Multi-area power system decentralized dispatching method based on newton method approximate dynamic programming

Abstract

The application discloses a multi-region power system scheduling method based on Newton method approximate dynamic programming, and comprises the following steps: S1, a multi-region power system scheduling model is constructed, a power system scheduling cost minimization is taken as an objective function, the multi-region power system scheduling model is divided into a plurality of regional sub-models, and a value function of each regional sub-model is determined; S2, the value function of each regional sub-model is subjected to second-order Taylor expansion based on the Newton method, and an approximate value function of each regional sub-model is obtained; S3, derivatives of the approximate value function of each regional sub-model in the multi-region power system scheduling model are calculated, and a second-order derivative matrix and a first-order derivative matrix of the approximate value function of each regional sub-model are obtained; S4, an approximate dynamic programming method based on the Newton method is adopted to update the approximate value function of each regional sub-model, an optimal scheduling strategy of the multi-region power system scheduling model is obtained, and the power system is scheduled according to the optimal scheduling strategy. The solving speed and accuracy are improved.

Description

Technical Field

[0001] This invention relates to the field of power system dispatching technology, and more specifically, to a distributed dispatching method for multi-regional power systems based on Newton's method and approximate dynamic programming. Background Technology

[0002] Interconnection of multiple regional power systems is a prominent feature of modern power systems, and efficient dispatch is of great significance to the economic and safe operation of modern power systems. Traditional centralized dispatch methods require a centralized dispatch center to collect detailed data from all regions and use a centralized optimization model for solution. However, with the continuous increase in the scale of power systems and the increasing complexity of regional interconnection, centralized optimization methods have significant limitations for the following reasons: (1) the dispatch center has difficulty accurately collecting and processing the massive amounts of data from each region; (2) each region, for the sake of protecting information privacy, should not upload all its information to the centralized dispatch center; (3) each region needs to operate independently, that is, the economic dispatch of its own region is the responsibility of its own dispatch center. Therefore, it is essential to use a decentralized dispatch method to solve the economic dispatch problem of multi-regional power systems.

[0003] Commonly used distributed scheduling methods mainly fall into two categories: dual decomposition methods and optimality conditional decomposition methods. Dual decomposition methods include Lagrange relaxation and augmented Lagrange relaxation. These methods construct decomposable dual subproblems by relaxing the coupling constraints between regions into the objective function, thus enabling distributed solutions to multi-region scheduling problems. However, these methods involve updating Lagrange multipliers, so their convergence depends on parameter adjustment, which significantly reduces the solution efficiency. Optimality conditional decomposition methods decouple KKT conditions by setting diagonal block elements to zero, constructing distributed subproblems corresponding to each region. However, this decomposition process is based on an approximate Newtonian direction, and its accuracy and convergence speed depend on the network partitioning, which greatly limits the application of this method.

[0004] The approximate dynamic programming method applies the Bellman equation to decompose the multi-region power system scheduling problem into subproblems corresponding to each region, and uses approximate value functions to reflect the influence between subproblems. The efficiency of solving the multi-region scheduling problem depends on the accuracy of the approximation of the value function; therefore, accurate value function approximation techniques are particularly important. Currently, value function approximation techniques based on piecewise linear functions and Benders cut functions have been used in multi-region power system scheduling problems. However, since these value function approximation techniques are linear, they are only suitable for solving DC power flow models. For nonlinear AC power flow models that more accurately describe power grid operation, these value function approximation techniques cannot achieve accurate solutions, greatly limiting their application. Therefore, exploring new value function approximation techniques to solve large-scale nonlinear AC power flow optimization scheduling problems in multi-region power systems more quickly and accurately remains a research focus. Summary of the Invention

[0005] The purpose of this invention is to solve the problem of distributed scheduling of multi-regional power systems in the prior art, and to provide a multi-regional power system scheduling method based on Newton's method and approximate dynamic programming, which improves the update efficiency and approximate accuracy of the value function. The approximate dynamic programming algorithm based on Newton's method improves the solution speed and accuracy of the large-scale nonlinear AC power flow optimization scheduling problem of multi-regional power systems.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A distributed dispatching method for multi-regional power systems based on Newton's method and approximate dynamic programming includes the following steps:

[0008] S1. Construct a multi-regional power system dispatch model, with the goal of minimizing power system dispatch costs. Divide the multi-regional power system dispatch model into multiple regional sub-models and determine the value function for each regional sub-model.

