Rapid and safe load recovery strategy based on state awareness

Abstract

The invention relates to a fast and secure load recovery strategy based on state awareness. Statistical information about unrecovered load blocks obtained from historical data is perfected by using real-time measurement data of recovered load blocks, so that the conservative degree of a load recovery plan is reduced without compromising safety. Specifically, along with the advancement of the load recovery process and the recovery of more loads, a Kalman filter is used to update the probability distribution of unrecovered loads with new measurement data obtained from recovered loads. And making a load recovery decision-making method according to a given confidence coefficient under the constraint conditions of frequency, voltage and power by utilizing the updated distribution. Case research is carried out on a certain test system, and the effectiveness of the method is verified. The result shows that compared with a traditional method, the proposed method can recover the load faster and more safely under the condition that the load is uncertain.

Description

Technical Field

[0001] This invention proposes a fast and safe load restoration strategy based on state awareness, which belongs to the field of power system restoration control. Background Technology

[0002] With the continuous growth of electricity demand, the operating pressure on power systems is increasing, and the risk of power outages and blackouts is also rising significantly. The main causes of power outages are considered to be extreme weather conditions and cascading failures. Although the likelihood of large-scale and prolonged power outages is relatively low, they can have serious negative impacts on society and the economy, and even threaten human lives. While conducting extensive research on power system stability, it is also essential to develop safe and rapid system recovery plans to improve the power system's resilience to fault events.

[0003] Generally, the power system restoration process after a power outage can be divided into three stages: system preparation, system restoration, and load restoration. The system preparation stage includes identifying and isolating the fault area, as well as restarting and black-starting generating equipment. In the system restoration stage, the transmission network architecture is established by energizing transmission lines and synchronizing all parts. In the first two stages of system restoration, a small amount of load is removed to maintain system stability. The final stage, the load restoration stage, focuses on efficiently receiving the majority of the remaining load. This article focuses on the load restoration stage. In this stage, operators need to answer three key questions: 1) How much load to restore (number of loads to restore); 2) When to restore (restore load time); 3) Which loads to restore (restore load location).

[0004] Traditionally, system operators follow pre-planned offline restoration strategies based on assumed power outage scenarios. This approach is unsuitable for active power operation conditions and fails to provide optimal solutions for scenarios requiring the restoration of large loads. Therefore, it is necessary to develop an online restoration planning tool that incorporates real-time measurement information to understand the situation and enhance decision-making. Summary of the Invention

[0005] Purpose of the invention: This invention proposes a state-aware load recovery strategy that takes into account uncertainty and correlation, which can effectively achieve a recovery process that is both fast and safe.

[0006] Technical solution: The technical solution adopted in this invention is a state-aware load recovery strategy that takes into account uncertainty and correlation, and adopts the following common assumptions.

[0007] - Generators and transmission lines have been restored. It is assumed that a sufficient number of generators and transmission lines, along with a small portion of the load, have been restored in the first two phases of the restoration process.

[0008] - Load distribution. Assume the bus load is divided into multiple load blocks. For each load block, assume the probability distribution at a given time follows an approximately Gaussian distribution.

[0009] - Correlation between load blocks. The load of a block depends on the social, economic, and meteorological conditions of that geographic area. It is reasonable to assume spatial correlation between adjacent load blocks. This paper assumes that load blocks located on the same or adjacent busbars have a high correlation coefficient. The correlation between different load blocks can be determined using historical load data.

[0010] - The impact of process noise. Because the load has time-varying characteristics, process noise is used to describe the temporal uncertainty. The probability distribution of process noise is modeled as a zero-mean Gaussian distribution with a full covariance matrix. This means that the process noise of different load blocks is correlated.

[0011] - The impact of measurement noise. Due to the non-ideal nature of sensing and communication, real-time measurements (such as active and reactive power of a restored load block) are not error-free. Since the measurement process for different load blocks is independent, measurement noise is modeled as a zero Gaussian distribution with a diagonal covariance matrix. It is important to note that although measurement noise exists, its uncertainty is much lower than the prior assumptions about the unrestored load.

