A distributed solution method for multi-region interconnected system with carbon emission constraints

Abstract

The application provides a distributed solving method for a multi-region interconnected system with carbon emission constraints, which has the characteristics of including multi-region interconnected system low-carbon economic dispatching model construction, low-carbon economic dispatching model decomposition, information network topology structure building, distributed iteration optimization solving framework design and evaluation index establishment, and evaluating the algorithm convergence and system emission reduction effect. The method is scientific and reasonable, has strong applicability and good effect, and the like.

Description

Technical Field

[0001] This invention belongs to the field of power system dispatch optimization, and in particular relates to a distributed solution method for multi-region interconnected systems with carbon emission constraints. Specifically, it utilizes the interaction of limited information between interconnected regions to achieve distributed dispatch optimization of multi-region interconnected systems. Background Technology

[0002] To accelerate carbon emission reduction, the shift towards low-carbon economic dispatch in power systems is an inevitable trend. In multi-regional interconnected power systems, the economic efficiency and reliability of system operation can be improved through load shifting and reserve sharing. Inter-regional information exchange enables carbon emission complementarity among power output units within each region, allowing for the formulation of corresponding low-carbon economic dispatch strategies based on reasonable emission reduction targets. This approach is most common in centralized optimal dispatch, but with the continuous development of power systems, the number of callable units in multi-regional interconnected power systems is gradually increasing, making it difficult to meet the extremely high communication bandwidth required by centralized economic dispatch. Furthermore, the demands for computation and information storage are increasing dramatically, resulting in poor scalability and susceptibility to single points of failure. Distributed economic dispatch, while ensuring information privacy in each region, reduces the demand for communication bandwidth and information storage, and has become a research hotspot. Research on distributed economic dispatch in multi-regional interconnected power systems has achieved some success, but the methods involved can only handle economic dispatch problems with one global equality constraint and several local constraints. These methods are not very applicable to economic dispatch problems with other global inequality constraints (such as reserve constraints and system carbon emission constraints). Summary of the Invention

[0003] To address the aforementioned problems, this invention provides a scientifically sound, highly applicable, and effective distributed solution method for multi-regional interconnected systems constrained by carbon emissions. Its aim is to achieve independent optimization for each interconnected region through limited information exchange, satisfying the requirements of information independence and privacy for each region, while also meeting the "plug-and-play" requirement for optimization unit units. This method first decomposes the centralized low-carbon economic scheduling model, breaking down the interconnected system problem into sub-problems for each unit, and then constructs an iterative optimization solution framework for solving the problem.

[0004] To address the existing problems, the technical solution adopted in this invention is: a distributed solution method for multi-regional interconnected systems constrained by carbon emissions, characterized by including: construction of a low-carbon economic scheduling model for the multi-regional interconnected system, decomposition of the low-carbon economic scheduling model, construction of the information network topology, design of a distributed iterative optimization solution framework, and establishment of evaluation indicators.

[0005] Furthermore, the low-carbon economic dispatch model for the multi-regional interconnected system is constructed.

[0006] With the goal of minimizing the overall operating cost of a multi-region interconnected system, and considering power balance, reserve constraints, system carbon emission constraints, upper and lower limits of output power constraints, and ramping constraints, its economic scheduling problem can be expressed as a linear programming problem as shown in equations (1) and (2), defined as model A:

[0007]

[0008] stAx∝b (2)

[0009] Where f is the overall operating cost of the regional interconnection system; c is a column vector composed of the marginal power generation cost coefficients of the power output units in each region; x is a column vector composed of the power output power decisions of each power output unit; A and b are constant matrices and column vectors formed by constraints; “∝” indicates the size relationship between matrices, where “∝” related to power balance constraints is “=”, and “∝” related to other constraints is “≤”. The forms of c, A, and b are as follows:

[0010]

[0011]

[0012] Where n is the number of regions, let the set of regions be v = {v1, ..., v2}. n};c j The marginal generation cost coefficient matrix is ​​given for the j-th region, j = 1, 2…n; A j b represents the coefficient matrix related to global constraints, namely power balance, reserve constraints, and system carbon emission constraints; A j b j For the coefficient matrix related to local constraints, namely the upper and lower limits of output and the climbing constraint, b, c j A j A j b j The specific form is:

[0013]

[0014] Among them, v j ={1,...,m j} represents the set of elements in region j, m j Let j be the number of units within region j; Let j be the set of units containing schedulable devices in region j; This is the predicted load of the i-th unit in region j; if there is no load, it is zero. This represents the lower limit of the output of the i-th power unit in region j; This represents the upper limit of the output of the i-th power output unit in region j; R is the set of units in region j that participate in AGC adjustment; up R dn These are the required upward and downward backup capacities for the system, respectively. Let be the carbon emission coefficient of the i-th output unit in region j. If unit i does not contain conventional units, =Zero; γ is the set emission reduction coefficient; ζ = {1,...,T} is the set of time periods; 1 T Let be a column vector of dimension T with all elements equal to 1; ε0 is the carbon emission coefficient calculated from the baseline carbon emissions and system load, and its expression is:

[0015]

[0016]

[0017] like

[0018]

[0019]

[0020]

[0021] in, Linearize the marginal cost function of generator generation in the i-th output unit of region j to calculate the power generation operating cost of the k-th segment; For dimension identity matrix Let be the number of segments into which the marginal power generation cost of the j-th regional output unit i is divided; D is a square matrix of dimension T rows and T columns, in the following form.

[0022]

[0023]

[0024]

[0025] Among them, 1 T-1 ∈R T A column vector of dimension T with all elements equal to 1; 0 ∈ R T It is a column vector whose elements are all 0; Δt represents the maximum climbing rate of the i-th regional unit; Δt is the length of a single time interval.

[0026]

[0027] like

[0028]

[0029] like

[0030]

[0031] Where 0 represents the number of rows (2T) and the number of columns (...). A matrix whose elements are all zero; If i represents wind power

[0032]

[0033]

[0034] in, Let i be the predicted output value of wind turbine i in region j at time t;

[0035] like

[0036] Then c j,i ∈R 0×0 A j,i ∈R 0×0 A j,i ∈R 0×0 b j,i ∈R 0×0 ;

[0037] Where R 0×0 It is an empty matrix.

[0038] Furthermore, the decomposition of the low-carbon economic dispatch model includes:

[0039] Step 1: Solve the dual problem of model A, as shown in equations (4) and (5):

[0040]

[0041]

[0042] Where λ is the multiplier associated with constraint (2), λ T For multipliers related to global constraints, λ j Ω is the multiplier associated with the local constraints of the j-th region. λ Let λ be the range of values. The range of values ​​for multipliers related to equality constraints is (-∞, +∞), and the range of values ​​for multipliers related to other constraints is (-∞, 0].

[0043] Step 2: Decompose λ and b;

[0044] λ represents the multiplier related to power, reserve constraints, and carbon emission constraints, which is decomposed into local variables related to each region:

[0045]

[0046] Where, λ j (j=1,...,n) are the local variables related to the j-th region after decomposing λ.

[0047] b represents the system's load forecast, reserve demand, and carbon emission allowance, and can be decomposed into a coefficient matrix related to each region:

[0048]

[0049] Among them, b j ∈R 4T Let the i-th region be... R From the individual units, we can see that the overall backup configuration of the system is as follows:

[0050] like That is, there are units in region j.

[0051]

[0052] like However, there are units in region j.

[0053]

[0054] like

[0055]

[0056] in, The reserve requirement of the entire system is determined by whether the j-th regional unit i can know the overall reserve requirement. If i = i R ,but If i ≠ i R ,but

[0057] Through the first and second steps, we obtain model B, which can be solved in a distributed manner, as shown in equations (6) to (7):

[0058]

[0059]

[0060] Where, λ z b z A z c zThe form is:

[0061]

[0062]

[0063]

[0064] Where E is the inter-regional association information matrix;

[0065] At this point, each region corresponds to a subproblem, as shown in equations (8) to (9):

[0066]

[0067]

