Enhanced resource allocation method for substations considering the uncertainty of component failure numbers

Abstract

This invention relates to a substation enhanced resource allocation method considering the uncertainty of the number of component failures, comprising the following steps: S1, classifying the perceived uncertainty of the number of substations damaged; S2, evaluating the probability of random scenarios with different numbers of substations damaged; S3, fusing different expert probability assessments using an improved D-S evidence theory; S4, based on the classification of the uncertainty of the number of substations damaged, calculating the corresponding SSDAD model using NFE C&CG to obtain the substation enhanced resource allocation scheme that minimizes system load shedding loss. The substation enhanced resource allocation stochastic optimization model of this invention enables the optimal substation repair and enhanced resource allocation scheme that minimizes expected load loss under extreme events. Embedding the network flow two-stage robust optimization C&CG algorithm can improve the solution speed by several orders of magnitude, allowing more time for the actual deployment and execution of the optimal pre-disaster substation enhanced resource allocation scheme.

Description

Technical Field

[0001] This invention relates to power system safety, and more specifically, to a substation enhanced resource allocation method that takes into account the uncertainty of the number of component failures. Background Technology

[0002] In recent years, extreme events have occurred frequently, such as floods, typhoons, earthquakes, and even cyberattacks, posing a significant threat to the safe and reliable operation of the power grid. These extreme scenarios are low-probability, high-impact events. Due to their low probability of occurrence, effective historical data is lacking. Therefore, planners find it difficult to determine the specific number of power grid components that may be damaged in extreme events; that is, planners face uncertainty regarding the number of faulty components. To address the uncertainty of the number of component failures in extreme events, three common methods are robust optimization, stochastic optimization, and distributed robust optimization.

[0003] Classical robust optimization methods use the Defender-Attacker-Defender (DAD) model to determine the optimal reinforcement resource allocation. This model assumes the worst-case scenario; for example, if planners are uncertain whether K or K+3 components will fail in an extreme event, they will consider the possibility of K+3 components failing. Stochastic optimization based on the classic DAD model assumes that the number of component failures follows a known probability distribution, thus determining the reinforcement scheme that minimizes the system's load shedding loss. Distributed robust optimization further considers the uncertainty of the probability distribution, constructing a fuzzy set containing all possible probability distributions, and then searching for the optimal reinforcement strategy in the worst-case scenario based on this set.

[0004] However, robust optimization is often too conservative and does not guarantee an optimal defense strategy. While classic stochastic optimization and sub-Brutal robust optimization methods can handle the uncertainty of the number of component failures, solving the NK test problem in simulated extreme events is already NP-hard. Solving multi-scenario defense-attack-defense DAD models based on stochastic and sub-Brutal robust optimization frameworks is even more challenging due to the need to handle more uncertainties and more complex scenarios. For example, classic robust optimization considers selecting two lines from 100 branches... There are various combinations. In the stochastic optimization DAD model, if the planner believes that there could be 2, 3, 4, or 5 lines that are damaged, then it is necessary to consider... This involves various combinations of fault scenarios. Furthermore, existing research only considers the uncertainty of the number of damaged lines. However, considering the fault coupling of cascaded components in some extreme scenarios, such as floods and cyberattacks, where a substation fault leads to line tripping, the uncertainty of the number of substation faults also needs to be considered. If planners cannot determine whether 2 or 3 out of 50 substations will be successfully attacked, then further consideration is needed beyond the original plan. Such attack combinations can make problem-solving extremely complex. Often, the faster a solution to the enhanced resource allocation scheme is found, the more time can be gained for actual deployment.

[0005] Therefore, considering the uncertainty of the number of cascaded component failures in extreme events, how to quickly calculate and determine the substation defense scheme that minimizes the expected load shedding loss of the system is an important issue that needs to be studied. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a substation enhanced resource allocation method that considers the uncertainty of the number of component failures. This method can determine the optimal substation emergency repair and enhanced resource allocation scheme that minimizes the expected load loss of the system under extreme events. The proposed embedded network flow two-stage robust optimization C&CG algorithm can improve the solution speed by several orders of magnitude, thus gaining more time for the actual deployment and execution of the optimal substation enhanced resource allocation scheme before disasters.

[0007] The technical solution adopted by this invention to solve its technical problem is: to construct a substation enhanced resource allocation method that considers the uncertainty of the number of component failures, including the following steps:

[0008] S1. Classify the uncertainty in the number of substations damaged;

[0009] S2. Evaluate the probability of random scenarios involving different numbers of substations being damaged;

[0010] S3. Integrate the probability assessments of different experts using the improved DS evidence theory;

[0011] S4. Based on the uncertainty of the number of substations damaged, the corresponding SSDAD models are calculated using NFE C&CG to obtain the substation enhanced resource allocation scheme that minimizes the system load shedding loss.