[0012] - Load uncertainty. Under normal operating conditions, the switching cycles of a group of electrical appliances are not consistent; this is known as load uncertainty. However, when the load is restored after a prolonged power outage, this uncertainty may be lost, resulting in a larger time-dependent load even when many appliances are turned on simultaneously. This state of non-uncertainty persists for a period of time before the uncertainty is restored. Assume that after the load is restored, the non-uncertain load increases several times over before returning to the uncertain state.

[0013] Based on the above assumptions, the development includes the following steps:

[0014] 2) State-aware load restoration planning program

[0015] The state-aware load recovery planning program integrates the load estimation model and the load recovery model in an iterative manner within a rolling scope. Figure 1The flowchart of the procedure is outlined. Initially, the system operator sets hyperparameters such as time span length, process noise covariance matrix, measurement noise covariance matrix, correlation matrix between all load blocks, initial covariance matrix of all load blocks, system inertia constant, total boost limit of system generators, frequency response characteristics of system loads, nominal system frequency, and minimum system frequency. These hyperparameters remain constant throughout the recovery process. Based on historical data, the prior probability distribution for each load block is calculated. Using the prior probability distribution for each load block, the load values ​​for the load recovery model are calculated. With this load model, the load recovery problem within the time span can be formulated and solved. Some load blocks are recovered according to the solution strategy for the load recovery problem, and new measurement data are collected. Then, the load estimation model is executed to obtain the posterior probability distribution of the unrecovered load blocks. This information will be used to allocate load in the load recovery model. Subsequently, the load recovery model is solved again to obtain the recovery strategy for the next time span. The entire process is iteratively executed until all load blocks are recovered.

[0016] 3) Load estimation model for unrecovered load areas based on Kalman filter and considering system uncertainties

[0017] The model uses available measurement data from recovered load blocks to iteratively refine the posterior probability distribution of unrecovered load blocks. Available measurement data can come from a monitoring and data acquisition system (sCADA) or a phase measurement unit (PMU).

[0018] The index set for all load blocks in the system is defined as follows:

[0019] load T ={(1,1),...,(1,n1),...,(i,1),...,(i,n i ),...,(m,1),...,(m,n m (1)

[0020] Then, the average load of all blocks in the system at time step t can be aggregated into a state vector μ. t as follows:

[0021]

[0022] The load transition from time step (t-1) to time step t can be written as the following stochastic process:

[0023] μ t =Fμ (t-1) +η (t-1) (3)

[0024] F can be estimated from historical data. For a time step (t-1), the process noise vector η(t-1) The syntax is as follows:

[0025]

[0026] The process noise covariance matrix A can be obtained from the standard deviation of the process noise and the correlation matrix of the load block:

[0027] Λ=Ω′ η *Corr*Ω′ η (5)

[0028] The correlation matrix Corr of a load block can be obtained from historical load data. The historical dataset for all load blocks can be sorted by date and time. For any load block φ, the variance of the load block can be estimated using the following methods:

[0029]

[0030] Similarly, the covariance between the two load blocks φ and χ can be estimated using the following method:

[0031]

[0032] Covariance matrix of the load block It can be written in the following form:

[0033]

[0034] Based on the covariance matrix of the load block, the Pearson correlation matrix of the load block can be calculated as follows:

[0035]

[0036] Where r φx This is the (φ, χ)th entry of the matrix Corr, defined as follows:

[0037]

[0038] Assume that the newly recovered load block at time step t uses the load index set M t This is represented as follows:

[0039]

[0040] Load set S t It was obtained by solving the load recovery problem.

[0041] Measurement vector z t The load measurement results of all recovery blocks at time step t are combined and defined as follows:

[0042]

[0043] Each time step z t The dimension t is updated based on the available measurement dataset, i.e., the load M. t As more load blocks recover, more measurements will become available.

