CN111027807A - Distributed power generation site selection and volume fixing method based on power flow linearization - Google Patents
Distributed power generation site selection and volume fixing method based on power flow linearization Download PDFInfo
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Abstract
The invention discloses a distributed power generation site selection and volume fixing method based on trend linearization, which comprises the steps of firstly, establishing a double-layer planning model of distributed power generation site selection and volume fixing by simultaneously considering the economic benefit of wind and light investment and the economic cost of a power distribution network, and enabling the model to be closer to the actual operation scene of a power grid, so that the method has better feasibility, higher accuracy and better robustness; then based on a convex relaxation method, a variable linearization method, a second order cone approximation and a KKT optimality condition, the nonlinear items in the originally proposed non-convex model distributed power generation site selection constant volume double-layer programming model are linearized and further converted into a completely linear solvable single-layer multi-target linear programming model, so that the model solving complexity is greatly reduced, the calculation complexity is lower, the model is simpler and faster, the converted solving result is very close to the solving result for linearization conversion, and the calculation complexity can be greatly reduced under the condition of ensuring the accuracy.
Description
Technical Field
The invention belongs to the technical field of distributed power generation site selection and volume fixing, and particularly relates to a distributed power generation site selection and volume fixing method based on power flow linearization.
Background
With the continuous opening of the electric power market, the continuous increase of the electric power demand and the gradual exhaustion of the traditional fossil energy, the distributed energy such as wind energy, solar energy and the like starts to play an increasingly important role in the electric power system. In recent years, the national energy agency has issued a plurality of policy documents such as 'notice about relevant matters of construction of wind power and photovoltaic power generation projects in 2019', which indicates that the policy of distributed power generation projects in China is further improved. By the end of 2018, the national wind power and photovoltaic installation reaches 3.6 hundred million kilowatts, and accounts for nearly 20 percent of the whole installation. The electricity generation of wind power and photovoltaic is 6000 hundred million kilowatt hours all the year round, and the electricity generation accounts for nearly 9 percent of the total electricity generation. Meanwhile, the problem of wind and light abandonment is particularly serious, and the wind and light abandonment power in 2018 of three provinces of Xinjiang, Gansu and inner Mongolia exceeds 300 hundred million kilowatt hours. With the continuous increase of the access capacity of the distributed power supply of the distribution network, the disordered access of the distributed power supply causes a series of adverse effects such as voltage rise, difficulty in consumption, low power quality and the like on the distribution network system, and the uncertain factors of the distribution network are increased to a great extent. Factors such as unreasonable site selection and volume fixing of the distributed power supply severely restrict the new energy consumption level.
The distributed power supply is accessed into the power grid in an optimized and friendly manner through site selection and volume fixing, and the effective measures for solving the problems of wind and light abandonment in a large scale and improving the consumption level of new energy are achieved. The traditional fixed weight method for processing the multi-target power grid planning problem of the multi-type distributed investors has the defect that the potential interest competition relationship of each actual distributed power generator cannot be reflected. Because conditions such as load requirements, climate factors and the like are dynamically changed, the investment income and the investment intention of each distributed investor are likely to change, the fixed weight method cannot well reflect the dynamic characteristics of the actual power distribution network, and the planning result is inaccurate. The existing method mainly adopts a heuristic algorithm to solve, the heuristic algorithm can perform calculation in an iterative mode, but the calculation real-time performance is sacrificed to a certain extent, the precision is still to be examined, the model has a series of problems of overhigh dimensionality, difficult optimization, long solving time and the like, and the practicability of the model is relatively limited.
In summary, it is an urgent need to solve the problem of providing a distributed power generation site selection and sizing method with low computational complexity and accurate planning.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a distributed power generation site selection and volume fixing method based on power flow linearization, and aims to solve the technical problem of high calculation complexity caused by repeated iteration due to adoption of a heuristic algorithm in the prior art.
In order to achieve the purpose, the invention provides a distributed power generation site selection and volume fixing method based on power flow linearization, which comprises the following steps:
s1, on the basis of an actual power distribution network operation scene, by considering the economic benefit of wind and light investment and the economic cost of a power distribution network, taking the optimal economic benefit of wind and light investment as an upper-layer optimization target, and taking the minimum annual operation economic cost of the power distribution network as a lower-layer optimization target, establishing a distributed power generation site selection and volume fixing double-layer planning model;
s2, based on a convex relaxation method, a variable linearization method, a second-order cone approximation and a KKT optimality condition, carrying out linearization processing on a nonlinear item in a double-layer planning model of distributed power generation site selection and volume fixing, and converting the double-layer planning model into a single-layer multi-target linear planning model;
and S3, acquiring grid structure data and actual distributed power generation output data of each typical day in the last year, inputting the data into the multi-target linear programming model, and solving the multi-target linear programming model to obtain the optimal distributed power generation site selection and volume fixing scheme.
Further preferably, the method of step S1, includes the following steps:
s11, establishing an upper-layer distributed investment capacity optimization model by taking the optimal wind and light investment economy as a target and considering investment budget and economic benefit constraints;
s12, with the goals of lowest annual economic operation cost of the power distribution network and the maximum clean energy consumption level, considering power flow constraint, stability constraint and distributed power supply capacity constraint of the power distribution network, deciding the built-in address of the distributed power supply and the built-in capacity of each corresponding point, and establishing a location and volume selection optimization model of the distributed power supply of the lower power distribution network;
and S13, integrating the upper-layer distributed investment capacity optimization model and the lower-layer distribution network distributed power source location and volume optimization model to obtain a distributed power generation location and volume double-layer planning model.
