Evaluation method for dynamic characteristics of ring microgrid with high proportion of distributed photovoltaic penetration

Abstract

The present invention relates to a method for evaluating the dynamic characteristics of a ring microgrid with a high proportion of distributed photovoltaic penetration, comprising the following steps: S1, segmenting the photovoltaic and load prediction curves according to the scheduling period, and obtaining all decision variables Ψ in the ring microgrid at the same time D and constraint EΨ D ≤F; S2, the output value of each decision variable in each period is modeled as a curve C(t)(t∈[0,1]) based on the fourth Bernstein interpolation and divided into segments according to the scheduling period, C B =[C B0 ,C B1 ,C B2 ,C B3 ] is the vector composed of the interpolation of the curve C(t) in each time period; S3, according to the power values ​​C(0), C(1) and the slopes C′(0), C′(1) at the beginning and end of the curve C(t), C B ; S4, convert all constraints into constraints on interpolation E B C B ≤F B , obtain a continuous-time microgrid model and solve it; S5, arrange the resources that need to be determined on the day before according to the power curves obtained from the solution results. The present invention can make full use of the day-ahead distributed photovoltaic power output forecast value, and can accurately evaluate the dynamic characteristics of the ring microgrid, with high accuracy and suitable for economic dispatch.

Description

Technical Field

[0001] The present invention relates to the field of electrical engineering, and more particularly to a method for evaluating dynamic characteristics of a ring microgrid with a high proportion of distributed photovoltaic penetration. Background Art

[0002] Microgrid (MG), as an important component of the new power system, is an important part of achieving the "30-60" goal. Microgrid is a self-controlled entity that operates in grid-connected or island mode and is used to manage the distributed energy resource (DER) with increasing penetration in the distribution network. Its concept diagram is shown in the figure below. Figure 2 As shown. It must also be pointed out that the traditional radial topology may not be the best choice for MG. New research shows that ring MG can improve power supply reliability and economy, especially for grid fault reconstruction, ensuring power supply stability and island operation.

[0003] Among all types of DER, photovoltaics are favored for their clean and pollution-free characteristics. With the advancement of photovoltaic technology, distributed photovoltaics directly connected to the grid have developed rapidly. According to statistics, the newly installed capacity of distributed photovoltaics in my country in 2021 has exceeded that of centralized photovoltaics. However, the high proportion of distributed photovoltaic penetration has also brought many problems, mainly because photovoltaic power generation is significantly affected by the environment and has large fluctuations, which introduces dynamic characteristics to MG. The dynamic characteristics of distributed photovoltaics in time and space, such as sufficient power generation at noon and less power generation after nightfall and on cloudy days, have caused the original unidirectional power flow at the point of common coupling (PCC) between MG and the upper-level power grid to change after it is connected to the grid, and then a bidirectional power flow appears.

[0004] When a large number of distributed photovoltaics are integrated into MG, their dynamic characteristics will be significantly increased, which will cause their impact on the power system to become increasingly complex. In the traditional discrete time scheduling method, the daily scheduling cycle is divided into 24 or 96 periods, and it is assumed that each period corresponds to a certain value. The power curve is modeled as Figure 3 The step curve in the figure. It can be seen that the step curve has a low degree of fit to the actual power curve, which will lose the power changes within the time period as shown in areas 1-5 in the figure. There is only a power jump at the junction of the time period, and the dynamic characteristics brought by distributed photovoltaics are mainly reflected in the power changes within the time period. The study of the dynamic characteristics of the power system shows that the finer the granularity of the scheduling time period, the more accurately the dynamic characteristics of the MG are captured. If the length of these time periods is reduced to infinitesimal, the MG model is close to continuous time, and a smooth curve is obtained to describe the MG's intraday power. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for evaluating the dynamic characteristics of a ring microgrid with a high proportion of distributed photovoltaic penetration. The method is suitable for a ring microgrid with a high proportion of distributed photovoltaic access, can make full use of the day-ahead distributed photovoltaic power output forecast value, and can accurately evaluate the dynamic characteristics of the ring microgrid. It has the characteristics of high precision and is suitable for economic dispatch.

