CN106815657B - Power distribution network double-layer planning method considering time sequence and reliability - Google Patents
Power distribution network double-layer planning method considering time sequence and reliability Download PDFInfo
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Abstract
The invention relates to a power distribution network double-layer planning method considering time sequence and reliability. The method comprises the following steps: obtaining typical daily power time sequence curves of wind power, photovoltaic output and load in different seasons according to meteorological data and load power statistical data; establishing a power distribution network frame and distributed power supply capacity double-layer planning mathematical model based on an opportunity constraint planning method, wherein the mathematical model comprises a target function and constraint conditions; solving the model by utilizing a particle swarm optimization algorithm, and ensuring the radiation and connectivity structure of the power distribution network in the iterative process by utilizing a minimum spanning tree algorithm; and obtaining a Pareto optimal solution set of the target network frame and the capacity of the distributed power supply, and generating an optimal planning scheme. The method solves the problem of unnecessary construction investment of the power distribution network caused by the fact that the traditional power distribution network planning method containing the distributed power supply cannot reflect the typical output characteristics of the distributed new energy; (2) the power supply reliability of the power distribution network is brought into a model objective function, so that a certain reliability target is realized in a planning stage.
Description
Technical Field
The invention belongs to the technical field of power distribution network planning, and particularly relates to a power distribution network double-layer planning method considering time sequence and reliability.
Background
The increasing weight of Distributed Generation (DG) in the grid increases the uncertainty in the planning of the distribution network. Traditional power distribution network planning processes distributed power sources into fixed power sources, which obviously do not conform to the operating characteristics of the distributed power sources; or assuming that the wind power or photovoltaic output obeys certain distribution characteristics, then randomly sampling the DG by using a Monte Carlo sampling method and other sampling methods to simulate the output of the DG, but the variation of the DG output along with the power supply season and time period is not reflected, and the uncertainty of the load is usually ignored. In addition, a general power distribution network planning model usually takes economic indicators as a core, and people pay more and more attention to the reliability of a power distribution network along with the development of power technologies. To improve the reliability of the distribution network, consideration of achieving deterministic reliability goals in the planning phase is a recent technical challenge in planning.
The large-scale DG (particularly renewable energy power generation) is concentrated on a medium-voltage distribution network, so that the traditional passive unidirectional power supply distribution network is changed into a bidirectional multi-power supply distribution network, the traditional distribution network planning method cannot solve the technical problem caused by the change, and the active planning technology is developed. The double-layer planning method brings active planning into a lower-layer model, and is different from the traditional power distribution network planning method in that active management and planning on various controllable resources (such as distributed power supplies, transformer taps, reactive compensation equipment and the like) are considered more.
For solving problems of the planning model, most of common methods adopt an intelligent optimization algorithm to solve, but the intelligent algorithm has the defect that a plurality of infeasible solutions are easy to generate in the solving process. In order to ensure the connectivity and the radiancy of the power distribution network in the solving process, most methods carry out manual radiation type repair on the infeasible solutions generated in the calculating process, but the calculating process is complicated.
Disclosure of Invention
The invention aims to provide a power distribution network double-layer planning method considering time sequence and reliability, which solves the problem that the existing power distribution network planning method does not consider the time sequence of DGs and loads, realizes a certain reliability target in a planning stage, solves the problem of complex infeasible solution and repair in a model solving algorithm, improves the technical economy of a power distribution network planning scheme, and realizes a set power supply reliability target while realizing the optimal configuration of a distributed power supply.
In order to achieve the purpose, the technical scheme of the invention is as follows: a power distribution network double-layer planning method considering time sequence and reliability comprises the following steps,
s1, respectively establishing corresponding four-season typical time-series curve models for the wind power generation and photovoltaic power generation output and load power in the power distribution network;
s2, carrying out multi-scene chance constraint processing on the model in the step S1;
s3, establishing a power distribution network double-layer planning mathematical model considering time sequence and reliability, wherein the power distribution network double-layer planning mathematical model comprises a target function and a constraint condition;
and S4, solving the mathematical model in the step S3 by applying a particle swarm optimization algorithm, and ensuring the radiation and connectivity structure of the power distribution network in the iterative process by using a minimum spanning tree method.
