of the network loss cost.
The invention has the beneficial effects that:
(1) the method is characterized in that a power distribution network planning model based on a credibility theory is established based on a fuzzy mathematical theory, fuzzy uncertainty of loads is considered at first, a target function with minimum fixed investment and fuzzy expected network loss cost of a power distribution network in a planning period is used, a credibility index is introduced, and branch power and node voltage constraints are processed by adopting fuzzy opportunity constraints, so that the effect of controlling system risks is achieved, and the obtained optimal scheme is prevented from being over conservative; secondly, a power distribution network planning model under the credibility index is equivalent to a power distribution network planning model under the interval load by adopting the credibility index equivalence theorem, so that an intercept set corresponding to the fuzzy load distribution can be represented by an intuitive interval, and a fuzzy load flow calculation and a genetic algorithm are adopted for solving, so that the model solving difficulty is reduced, and the model solving time is shortened;
(2) the method for planning the grid structure is suitable for planning the distribution grid structure by similarly considering the fuzzy uncertain factors in the power grid, and has better normative and generalizable properties.
Drawings
FIG. 1 is a flow chart of a distribution network planning method based on credibility theory according to the present invention;
fig. 2 is a flow chart of the genetic algorithm.
Detailed Description
The following detailed description of the preferred embodiments of the present invention, taken in conjunction with the accompanying drawings, will make the advantages and features of the invention easier to understand by those skilled in the art, and thus will clearly and clearly define the scope of the invention.
Referring to fig. 1, an embodiment of the present invention includes:
a power distribution network planning method based on a credibility theory comprises the following steps:
s1: establishing a power distribution network fuzzy planning model based on a credibility theory:
the credibility concept introduced by the fuzzy theory rationalization system based on the measure theory enables all operations of fuzzy numbers to be based on the credibility, and therefore fuzzy evaluation is quantized. The method takes the minimum of fixed investment and fuzzy expected network loss cost of the power distribution network in a planning period as an objective function, considers power balance constraint, voltage constraint, power flow constraint and connectivity radiation constraint, introduces credibility indexes, and processes branch power constraint and node voltage constraint by adopting fuzzy opportunity constraint; the objective function is:
minZcost＝Z1+β·Z2 (1)
the branch power constraint and the node voltage constraint are respectively as follows:
wherein,
Pjmaxfuzzy active power of each line and upper limit of allowable line power;
Vimax、Viminfuzzy voltage values and allowable voltage upper and lower limit values of each node are respectively; alpha is an introduced modelRisk assessment indexes, namely reliability indexes;
respectively, line fuzzy reactive power, node fuzzy active power and reactive power; l is the number of branch circuits of the power distribution network in a certain planning scheme; and N is the number of nodes of the power distribution network in a certain planning scheme.
Equations (4) and (5) are in the form of fuzzy chance constraint programming. The constraint requires that the reliability of the power distribution network branch power and the node voltage which are not out-of-limit is not less than the confidence level preset by a decision maker, the problem that a planning scheme obtained under the conventional constraint condition is too conservative is avoided, and meanwhile, the function of controlling out-of-limit risks is also achieved.
S2: establishing an equivalent model of a given reliability index:
based on the credibility index equivalence theorem, the fuzzy planning model under the given credibility index can be equivalent to an interval planning model. Therefore, given the confidence indicator α (≧ 0.5), equations (1) -6 can be converted to equations (7) -13 for solution:
minZcost＝Z1+β·Z2 (7)
wherein, muξ(y) is a membership function of the fuzzy load; y is fuzzy load
All load values that can be obtained;
the interval expressions corresponding to the fuzzy variables in (expression (1) - (expression (6)) are shown. Due to fuzzy network loss
The fuzzy expectation method is adopted for calculation, so that the method is not equivalent to the interval number; wherein, the confidence index α is required to be greater than 0.5 according to the formula (12) to avoid an inappropriate out-of-limit risk.
The power distribution network planning model under the credibility index is equivalent to the power distribution network planning model under the interval load by adopting the credibility index equivalence theorem, so that the intercept set corresponding to the fuzzy load distribution can be represented by a visual interval;
s3: and solving the model by adopting fuzzy load flow calculation and a genetic algorithm.
