A multi-objective reactive power optimization scheduling method based on an improved normalization method and plane constraint method

Abstract

The present invention discloses a multi-objective reactive power optimization scheduling method based on an improved normalization method and a plane constraint method. First, a three-objective reactive power optimization model of a power system that meets the constraint conditions and determines the minimization of network losses, the minimization of the action times of reactive power equipment, and voltage qualification is established. Then, according to the multi-objective optimization model, the three objective functions are optimized respectively to obtain the optimal solutions, which are normalized and a utopia plane is constructed. Points uniformly distributed are generated inside the triangle on the utopia plane, and new points are added between the triangle and the boundary curve at the same time, and the Pareto optimal points inside and outside the boundary curve of the utopia plane are solved. Finally, a compromise solution is selected on the complete Pareto front of the three-objective optimization problem as the final scheduling strategy. The present invention can not only effectively solve the multi-objective optimization problem of the power grid, but also obtain a complete Pareto front with uniform distribution, which is beneficial to improving the scientificity of the decision-making of dispatchers.

Description

Technical Field

[0001] The present invention belongs to the technical field of reactive power optimization of power systems, and particularly relates to a multi-objective reactive power optimization scheduling method based on an improved normalized normal constraint method Background Art

[0002] Reactive power optimization of power systems is an effective means to ensure the safe and economic operation of the system and is one of the important measures to improve the voltage quality of power systems. The so-called reactive power optimization means that when the structural parameters and load conditions of the system are determined, by optimizing certain control variables, the system can adjust reactive power to make one or some performance indicators of the system reach the optimal value on the basis of satisfying all given constraint conditions. The power system is a large-scale, time-varying complex system and is a very important basic industry in the national economy. With the development of the power industry, the scale of the power system is getting larger and larger, and the safety, reliability and economy of the system have received more and more attention.

[0003] In the single-objective reactive power optimization problem, only one objective function is considered, that is, only the optimal value of a single objective can be achieved. However, in engineering applications, considering a single objective often cannot meet the actual needs. Therefore, the proposal of multi-objective problems is of great significance for solving practical problems. Different from single-objective problems, in the fields of scientific research and practice, there are often mutual constraints among the decision variables of multiple objectives. Optimizing one of the objectives often comes at the expense of other objectives. As a result, multiple objective values cannot reach the optimal at the same time, and there is only a set of compromise solutions, that is, the Pareto solution set. The multi-objective optimization method based on Pareto can solve some objectives that cannot reach the optimal at the same time for decision-makers.

[0004] The normalized normal constraint (NNC) method is to transform the multi-objective optimization problem into the problem of solving the Pareto front optimal point corresponding to each equally spaced division point by making a normal line at each equally spaced division point on the utopia line in the solution space of the normalized objective function, and obtain a relatively evenly distributed Pareto solution set. However, since points are only evenly taken inside the triangle on the utopia plane, the Pareto front obtained by projecting these points along the normal direction of the utopia plane is incomplete. Therefore, the present invention proposes an improved normalized normal constraint algorithm to obtain a complete Pareto front. Summary of the Invention

[0005] Object of the Invention: The present invention aims to solve the above prior art problems and proposes a multi-objective reactive power optimization method for power systems based on an improved normalized normal constraint algorithm to obtain a complete Pareto front with uniform distribution.

[0006] Technical solution: To solve the above problems, the present invention proposes a multi-objective reactive power optimization scheduling method based on an improved normalized method plane constraint algorithm, and the method includes the following steps:

[0007] Step 1, establish a three-objective reactive power optimization model of the power system that satisfies the constraint conditions for minimizing the network loss, minimizing the number of operations of reactive power equipment, and voltage qualification of the power system;

[0008] Step 2, according to the multi-objective optimization model, optimize the three objective functions respectively to obtain the optimal solution, normalize it, and construct the utopia plane;

[0009] Step 3, generate uniformly distributed points inside the triangle on the utopia plane, add points between the triangle and the boundary curve, and solve the Pareto optimal points inside and outside the boundary curve of the utopia plane;

[0010] Step 4, select a compromise solution based on the complete Pareto front of the three-objective optimization problem in Step 3 as the final scheduling strategy.