In an embodiment of the present invention, the step S2 specifically includes: processing the time series curve data generated in the step S1, and taking the wind, the luminous output and the load power of each hour of each quarter as a scene, wherein the total number of the scenes is 96; carrying out load flow calculation under each scene, verifying whether a calculation result meets a constraint condition, counting the number of the scenes meeting the constraint condition, and dividing the number by the total number of the scenes to obtain the probability of meeting the constraint condition; if the probability reaches a preset value, the chance constraint condition is satisfied.
In an embodiment of the present invention, the mathematical model for double-layer planning of the power distribution network established in step S3 includes
1) Upper layer model
The objective function of the upper layer model is
In the formula: f. of1Expressed as an economic objective, where Cline、CDG、Cen、Closs、CuRespectively investment and operation and maintenance cost of a circuit, investment and operation and maintenance cost of a distributed power supply, power purchasing cost to an upper-level power grid, grid loss cost, environment-friendly and energy-saving benefits of renewable energy sources; f. of2Denotes the reliability target, λreliabilityRepresenting the power supply reliability of the power distribution network;
the constraint conditions of the upper layer model are as follows:
a. power balance constraint
In the formula: piInjecting power for the node i active power; qiReactive power injection for node i, j ∈ i is the set of all nodes directly connected to node i, UiNode/voltage amplitude; gijIs the real part of the nodal admittance matrix; b isijIs the imaginary part of the node admittance matrix; thetaijIs the voltage phase angle difference between nodes i and j;
b. probability constraint of upper and lower limits of node voltage
P{Umin≤U≤Umax}＝ku/N≥βu(3)
In the formula: u shapemaxAnd UminThe upper limit and the lower limit of the node voltage are respectively; k is a radical ofuThe number of scenes satisfying the voltage upper and lower limit constraint in all scenes βuA confidence level for node voltage constraints;
c. branch power probability constraint
P{Pl≤Plmax}＝kl/N≥βl(4)
In the formula: plIs the branch power; plmaxAn upper power limit allowed for the branch; k is a radical oflFor the number of scenarios satisfying the branch power constraint among all scenarios βlIs a confidence level of the branch power constraint;
d. inhibiting reverse power probabilistic constraints
P{PΣDG≤PΣL}＝kB/N≥βB(5)
In the formula: pΣDGAnd PΣLRespectively representing DG total output and load active total demand; k is a radical ofBFor the number of scenarios satisfying the reverse power prohibition constraint among all scenarios βBA confidence level for disabling a reverse power constraint;
e. distributed power source installation capacity constraints
In the formula: pΣPVIs the PV total installation capacity; pΣWGWG total installed capacity; sigma is the maximum permeability of the DG as a renewable energy source; pΣLmaxThe sum of the maximum active load of the distribution network; pPVimaxThe maximum PV installation capacity of the grid-connected node i to be selected is obtained;
PWGimaxthe maximum WG installation capacity of the grid-connected node i to be selected is obtained;
2) lower model
The lower layer model objective function is that the expected value of DG annual active power removal is minimum, namely
In the formula: pcur,z-DGiThe active power removal amount of the ith DG under a scene z is obtained;
the lower layer model constraint conditions are as follows:
a. DG output resection constraint
In the formula:
and
respectively representing the lower limit and the upper limit of the ith DG output excision;
b. reactive compensation equipment switching amount constraint
In the formula: qCiRepresents the switching amount of the reactive compensation equipment at the ith DG installation node,
and
respectively representing the lower limit and the upper limit of the switching quantity of the reactive compensation equipment;
c. transformer tap adjustment range constraints
In the formula: t iskRepresents the switching amount of the reactive compensation equipment at the ith DG installation node,
and
respectively representing the lower and upper limits of the transformer tap adjustment range.
