Analytic analysis method for equipment replacement scheme and reliability improvement level of power system

Abstract

The invention relates to the field of power system reliability optimization methods, in particular to an equipment replacement scheme and power system reliability improvement level analytic analysis method, which comprises the following steps: step 1, analyzing and counting aging failure data of a plurality of pieces of power equipment, and establishing an aging failure reliability model of the power equipment; step 2, based on the power equipment aging failure reliability model, establishing a power equipment aging failure unavailability analytical expression containing replacement plan influence; 3, based on the equipment unavailability parameter, combining the unavailability parameter with load uncertainty for modeling, and constructing an optimal load reduction model-based mathematical calculation model for predicting the reliability of the power system; and step 4, establishing an analytical model between the system reliability index predicted value and the unavailability parameter of the target equipment, and calculating the system reliability index predicted value of each year in the planning period. According to the method, input data for reliability prediction can be more accurate, the calculation amount is reduced, and the method is suitable for rapid equipment replacement scheme optimization in engineering practice.

Description

Technical Field

[0001] The present invention relates to the field of power system reliability optimization methods, and in particular to an analytical method for equipment replacement schemes and power system reliability improvement levels. Background Art

[0002] As the power demand of the power system becomes higher and higher, it is very important to strengthen the connection between power system reliability prediction and system planning and development (such as replacement of aging equipment), make up for the shortcomings of the power system grid structure, and ensure the adequacy and safety of the power system.

[0003] However, when evaluating the impact of aging power equipment replacement plans on the system reliability level, it is necessary to analyze a large number of system states during the planning period. The analysis of each system state must calculate the corresponding load shedding through the optimal power flow model, which makes the power system reliability prediction a high-dimensional, nonlinear problem that is difficult to solve quickly. In particular, the reliability parameters of aging equipment have time-varying characteristics during the planning period. In order to evaluate the impact of any aging equipment replacement plan, the system reliability level during the planning period must be predicted year by year, resulting in a huge amount of calculation. This also makes it difficult to accurately evaluate the improvement effect of different aging equipment replacement plans on system reliability within a limited decision-making time, and thus it is impossible to achieve the optimization of aging equipment replacement plans. In addition, if the uncertainty of system load is further considered, the analysis time will increase significantly.

[0004] From the perspective of causal analysis, the replacement plan of aging equipment directly affects its reliability level during the planning period, which in turn affects the reliability level of the entire power system during the planning period. However, the analysis and research of this causal chain has the following deficiencies:

[0005] (1) In terms of reliability parameters of aging power equipment: Existing models can usually only evaluate the unavailability rate of aging equipment in the short term or in the current year, and it is difficult to effectively predict the time-varying unavailability rate of equipment in the next few years. In addition, existing models also fail to take into account the impact of equipment replacement plans on the time-varying unavailability rate of aging equipment, and therefore cannot provide accurate data input for system reliability prediction models.

[0006] (2) In terms of system reliability prediction models: the existing models have not yet established an analytical mathematical relationship between the system reliability level and the unavailability rate of aging equipment during the planning period. This means that when the reliability parameters of aging equipment change year by year, complex reliability predictions must be performed year by year, resulting in a huge amount of calculations that are difficult to meet the time and resource requirements of actual engineering.

[0007] (3) In addition, when constructing existing reliability prediction models, the impact of load uncertainty on system reliability during the planning period is not fully considered, which may lead to deviations in the prediction results and thus affect the accuracy of decision-making. Summary of the invention

[0008] The present invention aims to provide an analytical method for equipment replacement schemes and power system reliability improvement levels to solve the problems of inaccurate data input into system reliability prediction models and large amount of calculation for reliability prediction.

[0009] The analytical method for the equipment replacement plan and the reliability improvement level of the power system in this plan includes the following steps:

[0010] Step 1, analyzing and statistically collecting aging failure data of multiple power equipment, using a grey prediction model to estimate the parameters of a three-parameter Weibull distribution, and establishing a power equipment aging failure reliability model based on a three-parameter Weibull distribution;

[0011] Step 2: Based on the reliability model of power equipment aging failure established in step 1, considering the influence of replacement plan, establish an analytical expression of unavailability rate of power equipment aging failure including the influence of replacement plan;

[0012] Step 3: Based on step 2, the equipment unavailability rate parameter after considering the impact of the replacement plan is obtained, the unavailability rate parameter is combined with the load uncertainty modeling, and a mathematical calculation model for power system reliability prediction based on the optimal load reduction model is constructed;

[0013] Step 4: Establish an analytical model between the predicted value of the system reliability index and the target equipment unavailability rate parameter, and use the analytical model to calculate the predicted value of the system reliability index for each year within the planning period.

[0014] The beneficial effects of this program are:

[0015] For the aging failure data during the operation of the power system, the analytical modeling expression of the reliability parameter "aging failure unavailability rate" of the power equipment is carried out under the influence of the aging equipment replacement plan, so that the input data of the subsequent system reliability prediction based on the aging unavailability rate of the power equipment is more accurate; then, considering the influence of the uncertainty of the system load during the actual operation, based on the conditional probability theory and the interval linear programming method, an analytical model between the reliability index of the power system and the equipment unavailability rate is established, and the corresponding reliability index prediction is carried out, so as to improve the accuracy of the reliability prediction results while simplifying the calculation process and reducing the amount of calculation; the present invention establishes an analytical model, which can directly realize the analytical quantitative analysis between the "aging equipment replacement plan" to the "equipment aging failure unavailability rate parameter" and then to the "system reliability improvement level". In engineering practice, equipment operation and maintenance personnel usually face a large number of aging equipment replacement plan options. The method of the present invention can quickly and accurately determine the improvement level of system reliability by implementing each aging equipment replacement plan, and then guide the operation and maintenance to select the equipment replacement plan that can maximize the improvement of the system reliability level.