[0012] According to the above scheme, in step S1, the uncertainty of the number of substations damaged in extreme scenarios can be divided into three types:

[0013] 1) If planners are completely unable to determine how many substations will be destroyed;

[0014] 2) The planners judged that the number of substations damaged was insufficient, but could not determine the exact number of substations that would be damaged;

[0015] 3) Planners predicted that a large number of substations would be destroyed.

[0016] According to the above scheme, in step S2, different random scenarios are analyzed using generalized stochastic Petri nets, Bayesian networks, and Markov models as needed to evaluate the probability of different extreme events; the different extreme events include floods, typhoons, earthquakes, and cyberattacks.

[0017] According to the above scheme, in step S3, the improved DS evidence theory is used to fuse the probability assessment results of different experts, specifically including the following steps:

[0018] S301. Input the probability assessment matrix of N experts on the success of destroying different numbers of components, and set i = 1;

[0019] S302. When i = 1, calculate the matrix probability fusion matrix. element m ij Let be the probability that the i-th expert believes that j components can be successfully destroyed.

[0020] S303. Calculate L1 = sum(R) - sum(dialog(R)), i = i + 1;

[0021] S304. When i>1, update the probability evaluation matrix R = [dialog(R)]. T ·m i +1;

[0022] S305. Calculate L2 = sum(R) - sum(dialog(R)), i = i + 1;

[0023] S306. Repeat steps 4-5 until the probability assessment fusion of N experts is completed;

[0024] S307. Calculate the conflict coefficient L = L1 + L2 + ... + L N ;

[0025] S308. If L < 0.95, the fusion result of the probability of different extreme scenarios is dialog(R) / (1-L); if L ≥ 0.95, the fusion result of the probability of the j-th element being successfully destroyed is: L×(dialog(R)[1]+,…,+dialog(R)[N]) / N+sum(dialog(R)).

[0026] According to the above scheme, in step S4, the SSDAD model is divided into three layers: the first layer determines the amount of enhanced resources for substations before a disaster, with the goal of minimizing the expected load shedding loss of the system; the second layer simulates all possible extreme scenarios, i.e., different numbers of substations and lines will be damaged, with the goal of maximizing the expected load loss of the system under all extreme scenarios; the third layer simulates the dispatcher taking corresponding load shedding, generator adjustment and other measures to deal with all possible fault scenarios, with the objective function being to minimize the load loss of the system under the corresponding extreme scenario.

[0027] According to the above scheme, the objective of the SSDAD model is to minimize the expected load loss of the system under all extreme scenarios. The specific mathematical model is as follows:

[0028]

[0029] A BL ·f l (s)=A BG ·P g (s)-A BD ·(D d -ΔD d (s)) (11)

[0030]

[0031] In the formula: n, l, g, d, and s are the indices of the node, line, generator, load, and extreme scenario, respectively.

[0032] Ω(s) represents the probability of different extreme scenarios occurring.

[0033] E Ω(s) To account for the expected losses caused by different numbers of components being destroyed;

[0034] w l (s) represents a 0-1 variable indicating a broken line in scenario s. If w l When (s)=1, then in extreme scenario s, line l will be disconnected; otherwise, line l will not be disconnected.

[0035] a n (s) is a 0-1 variable representing whether the substation is damaged under extreme scenario s. If a n When (s) = 1, the substation located at node n is destroyed in the extreme scenario s; otherwise, it is not destroyed.

[0036] u n (s) is a 0-1 variable representing the state of the substation located at node n, u n If (s) = 0, then substation n has been successfully destroyed; otherwise, the substation is in normal working condition.

[0037] f l (s) represents the branch current under extreme scenario s; P g (s) represents the generator output under extreme scenario s; ΔD d (s) represents the load shearing under extreme scenario s; θ n (s) represents the phase angle under extreme scenario s, G g,max F l,max D d θ n,max These represent the maximum output of generator g, the maximum transmission power of line l, the load at node d, and the voltage phase angle limit at node n, respectively. K1, K2(s), and K3(s) are the substation reinforcement resources, the estimated number of substations destroyed in extreme scenario s, and the estimated number of lines destroyed in extreme scenario s, respectively; A BL 、A BG 、A BD These are the node-line, node-generator, and node-load correlation matrices, respectively; T is a very large constant.

[0038] Equation (1) is the objective function of the model; Equation (2) is the budget constraint for the number of line reinforcement resources; Equation (3) is the constraint for the number of substations destroyed under different extreme scenarios s; Equation (4) represents the constraint for the number of lines destroyed under different extreme scenarios; Equation (5) represents that under different extreme scenarios s, if neither of the substations at both ends of the line is destroyed, then the line will not be destroyed; Equation (6) represents the state of whether the substation is destroyed under different extreme scenarios s; Equations (7)-(8) represent the maximum transmission power limit constraint of the line under different extreme scenarios s, considering the state of line destruction; Equations (9)-(10) represent the DC power flow constraint of the line under different extreme scenarios s; Equation (11) represents the node power balance equation under different extreme scenarios s; Equations (12)-(14) represent the limit constraints that all generator output, node load shedding, and node voltage phase angle must comply with under different extreme scenarios s.

