CN110504701B - Battery energy storage system scheduling method considering dynamic charge-discharge efficiency - Google Patents
Battery energy storage system scheduling method considering dynamic charge-discharge efficiency Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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Abstract
A battery energy storage system scheduling method considering dynamic charge-discharge efficiency comprises the following steps: A. acquiring basic information of a battery energy storage system, and performing piecewise linearization on a charge-discharge efficiency characteristic curve; B. acquiring scheduling information such as operation limit of a battery energy storage system, initial and final electric quantity, forecast time-of-use electricity price or price multiplier and the like; C. establishing a scheduling model; D. calculating dynamic upper and lower limits of the stored electric quantity of the battery energy storage system at each time interval; E. dynamic planning and reverse recursion are carried out, and an optimization model of the core subproblem needing to be solved repeatedly in each time period is obtained; F. sequentially solving the optimal path in each horizontal sub-region from bottom to top by using the geometric characteristics of the core sub-problem optimization model; G. solving an optimal path in the horizontal sub-area; H. processing the optimal path jump; I. dynamically planning forward recursion, and calculating the optimal charge and discharge electric quantity and power decision of each time period; J. and C, entering the next time interval along with the time development, updating the scheduling information in the step B and executing the step C. The method provides an effective way for the optimized operation of the battery energy storage system, and has engineering practical value.
Description
Technical Field
The invention relates to the technical field of battery energy storage, in particular to a battery energy storage system scheduling method considering dynamic charge and discharge efficiency.
Background
The uncertainties of the increasingly rapid access of renewable energy sources to the grid present new challenges to the control and management of electrical power systems. In recent years, energy storage has become a new industry hotspot. Through the wide application of the energy storage system, the power fluctuation can be stabilized, the power quality is improved, and the operation reliability of a power grid system is enhanced.
In general, the charge-discharge efficiency of stored energy dynamically changes with the charge-discharge power. For example, lead acid batteries and lithium battery energy storage systems have a state of charge (SOC) of 20% to 95% when discharged, in which the voltage is substantially constant when discharged and the efficiency decreases to some extent as the discharge current increases. The charging process is regarded as the reverse process of discharging, the efficiency change is similar to discharging, and when the rated working condition is deviated, the loss is increased, and the efficiency is reduced.
The existing scheduling method of the battery energy storage system generally comprises the steps of making an energy storage operation plan according to predicted data of a future day, and correcting according to a set amount when actual operation deviates from the operation plan so as to optimize the operation benefit of the battery energy storage system. However, general commercial optimization software is generally adopted to solve the scheduling model of the battery energy storage system at present, and a special solution algorithm with pertinence and strong adaptability is lacked.
Therefore, at present, a special algorithm aiming at the structural characteristics of the scheduling model is urgently needed to realize the efficient solution of the scheduling problem.
Disclosure of Invention
The invention aims to provide a battery energy storage system scheduling method considering dynamic charge and discharge efficiency, provides an effective way for the optimal operation of a battery energy storage system, and has engineering practical value.
In order to realize the purpose, the technical scheme adopted by the invention comprises the following steps:
a battery energy storage system scheduling method considering dynamic charge-discharge efficiency can make an optimal operation decision of a battery energy storage system and improve the operation economy of the battery energy storage system, and comprises the following steps:
A. determining the capacity of the battery energy storage system, the relation between dynamic charge-discharge power and efficiency, the limit of charge-discharge power and the upper and lower limits of the capacity of the battery energy storage system, and selecting a proper number of sections according to the scheduling precision requirement to perform section linearization on the charge-discharge power-efficiency relation of the battery energy storage system;
B. acquiring initial storage capacity of a battery energy storage system, target storage capacity at the end of scheduling, online capacity constraint at each time interval and time-of-use predicted electricity price or equivalent value multiplier;
C. establishing a scheduling model of the battery energy storage system, wherein the optimization goal of the scheduling model is to make a charge-discharge power decision of the battery energy storage system at each time interval so as to maximize the total power generation income of the battery energy storage system, and the objective function of the scheduling model is as follows:
wherein T is the total number of scheduling periods, T is the number of scheduling periods, and λ t For the predicted electricity prices or equivalent value multipliers of the t-th period, q t The charging and discharging electric quantity of the battery energy storage system in the t-th time period is positive, negative and p (q) t ) The charging and discharging power of the battery energy storage system in the t-th time period is q t Delta is the length of the scheduling period;
the constraints of the scheduling model include:
1) Electric quantity balance constraint of battery energy storage system
In the formula, e t The stored electric quantity L of the battery energy storage system at the end of the t-th period t The fixed loss electric quantity of the battery energy storage system in the known t-th time period is a negative value;