[0016] Furthermore, in step 1, the process of establishing the reliability model of power equipment aging failure includes the following sub-steps:

[0017] Sub-step 1.1, count the aging failure time of various types of power equipment in the power equipment historical ledger data, and arrange them in chronological order from small to large, expressed as:

[0018] T=(t1,t2,...,t n );

[0019] Where: t n is the time when the nth power equipment fails due to aging, and t1≤t2≤...≤t n ;

[0020] Sub-step 1.2, using the three-parameter Weibull distribution to construct the time-varying aging failure probability function F(x) of power equipment, expressed as:

[0021]

[0022] The corresponding aging failure probability density function is:

[0023]

[0024] Where: variable t is the operating time of the power equipment, F(t) and f(t) represent the aging failure probability function and aging failure probability density function of the power equipment respectively; η is the scale parameter; m is the shape parameter; γ is the location parameter;

[0025] Sub-step 1.3, the grey prediction model GM(1,1) estimates the scale parameter η, shape parameter m and location parameter γ of the three-parameter Weibull distribution. First, the data preprocessing of the inverse transformation of the time-varying aging failure probability function of power equipment constructed in sub-step 1.2 is expressed as:

[0026]

[0027]

[0028] Sub-step 1.4, calculate w and x in combination with the aging failure time data T of the power equipment, and then rewrite the formula in sub-step 1.3 as follows:

[0029]

[0030]

[0031] Substep 1.5, let a = 1 / m, c = η, u = a / b = γ, and replace the formula in substep 1.4 with the differential equation of the model GM(1,1) The time response function Corresponding.

[0032] The beneficial effect is that the model is built based on the aging failure data of the equipment, which can be applied to the accurate modeling of major power equipment such as generator sets, power transformers, and transmission lines while considering replacement plans and reliability goals.

[0033] Further, in the sub-step 1.5, replace (t i ,w i ) is equivalent to a general time series, and combined with the least squares method, the aging failure time data T is used to estimate the three parameters η, m and γ, which can be expressed as:

[0034]

[0035] Where:

[0036]

[0037]

[0038] Where: are the estimated values ​​of the three parameters η, m and γ respectively.

[0039] Further, the step 2 includes the following sub-steps:

[0040] Sub-step 2.1, the aging failure probability function of power equipment taking into account the impact of the replacement plan is expressed by the formula in sub-step 1.2:

[0041]

[0042] Where: variable t also represents the operating time of the power equipment; r rp Indicates the time to implement the replacement plan for power equipment;

[0043] Sub-step 2.2: for power equipment that has been in service for H years, the impact of equipment aging failure occurring at different time periods during the planning period on its expected unavailability time in the H+k year is evaluated by discrete method, and an analytical formula for aging failure unavailability rate is established;

[0044] Sub-step 2.3, calculate the probability of aging failure of the equipment in each period and the duration of unavailability caused in the H+k year, and obtain the aging failure unavailability rate of the equipment in the H+k year as:

[0045]

[0046] In the formula, ζ k (i) The impact of the replacement period on the expected unavailability time in year H+k;

[0047] In sub-step 2.4, the comprehensive unavailability rate in year H+k is given by the random failure unavailability rate U random The calculation is based on the union of (H+k) and the aging failure unavailability rate calculated in sub-step 2.3:

[0048] U all (H+k)=U random +U aging (H+k)-U random ·U aging (H+k);

[0049]

[0050] In the formula, and They are the average time before random failure of equipment and the average repair time, and their values ​​are constants.

[0051] The beneficial effect is that an analytical expression for the unavailability rate of power equipment aging failure including the influence of replacement plan is derived, which is used to quantitatively evaluate the impact of different replacement plans on the time-varying unavailability rate of aging power equipment in each year during the planning period, and provide accurate data input for subsequent system reliability prediction.

[0052] Furthermore, in the sub-step 2.2, the process of establishing the analytical formula of the aging failure unavailability rate includes:

[0053] Sub-step 2.2.1, divide the total planning period K years into N time periods according to the time length Δx, and each segment is marked with i (i = 1, 2, ..., N). The probability of irreparable aging failure of power equipment in the i-th time period can be analytically expressed as:

[0054]

[0055] Where F(·) is the aging failure probability function established in sub-step 2.1 after considering the impact of equipment replacement plan;

[0056] Sub-step 2.2.2: Examine the time L required to perform corrective replacement operations after the equipment fails due to aging in each period. repace The expected unavailable time ζ for the H+kth year k Assuming that the equipment fails due to aging in the i-th period, the period during which the equipment is unavailable due to replacement is from H+(2i-1)·Δx / 2 to H+(2i-1)·Δx / 2+L replace ;

[0057] Sub-step 2.2.3, for any stage of the planning period that time period i may be in, where i = 1, 2, ..., N, the impact of the replacement period on the expected unavailability time in year H+k ζ k (i) Including the following situations:

[0058] When the equipment fails due to aging in the i-th period and is replaced before the year H+k:

[0059] ζ k (i) = 0, if (H + (2i-1) · Δx / 2 + L replace )≤H+k;

[0060] When the aging failure of the equipment in the i-th period occurs before the H+k year but the replacement operation is completed within the H+k year:

[0061]

[0062] When the aging failure of the equipment in the i-th period is within the H+k year and the replacement operation is completed within the H+k year:

[0063]

[0064] When the aging failure of the equipment in the i-th period occurs within the H+k year and the replacement operation is completed after the H+k year:

[0065] ζ k (i)=(T+k+1)-(T+(2i-1)·Δx / 2)

[0066] if T+k≤(T+(2i-1)·Δx / 2)≤T+k+1&(T+(2i-1)·Δx / 2+L replace )>T+k+1;

[0067] When the aging failure occurred in the i-th period is after T+k years:

[0068] ζ k (i)=0, if (H+(2i-1)·Δx / 2)>H+k+1.

[0069] The beneficial effect is that the length of unavailability caused by equipment aging and failure is mainly limited by the time of equipment selection, procurement and transportation. Considering failure at any point in the time period can fully take into account the actual failure situation of the equipment.

[0070] Furthermore, in step 3, the construction of a mathematical calculation model for power system reliability prediction includes:

[0071] Sub-step 3.1, model the load uncertainty of the power system based on the interval model. In the kth year, the load uncertainty model of the power system at any hour is represented as:

[0072]

[0073] Where: Represents the load variable M i The value range of and Respectively represent the interval The previous and next term;

[0074] Sub-step 3.2, based on the load interval uncertainty model established in step 3.1, the optimal load reduction model based on DC power flow and the interval linear programming method are used to predict the system reliability in the kth year. The prediction steps include: system state generation, system state analysis, and reliability index calculation;

[0075] Sub-step 3.3, repeat step 3.2 until the predetermined termination criteria are met, and then calculate the predicted value of the system reliability indicator expected power shortage EENS in the kth year, which is expressed as:

[0076]

[0077] In the formula: EENS k represents the predicted value of the reliability index of the system in the kth year, LC s,aver represents the optimal average load reduction corresponding to system state s, Q sam,k represents the total number of system states generated to predict the system reliability index in the kth year;

[0078] Sub-step 3.4, calculate the improvement of the system reliability level in the kth year after implementing the given aging equipment replacement plan, expressed as:

[0079]

[0080] In the formula: EENS k,before It represents the predicted value of the reliability index of the system in the kth year before the aging equipment replacement plan is implemented, which is calculated by ignoring the impact of the aging equipment replacement plan.