[0068] The augmented Lagrangian function corresponding to model B is shown in equation (10):

[0069]

[0070] Where σ is a constant penalty factor, i.e., the iteration step size, used to improve the convergence of the algorithm; W T To be in accordance with constraints The relevant multiplier vector is of the following form:

[0071]

[0072] Among them, w (j,h) Multipliers related to the correlation constraints between subproblems in the interconnected region optimization; w j The multiplier associated with the local constraints of the optimization subproblem in a single region is equivalent to the output matrix of each region element;

[0073] A z W, c z Decomposed into the forms shown in equations (11) to (13):

[0074]

[0075]

[0076]

[0077] Among them, A z,j For A z,j The j-th column; W (j,h) W j c z,j The format is:

[0078]

[0079] Substituting equations (11) to (13) into equation (10) and simplifying, we obtain the augmented Lagrangian functions corresponding to the optimization subproblems of each region:

[0080]

[0081] Among them, 1 4T It is a column vector with all elements being 1 and a dimension of 4T;

[0082] make Then, rearranging equation (14), we obtain the Lagrangian function corresponding to the single-region optimization subproblem as follows:

[0083]

[0084] Among them, H j , The Lagrangian function corresponding to the optimization subproblem of a single region can be calculated based on the local information of region j and the correlation information of adjacent regions.

[0085] Furthermore, the information network topology is constructed.

[0086] The information network topology is represented as a directed graph: G = (v, ε), where v is the set of vertices, representing each region, v = {1, 2, ..., n}; ε = v × v is the set of edges, representing the information topology relationships between regions; the set of vertices adjacent to vertex j is denoted by N. j It means that N j ={N j + N j -}, where N j + N is the set of points connected to and pointed to by point j; j - Let G be the set of points connected to and pointing to point j; the point-edge incidence matrix G = (v, ε) is represented by matrix E. All regions are divided into two categories: the set of regions in the first category is P1, and the set of regions in the second category is P2, with N = {P1 ∪ P2} and... The requirement that adjacent areas be classified differently can be met by rationally planning the information network topology.

[0087] Furthermore, the distributed iterative optimization solution framework is designed...

[0088] (a) Initialize the data for each region, λ z,j =0、 w j =0;

[0089] (b) Solve the optimization model for each region to obtain the correlation between the k-th iteration and each region.

[0090] (c) Information is exchanged and updated between adjacent areas.

[0091] (d) Determine if the number of iterations meets the initial setting. If not, return to step (b); otherwise, end the iteration.

[0092] in, w for the kth iteration j w (j,h) w (h,j) .

[0093] Furthermore, the establishment of evaluation indicators

[0094] ①Dual residuals

[0095]

[0096] In the formula, s (k) Let be the dual residual of the k-th iteration; kind equals 1 or 2; Representing the k-th and (k+1)-th iterations, respectively. The algorithm's convergence and the system's emission reduction effect were evaluated.

[0097] This invention designs a distributed solution method for multi-regional interconnected systems with carbon emission constraints, including: establishing a low-carbon economic scheduling model for the multi-regional interconnected system, dualizing the economic scheduling model, decomposing the dual model, designing an iterative optimization solution framework, and evaluating the system's emission reduction effect. By decomposing the centralized low-carbon economic scheduling model of the multi-regional interconnected system, distributed low-carbon economic scheduling optimization of the system is achieved. This method solves economic scheduling problems containing both global equality constraints (e.g., power balance constraints) and global inequality constraints (e.g., reserve constraints, system carbon emission constraints), and is more universal than existing distributed economic scheduling methods. Each region only needs to use the operating status of its internal units and the Lagrange multiplier information of adjacent regions to achieve overall optimization, without requiring the exchange of power deficit information between adjacent regions. This fully satisfies the requirements of information independence and privacy for each region, while also meeting the "plug-and-play" requirement for optimized regional units. Attached Figure Description

[0098] Figure 1 Here is a flowchart of a distributed solution method for multi-regional interconnected systems constrained by carbon emissions.