2) Network power constraint
In the formula (I), the compound is shown in the specification,
and
the upper limit and the lower limit of the online electric quantity of the battery energy storage system in the t-th time period are respectively set;
3) Charge-discharge power constraint of battery energy storage system
In the formula, P max And P min The physical upper limits of the discharge power and the charge power of the battery energy storage system are respectively, the function p is a monotonous piecewise linear function, and the charge and discharge power constraint (4) can be converted into a constraint of charge and discharge amount:
in the formula, the function P 'is an inverse function of the function P, P' (P) max ) And P' (P) min ) Physical upper limits of the discharge electric quantity and the charge electric quantity of the battery energy storage system are respectively set;
4) SOC constraint of electric quantity
In the formula, E max And E min Respectively the upper limit and the lower limit of the stored electric quantity of the battery energy storage system;
5) Initial and final electric quantity restraint of battery energy storage system
e 0 ＝E 0 ,e T ＝E T (7)
In the formula, E 0 And E T Respectively the electric quantity of the battery energy storage system at the initial moment and the target electric quantity at the end of scheduling, e 0 And e T The stored electric quantity of the battery energy storage system at the starting moment of the dispatching and at the end of the T-th period respectively;
the dispatching model of the battery energy storage system is formed by formulas (1), (2), (3), (5), (6) and (7);
D. calculating dynamic upper and lower limit constraints of the storage electric quantity of the battery energy storage system at each time interval, and according to the target storage electric quantity E when the scheduling of the battery energy storage system is finished at the end of scheduling T And the upper and lower limits of the storage electric quantity of the battery energy storage system in each time interval are constrained (2) and (5), and the dynamic upper and lower limits of the storage electric quantity of the battery energy storage system in each time interval are calculated by starting reverse recursion from the T time interval:
in the formula, j is a time variable,
and
dynamic upper and lower limits of the storage capacity of the battery energy storage system at each time interval obtained by reverse derivation respectively T For the target stored charge, L, of the battery energy storage system at the end of the schedule j The fixed loss capacity of the battery energy storage system in the known j-th time period is a negative value, P' (P) max ) And P' (P) min ) Respectively the physical upper limits of the discharge capacity and the charge capacity of the battery energy storage system,
and
respectively is the upper limit and the lower limit of the online electric quantity of the battery energy storage system in the j time period;
according to the initial electric quantity E of the battery energy storage system 0 And the upper and lower limits of the storage electric quantity of the battery energy storage system in each time interval are constrained (2) and (5), forward recursion is carried out from the scheduling starting time interval, and the dynamic upper and lower limits of the storage electric quantity of the battery energy storage system in each time interval are calculated as follows:
in the formulaJ is a time variable,
and
dynamic upper and lower limits of the storage capacity of the battery energy storage system at the end of the t period, E, obtained by forward derivation 0 For the stored energy of the battery energy storage system at the beginning of the schedule, L j Is the known fixed loss capacity of the battery energy storage system in the j (th) period, P' (P) max ) And P' (P) min ) The physical upper limits of the discharge capacity and the charge capacity of the battery energy storage system are respectively,
and
respectively is the upper limit and the lower limit of the online electric quantity of the battery energy storage system in the j time period;
and combining the forward derivation and the backward derivation, and calculating the dynamic upper and lower limits of the storage capacity of the battery energy storage system as follows:
in the formula (I), the compound is shown in the specification,
and e t And (3) combining the dynamic upper and lower limits of the storage capacity of the battery energy storage system in each time interval obtained by calculation in the t-th time interval with the formula (6) to obtain the new upper and lower limits of the storage capacity of the battery energy storage system in each time interval as follows:
in the formula, e t The stored electric quantity of the battery energy storage system at the end of the t-th period, E max And E min Respectively of battery energy storage systemsStoring physical upper and lower limits of the electric quantity;
through equivalent transformation, the dispatching model of the battery energy storage system is formed by the formulas (1), (2), (3), (5), (7) and (13);
E. a reverse recursion phase of dynamic planning is obtained according to the dynamic planning principle
In the formula (f) t (e t ) Setting f for the maximum benefit from the end of the t-th scheduling period to the end of the scheduling T (E T ) And =0, substituting (14) the power balance constraint (2) of the battery energy storage system to obtain a dynamic programming cost-to-go function which needs to be solved repeatedly in each time interval:
(15) The formula is constrained by the formulas (2), (3), (5), (7) and (13) in the solving process, and the formula (15) is defined as a core subproblem in the dynamic programming reverse recursion phase, wherein an optimization model of the core subproblem is formed by the formulas (2), (3), (5), (7), (13) and (15);
F. performing variable substitution on the formula (15) to obtain a decision quantity q t+1 Is denoted by x, e t Expressed as y, maximum profit f t (e t ) Denoted as h (x) while f is represented t+1 (e t -L t+1 -q t+1 ) Translation L t+1 Obtaining a function g (y-x), and performing equivalent transformation on an optimization model of the core subproblem in a reverse recursion phase of dynamic planning;