Further preferably, the objective function of the upper distributed investment planning capacity optimization model is expressed as follows:
wherein, F1(x) Annual profit for wind power supplier, F2(x) T represents a time period set, omega represents a site selection site set of wind power and photovoltaic power stations, each site selection site is a power grid node,
the actual wind power access quantity d of the power grid in the time period t of the kth nodefIs the power price of the unit wind power, delta t is the duration of each time interval in the operation period, RfIs the investment cost, k, of the installed capacity of a unit wind turbinefF (A/P) is the annual fund present value coefficient, CFFor the total installed capacity of wind power, cfwFor the maintenance cost factor of the wind turbine,
the actual photovoltaic access quantity d of the power grid in the time period t at the kth nodegOn-line electricity price per unit photovoltaic electricity quantity, RgIs the investment cost, k, of installed capacity of a unit of photovoltaic unitgIs the residual value rate, C, of the photovoltaic unitGTo the total installed photovoltaic capacity, cgwThe investment cost R of unit installed capacity of the wind turbine is the maintenance cost coefficient of the photovoltaicfAnd the investment cost R of installed capacity of unit photovoltaic unitgAnd the investment budget constraint is met.
Further preferably, an objective function of the lower-layer power distribution network distributed power supply location capacity optimization model is represented as follows:
minf(x)＝Ccost+Cpub
wherein f (x) is the total power supply cost of the distribution company, CcostPurchase cost of electricity for distribution network, CpubIn order to avoid punishment cost of wind and light abandonment, T represents a time period set, omega represents a site selection set of wind power and photovoltaic power stations, each site selection is a power grid node,
d is the actual wind power access quantity of the power grid in the time period t of the ith nodefThe unit wind power electricity quantity is the power price on the internetffIs the operation and maintenance cost of unit wind power, delta t is the time length of each time interval in the operation period,
the actual photovoltaic access quantity d of the power grid in the time period t at the ith nodegElectricity price for the unit photovoltaic powergfIs the operation and maintenance cost per photovoltaic power, dgridTo purchase a price per unit of electricity from the main network,
purchasing electric quantity k for the power grid in the t time period at the ith nodepubAs a penalty factor, Ci fThe installed capacity of the wind power at the ith node is foutput (t), which is the output of a typical daily power curve of the wind power at the time t, FfFor the reference capacity of the typical solar output curve of wind power, goutput (t) is the output of the typical solar output curve of photovoltaic at the moment t, FgIs the baseline capacity of a typical solar output curve of a photovoltaic,
the installed photovoltaic capacity at the ith node is obtained.
Further preferably, the lower-layer power distribution network distributed power supply location capacity optimization model meets power balance constraint, power flow constraint, distributed power supply output constraint, node voltage constraint, power grid purchase power constraint, line current-carrying capacity constraint, distributed power supply total capacity constraint and power grid transformer capacity constraint.
Further preferably, the method of step S2, includes the following steps:
s21, combining a convex relaxation method and a variable linearization method, performing second-order conical linear approximation on a nonlinear term of power flow constraint in the distributed power generation localization and sizing double-layer planning model to obtain a double-layer linear planning model;
and S22, processing the double-layer linear programming model based on the KKT optimality condition, and converting the lower-layer programming model into the upper-layer programming model to obtain a completely linear solvable single-layer multi-target linear programming model.
The method greatly reduces the solving complexity of the double-layer planning model of the distributed power generation site selection constant volume, has lower calculating complexity, is simpler and quicker, and can greatly reduce the calculating complexity under the condition of ensuring the accuracy, and the converted solving result is very close to the solving result for linear conversion.
Further preferably, the pareto optimal front edge of the single-layer multi-target linear programming model is solved, and the solution with the highest comprehensive fitness in the pareto optimal front edge solution set serves as the optimal distributed power generation site selection constant volume scheme. Solving the pareto optimal front edge can better reflect the dynamic change of each distributed investor in the power grid, and can also better reflect the interest competition relationship of each investor in the model.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
1. the invention provides a distributed power generation site selection constant volume method based on power flow linearization, which realizes approximate convexity of a non-convex model, approximate linearization of a non-linear model and single-layer formation of the model by a convex relaxation method, a variable linearization method, a second-order cone approximation and a KKT optimality condition, so that nonlinear items in a double-layer planning model of the non-convex model distributed power generation site selection constant volume originally provided by the invention are subjected to linearization processing and further converted into a completely linear solvable single-layer multi-target linear programming model, the model solving complexity is greatly reduced, the calculation complexity is lower, the method is simpler and faster, the converted solving result is very close to the solving result for linearization conversion, and the calculation complexity can be greatly reduced under the condition of ensuring the accuracy.
2. According to the distributed power generation site selection and volume fixing method based on the trend linearization, the economic benefit of wind and light investment and the economic cost of the power distribution network are considered at the same time, the optimal economic benefit of the wind and light investment is taken as an upper-layer optimization target, the minimum annual operation economic cost of the power distribution network is taken as a lower-layer optimization target, a distributed power generation site selection and volume fixing double-layer planning model is established, the distributed power generation site selection and volume fixing double-layer planning model is closer to the actual operation scene of the power distribution network, and the distributed power generation site selection and volume fixing.
3. The upper-layer distributed investment capacity optimization model provided by the invention takes the profit competition relationship of multiple distributed investors into consideration, considers the investment budget and economic benefit constraints, and better meets the actual engineering requirements.
4. The lower-layer power distribution network distributed power supply location and volume optimization model provided by the invention meets the target requirement of lowest annual economic operation cost of the power distribution network, considers the power distribution network stability constraint, the power flow constraint and the distributed power supply commissioning capacity constraint, can better reflect the actual operation scene of the power distribution network, and has higher accuracy of planning accurate results.
