A Method for Evaluating the Resilience of Power Grids and Differentiated Planning under Extreme Typhoon Disasters

Abstract

The present invention relates to the technology of differential planning for power systems, and specifically relates to a method for evaluating the resilience of a power grid and differential planning under extreme typhoon disasters, which specifically includes: constructing a Batts wind field model to simulate typhoon disasters, constructing a power grid line fault recovery model and a power grid resilience evaluation index considering the power supply of important loads; constructing a two-stage optimization model for differential planning of the power grid with the return rate of power grid resilience improvement as the objective function, and using an improved PSO algorithm for solution to obtain a differential strengthening plan for the protection levels of power grid transmission lines. This method can effectively improve the resilience of the power grid and the supporting ability for resilience resources, while saving the investment scale. This method is of great significance for enhancing the disaster resistance ability of the power grid and ensuring the safe and reliable operation of the power grid under severe natural disasters. At the same time, it provides a reference for the power grid planning department to formulate differential planning schemes, which is conducive to enhancing the disaster resistance ability of the power grid and ensuring the safety of social power consumption.

Description

Technical Field

[0001] The present invention belongs to the technical field of differential planning of power systems, and particularly relates to a method for evaluating the resilience of a power grid and differential planning under extreme typhoon disasters. Background Art

[0002] Typhoon disasters are likely to cause group outages of power grids, which may evolve into large-scale power outages and result in huge economic losses. In recent years, the power grid department has introduced the concept of "resilience" to evaluate the ability of the power grid to reduce fault losses and quickly restore normal power supply under extreme disasters. However, the existing resilience evaluation methods are relatively subjective in distinguishing the importance of loads. In terms of resilience improvement measures, the differential planning method has good application potential. At the same time, it is necessary to verify the supporting role of the planning scheme for the utilization of system resilience resources. Summary of the Invention

[0003] Aiming at the problems existing in the background art, the present invention provides a method for evaluating the resilience of a power grid and differential planning under extreme typhoon disasters.

[0004] To solve the above technical problems, the present invention adopts the following technical solutions: A method for evaluating the resilience of a power grid and differential planning under extreme typhoon disasters, comprising the following steps:

[0005] Step 1: Simulate typhoon disasters based on the Batts wind field model;

[0006] Step 2: Construct a transmission line fault recovery model, and calculate the line failure rate and recovery time;

[0007] Step 3: Construct a power grid resilience evaluation index considering the power supply of important loads;

[0008] Step 4: Construct a two-stage optimization model for power grid differential planning with the power grid resilience improvement rate of return as the objective function;

[0009] Step 5: Use an improved PSO algorithm to solve the constructed model to obtain a power grid differential planning scheme.

[0010] In the above method for evaluating the resilience of a power grid and differential planning under extreme typhoon disasters, the implementation of Step 1 includes the following specific steps:

[0011] Step 1.1: Calculate the maximum wind speed radius R max and the gradient wind speed V gx ;

[0012] Step 1.1.1: Calculate the maximum wind speed radius R max ;

[0013] The forecast information required for the Batts wind field model includes the pressure difference ΔP hPa between the cyclone center and the periphery at the time of typhoon landing and the typhoon movement speed V T m / s; and the distance R from the cyclone center of the wind field to the strongest wind belt can be calculated through the central pressure difference max , and the calculation formula is as follows:

[0014]

[0015] In the formula: ΔP is the pressure difference between the cyclone center and the periphery, and the peripheral pressure of the cyclone takes the standard atmospheric pressure of 1013 hPa;

[0016] Step 1.1.2, calculate the gradient wind speed V gx ;

[0017] According to the maximum wind speed radius R max , calculate the gradient wind speed V gx caused by the pressure gradient force of the wind field, and the calculation formula is as follows:

[0018]

[0019] In the formula: θ is the empirical coefficient, taking 6.72; f is the Coriolis force coefficient of the earth's rotation;

[0020] Step 1.2, calculate the maximum wind speed V Rmax within the wind field and the wind speed V r at each point;

[0021] Step 1.2.1, calculate the maximum wind speed V Rmax within the wind field;

[0022] The maximum wind speed V Rmax within the wind field appears at the maximum wind speed radius R max , and the calculation formula is as follows:

[0023]

[0024] In the formula: V T is the typhoon movement speed;

[0025] Step 1.2.2, calculate the wind speed V r at each point within the wind field;

[0026] The instantaneous wind speed at each point in the wind field is calculated from the distance r from the research point to the wind field center:

[0027]

[0028] In the formula: r is the distance from the research point to the wind field center; V rin and V rout are respectively less than and greater than R maxThe instantaneous wind speed at the research point at that time; x is the typhoon radial intensity attenuation parameter, taking 0.5;

[0029] Step 1.3: Obtain the Batts wind field spatio-temporal model according to the typhoon intensity attenuation;

[0030] The pressure difference ΔP between the cyclone center and the periphery in the corrected wind field is a function of the typhoon landing time t, ΔP(t), as follows:

[0031] ΔP(t) = ΔP0(1 - e τt )

[0032] In the formula: t is the time constant for the increase of the cyclone pressure at the center of the wind field, and ΔP0 is the initial central pressure difference when the typhoon lands.