[0011] Furthermore, the specific method of Step 1 is as follows:

[0012] Select the minimum total loss in the actual network in a day as the first objective function f1, which is expressed as:

[0013]

[0014] where P loss is the actual power loss of the system; N is the total number of network branches; G ij is the conductance of branch ij; V i , V j are the voltages at nodes i and j respectively; θ ij is the voltage phase difference between nodes i and j;

[0015] Introduce a membership function to represent the voltage of node i at time t;

[0016]

[0017] where V i (t) is the voltage of node i at time t; V B0 and V G0 are the unacceptable voltage limits respectively, V B1 and V G1 are the acceptable voltage limits respectively; f Vi(t) is the range of deviation of the voltage of node i from the expected value;

[0018] Take the voltage qualification index of the entire system every day as the second objective function f2, which is expressed as:

[0019]

[0020] Taking the number of switching operations of the system OLTC and capacitors in a day as the third objective function f3, it is expressed as:

[0021]

[0022] In the formula, T m (t) is the tap position of the m-th OLTC at time t, X l (t) is the state of the l-th capacitor at time t, is the exclusive OR operation. When X l (t) ≠ X l (t - 1), When X l (t) = X l (t - 1), N T is the number of OLTCs in the system; N C is the number of capacitor banks in the system;

[0023] The relevant operating constraints for establishing the multi-objective reactive power optimization model are as follows:

[0024] 1) Power flow balance constraint

[0025]

[0026] In the formula, P Gi is the active power output of generator i; Q Gi is the active power output of the i-th generator; P Li is the active power load of the i-th node; Q Li is the reactive power load of the i-th node; V i is the voltage amplitude of the i-th node, V j is the voltage amplitude of the j-th node; G ij is the conductance of branch ij; B ij is the susceptance of branch ij; θ ij is the voltage phase angle between node i and node j; N is the number of nodes in the system;

[0027] 2) Inequality constraint

[0028]

[0029] In the formula, T i is the tap position of the i-th OLTC; Q Ci is the reactive power output of capacitor bank i; V Gi is the voltage amplitude of generator i; N T is the number of OLTCs in the system; N GThe number of generators in the system; N C The number of capacitor banks in the system; N is the number of nodes in the system; T imin 、T imax Are the lower and upper limits of the tap position of the i-th OLTC respectively; V iB0 、V iG0 Are the lower and upper limits of unacceptable voltage respectively; Q Gimin 、Q Gimax Are the lower and upper limits of the active power output of generator i respectively; Q Cimin 、Q Cimax Are the lower and upper limits of the reactive power output of capacitor bank i respectively; V Gimin 、V Gimax Are the lower and upper limits of the voltage amplitude of generator i respectively;

[0030] 3) Reactive power compensation equipment operation constraints

[0031]

[0032] In the formula, K T Is the maximum number of allowable tap operations per day; M T Is the maximum number of allowable tap operations per continuous hour; K C Is the maximum number of allowable switch operations per day per capacitor bank;

[0033] The multi-objective reactive power optimization model is:

[0034]

[0035] Furthermore, the specific method of step 2 is as follows:

[0036] When performing single-objective optimization considering only the minimum active power loss f1 of the power system, the optimal solution x 1* is obtained. Substitute the optimal solution x 1* into the other two objective functions to obtain the function values f2(x 1* ), f3(x 1* ). At this time, the endpoint coordinates corresponding to the three objective functions in the space coordinate system are f 1* (f1(x 1* ), f2(x 1* ), f3(x 1* ). Similarly, perform single-objective optimization on the other two objective functions respectively to obtain the optimal solutions when only considering the minimum of f2 and f3 respectively, and the corresponding endpoint coordinates in the space coordinate system are: f 2* (f1(x 2* ), f2(x 2* ), f3(x 2* )) and f 3* (f1(x3* ), f2(x 3* ), f3(x 3* ))), the plane formed by connecting the above three endpoints is called the utopia plane, and the Pareto front corresponds to the part between the utopia plane and the utopia point on the boundary surface of the feasible region in the objective function space;

