A node load reverse modeling method based on incomplete information

Abstract

The application provides a node load reverse modeling method based on incomplete information, comprising: constructing a double-layer optimization model for node price calculation; the double-layer optimization model comprises an upper model and a lower model; the upper model takes minimizing the difference between calculated price and real price as an objective, and obtains node load distribution according to system operation constraints; the lower model performs economic dispatch calculation based on the node load distribution, obtains node marginal price and returns to the upper model; the double-layer optimization model is converted into a single-layer model for solving, and the reverse modeling result of the node load is obtained; the credibility of the reverse modeling result is evaluated based on the capacity utilization rate deviation degree; and the reverse modeling result is fused and corrected with prior load information according to the credibility, and the final node load value is obtained. Under the condition of incomplete information that cannot directly obtain node load information, the load distribution of each node in the power grid is accurately speculated, and the vulnerable node susceptible to deliberate attack is identified.

Description

Technical Field

[0001] This invention relates to the field of power system security analysis technology, and in particular to a method for reverse modeling of node loads based on incomplete information. Background Technology

[0002] In recent years, the frequent occurrence of extreme disasters and deliberate attacks has driven vulnerability assessment research to expand its perspective to extreme scenarios. Most existing studies on extreme deliberate attack scenarios assume that attackers possess complete system information, which does not reflect the reality that attackers have limited information access. Therefore, some scholars have conducted research on deliberate attacks under conditions of incomplete information, mainly focusing on premises such as incomplete topology, possession of only local network information, and unknown local line reactance.

[0003] However, most of the aforementioned studies have not considered the condition that attackers are unaware of load information. In high-voltage transmission networks, attackers can obtain the static topological connections of the power grid through surface facility features and can make high-precision estimates of electrical parameters based on the parameters of similar equipment. In contrast, node load information is highly protected and has a strong dependence on power flow. Its absence or distortion will reduce the reliability of vulnerability identification and thus affect the effectiveness of defense measures. Summary of the Invention

[0004] This invention provides a node load reverse modeling method based on incomplete information to solve the problem in the prior art that it is impossible to accurately identify vulnerable nodes in the power grid when node load information is missing.

[0005] On one hand, the present invention provides a method for reverse modeling of node load based on incomplete information, comprising: A two-layer optimization model for calculating nodal electricity prices is constructed. The two-layer optimization model includes an upper-layer model and a lower-layer model. The upper-layer model aims to minimize the difference between the calculated electricity price and the actual electricity price, and obtains the nodal load distribution based on system operation constraints. The lower-layer model performs economic dispatch calculations based on the nodal load distribution to obtain the nodal marginal electricity price and returns it to the upper-layer model. The two-layer optimization model is transformed into a single-layer model for solution, and the inverse modeling results of node load are obtained. The reliability of the reverse modeling results is assessed based on the degree of deviation from capacity utilization. Based on the stated confidence level, the reverse modeling results are fused and corrected with prior load information to obtain the final node load value.

[0006] Optionally, the system operating constraints include total load constraints and main transformer N-1 safety constraints; The total load constraint includes: The sum of the loads generated at each node is equal to the total load disclosed in the electricity market; The main transformer N-1 safety constraint includes: The actual load of each substation is less than or equal to the product of the number of remaining main transformers in the substation and the rated capacity and overload factor of a single transformer; where the number of remaining main transformers is the total number of main transformers in the substation minus one; N is an integer greater than 1.

[0007] Optionally, the lower-level model performs economic dispatch calculations based on the node load distribution to obtain the node marginal electricity price, including: Based on DC power flow, an economically optimal power system operation model is constructed with the goal of minimizing power generation costs, while satisfying line power flow constraints, node power balance constraints, generator output constraints, and line capacity constraints. Construct the Lagrangian function of the economically optimal operating model; Based on the Lagrange function, the nodal marginal electricity price is obtained.

[0008] Optionally, after obtaining the nodal marginal electricity price based on the Lagrange function, the method further includes: Determine the active power loss of each line and express it as a quadratic function of the node phase angle; Based on the quadratic function, the reference node is deleted to reduce the order, resulting in the reduced network loss expression. Based on the reduced network loss expression and the relationship between node injection power and node phase angle, the marginal impact of each node injection power on the total network loss of the system is obtained, which serves as the marginal network loss coefficient of each node. Based on the marginal network loss coefficient of each node, the node marginal electricity price under DC power flow is corrected to obtain the corrected node marginal electricity price.

