A refined identification method for critical hyperplanes at the boundary of static safety domain of distribution network

Abstract

The invention discloses a method for fine identification of critical hyperplanes of the boundary of a static safety domain of a distribution network. The method mainly comprises the following steps: 1) defining a static safety domain of a distribution network in a complex power injection space; 2) generating a rough hyperplane of the boundary of the safety domain of the distribution network; 3) providing an initial operating point and an engineering practical boundary; 4) providing a strict criterion for determining whether a safety domain boundary hyperplane is a critical hyperplane; 5) preliminarily selecting the safety domain boundary hyperplane; 6) defining a search frontier of a critical hyperplane of the safety domain boundary and initializing it; 7) searching and judging the critical hyperplane; 8) correcting the critical hyperplane of the safety domain boundary based on power flow calculation; 9) verifying the critical hyperplane and providing a final identification result. The method can perform fine identification in a large number of safety domain boundary hyperplanes corresponding to all node voltage constraints and branch power flow constraints of the distribution network, obtain a few critical hyperplanes, and thus improve the calculation speed of solving the optimization problem.

Description

Technical field:

[0001] The present invention belongs to the field of distribution network security analysis, and in particular relates to a method for fine-tuning the critical hyperplane identification of the boundary of a static security domain of a distribution network. Background technology:

[0002] The safety region method is of great significance in power system analysis and will bring advantages in many aspects such as computational efficiency and visualization. Existing research has proposed the concept of static safety region of distribution network in complex power injection space, given a fast calculation method of the safety region boundary, and applied it to the operation optimization of power system. Research shows that the safety region method can optimize the dispatching of transmission and distribution network. [1] and risk assessment [2] The calculation speed is increased by several orders of magnitude. The prerequisite for achieving such superior results is to be able to finely identify the key hyperplane of the safety zone boundary.

[0003] The static safety domain of the distribution network is obtained by finding the intersection of the space surrounded by the static voltage safety domain that satisfies the node voltage constraint, the thermal stability safety domain that satisfies the branch flow constraint, and the engineering practical boundary that represents the value range of the node injection power in the complex power injection space. In other words, the boundary of the static safety domain of the distribution network starts from the initial operating point and continuously expands outward. The boundary corresponding to the node voltage limit or the thermal stability limit of the branch flow that is reached for the first time, together with the continuity of the flow relationship, can be judged: There are no holes inside the static safety domain of the distribution network. Within the scope of the engineering practical boundary, the boundary of the static safety domain of the distribution network can be approximately described by a few hyperplanes, which are referred to as the key hyperplanes of the boundary of the static safety domain of the distribution network in the present invention. The above characteristics of the static safety domain of the distribution network are an important basis for developing a refined identification method for the key hyperplane of the boundary of the static safety domain of the distribution network. Summary of the invention:

[0004] In view of the problems existing in the prior art, the present invention provides a method for fine-grained identification of key hyperplanes at the boundary of the static safety domain of a distribution network. The method can perform fine-grained identification among a large number of static safety domain boundary hyperplanes corresponding to all node voltage constraints and branch flow constraints of the distribution network, and obtain a few key hyperplanes. By compressing the scale of the distribution network optimization scheduling problem, the speed of solving the optimization scheduling problem is improved, thereby ensuring the efficient operation of the distribution network.

[0005] The present invention solves the practical problem by adopting the following technical solutions:

[0006] A refined identification method for critical hyperplanes at the boundary of static safety domain of distribution network.

[0007] 1) Define the static security domain of complex power injection spatial distribution network;

[0008] 2) Generate a rough hyperplane of the static safety domain boundary of the distribution network;

[0009] 3) Given the initial operating point and engineering practical boundary;

[0010] 4) Provide a strict criterion for determining whether the boundary hyperplane of the static safety domain of the distribution network is a critical hyperplane;

[0011] 5) Preliminary selection of the boundary hyperplane of the static safety domain of the distribution network;

[0012] 6) Define the search frontier of the critical hyperplane of the static safety domain boundary of the distribution network and initialize it;

[0013] 7) Search and judge the key hyperplane of the static safety domain boundary of the distribution network;

[0014] 8) Correct the critical hyperplane of the static safety domain boundary of the distribution network based on power flow calculation;

[0015] 9) Verify the critical hyperplane of the static safety domain boundary of the distribution network and give the final identification result.