[0039] According to the above scheme, the SSDAD optimization model is decomposed into a main problem and sub-problems under different scenarios s.

[0040] 1) Main Problem: Given a set of damaged cascaded components under different extreme scenarios in the k-th iteration, solve the main problem to determine a substation enhanced resource allocation scheme to reduce the expected load shedding loss of the system. Its mathematical expression is as follows:

[0041]

[0042] st∑ n z n ≤K3 (18)

[0043]

[0044]

[0045] In the formula: This represents the worst-case component failure scenarios under different extreme conditions obtained by solving the subproblem in the kth iteration; These are the substation state variables and scheduling variables added to the main problem during the k-th iteration;

[0046] 2) Sub-problem: Given a substation defense resource allocation strategy The worst-case component failure scenario is obtained by solving the subproblems, and its mathematical expression is as follows:

[0047]

[0048] st constraints (3)-(5)(16)

[0049]

[0050] Constraints (7)-(8), (11)-(13) (18)

[0051] Using the strong duality condition, the model is transformed into a single-layer model as follows:

[0052]

[0053] st constraint(3)-(5) (20)

[0054]

[0055] In the formula w l (s),λ n (s), β g (s),, α d (s) is the dual variable corresponding to (7)-(8) and (11)-(13);

[0056] Analyzing constraint (22), since its constraint parameter matrix is ​​a fully simple modulus matrix, therefore w l (s), β g (s), α d (s) and |λ n The upper bound of (s)| is 1.

[0057] According to the above scheme, in order to ensure the accuracy of the solution and speed up the solution process, the solution of the two-layer model of the subproblem is adopted using the following robust optimization algorithm based on the network flow model stage:

[0058] a. Input all grid parameters, including generator maximum output, load, line maximum power capacity, maximum phase angle, and topology parameters;

[0059] b. Solve the single-layer model equations (19)-(22) under different extreme scenarios to obtain the worst-case component failure.

[0060] c. Solve the DCOPF model fixed under different scenarios s to obtain

[0061] d. Return the results of the screening of damaged components. Compared with load shedding loss and expected load loss;

[0062] e. By embedding the solution process of the network flow model into a two-stage robust column generation algorithm, the final output result can be obtained.

[0063] The substation enhanced resource allocation method considering the uncertainty of the number of component failures according to the present invention has the following beneficial effects:

[0064] 1. This invention classifies the uncertainty of the number of different cascaded components destroyed in extreme events, and strengthens resource allocation calculation according to the corresponding uncertainty level, which can reduce the computational scale of large-scale systems.

[0065] 2. The enhanced resource allocation stochastic optimization model proposed in this invention, which considers the uncertainty of the number of substations damaged, can minimize the expected load shedding loss of the system when the substation defense resource allocation scheme calculated using this model is used.

[0066] 3. The C&CG algorithm for network flow embedding proposed in this invention can improve the solution speed of the model by several orders of magnitude. Attached Figure Description

[0067] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0068] Figure 1 This is a calculation framework diagram of the SSDAD model for the substation enhanced resource allocation method that considers the uncertainty of the number of component failures in this invention.

[0069] Figure 2 This is a calculation framework diagram of the SSDAD model for a completely uncertain number of substations damaged according to the present invention;

[0070] Figure 3This is a flowchart of the SSDAD model calculation based on cognitive uncertainty of the present invention;

[0071] Figure 4 This is a flowchart of the NFE C&CG algorithm of the present invention. Detailed Implementation

[0072] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0073] like Figure 1-4 As shown, the present invention presents a stochastic substation-based Defender-Attacker-Defender (SSDAD) method for pre-disaster reinforcement resource allocation in substations, considering the uncertainty of the number of cascaded component failures. This model is based on a min-max-min three-layer structure and improves upon the classic three-layer DAD stochastic optimization model framework. It is applied to the optimization problem of how to pre-allocate substation reinforcement resources to minimize the final expected load shedding loss, considering the uncertainty of the number of substations damaged. A new algorithm is proposed to improve the solution rate of the new model, including the following steps:

[0074] S1. Classify the uncertainty regarding the number of substations damaged. In extreme scenarios, the uncertainty regarding the number of substations damaged can be divided into three types:

[0075] 1) If planners are completely unable to determine how many substations will be destroyed;

[0076] 2) The planners judged that the number of substations damaged was insufficient, but could not determine the exact number of substations that would be damaged;

[0077] 3) Planners predicted that a large number of substations would be destroyed.

[0078] In the first case, planners only need to consider two stochastic scenarios: the substation is damaged and resources are insufficient, and the substation resources are sufficient. In the second case, each scenario of insufficient substation damage needs to be considered. In the third case, the extreme scenario failures simulated in the proposed stochastic optimization model for enhanced substation resource allocation are equivalent to the classic three-layer robust optimization defense-attack-defender (DAD) model that only considers the uncertainty of the number of lines damaged.