[0009] Optionally, the two-layer optimization model is transformed into a single-layer model for solution, yielding the inverse modeling results of node loads, including: Based on the KKT conditions of the lower-level model, the two-level optimization model is transformed into a single-level optimization model; wherein, the KKT conditions include stationary point conditions, nonnegativity conditions, and complementary relaxation conditions; The complementary relaxation conditions are processed using a linearization method to obtain a single-layer mixed integer programming model; Solving the single-layer mixed integer programming model yields the inverse modeling results of node load.

[0010] Optionally, the assessment of the reliability of the reverse modeling results based on the degree of deviation in capacity utilization includes: Calculate the capacity utilization rate of each substation; The median capacity utilization rate of each substation is determined as a reference benchmark for the system capacity utilization rate. Calculate the deviation between the capacity utilization of each node and the reference baseline; A Gaussian mapping function is used to map the deviation into node credibility.

[0011] Optionally, calculating the deviation between the capacity utilization of each node and the reference benchmark includes: Calculate the ratio of each node's utilization to the reference baseline; Convert the ratio to the logarithmic domain; Using the median of all logarithmic fields as a benchmark, calculate the absolute deviation of each node from the benchmark.

[0012] Optionally, the step of fusing and correcting the reverse modeling result with prior load information based on the confidence level to obtain the final node load value includes: The prior load of each node is calculated based on the proportional allocation of the substation's rated capacity. Using the credibility as a weight, the node load of the reverse modeling result and the prior load information are weighted and fused to obtain the weighted fused node load value; The weighted and merged node load values ​​are normalized to obtain the final node load values.

[0013] Optionally, the Lagrange function is expressed as: ; in, It is a Lagrange function; The total cost of generating electricity from all power plants; Index for power plants; For power plants; For power plants The power generation cost function; For power plants The power generation capacity; N is the index of the bus node; N is the set of bus nodes; For nodes Lagrange multipliers constrained by power balance; For connection at node A collection of power plants on the ground; For nodes The load; For route indexing; For the set of routes; Elements of the node-branch association matrix; For the line The meritorious trend; For power plants Lagrange multipliers with output upper limit constraints; For power plants The upper limit of output; For power plants Lagrange multipliers with output lower bound constraints; For power plants The lower limit of output; For the line Lagrange multipliers with transmission upper limit constraints; For the line Head bus The voltage phase angle; For the line The voltage phase angle of the first bus n; For the line The reactance; For the line The upper limit of transmission; For the line Lagrange multipliers with transmission lower bound constraints; For the line The lower limit of transmission.

[0014] Optionally, the objective function of the single-layer mixed-integer programming model is expressed as: (34); in, Let N be the objective function of a single-level mixed-integer programming model; N is the set of bus nodes. For nodes Lagrange multipliers constrained by power balance; Lagrange multipliers for the power balance constraints of reference node s; Let be the marginal network loss coefficient of node i; The voltage phase angle vector of the node; Let be the actual electricity price at node i.

[0015] This invention provides a method for inverse node load modeling based on incomplete information. It constructs a two-layer optimization model for calculating node electricity prices. The two-layer optimization model includes an upper-layer model and a lower-layer model. The upper-layer model aims to minimize the difference between the calculated electricity price and the actual electricity price, and obtains the node load distribution based on system operating constraints. The lower-layer model performs economic dispatch calculations based on the node load distribution, obtains the node marginal electricity price, and returns it to the upper-layer model. The two-layer optimization model is then transformed into a single-layer model for solution, yielding the inverse modeling results of the node load. The reliability of the inverse modeling results is evaluated based on the deviation of capacity utilization. Based on the reliability, the inverse modeling results are fused and corrected with prior load information to obtain the final node load value. This method enables accurate inverse modeling of node loads even when attackers cannot directly obtain incomplete information about the node loads. Furthermore, by evaluating the reliability of the modeling results based on the deviation of capacity utilization and fusing and correcting them with prior load information, the accuracy and robustness of the inverse node load modeling results are effectively improved. Under the condition that attackers cannot directly obtain incomplete information about node load, the load distribution of each node in the power grid can be accurately inferred, thereby identifying vulnerable nodes in the power grid that are susceptible to deliberate attacks. This provides a reliable basis for power grid defenders to optimize the deployment of defense resources and formulate targeted reinforcement measures. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating the node load reverse modeling method based on incomplete information provided in this embodiment of the invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0019] See Figure 1 The node load reverse modeling method based on incomplete information may include the following steps 101 to 104.