In an embodiment of the present invention, the step S4 of solving the mathematical model is as follows,
s41, initializing data; outputting original data of the power distribution network for planning, and setting parameter values;
s42, initializing a particle population; performing mixed coding according to the upgrading branch variable and the DG capacity variable, and randomly generating an initial population;
s43, obtaining an initial radial network topological structure by adopting a Kruskal algorithm;
s44, load flow calculation; calculating the power flow of the power distribution network by using MATPOWER according to the PV, WG and load power under each scene, and checking whether the constraint conditions of the formulas (2) to (4) are met; if the lower layer model meets the requirement, directly performing the next step, and if the lower layer model does not meet the requirement, starting the lower layer model;
s45, calculating a fitness value; calculating upper-layer objective function values of all individuals according to the load flow calculation result, and setting the fitness to be infinite for the individuals not meeting the probability constraint condition so as to eliminate the individuals in the iteration process; when calculating the power supply reliability of the power distribution network, firstly, carrying out breadth search on the network frame to find out a main feeder line and a branch feeder line, wherein the default longest generalized path is the main feeder line, and then, calculating according to the reliability calculation method in the step S43;
s46, selecting an individual optimal solution and a population optimal solution;
s47, constructing a Pareto optimal solution set of the population, calculating the crowdedness degree of individuals in the Pareto solution set, cutting, and storing the initial Pareto optimal solution set into a Pareto archive set;
s48, iteration, updating the dynamic weight and the learning factor of the particle, and updating the velocity and the position of the particle;
s49, revising the line parameters according to the updated particles, recalculating the branch weight, and obtaining a new network structure by using a minimum spanning tree algorithm; calculating the load flow, judging whether opportunity constraint conditions are met or not, starting a lower layer model if the opportunity constraint conditions are not met, calculating particle fitness values, and updating individual optimal solutions and population optimal solutions;
s410, storing the Pareto optimal solution set of the iterative population into a Pareto file set, processing the Pareto file set, deleting inferior solutions in the Pareto file set, calculating the crowding degree of individuals in the Pareto file set, and cutting the Pareto file set;
s411, judging whether an iteration termination condition is met, if so, outputting a Pareto archive set and ending, otherwise, repeating the steps S48 to S410 until an iteration termination standard is met;
and S42, sequencing the individuals on the Pareto frontier by utilizing an approximate ideal solution sequencing method, and selecting an optimal scheme.
Compared with the prior art, the invention has the following beneficial effects: the invention converts a complex power distribution system into a simple radial power distribution system by using an extent traversal algorithm, directly searches the position of a protection action by using a switch level matrix, analyzes the load fault type through a power accessibility result, calculates the reliability index, and can avoid repeatedly traversing the network topology, thereby greatly improving the efficiency of calculating the reliability of the power distribution network.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a flowchart illustrating the mathematical model solving process of step S4 according to the present invention.
FIG. 3 is an exemplary topology according to the present invention.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
As shown in fig. 1, the method for planning a power distribution network in two layers in consideration of time sequence and reliability of the present invention includes the following steps,
s1, respectively establishing corresponding four-season typical time-series curve models for the wind power generation and photovoltaic power generation output and load power in the power distribution network;
s2, carrying out multi-scene chance constraint processing on the model in the step S1;
s3, establishing a power distribution network double-layer planning mathematical model considering time sequence and reliability, wherein the power distribution network double-layer planning mathematical model comprises a target function and a constraint condition;
and S4, solving the mathematical model in the step S3 by applying a particle swarm optimization algorithm, and ensuring the radiation and connectivity structure of the power distribution network in the iterative process by using a minimum spanning tree method.