[0006] The technical solution adopted by the present invention to solve the technical problem is: constructing a method for evaluating the dynamic characteristics of a ring microgrid with a high proportion of distributed photovoltaic penetration, comprising the following steps:

[0007] S1. Segment the photovoltaic and load forecast curves according to the scheduling period, and obtain all decision variables Ψ in the ring microgrid D and constraint EΨ D ≤F;

[0008] S2. The output value of each decision variable in each period is modeled as a curve C(t)(t∈[0,1]) based on the fourth Bernstein interpolation and divided into segments according to the scheduling period, C B =[C B0 ,C B1 ,C B2 ,C B3 ] is the vector composed of the interpolation of the curve C(t) in each time period;

[0009] S3. Calculate C according to the power values ​​C(0), C(1) and slopes C′(0), C′(1) at the beginning and end of the curve C(t). B ;

[0010] S4. Convert all constraints into constraints on interpolation E B C B ≤F B , the continuous-time microgrid model is obtained and solved;

[0011] S5. Arrange the resources that need to be determined the day before according to the power curves obtained from the solution results.

[0012] According to the above scheme, in step S1, each component of the discrete-time ring microgrid contains its decision variables and parameters, and all decision variables obtained are the unit output value P G , unit start and stop status μ g , photovoltaic output value P pv , the amount of abandoned light P pvd , the transmission line power P L , power purchase quantity P ex ; Other parameters are the unit climbing / climbing rate R up / R low , unit operation cost coefficient α, unit start-up and shutdown cost coefficient β, electricity price γ, abandoned light ratio coefficient delta, transmission line capacity PLmax , the upper limit of power purchase and sale capacity P max .

[0013] According to the above scheme, in step S1, the constraints that need to be considered include the output constraint and ramp constraint of the unit, the distributed photovoltaic abandonment constraint, the transmission line flow constraint, the upper power grid purchase constraint and the power balance constraint. The specific forms of the constraints involved are:

[0014]

[0015] μ g P i Gmin ≤P i G ≤μ g P i Gmax (2)

[0016]

[0017] -P max ≤P ex ≤P max (4)

[0018]

[0019] 0≤delta≤1 (7)

[0020]

[0021] Among them, formula (1) is the power balance constraint, formulas (2)-(3) are the output constraints and ramp constraints of the unit, formula (4) is the power purchase constraint of the upper power grid, formula (5) is the transmission line flow constraint, and formulas (6)-(8) are the distributed photovoltaic abandonment constraints.

[0022] According to the above scheme, in step S1, the ring microgrid is connected to the upper grid via a common coupling point.

[0023] According to the above scheme, in step S2, all decision variables and prediction curves in the ring microgrid are modeled as continuous time curves C(t), which are Bezier curves; the discrete time ring microgrid modeling includes each component and its related constraints.

[0024] According to the above scheme, in step S2, the interpolation vector of curve C(t) is obtained based on the quartic Bernstein interpolation. B =[C B0 ,C B1 ,C B2 ,C B3 ], where C Bi(i=0,1,2,3) is interpolation,

[0025] The curve C(t) is uniquely determined by its set of control points in each time period t∈[0,1]. The control points of the curve C(t) and its interpolation vector C B =[C B0 ,C B1 ,C B2 ,C B3 ] one-to-one correspondence, the control points are:

[0026]

[0027] The analytical expression of the curve in the time period t∈[0,1] is given by its interpolation vector C B The only way to determine is as follows:

[0028]

[0029] Each interpolation value is calculated from the values ​​C(0), C(1) and the slopes C'(0), C'(1) at the beginning and end of the curve C(t) in the time period t∈[0,1]:

[0030]

[0031] After integration over t∈[0,1], C(t) has nothing to do with time t and only with the interpolation vector C B related:

[0032]

[0033] The differential curve C'(t) of the curve C(t) corresponds to the Bernstein interpolation after reducing the order by one:

[0034]

[0035] If the curve C(t) is always equal to 0, then its interpolated values ​​must also be 0:

[0036]

[0037] If the curve C(t) is always less than a certain positive constant α, then the interpolation value is also always less than α:

[0038]

[0039] All decision variables except energy storage Ψ D , and the corresponding curves all correspond to the quartic Bernstein interpolation coefficient vector (·) B ;