[0044] The relationship between active load and the corresponding measured value of time step t can be written as follows:

[0045] z t =D t μ t +v t (13)

[0046] Wherein, measurement matrix D t Used to map the real state space to the measurement space; denoted by the identity matrix. Then at time step t, the measurement matrix D t Given by the following formula:

[0047]

[0048] Measurement matrix D t It will increase with the acquisition of newly recovered load block measurement data; the measurement noise vector v of all recovered load blocks t It can be represented as follows:

[0049]

[0050] The load estimation model achieves the goal of determining the mean vector and covariance matrix of the load at each time step t by using a Kalman filter.

[0051] μ t and z t The prior estimate can be written as follows:

[0052]

[0053] In this diagram, the hat symbol (∧) represents the estimated value of the variable, and the subscripts (-) and (+) represent the prior (predicted) estimate and the posterior (updated) estimate, respectively. The prior covariance matrix at time step t... The following can be calculated:

[0054]

[0055] After receiving the measurement results at time t, the prior estimate can be improved. μ t The posterior estimate at time step t can be written as follows:

[0056]

[0057] After incorporating new measurement data, the posterior covariance matrix of time step t It can be calculated using the following formula:

[0058]

[0059] Posterior estimation and Updated mean and variance information is provided, defining the posterior probability distribution for each unrepaired load block at a given time step t. It's important to note that the measurement vector zt only includes measurements for repaired load blocks, while the load estimation vector... and This includes estimates for all load blocks, including repaired load blocks for which measurements are available and unrepaired load blocks for which measurements are not available. By applying this load estimation model, the statistics for unrepaired blocks are updated by the measurements based on the correlation between load blocks, which helps reduce the uncertainty of the load in unrepaired load blocks. and The information provided will be used for load allocation in the rolling horizontal load recovery planning problem, which will be discussed in the next subsection.

[0060] The proposed Kalman filter-based load estimation model assumes that the load in each block follows a Gaussian distribution. If the load probability distribution is strongly non-Gaussian, the particle filter can be used in the proposed load estimation model without altering the overall framework of situation-aware load recovery planning.

[0061] 4) Load recovery model using posterior statistics of unrecovered load

[0062] The posterior probability distribution of the load obtained in the previous section is used to ensure system safety and improve recovery speed. The solution of the developed load recovery model will provide grid operators with the optimal sequence of load recovery actions, reactive power compensation equipment switching actions, and generation dispatch actions.

[0063] The index set gen of all generators in the system _ T can be defined as follows:

[0064] gen_T={(1,1),...,(1,n g1 ,),...,(i,1),...,(i,n gi ),...,(m,1),...,(m,n gm )} (twenty two)

[0065] Since load restoration is a sequential decision problem, it needs to be divided into multiple time steps. Assume the total number of time steps required to restore the load is T. To recursively incorporate the load estimation results, a rolling time-domain optimization framework is adopted. This means that at any time step t, the next N needs to be planned. s Time step recovery strategy. x t (t = 1, 2, ..., T) is defined as a binary decision vector, representing the recovery state of the load block after each time step:

[0066]

[0067] For example, for a time step t, consider the first s steps (1≤s≤N). s The recovery state of load block l located on bus i is determined by... The first entry is defined as follows:

[0068]

[0069] The recovered load block does not exhibit uncertainty for a certain period after recovery. Defined as a binary decision vector, representing the uncertainty state t of the recovered load block after each recovery time step:

[0070]

[0071] Then, the uncertain state of the recovery load block l located at bus i at time step (t+s) can be determined by the binary decision vector. The item is represented as follows:

[0072]

[0073] 1. Constraints of Uncertain Loads. To prevent security vulnerabilities in the system under various possible load levels, the mean vector obtained from the load estimation model should be used. Covariance Matrix The posterior estimate is used to simulate the load of unrecovered blocks.

[0074] Suppose that the random variable α has a standard normal distribution with a mean of 0 and a variance of 1, i.e., α: N(0, 1). The cumulative distribution function of the standard normal variable α can be defined as the probability that α is less than or equal to a specific value τ.