[0099] Figure 2 A partitioned and information network topology diagram of the IEEE-6 node system;

[0100] Figure 3 Forecast curves of node load and wind power output for each time period;

[0101] Figure 4 A graph showing the output curves of each generator unit under Japan's economic dispatch.

[0102] Figure 5 This is a graph showing the iterative change curves of the dual residuals.

[0103] Figure 6 The graph shows the iterative change curve of the unit's power generation decision value;

[0104] Figure 7 A graph showing the difference in power generation decisions between distributed and centralized dispatching for each generating unit;

[0105] Figure 8 This is a comparison chart of the daily operating costs for different energy storage capacities. Detailed Implementation

[0106] The following description, using accompanying drawings and examples, further illustrates a distributed solution method for multi-regional interconnected systems constrained by carbon emission limits, in accordance with the present invention.

[0107] Reference Figure 1 The present invention provides a distributed solution method for multi-regional interconnected systems constrained by carbon emissions, characterized by including: constructing a low-carbon economic scheduling model for the multi-regional interconnected system, decomposing the low-carbon economic scheduling model, building an information network topology, designing a distributed iterative optimization solution framework, and establishing evaluation indicators.

[0108] Furthermore, the low-carbon economic dispatch model for the multi-regional interconnected system is constructed.

[0109] With the goal of minimizing the overall operating cost of a multi-region interconnected system, and considering power balance, reserve constraints, system carbon emission constraints, upper and lower limits of output power constraints, and ramping constraints, its economic scheduling problem can be expressed as a linear programming problem as shown in equations (1) and (2), defined as model A:

[0110]

[0111] stAx∝b (2)

[0112] Where f is the overall operating cost of the regional interconnection system; c is a column vector composed of the marginal power generation cost coefficients of the power output units in each region; x is a column vector composed of the power output power decisions of each power output unit; A and b are constant matrices and column vectors formed by constraints; “∝” indicates the size relationship between matrices, where “∝” related to power balance constraints is “=”, and “∝” related to other constraints is “≤”. The forms of c, A, and b are as follows:

[0113]

[0114]

[0115] Where n is the number of regions, let the set of regions be v = {v1, ..., v2}. n};c j The marginal generation cost coefficient matrix is ​​given for the j-th region, j = 1, 2…n; A j b represents the coefficient matrix related to global constraints, namely power balance, reserve constraints, and system carbon emission constraints; A j b j For the coefficient matrix related to local constraints, namely the upper and lower limits of output and the climbing constraint, b, c j A j A j b j The specific form is as follows:

[0116]

[0117] Among them, v j ={1,...,m j} represents the set of elements in region j, m j Let j be the number of units within region j; Let J be the set of units containing schedulable devices in region J; This is the predicted load of the i-th unit in region j; if there is no load, it is zero. This represents the lower limit of the output of the i-th power unit in region j; This represents the upper limit of the output of the i-th output unit in region j; R is the set of units in region j that participate in AGC adjustment; up R dn These are the required upward and downward backup capacities for the system, respectively. Let be the carbon emission coefficient of the i-th output unit in region j. If unit i does not contain conventional units, =Zero; γ is the set emission reduction coefficient; ζ = {1,...,T} is the set of time periods; 1 T Let be a column vector of dimension T with all elements equal to 1; ε0 is the carbon emission coefficient calculated from the baseline carbon emissions and system load, and its expression is:

[0118]

[0119]

[0120] like

[0121]

[0122]

[0123]

[0124] in, Linearize the marginal cost function of generator generation in the i-th output unit of region j to calculate the power generation operating cost of the k-th segment; For dimension identity matrix Let be the number of segments into which the marginal power generation cost of the j-th regional output unit i is divided; D is a square matrix of dimension T rows and T columns, in the following form.

[0125]

[0126]

[0127]

[0128] Among them, 1 T-1 ∈R T A column vector of dimension T with all elements equal to 1; 0 ∈ R T It is a column vector whose elements are all 0; Δt represents the maximum climbing rate of the i-th regional unit; Δt is the length of a single time interval.