[0081] The beneficial effect is that by combining the unavailability parameter with load uncertainty modeling, the expected reliability level of the system under any given replacement plan can be accurately predicted.

[0082] Further, the prediction step in the sub-step 3.2 includes:

[0083] Sub-step 3.2.1, randomly generate the status of any system component in the kth year. Based on the analytical calculation model of equipment unavailability established in step 2, a random number q in [0,1] is randomly generated to determine the operating status of each system device. For each device: if q all (H+k), the equipment is in a failed shutdown state, otherwise the equipment is in a normal operating state;

[0084] Sub-step 3.2.2, based on the load interval uncertainty model established in sub-step 3.1, randomly select a load interval of any hour in a year as the system load level corresponding to the system component state generated in sub-step 3.2.1;

[0085] In sub-step 3.2.3, the optimal load reduction model based on DC power flow and the interval linear programming method are used to analyze the system states generated by sub-steps 3.2.1 and 3.2.2, determine the optimal load reduction interval corresponding to the system state, and calculate the optimal average load reduction; assuming that the generated system state is s, the upper and lower optimal load reduction intervals are calculated using the preset optimal load reduction model, including the objective function and constraints.

[0086] The beneficial effect is that the optimal load reduction model based on DC power flow and the interval linear programming method can reduce the model error while ensuring the calculation speed, and can improve the accuracy and efficiency of power system reliability assessment.

[0087] Furthermore, in the sub-step 3.2.3, in the optimal load reduction model, the sum of the load reduction amounts on each bus of the system LC s Minimum is the objective function of the model, and the objective function is expressed as:

[0088] ​

[0089] Where: P s,i,cut represents the optimal load reduction of node i under system state s; Ψ bus Represents a collection of system nodes;

[0090] The constraints are expressed as:

[0091] 1. The system power balance constraint is expressed as:

[0092]

[0093] Where: P s,g represents the output of the g-th generator; Ψ g represents the set of generators in the system; P i,peak represents the annual peak load of node i; M s ·P i,peak represents the load demand of node i in state s; M s Take the value of system load;

[0094] 2. The node power balance constraint is expressed as:

[0095]

[0096] Where: g,i represents the set of generators connected to node i; P s,i,in represents the injected power of node i;

[0097] 3. The node load reduction constraint is expressed as:

[0098]

[0099] 4. The node injection power calculation is expressed as:

[0100]

[0101] Where: n represents the number of system nodes; θ s,j represents the voltage phase angle of node j; b s,ij represents the element in the i-th row and j-th column of the node admittance matrix B;

[0102] 5. The DC power flow equation of the transformer / line branch is expressed as:

[0103]

[0104] Where: θ s,i and θ s,j Respectively represent the voltage phase angles of the first and last nodes i and j of branch r; s,r Represents the reactance of branch r; PL s,rrepresents the power flow of branch r; branch Represents a set of system branches;

[0105] 6. Transformer / line branch transmission capacity constraint is expressed as:

[0106]

[0107] Where: Indicates the maximum transmission capacity of branch r; state identification variable υ s,r Used to describe the operating status of branch r: When the sampling status of branch r is failure and shutdown, υ s,r The value is 0, otherwise s,r is 1;

[0108] 7. The unit output constraint is expressed as:

[0109]

[0110] Where: Indicates the maximum output of the generator g, which is taken as the rated capacity; υ s,g Used to describe the operating status of generator g: When the sampling status of unit g is failure shutdown, υ s,g The value is 0, otherwise s,g is 1.

[0111] The beneficial effect is that the setting of the objective function and the constraint conditions can take into account multiple aspects of the equipment, improve the accuracy of the calculation and reduce the amount of calculation.

[0112] Further, in the sub-step 3.2.3, when M s When the value is taken as the upper limit of the load range, the obtained is the upper bound of the optimal load reduction interval, when M s When the value is taken as the lower limit of the load range, the obtained is the lower bound of the optimal load reduction interval. Therefore, the optimal average load reduction corresponding to the system state s is:

[0113]

[0114] Furthermore, in step 4, the step of calculating the predicted value of the system reliability index includes:

[0115] Sub-step 4.1, for the G components contained in the system, since only M target devices will be replaced during the planning period, the unavailability rate parameters of the remaining GM system components in each year during the planning period are constants, and the system reliability index is expressed as:

[0116]

[0117] Where, H1, ..., H M is the running time of M target devices. From the mathematical optimization model of step 3, we can know that About U all (H1+k),…,U all (H M +k) nonlinear function;

[0118] Sub-step 4.2, based on the proposed complete event group division principle, classify all system states generated in the process of predicting the reliability index of the kth year in step 3;

[0119] Since each device has only two states, working and failing, and the failures of each device are independent of each other, the number of combined states of M target devices is Y = 2 M , and these Y mutually exclusive combination states are recorded as F y , where y = 1, 2, ..., Y, let Y states constitute a complete event group;

[0120] Φ y , where y = 1, 2, ..., Y, represents the system event set of M target devices in the yth combination state, which is divided into Y subsets based on the system state generated in step 3, namely: Φ1, Φ2, ..., Φ Y ;

[0121] Rewrite the formula in substep 4.1 as:

[0122]

[0123] Where Y k (b) is the optimal load reduction corresponding to event b, which is calculated by the mathematical optimization model proposed in step 3;

[0124] Sub-step 4.3, based on the definition of independent failures between devices and conditional probability, rewrite the formula in step 4.2 as follows:

[0125]

[0126] In the formula, Indicates that in event F y The probability of event b occurring under the condition that For event F y The probability of occurrence, where y = 1, 2, ..,, Y;

[0127] Substep 4.4, let Rewrite the formula in substep 4.3 as:

[0128]

[0129] When the system network topology, operating parameters and GM non-target device unavailability rate parameters remain unchanged, the coefficients in the above formula It is only related to the state of non-target components and is a constant;

[0130] Sub-step 4.5, the failures of each component are independent of each other, and event F y Probability of occurrence The calculation formula is:

[0131]

[0132] Where: ε u and ε a They are the combined states F y A collection of devices in working and faulty states.