[0020] Step 101: Construct a two-layer optimization model for nodal electricity price calculation; wherein, the two-layer optimization model includes an upper-layer model and a lower-layer model; the upper-layer model aims to minimize the difference between the calculated electricity price and the actual electricity price, and obtains the nodal load distribution according to the system operation constraints; the lower-layer model performs economic dispatch calculation based on the nodal load distribution according to the power grid structure information, obtains the nodal marginal electricity price, and returns it to the upper-layer model.

[0021] Generally, a power transmission network mainly consists of power plants, high-voltage substations, and power lines. The power transmission network can be abstracted as a phase-free graph composed of nodes and edges, as shown in the following formula (1): (1); in, It is a phaseless graph; L Let it be a set of edges, where an edge can also be understood as a path; V A set of nodes; G For the set of power plant nodes; N This refers to the set of bus nodes. Power grid structure information can be obtained in advance, including grid topology connections, line reactance parameters, generator output limits, line transmission capacity limits, and substation transformer rated capacity.

[0022] The objective function of the upper-level model is expressed as formula (2): (2); in, Indicates minimization; The total number of nodes in the power grid; For node indexing; A set of nodes; For nodes Calculate the electricity price; For nodes The actual electricity price.

[0023] System operating constraints include total load constraints and main transformer N-1 safety constraints; Total load constraints include: The sum of the generated loads at each node is equal to the total load disclosed in the electricity market, as expressed in formula (3); (3); in, For nodes i The node load, Total load; The main transformer N-1 safety constraints include: The actual load of each substation is less than or equal to the product of the number of remaining main transformers in the substation and the rated capacity and overload factor of a single transformer; wherein, the number of remaining main transformers is the total number of main transformers in the substation minus one.

[0024] (4); in: For substation i Total number of main transformers within the station; For substation i The rated capacity of a single transformer.

[0025] The lower-level model performs economic dispatch calculations based on node load distribution to obtain the node marginal electricity price, including: Based on DC power flow, an economically optimal operation model of the power system is constructed with the goal of minimizing power generation costs, satisfying line power flow constraints, node power balance constraints, generator output constraints, and line capacity constraints, as shown in the following formulas (5) to (9): (5); (6); (7); (8); (9); in, For power plants g The power generation cost function; For power plants g The power generation capacity; Formula (6) is the power flow equation of the line, For the line The meritorious trend, , The lines are respectively Connecting the first and last busbars m and n phase angle, For the line The reactance, L is the line set; Equation (7) is the node power balance constraint, For nodes i The set of generators included; For nodes i Active load; A is the node-branch correlation matrix; N is the set of bus nodes; Equations (8)-(9) are the power plant output constraints and line capacity constraints, respectively; , Generator g Output upper limit and lower limit; , Showing the line Upper and lower limits for thermally stable transmission.

[0026] The Lagrangian function for constructing the economically optimal operating model is shown in the following formula (10): (10); In the formula, , , , , These are the Lagrange multipliers for node power balance constraints, generator upper and lower limit constraints, and line power flow upper and lower limit constraints, respectively. It is a Lagrange function.

[0027] The Lagrange multipliers of the nodal power balance constraint are used as the nodal marginal electricity price under DC power flow.

[0028] At the optimal solution, the minimum operating cost of the system is a function of the node load. i The active node price is defined as the marginal rate of change of the system's optimal cost for that node's load. The node price under DC power flow is obtained and expressed as formula (11): (11); in, For nodes Nodal marginal electricity price under DC power flow model; To achieve the optimal operating cost of the system; Let be the value of the Lagrange function at the optimal solution.

[0029] Formula (11) is the nodal price expression that ignores network losses. Using this model to solve the problem may cause distortion of the price signal, and network losses need to be further considered to correct it.