The method described in step S2 is as follows:
the time series curve data generated in step S1 is processed, and the wind, the luminous output, and the load power for each hour of each quarter are treated as one scene for a total of 96 scenes. And performing load flow calculation in each scene, verifying whether the calculation result meets the constraint condition, counting the number of the scenes meeting the constraint condition, and dividing the number by the total number of the scenes to obtain the probability of meeting the constraint condition. If the probability reaches a predetermined value (e.g., 90%), the chance constraint is satisfied.
The power distribution network double-layer planning mathematical model established in the step S3 comprises
1) Upper layer model
The objective function of the upper model is that the decision variables are the line model to be upgraded, the line to be newly built and the installation capacity of the DG;
in the formula: f. of1Expressed as an economic objective, where Cline、CDG、Cen、Closs、CuRespectively investment and operation and maintenance cost of a circuit, investment and operation and maintenance cost of a distributed power supply, power purchasing cost to an upper-level power grid, grid loss cost, environment-friendly and energy-saving benefits of renewable energy sources; f. of2Denotes the reliability target, λreliabilityRepresenting the power supply reliability of the power distribution network;
in the formula (1) f1Including the following cost charges:
(1.1) investment and operation and maintenance costs of the line, the calculation formula is shown as formula (2) and formula (3), the line comprises an upgraded line and a newly-built line
Cline＝CIline+COMline(2)
In the formula: cIlineThe equal annual value of investment is fixed for the line; cOMlineAnnual operating and maintenance costs for the line; omegaL1A set of newly-built lines is created; omegaL2Is a collection of upgrade lines; omegaLIs the set of all lines;
investment cost for newly building a line in unit length;
upgrading cost for upgrading the unit length of the line; l is the line length; r is the discount rate; n islineThe investment recovery period is fixed for the line; omegaLIs the set of all lines; gamma is the line maintenance costRate;
(1.2) investment and operation and maintenance costs of the distributed power supply, the calculation formula is shown as formula (4) and formula (5)
CDG＝CIDG+COMDG(4)
In the formula, CIDGThe equal annual value of investment is fixed for renewable energy DG; cOMDGAnnual operating and maintenance costs for the renewable energy DG; cfPVInstallation cost per unit capacity of Photovoltaic (PV); omegapvCreating a new PV set; pPVjA PV mounting capacity; cfWGInstallation cost per unit capacity for wind power (WG); omegaWGCreating a WG set; pWGkInstalling capacity for WG; n isDGA fixed investment recovery period for DG; comPVTransportation and maintenance cost of PV unit electric quantity; comWGThe operating and maintenance cost of the WG unit electricity quantity. OmegazIs a collection of scenes; tau iszAccumulating the running time of the distribution network in the scene z; pz-PVjThe active output of the jth PV under the scene z is; pz-WGkThe active output of the kth WG in a scene z;
(1.3) cost of purchasing electricity to the upper-level power grid
In the formula: ceEnergy cost per unit of electricity; n is the total number of the distribution network load nodes; pz-LiThe active load power of the distribution network nodes under the scene z is obtained;
(1.4) loss on line cost
In the formula, △ Pz-iThe active power loss of the line i under the scene z;
(1.5) environmental protection and energy saving benefits of renewable energy
Expressed by government subsidies on renewable energy generation
In the formula: pz-DGiThe active output of the ith DG under the scene z;
in the formula (1) f2The calculation method of (2) is as follows:
f2middle lambdareliabilityI.e. the power supply reliability, the greater the power supply reliability for the distribution network, the better, here by f2Converting the power supply reliability index into a smaller and more optimal form, namely lambdareliabilityThe calculation procedure is as follows.
1. Inputting net rack topology parameters, fault rate, fault repair time, line length and load parameters;
2. establishing a feeder area by taking the switch element as a boundary;
3. enumerating faults in a feeder line area in sequence, and disconnecting an action breaker and an isolating switch;
4. from the DG access point, adopting the principle of near recovery, and searching the load capable of recovering power supply in a wide range;
5. and calculating a reliability index.