[0133] The beneficial effect is that: considering the changes in the replacement plan of aging equipment, the unavailability rate parameters of aging equipment calculated in step 2 will also change accordingly. The establishment of the model can accurately calculate the predicted values ​​of system reliability indicators for each year within the planning period. BRIEF DESCRIPTION OF THE DRAWINGS

[0134] Figure 1 A flow chart for modeling in an embodiment of a method for analyzing equipment replacement scheme and power system reliability improvement level of the present invention;

[0135] Figure 2 The single-line diagram of the RTS-79 system in the embodiment of the analytical analysis method for equipment replacement scheme and power system reliability improvement level of the present invention;

[0136] Figure 3 It is an error diagram of the reliability level improvement calculation results in the embodiment of the analytical analysis method for equipment replacement scheme and power system reliability improvement level of the present invention. DETAILED DESCRIPTION

[0137] The following is further explained in detail through specific implementation methods.

[0138] Example

[0139] Analytical methods for equipment replacement schemes and power system reliability improvement levels, such as Figure 1 As shown:

[0140] Step 1: Analyze and statistically collect aging failure data of multiple power equipment, use the grey prediction model to estimate the parameters of the three-parameter Weibull distribution, and establish a power equipment aging failure reliability model based on the three-parameter Weibull distribution. In step 1, the process of establishing the power equipment aging failure reliability model includes the following sub-steps:

[0141] Sub-step 1.1, count the aging failure time of various types of power equipment in the historical ledger data of power equipment, and arrange them in chronological order from small to large, expressed as:

[0142] T=(t1,t2,...,t n );

[0143] Where: t n is the time when the nth power equipment fails due to aging, and t1≤t2≤...≤t n .

[0144] Sub-step 1.2, using the three-parameter Weibull distribution to construct the time-varying aging failure probability function F(x) of power equipment, expressed as:

[0145]

[0146] The corresponding aging failure probability density function is:

[0147]

[0148] Wherein: variable t is the operating time of the power equipment, F(t) and f(t) represent the aging failure probability function and aging failure probability density function of the power equipment respectively; η is the scale parameter; m is the shape parameter; γ is the location parameter; the three parameters η, m, and γ need to be estimated by fitting the historical data of aging failure of the power equipment.

[0149] Sub-step 1.3, the grey prediction model GM(1,1) estimates the scale parameter η, shape parameter m and location parameter γ of the three-parameter Weibull distribution. First, the data preprocessing of the inverse transformation of the time-varying aging failure probability function of power equipment constructed in sub-step 1.2 is expressed as:

[0150]

[0151]

[0152] Sub-step 1.4, calculate w and t in combination with the aging failure time data X of the power equipment, and then rewrite the formula in sub-step 1.3 as follows:

[0153]

[0154]

[0155] Substep 1.5, let a = 1 / m, c = η, u = a / b = γ, and replace the formula in substep 1.4 with the differential equation of the model GM(1,1) The time response function Correspondingly, replace (t i ,w i ) is equivalent to a general time series, and combined with the least squares method, the aging failure time data T is used to estimate the three parameters η, m and γ, which can be expressed as:

[0156]

[0157] Where:

[0158]

[0159]

[0160] Where: are the estimated values ​​of the three parameters η, m and γ respectively.

[0161] Step 2: Based on the power equipment aging failure reliability model established in step 1, considering the impact of the replacement plan, establish an analytical expression for the unavailability rate of power equipment aging failure including the impact of the replacement plan, including the following sub-steps:

[0162] Sub-step 2.1, after the replacement of long-life power equipment such as generator sets, transformers and transmission lines, they usually will not enter the aging stage within 10 to 20 years. Unlike the post-corrective replacement measures taken after the aging and failure of equipment, the replacement plan of power equipment is a pre-emptive preventive measure. Enterprises usually complete the preparation work such as equipment selection, procurement and transportation before implementing the replacement plan. Therefore, the time required for the implementation of the replacement plan can usually be ignored in the medium-term planning. The aging failure probability function of power equipment taking into account the impact of the replacement plan is expressed by the formula in sub-step 1.2:

[0163]

[0164] Where: variable t also represents the operating time of the power equipment; r rp Indicates the time to implement the replacement plan for power equipment. This formula means that after the replacement plan is completed, there will be no aging failure of the power equipment during the planning period.

[0165] Sub-step 2.2, the definition of equipment aging failure unavailability rate is that for power equipment that has been in service for H years, the ratio of the mathematical expectation of the length of unavailability time caused by aging failure during the subsequent inspection period to the total evaluation time (usually one year) is the unavailability rate. The length of unavailability time caused by equipment aging failure is mainly limited by the time of equipment selection, procurement and transportation. For power equipment that has been in service for H years, a discrete method is used to evaluate the impact of equipment aging failure occurring at different time periods during the planning period on the expected unavailability time in the H+k year, and establish an analytical formula for aging failure unavailability rate. In the sub-step 2.2, the process of establishing the analytical formula for aging failure unavailability rate includes:

[0166] Sub-step 2.2.1, divide the total planning period K years into N time periods according to the time length Δx, and each segment is marked with i (i = 1, 2, ..., N). The probability of irreparable aging failure of power equipment in the i-th time period can be analytically expressed as:

[0167]

[0168] Where F(·) is the aging failure probability function established in sub-step 2.1 after considering the impact of equipment replacement plan;

[0169] Sub-step 2.2.2: Examine the time L required to perform corrective replacement operations after the equipment fails due to aging in each period. repace The expected unavailable time ζ for the H+kth year k Assuming that the equipment fails due to aging in the i-th period, the period during which the equipment is unavailable due to replacement is from H+(2i-1)·Δx / 2 to H+(2i-1)·Δx / 2+L replace ;

[0170] Sub-step 2.2.3, for any stage of the planning period that time period i may be in, where i = 1, 2, ..., N, the impact of the replacement period on the expected unavailability time in year H+k ζ k (i) Including the following situations:

[0171] When the equipment fails due to aging in the i-th period and is replaced before the year H+k:

[0172] ζ k (i) = 0, if (H + (2i-1) · Δx / 2 + L replace )≤H+k;

[0173] When the aging failure of the equipment in the i-th period occurs before the H+k year but the replacement operation is completed within the H+k year:

[0174]

[0175] When the aging failure of the equipment in the i-th period is within the H+k year and the replacement operation is completed within the H+k year:

[0176]

[0177] When the aging failure of the equipment in the i-th period occurs within the H+k year and the replacement operation is completed after the H+k year:

[0178] ζ k (i)=(T+k+1)-(T+(2i-1)·Δx / 2)

[0179] if T+k≤(T+(2i-1)·Δx / 2)≤T+k+1&(T+(2i-1)·Δx / 2+L replace )>T+k+1;

[0180] When the aging failure occurred in the i-th period is after T+k years:

[0181] ζ k (i)=0, if (H+(2i-1)·Δx / 2)>H+k+1.