[0075] Φ(τ)=Pr(α≤τ). (29)

[0076] If the probability that a is less than or equal to τ should be equal to the given value ρ, then τ can be written as

[0077] T = Φ-1 (ρ). (30)

[0078] Suppose β is a normally distributed random variable β: N(μ, σ) 2 By shifting and scaling the random variable, β can be transformed into a standard normal random variable a, as shown below:

[0079]

[0080] Combining (30) and (31), if the probability that β is less than or equal to T should be equal to the confidence level ρ, then τ can be written as

[0081] T=μ+Φ -1 (ρ)σ. (32)

[0082] In the load recovery model, a load value should be assigned to each block such that the active load is less than or equal to the expected probability of the assigned load. In the recovery planning problem, the uncertain load amount assigned to block l located on bus i at recovery time step (t+s) should be determined as follows:

[0083]

[0084] in Using (19) to obtain; The estimated standard deviation vector of all load blocks can be obtained. Extract from, as shown below:

[0085]

[0086] Based on the posterior covariance matrix obtained using (21), the following results can be obtained.

[0087]

[0088] Similarly, σ η，il It is process noise σ η The standard deviation vector is shown below:

[0089]

[0090] The covariance matrix A of the process noise can be determined as follows:

[0091] σ η =diag(A -1 / 2 (37)

[0092] Since the load changes at each time step, the standard deviation of the process noise at time step (t+s) is the cumulative standard deviation from time step (t) to (t+s), which is equal to... Equation (33) ensures that at time step (t+s), the active power uncertainty load of load block l is equal to or less than the allocated value in the load recovery problem. The confidence level is ρ. In other words, if the recovery strategy obtains the assignment value under security constraints... This ensures safety with a confidence level of ρ, because the active load is less than or equal to the allocated value. The confidence level is p.

[0093] 2. Constraints on deterministic loads. If load block l located at bus i becomes uncertain after time step td, the following constraints must be satisfied:

[0094]

[0095] The load amount of a non-uncertain load can be expressed as follows:

[0096]

[0097] Uncertainty coefficient ζ f It can be determined by the system operator based on historical data.

[0098] 3. Frequency stability constraints. In order to maintain the system frequency within the ideal range, the total load recovery amount within each recovery time step should be limited to an allowable range.

[0099] Table I. Operational Constraints

[0100]

[0101] (40) As shown in Table I. It can be calculated using (41) in Table I.

[0102] 4. Constraints in Load Modeling. The static zIP load model is used to represent the voltage dependence of the load. It combines constant impedance, current, and power components in a polynomial equation to represent the relationship between voltage magnitude and power. The original nonlinear zIP model can be approximated by a linearized form, as shown below:

[0103]

[0104] System operators can set constant impedance based on their system's load model database. constant current and constant power The participating factors. The load model database can be developed and calibrated using existing load modeling algorithms.

[0105] If the load is restored at any time step, there will be no further power outages in all subsequent time steps. This can be ensured by the following constraints:

[0106]

[0107] 5. Power balance and power flow constraints. The linear power balance equations for active and reactive power can be written as (42), (43), (44) and (45), as shown in Table I. Depending on the recovery state and uncertainty state of the load block, as shown below:

[0108]

[0109] same, Depending on the recovery state and uncertainty state of the load block, as shown below:

[0110]

[0111] Nonlinear terms in (44) and (45) and Two new decision variables can be used and The terms are respectively replaced, and defined as follows:

[0112]

[0113] To be and The following constraints were added to the problem:

[0114]

[0115] Since the typical voltage angle limit is Therefore, the cosine function can be linearized, and the slope and intercept can be determined using linear regression. If the cosine function is divided into n... γ Divide into equal segments, then Fragment linearization can be used Represented as:

[0116]

[0117] As shown in Table I, the linear approximations of the active and reactive power flow equations can be written as (46) and (47).

[0118] 6. Operational Constraints. In addition to the constraints described above, the recovery planning problem also requires the implementation of some safety and operational constraints, as listed in Table I. The bus voltage constraint is shown in (48). The power generation constraint is given by (49) and (50). The generator ramp rate constraint is (51). Finally, the line flow constraint is given by (52).