[0009] S2. Based on Newton's method, perform a second-order Taylor expansion on the value function of each regional sub-model to obtain the approximate value function of each regional sub-model;

[0010] S3. Calculate the derivative of the approximate function of each regional sub-model in the multi-regional power system dispatch model, and obtain the second-order derivative matrix and the first-order derivative matrix of the approximate function of each regional sub-model;

[0011] S4. An approximate dynamic programming method based on Newton's method is adopted to update the approximate function of each regional sub-model, obtain the optimal scheduling strategy of the multi-regional power system scheduling model, and schedule the power system according to the optimal scheduling strategy.

[0012] Furthermore, the multi-regional power system dispatch model aims to minimize generator operating costs while satisfying unit output constraints, voltage safety constraints, line capacity constraints, and AC power flow constraints. The objective function is:

[0013]

[0014] In the formula, Represents a set of generators; a g b g and c g This represents the power generation cost coefficient of generator g; This represents the active power output of generator g;

[0015] The constraints are:

[0016]

[0017] In the formula, and These represent the lower and upper limits of the active power output of generator g, respectively. This represents the reactive power output of generator g; and These represent the lower and upper limits of the reactive power output of generator g, respectively. Represents a set of nodes; e i and f i V represents the real and imaginary parts of the voltage phasor at node i, respectively; i,min and V i,max P represents the lower and upper limits of the voltage amplitude at node i, respectively; ij,max G represents the upper limit of line transmission capacity for line ij; ij and B ij Let represent the real and imaginary parts of the nodal admittance matrix, respectively; and M represents the active and reactive loads of node i, respectively; i,g This represents the ig-th element of the node-generator association matrix.

[0018] Furthermore, the multi-regional power system dispatch model is divided into multiple regional sub-models, and the value function for each regional sub-model is determined, specifically as follows:

[0019] S11. Divide the multi-regional power system dispatch model into n regional sub-models according to geographical zoning;

[0020] S12. Arbitrarily determine a regional decision-making sequence to transform the multi-regional power system dispatching problem into a multi-stage decision-making process;

[0021] S13. The value function and constraints for each region's sub-model are as follows:

[0022] V a (S a )=min{C a (S a ,x a )+V a+1 (S a+1 )}

[0023]

[0024] Among them, V a (S a V represents the value function of region a; a+1 (S a+1 ) represents the value function of the region a+1; C a (S a ,x a S represents the power generation cost of region a; a S represents the state variables of region a; a+1 The state variable representing region a+1; x a G represents the decision variable for region a; a (S a ,x a ,S a+1 ) represents the equality constraint in region a; h a (S a ,x a ,S a+1 ) represents the inequality constraint in region a; h a This represents the lower bound of the inequality constraints in region a; This represents the upper limit of the inequality constraints in region a.

[0025] Furthermore, to obtain the approximate function of each regional sub-model, a Lagrange equation is constructed. for:

[0026]

[0027] Where, λ a Represents the Lagrange multiplier of region a; μ represents the potential barrier coefficient; N a,h This indicates the number of inequality constraints.

[0028] Furthermore, after introducing the Kuhn-Tak condition, the value function of each regional sub-model is described as follows:

[0029]

[0030] In the formula, This represents the Kuhn-Tak condition for the Lagrange equation.

[0031] Furthermore, the decision variable x for region aa The state variable S of region a+1 a+1 and the Lagrange multiplier λ of region a a Unified by variable ω a This means that ω is obtained. a =(x a S a+1 ;λ a ).