5. The distributed power generation site selection and volume fixing method based on the power flow linearization, which is provided by the invention, obtains the optimal distributed power generation site selection and volume fixing scheme by solving the pareto optimal front edge of the single-layer multi-target linear programming model, can better reflect the dynamic change of each distributed investor in a power grid, and can better reflect the interest competitive relationship of each investor in the model.
6. The distributed power generation site selection and volume fixing method based on the power flow linearization, provided by the invention, can obtain a practical and feasible optimal site selection and volume fixing planning result in different scenes, and has better robustness.
Drawings
FIG. 1 is a flow chart of a distributed power generation site selection and sizing method based on power flow linearization, which is provided by the invention;
FIG. 2 is a schematic diagram of a two-tier planning model for a distributed power generation siting volume.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
In order to achieve the above object, the present invention provides a distributed power generation site selection and sizing method based on power flow linearization, as shown in fig. 1, including the following steps:
s1, on the basis of an actual power distribution network operation scene, by considering the economic benefit of wind and light investment and the economic cost of a power distribution network, taking the optimal economic benefit of wind and light investment as an upper-layer optimization target, and taking the minimum annual operation economic cost of the power distribution network as a lower-layer optimization target, establishing a distributed power generation site selection and volume fixing double-layer planning model;
specifically, the distributed power generation site selection and volume fixing double-layer planning model is shown in fig. 2 and comprises an upper-layer distributed investment capacity optimization model and a lower-layer distribution network distributed power source site selection and volume fixing optimization model.
Specifically, the method for establishing the distributed power generation site selection constant volume double-layer planning model comprises the following steps:
s11, establishing an upper-layer distributed investment capacity optimization model by taking the optimal wind and light investment economy as a target and considering investment budget and economic benefit constraints;
specifically, the objective function of the upper-layer distributed investment planning capacity optimization model is expressed as follows:
wherein, F1(x) Annual profit for wind power supplier, F2(x) T represents a time period set, omega represents a site selection site set of wind power and photovoltaic power stations, each site selection site is a power grid node,
the actual wind power access quantity d of the power grid in the time period t of the kth nodefIs the power price of the unit wind power, delta t is the duration of each time interval in the operation period, RfIs the investment cost, k, of the installed capacity of a unit wind turbinefF (A/P) is the annual fund present value coefficient, CFFor the total installed capacity of wind power, cfwFor the maintenance cost factor of the wind turbine,
the actual photovoltaic access quantity d of the power grid in the time period t at the kth nodegOn-line electricity price per unit photovoltaic electricity quantity, RgIs the investment cost, k, of installed capacity of a unit of photovoltaic unitgIs the residual value rate, C, of the photovoltaic unitGTo the total installed photovoltaic capacity, cgwIs the maintenance cost coefficient of the photovoltaic.
The constraint of the upper-layer distributed investment capacity optimization model is mainly investment budget constraint, and for a distributed investor, the total one-time investment of the distributed investor is required to be within the fund range, namely:
wherein R isfInvestment cost per installed capacity of the wind turbine, CFFor the total installed capacity of wind power, FTmaxMaximum investable capital, R, for wind power and photovoltaic investorsgInvestment cost for installed capacity of photovoltaic unit, CGGT of the total photovoltaic installed capacitymaxThe method is the maximum investable capital of the photovoltaic investor. Therein, taking into account the distributionFormula electricity generation economic benefits, occupation of land factor, wind power total installed capacity CFAnd total photovoltaic installed capacity CGThe following constraints should also be satisfied:
wherein, CFmax、CFminRespectively representing the upper limit and the lower limit of the total wind power access capacity, CGmax、CGminRepresents the upper and lower limits of the total photovoltaic access capacity.
S12, with the goals of lowest annual economic operation cost of the power distribution network and the maximum clean energy consumption level, considering power flow constraint, stability constraint and distributed power capacity constraint of the power distribution network, deciding the built-in addresses of the distributed power and the built-in capacity of each corresponding point, and building a location and volume selection optimization model of the distributed power of the lower power distribution network.
The main body of the lower-layer power distribution network distributed power supply location and volume optimization model is a power distribution network, and the economic cost of the whole-year operation of the power distribution network is the minimum. The economy of the lower-layer main body in the model mainly considers the electricity purchasing cost of the power distribution network to the distributed power generation party, the electricity purchasing cost of the power distribution network to the upper-layer main network and the wind and light abandoning cost, and therefore the objective function of the lower-layer power distribution network distributed power locating and volume optimizing model is expressed as follows:
minf(x)＝Ccost+Cpub
wherein f (x) is the total power supply cost of the distribution company, CcostPurchase cost of electricity for distribution network, CpubIn order to avoid punishment cost of wind and light abandonment, T represents a time period set, omega represents a site selection set of wind power and photovoltaic power stations, each site selection is a power grid node,
d is the actual wind power access quantity of the power grid in the time period t of the ith nodefThe unit wind power electricity quantity is the power price on the internetffIs the operation and maintenance cost of unit wind power, delta t is the time length of each time interval in the operation period,
the actual photovoltaic access quantity d of the power grid in the time period t at the ith nodegElectricity price for the unit photovoltaic powergfIs the operation and maintenance cost per photovoltaic power, dgridTo purchase a price per unit of electricity from the main network,
purchasing electric quantity k for the power grid in the t time period at the ith nodepubIn order to be a penalty factor,
the installed capacity of the wind power at the ith node is foutput (t), which is the output of a typical daily power curve of the wind power at the time t, FfFor the reference capacity of the typical solar output curve of wind power, goutput (t) is the output of the typical solar output curve of photovoltaic at the moment t, FgIs the baseline capacity of a typical solar output curve of a photovoltaic,
the installed photovoltaic capacity at the ith node is obtained.
