CN111027807B - Distributed power generation site selection and volume determination method based on tide linearization - Google Patents
Distributed power generation site selection and volume determination method based on tide linearization Download PDFInfo
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Abstract
The invention discloses a distributed power generation site-selection and volume-fixation method based on tide linearization, which comprises the steps of firstly, establishing a double-layer planning model of distributed power generation site-selection and volume-fixation by considering the economic benefit of wind-light investment and the economic cost of a power distribution network at the same time, and being more close to the actual operation scene of the power grid, and having better feasibility, higher accuracy and better robustness; and then, based on a convex relaxation method, a variable linearization method, a second order cone approximation and a KKT optimality condition, carrying out linearization treatment on nonlinear items in a non-male-type distributed power generation site-selection and volume-fixing double-layer planning model which is originally provided by the invention, and further converting the nonlinear items into a fully linear solvable single-layer multi-target linear planning model, thereby greatly reducing the complexity of model solving, ensuring lower computational complexity, being simpler and faster, leading the converted solving result to be very close to the solving result for carrying out linearization conversion, and greatly reducing the computational complexity under the condition of ensuring accuracy.
Description
Technical Field
The invention belongs to the technical field of distributed power generation site selection and volume determination, and particularly relates to a power flow linearization-based distributed power generation site selection and volume determination method.
Background
With the continuous opening of the electric power market in China, the continuous increase of electric power demand and the increasing exhaustion of traditional fossil energy, distributed energy such as wind energy, solar energy and the like plays an increasingly important role in an electric power system. The national energy agency recently promulgates a plurality of policy files such as a report about the construction of related matters in the wind power and photovoltaic power generation project in 2019, which indicates that the policy of the distributed power generation project in China is further perfected. By 2018 years, the national wind power and photovoltaic installation reaches 3.6 hundred million kilowatts, which accounts for approximately 20% of the total installation proportion. The annual energy generation of wind power and photovoltaic is 6000 hundred million kilowatt-hours, which is close to 9% of the total energy generation. Meanwhile, the problem of wind and light discarding is particularly serious, and the wind and light discarding electric quantity in 2018 of three areas 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 unordered access of the distributed power supply causes a series of adverse effects of voltage rise, difficult digestion, low power quality and the like to the power distribution network system, and greatly increases the uncertainty factor of the power distribution network. The new energy consumption level is severely restricted by factors such as irrational property of distributed power supply site selection and volume determination.
The distributed power supply is optimally and friendly connected into the power grid through site selection and volume fixation, so that the method is an effective measure for solving the problems of large-scale wind and light abandoning and improving the new energy consumption level. Traditional fixed weight method processing accounts for the multi-objective power grid planning problem of multi-type distributed investors, and has the defect that potential benefit competition relation of each actual distributed generator cannot be embodied. Because conditions such as load demands, climate factors and the like are dynamically changed, investment benefits and investment intentions of all distributed investors are possibly changed, the fixed weight method cannot better reflect the dynamic characteristics of an actual power distribution network, and planning results are inaccurate. The double-layer planning model of the power distribution network for distributed power generation belongs to a high-dimensional non-convex optimization problem, the existing method mainly adopts a heuristic algorithm to solve, the heuristic algorithm can calculate through an iterative mode, the calculation instantaneity is sacrificed to a certain extent, the accuracy is also to be checked, the model has a series of problems of overhigh dimension, difficulty in optimizing, long solving time and the like, and the practicability of the model is limited.
In summary, the problem to be solved is to provide a distributed power generation site selection and volume determination method with low computational complexity and accurate planning.
Disclosure of Invention
Aiming at the defects or improvement demands of the prior art, the invention provides a distributed power generation site selection and volume determination method based on trend linearization, which aims to solve the technical problem of high computational complexity caused by repeated iteration in the prior art by adopting a heuristic algorithm.
In order to achieve the above purpose, the invention provides a distributed power generation site-selection and volume-fixing method based on tide linearization, which comprises the following steps:
s1, on the basis of an actual power distribution network operation scene, establishing a double-layer planning model for distributed power generation site selection and volume fixation by taking the economic benefit of wind and light investment and the economic cost of the power distribution network into consideration, taking the 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;
s2, linearizing nonlinear terms in a double-layer planning model for distributed power generation site selection and volume determination based on a convex relaxation method, a variable linearization method, a second order cone approximation and a KKT optimality condition, and converting the double-layer planning model into a single-layer multi-target linear planning model;
s3, acquiring grid structure data and distributed power generation actual 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 an optimal distributed power generation site selection and volume determination scheme.
Further preferably, the method of step S1 comprises the steps of:
s11, establishing an upper distributed investment capacity optimization model by taking optimal wind and light investment economy as a target and considering investment budget and economic benefit constraint;
s12, taking the lowest annual economic operation cost and the maximum clean energy consumption level of the power distribution network as targets, taking power flow constraint, stability constraint and distributed power capacity constraint of the power distribution network into consideration, deciding a distributed power supply construction address and corresponding point construction capacity, and establishing a lower-layer distributed power supply site selection constant volume optimization model;
and S13, integrating an upper distributed investment capacity optimization model and a lower distribution network distributed power supply location and volume-fixing optimization model to obtain a distributed power generation location and volume-fixing double-layer planning model.