[0030] After obtaining the nodal marginal electricity price from the lower-level model, the process also includes a step to correct the nodal marginal electricity price by considering transmission losses. Specifically, this includes: Determine the active power loss of each line and express it as a quadratic function of the node phase angle; Based on the quadratic function, the order is reduced by deleting the reference node, resulting in the reduced network loss expression. Based on the reduced network loss expression and the relationship between node injection power and node phase angle, the marginal impact of each node injection power on the total network loss of the system is obtained, which serves as the marginal network loss coefficient of each node. Based on the marginal network loss coefficient of each node, the node marginal electricity price under DC power flow is corrected to obtain the corrected node marginal electricity price.

[0031] branch road l The active power loss can generally be approximated by formula (12): (12); in, branch road l Active power loss; For the line l The resistance; branch road l Active power loss.

[0032] Substituting formula (6) into formula (12), we get formula (13). (13); The cumulative losses of each line can be expressed as a quadratic form of the node phase angle, as shown in the following formula (14): (14); In the formula, This is the sum of active power losses across all lines, which is also the total network loss. C is the column vector of voltage phase angles for all nodes; C is the loss matrix, whose elements are... .

[0033] Delete reference node s The corresponding rows and columns yield a reduced-order matrix. and non-reference node phase angle vector The total network loss at this point can be expressed as formula (15): (15); in, This is the reduced-order node phase angle vector, i.e., after deleting the reference node. After the corresponding rows and columns, the phase angle vectors of the remaining non-reference nodes are given. The reference nodes can be selected according to the actual situation, and no specific restrictions are made here.

[0034] In the DC power flow model, power and phase angle satisfy formula (16): (16); In the formula, B is the active power injection vector of the node; B is the node susceptance matrix.

[0035] Equation (16) can be written as formula (17). (17); in, The reduced nodal susceptance matrix The inverse matrix; Inject a power vector into the active power of the nodes after the order reduction; Substituting equation (17) into equation (15), we can obtain the marginal sensitivity of non-reference node injection to total network loss, expressed as formula (18): (18); Let the constant matrix This leads to formula (19): (19); in, This is a vector-valued function, representing the marginal impact of non-reference node injected power on the total network loss of the system at the current operating point.

[0036] Then its first Each component This indicates that at the current running point, the non-reference node... The marginal impact of injected active power on the total network loss of the system.

[0037] Power system operation must constantly maintain system energy balance. In DC power flow models, the reference node is responsible for balancing the entire network power, including compensating for changes in network losses. If the node... i Increasing the injected power by 1 unit requires adjusting the reference node by -(1+ Unit power to maintain net power balance, where This is the adjustment amount corresponding to the newly added network loss. Therefore, the sum of the marginal network loss coefficients of all nodes is zero, as expressed in formula (20): (20); in, Let be the marginal network loss coefficient of node i; Therefore, the marginal network loss coefficient of the reference node can be expressed as formula (21); (twenty one); in, is the marginal network loss coefficient of the reference node s.

[0038] This yields the network loss correction coefficient vector for all nodes, expressed as formula (22): (twenty two); in, Let be the marginal network loss coefficient of the reference node. Based on this, the electricity price at the node considering network loss can be expressed as formula (23): (twenty three); In the formula, The marginal electricity price for node i after considering network losses. The Lagrange multiplier for the nodal power balance constraint of the reference node.

[0039] Step 102: Convert the two-layer optimization model into a single-layer model for solution to obtain the inverse modeling results of node load.

[0040] Step 102 above may include: Based on the KKT conditions of the lower-level model, the bi-level optimization model is transformed into a single-level optimization model; the KKT conditions include stationary conditions, nonnegativity conditions, and complementary relaxation conditions. A linearization method is used to process the complementary relaxation conditions to obtain a single-layer mixed integer programming model; The solver is used to solve a single-layer mixed integer programming model to obtain the inverse modeling results of node loads.

[0041] Specifically, for the above load modeling model, the original two-layer structure is transformed into a single-layer problem using KKT conditions for solution. At the optimal point of the lower-layer problem, in addition to the original feasibility formulas (6) to (9), the following KKT conditions must also be satisfied: Condition 1, for The stationary conditions are shown in the following formula (24): (twenty four); Condition 2, for The stationary conditions are shown in the following formula (25): (25); In the formula, To indicate a branch l Meritorious current to node i Sensitivity of phase angle.