The constraint conditions of the upper layer model are as follows:
a. power balance constraint
In the formula: piInjecting power for the node i active power; qiReactive power injection for node i, j ∈ i is the set of all nodes directly connected to node i, UiNode/voltage amplitude; gijIs the real part of the nodal admittance matrix; b isijIs the imaginary part of the node admittance matrix; thetaijIs the voltage phase angle difference between nodes i and j;
b. probability constraint of upper and lower limits of node voltage
P{Umin≤U≤Umax}＝ku/N≥βu(10)
In the formula: u shapemaxAnd UminThe upper limit and the lower limit of the node voltage are respectively; k is a radical ofuThe number of scenes satisfying the voltage upper and lower limit constraint in all scenes βuA confidence level for node voltage constraints;
c. branch power probability constraint
P{Pl≤Plmax}＝kl/N≥βl(11)
In the formula: plIs the branch power; plmaxAn upper power limit allowed for the branch; k is a radical oflFor the number of scenarios satisfying the branch power constraint among all scenarios βlIs a confidence level of the branch power constraint;
d. inhibiting reverse power probabilistic constraints
P{PΣDG≤PΣL}＝kB/N≥βB(12)
In the formula: pΣDGAnd PΣLRespectively representing DG total output and load active total demand; k is a radical ofBFor the number of scenarios satisfying the reverse power prohibition constraint among all scenarios βBA confidence level for disabling a reverse power constraint;
e. distributed power source installation capacity constraints
In the formula: pΣPVIs the PV total installation capacity; pΣWGWG total installed capacity; sigma is the maximum permeability of the DG as a renewable energy source; pΣLmaxThe sum of the maximum active load of the distribution network; pPVimaxThe maximum PV installation capacity of the grid-connected node i to be selected is obtained;
PWGimaxthe maximum WG installation capacity of the grid-connected node i to be selected is obtained;
2) lower model
The lower layer model objective function is that the expected value of DG annual active power removal is minimum, namely
In the formula: pcur,z-DGiThe active power removal amount of the ith DG under a scene z is obtained;
the lower layer model constraint conditions are as follows:
a. DG output resection constraint
In the formula:
and
respectively representing the lower limit and the upper limit of the ith DG output excision;
b. reactive compensation equipment switching amount constraint
In the formula: qCiRepresents the switching amount of the reactive compensation equipment at the ith DG installation node,
and
respectively representing the lower limit and the upper limit of the switching quantity of the reactive compensation equipment;
c. transformer tap adjustment range constraints
In the formula: t iskRepresents the switching amount of the reactive compensation equipment at the ith DG installation node,
and
respectively representing the lower and upper limits of the transformer tap adjustment range.