[0119] 7. Objective Function. The primary objective of the load restoration problem is to maximize the cumulative restored load over the entire restoration period; other objectives, such as generation cost and voltage deviation, can also be added. In this paper, the objective function component related to the time step (t+s) is defined at time step t (1≤s≤N). s It can be written in the following form:

[0120]

[0121] The first term maximizes load recovery, the second term minimizes generation costs, and the third term penalizes voltage deviations from the reference value. The third term, in absolute value form, can be derived from a new decision variable defined as follows. replace:

[0122]

[0123] Then add the following three constraints to the problem:

[0124]

[0125] and This allows for an ideal trade-off between these three objectives. System operators can set these parameters based on real-time operating conditions and demands during the load restoration process. Generally, since the primary objective of this problem is to maximize the amount of load restored, therefore... The value should be higher than and If the physical variables of the target are of different orders of magnitude, the target should be normalized before weighting.

[0126] 8. Proposed Load Restoration Model. Combining all established constraints and objective functions, the load restoration planning problem can be modeled as a MILP problem. At restoration time step t, the next N... s There are 1 time steps (i.e., from time step t+1 to time step (t+N)). s The load recovery model can be modeled as follows:

[0127]

[0128] Solution variables and The optimal recovery action and uncertainty state of load block l located at bus i are provided respectively, as well as the generator g located at bus i. i The active power generation and the number of compensation steps of the compensator located at bus i. The index set load_S of the recovered load block. (t+s) From the solution vector Obtained:

[0129]

[0130] Then use load_S (t+s) To expand the measurement set load_M (t+s) and measurement vector z t To execute the load estimation model.

[0131] Beneficial Effects: This invention proposes a state-aware load recovery planning framework that considers load uncertainty and correlation. It combines a rolling time-domain load recovery model with a Kalman filter-based load estimation model. The load estimation model continuously derives statistical data of unrecovered loads using real-time measurement data of recovered loads. The latest statistical knowledge about unrecovered loads helps the load recovery model obtain a safe and rapid recovery strategy. Using the load estimation model, the uncertainty of unrecovered loads can be significantly reduced even before recovery and measurement. In terms of recovery speed, the proposed method performs comparably to the aggressive baseline method; in terms of system safety, it performs comparably to the conservative baseline method. Through theoretical analysis and numerical examples, it is shown that the state-aware load recovery planning framework considering load uncertainty and correlation proposed in this invention provides a safe and rapid load recovery strategy. Attached Figure Description

[0132] Appendix Figure 1 Flowchart of the proposed load restoration planning procedure

[0133] Appendix Figure 2 A comparison of the radical baseline approach, the conservative baseline approach, and the recommended approach. Detailed Implementation

[0134] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only for illustrating the present invention and are not intended to limit the scope of the present invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0135] To evaluate the effectiveness of the proposed situation-aware load restoration planning method, it was implemented on the IEEE 39 bus test system. The proposed problem was formulated using MATLAB 2019b, and the restoration solution was obtained using the MILP solver Gurobi 9.1.1.

[0136] (1) Comparison between baseline method and proposed method

[0137] To verify the effectiveness of the proposed method in rapidly and safely restoring load, we compared it with two baseline methods consistent with recent publications. In these studies, real-time measurements were iteratively updated after the restoration strategy was implemented and used to monitor safety performance. However, these studies used deterministic load models, ignoring the uncertainty of unrestored load. To compare the proposed method with existing research, the first baseline method was formulated without considering the uncertainty / variation of unrestored load, i.e., the load values ​​assigned in the restoration model were simply the average of the active unrestored load. This approach is considered positive because it can quickly restore system load, but at the cost of high safety risks when the active load is greater than the average. Simultaneously, we also created a conservative baseline method as a second baseline method, in which we considered a statistical load model and applied the same Φ to the assigned load values. -1 (ρ), but it only uses the prior probability distribution of the load and does not receive updates from the real-time load estimation model.

