CN117096873A - Transportation and storage multi-stage coordinated planning method considering carbon transaction cost - Google Patents

Transportation and storage multi-stage coordinated planning method considering carbon transaction cost Download PDF

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CN117096873A
CN117096873A CN202311120555.5A CN202311120555A CN117096873A CN 117096873 A CN117096873 A CN 117096873A CN 202311120555 A CN202311120555 A CN 202311120555A CN 117096873 A CN117096873 A CN 117096873A
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胡迎迎
李强
张琳娜
吉喆
高玮
邵亚林
张静宇
郑晓明
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Economic and Technological Research Institute of State Grid Shanxi Electric Power Co Ltd
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Abstract

The application provides a multi-stage coordinated planning method for output and storage, which takes carbon transaction cost into consideration, and aims to fully quantify uncertainty of wind power output, load demand and wind power plant output under annual period are generated into a typical scene set through scene clustering, and a two-stage distribution robust planning optimization model under data driving is provided on the basis of wind power output annual history data, and the method comprises the steps ofThe method comprises the steps of optimizing and solving comprehensive cost optimal decision results based on worst wind power probability scenes in one stage, searching probability distribution of the worst wind power scenes in the second stage, and optimizing and solving a two-stage model by adopting a column and constraint algorithm; build L-based 1 -norms and L ∞ The scene probability distribution uncertainty set of norms realizes the function of minimum sum of investment cost and operation cost of a power transmission line, a wind farm and energy storage, considers the randomness of the load in a annual period, avoids the planning thought based on load blocks, and effectively improves the reasonable capacity of the system for absorbing wind power resources.

Description

Transportation and storage multi-stage coordinated planning method considering carbon transaction cost
Technical Field
The application belongs to the technical field of novel power systems, and particularly relates to a transportation and storage multi-stage coordination planning method considering carbon transaction cost.
Background
With the continuous promotion of the national 'double carbon' target, new energy power generation mainly comprising wind power and photovoltaic is vigorously developed, and the fluctuation of the output of the new energy power generation requires the power grid to be flexibly transformed so as to adapt to high-proportion new energy grid connection. Under a short-term time scale operation framework, the adaptability of the power system is enhanced by a random unit combination, a robust unit combination, increased rotation standby and the like; under a long-time scale planning framework, the adaptability of the power system is improved through power plant extension, transmission network line extension, energy storage optimization configuration and the like. Because of the high cost of transmission line and energy storage construction and the high investment risk, it is necessary to coordinate the grid planning and energy storage planning to accommodate the uncertainty of load growth.
The documents related to the power transmission network expansion planning research are numerous, and some documents review the model, the solving method and the like of the power transmission network expansion planning and point out the development direction of the power transmission network and energy storage coordination planning. The novel energy storage is used as a regulator in a power system and is gradually commercialized and popularized in a power transmission network. The research on novel energy storage planning mainly comprises the steps of establishing an energy storage planning model from an energy storage cost model, attenuation characteristics and the like, for example, some documents analyze the necessity of energy storage configuration in a power transmission network, and establish a two-stage robust optimization model aiming at energy storage capacity cost minimization; some documents consider the influence of the charge and discharge process on the cycle life, the charge and discharge depth in actual operation is calculated to the full charge and discharge depth, a battery energy storage cost model based on the equivalent full cycle time life is provided, and a two-stage robust optimization model for minimizing the comprehensive daily chemical energy storage capacity cost and the operation cost is established.
In order to better coordinate the power transmission network and the energy storage planning, a minimum target of a comprehensive circuit, minimum energy storage investment and system wind abandoning cost is established, and the fact that along with the reduction of the energy storage cost, the power transmission and storage coordination planning benefit is better is verified. At present, scholars consider the attenuation characteristic of energy storage and establish the energy storage and power transmission network joint planning model with the energy storage life broken according to fixed proportion. Further documents establish robust planning models for transmission networks and energy storage expansion, and solve the robust planning models by adopting an original section decomposition algorithm. The probability distribution uncertainty set based on wind power output is studied to establish a robust joint planning model of the power transmission network and the energy storage distribution based on scene probability driving.
Most of the transportation and storage coordination planning researches take the comprehensive cost of a period of years as an objective function, belong to single-stage static coordination planning, and lack multi-stage dynamic coordination planning taking 10 years or even 20 years as a period. On the time scale, the single-stage static planning of coordination of transmission and storage belongs to short-term planning, and the multi-stage dynamic planning of coordination of transmission and storage belongs to long-term planning, so that the time sequence of investment can be more comprehensively considered, and repeated investment is avoided. Because the annual period dimension is increased by the long-term planning taking the year as the period, the existing long-term planning method of the power transmission network mainly divides the load demand, the wind power output and the like in one year into a plurality of load blocks and wind power blocks, and gives the duration of each load block and wind power block, so that short-term operation constraint is easy to establish, and the annual operation cost is acquired. While the load block-based long-term planning approach reduces the solution dimension, there is a lack of uncertainty factors that consider the load's randomness factor and load growth over a year period.
In addition, in order to further promote the control of the total carbon emission amount of the electric power system, the carbon trade market has been gradually promoted in the electric power system, and the initial carbon emission amount distribution is mainly performed in a gratuitous distribution manner in China at present, on the basis of which a rewarding and punishing mechanism is introduced to restrict the carbon emission, namely, when the total carbon emission amount of the power generation enterprises is lower than the carbon emission amount distributed freely, the government gives a certain rewarding and subsidy, and when the total carbon emission amount of the power generation enterprises is higher than the carbon emission amount distributed freely, the power generation enterprises need to purchase the carbon emission amount through the carbon trade market. Therefore, in a two-carbon context, it is necessary to consider carbon trade constraints in a coordinated storage planning process.