[0016] Furthermore, in step 2), the static safety domain boundary of the distribution network is generated in the form of a hyperplane, including a rough hyperplane of the static voltage safety domain boundary and a rough hyperplane of the thermal stability safety domain boundary, wherein:

[0017] 2.1. The rough hyperplane of the static voltage safety region boundary is

[0018]

[0019] Where: P i and Q i denote the active power injection and reactive power injection of node i respectively, and They represent the coefficients corresponding to the active power injection and reactive power injection of node i in the hyperplane expression of the static voltage safety region boundary of the distribution network corresponding to the voltage upper limit of node k, respectively. Node k and node i are both elements in the node set N except the root node in the distribution network. and They respectively represent the coefficients corresponding to the active power injection and reactive power injection of node i in the hyperplane expression of the boundary of the static voltage safety region of the distribution network corresponding to the voltage lower limit of node k;

[0020] 2.2. The rough hyperplane of the thermal stability safety region boundary is

[0021]

[0022] Where: and Respectively represent a line l in the distribution network jh The coefficients corresponding to the active power injection and reactive power injection of node i in the hyperplane expression of the thermal stability safety region boundary corresponding to the forward power flow are: and Respectively represent line l jh The coefficients corresponding to the active power injection and reactive power injection of node i in the hyperplane expression of the thermal stability safety region boundary corresponding to the reverse power flow.

[0023] Further, step 5) preliminarily selects the hyperplane of the static safety domain boundary of the distribution network to determine whether the rough hyperplane of the static safety domain boundary of the distribution network obtained in step 2) can penetrate the hypercube Φ formed by the engineering practical boundary in step 3):

[0024] make and The two most extreme operating points on the hypercube Φ that represents the engineering practical boundary of node injection, where the superscript M represents the maximum limit of node injection power and the subscript m represents the minimum limit of node injection power; the vector z is calculated as follows:

[0025]

[0026]

[0027] Assume that the distribution network has n+1 nodes, n b branches, node 0 is the root node, then Y is a (2n+2n b )×2n-dimensional matrix, all coefficients of each distribution network static safety region boundary hyperplane obtained in step 2 constitute a row in the matrix Y, and z are both (2n+2n b )-dimensional column vector;

[0028] If the jth element in z is less than 1, it means that the rough hyperplane of the static safety domain boundary of the distribution network corresponding to the jth row in the Y matrix will not penetrate Φ, otherwise it means that it can penetrate Φ.

[0029] Furthermore, the key hyperplane search model for the static safety domain boundary of the distribution network constructed in step 7) is:

[0030] The critical hyperplane search model for the static safety domain boundary of the distribution network is constructed by the following formula:

[0031]

[0032] stc u x=1

[0033] Where: represents the node complex power injection vector, ‖·‖2 represents the L2 norm, x 0 represents the initial operating point given by step 3, K represents the critical hyperplane search frontier of the static safety region boundary of the distribution network defined in step 6, and is the currently identified n c The intersection of the space enclosed by the key hyperplanes of the static safety domain boundary of the distribution network; the n re The coefficients of the hyperplane expressions of the static safety region boundaries of the distribution network form an n re ×2n-dimensional matrix C re , where n re =(n V +n T -n c ), U={1,2,…,n re} represents the matrix C re The set of row vector numbers, c u Represents the matrix C re The u-th row vector of .

[0034] Furthermore, the method for determining the critical hyperplane of the boundary of the static safety domain of the distribution network in step 7) is as follows:

[0035] The distribution network static safety domain boundary hyperplanes are grouped according to physical meanings: the distribution network static voltage safety domain boundary hyperplanes are divided into voltage upper limit group and voltage lower limit group, and the thermal stability safety domain boundary hyperplanes are divided into forward power flow group and reverse power flow group; Search for the operating point x2 where the expression of the distribution network static safety domain boundary hyperplane to be judged is greater than 1, and the expressions of other distribution network static safety domain boundary hyperplanes in the same group are not greater than 1; if such an operating point exists, the distribution network static safety domain boundary hyperplane to be judged is a key hyperplane, otherwise it is not;

[0036] To determine whether the boundary hyperplane of the static safety region of the distribution network belongs to the voltage upper limit group or the positive power flow group, solve the following model:

[0037]

[0038] To determine whether the boundary hyperplane of the static safety region of the distribution network belongs to the voltage lower limit group or the reverse power flow group, solve the following model:

[0039]

[0040] Substitute the solution of the above model into the distribution network static safety domain boundary hyperplane expression in the same group, let s0 represent the number of expressions greater than 1, and resolve the above model with these s0 distribution network static safety domain boundary hyperplane expressions as the objective function, and construct a convex envelope with the solved s0 operating points as vertices. The convex envelope is continuously divided evenly until x2 is searched, and the distribution network static safety domain boundary hyperplane to be judged is judged as a critical hyperplane or the set upper limit of the number of divisions is reached, and the distribution network static safety domain boundary hyperplane to be judged is judged as non-critical.