The power distribution network is one of the most important parts in the power system, and should meet the basic operation constraints of the system, namely power balance constraint, node voltage constraint, line current-carrying capacity constraint and the like. Specifically, the constraint of the lower-layer power distribution network distributed power supply location and volume optimization model comprises the following steps:
1. power balance constraint
The power balance constraint is the most basic constraint of a power system, and the active and reactive power balance constraints of the system must be considered when the power distribution network runs:
wherein the content of the first and second substances,
the actual wind power access quantity of the power grid in the time period t at the ith node is obtained,
the actual photovoltaic access amount of the power grid in the t time period at the ith node is,
purchasing electric quantity for the power grid in the t time period at the ith node,
is the total load active power, P, corresponding to the system at the moment t of the ith nodeij,tThe active power flowing on branch i-j at time t,
the reactive power of the wind power in the t time period at the ith node is,
the reactive power of the photovoltaic in the t time period at the ith node,
for the reactive power purchased from the main network at time t at the ith node,
for the total load reactive power, Q, corresponding to the system at the moment t of the ith nodeij,tThe reactive power flowing on the branch i-j at time t.
2. Flow restraint
The branch power flow constraint of the power distribution network can be expressed by the following node voltage and branch phase difference:
wherein, Pij,tActive power, G, flowing on branch i-j at time tijFor the conductance of the branches i-j, Ui,tIs the voltage at the ith node at time t, Uj,tRespectively represents the voltage magnitude at the jth node at the time t, thetaij,tIs the voltage phase difference between the ith and jth nodes at time t, BijSusceptance value, Q, for branch i-jij,tThe reactive power flowing on the branch i-j at time t.
3. Distributed power supply output constraint
In order to ensure the economical efficiency and stability of the power distribution network, a certain amount of wind and light abandoning phenomena can be generated in the power grid. For various types of wind and light power supplies, the access quantity is limited by the access capacity of each point, the real-time wind and light output and other factors, namely:
wherein the content of the first and second substances,
the actual wind power access amount of the power grid in the t time period at the ith node is obtained,
the installed capacity of the wind power at the ith node is foutput (t), which is the output of a typical daily power curve of the wind power at the time t, FfIs the reference capacity of the typical sunrise curve of wind power,
the actual photovoltaic access amount of the power grid in the t time period at the ith node is,
the installed photovoltaic capacity at the ith node is shown as Goutput (t), the output of a typical photovoltaic daily force curve at the moment t is shown as FgIs a photovoltaic systemThe baseline capacity of the model sunrise force curve.
4. Node voltage constraint
Each node in the power distribution network should satisfy node voltage constraints, namely:
Umin≤Ui,t≤Umax
in the formula of Ui,tRepresenting the magnitude of the voltage at the ith node during a period of time t, UmaxAnd UminRespectively representing the upper and lower limits of the node voltage.
5. Electric quantity restriction for electric network purchase
For satisfying the power balance constraint, the power grid may need to purchase power to the upper level power grid in addition to consuming part of the electric energy of the distributed power generation party, and the power purchase amount of each node to the upper level power grid has certain limitation, that is:
wherein the content of the first and second substances,
purchasing electric quantity for the power grid in the t time period at the ith node,
an upper limit of the amount of real regulation purchased from the i-th node to the upper grid,
for the reactive power purchased from the main network at time t at the ith node,
and (4) purchasing an upper limit of reactive power regulation quantity from the upper-level power grid for the ith node.
6. Line ampacity constraint
For each power transmission line of a power grid, the control circuit generates heat, stable operation of the circuit is ensured, and basic circuit current-carrying capacity constraint needs to be met, namely:
0≤Iij≤Iij,max
wherein, IijThe magnitude of the current-carrying capacity of branch I-j, Iij,maxThe upper limit of the current-carrying capacity of the branch i-j.
7. Distributed power supply total capacity constraint
The sum of the construction capacities of the wind and light points is required to meet the following requirements:
wherein the content of the first and second substances,
is the installed capacity of wind power at the ith node, CFFor the size of the total installed capacity of wind power,
is the magnitude of the installed photovoltaic capacity at the ith node, CGThe total photovoltaic installed capacity is obtained.
8. Power grid transformer capacity constraints
The wind and light access capacity of each point is limited by the capacity of a power grid transformer, and in order to ensure that the power grid transformer has certain margin, the capacity constraint of the power grid transformer can be expressed as follows:
wherein the content of the first and second substances,
the installed wind power capacity at the ith node is the size,
the device limits the capacity of the device to a certain extent,
for light at the ith nodeAnd the installed capacity is large.
And S13, integrating the upper-layer distributed investment capacity optimization model and the lower-layer distribution network distributed power source location and volume optimization model to obtain a distributed power generation location and volume double-layer planning model.
Based on the process, a double-layer planning model of distributed power generation site selection and volume determination is established, the model takes the economic benefits of the power distribution network and the main bodies of the plurality of distributed power generation parties into account, the competitive relationship of each distributed power generation party is reflected, and the actual operation state of the power grid can be well reflected.
S2, based on a convex relaxation method, a second-order cone approximation and a KKT optimality condition, carrying out linearization processing on a nonlinear item in a distributed power generation site selection constant volume double-layer programming model, and converting the double-layer programming model into a single-layer multi-target linear programming model;
the method comprises the following steps:
s21, combining a convex relaxation method, and performing second-order conic linear approximation on a nonlinear term of power flow constraint in the distributed power generation localization and sizing double-layer planning model to obtain a double-layer linear planning model;
specifically, as can be known from the foregoing derivation, the branch power flow constraint of the power distribution network includes a large number of voltage square terms, product terms, and trigonometric function terms, so that the solution of the double-layer planning model including the power flow constraint belongs to a typical non-convex problem, and is difficult to accurately solve. In recent years, some scholars adopt a heuristic algorithm to solve the non-convex problem, but the solution effect and the time complexity are not ideal. According to the method, the nonlinear quantity in the branch tide constraint of the power distribution network is subjected to linear treatment by adopting a convex relaxation method and second-order cone approximation, and an original optimization problem is converted into a convex optimization problem which is easier to solve.