[0042] Condition 3: The nonnegativity and complementary relaxation conditions are as follows: (26) to (29): (26); (27); (28); (29); (30); (31); (32); (33); Through binary variables and large The method linearizes the nonlinear constraint formulas (30)-(33), and the transformed problem and constraints are as follows: formulas (34)-(44): (34); in, To minimize the objective function, which is the objective function of the transformed single-layer optimization model; st formula (3)-(4), (6)-(9), (24)-(29); (35); (36); (37); (38); (39) (40); (41); (42); (43); (44); In the formula, , , , It is a 0-1 variable. "M" in the Big M method refers to a sufficiently large positive integer.

[0043] This transforms the original two-layer optimization model into a single-layer non-convex mixed-integer quadratic programming (MIQP) problem. Its non-convexity primarily stems from the bilinear terms. It can be solved using the non-convex quadratic module of the commercial solver Gurobi.

[0044] Step 103: Assess the credibility of the reverse modeling results based on the degree of deviation of capacity utilization.

[0045] Step 104: Based on the confidence level, fuse and correct the reverse modeling results with the prior load information to obtain the final node load value.

[0046] In this embodiment, a two-layer optimization model is constructed based on the formation mechanism of nodal electricity prices. This model includes an upper-layer model and a lower-layer model. The upper-layer model aims to minimize the difference between the calculated electricity price and the actual electricity price, and obtains the nodal load distribution based on system operating constraints. The lower-layer model performs economic dispatch calculations based on the nodal load distribution, obtains the nodal marginal electricity price, and returns it to the upper-layer model. The two-layer optimization model is then transformed into a single-layer model for solution, yielding the inverse modeling results of the nodal load. The reliability of the inverse modeling results is evaluated based on the deviation of capacity utilization. Based on the reliability, the inverse modeling results are fused and corrected with prior load information to obtain the final nodal load value. This approach enables accurate inverse modeling of nodal loads even when attackers cannot directly obtain incomplete information about the nodal loads. Furthermore, by evaluating the reliability of the modeling results based on the deviation of capacity utilization and fusing and correcting them with prior load information, the accuracy and robustness of the nodal load inverse modeling results are effectively improved. Under the condition that attackers cannot directly obtain incomplete information about node load, the load distribution of each node in the power grid can be accurately inferred, thereby identifying vulnerable nodes in the power grid that are susceptible to deliberate attacks. This provides a reliable basis for power grid defenders to optimize the deployment of defense resources and formulate targeted reinforcement measures.

[0047] In one embodiment of this specification, assessing the reliability of reverse modeling results based on the degree of deviation in capacity utilization may include: Calculate the capacity utilization rate of each substation; The median capacity utilization rate of each substation is determined as a reference benchmark for the system capacity utilization rate. Calculate the deviation of each node's capacity utilization rate from the reference baseline; A Gaussian mapping function is used to map the deviation to the node confidence, and the maximum value of the deviation of all nodes is used as the half-decay point of the mapping function.

[0048] In this embodiment, based on the obtained calculated load reverse modeling results, considering the multiple factors that affect node motors in the actual electricity market, such as network constraints and market clearing status, the load modeling may have certain uncertainties. Therefore, based on a node load reliability quantification method based on the relative deviation of substation capacity utilization, the calculated load information and prior load information are adaptively fused to improve the robustness of the optimization results.

[0049] In one embodiment of this specification, calculating the deviation between the capacity utilization of each node and a reference baseline may include: Calculate the ratio of each node's utilization to the reference baseline; Transform the ratio to the logarithmic field; Using the median of all logarithmic fields as a benchmark, calculate the absolute deviation of each node from the benchmark.

[0050] The credibility assessment rules are as follows: Based on the load distribution characteristics revealed by the electricity price signal, if the capacity utilization rate of a substation tends to be consistent with the overall system capacity utilization rate, it is assigned a high credibility; conversely, the credibility decreases exponentially with the increase of the deviation. Furthermore, when the deviation is within a reasonable threshold, the credibility remains basically stable; the exponential decline mechanism only becomes significant when the deviation continues to expand and exceeds the reasonable fluctuation range.

[0051] The capacity utilization rate of each substation is calculated as shown in the following formula (45): (45); in, The capacity utilization rate of substation i; This represents the rated capacity of substation i.

[0052] To ensure that the indicator is not sensitive to outliers, the median in robust statistics is used as the reference benchmark for system capacity utilization, as shown in formula (46): (46); For reference.