[0041] Beneficial effects:

[0042] The method for fine-grained identification of key hyperplanes at the boundary of the static safety domain of the distribution network proposed in the present invention can obtain a few accurate key hyperplanes with extremely low computational overhead to describe the static safety domain of the distribution network. The present invention makes the time-consuming critical operating point search in the entire calculation process of the boundary hyperplane of the static safety domain of the distribution network more targeted, thereby improving the analytical calculation speed of the boundary hyperplane of the safety domain. In addition, the few key hyperplanes given by the present invention can be used as safety constraints in the optimal scheduling and risk assessment of the distribution network based on the safety domain, avoiding the indiscriminate consideration of the safety domain boundary hyperplanes corresponding to all nodes and lines as safety constraints, thereby greatly reducing the scale of the mathematical model of these problems, avoiding the unnecessary computational burden brought by considering redundant safety constraints, and also avoiding the errors that may be caused by specifying a certain key hyperplane based on operating experience. Description of the drawings:

[0043] Figure 1 It is a flow chart of the present invention;

[0044] Figure 2 2. It is a two-dimensional cross-sectional schematic diagram of the meaning of the elements in the vector z of the present invention; wherein: (a) the jth element in z is less than 1; (b) the jth element in z is greater than 1;

[0045] Figure 3 It is a schematic diagram of searching for a hyperplane along the frontier K of the present invention;

[0046] Figure 4 Schematic diagram of the space segmentation method of the present invention; wherein: (a) a new operating point generated by the first segmentation; (b) a new operating point generated by the second segmentation. Specific implementation method:

[0047] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings. The examples described in the accompanying drawings are only used to explain the present invention and are not intended to limit the present invention.

[0048] The invention proposes a method for fine-tuning the critical hyperplane identification of the boundary of the static safety domain of a distribution network, comprising the following steps: Step (1): defining the static safety domain of the distribution network in the complex power injection space

[0049] Assume that the distribution network has n+1 nodes, n b branches, node 0 is the root node. N represents the node set without the root node N = {1, 2, ... n}, and B represents the set of all branches B = {1, 2, ..., n b}.make and They represent the node active and reactive injection vectors respectively (injection is defined as positive and output is negative), then represents the node power injection vector; and Then they represent the vectors composed of node voltage amplitude and phase angle respectively; represents the line current magnitude vector (the positive direction of the current is defined as the direction away from the root node). With f(V,θ) = x and f i (V,θ)=I represents the power flow mapping of the system. In the complex power injection space, the static voltage safety region (denoted as Ω) corresponding to any node k∈N in the distribution network V,k ) and any branch l jh ∈B (j and h represent the first and last nodes of the branch) corresponding to the thermal stability safety domain (denoted as Ω T,jh ) can be defined as:

[0050]

[0051]

[0052] In the formula represents the voltage amplitude constraint corresponding to node k, It means line l jh The current constraint is defined as follows:

[0053]

[0054]

[0055] Where V k represents the voltage amplitude of node i, and Respectively represent the upper and lower limits of the voltage at node i. jh Indicates branch l jh The current value, Then it means branch l jh The current limit.

[0056] Practical static security domain of distribution network (denoted as ΩPSSR ) can be obtained by the static voltage safety domain (denoted as Ω) corresponding to all node voltage constraints. V ) and the thermal stability safety region corresponding to all line current constraints (denoted as Ω T ) and engineering practical boundary range and The intersection of the enclosed space is expressed as:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] Step (2): Generate a rough hyperplane of the static safety domain boundary of the distribution network

[0063] In order to simplify the mathematical derivation process of the boundary hyperplane of the static safety domain of the distribution network, several assumptions are made in combination with the actual operation of the distribution network: ① It is assumed that the network loss can be ignored; ② It is assumed that the voltage amplitude of each node in the distribution network is approximately equal to the voltage amplitude of the root node; ③ The voltage phase angles of adjacent nodes in the distribution network are not much different, so the transverse component of the voltage drop can be ignored.

[0064] The calculation of the static safety domain boundary hyperplane of the distribution network is divided into two steps: first, based on the above simplified assumptions, the static safety domain boundary in the form of a hyperplane is directly derived, which is called a rough hyperplane in the present invention; on the basis of the rough hyperplane, the hyperplane coefficients are corrected by obtaining an accurate critical operating point through power flow calculation to obtain a corrected hyperplane. Although the above assumptions are applied in the derivation of the rough hyperplane, the accuracy of the safety domain boundary hyperplane after correction by power flow calculation can fully meet the actual needs of the project. Since the correction process occupies a major part of the overall computational overhead of the safety domain boundary hyperplane, in order to minimize the computational overhead, step 2 is not corrected first, and only a rough hyperplane is generated. The correction process will be completed in step 8 after the identification work is basically completed.

[0065] 2.1 Generate a rough hyperplane of the static voltage safety region boundary

[0066] Under the above three assumptions, the voltage difference between two adjacent nodes j and h can be expressed as follows:

[0067]

[0068] Where V0 represents the voltage amplitude of the root node.jh and X jh Indicates branch l jh The resistance and reactance values ​​of P jh and Q jh Then they represent branch l jh The transmission active power and reactive power.

[0069] The branch transmission power in equation (10) can be rewritten as the node power injection form. For the selected node k (k∈N), the following equation can be obtained by deducing from the root node to node k:

[0070]

[0071] in

[0072]

[0073] Where λ k and λ i They represent the branch sets contained in the power supply paths from the root node to node k and node i respectively. For a tree-like distribution network, the power supply branch from the root node to any node is uniquely determined.