Specifically, the SOCP is a convex plan in nature, and both the optimality of the solution and the efficiency of the calculation have excellent characteristics. The existing commercial software and algorithm package can well solve the second-order cone planning problem, and the solving process can be completed in polynomial time.
Specifically, the second order cone relaxation method firstly needs to carry out variable replacement, and J is replacedi,t、Jj,t、Kij,t、Hij,tThe following definitions are respectively made:
to further ensure the coupling relationship between the second order cone variables, constraints are added:
because the newly added second-order cone coupling constraint still has a nonlinear relation, the above formula is further relaxed into;
after the above formula is relaxed, the second-order cone standard form is further converted into:
bringing into the flow constraint, we can get:
meanwhile, according to the basic relation of branch current, the current-carrying capacity constraint of the line can be converted into:
the node voltage constraint, in turn, also translates into:
Ji,min≤Ji,t≤Ji,max
after the second-order cone relaxation is completed, the model complexity is simplified to a certain extent, but the defects of long calculation time and the like still exist when the function packet is used for solving the second-order cone constraint. In view of the above, the present invention further linearizes the second order cone constraint.
Specifically, the second order cone standard form is as follows:
for the second-order cone standard form, linear approximation processing can be adopted, and the linearization is expressed as:
to facilitate the second-order cone linearization analysis described above, a four-dimensional second-order cone is used
The constraint is converted to two second order cone standard forms:
based on the linearized representation of the second order cone standard form, the two second order cone standard forms described above can be further represented as:
therefore, second-order conic linear approximation of a nonlinear term in tidal constraint is completed, so that the original power flow constraint of the power distribution network with certain nonlinearity is converted into linear constraint, and the nonlinearity problem of a double-layer planning model for location selection and volume determination of distributed power generation is solved.
The existing method generally adopts an improved intelligent algorithm to solve the linear double-layer programming model, but the method needs to iterate the upper layer model and the lower layer model repeatedly, and simultaneously carries out data transmission between the upper layer model and the lower layer model, so that the calculation time is long, and the calculation complexity is high.
And S22, processing the double-layer linear programming model based on the KKT optimality condition, converting the lower-layer programming model into the upper-layer programming model to serve as the constraint condition of the upper-layer model, and obtaining a completely linear solvable single-layer multi-target linear programming model.
Specifically, for the obtained lower layer linear programming model, a lagrangian function L is constructed:
wherein F represents the objective function of the lower linear programming model, Fi,gjRespectively representing all inequality constraints and equality constraints of the lower-layer linear programming model, and respectively representing lower-layer lines I and EAn inequality constraint set and an equality constraint set of the sexual planning model; lambda [ alpha ]i,hjAnd respectively representing parameters corresponding to inequality constraints and equality constraints of the lower-layer linear programming model.
Thereby further converting the lower linear programming model to KKT conditions, including:
original feasible field:
dual feasible fields:
λi≥0,i∈I
complementary relaxation conditions:
λifi＝0,i∈I
stability conditions:
wherein, x is a linear lower layer decision variable and belongs to all decision variable sets of the lower layer.
The lower linear programming model is converted into the KKT optimality condition through the above process, but a nonlinear factor is further introduced into the above complementary relaxation condition, and needs to be further linearized. In this embodiment, the complementary relaxation condition is linearized by a large M method:
wherein M is a very large positive integer, YiThe variable is 0-1, and all the constraint conditions of the KKT condition can be ensured to be linear constraint by a large M method.
Through the processes, the finally obtained single-layer multi-target linear programming model is as follows:
after the model nonlinear constraint second-order cone relaxation and linearization and double-layer model KKT condition conversion are carried out, the linearly solvable single-layer multi-target linear programming model is finally obtained, so that the model can be conveniently solved after simplification, and the practicability of the model is improved.
And S3, acquiring grid structure data and actual distributed power generation output data of each typical day in the last year, inputting the data into the multi-target linear programming model, and solving the multi-target linear programming model to obtain the optimal distributed power generation site selection and volume fixing scheme.
Specifically, the main body of research in this embodiment is a 35kV power distribution network, 12 typical days are selected in a year, 8 time nodes in each typical day are respectively selected to represent the typical day, 96 time nodes are finally obtained to equivalently represent the wind and light output of the year, the distributed generation actual output data of each typical day in the last year are collected, the distributed generation actual output data and the grid structure data are input into a multi-target linear programming model, the pareto optimal front edge of the single-layer multi-target linear programming model is solved, then the comprehensive fitness of each solution in the pareto optimal front edge solution set is solved, the solution with the highest comprehensive fitness in the pareto optimal front edge solution set is taken as the optimal compromise, and the optimal distributed generation site selection constant volume scheme is obtained. Specifically, the actual output data of the distributed power generation comprises the output magnitude of a wind power typical daily force curve at each moment and the output magnitude of a photovoltaic typical daily force curve at each moment, and the grid structure data comprises the conductance, the susceptance value and the upper limit of the current-carrying capacity of a branch in the power system. The optimal distributed power generation site selection and volume fixing scheme is obtained by solving the pareto optimal front edge of the single-layer multi-target linear programming model, the dynamic change of each distributed investor in the power grid can be better reflected, and the benefit competition relationship of each investor in the model can also be better reflected.
