Power grid network attack-oriented phase-shifting transformer planning-operation joint optimization method

Abstract

The invention belongs to the technical field of transformer prediction optimization, and more specifically relates to a power grid network attack-oriented phase-shifting transformer planning-operation joint optimization method. The method comprises the steps of bringing T time stages of an operation stage into a planning stage for overall planning, and describing a defender, an attacker and a system as a three-layer optimization model; dividing a three-layer optimization problem into a main problem and a plurality of sub-problems, and solving a global optimal solution; carrying out sensitivity analysis on the load, and defining an index load similarity; the load similarity is used as a clustering index, multiple time stages of the whole day are classified, and the time stages are simplified according to a clustering result; and deploying the transformer according to the decided optimal position, applying the decided phase shift angle to the actual operation stage, and if the actual load curve greatly deviates from the predicted load curve, deciding the phase shift angle in real time. According to the method, the problem of insufficient attack influence elimination performance caused by planning and running discrete design is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of transformer prediction optimization, and more specifically, relates to a combined optimization method for the planning - operation of phase - shifting transformers facing power grid cyber - attacks. Background Art

[0002] With the wide application of communication and computing technologies, the power system integrates physical networks, information technology, and operation technology, significantly improving its efficiency and reliability. However, vulnerabilities in information systems also expose the power system to various cyber threats. For example, attackers can mislead the operation of the power system by tampering with the measurement data uploaded to the control center, causing the power system to enter uneconomic or dangerous operating states, leading to serious consequences such as a significant increase in costs or cascading power outages. According to the power network security monitoring data of a certain province in China, the power system in this province suffered more than 420,000 cyber - attacks in 2020, including 65.4% of high - risk cyber - attacks. Therefore, designing defense methods against power system cyber - attacks is of great significance for ensuring the safe and stable operation of the power system.

[0003] Among the known power system cyber - attacks, load re - distribution attack is one of the most practical and serious cyber - attacks. Load re - distribution attacks mislead economic dispatch applications by tampering with load measurement values, which can overload target transmission lines or significantly increase the operating cost of the power system. Although there are various defense methods against the above - mentioned load re - distribution attacks in the power system, the existing methods mainly focus on the attack detection level, and the methods for eliminating the impacts of cyber - attacks such as load re - distribution attacks are still in their infancy. For example, existing generalized low - frequency load shedding schemes, corrective dispatch schemes, network - resilient economic dispatch schemes, etc. mainly adjust equipment parameters or economic dispatch outputs during the operation stage to weaken the attack impact, without considering issues such as equipment deployment in the planning stage; existing critical equipment protection methods are limited to the selection of critical equipment in the planning stage and fail to effectively utilize problems such as the adjustment and optimization of equipment parameters during the operation stage of the power system. Although the existing load re - distribution attack defense methods based on phase - shifting transformers discuss the deployment of defense equipment and the online operation adjustment of related equipment, the above - mentioned defense strategies are designed separately for the planning and operation stages, failing to fully explore the performance of eliminating attack impacts, resulting in insufficient protection effect and high protection cost.

[0004] Chinese Patent Document CN116542368A discloses a low-carbon and resilient site selection optimization method for phase-shifting transformers based on an improved PageRank method. The method includes: Step 1: replacing the elements in the power transmission matrix with the corresponding elements in the active power flow betweenness index matrix; Step 2: considering the power transmission of the active power flow coefficient and the particularity of generator nodes and load nodes, adding virtual nodes between generator nodes and load nodes, and modifying the power transmission matrix and the power transfer probability matrix; Step 3: taking the low-carbon and resilient comprehensive evaluation value as the goal, combining the line fault set under extreme weather, and using the BCC optimization algorithm to optimize the installation location and phase angle of the phase-shifting transformer, so as to obtain the optimal low-carbon and resilient site selection result of the phase-shifting transformer for the power system under ice disaster extreme weather conditions. However, the above-mentioned document only involves the planning of transformers and does not involve the optimization of the operation stage, and cannot fully meet the requirements of the power system.

[0005] In view of this, the present invention designs a combined planning-operation optimization method for phase-shifting transformers facing grid cyberattacks. Summary of the Invention

[0006] The present invention aims to overcome at least one defect of the above-mentioned prior art, and provides a combined planning-operation optimization method for phase-shifting transformers facing grid cyberattacks, so as to solve the problem of insufficient performance in eliminating the impact of attacks caused by the separate design of planning and operation.

[0007] The detailed technical solution of the present invention is as follows:

[0008] A combined planning-operation optimization method for phase-shifting transformers facing grid cyberattacks, the method includes:

[0009] S1. Incorporate the T time stages in the operation stage into the planning stage for overall consideration, and describe the game among the defender, attacker, and system as a collaborative defense three-layer optimization model;

[0010] S2. Decompose the collaborative defense three-layer optimization model, use the column and constraint generation algorithm to divide the original problem into a master problem and multiple sub-problems, give the algorithm for the iteration of the master problem and the sub-problems, and obtain the global optimal solution;

[0011] S3. Conduct sensitivity analysis on the load and define the index load similarity;

[0012] S4. Use the load similarity as the clustering index to classify multiple time stages throughout the day, and simplify the time stages according to the clustering results;

[0013] S5. Deploy the phase-shifting transformer according to the optimal position of the decision, and apply the decision phase shift angle to the actual operation stage. If the actual load curve deviates significantly from the predicted load curve, then make a real-time decision on the phase shift angle according to the optimal power flow scheduling that integrates the phase-shifting transformer.