[0182] Sub-step 2.3, calculate the probability of aging failure of the equipment in each period and the duration of unavailability caused in the H+k year, and obtain the aging failure unavailability rate of the equipment in the H+k year as:

[0183]

[0184] In the formula, ζ k (i) is the impact of the replacement period on the expected unavailability time in year H+k.

[0185] In sub-step 2.4, the reliability of power equipment will be affected by two independent modes, random failure and aging failure. The comprehensive unavailability rate in the H+k year is determined by the random failure unavailability rate U random The calculation is based on the union of (H+k) and the aging failure unavailability rate calculated in sub-step 2.3:

[0186] U all (H+k)=U random +U aging (H+k)-U random ·U aging (H+k);

[0187]

[0188] In the formula, and They are the average time before random failure of equipment and the average repair time, which are constants. The average time before random failure of equipment and the average repair time are obtained through historical data statistics.

[0189] Step 3: Based on step 2, the equipment unavailability rate parameters after considering the impact of the replacement plan are obtained, and the unavailability rate parameters are combined with load uncertainty modeling to build a mathematical calculation model for power system reliability prediction based on the optimal load reduction model. The construction of the mathematical calculation model for power system reliability prediction includes:

[0190] Sub-step 3.1: In engineering practice, the statistical law of system historical load is relatively complex, and it is difficult to determine the precise probability distribution of system load, but its upper and lower bounds are easy to determine. Based on the interval model, the load uncertainty of the power system is modeled. In the kth year, the load uncertainty model of the power system at any hour is characterized as:

[0191]

[0192] Where: Represents the load variable M i The value range of and Respectively represent the interval The upper and lower bounds are determined based on historical statistical data.

[0193] Sub-step 3.2, based on the load interval uncertainty model established in step 3.1, the optimal load reduction model based on DC power flow and the interval linear programming method are used to predict the system reliability in the kth year. The prediction steps include: system state generation, system state analysis, and reliability index calculation.

[0194] The prediction steps include:

[0195] Sub-step 3.2.1, randomly generate the status of any system component in the kth year. Based on the analytical calculation model of equipment unavailability established in step 2, a random number q in [0,1] is randomly generated to determine the operating status of each system device. For each device: if q all (H+k), the equipment is in a failed shutdown state, otherwise the equipment is in a normal operating state;

[0196] Sub-step 3.2.2, based on the load interval uncertainty model established in sub-step 3.1, randomly select a load interval of any hour in a year as the system load level corresponding to the system component state generated in sub-step 3.2.1;

[0197] ​In sub-step 3.2.3, the optimal load reduction model based on DC power flow and the interval linear programming method are used to analyze the system states generated by sub-steps 3.2.1 and 3.2.2, determine the optimal load reduction interval corresponding to the system state, and calculate the optimal average load reduction; assuming that the generated system state is s, the upper and lower optimal load reduction intervals are calculated using the preset optimal load reduction model, including the objective function and constraints.

[0198] In the optimal load reduction model, the sum of the load reduction on each bus (node) of the system is LC s Minimum is the objective function of the model, and the objective function is expressed as:

[0199]

[0200] Where: P s,i,cut represents the optimal load reduction of node i under system state s; Ψ bus Represents a collection of system nodes;

[0201] The constraints are expressed as:

[0202] 1. The system power balance constraint is expressed as:

[0203]

[0204] Where: P s,g represents the output of the g-th generator; Ψ g represents the set of generators in the system; P i,peak represents the annual peak load of node i; M s ·P i,peak represents the load demand of node i in state s; M s Take the value of system load;

[0205] 2. The node power balance constraint is expressed as:

[0206]

[0207] Where: g,i represents the set of generators connected to node i; P s,i,in represents the injected power of node i;

[0208] 3. The node load reduction constraint is expressed as:

[0209]

[0210] 4. The node injection power calculation is expressed as:

[0211]

[0212] Where: n represents the number of system nodes; θ s,j represents the voltage phase angle of node j; b s,ij represents the element in the i-th row and j-th column of the node admittance matrix B;

[0213] 5. The DC power flow equation of the transformer / line branch is expressed as:

[0214]

[0215] Where: θ s,i and θ s,j Respectively represent the voltage phase angles of the first and last nodes i and j of branch r; s,r Represents the reactance of branch r; PL s,r represents the power flow of branch r; branch Represents a set of system branches;

[0216] 6. Transformer / line branch transmission capacity constraint is expressed as:

[0217]

[0218] Where: Indicates the maximum transmission capacity of branch r; state identification variable υ s,r Used to describe the operating status of branch r: When the sampling status of branch r is failure and shutdown, υ s,r The value is 0, otherwise s,r is 1;

[0219] 7. The unit output constraint is expressed as:

[0220]

[0221] Where: Indicates the maximum output of the generator g, which is taken as the rated capacity; υ s,g Used to describe the operating status of generator g: When the sampling status of unit g is failure shutdown, υ s,g The value is 0, otherwise s,g is 1.

[0222] When M s When the value is taken as the upper limit of the load range, the obtained is the upper bound of the optimal load reduction interval, when M s When the value is taken as the lower limit of the load range, the obtained is the lower bound of the optimal load reduction interval. Therefore, the optimal average load reduction corresponding to the system state s is:

[0223]

[0224] Sub-step 3.3, repeat step 3.2 until the predetermined termination criteria are met, and then calculate the predicted value of the system reliability indicator expected power shortage EENS in the kth year, which is expressed as:

[0225]

[0226] In the formula: EENS k represents the predicted value of the reliability index of the system in the kth year, LC s,aver represents the optimal average load reduction corresponding to system state s, Q sam,k represents the total number of system states generated to predict the system reliability index in the kth year.

[0227] The predetermined termination criterion is to generate a sufficient number of system states based on the equipment unavailability parameter obtained in step 2 until the following termination criterion is met:

[0228]

[0229] Convergence coefficient β EENS Should satisfy β EENS ≤0.05.

[0230] Sub-step 3.4, calculate the improvement of the system reliability level in the kth year after implementing the given aging equipment replacement plan, expressed as:

[0231]

[0232] In the formula: EENS k,before It represents the predicted value of the reliability index of the system in the kth year before the aging equipment replacement plan is implemented, which is calculated by ignoring the impact of the aging equipment replacement plan.