The construction of a novel power system taking renewable energy sources such as wind power, photovoltaic and the like as main bodies is a main direction for realizing a double-carbon target, but large-scale wind power grid connection with strong fluctuation and high uncertainty brings serious challenges to investment planning of a power transmission network. Therefore, on the basis of considering the carbon emission cost of the system, the cooperative expansion planning model is constructed by taking the minimum sum of the investment cost and the operation cost of the power transmission line, the wind farm and the energy storage as an optimization target.
Disclosure of Invention
The application aims to solve the technical problems that: the method is used for minimizing the sum of investment cost and operation cost of a power transmission line, a wind farm and energy storage.
The technical scheme adopted by the application for solving the technical problems is as follows: a transportation and storage multi-stage coordinated planning method considering carbon transaction cost comprises the following steps:
s1: constructing a transmission and storage multi-stage coordination planning model comprising system operation cost, carbon emission cost, energy storage investment cost and transmission line investment cost;
s2: acquiring actual probability distribution of wind power based on massive wind power historical data, and providing a two-stage distribution robust scheduling model based on data driving by combining a robust optimization method to quantify uncertainty;
s3: in the two-stage distributed robust scheduling model solving, the max-min problem is subjected to dual conversion by utilizing a strong dual theory, a planning result in the worst scene is found by adopting a column and constraint generation algorithm, modeling is performed by utilizing a Yalmip of a Matlab toolbox, and a business solver is called for solving.
According to the above scheme, in the step S1, the specific steps are as follows:
s11: the system operation cost, the carbon emission cost, the energy storage investment cost and the transmission line investment cost of the y-th year are respectively set asAnd if the total years of the planning period is Y, establishing an objective function of a transmission and storage multi-stage coordinated planning model as follows:
s12: the constraint conditions for establishing the transportation and storage multi-stage coordination planning model comprise unit operation constraint, unit standby constraint, energy storage power station operation constraint, energy storage construction constraint, branch flow constraint, line extension constraint, node power balance constraint and system standby constraint.
Further, in the step S11, the specific steps are as follows:
s111: let the probability corresponding to the y-th scene s be ρ y,s The running cost of the ith conventional unit in the period t under the scene s is as followsThe conventional unit is assembled into omega G The operation period is T, and the discount rate is r; the active output of the section b of the ith conventional unit in the period t under the scene s of the y-th year is +.>The segmentation cost coefficient of the ith conventional unit in b segments is k i,b The total number of segments of the unit cost curve is B, at the firstThe running state of the ith conventional unit in the period t under the scene s of y years is +.>If the device is in operation, the device is 1, and if the device is not in operation, the device is 0; let the starting cost of the ith conventional unit be U i No-load cost of the ith conventional unit is N i The method comprises the steps of carrying out a first treatment on the surface of the The operation cost of the ith conventional unit in the period t under the scene s of the y-th year ∈>The method comprises the following steps:
s112: according to the actual carbon emissionAnd gratuitous carbon emission quota->The relation between them establishes a ladder carbon trade mechanism, then carbon trade cost +.>The calculation model of (2) is as follows:
let the carbon emission allowance per unit power generation amount beGratuitous carbon emission quota->The method comprises the following steps:
let the actual carbon emission amount per unit power generation amount be phi, the actual carbon emission amountThe method comprises the following steps:
dividing the difference between the actual carbon emission and the gratuitous carbon emission quota into a plurality of intervals, wherein each interval corresponds to different carbon transaction prices; based on a ladder carbon transaction mechanism, when the actual carbon emission is smaller than the gratuitous carbon emission quota, the electric power system sells redundant quota in the carbon transaction market to obtain benefits, and the smaller the carbon emission is, the larger the difference value between the carbon emission and the quota is, the higher the quota selling price and the higher the income in the corresponding interval are; conversely, when the actual carbon emission is larger than the gratuitous carbon emission quota, the electric power system pays a certain fee to purchase the carbon emission right, and the more the carbon emission is, the larger the difference value between the carbon emission and the quota is, the higher the purchase price of the carbon emission right and the purchase fee of the carbon emission right in the corresponding interval are; let the reference price of carbon trade be c, the growth coefficient of carbon trade be alpha, the length of carbon trade price interval be v, then the cost of carbon tradeIs expressed as:
s113: let the service life of the energy storage power station be S T Annual cost interest rate alpha of nth energy storage power station n Is that;
let the investment cost of unit capacity and the investment cost of unit power of the energy storage power station be C respectively E And C P Annual investment cost k of unit capacity of energy storage power station e And annual investment cost per unit power k p The method comprises the following steps of:
let the initial capacity and power of the energy storage power station at node i be respectivelyAnd->The candidate energy storage node set is omega S The energy storage investment cost is:
s114: let the investment cost per unit capacity of the transmission line be C L The service life of the power transmission line is L T Annual investment cost per unit capacity c of transmission line ij ij The method comprises the following steps:
annual cost interest rate beta of nth year transmission line n The method comprises the following steps:
whether the power transmission line ij is built as the p candidate line in the y-th yearIf the construction is 1, if the construction is not, the construction is 0; the candidate transmission line set is omega L The number of candidate lines is p max The method comprises the steps of carrying out a first treatment on the surface of the The line investment costs are:
further, in the step S12, the specific steps are as follows:
s121: the active output of the ith conventional unit in the period t under the scene s of the y-th year is set asThe lower limit of the output of the ith conventional unit is i pThe upper limit of the output of the ith conventional unit in the section b is +.>The climbing speed of the ith conventional unit is delta i The method comprises the steps of carrying out a first treatment on the surface of the The unit operation constraint is as follows:
s122: the active reserve of the ith conventional unit in the period t under the scene s of the y-th year is set asThe upper limit of the output of the ith conventional unit is +.>The active standby response time is Δt; the unit standby constraint is:
s123: the capacity of the energy storage power station at the node i in the y-th scene s in the period t is set asThe charging power and the discharging power of the energy storage power station at the node i in the period t under the scene s of the y year are respectively +.>And->The charging efficiency and the discharging efficiency of the energy storage power station at the node i are respectively +.>And->The charging state and the discharging state of the energy storage power station at the node i in the period t under the scene s of the y year are respectively +.>And->The upper limit and the lower limit of the charge state of the energy storage power station are respectively +.>AndSocthe method comprises the steps of carrying out a first treatment on the surface of the The maximum capacity and maximum power of the energy storage station at node i of the y-th year are +.>And->Whether or not the energy storage power station at the construction node i is invested in the y-th year is +.>If the investment construction is 1, if the investment construction is not, the investment construction is 0; the active reserve of the energy storage station at node i in the period t under the scene s of the y-th year is +.>The energy storage power station operating constraints are:
s124: the total number of the energy storage power stations built in the y year is S y The total number of the energy storage power stations built in the whole planning period is S max The method comprises the steps of carrying out a first treatment on the surface of the The energy storage build constraint is:
s125: planning initial year y 0 The branch active power of the transmission line ij in the s scene t period is as followsPlanning initial year y 0 Whether or not the transmission line ij of (1) is operating as +.>If the device is in operation, the device is 1, and if the device is not in operation, the device is 0; in the scenario s of the y-th year the phase angle of node i in period t is +.>Reactance of transmission line is B ij Planning initial year y 0 The upper limit of the active power of the branch of the transmission line ij at the t period is xB ij The method comprises the steps of carrying out a first treatment on the surface of the The branch power flow constraint is:
setting the branch active power of the p candidate line of the power transmission line ij in the t period under the y-th scene s asWhether the power transmission line ij runs as +.f in the y-th scene s at t period p candidate line>If the device is in operation, the device is 1, and if the device is not in operation, the device is 0; the upper limit of the branch active power of the p candidate line of the transmission line ij in the period t of the y-th year is +.>Then after p candidate lines, the branch power flow constraint becomes:
let M be on the order of 10 6 And then linearizes the above formula to:
s126: the total number of the power transmission lines arranged in the whole planning period isThe line extension constraint is:
s127: the active output of the wind power plant at the node i in the y-th scene s in the period t isThe active demand of the load at node i in period t under the y-th scenario s is +.>The node power balancing constraint is:
s128: the system standby constraint is:
further, in the step S123, the capacity and the power annual attenuation factor of the nth energy storage power station are set to be a respectively n And b n The calendar aging decay rate and the cyclic aging decay rate of the energy storage power station are k respectively cal And k cycle The method comprises the steps of carrying out a first treatment on the surface of the Based on the operation constraint of the energy storage power station, the damage constraint of the cycle life of the energy storage power station is obtained according to the fixed attenuation factor conversion:
C＝1-k cal -k cycle ，
further, in the step S2, the specific steps are as follows:
s21: let the investment variable be x and the corresponding investment cost term be a T The feasible domain of x and x is χ; the operating variable is y, and the corresponding operating cost and carbon emission cost are b T y+c T The feasible domain of xi and y is gamma, and the random variable related to the predicted power of the wind turbine generator is xi; set A, B, d, z, C, D, E, F, G, H, f, J as matrix and vector in abstract form, representing the coefficients of objective function and constraint; converting the deterministic multi-stage coordination planning model of the storage and the transmission constructed in the step S1 into a two-stage distribution robust scheduling model, and simplifying the corresponding mathematical model into:
in the two-stage distributed robust scheduling model, the first stage obtains an optimal decision result by optimizing all investment decision variables and corresponding investment costs; the expected cost and the running cost of the predicted power xi of the wind turbine generator are optimized in the second stage, so that probability distribution of the worst scene of the predicted power of the wind turbine generator in the first stage is obtained; let the feasible domains of investment constraint polynomial and operation constraint formula be X respectively m 、Y m Meanwhile, the coupling relation of the covering variables in the first stage and the second stage under the fixed wind power output scene is also represented; the total operation scene is M; constructing a probability distribution function of wind power output as P { ζ };
s.t.Ax≤d，
the initial probability weight of the m-th typical scene extracted from a large amount of wind power operation data is set asWith scene probability p m Corresponding N s The vector consisting of positive real numbers is +.>The allowable probability deviations in the 1-norm and infinity-norm ranges are respectively θ 1 、θ ∞ The method comprises the steps of carrying out a first treatment on the surface of the The probability under the worst scene is further obtained by establishing 1-norm and infinity-norm as constraints to limit wind power fluctuation within a reasonable range, and the established comprehensive norm set is expressed as:
let the actual number of operating scenarios be Q, where:
θ ∞ ＝1/(2Q)·ln2M/(1-α ∞ )；
then for the mth scene p m Is expressed as:
according to the above scheme, in the step S3, the specific steps are as follows:
solving a two-stage distributed robust model by using a column and constraint generation algorithm CCG, decomposing a second-stage model into a main problem and a sub-problem, and continuously iterating alternately; the main problem is to find the optimal planning result under the probability distribution of the given worst scene, K is set as the iteration number, and the lower bound value of the objective function is obtained in the alternate kth iteration of the main problem and the sub-problem:
s.t.Ax s ≤d，
the sub-problem is the variable x after the kth iteration is obtained k Under the condition of (1), optimizing probability distribution of the worst scene, providing iterative input for the main problem, and providing the most suitable upper bound value for the main problem, thereby ensuring that the uncertainty of the scene is fully quantized; the expression of the sub-problem is:
the sub-problem is a double-layer max-min problem, the minimum optimization problem under different m scenes is a linear programming model, and the maximum problem and the minimum problem are mutually independent; the minimum problem is to minimize the running cost of M scenes in investment planning, and the maximum problem is to solve the probability distribution of the worst uncertainty scene under the given optimal running cost;
since the min-layer optimization problem in the sub-problem is independent of each other, the x is obtained in the first stage * Thereafter, the inner layer minimum optimization problem in the sub-problem is converted into f (x * ,ξ m ) The above formula is simplified to:
the above method converts the sub-problem into a linear programming problem, andand M scenes are not mutually influenced, so that O (x) is obtained through linear optimization * ) WhileWill be obtained during the k+1st iteration of the main problem; 2 0-1 auxiliary variables are introduced to represent probability +.>The negative offset and the positive offset of the constraint term containing absolute values are converted into linear constraint terms;
and transmitting the confidence probability distribution obtained by the lower layer to an upper layer planning model for iterative solution, and adopting direct current power flow in the upper layer model to treat the nonlinear problem in power flow calculation.