[0014] Preferably according to the present invention, the three-layer collaborative defense optimization model includes three layers: the defender, the attacker, and the system from top to bottom. The goal of the defender is to minimize the cost of phase-shifting transformers and the operating cost by deciding on the set of phase-shifting transformers for T time stages. The objective function of the defender is as follows:

[0015]

[0016]

[0017] In Equation (1), N l is the number of transmission lines in the system, c l is the cost of deploying a phase-shifting transformer on line l, d l is a binary variable representing whether a phase-shifting transformer is deployed on line l, and s.t. d l ∈ {0, 1}, l ∈ N l , when d l = 0, it means there is no phase-shifting transformer on the line. T is the total number of time stages in a future period, N g is the number of generators in the system, α i and β i are the power generation cost coefficients, P i,t represents the output of the i-th generator at time t. The superscript * represents the optimal value of the bottom layer, d represents the set of phase-shifting transformer deployments, and Σ represents the set of phase shift angles;

[0018] The value range of the phase shift angle σ l,t of the phase-shifting transformer on the l-th line at time t is as follows:

[0019]

[0020] In Equation (2), and are the upper and lower bounds of the phase shift angle, N l is the number of transmission lines in the system, and T is the total number of time stages in a future period;

[0021] The goal of the attacker is to maximize the system operating cost. The objective function of the attacker is as follows:

[0022]

[0023] To ensure the concealment of the attack, the sum of the load tampering amounts ΔD k,t is zero, which is specifically expressed as follows:

[0024]

[0025] Since there is a power flow equality relationship between the load and the line power flow, to ensure concealment, when the attacker tampers with the load measurement, the power flow measurement will be tampered with accordingly, which is specifically described as follows:

[0026] ΔF t =-L·A D ·ΔD t ,t∈T (5)

[0028] In Equation (5), ΔF t represents the tampering vector of the power flow at time t, L is the power transfer distribution factor matrix, A D is the topological association matrix between the bus and the load, and ΔD t represents the load tampering amount at time t;

[0029] To ensure the concealment of the attack, the tampering of the load does not exceed ζ times the load value, that is:

[0030] -ζ·D k,t ≤ΔD k,t ≤ζ·D k,t ,k∈N d ,t∈T

[0031]

[0032] The following formula is used to determine whether the load measurement and the line power flow measurement are attacked at time t:

[0033]

[0034] In Equations (7) and (8), ω D,k,t and ω F,l,t are binary variables representing whether the load measurement and the line power flow measurement are attacked at time t, respectively. That is, at time t, when the kth load measurement is attacked, ω D,k,t =1, otherwise ω D,k,t =0; when the lth line power flow is attacked, ω F,l,t =1, otherwise ω F,l,t =0; ΔD k,t is the tampering value of the attacker for the kth load measurement at time t, and ΔF l,t is the tampering value of the attacker for the power flow on the lth transmission line at time t, and N d is the number of load measurements in the system;

[0035] Since the resources available to the attacker are often limited, there is an upper limit to the number of meters that can be tampered with. The attacker's attack resource limitations are as follows:

[0036]

[0037] In Equation (9), R a is the maximum number of attacks that an attacker can launch and measure;

[0038] The goal of the system is to minimize the operating cost, and the objective function of the system is as follows:

[0039]

[0040] Since the power system needs to operate normally, the supply-demand balance equation that the generator output and the load need to maintain is as follows:

[0041]

[0042] In Equation (11), D k,t represents the k-th load value at time t of the load forecast;

[0043] The power flow equation in the form of the power flow distribution transfer factor is as follows:

[0044] s.t. F t = L·A P ·P t - L·A d ·(D t + ΔD * t ) + (X -1 ·N lB ·L T - X -1 )·σ t , t ∈ T (12)

[0046] In Equation (12), F t represents the power flow vector at time t; L is the power transfer distribution factor matrix, A P is the topological incidence matrix between buses and generators, P t represents the generator output vector at time t; A D is the topological incidence matrix between buses and loads; D t represents the load vector at time t of the load forecast; ΔD * t represents the optimal, i.e., the worst load tampering amount for the system, at time t; X is a diagonal matrix, and its diagonal elements are the impedances on each transmission line; N LB is the topological incidence matrix between buses and branches; T is the total number of time stages in a future period; σ t represents the phase shift angle at time t;

[0047] There are upper and lower limits on the output of the generator and the power flow on the transmission line, as follows:

[0048]

[0049] In equations (13) and (14), is the upper limit of the capacity of the transmission line, P i min and P i max are the upper and lower bounds of the generator output, P is the generator output vector, F is the power flow vector on the transmission line, and F l,t represents the power flow on the l-th line at time t.