[0129]

[0130] like

[0131]

[0132] like

[0133]

[0134] Where 0 represents the number of rows as 2T and the number of columns as... A matrix whose elements are all zero;

[0135] If i represents wind power

[0136]

[0137]

[0138] in, Let i be the predicted output value of wind turbine i in region j at time t;

[0139] like

[0140] Then c j,i ∈R 0×0 A j,i ∈R 0×0 A j,i ∈R 0×0 b j,i ∈R 0×0 ;

[0141] Where R 0×0 It is an empty matrix.

[0142] Furthermore, the decomposition of the low-carbon economic dispatch model includes:

[0143] Step 1: Solve the dual problem of model A, as shown in equations (4) and (5):

[0144]

[0145]

[0146] Where λ is the multiplier associated with constraint (2), λ T For multipliers related to global constraints, λ j Ω is the multiplier associated with the local constraints of the j-th region. λ Let λ be the range of values. The range of values ​​for multipliers related to equality constraints is (-∞, +∞), and the range of values ​​for multipliers related to other constraints is (-∞, 0].

[0147] Step 2: Decompose λ and b;

[0148] λ represents the multiplier related to power, reserve constraints, and carbon emission constraints, which is decomposed into local variables related to each region:

[0149]

[0150] Where, λ j (j=1,...,n) are the local variables related to the j-th region after decomposing λ.

[0151] b represents the system's load forecast, reserve demand, and carbon emission allowance, and can be decomposed into a coefficient matrix related to each region:

[0152]

[0153] Among them, b j ∈R 4T Let the i-th region be... R From the individual units, we can see that the overall backup configuration of the system is as follows:

[0154] like That is, there are units in region j.

[0155]

[0156] like However, there are units in region j.

[0157]

[0158] like

[0159]

[0160] in, The reserve requirement of the entire system is determined by whether the j-th regional unit i can know the overall reserve requirement. If i = i R ,but If i ≠ i R ,but

[0161] Through the first and second steps, we obtain model B, which can be solved in a distributed manner, as shown in equations (6) to (7):

[0162]

[0163]

[0164] Where, λ z b z A z c z The form is:

[0165]

[0166]

[0167]

[0168] Where E is the inter-regional association information matrix;

[0169] At this point, each region corresponds to a subproblem, as shown in equations (8) to (9):

[0170]

[0171]

[0172] The augmented Lagrangian function corresponding to model B is shown in equation (10):

[0173]

[0174] Where σ is a constant penalty factor, i.e., the iteration step size, used to improve the convergence of the algorithm; W T To be in accordance with constraints The relevant multiplier vector is of the following form:

[0175]

[0176] Among them, w (j,h) Multipliers related to the correlation constraints between subproblems in the interconnected region optimization; w j The multiplier associated with the local constraints of the optimization subproblem in a single region is equivalent to the output matrix of each region element;

[0177] A z W, c z Decomposed into the forms shown in equations (11) to (13):

[0178]

[0179]

[0180]

[0181] Among them, A z,j For A z,j The j-th column; W (j,h) W j c z,j The format is:

[0182]

[0183] Substituting equations (11) to (13) into equation (10) and simplifying, we obtain the augmented Lagrangian functions corresponding to the optimization subproblems of each region:

[0184]

[0185] Among them, 1 4T It is a column vector with all elements being 1 and a dimension of 4T;

[0186] make Then, rearranging equation (14), we obtain the Lagrangian function corresponding to the single-region optimization subproblem as follows:

[0187]

[0188] Among them, H j , The Lagrangian function corresponding to the optimization subproblem of a single region can be calculated based on the local information of region j and the correlation information of adjacent regions.

[0189] Furthermore, the information network topology is constructed.

[0190] The information network topology is represented as a directed graph: G = (v, ε), where v is the set of vertices, representing each region, v = {1, 2, ..., n}; ε = v × v is the set of edges, representing the information topology relationships between regions; the set of vertices adjacent to vertex j is denoted by N. j It means that N j ={N j + N j -}, where N j + N is the set of points connected to and pointed to by point j; j - Let G be the set of points connected to and pointing to point j; the point-edge incidence matrix G = (v, ε) is represented by matrix E. All regions are divided into two categories: the set of regions in the first category is P1, and the set of regions in the second category is P2, with N = {P1 ∪ P2} and... The requirement that adjacent areas be classified differently can be met by rationally planning the information network topology.