As shown in fig. 2, the mathematical model solving step of step S4 is as follows,
s41, initializing data; outputting original data of the power distribution network for planning, and setting parameter values;
s42, initializing a particle population; performing mixed coding according to the upgrading branch variable and the DG capacity variable, and randomly generating an initial population;
s43, obtaining an initial radial network topological structure by adopting a Kruskal algorithm;
s44, load flow calculation; calculating the power flow of the power distribution network by using MATPOWER according to the PV, WG and load power under each scene, and checking whether the constraint conditions of the formulas (2) to (4) are met; if the lower layer model meets the requirement, directly performing the next step, and if the lower layer model does not meet the requirement, starting the lower layer model;
s45, calculating a fitness value; calculating upper-layer objective function values of all individuals according to the load flow calculation result, and setting the fitness to be infinite for the individuals not meeting the probability constraint condition so as to eliminate the individuals in the iteration process; when calculating the power supply reliability of the power distribution network, firstly, carrying out breadth search on the network frame to find out a main feeder line and a branch feeder line, wherein the default longest generalized path is the main feeder line, and then, calculating according to the reliability calculation method in the step S43;
s46, selecting an individual optimal solution and a population optimal solution;
s47, constructing a Pareto optimal solution set of the population, calculating the crowdedness degree of individuals in the Pareto solution set, cutting, and storing the initial Pareto optimal solution set into a Pareto archive set;
s48, iteration, updating the dynamic weight and the learning factor of the particle, and updating the velocity and the position of the particle;
s49, revising the line parameters according to the updated particles, recalculating the branch weight, and obtaining a new network structure by using a minimum spanning tree algorithm; calculating the load flow, judging whether opportunity constraint conditions are met or not, starting a lower layer model if the opportunity constraint conditions are not met, calculating particle fitness values, and updating individual optimal solutions and population optimal solutions;
s410, storing the Pareto optimal solution set of the iterative population into a Pareto file set, processing the Pareto file set, deleting inferior solutions in the Pareto file set, calculating the crowding degree of individuals in the Pareto file set, and cutting the Pareto file set;
s411, judging whether an iteration termination condition is met, if so, outputting a Pareto archive set and ending, otherwise, repeating the steps S48 to S410 until an iteration termination standard is met;
and S42, sequencing the individuals on the Pareto frontier by utilizing an approximate ideal solution sequencing method, and selecting an optimal scheme.
The technical scheme of the invention is further explained by combining specific examples.
The method of the invention is applied to plan the line selection to be upgraded, the position of the newly-built line and the capacity of the distributed power supply for the power distribution network calculation example shown in figure 3. In fig. 3, the solid line is the established line and the line to be upgraded, the dotted line is the line to be newly established, the number represents the node number, and the number in the parenthesis represents the line number. Wherein 6 load nodes (nodes 34-39) are newly added, and 24 lines (branches 38-61) are to be newly built. The confidence level for all opportunity constraints is taken to be 90%. The installation reference capacity of the DGs is 100kW, and the maximum permeability is 50%. Table 1 shows the upper limit of the positions and the installation numbers of the nodes to be connected to the distributed power supply. The original line parameters are: the unit cost is 6 ten thousand yuan/km, the unit impedance is 0.85+ j0.42 omega/km, and the maximum current is 170A. The parameters of the upgrade line type 1 are: the unit cost is 8 ten thousand yuan/km, the unit impedance is 0.45+ j0.40 omega/km, and the maximum current is 380A. The parameters of upgrade line type 2 are: the unit cost is 10 ten thousand yuan/km, the unit impedance is 0.27+ j0.38 omega/km, and the maximum current is 275A. The line operation maintenance cost rate is 0.03, the fixed investment recovery period is 20 years, and the discount rate is 10%. The fixed investment recovery period of DG is 10 years, and the investment cost of unit electric quantity PV and WG is 0.8 and 0.6 ten thousand yuan/kW respectively; the operation and maintenance costs of the unit electric quantity PV and the unit electric quantity WG are 0.15 yuan/kW.h and 0.2 yuan/kW.h respectively; the energy cost per unit of electricity is 0.4 yuan/kW.h. To compare the timing of DG and load with the effect of random sampling on the planning, DG and load are set to obey the following distribution. WG: the shape parameter of Weibull distribution is 3.97, the scale parameter is 10.7, the cut-in wind speed is 3m/s, the rated wind speed is 14m/s, and the cut-off wind speed is 25 m/s; PV: beta has a shape parameter alpha of 2, Beta of 0.8 and a maximum illumination intensity of 600W/m 2; loading: obeying a normal distribution with a variance of 0.2Pload, expected to be Pload.
TABLE 1 upper limit of installation position and installation number of distributed power supplies
The planning scheme obtained by the method is marked as scheme 1; the time sequence is not considered, the DG and the load power are obtained by a random sampling method, and the obtained planning scheme is recorded as a scheme 2; regardless of reliability, the resulting planning scheme is denoted as scheme 3. The planning results are shown in table 2. Wherein, the numbers in brackets of the upgrade circuit and the model represent line types, and the numbers outside the number represent the circuit number; the newly-built line represents the serial number of the line to be newly built; the numbers in the brackets of the DG capacity indicate the node positions, and the numbers outside the brackets indicate the number of installations.