A computer storage medium having stored therein a computer program executable by a computer processor for performing a method of transportation and storage multi-stage coordinated planning taking into account carbon trade costs.
The beneficial effects of the application are as follows:
1. according to the input and storage multi-stage coordinated planning method considering the carbon transaction cost, in order to fully quantify the uncertainty of wind power output, a typical scene set is generated by using load demands and wind power plant output under a annual period through scene clustering, a two-stage distribution robust planning optimization model under data driving is provided on the basis of wind power output annual history data, the first stage is based on worst wind power probability scenes, the optimal decision result of comprehensive cost is optimized and solved, the second stage is the probability distribution of searching the worst wind power scenes, and the two-stage model is optimized and solved by adopting a column and constraint algorithm; build L-based 1 -norms and L ∞ The scene probability distribution uncertainty set of norms realizes the function of minimum sum of investment cost and operation cost of a power transmission line, a wind farm and energy storage, considers randomness of load under the annual cycle, and avoids planning thought based on load blocks.
2. Aiming at the problems of uncertainty and volatility in high-proportion wind power grid connection, the application establishes a transmission and storage multi-stage coordinated distribution robust planning model which is based on data driving and takes the minimum sum of the investment cost of a power transmission line, the investment cost of energy storage, the operation cost, the carbon transaction cost and the investment cost of a wind power plant as an optimization target, and adopts a column and constraint generation (column-and-constraint generation, C & CG) algorithm to convert the transmission and storage multi-stage coordinated distribution robust planning model into a main and sub problem iterative solution; and the carbon emission cost of the system is considered in the operation process, so that the reasonable capacity of the system for absorbing wind power resources is effectively improved under the condition of ensuring the safe and stable operation of the system.
3. Compared with the traditional mixed integer linear programming, the algorithm combines the advantages of random optimization and robust optimization, fully quantifies the uncertainty of representing the wind power output, remarkably reduces the air discarding quantity in the system operation, and realizes the optimal configuration of resources.
4. According to the application, the carbon emission cost is introduced into the model, so that the thermal power output can be guided to be reduced while emission reduction is satisfied, the wind power consumption level of the system is improved, and the method has important significance in promoting high-proportion renewable energy grid connection.
5. Along with the enhancement of wind power uncertainty, only planning of a power transmission grid is difficult to meet large-scale wind power grid connection requirements, enough thermal power, energy storage and other flexible resources are needed to match with the power transmission grid, and the deep coordinated interaction of source grid storage is realized, so that low-carbon transformation of a propulsion power grid is accelerated, and economic and green development of the industry is driven.
Drawings
FIG. 1 is a schematic diagram of a ladder carbon transaction mechanism according to an embodiment of the present application.
FIG. 2 is a two-stage model solution flow diagram of an embodiment of the present application.
Fig. 3 is a flow chart of an embodiment of the present application.
Detailed Description
The application will be described in further detail with reference to the drawings and the detailed description.
Referring to fig. 3, a method for multi-stage coordinated planning of transportation and storage considering carbon transaction cost according to an embodiment of the present application includes the following steps:
the first step: and constructing an input and storage multi-stage coordination planning model consisting of four parts including system operation cost, carbon emission cost, energy storage investment cost and transmission line investment cost.
1: objective function
The objective function of the transmission and storage multi-stage coordination planning model established by the patent comprises the total cost consisting of four parts, namely, the system operation cost, the carbon emission cost, the energy storage investment cost and the transmission line investment cost, namely:
wherein:respectively representing the system operation cost, the carbon emission cost, the energy storage investment cost and the transmission line investment cost of the y year; y represents the total number of years of the programming cycle.
(1) Annual operating costs
Wherein: ρ y,s Representing the probability that scene s corresponds to the y-th year,representing the running cost of the ith conventional unit in a period t under a scene s, and omega G Representing a conventional unit set, wherein T is an operation period, and r is a discount rate; />Representing the active output, k of the b segment of the ith conventional unit in the period t under the scene s of the y year i,b Representing the segmentation cost coefficient of the ith conventional unit in the B segments, wherein B is the total number of segments of the unit cost curve, [ the number of segments of the unit cost curve ]>The running state of the ith conventional unit in the period t under the scene s of the y year is 1 in running, otherwise, the running state is 0; u (U) i Represents the starting cost of the ith conventional unit, N i Indicating the no-load cost of the ith conventional unit.