[0191] Furthermore, the distributed iterative optimization solution framework is designed...

[0192] (a) Initialize the data for each region, λ z,j =0、 w j =0;

[0193] (b) Solve the optimization model for each region to obtain the correlation between the k-th iteration and each region.

[0194] (c) Information is exchanged and updated between adjacent areas.

[0195] (d) Determine if the number of iterations meets the initial setting. If not, return to step (b); otherwise, end the iteration.

[0196] in, w for the kth iteration j w (j,h) w (h,j) .

[0197] Furthermore, the establishment of evaluation indicators

[0198] ①Dual residuals

[0199]

[0200] In the formula, s (k) Let be the dual residual of the k-th iteration; kind equals 1 or 2; Representing the k-th and (k+1)-th iterations, respectively. The algorithm's convergence and the system's emission reduction effect were evaluated.

[0201] 6) Analysis of the effects of distributed low-carbon economic dispatch

[0202] This example uses the IEEE-6 node system. The IEEE-6 node system is divided into three regions, and the information network topology between the regions is as follows: Figure 2 As shown. Unit 3 contains a 50MW wind turbine, and a typical day is selected as the research object. Figure 3 The load and wind power output of each node are predicted, with a single time period length Δt of 15 mins and an emission reduction factor γ of 15%.

[0203] Table 1 shows the operating parameters of each unit.

[0204] Table 1 Power generation parameters of the IEEE-6 Node system

[0205]

[0206]

[0207] The initial value of the iteration step size σ is 0.1. Figure 4 To incorporate system carbon emission constraints into the daily power output decision curves of the gas turbine units, this study adds them to Example 1. With a low carbon emission coefficient, coal-fired power units, under carbon emission constraints, Compared to Example 1, the output decision value is significantly reduced. Furthermore, due to the unit... The power generation cost and carbon emission coefficient are relatively high, so it operates at minimum output.

[0208] Furthermore, convergence analysis was performed on the results of the first four time periods of a typical day's scheduling. Figure 5 The curve shows the variation of the dual residual with the number of iterations. Distributed computing reaches convergence around 500 iterations. The scheduling result at 500 iterations is analyzed. At this point, the distributed scheduling cost is 82284.36 yuan, with a relative error of 0.17% compared to the centralized scheduling cost (82144.38 yuan). The results achieved by both methods are very similar. Figure 6The curves showing the change in unit output decision with the number of iterations for the four time periods show that when the number of iterations reaches about 100, the unit output of the system has reached the power balance constraint. In subsequent iterations, the unit output gradually changes as the multipliers between nodes are continuously exchanged. Figure 7 This represents the difference in decision values ​​between distributed and centralized economic dispatch for each unit after considering carbon emission constraints. Compared to Example 1, the time periods with differences from centralized economic dispatch have increased, but the difference ranges from -0.06 to 0.07 in each time period, indicating a relatively small error. Figure 8 This chart compares the carbon emissions of each unit over the first four time periods. Thermal power units. Carbon emissions have been significantly reduced. Carbon emissions increased. The system's carbon emissions decreased from 224t to 190.41t, a reduction of 15%, meeting carbon emission constraints.

[0209] Based on the above, the method described in this invention introduces a global inequality constraint—system carbon emission constraint—into a multi-regional interconnected system containing multiple types of schedulable resources. It adjusts the output decisions of each power unit according to emission reduction requirements, achieving distributed low-carbon economic scheduling. For economic scheduling problems simultaneously containing global equality constraints (power balance constraints) and global inequality constraints (reserve constraints, system carbon emission constraints), a fully distributed scheduling model is constructed based on duality theory and variable decomposition methods, which is more universally applicable compared to existing distributed economic scheduling methods. During the iterative solution process, each interconnected region only needs to exchange Lagrange multiplier information with its neighboring regions to achieve overall optimization. This effectively reduces the amount of information transmitted between regions and fully protects the information privacy requirements of each region's units. Therefore, the distributed solution method in this invention is proven to be truly effective.