[0033] In the above method for evaluating the resilience of the power grid and differential planning under extreme typhoon disasters, the implementation of step 2 includes the following specific steps:

[0034] Step 2.1: Calculate the system line failure rate under extreme weather conditions through the component vulnerability curve;

[0035] Taking the typhoon wind speed as a characteristic, construct a line fault model under the typhoon operating conditions: when the wind speed v at the line research point is less than the line design wind speed V N at that time, the line failure rate is 0; when v > 2V N at that time, the line failure rate is 1; in other cases, the line failure rate increases exponentially, as follows:

[0036]

[0037] Step 2.2: Calculate the time required for line fault recovery through the β distribution;

[0038] After a line fault, the time required to restore power supply through operation follows a β distribution, and its expectation and standard deviation are as follows:

[0039]

[0040] In the formula: t c is the time required for the faulty line to restore power supply through operation; for each line operation, three duration estimates are made: the optimistic recovery time A, the most likely recovery time M, and the pessimistic recovery time B.

[0041] In the above method for evaluating the resilience of the power grid and differential planning under extreme typhoon disasters, the implementation of step 3 includes the following specific steps:

[0042] Step 3.1: Construct a differential resilience evaluation index considering the size of the system load loss, the fault duration, and the maximum loss of important loads;

[0043] The Differentiated Resilience DR index is used to evaluate the resilience of the power grid, as shown in the following formula:

[0044]

[0045] In the formula: E(·) represents the mathematical expectation; T is the research period; l R (t) is the operating curve of the system in the normal state; l I (t) is the operating curve of the system when it suffers from extreme disasters; the coefficient 1 / 2 makes the resilience evaluation result a floating-point number between [0,1];

[0046] Step 3.2: Calculate the differentiated resilience evaluation index of the power grid under discrete simulation;

[0047] During the simulation process, the DR index is calculated as shown in the following formula:

[0048]

[0049] In the formula: N is the number of sampling scenarios; T is the simulation duration, and ΔT is the simulation step size; is the system load retention in the i-th simulation step under the k-th sampling scenario; L total is the total system load; is the minimum retention of important loads under the k-th sampling scenario; L Stotal is the total amount of important loads in the system;

[0050] Step 3.3: The differentiated resilience evaluation process of the power grid:

[0051] The power grid resilience evaluation is based on the simulation of disaster faults and recovery, obtaining the dynamic changes of the network topology; according to the system fault response, that is, the optimal load shedding model, the system state changes are obtained; the system resilience is quantified according to the mean value of the system resilience under N Monte Carlo samplings.

[0052] In the above method for evaluating the resilience of the power grid and differentiated planning under extreme typhoon disasters, the implementation of step 4 includes the following specific steps:

[0053] Step 4.1: The first-stage optimization takes the maximum resilience improvement return rate as the objective function, and strengthens the protection levels of transmission lines differently through the differentiated planning method; the first-stage optimization model is:

[0054]

[0055] In the formula: DR ROI is the resilience improvement return rate; ΔDR is the magnitude of the resilience improvement obtained when the power grid adopts differentiated reinforcement; F LCC is the life cycle cost of this scheme; The life - cycle cost for all lines with the highest protection level; U i,t 、U j,t are the voltage magnitudes of nodes i and j at time t respectively; θ ij,t is the voltage phase - angle difference between nodes i and j at time t; g ij 、b ij are the conductance and susceptance between nodes i and j respectively; P ess,i,t 、P G,i,t 、P load,i,t are the active power output of energy storage, the active power output of the power source, and the active power consumed by the load of node i at time t respectively; Q ess,i,t 、Q G,i,t 、Q load,i,t are the reactive power output of energy storage, the reactive power output of the power source, and the reactive power consumed by the load of node i at time t respectively. In the first - stage optimization model, energy - storage discharging is not considered, so P ess,i,t 、Q ess,i,t are both 0; U i,min 、U i,max are the minimum and maximum values of the operating voltage of node i respectively; P l,t is the actual load of line l at time t; P l,max is the maximum load of line l; P G,i,min 、P G,i,max are the upper and lower limits of the active power output of generator set i respectively; R G,i is the upper limit of the allowable increase or decrease in the active power of generator set i per unit time;

[0056] The life - cycle cost F of the planning scheme LCC is calculated as follows:

[0057]

[0058] In the formula: F1 is the one - time investment cost for improving the protection level of the line; F2 is the additional daily maintenance, inspection, etc. costs after improving the protection level; F3 is the recovery cost after the line is taken out of service; r is the annual interest rate of funds; Year is the research period; α1, α2 are proportionality coefficients;

[0059] Step 4.2, Optimize the system resilience resources in the second stage to improve the resilience - improvement return rate of the differential planning scheme; The second - stage optimization model is as follows:

[0060]

[0061] In the formula: f1 is the value of the objective function of the first - stage optimization; ΔDR ess is the system resilience improved by energy - storage supporting the load; is the life - cycle cost of the first - stage differential planning scheme; \(g(x)=0, h(x)\leq0\) are the power grid operation constraints listed in the first - stage optimization model respectively; is the capacity of the energy storage device installed at node \(i\); are its upper and lower capacity limits; \(P\) ess,i,t is the discharge amount of the energy storage at node \(i\) at time \(t\); \(P\) ess,i,max is its upper discharge power limit; \(SOC\) min 、\(SOC\) max are the minimum and maximum state - of - charge values of the energy storage system respectively; \(E\) left,i,t is the remaining power of the energy storage at node \(i\) at time \(t\).