Further preferably, the objective function of the upper distributed investment-projected capacity optimization model is expressed as follows:
wherein F is 1 (x) Is thatNet annual profit of wind power investors, F 2 (x) For net annual profit of the photovoltaic sponsor, T represents a set of time periods, Ω is a set of site locations for wind power and photovoltaic power plants, each site location is a grid node,d, obtaining the actual wind power access quantity of the power grid in the t time period at the kth node f The online electricity price of the unit wind power electric quantity is delta t which is the duration of each period in the operation period, R f Investment cost k is unit of wind turbine installation capacity f F (A/P) is the annual gold present value coefficient, C F C, the capacity of the wind power assembly machine is equal to that of a wind power assembly machine fw For the maintenance cost factor of the wind turbine generator system, +.>D, the actual photovoltaic access quantity of the power grid in the t time period at the kth node g The online electricity price of the unit photovoltaic electric quantity is R g Investment cost, k, in units of photovoltaic unit assembly capacity g C is the residual value rate of the photovoltaic unit G C, the capacity of the photovoltaic assembly machine is equal to that of the photovoltaic assembly machine gw Investment cost R of unit wind turbine installation capacity as maintenance cost coefficient of photovoltaic f And investment cost per unit photovoltaic unit assembly capacity R g Meeting the investment budget constraints.
Further preferably, the objective function of the lower-layer distribution network distributed power supply location and volume-fixing optimization model is expressed as follows:
minf(x)＝C cost +C pub
wherein f (x) is the total power supply cost of the distribution company, C cost For the electricity purchasing cost of the distribution network,C pub for the penalty cost of wind and light discarding, T represents a time period set, Ω is a wind power and photovoltaic power station site set, each site is a grid node,d, obtaining the actual wind power access quantity of the power grid in the t time period at the ith node f The online electricity price of the unit wind power and electricity quantity is d ff The running cost of the unit wind power and electricity quantity is shown as delta t, and delta t is the duration of each period in the running period>D, the actual photovoltaic access quantity of the power grid in the t time period at the ith node g The online electricity price of the unit photovoltaic electric quantity is d gf The operation and maintenance cost of the unit photovoltaic electric quantity is d grid For the price of buying a unit of electricity from the main network, < > the price of->For the electricity purchasing quantity k of the power grid in the t time period at the ith node pub For penalty factor, C i f For the capacity of the wind power installation at the ith node, the output (t) is the output of a wind power typical solar power curve at the moment t, F f The output (t) is the output of the photovoltaic typical solar power curve at the moment t and F is the reference capacity of the wind power typical solar power curve g Reference capacity for a typical solar curve of photovoltaic, +.>Is the photovoltaic installed capacity size at the i-th node.
Further preferably, the lower-layer distribution network distributed power supply location and volume-determining optimization model meets power balance constraint, power flow constraint, distributed power supply output constraint, node voltage constraint, power grid purchase quantity constraint, line current capacity constraint, distributed power supply total capacity constraint and power grid transformer capacity constraint.
Further preferably, the method of step S2 comprises the steps of:
s21, combining a convex relaxation method and a variable linearization method, and performing second-order cone linear approximation on a nonlinear term of power flow constraint in a double-layer planning model for distributed power generation site selection and volume determination to obtain a double-layer linear planning model;
s22, processing the double-layer linear programming model based on the KKT optimality condition, and converting the lower-layer programming model into an upper-layer multi-objective linear programming model which is completely linear and solvable.
The method has the advantages that the solving complexity of the double-layer planning model for distributed power generation site selection and volume determination is greatly reduced through the steps, the calculating complexity is low, the method is simpler and quicker, the converted solving result is very close to the solving result for linearization conversion, and the calculating complexity can be greatly reduced under the condition of ensuring the accuracy.
Further preferably, solving the pareto optimal front edge of the single-layer multi-target linear programming model, and taking the solution with the highest comprehensive fitness in the pareto optimal front edge solution as an optimal distributed power generation addressing and volume-fixing scheme. Solving the pareto optimal front can better reflect the dynamic change of each distributed investor in the power grid, and can also better embody the benefit competition relationship of each investor in the model.
In general, the above technical solutions conceived by the present invention, compared with the prior art, enable the following beneficial effects to be obtained:
1. the invention provides a distributed power generation site-selection and volume-fixing method based on trend linearization, which realizes the approximate convexity of a non-convexity model, the approximate linearization of a non-linear model and the single-layer linearization of the model based on a convexity relaxation method, a variable linearization method, a second order cone approximation and a KKT optimality condition, so that the nonlinear term in the originally proposed non-convex model distributed power generation site-selection and volume-fixing double-layer planning model is subjected to linearization treatment and further converted into a fully linear solvable single-layer multi-target linear planning model, the model solving complexity is greatly reduced, the calculation complexity is lower, the method is simpler and quicker, the converted solving result is very similar to the solving result for carrying out linearization conversion, and the calculating complexity can be greatly reduced under the condition of ensuring the accuracy.