[0074] Set the voltage upper limit of node k to and lower limit Substituting into (11), we can get the following formula:

[0075]

[0076] Normalizing the right side of equation (13) can obtain the static voltage safety region boundary corresponding to node k (denoted as )’s rough hyperplane:

[0077]

[0078] Where P i and Q i denote the active power injection and reactive power injection of node i respectively; and They represent the coefficients corresponding to the active power injection and reactive power injection of node i in the safety domain boundary hyperplane expression corresponding to the voltage upper limit of node k; and They respectively represent the coefficients corresponding to the active power injection and reactive power injection of node i in the safety domain boundary hyperplane expression corresponding to the voltage lower limit of node k.

[0079] 2.2 Generating a rough hyperplane of the thermally stable safety region boundary

[0080] Line jhThe relationship between the current and the voltage at nodes j and h is:

[0081]

[0082] Since the voltage phase angles between adjacent nodes in the distribution network are not much different, it can be considered that cosθ jh ≈0, so we have:

[0083]

[0084] Therefore, substituting formula (11) into formula (16) yields:

[0085]

[0086] The line l jh Current limit and Substituting into formula (17), we can get:

[0087]

[0088] Normalizing the right side of equation (18) yields the line l jh The corresponding thermal stability safety domain boundary (denoted as ) is:

[0089]

[0090] In the formula and Respectively represent line l jh The coefficients corresponding to the active power injection and reactive power injection of node i in the hyperplane expression of the thermal stability safety region boundary corresponding to the forward power flow; and Respectively represent line l jh The coefficients corresponding to the active power injection and reactive power injection of node i in the safety domain boundary hyperplane expression corresponding to the reverse power flow.

[0091] So far, the present invention generates a rough hyperplane of the safety region boundary for subsequent identification. Since the accurate critical point has not been determined based on the power flow calculation and the hyperplane coefficient has not been corrected, the cost of generating the rough hyperplane of the safety region boundary is very small.

[0092] The present invention no longer emphasizes that the safety domain boundary hyperplane mentioned is a rough hyperplane in the subsequent text, but it should be made clear that before step 8 corrects the accurate critical point determined based on the flow calculation and corrects the hyperplane coefficient, the distribution network static safety domain boundary hyperplane mentioned in the present invention is an uncorrected rough hyperplane.

[0093] Step (3): Given the initial operating point and engineering practical boundary

[0094] Input the required historical information of node injection power, the forecast information for the next period, and the equipment capacity limit. Take the average of the forecast information of node injection power for the next period to determine the initial operation point.

[0095]

[0096] In the formula and represents the predicted value of active power injection and reactive power injection of node i at time t; T = {1,2,…,n t},n t Indicates the length of the period of interest.

[0097] The engineering practical boundary is given by:

[0098]

[0099]

[0100] In the formula and It represents the active capacity limit and reactive capacity limit of the w-th device accessing the node i, the superscript M represents the upper limit, and the superscript m represents the lower limit.

[0101] Geometrically, the engineering practical boundary constitutes a hypercube Φ in the complex power node injection space, as shown in Equation (23).

[0102]

[0103] Step (4): Give a strict criterion for whether the safety domain boundary hyperplane is critical

[0104] Combining the rough hyperplane obtained in step 2 and the engineering practical boundary obtained in step 3, Ω expressed in formula (9) PSSR It can also be specifically written in the form of formula (24). The identification of the critical hyperplane is to identify the Ω represented by formula (24). PSSR Filter out the many inequality constraints contained in .

[0105] The definition and strict criteria of the critical hyperplane are given below:

[0106] Definition: Delete Ω expressed in equation (24) PSSR After a certain safety domain boundary hyperplane constraint in the PSSR , if Ω' PSSR ≠Ω PSSR , then the deleted hyperplane is critical, otherwise it is non-critical.

[0107]

[0108] Criteria: If the assumption is that "at least one operating point can be found on the selected static safety region boundary hyperplane If the constraints corresponding to other static safety domain boundary hyperplanes in (22) are satisfied (abbreviated as p) is true, then the inference "the selected static safety domain boundary hyperplane is the critical hyperplane" (abbreviated as q) is also true. Proof: Proof by contradiction.

[0109] Assume that p is true, but the selected static safety domain boundary hyperplane is not a critical hyperplane. According to assumption p, after deleting the selected static safety domain boundary hyperplane, there must be The neighborhood Δ1 of is included in Ω' PSSR In other words, Ω' PSSR Compared to Ω PSSR "Expanded":

[0110]

[0111] However, if the selected static safety region boundary hyperplane is not a critical hyperplane, then according to the precise definition of the critical hyperplane above, Ω' PSSR =Ω PSSR , which obviously contradicts (25). This proves the proposition.

[0112] Step (5): Preliminary selection of the safety zone boundary hyperplane

[0113] The purpose of step 5 is to determine whether the safety domain boundary hyperplane obtained in step 2 can penetrate the hypercube Φ formed by the engineering practical boundary obtained in step 3.