[0062] In the above - mentioned power grid resilience assessment and differential planning method under extreme typhoon disasters, the implementation of step 5 includes the following specific steps:

[0063] Step 5.1: Construct a basic particle swarm optimization algorithm;

[0064] A group of particles search for the objective function at a certain speed in the \(N\) - dimensional space. The motion state of the particles is described by the position vector and the speed vector Each particle communicates and learns from each other through learning factors and inertia weights, and stores the current individual optimal position vector and the current global optimal position vector Adjust the speed vector for the search in the next iteration and correct the particle position vector as follows:

[0065]

[0066]

[0067] In the formula: \(w\) is the inertia weight; \(c_1\), \(c_2\) are the individual and social experience learning factors respectively; \(r_1\), \(r_2\) are random numbers uniformly distributed in \([0,1]\); are the speed vectors of particle \(i\) at the \(k\) - th and \((k + 1)\) - th iterations respectively; are the position vectors of particle \(i\) at the \(k\) - th and \((k + 1)\) - th iterations respectively; is the individual optimal position vector of particle \(i\) at the \(k\) - th iteration; \(g\) k global optimal position vector;

[0068] Step 5.2: An improved PSO algorithm based on elliptic - function - modified inertia weight;

[0069] The specific calculation of the inertia weight adjusted based on the elliptic - curve function is as follows:

[0070]

[0071] In the formula: \(w\)max The maximum value of the inertia weight; N wzero is the number of iterations when the inertia weight is 0; n is the current number of iterations.

[0072] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0073] 1. The resilience evaluation index constructed by the present invention takes into account the different impacts of hierarchical load loss on the system, so that the resilience evaluation result avoids the masking phenomenon. By improving this index, it is possible to improve the resilience of the power grid and the power supply capacity of the power grid for important loads at the same time.

[0074] 2. The line reinforcement method with differential planning of the present invention can greatly improve the resilience of the power grid, reduce investment and disaster losses. At the same time, the two-stage optimization method proposed in this paper can make the planning scheme take into account the supporting role of the existing resilience resources of the system, and further improve the benefits of differential planning.

[0075] 3. The improved particle swarm optimization algorithm that modifies the inertia weight with the elliptic curve function proposed by the present invention has certain advantages in terms of convergence speed and accuracy compared with other algorithms, and can more effectively solve the problem to provide accurate differential planning references for the power grid department.

[0076] 4. The method of the present invention can effectively improve the resilience of the power grid and the supporting ability for resilience resources, while saving the investment scale. It is of great significance for enhancing the disaster resistance ability of the power grid and ensuring the safe and reliable operation of the power grid under severe natural disasters. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 is the flow chart of differential planning for resilience improvement provided by an embodiment of the present invention;

[0078] Figure 2 is the flow chart of power grid resilience evaluation under typhoon disasters provided by an embodiment of the present invention;

[0079] Figure 3 is the two-stage optimization flow chart of differential planning provided by an embodiment of the present invention

[0080] Figure 4 is the flow chart of solving the IPSO algorithm provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0081] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0082] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0083] The present invention will be further described below in conjunction with specific embodiments, but it is not intended to limit the present invention.

[0084] In this embodiment, a Batts wind field model is constructed to simulate typhoon disasters, a power grid line fault recovery model and a power grid resilience evaluation index considering the power supply of important loads are constructed; a two-stage optimization model for power grid differential planning is constructed with the power grid resilience improvement return rate as the objective function, and an improved PSO algorithm is used for solution to obtain a differential reinforcement plan for the protection levels of power grid transmission lines. A resilience evaluation index considering the power supply of important loads is proposed; subsequently, a two-stage optimization model for differential planning is constructed, where in the first stage, the line reinforcement strategy is optimized based on the differential planning method; in the second stage, the load recovery strategy of the energy storage power supply is optimized to verify the support ability of the planning scheme for resilience resources; finally, the solution is carried out through a particle swarm algorithm that modifies the inertia weight by an elliptic function. The method for evaluating the resilience of the power grid and differential planning under extreme typhoon disasters can effectively improve the resilience of the power grid and the support ability for resilience resources, while saving the investment scale. This method is of great significance for enhancing the disaster resistance ability of the power grid and ensuring the safe and reliable operation of the power grid under severe natural disasters.