2. According to the distributed power generation site selection and volume determination method based on trend linearization, by considering the economic benefit of wind and light investment and the economic cost of the power distribution network, the economic benefit of wind and light investment is optimal as an upper optimization target, the annual operation economic cost of the power distribution network is minimum as a lower optimization target, a double-layer planning model of distributed power generation site selection and volume determination is established, the method is closer to the actual operation scene of the power grid, and the method has good feasibility and high accuracy.
3. The upper distributed investment capacity optimization model provided by the invention takes the benefit competition relationship of multiple distributed investors into account, considers investment budget and economic benefit constraint, and meets the actual engineering requirements better.
4. The lower-layer distribution network distributed power supply location and volume-fixing optimization model provided by the invention meets the target requirement of lowest annual economic operation cost of the distribution network, considers the stability constraint, the tide constraint and the distributed power supply project capacity constraint of the distribution network, can reflect the actual operation scene of the distribution network, and has higher accuracy of planning quasi-results.
5. According to the distributed power generation site selection and volume determination method based on trend linearization, the optimal distributed power generation site selection and volume determination scheme is obtained by solving the pareto optimal front edge of the single-layer multi-objective linear programming model, so that dynamic changes of all distributed investors in a power grid can be reflected well, and benefit competition relations of all investors in the model can be reflected well.
6. The distributed power generation site-selection and volume-fixation method based on trend linearization provided by the invention can obtain the practically feasible optimal site-selection and volume-fixation planning result under different scenes, and has better robustness.
Drawings
FIG. 1 is a flow chart of a distributed power generation site selection and volume determination method based on tide linearization;
FIG. 2 is a schematic diagram of a two-layer planning model for distributed generation site selection and sizing.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
In order to achieve the above purpose, the present invention provides a distributed power generation location and volume-determining method based on tide linearization, as shown in fig. 1, comprising the following steps:
s1, on the basis of an actual power distribution network operation scene, establishing a double-layer planning model for distributed power generation site selection and volume fixation by taking the economic benefit of wind and light investment and the economic cost of the power distribution network into consideration, taking the 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;
specifically, a double-layer planning model for distributed power generation site selection and volume fixation is shown in fig. 2, and comprises an upper-layer distributed investment capacity optimization model and a lower-layer distributed power supply site selection and volume fixation optimization model.
Specifically, the method for establishing the double-layer planning model for distributed power generation site selection and volume determination comprises the following steps:
s11, establishing an upper distributed investment capacity optimization model by taking optimal wind and light investment economy as a target and considering investment budget and economic benefit constraint;
specifically, the objective function of the upper distributed investment-projected capacity optimization model is expressed as follows:
wherein F is 1 (x) For the net annual profit of wind power investors, F 2 (x) Is a photovoltaic deviceThe net annual profit of the sponsor, T represents a set of time periods, Ω is a set of site locations for wind power and photovoltaic power plants, each site location is a grid node,d, obtaining the actual wind power access quantity of the power grid in the t time period at the kth node f The online electricity price of the unit wind power electric quantity is delta t which is the duration of each period in the operation period, R f Investment cost k is unit of wind turbine installation capacity f F (A/P) is the annual gold present value coefficient, C F C, the capacity of the wind power assembly machine is equal to that of a wind power assembly machine fw For the maintenance cost factor of the wind turbine generator system, +.>D, the actual photovoltaic access quantity of the power grid in the t time period at the kth node g The online electricity price of the unit photovoltaic electric quantity is R g Investment cost, k, in units of photovoltaic unit assembly capacity g C is the residual value rate of the photovoltaic unit G C, the capacity of the photovoltaic assembly machine is equal to that of the photovoltaic assembly machine gw Is a maintenance cost factor for photovoltaic.
The constraint of the upper distributed investment capacity optimization model is mainly investment budget constraint, and for a distributed investor, the total one-time investment is required to be within the fund range, namely:
wherein R is f Investment cost per unit of wind turbine installation capacity, C F For the capacity of the wind power total assembly machine, FT max Maximum investable funds for wind power and photovoltaic investors, R g Investment cost for capacity of photovoltaic machine assembly, C G GT is the capacity of the photovoltaic assembly machine max The maximum investable funds for photovoltaic investors. Wherein, the total installed capacity C of wind power accounts for the economic benefit and the occupation factor of distributed power generation F And photovoltaic total assembly machine capacity C G Also should satisfy the following aboutBeam:
wherein CF is as follows max 、CF min Upper and lower limits of wind power total access capacity are respectively represented, CG max 、CG min Representing the upper and lower limits of the total access capacity of the photovoltaic.
And S12, taking the lowest annual economic operation cost and the maximum clean energy consumption level of the power distribution network as targets, taking the power flow constraint, the stability constraint and the distributed power capacity constraint of the power distribution network into consideration, deciding the distributed power supply construction address and the construction capacity corresponding to each point, and establishing a lower-layer distributed power supply site selection constant volume optimization model.