[0050] Preferably according to the present invention, in step S2, the original problem is decomposed into the form of a master problem and a sub-problem according to the column and constraint generation algorithm, and the master problem is expressed as follows:

[0051]

[0052]

[0053] In the master problem, the subscript I is the iteration count, and N I is the upper limit of the number of iterations, η is the auxiliary variable in the column and constraint generation algorithm, formula (15) is the objective function of the master problem, (16) represents the relationship between the auxiliary variable η and the objective function of the original three-layer optimization problem, and (17)-(20) are the iterative forms of the constraints (2) and (12)-(14) in the aforementioned power grid;

[0054] The sub-problem is expressed as follows:

[0055]

[0056] ΔF = -L·A D ·ΔD (23)

[0058] -ζ·D k ≤ΔD k ≤ζ·D k k = 1,…,N d (24)

[0060]

[0061] s.t.F = L·A P ·P - L·A D ·(D + ΔD * ) + (X -1 ·N LB ·L T -X -1 )·σ (29)

[0063]

[0064] For the above sub - problems, (21)-(32) are the single - time - stage forms of the original three - layer optimization problems (3)-(14). Solve (21)-(32) for each time stage t respectively instead of solving (3)-(14) globally for all time stages T.

[0065] Preferably according to the present invention, in step S2, the algorithm for the iteration of the master problem and the sub - problems specifically refers to:

[0066] First, for a given initial value d 0 Solve T sub - problems to obtain the attack vector ΔD * , and the optimal value f of the objective function of the sub - problems * is used as the upper bound of the global optimal value. The formula is as follows:

[0067]

[0068] Secondly, for the obtained Solve the master problem to obtain the shunt transformer deployment set d and the phase - shift angle set Σ. The optimal value of the objective function of the master problem is used as the lower bound of the global optimal value. Iterate cyclically until the upper and lower bounds converge.

[0069] Preferably according to the present invention, in step S3, the sensitivity analysis of the load is specifically as follows:

[0070]

[0071]

[0072] Among them, is an added auxiliary variable, whose value is equal to the load value. Its relationship is described by equation (37), and λ k is the dual variable corresponding to the equation, which can reflect the influence of the load change on the objective function;

[0073] Based on the above sensitivity analysis, the load similarity is defined as:

[0074]

[0075] In formula (40), S represents the similarity between the load vectors at times t and t′. The vectors D t and D t′ represent the load vectors at times t and t′ respectively. The coefficient λ, as a weight coefficient vector, is used to balance the weights of different loads and is obtained from the sensitivity analysis.

[0076] Preferably according to the present invention, in step S4, using the load similarity as a clustering index to classify multiple time stages of the whole day specifically refers to:

[0077] Using the K-means method, with the similarity S as the clustering index, the time phases T after clustering are divided into K clusters. The k-th cluster has n time phases, that is:

[0078] T k ={t k,1 ,t k,2 ,...,t k,n} (41)

[0080] Then the objective functions of each layer in the original three-layer optimization problem can be replaced by:

[0081]

[0082] Through the clustering method based on load similarity, the number of three-layer optimization calculations is reduced from T to K. That is, when the number of clusters is much smaller than the time periods in the load curve, the computational complexity can be significantly reduced.

[0083] According to the preference of the present invention, the specific steps of step S5 are as follows:

[0084] Deploy the phase-shifting transformer according to the optimal position of the decision, and apply the decision phase-shift angle to the actual operation stage;

[0085] If the deviation degree between the actual load value D ture and the predicted load value D used in the three-layer optimization decision in the planning stage is greater than the threshold γ, that is:

[0086]

[0087] Then the phase-shift angle σ t decided in the planning stage will no longer be used, and instead the phase-shift angle is decided by the following optimal power flow scheduling problem:

[0088]

[0089] s.t.(29)-(32)

[0090]

[0091] In formula (47), d * is the deployment set of the phase-shifting transformer decided in the planning stage.

[0092] Compared with the prior art, the beneficial effects of the present invention are:

[0093] (1) The present invention designs a joint planning - operation deployment method of phase - shifting transformers based on grid load redistribution attacks. In the planning stage, the optimal deployment locations and phase - shift angles of phase - shifting transformers are determined according to the loads in the next T operation stages, and the phase - shift angles are adjusted in real - time during the operation stage. Compared with the existing defense strategies with separate planning and operation designs, it can significantly reduce the impact of attacks on the power system.

[0094] (2) The present invention designs an iterative solution algorithm based on the column - and - constraint generation algorithm, which can obtain the optimal deployment locations, quantities of phase - shifting transformers, and the corresponding phase - shift angles in each time stage.

[0095] (3) The present invention designs an approximate solution algorithm based on load clustering, which can significantly reduce the solution complexity of the joint planning - operation deployment optimization problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 FIG. is a schematic diagram of a joint optimization method of phase - shifting transformers for grid load redistribution attacks according to the present invention.