[0085] This embodiment is realized through the following technical solutions. A method for evaluating the resilience of a power grid and differential planning under extreme typhoon disasters includes the following steps:

[0086] S1. Simulate typhoon disasters based on the Batts wind field model;

[0087] S2. Construct a transmission line fault recovery model to calculate the line failure rate and recovery time;

[0088] S3. Evaluate the resilience of the power grid based on the constructed power grid resilience evaluation index and process;

[0089] S4. Construct a two-stage optimization model for power grid differential planning with the maximum resilience investment return rate as the objective function;

[0090] S5. Solve the constructed model based on the improved PSO algorithm to obtain a power grid differential planning scheme.

[0091] Moreover, the Batts wind field model includes calculating the maximum wind speed radius R according to the forecast information max and the gradient wind speed V gx , further calculating the maximum wind speed V within the wind field range Rmax and the wind speed V at each point r , and further obtaining the Batts wind field spatio-temporal model according to the typhoon intensity attenuation.

[0092] Moreover, the transmission line fault model under typhoon conditions is characterized by the component vulnerability curve. The horizontal axis is described by the disaster characteristic quantity, i.e., the typhoon wind speed; the vertical axis is the failure rate of the component corresponding to this extreme weather condition. After a line fault occurs, it takes a certain amount of time to locate and repair the fault to restore normal power supply. A stochastic model of the line recovery time is constructed through the beta distribution.

[0093] Moreover, the constructed resilience evaluation index reflects the size of the system load loss and the fault duration through the integration of the load curve, and also reflects the maximum loss of important loads. The power grid resilience evaluation is a dynamic process that changes continuously with the development of the typhoon, including the network topology changes caused by line disconnection, line maintenance and restoration, etc. during the typhoon accident, and the system state changes caused by the network topology changes. The change of the system state directly reflects the size of the system resilience. Based on the above analysis, the power grid resilience evaluation should be based on disaster fault and recovery simulation to obtain the dynamic changes of the network topology structure; then, according to the system fault response, i.e., the optimal load shedding model, the system state changes are obtained; finally, the system resilience is quantified according to the N - th system resilience mean value under Monte Carlo sampling.

[0094] Moreover, the constructed two - stage optimization model for differential planning aims at the maximum resilience improvement return rate. Among them, in the first stage, the line reinforcement strategy is optimized based on the differential planning method; in the second stage, the load recovery strategy supported by energy storage power supply is optimized to verify the support ability of the planning scheme for resilience resources.

[0095] Moreover, an IPSO algorithm with an inertia weight adjusted based on an elliptic curve is used to solve the two - stage optimization model for differential planning. The change rate of the inertia weight of this algorithm is slow in the early stage of iteration and fast in the later stage, which is more conducive to the switching between the global search and local development of the algorithm.

[0096] During specific implementation, as Figure 1 shown, a power grid resilience evaluation and differential planning method under extreme typhoon disasters includes the following steps:

[0097] S1: Conduct typhoon disaster simulation based on the Batts wind field model;

[0098] The specific steps of S1 for conducting typhoon disaster simulation based on the Batts wind field model include:

[0099] S1.1 Calculate the maximum wind speed radius R max and the gradient wind speed V gx .

[0100] The maximum wind speed radius R max :

[0101] The forecast information required by the Batts wind field model includes the pressure difference ΔP (hPa) between the cyclone center and the periphery at the time of typhoon landing and the typhoon movement speed V T (m / s). The distance R from the cyclone center of the wind field to the strongest wind belt can be calculated through the central pressure difference max , and the calculation formula is as follows:

[0102]

[0103] In the formula: ΔP is the pressure difference between the cyclone center and the periphery of the wind field, and the peripheral pressure of the cyclone takes the standard atmospheric pressure of 1013 hPa

[0104] Gradient wind speed V gx :

[0105] According to the maximum wind speed radius, further R max , calculate the gradient wind speed V gx caused by the pressure gradient force of the wind field, and the calculation formula is as follows:

[0106]

[0107] In the formula: θ is the empirical coefficient, taking 6.72; f is the Coriolis force coefficient of the earth's rotation

[0108] S1.2. Calculate the maximum wind speed V Rmax within the wind field and the wind speed V r at each point

[0109] The maximum wind speed V Rmax within the wind field:

[0110] The maximum wind speed V Rmax appears at the maximum wind speed radius R max , and the calculation formula is as follows:

[0111]

[0112] In the formula: V T is the typhoon movement speed

[0113] The wind speed V r at each point within the wind field:

[0114] The instantaneous wind speed at each point in the wind field can be calculated from the distance r from this point to the wind field center, as follows:

[0115]

[0116] In the formula: r is the distance from the research point to the wind field center; V rin , V rout are the wind speeds when r is less than and greater than R maxThe instantaneous wind speed at the research point at that time; x is the typhoon radial intensity attenuation parameter, taking 0.5.

[0117] S1.3. Obtain the Batts wind field spatio-temporal model according to the typhoon intensity attenuation;

[0118] The power grid resilience assessment is a time-related dynamic process. Therefore, the wind field model of only a certain section is not sufficient to support the resilience assessment. It is necessary to make certain corrections to the static wind field model. After the typhoon makes landfall, the central cyclone pressure of the typhoon continuously increases, and the typhoon intensity attenuates. Eventually, after the typhoon ends when it is the same as the atmospheric pressure, the corrected wind field cyclone peripheral and central pressure difference ΔP is a function of the typhoon landfall time t, ΔP(t), as follows:

[0119] ΔP(t) = ΔP0(1 - e τt )

[0120] In the formula: t is the time constant for the increase of the central cyclone pressure of the wind field, and ΔP0 is the initial central pressure difference when the typhoon makes landfall.