wherein a and b represent the charge and discharge amount q in the t +1 th period determined by the equations (3) and (5), respectively t+1 C and d respectively represent the stored electric quantity e of the battery energy storage system in each time period at the end of the t time period determined by the formulas (7) and (13) t Upper part ofThe lower limit, according to the formula (2), alpha and beta actually represent the upper and lower limits of the stored electric quantity of the battery energy storage system at the end of the t +1 time period respectively;
according to the geometric meaning of the formula (16), the segmented turning lines of the functions h (x) and g (y-x) divide the definition domain into a plurality of sub-domains, the optimal value can be proved to be obtained at the boundary in each parallelogram or the sub-domain similar to the parallelogram, the function value is linearly changed relative to the parameter x, namely the linear segmented turning point of the boundary relative to the function value can be obtained only at the end point of the parallelogram sub-domain, the end points of the parallelogram sub-domains are sorted according to the y value of each end point, the horizontal line of the adjacent end point divides the feasible domain of the problem into N horizontal sub-domains, and the optimal path in each horizontal sub-domain is sequentially searched from the lower N =1 to the upper N = N;
G. and (3) solving the optimal path of the horizontal subarea, starting from n =1, wherein L90-degree vertical lines and 45-degree oblique lines are arranged in the horizontal subarea and respectively correspond to segmented turning lines of functions h (x) and g (y-x), and the function values of intersection points of the segmented turning lines and the upper and lower boundaries of the horizontal subarea are respectively z l (y u ) And z l (y d ) Finding the maximum point z of the lower boundary function value l '(y d ) And corresponding paths l' and judging the function value z of the intersection point of the paths and the upper boundary l '(y u ) Whether the maximum point is the maximum point of all the upper boundary intersection point function values, if not, the jump of the optimal path occurs in the area, and the step H is executed; if yes, the path is the maximum path in the horizontal sub-area, and whether n is judged>N, if yes, ending the core subproblem solving process in the t-th time period, executing the step I, if not, setting N = N +1, and continuously solving the optimal path of the adjacent subarea above the horizontal subarea;
H. the optimal path jumping means that a point with the maximum function value of a lower boundary rises through an initial optimal path, jumps to another optimal path at a certain turning point to continue rising and then reaches a point with the maximum function value of an upper boundary, and initializes l '= l' by taking l 'as a reference path' s S =1, calculating the intersection point and slope of the earliest path intersected with l', and obtainingGet its intersecting path l' s+1 Coordinate of turning point (y) s+1 ，z l's+1 (y s+1 ) L' s+1 Function z at the intersection with the upper boundary l's+1 (y u ) Judgment of z l's+1 (y u ) If it is the upper bound maximum, if not let s = s +1, will l' s+1 As a new reference path, re-executing H; if yes, outputting the coordinates (y) of each turning point s+1 ，z l's+1 (y s+1 ) And z) and l' (y d ),z l's (y u ) Value to obtain the optimal path l' s S =1, 2.. Multidot.s, the solution of the optimal path of the horizontal subarea is finished, and whether n is judged>N, if yes, ending the core subproblem solving process in the t-th time period, executing the step I, if not, setting N = N +1, and continuously solving the optimal path of the adjacent subarea above the horizontal subarea;
I. setting t = t-1, judging whether t >0, returning to execute the step E, continuously solving the core subproblem in the t period, and executing the step J if t = 0;
J. dynamically planning the forward recursion phase, order
For T =1,2,.. T is calculated in sequence:
in the formula, q t * The optimal charging and discharging electric quantity of the battery energy storage system in the t period,
the optimal storage capacity L of the battery energy storage system in the t-th period t The fixed loss electric quantity of the battery energy storage system in the known t-th time period; the formula (17) is solved under the constraint of the formulae (3) to (6), and according to the dynamic programming principle, the maximization problem defined by the formulae (3) to (6) and (17) is solved to obtain the charge and discharge quantity decision of the battery energy storage system from the 1 st time period to the T time period
And corresponding charging and discharging power
The optimal solution of the scheduling problem of the battery energy storage system is obtained;
J. and C, entering the next time interval along with the time development, updating the initial stored electric quantity of the battery energy storage system, the target stored electric quantity at the end of scheduling, the online electric quantity constraint in each time interval and the time-sharing predicted electricity price or equivalent value multiplier in the step B, and continuously executing the step C.
Compared with the prior art, the invention has the following advantages:
the nonlinear charge-discharge efficiency characteristic curve of the battery energy storage system is subjected to piecewise linearization when the model is established, and a mixed integer linear programming model is established, so that the model is more accurate than the traditional model; in addition, when the mixed integer linear programming model is solved, efficient solving can be performed only by adopting commercial software packages such as CPLEX and the like, firstly, dynamic upper and lower limit constraints of the storage capacity of the battery energy storage system at each time interval are calculated through the step D, the understood feasible region range is reduced, and the solving time is shortened; secondly, aiming at the geometrical structure characteristics of the core subproblem needing to be solved repeatedly in the dynamic programming in the step F, a refinement algorithm which can be used for solving efficiently and can fully ensure the numerical stability in the calculation process is provided in the step G and the step H, so that commercial software can be replaced when the scheduling problem of the battery energy storage system is solved.