[0079] S2. Evaluate the probability of random scenarios involving different numbers of substations being damaged;

[0080] Different probability assessment methods exist for various extreme events, such as floods, typhoons, earthquakes, and cyberattacks. Generalized stochastic Petri nets, Bayesian networks, Markov models, and other methods can be used for analysis depending on specific needs.

[0081] S3. Integrate the probability assessments of different experts using the improved DS evidence theory;

[0082] In engineering practice, planners can only obtain limited information beforehand about the damage to components in extreme events. Even with the same data and information, different planners and experts may make different, even contradictory, judgments. Improving the DS evidence theory to fuse the probabilistic assessments of different experts can integrate their evaluation results.

[0083] S301. Input the probability assessment matrix of N experts on the success of destroying different numbers of components, and set i = 1;

[0084] S302. When i = 1, calculate the matrix probability fusion matrix. element m ij Let be the probability that the i-th expert believes that j components can be successfully destroyed.

[0085] S303. Calculate L1 = sum(R) - sum(dialog(R)), i = i + 1;

[0086] S304. When i>1, update the probability evaluation matrix R = [dialog(R)]. T ·m i +1;

[0087] S305. Calculate L2 = sum(R) - sum(dialog(R)), i = i + 1;

[0088] S306. Repeat steps 4-5 until the probability assessment fusion of N experts is completed;

[0089] S307. Calculate the conflict coefficient L = L1 + L2 + ... + L N ;

[0090] S308. If L < 0.95, the fusion result of the probability of different extreme scenarios is dialog(R) / (1-L); if L ≥ 0.95, the fusion result of the probability of the j-th element being successfully destroyed is: L×(dialog(R)[1]+,…,+dialog(R)[N]) / N+sum(dialog(R)).

[0091] S4. Based on the uncertainty of the number of substations damaged, the corresponding SSDAD models are calculated using NFE C&CG to obtain the substation enhanced resource allocation scheme that minimizes the system load shedding loss.

[0092] The two-stage robust optimization column generation (NFE C&CG) algorithm, which embeds a network flow model, relaxes the line DC power flow constraints and phase angle constraints in the underlying DC optimal power flow (DCOPF) model of the SSDAD model, transforming it into a network flow model. The underlying network flow model can be equivalently approximated to the original DCOPF model in actual power grids.

[0093] like Figure 1 As shown, the basic framework of the SSDAD model consists of three layers. The first layer determines the amount of pre-disaster reinforcement resources for substations, with the objective of minimizing the expected load shedding loss of the system. The second layer simulates all possible extreme scenarios, i.e., different numbers of substations and lines will be damaged, with the objective of maximizing the expected load loss of the system under all extreme scenarios. The third layer simulates the dispatcher's corresponding load shedding and generator adjustment measures to deal with all possible fault scenarios, with the objective function being to minimize the load loss of the system under the corresponding extreme scenario. The goal of the SSDAD model is to minimize the expected load loss of the system under all extreme scenarios. Its specific mathematical model is as follows:

[0094]

[0095]

[0096] A BL ·f l (s)=A BG ·P g (s)-A BD ·(D d -ΔD d (s)) (11)

[0097]

[0098] In the formula: n, l, g, d, and s are the indices of the node, line, generator, load, and extreme scenario, respectively. Ω(s) is the probability of different extreme scenarios occurring, and E Ω(s) To consider the expected losses caused by scenarios where different numbers of components are damaged; w l (s) represents a 0-1 variable indicating a broken line in scenario s. If w lWhen (s) = 1, then in the extreme scenario s, line l will be disconnected; otherwise, line l will not be disconnected. n (s) is a 0-1 variable representing whether the substation is damaged under extreme scenario s. If a n When (s) = 1, then in the extreme scenario s, the substation located at node n is destroyed; otherwise, it is not destroyed. n (s) is a 0-1 variable representing the state of the substation located at node n, u n If (s) = 0, then substation n has been successfully destroyed; otherwise, the substation is in normal working condition. l (s) represents the branch current under extreme scenario s; P g (s) represents the generator output under extreme scenario s; ΔD d (s) represents the load shearing under extreme scenario s; θ n (s) represents the phase angle under extreme scenario s. G g,max F l,max D d θ n,max These represent the maximum output of generator g, the maximum transmission power of line l, the load at node d, and the voltage phase angle limit at node n, respectively. K1, K2(s), and K3(s) are the substation reinforcement resources, the estimated number of substations destroyed in extreme scenario s, and the estimated number of lines destroyed in extreme scenario s, respectively; A BL 、A BG 、A BD These are the node-line, node-generator, and node-load correlation matrices, respectively; T is a very large constant.