[0037] Normalize the three objective functions so that their values are between [0, 1];

[0038]

[0039]

[0040]

[0041]

[0042] f1 N = max{f1(x 1* ), f1(x 2* ), f1(x 3* )} (13)

[0043]

[0044] f3 N = max{f3(x 1* ), f3(x 2* ), f3(x 3* )} (15)

[0045] In the formula, is the utopia point; is the preset worst point; is the solution space of the normalized objective function;

[0046] The three endpoints of the normalized utopia plane are

[0047] Furthermore, in step 3, assume that the N1 vector is from the point to the point The N2 vector is from the point to the point The N3 vector is from the point to the point First, take j uniformly distributed points p j in the triangle on the utopia plane, which is expressed as:

[0048]

[0049] Among them, β 1j= {0, 1 / 5, 2 / 5, 3 / 5, 4 / 5, 1}, β 2j = {0, 1 / 5, 2 / 5,..., 1 - β 1j}, β 3j = 1 - β 1j -β 2j , then determine the points taken in the feasible region part of the objective function outside the utopia surface triangle. The specific method of taking points is as follows: Let the distance of the equally divided points on the side be μ, draw perpendiculars at the points taken on the three sides of the triangle, and take an additional point every μ on the perpendiculars. If the newly added point is within the boundary curve where the utopia surface intersects the feasible region in the objective function space, it is the required newly added point, denoted as p k , through the point p j make a plane α1 perpendicular to the vector N1 and a plane α2 perpendicular to the vector N2, that is, α1⊥N1 and α2⊥N2. The above two planes divide the feasible region of the objective function space into the spatial feasible region and the spatial feasible region after adding constraints between the two planes. Solve the minimum value problem of f3 in the spatial feasible region after adding constraints through the solution model to obtain the point p j and the point p k corresponding points on the Pareto front, and denote the corresponding points on the Pareto front together as μ n , and, take μ n as the candidate operating points. The solution model is:

[0050]

[0051] In the formula, are the transposes of the vectors N i respectively; p j is the uniformly taken point within the utopia surface.

[0052] Furthermore, in step 4, calculate and compare the increments of each candidate operating point relative to the utopia point in the target direction, and take the candidate operating point with the smallest sum of squares of the increments in each direction as the fair compromise solution, and obtain the generator unit output plan and the action plan of the reactive power compensation equipment as the final scheduling decision.

[0053] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0054] The proposed method for solving the complete Pareto front overcomes the deficiency of the traditional method of only taking points inside the triangle on the utopia surface. By adding uniformly taken points between the outside of the triangle and the boundary curve of the utopia surface, the complete Pareto front can be solved, providing more complete decision-making information for decision-makers and being beneficial to improving the scientificity of the decision-making of dispatchers. Brief description of the drawings

[0055] Figure 1 is the flow chart of the method of the present invention.

[0056] Figure 2 It is a utopia surface illustration diagram.

[0057] Figure 3 It is a schematic diagram for solving the Pareto front.

[0058] Figure 4 It is a new point-taking diagram for solving the complete Pareto front.

[0059] Figure 5 It is a diagram of the IEEE 30-node test case.

[0060] Figure 6 It is a typical daily load curve diagram.

[0061] Figure 7 It is a complete Pareto front diagram.

[0062] Figure 8 It is a diagram of the number of operations of reactive power equipment. Specific implementation manners

[0063] As Figure 1 shown, the present invention proposes a multi-objective reactive power optimization scheduling method based on an improved normalized method plane constraint algorithm, and the method includes the following steps:

[0064] Step 1: Establish a three-objective reactive power optimization model of the power system that satisfies the constraint conditions for determining the minimum network loss, the minimum number of operations of reactive power equipment, and the voltage qualification of the power system;

[0065] Step 2: According to the multi-objective optimization model, optimize the three objective functions respectively to obtain the optimal solutions, normalize them, and construct a utopia plane;

[0066] Step 3: Generate uniformly distributed points inside the triangle on the utopia plane, add new points between the triangle and the boundary curve, and solve the Pareto optimal points inside and outside the boundary curve of the utopia plane;

[0067] Step 4: Select a compromise solution based on the complete Pareto front of the three-objective optimization problem in Step 3 as the final scheduling strategy.