Specifically, the comprehensive fitness of the kth pareto optimal solution is represented as:
wherein, fit (i, k) is the fitness of the kth pareto optimal solution of the ith objective function, N represents the number of objective functions in the multi-objective linear programming model, and M represents the number of pareto optimal solutions in the front edge of the pareto.
Specifically, the fitness fit (i, k) of the kth pareto optimal solution of the ith objective function is represented as:
wherein, Fi,max,Fi,minRespectively representing the maximum and minimum values of the ith objective function,
and an objective function value representing the kth pareto optimal solution of the ith objective function.
In the following, an actual distribution network system in a certain town is taken as an example. The main line of the power grid in the area to be planned is a 35kV outgoing line, and the number of the 110kV/35kV transformers is 1 in total, and the transformers are publicly accessible transformers; the 35kV power distribution network has 11 public accessible nodes. In this embodiment, the investment cost per unit capacity of the wind turbine is 7000 yuan/MW, the investment cost per unit capacity of the photovoltaic turbine is 6000 yuan/MW, the power rate of the wind power on-grid is 0.34 yuan/kw.h, the power rate of the photovoltaic on-grid is 0.34 yuan/kw.h, the power rate of the main grid is 0.568 yuan/kw.h, the discount rate is 3%, the depreciation period of the wind turbine is 20 years, the depreciation period of the photovoltaic turbine is 30 years, and the residual value rate of the wind turbine and the photovoltaic turbine is 5%.
The results of the wind power optimal solution, the photovoltaic optimal solution and the compromise optimal solution obtained by solving by adopting the method provided by the invention are shown in table 1.
TABLE 1
| Results | Optimal solution for wind power | Photovoltaic optimal solution | Optimal compromise solution |
| Electric network general objective function/ten thousand yuan | 5008.7 | 5535.7 | 5178.2 |
| Wind power objective function/ten thousand yuan | 236.1 | 78.6 | 214.1 |
| Photovoltaic objective function/ten thousand yuan | 5.3 | 137.5 | 49.0 |
| Total built-in capacity/MW of wind power | 20 | 5 | 14.4 |
| Total photovoltaic projected capacity/MW | 5.4 | 13.1 | 8.5 |
| Wind power total power generation capacity/MW & h | 31848 | 8536.5 | 24253.9 |
| Photovoltaic total power generation capacity/MW & h | 2959 | 9410.6 | 5357.9 |
| Total purchased electric quantity/MW & h of power grid | 66252 | 83236.7 | 71460.0 |
As can be seen from table 1, the optimal solution for wind power only considers the benefit maximization of the wind power investor, thus causing the situation that the benefit of the photovoltaic investor is extremely low; meanwhile, the photovoltaic optimal solution only considers the photovoltaic investors, and the benefits of the wind power investors are not well considered. Compared with the optimal solution of wind power and the optimal solution of photovoltaic power, the optimal compromise solution of the model can better integrate the economic benefits of wind power and photovoltaic investment businessmen, and the economic benefits of the wind power and the photovoltaic investment businessmen are balanced. When an actual power grid operates, the investment enthusiasm and the investment return rate of a wind and light investor can dynamically change along with the power grid and climate factors, so that the optimal solution and the optimal compromise solution of the distributed investors can be continuously updated, the pareto optimal solution set solved by the method better covers various possible distributed investment scenes of the power grid, and the advantage of the solving idea of the method in comparison with a fixed weight method is further proved.
In addition, the method combines a convex relaxation method to perform second-order conic linear approximation on the nonlinear terms of the power flow constraint in the distributed power generation localization and sizing double-layer planning model to obtain the double-layer linear planning model. As shown in table 2, the optimal result is obtained by solving the linearized second-order cone model and the original second-order cone model.
TABLE 2
| Results | Second order cone linearization model | Original second order cone model | Both errors |
| Electric network general objective function/ten thousand yuan | 4996.2 | 4991.6 | 0.0906％ |
| Wind power objective function/ten thousand yuan | 31847 | 31891 | 0.1392％ |
| Photovoltaic objective function/ten thousand yuan | 8683 | 8775 | 1.0484％ |
| Total purchased electric quantity/MW & h of power grid | 60490 | 60294 | 0.3235％ |
As can be seen from Table 2, the second-order cone linearization method adopted by the invention can better geometrically approximate the original second-order cone constraint, the difference between the second-order cone linearization and the solving result of the original second-order cone is within an acceptable range through a plurality of angle analyses of the total economic index of the power distribution network, the electric quantity purchased by wind power, photovoltaic and power grid and the like, and the nonlinear problem in the original model is better solved through the linear approximation of the second-order cone, so that the calculation complexity of the model is greatly reduced, and the feasibility of the model is improved.
In order to further verify the effectiveness and the practicability of the method provided by the invention, the solving result of the power distribution network double-layer planning model established by taking the maximum economic benefit of the wind and light investors and the minimum annual operation cost of the power distribution network as the targets is compared with the solving result of the power distribution network single-layer planning model established by taking the minimum annual operation economic cost of the power distribution network only by considering the operation constraint of the power distribution network without considering the benefit of wind and light investors in the conventional method, and the obtained result is shown in table 3.
TABLE 3
From table 3, it can be seen that the economic benefit of the wind and light investors in the single-layer planning model of the power grid is less than 0, the benefit of the distributed investors is not taken into account, and meanwhile, the wind and light on-grid electricity prices are all lower than the electricity purchasing price of the power distribution network to the superior power grid, so that the single-layer planning model enables the wind and light each-point investment capacity to reach the upper limit in order to ensure the optimal operation economy of the power distribution network, and the result of the double-layer planning model provided by the invention is more.