Drawings
Fig. 1 is a flowchart of the entire scheduling algorithm.
Fig. 2 is a battery discharge efficiency-power curve.
FIG. 3 is a geometric characterization of a core sub-problem in a dynamic programming algorithm.
Fig. 4 is a schematic diagram of a sub-method for processing "optimal path hopping".
FIG. 5 is a flowchart of an algorithm of a sub-method for processing the "optimal path hopping".
Detailed Description
The invention aims to provide a battery energy storage system scheduling method considering dynamic charge and discharge efficiency characteristics, which can make an optimal decision for the operation of a battery energy storage system in a future period of time according to the self characteristics of battery energy storage, operation constraints and a predicted market price, so as to guide the operation of the battery energy storage system and improve the operation efficiency and operation income of the system.
The following describes an embodiment of the scheduling method and the whole process in the present invention with reference to fig. 1.
A battery energy storage system scheduling method considering dynamic charge-discharge efficiency can make an optimal operation decision of an energy storage battery system and improve the operation economy of the battery energy storage system, and comprises the following steps:
A. and determining the capacity, the dynamic charge-discharge efficiency, the charge-discharge power limit and the upper and lower limits of the capacity of the battery energy storage system, referring to the attached figure 2, performing piecewise linearization on a charge-discharge power-efficiency relation graph of the battery energy storage system, and selecting a proper number of segments according to the precision requirement.
B. The method comprises the steps of obtaining initial storage capacity of a battery energy storage system, target storage capacity at the end of scheduling, online capacity constraint at each time interval and time-of-use predicted electricity price or equivalent value multiplier.
C. Establishing a dispatching model of the battery energy storage system, wherein the optimization goal of the dispatching model is to make a charge-discharge power decision of the battery energy storage system at each time interval so as to maximize the total power generation income of the battery energy storage system, and the objective function of the model is as follows:
wherein T is the total number of scheduling periods, T is the number of scheduling periods, and λ t For the predicted electricity price or equivalent value multiplier, q, of the t-th period t The charging and discharging electric quantity of the battery energy storage system in the t-th time period is positive, negative charging is performed, and p (q) t ) The charging and discharging power of the battery in the t period is q t Is the scheduling period length, δ is the unitary piecewise linear function of (1).
The scheduling model constraints include:
1) Electric quantity balance constraint of battery energy storage system
In the formula e t The stored electric quantity L of the battery energy storage system at the end of the t-th period t The fixed amount of power lost for storage of the battery energy storage system is known to be negative for the t-th time period.
2) Network power constraint
In the formula
And
the upper limit and the lower limit of the internet power of the battery energy storage system in the t-th time period are respectively.
3) Charge-discharge power constraint of battery energy storage system
In the formula P max And P min The physical upper limits of the discharge power and the charge power of the battery energy storage system are respectively, the function p is a monotonous piecewise linear function, and the charge and discharge power constraint (4) can be converted into a constraint of charge and discharge amount:
in which the function P 'is the inverse of the function P, P' (P) max ) And P' (P) min ) The physical upper limits of the discharge capacity and the charge capacity of the battery energy storage system are respectively set.
4) Electric quantity (SOC) constraint
In the formula E max And E min Respectively are the upper and lower limits of the stored electric quantity of the battery energy storage system.
5) Initial and final electric quantity restraint of battery energy storage system
e 0 ＝E 0 ,e T ＝E T (7)
In the formula E 0 And E T Respectively the electric quantity of the battery energy storage system at the initial moment and the target electric quantity at the end of scheduling, e 0 And e T The stored electric quantity of the battery energy storage system at the starting moment of the scheduling and at the end of the T-th period are respectively.
The dispatching model of the battery energy storage system is formed by the formulas (1), (2), (3), (5), (6) and (7).
D. Calculating dynamic upper and lower limit constraints of the storage capacity of the battery energy storage system at each time interval, and according to the target storage capacity E when the scheduling of the battery energy storage system is finished at the end of scheduling T And the upper and lower limits of the storage electric quantity of the battery energy storage system in each time interval are restricted (2) and (5), and the dynamic upper and lower limits of the storage electric quantity of the battery energy storage system in each time interval are calculated by reversely recursing from the T time interval:
in the formula, j is a time variable,
and
battery energy storage system obtained for reverse derivation at end of t time periodDynamic upper and lower limits of the amount of stored electricity at each time interval, E T For the target stored charge, L, of the battery energy storage system at the end of the schedule j Is the known fixed loss capacity of the battery energy storage system in the j (th) period, P' (P) max ) And P' (P) min ) Respectively the physical upper limits of the discharge capacity and the charge capacity of the battery energy storage system,
and
the upper limit and the lower limit of the online electric quantity of the battery energy storage system in the j-th time period are respectively.