[0040] The interpolation coefficient vector corresponding to all decision variables is the unit output value P GB , unit start and stop status Photovoltaic output value P pvB , the amount of abandoned light P pvdB , the transmission line power P LB , power purchase quantity P exB ; Other parameters are the unit climbing / climbing rate R up / R low , unit operation cost coefficient α, unit start-up and shutdown cost coefficient β, electricity price γ, transmission line capacity P Lmax , the upper limit of power purchase and sale capacity P max ; Photovoltaic prediction curve modeling is P pvAB , the load forecast curve is modeled as P DB ,all(·) B All the above-mentioned interpolation vectors C are observed B the nature of;

[0041] All the constraints of the discrete-time model are transformed into the continuous-time model according to equations (12)-(17) for each interpolation vector (·) B The analytical expressions of each curve are calculated according to equations (10) and (11).

[0042] According to the above scheme, the ring microgrid is modeled as follows:

[0043]

[0044] -P max ≤P exB ≤P max (25)

[0045]

[0046] 0≤delta≤1 (28)

[0047]

[0048] Among them, formula (18) is the optimization objective of the overall model after transformation; formulas (19)-(21) are the unit operation costs, ring microgrid power purchase costs, and photovoltaic abandonment penalties after transformation; formula (22) is the power balance constraint after transformation; formulas (23)-(24) are the output constraints and ramp constraints of the unit after transformation; formula (25) is the upper power grid power purchase and sales constraints after transformation; formula (26) is the transmission line flow constraint after transformation; formulas (27)-(29) are the distributed photovoltaic abandonment constraints after transformation; formulas (30)-(31) are the first-order continuity constraints to ensure that the beginning and end of the curve are smoothly and continuously connected.

[0049] The method for evaluating the dynamic characteristics of a ring microgrid with high-proportion distributed photovoltaic penetration according to the present invention has the following beneficial effects:

[0050] 1. The present invention can make full use of the forecast value of distributed photovoltaic power output on the day before, and can accurately evaluate the dynamic characteristics of the ring microgrid. It has the characteristics of high accuracy and suitability for economic dispatch, and can make full use of the forecast data of photovoltaic and load to make the result more accurate.

[0051] 2. The present invention provides a continuous-time model of a ring distribution network, which can fully characterize the dynamic characteristics of the ring distribution network, especially the power fluctuations on a sub-hourly scale, and is suitable for participating in the power market and economic dispatch. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0053] Figure 1 It is a conceptual diagram of a ring microgrid of the method for evaluating dynamic characteristics of a ring microgrid with high proportion of distributed photovoltaic penetration of the present invention;

[0054] Figure 2 It is a comparison diagram of the discrete time step power curve of the present invention and the actual curve;

[0055] Figure 3 is a flow chart of a method for evaluating dynamic characteristics of a ring microgrid with high proportion of distributed photovoltaic penetration according to the present invention;

[0056] Figure 4 1 is a schematic diagram of a fourth-order Bernstein interpolation corresponding to the Bezier curve of the present invention;

[0057] Figure 5 It is the improved IEEE-34 node ring microgrid topology diagram of the present invention;

[0058] Figure 6 It is a curve diagram of the total amount of abandoned light in a day of the ring microgrid of the present invention;

[0059] Figure 7 It is a daily unit output curve diagram of the ring microgrid of the present invention;

[0060] Figure 8 It is a curve diagram of power purchase and sale between the annular microgrid of the present invention and the upper-level power grid within a day. DETAILED DESCRIPTION

[0061] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0062] like Figure 1-8 As shown, the present invention segments the photovoltaic and load forecast curves according to the scheduling period, and simultaneously obtains all decision variables Ψ in the ring microgrid D and constraint EΨ D≤F; the output value of each decision variable in each period is modeled as a curve C(t)(t∈[0,1]) based on the fourth Bernstein interpolation and divided into segments according to the scheduling period, C B =[C B0 ,C B1 ,C B2 ,C B3 ] is the vector composed of the interpolation of the curve C(t) in each time period; C is calculated based on the power values ​​C(0), C(1) and the slopes C′(0), C′(1) at the beginning and end of the curve C(t). B ; Convert all constraints to constraints on interpolation E B C B ≤F B , obtain the continuous time microgrid model and solve it; arrange the resources that need to be determined on the day before according to the power curves obtained by the solution results. The present invention can make full use of the day-ahead distributed photovoltaic power output forecast value, and can accurately evaluate the dynamic characteristics of the ring microgrid, with high accuracy and suitable for economic dispatch.