[0032] Furthermore, performing a second-order Taylor expansion on the value function yields the approximate value function as follows:

[0033]

[0034] In the formula, Region a is based on a second-order approximation function; C represents the constant term of the expansion; ΔS a and Δω a Indicates the Newtonian direction; Q a,SS Q a,Sω Q a,ωS and Q a,ωω L represents the second derivative of the expansion; a,S and L a,ω It represents the first derivative of the expansion.

[0035] Furthermore, the formula for calculating the derivative of the approximate function is:

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] In the formula, Indicates the current point and Expand at the location; This indicates differentiation.

[0043] Furthermore, by linearizing the Kuhn-Tak conditions using the Newton-Raphson method, the relationship between the state variables and other variables is obtained as follows:

[0044]

[0045] The result derived from the relationship between the state variable and other variables is:

[0046] Δω a =Q a,ωω -1 (-L a,ω -Q a,ωS ΔS a )=aΔS a +b

[0047] In the formula, a and b are both coefficient matrices;

[0048] The formula for calculating 'a' is:

[0049] a = -Q a,ωω -1 Q a,ωS

[0050] The formula for calculating b is:

[0051] b = -Q a,ωω -1 L a,ω

[0052] In the second-order approximation function based on Newton's method, by eliminating variables other than the state variable and combining like terms, we obtain:

[0053]

[0054] In the formula, Q' a N represents the approximate value function a,S ×N a,S L' is a second-order derivative matrix. a N represents the approximate function a,S A 1×1-dimensional first-order derivative matrix; N a,S Indicates the number of state variables;

[0055] Among them, Q' a The calculation formula is:

[0056]

[0057] L' a The calculation formula is:

[0058]

[0059] Furthermore, the approximate dynamic programming method based on Newton's method is specifically as follows:

[0060] S41. Initialize the data, let the iteration index k = 0, set the convergence values ​​ε1 > 0, ε2 > 0, the reduction coefficient σ satisfy 0 < σ < 1, and the initial value of the Lagrange multiplier λ. (0) =0, initial value of barrier coefficient μ (0) >1;

[0061] S42. Solve each region sub-model from back to front, and calculate Q'. a (k) and L' a (k) and put Q' a (k) and L' a (k) The value functions of all sub-models in all regions are solved.

[0062] Among them, Q' a (k) L' represents the second derivative matrix of the approximate function of region a in the k-th iteration; a (k) The matrix representing the first derivative of the approximate function of region a in the k-th iteration;

[0063] S43. Update the state and decision of each region sub-model from front to back, and calculate ΔS. a (k) and Δω a (k) and ΔS a+1 (k) The changes are passed to the next region, and finally, the variables in all regions are updated using a formula: The update formula is:

[0064]

[0065] in, and This represents the initial value for the (k+1)th iteration; and Denotes the initial value of the k-th iteration; ΔS a (k) and Δω a (k) Indicates the Newton direction in the k-th iteration;

[0066] S44. Determine whether the convergence criterion is met. The convergence criterion is:

[0067] μ (k) ≤ε1

[0068] ||(ΔS (k) ;Δω (k) )|| ∞ <ε2

[0069] If satisfied, terminate the program; otherwise, let k = k + 1, μ (k+1) =σ×μ (k) Repeat steps S42 to S44.

[0070] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0071] 1. This invention proposes for the first time a second-order value function approximation technique based on Newton's method, which extends the information of the approximate value function from the first order to the second order, thereby improving the update efficiency and approximation accuracy of the value function.

[0072] 2. This invention proposes for the first time a distributed scheduling method based on Newton's method and approximate dynamic programming, which improves the solution speed and accuracy of large-scale nonlinear AC power flow optimization scheduling problems in multi-regional power systems.