[0138] Figure 2 This section explains the differences between the proposed method and the two baseline methods. It assumes that the prior estimate of the mean and standard deviation of the load block 1 distribution at bus i are respectively... and At the recovery time step t, the posterior estimate mean and standard deviation obtained from the load estimation model are respectively... and Because it integrates real-time measurement data, the posterior distribution has a narrower shape, reflecting a reduction in the uncertainty of the unrecovered load. Details of the proposed method and the two baseline methods will be discussed below.

[0139] 1. Aggressive Baseline Method: The aggressive baseline method does not consider the uncertainty of the load. For example... Figure 2 As shown, if load block l is not recovered at time step t, then the uncertain load amount of the load block at time step (t+s) is... It can be calculated through (33), assuming Φ -1 (ρ) = 0. This means that (ρ) = 0. equal to the prior distribution The average value.

[0140] Table II. Technical Characteristics of Generators

[0141]

[0142] However, at a confidence level of 50%, the amount of active power uncertainty in the load block may be greater than the average of the prior distribution, thus leading to a high risk of violating safety regulations.

[0143] 2. Conservative Baseline Method (base-cnsv.) The conservative baseline method considers the uncertainty of unrecovered load. However, it only uses the prior probability distribution of historical load data, i.e. and Instead of using the posterior distribution derived from real-time measurements, the mean and standard deviation of the unrecovered load block remain constant throughout the recovery process. If load block l is not recovered at time step t, assumption Φ (33) can be used. -1 If (ρ)>0, calculate the uncertain load amount of the load block at time step (t+s). Thus, the uncertain load amount of load block l at time step (t+s) is very likely to be higher than the active load amount (confidence level of 99.7%). Therefore, the conservative baseline method has a lower probability of safety violations, but at the cost of slower load extraction speed.

[0144] 3. Proposed Method. The proposed method also employs a statistical loading model, but it uses the posterior probability distribution of the loading, i.e. and These posterior probability distributions are updated at each step by real-time measurement results.

[0145] To take into account the stochastic characteristics of active load, the three methods were repeated 100 times for the IEEE 39 bus system and 30 times for the NPCC 140 bus system under different load conditions, and the average results were compared.

[0146] (2) Indicators of severity of violation

[0147] To compare the performance of the three methods, we defined several metrics. In addition to metrics with direct meaning, namely average recovery steps, average recovery duration (minutes), and average security violation per simulation, we also introduced metrics that quantify the severity of security violations in the AC power flow solution.

[0148] The Voltage Limit Exceedance Severity Index is used to define the severity of voltage limits exceeded during load restoration. It considers the voltage deviation of each bus in the system across all restoration time steps. The formula for calculating the Voltage Limit Exceedance Severity Index is as follows:

[0149]

[0150] The average voltage exceedance severity is defined as the average of the voltage exceedance severity index across all simulation tests.

[0151] The Active Power Flow Limit Exceedance Severity Index can be used to quantify the severity of active power flow limit exceedances during load restoration. It considers the deviation of the active power flow from the limit for each branch of the system across all restoration time steps. The Active Power Flow Limit Exceedance Severity Index is expressed as a percentage value, and the calculation formula is as follows:

[0152]

[0153] The average active power flow exceedance is defined as the average of the active power flow exceedance severity index in all simulation tests.

[0154] The reactive power flow exceedance severity index can be used to quantify the severity of reactive power flow exceedances during load restoration. It considers the deviation of the reactive power flow from the limit value for each branch of the system across all restoration time steps. The reactive power flow exceedance severity index is expressed as a percentage, and the calculation formula is as follows:

[0155]

[0156] The average reactive power flow limit exceedance is defined as the average of the reactive power flow limit exceedance severity index across all simulation tests.