[0114] make and Represent the two most extreme operating points on the hypercube Φ. The vector z used to characterize whether the safety domain boundary hyperplane can penetrate the hypercube Φ formed by the engineering practical boundary is calculated as follows:

[0115]

[0116] Where Y is a (2n+2n b )×2n-dimensional hyperplane coefficient matrix, which is composed of all static safety domain boundary hyperplane coefficients obtained in step 2. The 2n coefficients of each safety domain boundary hyperplane expression constitute a row in the matrix Y. Therefore, and z are both (2n+2n b )-dimensional column vector. Column vector and The maximum of the two corresponding elements of is the corresponding element value of the column vector z.

[0117] If the jth element in z is less than 1, it means that the safety zone boundary hyperplane corresponding to the jth row in the Y matrix will not penetrate Φ, such as Figure 2 (a), so it cannot be critical; on the contrary, if the jth element in z is greater than 1, it means that part of the security domain boundary corresponding to the jth row in the Y matrix is ​​within Φ and can penetrate Φ, as shown in Figure 2 As shown in (b), it is necessary to make another judgment in the subsequent steps. Assume that after the preliminary screening in step 5, the number of static voltage safety region boundary hyperplanes retained is n V , the number of hyperplanes on the boundary of the thermally stable safety region that can be retained is n T .

[0118] Step (6): Define the critical hyperplane search frontier of the safety domain boundary and initialize it

[0119] 6.1 Defining the critical hyperplane search frontier K of the safety domain boundary

[0120] Define the search frontier K as all n currently identified c The intersection of the hyperplanes of the critical safety domain boundaries. Obviously, K will be continuously updated in the identification process. c It is also incremented by 1 in each recognition.

[0121]

[0122] In the formula Indicates n c dimensional unit column vector, A is n c ×2n-dimensional matrix, consisting of all n currently identified c The coefficients of the key hyperplanes are composed of all 2n coefficients of each hyperplane expression, forming a row of the matrix A. re The coefficients of the safety region boundary hyperplane expressions form an n re ×2n-dimensional matrix C re , all 2n coefficients of each hyperplane expression form the matrix C re A row, n re =(n V +n T -n c ).

[0123] 6.2 Initializing the critical hyperplane search frontier K of the safety domain boundary

[0124] The boundary of the static safety domain of the distribution network is the boundary corresponding to the node voltage limit or line flow limit that is first encountered and continuously expanded outward from the initial operating point. Therefore, if we start from the critical hyperplane closest to the initial operating point and continuously search for the hyperplane that first intersects with the frontier K until the obtained hyperplane is non-critical, the search can be completed. Therefore, the initial search frontier K is composed of the operating points on the hyperplane closest to the initial operating point. Correspondingly, n c The initial value of is 1.

[0125] The distance from the initial operating point to the hyperplane of each safety zone boundary is defined by the Euclidean distance, which is determined by the following formula:

[0126]

[0127] Where a i and b i They respectively represent the coefficient corresponding to the active power injection and the coefficient corresponding to the reactive power injection of the i-th node in the selected safety domain boundary hyperplane expression.

[0128] Calculate all n retained in step 5 separately V +n T The Euclidean distance from the static safety domain boundary hyperplane to the initial operating point is calculated, and the static safety domain boundary hyperplane closest to the initial operating point is selected to complete the initialization of the search frontier K of the key hyperplane of the safety domain boundary.

[0129] Step (7): Search and determine the critical hyperplane

[0130] The basic logic of step 7 is: continue searching along the critical hyperplane search frontier K defined in step 6, and judge whether the static safety domain boundary hyperplanes obtained by the search are critical one by one, until the static safety domain boundary hyperplanes obtained by the search are judged to be non-critical.

[0131] 7.1 Constructing a static safety zone boundary hyperplane search model

[0132] Keep looking for the hyperplane that intersects with the search frontier K first ("first" means: the Euclidean distance between the intersection point and the initial running point is the smallest), and then determine whether it is the key hyperplane. Figure 3As shown, in the schematic three-dimensional space, if the key hyperplanes are known to be labeled 1 and 2 (indicated by dark colors), the search frontier K is the intersection of the two planes (indicated by the dotted line in the figure). The intersection point of the unidentified hyperplane 3 (indicated by light colors) and the search frontier K is intersection point 1, and the intersection point of the unidentified hyperplane 4 (indicated by light colors) and the search frontier K is intersection point 2. Obviously, intersection point 1 is closest to the initial running point, and hyperplane 3 should be selected for subsequent judgment. If it is a key hyperplane, the search frontier K is updated and the step is repeated, otherwise the search process is terminated.

[0133] Therefore, the security domain boundary search model is shown as follows.

[0134]

[0135] Where ‖·‖2 represents the L2 norm, U={1,2,…,n re} represents the matrix C re The set of row vector numbers, c u is the matrix C re The u-th row vector of the matrix C re The row vector consisting of all 2n coefficients of the unjudged safety region boundary hyperplane corresponding to the u-th row of .