The main body of the lower-layer distribution network distributed power supply locating and sizing optimization model is a distribution network, and the aim is that the annual operation economic cost of the distribution network is minimum. In the model, the lower-layer main body economy mainly considers the electricity purchasing cost of the power distribution network to the distributed power generation party, and the electricity purchasing cost of the power distribution network to the upper-layer main network and the abandoned wind and abandoned light cost, so that the objective function of the lower-layer power distribution network distributed power supply location and volume-fixing optimization model is expressed as follows:
minf(x)＝C cost +C pub
wherein f (x) is the total power supply cost of the distribution company, C cost C for purchasing electricity cost of power distribution network pub For the penalty cost of wind and light discarding, T represents a time period set, Ω is a wind power and photovoltaic power station site set, each site is a grid node,for the t time period at the ith nodeActual wind power access quantity of internal power grid, d f The online electricity price of the unit wind power and electricity quantity is d ff The running cost of the unit wind power and electricity quantity is shown as delta t, and delta t is the duration of each period in the running period>D, the actual photovoltaic access quantity of the power grid in the t time period at the ith node g The online electricity price of the unit photovoltaic electric quantity is d gf The operation and maintenance cost of the unit photovoltaic electric quantity is d grid For the price of buying a unit of electricity from the main network, < > the price of->For the electricity purchasing quantity k of the power grid in the t time period at the ith node pub For penalty factor, +.>For the capacity of the wind power installation at the ith node, the output (t) is the output of a wind power typical solar power curve at the moment t, F f The output (t) is the output of the photovoltaic typical solar power curve at the moment t and F is the reference capacity of the wind power typical solar power curve g Reference capacity for a typical solar curve of photovoltaic, +.>Is the photovoltaic installed capacity size at the i-th node.
The power distribution network is one of the most important parts in the power system, and the basic operation constraint of the system, namely the power balance constraint, the node voltage constraint, the line current-carrying capacity constraint and the like, should be met, and in addition, the lower planning model should also meet the processing constraint of the distributed power supply. Specifically, constraints of the lower-layer distribution network distributed power supply locating and sizing optimization model include:
1. power balance constraint
The power balance constraint is the most basic constraint of the power system, and the active and reactive balance constraint of the system must be considered when the power distribution network operates:
wherein,for the actual wind power access quantity of the power grid in the t time period at the ith node, +.>For the actual photovoltaic access quantity of the power grid in the t time period at the ith node, +.>For the power purchase amount of the power grid in the t time period at the ith node,/>The total load active power corresponding to the system at the t moment of the ith node, P ij,t For the active power flowing on branch i-j at time t,/>For reactive power of wind power in the t period of time at the ith node, +.>For reactive power of photovoltaic in the t period at the ith node, +.>For reactive power purchased from the main network at time t at the ith node,/for example>For the total load reactive power corresponding to the system at the t moment of the ith node, Q ij,t And the reactive power flowing through the branch i-j at the moment t.
2. Tidal current constraint
The branch tidal current constraint available node voltage and branch phase difference of the power distribution network are expressed as:
wherein P is ij,t For the active power flowing through branch i-j at time t, G ij For conductance of branch i-j, U i,t For the voltage at the ith node at time t, U j,t Respectively represent the voltage at the j-th node at the time t, theta ij,t B is the voltage phase difference between the ith node and the jth node at the moment t ij Susceptance value for branch i-j, Q ij,t And the reactive power flowing through the branch i-j at the moment t.
3. Distributed power supply output constraint
To ensure the economic and stability requirements of the power distribution network, a certain amount of "wind and light discarding" phenomena may occur in the power grid. For various wind-light power supplies, the access quantity is limited by the access capacity of each point, the real-time output of wind-light and other factors, namely:
wherein,for the actual wind power access quantity of the power grid in the t time period at the ith node,/for the power grid>For the capacity of the wind power installation at the ith node, the output (t) is the output of a wind power typical solar power curve at the moment t, F f Reference capacity of typical daily output curve of wind power, < + >>For the actual photovoltaic access quantity of the power grid in the t time period at the ith node, +.>Is large in photovoltaic installed capacity at the ith nodeSmall, goutput (t) is the output of the photovoltaic typical solar power curve at the moment t, F g Is the reference capacity of a typical sunrise force curve of a photovoltaic.
4. Node voltage constraint
Each node in the power distribution network should meet node voltage constraint, namely:
U min ≤U i,t ≤U max
in U i,t Indicating the voltage level at the ith node in the t period, U max And U min Respectively representing the upper and lower limits of the node voltage.
5. Power grid purchase quantity constraint
In order to meet the power balance constraint, the power grid may need to purchase power to the upper power grid in addition to the power consumption of part of the distributed power generation parties, and each node has a certain limit on the purchase power to the upper power grid, namely:
wherein,for the power purchase amount of the power grid in the t time period at the ith node,/>Upper limit of active regulation purchased for the ith node towards the upper grid, +.>For reactive power purchased from the main network at time t at the ith node,/for example>An upper limit for the amount of reactive power regulation purchased for the ith node to the upper grid.
6. Line current-carrying capacity constraints
For each power transmission line of the power grid, in order to control the line to generate heat and ensure the stable operation of the line, the current-carrying capacity constraint of the basic line needs to be met, namely:
0≤I ij ≤I ij,max
wherein I is ij The current-carrying capacity of the branch I-j is I ij,max Is the upper limit of the current-carrying capacity of branch i-j.
7. Distributed power supply total capacity constraint
The sum of the projection capacity of each point of the wind and the light meets the following conditions:
wherein,c, for the size of the wind power installation capacity at the ith node F Capacity of wind power total assembly machine, < >>C is the photovoltaic installed capacity size at the ith node G The capacity of the photovoltaic total assembly machine is equal to that of the photovoltaic total assembly machine.