(2) Stepped carbon trade cost
According to the relation between the actual carbon emission and the gratuitous carbon emission quota, a ladder carbon transaction mechanism established by the embodiment of the application is shown in the attached figure 1. In the figure, c is the carbon trade reference price; an alpha carbon trade price growth factor; v is the length of the carbon trade price interval. The difference between the actual carbon emission and the gratuitous carbon emission allowance is divided into a plurality of intervals, and each interval corresponds to different carbon transaction prices. Based on the carbon transaction mechanism, when the actual carbon emission is smaller than the gratuitous carbon emission quota, the electric power system can sell redundant quota in the carbon transaction market to obtain certain benefits, and the smaller the carbon emission, the larger the difference value between the carbon emission and the quota, the higher the quota selling price of the corresponding interval and the higher the income; conversely, when the actual carbon emission is greater than the gratuitous carbon emission allowance, the electric power system needs to pay a certain fee to purchase the carbon emission right, and accordingly, the more the carbon emission is, the greater the difference between the carbon emission and the allowance is, the higher the purchase price of the carbon emission right in the corresponding interval is, and the higher the purchase fee of the carbon emission right is. Overall, carbon trade costsThe calculation model of (2) is as follows:
(3) Cost of energy storage investment
Wherein: k (k) e 、k p Representing annual investment cost of unit capacity and annual investment cost of unit power of energy storage power station, C E 、C P Respectively representing the unit capacity investment cost and the unit power investment cost of the energy storage power station; s is S T The service life of the energy storage power station is prolonged;the initial capacity and power of the energy storage power station at the node i are respectively; alpha n Annual cost interest rate for the nth energy storage power station. Omega shape S Representing a set of candidate storage nodes.
(4) Line investment cost
Wherein: c ij Representing annual investment cost per unit capacity of the power transmission line ij, C L Is the investment cost of the unit capacity of the transmission line,indicating whether the power transmission line ij is constructed in the p candidate line of the y-th year, wherein the construction is 1, otherwise, the construction is 0; beta n Annual cost interest rate of the nth year transmission line; l (L) T The service life of the power transmission line is prolonged; omega shape L Representing a candidate transmission line set, p max Is the number of candidate lines.
2: constraint conditions
The constraint conditions of the transmission and storage multi-stage coordination planning model established by the method comprise seven groups of constraints including unit operation constraint, unit standby constraint, energy storage power station operation constraint, energy storage construction constraint, branch flow constraint, line extension constraint, node power balance constraint and system standby constraint.
(1) Unit operation constraint
Wherein:representing the ith conventional machine in the scene s of the y-th yearThe active force of the group during period t, i pindicating the lower limit of the output of the ith conventional unit, < ->The upper limit of the output of the ith conventional unit in the section b is shown, delta i And the climbing speed of the ith conventional unit is represented.
(2) Standby constraint of unit
Wherein:indicating the active standby of the ith conventional unit in period t under the scene s of the y-th year,/->And the upper limit of the output of the ith conventional unit is represented, and deltat is the active standby response time.
(3) Energy storage operation constraint
Wherein:representing the capacity of the energy storage station at node i in period t under the scenario s of the y-th year, +.> Respectively representing the charging power and the discharging power of the energy storage power station at the node i in the period t under the scene s of the y year; />Charging efficiency and discharging efficiency of the energy storage power station at the node i are respectively +.>Respectively representing the charging state and the discharging state of the energy storage power station at the node i in the period t under the scene s of the y year; /> SocRespectively representing upper and lower limits of the state of charge of the energy storage power station;respectively representing the maximum capacity and the maximum power of the energy storage power station at the node i of the y year; />Energy storage station indicating whether or not to invest in construction node i in the y-th year, +>And (3) active standby of the energy storage power station in the period t at the node i in the scene s of the y year.
Based on the operation constraint of the energy storage power station, the damage constraint of the cycle life of the energy storage power station is further considered, and the energy storage power station is converted according to a fixed attenuation factor, as follows:
C＝1-k cal -k cycle
wherein: a, a n 、b n The capacity and the power annual attenuation factors k of the energy storage power station in the nth year are respectively cal 、k cycle Respectively representing the calendar aging decay rate and the cyclic aging decay rate of the energy storage power station.
(4) Energy storage construction constraint
Wherein: s is S y Representing the total number of energy storage power stations built in the y-th year, S max Representing the total number of energy storage power stations built throughout the planning cycle.
(5) Branch tide constraint
Wherein:representing the planning initial year y 0 Branch active power of transmission line ij in s scene t period, l ij y0 is the initial year y of planning 0 If the power transmission line ij is running, the running power is 1, otherwise, the running power is 0; />Representing the phase angle of node i in period t, B, under the scenario s of the y-th year ij For reactance of transmission line, xB ij To plan the initial year y 0 The upper limit of the branch active power of the transmission line ij in the t period.
After p candidate lines, the branch power flow also becomes:
wherein:representing the branch active power of the p candidate line of the power transmission line ij in the t period under the scene s of the y year, < ->Indicating whether the power transmission line ij runs in the y-th scene s at the t period of the p candidate line, wherein the running is 1, otherwise, the running is 0; />And (3) the upper limit of the active power of the branch of the p candidate line of the transmission line ij in the period t of the y-th year. Further the above formula can be linearized as:
(6) Line extension constraints
Wherein:representing the total number of transmission lines over the entire planning period.
(7) Node power balancing constraints
/>
Wherein:representing the active force,/-for period t of the wind farm at node i in the y-th scenario s>Representing the active demand of the load at node i for period t in the y-th scenario s.
(8) System standby constraints
And a second step of: based on massive wind power historical data, the actual probability distribution of wind power is obtained, and the uncertainty of the wind power is quantified by a two-stage distribution robust optimization method based on data driving by further combining the robust optimization method.
Firstly, converting the deterministic power transmission network and wind power collaborative planning model constructed in the first step into a corresponding two-stage distributed robust scheduling model, wherein a corresponding mathematical model can be simplified into:
wherein: x is investment variable, a T x is the corresponding investment cost term, χ is the feasible region of x; y is an operating variable, b T y+c T ζ is the corresponding running cost and carbon emission cost, and γ is the feasible region of y, and ζ represents the random variable related to the predicted power of the wind turbine generator; A. b, d, z, C, D, E, F, G, H, f, J is a matrix and vector in abstract form, representing the coefficients of the objective function and constraints.