[0097] Figure 2 FIG. shows the protection effect of the method according to the present invention in a 14 - node test system in the embodiment.

[0098] Figure 3 FIG. shows the protection effect of the method according to the present invention in a 30 - node test system in the embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0099] The following further describes the present disclosure in conjunction with the drawings and embodiments.

[0100] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present disclosure belongs.

[0101] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0102] In the case of no conflict, the embodiments and features in the present disclosure can be combined with each other.

[0103] Embodiment 1

[0104] ReferFigure 1 , this embodiment provides a joint optimization method for phase-shifting transformer planning and operation facing grid load reallocation attacks, proposes the concept of coordinated planning and operation design, optimizes the deployment of defense equipment according to possible system states in the planning stage, and significantly improves the performance of attack impact elimination compared with the separately designed attack impact elimination strategy. The method includes the following steps:

[0105] Step S1: Incorporate the T time stages in the operation stage into the planning stage for overall consideration, and describe the game among the defender, attacker, and system as a three-layer optimization model;

[0106] Step S2: Decompose the three-layer coordinated defense optimization problem, use the column and constraint generation algorithm to divide the original problem into a master problem and multiple sub-problems, give the algorithm for the iteration of the master problem and sub-problems, and obtain the global optimal solution;

[0107] Step S3: Conduct sensitivity analysis on the load, define the index load similarity, and evaluate the correlation of the load among multiple time stages;

[0108] Step S4: Use the load similarity as the clustering index to classify multiple time stages throughout the day, simplify the time stages according to the clustering results, and improve the calculation efficiency of the three-layer coordinated defense optimization problem;

[0109] Step S5: Deploy the phase-shifting transformer according to the optimal decision position, and apply the decision-making phase shift angle to the actual operation stage. If the actual load curve deviates significantly from the predicted load curve, then make a real-time decision on the phase shift angle according to the optimal power flow scheduling integrating the phase-shifting transformer.

[0110] Step S1: In the coordinated optimization framework, the defender will simultaneously make decisions on the set of phase-shifting transformer equipment, that is, the number and location of PST equipment and the corresponding sequence of phase shift angles, for a given typical load curve within the time period T. After determining the deployment scheme of these PST equipment, the attacker will search for the optimal but worst LR attack vector for the system, while the system optimizes the power generation scheduling under the influence of the defender and the attacker. The above game among the defender, attacker, and system can be described as the following three-layer optimization model:

[0111]

[0112] s.t.d l ∈{0,1},l∈N l (2)

[0114]

[0115] ΔF t =-L·AD ·ΔD t , t ∈ T 6)

[0117] -ζ·D k,t ≤ ΔD k,t ≤ ζ·D k,t , k ∈ N d , t ∈ T (7)

[0119]

[0120] s.t. F t =L·A P ·P t -L·A D ·(D t +ΔD * t )+(X -1 ·N LB ·L T -X -1 )·σ t , t ∈ T (13)

[0122]

[0123] Where T is the total number of time stages in a future period, N g is the number of generators in the system, N d is the number of load measurements in the system, N l is the number of transmission lines in the system, N LB is the topological incidence matrix of buses and branches; c l is the cost of deploying a phase-shifting transformer on line l, α i and β i are the generation cost coefficients, is the upper limit of the capacity of the transmission line, and are the upper and lower bounds of the generator output, and are the upper and lower bounds of the phase-shift angle; A P is the topological incidence matrix of buses and generators, A D is the topological incidence matrix of buses and loads, L is the power transfer distribution factor matrix, X is a diagonal matrix whose diagonal elements are the impedances on each transmission line, D k is the actual k-th load; in terms of variables, P is the output of the generator, F is the power flow on the transmission line, ΔD k,t is the tampering value of the attacker for the k-th load measurement at time t, ΔF l,t is the tampering value of the attacker for the power flow on the l-th transmission line at time t, Pi,t Denote the output of the \(i\)-th generator at time \(t\), with the superscript \(*\) representing the optimal value of the bottom layer, and \(\sigma\) l,t is the phase shift angle of the phase-shifting transformer on the \(l\)-th line at time \(t\), and \(\omega\) D,k,t and \(\omega\) F,l,t are binary variables representing whether the load measurement and line power flow measurement are attacked at time \(t\). That is, at time \(t\), when the \(k\)-th load measurement is attacked, \(\omega\) D,k,t = 1, otherwise \(\omega\) D,k,t = 0; when the \(l\)-th line power flow is attacked, \(\omega\) F,l,t = 1, otherwise \(\omega\) F,l,t = 0, and \(R\) a is the maximum number of measurements that the attacker can attack, and \(d\) l is a binary variable representing whether a phase-shifting transformer is deployed on line \(l\); in addition, in the present invention, unless otherwise stated, letters without subscripts represent vector forms of corresponding variables, and their elements are represented by letters with the same letter and subscripts;