[0121] S2: Construct a transmission line fault recovery model to calculate the line failure rate and recovery time;

[0122] The specific steps for constructing the transmission line fault recovery model to calculate the line failure rate and recovery time described in S2 are as follows:

[0123] S2.1. Calculate the system line failure rate under extreme weather conditions through the component vulnerability curve:

[0124] Under typhoon weather, wind damage is most likely to cause line faults. Taking the typhoon wind speed as the characteristic, construct a line fault model under the typhoon operating conditions: when the wind speed v at the line research point is less than the line design wind speed V N at that time, the line failure rate is 0; when v > 2V N at that time, the line failure rate is 1; in other cases, the line failure rate increases exponentially, as follows:

[0125]

[0126] S2.2. Calculate the time required for line fault recovery through the β distribution:

[0127] After a line fault, it takes a certain amount of time to locate and repair the fault to restore normal power supply. It is considered that the time to restore power supply through operation follows the β distribution, and its expectation and standard deviation are as follows:

[0128]

[0129] In the formula: t cThe time required for the faulty line to resume power supply through operation; for each line operation, three durations are estimated: the optimistic recovery time A, the most likely recovery time M, and the pessimistic recovery time B.

[0130] S3: Evaluate the power grid resilience based on the constructed power grid resilience evaluation indicators and processes;

[0131] The specific steps for evaluating the power grid resilience by the power grid resilience evaluation indicators and processes described in S3 include:

[0132] S3.1: Construct a differentiated resilience evaluation indicator considering the magnitude of system load loss, fault duration, and the maximum loss of important loads.

[0133] When society suffers from natural disasters such as typhoons, the absence of important loads such as important transportation hubs will further expand the disaster losses and affect the restoration of the power system at the same time. If this part of the load is considered equivalent to the rest of the loads, the resilience evaluation result will be higher than the actual situation, resulting in a masking phenomenon. To make the resilience evaluation result more accurate, the DR (Differentiated Resilience) indicator is proposed to evaluate the power grid resilience, as shown in the following formula:

[0134]

[0135] In the formula: E(·) represents the mathematical expectation; T is the research period; l R (t) is the system normal state operation curve; l I (t) is the system operation curve when the system suffers from extreme disasters; the coefficient 1 / 2 makes the resilience evaluation result a floating-point number between [0,1].

[0136] S3.2: Calculation of the differentiated resilience evaluation indicator of the power grid under discrete simulation.

[0137] In the actual simulation process, a continuous and smooth system state curve l I(t) cannot be obtained, but the total amount of system retained load L i and the total amount of important loads L i discrete within each simulation step T Si are obtained. At the same time, the expected value in the evaluation indicator is characterized by the mean value of the evaluation indicators of a number of sampled scenarios. During the simulation process, the DR indicator is calculated as follows

[0138]

[0139] In the formula: N is the number of sampled scenarios; T is the simulation duration, and ΔT is the simulation step; is the system load retention at the i-th simulation step in the k-th sampled scenario; L total is the total system load; is the minimum retention of important loads in the k-th sampling scenario; L Stotal is the total amount of important loads in the system.

[0140] S3.3. Power grid differential resilience assessment process:

[0141] The power grid resilience assessment is a dynamic process that changes with the development of typhoons, including the topological changes of the network caused by line disconnections, line repair and restoration, etc. during typhoon accidents, and the system state changes caused by the topological changes of the network. The changes in the system state directly reflect the size of the system resilience. Based on the above analysis, the power grid resilience assessment should be based on disaster fault and recovery simulation to obtain the dynamic changes of the network topological structure; then, according to the system fault response, that is, the optimal load shedding model, the system state changes are obtained; finally, the system resilience is quantified according to the N -th system resilience mean value under Monte Carlo sampling.

[0142] Specifically, when implemented, the power grid resilience assessment process under typhoon disasters is as Figure 2 shown: 1) Input typhoon wind field data and power grid data;

[0143] 2) Start the simulation, and the sampling times k = 1;

[0144] 3) Calculate the line failure rate within the step size;

[0145] 4) Randomly generate faults according to the failure rate;

[0146] 5) Generate the fault recovery time according to the line recovery model;

[0147] 6) Form a line fault status table;

[0148] 7) After t = 1 second, the system conducts a fault impact analysis;

[0149] 8) Generate an optimal load shedding model;

[0150] 9) Count the load shedding and important load shedding situations;

[0151] 10) Calculate the system resilience under a single sampling;

[0152] 11) Judge whether the sampling times are satisfied. If the sampling times satisfy k = k + 1, then return to step 3); otherwise, continue with step 12);

[0153] 12) Calculate the system resilience mean value as the final resilience assessment result.