[0233] Step 4. Once the replacement plan for aging equipment changes, the aging equipment unavailability rate parameters calculated in step 2 will also change accordingly, thereby affecting the prediction results of the system reliability index in step 3. At this time, the update of the system reliability index needs to be completed by repeatedly generating and analyzing a large number of system states. However, since the target equipment of the aging equipment replacement plan is predetermined, only the specific replacement time in each replacement plan is different. Therefore, this step 4 is to establish an analytical model between the predicted values ​​of the system reliability index and the unavailability rate parameters of these target equipment. Establish an analytical model between the predicted values ​​of the system reliability index and the unavailability rate parameters of the target equipment, and use the analytical model to calculate the predicted values ​​of the system reliability index for each year during the planning period.

[0234] The calculation step of the system reliability index prediction value includes:

[0235] Sub-step 4.1, for the G components contained in the system, since only M target devices will be replaced during the planning period, the unavailability rate parameters of the remaining GM system components in each year during the planning period are constants, and the system reliability index is expressed as:

[0236]

[0237] Where, H1, ..., H M is the running time of M target devices. From the mathematical optimization model of step 3, we can know that About U all (H1+k),…,U all (H M +k) nonlinear function;

[0238] Sub-step 4.2, based on the proposed complete event group division principle, classify all system states generated in the process of predicting the reliability index of the kth year in step 3;

[0239] Since each device has only two states, working and failing, and the failures of each device are independent of each other, the number of combined states of M target devices is Y = 2 M , and these Y mutually exclusive combination states are recorded as F y , where y = 1, 2, ..., Y, let Y states constitute a complete event group;

[0240] Φ y , where y = 1, 2, ..., Y, represents the system event set of M target devices in the yth combination state, which is divided into Y subsets based on the system state generated in step 3, namely: Φ1, Φ2, ..., Φ Y ;

[0241] Rewrite the formula in substep 4.1 as:

[0242]

[0243] Where Y k (b) is the optimal load reduction corresponding to event b, which is calculated by the mathematical optimization model proposed in step 3;

[0244] Sub-step 4.3, based on the definition of independent failures between devices and conditional probability, rewrite the formula in step 4.2 as follows:

[0245]

[0246] In the formula, Indicates that in event F y The probability of event b occurring under the condition that For event Fy The probability of occurrence, where y = 1, 2, ..,, Y;

[0247] Substep 4.4, let Rewrite the formula in substep 4.3 as:

[0248]

[0249] When the system network topology, operating parameters and GM non-target device unavailability rate parameters remain unchanged, the coefficients in the above formula It is only related to the state of non-target components and is a constant;

[0250] Sub-step 4.5, the failures of each component are independent of each other, and event F y Probability of occurrence The calculation formula is:

[0251]

[0252] Where: ε u and ε a They are the combined states F y A collection of devices in working and faulty states.

[0253] Compared with the existing analysis methods, this embodiment is based on the statistically collected aging failure data of power equipment such as transformers, transmission lines, and generators, and with the help of a three-parameter Weibull distribution model and a gray prediction model, an aging failure reliability model that can accurately describe the time-varying aging failure probability and performance degradation process of power equipment is established; on this basis, based on the integral discretization method, an analytical calculation model for the unavailability rate of power equipment taking into account the influence of the replacement plan is derived, and then the precise mathematical relationship between the "aging equipment replacement plan" and the "aging equipment unavailability rate" is established; then, based on the interval model, the uncertainty of the system load is analytically characterized, and then with the help of the interval linear programming method, a power system reliability prediction method based on the optimal load shedding flow is established, and then the precise mathematical relationship between the "aging equipment unavailability rate" and the "system reliability improvement level" is established; on this basis, based on the complete event group division principle and conditional probability theory, an analytical calculation formula between the "target aging equipment unavailability rate" and the "system reliability improvement level" is established. Based on the above model, a analytical quantitative analysis model between the aging equipment replacement plan and the reliability improvement level of the power generation and transmission system is finally established, realizing a rapid and accurate analysis of the system reliability improvement level for any aging equipment replacement plan.

[0254] In order to verify the accuracy and efficiency of the analytical quantitative analysis method between the proposed replacement plan for aging equipment and the reliability improvement level of the power generation and transmission system, the improved IEEE RTS-79 reliability system is used as a test system for verification and analysis. The test system includes 32 generator sets, 33 transmission lines, and 37 power transformers (32 step-up transformers and 5 interconnection transformers). The specific topology structure is shown in the figure below. Figure 2 shown.

[0255] For the convenience of analysis, the six step-up transformers connected to Bus7 and Bus13 are selected as the aging equipment to be replaced. Assuming that the six transformers are replaced at the same time, 50 equipment replacement plans are generated by random sampling according to the replacement time. The accuracy of the traditional method and the method of this embodiment in evaluating the improvement of system reliability by the 50 transformer replacement plans is compared, and the difference in calculation efficiency between the two methods is analyzed. The specific analysis results are as follows.

[0256] Taking the reliability level improvement calculation result obtained by the traditional method as the true value, the reliability level improvement calculation result error obtained by the method of this embodiment is as follows: Figure 3 shown.

[0257] Depend on Figure 3 It can be seen that under each group of aging equipment replacement schemes, the average error of the reliability level of the power generation and transmission system obtained by the method of this embodiment compared with the results of the traditional method is less than 3.5%, which proves the accuracy of the analytical method model proposed by the method of this embodiment in the evaluation results. Furthermore, Table 1 shows the calculation time comparison results of the method of this embodiment and the traditional method.

[0258] Table 1 Comparison of calculation time between the method of this embodiment and the traditional method

[0259]

[0260] As can be seen from Table 1, in order to obtain the analysis results of the reliability improvement level of the power generation and transmission system under 50 scenarios, the total calculation time of the traditional method is about 4.3 hours. This is because: for each set of aging equipment replacement plans, the traditional method needs to perform two complete reliability assessments based on the optimization model solution to obtain the system's optimal load reduction when the load values ​​are the lower and upper limits of the interval, and then calculate the reliability improvement level of the power generation and transmission system. However, the analytical model of the method of this embodiment only needs to perform two preliminary reliability assessments based on the optimization model solution to determine the model coefficients. Once the coefficients are determined, the calculation of the analytical model based on the method of this embodiment takes very little time, and the total time required to evaluate the reliability improvement level of the power generation and transmission system under 50 different scenarios does not exceed 1 second, which verifies the high efficiency of the analytical analysis method proposed in this patent in terms of computational efficiency.