8. Power grid transformer capacity constraint
The wind-light access capacity of each point is limited by the capacity of a power grid transformer, and the capacity constraint of the power grid transformer can be expressed as follows in order to ensure that a certain margin exists in the power grid transformer:
wherein,wind power installation capacity at ith node, < > for the size of the wind power installation capacity at the ith node, < >>Capacity limiter>Is the photovoltaic installed capacity size at the i-th node.
And S13, integrating an upper distributed investment capacity optimization model and a lower distribution network distributed power supply location and volume-fixing optimization model to obtain a distributed power generation location and volume-fixing double-layer planning model.
Based on the above process, a double-layer planning model for distributed power generation site selection and volume determination is established, and the model simultaneously accounts for the economic benefits of the power distribution network and a plurality of distributed power generation party main bodies, simultaneously embodies the competition relationship of each distributed power generation party, and can better reflect the actual running state of the power grid.
S2, linearizing nonlinear terms in a double-layer planning model for distributed power generation site selection and volume determination based on a convex relaxation method, second order cone approximation and KKT optimality conditions, and converting the double-layer planning model into a single-layer multi-target linear planning model;
the method comprises the following steps:
s21, combining a convex relaxation method, and performing second-order cone linear approximation on a nonlinear term of power flow constraint in a double-layer planning model of distributed power generation site selection and volume determination to obtain a double-layer linear planning model;
specifically, as can be seen from the above deduction, the branch flow constraint of the power distribution network includes a large number of square voltage terms, product terms and trigonometric function terms, so that the solution of the double-layer planning model including the flow constraint belongs to a typical non-convex problem, and is difficult to accurately solve. In recent years, partial scholars adopt heuristic algorithm to solve the non-convex problem, but the solution effect and the time complexity are not ideal. According to the invention, the nonlinear quantity in the branch power flow constraint of the power distribution network is subjected to linearization treatment by adopting a convex relaxation method and second order cone approximation, and the original optimization problem is converted into a convex optimization problem which is easier to solve.
Specifically, SOCP is essentially a convex program with excellent characteristics of both solution optimality and computational efficiency. The existing part of commercial software and algorithm packages can solve the second order cone planning problem well, and the solving process can be completed in polynomial time.
Specifically, the second order cone relaxation method firstly needs to perform variable substitution to obtain J i,t 、J j,t 、K ij,t 、H ij,t The following definitions are respectively made:
to further ensure the coupling relationship between the second order cone variables, add constraints:
the added second order cone coupling constraint still has a nonlinear relation, so that the above formula is further relaxed;
after the above formula is relaxed, the standard form of the second order cone is further converted into:
bringing into tidal current constraints, the following can be obtained:
meanwhile, according to the basic relation of the branch current, the line current-carrying capacity constraint can be converted into:
the node voltage constraint is then also converted into:
J i,min ≤J i,t ≤J i,max
after the second-order cone relaxation is completed, the complexity of the model is simplified to a certain extent, but the problem that the calculation time is long still exists when the second-order cone constraint is solved by using a function package is solved. 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, a linear approximation process can be used, and the linearization of the second order cone standard form is expressed as:
to facilitate the linearization analysis of the second order cone, a four-dimensional second order cone is adoptedThe constraint is converted into 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 may be further represented as:
the method and the device complete the second order cone linear approximation of the nonlinear term in the tidal constraint, so that the power flow constraint of the power distribution network which originally has certain nonlinearity is converted into the linear constraint, and the nonlinearity problem of the double-layer planning model for distributed power generation site selection and volume determination 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 meanwhile, data transmission between the upper layer model and the lower layer model is carried out, so that the calculation time is long, and the calculation complexity is high.
S22, processing the double-layer linear programming model based on the KKT optimality condition, and converting the lower-layer programming model into an upper-layer programming model to serve as a constraint condition of the upper-layer model, so that a single-layer multi-target linear programming model which is completely linear and solvable is obtained.
Specifically, a lagrangian function L is constructed for the resulting lower linear programming model:
wherein F represents an objective function of the lower linear programming model, F i ,g j Respectively representing all inequality constraints and equality constraints of the lower linear programming model, wherein I and E respectively represent an inequality constraint set and an equality constraint set of the lower linear programming model; lambda (lambda) i ,h j Respectively representing parameters corresponding to inequality constraint and equality constraint of the lower linear programming model.
Thereby further converting the underlying linear programming model to a KKT condition, comprising:
original feasible region:
dual feasible domain:
λ i ≥0,i∈I
complementary relaxation conditions:
λ i f i ＝0,i∈I
stability conditions:
wherein x is a linear lower layer decision variable, and belongs to all lower layer decision variable sets.
The underlying linear programming model is transformed into the KKT optimality condition by the procedure described above, but further nonlinear factors are introduced into the complementary relaxation condition described above, which requires further linearization. The present example linearizes the complementary relaxation conditions using the large M method:
wherein M is a great positive integer, Y i And 0-1 variable, and ensuring that all constraint conditions of the KKT condition are linear constraint through a large M method.