[0154] S4: Construct a two - stage optimization model for power grid differential planning with the maximum resilience return on investment as the objective function;

[0155] As Figure 3As shown in the figure, the specific construction steps of the two-stage optimization model for grid differential planning described in S4 are as follows:

[0156] 1) Input the electrical, geographical, and typhoon parameters of the system;

[0157] 2) Input the initial grid reinforcement plan of the system;

[0158] 3) The IPSO solves the first-stage optimization model;

[0159] 4) Obtain the first-stage optimization results;

[0160] 5) Alternative differential planning schemes;

[0161] 6) Input the existing energy storage parameters of the system;

[0162] 7) The IPSO solves the second-stage optimization model;

[0163] 8) Correct the first-stage optimization results of the alternative schemes;

[0164] 9) Output the optimal differential planning scheme of the system and the resilience evaluation results.

[0165] The specific steps are as follows:

[0166] S4.1. The first-stage optimization takes the maximum return rate of resilience improvement as the objective function, and the protection levels of transmission lines are differentially strengthened through the differential planning method. The first-stage optimization model is as follows:

[0167]

[0168] In the formula: DR ROI is the return rate of resilience improvement; ΔDR is the magnitude of resilience improvement obtained when the grid adopts differential reinforcement; F LCC is the life-cycle cost of this scheme; is the life-cycle cost when all lines adopt the highest protection level; U i,t and U j,t are the voltage amplitudes of nodes i and j at time t, respectively; θ ij,t is the voltage phase angle difference between nodes i and j at time t; g ij and b ij are the conductance and susceptance between nodes i and j, respectively; P ess,i,t and P G,i,t and P load,i,t are the active power output of the energy storage, the active power output of the power source, and the active power consumed by the load at node i at time t, respectively; Q ess,i,t and Q G,i,t and Q load,i,tare the reactive power output of the energy storage, the reactive power output of the power source, and the reactive power consumption of the load at node i at time t. In the first-stage optimization model, energy storage discharge is not considered, so P ess,i,t , Q ess,i,t are both 0; U i,min , U i,max are the minimum and maximum values of the operating voltage of node i respectively; P l,t is the actual load of line l at time t; P l,max is the maximum load of line l; P G,i,min , P G,i,max are the upper and lower limits of the active power output of generator set i respectively. R G,i is the upper limit of the allowable increase or decrease of the active power of generator set i per unit time.

[0169] The life-cycle cost F LCC of the planning scheme is calculated as follows:

[0170]

[0171] In the formula: F1 is the one-time investment cost for improving the line protection level; F2 is the additional daily maintenance, inspection, etc. costs after improving the protection level; F3 is the recovery cost after the line is taken out of service; r is the annual interest rate of funds; Year is the research period; α1, α2 are proportionality coefficients.

[0172] S4.2. In the second stage, optimize the system resilience resources to further improve the resilience improvement return rate of the differential planning scheme. The second-stage optimization model is as follows:

[0173]

[0174] In the formula: f1 is the value of the objective function of the first-stage optimization; ΔDR ess is the system resilience improved by supporting the load through energy storage; is the life-cycle cost of the first-stage differential planning scheme; g(x)=0, h(x)≤0 are the grid operation constraints listed in the first-stage optimization model respectively; is the capacity of the energy storage device installed at node i; are its upper and lower limits of capacity; P ess,i,t is the energy storage discharge at node i at time t; P ess,i,max is its upper limit of discharge power; SOC min , SOC max are the minimum and maximum state of charge values of the energy storage system respectively; E left,i,t is the remaining energy of the energy storage at node i at time t.

[0175] As Figure 4 shown, the solution process of the IPSO algorithm is as follows:

[0176] 1) Initialize the algorithm parameters;

[0177] 2) The iteration number n = 1;

[0178] 3) Randomly initialize the particle positions and velocities, and calculate the fitness of each particle;

[0179] 4) Obtain the global extreme value and the individual extreme value of the population respectively;

[0180] 5) Update the positions and velocities of the particles by cyclic iteration, and update the magnitude of the inertia weight;

[0181] 6) Update the global extreme value and the individual extreme value of the population according to the fitness values of the new particles;

[0182] 7) When the iteration number reaches the set value, output the optimal position of the population and the corresponding fitness magnitude.

[0183] The specific steps of the improved binary ISO algorithm for solving the model described in S5 are as follows:

[0184] S5.1, Construct the basic particle swarm optimization algorithm:

[0185] The basic particle swarm optimization algorithm is as follows: A group of particles search for the objective function in the N-dimensional space at a certain speed, and describe the motion state of the particles through the position vector and the velocity vector Each particle can communicate and learn from each other through the learning factor and the inertia weight, and store the current individual optimal position vector and the current global optimal position vector so as to adjust the velocity vector for searching in the next iteration, and correct the particle position vector, as shown in the following formula:

[0186]

[0187]

[0188] In the formula: w is the inertia weight; c1 and c2 are the individual and social experience learning factors respectively; r1 and r2 are random numbers uniformly distributed in [0,1]; are the velocity vectors of particle i at the k-th and (k + 1)-th iterations respectively; are the position vectors of particle i at the k-th and (k + 1)-th iterations respectively; is the individual optimal position vector of particle i at the k-th iteration; g k The global optimal position vector.