[0073] 3. This invention improves the optimization accuracy and solution efficiency of distributed dispatching in multi-regional power systems, reduces the operating costs of power systems, and enhances the coordination and decision-making efficiency of multi-regional power systems. This aligns with the trend of regionalized development of power systems under the background of widespread access to distributed power sources, thereby bringing about good social and economic benefits. Attached Figure Description

[0074] Figure 1 This is a flowchart illustrating the distributed scheduling method for multi-regional power systems based on Newton's method and approximate dynamic programming, as presented in this invention. Detailed Implementation

[0075] The following description, in conjunction with the accompanying drawings and specific embodiments, further illustrates the distributed dispatching method for multi-regional power systems based on Newton's method and approximate dynamic programming.

[0076] Please see Figure 1 This invention discloses a distributed dispatching method for multi-regional power systems based on Newton's method and approximate dynamic programming, comprising the following steps:

[0077] S1. Construct a multi-regional power system dispatch model, with the goal of minimizing power system dispatch costs. Divide the multi-regional power system dispatch model into multiple regional sub-models and determine the value function for each regional sub-model.

[0078] S2. Based on Newton's method, perform a second-order Taylor expansion on the value function of each regional sub-model to obtain the approximate value function of each regional sub-model.

[0079] S3. Calculate the derivative of the approximate function of each regional sub-model in the multi-regional power system dispatch model, and obtain the second-order derivative matrix and the first-order derivative matrix of the approximate function of each regional sub-model.

[0080] S4. An approximate dynamic programming method based on Newton's method is adopted to update the approximate function of each regional sub-model, obtain the optimal scheduling strategy of the multi-regional power system scheduling model, and schedule the power system according to the optimal scheduling strategy.

[0081] This invention uses Newton's method and approximate dynamic programming as basic theoretical tools, and proposes a second-order value function approximation technique to improve the update efficiency and approximation accuracy of the value function. Then, based on this second-order value function approximation technique, a distributed scheduling method based on Newton's method and approximate dynamic programming is proposed, which improves the solution speed and accuracy of the nonlinear AC power flow optimization scheduling problem in multi-regional power systems.

[0082] For an n-region power system, the centralized model of its dispatching problem aims to minimize generator operating costs while satisfying unit output constraints, voltage safety constraints, line capacity constraints, and AC power flow constraints. The objective function is:

[0083]

[0084] In the formula, Represents a set of generators; a g b g and c g This represents the power generation cost coefficient of generator g; This represents the active power output of generator g;

[0085] The constraints are:

[0086]

[0087] In the formula, and These represent the lower and upper limits of the active power output of generator g, respectively. This represents the reactive power output of generator g; and These represent the lower and upper limits of the reactive power output of generator g, respectively. Represents a set of nodes; e i and f i V represents the real and imaginary parts of the voltage phasor at node i, respectively; i,min and V i,max P represents the lower and upper limits of the voltage amplitude at node i, respectively; ij,max G represents the upper limit of line transmission capacity for line ij; ij and B ij Let represent the real and imaginary parts of the nodal admittance matrix, respectively; and M represents the active and reactive loads of node i, respectively; i,g This represents the ig-th element of the node-generator association matrix.

[0088] This invention employs approximate dynamic programming theory to decouple each regional sub-model. First, the centralized model is divided into n sub-models based on geographical partitioning, with boundary voltage variables used as state variables. Second, an arbitrary regional decision-making order is determined, transforming the multi-regional power system dispatching problem into a multi-stage decision-making process. Finally, according to the Bellman equations, the value function and constraints of each regional sub-model are as follows:

[0089] V a (S a )=min{C a (S a ,x a )+V a+1 (S a+1 )} (3a)

[0090]

[0091] Among them, V a (S a V represents the value function of region a; a+1 (S a+1 ) represents the value function of the region a+1; C a (S a ,x a S represents the power generation cost of region a; a S represents the state variables of region a; a+1 The state variable representing region a+1; x a G represents the decision variable for region a; a (S a ,x a ,S a+1 ) represents the equality constraint in region a; h a (S a ,x a ,S a+1 ) represents the inequality constraints in region a; h a This represents the lower bound of the inequality constraints in region a; This represents the upper limit of the inequality constraints in region a.