According to the initial electric quantity E of the battery energy storage system 0 And the battery energy storage system carries out forward recursion from the scheduling starting time interval by using upper and lower limit constraints (2) and (5) of the storage electric quantity at each time interval, and calculates the dynamic upper and lower limits of the storage electric quantity at each time interval of the battery energy storage system as follows:
in the formula, j is a time variable,
and
dynamic upper and lower limits of the storage capacity of the battery energy storage system at the end of the t period, E, obtained by forward derivation 0 For the stored energy of the battery energy storage system at the beginning of the scheduling, L j The fixed loss electric quantity of the battery energy storage system in the known j time period is a negative value, P' (P) max ) And P' (P) min ) The physical upper limits of the discharge capacity and the charge capacity of the battery energy storage system are respectively,
and
the upper limit and the lower limit of the online electric quantity of the battery energy storage system in the j-th time period are respectively.
And combining the forward derivation result and the backward derivation result, and calculating dynamic upper and lower limits of the storage capacity of the battery energy storage system as follows:
in the formula
Ande t and (3) combining the dynamic upper and lower limits of the storage capacity of the battery energy storage system in each time interval obtained by calculation in the t-th time interval with the formula (6) to obtain the new upper and lower limits of the storage capacity of the battery energy storage system in each time interval as follows:
in the formula, e t The stored electric quantity of the battery energy storage system at the end of the t-th period, E max And E min The physical upper and lower limits of the stored electric quantity of the battery energy storage system are respectively set;
through equivalent transformation, the dispatching model of the battery energy storage system is formed by the formulas (1), (2), (3), (5), (7) and (13).
E. A reverse recursion phase of dynamic planning is obtained according to the dynamic planning principle
In the formula f t (e t ) The maximum profit from the end of the t-th scheduling period to the end of the schedule. Put f T (E T ) =0, bringing (14) the cell energy storage system charge balance constraint (2) into the demandAnd (3) dynamically planning a cost-to-go function repeatedly solved in each time interval:
(15) The formula (15) is defined as a core subproblem in the dynamic programming backward recursion phase, and an optimization model of the core subproblem is formed by the formulas (2), (3), (5), (7), (13) and (15).
F. Performing variable substitution on the formula (15) to obtain a decision quantity q t+1 Is denoted by x, e t Expressed as y, maximum gain f t (e t ) Denoted as h (x) while f is t+1 (e t -L t+1 -q t+1 ) Translation L t+1 Obtaining a function g (y-x), and performing equivalent transformation on an optimization model of the core subproblem in the dynamic programming reverse recursion stage to obtain:
wherein a and b represent the charge and discharge amount q during the t +1 th period determined by the equations (3) and (5), respectively t+1 C and d respectively represent the stored electric quantity e of the battery energy storage system in each time period at the end of the t time period determined by the formulas (7) and (13) t According to the formula (2), alpha and beta actually represent the upper and lower limits of the storage capacity of the battery energy storage system at the end of the t +1 th time period respectively.
Referring to fig. 3, according to the geometric meaning of the optimization model of the core subproblem, the piecewise turning line of the function h (x) is x = x θ θ =1,2,3.. Φ, Φ being the function h (x) as the number of segments, corresponding to the 90 ° numeric dash-dot line in the figure; g (y-x) has a segment break line of y-x = ρ ν V =1,2,3.. V, V being the number of segments of the function g (y-x), corresponding to the 45 ° dashed line in the figure. The piecewise inflexion lines of the functions h (x) and g (y-x) subdivide the domain into sub-regions, at each parallelogram or parallelogram-like sub-region, it can be shown that the optimum must be taken at the boundary, the function values being relative to the reference variablesx is linearly changed, namely the sectional turning point of the straight line of the boundary relative to the function value can only be obtained at the end points of the parallelogram subareas, the end points of the parallelogram subareas are sequenced according to the y value of each end point, the horizontal line of the adjacent end point divides the feasible domain of the problem into N horizontal subareas, and the optimal path in each horizontal subarea is sequentially searched from the lower N =1 to the upper N = N.