[0189] S5.2, The improved PSO algorithm based on the elliptic function to correct the inertia weight

[0190] In the basic PSO algorithm, the inertia weight w is a constant. However, a constant weight cannot balance the contradiction between global search in the early stage and local fine search in the later stage. To address this defect, an IPSO algorithm with an inertia weight adjusted based on an elliptic curve is proposed. In this algorithm, the change rate of the inertia weight is slow in the early stage of iteration and fast in the later stage, which is more conducive to the switching between global search and local development of the algorithm.

[0191] The specific calculation of the inertia weight adjusted based on the elliptic curve function is as follows:

[0192]

[0193] In the formula: w max are the maximum values of the inertia weight respectively; N wzero is the number of iterations when the inertia weight is 0; n is the current number of iterations.

[0194] S5.3. Set the population size of the algorithm parameters to 20 and the number of iterations to 300 to solve this model.

[0195] The above are only preferred embodiments of the present invention, and do not limit the implementation manners and protection scope of the present invention accordingly. For those skilled in the art, it should be able to realize that all the solutions obtained by equivalent substitution and obvious changes made by using the content of the specification of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for evaluating the resilience of power grids and differential planning under extreme typhoon disasters, characterized in that: It includes the following steps: Step 1: Simulate typhoon disasters based on the Batts wind field model; Step 2: Construct a transmission line fault recovery model to calculate the line failure rate and recovery time; Step 3: Construct grid resilience evaluation indicators considering the power supply of important loads; Step 4: Take the grid resilience improvement return rate as the objective function to construct a two-stage optimization model for grid differential planning; the specific steps are as follows: The first-stage optimization takes the maximum grid resilience improvement return rate as the objective function, and differentially strengthens the protection levels of transmission lines through differential planning methods; the first-stage optimization model is: Where: DR ROI is the resilience improvement return rate; ΔDR is the magnitude of resilience improvement obtained when the power grid adopts differential reinforcement; F LCC is the life cycle cost of the scheme; is the life cycle cost when all lines adopt the highest protection level; U i,t and U j,t are the voltage amplitudes of nodes i and j at time t respectively; θ ij,t is the voltage phase angle difference between nodes i and j at time t; g ij , b ij are the conductance and susceptance between nodes i and j respectively; P ess,i,t , P G,i,t , P load,i,t are the active power output of the energy storage, the active power output of the power source, and the active power consumption of the load at node i at time t respectively; Q ess,i,t , Q G,i,t , Q load,i,t are the reactive power output of the energy storage, the reactive power output of the power source, and the reactive power consumption of the load at node i at time t respectively. In the first-stage optimization model, the energy storage discharge is not considered, so P ess,i,t , Q ess,i,t are both 0; U i,min , U i,max are the minimum and maximum values of the operating voltage of node i respectively; P l,t is the actual load of line l at time t; P l,max is the maximum load of line l; R G,i is the upper limit of the active power that the generator set i is allowed to increase or decrease per unit time; The full life cycle cost F of the planning scheme LCC The calculation method is as follows: In the formula: F1 is the one-time investment cost for improving the line protection level; F2 is the new daily maintenance and inspection cost after improving the protection level; F3 is the recovery cost after the line is taken out of service; r is the annual interest rate of funds; Year is the research period; α1, α2 are proportionality coefficients; The second-stage optimizes the system resilience resources to improve the resilience improvement return rate of the differential planning scheme; Step 5: Use the improved PSO algorithm to solve the constructed model to obtain the grid differential planning scheme.

2. The method for evaluating the resilience of the power grid and differential planning under extreme typhoon disasters according to claim 1, wherein: The implementation of Step 1 includes the following specific steps: Step 1.

1. Calculate the maximum wind speed radius R based on the forecast information max and the gradient wind speed V gx ; Step 1.1.1, calculate the maximum wind speed radius R max ; The forecast information required for the Batts wind field model includes the pressure difference ΔP, hPa between the cyclone center and the periphery at the time of typhoon landing, and the typhoon movement speed V T , m / s; and the distance R from the cyclone center of the wind field to the strongest wind belt can be calculated through the central pressure difference max , and the calculation formula is as follows: In the formula: ΔP is the air pressure difference between the cyclone center and the periphery, and the air pressure at the cyclone periphery takes the standard atmospheric pressure of 1013 hPa; Step 1.1.2, calculate the gradient wind speed V gx ; According to the maximum wind speed radius R max , calculate the gradient wind speed V gx caused by the pressure gradient force of the wind field. The calculation formula is as follows: In the formula: θ is the empirical coefficient, taking 6.72; f is the Coriolis force coefficient of the earth's rotation; Step 1.2, calculate the maximum wind speed V within the wind field Rmax and the wind speed V at each point r ; Step 1.2.

1. Calculate the maximum wind speed V within the wind field Rmax ; The maximum wind speed V within the wind field Rmax appears at the maximum wind speed radius R max at the location, and the calculation formula is as follows: Where: V T is the typhoon moving speed; Step 1.2.