[0053] Calculate the ratio of each node's utilization to the reference baseline and convert it to the logarithmic domain to normalize the distribution, as shown in Equations (47) and (48). (47); (48); In the formula, This is the ratio of the capacity utilization of node i to the reference baseline. It is a very small positive number. Let i be the logarithmic field transformation value of node i.

[0054] Using the center of the logarithmic sequence as a reference, the following formula (49) is given: (49); in, This is the median of all logarithmic fields.

[0055] node i The absolute deviation from this center is defined by formula (50): (50); in, For nodes i The absolute deviation relative to the benchmark; Based on deviation samples of all nodes Its empirical distribution function is given by formula (51): (51); in, Deviation The empirical distribution function; For indicator functions, when The value is 1 if the condition is met, and 0 otherwise. The threshold variable is the deviation.

[0056] Set deviation threshold The quantiles of this empirical distribution are given by formula (52): (52); in, For deviation quantiles; This is a quantile function; in this embodiment, the quantile parameters are taken. At this point, equation (54) requires finding a solution that satisfies... The smallest x That is, the deviation does not exceed x The node ratio reached 100%. Therefore, Essentially, it is the maximum value of the deviation of all nodes, that is... This extends the boundary of the reasonable fluctuation range to cover all nodes, thereby avoiding prior distinctions between nodes based on preset local thresholds and reducing the impact of subjective threshold selection on the utilization of overall electricity price information.

[0057] Deviation Mapped to node credibility Define a Gaussian mapping with half-decay point locking, nodes i The credibility is expressed by formula (53): (53); in, Let be the credibility of node i. From equation (53), it can be calculated that when... hour, That is, using quantile threshold As a measure of confidence level, the half-decay point of confidence level is determined by the definition of quantiles, meaning that the confidence level of all nodes is not lower than 0.5.

[0058] Considering that substation capacity is usually positively correlated with the size of the load it carries, in the absence of historical data, a proportional allocation based on rated capacity can be used as a priori, with nodes... The prior load is given by formula (54): (54); in, The prior load of node i; This represents the total system load.

[0059] Based on the reliability, the reverse modeling results are fused and corrected with prior load information to obtain the final node load values, including: The prior load of each node is calculated based on the proportional allocation of the substation's rated capacity: the prior load of a node is equal to the total load multiplied by the proportion of the rated capacity of that node's substation to the sum of the rated capacities of all node substations. Using credibility as the weight, the node load of the reverse modeling result and the prior load information are weighted and fused to obtain the weighted fused node load value; The weighted and merged node load values ​​are normalized so that the sum of the loads of each node is equal to the total load disclosed in the electricity market, thus obtaining the final node load value.

[0060] Specifically, the load correction value is obtained by weighted fusion based on credibility, as shown in the following formula (55): (55); in, The weighted and merged load value for node i; Since equation (55) is a point-by-point independent correction, it theoretically does not satisfy the total load constraint of equation (3). Therefore, normalization is required to ensure consistency of the total load and the nodes. i The final corrected load is shown in formula (56): (56); in, is the node load value of node i after normalization.

[0061] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units.

[0062] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0063] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for reverse modeling of node loads based on incomplete information, characterized in that, include: A two-layer optimization model for calculating nodal electricity prices is constructed. The two-layer optimization model includes an upper-layer model and a lower-layer model. The upper-layer model aims to minimize the difference between the calculated electricity price and the actual electricity price, and obtains the nodal load distribution based on system operation constraints. The lower-layer model performs economic dispatch calculations based on the nodal load distribution to obtain the nodal marginal electricity price and returns it to the upper-layer model. The two-layer optimization model is transformed into a single-layer model for solution, and the inverse modeling results of node load are obtained. The reliability of the reverse modeling results is assessed based on the degree of deviation from capacity utilization. Based on the stated confidence level, the reverse modeling results are fused and corrected with prior load information to obtain the final node load value.

2. The method according to claim 1, characterized in that, The system operation constraints include total load constraints and main transformer N-1 safety constraints; The total load constraint includes: The sum of the loads generated at each node is equal to the total load disclosed in the electricity market; The main transformer N-1 safety constraint includes: The actual load of each substation is less than or equal to the product of the number of remaining main transformers in the substation and the rated capacity and overload factor of a single transformer; where the number of remaining main transformers is the total number of main transformers in the substation minus one; N is an integer greater than 1.