Through the above process, the single-layer multi-target linear programming model finally obtained is:
after the model nonlinear constraint second order cone relaxation, linearization and double-layer model KKT condition transformation, the invention finally obtains the linearly solvable single-layer multi-target linear programming model so as to ensure that the simplified model can be conveniently solved and improve the practicability of the model.
S3, acquiring grid structure data and distributed power generation actual 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 an optimal distributed power generation site selection and volume determination scheme.
Specifically, the main body studied in the embodiment is a 35kV power distribution network, 12 typical days are selected in one year, 8 time nodes in each typical day are selected to represent the typical day, 96 time nodes are finally obtained to equivalently represent wind and light output in the year, distributed power generation actual output data of each typical day in the previous year are collected, the distributed power generation actual output data and grid structure data are input into a multi-target linear programming model, the pareto optimal front edge of a single-layer multi-target linear programming model is solved, the comprehensive adaptability of each solution in the pareto optimal front edge solution set is solved, and the solution with the highest comprehensive fitness in the pareto optimal front edge solution set is taken as the optimal compromise solution, namely the optimal distributed power generation site selection and volume fixing scheme. Specifically, the actual output data of the distributed power generation comprises the output of a wind power typical solar power curve at each moment and the output of a photovoltaic typical solar power curve at each moment, and the grid structure data comprises the conductance, susceptance value and current-carrying capacity upper limit of a branch in the power system. The optimal distributed power generation, site selection and volume determination scheme is obtained by solving the pareto optimal front edge of the single-layer multi-target linear programming model, so that the dynamic change of each distributed investor in a power grid can be better reflected, and the benefit competition relationship of each investor in the model can be better reflected.
Specifically, the overall fitness of the kth pareto optimal solution is expressed as:
wherein fit (i, k) is the fitness of the ith objective function, kth pareto optimal solution, 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 pareto front.
Specifically, the fitness fit (i, k) of the kth pareto optimal solution of the ith objective function is expressed as:
wherein F is i,max ,F i,min Representing the maximum and minimum of the ith objective function respectively,the objective function value of the kth pareto optimal solution of the ith objective function is represented. />
In the following, a practical distribution network system of a certain town is taken as an embodiment. The main line of the regional power grid to be planned is a 35kV outgoing line, and 1 110kV/35kV transformers are taken as public accessible transformers in total; the 35kV power distribution network has 11 public accessible nodes. In the embodiment, the investment cost per unit capacity of the wind turbine generator is 7000 yuan/MW, the investment cost per unit capacity of the photovoltaic turbine generator is 6000 yuan/MW, the wind power on-line electricity price is 0.34 yuan/kW.h, the photovoltaic on-line electricity price is 0.34 yuan/kW.h, the main network electricity purchasing electricity price is 0.568 yuan/kW.h, the survival rate is 3%, the depreciation period of wind power equipment is 20 years, the depreciation period of the photovoltaic equipment is 30 years, and the residual value rate of the wind power photovoltaic equipment is 5%.
The results of solving the obtained optimal solution of wind power, optimal solution of photovoltaic power and optimal solution of compromise by adopting the method provided by the invention are shown in table 1.
TABLE 1
| Results | Wind power optimal solution | Photovoltaic optimal solution | Optimal solution for compromise |
| Electrical network total 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 |
| Wind power total building capacity/MW | 20 | 5 | 14.4 |
| Photovoltaic total projected capacity/MW | 5.4 | 13.1 | 8.5 |
| Wind power total generating capacity/MW.h | 31848 | 8536.5 | 24253.9 |
| Total power generation of photovoltaic/MW.h | 2959 | 9410.6 | 5357.9 |
| Total power purchase/MW.h of electric network | 66252 | 83236.7 | 71460.0 |
As can be seen from table 1, the optimal solution of wind power only considers the maximization of the interests of the wind power investor, thus resulting in the situation that the interests of the photovoltaic investor are extremely low; meanwhile, the optimal solution of the photovoltaic is only considered by a photovoltaic investor, and the benefits of wind power investors are not considered well. Compared with the optimal solution of wind power and the optimal solution of photovoltaic, the optimal compromise solution of the model can better integrate the economic benefits of wind power and photovoltaic investors, and the two economic benefits are balanced. When the actual power grid runs, the investment enthusiasm, the return on investment and the like of the wind-light investors can be dynamically changed along with the power grid and the climate factors, so that the optimal solution and the optimal solution of the distributed investors can be continuously updated, and the pareto optimal solution set solved by the invention better covers various distributed investment scenes possibly appearing in the power grid, and further proves the advantages of the solution thinking of the invention compared with a fixed weight method.
In addition, the invention combines the convex relaxation method to perform second order cone linear approximation on the nonlinear term of the flow constraint in the double-layer planning model of distributed power generation site selection and volume determination, so as to obtain the double-layer linear planning model. As shown in table 2, the optimal results are obtained by solving the model after linearizing the second order cone and the original second order cone model respectively.