Specifically, a genetic algorithm based on Monte Carlo simulation is adopted to solve a fuzzy opportunity constraint power distribution network planning model, and a penalty function is used for processing constraint function out-of-limit. The main solving steps are as follows:
s3.1: inputting net rack original data and basic parameters of a genetic algorithm, wherein the basic parameters comprise the chromosome number, the crossover and variation probability and the like of an initial population, and the chromosome number of the initial population is determined according to the scale of a planned net rack;
s3.2: randomly generating a binary coded chromosome to carry out connected radiation detection, judging whether the connected radiation requirement is met, and if not, correcting the net rack. The correction process is divided into three cases: if the net rack has a ring, the circuit in the ring is randomly disconnected, and then the connectivity radiation inspection is carried out; if the net rack has an island, randomly selecting one line from the alternative lines which are not selected and connected with the island to add into the net rack, and then carrying out connected radiation inspection; if the net rack has an isolated chain, randomly selecting one line from the unselected alternative lines which are associated with any node in the isolated chain, adding the selected line into the net rack, and then carrying out connectivity radiation inspection until the requirement of connectivity radiation is met;
s3.3: sampling fuzzy loads by adopting fuzzy simulation according to the grid structure determined by the chromosome and the distribution of the fuzzy loads, performing deterministic load flow calculation on load data obtained by each sampling, judging whether node voltage fuzzy opportunity constraint and branch load flow fuzzy opportunity constraint are met, and if the constraint is met, taking the load data as an individual in an initial group;
the scheme meeting the node voltage fuzzy opportunity constraint and the branch power flow fuzzy opportunity constraint is a scheme for evaluating the risk level by adopting a fuzzy opportunity constraint verification method. The method comprises the following specific steps:
combining credibility equivalence theorem and checking in fuzzy simulation
Method of (1), can be examined
The method of (1).
Knowing the confidence measure α, for any given decision variable x, assume
Number of intervals of fuzzy vector of n dimension:
(1) setting k to be 0;
(2) are respectively provided with
2 (1-. alpha.)Randomly generating a set of sample values in a truncation interval
(3) If it is not
Satisfy the requirement of
Returning to the step (2); otherwise, the fuzzy chance constraint is not satisfied, and the decision variable x is an infeasible solution.
(4) When k reaches the maximum number of samples M,
can all satisfy
Then the fuzzy chance constraint holds and the decision variable x is a feasible solution.
S3.4: repeating steps S3.2-S3.3 until a defined number of chromosomes of the initial population are generated;
s3.5: calculating target function values of all chromosomes, namely expected values of net rack planning year fixed investment and network loss cost, and calculating fitness values of the chromosomes by adopting a penalty function method for a scheme which does not meet node voltage fuzzy opportunity constraints and branch flow fuzzy opportunity constraints;
specifically, the expected value of the network loss cost is calculated by adopting a fuzzy load flow calculation method,
to define a fuzzy load vector, net loss, over a likelihood space (Θ, p (Θ), Pos)
Is composed of
A function of (a), the function being derivable from a set of load flow calculation equations
The expected value of the loss is
The specific calculation process is as follows:
(1) setting e to be 0;
(2) uniformly generating theta from theta respectivelykMake Pos (theta)k) Greater than or equal to epsilon, let vk＝Pos(θk) K is 1,2 …, N, where epsilon is a sufficiently small number.
(3) Device for placing
(4) Uniformly generating r from [ a, b ];
(5) if r ≧ 0, then
(6) If r < 0, then
(7) Repeating the steps (4) to (6) for N times;
wherein r is not less than 0, and when N is sufficiently large, the reliability is high
Is approximately equal to
And for any r < 0, when N is sufficiently large,credibility
Is approximately equal to
S3.6: selecting the chromosome with the minimum fitness value in the population by adopting a roulette method;
s3.7: carrying out cross and variation operations on chromosomes in the population to obtain a new generation of chromosomes, and carrying out node voltage fuzzy opportunity constraint and branch flow fuzzy opportunity constraint test on the chromosomes;
s3.8: and (5) repeating the steps S3.5-S3.7 until the chromosome reaches the maximum allowable iteration number, so as to obtain the optimal scheme.