2. Calculate the wind speed V at each point within the wind field r ; The instantaneous wind speed at each point in the wind field is calculated from the distance r from the research point to the wind field center: where: r is the distance from the research point to the center of the wind field; V rin and V rout are the instantaneous wind speeds at the research point when r is less than and greater than R max respectively; x is the typhoon radial intensity attenuation parameter, taking 0.5; Step 1.3: Obtain the Batts wind field spatio-temporal model according to the typhoon intensity attenuation; Correct the air pressure difference ΔP between the cyclone center and the periphery of the wind field as a function of the typhoon landing time t, ΔP(t), as follows: ΔP(t) = ΔP0(1 - e τt ) In the formula: t is the time constant for the increase in the cyclone air pressure at the wind field center, and ΔP0 is the initial central air pressure difference at the time of typhoon landing.

3. The method for evaluating the resilience of the power grid and differential planning under extreme typhoon disasters according to claim 1, characterized in that: The implementation of Step 2 includes the following specific steps: Step 2.1: Calculate the system line failure rate under extreme weather conditions through the component vulnerability curve; Construct a line fault model under typhoon operating conditions characterized by typhoon wind speed: when the wind speed v at the line research point is less than or equal to the line design wind speed V N the line failure rate is 0; when v ≥ 2V N the line failure rate is 1; in other cases, the line failure rate increases exponentially, as shown in the following formula: Step 2.2: Calculate the time required for line fault recovery through the β distribution; After the line fails, the time for restoring power supply through operation follows the β distribution, and its expectation and standard deviation are as follows: where: t c is the time required for the faulty line to resume power supply through operation; for each line operation, three durations are estimated: the optimistic recovery time A, the most likely recovery time M, and the pessimistic recovery time B.

4. The method for evaluating the resilience of the power grid and differential planning under extreme typhoon disasters according to claim 1, characterized in that: The implementation of Step 3 includes the following specific steps: Step 3.1: Construct differential resilience evaluation indicators considering the size of system load loss, fault duration, and maximum loss of important loads; Use the Differentiated Resilience DR index to evaluate the grid resilience, as follows: Where: E( · ) represents the mathematical expectation; T is the research period; l R (t) is the normal state operation curve of the system; l I (t) is the system operation curve when the system suffers from extreme disasters; the coefficient 1 / 2 makes the resilience evaluation result a floating-point number between [0,1]; Step 3.2: Calculate the grid differential resilience evaluation indicators under discrete simulation; During the simulation process, the DR index is calculated as follows: Where: N is the number of sampling scenarios; T is the simulation duration, and ΔT is the simulation step size; is the system load retention at the i-th simulation step in the k-th sampling scenario; L total is the total system load; is the minimum retention of important loads in the k-th sampling scenario; is the total amount of important loads in the system; Step 3.3: Grid differential resilience evaluation process: The grid resilience evaluation is based on disaster fault and recovery simulation to obtain the dynamic changes in the network topology structure; according to the system fault response, that is, the optimal load shedding model, the system state changes are obtained; the system resilience is quantified according to the N - time system resilience mean under Monte Carlo sampling.

5. According to the method for evaluating grid resilience and differential planning under extreme typhoon disasters described in claim 1, it is characterized in that: The second-stage optimization model is as follows: Where: f1 is the optimization objective function value in the first stage; ΔDR ess is the system resilience improved by energy storage to support the load; is the life cycle cost of the first-stage differentiated planning scheme; g(x) = 0 and h(x) ≤ 0 are the power grid operation constraints listed in the first-stage optimization model respectively; is the capacity of the energy storage device installed at node i; are its upper and lower capacity limits; P ess,i,t is the discharge amount of the energy storage at node i at time t; P ess,i,max is its upper discharge power limit; SOC min and SOC max are the minimum and maximum state of charge values of the energy storage system respectively; E left,i,t is the remaining power of the energy storage at node i at time t.

6. The method for evaluating the resilience of the power grid and differential planning under extreme typhoon disasters according to claim 1, wherein: The implementation of Step 5 includes the following specific steps: Step 5.1: Construct a basic particle swarm algorithm; A group of particles searches for the objective function at a certain speed in the N-dimensional space, and describes the motion state of the particles through the position vector and the velocity vector ; each particle communicates and learns from each other through the learning factor and the inertia weight, and stores the current individual optimal position vector and the current global optimal position vector to adjust the velocity vector for searching in the next iteration, and correct the particle position vector, as shown in the following formula: Where: w is the inertia weight; c1 and c2 are the individual and social experience learning factors respectively; r1 and r2 are random numbers uniformly distributed in [0, 1]; are the velocity vectors of particle i at the k-th and (k + 1)-th iterations respectively; are the position vectors of particle i at the k-th and (k + 1)-th iterations respectively; is the individual optimal position vector of particle i at the k-th iteration; g k the global optimal position vector; Step 5.2: Improved PSO algorithm with inertia weight corrected based on elliptic function; The specific calculation of the inertia weight adjusted based on the elliptic curve function is as follows: where: w max is the maximum value of the inertia weight; is the number of iterations when the inertia weight is 0; n is the current number of iterations.

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