To further prove the robustness of the method proposed by the present invention, this embodiment sets 8 different scenarios, which are respectively:
scene 1: wind power total installed capacity CF20 and total photovoltaic installed capacity CG20, and giving appropriate wind and light abandoning constraints;
scene 2: wind power total installed capacity CF20 and total photovoltaic installed capacity CG20, giving a penalty cost of greatly abandoning wind and light to the power grid;
scene 3: wind power total installed capacity CF0 and the total installed photovoltaic capacity CG20, there is only a photovoltaic sponsor, no windAn electric supplier;
scene 4: wind power total installed capacity CF20 and total photovoltaic installed capacity CGWhen the wind power investment quotient is 0, only a wind power investment quotient exists, and no photovoltaic investment quotient exists;
scene 5: wind power total installed capacity CFTotal installed photovoltaic capacity C ═ 5G5, corresponding to negative investment of wind power and photovoltaic suppliers;
scene 6: wind power total installed capacity CFTotal installed photovoltaic capacity C ═ 5G20, corresponding to wind power negative investment and photovoltaic positive investment;
scene 7: wind power total installed capacity CF20 and total photovoltaic installed capacity CG5, photovoltaic negative investment and wind power positive investment;
scene 8: wind power total installed capacity CF20 and total photovoltaic installed capacity CGAnd (5) the wind power and photovoltaic investors all invest actively as 20.
The two-layer planning model for the distributed power generation site selection capacity proposed by the invention is solved under the above 8 scenes, and the obtained results are shown in tables 4 and 5. As can be seen from table 4, when the power grid imposes a very strict wind abandoning and light abandoning penalty (corresponding to scene 2), all the accessible wind power of the power grid is accessed to the power grid, and the photovoltaic electric quantity still has a certain amount of light abandoning due to the output characteristics and the stable constraints of the power flow. The punishment of wind abandoning and light abandoning of the power grid can greatly restrict the phenomenon of wind abandoning and light abandoning, but if the wind abandoning and light abandoning needs to be further restricted, the location and the volume of the distributed power supply need to be more reasonably determined.
TABLE 4
| Scene | Scene 1 | Scene 2 |
| Electric network general objective function/ten thousand yuan | 4996.2 | 5467.0 |
| Wind power total power generation capacity/MW & h | 31847 | 34377.3 |
| Photovoltaic total power generation capacity/MW & h | 8683 | 15839.8 |
| Total purchased electric quantity/MW & h of power grid | 60490 | 60298.5 |
| Air flow abandon rate/MW h | 2530.9 | 0 |
| Light rejection/MW & h | 10927 | 3774.4 |
As can be seen from Table 5, under different scenes, the method provided by the invention can provide an optimal distributed power generation location capacity scheme, and has good robustness.
TABLE 5
| Scene | Scene 3 | Scene 4 | Scene 5 | Scene 6 | Scene 7 | Scene 8 |
| Electric network general objective function/ten thousand yuan | 5728.0 | 5014.7 | 5549.1 | 5529.4 | 5011.7 | 4996.2 |
| Wind power total power generation capacity/MW & h | 0 | 31868 | 8512 | 8529 | 31826 | 31847 |
| Photovoltaic total power generation capacity/MW & h | 13876.0 | 0 | 4349 | 12605 | 2701 | 8683 |
| Total purchased electric quantity/MW & h of power grid | 87409 | 69211 | 88389 | 80037 | 66568 | 60490 |
In conclusion, compared with the traditional algorithm, the distributed power generation site selection and volume fixing method based on the trend linearization, provided by the invention, not only can simultaneously take multiple beneficial bodies into consideration, improve the new energy consumption level and the economic benefit of distributed power generators, but also reduce the annual economic operation cost of a power grid company, effectively reduce the model calculation complexity and show the practicability of the distributed power generation site selection and volume fixing method.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (7)
1. A distributed power generation site selection and volume fixing method based on power flow linearization is characterized by comprising the following steps:
s1, on the basis of an actual power distribution network operation scene, by considering the economic benefit of wind and light investment and the economic cost of a power distribution network, taking the optimal economic benefit of wind and light investment as an upper-layer optimization target, and taking the minimum annual operation economic cost of the power distribution network as a lower-layer optimization target, establishing a distributed power generation site selection and volume fixing double-layer planning model;
s2, based on a convex relaxation method, a variable linearization method, a second-order cone approximation and a KKT optimality condition, carrying out linearization processing on a nonlinear item in a double-layer planning model of distributed power generation site selection and volume fixing, and converting the double-layer planning model into a single-layer multi-target linear planning model;
and S3, acquiring grid structure data and actual distributed power generation output data of each typical day in the last year, inputting the data into the multi-target linear programming model, and solving the multi-target linear programming model to obtain the optimal distributed power generation site selection and volume fixing scheme.
2. The power flow linearization based distributed power generation siting volume method of claim 1, wherein the method of step S1 comprises the following steps:
s11, establishing an upper-layer distributed investment capacity optimization model by taking the optimal wind and light investment economy as a target and considering investment budget and economic benefit constraints;
s12, with the goals of lowest annual economic operation cost of the power distribution network and the maximum clean energy consumption level, considering power flow constraint, stability constraint and distributed power supply capacity constraint of the power distribution network, deciding the built-in address of the distributed power supply and the built-in capacity of each corresponding point, and establishing a location and volume selection optimization model of the distributed power supply of the lower power distribution network;
and S13, integrating the upper-layer distributed investment capacity optimization model and the lower-layer distribution network distributed power source location and volume optimization model to obtain a distributed power generation location and volume double-layer planning model.