Claims

1. A state-aware, fast, and safe load recovery strategy, characterized in that, The load restoration strategy includes: Initially, the hyperparameters were set by the system operator; Calculate the prior probability distribution for each load block based on historical data; The load value of the load recovery model is calculated using the prior probability distribution of each load block; With this load model, we can formulate and solve load recovery problems over a time span; Based on the solution strategy for the load recovery problem, some load blocks are recovered, and new measurement data are collected; Then, the load estimation model is executed to obtain the posterior probability distribution of the unrecovered load blocks; This information will be used to distribute the load in the load recovery model; Subsequently, the load recovery model is solved again to obtain the recovery strategy for the next time span; The entire process is executed iteratively until all load blocks are recovered.

2. The state-aware, fast, and secure load recovery strategy according to claim 1, characterized in that, Hyperparameters, such as time span length, process noise covariance matrix, measurement noise covariance matrix, correlation matrix between all load blocks, initial covariance matrix of all load blocks, system inertia constant, and total voltage boost limit of the system generators, are set by the system operator. The frequency response characteristics of the system load, the nominal system frequency, and the minimum system frequency; these hyperparameters remain constant throughout the recovery process.

3. The state-aware, fast, and secure load recovery strategy according to claim 2, characterized in that, The load estimation model is a load estimation model for the unrecovered load area based on a Kalman filter and taking into account system uncertainties.

4. The state-aware, fast, safe load recovery strategy according to claim 3, characterized in that, The load estimation model is as follows: The index set for all load blocks in the system is defined as follows: load t ={(1,1),...,(1,n1),...,(i,1),...,(i,n i ),...,(m,1),...,(m,n m )}. (1) Then, the average load of all blocks in the system at time step t can be aggregated into a state vector μ. t as follows: The load transition from time step (t-1) to time step t can be written as the following stochastic process: m t =Fμ (t-1) +n (t-1) . (3) F can be estimated from historical data; for a time step (t-1), the process noise vector η (t-1) The syntax is as follows: The process noise covariance matrix Λ can be obtained from the standard deviation of the process noise and the correlation matrix of the load block: L=Ω′ η *Corr*Ω′ η . (5) The correlation matrix Corr of a load block can be obtained from historical load data. The historical datasets of all load blocks can be sorted by date and time. For any load block φ, the variance of the load block can be estimated using the following methods: Similarly, the covariance between the two load blocks φ and χ can be estimated using the following method: Covariance matrix of the load block It can be written in the following form: Based on the covariance matrix of the load block, the Pearson correlation matrix of the load block can be calculated as follows: Where r φχ This is the (φ,χ)th entry of the matrix Corr, defined as follows: Assume that the newly recovered load block at time step t uses the load index set M t This is represented as follows: Load set S t It was obtained by solving the load recovery problem; Measurement vector z t The load measurement results of all recovery blocks at time step t are combined and defined as follows: Each time step z t The dimension t is updated based on the available measurement dataset, i.e., the load M. t As more load blocks recover, more measurements will become available; The relationship between active load and the corresponding measured value of time step t can be written as follows: z t =D t μ t +v t , (13) Wherein, measurement matrix D t Used to map the real state space to the measurement space; denoted by the identity matrix. Then at time step t, the measurement matrix D t Given by the following formula: Measurement matrix D t It will increase with the acquisition of newly recovered load block measurement data; the measurement noise vector v of all recovered load blocks t It can be represented as follows: The load estimation model achieves the goal of determining the mean vector and covariance matrix of the load at each time step t by using a Kalman filter; μ t and z t The prior estimate can be written as follows: Where, the hat symbol (∧) represents the estimated value of the variable, and the subscripts (-) and (+) represent the prior (predicted) estimate and the posterior (updated) estimate, respectively; the prior covariance matrix at time step t... The following can be calculated: After receiving the measurement results at time t, the prior estimate can be improved; μ t The posterior estimate at time step t can be written as follows: After incorporating new measurement data, the posterior covariance matrix of time step t It can be calculated using the following formula: Posterior estimation and It provides updated mean and variance information, which defines the posterior probability distribution of each unrepaired load block at a given time step t. It's important to note that the measurement vector z... t Only measurements of the repaired load blocks are included, while the load estimation vector... and This includes estimations for all load blocks, including repaired load blocks with available measurements and unrepaired load blocks without available measurements. By applying this load estimation model, the statistics for unrepaired blocks are updated from the measurement results based on the correlation between load blocks, which helps reduce the uncertainty of the load in unrepaired load blocks. and The information provided will be used for load allocation in the rolling horizontal load recovery planning problem.