[0092] In this embodiment, S a The boundary voltage variable of region a, g a (S a ,x a ,S a+1 This includes constraints on the flow of communication, h a (S a ,x a ,S a+1 This includes unit output constraints, voltage safety constraints, and line capacity constraints.

[0093] First, construct the following Lagrange equation. for:

[0094]

[0095] Where, λ a Represents the Lagrange multiplier of region a; μ represents the potential barrier coefficient; N a,h This indicates the number of inequality constraints.

[0096] After introducing the Karush-Kuhn-Tucker (KKT) conditions, the value function of each region sub-model is described as follows:

[0097]

[0098] For the sake of brevity, let the decision variable x of region a be... a The state variable S of region a+1 a+1 and the Lagrange multiplier λ of region a a Unified by variable ω a It means that it has been obtained.

[0099] ω a =(x a S a+1 ;λ a (6)

[0100] Then, by performing a second-order Taylor expansion on the value function, we can obtain...

[0101]

[0102] in, Region a is based on a second-order approximation function; C represents the constant term of the expansion; ΔS a and Δω a Indicates the Newtonian direction; Q a,SS Q a,Sω Q a,ωS and Q a,ωω L represents the second derivative of the expansion; a,S and L a,ω It represents the first derivative of the expansion.

[0103] The formula for calculating the derivative of an approximate function is:

[0104]

[0105]

[0106] In the formula, Indicates the current point and Expand at the location; This indicates differentiation.

[0107] Since the approximation function is only a function of the state variables, other variables besides the state variables should be eliminated in the second-order Taylor expansion (7). Using Newton's method to linearize the Karush-Kuhn-Tucker (KKT) conditions, the relationship between the state variables and other variables is obtained as follows:

[0108]

[0109] The following result can be derived from equation (9):

[0110] Δω a =Q a,ωω -1 (-L a,ω -Q a,ωS ΔS a )=aΔS a +b (10)

[0111] In the formula, a and b are both coefficient matrices.

[0112] The formulas for calculating a and b are as follows:

[0113] a = -Q a,ωω -1 Q a,ωS b = -Q a,ωω -1 L a,ω (11)

[0114] Substituting equation (10) into equation (7) to eliminate variables other than state variables and combining like terms, we get:

[0115]

[0116] In the formula, Q' a N represents the approximate value function a,S ×N a,S L' is a second-order derivative matrix. a N represents the approximate value function a,S A 1×1-dimensional first-order derivative matrix; N a,S This indicates the number of state variables.

[0117] Among them, Q' a and L' a The calculation formula is:

[0118]

[0119]

[0120] Based on the derived second-order approximation function form, we propose a distributed scheduling method based on Newton's method and approximate dynamic programming to improve the solution speed and accuracy of nonlinear AC power flow optimization scheduling problems in multi-regional power systems. The specific process is as follows:

[0121] S41. Initialize the data, let the iteration index k = 0, set the convergence values ​​ε1 > 0, ε2 > 0, the reduction coefficient σ satisfy 0 < σ < 1, and the initial value of the Lagrange multiplier λ. (0) =0, initial value of barrier coefficient μ (0) >1;

[0122] S42. Solve each region sub-model from back to front, and calculate Q'. a (k) and L' a (k) and put Q' a (k) and L' a (k) The value functions of all sub-models in all regions are solved;

[0123] Among them, Q' a (k) L' represents the second derivative matrix of the approximate function of region a in the k-th iteration; a (k) The matrix representing the first derivative of the approximate function of region a in the k-th iteration;

[0124] S43. Update the state and decision of each region sub-model from front to back, and calculate ΔS. a (k) and Δω a (k) and ΔS a+1 (k) The changes are passed to the next region, and finally, the variables in all regions are updated using a formula: The update formula is:

[0125]

[0126] in, and This represents the initial value for the (k+1)th iteration; and Denotes the initial value of the k-th iteration; ΔS a (k) and Δω a (k) Indicates the Newton direction in the k-th iteration;

[0127] S44. Determine whether the convergence criterion is met. The convergence criterion is:

[0128] μ (k) ≤ε1

[0129] ||(ΔS (k) ;Δω (k) )|| ∞ <ε2

[0130] If satisfied, terminate the program; otherwise, let k = k + 1, μ (k+1) =σ×μ (k) Repeat steps S42 to S44.