[0099] Equation (1) is the objective function of the model. Equation (2) is the budget constraint for the number of enhanced resources for the line. Equation (3) is the constraint for the number of substations destroyed under different extreme scenarios s. Equation (4) represents the constraint for the number of lines destroyed under different extreme scenarios. Equation (5) represents that under different extreme scenarios s, if neither of the substations at both ends of the line is destroyed, then the line will not be destroyed. Equation (6) represents the state of whether the substation is destroyed under different extreme scenarios s. Equations (7)-(8) represent the maximum transmission power limit constraint of the line under different extreme scenarios s, considering the state of line destruction. Equations (9)-(10) represent the DC power flow constraint of the line under different extreme scenarios s. Equation (11) represents the node power balance equation under different extreme scenarios s. Equations (12)-(14) represent the limit constraints that all generator output, node load shedding, and node voltage phase angle must comply with under different extreme scenarios s.

[0100] It is worth noting that when planners are completely uncertain about how many substations will be damaged, they only need to assess the probability of two random scenarios: substation damage due to insufficient resources and substation resource abundance. Figure 2 The calculation framework shown is as follows: When planners determine that the number of substations to be damaged is insufficient, but cannot determine the exact number of substations to be damaged, it is necessary to consider every scenario where the number of substations to be damaged is insufficient. In this case, the calculation framework is as follows: Figure 1 As shown; 3) If the planner judges that a large number of substations will be destroyed, then only the uncertainty of the number of lines destroyed needs to be considered. The classic enhanced resource stochastic optimization allocation model that considers the uncertainty of the number of lines can be used for calculation.

[0101] Given a graphical representation of a power system G(V,E), let V and E be the maximum and minimum line admittances in the power grid, respectively. If the following conditions are met:

[0102]

[0103] R = max(card(V) i ),...,card(V m (16)

[0104] In the formula, V represents the set of vertices in the system and E represents the set of edges represented by the line. Then, the constraints (9)-(10) in the DCoptimal power flow (DCOPF) model can be equivalently relaxed, thereby transforming the underlying DCOPF model into a network flow model.

[0105] In actual power systems, since the planned line capacity is often much larger than the rated power of the line during normal system operation, even considering the impact of changes in load demand and generator output cost on system operation, conditions (15)-(16) are easily satisfied. Therefore, constraints (9)-(10) and constraint (14) in the underlying DCOPF model of the subproblem can be removed. The SSDAD optimization model can be decomposed into a main problem and subproblems under different scenarios s.

[0106] 1) Main Problem: Given a set of damaged cascaded components under different extreme scenarios in the k-th iteration, solve the main problem to determine a substation enhanced resource allocation scheme to reduce the expected load shedding loss of the system. Its mathematical expression is as follows:

[0107]

[0108] st∑ n z n ≤K3 (18)

[0109]

[0110] In the formula: This represents the worst-case component failure scenarios under different extreme conditions obtained by solving the subproblem in the kth iteration; These are the substation state variables and scheduling variables added to the main problem during the k-th iteration.

[0111] 2) Sub-problem: Given a substation defense resource allocation strategy The worst-case component failure can be obtained by solving the subproblems, and its mathematical expression is as follows:

[0112]

[0113] st constraints (3)-(5)(16)

[0114]

[0115] Constraints (7)-(8), (11)-(13)(18)

[0116] Using the strong duality condition, the model is transformed into a single-layer model as follows:

[0117]

[0118] st constraint(3)-(5)(20)

[0119]

[0120] In the formula w l (s),λ n (s), β g (s),, α d (s) is the dual variable corresponding to (7)-(8) and (11)-(13).

[0121] Analyzing constraint (22), since its constraint parameter matrix is ​​a fully simple modulus matrix, therefore w l (s), β g (s), α d (s) and |λ n The upper bound of (s)| is 1.

[0122] In summary, to ensure solution accuracy and accelerate solution speed, the two-layer model of the subproblem can be solved using the following two-stage robust optimization algorithm based on the Network-flow based (NFB) model:

[0123] a. Input all grid parameters, including generator maximum output, load, line maximum power capacity, maximum phase angle, and topology parameters.

[0124] b. Solve the single-layer model equations (19)-(22) under different extreme scenarios to obtain the worst-case component failure.

[0125] c. Solve the DCOPF model fixed under different scenarios s to obtain

[0126] d. Return the results of the screening of damaged components. Compared with load shedding loss and expected load loss.

[0127] e. Embed the solution process of the above network flow model into a two-stage robust column generation algorithm, such as... Figure 3 As shown, the final output result can be obtained.

[0128] The calculation process of the SSDAD model based on the uncertainty of the perceived number of substations damaged is as follows: Figure 4 As shown.

[0129] The substation enhanced resource allocation method that takes into account the uncertainty of the number of component failures provided by this invention can be applied to specific scenarios through the following steps.