TABLE 2
| Results | Second order cone linearization model | Original second order cone model | Error of both |
| Electrical network total 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 power purchase/MW.h of electric network | 60490 | 60294 | 0.3235％ |
As can be seen from the table 2, the second order cone linearization method adopted by the invention can better geometrically approximate to the original second order cone constraint, and the difference between the second order cone linearization and the original second order cone solving result is in an acceptable range from the analysis of multiple angles such as the total economy index of the power distribution network, wind power, photovoltaic power grid purchase quantity and the like, and the nonlinear problem in the original model is better solved through the second order cone linearization approximation, 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 of the method and the practicability of the model, the method provided by the invention is used for comparing the solving result of the double-layer planning model of the power distribution network, which is established by taking the maximum economic benefit of a wind-light investor and the minimum annual operation cost of the power distribution network as targets, with the solving result of the single-layer planning model of the power distribution network, which is established by taking the minimum annual operation economic cost of the power distribution network as targets, without considering the benefits of wind-light investors in the existing method, only taking the operation constraint of the power distribution network into consideration, and the obtained results are shown in table 3.
TABLE 3 Table 3
From table 3, it can be seen that the economic benefit of the wind-light investor in the single-layer planning model of the power grid is less than 0, the benefits of the distributed investors are not considered, and meanwhile, the wind-light online electricity prices are lower than the electricity purchasing prices of the power distribution network to the upper power grid, so that the single-layer planning model ensures that the running economy of the power distribution network is optimal, the investment capacity of each wind-light point reaches the upper limit, and the result of the double-layer planning model provided by the invention is more accurate.
In order to further prove the robustness of the method proposed by the present invention, the present embodiment sets 8 different scenarios, respectively:
scene 1: total installed capacity C of wind power F =20 and photovoltaic total packaging machine capacity C G =20, and gives the appropriate reject-wind reject constraint;
scene 2: total installed capacity C of wind power F =20 and photovoltaic total packaging machine capacity C G =20, and gives the grid a very large wind and light curtailment penalty cost;
scene 3: total installed capacity C of wind power F =0 and photovoltaic total packaging machine capacity C G =20, only photovoltaic investors are present, no wind investors are present;
scene 4: total installed capacity C of wind power F =20 and photovoltaic total packaging machine capacity C G =0, only wind investors are present, no photovoltaic investors are present;
scene 5: total installed capacity C of wind power F =5 and photovoltaic total packaging machine capacity C G =5, corresponding to negative investments of both wind power and photovoltaic investors;
scene 6: total installed capacity C of wind power F =5 and photovoltaic total packaging machine capacity C G =20, corresponding to negative investment in wind power, positive investment in photovoltaic;
scene 7: total installed capacity C of wind power F =20 and photovoltaic total packaging machine capacity C G =5, photovoltaic negative investment, wind power positive investment;
scene 8: total installed capacity C of wind power F =20 and photovoltaic total packaging machine capacity C G =20, all the wind photovoltaic investors invested positively.
The double-layer planning model for distributed power generation site selection and volume determination provided by the invention is solved under the 8 scenes, and the obtained results are shown in tables 4 and 5. As can be seen from table 4, when the grid gives a very strict wind-discarding light-discarding penalty (corresponding to scenario 2), all the wind power accessible to the grid is connected to the grid, and the photovoltaic power still has a certain amount of light-discarding due to the output characteristics and the power flow stability constraint. The wind-discarding punishment of the power grid can greatly restrict the wind-discarding phenomenon, but if the wind-discarding punishment is required to be further restricted, the distributed power supply location and volume-fixing is required to be more reasonably carried out.
TABLE 4 Table 4
| Scene(s) | Scene 1 | Scene 2 |
| Electrical network total objective function/ten thousand yuan | 4996.2 | 5467.0 |
| Wind power total generating capacity/MW.h | 31847 | 34377.3 |
| Total power generation of photovoltaic/MW.h | 8683 | 15839.8 |
| Total power purchase/MW.h of electric network | 60490 | 60298.5 |
| Air rejection rate/MW.h | 2530.9 | 0 |
| Light rejection/MW.h | 10927 | 3774.4 |
As can be seen from Table 5, the method provided by the invention can provide an optimal distributed power generation site-selection and volume-fixing scheme under different scenes, and has better robustness.