[0063] The present invention provides a method for evaluating the dynamic characteristics of a ring microgrid with a high proportion of distributed photovoltaic penetration, comprising:

[0064] S1. Segment the photovoltaic and load forecast curves according to the scheduling period, and obtain all decision variables Ψ in the ring microgrid D and constraint EΨ D ≤F.

[0065] S2. The output value of each decision variable in each period is modeled as a curve C(t)(t∈[0,1]) based on the fourth Bernstein interpolation and divided into segments according to the scheduling period, C B =[C B0 ,C B1 ,C B2 ,C B3 ] is a vector composed of the interpolation of the curve C(t) in each time period.

[0066] S3. Calculate C according to the power values ​​C(0), C(1) and slopes C′(0), C′(1) at the beginning and end of the curve C(t). B .

[0067] S4. Convert all constraints into constraints on interpolation E B C B ≤F B , the continuous-time microgrid model is obtained and solved.

[0068] S5. Arrange the resources that need to be determined the day before according to the power curves obtained from the solution results.

[0069] like Figure 5As shown in the figure, the specific topology is that the ring microgrid is connected to the upper grid through the point of common coupling (PCC). The discrete-time ring microgrid modeling includes the components and constraints. The components of the discrete-time ring microgrid include their decision variables and parameters. The decision variable is the unit output value P. G , unit start and stop status μ g , photovoltaic output value P pv , the amount of abandoned light P pvd , the transmission line power P L , power purchase quantity P ex ; Other parameters are the unit climbing / climbing rate R up / R low , unit operation cost coefficient α, unit start-up and shutdown cost coefficient β, electricity price γ, abandoned light ratio coefficient delta, transmission line capacity P Lmax , the upper limit of power purchase and sale capacity P max .

[0070] The model of the discrete-time ring microgrid is as follows:

[0071]

[0072] μ g P i Gmin ≤P i G ≤μ g P i Gmax (34)

[0073]

[0074] -P max ≤P ex ≤P max (36)

[0075]

[0076] 0≤delta≤1 (39)

[0077]

[0078] Among them, formula (33) is the power balance constraint, formulas (34)-(35) are the output constraints and ramp constraints of the unit, formula (36) is the power purchase constraint of the upper power grid, formula (37) is the transmission line flow constraint, and formulas (38)-(40) are the distributed photovoltaic abandonment constraints.

[0079] All decision variables and prediction curves in the ring microgrid are modeled as continuous time curves C(t), which are Bezier curves. Each curve C(t) is a piecewise curve, which is segmented into each scheduling period t∈[0,1] based on the scheduling period. The interpolation vector of the curve C(t) is obtained based on the quartic Bernstein interpolation. B =[C B0 ,C B1 ,C B2 ,C B3 ], where C Bi (i=0,1,2,3) is interpolation. The curve C(t) is uniquely determined by its control point set in each time period t∈[0,1], such as Figure 4 As shown. The control points of the curve C(t) and its interpolation vector C B =[C B0 ,C B1 ,C B2 ,C B3 ] one-to-one correspondence, the control points are (0,C B0 ), (1,C B3 ).

[0080] The analytical expression of the curve in the time period t∈[0,1] is given by its interpolation vector C B The only way to determine is as follows:

[0081]

[0082] Each interpolation value can be calculated from the values ​​C(0), C(1) and the slopes C'(0), C'(1) at the beginning and end of the curve C(t) in the time period t∈[0,1]:

[0083]

[0084] After integration over t∈[0,1], C(t) has nothing to do with time t and only with the interpolation vector C B related:

[0085]

[0086] The differential curve C'(t) of the curve C(t) corresponds to the Bernstein interpolation after reducing the order by one:

[0087]

[0088] If the curve C(t) is always equal to 0, then its interpolated values ​​must also be 0:

[0089]

[0090] If the curve C(t) is always less than a certain positive constant α, then the interpolation value is also always less than α:

[0091]