3. The method according to claim 1, characterized in that, The lower-level model performs economic dispatch calculations based on the node load distribution to obtain the node marginal electricity price, including: Based on DC power flow, an economically optimal power system operation model is constructed with the goal of minimizing power generation costs, while satisfying line power flow constraints, node power balance constraints, generator output constraints, and line capacity constraints. Construct the Lagrangian function of the economically optimal operating model; Based on the Lagrange function, the nodal marginal electricity price is obtained.

4. The method according to claim 3, characterized in that, After obtaining the nodal marginal electricity price based on the Lagrange function, the method further includes: Determine the active power loss of each line and express it as a quadratic function of the node phase angle; Based on the quadratic function, the reference node is deleted to reduce the order, resulting in the reduced network loss expression. Based on the reduced network loss expression and the relationship between node injection power and node phase angle, the marginal impact of each node injection power on the total network loss of the system is obtained, which serves as the marginal network loss coefficient of each node. Based on the marginal network loss coefficient of each node, the node marginal electricity price under DC power flow is corrected to obtain the corrected node marginal electricity price.

5. The method according to claim 1, characterized in that, The two-layer optimization model is transformed into a single-layer model for solution, yielding the inverse modeling results of node loads, including: Based on the KKT conditions of the lower-level model, the two-level optimization model is transformed into a single-level optimization model; wherein, the KKT conditions include stationary point conditions, nonnegativity conditions, and complementary relaxation conditions; The complementary relaxation conditions are processed using a linearization method to obtain a single-layer mixed integer programming model; Solving the single-layer mixed integer programming model yields the inverse modeling results of node load.

6. The method according to claim 1, characterized in that, The assessment of the reliability of the reverse modeling results based on the degree of deviation in capacity utilization includes: Calculate the capacity utilization rate of each substation; The median capacity utilization rate of each substation is determined as a reference benchmark for the system capacity utilization rate. Calculate the deviation between the capacity utilization of each node and the reference baseline; A Gaussian mapping function is used to map the deviation into node credibility.

7. The method according to claim 6, characterized in that, The calculation of the deviation between the capacity utilization of each node and the reference benchmark includes: Calculate the ratio of each node's utilization to the reference baseline; Convert the ratio to the logarithmic domain; Using the median of all logarithmic fields as a benchmark, calculate the absolute deviation of each node from the benchmark.

8. The method according to claim 1, characterized in that, The step of fusing and correcting the reverse modeling result with prior load information based on the confidence level to obtain the final node load value includes: The prior load of each node is calculated based on the proportional allocation of the substation's rated capacity. Using the credibility as a weight, the node load of the reverse modeling result and the prior load information are weighted and fused to obtain the weighted fused node load value; The weighted and merged node load values ​​are normalized to obtain the final node load values.

9. The method according to claim 3, characterized in that, The Lagrange function is expressed as: ； in, It is a Lagrange function; The total cost of generating electricity from all power plants; Index for power plants; For the collection of power plants; For power plants The power generation cost function; For power plants The power generation capacity; N is the index of the bus node; N is the set of bus nodes; For nodes Lagrange multipliers constrained by power balance; For connection at node A collection of power plants on the ground; For nodes The load; For route indexing; For the set of routes; Elements of the node-branch association matrix; For the line The meritorious trend; For power plants Lagrange multipliers with output upper limit constraints; For power plants The upper limit of output; For power plants Lagrange multipliers with output lower bound constraints; For power plants The lower limit of output; For the line Lagrange multipliers with transmission upper limit constraints; For the line Head bus The voltage phase angle; For the line The voltage phase angle of the first bus n; For the line The reactance; For the line The upper limit of transmission; For the line Lagrange multipliers with transmission lower bound constraints; For the line The lower limit of transmission.

10. The method according to claim 5, characterized in that, The objective function of the single-layer mixed integer programming model is expressed as: ； in, Let N be the objective function of a single-level mixed-integer programming model; N is the set of bus nodes. For nodes Lagrange multipliers constrained by power balance; Lagrange multipliers for the power balance constraints of reference node s; Let be the marginal network loss coefficient of node i; The voltage phase angle vector of the node; Let be the actual electricity price at node i.

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