[0130] To facilitate comparison, explanation, and verification of the computational performance of large-scale systems, the IEEE RTS 24-node system and the IEEE 118-node system are analyzed. Since the uncertainty regarding the number of damaged lines has been studied and is not a contribution of this invention, the uncertainty of the number of damaged lines is not studied; K2 = 5 is fixed, and only the following two uncertainties are considered: 1) the first uncertainty: if the planner is completely unable to determine how many substations will be damaged; 2) the second uncertainty: the planner judges the number of damaged substations to be insufficient, but cannot determine the specific number of substations that will be damaged.

[0131] The first type of uncertainty:

[0132] If planners are completely uncertain about how many substations will be damaged, they can first assess two stochastic scenarios: whether the number of damaged substations is sufficient. Assuming an assessment of the uncertainty regarding the number of damaged substations, the initial probability assessment results are shown in Appendix Table 1:

[0133] Appendix 1: Expert Initial Probability Assessment and Fusion Results Regarding Whether the Number of Damaged Substations Was Sufficient

[0134]

[0135] The second type of uncertainty:

[0136] If planners can determine that substations will not be extensively damaged, but are unsure of the exact number of substations that will be damaged, then they need to assess the probability of different numbers of substations being damaged.

[0137] The first type of uncertainty:

[0138] If planners are completely unable to determine the number of substations damaged, they must first consider two scenarios: whether the number of damaged substations is sufficient. For the IEEE RTS 24-node system, scenario 1 is defined as insufficient substation damage (K1≤2); scenario 2 is defined as sufficient substation damage (K1>2). (The threshold value of 2 for whether the number of damaged substations is sufficient can be determined by continuously increasing K2 and recalculating the DAD model until the resulting load shedding loss remains constant). Using the probability assessment fusion results in Appendix 1, the probabilities of the two random scenarios of insufficient and sufficient substation damage are set to {0.6538, 0.3461}. The calculation results of the SSDAD model include substation reinforcement schemes, damaged schemes, load losses in both scenarios, and expected losses, as shown in Appendix 2.

[0139] Appendix Table 2: Calculation Results of the First Uncertainty SSDAD Model for the IEEE RTS 24-Node System

[0140]

[0141]

[0142] Table 2 shows that when planners cannot determine the number of substations damaged in the IEEE RTS 24-node system, the optimal solution is to reinforce substations 10, 12, 14, and 23, with an expected loss of 466.26 MW. This result is compared with the substation reinforcement schemes obtained under a single scenario. By setting the parameter K1 in the SDAD model to 2 and 5, the corresponding substation reinforcement schemes for a single scenario can be obtained. When K1 = 2, the substation reinforcement scheme obtained by the SDAD model is to reinforce substations at nodes 6, 10, 13, and 14; when K1 = 5, the protection scheme obtained by the SDAD model is to reinforce substations at nodes 10, 12, 20, and 23. Thus, the load loss and expected loss for each scenario under the three reinforcement schemes can be obtained, as shown in Appendix Table 3.

[0143] Appendix Table 3: Comparison of the effectiveness of the first uncertainty defense scheme for the IEEE RTS 24-node system

[0144]

[0145] As shown in Appendix Table 3, the expected loss obtained by the substation reinforcement scheme considering only a single scenario is higher than the expected loss corresponding to the scheme obtained by the SSDAD model. If reinforcement resources are deployed under the condition of insufficient substations, and a large number of substations are destroyed, the resulting load loss will be much greater than the other two schemes. However, even when considering only the worst-case scenario, i.e., a large number of substations are destroyed, the best reinforcement effect cannot be guaranteed. This is because if only two substations are destroyed, the resulting load loss will be greater than the other two schemes.

[0146] The second type of uncertainty:

[0147] If the planner determines that a large number of substations will not be forced to fail, but cannot determine the exact number of substations that will be damaged, then various scenarios where the number of damaged substations is insufficient can be considered. In the IEEE RTS 24-node system, this means considering two cases where K1 = 1 and K2, and formulating a substation protection scheme with the minimum expected loss. Since there are only two cases, the probability fusion results {0.6538, 0.3462} from Table 1 are still used, and the two scenarios are designated as Scenario 3 and Scenario 4. Figure 1 The results calculated by the SSDAD model shown include the substation enhanced resource allocation scheme, the corresponding substation and line damage, the load loss in the two scenarios, and the expected loss. The results are shown in Appendix Table 4.

[0148] Appendix Table 4: Calculation Results of the Second Uncertainty SSDAD Model for the IEEE RTS 24-Node System

[0149]

[0150] To illustrate the advantages of the SSDAD model in handling the second type of uncertainty, the results in Appendix 4 are compared with the substation protection schemes obtained under a single scenario. Setting the parameter K1 in the SDAD model to 1 and 2 yields the corresponding substation enhancement schemes for a single scenario. When K1 = 1, the substation protection scheme obtained by the SDAD model protects substations at nodes 3, 10, 14, and 19; when K1 = 2, the protection scheme obtained by the SDAD model protects substations at nodes 6, 10, 13, and 14. Thus, the load loss and expected loss for each scenario under the three protection schemes can be obtained, as shown in Appendix 5.