G. And (3) solving the optimal path of the horizontal subarea, starting from n =1, wherein L90-degree vertical lines and 45-degree oblique lines are shared in the horizontal subarea and correspond to the segmented turning lines of functions h (x) and g (y-x), and the segmented turning lines and the function values of the intersection points of the upper boundary and the lower boundary of the horizontal subarea, namely z l (y u ) And z l (y d ) Finding the maximum value z of the lower boundary function value l '(y d ) And corresponding paths l' and judging the function value z of the intersection point of the paths and the upper boundary l '(y u ) Whether the maximum point is the maximum point of all the upper boundary intersection point function values, if not, the jump of the optimal path occurs in the area, and the step H is executed; if yes, the path is the maximum path in the horizontal sub-area, and whether n is judged>And N, if yes, ending the core subproblem solving process in the t-th period, executing the step I, if not, setting N = N +1, and continuing to solve the optimal path of the adjacent subarea above the horizontal subarea.
H. The optimal path jumping means that the point with the maximum function value of the lower boundary ascends through the initial optimal path, jumps to another optimal path at a certain turning point to continuously ascend and then reaches the point with the maximum function value of the upper boundary; the idea of processing the optimal path "hop" method is illustrated by a simple example, see fig. 5: respectively recording the function values of the upper and lower boundaries in the horizontal subarea and the intersection points of all the paths as z l (y u ) And z l (y d ) A linear function z corresponding to the path l on the zoy plane can be obtained l (y) starting from the point a with the maximum lower boundary function value, before intersecting with other paths 1 For the optimal path, when it is summed with the path l 3 After the point b, due to l 3 Is rising ofThe speed is higher than the original optimal path l 1 Therefore, starting from point b, the optimal path changes to l 3 Similarly, at point c, the optimal path becomes l 4 Until reaching the point d with the maximum upper boundary function value; detailed calculation flow referring to fig. 4, l 'is used as a reference path, and l' = l 'is initialized' s And s =1, calculating the intersection point and the slope of the earliest intersected path l 'to obtain an intersected path l' s+1 Coordinate of turning point (y) s+1 ，z l's+1 (y s+1 ) L' s+1 Function z at the intersection with the upper boundary l's+1 (y u ) Judgment of z l's+1 (y u ) If it is an upper bound maximum, if not, let s = s +1, will l' s+1 As a new reference path, re-executing H; if yes, outputting the coordinates (y) of each turning point s+1 ，z l's+1 (y s+1 ) And z) and l' (y d ),z l's (y u ) Value to obtain the optimal path l' s S =1, 2.. Multidot.s, the solution of the optimal path of the horizontal subarea is finished, and whether n is judged>And N, if yes, ending the core sub-problem solving process in the t-th time period, executing the step I, if not, setting N = N +1, and continuing to solve the optimal path of the adjacent sub-area above the horizontal sub-area.
I. Setting t = t-1, judging whether t >0, returning to execute the step E, continuously solving the core subproblem at the stage of t, and executing the step J if t = 0;
J. dynamically planning the forward recursion phase, order
For T =1,2,.. T is calculated in sequence:
in the formula, q t * The optimal charging and discharging electric quantity of the battery energy storage system in the t-th period is obtained,
is the most important of the battery energy storage system in the t periodExcellent storage capacity, L t The fixed loss electric quantity of the battery energy storage system in the known t-th time period is obtained; the formula (17) is solved under the constraint of the formulae (3) to (6), and according to the dynamic programming principle, the maximization problem defined by the formulae (3) to (6) and (17) is solved to obtain the charge and discharge quantity decision of the battery energy storage system from the 1 st time period to the T time period
And corresponding charging and discharging power
The method is the optimal solution of the scheduling problem of the battery energy storage system.
J. And C, entering the next time interval along with the time development, updating the initial storage electric quantity of the battery energy storage system, the target storage electric quantity at the end of scheduling, the online electric quantity constraint in each time interval and the time-of-use predicted electricity price or equivalent value multiplier in the step B, and continuously executing the step C.