[0210] The calculation conditions, illustrations, tables, etc. in the embodiments of this invention are only used to further illustrate the invention and are not exhaustive. They do not constitute a limitation on the scope of protection of the claims. Those skilled in the art, based on the inspiration gained from the embodiments of this invention, can conceive of other substantially equivalent alternatives without creative effort, all of which are within the scope of protection of this invention.

Claims

1. A distributed solution method for multi-regional interconnected systems constrained by carbon emissions, characterized in that, The method includes: constructing a low-carbon economic scheduling model for a multi-regional interconnected system, decomposing the low-carbon economic scheduling model, building an information network topology, designing a distributed iterative optimization solution framework, and establishing evaluation indicators. Construction of the low-carbon economic dispatch model for the multi-regional interconnected system: With the goal of minimizing the overall operating cost of a multi-region interconnected system, and considering power balance, reserve constraints, system carbon emission constraints, upper and lower limits of output power constraints, and ramping constraints, its economic scheduling problem can be expressed as a linear programming problem as shown in equations (1) and (2), defined as model A: （1） （2） Where f is the overall operating cost of the regional interconnection system; c is a column vector composed of the marginal power generation cost coefficients of the power output units in each region; x is a column vector composed of the power output decisions of each power output unit; A and b are a constant matrix and a column vector formed by constraints. "This indicates the size relationship between matrices, where the relationship is related to power balance constraints." "for "=", related to other constraints "≤ ", c, A, b are in the following forms: ； Where n is the number of regions, and let the set of regions be v = {v1, ..., v}. n };c j The marginal generation cost coefficient matrix is ​​given for the j-th region, j=1,2…n; , A is a coefficient matrix related to global constraints, namely power balance, reserve constraints, and system carbon emission constraints; j b j This is the coefficient matrix related to local constraints, namely the upper and lower limits of output and the climbing constraint. c j , A j b j The specific form is: ； Among them, v j ={1,...,m j } represents the set of elements in region j, m j Let j be the number of units within region j; Let j be the set of units containing schedulable devices in region j; This is the predicted load of the i-th unit in region j; if there is no load, it is zero. This represents the lower limit of the output of the i-th power unit in region j; This represents the upper limit of the output of the i-th power output unit in region j; R is the set of units in region j that participate in AGC adjustment; up R dn These are the required upward and downward backup capacities for the system, respectively. Let be the carbon emission coefficient of the i-th output unit in region j. If unit i does not contain conventional units, It is zero; The set emission reduction coefficient; ζ={1,...,T} is the set of time periods; It is a column vector with all elements being 1 and a dimension of T; The carbon emission factor, calculated based on baseline carbon emissions and system load, is expressed as follows: （3） ， like : ； ； ； in, Linearize the marginal cost function of generator generation in the i-th output unit of region j to calculate the power generation operating cost of the k-th segment; For dimension identity matrix Let be the number of segments into which the marginal power generation cost of the j-th regional output unit i is divided; D is a square matrix of dimension T rows and T columns, in the following form. ； ； ； in, It is a column vector with all elements being 1 and a dimension of T; It is a column vector whose elements are all 0; The maximum climbing rate for the i-th region unit; The length of a single time period; ； like : ； like : ； Where 0 represents the number of rows (2T) and the number of columns (...). A matrix whose elements are all zero; ; If i represents wind power: ； ； in, Let i be the predicted output value of wind turbine i in region j at time t; like : but , , , ; in It is an empty matrix.