Compared with the two-stage optimization variables, the first stage in the two-stage distribution robust model is to optimize all investment decision variables and corresponding investment costs, so as to obtain an optimal decision result. And the second stage is to optimize the expected cost and the running cost of the predicted power xi of the wind turbine generator, so as to obtain the probability distribution of the worst scene of the predicted power of the wind turbine generator in the first stage.
s.t.Ax≤d
Wherein: x is X m 、Y m The method respectively represents the feasible domains of investment constraint polynomials and operation constraint formulas, and simultaneously represents the coupling relation of covering variables in the first stage and the second stage under the fixed wind power output scene; m represents the total operation scene; p { ζ } is a probability distribution function (such as Weibull distribution) for constructing wind power output.
The probability under the worst scene is further obtained by establishing 1-norm and infinity-norm as constraints to limit the wind power fluctuation within a reasonable range, and the established comprehensive norm set can be expressed as
/>
Wherein:representing the initial probability weight of the m-th typical scene extracted from a large amount of wind power operation data;for and scene probability p m Corresponding N s Vector of positive real numbers, θ 1 、θ ∞ The allowable probability deviations in the 1-norm and infinity-norm intervals are shown, respectively. And for the mth scene p m The confidence level of (2) can be expressed as:
wherein:
θ ∞ ＝1/(2Q)·ln2M/(1-α ∞ )
wherein: q number of actual running scenes.
And a third step of: in solving a two-stage distributed robust model, performing dual conversion on a max-min problem by using a strong dual theory, searching a planning result in the worst scene by using a column and constraint generation algorithm, modeling by using a Yalmip of a Matlab toolbox, and calling a commercial solver to solve.
For the two-stage distributed robust model, which belongs to a typical two-layer optimization problem, a decomposition type algorithm is generally adopted for solving, and the method solves the problem by using a column and constraint generation algorithm (column and constraint generation, CCG), so that the CCG has better convergence characteristic. The CCG algorithm decomposes the second step model into two parts, namely a main problem and a sub problem, and iterates continuously. The main problem is essentially a deterministic optimization problem, i.e. an optimal planning result is found given the probability distribution of the worst scene, and in the alternate kth iteration of the main problem and the sub-problem, the lower bound value of the objective function can be obtained:
s.t.Ax s ≤d
where K is the number of iterations.
The sub-problem is the variable x after the kth iteration is obtained k In the case of (2), the probability distribution of the worst scene is optimized and iterative inputs are provided for the main problem. It can be seen that the sub-problem is essentially to provide the most appropriate upper bound to the main problem, thus ensuring that the uncertainty of the scene is sufficiently quantified, expressed as:
/>
it can be seen from the formula that the sub-problem belongs to the double-layer 'max-min' problem, and the minimum optimization problem under different m scenes is a linear programming model, and the maximum problem and the minimum problem are mutually independent. The minimum problem is understood to be minimizing the running costs of M scenarios in the investment plan, and the maximum problem is solving the probability distribution of the worst uncertainty scenario given the optimal running cost.
Since the min-layer optimization problem in the sub-problem is independent of each other, x can be obtained in the first stage * Thereafter, the inner layer minimum optimization problem in the sub-problem is converted into f (x * ,ξ m ) The above is simplified into
The above method can convert the sub-problem into linear programming problem, and M scenes are not affected each other, so that O (x) can be obtained through linear optimization * ) WhileWill be obtained during the k+1st iteration of the main problem. Furthermore, the probability ++1 is expressed by taking into account the introduction of 2 auxiliary variables from 0 to 1>And the negative and positive offsets of (a) to convert the constraint term containing absolute values into a linear constraint term.
The confidence probability distribution obtained by the lower layer is transmitted to the upper layer planning model for iterative solution, and the nonlinear problem in the power flow calculation is processed by adopting the direct current power flow in the upper layer model, so that the two-stage distribution robust model optimization solution process provided by the patent can be shown as a figure 2.
It should be understood that the sequence number of each step in the foregoing embodiment does not mean that the execution sequence of each process should be determined by the function and the internal logic, and should not limit the implementation process of the embodiment of the present application.
The above embodiments are merely for illustrating the design concept and features of the present application, and are intended to enable those skilled in the art to understand the content of the present application and implement the same, the scope of the present application is not limited to the above embodiments. Therefore, all equivalent changes or modifications according to the principles and design ideas of the present application are within the scope of the present application.

Claims (8)

1. A transportation and storage multi-stage coordinated planning method considering carbon transaction cost is characterized in that: the method comprises the following steps:
s1: constructing a transmission and storage multi-stage coordination planning model comprising system operation cost, carbon emission cost, energy storage investment cost and transmission line investment cost;
s2: acquiring actual probability distribution of wind power based on massive wind power historical data, and providing a two-stage distribution robust scheduling model based on data driving by combining a robust optimization method to quantify uncertainty;
s3: in the two-stage distributed robust scheduling model solving, the max-min problem is subjected to dual conversion by utilizing a strong dual theory, a planning result in the worst scene is found by adopting a column and constraint generation algorithm, modeling is performed by utilizing a Yalmip of a Matlab toolbox, and a business solver is called for solving.
2. The method for multi-stage coordinated planning of transportation and storage considering carbon trade costs according to claim 1, wherein: in the step S1, the specific steps are as follows:
s11: the system operation cost, the carbon emission cost, the energy storage investment cost and the transmission line investment cost of the y-th year are respectively set asAnd if the total years of the planning period is Y, establishing an objective function of a transmission and storage multi-stage coordinated planning model as follows:
s12: the constraint conditions for establishing the transportation and storage multi-stage coordination planning model comprise unit operation constraint, unit standby constraint, energy storage power station operation constraint, energy storage construction constraint, branch flow constraint, line extension constraint, node power balance constraint and system standby constraint.