The method is characterized by establishing a power distribution network planning model based on a credibility theory based on a fuzzy mathematical theory, considering fuzzy uncertainty of loads, introducing a credibility index by taking the minimum fixed investment and fuzzy expected network loss cost of the power distribution network in a planning period as a target function, and adopting fuzzy opportunity constraint to process branch power and node voltage constraint, thereby achieving the effect of controlling system risk and preventing the obtained optimal scheme from being over conservative; secondly, a power distribution network planning model under the credibility index is equivalent to a power distribution network planning model under the interval load by adopting the credibility index equivalence theorem, so that an intercept set corresponding to the fuzzy load distribution can be represented by an intuitive interval, and a fuzzy load flow calculation and a genetic algorithm are adopted for solving, so that the model solving difficulty is reduced, and the model solving time is shortened; the method for planning the grid structure is suitable for planning the distribution grid structure by similarly considering the fuzzy uncertain factors in the power grid, and has better normative and generalizable properties.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (5)
1. A power distribution network planning method based on a credibility theory comprises the following steps:
s1: establishing a power distribution network fuzzy planning model based on a credibility theory: the method comprises the steps of taking the minimum of fixed investment and fuzzy expected network loss cost of a power distribution network in a planning period as a target function, introducing a reliability index, and processing branch power constraint and node voltage constraint by adopting fuzzy opportunity constraint;
the objective function is:
min Zcos t＝Z1+β·Z2 (1)
wherein Z iscostThe total cost of fixed investment and loss of the power distribution network in a planning period is saved; z1The construction cost for the net rack; z2The annual network loss cost; beta is a network loss cost conversion coefficient, namely a planning year limit; cj、LjInvestment cost and line length are respectively unit length; x is the number ofjIs a decision variable; d is an alternative line set; c0Is unit electricity price; tau isjThe maximum load loss hours of each line;
the loss of each line is blurred;
the branch power constraint and the node voltage constraint are respectively as follows:
wherein,
Pjmaxfuzzy active power of each line and upper limit of allowable line power;
Vimax、Viminfuzzy voltage values and allowable voltage upper and lower limit values of each node are respectively; alpha is an introduced model risk assessment index, namely a reliability index;
respectively, line fuzzy reactive power, node fuzzy active power and reactive power; l is the number of branch circuits of the power distribution network in a certain planning scheme; n is the number of nodes of the power distribution network in a certain planning scheme;
s2: establishing an equivalent model of a given reliability index: the power distribution network planning model under the credibility index is equivalent to the power distribution network planning model under the interval load by adopting the credibility index equivalence theorem, so that the intercept set corresponding to the fuzzy load distribution can be represented by a visual interval;
under the condition that the given reliability index sigma is larger than or equal to 0.5, the equations (1) to (6) are converted into equations (7) to (13) to be solved:
min Zcos t＝Z1+β·Z2 (7)
wherein, muξ(y) is a membership function of the fuzzy load; y is fuzzy load
All the obtained load values;
the interval expressions corresponding to the fuzzy variables in (formula (1) to (6));
s3: solving the model by adopting fuzzy load flow calculation and a genetic algorithm;
and solving a fuzzy opportunity constraint power distribution network planning model by adopting a genetic algorithm based on Monte Carlo simulation, and processing the constraint function out-of-limit by using a penalty function.
2. The method for planning a power distribution network based on the credibility theory as claimed in claim 1, wherein the specific step of step S3 comprises:
s3.1: inputting net rack original data and basic parameters of a genetic algorithm, including the number of chromosomes of an initial population;
s3.2: randomly generating a binary coded chromosome to carry out connected radiation detection, judging whether the connected radiation requirement is met, and if not, correcting the net rack;
s3.3: sampling fuzzy loads by adopting fuzzy simulation according to the grid structure determined by the chromosome and the distribution of the fuzzy loads, performing deterministic load flow calculation on load data obtained by each sampling, judging whether node voltage fuzzy opportunity constraint and branch load flow fuzzy opportunity constraint are met, and if the constraint is met, taking the load data as an individual in an initial group;
s3.4: repeating steps S3.2-S3.3 until a defined number of chromosomes of the initial population are generated;
s3.5: calculating target function values of all chromosomes, namely expected values of net rack planning year fixed investment and network loss cost, and calculating fitness values of the chromosomes by adopting a penalty function method for a scheme which does not meet node voltage fuzzy opportunity constraints and branch flow fuzzy opportunity constraints;
s3.6: selecting the chromosome with the minimum fitness value in the population by adopting a roulette method;
s3.7: carrying out cross and variation operations on chromosomes in the population to obtain a new generation of chromosomes, and carrying out node voltage fuzzy opportunity constraint and branch flow fuzzy opportunity constraint test on the chromosomes;
s3.8: and (5) repeating the steps S3.5-S3.7 until the chromosome reaches the maximum allowable iteration number, so as to obtain the optimal scheme.
3. The credibility theory-based power distribution network planning method according to claim 2, wherein the number of chromosomes of the initial population is determined according to the scale of a planning grid frame.
4. The power distribution network planning method based on the credibility theory as claimed in claim 2, wherein the scheme satisfying the node voltage fuzzy opportunity constraint and the branch power flow fuzzy opportunity constraint is a scheme for evaluating a risk level by using a fuzzy opportunity constraint verification method.
5. The credibility theory-based power distribution network planning method of claim 2, wherein the expected value of the network loss cost is calculated by a fuzzy load flow calculation method.
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