[0124] For the three-layer optimization, (1)-(3) represent the defender. (1) is the objective function of the defender, which minimizes the cost of phase-shifting transformers and operating costs by deciding the set of phase-shifting transformers for \(T\) time stages; (2) is the value constraint of \(d\) l , and (3) represents the value range of the phase shift angle of the phase-shifting transformer on line \(l\). When \(d\) l = 0, it means there is no phase-shifting transformer on the line; (4)-(10) represent the defender. Its objective function (4) maximizes the operating cost of the system. The equation in (5) represents that the sum of all load tampering amounts should be zero to ensure the concealment of the attack. The equation in (6) represents that to ensure concealment, when the attacker tampers with the load measurement, it needs to respond with tampering of the power flow measurement because there is a power flow equation relationship between the load and the line power flow. (8) and (9) are logical constraints representing the relationship between the attack vectors \(\Delta D\) k , \(\Delta F\) l and the binary variable \(\omega\) D,k,t , \(\omega\) F,l,t . (10) represents the attack resource limitation of the attacker; (11)-(15) represent the optimal power flow scheduling of the system, where (11) is the objective function of the system - minimizing the operating cost, the constraint (12) is the power supply-demand balance equation, the constraint (13) is the power flow equation in the form of a power flow distribution transfer factor, and (14)-(15) are the upper and lower limit constraints of the variables.

[0125] Step S2: The three-layer optimization problem of eliminating the impact of load redistribution attacks based on phase-shifting transformers can be decomposed into a master problem and a sub-problem according to the column generation and constraint algorithm. The master problem can be described as:

[0126]

[0127]

[0128] where the subscript \(I\) is the iteration count, \(N\) I is the upper limit of the number of iterations, \(\eta\) is an auxiliary variable in the column and constraint generation algorithm; (16) is the objective function of the master problem, constraint (17) characterizes the relationship between the auxiliary variable \(\eta\) and the objective function of the original three-layer optimization problem, and (18)-(21) are the iterative forms of the aforementioned power grid constraints (3) and (13)-(15).

[0129] Since the attack vectors are independently generated at each time stage \(t\), the subproblems within the framework of the column and constraint generation algorithm must be decomposed into the following \(T\) subproblems. For each time period \(t\), the subproblem can be expressed as follows:

[0130]

[0131] \(\Delta F=-L\cdot A\) D \(\cdot\Delta D\) (24)

[0133] \(-\zeta\cdot D\) k \(\leq\Delta D\) k \(\leq\zeta\cdot D\) k \(k = 1,\ldots,N\) d (25)

[0135]

[0136]

[0137] s.t. \(F = L\cdot A\) P \(\cdot P - L\cdot A\) D \(\cdot(D+\Delta D\) * )+(X -1 \(\cdot N\) LB \(\cdot L\) T \(-X\) -1 )\(\cdot\sigma\) (30)

[0139]

[0140] Based on the above master problem and subproblems, an algorithm for solving the global optimal solution is given: First, for a given initial value \(d\) 0 Solve the \(T\) subproblems to obtain the attack vector \(\Delta D\) * , and the optimal value is used as the upper bound of the global optimal value. Second, for the obtained Solve the master problem to obtain the shunt transformer deployment set \(d\) and the phase shift angle set \(\sum\), and the optimal value is used as the lower bound of the global optimal value. Iterate cyclically until the upper and lower bounds converge.

[0141] Step S3: Conduct sensitivity analysis on the load:

[0142]

[0143]

[0144] wherein, is a newly added auxiliary variable, whose value is equal to the load value, and its relationship is described by equation (37), λ k is the dual variable corresponding to the equation, which can reflect the influence of the change of the load on the objective function.

[0145] Based on the above sensitivity analysis, the load similarity is defined as:

[0146]

[0147] where the vector D t and D t′ represent the load vectors at times t and t′ respectively. S represents the similarity between the load vectors at times t and t′. The coefficient λ, as a weight coefficient vector, is used to balance the weights of different loads and is obtained from the above sensitivity analysis.

[0148] Step S4: Use the above load similarity as a clustering index to classify multiple time stages throughout the day.

[0149] Using the K-means method and adopting (40) as the clustering index, assume that the time stage T after clustering is divided into K clusters, and the k-th cluster has n time stages, that is:

[0150] T k ={t k,1 ,t k,2 ,...,t k,n} (41)

[0152] Then the objective functions of each layer in the original three-layer optimization problem can be replaced by:

[0153]

[0154] Through the clustering method based on load similarity, the number of three-layer optimizations calculated is reduced from T to K. That is, when the number of clusters is much smaller than the time periods in the load curve, the computational complexity can be significantly reduced.

[0155] Step S5: Deploy the phase-shifting transformer according to the optimal position of the decision, and apply the decision phase-shift angle to the actual operation stage.

[0156] If the actual load D tureThe deviation from the predicted load D used in the three-layer optimization decision in the planning stage is greater than the threshold γ, i.e.:

[0157]

[0158] Then the phase shift angle σ decided in the planning stage will no longer be used t , and instead, the phase shift angle is decided by the following optimal power flow scheduling problem:

[0159]

[0160] s.t. (30)-(33)

[0161]

[0162] where d * is the set of shunt transformer deployments decided in the planning stage.