[0261] The above is only an embodiment of the present invention, and the common knowledge such as the known specific structure and characteristics in the scheme is not described in detail here. It should be pointed out that for those skilled in the art, several deformations and improvements can be made without departing from the structure of the present invention, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. The analytical method for equipment replacement scheme and power system reliability improvement level is characterized by: The following steps are involved: Step 1, analyzing and statistically collecting aging failure data of multiple power equipment, using a grey prediction model to estimate the parameters of a three-parameter Weibull distribution, and establishing a power equipment aging failure reliability model based on a three-parameter Weibull distribution; Step 2: Based on the reliability model of power equipment aging failure established in step 1, considering the influence of replacement plan, an analytical expression of unavailability rate of power equipment aging failure including the influence of replacement plan is established; Step 3: Based on step 2, the equipment unavailability rate parameter after considering the impact of the replacement plan is obtained, the unavailability rate parameter is combined with the load uncertainty modeling, and a mathematical calculation model for power system reliability prediction based on the optimal load reduction model is constructed; Step 4: Establish an analytical model between the predicted value of the system reliability index and the target equipment unavailability rate parameter, and use the analytical model to calculate the predicted value of the system reliability index for each year within the planning period.

2. The analytical method for equipment replacement scheme and power system reliability improvement level according to claim 1 is characterized by: In step 1, the process of establishing the reliability model of power equipment aging failure includes the following sub-steps: Sub-step 1.1, count the aging failure time of various types of power equipment in the power equipment historical ledger data, and arrange them in chronological order from small to large, expressed as: T=(t1,t2,...,t n ); Where: t n is the time when the nth power equipment fails due to aging, and t1≤t2≤...≤t n ; Sub-step 1.2, using the three-parameter Weibull distribution to construct the time-varying aging failure probability function F(x) of power equipment, expressed as: The corresponding aging failure probability density function is: Where: variable t is the operating time of the power equipment, F(t) and f(t) represent the aging failure probability function and aging failure probability density function of the power equipment respectively; η is the scale parameter; m is the shape parameter; γ is the location parameter; Sub-step 1.3, the grey prediction model GM(1,1) estimates the scale parameter η, shape parameter m and location parameter γ of the three-parameter Weibull distribution. First, the data preprocessing of the inverse transformation of the time-varying aging failure probability function of power equipment constructed in sub-step 1.2 is expressed as: Sub-step 1.4, calculate w and t in combination with the aging failure time data X of the power equipment, and then rewrite the formula in sub-step 1.3 as follows: Substep 1.5, let a = 1 / m, c = η, u = a / b = γ, and replace the formula in substep 1.4 with the differential equation of the model GM(1,1) The time response function Corresponding.

3. The analytical method for equipment replacement scheme and power system reliability improvement level according to claim 2 is characterized by: Sub-step 1.4 formula (t i ,w i ) is equivalent to a general time series, and combined with the least squares method, the aging failure time data T is used to estimate the three parameters η, m and γ, which can be expressed as: Where: Where: are the estimated values ​​of the three parameters η, m and γ respectively.

4. The analytical method for equipment replacement scheme and power system reliability improvement level according to claim 2 is characterized by: The step 2 includes the following sub-steps: Sub-step 2.1, the aging failure probability function of power equipment taking into account the impact of the replacement plan is expressed by the formula in sub-step 1.2: Where: variable t also represents the operating time of the power equipment; r rp Indicates the time to implement the replacement plan for power equipment; Sub-step 2.2: for power equipment that has been in service for H years, the impact of equipment aging failure occurring at different time periods during the planning period on its expected unavailability time in the H+k year is evaluated by discrete method, and an analytical formula for aging failure unavailability rate is established; Sub-step 2.3, calculate the probability of aging failure of the equipment in each period and the duration of unavailability caused in the H+k year, and obtain the aging failure unavailability rate of the equipment in the H+k year as: In the formula, ζ k (i) The impact of the replacement period on the expected unavailability time in year H+k; In sub-step 2.4, the comprehensive unavailability rate in year H+k is given by the random failure unavailability rate U random The calculation is based on the union of (H+k) and the aging failure unavailability rate calculated in sub-step 2.3: IN all (H+k)=U random +U aging (H+k)-U random ·IN aging (H+k); In the formula, and They are the average time before random failure of equipment and the average repair time, and their values ​​are constants.

5. The analytical method for equipment replacement scheme and power system reliability improvement level according to claim 4 is characterized by: In the sub-step 2.2, the process of establishing the analytical formula of the aging failure unavailability rate includes: Sub-step 2.2.1, divide the total planning period K years into N time periods according to the time length Δx, and each segment is marked with i (i = 1, 2, ..., N). The probability of irreparable aging failure of power equipment in the i-th time period can be analytically expressed as: Where F(·) is the aging failure probability function established in sub-step 2.1 after considering the impact of equipment replacement plan; Sub-step 2.2.2: Examine the time L required to perform corrective replacement operations after the equipment fails due to aging in each period. repace The expected unavailable time ζ for the H+kth year k Assuming that the equipment fails due to aging in the i-th period, the period during which the equipment is unavailable due to replacement is from H+(2i-1)·Δx / 2 to H+(2i-1)·Δx / 2+L replace ; Sub-step 2.2.3, for any stage of the planning period that time period i may be in, where i = 1, 2, ..., N, the impact of the replacement period on the expected unavailability time in year H+k ζ k (i) Including the following situations: When the equipment fails due to aging in the i-th period and is replaced before the year H+k: ζ k (i)=0,if(H+(2i-1)·Δx / 2+L replace )≤H+k; When the aging failure of the equipment in the i-th period occurs before the H+k year but the replacement operation is completed within the H+k year: When the aging failure of the equipment in the i-th period is within the H+k year and the replacement operation is completed within the H+k year: When the aging failure of the equipment in the i-th period occurs within the H+k year and the replacement operation is completed after the H+k year: ζ k (i)=(T+k+1)-(T+(2i-1)·Δx / 2) if T+k≤(T+(2i-1)·Δx / 2)≤T+k+1&(T+(2i-1)·Δx / 2+L replace )>T+k+1; When the aging failure occurred in the i-th period is after T+k years: ζ k (i)=0,if(H+(2i-1)·Δx / 2)>H+k+1。 6. The analytical method for equipment replacement scheme and power system reliability improvement level according to claim 4 is characterized by: In step 3, the construction of the mathematical calculation model for power system reliability prediction includes: Sub-step 3.1, model the load uncertainty of the power system based on the interval model. In the kth year, the load uncertainty model of the power system at any hour is represented as: Where: Represents the load variable M i The value range of and Respectively represent the interval The previous and next term; Sub-step 3.2, based on the load interval uncertainty model established in step 3.1, the optimal load reduction model based on DC power flow and the interval linear programming method are used to predict the system reliability in the kth year. The prediction steps include: system state generation, system state analysis, and reliability index calculation; Sub-step 3.3, repeat step 3.2 until the predetermined termination criteria are met, and then calculate the predicted value of the system reliability indicator expected power shortage EENS in the kth year, which is expressed as: In the formula: EENS k represents the predicted value of the reliability index of the system in the kth year, LC s,aver represents the optimal average load reduction corresponding to system state s, Q sam,k represents the total number of system states generated to predict the system reliability index in the kth year; Sub-step 3.4, calculate the improvement of the system reliability level in the kth year after implementing the given aging equipment replacement plan, expressed as: In the formula: EENS k,before It represents the predicted value of the reliability index of the system in the kth year before the aging equipment replacement plan is implemented, which is calculated by ignoring the impact of the aging equipment replacement plan on the equipment unavailability parameter.