3. The power flow linearization-based distributed power generation siting volume method according to claim 2, wherein the objective function of the upper distributed investment commissioning capacity optimization model is expressed as follows:
wherein, F1(x) Annual profit for wind power supplier, F2(x) T represents a time period set, omega represents a site selection site set of wind power and photovoltaic power stations, each site selection site is a power grid node,
the actual wind power access quantity d of the power grid in the time period t of the kth nodefIs the power price of the unit wind power, delta t is the duration of each time interval in the operation period, RfIs the investment cost, k, of the installed capacity of a unit wind turbinefF (A/P) is the annual fund present value coefficient, CFFor the total installed capacity of wind power, cfwFor the maintenance cost factor of the wind turbine,
the actual photovoltaic access quantity d of the power grid in the time period t at the kth nodegOn-line electricity price per unit photovoltaic electricity quantity, RgIs the investment cost, k, of installed capacity of a unit of photovoltaic unitgIs the residual value rate, C, of the photovoltaic unitGTo the total installed photovoltaic capacity, cgwThe investment cost R of unit installed capacity of the wind turbine is the maintenance cost coefficient of the photovoltaicfAnd the investment cost R of installed capacity of unit photovoltaic unitgAnd the investment budget constraint is met.
4. The distributed power generation localization and sizing method based on power flow linearization as claimed in claim 2, wherein the objective function of the lower distribution network distributed power supply localization and sizing optimization model is expressed as follows:
min f(x)＝Ccost+Cpub
wherein f (x) is the total power supply cost of the distribution company, CcostPurchase cost of electricity for distribution network, CpubPenalty cost for abandoning wind and light, T represents a time period set, and omega represents wind power and lightThe site selection sites of the photovoltaic power station are aggregated, each site selection site is a power grid node,
d is the actual wind power access quantity of the power grid in the time period t of the ith nodefThe unit wind power electricity quantity is the power price on the internetffIs the operation and maintenance cost of unit wind power, delta t is the time length of each time interval in the operation period,
the actual photovoltaic access quantity d of the power grid in the time period t at the ith nodegElectricity price for the unit photovoltaic powergfIs the operation and maintenance cost per photovoltaic power, dgridTo purchase a price per unit of electricity from the main network,
purchasing electric quantity k for the power grid in the t time period at the ith nodepubIn order to be a penalty factor,
the installed capacity of the wind power at the ith node is foutput (t), which is the output of a typical daily power curve of the wind power at the time t, FfFor the reference capacity of the typical solar output curve of wind power, goutput (t) is the output of the typical solar output curve of photovoltaic at the moment t, FgIs the baseline capacity of a typical solar output curve of a photovoltaic,
the installed photovoltaic capacity at the ith node is obtained.
5. The distributed power generation site selection and volume fixing method based on the power flow linearization as claimed in claim 4, wherein the distributed power supply site selection and volume fixing optimization model of the lower-layer power distribution network meets power balance constraint, power flow constraint, distributed power supply output constraint, node voltage constraint, power grid purchase power constraint, line current-carrying capacity constraint, distributed power supply total capacity constraint and power grid transformer capacity constraint.
6. The power flow linearization based distributed power generation siting volume method of claim 1, wherein the method of step S2 comprises the following steps:
s21, combining a convex relaxation method and a variable linearization method, performing second-order conical linear approximation on a nonlinear term of power flow constraint in the distributed power generation localization and sizing double-layer planning model to obtain a double-layer linear planning model;
and S22, processing the double-layer linear programming model based on the KKT optimality condition, and converting the lower-layer programming model into the upper-layer programming model to obtain a completely linear solvable single-layer multi-target linear programming model.
7. The distributed power generation site selection and volume fixing method based on the power flow linearization as claimed in claim 1, characterized in that the pareto optimal front edge of the single-layer multi-target linear programming model is solved, and the solution with the highest comprehensive fitness in the pareto optimal front edge solution set is used as the optimal distributed power generation site selection and volume fixing scheme.
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| CN112132363A (en) * | 2020-10-16 | 2020-12-25 | 国网湖北省电力有限公司十堰供电公司 | Energy storage site selection and volume fixing method for enhancing system operation robustness |
| CN112491037A (en) * | 2020-11-09 | 2021-03-12 | 四川大学 | Multi-target multi-stage dynamic reconstruction method and system for urban power distribution network |
| CN112668186A (en) * | 2020-12-30 | 2021-04-16 | 华中科技大学 | Site selection and volume fixing cooperative optimization method for transmission and distribution integrated energy storage system based on ELM |
| CN113421123A (en) * | 2021-06-29 | 2021-09-21 | 国网安徽省电力有限公司电力科学研究院 | Design method and device for point-to-point electric energy trading market containing shared energy storage |
| CN113421123B (en) * | 2021-06-29 | 2024-04-09 | 国网安徽省电力有限公司电力科学研究院 | Point-to-point electric energy transaction market design method and device containing shared energy storage |
| CN115564142A (en) * | 2022-11-03 | 2023-01-03 | 国网山东省电力公司经济技术研究院 | Site selection and volume fixing optimization method and system of hybrid energy storage system |
| CN115907227A (en) * | 2022-12-30 | 2023-04-04 | 天津大学 | Double-layer collaborative optimization method for fixed and movable charging facilities of expressway |
| CN116451978A (en) * | 2023-06-15 | 2023-07-18 | 山东泰霖环保科技有限公司 | Wind-solar-electric energy grid planning analysis system based on double-carbon targets |
| CN116451978B (en) * | 2023-06-15 | 2023-09-12 | 山东泰霖环保科技有限公司 | Wind, light and electric energy source net rack planning analysis system |
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