[0163] To verify the protection ability of the power grid load reallocation attack plan and operation collaborative defense method and device proposed in this application, the experiment compared the costs of power systems with two typical load curves (NYISO real load data) in 4 cases. Specifically, the operating cost of the power system in the normal operating state is given in Case 1, where there is no attack. In Case 2, the situation of the power system suffering from a load reallocation attack without adopting any defense scheme is simulated to show the impact of the attack. In Case 3, the attack impact elimination method based on shunt transformers is simulated, where the deployment of shunt transformer equipment and the phase shift angle of shunt transformer equipment are designed and optimized separately. Finally, in Case 4, the proposed planning and operation collaborative defense method is simulated, and the column and constraint generation algorithm is applied to solve it. The simulation results of the IEEE14-node and IEEE 30-node test systems are shown in Table 1.

[0164] Table 1 Simulation results of the collaborative defense method for the IEEE 14-node and IEEE 30-node test systems under typical load curves

[0165]

[0166] As shown in Table 1, the load reallocation attack can significantly increase the operating cost of the power system, thereby reducing the economic benefits of the power system. For example, on the typical load curve 1 of the IEEE 14-node test system, in Case 2, the operating cost under the load reallocation attack is $197,731.41 per day, which is $2,871.16 higher than the cost of the power system in the normal operating state in Case 1. On the typical load curve 2 of the IEEE 14-node test system, the impact of the load reallocation attack is more severe. When there is no defense strategy, the cost of the power system under the load reallocation attack in Case 2 is $11,198.28 higher than the cost in the normal operating state. By comparing the results of Case 2 and Case 4, the proposed method for eliminating the impact of coordinated attacks can significantly reduce the destructive impact of the load reallocation attack in the test system. Specifically, for the typical load curve 1, after applying the method for eliminating the impact of coordinated attacks, the operating cost of the power system affected by the load reallocation attack in the IEEE 14-node test system in Case 4 is $194,863.84. Compared with the cost in Case 2, the operating cost when affected by the load reallocation attack is reduced by $2,867.57, which eliminates 99.87% of the economic losses caused by the load reallocation attack. In the IEEE 30-node test system, the operating cost affected by the load reallocation attack is reduced by $47,255.86 compared with the cost in Case 2, which eliminates 100.91% of the economic losses caused by the load reallocation attack. Since a phase-shifting transformer device is deployed in the method for eliminating the impact of coordinated attacks, the operating cost in the coordinated mitigation plan is even lower than the normal operating state (Case 1, without a phase-shifting transformer device in the normal operating state). Similarly, thanks to the method for eliminating the impact of coordinated attacks, for the typical load curve 2, in the IEEE 14-node test system, the operating cost of the power system in Case 4 is $228,781.26, which is $10,535.06 lower than the operating cost in Case 2. In the IEEE 30-node test system, compared with the cost affected by the load reallocation attack, the operating cost under the method for eliminating the impact of coordinated attacks is reduced by $59,326.43. Compared with the operating costs in Case 3 and Case 4, the proposed method for eliminating the impact of coordinated attacks has more advantages than the method of separately designing the deployment of the phase-shifting transformer device and its device control. Specifically, in the method for eliminating the impact of coordinated attacks in Case 4, for the typical load curve 1, in the IEEE 14-node and IEEE 30-node test systems, the operating costs of the power systems affected by the load reallocation attack are $880.63 and $1,712.14 lower than those in the method for eliminating the impact of the phase-shifting transformer-based attack in Case 3, respectively. For the typical load curve 2, the reduced operating costs are $1,888.93 and $5,093.78, respectively, which clearly shows the advantages of the method for eliminating the impact of coordinated attacks over the existing method for eliminating the impact of the phase-shifting transformer-based attack.In addition, the number of phase-shifting transformer devices deployed in the collaborative attack impact elimination method can be much less than that in the attack impact elimination method based on phase-shifting transformers, which can further reduce the cost of deploying the attack impact elimination method. For example, in the IEEE 14-bus test system, for the typical load curve 1, the number of phase-shifting transformer devices deployed in the attack impact elimination method based on phase-shifting transformers is 13, while the number of phase-shifting transformer devices deployed in the collaborative attack impact elimination method is 3. Therefore, the proposed collaborative attack impact elimination method may significantly reduce the cost of deploying the attack impact elimination method, which is also an advantage of the proposed collaborative attack impact elimination method compared with the attack impact elimination method with separate designs of phase-shifting transformer device deployment and phase-shift angle.