7. The analytical method for equipment replacement scheme and power system reliability improvement level according to claim 6 is characterized by: The prediction step in the sub-step 3.2 includes: Sub-step 3.2.1, randomly generate the status of any system component in the kth year, and determine the operating status of each system device by randomly generating a random number q in [0,1] based on the device unavailability analysis calculation model established in step 2. For each device: if q all (H+k), the equipment is in a failed shutdown state, otherwise the equipment is in a normal operating state;​ Sub-step 3.2.2, based on the load interval uncertainty model established in sub-step 3.1, randomly select a load interval of any hour in a year as the system load level corresponding to the system component state generated in sub-step 3.2.1; In sub-step 3.2.3, the optimal load reduction model based on DC power flow and the interval linear programming method are used to analyze the system states generated by sub-steps 3.2.1 and 3.2.2, determine the optimal load reduction interval corresponding to the system state, and calculate the optimal average load reduction; assuming that the generated system state is s, the upper and lower optimal load reduction intervals are calculated using the preset optimal load reduction model, including the objective function and constraints.

8. The analytical method for equipment replacement scheme and power system reliability improvement level according to claim 7 is characterized by: In the sub-step 3.2.3, in the optimal load reduction model, the sum of the load reduction amounts on each bus of the system LC s Minimum is the objective function of the model, and the objective function is expressed as: Where: P s,i,cut represents the optimal load reduction of node i under system state s; Ψ bus Represents a collection of system nodes; The constraints are expressed as: The system power balance constraint is expressed as: Where: P s,g represents the output of the g-th generator; Ψ g represents the set of generators in the system; P i,peak represents the annual peak load of node i; M s ·P i,peak represents the load demand of node i in state s; M s Take the value of system load; The node power balance constraint is expressed as: Where: g,i represents the set of generators connected to node i; P s,i,in represents the injected power of node i; The node load reduction constraint is expressed as: The node injection power calculation is expressed as: Where: n represents the number of system nodes; θ s,j represents the voltage phase angle of node j; b s,ij represents the element in the i-th row and j-th column of the node admittance matrix B; The DC power flow equation for the transformer / line branch is expressed as: Where: θ s,i and θ s,j Respectively represent the voltage phase angles of the first and last nodes i and j of branch r; x s,r Represents the reactance of branch r; PL s,r represents the power flow of branch r; branch Represents a set of system branches; The transformer / line branch transfer capacity constraint is expressed as: Where: represents the maximum transmission capacity of branch r; Status indicator variable υ s,r Used to describe the operating status of branch r: When the sampling status of branch r is failure and shutdown, υ s,r The value is 0, otherwise s,r is 1; The unit output constraint is expressed as: Where: Indicates the maximum output of the generator g, which is taken as the rated capacity; υ s,g Used to describe the operating status of generator g: When the sampling status of unit g is failure shutdown, υ s,g The value is 0, otherwise s,g is 1.

9. The analytical method for equipment replacement scheme and power system reliability improvement level according to claim 8 is characterized by: In the sub-step 3.2.3, when M s When the value is taken as the upper limit of the load range, the obtained is the upper bound of the optimal load reduction interval, when M s When the value is taken as the lower limit of the load range, the obtained is the lower bound of the optimal load reduction interval, and the optimal average load reduction corresponding to the system state s is:

10. The analytical method for equipment replacement scheme and power system reliability improvement level according to claim 6 is characterized by: In step 4, the step of calculating the predicted value of the system reliability index includes: Sub-step 4.1, for the G components contained in the system, since only M target devices will be replaced during the planning period, the unavailability rate parameters of the remaining GM system components in each year during the planning period are constants, and the system reliability index is expressed as: Where, H1, ..., H M is the running time of M target devices; from the mathematical optimization model of step 3, we can know that About U all (H1+k),…,U all (H M +k) nonlinear function; Sub-step 4.2, based on the proposed complete event group division principle, classify all system states generated in the process of predicting the reliability index of the kth year in step 3; Since each device has only two states, working and failing, and the failures of each device are independent of each other, the number of combined states of M target devices is Y = 2 M , and these Y mutually exclusive combination states are recorded as F y , where y = 1, 2, ..., Y, let Y states constitute a complete event group; Φ y , where y = 1, 2, ..., Y, represents the system event set of M target devices in the yth combination state, which is divided into Y subsets based on the system state generated in step 3, namely: Φ1, Φ2, ..., Φ Y ; Rewrite the formula in substep 4.1 as: Where Y k (b) is the optimal load reduction corresponding to event b, which is calculated by the mathematical optimization model proposed in step 3; Sub-step 4.3, based on the definition of independent failures between devices and conditional probability, rewrite the formula in step 4.2 as follows: In the formula, Indicates that in event F y The probability of event b occurring under the condition that For event F y The probability of occurrence, where y = 1, 2, ..,, Y; Substep 4.4, let Rewrite the formula in substep 4.3 as: Under the condition that the system network topology, operation parameters and GM non-target device unavailability rate parameters remain unchanged; Sub-step 4.5, the failures of each component are independent of each other, and event F y Probability of occurrence The calculation formula is: Where: ε u and ε a They are the combined states F y A collection of devices in working and faulty states.

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