3. The method for multi-stage coordinated planning of transportation and storage considering carbon trade costs according to claim 2, wherein: in the step S11, the specific steps are as follows:
s111: let the probability corresponding to the y-th scene s be ρ y,s The running cost of the ith conventional unit in the period t under the scene s is as followsThe conventional unit is assembled into omega G The operation period is T, and the discount rate is r; the active output of the section b of the ith conventional unit in the period t under the scene s of the y-th year is +.>The segmentation cost coefficient of the ith conventional unit in b segments is k i,b The total number of segments of the unit cost curve is B, and the running state of the ith conventional unit in the period t under the scene s of the y-th year is +.>If the device is in operation, the device is 1, and if the device is not in operation, the device is 0; let the starting cost of the ith conventional unit be U i No-load cost of the ith conventional unit is N i The method comprises the steps of carrying out a first treatment on the surface of the The operation cost of the ith conventional unit in the period t under the scene s of the y-th year ∈>The method comprises the following steps:
s112: according to the actual carbon emissionAnd gratuitous carbon emission quota->The relation between them establishes a ladder carbon trade mechanism, then carbon trade cost +.>The calculation model of (2) is as follows:
let the carbon emission allowance per unit power generation amount beGratuitous carbon emission quota->The method comprises the following steps:
let the actual carbon emission per unit power generation amount bePhi, the actual carbon emissionThe method comprises the following steps:
dividing the difference between the actual carbon emission and the gratuitous carbon emission quota into a plurality of intervals, wherein each interval corresponds to different carbon transaction prices; based on a ladder carbon transaction mechanism, when the actual carbon emission is smaller than the gratuitous carbon emission quota, the electric power system sells redundant quota in the carbon transaction market to obtain benefits, and the smaller the carbon emission is, the larger the difference value between the carbon emission and the quota is, the higher the quota selling price and the higher the income in the corresponding interval are; conversely, when the actual carbon emission is larger than the gratuitous carbon emission quota, the electric power system pays a certain fee to purchase the carbon emission right, and the more the carbon emission is, the larger the difference value between the carbon emission and the quota is, the higher the purchase price of the carbon emission right and the purchase fee of the carbon emission right in the corresponding interval are; let the reference price of carbon trade be c, the growth coefficient of carbon trade be alpha, the length of carbon trade price interval be v, then the cost of carbon tradeIs expressed as:
s113: let the service life of the energy storage power station be S T Annual cost interest rate alpha of nth energy storage power station n Is that;
let the investment cost of unit capacity and the investment cost of unit power of the energy storage power station be C respectively E And C P Annual investment cost k of unit capacity of energy storage power station e And annual investment cost per unit power k p The method comprises the following steps of:
let the initial capacity and power of the energy storage power station at node i be respectivelyAnd->The candidate energy storage node set is omega S The energy storage investment cost is:
s114: let the investment cost per unit capacity of the transmission line be C L The service life of the power transmission line is L T Annual investment cost per unit capacity c of transmission line ij ij The method comprises the following steps:
annual cost interest rate beta of nth year transmission line n The method comprises the following steps:
whether the power transmission line ij is built as the p candidate line in the y-th yearIf the construction is 1, if the construction is not, the construction is 0; candidate transmission line setIs combined into omega L The number of candidate lines is p max The method comprises the steps of carrying out a first treatment on the surface of the The line investment costs are:
4. the method for multi-stage coordinated planning of transportation and storage considering carbon trade costs according to claim 2, wherein: in the step S12, the specific steps are as follows:
s121: the active output of the ith conventional unit in the period t under the scene s of the y-th year is set asThe lower limit of the output of the ith conventional unit is i pThe upper limit of the output of the ith conventional unit in the section b is +.>The climbing speed of the ith conventional unit is delta i The method comprises the steps of carrying out a first treatment on the surface of the The unit operation constraint is as follows:
s122: the ith conventional unit is arranged in the period t under the scene s of the y-th yearActive standby asThe upper limit of the output of the ith conventional unit is +.>The active standby response time is Δt; the unit standby constraint is:
s123: the capacity of the energy storage power station at the node i in the y-th scene s in the period t is set asThe charging power and the discharging power of the energy storage power station at the node i in the period t under the scene s of the y year are respectively +.>And->The charging efficiency and the discharging efficiency of the energy storage power station at the node i are respectively +.>And->The charging state and the discharging state of the energy storage power station at the node i in the period t under the scene s of the y year are respectively +.>And->The upper limit and the lower limit of the charge state of the energy storage power station are respectively +.>AndSocthe method comprises the steps of carrying out a first treatment on the surface of the The maximum capacity and maximum power of the energy storage station at node i of the y-th year are +.>And->Whether or not the energy storage power station at the construction node i is invested in the y-th year is +.>If the investment construction is 1, if the investment construction is not, the investment construction is 0; the active reserve of the energy storage station at node i in the period t under the scene s of the y-th year is +.>The energy storage power station operating constraints are:
s124: the total number of the energy storage power stations built in the y year is S y The total number of the energy storage power stations built in the whole planning period is S max The method comprises the steps of carrying out a first treatment on the surface of the The energy storage build constraint is:
s125: planning initial year y 0 The branch active power of the transmission line ij in the s scene t period is as followsPlanning initial year y 0 Whether or not the transmission line ij of (1) is operating as +.>If the device is in operation, the device is 1, and if the device is not in operation, the device is 0; in the scenario s of the y-th year the phase angle of node i in period t is +.>Power transmission line electricityThe resistance is B ij Planning initial year y 0 The upper limit of the active power of the branch of the transmission line ij at the t period is xB ij The method comprises the steps of carrying out a first treatment on the surface of the The branch power flow constraint is:
setting the branch active power of the p candidate line of the power transmission line ij in the t period under the y-th scene s asWhether the power transmission line ij runs as +.f in the y-th scene s at t period p candidate line>If the device is in operation, the device is 1, and if the device is not in operation, the device is 0; the upper limit of the branch active power of the p candidate line of the transmission line ij in the period t of the y-th year is +.>Then after p candidate lines, the branch power flow constraint becomes:
let M be on the order of 10 6 And then linearizes the above formula to:
s126: the total number of the power transmission lines arranged in the whole planning period isThe line extension constraint is:
s127: the active output of the wind power plant at the node i in the y-th scene s in the period t isThe active demand of the load at node i in period t under the y-th scenario s is +.>The node power balancing constraint is:
s128: the system standby constraint is:
5. the method for multi-stage coordinated planning of transportation and storage considering carbon trade costs according to claim 4, wherein: in the step S123, the capacity and the power annual attenuation factor of the nth energy storage power station are respectively set as a n And b n The calendar aging decay rate and the cyclic aging decay rate of the energy storage power station are k respectively cal And k cycle The method comprises the steps of carrying out a first treatment on the surface of the Based on the operation constraint of the energy storage power station, the energy storage electricity is obtained according to the conversion of the fixed attenuation factorLoss of station cycle life constraint:
C＝1-k cal -k cycle ，
6. the method for multi-stage coordinated planning of transportation and storage considering carbon trade costs according to claim 2, wherein: in the step S2, the specific steps are as follows:
s21: let the investment variable be x and the corresponding investment cost term be a T The feasible domain of x and x is χ; the operating variable is y, and the corresponding operating cost and carbon emission cost are b T y+c T The feasible domain of xi and y is gamma, and the random variable related to the predicted power of the wind turbine generator is xi; set A, B, d, z, C, D, E, F, G, H, f, J as matrix and vector in abstract form, representing the coefficients of objective function and constraint; converting the deterministic multi-stage coordination planning model of the storage and the transmission constructed in the step S1 into a two-stage distribution robust scheduling model, and simplifying the corresponding mathematical model into:
in the two-stage distributed robust scheduling model, the first stage obtains an optimal decision result by optimizing all investment decision variables and corresponding investment costs; the expected cost and the running cost of the predicted power xi of the wind turbine generator are optimized in the second stage, so that probability distribution of the worst scene of the predicted power of the wind turbine generator in the first stage is obtained; let the feasible domains of investment constraint polynomial and operation constraint formula be X respectively m 、Y m Meanwhile, the coupling relation of the covering variables in the first stage and the second stage under the fixed wind power output scene is also represented; the total operation scene is M; constructing a probability distribution function of wind power output as P { ζ };
s.t.Ax≤d，
the initial probability weight of the m-th typical scene extracted from a large amount of wind power operation data is set asWith scene probability p m Corresponding N s The vector consisting of positive real numbers is +.>The allowable probability deviations in the 1-norm and infinity-norm ranges are respectively θ 1 、θ ∞ The method comprises the steps of carrying out a first treatment on the surface of the The probability under the worst scene is further obtained by establishing 1-norm and infinity-norm as constraints to limit wind power fluctuation within a reasonable range, and the established comprehensive norm set is expressed as:
let the actual number of operating scenarios be Q, where:
θ ∞ ＝1/(2Q)·ln2M/(1-α ∞ )；
then for the mth scene p m Is expressed as:
7. the method for multi-stage coordinated planning of transportation and storage considering carbon trade costs according to claim 1, wherein: in the step S3, the specific steps are as follows:
solving a two-stage distributed robust model by using a column and constraint generation algorithm CCG, decomposing a second-stage model into a main problem and a sub-problem, and continuously iterating alternately; the main problem is to find the optimal planning result under the probability distribution of the given worst scene, K is set as the iteration number, and the lower bound value of the objective function is obtained in the alternate kth iteration of the main problem and the sub-problem:
s.t.Ax s ≤d，
the sub-problem is the variable x after the kth iteration is obtained k Under the condition of (1), optimizing probability distribution of the worst scene, providing iterative input for the main problem, and providing the most suitable upper bound value for the main problem, thereby ensuring that the uncertainty of the scene is fully quantized; the expression of the sub-problem is:
the sub-problem is a double-layer max-min problem, the minimum optimization problem under different m scenes is a linear programming model, and the maximum problem and the minimum problem are mutually independent; the minimum problem is to minimize the running cost of M scenes in investment planning, and the maximum problem is to solve the probability distribution of the worst uncertainty scene under the given optimal running cost;
since the min-layer optimization problem in the sub-problem is independent of each other, the x is obtained in the first stage * Thereafter, the inner layer minimum optimization problem in the sub-problem is converted into f (x * ,ξ m ) The above formula is simplified to:
the sub-problem is converted into a linear programming problem, and M scenes are not mutually influenced, so that O (x) is obtained through linear optimization * ) WhileWill be obtained during the k+1st iteration of the main problem; 2 0-1 auxiliary variables are introduced to represent probability +.>The negative offset and the positive offset of the constraint term containing absolute values are converted into linear constraint terms;
and transmitting the confidence probability distribution obtained by the lower layer to an upper layer planning model for iterative solution, and adopting direct current power flow in the upper layer model to treat the nonlinear problem in power flow calculation.
8. A computer storage medium, characterized by: a computer program executable by a computer processor to perform a transportation and storage multi-stage coordinated planning method according to any one of claims 1 to 7 in consideration of carbon trade costs is stored therein.
CN202311120555.5A 2023-08-31 2023-08-31 Transportation and storage multi-stage coordinated planning method considering carbon transaction cost Pending CN117096873A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117332997A (en) * 2023-12-01 2024-01-02 国网江苏省电力有限公司经济技术研究院 Low-carbon optimal scheduling method, device and equipment for comprehensive energy system

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117332997A (en) * 2023-12-01 2024-01-02 国网江苏省电力有限公司经济技术研究院 Low-carbon optimal scheduling method, device and equipment for comprehensive energy system
CN117332997B (en) * 2023-12-01 2024-02-23 国网江苏省电力有限公司经济技术研究院 Low-carbon optimal scheduling method, device and equipment for comprehensive energy system

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