[0167] Subsequently, the simulation results of the performance of the clustering-based approximate solution method are given in Table 2. The sum of squared load similarities is used as an index for selecting the number of clusters in the approximate solution method and is defined by the load similarity S in Equation (40). When the change rate of the normalized sum of squared load similarities is less than the set threshold of 1.5%, the number of clusters at this time is selected. The sum of squared load similarities and the change rate of the normalized sum of squared load similarities in the IEEE 14-bus and IEEE 30-bus test systems are shown in Figure 2 and Figure 3 。

[0168] Table 2 Simulation Results of the Clustering-Based Approximate Method

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[0171] Since the column-and-constraint generation algorithm can obtain the global optimal solution of the three-layer optimization problem, the optimal values obtained by using the column-and-constraint generation algorithm and the approximate algorithm are experimentally compared to evaluate the optimality of the approximate algorithm. As shown in Table 2, for load curve 1, in the IEEE 14-bus and IEEE 30-bus test systems, the optimal values obtained by the approximate algorithm are the same as those obtained by the column-and-constraint generation algorithm. In addition, for load curve 2, in the IEEE 14-bus test system, the optimal value obtained by the approximate algorithm is $228,784.37, and the deviation between the obtained value and the optimal value is less than 0.01%. At the same time, in the IEEE 30-bus test system, the operating cost obtained by the approximate algorithm is $146,029.18, and the deviation between the obtained value and the optimal value is approximately 0.64% of the optimal value. Therefore, the solution obtained by using the approximate algorithm is very close to the optimal solution, which demonstrates the optimality of the proposed approximate algorithm.

[0172] In summary, the joint deployment method of phase-shifting transformer planning and operation designed in this application for grid load reallocation attacks is modeled as a three-layer optimization problem. Subsequently, a clustering-based approximation algorithm is proposed to reduce the computational complexity by clustering load similarities, and a metric for load similarity is proposed. The simulation results in the IEEE 14-bus and 30-bus test systems verify the performance and effectiveness of the proposed collaborative attack impact elimination method.

[0173] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the technical solutions of the present invention, rather than limitations on the specific implementation manners of the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the claims of the present invention shall be included within the protection scope of the claims of the present invention.

Claims

1. A phase-shifting transformer planning-operation joint optimization method for power grid network attacks, characterized in that: The method comprises: S1. Incorporate the T time phases of the operation phase into the planning phase, and describe the game between defenders, attackers, and systems as a three-layer optimization model of collaborative defense. S2. Decompose the three-layer optimization model of collaborative defense, use the column and constraint generation algorithm to divide the original problem into a main problem and multiple sub-problems, and provide an algorithm for iterating the main problem and sub-problems to obtain the global optimal solution; S3, perform sensitivity analysis on the load and define the index load similarity; S4, using load similarity as a clustering indicator, classifying multiple time stages throughout the day, and simplifying the time stages according to the clustering results; S5. Deploy the phase-shifting transformer according to the optimal position decided, and apply the decided phase-shifting angle to the actual operation stage. If the actual load curve deviates significantly from the predicted load curve, the phase-shifting angle is decided in real time according to the optimal power flow dispatching of the integrated phase-shifting transformer.

2. The phase-shifting transformer planning-operation joint optimization method for power grid network attacks according to claim 1 is characterized in that: The collaborative defense three-layer optimization model includes three layers from top to bottom: defender, attacker, and system. The goal of the defender is to minimize the cost and operating cost of the phase-shifting transformer by deciding the set of phase-shifting transformers in T time stages. The objective function of the defender is as follows: In formula (1), N l is the number of transmission lines in the system, c l is the cost of deploying a phase-shifting transformer on line l, d l is a binary variable, representing whether the line l is equipped with a phase-shifting transformer, and std l ∈{0,1},l∈N l , when d l =0 means there is no phase-shifting transformer on the line, T is the total number of time stages in the future, N g is the number of generators in the system, α i and β i is the power generation cost coefficient, P i,t represents the output of the i-th generator at time t, the superscript * represents the optimal value of the lowest layer, d represents the phase-shifting transformer deployment set, and Σ represents the phase-shifting angle set; The phase shift angle σ of the phase-shifting transformer on the lth line at time t l,t The value range of is as follows: (2) In formula (2), and is the upper and lower bounds of the phase shift angle, N l is the number of transmission lines in the system, T is the total number of time stages in the future; The attacker's goal is to maximize the system operation cost. The attacker's objective function is as follows: Load tampering amount ΔD k,t The sum of is zero, which is expressed as follows: When an attacker tampers with load measurements, he or she will also tamper with power flow measurements accordingly. The specific description is as follows: ΔF t =-L·A D ·ΔD t ,t∈T (5) In formula (5), ΔF t represents the tampering vector of the power flow at time t, L is the power transfer distribution factor matrix, A D is the topological correlation matrix between busbar and load, ΔD t represents the load tampering amount at time t; The tampering of the load shall not exceed ζ times the load value, that is: The following formula is used to determine whether the load measurement and line flow measurement are attacked at time t: In formulas (7) and (8), ω D,k,t and ω F,l,t are binary variables that characterize whether the load measurement and line flow measurement are attacked at time t. That is, at time t, when the kth load measurement is attacked, ω D,k,t =1, otherwise ω D,k,t =0; when the lth line flow is attacked, ω F,l,t =1, otherwise ω F,l,t =0; ΔD k,t is the tampered value measured by the attacker for the kth load at time t, ΔF l,t is the attacker's tampered value of the power flow on the lth transmission line at time t, N d The quantity measured for the load in the system; The attacker's attack resource restrictions are as follows: In formula (9), R a The maximum number of measurements that an attacker can attack; The goal of the system is to minimize the operating cost. The objective function of the system is as follows: The supply and demand balance equation that the generator needs to maintain for power generation and load is as follows: In formula (11), D k,t represents the kth load value at time t in load forecast; The power flow equation in the form of power flow distribution transfer factor is as follows: s.t.F t =L·A P ·P t -L·A D ·(D t +ΔD * t )+(X -1 ·N LB ·L T -X -1 )·σ t ,t∈T (12) In formula (12), F t represents the power flow vector at time t; L is the power transfer distribution factor matrix, A P is the topological correlation matrix between the busbar and the generator, P t A represents the generator output vector at time t; D is the topological correlation matrix between busbar and load; D t represents the load vector at time t of load forecast; ΔD * t represents the optimal load tampering at time t, that is, the worst load tampering for the system; X is a diagonal matrix, and its diagonal elements are the impedances on each transmission line; N LB is the topological association matrix of busbars and branches; T is the total number of time stages in the future; σ t represents the phase shift angle at time t; There are upper and lower limits on the output of the generator and the power flow on the transmission line, as follows: In formulas (13) and (14), is the upper capacity limit of the transmission line, and are the upper and lower bounds of the generator output, P is the generator output vector, F is the power flow vector on the transmission line, and F l,t represents the power flow on the lth line at time t.