[0151] Appendix 5: Comparison of the effectiveness of the second uncertainty defense scheme for the IEEE RTS 24-node system

[0152]

[0153] As shown in Appendix 5, although the probability of a single substation being successfully damaged is relatively high, if reinforcement resources are deployed according to this scenario, and more than one substation is actually damaged, a maximum load loss of 431MW will occur. Note that the defense effect of protecting substations at protection nodes 6, 10, 13, and 14 is the same as that at protection nodes 6, 10, 14, and 23. Therefore, in this case, a substation reinforcement resource allocation scheme can be considered based on the assumption that a sufficient number of substations are damaged.

[0154] Comparison of algorithm solution performance:

[0155] A two-stage robust C&CG optimization algorithm for network flow embedding is compared with the classic two-stage robust C&CG optimization algorithm. The solution time for the main problem and subproblems is set to 12 hours each. The computation time based on the IEEE RTS 24-node system and the IEEE 118-node system is shown in Appendix Tables 6-7. The results show that the NFE C&CG algorithm is several orders of magnitude faster than the classic two-stage robust C&CG algorithm.

[0156] Appendix Table 6 Comparison of Algorithm Computation Efficiency in IEEE RTS 24-Node System

[0157]

[0158] Appendix Table 7 Comparison of Algorithm Computation Efficiency in IEEE 118-Node System

[0159]

[0160] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are protected by the present invention.

Claims

1. A substation enhanced resource allocation method considering the uncertainty of the number of component failures, characterized in that, Includes the following steps: S1. Classify the uncertainty in the number of substations damaged; S2. Evaluate the probability of random scenarios involving different numbers of substations being damaged; S3. Integrate the probability assessments of different experts using the improved DS evidence theory; S4. Based on the uncertainty of the number of substations damaged, the corresponding stochastic optimization model for substation pre-disaster reinforcement resource allocation, which takes into account the uncertainty of the number of cascaded component failures, is calculated by the two-stage robust optimization column generation algorithm embedded in the network flow model. The substation reinforcement resource allocation scheme that minimizes the system load shedding loss is obtained.

2. The substation enhanced resource allocation method considering the uncertainty of the number of component failures according to claim 1, characterized in that, In step S1, the uncertainty of the number of substations damaged in extreme scenarios can be categorized into three types: 1) If planners are completely unable to determine how many substations will be destroyed; 2) The planners judged that the number of substations damaged was insufficient, but could not determine the exact number of substations that would be damaged; 3) Planners predicted that a large number of substations would be destroyed.

3. The substation enhanced resource allocation method considering the uncertainty of the number of component failures according to claim 1, characterized in that, In step S2, different random scenarios are analyzed using generalized stochastic Petri nets, Bayesian networks, and Markov models as needed to evaluate the probability of different extreme events; the different extreme events include floods, typhoons, earthquakes, and cyberattacks.

4. The substation enhanced resource allocation method considering the uncertainty of the number of component failures according to claim 1, characterized in that, In step S3, the improved DS evidence theory is used to fuse the probability assessment results of different experts, specifically including the following steps: S301. Input the probability assessment matrix of N experts on the success of destroying different numbers of components, and set i = 1; S302. When i = 1, calculate the matrix probability fusion matrix. element m ij Let be the probability that the i-th expert believes that j components can be successfully destroyed. S303. Calculate L1 = sum(R) - sum(dialog(R)), i = i + 1; S304. When i>1, update the probability evaluation matrix R = [dialog(R)]. T ·m i +1; S305. Calculate L2 = sum(R) - sum(dialog(R)), i = i + 1; S306. Repeat steps 4-5 until the probability assessment fusion of N experts is completed; S307. Calculate the conflict coefficient L = L1 + L2 + ... + L N ; S308. If L < 0.95, the fusion result of the probability of different extreme scenarios is dialog(R) / (1-L); if L ≥ 0.95, the fusion result of the probability of the j-th element being successfully destroyed is: L×(dialog(R)[1]+,…,+dialog(R)[N]) / N+sum(dialog(R)).

5. The substation enhanced resource allocation method considering the uncertainty of the number of component failures according to claim 1, characterized in that, In step S4, the substation pre-disaster reinforcement resource allocation stochastic optimization model, which considers the uncertainty of the number of cascaded component failures, is divided into three layers: the first layer determines the amount of reinforcement resources for the substation before a disaster, with the objective of minimizing the expected load shedding loss of the system; the second layer simulates all possible extreme scenarios, i.e., different numbers of substations and lines will be damaged, with the objective of maximizing the expected load loss of the system under all extreme scenarios; the third layer simulates the dispatcher taking corresponding load shedding, generator adjustment and other measures to deal with all possible failure scenarios, with the objective function of minimizing the load loss of the system under the corresponding extreme scenario.