Table 2 plan scheme results comparison
As can be seen from table 2, the method adopted by the present invention ensures the reliability of the distribution network while reducing the planning economic cost, and although the scheme 3 reduces the economic cost, the reliability is also reduced.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (3)
1. A power distribution network double-layer planning method considering time sequence and reliability is characterized in that: comprises the following steps of (a) carrying out,
s1, respectively establishing corresponding four-season typical time-series curve models for the wind power generation and photovoltaic power generation output and load power in the power distribution network;
s2, carrying out multi-scene chance constraint processing on the model in the step S1;
s3, establishing a power distribution network double-layer planning mathematical model considering time sequence and reliability, wherein the power distribution network double-layer planning mathematical model comprises a target function and a constraint condition;
s4, solving the mathematical model in the step S3 by applying a particle swarm optimization algorithm, and ensuring the radiation and connectivity structure of the power distribution network in the iterative process by using a minimum spanning tree method;
the power distribution network double-layer planning mathematical model established in the step S3 comprises
1) Upper layer model
The objective function of the upper layer model is
In the formula: f. of1Expressed as an economic objective, where Cline、CDG、Cen、Closs、CuRespectively investment and operation and maintenance cost of a circuit, investment and operation and maintenance cost of a distributed power supply, power purchasing cost to an upper-level power grid, grid loss cost, environment-friendly and energy-saving benefits of renewable energy sources; f. of2Denotes the reliability target, λreliabilityRepresenting the power supply reliability of the power distribution network;
the constraint conditions of the upper layer model are as follows:
a. power balance constraint
In the formula: piInjecting power for the node i active power; qiReactive power injection for node i, j ∈ i is the set of all nodes directly connected to node i, UiIs the voltage amplitude of node i, UjIs the voltage amplitude of node j; gijIs the real part of the nodal admittance matrix; b isijIs the imaginary part of the node admittance matrix; thetaijIs the voltage phase angle difference between nodes i and j;
b. probability constraint of upper and lower limits of node voltage
P{Umin≤U≤Umax}＝ku/N≥βu(3)
In the formula: u shapemaxAnd UminThe upper limit and the lower limit of the node voltage are respectively; k is a radical ofuThe number of scenes satisfying the voltage upper and lower limit constraint in all scenes βuA confidence level for node voltage constraints; n is the total number of scenes;
c. branch power probability constraint
P{Pl≤Plmax}＝kl/N≥βl(4)
In the formula: plIs the branch power; plmaxAn upper power limit allowed for the branch; k is a radical oflFor the number of scenarios satisfying the branch power constraint among all scenarios βlIs a confidence level of the branch power constraint;
d. inhibiting reverse power probabilistic constraints
P{PΣDG≤PΣL}＝kB/N≥βB(5)
In the formula: pΣDGAnd PΣLRespectively representing DG total output and load active total demand; k is a radical ofBFor the number of scenarios satisfying the reverse power prohibition constraint among all scenarios βBA confidence level for disabling a reverse power constraint;
e. distributed power source installation capacity constraints
In the formula: pΣPVIs the PV total installation capacity; pΣWGWG total installed capacity; sigma is the maximum permeability of the DG as a renewable energy source; pΣLmaxThe sum of the maximum active load of the distribution network; pPVimaxThe maximum PV installation capacity of the grid-connected node i to be selected is obtained; pWGimaxThe maximum WG installation capacity of the grid-connected node i to be selected is obtained; wherein PV represents photovoltaic and WG represents wind power;
2) lower model
The lower layer model objective function is that the expected value of DG annual active power removal is minimum, namely
In the formula: f is the lower model objective function, τZCumulative running time of distribution network in scene zcur,z-DGiIs the active power removal amount, omega, of the ith DG under the scene zzFor the set of all scenes, ΩDGIs the set of all DGs;
the lower layer model constraint conditions are as follows:
a. DG output resection constraint
In the formula: pcur,z-DGiFor the amount of active power cut of the ith DG in scene z,
and
respectively representing the lower limit and the upper limit of the ith DG output excision;
b. reactive compensation equipment switching amount constraint
In the formula: qCiRepresents the switching amount of the reactive compensation equipment at the ith DG installation node,
and
respectively representing the lower limit and the upper limit of the switching quantity of the reactive compensation equipment;
c. transformer tap adjustment range constraints
In the formula: t iskRepresents the switching amount of the reactive compensation equipment at the ith DG installation node,
and
respectively representing the lower and upper limits of the transformer tap adjustment range.