3. The phase-shifting transformer planning-operation joint optimization method for power grid network attacks according to claim 2 is characterized in that: In step S2, the original problem is decomposed into a main problem and sub-problems according to the column and constraint generation algorithm. The main problem is expressed as follows: In the main problem, the subscript I is the iteration count, and N is I is the upper limit of the number of iterations, η is the auxiliary variable in the column and constraint generation algorithm, formula (15) is the objective function of the main problem, (16) represents the relationship between the auxiliary variable η and the objective function of the original three-layer optimization problem, (17)-(20) are the iterative forms of constraints (2) and (12)-(14) in the aforementioned power grid; The sub-problem is expressed as follows: ΔF=-L·A D ·ΔD (23) s.t.F=L·A p ·P-L·A D ·(D+ΔD * )+(X -1 ·N LB ·L T -X -1 )·σ (29) For the above subproblems, (21)-(32) are the single-time stage forms of the original three-level optimization problems (3)-(14). (21)-(32) are solved separately for each time stage t instead of solving (3)-(14) as a whole for all time stages T.

4. The phase-shifting transformer planning-operation joint optimization method for power grid network attacks according to claim 3 is characterized in that: In step S2, the algorithm for iterating the main problem and the sub-problems specifically refers to: First, for the given initial value d0, solve T sub-problems and obtain the attack vector ΔD * , the optimal value of the sub-problem objective function f * As the upper bound of the global optimal value, the formula is as follows: Secondly, for the obtained Solve the main problem, obtain the phase-shift transformer deployment set d and the phase shift angle set Σ, and use the optimal value of the main problem objective function as the lower bound of the global optimal value. Iterate until the upper and lower bounds converge.

5. The phase-shifting transformer planning-operation joint optimization method for power grid network attacks according to claim 2 is characterized in that: In step S3, the sensitivity analysis of the load is performed as follows: in, is a newly added auxiliary variable, whose value is equal to the load value, and its relationship is described as equation (37), λ k It is the dual variable corresponding to the equation, which can reflect the impact of load changes on the objective function; Based on the above sensitivity analysis, the load similarity is defined as: In formula (40), S represents the similarity between the load vectors at time t and t′, and the vector D t and D t′ represent the load vectors at time t and t′ respectively, and the coefficient λ is used as a weight coefficient vector to balance the weights of different loads, which is obtained by sensitivity analysis.

6. The phase-shifting transformer planning-operation joint optimization method for power grid network attacks according to claim 2 is characterized in that: In step S4, using load similarity as a clustering indicator to classify multiple time stages throughout the day specifically means: Using the K-means method, the similarity S is used as the clustering index, and the clustered time period T is divided into K clusters. The kth cluster has n time periods, that is: T k ={t k,1 ,t k,2 ,...,t k,n } (41) Then the objective function of each layer in the original three-layer optimization problem can be replaced by: Through the clustering method based on load similarity, the calculated number of three-layer optimizations is reduced from T to K.

7. The phase-shifting transformer planning-operation joint optimization method for power grid network attacks according to claim 2 is characterized in that: The step S5 is specifically as follows: Deploy the phase-shifting transformer according to the optimal position decided, and apply the decided phase-shifting angle to the actual operation stage; If the actual load value D ture The deviation from the predicted load value D used in the three-level optimization decision-making in the planning stage is greater than the threshold γ, that is: Then the phase shift angle σ determined in the planning phase will no longer be used t , and use the following optimal power flow scheduling problem to decide the phase shift angle: s.t.(29)-(32) In formula (47), d * A collection of phase-shift transformer deployments for planning stage decisions.

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