5. A state-aware, fast, safe load recovery strategy according to claim 4, characterized in that, Load recovery model using posterior statistics of unrecovered load: The index set gen_T for all generators in the system can be defined as follows: gen_T={(1,1),…,(1,n g1 ,),...,(i,1),...,(i,n gi ),...,(m,1),...,(m,n gm )} (22) Since load restoration is a sequential decision problem, it needs to be divided into multiple time steps. Assuming the total number of time steps required to restore the load is T, a rolling time-domain optimization framework is adopted to recursively incorporate the load estimation results. This means that at any time step t, the next N needs to be planned. s The time-step recovery strategy will x t (t=1,2,...,T) is defined as a binary decision vector, representing the recovery state of the load block after each time step: For time step t, consider the first s steps (1≤s≤N) s The recovery state of load block l located on bus i is determined by... The l-th entry is represented by the following definition: The recovered load block still does not have uncertainty for a certain period of time after recovery. Defined as a binary decision vector, representing the uncertainty state t of the recovered load block after each recovery time step: Then, the uncertain state of the recovery load block l located at bus i at time step (t+s) can be determined by the binary decision vector. The item is represented as follows:

6. A state-aware, fast, safe load recovery strategy according to claim 5, characterized in that, To address the constraints of uncertain loads and prevent system vulnerabilities under various possible load levels, the mean vector obtained from the load estimation model should be used. Covariance Matrix The posterior estimate is used to simulate the load on unrecovered blocks; Suppose that the random variable α has a standard normal distribution with a mean of 0 and a variance of 1, i.e., α:N(0,1). The cumulative distribution function of the standard normal variable α can be defined as the probability that α is less than or equal to a specific value τ. Φ(τ)=Pr(α≤τ). (29) If the probability that α is less than or equal to τ should be equal to the given value ρ, then τ can be written as τ=Φ -1 (p). (30) Suppose β is a normally distributed random variable β:N(μ,σ) 2 By shifting and scaling the random variable, β can be transformed into a standard normal random variable α, as shown below: Combining (30) and (31), if the probability that β is less than or equal to τ should be equal to the confidence level ρ, then τ can be written as τ=μ+Φ -1 (r)s. (32) In the load recovery model, a value should be assigned to the load of each block such that the active load is less than or equal to the expected probability of the assigned load; in the recovery planning problem, the uncertain load amount assigned to block l located on bus i at the recovery time step (t+s) should be determined as follows: in Using (19) to obtain; The estimated standard deviation vector of all load blocks can be obtained. Extract from, as shown below: Based on the posterior covariance matrix obtained using (21), the following results can be obtained. Similarly, σ η,il It is process noise σ η The standard deviation vector is shown below: The following can be determined based on the covariance matrix Λ of the process noise: s η =diag(Λ -1 / 2 (37) Since the load changes at each time step, the standard deviation of the process noise at time step (t+s) is the cumulative standard deviation from time step (t) to (t+s), which is equal to... Equation (33) ensures that at time step (t+s), the active power uncertainty load of load block l is equal to or less than the allocated value in the load recovery problem. The confidence level is ρ.

7. A state-aware, fast, safe load recovery strategy according to claim 5, characterized in that, The constraint condition for deterministic loads is that if the load block l located at bus i is at t d If uncertainty arises after a time step, the following constraints must be met: The load amount of a non-uncertain load can be expressed as follows: Uncertainty coefficient ζ f It can be determined by the system operator based on historical data.

8. A state-aware, fast, and secure load recovery strategy according to claim 6, characterized in that, Frequency stability constraints require that, in order to maintain the system frequency within the ideal range, the total load recovery amount within each recovery time step should be limited to the allowable range.

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