[0136] 7.2 Search Model for Solving the Static Safety Region Boundary Hyperplane

[0137] Model (29) is a two-level optimization problem, which theoretically requires complex calculations. However, in practice, model (29) has special characteristics and can be solved quickly. The solution method of model (29) is given below.

[0138] First, we analyze the lower optimization problem with a fixed u value (30)

[0139]

[0140] In the formula Indicates (n c +1)-dimensional unit column vector, abbreviated as e'. Matrix J is based on matrix A with the addition of row vector c u The matrix after the sorting is thus a (n c +1)×2n-dimensional matrix.

[0141] Let Δx = xx 0 , formula (30) can be organized into a more concise incremental form:

[0142]

[0143] Where E 2n Represents a unit square matrix of dimension 2n.

[0144] Model (31) is a standard quadratic programming problem (QP). Write down the KKT (Karush-Kuhn-Tucker) conditions of the problem and solve it:

[0145]

[0146] Where x * represents the optimal solution of model (31), ν * Represents the dual variable corresponding to the equality constraint when x takes the optimal solution.

[0147] According to the properties of block matrix inversion, x * It can be expressed as:

[0148]

[0149] In summary, the computational overhead of the lower-level optimization problem is mainly the calculation of formula (33), that is, the calculation of JJ T Find the inverse. It should be pointed out that JJ T is a (n c +1)×(n c +1)-dimensional matrix, and since the number of hyperplanes judged as critical is very limited in the entire identification process, JJ T The size of is always small, and the computational cost of its inversion is also small. Given that the underlying problem can be solved quickly, it is feasible to traverse all possible values ​​of parameter u, solve model (30) separately, and select the minimum value of all optimization results as the solution of model (29).

[0150] 7.3 Determination of the critical hyperplane

[0151] 7.3.1 Relaxation of the strict criteria

[0152] Theoretically, if the hyperplane to be judged is a critical hyperplane, then the optimal solution x in 7.2 is * That is, the operating point that satisfies the strict criterion given in step 4. However, the rough hyperplane obtained in step 2 has not been corrected by the accurate critical operating point obtained by the power flow calculation, so the judgment according to the strict criterion may result in missed judgment (judging the critical hyperplane as non-critical), thereby terminating the search process in advance. To avoid missed judgment, the present invention relaxes the strict criterion given in step 4 to obtain a relaxed criterion.

[0153] The static safety domain boundary hyperplanes are grouped according to their physical meanings: the static voltage safety domain boundary is divided into the voltage upper limit group and the voltage lower limit group; the thermal stability safety domain boundary is divided into the forward power flow group and the reverse power flow group. The strict criterion given in step 4 is relaxed and rewritten as follows: If there is at least one operating point x2 in the complex power injection space, so that the constraint corresponding to the safety domain boundary hyperplane to be judged is violated, and the constraints corresponding to all other safety domain boundary hyperplanes in the same group are not violated, then the current hyperplane to be judged can be regarded as a critical hyperplane.

[0154] 7.3.2 Judging whether the rough hyperplane of the safety region boundary is critical based on the relaxation criterion

[0155] If the rough hyperplane to be determined is the boundary of the static voltage safety region, execute step 7.3.2.

[0156] For the node voltage of the tree-like distribution network, the following proposition holds true: In the tree-like distribution network, the increase of active power injection and reactive power injection will not cause the voltage of any node to decrease, nor will it cause the forward current of any branch to decrease or the reverse current to increase. Similarly, the reduction of active power injection and reactive power injection will not cause the voltage of any node to increase, nor will it cause the forward current of any branch to increase or the reverse current to decrease. Based on the voltage expression of node k shown in equation (11) and the line l shown in equation (19), jh The current expression of node i is used to find the partial derivative of the injected power. The obtained sensitivity coefficient can be approximately expressed by the following formula:

[0157]

[0158]

[0159] As shown in equations (34) and (35), under the premise of setting the positive direction of node injection and the positive direction of current, the sensitivity of active injection power and reactive injection power of any node to any node voltage and line current is non-negative, so the above proposition holds. This provides a clear direction for the search of operating point x2. The following takes a static voltage safety domain boundary hyperplane belonging to the voltage upper limit group as an example to illustrate the search method of x2:

[0160] To determine whether the boundary hyperplane of the static safety region of the distribution network belongs to the voltage upper limit group or the positive power flow group, solve the following model:

[0161]

[0162] To determine whether the boundary hyperplane of the static safety region of the distribution network belongs to the voltage lower limit group or the reverse power flow group, solve the following model:

[0163]

[0164] In the formula represents the node complex power injection vector.