TABLE 5
| Scene(s) | Scene 3 | Scene 4 | Scene 5 | Scene 6 | Scene 7 | Scene 8 |
| Electrical network total objective function/ten thousand yuan | 5728.0 | 5014.7 | 5549.1 | 5529.4 | 5011.7 | 4996.2 |
| Wind power generation capacity-MW·h | 0 | 31868 | 8512 | 8529 | 31826 | 31847 |
| Total power generation of photovoltaic/MW.h | 13876.0 | 0 | 4349 | 12605 | 2701 | 8683 |
| Total power purchase/MW.h of electric network | 87409 | 69211 | 88389 | 80037 | 66568 | 60490 |
In summary, compared with the traditional algorithm, the distributed power generation site selection and volume determination method based on trend linearization, provided by the invention, not only simultaneously considers multiple benefit subjects, reduces the annual economic operation cost of power grid companies while improving the new energy consumption level and the economic benefit of distributed power generators, but also effectively reduces the model calculation complexity, and shows the practicability of the method.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (3)
1. A distributed power generation site-selection and volume-fixing method based on tide linearization is characterized by comprising the following steps:
s1, on the basis of an actual power distribution network operation scene, establishing a double-layer planning model for distributed power generation site selection and volume fixation by taking the economic benefit of wind and light investment and the economic cost of the power distribution network into consideration, taking the 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; the economic benefits of the wind and light investment include: net annual profit of the wind sponsor and net annual profit of the photovoltaic sponsor;
the model corresponding to the upper layer optimization target is an upper layer distributed investment construction capacity optimization model, and is expressed as follows:
wherein F is 1 (x) For the net annual profit of wind power investors, F 2 (x) For net annual profit of the photovoltaic sponsor, T represents a set of time periods, Ω is a set of site locations for wind power and photovoltaic power plants, each site location is a grid node,d, obtaining the actual wind power access quantity of the power grid in the t time period at the kth node f The online electricity price of the unit wind power electric quantity is delta t which is the duration of each period in the operation period, R f Investment cost k is unit of wind turbine installation capacity f F (A/P) is the annual gold present value coefficient, C F C, the capacity of the wind power assembly machine is equal to that of a wind power assembly machine fw For the maintenance cost factor of the wind turbine generator system, +.>D, the actual photovoltaic access quantity of the power grid in the t time period at the kth node g The online electricity price of the unit photovoltaic electric quantity is R g Investment cost, k, in units of photovoltaic unit assembly capacity g C is the residual value rate of the photovoltaic unit G C, the capacity of the photovoltaic assembly machine is equal to that of the photovoltaic assembly machine gw Investment cost R of unit wind turbine installation capacity as maintenance cost coefficient of photovoltaic f And investment cost per unit photovoltaic unit assembly capacity R g Meeting investment budget constraints;
the model corresponding to the lower-layer optimization target is a lower-layer distribution network distributed power supply site-selection and volume-fixation optimization model, and is expressed as follows:
minf(x)＝C cost +C pub
wherein f (x) is the total power supply cost of the distribution company, C cost C for purchasing electricity cost of power distribution network pub For the penalty cost of wind and light discarding, T represents a time period set, Ω is a wind power and photovoltaic power station site set, each site is a grid node,d, obtaining the actual wind power access quantity of the power grid in the t time period at the ith node f The online electricity price of the unit wind power and electricity quantity is d ff The running cost of the unit wind power and electricity quantity is shown as delta t, and delta t is the duration of each period in the running period>For the t time period at the ith nodeActual photovoltaic access quantity of internal power grid, d g The online electricity price of the unit photovoltaic electric quantity is d gf The operation and maintenance cost of the unit photovoltaic electric quantity is d grid For the price of buying a unit of electricity from the main network, < > the price of->For the electricity purchasing quantity k of the power grid in the t time period at the ith node pub For penalty factor, +.>For the capacity of the wind power installation at the ith node, the output (t) is the output of a wind power typical solar power curve at the moment t, F f The output (t) is the output of the photovoltaic typical solar power curve at the moment t and F is the reference capacity of the wind power typical solar power curve g Reference capacity for a typical solar curve of photovoltaic, +.>The photovoltaic installed capacity at the ith node;
constraint conditions of the lower-layer distribution network distributed power supply location and volume-fixing optimization model comprise: and (3) load flow constraint:
wherein P is ij,t For the active power flowing through branch i-j at time t, G ij For conductance of branch i-j, U i,t For the voltage at the ith node at time t, U j,t Respectively represent the voltage at the j-th node at the time t, theta ij,t B is the voltage phase difference between the ith node and the jth node at the moment t ij Susceptance value for branch i-j, Q ij,t The reactive power flowing through the branch i-j at the moment t;
s2, linearizing nonlinear terms in a double-layer planning model for distributed power generation site selection and volume determination based on a convex relaxation method, a variable linearization method, a second order cone approximation and a KKT optimality condition, and converting the double-layer planning model into a single-layer multi-target linear planning model;
s3, acquiring grid structure data and actual output data of distributed power generation on 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 an optimal distributed power generation site selection and volume determination scheme;
the method of step S2, comprising the steps of:
s21, combining a convex relaxation method and a variable linearization method, and performing second-order cone linear approximation on a nonlinear term of power flow constraint in a double-layer planning model for distributed power generation site selection and volume determination to obtain a double-layer linear planning model; firstly, performing second-order cone relaxation on a double-layer planning model, and then performing second-order cone constraint linearization on the model with the second-order cone relaxation to obtain a double-layer linear planning model;
s22, processing the double-layer linear programming model based on the KKT optimality condition, and converting the lower-layer programming model into an upper-layer multi-objective linear programming model which is completely linear and solvable.
2. The power flow linearization-based distributed power generation site-selection and volume-fixation method as claimed in claim 1, wherein the constraint condition of the lower-layer distribution network distributed power source site-selection and volume-fixation optimization model further comprises: power balance constraint, distributed power supply output constraint, node voltage constraint, power grid purchase quantity constraint, line current-carrying capacity constraint, distributed power supply total capacity constraint and power grid transformer capacity constraint.
3. The distributed power generation site selection and volume determination method based on trend linearization according to claim 1, wherein the pareto optimal front edge of the single-layer multi-objective linear programming model is solved, and a solution with highest fitness in the pareto optimal front edge solution set is used as an optimal distributed power generation site selection and volume determination scheme.
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