[0131] In summary, the present invention has the following advantages and beneficial effects:

[0132] 1. This invention proposes for the first time a second-order value function approximation technique based on Newton's method, which extends the information of the approximate value function from the first order to the second order, thereby improving the update efficiency and approximation accuracy of the value function.

[0133] 2. This invention proposes for the first time a distributed scheduling method based on Newton's method and approximate dynamic programming, which improves the solution speed and accuracy of large-scale nonlinear AC power flow optimization scheduling problems in multi-regional power systems.

[0134] 3. This invention improves the optimization accuracy and solution efficiency of distributed dispatching in multi-regional power systems, reduces the operating costs of power systems, and enhances the coordination and decision-making efficiency of multi-regional power systems. This aligns with the trend of regionalized development of power systems under the background of widespread access to distributed power sources, thereby bringing about good social and economic benefits.

[0135] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit disclosed in the present invention should fall within the patent scope covered by the present invention.

Claims

1. A distributed dispatching method for multi-regional power systems based on Newton's method and approximate dynamic programming, characterized in that, Includes the following steps: S1. Construct a multi-regional power system dispatch model, with the goal of minimizing power system dispatch costs. Divide the multi-regional power system dispatch model into multiple regional sub-models and determine the value function for each regional sub-model. S2. Based on Newton's method, perform a second-order Taylor expansion on the value function of each regional sub-model to obtain the approximate value function of each regional sub-model; S3. Calculate the derivative of the approximate function of each regional sub-model in the multi-regional power system dispatch model, and obtain the second-order derivative matrix and the first-order derivative matrix of the approximate function of each regional sub-model; S4. An approximate dynamic programming method based on Newton's method is adopted to update the approximate function of each regional sub-model, obtain the optimal scheduling strategy of the multi-regional power system scheduling model, and schedule the power system according to the optimal scheduling strategy. The multi-regional power system dispatch model aims to minimize generator operating costs while satisfying unit output constraints, voltage safety constraints, line capacity constraints, and AC power flow constraints. The objective function is: ； In the formula, Represents a set of generators; a g b g and c g This represents the power generation cost coefficient of generator g; This represents the active power output of generator g; The constraints are: ； In the formula, and These represent the lower and upper limits of the active power output of generator g, respectively. This represents the reactive power output of generator g; and These represent the lower and upper limits of the reactive power output of generator g, respectively. Represents a set of nodes; e i and f i V represents the real and imaginary parts of the voltage phasor at node i, respectively; i,min and V i,max These represent the lower and upper limits of the voltage amplitude at node i, respectively; P ij,max G represents the upper limit of line transmission capacity for line ij; ij and B ij Let represent the real and imaginary parts of the nodal admittance matrix, respectively; and These represent the active load and reactive load of node i, respectively; This represents the ig-th element of the node-generator association matrix.

2. The distributed dispatching method for multi-regional power systems based on approximate dynamic programming using Newton's method according to claim 1, characterized in that, The multi-regional power system dispatch model is divided into multiple regional sub-models, and the value function for each regional sub-model is determined as follows: S11. Divide the multi-regional power system dispatch model into n regional sub-models according to geographical zoning; S12. Arbitrarily determine a regional decision-making sequence to transform the multi-regional power system dispatching problem into a multi-stage decision-making process; S13. The value function and constraints for each region's sub-model are as follows: ； ； in, The function representing the value of region a; The function representing the value of region a+1; This represents the power generation cost of region a; Represents the state variables of region a; Represents the state variables of region a+1; The decision variables for region a; Represents the equality constraints in region a; Represent the inequality constraints for region a; This represents the lower bound of the inequality constraints in region a; This represents the upper limit of the inequality constraints in region a.