Claims (1)
1. A battery energy storage system scheduling method considering dynamic charge-discharge efficiency is characterized in that: by using the method, an optimal operation decision of the battery energy storage system can be made, and the operation economy of the battery energy storage system is improved, wherein the method comprises the following steps:
A. determining the capacity, the dynamic charge-discharge efficiency, the charge-discharge power limit and the upper and lower capacity limits of the battery energy storage system, and selecting a proper number of segments according to the scheduling precision requirement to perform segment linearization on the charge-discharge power-efficiency relation of the battery energy storage system;
B. acquiring initial storage capacity of a battery energy storage system, target storage capacity at the end of scheduling, online capacity constraint at each time interval and time-of-use predicted electricity price or equivalent value multiplier;
C. establishing a scheduling model of the battery energy storage system, wherein the optimization goal of the scheduling model is to make a charge-discharge power decision of the battery energy storage system at each time interval so as to maximize the total power generation income of the battery energy storage system, and the objective function of the scheduling model is as follows:
wherein T is the total number of scheduling periods, T is the number of scheduling periods, and lambda t For the predicted electricity prices or equivalent value multipliers of the t-th period, q t The charging and discharging electric quantity of the battery energy storage system in the t-th time period is positive, negative and p (q) t ) The charging and discharging power of the battery energy storage system in the t-th time period is q t Delta is the length of the scheduling period;
the constraints of the scheduling model include:
1) Electric quantity balance constraint of battery energy storage system
In the formula, e t The stored electric quantity L of the battery energy storage system at the end of the t period t The fixed loss electric quantity of the battery energy storage system in the known t-th time period is a negative value;
2) Network power constraint
In the formula (I), the compound is shown in the specification,
and
the upper limit and the lower limit of the online electric quantity of the battery energy storage system in the t-th time period are respectively set;
3) Charge-discharge power constraint of battery energy storage system
In the formula, P max And P min The physical upper limits of the discharge power and the charge power of the battery energy storage system are respectively, the function p is a monotonous piecewise linear function, and the charge and discharge power constraint (4) can be converted into a constraint of charge and discharge amount:
in the formula, the function P 'is an inverse function of the function P, P' (P) max ) And P' (P) min ) Physical upper limits of the discharge electric quantity and the charge electric quantity of the battery energy storage system are respectively set;
4) SOC constraint of electric quantity
In the formula, E max And E min The upper limit and the lower limit of the stored electric quantity of the battery energy storage system are respectively set;
5) Initial and final electric quantity restraint of battery energy storage system
e 0 ＝E 0 ,e T ＝E T (7)
In the formula, E 0 And E T Respectively the electric quantity of the battery energy storage system at the initial moment and the target electric quantity at the end of scheduling, e 0 And e T The stored electric quantity of the battery energy storage system at the starting moment of the dispatching and at the end of the T-th period respectively;
the dispatching model of the battery energy storage system is formed by formulas (1), (2), (3), (5), (6) and (7);
D. calculating dynamic upper and lower limit constraints of the storage capacity of the battery energy storage system at each time interval, and according to the target storage capacity E when the scheduling of the battery energy storage system is finished at the end of scheduling T And the upper and lower limits of the storage electric quantity of the battery energy storage system in each time interval are constrained (2) and (5), and the dynamic upper and lower limits of the storage electric quantity of the battery energy storage system in each time interval are calculated by starting reverse recursion from the T time interval:
in the formula, j is a time variable,
and
dynamic upper and lower limits of the storage capacity of the battery energy storage system at each time interval obtained by reverse derivation respectively T For the target stored charge, L, of the battery energy storage system at the end of the schedule j The fixed loss electric quantity of the battery energy storage system in the known j time period is a negative value, P' (P) max ) And P' (P) min ) Respectively the physical upper limits of the discharge capacity and the charge capacity of the battery energy storage system,
and
respectively the upper limit and the lower limit of the online electric quantity of the battery energy storage system in the jth time period;
according to the initial electric quantity E of the battery energy storage system 0 And the battery energy storage system carries out forward recursion from the scheduling starting time interval by using upper and lower limit constraints (2) and (5) of the storage electric quantity at each time interval, and calculates the dynamic upper and lower limits of the storage electric quantity at each time interval of the battery energy storage system as follows:
in the formula, j is a time variable,
and
dynamic upper and lower limits of the storage capacity of the battery energy storage system at the end of the t period, E, obtained by forward derivation 0 For the stored energy of the battery energy storage system at the beginning of the schedule, L j Is the known fixed loss electric quantity of the battery energy storage system in the j time period, P' (P) max ) And P' (P) min ) Respectively the physical upper limits of the discharge capacity and the charge capacity of the battery energy storage system,
and
respectively the upper limit and the lower limit of the online electric quantity of the battery energy storage system in the jth time period;
and combining the forward derivation and the backward derivation, and calculating the dynamic upper and lower limits of the storage capacity of the battery energy storage system as follows:
in the formula (I), the compound is shown in the specification,
ande t and (3) combining the dynamic upper and lower limits of the storage capacity of the battery energy storage system in each time interval obtained by calculation in the t-th time interval with the formula (6) to obtain the new upper and lower limits of the storage capacity of the battery energy storage system in each time interval as follows:
in the formula, e t The stored electric quantity of the battery energy storage system at the end of the t-th period, E max And E min The physical upper and lower limits of the stored electric quantity of the battery energy storage system are respectively set;
through equivalent transformation, the dispatching model of the battery energy storage system is formed by the formulas (1), (2), (3), (5), (7) and (13);
E. a reverse recursion phase of dynamic planning is obtained according to the dynamic planning principle
In the formula (f) t (e t ) Setting f for the maximum benefit from the end of the t-th scheduling period to the end of the scheduling T (E T ) And (5) bringing (14) the power balance constraint (2) of the battery energy storage system into (0) to obtain a dynamic programming cost-to-go function which needs to be solved repeatedly in each time interval:
(15) The formula is constrained by the formulas (2), (3), (5), (7) and (13) in the solving process, and the formula (15) is defined as a core subproblem in the dynamic programming reverse recursion phase, wherein an optimization model of the core subproblem is formed by the formulas (2), (3), (5), (7), (13) and (15);
F. performing variable substitution on the formula (15), and converting the decision quantity q t+1 Is denoted by x, e t Expressed as y, maximum profit f t (e t ) Denoted as h (x) while f is represented t+1 (e t -L t+1 -q t+1 ) Translation L t+1 Obtaining a function g (y-x), and performing equivalent transformation on an optimization model of the core subproblem in a reverse recursion phase of dynamic planning;
in which a andb represents the charge and discharge amount q in the t +1 th period determined by the equations (3) and (5), respectively t+1 C and d respectively represent the stored electric quantity e of the battery energy storage system in each time period at the end of the t time period determined by the formulas (7) and (13) t According to the formula (2), alpha and beta actually respectively represent the upper and lower limits of the electric quantity stored by the battery energy storage system at the end of the t +1 time period;
according to the geometric meaning of the formula (16), the segmented turning lines of the functions h (x) and g (y-x) divide the definition domain into a plurality of subregions, the optimal values can be proved to be obtained at the boundary of each parallelogram or the subregions similar to the parallelogram, the function values are linearly changed relative to the parameter x, namely the segmented turning points of the straight line of the boundary relative to the function values can only be obtained at the end points of the parallelogram subregions, the end points of the parallelogram subregions are sequenced according to the y values of the end points, the feasible region of the problem is divided into N horizontal subregions by the horizontal line of the adjacent end points, and the optimal path in each horizontal subregion is searched in turn from the lower N =1 to the upper N = N;
G. and (3) solving the optimal path of the horizontal subarea, starting from n =1, wherein L90-degree vertical lines and 45-degree oblique lines are arranged in the horizontal subarea and respectively correspond to the segmented turning lines of functions h (x) and g (y-x), and the function values of intersection points of the segmented turning lines and the upper and lower boundaries of the horizontal subarea are respectively z l (y u ) And z l (y d ) Finding the maximum point z of the lower boundary function value l '(y d ) And corresponding paths l' and judging the function value z of the intersection point of the paths and the upper boundary l '(y u ) Whether the maximum point is the maximum point of all the upper boundary intersection point function values, if not, the jump of the optimal path occurs in the area, and the step H is executed; if yes, the path is the maximum path in the horizontal sub-area, and whether n is judged>N, if yes, ending the core subproblem solving process in the t-th time period, executing the step I, if not, setting N = N +1, and continuously solving the optimal path of the adjacent subarea above the horizontal subarea;
H. the optimal path jump means that the point with the maximum function value of the lower boundary rises through the initial optimal path and at a certain turning pointJumping to another optimal path to continue rising and then reach the point with the maximum upper boundary function value, taking l ' as a reference path, and initializing l ' = l ' s S =1, calculating the intersection point and slope of the earliest path intersected with l ', and obtaining the path l ' intersected with l ' s+1 Coordinate of turning point (y) s+1 ，z l's+1 (y s+1 ) L' s+1 Function z at the intersection with the upper boundary l's+1 (y u ) Judgment of z l's+1 (y u ) If it is the upper bound maximum, if not let s = s +1, will l' s+1 As a new reference path, re-executing H; if yes, outputting the coordinates (y) of each turning point s+1 ，z l's+1 (y s+1 ) And z) and l' (y d ),z l's (y u ) Value to obtain the optimal path l' s S =1, 2.. Said, S are the total number of the optimal paths, the solution of the optimal paths of the horizontal sub-region is finished, and whether n is judged>N, if yes, ending the core subproblem solving process in the t-th time period, executing the step I, if not, setting N = N +1, and continuously solving the optimal path of the adjacent subarea above the horizontal subarea;
I. setting t = t-1, judging whether t >0, returning to execute the step E, continuously solving the core subproblem in the t period, and executing the step J if t = 0;
J. dynamically planning the forward recursion phase, order
For T =1,2,.. T is calculated in sequence:
in the formula, q t * The optimal charging and discharging electric quantity of the battery energy storage system in the t-th period is obtained,
the optimal storage capacity L of the battery energy storage system in the t-th period t For the known t-th time period of the battery energy storage systemThe fixed loss of power of the system; the formula (17) is solved under the constraint of the formulas (3) - (6), and according to the dynamic programming principle, the maximum problem defined by the formulas (3) - (6) and (17) is solved to obtain the charge and discharge amount of the battery energy storage system from the 1 st period to the T th period
And corresponding charging and discharging power
The optimal solution of the scheduling problem of the battery energy storage system is obtained;
J. and C, entering the next time interval along with the time development, updating the initial stored electric quantity of the battery energy storage system, the target stored electric quantity at the end of scheduling, the online electric quantity constraint in each time interval and the time-sharing predicted electricity price or equivalent value multiplier in the step B, and continuously executing the step C.
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