2. The distributed solution method for multi-regional interconnected systems constrained by carbon emission limits as described in claim 1, characterized in that, The decomposition of the low-carbon economic dispatch model includes: Step 1: Solve the dual problem of model A, as shown in equations (4) and (5): （4） （5） Where λ is the multiplier associated with constraint (2), , For multipliers related to global constraints, λ j Ω is the multiplier associated with the local constraints of the j-th region. λ Let λ be the range of values. The range of values ​​for multipliers related to equality constraints is (-∞, +∞), and the range of values ​​for multipliers related to other constraints is (-∞, 0]. Step 2: [The sentence is incomplete and requires more context.] , Decomposition; The multipliers, representing those related to power, reserve constraints, and carbon emission constraints, are decomposed into local variables relevant to each region: ； in, To be After decomposition, the local variables related to the j-th region, j=1,...,n, This represents the constraint values ​​related to the system's load forecast, reserve demand, and carbon emission allowances. Decomposed into a coefficient matrix related to each region: ； in, Let the i-th region be... R From the individual units, we can see that the overall backup configuration of the system is as follows: like That is, there are units in region j. : ； like However, there are units in region j. : ； like : ； in, The reserve requirement of the entire system is determined by whether the j-th regional unit i knows the overall reserve requirement. If i = i R ,but If i ≠ i R ,but ; Through the first and second steps, we obtain model B, which can be solved in a distributed manner, as shown in equations (6) to (7): （6） （7） Where, λ z b z A z c z The form is: ； ； Where E is the inter-regional association information matrix; n is the number of regions; At this point, each region corresponds to a subproblem, as shown in equations (8) to (9): （8） （9） The augmented Lagrangian function corresponding to model B is shown in equation (10): （10） in, This is a constant penalty factor, i.e., the iteration step size, used to improve the convergence of the algorithm; To be in accordance with constraints The relevant multiplier vector is of the following form: ； Among them, w (j,h) Multipliers related to the correlation constraints between subproblems in the interconnected region optimization; w j The multiplier associated with the local constraints of the optimization subproblem of a single region is equivalent to the output matrix of each region element; η is the set of interconnected regions (j,h); A z W, c z Decomposed into the forms shown in equations (11) to (13): （11） （12） （13） Among them, A z,j For A z,j The j-th column; W (j,h) W j c z,j The format is: ； Substituting equations (11) to (13) into equation (10) and simplifying, we obtain the augmented Lagrangian functions corresponding to the optimization subproblems of each region: （14） in, It is a column vector with all elements being 1 and a dimension of 4T; make , , Then, by rearranging equation (14), we obtain the Lagrangian function corresponding to the single-region optimization subproblem as follows: （15） Among them, H j , The Lagrangian function corresponding to the optimization subproblem of a single region can be calculated based on the local information of region j and the correlation information of adjacent regions.

3. The distributed solution method for multi-regional interconnected systems constrained by carbon emission limits as described in claim 1, characterized in that, The aforementioned information network topology construction: The information network topology is represented as a directed graph: G=(v, ε), where v is the set of vertices, representing each region, v={1, 2,…,n}; ε=v×v is the set of edges, representing the information topology relationships between regions; the set of vertices adjacent to vertex j is denoted by N. j It means that N j ={ N j + N j - }, where N j + N is the set of points connected to and pointed to by point j; j - Let G be the set of points connected to and pointing to point j; the point-edge incidence matrix G=(v, ε) is represented by matrix E. All regions are divided into two categories: the set of regions in the first category is P1, and the set of regions in the second category is P2, with N={P1∪P2} and P1∩P2= The requirement that adjacent areas be classified differently can be met by rationally planning the information network topology.

4. The distributed solution method for multi-regional interconnected systems constrained by carbon emissions, as described in claim 1, is characterized in that... The distributed iterative optimization solution framework design is as follows: (a) Initialize the data for each region. , , , ; (b) Solve the optimization model for each region to obtain the correlation between the k-th iteration and each region. ; (c) Information is exchanged and updated between adjacent areas. , , ; (d) Determine if the number of iterations meets the initial setting. If not, return to step (b); otherwise, end the iteration. in, , , For the k-th iteration , , .

5. The distributed solution method for multi-regional interconnected systems constrained by carbon emission limits as described in claim 1, characterized in that, The establishment of evaluation indicators ①Dual residuals （16） In the formula, Let be the dual residual of the k-th iteration; , kind equals 1 or 2; , Representing the k-th and (k+1)-th iterations, respectively. The algorithm's convergence and the system's emission reduction effect were evaluated.

Images