[0165] Substitute the solution of the above model into the distribution network static safety domain boundary hyperplane expression in the same group, let s0 represent the number of expressions greater than 1, and re-solve the above model with these s0 distribution network static safety domain boundary hyperplane expressions as the objective function, and construct a convex envelope with the s0 operating points obtained as vertices, segment the convex envelope, and continuously generate new operating points until the operating point found meets the relaxation criterion (the safety domain boundary hyperplane is considered to be a critical hyperplane) or the number of segmentations has reached the set upper limit (the safety domain boundary hyperplane is considered to be non-critical). These s0 operating points are denoted as x 0,1 ,x 0,2 ,……, The first digit of the subscript indicates the number of divisions, and the second digit indicates the sequence number of the operating point generated by the division. Since the above operating points have not been divided, the first digit of the subscript is 0.

[0166] In order to ensure uniform point selection, the present invention designs the following space segmentation method:

[0167] (1) Generate the new operating point for the first split according to formula (38):

[0168]

[0169] (2) Replace any operating point on the right side of equation (39) with x 1,1 , continue to split, can generate s0 new operating points, where the i-th new operating point can be expressed as:

[0170]

[0171] (3) On this basis, the kth segmentation will give A new operating point.

[0172] Figure 3 A schematic diagram of a simple example of s0=2 is given to illustrate the segmentation method.

[0173] Assume that the static voltage safety region boundary hyperplane determined as the critical hyperplane in step 7 has n′ V The thermal stability safety region boundary hyperplane has n′ T Then the matrix A' consists of n' V +n′ T The coefficient of the retained HP is composed of .

[0174] Step (8): Correct the safety zone boundary hyperplane coefficient based on power flow calculation

[0175] In order to correct the rough hyperplane of the static safety domain boundary in step 2 and improve the accuracy, it is necessary to determine the precise critical point corresponding to the safety domain boundary through power flow calculation and substitute it into the rough hyperplane for correction. The following takes the static voltage safety domain boundary hyperplane corresponding to the voltage upper limit of node k as an example. The critical point Substituting the rough hyperplane of the safety region boundary given by equation (14) into the formula, we get a correction coefficient c close to 1. V,M :

[0176]

[0177] make and Then the static voltage safety region boundary hyperplane corresponding to the voltage upper limit of node k corrected based on power flow calculation can be obtained:

[0178]

[0179] The following is a fast calculation method for the critical point. We still take the rough hyperplane of the static voltage safety region boundary corresponding to the voltage upper limit of node k as an example. Since the operating point x2 that satisfies the relaxation criterion obtained in the judgment process is actually very close to the accurate critical operating point, we use this operating point as the search starting point and perform an iterative search for the critical operating point according to formula (42):

[0180]

[0181] In the formula and They represent the active power injection and reactive power injection of node j at the tth iteration, It represents the voltage value of node k at the t-1th iteration.

[0182] Perform the above search until ε is the set convergence threshold, which is set to ε = 0.001 in the present invention. Since the selected search starting point is already very close to the real critical operating point, it generally only takes a few iterations to converge quickly. Step (9): Check the key hyperplane and give the final identification result

[0183] After obtaining the corrected safety region boundary hyperplane, execute step 9 to eliminate misjudgment caused by the relaxed criterion (judging a non-critical hyperplane as a critical hyperplane).

[0184] Starting from the critical hyperplane of the security domain boundary that was finally judged as critical in step 7, the verification is performed in a backward order until the verification result shows that the current security domain boundary hyperplane is indeed critical. The verification model is shown in formula (43):

[0185]

[0186] Where A′ k is the kth row of A', and A' -k It means that A' is the matrix obtained by deleting the kth row, so A' -k is (n′ V +n′ T -1)×2n dimensional matrix. If the solution of model (43) is greater than 1, the kth identified critical hyperplane is indeed critical, otherwise it is a misjudgment.

[0187] If the solution of model (43) is greater than 1, then the currently verified safety domain boundary hyperplane is indeed critical, otherwise it is non-critical. Since model (43) is a linear convex optimization problem with a small scale, only (n′ V +n′ T -1) constraints, which can be solved quickly using the simplex method.

[0188] The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solution of the present invention. The above specific embodiments are merely illustrative and not restrictive. Without departing from the scope of the present invention and the scope of protection of the claims, a person of ordinary skill in the art can also make many forms of specific changes under the guidance of the present invention, which all fall within the scope of protection of the present invention.