[0092] All decision variables except energy storage Ψ D , and the corresponding curves all correspond to the quartic Bernstein interpolation coefficient vector (·) B The interpolation coefficient vector corresponding to all decision variables is the unit output value P GB , unit start and stop status Photovoltaic output value P pvB , the amount of abandoned light P pvdB , the transmission line power P LB , power purchase quantity P exB ; Other parameters are the unit climbing / climbing rate R up / R low , unit operation cost coefficient α, unit start-up and shutdown cost coefficient β, electricity price γ, transmission line capacity P Lmax , the upper limit of power purchase and sale capacity P max The photovoltaic prediction curve is modeled as P pvAB , the load forecast curve is modeled as P DB .all(·) B All the above-mentioned interpolation vectors C are observed B nature.

[0093] Among them, all the constraints of the discrete-time model can be transformed into the continuous-time model for each interpolation vector (·) according to equations (44)-(49): B Constraints, the analytical expressions of each curve can be calculated according to equations (42)-(43).

[0094] The ring microgrid is modeled as follows:

[0095]

[0096] -P max ≤P exB ≤P max (57)

[0097]

[0098] 0≤delta≤1 (60)

[0099]

[0100] Among them, formula (50) is the optimization objective of the overall model after transformation; formulas (51)-(53) are the unit operating costs, ring microgrid power purchase costs, and photovoltaic abandonment penalties after transformation; formula (54) is the power balance constraint after transformation; formulas (55)-(56) are the output constraints and climbing constraints of the unit after transformation; formula (57) is the upper power grid power purchase and sales constraints after transformation; formula (58) is the transmission line flow constraint after transformation; formulas (59)-(61) are the distributed photovoltaic abandonment constraints after transformation; formulas (62)-(63) are the first-order continuity constraints to ensure that the beginning and end of the curve are smoothly and continuously connected.

[0101] The following further describes the beneficial effects that can be achieved by this embodiment in conjunction with a specific application scenario.

[0102] This embodiment is verified in an improved IEEE-34 node ring microgrid. The node system includes 3 cogeneration units and 12 distributed photovoltaic units. The topology diagram is as follows: Figure 5 As shown. The corresponding program was written on the computing software MATLAB R2024a, and the Yalmip solver equipped with Gurobi was called for solution. To solve the optimization problem, the computing device used was: a HUAWEI matebook laptop equipped with an Intel Core i7-10510U processor, 16GB of running memory, and running the Windows 10 Professional operating system. The solution results are shown in Table 1 and Figure 6-Figure 8 shown.

[0103] Table 1 Comparison of running results under continuous time and discrete time modeling

[0104]

[0105] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A method for evaluating the dynamic characteristics of a ring microgrid with high proportion of distributed photovoltaic penetration, characterized in that: The following steps are involved: S1. Segment the photovoltaic and load forecast curves according to the scheduling period, and obtain all decision variables Ψ in the ring microgrid D and constraint EΨ D ≤F; S2. The output value of each decision variable in each period is modeled as a curve C(t)(t∈[0,1]) based on the fourth Bernstein interpolation and divided into segments according to the scheduling period, C B =[C B0 ,C B1 ,C B2 ,C B3 ] is the vector composed of the interpolation of the curve C(t) in each time period; S3. Calculate C according to the power values ​​C(0), C(1) and slopes C′(0), C′(1) at the beginning and end of the curve C(t). B ; S4. Convert all constraints into constraints on interpolation E B C B ≤F B , the continuous-time microgrid model is obtained and solved; S5. Arrange the resources that need to be determined the day before according to the power curves obtained from the solution results.

2. The method for evaluating dynamic characteristics of a ring microgrid with high proportion of distributed photovoltaic penetration according to claim 1 is characterized in that: In step S1, each component of the discrete-time ring microgrid contains its decision variables and parameters, and all decision variables obtained are the unit output value P G , unit start and stop status μ g , photovoltaic output value P pv , the amount of abandoned light P pvd , the transmission line power P L , power purchase quantity P ex ; Other parameters are the unit climbing / climbing rate R up / R low , unit operation cost coefficient α, unit start-up and shutdown cost coefficient β, electricity price γ, abandoned light ratio coefficient delta, transmission line capacity P Lmax , the upper limit of power purchase and sale capacity P max .