6. The substation enhanced resource allocation method considering the uncertainty of the number of component failures according to claim 5, characterized in that, The objective of the substation pre-disaster enhanced resource allocation stochastic optimization model considering the uncertainty of the number of cascaded component failures is to minimize the expected load loss of the system under all extreme scenarios. The specific mathematical model is as follows: A BL ·f l (s)=A BG ·P g (s)-A BD ·(D d -ΔD d (s)) (11) In the formula: n, l, g, d, and s are the indices of the node, line, generator, load, and extreme scenario, respectively. Ω(s) represents the probability of different extreme scenarios occurring; E Ω(s) To account for the expected losses caused by different numbers of components being destroyed; w l (s) represents a 0-1 variable indicating a broken line in scenario s. If w l When (s)=1, then in extreme scenario s, line l will be disconnected; otherwise, line l will not be disconnected. a n (s) is a 0-1 variable representing whether the substation is damaged under extreme scenario s. If a n When (s) = 1, the substation located at node n is destroyed in the extreme scenario s; otherwise, it is not destroyed. u n (s) is a 0-1 variable representing the state of the substation located at node n, u n If (s) = 0, then substation n has been successfully destroyed; otherwise, the substation is in normal working condition. f l (s) represents the branch current under extreme scenario s; P g (s) represents the generator output under extreme scenario s; ΔD d (s) represents the load shearing under extreme scenario s; θ n (s) represents the phase angle under extreme scenario s, G g,max F l,max D d θ n,max These represent the maximum output of generator g, the maximum transmission power of line l, the load of node d, and the voltage phase angle limit of node n, respectively; K1, K2(s), and K3(s) are the substation reinforcement resources, the estimated number of substations destroyed in extreme scenario s, and the estimated number of lines destroyed in extreme scenario s, respectively; A BL 、A BG 、A BD These are the node-line, node-generator, and node-load correlation matrices, respectively; T is a very large constant. Equation (1) is the objective function of the model; Equation (2) is the budget constraint for the number of line reinforcement resources; Equation (3) is the constraint for the number of substations destroyed under different extreme scenarios s; Equation (4) represents the constraint for the number of lines destroyed under different extreme scenarios; Equation (5) represents that under different extreme scenarios s, if neither of the substations at both ends of the line is destroyed, then the line will not be destroyed; Equation (6) represents the state of whether the substation is destroyed under different extreme scenarios s; Equations (7)-(8) represent the maximum transmission power limit constraint of the line under different extreme scenarios s, considering the state of line destruction; Equations (9)-(10) represent the DC power flow constraint of the line under different extreme scenarios s; Equation (11) represents the node power balance equation under different extreme scenarios s; Equations (12)-(14) represent the limit constraints that all generator output, node load shedding, and node voltage phase angle must comply with under different extreme scenarios s.

7. The substation enhanced resource allocation method considering the uncertainty of the number of component failures according to claim 6, characterized in that, The substation pre-disaster enhanced resource allocation stochastic optimization model considering the uncertainty of the number of cascaded component failures is decomposed into a main problem and sub-problems under different scenarios s. 1) Main Problem: Given a set of damaged cascaded components under different extreme scenarios in the k-th iteration, solve the main problem to determine a substation enhanced resource allocation scheme to reduce the expected load shedding loss of the system. Its mathematical expression is as follows: s.t.∑ n z n ≤K3 (18) In the formula: This represents the worst-case component failure scenarios under different extreme conditions obtained by solving the subproblem in the kth iteration; These are the substation state variables and scheduling variables added to the main problem during the k-th iteration; 2) Sub-problem: Given a substation defense resource allocation strategy The worst-case component failure scenario is obtained by solving the subproblems, and its mathematical expression is as follows: st constraints (3)-(5)(16) Constraints (7)-(8), (11)-(13)(18) Using the strong duality condition, the model is transformed into a single-layer model as follows: st constraint(3)-(5)(20) In the formula w l (s),λ n (s), β g (s), α d (s) is the dual variable corresponding to (7)-(8) and (11)-(13); Analyzing constraint (22), since its constraint parameter matrix is ​​a fully simple modulus matrix, therefore w l (s), β g (s), α d (s) and |λ n The upper bound of (s)| is 1.

8. The substation enhanced resource allocation method considering the uncertainty of the number of component failures according to claim 7, characterized in that, The solution to the two-layer model of the sub-problem is obtained using the following robust optimization algorithm based on the network flow model stage: a. Input all grid parameters, including generator maximum output, load, line maximum power capacity, maximum phase angle, and topology parameters; b. Solve the single-layer model equations (19)-(22) under different extreme scenarios to obtain the worst-case component failure. c. Solve the DCOPF model fixed under different scenarios s to obtain d. Return the results of the screening of damaged components. Compared with load shedding loss and expected load loss; e. By embedding the solution process of the network flow model into a two-stage robust column generation algorithm, the final output result can be obtained.

Images