2. The power distribution network double-layer planning method considering time sequence and reliability according to claim 1, characterized in that: the step S2 specifically includes: processing the time series curve data generated in the step S1, and taking the wind, the luminous output and the load power of each hour of each quarter as a scene, wherein the total number of the scenes is 96; carrying out load flow calculation under each scene, verifying whether a calculation result meets a constraint condition, counting the number of the scenes meeting the constraint condition, and dividing the number by the total number of the scenes to obtain the probability of meeting the constraint condition; if the probability reaches a preset value, the chance constraint condition is satisfied.
3. The power distribution network double-layer planning method considering time sequence and reliability according to claim 1, characterized in that: the step S4 solving the mathematical model is as follows,
s41, initializing data; outputting original data of the power distribution network for planning, and setting parameter values;
s42, initializing a particle population; performing mixed coding according to the upgrading branch variable and the DG capacity variable, and randomly generating an initial population;
s43, obtaining an initial radial network topological structure by adopting a Kruskal algorithm;
s44, load flow calculation; calculating the power flow of the power distribution network by using MATPOWER according to the PV, WG and load power under each scene, and checking whether the constraint conditions of the formulas (2) to (4) are met; if the lower layer model meets the requirement, directly performing the next step, and if the lower layer model does not meet the requirement, starting the lower layer model;
s45, calculating a fitness value; calculating upper-layer objective function values of all individuals according to the load flow calculation result, and setting the fitness to be infinite for the individuals not meeting the probability constraint condition so as to eliminate the individuals in the iteration process; when calculating the power supply reliability of the power distribution network, firstly, carrying out breadth search on the network frame to find out a main feeder line and a branch feeder line, wherein the default longest generalized path is the main feeder line, and then, calculating according to the reliability calculation method in the step S43;
s46, selecting an individual optimal solution and a population optimal solution;
s47, constructing a Pareto optimal solution set of the population, calculating the crowdedness degree of individuals in the Pareto solution set, cutting, and storing the initial Pareto optimal solution set into a Pareto archive set;
s48, iteration, updating the dynamic weight and the learning factor of the particle, and updating the velocity and the position of the particle;
s49, revising the line parameters according to the updated particles, recalculating the branch weight, and obtaining a new network structure by using a minimum spanning tree algorithm; calculating the load flow, judging whether opportunity constraint conditions are met or not, starting a lower layer model if the opportunity constraint conditions are not met, calculating particle fitness values, and updating individual optimal solutions and population optimal solutions;
s410, storing the Pareto optimal solution set of the iterative population into a Pareto file set, processing the Pareto file set, deleting inferior solutions in the Pareto file set, calculating the crowding degree of individuals in the Pareto file set, and cutting the Pareto file set;
s411, judging whether an iteration termination condition is met, if so, outputting a Pareto archive set and ending, otherwise, repeating the steps S48 to S410 until an iteration termination standard is met;
and S42, sequencing the individuals on the Pareto frontier by utilizing an approximate ideal solution sequencing method, and selecting an optimal scheme.
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