3. The method for evaluating dynamic characteristics of a ring microgrid with high proportion of distributed photovoltaic penetration according to claim 2 is characterized in that: In step S1, the constraints to be considered include the output constraint and ramp constraint of the unit, the distributed photovoltaic abandonment constraint, the transmission line flow constraint, the upper power grid purchase constraint and the power balance constraint. The specific forms of the constraints involved are: Among them, formula (1) is the power balance constraint, formulas (2)-(3) are the output constraints and ramp constraints of the unit, formula (4) is the power purchase constraint of the upper power grid, formula (5) is the transmission line flow constraint, and formulas (6)-(8) are the distributed photovoltaic abandonment constraints.

4. The method for evaluating dynamic characteristics of a ring microgrid with high proportion of distributed photovoltaic penetration according to claim 3 is characterized in that: In step S1, the ring microgrid is connected to the upper grid via a common coupling point.

5. The method for evaluating dynamic characteristics of a ring microgrid with high proportion of distributed photovoltaic penetration according to claim 1 is characterized in that: In step S2, all decision variables and prediction curves in the ring microgrid are modeled as continuous time curves C(t), which are Bezier curves; the discrete time ring microgrid modeling includes each component and its related constraints.

6. The method for evaluating dynamic characteristics of a ring microgrid with high proportion of distributed photovoltaic penetration according to claim 5 is characterized in that: In step S2, the interpolation vector of the curve C(t) is obtained based on the quartic Bernstein interpolation. B =[C B0 ,C B1 ,C B2 ,C B3 ], where C Bi (i=0,1,2,3) is interpolation, The curve C(t) is uniquely determined by its set of control points in each time period t∈[0,1]. The control points of the curve C(t) and its interpolation vector C B =[C B0 ,C B1 ,C B2 ,C B3 ] one-to-one correspondence, the control points are: The analytical expression of the curve in the time period t∈[0,1] is given by its interpolation vector C B The only way to determine is as follows: Each interpolation value is calculated from the values ​​C(0), C(1) and the slopes C'(0), C'(1) at the beginning and end of the curve C(t) in the time period t∈[0,1]: After integration over t∈[0,1], C(t) has nothing to do with time t and only with the interpolation vector C B related: The differential curve C'(t) of the curve C(t) corresponds to the Bernstein interpolation after reducing the order by one: If the curve C(t) is always equal to 0, then its interpolated values ​​must also be 0: If the curve C(t) is always less than a certain positive constant α, then the interpolation value is also always less than α: All decision variables except energy storage Ψ D , and the corresponding curves all correspond to the quartic Bernstein interpolation coefficient vector (·) B ; The interpolation coefficient vector corresponding to all decision variables is the unit output value P GB , unit start and stop status Photovoltaic output value P pvB , the amount of abandoned light P pvdB , the transmission line power P LB , power purchase quantity P exB ; Other parameters are the unit climbing / climbing rate R up / R low , unit operation cost coefficient α, unit start-up and shutdown cost coefficient β, electricity price γ, transmission line capacity P Lmax , the upper limit of power purchase and sale capacity P max ; Photovoltaic prediction curve modeling is P pvAB , the load forecast curve is modeled as P DB ,all(·) B All the above-mentioned interpolation vectors C are observed B the nature of; All the constraints of the discrete-time model are transformed into the continuous-time model according to equations (12)-(17) for each interpolation vector (·) B The analytical expressions of each curve are calculated according to equations (10) and (11).

7. The method for evaluating dynamic characteristics of a ring microgrid with high proportion of distributed photovoltaic penetration according to claim 5 is characterized in that: The ring microgrid is modeled as follows: Among them, formula (18) is the optimization objective of the overall model after transformation; formulas (19)-(21) are the unit operation costs, ring microgrid power purchase costs, and photovoltaic abandonment penalties after transformation; formula (22) is the power balance constraint after transformation; formulas (23)-(24) are the output constraints and ramp constraints of the unit after transformation; formula (25) is the upper power grid power purchase and sales constraints after transformation; formula (26) is the transmission line flow constraint after transformation; formulas (27)-(29) are the distributed photovoltaic abandonment constraints after transformation; formulas (30)-(31) are the first-order continuity constraints to ensure that the beginning and end of the curve are smoothly and continuously connected.

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