[0068] Furthermore, the specific method of Step 1 is as follows:

[0069] Select the minimum total loss in the actual network in a day as the first objective function f1, which is expressed as:

[0070]

[0071] In the formula, P loss is the actual power loss of the system; N is the total number of network branches; G ij is the conductance of branch ij; Vi , V j are the voltages at nodes i and j respectively; θ ij is the voltage phase difference between nodes i and j;

[0072] A membership function is introduced to represent the voltage of node i at time t;

[0073]

[0074] In the formula, V i (t) is the voltage of node i at time t; V B0 and V G0 are the unacceptable voltage limits respectively, and V B1 and V G1 are the acceptable voltage limits respectively; f Vi(t) is the range of the voltage deviation of node i from the expected value;

[0075] Taking the daily voltage qualification index of the entire system as the second objective function f2, it is expressed as:

[0076]

[0077] Taking the number of switching operations of the system OLTC and capacitors during a day as the third objective function f3, it is expressed as:

[0078]

[0079] In the formula, T m (t) is the tap position of the m-th OLTC at time t, and X l (t) is the state of the l-th capacitor at time t, is the exclusive OR operation. When X l (t) ≠ X l (t - 1), When X l (t) = X l (t - 1), N T is the number of OLTCs in the system; N C is the number of capacitor banks in the system;

[0080] The relevant operation constraints for establishing the multi-objective reactive power optimization model are as follows:

[0081] 1) Power flow balance constraint

[0082]

[0083] In the formula, P Gi is the active power output of generator i; Q Gi is the active power output of the i-th generator; PLi is the active power load of the i-th node; Q Li is the reactive power load of the i-th node; V i is the voltage magnitude of the i-th node, V j is the voltage magnitude of the j-th node; G ij is the conductance of branch ij; B ij is the susceptance of branch ij; θ ij is the voltage phase angle between node i and node j; N is the number of nodes in the system;

[0084] 2) Inequality constraints

[0085]

[0086] In the formula, T i is the tap position of the i-th OLTC; Q Ci is the reactive power output of capacitor bank i; V Gi is the voltage magnitude of generator i; N T is the number of OLTCs in the system; N G is the number of generators in the system; N C is the number of capacitor banks in the system; N is the number of nodes in the system; T imin 、T imax are the lower and upper limits of the tap position of the i-th OLTC respectively; V iB0 、V iG0 are the lower and upper limits of the unacceptable voltage respectively; Q Gimin 、Q Gimax are the lower and upper limits of the active power output of generator i respectively; Q Cimin 、Q Cimax are the lower and upper limits of the reactive power output of capacitor bank i respectively; V Gimin 、V Gimax are the lower and upper limits of the voltage magnitude of generator i respectively;

[0087] 3) Reactive power compensation equipment operation constraints

[0088]

[0089] In the formula, K T is the maximum number of tap operations allowed per day; M T is the maximum number of tap operations allowed per continuous hour; K C is the maximum number of switch operations allowed per day for each capacitor bank;

[0090] The multi-objective reactive power optimization model is:

[0091]

[0092] Further, the specific method for step 2 is as follows:

[0093] When performing single-objective optimization considering only the minimum active power loss f1 of the power system, the optimal solution x is obtained 1* , and substitute the optimal solution x 1* into the other two objective functions to obtain the function values f2(x 1* ), f3(x 1* ). At this time, the endpoint coordinates corresponding to the three objective functions in the space coordinate system are f 1* (f1(x 1* ), f2(x 1* ), f3(x 1* ))). Similarly, perform single-objective optimization on the other two objective functions respectively to obtain the optimal solutions when only considering the minimum of f2 and f3 respectively, and the corresponding endpoint coordinates in the space coordinate system are: f 2* (f1(x 2* ), f2(x 2* ), f3(x 2* )) and f 3* (f1(x 3* ), f2(x 3* ), f3(x 3* ))). Connecting the above three endpoints to obtain a plane is called the utopia plane, and the Pareto front corresponds to the part of the boundary surface of the feasible region in the objective function space that lies between the utopia plane and the utopia point;

[0094] Normalize the three objective functions so that their values are between [0, 1];

[0095]

[0096]

[0097]

[0098]

[0099] f1 N = max{f1(x 1* ), f1(x 2* ), f1(x 3* )} (13)

[0100]

[0101] f3 N = max{f3(x 1* ), f3(x 2* ), f3(x 3* )} (15)

[0102] In the formula, is the utopia point; is the preset worst point; is the normalized objective function solution space;

[0103] The three endpoints of the normalized utopia surface are

[0104] Furthermore, in step 3, assume that the N1 vector is the point pointing to the point The N2 vector is the point pointing to the point The N3 vector is the point pointing to the point First, take j uniformly distributed points p j in the triangle on the utopia plane, which are expressed as:

[0105]

[0106] where, β 1j ={0, 1 / 5, 2 / 5, 3 / 5, 4 / 5, 1}, β 2j ={0, 1 / 5, 2 / 5,..., 1 - β 1j}, β 3j =1 - β 1j - β 2j . Then, determine the points taken in the feasible region part of the objective function outside the utopia plane triangle. The specific method of taking points is as follows: Let the distance of the equally divided points on the side be μ. Draw perpendicular lines on the points taken on the three sides of the triangle, and take an additional point every μ on the perpendicular lines. If the new point is within the boundary curve where the utopia plane intersects the feasible region in the objective function space, it is the required new point, denoted as p k . Pass a plane α1 perpendicular to the vector N1 and a plane α2 perpendicular to the vector N2 through the point p j , that is, α1⊥N1 and α2⊥N2. The above two planes divide the feasible region of the objective function space into the spatial feasible region and the spatial feasible region with constraints added between the two planes. Solve the minimum value problem of f3 through the solution model in the spatial feasible region with constraints added to obtain the points on the Pareto front corresponding to the point p j and the point p k . Denote the points on the corresponding Pareto front together as μ n . And, regard all μ n as candidate operating points. The solution model is:

[0107]

[0108] In the formula, are the transposes of the vectors N i respectively; pj Uniformly sampling points within the utopia plane.

[0109] Furthermore, in step 4, calculate and compare the increments of each candidate operating point relative to the utopia point in the target direction, and take the candidate operating point with the minimum sum of squares of the increments in each direction as the fair compromise solution, obtaining the generator unit output plan and the action plan of the reactive power compensation equipment as the final scheduling decision.

[0110] Case study

[0111] The present invention adopts Figure 5 The IEEE 30-node system case shown, including 6 generators, 4 OLTCs with a tap step of 0.9 + 16×0.0125, and 1 capacitor bank each at buses 10 and 24. All parameters in the case study are in per-unit values, the base capacity is 100 MVA, the acceptable voltage range is [1.00 p.u, 1.05 p.u], and the unacceptable voltage range is [0.98 p.u, 1.07 p.u]. At the same time, the maximum number of allowed operations of the OLTC per day is 12 times, and the maximum number of allowed switchings of the capacitor bank per day is 10 times. Figure 6 It is a typical daily load curve for predicting load changes. This description is implemented through the GAMS optimization platform and solved using the CONOPT solver.