3. The distributed dispatching method for multi-regional power systems based on approximate dynamic programming using Newton's method according to claim 2, characterized in that, To obtain approximate functions for each regional sub-model, a Lagrange equation is constructed. for: ； in, Denote the Lagrange multipliers of region a; Represents the potential barrier coefficient; This indicates the number of inequality constraints.

4. The distributed dispatching method for multi-regional power systems based on approximate dynamic programming using Newton's method according to claim 3, characterized in that, After introducing the Kuhn-Tak condition, the value function of each regional sub-model is described as follows: ； In the formula, This represents the Kuhn-Tak condition for the Lagrange equation.

5. The distributed dispatching method for multi-regional power systems based on approximate dynamic programming using Newton's method according to claim 4, characterized in that, Decision variables for region a The state variables of region a+1 Lagrange multipliers of region a Unified by variables It means that it has been obtained. .

6. The distributed dispatching method for multi-regional power systems based on approximate dynamic programming using Newton's method according to claim 5, characterized in that, Performing a second-order Taylor expansion on the value function yields the approximate value function as follows: ； In the formula, Region a is based on a second-order approximation function; C represents the constant term of the expansion; and Indicates Newtonian direction; , , and The second derivative of the expansion; and It represents the first derivative of the expansion.

7. The distributed dispatching method for multi-regional power systems based on approximate dynamic programming using Newton's method according to claim 6, characterized in that, The formula for calculating the derivative of an approximate function is: ； ； In the formula, Indicates the current point and Expand at the location; To express differentiation; The approximation function is only a function of the state variables; other variables besides the state variables should be eliminated in the second-order Taylor expansion.

8. The distributed dispatching method for multi-regional power systems based on approximate dynamic programming using Newton's method according to claim 7, characterized in that, Linearizing the Kuhn-Tak conditions using Newton's method yields the following relationship between the state variables and other variables: ； The result derived from the relationship between the state variable and other variables is: ； In the formula, a and b are both coefficient matrices; The formula for calculating 'a' is: ； The formula for calculating b is: ； In the second-order approximation function based on Newton's method, by eliminating variables other than the state variable and combining like terms, we obtain: ； In the formula, N represents the approximate function a,S ×N a,S 2D second-order derivative matrix; N represents the approximate function a,S A 1×1-dimensional first-order derivative matrix; N a,S Indicates the number of state variables; in, The calculation formula is: ； The calculation formula is: 。 9. The distributed dispatching method for multi-regional power systems based on approximate dynamic programming using Newton's method according to claim 8, characterized in that, The approximate dynamic programming method based on Newton's method is as follows: S41. Initialize the data, let the iteration index k=0, set the convergence values ​​ε1 > 0, ε2 > 0, the reduction coefficient σ satisfy 0 < σ < 1, and the initial value of the Lagrange multiplier λ. (0) = 0, initial value of barrier coefficient μ (0) > 1; S42. Solve each region sub-model from back to front, and calculate Q'. a (k) and L' a (k) and put Q' a (k) and L' a (k) The value functions of all sub-models in all regions are solved; Among them, Q' a (k) L' represents the second derivative matrix of the approximate function of region a in the k-th iteration; a (k) The matrix representing the first derivative of the approximate function of region a in the k-th iteration; S43. Update the state and decision of each region sub-model from front to back, and calculate ΔS. a (k) and Δ a (k) and ΔS a+1 (k) The changes are passed to the next region, and finally, the variables in all regions are updated using a formula: The update formula is: ； in, and This represents the initial value for the (k+1)th iteration; and Denotes the initial value of the k-th iteration; ΔS a (k) and Δ a (k) Indicates the Newton direction in the k-th iteration; S44. Determine whether the convergence criterion is met. The convergence criterion is: ； ； If satisfied, terminate the program; otherwise, let k = k + 1, μ (k+1) =σ× μ (k) Repeat steps S42 to S44.

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