Claims

1. A method for fine-grained identification of critical hyperplanes at the boundary of static safety domain of distribution network, characterized in that: 1) Define the static security domain of complex power injection spatial distribution network; 2) Generate a rough hyperplane of the static safety domain boundary of the distribution network; 3) Given the initial operating point and engineering practical boundary; 4) Provide a strict criterion for determining whether the boundary hyperplane of the static safety domain of the distribution network is a critical hyperplane; 5) Preliminary selection of the distribution network static safety domain boundary hyperplane; wherein: the preliminary selection of the distribution network static safety domain boundary hyperplane is to determine whether the rough hyperplane of the distribution network static safety domain boundary obtained in step 2) can penetrate the hypercube Φ formed by the engineering practical boundary in step 3): make and The two most extreme operating points on the hypercube Φ that represents the engineering practical boundary of node injection, where the superscript M represents the maximum limit of node injection power and the subscript m represents the minimum limit of node injection power; the vector z is calculated as follows: Assume that the distribution network has n+1 nodes, n b branches, node 0 is the root node, then Y is a (2n+2n b )×2n-dimensional matrix, all coefficients of each distribution network static safety region boundary hyperplane obtained in step 2 constitute a row in the matrix Y, and z are both (2n+2n b )-dimensional column vector; If the jth element in z is less than 1, it means that the rough hyperplane of the static safety region boundary of the distribution network corresponding to the jth row in the Y matrix will not penetrate Φ, otherwise it means that it can penetrate Φ; 6) Define the search frontier of the critical hyperplane of the static safety domain boundary of the distribution network and initialize it; 7) Search and judge the key hyperplane of the boundary of the static safety domain of the distribution network; Among them: The constructed key hyperplane search model of the boundary of the static safety domain of the distribution network is: The critical hyperplane search model for the static safety domain boundary of the distribution network is constructed by the following formula: Where: represents the node complex power injection vector, ‖·‖2 represents the L2 norm, x 0 represents the initial operating point given by step 3, K represents the critical hyperplane search frontier of the static safety region boundary of the distribution network defined in step 6, and is the currently identified n c The intersection of the space enclosed by the key hyperplanes of the static safety domain boundary of the distribution network; the n re The coefficients of the hyperplane expressions of the static safety region boundaries of the distribution network form an n re ×2n-dimensional matrix C re , where n re =(n V +n T -n c ), U={1,2,…,n re } represents the matrix C re The set of row vector numbers, c u Represents the matrix C re The u-th row vector of ; 8) Correct the critical hyperplane of the static safety domain boundary of the distribution network based on power flow calculation; 9) Verify the critical hyperplane of the static safety domain boundary of the distribution network and give the final identification result.

2. According to claim 1, a method for fine-grained identification of critical hyperplanes at the boundary of a static safety domain of a distribution network is characterized in that: In the step 2), the static safety domain boundary of the distribution network is generated in the form of a hyperplane, including a rough hyperplane of the static voltage safety domain boundary and a rough hyperplane of the thermal stability safety domain boundary, wherein: 2.

1. The rough hyperplane of the static voltage safety region boundary is Where: P i and Q i denote the active power injection and reactive power injection of node i respectively, and They represent the coefficients corresponding to the active power injection and reactive power injection of node i in the hyperplane expression of the static voltage safety region boundary of the distribution network corresponding to the voltage upper limit of node k, respectively. Node k and node i are both elements in the node set N except the root node in the distribution network. and They respectively represent the coefficients corresponding to the active power injection and reactive power injection of node i in the hyperplane expression of the boundary of the static voltage safety region of the distribution network corresponding to the voltage lower limit of node k; 2.

2. The rough hyperplane of the thermal stability safety region boundary is Where: and Respectively represent a line l in the distribution network jh The coefficients corresponding to the active power injection and reactive power injection of node i in the hyperplane expression of the thermal stability safety region boundary corresponding to the forward power flow are: and Respectively represent line l jh The coefficients corresponding to the active power injection and reactive power injection of node i in the hyperplane expression of the thermal stability safety region boundary corresponding to the reverse power flow.

3. According to claim 1, a method for fine-grained identification of critical hyperplanes at the boundary of a static safety domain of a distribution network is characterized in that: The method for determining the critical hyperplane of the boundary of the static safety domain of the distribution network in step 7) is as follows: The distribution network static safety domain boundary hyperplanes are grouped according to physical meanings: the distribution network static voltage safety domain boundary hyperplanes are divided into voltage upper limit group and voltage lower limit group, and the thermal stability safety domain boundary hyperplanes are divided into forward power flow group and reverse power flow group. Search for an operating point x2 where the hyperplane expression of the boundary of the static safety region of the distribution network to be judged is greater than 1, and the hyperplane expressions of the boundary of the static safety region of other distribution networks in the same group are not greater than 1; If such an operating point exists, the distribution network static safety domain boundary hyperplane to be judged is the critical hyperplane, otherwise it is not; To determine whether the boundary hyperplane of the static safety region of the distribution network belongs to the voltage upper limit group or the positive power flow group, solve the following model: To determine whether the boundary hyperplane of the static safety region of the distribution network belongs to the voltage lower limit group or the reverse power flow group, solve the following model: Substitute the solution of the above model into the distribution network static safety domain boundary hyperplane expression in the same group, and re-solve the above model with the distribution network static safety domain boundary hyperplane expression whose value is greater than 1 after substituting the solution of the above model as the objective function, and construct a convex envelope with the solved operating points as vertices. The convex envelope is continuously divided evenly until x2 is searched, and the distribution network static safety domain boundary hyperplane to be judged is judged as a critical hyperplane or the set upper limit of the number of divisions is reached, and the distribution network static safety domain boundary hyperplane to be judged is judged as non-critical.

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