[0112] Based on this case, the values of β in the present invention are respectively:

[0113] β 1j ={0, 1 / 5, 2 / 5, 3 / 5, 4 / 5, 1}, β 2j ={0, 1 / 5, 2 / 5,..., 1 - β 1j}, β 3j = 1 - β 1j - β 2j , a total of 21 points are sampled inside the utopia plane triangle, and 18 points are sampled outside the triangle. The obtained Pareto front is as Figure 7 . Calculate and compare the increments of each point relative to the ideal point in the target direction, and take the operating point with an increment ratio close to 1 as the fair compromise solution. The comparison between the compromise optimal solution scheduling scheme and the single-objective optimal solution scheduling scheme is shown in Table 1. It can be seen that compared with the single-objective optimal solution, the compromise solution has a higher degree of optimization and is more scientific.

[0114] Table 1 Comparison of single-objective and compromise solutions for the IEEE 30-node system

[0115]

[0116] The present invention provides more options for users to schedule the tap position of the OLTC and the status of shunt capacitors based on daily load forecasting. Compared with the initial state of the power grid, after reactive power optimization measures, the network loss is greatly reduced, the voltage quality is significantly improved after network loss optimization, and the economy, safety and stability of the system are improved.

[0117] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A multi-objective reactive power optimal scheduling method based on an improved normalized method plane constraint algorithm, characterized in that It includes the following steps: Step 1: Establish a three-objective reactive power optimization model of the power system that satisfies the constraints of minimizing the network loss of the power system, minimizing the operation times of reactive power equipment, and voltage qualification. Step 2: According to the multi-objective optimization model, optimize the three objective functions respectively to obtain the optimal solutions, normalize them, and construct the utopia plane. Step 3: Generate uniformly distributed points inside the triangle on the utopia plane, add points between the triangle and the boundary curve, and solve the Pareto optimal points inside and outside the boundary curve of the utopia plane. Step 4: Select a compromise solution based on the complete Pareto front of the three-objective optimization problem in Step 3 as the final scheduling strategy. In Step 1, select the minimum total loss in the actual network in a day as the first objective function f1, which is expressed as: Where, P loss is the actual power loss of the system; N is the total number of network branches; G ij is the conductance of branch ij; V i , V j are the voltages at nodes i and j respectively; θ ij is the voltage phase difference between nodes i and j; Introduce a membership function to represent the voltage of node i at time t. Where, V i (t) is the voltage of node i at time t; V B0 and V G0 are respectively the unacceptable bounds of voltage, V B1 and V G1 are respectively the acceptable bounds of voltage; f Vi(t) is the range of deviation of the voltage of node i from the expected value; Take the voltage qualification index of the whole system every day as the second objective function f2, which is expressed as: Take the switching operation times of the OLTC and capacitors in the system in a day as the third objective function f3, which is expressed as: Where, T m (t) is the tap position of the m-th OLTC at time t, X l (t) is the state of the first capacitor at time t, is the exclusive OR operation. When X l (t) ≠ X l (t - 1), When X l (t) = X l (t - 1), N T is the number of OLTCs in the system; N C is the number of capacitor banks in the system.

2. The multi-objective reactive power optimization scheduling method based on the improved normalization method plane constraint algorithm according to claim 1, characterized in that The constraints in Step 1 are as follows: The relevant operation constraints for establishing the multi-objective reactive power optimization model are as follows: 1) Power flow balance constraint Where, P Gi is the active power output of generator i; Q Gi is the active power output of the i-th generator; P Li is the active power load of the i-th node; Q Li is the reactive power load of the i-th node; V i is the voltage magnitude of the i-th node, V j is the voltage magnitude of the j-th node; G ij is the conductance of branch ij; B ij is the susceptance of branch ij; θ ij is the voltage phase angle between node i and node j; N is the number of nodes in the system; 2) Inequality constraint where T i is the tap of the i-th OLTC; Q Ci is the reactive power output of capacitor bank i; V Gi is the voltage magnitude of generator i; N T is the number of OLTCs in the system; N G is the number of generators in the system; N C is the number of capacitor banks in the system; N is the number of nodes in the system; T imin and T imax are the lower and upper limits of the tap of the i-th OLTC respectively; V iB0 and V iG0 are the lower and upper limits of unacceptable voltage respectively; Q Gimin and Q Gimax are the lower and upper limits of the active power output of generator i, respectively; Q Cimin and Q Cimax are respectively the lower limit and the upper limit of the reactive power output by the capacitor bank i; V Gimin and V Gimax are the lower and upper limits of the voltage amplitude of generator i, respectively; 3) Reactive power compensation equipment operation constraint Where K T is the maximum number of tap operations allowed per day; M T is the maximum number of tap operations allowed per continuous hour; K C is the maximum number of switch operations allowed per capacitor bank per day; The multi-objective reactive power optimization model is:

3. A multi-objective reactive power optimal scheduling method based on an improved normalization method plane constraint algorithm according to claim 2, characterized in that, The specific method of Step 2 is as follows: When performing single-objective optimization considering only the minimum active power loss f1 of the power system, the optimal solution x is obtained. 1* Substitute the optimal solution x 1* into the other two objective functions to obtain the function values f2(x 1* ), f3(x 1* ). At this time, the endpoint coordinates of the corresponding three objective functions in the space coordinate system are f 1* (f1(x 1* ), f2(x 1* ), f3(x 1* ))). Similarly, perform single-objective optimization on the other two objective functions respectively to obtain the optimal solutions when only considering the minimum of f2 and f3. The corresponding endpoint coordinates in the space coordinate system are: f 2* (f1(x 2* ), f2(x 2* ), f3(x 2* )) and f 3* (f1(x 3* ), f2(x 3* ), f3(x 3* ))). The plane formed by connecting the above three endpoints is called the utopia plane. The Pareto front corresponds to the part of the boundary surface of the feasible region in the objective function space that lies between the utopia plane and the utopia point. Perform per-unit processing on the three objective functions to make their values between [0, 1]. f1 N = max{f1(x 1* ), f1(x 2* ), f1(x 3* )}(13) In the formula, is the utopia point; is the preset worst point; is the per-unitized solution space of the objective function; The three endpoints of the per-unit utopia plane are 4. A multi-objective reactive power optimal scheduling method based on an improved normalization method plane constraint algorithm according to claim 3, characterized in that, In step 3, assume that the N1 vector is the point pointing to the point The N2 vector is the point pointing to the point The N3 vector is the point pointing to the point First, take j uniformly distributed points p in the triangle on the utopia plane j , expressed as: Among them, β 1j = {0, 1 / 5, 2 / 5, 3 / 5, 4 / 5, 1}, β 2j = {0, 1 / 5, 2 / 5,..., 1 - β 1j}, β 3j = 1 - β 1j - β 2j , then determine the points taken in the feasible region part of the objective function outside the utopia surface triangle. The specific method for taking points is as follows: Let the distance of the equally divided points on the side be μ, draw perpendiculars at the points taken on the three sides of the triangle, and take an additional point every μ on the perpendiculars. If the additional point is within the boundary curve where the utopia surface intersects the feasible region in the objective function space, it is the required additional point, denoted as p k . Pass a plane α1 perpendicular to the vector N1 and a plane α2 perpendicular to the vector N2 through the point p j , that is, α1⊥N1 and α2⊥N2. The above two planes divide the feasible region of the objective function space into the spatial feasible region and the spatial feasible region with constraints added between the two planes. Solve the minimum value problem of f3 by solving the model within the spatial feasible region with constraints added to obtain the points p j and the points on the Pareto front corresponding to the point p k . Denote the points on the corresponding Pareto front together as μ n . And, take all μ n as candidate operating points. The model to be solved is: In the formula, are respectively the transposes of the vector N i ; p j is the uniformly sampled point within the utopia plane.

5. A multi-objective reactive power optimization scheduling method based on an improved normalized method plane constraint algorithm according to claim 4, characterized in that, In Step 4, calculate and compare the increments of each candidate operating point relative to the utopia point in the target direction, and take the candidate operating point with the minimum sum of the squares of the increments in each direction as the fair compromise solution, and obtain the generator unit output plan and the operation plan of the reactive power compensation equipment as the final scheduling decision.

Images